Bp Frac Manual

Table of Contents 1.1 1.2 1.3 1.4 2.1 2.2 2.3 3.1 3.2 3.3 3.4 3.5 3.6 4.1 4.2 4.3 4.4 5.1 5.2 5.3 5.4 5.5 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 7.1 7.2 7.3 7.4 7.5 7.6 8.1 8.2 8.3 8.4 8.5 8.6 June 1997

History of Hydraulic Fracturing .................................................................................. 1-1 Amoco Hydraulic Fracturing Course Outline ........................................................... 1-11 Nomenclature ............................................................................................................ 1-14 References ................................................................................................................. 1-17 The Continuity Equation ............................................................................................. 2-1 Model Differences and the Elasticity Equation .......................................................... 2-4 References ................................................................................................................... 2-8 Reservoir Response To Fracture Stimulation ............................................................. 3-1 Steady-State Reservoir Response .............................................................................. 3-10 Transient Reservoir Response .................................................................................. 3-24 Bilinear Flow - Liquid Reservoirs (Reproduction of PTA Course Material) ........... 3-27 Bilinear Flow - Gas Reservoirs ................................................................................. 3-40 References ................................................................................................................ 3-49 Elastic Properties of the Formation ............................................................................. 4-1 Fracture Toughness .................................................................................................... 4-7 Hardness ................................................................................................................... 4-10 References ................................................................................................................. 4-11 Fracture Height/Fracture Height Growth - 3-D Modeling/Design ............................. 5-1 Fluid Loss .................................................................................................................. 5-20 Fluid Viscosity ......................................................................................................... 5-27 Treatment Pumping ................................................................................................... 5-36 References ................................................................................................................. 5-43 Fluid Selection .......................................................................................................... 6-1 Fluid Classification ..................................................................................................... 6-1 Fluid Selection Criteria .............................................................................................. 6-3 Description of Fracturing-Fluid Types ..................................................................... 6-30 Rheological Testing Of Fracturing Fluids ................................................................ 6-49 Service Company Trade Names ............................................................................... 6-52 Fluid Scheduling ...................................................................................................... 6-70 References ................................................................................................................ 6-80 Introduction ................................................................................................................. 7-1 Proppant Properties ..................................................................................................... 7-4 Conductivity/Permeability ....................................................................................... 7-19 Proppant Transport .................................................................................................... 7-26 Non-Darcy Flow ........................................................................................................ 7-29 References ................................................................................................................. 7-32 Introduction To Fracturing Pressure Analysis ........................................................... 8-1 Fracture Closure Stress ............................................................................................... 8-4 Bottomhole Treating Pressure .................................................................................. 8-14 Pressure Decline Analysis ........................................................................................ 8-25 Pressure History Matching ....................................................................................... 8-46 Proppant/Fluid Schedule From Pressure Decline ..................................................... 8-55

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8.7 Nomenclature .............................................................................................................8-68 8.8 References ..................................................................................................................8-70 9.1 Introduction ..................................................................................................................9-1 9.2 General Economic Criteria ...........................................................................................9-3 9.3 Elements Of Fracturing Treatment Costs ...................................................................9-20 9.4 References. .................................................................................................................9-21 10.1 Fracturing Tests ..........................................................................................................10-3 10.2 Introduction To TerraFrac ........................................................................................10-29 10.3 References ................................................................................................................10-49 11.1 Introduction ................................................................................................................11-1 11.2 Stimulation Design and Planning ...............................................................................11-2 11.3 Water Quality Control ................................................................................................11-4 11.4 Proppant Quality Control ...........................................................................................11-6 11.5 Fracture Treatment Setup ...........................................................................................11-8 11.6 Fracture Treatment Execution ..................................................................................11-10 11.7 Post-Frac Cleanup ....................................................................................................11-13 11.8 Frac Treatment Reporting Requirements .................................................................11-14 FRAC School Problem No. 1 ............................................................................................... P-1 FRAC School Problem No. 1 ............................................................................................... P-2 9.9 History of Hydraulic Fracturing....................................................................................1-1

Chapter 1 Introduction

9.10 9.11 9.12 9.13

Developments in Hydraulic Fracturing .......................................................................1-3 Fracture Orientation: ..............................................................................................1-3 Fracturing Fluid: .....................................................................................................1-4 Proppants: ................................................................................................................1-5 Fracture Treatment: .................................................................................................1-6 Early Fracture Design ...................................................................................................1-8 Amoco Hydraulic Fracturing Course Outline .............................................................1-11 Nomenclature ..............................................................................................................1-14 References ...................................................................................................................1-17 The Continuity Equation ...............................................................................................2-1

Chapter 2 Fracturing Models 9.14 Model Differences and the Elasticity Equation ............................................................2-4 9.15 References .....................................................................................................................2-8 9.16 Reservoir Response To Fracture Stimulation ...............................................................3-1 Fracture Length ............................................................................................................3-1

Chapter 3 Reservoir Analysis Reservoir Permeability .................................................................................................3-2 Fracture Flow Capacity ................................................................................................3-3 Hydraulic Fracturing Theory Manual

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9.17

9.18 9.19

9.20

9.21 9.22

June 1997

Fracture Orientation ................................................................................................ 3-8 Steady-State Reservoir Response .............................................................................. 3-10 Effective Wellbore Radius, r'w ................................................................................... 3-10 A Direct Way Of Finding FOI ................................................................................... 3-14 Optimizing Fractures for Secondary Recovery ......................................................... 3-15 Acid Fracturing .......................................................................................................... 3-22 Transient Reservoir Response ................................................................................... 3-24 Bilinear Flow - Liquid Reservoirs (Reproduction of PTA Course Material)............. 3-27 Flow Periods For A Vertically Fractured Well .......................................................... 3-27 Fracture Linear Flow ........................................................................................... 3-27 Bilinear Flow ....................................................................................................... 3-27 Formation Linear Flow ........................................................................................ 3-27 Pseudo-Radial Flow ............................................................................................. 3-27 Bilinear Flow Equations ........................................................................................... 3-28 Constant Formation Face Rate ............................................................................ 3-28 Constant Formation Face Pressure ...................................................................... 3-29 Bilinear Flow Graphs ................................................................................................ 3-30 Constant Formation Face Rate ............................................................................. 3-30 Constant Formation Face Pressure ....................................................................... 3-31 End of Bilinear Flow ................................................................................................. 3-33 Constant Formation Face Rate ............................................................................. 3-33 Constant Formation Face Pressure ....................................................................... 3-33 Analysis of Bilinear Flow Data ................................................................................ 3-35 Liquid-Constant Rate ........................................................................................... 3-35 Liquid-Constant Pressure .................................................................................... 3-36 Effect of Flow Restrictions ....................................................................................... 3-37 Effect of Wellbore Storage ....................................................................................... 3-37 Bilinear Flow - Gas Reservoirs .................................................................................. 3-40 Bilinear Flow Equations ............................................................................................ 3-40 Constant Formation Face Rate ............................................................................. 3-40 Constant Formation Face Pressure ....................................................................... 3-40 Bilinear Flow Graphs ................................................................................................ 3-41 Constant Formation Face Rate ............................................................................ 3-41 Constant Formation Face Pressure ...................................................................... 3-42 End of Bilinear Flow ................................................................................................. 3-43 Constant Formation Face Rate ............................................................................. 3-43 Constant Formation Face Pressure ...................................................................... 3-44 Analysis of Bilinear Flow Data ........................................................................... 3-46 Gas-Constant Rate ............................................................................................... 3-47 Gas-Constant Pressure ......................................................................................... 3-47 References ................................................................................................................ 3-49 Elastic Properties of the Formation ............................................................................. 4-1

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Chapter 4 Formation Mechanical Properties

9.23 9.24 9.25 9.26

Effect Of Modulus On Fracturing ................................................................................4-4 Typical Modulus Values .............................................................................................4-4 Fracture Toughness ...................................................................................................... 4-7 Hardness ....................................................................................................................4-10 References ..................................................................................................................4-11 Fracture Height/Fracture Height Growth - 3-D Modeling/Design ..............................5-1 Factors Controlling Fracture Height ............................................................................5-1

Chapter 5 Design of Pseudo 3-D Hydraulic Fracturing Treatments

9.27

9.28

9.29

9.30 9.31 9.32

Factors Controlling Fracture Height ............................................................................5-2 Effect Of Closure Stress Profile On Fracture Height Growth .....................................5-3 Effect Of Bed Thickness On Fracture Height Growth .................................................5-6 Effect Of Other Factors On Fracture Height Growth .................................................5-10 Picking Fracture Height ..............................................................................................5-12 (Estimating the In-situ Stress Profile) ........................................................................5-12 Factors Which Dominate In-situ Stress Differences ..................................................5-12 3-D Fracture Modeling/3-D Fracture Design .............................................................5-15 Measuring Fracture Height .........................................................................................5-17 Fluid Loss Height .......................................................................................................5-18 Fluid Loss ...................................................................................................................5-20 Fluid Loss Coefficient, Ct ..........................................................................................5-20 Spurt Loss ...................................................................................................................5-24 Fluid Viscosity ..........................................................................................................5-27 Viscosity Determination and Rheological Models .....................................................5-27 Fluid Entry Conditions and Temperature Considerations ..........................................5-29 Reservoir Temperatures .............................................................................................5-32 Effect of Proppant on Viscosity .................................................................................5-33 Summary For Fluid Viscosity ....................................................................................5-34 Treatment Pumping ....................................................................................................5-36 Fracture Radius ..........................................................................................................5-36 Pump Rate ..................................................................................................................5-36 Fluid Volume: ......................................................................................................5-37 Transport and Viscosity: ......................................................................................5-38 Summary for Pump Rate: ......................................................................................5-40 Depth .........................................................................................................................5-40 Friction Pressure ........................................................................................................5-40 References ..................................................................................................................5-43 Fluid Selection ...........................................................................................................6-1 Fluid Classification ......................................................................................................6-1 Water-Base Fracturing Fluid Systems .........................................................................6-1

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Chapter 6 Fluid Selection and Scheduling Hydrocarbon-Base Fracturing Fluid Systems ............................................................. 6-2 9.33 Fluid Selection Criteria ............................................................................................... 6-3 Safety and Environmental Compatibility .............................................................. 6-5 Compatibility with Formation, Formation Fluids, and Chemical Additives ......... 6-6 Simple Preparation and Quality Control ............................................................... 6-7 Low Pumping Pressure .......................................................................................... 6-9 Appropriate Viscosity .......................................................................................... 6-11 Low Fluid Loss .................................................................................................... 6-14 Good Flow Back and Cleanup ............................................................................. 6-18 Economics ........................................................................................................... 6-23 9.34 Description of Fracturing-Fluid Types ..................................................................... 6-30 Water-Base Polymer Solutions ............................................................................. 6-30 Fast-Crosslinking Water-Base Gels .................................................................... 6-32 Delayed Crosslinked Fluids ................................................................................. 6-38 Polymer Emulsion Fluid ...................................................................................... 6-40 Foamed Frac Fluids ............................................................................................. 6-41 Gelled Hydrocarbons ........................................................................................... 6-46 Gelled Methanol .................................................................................................. 6-48 9.35 Rheological Testing Of Fracturing Fluids ................................................................ 6-49 9.36 Service Company Trade Names ............................................................................... 6-52 9.37 Fluid Scheduling ....................................................................................................... 6-70 Fluid Scheduling Given the Fluid Rheology ............................................................ 6-70 Fluid Scheduling Using Constrained Rheology ....................................................... 6-71 Warning: .................................................................................................................... 6-73 9.38 References ................................................................................................................ 6-80 9.39 Introduction ................................................................................................................. 7-1 Why Do We Need Proppants? ..................................................................................... 7-1 Types of Proppants Available ...................................................................................... 7-1 Calculating the Stress on Proppant ............................................................................. 7-1

Chapter 7 Proppants What Causes A Proppant To Be Substandard? ............................................................ 7-3 Overview of Chap. 7 .................................................................................................... 7-3 9.40 Proppant Properties ..................................................................................................... 7-4 Sphericity and Roundness ........................................................................................... 7-4 Hardness ..................................................................................................................... 7-4 Size Distribution ......................................................................................................... 7-5 Crush Resistance ......................................................................................................... 7-9 Bulk and Grain Density ............................................................................................ 7-11 Acid Solubility .......................................................................................................... 7-11 Turbidity ................................................................................................................... 7-13 Resin-Coated Proppant ............................................................................................. 7-16 June 1997

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9.41

9.42 9.43 9.44 9.45

Precured Resin-Coated Proppant ..........................................................................7-16 Curable Resin-Coated Proppant ............................................................................7-16 Conductivity/Permeability ........................................................................................7-19 Laboratory Methods of Measuring Fracture Conductivity .........................................7-19 Radial Flow Cell ...................................................................................................7-19 Cylindrical Pack ....................................................................................................7-20 Cylindrical Cell With Platens ...............................................................................7-20 Cooke-Type Cell (API Cell) .................................................................................7-20 Long-Term Conductivity: Baseline Data ..................................................................7-20 Long-Term Conductivity: Damage Caused By Frac Fluids and Additives ...............7-23 Proppant Transport .....................................................................................................7-26 Non-Darcy Flow ........................................................................................................7-29 References ..................................................................................................................7-32 Introduction To Fracturing Pressure Analysis ............................................................8-1 History ..........................................................................................................................8-1

Chapter 8 Fracture Treating Pressure Analysis 9.46

9.47

9.48

9.49

Similarity to Pressure Transient Analysis ....................................................................8-2 Fracture Closure Stress ................................................................................................8-4 Microfrac Tests ............................................................................................................8-4 Pump-In/Decline Test ..................................................................................................8-7 Pump-In/Flowback Test ..............................................................................................8-9 Step-Rate Injection Test .............................................................................................8-10 Bottomhole Treating Pressure ...................................................................................8-14 Nolte-Smith Log-Log Interpretation .........................................................................8-14 Critical Pressure ........................................................................................................8-20 BHTP Measuring Techniques ...................................................................................8-22 BHTP Measuring Devices .........................................................................................8-23 Pressure Decline Analysis .........................................................................................8-25 Fracture Stiffness .......................................................................................................8-26 Fluid Loss Rate ..........................................................................................................8-27 ∆P* - Pressure Decline Analysis ...............................................................................8-30 Type Curve Analysis .................................................................................................8-32 'G' Function Plot for ∆P* ...........................................................................................8-35 Fluid Efficiency .........................................................................................................8-36 Example/Guidelines ..................................................................................................8-38 Example - Pressure Decline Analysis: ..................................................................8-38 Pitfalls .........................................................................................................................8-39 Post-propped-Frac Pressure Decline Analysis ..........................................................8-42 Pressure History Matching ........................................................................................8-46 Simple History Matching ..........................................................................................8-48 Simple History Matching Procedure & Example .......................................................8-49

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9.50

9.51 9.52 9.53

Complex Geology Effects .......................................................................................... 8-50 Problem Definition .................................................................................................... 8-52 Pressure Decline Analysis Variables ......................................................................... 8-52 Proppant/Fluid Schedule From Pressure Decline ...................................................... 8-55 Advantages of an Efficiency Derived Schedule ........................................................ 8-56 Disadvantages of an Efficiency Derived Schedule .................................................... 8-56 Determining Fracture Fluid Efficiency ..................................................................... 8-58 Pad Volume .............................................................................................................. 8-59 Proppant Addition Schedule ..................................................................................... 8-62 Effect of Treatment Volume ..................................................................................... 8-64 Example ..................................................................................................................... 8-65 Find Actual Job “Expected” Efficiency ..................................................................... 8-65 Treatment Pad Percentage ........................................................................................ 8-66 Proppant Addition Schedule ..................................................................................... 8-66 Time/Temperature History ....................................................................................... 8-67 Nomenclature ............................................................................................................ 8-68 References ................................................................................................................. 8-70 Introduction ................................................................................................................. 9-1

Chapter 9 Economic Optimization of Hydraulic Fracture Treatments 9.54 General Economic Criteria .......................................................................................... 9-3 The Present Worth Concept ......................................................................................... 9-4 Profitability Index ....................................................................................................... 9-7 Discounted Return on Investment (includes Fracture Discounted Return on Investment) .......................................................................................................... 9-8 Payout ........................................................................................................................ 9-10 Return on Investment ................................................................................................. 9-11 Incremental Economics .............................................................................................. 9-12 Present Worth Vs. the Profitability Index ................................................................. 9-14 Yet-to-Spend (Point Forward Evaluation) Vs. Full-Cycle Economics ...................... 9-17 9.55 Elements Of Fracturing Treatment Costs .................................................................. 9-20 Stimulation Service Company Costs ......................................................................... 9-20 9.56 References. ................................................................................................................ 9-21

Chapter 10 Special Topics 9.57 Fracturing Tests ......................................................................................................... 10-3 Introduction ................................................................................................................ 10-3 Core Tests to Determine Mechanical Rock Properties and Fluid Loss Coefficient ...................................................................................................... 10-3 Prefrac Logging Program ........................................................................................... 10-5 Borehole Geometry Log ............................................................................................ 10-5 Long Spaced Digital Sonic Log (LSDS) .................................................................. 10-6 Downhole Television and Borehole Televiewer ...................................................... 10-7 June 1997

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Cement Bond Log ......................................................................................................10-7 Temperature Logs .......................................................................................................10-8 Perforating and Permeability Determination ............................................................10-10 Bottomhole Treating Pressure Measurement ..........................................................10-11 Procedure for Measurement of Static Pressure Tubing/Annulus .............................10-12 Procedure for Recording Downhole with Surface Readout .....................................10-12 Procedure for Downhole Pressure Measurement .....................................................10-13 Pressure Measurement Devices ................................................................................10-13 Closure Stress Tests ..................................................................................................10-13 Minifracs .................................................................................................................10-17 Postfrac Logging Program ........................................................................................10-18 Temperature Decay Profiles ................................................................................10-18 Postfrac Temperature Log Interpretation .................................................................10-18 Postfrac Gamma Ray Logs ......................................................................................10-21 Fracture Azimuth Determination ..............................................................................10-21 Tiltmeters .................................................................................................................10-22 Borehole Geophones ...............................................................................................10-24 Oriented Core Analysis ...........................................................................................10-26 Borehole Geometry .................................................................................................10-28 9.58 Introduction To TerraFrac ........................................................................................10-29 General Description of the TerraFrac Simulator ......................................................10-29 Input To Terrafrac ....................................................................................................10-31 Terrafrac Simulation Runs .......................................................................................10-32 Confined Fracture Growth .................................................................................10-32 Unconfined Fracture Growth .............................................................................10-36 Summary ..................................................................................................................10-41 9.59 References ................................................................................................................10-49 9.60 Perforating .......................................................................................................................1 Hole Diameter .................................................................................................................1

Chapter 11 Fracture Stimulation Guidelines and Quality Control Chapter 12 Number of Perforations ...................................................................................................3 Perforation Phasing .........................................................................................................4 Perforating for Deviated/Horizontal Well Fracturing .....................................................4 Over-Pressured Perforating .............................................................................................8 Other Considerations .......................................................................................................9 9.61 WELLBORE CONFIGURATION 10 Fracturing Down Casing ...............................................................................................11

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9.62

9.63

9.64

9.65

9.66

9.67 9.68

9.69

June 1997

Fracturing Down Tubing with a Packer .........................................................................11 Fracturing Down Open-Ended Tubing ..........................................................................12 Methods of Obtaining Fracturing BHP ..........................................................................12 Considerations for Frac-Pack Completions ...................................................................14 PRE-TREATMENT PLANNING 16 Data Collection Requirements .......................................................................................16 Preliminary Treatment Design .......................................................................................17 Frac “Brief” Procedure ..................................................................................................18 Service Co./Operator Interaction ...................................................................................18 FRACTURING FLUID QC 20 Base Mixing Fluid .........................................................................................................21 Transport and Storage of Fluid ......................................................................................23 Quality Controlling Water-Based Gels ..........................................................................24 Quality Controlling Oil-Based Gels ..............................................................................30 Quality Controlling Foam Fracturing Fluids .................................................................33 Additional Fluid Quality Control Measures ..................................................................34 PROPPANT QC 36 Closure Stress and Proppant Strength ............................................................................36 Proppant Particle Size ....................................................................................................36 Proppant Grain Shape ....................................................................................................41 Proppant Fines ...............................................................................................................42 Interpretation ............................................................................................................43 Additional Proppant Quality Control Measures ............................................................45 TREATMENT EXECUTION 46 Lines of Authority and Communication ........................................................................46 Safety Meeting ...............................................................................................................46 Pressure Testing .............................................................................................................47 Treating Problems ..........................................................................................................47 Flushing the Treatment ..................................................................................................49 When to Flowback .........................................................................................................50 POST-FRAC LOGGING 51 Temperature Logs ..........................................................................................................51 Gamma-Ray Logs ..........................................................................................................54 FRAC School Problem No. 1 P-1 FRAC School Problem No. 2 P-2 Abstract ........................................................................................................................ P-2 Purpose ........................................................................................................................ P-2 Description ................................................................................................................... P-2 Procedure: .................................................................................................................... P-9 Workshop Problem 3 P-10 Abstract ...................................................................................................................... P-10 Description ................................................................................................................. P-10 Objective .................................................................................................................... P-10

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Procedure: .................................................................................................................. P-11 9.70 Workshop Problem 4 P-15 Abstract ..................................................................................................................... P-15 Purpose ...................................................................................................................... P-15 Geologic Setting ........................................................................................................ P-15 Description ................................................................................................................ P-15 9.71 Workshop Problem No. 5 P-23 Abstract ..................................................................................................................... P-23 Description ................................................................................................................ P-23 Objective: .................................................................................................................. P-23 Procedure: .................................................................................................................. P-29 9.72 Water Injection Well Problem 6 P-30 Pressure Falloff Test .................................................................................................. P-30 “Mini-Frac” Pressure Data ........................................................................................ P-34 9.73 Tight Gas Problem 7 P-39 9.74 Oil Well Problem 8 P-43 Other Pertinent Information ...................................................................................... P-43 Pressure Build-Up Data from Offset Well ................................................................ P-43 Results from Minifrac Treatment .............................................................................. P-48 9.75 Bili near FLow Problem 9 P-49 P-49 P-49 P-49

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Chapter

1

Introduction

1.1 History of Hydraulic Fracturing Hydraulic fracturing has made a significant contribution to the oil and gas industry as a primary means of increasing well production. Since fracturing was introduced by Stanolind (Amoco) in 1947, over one million fracture treatments have been performed and currently about 40% of all wells drilled are stimulated using hydraulic fracture treatments. Fracture stimulation treatments not only increase production rates, but are also credited for adding to the United States reserves an additional seven billion barrels of oil and over 600 trillion scf of gas which would have otherwise not been economical to develop. In addition, hydraulic fracturing has accelerated recovery and significantly increased the present worth of U.S. reserves. As we move towards the next century, we are challenged with applying this technology domestically in an attempt to offset large domestic trade deficits and declining production. In addition, as our industry’s focus moves internationally, methods of accelerating recovery, such as fracturing, must be explored. Fig. 1.1 presents a world cross section of producing oil wells, their average production and the total production of each country. This logarithmic plot shows that fracturing applications will continue to be important throughout North America, driven by the large number of wells available and the corresponding low producing rates presently experienced by these wells. PRODUCING WELLS & AVERAGE PRODUCTION Likelihood of Fracturing No. Wells/Av. Production-bbl/d

Total Daily Production-bbl

1000000

10

100000

8

10000

6

1000

4

100

2

10

0 Saudi Arabia

U. K.

Nigeria

Mexico

China

Canada

U. S.

Country # Oil Wells

Well Rate

Total Production Excerpted DOE/FE-0139

Fig. 1.1 - Producing Wells and Average Production

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Introduction

The idea of hydraulically fracturing a formation to enhance the production of oil and gas was conceived by Floyd Farris1 of Stanolind Oil and Gas Corporation (Amoco) after an extensive study of the pressures encountered while squeezing cement, oil and water into formations. The first experimental treatment intentionally performed to hydraulically fracture a well for stimulation was performed by Stanolind in the Hugoton gas field in Grant County, Kansas, in 1947 as shown in Fig. 1.2. A total of 1,000 gallons of napalm thickened gasoline was injected, followed by a gel breaker, to stimulate a gas producing limestone formation at 2,400 ft. However, the deliverability of the well was not changed appreciably. The hydraulic fracturing process was first introduced to the industry in a paper written by J. B. Clark2 of Stanolind in 1948 and patented and licensed in 1949. These patents resulted in royalty income to Amoco in the 17 years following and essentially funded the construction of the Amoco Production Research (APR) complex in Tulsa, Oklahoma (i.e., APR is the house that fracturing built).

Fig. 1.2 - Hugoton Gas Field in Grant County, Kansas, 1947.

Halliburton Oil Well Cementing Company was given an exclusive license on the new process. The first two commercial fracturing treatments were performed in Stephens County, Oklahoma, and Archer County, Texas, on March 17, 1949, using lease crude oil or a blend of crude and gasoline, and approximately 100 to 150 pounds of sand. Both wells were successful and thereafter application of the fracturing process grew rapidly, peaking, as shown in Fig. 1.3, at an average of +3,000 wells per month by the mid-1950s and increasing the supply of oil in the United States far beyond our early projections.3 The first one-half million pound fracturing job in the free world was performed in Stephens County, Oklahoma, in October 1968, by Pan American Petroleum Corporation, now Amoco. Hydraulic Fracturing Theory Manual

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History of Hydraulic Fracturing

AVERAGE NUMBER OF JOBS PER MONTH

Today, fracture treatments are performed regularly in all petroleum producing countries, including the Soviet Union. It is estimated that at least 30% of the recoverable oil and gas reserves in the United States can be attributed to the application of hydraulic fracturing.

5000

4000

3000

2000

1000

1949

1955

1960

1965

1970

1975

1980

1985

YEARS

Fig. 1.3 - Average Number of Fracturing Treatments per Month United States.

Significant technical advancements have been made during the four plus decades since the first commercial treatments. After the first few jobs, the average fracture treatment consisted of about 750 gallons of fluid and 400 pounds of sand. Today, treatments average about 43,000 gallons of fluid and 68,000 pounds of propping agent with the largest treatments exceeding one million gallons of fluid and three million pounds of proppant. This reflects advancements made by the industry in both theory and practice which have resulted in a better understanding of the fracturing process. As this process evolved; cleaner and more suitable fluid systems were developed; sand quality increased and higher concentrations were pumped; higher strength synthetic proppants were developed for deep-well fracturing; pumping and monitoring equipment were improved and computerized; and fracture design and evaluation techniques grew in sophistication. Developments in Hydraulic Fracturing Fracture Orientation: The original, shallow fracture treatments were thought to be horizontal, even though some of the deep wells that had been squeeze cemented showed cement in vertical fractures. The theory was that the overburden was lifted and the fracture was inserted in a horizontal plane. Clark et al.4 reported on a method of forming a vertical fracture in 1953 by plastering the walls of the wellbore to where it became a thick wall cylinder. Pressures were then applied to obtain vertical fractures, otherwise it was theorized horizontal fractures were obtained. Huitt et al.5-7 extended the theories in the late 1950s that the best fracture systems were horizontal and they could be obtained by notching the formation. Hubbert and Willis8 with Shell Oil Company presented a paper in 1956 reporting on the work they had done in a gelatin model. This work indicated that all fractures were February 1993

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Introduction

vertical, creating quite a controversy. In spite of this, it was not until the mid-1960s that the industry accepted the theory that practically all fractures were vertical and that only a few were horizontal. Prior to this time, theories were advanced that all fractures with a treating gradient of over 0.8 or 0.9 psi per foot of depth were vertical. All those with treating gradients less than this were horizontal. Work initiated by Cochran, Heck and Waters and reported on by Anderson and Stahl9 proved, without a doubt, that the majority of fractures were in fact vertical and it was a rare exception when a horizontal fracture was obtained. 100

PERCENT OF TREATMENT

90

AQUEOUS BASE FLUID

80 70 60 50 40 30 20

OIL BASE FLUID

10

1949

1953

1957

1961

1965

1969

1973

1977

1981

1985

1989

YEAR

Fig. 1.4 - Trend of Fracturing Base Fluids.

Fracturing Fluid: Hydraulic fracturing fluids have varied considerably over time as shown in Fig. 1.4. The first fracture treatments were performed with gelled lease crude, later, gelled kerosene was used. In 1952, refined and lease crude oils began to gain momentum, and by the latter part of 1952, a large portion of all fracturing treatments were performed with refined and lease crude oils. These fluids were inexpensive and safer, permitting greater volumes to be pumped at a lower cost. Their lower viscosities exhibited less friction than the original viscous gel, thus injection rates could be obtained at lower treating pressures. Higher injection rates, though, were necessary to transport the sand due to the lower viscosity and high rates of leakoff for these fluids. In 1953, with the advent of water as a fracturing fluid, a number of different gelling systems were developed. Surfactants were added to minimize emulsions with the formation fluid and potassium chloride was added to minimize the effect on clays and other water sensitive constituents of the formation. Later, other clay stabilizing agents were developed that enhanced the potassium chloride and permitted the use of water in a greater number of formations. Other new innovations, such as foams and addition of alcohol, have enhanced the use of water in a number of formations. Aqueous fluids such as acid, water and brines are now used as the base fluid in over 70% of all fracturing treatments employing a propping agent. In the early 1970s, a major innovation in fracturing fluids Hydraulic Fracturing Theory Manual

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February 1993

History of Hydraulic Fracturing

was to use crosslinking agents to enhance the viscosity of gelled water base fracturing fluids. Less pounds of gelling agent were required to reach the desired pumping viscosity, thus reducing cost. In many cases, however, too high a viscosity was obtained and pumping problems resulted. This system was soon perfected by reducing the concentration of gelling agents and crosslinker, resulting in an economically satisfactory fracturing fluid system. During the mid 1970s, fracture stimulations were designed for deeper formations. Gel stabilizers were developed to maintain the properties of the fluid system at the higher temperatures at these greater depths. The first of these temperature stabilizers was 5% methanol. Later chemical stabilizers were developed that could be used alone, or with the methanol. There was a synergistic effect obtained when the chemical and the methanol were used together as stabilizers. Recently, a new innovation was introduced which gives even greater temperature stability. As the gelled fluid reaches the bottom of the hole and the temperature is increasing, a secondary gelling agent reacts giving a more uniform viscosity than previous surface crosslinked fluids. Improvements in crosslinkers involve a delayed effect, thus permitting the fluid to reach the bottom of the hole in high temperature wells prior to crosslinking. This system gives adequate viscosity for moving the propping agent through the surface equipment and into the tubing, reducing the shearing effect caused by tubulars, and supplying a good fluid in the hydraulically created fracture to ensure adequate proppant transport. These are only a few of the highlights of fracturing fluid developments. Many other developments have enhanced the performance of fracturing fluids. Proppants: To keep the artificially created hydraulic fractures open, proppants of many different kinds have been used. The first fracturing treatment used a northern type sand for proppant; however, screened river sand was also employed on many early treatments. In fact, on some of these treatments, construction sand sieved through a window screen was employed as the propping agent. It was soon realized, however, that a high quality sand was desirable and specifications were established on the type of sand to be used. There have been a number of trends in the size of sand, from very large down to small. From the very beginning a 20 to 40 U.S. standard mesh sand has been the most popular and at the present time approximately 85% of the sand used is of this size. Numerous propping agents have been evaluated throughout the years, including plastic pellets, steel shot, Indian glass beads, aluminum pellets, high strength glass beads, rounded nut shells, resin coated sands, sintered bauxite and fused zirconium. Fig. 1.5 shows that the amount of sand used per fracture treatment has steadily increased through time. As shown, the concentration of sand (lb/fluid gal) remained low until the mid-1960s when the use of viscous fluids, such as complexed water base gel and viscous refined oil were introduced. At that time, large size propping agents were advocated to improve well deliverability. Proppant design techniques at low sand concentration changed from the monolayer or partial monolayer concept to pumping sand at multiple grain diameters and high concentrations. Over the last decade, there has been another sharp increase in sand concentrations used corresponding with improved hydraulic fracturing fluids and advanced pumping equipment.10 It is not infrequent to February 1993

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Hydraulic Fracturing Theory Manual

Introduction

2.0 100

100

1.8 90

90

1.6 80

80 Sand Concentration

1.2 60 1.0 50 0.8 40 0.6 30 0.4 20

Pounds Sands (Thousand)

Sand Concentration

1.4 70

70 60 50

Fluid/treatment

40 30 Sand/treatment

Gallons of Fluid (Thousands)

1

20

10

10

0 1949

1953

1957

1961

1965

1969

Years

1973

1977

1981

0 1989

1985

Fig. 1.5 - Trend of Average Fracture Treatments in the United States.

see proppant concentrations averaging 10 to 12 lbm/gal used throughout the treatment. This means that low concentrations are used at the start of the job and rapidly increased to concentrations of 15 lbm/gal or more. Corresponding to increased fluid viscosity, higher pump rates and deeper well applications, the hydraulic horsepower (hhp) used in treatments has increased from an average of about 75 to over 1500 hhp as shown in Fig. 1.6. 3000

30

2500

25

20

2000 INJECTION RATE

15

1500 HHP/JOB 1000

10

500

5

RATE, bbl/min

HYDRAULIC HORSEPOWER

a

0 0 1949 1953 1957 1961 1965 1969 1973 1977 1981 1985 1989

YEARS

Fig. 1.6 - Evolution of Fracturing Techniques.

Fracture Treatment: There are cases where as much as 15,000 hhp has been available on jobs with over 10,000 hhp actually being utilized. Contrast this to some of the early jobs where only 10 to 15 hhp was required. The initial jobs were performed at rates of two to three barrels per minute (bpm). Rates Hydraulic Fracturing Theory Manual

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February 1993

History of Hydraulic Fracturing

increased rapidly until the early 1960s where rates around 20 bpm became popular. Today, jobs are performed at a low rate of about 5 bpm, to a high rate of over 100 bpm. At one time in the Hugoton gas field, pumping rates of over 300 bpm were employed. Surface treating pressures sometimes are less than 100 psi, yet others may approach 20,000 psi. Today, as treatment size, pressure and pump rate increase, treatment costs have also increased, ranging from less than $10,000 to over $1,000,000. The first two commercial treatments cost between $900 and $1,000. Conventional cement and acid pumping equipment were utilized initially to execute fracturing treatments. One to three units equipped with a jet mixer and one pressure pump delivering 75 to 125 hhp were adequate for the small volumes injected at the low rates. Amazingly, many of these treatments gave phenomenal production increases. As the treating volumes increased, accompanied with demand for greater injection rates, purpose built pumping and blending equipment was developed to perform these specialized functions. Today, the development of fracturing equipment continues, including intensifiers, high pressure manifolds, and computer control systems. Large, massive hydraulic fracturing (MHF) treatments as illustrated in Fig. 1.7, were developed by Amoco in the Hydraulic Fracturing Department, Amoco Production Research in Tulsa. The treatments were developed to convert non-commercial, tight gas deposits found throughout North America into viable, commercial properties. MHF treatments require several million dollars worth of equipment, utilize in excess of one million gallons of fluid and have placed over 3.3 million pounds of sand, injected in one continuous operation pumped over 10 hours at rates of approximately 40 bpm.

Fig. 1.7 - Massive Hydraulic Fracture Treatment.

Sand and fluid are mixed in a piece of fracturing equipment called a blender. For the first few years, sand was added to the fracturing fluid by pouring it into a tank or jet mixer containing fracFebruary 1993

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Introduction

turing fluid and connected to the pump suction. Later with less viscous fluid, a ribbon or paddle type batch blender was employed. Finally, the continuous proportioner and blender was developed. Blending equipment has become very sophisticated to meet the need for proportioning a large number of dry and liquid additives, then properly blending them into the base fluid with the specified concentrations of sand or other propping agents. In order to handle large volumes of propping agents required in large treatments, special storage facilities have been developed to facilitate storing and moving the propping agents at the proper rate to the blender. Proportioning and mixing of the gelling agents has become a very sophisticated procedure utilizing computer control systems to step or ramp sand concentrations in the blender as shown in Fig. 1.8. It is necessary to blend them in a uniform method to give the maximum yield viscosity. One procedure is to use a concentrated gelling agent prepared prior to the treatment, then taken to the field where it is proportioned into the base fluid in a semi-continuous method. A very uniform high yield viscosity is obtained. With the advent of larger size treatments, it has become necessary to have a computer control center (Fig. 1.9) to coordinate all of the activities that are transpiring simultaneously, each of which is critical. FRACTURING FLUID METERING PUMP PROPORTIONING CONTROL SAND BULK OR SACK

AGITATOR

SAND - FLUID MIXTURE TO PUMP TRUCK PRESSURIZER

Fig. 1.8 - Schematic Diagram of Sand Fluid Proportioner.

Early Fracture Design The first treatments were designed by very complex application charts, nomographs and calculations to arrive at the treatment size to be pumped. The calculations generally predicted a treatment size of 800 gallons, or multiples thereof, of fluid, and the sand at concentrations of around one-half to three-fourths lbm/gal. A hit and miss method of designing treatments was employed until the mid-1960s when programs were developed for use on simple computers. The original programs, based on work developed by Howard and Fast11 on fluid efficiency and the shape of a fracture system, were a great improvement. Since that time, many innovations have been introduced through

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February 1993

History of Hydraulic Fracturing

Fig. 1.9 - Computer Control Console.

mathematical modeling in both fixed height, two-dimensional and variable height, three-dimensional solutions. Today, programs are capable of determining temperature profiles of the treating fluid during a fracturing treatment. Such a profile can assist in designing the gel concentrations, gel stabilizer concentrations, breaker concentrations and propping agent concentrations during the various stages of the treatment. Models have been developed to simulate the way fluids move through the fracture and how the propping agent is distributed. From these simulations, production increases can be determined. Following a fracturing treatment, reservoir models and pressure transient analysis methods can then be used to history match the pressure and production performance to determine what type of treatment was actually achieved. The history of fractured reservoir response analysis dates from the late 1960s. Tinsley et al.12 did work on an electrolytic model to determine the effect fracture lengths and flow capacity would have on the production increase obtained from wells with a different drainage radius. Several others developed mathematical models for similar projections. Nolte and Smith13 developed procedures to correlate between observations made during fracturing treatments and Britt14,15 and Veatch16-18 presented methods to optimize the fracturing process. Several theories have been advanced by this work which added considerably to the understanding of the hydraulic fracturing process. This technology added considerably to the understanding of the hydraulic fracturing process and is summarized in the SPE Monograph Volume 12.19 Marked advancements were achieved by Amoco and the industry during the 1970s and early 1980s. Much of what was learned during this period is now being applied to fracturing oil and gas formations. The most notable contribution was field test procedures and data collection programs developed to better estimate fracture design parameters. These include prefrac stress tests, minifrac February 1993

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Hydraulic Fracturing Theory Manual

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Introduction

calibration treatments and the measurement of bottomhole treating pressures during fracturing. Observations from these tests indicate lateral fracture extension rate, vertical growth behavior, fracturing fluid leakoff rate, and general characteristics associated with defining fracture geometry. This information has led Amoco and the industry to a more precise and systematic approach to fracture treatment design. Well stimulation by hydraulic fracture treatment is an important production engineering process to Amoco Production Company. There are many fields in the United States that would not be in existence today if it had not been for hydraulic fracturing. Some of these include the Sprayberry trend in west Texas; the Pine Island field in Louisiana; many wells in the Anadarko Basin, the Bruy River and Cardinal Fields in Canada, a large number of Morrow wells in northwestern Oklahoma; the entire San Juan basin of New Mexico; the Denver Julesburg basin of Colorado; the East Texas and north Louisiana trend in the Cotton Valley; the tight gas sands of south Texas and western Colorado; the tight gas sands of southwestern Wyoming and many of the producing areas of the northeastern part of the United States. Recent economic developments and the constant fluctuation in petroleum prices have led to a near-halt in the development of tight gas fields until recently. The industry has turned its attention more to low risk, high profit type projects. Still, fracturing remains as important to many of these projects as to the earlier tight gas developments. With continuing advancements in technology, hydraulic fracturing promises to continue playing a vital role in unlocking otherwise unobtainable reserves and extending field life accordingly. For additional information on current hydraulic fracturing technology, refer to the technical references at the end of this chapter.

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Amoco Hydraulic Fracturing Course Outline

1.2 Amoco Hydraulic Fracturing Course Outline The purpose of this course is twofold. The course will present the principles behind the fracturing process which will assist you in understanding the dependencies between fluid hydraulics, rock properties, resulting fracture geometry and associated reservoir response. The second, and most important purpose, is to provide a technical understanding to evaluate the results you achieve. This understanding will allow you to improve field applications and develop new techniques for application. Significant financial benefits are possible by diligently applying the current state of technology, and overcoming arbitrary and poorly implemented procedures and attitudes. A question often asked today is, “What can be changed to maximize profits?” As shown in Fig. 1.10, the optimum treatment results from balancing different parameters, i.e., fracture conductivity, fracture length and reservoir permeability, to achieve the maximum profit. Generally speaking, the desired fracture length for optimal production is bigger for lower permeability formations as shown in Fig. 1.11. Conversely, the desired fracture conductivity for optimal production is greater for higher permeability reservoirs.

Fig. 1.10 - Critical Factors to Optimum Fracture Stimulation.

The optimum treatment will differ from field to field and from one area of a field to another based on reservoir characteristics and treatment cost. Recognize that the amount of fluid and proppant required to achieve a desired penetration will vary greatly from location to location as a function of lithology, wellbore stresses and fracture containment. Therefore, it is very important for overall financial optimization, that the optimization process be completed for each different situation and that at least two or three different fluid and proppant systems be evaluated for each situation. Fig. 1.12, illustrates a simplified schematic of the optimization process used in the design of hydraulic fracture stimulations. The upper portion of Fig. 1.12 considers the reservoir response resulting from fracturing and the revenue produced. The detailed aspects of reservoir behavior are covered in other courses, however, a general discussion of how these topics relate to optimizing revenue through fracture design is included in this manual in Chap. 3 and Chap. 9. The lower porFebruary 1993

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Hydraulic Fracturing Theory Manual

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Introduction

4 3

Frac. 1/2 Length 1000’s Feet

2 1 0 Extremely Very Tight Tight

MD .0001 Micro .1 Darcies

Tight

Near Tight

Conventional

.001 .005 .01 .05 .1 1.0 1 5 10 50 100 1000 In-Situ Gas Permeability

10.0 10,000

100. 100,000

Fig. 1.11 - Desired Fracture Half-lengths for Different Formation Permeabilities.

$ Revenue

Reservoir Simulator

Cum. Prod.

tion of Fig. 1.12, relates to creating the fracture (i.e., the cost aspect). Unlike reservoirs, fractures are created by humans and therefore can be changed and made both longer and wider as required. The design and implementation of a propped hydraulic fracture stimulation treatment is the primary topic of this course.

Years

Length

Fracture Length $ Cost

Fracturing Hydrafrac Simulator

Treatment Vol.

$ Revenue Less $ Cost

Fracture Length

Length

Fig. 1.12- Fracture Stimulation Design--The Total Concept for Optimization.

The topics detailed in this course include how a fracture is created, what proppants should be used to hold it open and how the fluid flow in a reservoir is altered. The effect of fracture penetration, the importance of fracture height development, the concepts of effective wellbore radius, dimensionless fracture conductivity (FCD) and folds of increase (FOI) for steady-state conditions are discussed. The effect of early time transient production and bilinear flow, and the application of economic analysis and revenue optimization are elements of coupled reservoir analysis and

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February 1993

Amoco Hydraulic Fracturing Course Outline

hydraulic fracture treatment designs covered in this course. The financial results obtained in fracturing can be significantly increased, over the standard practice of the industry, through a better understanding of the fracturing process, how to optimize a treatment design, and the implementation of quality control in the field. The nomenclature which follows on the next pages summarizes the most important and frequently used terms in the manual. The SPE Monograph Volume 1219 provides a comprehensive review and list of references on many of the aspects covered in this course.

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Introduction

1.3 Nomenclature BHCP

Bottomhole closure pressure in psi. It is equal to fracture pressure; it is also σc.

BHTP

Bottomhole treating pressure in psi. It is equal to surface treating pressure plus hydrostatic pressure minus friction pressure. It is also equal to BHCP plus PN.

bpm

Barrels per minute.

C

Fracturing fluid leakoff coefficient. It is also equal to Ct in ft/ minute .

CI

Part of Ct. It is the effects of the frac fluid viscosity and relative permeability in ft/ minute .

CII

Part of Ct. It is the effects of the reservoir fluid viscosity and compressibility in ft/ minute .

CIII

Part of Ct. It is the effects of the wall building properties of the frac fluid in ft/ minute .

Ct

The total effects of the frac fluid leakoff coefficient in ft/ minute .

Ct

It is the total compressibility factor of the reservoir and fluid in psi-1. It is used to calculate part of CIII.

E

Modulus of Elasticity in psi.

FCD

A dimensionless fracture capacity. It is related to the contrast in permeability between the fracture and the formation.

FOI

Folds of Increase. It is the ratio of the stabilized production after fracturing to the production before fracturing. It is equal to QFRAC/QUNFRAC.

φ

Rock porosity in decimal percent.

H

Total or gross fracture height in feet.

hhp

Hydraulic Horse Power in hp.

Hp

Permeability Height. That portion of the frac height, H, to which frac fluids may be lost.

k

Reservoir permeability in millidarcies (md).

kf

Fracture permeability in md.

kfw

Fracture conductivity in md-ft.

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February 1993

Nomenclature

K'

A property of gelled frac fluids called consistency index and is shear stress at a strain rate of 1 sec-1. Data supplied by service companies.

L

Hydraulic fracture length from tip to tip. It is equal to 2 times the hydraulic frac radius, xf, in feet.

µ

Viscosity in cp.

n'

A property of gelled frac fluids called Power Law Exponent or Flow Behavior Index. Data supplied by service companies. Related to K'.

OB

Overburden pressure in psi. Generally, it is one times TVD in psi.

∆p

The difference between the pressure in the fracture and reservoir pressure in psi, used in CI and CII.

Pc

Critical Pressure or Pressure Capacity. It is the net pressure above closure pressure where a fracture may become unconfined.

PFCF

Proppant Fall Correction Factor. It is a term used to tell the computer that a proppant other than 20-40 mesh is being used, or that fall is through a crosslinked fluid.

PN

Net Pressure. The pressure in the fracture above closure pressure. It is equal to BHTP minus BHCP.

PPG

Pounds of Proppant Per Gallon of liquid in lb/gal.

PPSG

Pounds of Proppant Per Gallon of Slurry in lb/gal.

Q

Pump rate in barrels per minute (bpm).

Q FRAC --------------------Q UNFRAC

Same as FOI. A measure of the results of the fracture stimulation.

re

Drainage radius in feet. Generally, it is one-half the distance to the next well.

rw

Wellbore radius in feet.

r'w

The stimulated wellbore radius effect due to the fracture in feet. It is the effective or pseudo-wellbore flow radius resulting from the fracture.

S.G.

Specific Gravity relative to water.

SIBHP

Shut In Bottomhole Pressure, PR, in psi.

SIBHT

Shut In Bottomhole Temperature in ° F.

SPF

Perforation density in Shots Per Foot.

February 1993

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Introduction

t

Time in minutes.

σc

Closure Stress. Equal to BHCP.

TVD

True Vertical Depth in feet.

VFRAC

Volume of fracture cavity in cubic feet.

VIN

Volume of frac fluid pumped into the well in cubic feet.

VLOST

Volume of frac fluid leaked from the crack into the formation in cubic feet.

w

Fracture Width in feet (may also be in inches).

w

Average Fracture Width in feet (may also be in inches).

xf

Fracture radius in feet (or fracture half-length). Measured from the center of the wellbore to the end of the proppant on one wing of the fracture.

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February 1993

References

1.4 References 1. Farris, R. F.: U. S. Patent reissued Nov. 10, 1953, Re 23733. 2. Clark, J. B.: “A Hydraulic Process for Increasing the Productivity of Oil Wells,” Trans., AIME (1949) 186, 1-8. 3. Maly, J. W. and Morton, T. E.: “Selection and Evaluation of Wells for Hydrafrac Treatment,” Oil & Gas J, (May 3, 1951) No. 52, 126. 4. Clark, R. C. et al.: “Application of Hydraulic Fracturing to the Stimulation of Oil and Gas Production,” Drill. & Prod. Prac., API (1953) 113-22. 5. Huitt, J. L. and McGlothin, B. B. Jr.: “The Propping of Fractures in Formations Susceptible to Propping-Sand Embedment,” Drill. & Prod. Prac., API (1958) 115. 6. Huitt, J. L., McGlothin, B. B. Jr., and McDonald, J. F.: “The Propping of Fractures in Formations in Which Propping Sand Crushes,” Drill. & Prod. Prac., API (1958) 115. 7. Huitt, J. L.: “Hydraulic Fracturing with Single Point Entry Technique,” JPT, (March 1960) XII, No. 3, 11. 8. Hubbert, M. K. and Willis, D. G.: “Mechanics of Hydraulic Fracturing,” Trans., AIME (1957) 210, 153-66. 9. Anderson, T. O. and Stahl, E. J.: “A Study of Induced Fracturing Using an Instrumental Approach,” JPT (Feb. 1967) 261-67; Trans., AIME, 240. 10. Coulter, G. R. and Wells, R. D.: “The Effect of Fluid pH on Clays and Resulting Formation Permeability,” presented at the Southwestern Petroleum Short Course, Dept. of Petroleum Engineering, Texas Tech University, Lubbock, Texas, April 17-18, 1975. 11. Howard G. C. and Fast, C. R.: “Optimum Fluid Characteristics for Fracture Extension,” Drill. & Prod. Prac., API (1957) 261-70. 12. Tinsley, J. M. et al.: “Vertical Fracture Height--Its Effect on Steady-State Production Increase,” JPT (May 1969) 633-38; Trans., AIME, 246. 13. Nolte, K. G. and Smith, M. B.: “Interpretation of Fracturing Pressures,” JPT, (Sept. 1981), 1767-75. 14. Britt, L. K.: “Optimized Oil Well Fracturing, Phase I Report,” Amoco Production Company Report F84-P-23 (May 25, 1984). 15. Britt, L. K.: “Optimized Oil Well Fracturing, Phase II Report,” Analysis of the Effects of Fracturing on the Secondary Recovery Process; Amoco Production Company Report F85-P-7 (Jan. 24, 1985). 16. Veatch, R. W. Jr.: “Overview of Current Hydraulic Fracturing Design and Treatment Technology--Part 1,” JPT (April 1983) 677-87. 17. Veatch, R. W. Jr.: “Overview of Current Hydraulic Fracturing Design and Treatment Technology--Part 2,” JPT (May 1983) 853-64. 18. Veatch, Ralph W. Jr.: “Economics of Fracturing Some Methods and Case Study Examples,” Amoco Production Company Report F89-P-58 (Aug. 3, 1989).

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Introduction

19. Gidley, J. L., Holditch, D. E., Nierode, D. E., and Veatch, R. W., Jr.:, Monograph Series, SPE, Richardson, TX (1989) 12.

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February 1993

Chapter

2

Fracturing Models

Fracture design models attempt to simulate the natural phenomena associated with the hydraulic fracturing process. They account for the total volume of fluid injected in the ground (continuity equation) and estimate the fluid volume that leaks off in the formation and the fluid volume that remains within the fracture; they relate fracture width to the applied hydraulic pressure (elasticity equation); they account for pressure loss due to flow within the fracture (fluid flow equation); and they predict fracture dimensions due to fluid pressure by satisfying a fracture propagation criterion at the fracture tip. In many cases, the consideration of continuity and elasticity equations provides insight into the basic relationship between directly measured qualities of the fracturing process, such as injected volume and treating pressure.

2.1 The Continuity Equation The continuity (or volume balance) equation expresses the relationship: Volume Pumped = Volume Lost + Volume in Fracture or V IN = V LOST + V FRAC

(2.1)

.

It states that the volume pumped into the fracture is equal to the volume lost to the formation by fluid loss plus the volume remaining or stored in the fracture. The individual terms (for a constant height fracture, pumped at a constant rate) are defined as follows: V IN = Qt ( proportional to total cost )

(2.2)

V LOST ≅ 3CH p L t ( proportional to lost cost )

(2.3)

V FRAC = wHL ( proportional to effective cost)

(2.4)

Substituting Eqs. (2.2) - (2.4) into Eq. (2.1) , and solving for the tip to tip length, L, gives Qt L = ------------------------------------3CH p t + wH

July 1993

2-1

(2.5)

Hydraulic Fracturing Theory Manual

2

Fracturing Models

where Q = pump rate in cubic feet per minute (5.6 cu. ft. = 1bbl), t= pump time in minutes, C = fluid loss coefficient in ft/ min , Hp = permeable fracture height in feet, w = average fracture width in feet, and H = total fracture height in feet. Eq. (2.5) determines the length which will result for a fracture treatment in terms of the other variables and compares within 10-15% of computer fracture models. Also this equation can be rearranged to form a quadratic equation in terms of t . Solving this equation gives the pumping time (i.e., VIN) to obtain a desired fracture length. Inspection of Eq. (2.5) indicates that increasing any of the terms in the denominator (except time) will decrease the fracture length. In particular, changing the height, H, and/or fluid loss coefficient, C, can have dramatic effects on fracture length. Fig. 2.1 shows an example of the relationship between fracture height and length for a given treatment volume. Fig. 2.2 shows a similar relationship between fluid loss coefficient and length. 600

Height - Feet

500 400 300 200 100 0 0

1000

2000

3000

Fracture Length - Feet Fig. 2.1 - Fracture Height vs. Fracture Length 300,000 Gallon Treatment Design.

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July 1993

The Continuity Equation

Low Fluid Loss Polymer Emulsion

Length

Fracture Length (ft)

2000

Height High Fluid Loss

1500 Water & Oil Base Gels

1000

150 ft Fracture Height 20 BPM

500

0 20

60

100

140

180

220

260

Volume (1000s Gallons) Fig. 2.2 - Fracture Length vs. Volume Pumped for Low (emulsion) and High (base gels) Fluid Loss Behavior.

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Hydraulic Fracturing Theory Manual

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Fracturing Models

2.2 Model Differences and the Elasticity Equation The width term, w , in Eq. (2.5) , has caused the industry many problems because two fundamentally different model assumptions are used for constant height designs which give significantly different results. The two models are commonly termed the Perkins and Kern (PK)1 and the Khristianovic (K) model.2 The differences in the models result from their different applications of the theory of elasticity to hydraulic fracturing. It should be noted that the Perkins and Kern model was later extended by Nordgren,3 while the Khristianovic model was extended by Geertsma and de Klerk.4 As a result, “PK” and “PKN” are used synonymously for the Perkins and Kern model as “K” and “GDK” are for the Kristianovic model. A classical solution in the theory of elasticity predicts that, for an infinite, elastic slab, in planestrain (i.e., deformation restricted between parallel planes in the slab), with a pressurized slit through the slab, the slit will deform into the shape of an ellipse. The ellipse will have a major axis equal to the slit half-length and a minor axis proportional to the pressure and slit length, and inversely proportional to the elastic modulus as seen in the upper portion of Fig. 2.3. This elastic solution was applied to hydraulic fracturing, but in different directions as seen in the bottom portion of Fig. 2.3. As shown, the ellipse in the PK model is vertical while the ellipse in the K model is horizontal. As a result, a continuing debate has been waged during the last 30 years as to which is correct. This debate is more than academic since the two models predict significantly different fluid volumes to achieve a desired fracture length. In this regard, the K model requires greater volume per foot of length. Additionally, the K model implicitly assumes free slip between the fractured bed and bounding beds which is physically improbable at depth.

Fracture Pressure and Width VOLIN = VOLLOST + VOLFRAC

WHL

ELLIPSE

ELASTICITY

D W~ _ p E

P=S+p

TWO MODELS

L=D

L/2 ELLIPSE

“PERKINS & KERN” MODEL

ELLIPSE

“KHRISTIANOVIC” MODEL

Fig. 2.3 - Two Very Different Models.

The prevailing thought within Amoco is that the PKN model is most applicable for fractures which are long when compared to their height and that the GDK model is more applicable for fractures

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July 1993

Model Differences and the Elasticity Equation

which are short compared to their height. In this latter scenario, a “penny frac” or a 3 Dimensional model would be more appropriate. Fig. 2.4 shows the resulting difference between the PKN and GDK models as a result of the different application of the elasticity relation. Note that their relationships for viscosity (for flow of a Newtonian fluid), rate, and rock modulus are the same. However, the relationships for pressure and width are very different as shown in Table 2.1. Table 2.1 - Comparison of Perkins and Kern and Khristianovic Models. Elasticity

Fluid Flow (Newtonian)

Perkins and Kern

W∼H

p ~ L1/4

Khristianovic

W∼L

p ~ --------1/2

1

L

P&K Model

W

I. Elasticity

W

II. Friction From Fluid Flow (Newtonian)

III. Combining I & II

W

∼ H--E- p

L _ W~ p P

= -4π W

QL -) ∼ ( µ------E

3/4

p

Khrist. Model

2 1/4

1/4

- ( µ QL ) ∼ E-------H

W

1/4

QL  ∼  µ--------- EH 

3/4

p

E - ( µ QL ) ∼ -------1/2 L

1/4

Fig. 2.4 - Comparison of Perkins and Kern and Khristianovic Models.

For the general case with length greater than height, the PKN model will predict less width; thus from Eq. (2.5) , the PKN model will generally predict more length. Also, the PKN model predicts that the net pressure (fluid pressure in fracture minus formation closure pressure) increases as length, L, (or time, t,) increases, while the GDK model predicts net pressure decreases with length, L, (or time, t,) as shown on Fig. 2.5. Bottomhole pressure measurements indicate that, if height is relatively constant and significantly smaller than fracture length, the pressure will increase as predicted by the PKN model. Also, downhole televiewer pictures obtained by Amoco, which directly measured the fracture width in an open hole completion, indicated that the pressure-width relationship of the PKN model was most applicable.

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Fracturing Models

PKN Model p

∼L

1/4

GDK Model p

∼ (µQ )

1/4

p

1 ∼ -----1/2

log p

log p

L

log L ) (TIME

log L

“PKN” log L

“GDK”

log t (or VOL.)

Fig. 2.5 - “Perkins & Kern” (PKN) Model and “Khristianovic” (GDK) Model.5

The consequence of the different width assumptions in the models can be seen by a comparison of service company designs based on exactly the same requested input. This comparison was made by Amoco in 1980. The input variables supplied to the service companies are shown in Table 2.2. Table 2.2 - Input Values - Service Company Designs. Input Variables

Input Values

Propped Radius

2000 ft

Frac Height

200 ft

Leakoff Height

100 ft

Modulus

6x10 psi

Loss Coefficient

0.001 ft/min

Pump Rate

25 BPM

Viscosity

100 CP

Proppant Concentration

1 lb/ft

Frac gradient, depth, surface and reservoir temperatures, and rock type also specified.

Table 2.3 shows the dramatic variations in the results because of the different schools of thought in each company at that time. As shown, the Halliburton and Dowell Programs were based on the GDK model, while the Western, Smith and Amoco programs were based on the PKN model. It is noted that the BJ program set the leakoff height to 200 ft instead of 100 ft and the Western model assumed that the fracture width down the complete length was the maximum value at the wellbore. The large differences in the output indicate the impact of modeling assumptions associated with Hydraulic Fracturing Theory Manual

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Model Differences and the Elasticity Equation

comparing service company bids and highlight the importance of knowledgably designing your own treatments. However, many oil companies still rely on the service companies for designs. Table 2.3 - Results - Service Company Designs.

Model Type

Average Width Inches

Sand, M lb

Volume, M gal

Pad, M gal

Amoco

PKN

0.24

715

250

110

B-J

PKN

0.39

800

630

125

Dowell

GDK

0.51

1280

420

110

Halliburton

GDK

0.69

1150

535

150

Smith

PKN

0.29

657

166

36

Western

PKN

0.40

1425

400

80

Company

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Fracturing Models

2.3 References 1. Perkins, T. K. Jr. and Kern, L. R.: “Widths of Hydraulic Fractures,” JPT (Sept. 1961) 937-49; Trans., AIME, 222. 2. Khristianovic, S. A. and Zheltov, Y. P.: “Formation of Vertical Fractures by Means of Highly Viscous Fluids,” Proc., Fourth World Pet. Cong., Rome (1955) II, 579. 3. Nordgren, R. P.: “Propagation of a Vertical Hydraulic Fracture,” SPEJ (Aug. 1972) 306-14; Trans., AIME, 253. 4. Geertsma, J. and de Klerk, F.: “A Rapid Method of Predicting Width and Extent of Hydraulically Induced Fractures,” JPT (Dec. 1969) 1571-81; Trans., AIME, 246. 5. Nolte, K. G. and Smith, M. B.: “Interpretation of Fracturing Pressures,” JPT (Sept. 1981) 1767-75.

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Chapter

3

Reservoir Analysis

3.1 Reservoir Response To Fracture Stimulation To understand the reservoir response to fracture stimulations, one must understand the interrelationship between the important reservoir and fracture variables. These variables include reservoir permeability, fracture conductivity, and fracture half length. The Dimensionless Fracture Capacity, FCD, describes this interrelationship. This equation: kfw F CD = --------k xf

(3.1)

relates the fracture's ability to flow fluids to the wellbore to the reservoir's ability to flow fluids to the fracture. If, for example, FCD is low (FCD ≤ 1.6) the fracture has finite conductivity and the reservoir fluids would rather flow towards the wellbore than the fracture. It further indicates that increasing fracture length would not result in improved reservoir response. Conversely, if FCD is high (FCD ≥ 500), the fracture has infinite conductivity. As a result, increasing fracture conductivity would not improve reservoir response. For practical purposes, fractures having FCD > 30 act as infinite conductivity fractures. The parameters used to define FCD are illustrated in Fig. 3.1. • Fracture Length, xf, feet • Formation Permeability, k, md • Fracture Flow Capacity, kfw, md-ft k kf w xf

Fig. 3.1 - Major Factors Affecting Performance.

Fracture Length Fracture length or penetration generally has the greatest impact on low permeability reservoirs. The following examples are from the Wattenberg Field, which is operated by Amoco Production

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Reservoir Analysis

Company. This field is located north of Denver, Colorado, and has a permeability of about 0.005 md. Fig. 3.2 shows the effect of fracture half-length, xf, on cumulative gas production. As shown, increasing fracture half length results in significant incremental gas recovery over a 25-year period. 2000

Cummulative Gas Production - MMCF

1800 1600

FRACTURE LENGTH

1400 1200 1500 ft

ADDITIONAL RECOVERY BY INCREASING FRACTURE LENGTH

1000 1000 ft

800 600

400 ft

400

RADIAL FLOW

200 0

2

4

6

8

10

12

14

16

18

20

22

24

Time (years)

Fig. 3.2 - Effect of Fracture Length Cumulative Gas Produced (25 Years).

Reservoir Permeability Reservoir permeability, k, and its effect on fractured well performance is illustrated in Fig. 3.3 and Fig. 3.4. Shown in the figures is the pressure distribution map for only one quadrant of a fractured well. The pressure distribution map was obtained from a computer simulation after the well, located in the upper left corner, was produced for a period of time. The simulated fracture in Fig. 3.3 is located vertically on the left and has a high fracture flow capacity, kfw. The formation permeability, k, in the computer simulator was very low at 0.005 md (5 micro darcies). Contours of the pressure profile in psi were made and because gas flows perpendicular to these pressure contour lines, “streamlines” which represent the path by which the gas travels to the well can be drawn. Since the formation permeability is extremely low relative to the fracture flow capacity (kfw), the flow is nearly linear and the fracture acts as an infinite conductivity fracture. As a result, the fracture carries almost all the total gas flow to the well. The path of least resistance is the shortest distance to the fracture. Fig. 3.4 shows a pressure distribution map for a fractured well with the same fracture flow capacity as in Fig. 3.3, but this time the formation permeability is significantly higher at 100 md. Since the formation permeability more nearly approximates the fracture flow capacity, equal pressure lines become circular and the flow is nearly radial as can be seen by converging flow lines. In this case, the fracture carries a relatively small fraction of the total gas flow which indicates that the benefit Hydraulic Fracturing Theory Manual

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Reservoir Response To Fracture Stimulation

1200 psi

1000 psi

800 psi

600 psi

Well

400 psi

1200 1200psi psi

1000 1000psi psi

800 psi 800 psi

Well

600 psi 600 psi

400 psi 400 psi

realized from the fracture stimulation was minimal. In this case, the path of least resistance is primarily via the reservoir.

Pressure Contour PRESSU Lines F R A C T U R E

Pressure Contour Lines F R A C T U R E

Streamlines

Flow is nearly linear FCD > 25 (Inifinite Conductivity) Fracture carries almost the total gas flow to the well

Fig. 3.3 - Pressure Distribution and Approximate Streamlines, Reservoir K = 0.005 md.

Streamlines

Flow is nearly radial FCD << 25 (Finite Conductivity) Fracture carries almost no gas to the well

Fig. 3.4 - Pressure Distribution and Approximate Streamlines, Reservoir K = 100 md.

Fracture Flow Capacity The key difference in Fig. 3.3 and Fig. 3.4 is the ratio of the fracture flow capacity to the reservoir permeability, k. Fracture flow capacity is defined as the product of the permeability in the fracture, kf, and the fracture width, w, with dimensions of md-ft. It is also referred to as fracture conductivity. Shown in Fig. 3.5 are three types of fracture flow capacity. An infinite flow capacity fracture is a fracture that acts similar to a large diameter pipeline where there is essentially no pressure drop from the tip of the fracture to the wellbore. A finite flow capacity fracture has a pressure drop along the fracture that is proportional to the fracture flow capacity, kfw. Nearly all created fractures have finite capacity. The reservoir response associated with variable conductivity fractures is governed by the arithmetic average flow capacity. Estimates of kfw are available from the service companies and Amoco's Production Research (APR) Department. The STIM-LAB data in Fig. 3.6 shows the effect of proppant type on liquid permeability. The entire set of Stimlab data can be accessed in the Proppants Manual or from APR. Fig. 3.6 shows that the manufactured proppants bauxite, intermediate density proppant and zirconia have high permeability up to very high closure stresses.

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Reservoir Analysis

(Fracture Perm. x Fracture Width)

kf INFINITE CAPACITY

kf FINITE CAPACITY

k f1

k f2

VARIABLE FINITE CAPACITY

Fig. 3.5 - Fracture Flow Capacity.

The resin coated sand has intermediate permeability values, and the sands (Brady and Ottawa) have the lowest values at higher stresses. Fig. 3.6 indicates that the “Brady” sand has higher permeability for closure pressure less than 5000 psi (i.e., nominally 6000 to 7000 ft) than the more pure silica sand of the “Ottawa” type. This results because the Brady sand tends to be coarser (i.e., more toward 20 mesh) and more angular. At higher stresses the less pure and more angular sand has less permeability (i.e., more crushing). Fig. 3.7 shows laboratory values of conductivity, kfw for both Brady and Ottawa type sands. Note that the Ottawa types are not available in the coarser sizes, while Brady is not available for the finer sizes. Notice that at 4000 psi, the 8/16 Brady sand has about 5 times more conductivity or capacity than the commonly used 20/40 Ottawa (i.e., 15,000 vs 2800 md ft). Post treatment evaluation experience indicates that in-situ capacity is dramatically less than these laboratory values. This results from gel residues, fluid loss additives and potentially rock debris. Indicated values are about 1/3 - 1/10 of the lab values. In addition, Amoco's design program indicates that propped widths of more than 1 lb/ft2 are difficult to achieve. It is noted that some service companies claim they achieve 4 lb/ft2. Since the laboratory standard (i.e., Fig. 3.7 is 2 lb/ft2); a further reduction for width must be made. The best method to determine in-situ capacity is to perform well tests in the field and use the bilinear flow analysis techniques discussed in Section 3.3. If actual in-situ values are not available, the following guideline for capacity should be used. k f w lab data 2 expected k f w = 0.3 ---------------------------------lb/ft expected 2 lb/ft lab data

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(3.2)

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Reservoir Response To Fracture Stimulation

Fig. 3.6 - Effect of Proppant Type on Flow Capacity.

Most lab tests are run at 2 lb/ft2. However, your test data may be different. Proppant concentration at which the tests were run should be available, or the data should not be used. The 0.30 factor is a permeability reduction applied to the lab data to correct for inherent differences in in-situ fracture conditions and idealized laboratory conditions. This is nothing but a “fudge-factor” and varies widely. This correction may be used for scoping studies, but pressure transient testing is still the preferred technique to obtain the actual in-situ value of kfw. The importance of fracture conductivity and fracture length are illustrated in Fig. 3.8 through Fig. 3.10. These figures show the results of simulations which combine variations of conductivity and length with reservoir permeabilities of 0.005, 0.08, and 5.0 md, respectively. The results are shown as the ratio of flow rate after fracturing to that before stimulation. This ratio is known as “Folds of Increase,” FOI.

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40

60

80

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3-6

1.0

1 9 8 7 6

0

2

2

0.4

0.3

0.2

3

2

0.6

4

5

3

3

0.8

4

6

4

5

10

1 9 8 7 6

8

20

2

3 30

4

5

0 9 8 7 6

Fracture FractureConductivity, Conducitivty,klklxxWf, Wf,darcy darcyxxfoot, foot,DDxxftft

2

4

“Brady” Sand

Closure Stress, psi in 1000’s 6 8

Note: No allowances have been made for embedment or any form of pack damage.

20/40

16/30

12/20

8/16

API Mesh Size 6/12

10

12

14JUL83 RWA

Specific Gravity: 2.65 (22.1 lb/gal) Bulk Density: 1.61 g/cm (100.5 lb/ft3

Class D “brady” Frac Sand Hickory Sandstone 12/20 & 20/40 Bidahochi Formation 6/12-12/20 Aeolian dune sand

Effect of Proppant Size on Flow Cpacity

14

1

2

3

4

5

1 9 8 7 6

2

3

4

5

0.2

0.3

0.4

0.6

0.8

1.0

2

3

4

6

8

10

20

2

1 9 8 7 6

30

40

3

4

5

10 100 9 8 80 7 6 60

2

4

70/140

40/70

30/50

20/40

16/30

12/20

“Ottawa” Sand

10

12

12JUL83 RWA

Note: No allowances have been made for embedment or any form of pack damage.

Closure Stress, psi in 1000’s 6 8

API Mesh Size

Proppant Concentration 2.0 lb/ft2

Specific Gravity: 2.65 (22.1 lb/gal) Bulk Density: 1.65 g/cm3 (102.7 lb/ft3)

Galesville Sandstone Ironton/Galesville Sandstone Jordan Sandstone Saint Peter Sandstone

Class E “ottawa” Frac Sand

Effect of Proppant Size on Flow Capacity

3 Reservoir Analysis

Fig. 3.7 - Laboratory Fracture Conductivity for Frac Sands.

July 1999

Fracture Conductivity, kl x Wf, darcy x foot, D x ft

Reservoir Response To Fracture Stimulation

Fig. 3.8 shows for a formation permeability equal to 0.005 md that as the fracture flow capacity, kfw, is reduced from 1000 md-ft to 1.0 md-ft, the effect of improved flow rate due to increased fracture length is diminished. However, the effect becomes significant when kfw is increased from 1 to 10 and 100 md-ft. Beyond a kfw = 100 md-ft, the effect of increasing fracture flow capacity has diminishing returns. Fig. 3.9 and Fig. 3.10 show that as formation permeability increases, the effect of improved flow rate due to increasing the fracture length diminishes further. 12 12

11

11

10

K=0.005 MD

10

Qfrac/Qunfrac

Qfrac/Qunfrac

8 7

kfw = 10 Md-ft

6

Kfw=1000 Md-ft

9

kfw = 1000 Md-ft kfw = 100 Md-ft

9

K=0.05 MD

5

8 7 Kfw=100 Md-ft

6 5 4

4

Kfw=10 Md-ft

3

3

2

2

Kfw=1 Md-ft

kfw = 1 Md-ft

1 0

100

200

300

400

500

600

700

1 0

800

100

200

300

400

500

600

700

800

Fracture-Half Length

Fracture-Half Length

Fig. 3.8 - Formation Permeability Equal to 0.005 md.

Fig. 3.9 - Formation Permeability Increased to 0.05 md.

12 11

K=5.0 MD

10 9

Qfrac/Qunfrac

8 7 6 5 4 3

Kfw = 1000 Md-ft

2

Kfw = 100 Md-ft Kfw = 10 Md-ft

1 0

100

200

300

400

500

600

700

800

Fracture-Half Length

Fig. 3.10 - Formation Permeability Equal to 5.0 md.

Fig. 3.9 shows a similar graph where formation permeability, k, is increased to 0.05 md. Notice that increasing the flow capacity, kfw, above 100 md-ft will still have an effect on improving flow rate. This was not the case when k was 0.005 md. Also note that for fracture flow capacities equal to 10 md-ft or lower, there is little rate improvement as the fracture length increases.

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Reservoir Analysis

Fig. 3.10 shows a similar plot with formation permeability, k, of 5.0 md. This plot shows that increasing fracture length beyond 200 ft in a 5 md reservoir, has little productivity advantage. Fig. 3.10 exposes the myth that fractures are only for low permeability wells. As reservoir permeability increases, the Qfrac/Qunfrac ratio decreases for a given fracture length and conductivity. But since for radial flow, the base rate is directly proportional to permeability, the base rate (Qunfrac) is increasing. Would you invest in a frac for a 5 md well making 10 MMCFD? Fig. 3.10 indicates that a 100 ft, 1000 md-ft frac would make it a 25 MMCFD well. When the importance of short, high conductivity fractures is better understood, many high permeability wells will be fractured in the future. In general, wells in high permeability reservoirs are the least expensive to stimulate and often provide the greatest incremental benefit. Fracture Orientation As a reservoir's permeability decreases, the drainage pattern becomes more elliptical (i.e., smaller aspect ratio) for an optimum fracture. This results because of two reasons: first, the drainage perpendicular to the fracture face decreases, and second, the optimum fracture length is longer. Fig. 3.11 shows the effect of fracture orientation on reservoir drainage. This figure shows the elliptical patterns after 10 and 25 years for Wattenberg reservoir conditions on 320 acre spacing. The upper portion of Fig. 3.11, shows fractures placed properly with respect to the fracture orientation. As shown, there is little interference and relatively complete drainage would occur. However on the lower portion of Fig. 3.11, for a 45° azimuth, there is significant overlap of the patterns and substantial areas of the reservoir that will not be drained. Also note that the contours are for a 300 psi drawdown at 10 and 25 years - very far from depletion. If a similar contour map of the well configuration (unfavorably oriented) shown in the lower portion of Fig. 3.11, was made after 100 years of production, it might show as complete a coverage or drainage as the well configuration in the upper portion of Fig. 3.11 has shown in 25 years. It suffices to say that fracture orientation can have a significant affect on both ultimate recovery and rate acceleration benefits derived from fracturing. It is obvious that to generally benefit from knowing the orientation, well placement must be selected in a manner that differs from normal practices. The required spacing is with wells closer in the direction perpendicular to the fracs and farther apart in the direction of the fracs. Also since the orientation is likely not to be near 0° or 45° , the optimum well placement will be quite different than normal patterns of subsequent quartering sections. An SPE paper by M. B. Smith1 gives an excellent study of the effect of fracture azimuth, well spacing, and lost production for Wattenberg.

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Reservoir Response To Fracture Stimulation

DRAINAGE AREAS INITIAL PRESSURE - 2800 PSI FORMATION PERMEABILITY = 0.004 md

10 YEARS 25 YEARS

5280'

2500 PSI

5280

2500 PSI 10 YEARS

5280

DRAINAGE AREAS INITIAL PRESSURE - 2800 PSI FORMATION PERMEABILITY = 0.004 md

25 YEARS

5280

Fig. 3.11 - Optimum Well Placement vs. Fracture Orientation.

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Reservoir Analysis

3.2 Steady-State Reservoir Response The fracturing response for wells in moderate to high permeability reservoirs quickly reaches a pseudo steady-state condition which can be modeled by radial flow behavior. This is not the case for very low permeability formations which are in transient flow for a significant part of their productive life. Transient flow will be addressed in Section 3.3. The pseudo steady-state radial flow for fractures in moderate-to-high permeability reservoirs permits modeling by the “effective wellbore” concept. This concept was introduced by Prats2 along with the term, FCD, discussed previously (page 3-1). Effective Wellbore Radius, r'w This powerful tool indicates that fracturing wells in moderate-to-high permeability reservoirs is equivalent to increasing the area of the wellbore, i.e., a giant “under-reaming” job. Thus fracturing in moderate-to-high permeability reservoirs is equivalent to enlarging the wellbore. Consequently the relative benefits of fracturing are the same for heavy or light oils. Theoretically, for an infinite conductivity fracture, Prats found that r' w = ( 0.5 ) x f ; F CD large

(3.3)

Taking the wellbore analog further and using the steady-state radial flow equation, the ratio of production after and before fracturing is ln ( r e /r w ) q -----f = FOI = ----------------------qo ln ( r e /r' w )

(3.4)

where FOI= folds of increase, qf = postfrac production rate, qo = prefrac production rate, re = external drainage radius, rw = actual wellbore radius, and r'w = effective wellbore radius. When evaluating the ratio of production in Eq. (3.4), the drawdown pressure, permeability and viscosity are assumed the same before and after fracturing. Prats also gave the theoretical relationship between r'w and dimensionless flow capacity. Fig. 3.12 gives this relationship in terms of FCD. The figure shows that for FCD > 30, that r'w = 0.5 xf; i.e., the fracture acts as an infinitely conductive fracture and there is no benefit from increasing FCD. Fig. 3.12 also shows for small FCD (i.e., less than 0.3) that r'w is independent of the fracture length and depends only on conductivity. Studying Fig. 3.12 will reveal where the producer should be spending his money to increase the results of a fracture stimulation. For example, if the reservoir permeability is 10 md, the fracture has a conductivity of 1000 md-ft, the fracture half length is 500 ft, wells are 2000 ft apart, and borehole diameter is 5.5 in: Hydraulic Fracturing Theory Manual

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July 1999

Steady-State Reservoir Response

F CD = 1000/10 × 500 = .2 From Fig. 3.12, for an FCD = 0.2, r' w /x f = .048 Therefore, r' w = .048x f = .048 × 500 = 24' The FOI = (ln 1000/0.229(ID of 5.5 in CSG))/(ln 1000/24) FOI = 7.6/3.73 = 2.04 Assuming that this FOI is not acceptable, will a bigger frac help? x f = 1000 ft F CD = 1000/10 × 1000 = .1 From Fig. 3.12 r' w /x f = .024 for F CD = .1 r' w = .024 x f = .024 × 1000 = 24 ft . Therefore, FOI = (ln 1000/0.229)/(ln 1000/24) is the same as before. FOI = 2.04 Notice that the cost of the fracture stimulation would have more than doubled by going from xf = 500 ft to xf = 1000 ft with NO increase in r'w or FOI. Suppose, instead of a longer frac, the decision is made to improve kfw. If kfw = 2000 md-ft instead of 1000 md-ft. F CD = 2000/10 × 500 = .4 r' w /x f = .09 r' w = .09 x f = .09 × 500 = 45 ( ln 1000/0.229 ) FOI = -------------------------------------( ln 1000/45 ) = 7.6/3.1 = 2.45 July 1999

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Reservoir Analysis

Fig. 3.12 - Effective Wellbore Radius vs. FCD.

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July 1999

Steady-State Reservoir Response

Notice by doubling conductivity, a productivity increase of 20% has been accomplished. A review of Fig. 3.7 indicates that conductivity could be doubled simply by changing from 20/40 to 16/30 mesh sand. In summary, for FCD less than 0.5, increasing xf is a total waste of time and investment. The investment should be made on a higher conductivity proppant. Another example, if k = 0.02 md, kfw = 1000 md-ft, xf = 1000 ft, r e = 2000 ft, r w = 0.229 ft F CD = 1000/.02 × 1000 = 50 r' w /x f = .5 r' w = .5 x f = .5 × 1000 = 500 ft ( ln 2000/0.229 ) FOI = -------------------------------------( ln 2000/500 ) = 8.294/1.386 FOI = 5.98 The decision is made to improve fracture conductivity, kfw from 1000 to 2000. F CD = 2000/.02 × 1000 = 100 r' w /x f = .5 ( ln 2000/0.229 ) FOI = -------------------------------------- which is the same as before ( ln 2000/500 ) = 5.98 Notice, greatly improving fracture conductivity, kfw, had NO effect on increasing FOI. However, if xf is doubled to 2000 ft, F CD = 1000/.02 × 2000 = 25 r' w /x f = .48 r' w = .48 x f = .48 × 2000 = 960 ft

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Reservoir Analysis

( ln 2000/0.229 ) FOI = -------------------------------------( ln 2000/960 ) = 8.294/.734 FOI = 11.3 It is evident from the above, that if FCD is greater than 25 to 30, improving fracture conductivity is not helpful. The investment should be made to achieve more fracture length to increase FOI, if the increased production offsets the increased cost of the treatment (i.e., economics, addressed in Chap. 9). When FCD's are between 0.5 and 25, FOI will experience an increase if xf or kfw is increased. Therefore when FCD's fall in the range of 0.5 to 25, economics must be used to determine whether improving conductivity or creating longer fractures, or some combination of both, is the most cost effective (i.e., profitable). A Direct Way Of Finding FOI In using the FOI technique just shown, xf must be determined by trial and error for a design. That is, once a FOI is selected, a r'w can be calculated that will be required to effect a given production increase. However, since for finite conductivity fractures, xf affects both r'w and FCD, the xf is required to yield the desired FOI. Fig. 3.13 shows a modified version of Fig. 3.12 which includes the conversion of ( ln r e /r w ) FOI = ------------------------( ln r e /r' w ) on the left vertical axis. On the right vertical axis are various xf /re curves. The horizontal axis is kfw/kre. This parameter should be known for specific proppant size and concentration (i.e., kfw) since the k and re should be known. Also from xf /re on Fig. 3.13, xf can then be determined from the known re. Fig. 3.14 shows the use of Fig. 3.13 for a case with a desired FOI = 5 (denoted by “a”), 160 acre spacing (denoted by “b”), a horizontal line (denoted by “c”), the value of kfw/kre = 1.1 (denoted by “d”), the intersection (denoted by “e”), and finally the indicated xf /re of 0.75 (denoted by “f”) to achieve the FOI. Fig. 3.13 can also be used in reverse; i.e., find the FOI for a given xf /re. Another example, the objective is an FOI = 4, well spacing is 640 acres (re = 2640), k is 0.1 md and the proppant selected will have a kfw of 1320 md-ft at the proposed concentration and closure stress. This gives kfw/kre = 5

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Steady-State Reservoir Response

What frac radius will be required to achieve this FOI? Enter Fig. 3.13 from the left vertical axis with FOI. Find the intersection for FOI of 4 and the well spacing of 640 acres. This determines r'w/re. A horizontal line should be drawn from the intersection of the FOI and the spacing line, completely across the graph. Then enter Fig. 3.13 from the bottom with kfw/kre of 5. Draw a vertical line up to intersect the r'w /re line. A curved line should be drawn to the right vertical axis from the intersection of kfw/kre and r'w/re parallel to the xf /re lines, xf/re is then determined to be 0.2. Therefore, x f /r e = 0.2 x f = 0.2 ( r e ) = 0.2 ( 2640 ft ) x f = 528 ft Notice, that by varying kfw on the horizontal axis, xf /re and therefore xf will change. Studying this graph will also show quickly where to invest time, effort and money. When the xf /re curves become horizontal, increasing kfw will not result in an increase in FOI. Also, when kfw/kre is very small, increasing xf has a minimal effect on FOI. Optimizing Fractures for Secondary Recovery When designing any fracture stimulation, engineers must consider two primary factors: (1) designing the treatment to yield the highest productivity or injectivity per dollar cost, and (2) designing the treatment to minimize any loss in reserves. For moderate permeability wells under primary recovery, fracture length should be optimized to reservoir permeability and fracture conductivity. For reservoirs under secondary recovery, the fracture length must not only be economically optimized as above, but other factors such as the impact of fracture length and fracture orientation upon recovery must be addressed. Two research reports by L. K. Britt,3,4 have been published which provide significant insight into the importance of length and fracture orientation on secondary recovery projects.These reports drew several conclusions that are pertinent to fracture stimulation design in waterfloods: 1. The older potentiometric reservoir response models, such as McGuire and Sikora are invalid. 2. Prats' “effective wellbore radius” concept (Fig. 3.12), whereby the effect of a fracture upon reservoir response is modeled as an increased wellbore radius, is valid if frac lengths are less than 25% of the interwell distance. 3. Short fractures cause no loss in reserves, and can contribute significantly to rate acceleration. July 1999

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Fig. 3.13 - Folds of Increase vs. Relative Conductivity.

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Steady-State Reservoir Response

Fig. 3.14 - Folds of Increase vs. Relative Conductivity.

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Reservoir Analysis

4. Fracture length (radius) greater than 25% of the distance between injector and producer may reduce reservoir recovery when the fracture orientation is unfavorable (injector or producer) and improve recovery when the fracture orientation is favorable (injector to injector). 5. The economically optimum fracture stimulation for moderate permeability reservoirs (1-50 md) is short, with very high conductivity. 6. In-situ fracture proppant conductivity is on the order of 10-30% of published laboratory data. To verify that Prats' results were correct using Amoco's reservoir simulators, the Coning model was used to simulate primary recovery from a fractured moderate-permeability reservoir. Runs were made comparing productivity by combining a radial model using Prats' effective wellbore radius to simulate the effect of the fracture, and an areal gridded model using the Coning model with actual fracture parameters. The results were found to be nearly identical. This comparison was further evaluated for secondary recovery by using a model to compare a fracture simulated in a radial mode using Prats' effective wellbore radius to an areal model for a fivespot waterflood pattern with both injectors and producers stimulated with identical fractures (Fig. 3.15). FRACTURE VS. EFF. WELL RADIUS FIVE SPOT PATTERN DEVELOPMENT XFP/XFI EQUALS 1 100

PERCENT ERROR (%)

80 PERCENT ERROR IN WATER/OIL RATIO EVALUATED AT THE ECONOMIC LIMIT OF 2 BDPD

60

40

20

0 0.2

0

0.4

0.6

0.8

1

FRACTURE HALF LENGTH/INTERWELL DISTANCE

Fig. 3.15 - Validation of the Effective Wellbore Radius Concept.

Increasing the fracture length on the gridded model provides the “correct” answer used as the basis for the evaluation. Increasing the effective wellbore radius in the radial model to compare to that

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Steady-State Reservoir Response

in the areal model introduces about 10% error when the fracture length for each well reaches 25% of the interwell distance, implying that Prats' radial flow curves are in error beyond this point. The effect of fracture length on recovery was also evaluated for a five-spot moderate permeability waterflood pattern. Fig. 3.16 shows the results of increasing fracture length on recovery. Recovery is relatively unaffected for fracture lengths up to about 25% of the interwell distance. This data is for the most unfavorable fracture orientation, where the producing well fracture is directly in line with the injection well fracture.

PERCENT LOSS IN RECOVERY

50

40

30

20

10

0 0

10

20

30

40

50

FRAC RADIUS/INTERWELL DISTANCE, %

Fig. 3.16 - Loss in Secondary Recovery vs. FRAC Radius.

It should be noted that even though recovery is about the same for short fractures, the rate of recovery can be significantly different. For moderate permeability, and a maximum fracture length of 25% of the interwell distance, 2 HCPV of water could be injected 20-30 years sooner than if the well were unfractured, significantly increasing the economic viability of the project. Note also that results of a study conducted by Connie Bargas5 indicate that unfavorable mobility recovery processes (i.e., CO2 floods) are even more sensitive to fracture length and orientation. When fracture stimulation is used to work over wells to restore lost injectivity or productivity, we must ensure that the two goals stated at the beginning of this section are met. That is, fractures must be designed to yield the maximum rate of return on investment, and must not reduce recovery due to excessive length. In most cases, the economically optimum length will be less than the maximum to affect recovery. To assure that secondary recovery is not affected by the placement of fractures in the reservoir, the design fracture radius should not exceed the maximums shown in Table 3.1 unless wells are favorably oriented. In any situation where the potential to infill drill a field is high, some guidelines must be established for the tightest well spacing that might be drilled. The maximum design frac length should not be allowed to exceed 25% of that interwell distance. Once a hydraulic fracture is created, and July 1999

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Reservoir Analysis

conductivity established either by proppant or by acidizing, we obviously cannot reduce that frac length. Table 3.1 - Maximum Design Fracture Radius.

Hydraulic Fracturing Theory Manual

Well Spacing

Frac Half-Length

10 ac

165 ft

20 ac

233 ft

40 ac

330 ft

80 ac

466 ft

160 ac

660 ft

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Steady-State Reservoir Response

Class Problem Find:

xf

Given:

k = 1 md, 160 acre spacing, Depth = 6000 ft (normal grad.), re = 1320 ft

Find:

xf for 20-40, 12-20, 6-12 Brady sand to obtain 5-fold increase in production over nondamaged or stimulated wellbore.

Solution: kre = 1 x 1320 = 1320 md-ft Use capacity guidelines (1 lb/ft) @ 6000 ft = 4000 psi kfw - 20-40 500 md-ft [Fig. 3.7 and Eq. (3.2)] 12-20 ____________ 8-16 ____________ Mesh

kfw'

20-40

500

kfw/kre

re/r‘w

xf/re

xf

12-20 8-16

What is the optimum proppant size, and why?

Explain:

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Reservoir Analysis

Acid Fracturing Fracturing with acid in carbonates creates a highly-conductive, etched fracture. Fig. 3.13 can be used for predicting performance of an acid fracturing treatment by assuming FCD = ∞ (i.e., infinite) or effectively greater than 30. The line shown on Fig. 3.17 represents an infinite conductivity fracture (FCD > 30), and is equivalent to the vertical line for a specific kfw/kre for a propped fracture (i.e., line “d” on Fig. 3.14). Equivalently for a given xf /re or FOI a horizontal line can be drawn directly across Fig. 3.17 to determine the relationship between FOI and xf /re. Many carbonate wells are initially acidized and later fractured with proppant. This causes a sand production problem after the fracture treatment because any sand in an acid channel will not be trapped and is eventually washed into the wellbore by production fluids. Therefore, if a propped fracture would give a larger FOI, it would be desirable to conduct this fracture initially, thereby saving the cost of an acid treatment, obtaining more production, and reducing sand production problems. For 40 acre spacing, maximum acid xf = 150 ft, maximum kfw = 1300 md-ft for proppant, find if an acid frac or propped frac appears more optimum for k = 1 md and k = 5 md.

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Steady-State Reservoir Response

Fig. 3.17 - Use of FOI Curves for Acid Fractures.

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Reservoir Analysis

3.3 Transient Reservoir Response The fracturing response for low permeability reservoirs can exhibit a substantial period of time during which steady-state conditions (i.e., a constant folds of increase or effective wellbore radius) do not hold. Steady-state conditions, as discussed in Section 3.2, first become applicable for dimensionless time of about 3, as shown on Fig. 3.18 by the indication of the start of i.e., pseudo radial flow (i.e., semilog straight line). For the period prior to the start of the semilog straight line, the reservoir response must be analyzed using transient conditions such as an aerial extent type curve, as shown in Fig. 3.18, or a reservoir simulator such as Amoco’s GAS3D. aa

Infinite Conductivity Transient Flow

Pseudo Radial Flow

Unstimulated

η defines the degree of stimulation

Fig. 3.18 - Production Decline Analysis.

Fig. 3.18 also shows that fracture conductivity is even more important for transient flow than pseudo steady-state flow. For the steady-state case of Prats (Fig. 3.12), there was little improvement for FCD greater than 10; however, Fig. 3.18 shows that for tDf < 0.1, there is a dramatic reduction in qD (approximately proportional to the inverse of flow rate), or a dramatic increase in rate if η is increased from 1.004 to 1.234. This approximate doubling of flow rate is very significant for fractures in very low permeability reservoirs which can stay in transient flow for a substantial portion of their productive life. The dimensionless time (tDf) on Fig. 3.18 is proportional to k/xf2. Therefore, low permeability reservoirs which require large xf's tend to fall on the left side of Fig. 3.18, while higher permeability reservoirs which require only short, but highly conductive fractures, tend to fall on the right side where the much simpler steady-state analyses are applicable.

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Transient Reservoir Response

Fig. 3.18 also shows finite capacity fracture behavior (i.e., η ≥ 1.045 ≤ 1.234). In finite capacity fractures, bilinear flow can occur. During bilinear flow, the pressure transient has not reached the tip of the fracture; both linear flow from the reservoir to the fracture and linear flow down the length of the fracture are occurring. The bilinear flow region, is very important for two reasons: (1) unique fracture length cannot be found from the production response, and (2) the actual value of conductivity in-situ, kfw can be determined. The log-log curves, either constant rate or pressure, have a 1/4 slope for bilinear flow. Fig. 3.19 shows a plot of pressure change vs. the fourth root of time for fractures with an FCD of greater than 1.6, equal to 1.6, and less than 1.6, respectively. In addition, the lower portion of Fig. 3.19 shows the effect of damage on the fourth root of time behavior. The upper plot on Fig. 3.19 shows that a straight line should result on a pressure change vs. fourth root of time if the fracture is in bilinear flow. It also shows how the data deviates from the straight line (bilinear flow) is a qualitative indicator of FCD. If, for example, the data deviates up from the bilinear flow line this indicates that FCD is greater than 1.6. Conversely, if the data deviates downward from the bilinear flow line the FCD < 1.6. The lower plot on Fig. 3.19 indicates that if the bilinear flow line does not go through the origin, the entrance to the fracture is damaged. This loss of production can result from: • inadequate perforations - reperforate and/or redesign perforations on subsequent wells, • turbulent flow - increase proppant size/concentration, • over displacement of proppant - do not overflush, • kill fluid was dumped into the fracture - let fracture “clean up” before conducting test. Fig. 3.20 shows an example of these plots and the indicated kfw. The data in Fig. 3.20 deviates downward from the bilinear flow line qualitatively indicating that the FCD is less than 1.6. Since FCD is low, efforts should be made to either increase fracture conductivity, reduce fracture length, or both. A more complete presentation of the transient response of fractured wells is included in the Pressure Transient Analysis manual from the PTA course given by the Training Center. Because of the importance of bilinear flow in the analysis of fractured reservoirs and the improvement of treatment design, the section on bilinear flow from the PTA course is included in this chapter for ease of reference.

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Reservoir Analysis

FCD > 1.6

∆p, psi

SLOPE = mbf

FCD < 1.6

BILINEAR END OF FLOW

t1/4, hours1/4

∆p, psi

DAMAGE OR CHOKED FRACTURE

∆ps 0

IDEAL

0

t1/4, hours1/4

Fig. 3.19 - Bilinear Flow on Fourth Root of Time Plot. BILINEAR FLOW ANALYSIS NORTH COWDEN UNIT WELL - A

AMERADA BOMB

Downward Deviation From Bilinear Flow Line indicates FCD is less than 1.6 Mbf = 134 Kfw = 1168/RcD = 1320 mdft

Fig. 3.20 - Example of Bilinear Flow Analysis.

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Bilinear Flow - Liquid Reservoirs (Reproduction of PTA Course Material)

3.4 Bilinear Flow - Liquid Reservoirs (Reproduction of PTA Course Material) Flow Periods For A Vertically Fractured Well Fig. 3.21 depicts the various flow periods which are associated with finite conductivity vertical fractures. Fracture Linear Flow The “Fracture Linear Flow”, (a) on Fig. 3.21, is the first flow period which occurs in a fractured system. Most of the fluid which enters the wellbore during this period of time is a result of expansion within the fracture, i.e., there is negligible fluid coming from the formation. Flow within the fracture during this time period is linear. Equations which can be used to predict the following formation face pressure, pwf, during fracture linear flow are presented by Cinco-Ley et al.,6 for the constant rate case. This reference also presents an equation which predicts the time when this flow period ends. Unfortunately, fracture linear flow occurs at a time which is too early to be of practical use in well test analysis. Bilinear Flow The next flow period to occur is called “Bilinear Flow,” (b) on Fig. 3.21, because two types of linear flow simultaneously occur. One flow is linear incompressible flow within the fracture and the other is linear compressible flow in the formation. Most of the fluid which enters the wellbore during this flow period comes from the formation. Fracture tip effects do not affect well behavior during bilinear flow; accordingly, unless a well test is run sufficiently long for bilinear flow to end, it will not be possible to determine fracture length from the data. Bilinear flow was first recognized by Cinco-Ley et al.6 Since its introduction into literature, the use of bilinear flow analysis to characterize both formation and fracture properties has been documented.7-11 The details of analyzing bilinear flow data will be detailed in subsequent discussions beginning on page 3-35. Formation Linear Flow The analysis of “Formation Linear Flow”, (c) on Fig. 3.21, is covered in the Pressure Transient Analysis course manual. Pseudo-Radial Flow The analysis of “Pseudo-Radial Flow”, (d) on Fig. 3.21, is covered in the Pressure Transient Analysis course manual.

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Reservoir Analysis

WELL WELL

FRACTURE

FRACTURE (a) FRACTURE LINEAR FLOW

(b) BILINEAR FLOW

FRACTURE FRACTURE WELL

(c) FORMATION LINEAR FLOW

(d) PSEUDO-RADIAL FLOW

Fig. 3.21 - Flow Periods for a Vertically Fractured Well.

Bilinear Flow Equations Constant Formation Face Rate Dimensionless Pressure: kh ( p i – p wf ) kh∆m ( p ) P D = ------------------------------- ( oil ) P D = ----------------------- ( gas ) 1424T q 141.2qBµ

(3.5)

0.0002637kt t Dxf = ----------------------------2 φµc t x f

(3.6)

Dimensionless Time:

Dimensionless Fracture Conductivity: kfw F CD = --------kx f

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(3.7)

July 1999

Bilinear Flow - Liquid Reservoirs (Reproduction of PTA Course Material)

Bilinear Flow Equation:

PD

1/4 2.45 t Dx = ---------------------f 1\/2 F CD

(3.8)

44.1qBµ 1/4 - t p i – p wf = -----------------------------------------------------1/2 1/4 ( φµc t k ) h(k f w)

(3.9)

Bilinear Slope (graph of pi-pwf vs. t1/4): 494qT m bf = ------------------------------------------------1/2 1/4 h ( k f w ) ( kφµc t )

(3.10)

Constant Formation Face Pressure Dimensionless Rate: 141.2qBµ 1424Tq q D = ------------------------------- (oil) q D = ----------------------- (gas) kh ( p i – p wf ) kh∆m ( p )

(3.11)

Bilinear Flow Equation: 2.72 t 1/4 Dx f 1 ------ = ----------------------qD F 1/2

(3.12)

CD

1/4 1 48.9Bµ - = t ( oil ) --- = -------------------------------------------------------------------------1/2 1/4 q ( p i – p wf )h ( k f w ) ( φµc t k ) 1/4 1 494T --- = -------------------------------------------------------------------- = t (gas) 1/2 1/4 q h ( k f w ) ( kφµc t ) ∆m ( p )

(3.13)

Bilinear Slope (graph 1/q of vs. t1/4): 48.9Bµ - (oil) m bf = -------------------------------------------------------------------------1/2 1/4 ( p i – p wf )h ( k f w ) ( φµc t k ) 494T m bf = ------------------------------------------------------------------(gas) 1/2 1/4 h ( k fw ) ( kφµc t ) ∆m ( p )

(3.14)

Note: The equations presented in this section are written specifically for pressure drawdown tests. These equations can be modified for pressure buildup tests by replacing the pressure differJuly 1999

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Reservoir Analysis ential ∆p = p i – p wf , and the producing time, t, with appropriate values as shown in the following table: Test

Differential

Time

Drawdown

∆p = pi-pwf

t

Buildup

∆p = pws-pwf

∆t or ∆te

Bilinear Flow Graphs Constant Formation Face Rate When the rate of a well is maintained constant, the pressure change at the formation face is described by Eq. (3.9). This equation indicates that a plot of pi-pwf (pws-pwf) for buildup tests) vs. t1/4 (∆t1/4 for buildup tests) will yield a straight line with slope, mbf, predicted by Eq. (3.10). The plot of pressure change vs. fourth root of time is illustrated by Fig. 3.22. When bilinear flow ends, the straight line will end and the plot will exhibit curvature which is concave upward or downward depending upon the value of the dimensionless fracture conductivity, FCD. When FCD ≤ 1.6, the curve will be concave downward; a value of FCD > 1.6 will cause the curve to be concave upward.

FCD > 1.6

SLOPE = mbf

∆p, psi

FCD < 1.6

END OF BILINEAR FLOW

t1/4, hours1/4

Fig. 3.22 - Bilinear Flow Graph for a Constant Rate Well.

When FCD > 1.6, bilinear flow ends because the fracture tip begins to affect wellbore behavior. If a pressure transient test is not run sufficiently long for bilinear flow to end when FCD > 1.6, it is not possible to determine the length of the fracture. When FCD ≤ 1.6, bilinear flow in the reservoir changes from predominately one-dimensional (linear) to a two-dimensional flow regime. In this case, it is not possible to uniquely determine fracture length even if bilinear flow does end during the test. Hydraulic Fracturing Theory Manual

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Bilinear Flow - Liquid Reservoirs (Reproduction of PTA Course Material)

A more diagnostic plot to recognize the occurrence of bilinear flow is the log-log plot. From Eq. (3.9), 1 44.1qBµ --- log t . + log ( p i – p wf ) = log ------------------------------------------------1/2 1/4 4 h ( k f w ) ( φµc t k )

(3.15)

Eq. (3.15) indicates that a log-log plot of pi-pwf vs. t will yield a straight line with a one-fourth slope; this is illustrated by Fig. 3.23.

∆p, psi

SLOPE = 1/4

t, hours

Fig. 3.23 - Log-log Plot Illustrating the Effect of Ideal Bilinear Flow for the Constant Rate Case.

Constant Formation Face Pressure When formation face pressure remains constant, the formation face rate will change with time as described by Eq. (3.13). According to Eq. (3.13), a plot of 1/q vs. t1/4 should yield a straight line with slope, mbf, defined by Eq. (3.14) this plot is depicted by Fig. 3.24. Following the end of the bilinear flow period, the curve for F CD ≤ 2.8 will be concave downward and the curve for FCD > 2.8 will be concave upward. The straight line caused by bilinear flow ends for the same reasons as described for the constant rate case. Eq. (3.13) also indicates that a log-log plot of 1/q vs. t should yield a straight line with a slope of one-fourth: 1 1 48.9Bµ --- log t . + log  --- = log -------------------------------------------------------------------------1/2 1/4  q 4 ( p i – p wf )h ( k f w ) ( φµc t k )

(3.16)

The plot illustrated by Fig. 3.25, is the primary diagnostic tool by which bilinear flow can be recognized.

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Dp, psi

FCD > 2.8

SLOPE = mbf

1/q

FCD < 2.8

END OF BILINEAR FLOW

t1/4, hours1/4

Fig. 3.24 - Bilinear Flow Graph for a Constant Pressure Well.

Dp, psi

SLOPE = 1/4

1/q

t, hours

Fig. 3.25 - Log-log Plot Showing Effect of Ideal Bilinear Flow for the Constant Rate Case.

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Bilinear Flow - Liquid Reservoirs (Reproduction of PTA Course Material)

End of Bilinear Flow Constant Formation Face Rate The relationship between (tDxf)ebf and FCD is depicted graphically by Fig. 3.26. This relationship can be approximated as: F CD ≥ 3: 1.6 < F CD < 3: F CD ≤ 1.6:

0.1 ( t Dxf ) ebf ≅ --------2 F CD

(3.17)

( t Dxf ) ebf ≅ 0.0205 ( F CD – 1.5 )

– 1.53

–4 4.55 ( t Dxf ) ebf ≅  -------------- – 2.5  F  CD

(3.18)

(3.19)

For the case where FCD ≥ 3, the dimensionless pressure at the end of bilinear flow is 1.38 ( p D ) ebf = ---------- . F CD

(3.20)

1.38 F CD = -----------------( p D ) ebf

(3.21)

194.9qBµ F CD = ------------------------------------- . kh ( p i – p wf ) ebf

(3.22)

Therefore,

and,

Constant Formation Face Pressure The relationship between (tDxf)ebf and FCD is presented graphically by Fig. 3.27. This relationship can be approximated by the following equations: F CD ≥ 5:

( t Dxf ) ebf

–2

6.94 × 10 = -------------------------2 F CD

(3.23)

2 < FCD < 5: See Fig. 3.27 – 3 1.6

0.5 ≤ F CD ≤ 2: ( t Dxf ) ebf = 1.58 × 10 F CD

(3.24)

For the case where FCD ≥ 5, July 1999

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1

10-1

(tDxf) ebf

10-2

10-3

10-4

10-5 -1 10

1 FCD

101

102

Fig. 3.26 - Dimensionless Time for the End of the Bilinear Flow Period vs. Dimensionless Fracture Conductivity, Constant Rate Case.6

1.40 1 ------------------ = ---------- . F CD ( q D ) ebf

(3.25)

F CD = 1.40 ( q D ) ebf

(3.26)

197.7q ebf Bµ F CD = --------------------------------- . kh ( p i – p wf )

(3.27)

Therefore,

and,

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Bilinear Flow - Liquid Reservoirs (Reproduction of PTA Course Material)

Analysis of Bilinear Flow Data The conventional analysis of bilinear flow data requires two plots - a log-log plot of the appropriate rate or pressure function vs. t, and a cartesian plot of the appropriate rate or pressure function vs. t1/4. Liquid-Constant Rate The following procedure can be used to analyze bilinear flow data for fracture conductivity and fracture length when the production rate is constant: 1. Make a log-log plot of (pi-pwf) vs. equivalent producing time, tp. 2. Determine if any data fall on a straight line of quarter slope. 3. If any data form a quarter slope in Step 2, plot pi-pwf vs. t1/4 on cartesian paper and identify the data which form the bilinear flow straight line. 4. Determine the slope, mbf, of the bilinear flow straight line. 5. Using the slope, mbf, from Step 4, compute the fracture conductivity, kfw, using Eq. (3.10): 44.1qBµ k f w = ------------------------------------1/4 m bf h ( φµc t k )

2

.

(3.28)

It should be noted that this calculation can only be made if k is known from a prefrac test. 6. If the bilinear flow straight line ends and the data rise above the straight line, determine the value of ∆p, i.e., ∆pebf, at which the line ends. Then, from Eq. (3.24), FCD can be computed as 194.9qBµ F CD = ------------------------------------- . kh ( p i – p wf ) ebf

(3.24)

with FCD known, the fracture length can be computed using Eq. (3.7): kfw x f = ------------- . kF CD

(3.29)

It should be noted that Eq. (3.24) assumes FCD ≥ 3. If enough data is available beyond bilinear flow, a type curve match should be attempted to verify that this is true.

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10-1

10-2

(tDxf)ebf

FCD = 5

10-3

10-4

10-5 -1 10

1

2.8

10

10-2

FCD

Fig. 3.27 - Dimensionless Time to the End of Bilinear Flow for Constant Pressure Production.9

Liquid-Constant Pressure When formation face pressure remains constant during a test, the following procedure can be used to analyze the bilinear flow data for fracture conductivity and fracture length: 1. Make a log-log plot of 1/q vs. t. 2. Determine if any data fall on a straight line of quarter slope. 3. If any data in Step 2 form a quarter slope, plot 1/q vs. t1/4 on cartesian paper and determine the slope, mbf, of the bilinear flow straight line. 4. Using the slope, mbf, from Step 3, compute the fracture conductivity, kfw, using Eq. (3.14)

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Bilinear Flow - Liquid Reservoirs (Reproduction of PTA Course Material)

48.9Bµ k f w = -------------------------------------------------------------1/4 m bf ( p i – p wf )h ( φµc t h )

2

.

(3.30)

5. If the bilinear flow line ends and the data rise above the straight line, determine the value of q where the line ends, i.e., qebf. Then, from Eq. (3.27), FCD can be computed as 197.7q ebf Bµ F CD = ------------------------------- . kh ( p i – p wf )

(3.27)

With FCD known, the fracture length can be computed using Eq. (3.24): kfw x f = --------------- . k F CD

(3.29)

Eq. (3.27) assumes FCD ≥ 5 ;accordingly, if enough data are available beyond bilinear flow, a type curve match should be attempted to verify that this is true. Effect of Flow Restrictions When a flow restriction exists in the formation adjacent to the fracture, or when a restriction occurs in the fracture near the wellbore, the ideal bilinear flow behavior discussed previously, shown by Fig. 3.22 and Fig. 3.24 will be altered. Ideal bilinear flow results in a straight line on a cartesian plot of ∆p (constant rate) or 1/q (constant pressure) vs. t; further, this line passes through the origin. Bilinear flow still exists when a flow restriction is present; however, the restriction causes an extra pressure drop, ∆ps, in the system. This additional pressure loss does not alter the slope, mbf, of the bilinear flow straight line; instead, rather than passing through the origin, the line will have an intercept equal to ∆ps for the constant rate case. This behavior is depicted by Fig. 3.28.

∆p, psi

DAMAGE OR CHOKED FRACTURE

{

∆ps

0

IDEAL

0

t1/4, hours1/4

Fig. 3.28 - Effect of a Flow Restriction on Bilinear Flow, Constant Rate Case. July 1999

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A log-log plot of ∆p (constant rate) or 1/q (constant pressure) vs. t will exhibit a straight line with quarter slope for ideal bilinear flow. The slope of this line will be altered, however, when a flow restriction is present. This non-ideal behavior is depicted by Fig. 3.25 for the constant rate case.

∆p, psi

DAMAGE OR CHOKED FRACTURE

SLOPE = 1/4

t, hrs

Fig. 3.29 - Effect of a Flow Restriction on the Log-log Plot for the Constant Rate Case.

Effect of Wellbore Storage Wellbore storage will alter or completely mask the bilinear flow straight lines ideally expected on the cartesian and log-log plots of ∆p or 1/q vs. t1/4 and ∆p or 1/q vs. time, respectively. Fig. 3.30 depicts the effect of storage on a plot of ∆p vs. t1/4 for the constant rate case. The corresponding effect of storage on the log-log plot is shown in Fig. 3.31. It has been reported by Cinco-Ley et al.,6 that the end of wellbore storage effects occurs approximately three log cycles after the end of the unit slope line.

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∆p, psi

Bilinear Flow - Liquid Reservoirs (Reproduction of PTA Course Material)

IDEAL BILINEAR FLOW

EFFECT OF WELLBORE STORAGE

t, hrs

Fig. 3.30 - Effect of Wellbore Storage on a Plot of ∆p vs. t1/4 for the Constant Rate Case.

SLOPE = 1/4

∆p, psi

UNIT SLOPE

= 3 LOG CYCLES

t, hrs

Fig. 3.31 - Effect of Wellbore Storage on the Log-log Plot for the Constant Rate Case.

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3.5 Bilinear Flow - Gas Reservoirs Bilinear Flow Equations Constant Formation Face Rate Dimensionless Pressure: kh [ m ( p i ) – m ( p wf ) ] P D = ------------------------------------------------1424qT

(3.31)

Dimensionless Time: 0.0002637kt t Dxf = ----------------------------2 φµc t x f

(3.6)

Dimensionless Fracture Conductivity: kfw F CD = --------kx f

(3.7)

Bilinear Flow Equation:

PD

1/4 2.45 t Dx = ---------------------f 1\/2 F CD

444.6qT 1/4 -t m ( p i ) – m ( p wf ) = ------------------------------------------------1/2 1/4 h ( k f w ) ( φµc t k )

(3.8)

(3.32)

Bilinear Slope (graph of ∆m(p) vs. t1/4): 444.6qT m bf = ------------------------------------------------1/2 1/4 h ( k f w ) ( φµc t k )

(3.33)

Constant Formation Face Pressure Dimensionless Rate: 1424qT q D = -------------------------------------------------kh [ m ( p i ) – m ( p wf ) ]

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(3.34)

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Bilinear Flow - Gas Reservoirs

Bilinear Flow Equation: 2.72 t 1/4 Dx f 1 ------ = ----------------------qD F 1/2

(3.12)

493.6T 1/4 1 --- = --------------------------------------------------------------------------------------------t 1/2 1/4 q h ( k f w ) ( φµc t k ) [ m ( p i ) – m ( p wf ) ]

(3.35)

CD

Bilinear Slope (graph of 1/q vs. t1/4): 493.6T m bf = --------------------------------------------------------------------------------------------1/2 1/4 h ( k f w ) ( φµc t k ) [ m ( p i ) – m ( p wf ) ]

(3.36)

NOTE: The equations presented in this section are written specifically for pressure drawdown tests. These equations can be modified for pressure buildup tests by replacing the pseudopressure differential, ∆m(p), and the producing time, t, with appropriate values as shown in the following table: Test

Pseudopressure Differential

Time

Drawdown

∆m(p) = m (pi)-m(pwf)

t

Buildup

∆m(p) = m(pws)-mp(pwf)

∆t or ∆te

Bilinear Flow Graphs Constant Formation Face Rate When the rate of a gas well is maintained constant, the pressure change at the formation face is described by Eq. (3.32). This equation indicates that a plot of m(pi)-m(pwf) vs. t1/4 for drawdown tests, or m(pws)-m(pwf) for buildup tests, will yield a straight line with slope, mbf, predicted by Eq. (3.33). This plot described by Eq. (3.32) is illustrated by Fig. 3.24. When bilinear flow ends, the straight line will end and the data will exhibit curvature which is concave upward or downward depending upon the value of the dimensionless fracture conductivity, FCD. When FCD ≤ 1.6, the curve will be concave downward, a value of FCD > 1.6 will cause the curve to be concave upward . When FCD > 1.6, bilinear flow ends because the fracture tip begins to affect wellbore behavior. If a pressure transient test is not run sufficiently long for bilinear flow to end when FCD > 1.6, it is not possible to determine the length of the fracture. When FCD ≤ 1.6, bilinear flow in the reservoir changes from predominately one-dimensional (linear) to a two-dimensional flow regime. In this case, it is not possible to uniquely determine fracture length even if bilinear flow does end during the test. A more diagnostic plot to recognize bilinear flow is the log-log plot. From Eq. (3.32) July 1999

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∆p, psi

FCD > 1.6

SLOPE = mbf

FCD < 1.6

END OF BILINEAR FLOW

t1/4, hours1/4

Fig. 3.32 - Bilinear Flow Graph for a Constant Pressure Well.

444.6qT 1 - + --- log t . log [ m ( p i ) – m ( p wf ) ] = log ------------------------------------------------1/2 1/4 4 h ( k f w ) ( φµc t k )

(3.37)

Eq. (3.37) indicates that a log-log plot of m(pi)-m(pwf) vs. t will yield a straight line with a onefourth slope; this is illustrated by Fig. 3.35. Constant Formation Face Pressure When formation face pressure remains constant, the formation face rate will change with time as described by Eq. (3.35). According to Eq. (3.35), a plot of 1/q vs. t1/4 should yield a straight line with slope, mbf, defined by Eq. (3.36) this graph is depicted by Fig. 3.24. Following the end of the bilinear flow period, the curve for FCD ≤ 2.8 will be concave downward and the curve for FCD > 2.8 will be concave upward. The straight line for bilinear flow ends for the same reasons presented for the constant rate case on page 3-41. Eq. (3.35) also indicates that a log-log plot of 1/q vs. t should yield a straight line with a slope of one-fourth: 493.6T 1 - + --- log t . log ( 1 of q ) = log ---------------------------------------------------------------------------------------1/2 1/4 4 h ( k f w ) ( φµc t k ) m ( p i ) – m ( p wf )

(3.38)

The log-log plot of pressure change vs. time, illustrated by Fig. 3.35, is the primary diagnostic tool by which bilinear flow can be recognized.

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Bilinear Flow - Gas Reservoirs

∆p, psi

SLOPE = 1/4

t, hours

Fig. 3.33 - Log-log Plot Showing Effect of Ideal Bilinear Flow for the Constant Gas Rate Well.

∆p, psi

FCD > 1.6

SLOPE = mbf FCD < 1.6

END OF BILINEAR FLOW

t1/4, hours1/4

Fig. 3.34 - Bilinear Flow Graph for a Constant Pressure Well.

End of Bilinear Flow Constant Formation Face Rate The relationship between (tDxf)ebf and FCD for constant formation face rate is depicted graphically by Fig. 3.37. This relationship can be approximated as: (3.17)

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∆p, psi

SLOPE = 1/4

t, hours

Fig. 3.35 - Log-log Plot Illustrating the Effect of Ideal Bilinear Flow for the Constant Pressure Case.

1.6 < F CD < 3: ( t Dxf ) ebf ≅ 0.0205 ( F CD – 1.5 )

– 1.53

–4 4.55 F CD ≤ 1.6: ( t Dxf ) ebf ≅  ---------- – 2.5  F CD 

(3.19)

(3.20)

For the case where FCD ≥ 3, the dimensionless pressure at the end of bilinear flow is 1.38 ( p D ) ebf = ---------- . F CD

(3.39)

1.38 F CD = -----------------( p D ) ebf

(3.40)

1965.1qT F CD = --------------------------------------------------------- . kh [ m ( p i ) – m ( p wf ) ] ebf

(3.41)

Therefore,

and,

Constant Formation Face Pressure The relationship between (tDxf)ebf and FCD for constant formation face pressure is presented graphically by Fig. 3.37. This relationship can be approximated by the following equations:

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Bilinear Flow - Gas Reservoirs

1

10-1

(tDxf) ebf

10-2

10-3

10-4

10-5 -1 10

1 FCD

102

101

Fig. 3.36 - Dimensionless Time for the End of the Bilinear Flow Period vs. Dimensionless Fracture Conductivity, Constant Formation Face Rate Case.6 –2

6.94 × 10 F CD ≥ 5: ( t Dxf ) ebf ≅ -------------------------2 F CD

(3.23)

2 < FCD < 5: See Fig. 3.37 (3.24)

For the case where FCD ≥ 5, 1.40 1 ------------------ = ---------- . F CD ( q D ) ebf

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(3.25)

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Reservoir Analysis

10-1

10-2

(tDxf)ebf

FCD = 5

10-3

10-4

10-5 -1 10

1

2.8

10

10-2

FCD

Fig. 3.37 - Dimensionless Time to the End of the Bilinear Flow for Constant Pressure Production.9

Therefore, F CD = 1.40 ( q D ) ebf

(3.26)

1988T q ebf F CD = -------------------------------------------------- . kh [ m ( p i ) – m ( p wf ) ]

(3.42)

and

Analysis of Bilinear Flow Data The conventional analysis of bilinear flow data requires two plots - a log-log plot of the appropriate rate or pressure function vs. t, and a cartesian plot of the appropriate rate or pressure function vs. t1/4.

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Bilinear Flow - Gas Reservoirs

Gas-Constant Rate The following procedure can be used to analyze bilinear flow data for fracture conductivity and fracture length. When rate is constant: 1. Make a log-log plot of m(pi)-m(pwf) vs. t. 2. Determine if any data fall on a straight line of quarter-slope. 3. If any data in Step 2 form a quarter-slope, plot m(pi)-m(pwf) vs. t1/4 on cartesian paper and identify the data which form the bilinear flow straight line. 4. Determine the slope, mbf, of the bilinear flow straight line. 5. Using the slope, mbf, from Step 4, compute the fracture conductivity, kfw, using Eq. (3.33): 444.6qT k f w = ------------------------------------1/4 m bf h ( φµc t k )

2 (3.43)

It should be noted that this calculation can only be made if k is known from a prefrac test. 6. If the bilinear flow straight line ends and the data rise above the straight line, determine the value of ∆m(p), i.e., [∆m(p)]ebf, at which the line ends. Then, from Eq. (3.42), FCD can be computed as 1965.1qT F CD = --------------------------------------------------------- . kh [ m ( p i ) – m ( p wf ) ] ebf

(3.42)

With FCD known, the fracture length can be computed using Eq. (3.7): kfw x f = ------------- . kF CD

(3.29)

It should be noted that Eq. (3.43) assumes FCD ≥ 3. If enough data is available beyond bilinear flow, a type curve match should be attempted to verify that this is true. Gas-Constant Pressure When formation face pressure remains constant during a test, the following procedure can be used to analyze the bilinear flow data for fracture conductivity and fracture length: 1. Make a log-log plot of 1/q vs. t. 2. Determine if any data fall on a straight line of quarter slope.

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3. If any data in Step 2 form a quarter-slope, plot 1/q vs. t1/4 on cartesian paper and determine the slope, mbf, of the bilinear flow straight line. 4. Using the slope, mbf, from Step 3, compute the fracture conductivity, kfw, using Eq. (3.38): 493.6T k f w = --------------------------------------------------------------------------------1/4 m bf h ( φµc t k ) [ m ( p i ) – m ( p wi ) ]

2 (3.44)

5. If the bilinear flow line ends and the data rise above the straight line, determine the value of q where the line ends, i.e., qebf. Then, from Eq. (3.43), FCD can be computed as 1988T q ebf F CD = -------------------------------------------------- . kh [ m ( p i ) – m ( p wf ) ]

(3.42)

With FCD known, the fracture length can be computed using Eq. (3.29): kfw x f = ------------- . kF CD

(3.29)

Eq. (3.29) assumes FCD ≥ 5; accordingly, if enough data are available beyond bilinear flow, a type curve match should be attempted to verify that this is true.

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References

3.6 References 1. Smith, M. B.: “Effect of Fracture Azimuth on Production With Application to the Wattenberg Gas Field,” paper SPE 8298 presented at the 1979 SPE Annual Technical Conference and Exhibition, Las Vegas, Sept. 23-26 2. Prats, M.: “Effect of Vertical Fractures on Reservoir Behavior - Incompressible Fluid Case,” SPEJ (June 1961) 105-18; Trans., AIME, 222. 3. Britt, L. K.: “Optimized Oil Well Fracturing, Phase I Report,” Amoco Production Company Report F84-P-23 (May 25, 1984). 4. Britt, L. K.: “Optimized Oil Well Fracturing, Phase II Report,” Analysis of the Effects of Fracturing on the Secondary Recovery Process; Amoco Production Company Report F85-P-7 (Jan. 24, 1985). 5. Bargas, C. L.: “The Effects of Vertical Fractures on the Areal Sweep Efficiency and Relative Injectivity of Adverse Mobility Ratio Displacements,” Amoco Production Company Report F89-P-13 (Feb. 13, 1989). 6. Cinco-Ley, H. and Samaniego-V., F.: “Transient Pressure Analysis for Fractured Wells,” JPT (Sept. 1981) 174966. 7. Cinco-Ley, H. and Samaniego-V., F.: “Transient Pressure Analysis: Finite Conductivity Fracture Case vs. Damaged Fracture Case; paper SPE 10179, presented at the 1981 Annual Technical Conference and Exhibition, San Antonio, Oct. 5-7. 8. Cinco-Ley, H.: “Evaluation of Hydraulic Fracturing by Transient Pressure Analysis Methods,” paper SPE 10043, presented at the 1982 SPE Intl. Petroleum Exhibition and Technology Symposium, Beijing, March 19-22. 9. Bennett, C. O., Reynolds, A. C., and Raghavan, R.: “Performance of Finite-Conductivity, Vertically Fractured Wells in Single-Layer Reservoirs,” SPEFE (Aug. 1986) 399-412; Trans., AIME, 281. 10. Guppy, K. H., Cinco-Ley, H., and Ramey, H. J. Jr.: “Pressure Buildup Analysis of Fractured Wells Producing at High Flow Rates,” JPT (Nov. 1982) 2656-66. 11 Rodiquez, F., Horne, R. N., and Cinco-Ley, H.: “Partially Penetrating Vertical Fractures: Pressure Transient Behavior of Finite Conductivity Fracture,” paper SPE 13057, presented at the 1984 SPE Annual Technical Conference and Exhibition, Houston, Sept. 16-19.

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Chapter

4

Formation Mechanical Properties

The following mechanical properties are of interest in fracturing: (1) Elastic Properties of the Formation (i.e., Modulus of Elasticity and Poisson’s Ratio), (2) Fracture Toughness, and (3) Hardness. Rock strength plays only a small role in the fracturing process and is not included in the fracture design calculations.

4.1 Elastic Properties of the Formation As an engineering simplification, the formation is often assumed to be a linearly elastic homogeneous material. This simplification allows the use of solutions from the theory of elasticity to estimate, for example, fracture widths and stresses in the formation. However, it should always be remembered that the formation is neither homogeneous nor isotropic. Therefore, the assumption of a linearly elastic isotropic formation may be grossly violated, especially in poorly consolidated formations. Based on this simplifying assumption, formation properties can be characterized by two elastic constants, the modulus of elasticity (or Young’s modulus), E, given in psi or units of pressure, and Poisson’s ratio (in honor of the great French mathematician), ν , a dimensionless number as its name implies. The modulus characterizes how “stiff” the formation is and quantifies how easily a core is deformed by an axial stress (tension or compression). Poisson’s ratio quantifies how a core “bulges” (expands or contracts laterally) by an axial compression or tension and it characterizes (together with E) the transmittal of horizontal pressure due to the overburden. Fracture design is greatly affected by how much the formation opens for a given pressure inside a fracture. Fracture width depends on both fracture dimensions and formation stiffness. Fracture width is inversely proportional to the formation plane strain modulus, E ′ , given by E -. E′ = -----------------( 1 – ν2 )

(4.1)

Fig. 2.3 in Chap. 2 expressed this spring stiffness type relation as D W ∼ ---- p E

(4.2)

where, for simplicity’s sake, E was used instead of E ′ . This is usually a good approximation since a rough estimate for the Poisson’s ratio for most rocks is between 0.20 to 0.35. Therefore, E ′ is expected to be about 4 to 12% larger than E. Note that the theoretically expected values for ν are

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Formation Mechanical Properties

between 0 and 0.5 while moduli could have a much greater variability, from a few hundred thousand psi to over 10 million psi. Both of the elastic constants of a formation can be measured in the laboratory using a single compression test. This test gives the modulus and the Poisson’s ratio under “quasi” static conditions. These static properties characterize rock behavior under “slowly” varying loading, such as the one resulting from the hydraulic fracturing process. Different values for the elastic constants can be inferred (using elasticity relations) from the travel times of the compressional and shear sonic waves (e.g. sonic logs) under dynamic conditions. The differences between dynamic and static elastic constants are primarily of practical significance for the modulus. Dynamic moduli may be much larger than static moduli and some correlation is usually needed to infer the static moduli needed for fracturing design; in some cases the static moduli are 50 to 75% of the dynamic moduli. Fig. 4.1 shows the typical result of a compression test (in this case, Bedford limestone). A small core plug is jacketed and subjected to a confining pressure (usually equal to the overburden minus reservoir pressure) in the triaxial cell; it is then loaded axially to produce plots of axial, lateral, and volumetric strain vs. axial stress in excess of the confining pressure (Effective Axial Stress). Both the axial and lateral strains are quantities calculated from measuring the decrease of the core length and the increase of the core diameter using strain transducers that are mounted on the core. 12000

SECANT MODULUS (DO NOT USE)

TANGENT MODULUS

10000

EFFECTIVE AXIAL STRESS, PSI

AXIAL ULTIMATE LOADS

8000 CONFINING PRESSURE

6000

4000

AXIAL STRAIN

YIELD

LATERAL STRAIN

2000

VOLUMETRIC STRAIN 0 -2.0

-1.0

0.0

2.0

1.0

STRAIN

3.0

4.0

5.0

*10-3

Fig. 4.1 - Typical Stress-Strain Curve for Brittle Rocks.

The axial strain represents the ratio of the core “shortening” (length decrease) over its original length and is a dimensionless number which is plotted positive for a length decrease (contraction). The lateral strain represents the ratio of the core “bulging” (diameter increase) over its original Hydraulic Fracturing Theory Manual

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March 1993

Elastic Properties of the Formation

diameter and is a dimensionless number which is plotted negative for core diameter increase (expansion). The volumetric strain, also shown on Fig. 4.1, is a calculated quantity given by the following algebraic sum volumetric strain = axial strain + 2 × lateral strain .

(4.3)

It represents the ratio of the volume change over the original volume of the core, and is plotted positive for contraction. By definition, the initial slope of the axial strain curve is the modulus of elasticity or Young’s modulus, E, in psi. It is also called a “tangent” modulus because it is the slope of the dashed line drawn tangent to the stress-strain curve at the origin (Fig. 4.1). Since the compression test was performed at a confining stress approximating the in-situ conditions, this is the value that should be used for modulus in a fracture design. By this, we mean that the formation in-situ is at a state of stress comparable to the one near the origin of the plot; any loading due to fracturing would make the stress state go up or down on the curves near the origin. However, modulus depends on the confining pressure, and some judgement should be exercised when data for the specific in-situ conditions are not available. Modulus data should be used with a good understanding of what the testing conditions represent because some labs draw, for example, a straight line from the origin to the point of failure and report the slope of that line as modulus. This value is called, the “Secant” Modulus of Elasticity and should not be used for fracture design calculations. Poisson’s ratio, ν , represents the ratio of the lateral strain over the axial strain, both taken from the linear behavior of the core near the origin, (i.e., over the range that the modulus straight line is determined). Poisson’s Ratio ν = - lateral strain / axial strain

(4.4)

For the Bedford Limestone example in Fig. 4.2, at an effective axial stress of 4,000 psi the lateral strain is -0.25 x 10-3 and the axial strain is 0.9 x 10-3. The Poisson’s ratio from Eq. (4.4) is 0.277. Poisson’s Ratio quantifies the tendency of the material to “bulge” out for a given axial strain and therefore how the material “pushes” laterally when it is subjected to an overburden pressure. The theoretical range of Poisson’s ratio for uniform materials is between 0 and 0.5. Rocks which have a competent structure (i.e. rocks with porosity that does not change significantly with loading) are expected to have Poisson’s ratios in the same range. Good approximate values for Poisson’s ratio for fracture width calculations are 0.25 for sandstone formations and 0.33 for carbonate formations. However, Poisson’s ratio strongly affects how the closure stress is related to overburden pressure. For example, a formation with ν ≅ 0 will develop almost no horizontal closure stress when subjected to overburden; in contrast, a formation with ν ≅ 0.5 will develop a horizontal closure stress almost equal to overburden, and will behave like a liquid! Real rocks fall somewhere between those values, with the more ductile and plastic rocks having a higher Poisson’s ratio. Note that rocks that have high porosity and low cementation (e.g. Valhall chalk) may have a ν close to zero.

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Formation Mechanical Properties

This is because their porosity changes considerably with loading, and the bulging of the core is accommodated by porosity reduction. Effect Of Modulus On Fracturing Though the predicted fracture width and penetration for a fixed fracture height and fluid volume are relatively insensitive to modulus, the relation between fracturing pressure and modulus makes modulus one of the more important variables considered in fracture design. Fig. 4.2 shows an example of the dependence of net fracturing pressure (injection pressure minus closure stress) on the modulus of elasticity; generally speaking, as modulus increases, net pressure increases. Therefore, if a stimulation is designed with a value for “E” that is smaller than the actual value, the net pressure during a job will be higher than predicted, possibly leading to unanticipated height growth.

800

20

600

15

400

10

200

5

2

4

6

Slurry Volume Required (1000 gal)

Net Fracturing Pressure (psi)

Example Data H = 100 ft Fluid Loss H = 100 ft C = .001 Spurt = 0 Q = 20 bpm Viscosity = 100 cp (n' = 1) Design Penetration (1/2 Length) = 500 ft

8

Young’s Modulus (106 psi) Fig. 4.2 - Example of the Effect of Modulus on Net Fracturing Pressure.

Typical Modulus Values Fig. 4.3 and Fig. 4.4 show typical ranges of values for modulus for sands and carbonates. Modulus usually increases with confining pressure and decreases with increasing porosity and increasing grain size. If nothing else is known, these figures may be used to determine an estimate of modulus. However, significant variations from either figure can exist due to mineralogical compositions and depositional differences.

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Elastic Properties of the Formation

Young’s Modulus (million psi)

Young's Modulus (million psi)

10 8 Low Porosity (< 10%), Very Fine Grained

6

4 High Porosity (> 25%), Coarse Grained

2

5

Low Porosity, Dolomite 8

6

4

High Porosity

2

10 5

Overburden-Pore Pressure (1000 psi)

10

Overburden-Pore Pressure (1000 psi)

Fig. 4.3 - Modulus of Elasticity for Sandstones.

Fig. 4.4 - Modulus of Elasticity for Carbonates.

Also, the modulus values in Fig. 4.3 and Fig. 4.4 are for small samples. Many carbonate formations are naturally fractured; and in such a case, the modulus for the “bulk” in-situ rock would be lower than a value for a small sample. A similar chart for shales is not practical since Young’s Modulus for shales can vary from 500,000 psi for a high porosity, clay rich, shale to 6-8 million psi for a quartz cemented siltstone. If no core is available for shales, sonic logs have been used to predict the modulus of the shales relative to the modulus of the pay formation where core is available and modulus has been measured. Table 4.1 lists typical modulus values for two “special” formation types. Table 4.1 - Typical Modulus Values for Two “Special” Formation Types.

Porosity

Modulus (106 psi)

Chalk (North Sea)

35 - 50%

0.5 to 1.5

Diatomaceous Earth

40 - 50%

0.4 to 1.0

Formation

Fig. 4.5 is a plot that allows the use of conventional Sonic Log data (compressional wave) to estimate modulus. This “dynamic” modulus (i.e., estimated from correlation based on compressional wave velocity in the formation) is greater than the “static” modulus needed for fracture design, but, if laboratory tests are not available, the dynamic modulus sets an upper bound for modulus and is preferable to Fig. 4.3 and Fig. 4.4. It can also be used to estimate the modulus in formations where core is not available if lab data is available from other formations in the same well. A better technique than conventional Sonic Logs is to calculate Young’s Modulus, “E,” from Long Spaced Sonic Log data, using the compressional and shear wave velocities of the formation.

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Formation Mechanical Properties

Acoustic Travel Time (microseconds/ft)

4

100

80

60

Sand Dolomite Lime

40 2

4

8

6 Ex

10

106

12

14

16

- psi

Fig. 4.5 - Young’s Modulus (E) vs. Acoustic Travel Time.

Again, this dynamic modulus will be an upper bound for the static modulus used for fracture design. The best solution is to obtain core samples and have tangent modulus measured in a lab. If this is impossible and E must be estimated, try to estimate on the high side. This will result in a design with a narrower fracture width, higher net pressure and greater fracture height than should actually occur, providing a conservative “safe” approach to fracture design.

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Fracture Toughness

4.2 Fracture Toughness Fracture toughness is one of the most elusive material properties that comes from linear fracture mechanics. It is discussed here because it is often used in numerical simulators as a matching parameter of the treating pressure and because there are many near fracture tip phenomena that could appear as “apparent” fracture toughness. Without getting too deep into theory, the fracture toughness concept comes from Griffith’s1 work on the fracture of brittle solids. The fracture toughness of a material represents its natural ability to resist the propagation of a fracture. To quote an article by Srawley and Brown,2 “In the simplest terms, the fracture toughness of a material determines how big a crack the material is able to tolerate without fracturing when loaded to a level approaching that at which it would fail by excessive plastic deformation.” Fracture toughness can be quantified by lab experiments (such as the three point loading of the Chevron notch) from which the loading vs. deformation curve is plotted until failure, and the energy spent to fracture the specimen can be calculated from this diagram. It may be noted that loading capacity of a specific specimen depends not only on crack size, but also on crack shape, bulk of the specimen, crack orientation with respect to layering of material (e.g. formation), temperature, rate of loading, etc. For this reason, it is very difficult to extrapolate laboratory results to the field, and an indirect assessment of “apparent” fracture toughness is done in the field from treating pressure behavior using fracturing simulators, as described below. The fracture toughness is quantified by either of two related parameters: (1) the critical strain energy release rate, G, expressed in energy per area of created fracture (not the area of the fracture faces) in units of force/length; and (2) the critical stress intensity factor, Kc, expressed in units of pressure times square root of length. The relation between the two parameters for hydraulic fracturing problems (plane strain problems) is 2

G = Kc /E'.

(4.5)

Typical laboratory range of Kc values are given by Thiercelin3 in Table 4.2. From Table 4.2 we see that typical laboratory Kc’s are of the order of 900 to 2000 psi in with a value of about 1500 psi in being a good rough estimate. A corresponding rough estimate of fracture energy is about 1 psi-in. Note that some simulators require Kc and some require G as input. Fracture toughness relates the pressure required to propagate a fracture with the dimensions of the fracture. Let us consider an example from the Wattenberg field,4 where fractures in the Muddy J formation are highly confined by shale layers above and below the pay. Stress tests, minifrac and fracturing treatments in the example well show that a fracture height of 90 ft is representative for these type of calculations. Furthermore, net pressures, PN, on the order of 400 to 550 psi for minifrac treatments and 2100 psi for the main fracture treatments are typical. These observations indicate the magnitudes of the formation toughness (i.e., critical stress intensity factor Kc), the confining stress contrast ∆σc between layers, and other rock mechanics considerations. Consider-

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Formation Mechanical Properties

Table 4.2 Fracture Toughness and Properties as a Function of Confining Pressure. Confining Pressure

Young’s Modulus

Lithology

Porosity %

±

106 psi

MPa

psi

11%

4.8

0. 13.8 20.7

0 2068 3102

2.12 (2) 2.4 (2) 3.6 (1)

Error MPa

KIc % Error MPa

m

±

11% 17%

psi

in

Mesa Verde Sandstone -

5-10 -

32,000 (3)

1993 2256 3384

Mesa Verde Mudstone

-

45,000 (2)

9%

6.7

0. 20.7

0 3102

2.12 (1) 2.6 (1)

Cardium Sandstone

13 -

25,500 (2)

31%

3.8

0. 21.0

0 3147

0.98 (3) 3.3 (2)

14% 6%

921 3102

Berea Sandstone -

23 -

19,400 (2) 20,500 (1)

2%

2.9 3.1

0. 5.0 10.0 20.0

0 74 9 1499 2997

1.11 (2) 1.3 (2) 1.3 (2) 1.5 (3)

5% 8% 8% 13%

1043 1222 1222 1410

1993 2444

Note: the figures in parentheses show the number of samples tested.

ing the lateral propagation of the fracture tip of this highly confined fracture gives estimates of the Muddy J pay toughness, or, better, its “apparent” toughness. The fracture tip is essentially a penny shaped fracture that is subjected to the net treating pressure PN. There is no stress contrast confining the fracture in the horizontal direction. Therefore, fracture toughness is expected to be a dominant confining mechanism in the horizontal direction. From fracturing mechanics,5 the stress intensity factor, K, in the opening mode of a penny shaped crack under uniform pressure is given by R K = 2 P N --π

(penny crack)

(4.6)

where R is the radius and PN the uniform net pressure. The fracture propagates when K is equal to the formation fracture toughness, Kc (which is a material property), and remains stationary when K < Kc. The fracture tip geometry of the Wattenberg fractures is characterized by R = 45 ft = 540 in and PN = 500 psi. This value of net pressure is estimated from the minifrac treatment which does not have the additional friction due to a proppant. With these values, Eq. (4.6) gives Kc = 13110 psi in . This estimate is approximately 10 times greater than the fracture toughness of rocks measured in the lab which have a typical toughness value of 1000 to 1500 psi in . Note that this discrepancy is a common phenomenon and consequently the calculated Kc is called an “apparent” formation toughness.

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Fracture Toughness

Several near fracture tip hypotheses contribute to an increased net fracturing pressure and could contribute to an increased Kc. The most popular within the research community are (1) formation plasticity, (2) non-penetrated (“dry”) zone near the tip, and (3) process zone (microfracture zone) around the tip. Hypotheses (1) and (3) contribute to increased energy expenditure near the tip due to plastic flow and intense microfracturing. Hypothesis (2) assumes a region where the hydraulic pressure is not easily transmitted to the fracture tip due to asperities, gel plugging, increased gel viscosity due to dehydration, and great frictional losses within very narrow crack opening. For all the above reasons, it is quite common to input increased fracture toughness in the hydraulic fracturing simulators to match treating pressures and predict fracturing geometry.

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Formation Mechanical Properties

4.3 Hardness Rock hardness is important to fracture conductivity. The proppant may imbed into soft rocks, causing the fracture conductivity to decrease and the propped fracture to lose its effectiveness. For most rock types, this is not a problem if a nominal design guideline of one pound of proppant per square foot of fracture is achieved. For very soft formations (chalks are one example as seen in Fig. 4.6), this is not sufficient and special fracture designs are required. If proppant embedment is suspected due to productivity declines or pressure transient tests showing a loss of fracture capacity with time, special lab tests are available to test core samples with various amounts and types of proppant.

TEMP = 200F 2X2 DANIAN CHALK

TOTAL CORE PERMEABILITY MD

1000

100

Legend 0.4" PROPPED FRAC

10

0.25" PROPPED FRAC 0.1" PROPPED FRAC MATRIX FLOW 1

10096-97

0.1 0

1000

2000

3000

4000

5000

6000

7000

8000

9000

GROSS CONFINING PRESSURE PSI Fig. 4.6 - Effect of Propped Fracture Thickness on Flow Rate.

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References

4.4 References 1. Griffith, A. A.: “The Phenomena of Rupture and Flow in Solids,” Phil. Trans., Royal Soc. of London (1920) Ser. A, 221, 163-98. 2. Srawley, John E., and Brown, William F., Jr.: “Fracture Toughness Testing Methods”, Fracture Toughness Testing and Its Applications Symposium, 1964 Annual Meeting of ASTM, Chicago, June 21-26. 3. Thiercelin, M.: “Fracture Toughness Under Confining Pressure Using the Modified Ring Test”, Proceedings of the 1987 US Symposium of Rock Mechanics, 149-56, June 29-July 1. 4. Moschovidis, Z.A., Broacha, E., and Gardner, D.: APR, “Tectonic Correction of Closure Stress Profiles and Field Data Analysis for Fracture Design for Wattenberg Gas Field, Colorado;” Amoco Production Company Report F91-P-59 (Nov. 1990). 5. Warpinski, N. R., and Smith, M. B.: “Rock Mechanics and Fracture Geometry,” Monograph Series, SPE, Richardson, TX (1989) 12, vi, 57-80.

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Formation Mechanical Properties

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Chapter

5

Design of Pseudo 3-D Hydraulic Fracturing Treatments

5.1 Fracture Height/Fracture Height Growth - 3-D Modeling/Design As emphasized in Chap. 2 in the discussion of the basic fracture models, fracture height and fracture height growth are the major variables governing treatment design or analysis. This is easily seen in the simple relation derived from conservation of mass for a confined fracture Q tp L = ---------------------------------------------3 C Hp tp + w H

(5.1)

where fracture height, H, and fluid loss height, Hp, appear in the denominator and have a great effect on fracture length. H is the total or “gross” fracture height which, of course, changes with time during a treatment. A reasonable estimate of the “initial” fracture height, and of the variables governing height growth is critical to an accurate solution for fracture length since, as seen in the relation above, length, L, and height, H, are inversely proportional. It is usually desirable to maintain frac height within a reasonable distance above and below the pay zone, to minimize “useless” fracture area (created and propped fracture area which will not contribute to production) or to avoid fracturing into water bearing layers. The fracture height obtained is largely controlled by formation properties. We have some influence over the height obtained through controls on pump rate and fluid viscosity, but must recognize the limits to which we can control height development. Factors Controlling Fracture Height Numerous oil field techniques and wellbore arrangements have been proposed in the past for limiting fracture height: •

Perforate a limited section and only frac where the perfs are

•

Set a packer in the wellbore so that you do not frac up

•

Perforate low in the wellbore, since everybody knows that you cannot frac below Total Depth (TD)

•

Perforate high in the wellbore, so that you do not frac into water below.

•

Everybody knows that fracs grow up!

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•

Pump at low rate so that the frac will stay in zone.

•

Pump at high rate so that you get the job pumped before the fracture has a chance to grow out of the zone.

•

Use of a 2D model, then height won’t change!

Though these approaches may sound silly, we have all probably tried to use these or others in some form or fashion. Some of them have limited application and may exert some influence over the ultimate frac height obtained, but overall, they have minimal impact on frac height. Fig. 5.1 shows a schematic of a fracture which basically grows where it wants to. The only wellbore condition that can have a significant impact on frac height is the cement bond. A poor cement bond can allow annular communication with another zone, and thus bypass a potential confining bed. Pump rate and fluid viscosity do affect frac height through their indirect control on pressure, but to a very small degree when compared to formation properties.

Fracture Height = ?

Design

Pay

Water

Actual

Not Perforated Height! Fig. 5.1 - A Frac Grows Where It Wants To!!

Vertical fracture growth and resulting fracture height is controlled by the interaction of hydraulic pressure inside the fracture with mechanical properties of the rocks and in-situ stresses. The dominant factors controlling frac height are listed below in order of decreasing importance. Factors Controlling Fracture Height •

Closure stress differences between pay and bounding beds

•

Thickness of bounding beds & Thickness of “pay”

•

Fracture pressure from high modulus (naturally high/low closure stress, etc.)

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Fracture Height/Fracture Height Growth - 3-D Modeling/Design

•

Modulus contrast between pay and bounding beds

•

Interface or bedding plane slip - applicable at shallow depth?

•

Ductility of bounding bed - may facilitate bedding plane slip, (small coal seams)

•

Stress gradient due to fluid pressure - generally insignificant

•

Fracture toughness or strength differences - probably not a barrier

Effect Of Closure Stress Profile On Fracture Height Growth The most dominant controlling mechanism for frac height is vertical variations in closure stress through strata of varying lithology and rock properties.1 Closure stress is the minimum, compressive, in-situ stress. Pressure in the fracture must exceed this before a hydraulic fracture can open. Fig. 5.2 shows a simplistic, idealized case of three zones of different stress. In this case, the bounding beds (Zones 2 and 3) are assumed to be of infinite thickness and have the same closure stress. The stress in the bounding beds is greater than that in the pay zone (Zone 1). Zone 1 is perforated and a fracture is initiated. The fracture grows unrestricted to the height of Zone 1. At this point, the relationship shown in Fig. 5.2 goes to work (Point A). As injection continues, the fracture begins elongating and extending laterally from the wellbore. Net fracture pressure, Pn, (bottomhole treating pressure outside the perforations minus the formation closure pressure, discussed in more detail in Chap. 8), begins to increase as the fracture extends. During this period, the fracture is essentially acting as a “pipeline” carrying high viscosity fluid from the wellbore to the fracture tip. As the pipeline grows longer, the pressure at the wellbore must increase to overcome the increased friction drop along the ever lengthening fracture. As net pressure, Pn, increases, the ratio of net pressure to the closure stress differential between the pay zone and bounding beds begins to increase, moving one “up the curve” (Point B). When net pressure has increased to about 50% of the stress differential between Zone 1 and Zones 2 and 3, fracture height has increased to about 135% of the initial frac height (Zone 1). As net pressure in the fracture increases, frac height continues to grow, until the frac height is twice the initial height at a net pressure equal to 70% of the stress differential (Point D). The thickness of Zone 1 and the absolute values of the stresses are independent of this relationship for a three zone system with infinite bounding beds. Obviously, after net pressure reaches 70-80% of the stress differential between the pay zone and bounding beds, small increases in net pressure (the net pressure to stress difference ratio) can add much additional frac height. The fracture height cannot be contained, and the fracture grows uncontrollably out of zone. Note, however, that after this point is reached, fracture length growth does not stop though it is slowed considerably. Thus, if no danger exists of the fracture breaking into another (possibly undesirable) low stress zone - pumping may safely continue in order to create a longer fracture. The “economics” of creating this additional fracture length will be affected though, with significantly greater treatment volumes now being needed to create addi-

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Sand

σ c1

Zone 2

0.8

D C

0.6

Hi Zone 1

σ c2

Shale

b

1.0

Zone 3

Stress Difference

σ c2

Shale

a Pn  ------  ∆σ c

Gamma Ray Closure Stress

Ratio Net Pressure:

5

B

0.4 0.2 0

A 0

1

2

3

4

5

Ratio Frac Height:

∆σ c = σ c2 – σ c1

Initial Frac Height

H ( ---) H i

c

d Pressure C B

A

B

C

D

D

A

Time Fig. 5.2 - Effect of Closure Stress Variations on Fracture Height.

tional length. Similarly, sand is distributed over a greater and greater height, reducing the sand concentration per unit area. This means that if we are to contain a fracture within zone, we must have some idea of closure stress in the pay zone and bounding beds. If stress differences are only 700-800 psi, then we can expect the fracture to grow uncontrollably out of zone at about 500-600 psi net fracture pressure. Fracture treatments could be designed to stay within this net pressure limitation. On the other hand, it may be difficult to achieve the length desired at these net pressures (since net pressure depends on fracture length), and the treatment would have to be designed with this fracture height growth in mind. Conversely, if the stress differential is on the order of 1500 psi, net pressure can be

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Fracture Height/Fracture Height Growth - 3-D Modeling/Design

allowed to rise to 1000-1100 psi before the fracture will begin to grow significantly out of zone. This would allow an ample pressure limitation for designing most fracture treatments. Obviously, an in-situ fracture closure stress profile, as seen in Fig. 5.3, is the major input data for 3-D or Pseudo 3-D fracture treatment design. The example in Fig. 5.3 illustrates a stress profile generated by conducting multiple small volume, microfrac stress tests. Generally, such multiple stress data are not available and some form of log-stress correlation will be required. However, this example illustrates another important item - namely “typical” (or “maximum”) values for in-situ stress differences. Consider data from the sandstone at ± 7500 ft showing a fracture closure pressure (closure stress) of ± 6500 psi. Then consider the stress of ± 8000 psi at a depth of about 7650 ft in the Mancos Tongue Shale. This stress difference of ± 1500 psi at this depth represents a stress difference of ± 0.2 psi/ft - and this is about the maximum stress difference which has been recorded, verified, and published. Thus, assuming some lithology differences exist, an optimistic estimate for in-situ stress differences might be: Max Stress Difference, ∆σ = 0.2 psi/ft of depth.

PALUDAL

7400 (2255m)

7700 (2347m)

7900 (2408m) 8000 (2438m) 8100 (2459m)

ROLLINS

9000

2350

2400

MANCOS TONGUE COZZETTE

SHALE

7800 (2377m)

2300

MANCOS TONGUE

SILT

m

2250 Estimated overburden stress (1.05 psi/ft)

COAL

7500 (2286m) 7600 (2315m)

7000

6000

0.1

0.0

0.1

0.2

ft 7300 (2225m)

8000

STRESS (psi)

POROSITY 0.3

200.0

150.0

100.0

50.0

00.0

GAMMA (GAPI)

SAND

2450

45

50

55

60 MPa

Fig. 5.3 - Variations in Fracture Closure Stress in a Sand/Shale Sequence.

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The effects of lithology on in-situ stress (fracture closure stresses or closure pressure) along with the effect of closure stress variations on fracture geometry may also be seen in Fig. 5.4, a set of field data presented by Esso Canada.2 Fig. 5.4 compares two cases (within the same wellbore) showing measured in-situ stresses along with pre and postfrac radioactivity logs for fracture height growth. For Case 1, several stress tests (microfrac type stress tests) were conducted in zones with (based on differing gamma ray readings) varying lithology. This stress data showed basically a ± 0.7 psi/ft (e.g. normal) stress gradient - and the postfrac logs suggest massive height growth outof-zone. Case 2 shows stress data collected from two zones, both of which were perforated, and a propped fracture treatment was conducted attempting to stimulate the two zones simultaneously. The upper zone shows a significantly higher closure stress (associated with a different lithology) and the postfrac logs indicate that the entire treatment entered the deeper, lower stress zone. Thus we see examples - in the same wellbore - of lithology changes with and without associated differences in fracture closure pressure. A guideline for interpreting stress profiles where no other information exists might be: There must be some change in lithology in order to expect some variations in closure pressure - and thus some degree of fracture height confinement. However, do not try to quantify lithology logs. That is, relatively minor apparent lithology changes could signify significant stress differences, OR a major lithology change might have no associated stress differences. As discussed in Chap. 4, the one exception to this would be for stress changes created by artificial changes in reservoir pressure (e.g. depletion). Effect Of Bed Thickness On Fracture Height Growth In addition to the stress difference in the beds, bed thickness is important. If the bounding beds are not infinitely thick, then we must consider their thickness to determine if the fracture might grow completely through the bounding beds and into zones of lower stress. A 2 ft shale bounding a 10 ft pay zone is obviously not going to stop a fracture from growing out of zone, nor will a 20 ft shale bounding a 50 ft zone. A good rule for beds immediately bounding a zone to be fractured, is that they should be at least as thick as the zone being stimulated to confine frac height; the “basis” for this “rule-of-thumb” is discussed under Picking Fracture Height on page 5-12. Consider the “Pressure-Height Curve” as seen in Fig. 5.2b. At the point where the fracture has tripled in height (e.g., H/Hi = 1 and the fracture has grown “upwards” a distance equal to one initial height and “downwards” one initial height), net pressure has reached ± 80 % of the in-situ stress difference. Also at this point, pressure-height behavior is fairly “flat”, that is, relatively large amounts of height growth begin to occur for small increases in bottomhole treating pressure. Thus, even for “infinite” bounding beds, fracture height will begin to increase rapidly after an “upward” or “downward” growth about equal to one original formation thickness.

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Fracture Height/Fracture Height Growth - 3-D Modeling/Design

Case 1 Apparent Lithology No Stress Difference Collar Locations

2700

Parts

Depth (meters)

2675

Base Gamma Ray

0.7 psi/ft gradient

2725

6000

7000

Post-Frac Gamma Ray

2750 Closure Stress (psi)

Increasing Gamma Activity

Case 2 Large Stress Differences No FRAC in High Stress Interval

2060

4000

Base GR

5000

Perfs

Lower Zone Upper Zone

Collar Locations

2060

Perfs

Depth (meters)

2060

Post-Frac GR

Increasing Gamma Activity

Closure Stress (psi)

Fig. 5.4 - Examples of Lithology Changes, With and Without Associated Stress Differences.

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The first important effect of bed thickness then is the thickness of bounding formations as illustrated by the four drawings in Fig. 5.5. This figure repeats the “three-layer” behavior discussed above until “point C” is reached - e.g. the fracture has approximately tripled in height and the top of the fracture has just reached the top of the barrier formation. At that point in time, the treating pressure inside the fracture, near the wellbore, is considerably greater than the pressure needed to propagate a fracture into the shallower low stress zone. Thus treating pressure will begin to drop (sometimes fairly rapidly) as the fracture preferentially migrates into this new formation.

Fig. 5.5 - Fracture Height Growth Through Finite Bounding Beds. Hydraulic Fracturing Theory Manual

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Fracture Height/Fracture Height Growth - 3-D Modeling/Design

This can, in extreme cases, even lead to the main fracture beginning to grow shorter and can have major (usually undesirable) effects on the ability to pump proppant, proppant placement, and on stimulation effectiveness. Some of the treatment pumping problems which can arise from such height growth behavior are discussed in Chap. 8. Also, some of the fracture modeling/fracture design issues raised by such a fracture geometry are briefly discussed below. The second major importance of bed thickness is thickness of the pay zone itself. The net pressure which the stress and thickness of the bounding beds must counteract depends on the thickness of the pay zone. Fig. 5.6 illustrates the net pressure required to create a 500 ft fracture for several pay zone thicknesses. This figure shows that height growth would probably not be expected to be confined to a 20 ft zone at 2000 psi, but height confinement could be expected for a 200 ft zone at 200 psi. While the actual net pressures tabulated in Fig. 5.6 are for a specific case, the figure can also be used, in a general, qualitative, sense to estimate the potential for height confinement for particular zones.

Fig. 5.6 - Net Pressure Required to Create a 500 ft (1/2 Length) Fracture.

The actual net pressures tabulated in Fig. 5.6 are for a specific case. However, they might also be viewed as “typical” values of net treating pressure for various gross zone thicknesses. Thus, if a formation being considered for fracturing has a gross thickness on the order of 30 ft - then net treating pressure will probably be ± 1500 psi, and stress differences on the order of 1600 psi will be needed to give reasonable height confinement. Assuming a formation depth of 6000 ft, the required “gradient” of stress difference would be 0.27 psi/ft - good height confinement is unlikely and extensive height growth would be expected. On the other hand, a typical net pressure for fracturing a zone with a gross thickness of 60 ft might be on the order of 800 psi - with stress differences of ± 900 psi needed for reasonable height confinement. For a formation depth of 8000 ft, the required

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gradient difference is “only” 0.1 psi/ft - and assuming some lithology differences exist - then fairly good height confinement may be a reasonable possibility. Effect Of Other Factors On Fracture Height Growth •

Modulus contrast between pay and bounding beds

•

Interface or bedding plane slip - applicable at shallow depth?

•

Ductility of bounding bed-may facilitate bedding plane slip, rare

•

Stress gradient due to fluid pressure - generally insignificant

•

Fracture toughness or strength differences-probably not a barrier

Fig. 5.7 - Effect of Modulus Contrast on Fracture Containment.

Probably the most important of the remaining variables which affects frac height (after the stress and pressure behavior), are modulus contrasts (Fig. 5.7), and bedding plane slip (Fig. 5.8 and Fig. 5.9). Though not as strong a barrier as once thought, bounding beds with higher modulus than the pay zone can retard height growth by causing fracture width in the bounding formations to be very narrow. However, as seen in Fig. 5.7, the maximum possible L to H ratios are fairly small - that is the height confining effect of modulus contrasts is actually quite minimal. For shallow depths, overpressured formations, or highly jointed formations such as coals, slip may occur along bedding planes at the top or bottom tip of the fracture, Fig. 5.8, blunting the fracture and arresting height growth. This would be a very strong barrier; however, it probably does not occur often in oil and gas well fracturing except possibly at the interfaces with coal seams. Slip of this type would be required for the Geerstma de Klerk model to be applicable for fractures with lengths greater than their height (L/H > 1). Fig. 5.9 presents the results of a series of lab tests conducted to determine the “likelihood” of a hydraulic fracture stopping at an unbonded interface between two rock layers. As seen from these Hydraulic Fracturing Theory Manual

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Fracture Height/Fracture Height Growth - 3-D Modeling/Design

Fig. 5.8 - Illustration of Fracture Interface Slip.

Fig. 5.9 Interface Slip vs. Stress.

results, for an effective vertical stress across the interface (e.g. overburden weight minus pore pressure) of only ± 1000 psi the fracture crossed the interface for almost all rock types. Since an effective vertical stress of this magnitude would correspond to a depth of only about 2000 ft - it is clear that interface slip will not be an effective barrier to vertical frac height growth for most oil and gas well situations. Fracture closure pressure or closure stress generally increases with depth, with a typical gradient of ± 0.7 psi/ft - e.g. for each 100 ft increase in depth, closure pressure will increase by 70 psi. This increase in closure stress is generally greater than the increase (with depth) in fluid pressure inside the fracture due to the hydrostatic gradient of the fluid. As an example, consider a fracture 200 ft in height which is filled with a water based fluid. Closure stress at the bottom of the fracture is greater by about 140 psi than closure stress at the top; at the same time the driving fluid pressure at the bottom is greater by ± 86 psi (assuming a hydrostatic gradient of 0.43 psi/ft for water). Thus net pressure (e.g. driving fluid pressure minus closure pressure) is about 54 psi less at the bottom of the fracture than at the top. Thus the fracture would have some tendency to grow upward rather than downward. However, for many (most?) fracturing cases net pressure may have a typical value on the order of 500 to 1000 psi - thus a difference (over the height) of ± 50 psi in net pressure is relatively insignificant. Stress gradients, then, only become significant in affecting fracture height growth for cases where significant height already exists (e.g. several hundred feet), or for cases of very low net pressure (e.g. typically associated with low modulus formations and/or the pumping of very low viscosity fluids).

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Generally Insignificant Except in Case of Unrestrained Vertical Growth Where Height Becomes Very Big

Fig. 5.10 - Illustration of Stress Gradient Effect on Frac Height Growth.

Picking Fracture Height (Estimating the In-situ Stress Profile) Obviously, normal strata are not as simple as the idealized case described in Fig. 5.10, but the principles are still applicable. If the bounding beds are not infinitely thick, then we must ensure that they are of adequate thickness so the fracture does not grow completely through them and into a zone of lower stress. A 2 ft shale bounding a 10 ft pay zone is obviously not going to stop a fracture from growing out of zone. As discussed on page 5-6, a good rule for beds immediately bounding a zone to be fractured is that they must be at least as thick as the zone being treated. Still, there will be some height growth into the bounding layers with the final magnitude of fracture height being predominantly determined by the stress difference between the “pay” and the bounding formations. Thus predicting or picking fracture height becomes an exercise in estimating (or measuring) the in-situ closure stress for various zones. There are tools which may, under some conditions, possibly aid in determining the in-situ stress “profile.” However, in general, consideration of two dominant parameters will aid in constructing reasonable estimates of in-situ stresses. Factors Which Dominate In-situ Stress Differences •

Lithology Changes

•

Pore Pressure

•

Pore Pressure Variations

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Fracture Height/Fracture Height Growth - 3-D Modeling/Design

One minimum consideration for height confinement is significant lithology changes as seen with a Gamma Ray log. Shales often have higher closure stresses than clean sands so thick boundary shales can confine fractures. Such confinement is not always the case, but the lack of lithology changes virtually ensures unrestricted height growth or radially shaped fractures. Thus a change in lithology makes it possible for stress differences to exist. However, one should not try to “quantify” a Gamma Ray log, e.g., if a lithology difference exists, then stress differences may exist and fracturing pressure analysis (as discussed in Chap. 8) must be used to determine the magnitude of the stress differences. As discussed, closure stress is related to reservoir pressure. Therefore, a reservoir that has been drawn down, as in a producing well, is likely to have a lower closure stress than normal in the pay zone, and consequently a higher stress differential between pay and the bounding beds, improving chances for height confinement. On the other hand, height confinement could be more difficult to achieve in an injection well due to pressuring up of the pay zone. Thus pore pressure and pore pressure differences between zones (e.g. due to partial depletion from offset production) is a major factor to consider in estimating in-situ stresses. Fracture closure stress is generally related to pore pressure by3 ν σ c =  ------------ ( OB – p ) + p  1 – ν

(5.2)

where OB = Overburden Pressure ≈ 1 psi/ft, p = pore pressure, ν = Poisson’s ratio, Sandstones ν = 25, and Carbonates ν = .33. Inspection of Eq. (5.2) for a “typical” sandstone reservoir with a Poisson’s ratio, ν of 0.25 indicates that for every psi change in reservoir pressure there is a corresponding 2/3 of a psi change in closure pressure. Thus a depletion of 1500 psi in a sandstone will typically cause a reservoir closure pressure to decrease by about 1000 psi. Since there should presumably be no pore pressure reduction in the surrounding impermeable shales, this 1000 psi decrease in the pay zone closure pressure would be added to any “naturally” existing stress differences and very good height confinement can exist in depleted formations. Further inspection of Eq. (5.2) for a “typical” carbonate reservoir would show a 1/2 psi change in closure pressure for every psi change in reservoir pressure. Special logs have been developed and marketed which may, sometimes be of value in determining the in-situ stress profile (see Chap. 10). However, these logs are based on simple, elasticity assumptions and should be treated with extreme caution. For sand/shale sequence geology, there is often some “relative truth” in the logs and the actual stresses can frequently be successfully “calibrated” against the log derived stress values. Carbonate geology tends to be more complex and the value of the logs is more questionable. In either case, however, the raw information from the logs should never be used. If test procedures are not planned in order to calibrate the logs - then the logs should not be run. December 1995

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An example of a stress/log calibration is shown in Fig. 5.11, showing a comparison of measured stress vs. log stress from several sand/shale sequence formations. It is important to note two things on Fig. 5.11: (1) the correlation, which is reasonably strong, is not 1:1, e.g. the absolute values of log stresses are probably never correct, and (2) this data is not intended for application, but merely as an example of how one might proceed to calibrate such special logs. Finally, it should be noted that while on a scale of “absolute stress,” the correlation appears very good. Examining the fine detail shows that the actual stress sometimes differs from the “correlation” by 500 to 1000 psi. Since the stress of interest is not the absolute value but instead is the difference - such a deviation represents as much as a 50 to 100% error. Thus any type of “general” stress correlation must be treated with care.

Fig. 5.11 - Stress/Log-Stress Correlation.

A measured/log stress correlation can be based on stresses actually measured in several zones in the wellbore using closure stress tests as described in Chap. 8. This technique is the only one which provides quantitative, in-situ data by which to determine the potential for height confinement, but

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Fracture Height/Fracture Height Growth - 3-D Modeling/Design

requires perforating and testing multiple zones in the well. If a number of fracture stimulations are to be performed in the field, and height confinement is questionable and critical to the outcome of the stimulations, then such testing coupled with running sonic logs as described above may be warranted. Alternatively, a 3-D type fracture simulator may be used to infer the in-situ stresses through history matching actual bottomhole treating pressure (BHTP) data. This is also discussed in Chap. 8. In summary, fracture height is the most critical variable to successful fracture treatment design, and yet is one of the most difficult variables to measure. The three variables most strongly affecting the ultimate frac height achieved during a treatment are: (1) closure stress differentials, (2) thickness of the bounding beds, and (3) net fracture pressure. Several techniques exist by which to better quantify frac height, involving everything from qualitative guesses to detailed quantitative measurement. Finally, there is no substitute for experience in an area for picking fracture height or estimating the in-situ closure stress profile, but whether an established field or a wildcat, there is plenty of room for sound, engineering judgments. 3-D Fracture Modeling/3-D Fracture Design Since fracture height and fracture height growth are the dominant variables affecting successful propped fracture treatment design, fracture models which can account for height growth become powerful, even indispensable, tools for modern job design or analysis. This is true in spite of the common statement - “We never have the data required to really use such fracture models.” In fact, one must realize that, in reality, 2-D fracture models are much harder to accurately use since there is never, under any conditions, any way of accurately estimating fracture height in advance. However, we can make reasonable estimates for the in-situ stress distribution. Also, since in many cases the bottomhole pressure during a treatment is a strong function of the in-situ stresses and the stress profile, we can use pressure data along with 3-D models to verify or modify these estimates, finally arriving at a reasonably accurate description of the formation(s). This is most efficiently done via a pressure history matching procedure as discussed in Chap. 8. It is important to realize, however, that there are two “types” of 3-D fracture simulators. Fully (or true) 3-D models calculate fracture width and fracture propagation at every point as a function of the fluid pressure distribution everywhere inside the fracture. Among other things, this ensures that the fully 2-dimensional flow field inside the fracture is used in calculating fluid pressure and fracture width at each point. Models such as this are powerful tools and can be used for analyzing quite complex geologic settings and complicated fracture geometry. Such models also require extensive computer resources and are not usable for any type of “routine” well completion designs. TerraFrac is one commercial fracture simulator of this type and this model is available in Amoco. The TerraFrac model is discussed and some of its capabilities are briefly described in Section 10.2 of this manual. Also, a few different fracture geometry cases are briefly reviewed below along with some notes as to which “geometry types” require such “fully 3-D” modeling. December 1995

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Design of Pseudo 3-D Hydraulic Fracturing Treatments

A more common, and usable, type of fracture simulator has been termed a pseudo 3-D model. Such models are made more “usable” (in terms of time and required computer resources) through several simplifying assumptions including: 1. The fracture length is at least equal to the fracture height, though through analytical approximations, such models can also give at least rough estimates of fracture geometry where vertical height growth may be somewhat greater than fracture length. 2. Fracture height growth at any point along the length of the fracture is related only to the net pressure at that point. Also, fracture width (and the vertical fracture width profile) at any point along the fracture length is assumed to be related only to the net pressure at that point. 3. The greatest fracture penetration is occurring in the zone where the fracture initiates. Even with these simplifying assumptions, however, pseudo 3-D models have proven in field practice and through comparison with fully 3-D models, capable of handling many realistic and common cases. Schematically, a pseudo 3-D type fracture model proceeds as pictured in Fig. 5.12. Fracture length propagation is calculated using calculations and assumptions similar to the traditional, 2-D, Perkins & Kern (PKN) fracture geometry. Along the fracture length the fracture is broken into individual segments or cells, and the vertical fracture height growth for each “cell” is calculated as if this cell represented a single Geertsma de Klerk (GDK) fracture geometry. As mentioned above, the fracture width and width profile along with the height growth for each cell is assumed to be related solely to the net pressure in that particular fracture segment or cell.

Geertsma deKlerk Solution

Perkins & Kern Solution

Fracture Length is Broken Into Segments and Height Growth and Width of Each Segment is Calculated Independently

Theoretical Basis of Pseudo 3-D Type Fracture Models

Fig. 5.12 - Pseudo 3-D Fracture Modeling.

While pseudo 3-D models are good, usable tools, it is important to realize that limitations do exist and to recognize when the use of more sophisticated models is necessary. Fig. 5.13 illustrates sev-

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Fracture Height/Fracture Height Growth - 3-D Modeling/Design

eral possible fracture geometries and briefly comments on the applicability of “Pseudo 3-D” models to each case.

Radial Frac

Ideal “P3D” Geometry

OK for “P3D” Modeling

Stress Profile

Requires “Full 3-D” Model OK for “P3D” Model

Fig. 5.13 - Fracture Geometries.

Measuring Fracture Height Just as it is difficult to pick a fracture height or to estimate the stress profile controlling height growth, it is also difficult to measure fracture height after a job. However, several tools are available and these should be employed whenever possible to allow post-job evaluation and to improve future jobs. The primary techniques for measuring height include temperature and Gamma Ray logs (GR log); when conditions allow, an open hole completion; and, when the situation warrants it, downhole televiewer logging. Procedures involved in running these logs are discussed in Section 10.1 of this manual.

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Design of Pseudo 3-D Hydraulic Fracturing Treatments

Temperature logs are, and will probably remain, the most widely used logs for measuring fracture height. However, one significant restriction of the log should always be considered. Temperature logs are very shallow investigative tools; and if the fracture deviates from the wellbore, it will quickly become “invisible.” In general, a temperature log (or postfrac Gamma Ray log) showing fracture height confined exactly to the perforated interval should be treated with extreme skepticism. Fluid Loss Height The prediction of fluid loss height, Hp, is important for the design of a fracture treatment. The loss height represents the net height in the fracture which will dominate the fluid lost to permeable zones. One method of selecting Hp, is illustrated in Fig. 5.14, where an Spontaneous Potential (SP) log is used. For this procedure, the net section to the left of a line 1/3 the distance from the “shale” line to the maximum “sand” deflection. This procedure neglects potential (if any) loss to “shale” and “dirty” sands. A Gamma Ray Log might be used in a similar manner, with fluid loss height being the net section to the left of a line 1/3 the distance from the “shale” line and the maximum “sand” line. If adequate definition from a SP or GR log cannot be obtained, other cutoffs (porosity) can be used.

Selecting Fluid Loss Height

Max. “Sand” Line

“Shale” Line

Fluid Loss Or “Permeable” Line

Fluid Loss Height = Net section height to left of “permeable” line Neglect Shales, ?

Fig. 5.14 - Selecting Fluid Loss Height.

For a given field, the potentially arbitrary nature of this procedure is overcome if the procedure is consistently used for fluid loss coefficients determined from minifrac pressure-decline analysis or calibrated along with loss coefficients from the success or failure on past designs of offset wells. This works because fluid loss height and fluid loss coefficient are multiplied together to arrive at

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Fracture Height/Fracture Height Growth - 3-D Modeling/Design

a “fluid loss capacity” analogous to reservoir flow capacity (kh). Doubling fluid loss height and halving fluid loss coefficient yields exactly the same results as the base values. The fluid loss height is commonly and wrongly confused with net pay height. Fluid loss height will always be greater than the pay height. In many reservoirs where the net pay cutoffs from porosity logs are well established, one should ensure that all net pay is included as fluid loss height.

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Design of Pseudo 3-D Hydraulic Fracturing Treatments

5.2 Fluid Loss This section discusses the values for the fluid loss coefficient and spurt loss used in fracture design and/or analysis. The amount of fluid lost to the formation during a treatment is a primary design consideration. The lost fluid is essentially wasted and represents a significant portion (i.e., generally 30 to 70%) of the total fluid and cost of treatment. The rate of fluid loss is described by the expression C A q l = ---------t

(5.3)

where C is the fluid loss coefficient, A is the fracture wall area and t is the time since the area A was exposed to fluid. The loss coefficient depends on three separate effects as shown on Fig. 5.15 and each of the three have the square root of time relationship given in Eq. (5.3). These effects and how they are determined are discussed below. The best estimate of fluid loss is obtained from the pressure decline analysis of a calibration treatment (discussed in Chap. 8). Fluid Loss Coefficient, Ct The composite fluid-loss coefficient depends on three separate linear flow mechanisms with the separate coefficients, CI - fracturing fluid viscosity relative permeability effects, CII - reservoir fluid viscosity-compressibility effects, and CIII - wall building effects. In any fracturing treatment, each of these mechanisms acts simultaneously to varying extents and complements the other. These mechanisms act analogously to a series of electrical conductors and their coefficients are combined as shown in the following equation: 1 1 1 1 ----- = ------ + ------- + --------Ct C I C II C III

(5.4)

The fracturing fluid viscosity and relative permeability (i.e., filtrate) effect can be obtained from the following equation: C I = 0.0469

k f Φ ∆p -----------------------1000 µ f

(5.5)

Permeability, kf (md), to the fracturing fluid filtrate may be obtained by correcting pressure transient test derived permeabilities (ko, kw or kG) by reducing the value by a factor of about 5. HowHydraulic Fracturing Theory Manual

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Fluid Loss

∆P = P f – P p : p – pore, f – filtrate, c – Cake CII =

∆P

CI =

2 µp ∆ Pk

-------2 µf

(OIL) (CARTER, SPE 1957) (GAS)

k ∆P

c ------------ (POLYMER, SOLIDS) 2 µf f c

Fracture

CIII =

kc φ ------

CIII

fc FRACTION OF FLUID LOSS ON CAKE

Reservoir Three Components of Fluid Loss: CI = Frac Fluid Effect CI

CII

CII = Reservoir Fluid Effect CIII = Wall Building Effect

Wall Cake

Invaded Zone (usually ~ 2-3 in.) Fig. 5.15 - Fluid Loss.

ever, if the filtrate from the frac fluid is similar to the reservoir fluid, than this reduction is not necessary (i.e., water frac on a water injection well). The purpose of the reduction factor is to account for relative permeability effects. If relative permeability curves are available they can be used to determine kf. Effective porosity should be obtained by correcting the formation porosity for in-place fluid saturations. If, for example, a water based fluid is being used to frac a reservoir, the effective porosity is reservoir porosity multiplied by (1-So-Sg). If a hydrocarbon based fluid is used; the effective porosity is the reservoir porosity multiplied by (1-sw). Pressure differential, ∆p (psi), across the fracture face is the difference between bottomhole treating pressure (i.e., ∆p = BHCP + P N – P R ) and reservoir pressure. Since polymers are generally filtered from the base fluid by a low permeability matrix, the base leakoff fluid viscosity, µ f , is usually that of 2% KCl water containing a slight amount of polymer. A maximum value for µ f might be 5 cp with a minimum value of 0.5 cp, depending on formation temperature. December 1995

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The CI effect is primarily governed by the viscosity of the filtrate of the fracturing fluid. Since the viscosity is generally very small (i.e., < 1 cp), the CI term is generally large for current fracturing fluids and is not effective for fluid loss control. This is not the case for very viscous oils such as those used during the 50s and 60s. The reservoir fluid viscosity-compressibility (i.e., formation fluid) effect can be obtained from the following equation: k HC c t Φ HC C II = 0.374 ∆p ------------------------------1000 µ HC

(5.6)

The CII effect is primarily governed by the compressibility, ct and therefore is very important for liquid filled reservoirs such as oil wells or water injection wells. These generally have a very low ct compared to gas reservoirs. However, the CII term has negligible control in gas reservoirs which have a relatively high ct (ct gas = 1/pr gas). Permeability to the reservoir fluids (kHC) (millidarcies) should be measured by a pressure transient test. Viscosity and compressibility of the reservoir fluids should be determined as in a pressure transient analysis (e.g., lab tests, tables, or calculations). The wall building effect for the fluid loss coefficient is determined from data obtained experimentally in a laboratory as shown in Fig. 5.16. A standard fluid loss test is conducted in a high pressure-high temperature Baroid filter press containing core samples or filter paper. The fluid loss test is run with a pressure differential of 1000 psi as standard, although ∆p may be much larger, i.e., 3000 psi. Additional work is required on the effect of ∆p which is currently assumed to be negligible. For very low k rocks (< .1 md), the tests should be run using filter paper instead of cores. Otherwise, the data for CIII will be erroneous due ∆ p of the filtrate through the core during the early portion of the test which has a high loss rate. The fluid loss in cubic centimeters is measured at time intervals of 1, 4, 9, 16, 25, and 36 minutes; and these fluid loss values are then plotted on straight coordinate paper against the square root of time in minutes (Fig. 5.16). The experimental fluid loss coefficient is then calculated as follows: C III = 0.0164m/A

(5.7)

where m is the slope of the plotted data (cc/ t ) and A is the cross sectional area (cm2) of the core wafer. Normally, CIII is furnished by the fracturing service company. For critical treatments, fluid loss tests for the specific fluid and in-situ conditions should be requested.

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Fluid Loss

WALL BUILDING FLUID LOSS TEST

Fig. 5.16 - Standard Fluid Loss Test.

Fig. 5.17 shows a qualitative comparison of CIII values for different fluids based on laboratory data from low permeability cores. These test data were run at 150 ° F and one polymer loading. At 250 ° F, it has been found that the CIII values for most frac fluids increased by a factor of 1.5 to 2 because of the reduced viscosity of the filtrate through the wall (Fig. 5.15). Keep in mind that the data in Fig. 5.17 is approximate and the wall building ability of a fracturing fluid depends on formation temperature, and the fracturing fluid type and polymer loading under consideration. The addition of 5% hydrocarbon to crosslinked water systems (Type III, on Fig. 5.17) can be a very effective loss control additive for permeabilities less than 1 md and is generally recommended. The addition of a hydrocarbon dispersion works primarily by reducing the relative permeability of the polymer cake to water and by droplet plugging of pore throats. Adding the second (oil) phase reduces the relative permeability to water. Since the hydrocarbon works primarily in the polymer cake, this technique provides little benefit if most of the fluid loss is CI or CII controlled, as in high permeability reservoirs. The effect of droplet plugging on a low permeability formation also makes wall building fluid loss control important for emulsion and foam fluids. Solid fluid loss additives are sometimes required for efficient fracturing in moderate to high permeability or naturally fractured reservoirs. These agents work by blocking the larger pore throats (i.e., required to form wall building) and fractures. Fig. 5.18 shows the effect of silica flour (Halliburton's WAC-9) on CIII. Such agents are silica flour, 100 mesh sand and manufactured mixtures. These additives must be used with extreme caution if they are mixed with the proppant, since they can plug the proppant, unless they are designed to dissolve in the produced fluid. Use of these additives with proppant laden fluid is not recommended unless absolutely required and then such that the total does not exceed 1% of the total proppant during the treatment. The addition of silica flour to the pad at a loading of 15 lb/1000 gal has been used to seal off closed natural fractures.

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Design of Pseudo 3-D Hydraulic Fracturing Treatments

Fig. 5.17 - Wall Building for Various Fluid Systems.

Also, 100 mesh sand for the initial sand stage (1/4 to 1 lbm/gal) is effective for sealing open natural fractures. Spurt Loss The total fluid lost when wall building dominates is a combination of the fluid lost before a filter cake has begun to form (spurt loss) and the fluid lost through the filter cake during the treatment. The point where the fluid loss curve intersects the ordinate on a fluid loss plot is known as the spurt loss (see Fig. 5.16). For fluids that build effective wall cakes and low permeability formations, the spurt loss is low. In this case, a value of zero (0) is used for spurt loss if the permeability is very low (i.e., less than 0.05 md). Generally, the service company supplies the spurt loss values for their various fluids. Table 5.1 is an example from the Dowell “Fracturing Fluids” book showing CIII (i.e., Cw) and spurt for a non-wall building fluid for various high permeability rocks (i.e., relatively high spurt) and amounts of silica flour. Spurt loss can be significant for moderate to high permeability formations. For example, assume a 500 ft fracture radius, 50 ft fluid loss height, and 5 md permeability. Table 5.1 shows 20 gals/100 ft2 spurt loss even with 20 lb/1000 gal silica flour. This equates to an additional 20,000 gal of fluid loss which must be included in the treatment design.

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Fluid Loss

0.005 0.004 0.003 CW -- ft/min1/2

0.002 Permeability 0.1 - 150 md 0.001 0.0005 0.0004 0.0003 0.0002 0.0001 0

20

30

40

50

60

70

80

90

100

WAC-9 Concentration -- lb/1000 gal water Fig. 5.18 - Silica Flour for Moderate to High Permeability. Table 5.1 - Spurt Loss Dependence on Permeability and Additives. FLUID LOSS OF FLUIDS PREPARED WITH J160 THICKENER J84 (lb/1,000 gal) (Silica Flour)

Cw X 1000 (ft/ min

Spurt (gal/100 ft2)

2.2 1.5 22.5

0 20 50

30.0 9.9 6.0

0.0 7.9 59.0

125 125

1.0 4.8

20 20

5.0 4.2

1.8 19.5

40 40

125 125

1.0 4.8

20 20

5.0 4.2

1.8 19.5

60 60

125 125

2.9 3.1

20 20

4.9 4.1

15.5 19.8

80 80 80 80

125 125 125 125

3.7 3.9 5.1 25.0

20 30 40 50

3.3 1.8 3.1 3.0

5.9 5.9 9.3 44.0

J160 (lb/1,000 gal)

Temperature ( ° F)

20 20 20

125 125 125

30 30

December 1995

K (md)

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Design of Pseudo 3-D Hydraulic Fracturing Treatments

FLUID LOSS PROBLEM

Find:

The Combined Fluid Loss Coefficient

Given:

Gas Reservoir: 170 ° F; Pr = 2300 psi, Φ HC = 0.125 ; Sg = 0.50; k = 0.1 md (buildup test) µ g = 0.0174 cp ; BHTP = 4000 psi

Lab Data:C III = 0.001 ft\/ min @ 150 ° F (For Water Filtrate: 0.45 cp @ 150 ° F 0.21 cp @ 250 ° F)

U L T R A F R A C 09:23:40

2 . 0 User ID: ZWXY01

03/04/92

File : UFDEMOS

FRC

UFCIII:

Well Name: CARTHAGE (COTTON VALLEY) FIELD Calculate Total Fluid Loss Coefficient

Res Fluid Visc (cp) Filtrate Visc (cp) Formation Temp (deg F) Pressure Diff C-III

(psi)

0.017 2.4 170.

1700. 0.001

Permeability (md) Porosity (fraction) Compressibility (lbs/gal)

0.100 0.125 200.0

((Clos Pres + 500 (psi) - Res Pres) @ Test Temp (deg F) 150.

C-I = 0.004463 C-II = 0.026517 C-III = 0.001090

ft/min**.5

at 170. (deg F)

Harmonically Weighted Ct = 0.00085 PF3 Continue

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Fluid Viscosity

5.3 Fluid Viscosity For most fracture treatments, a significant portion of the cost is for chemicals to create a fluid which will maintain a relatively high viscosity throughout the treatment. As the treatment time and formation temperature increase, the relative cost for the required chemical additives also increase. Fluid viscosity is required primarily to transport the proppant from the wellbore to the tip of the fracture. Fluid viscosity also affects the fracture width which is a consideration for proppant admittance; however, sufficient width is normally created for proppant entry by a fluid which has sufficient viscosity for proppant transport and/or as a result of the fracture length created by a sufficient pad. Viscosity Determination and Rheological Models The viscosity values of fluids are determined by laboratory tests. The simplest, but idealized, experiment of fluid flow is fluid being sheared between plates moving parallel and relative to each other. The shear stress on the fluid is the shear force exerted on the plates divided by their area with the units of pressure. The shear rate or velocity gradient is the relative velocity divided by distance of separation and has the units of 1/time, usually in sec-1. The viscosity is defined as the shear stress/shear rate. The rotating cup/bob viscometer has been popularized in the industry by the Fann Instrument Co. (now under the ownership of NL Baroid). As shown in the idealized drawing, Fig. 5.19, the shear stress is the force exerted on the walls (sensed by the torque on the bob) divided by the surface area, and the shear rate is the relative velocity of the stationary bob and the rotating cup divided by the gap distance. For the standard system, i.e., the R1-B1 Rotor-Bob Geometry, a rotating speed of 100 RPM represents a shear rate of 170 sec-1, and a speed of 300 RPM represents a shear rate of 511 sec-1. Unfortunately, this device is not suited to some crosslinked polymer fluids, e.g. borate crosslinked gels, because of their viscoelastic nature. Borate gels can “crawl” up and out of the cup. In spite of this, most published data for borate gels are determined using cup and bob viscometers. Viscosity is sufficient to characterize the stress-flow behavior, i.e., the rheological character, of some simple fluids such as water and refined oils. These simple fluids have shear rate independent viscosity. Most fracturing fluids, however, show shear-dependent viscosities, usually decreasing with increasing shear rate, i.e., shear thinning, and thus more than one parameter is required to characterize the rheology. Experimental shear stress and shear rate data are usually correlated by some approximating rheological model. The rheological models commonly used in the industry for many types of fluids are the Newtonian, Bingham Plastic, and Power Law Models, as shown in Fig. 5.20. These models are selected because they yield straight lines on linear or log-log graphs of shear stress vs. shear rate.

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Design of Pseudo 3-D Hydraulic Fracturing Treatments

Fluid Flow (Rheology)

II. Rotating Cup & Bob (e.g., Fan Viscometer: Industry Standard)

I. Idealized

T W

A

Turn Cup: W Torque on Bob: T

F, ν x

d

Fluid

H

ν(x)

Ri Ro

τ = Shear Stress = F/A (Pressure)

wR

o ϒ˙ = --dν ≅ --------------Ro – Ri

dν 1 ϒ˙ = Shear Rate = --ν = ---- ( --------) d dx time

τ

T /R

T = F--A = ------------i - = -----------2πRi H

2πR i H

Fig. 5.19 Fluid Testing.

Rheological Models I. Newtonian

II. Bingham

III. Power Law log τ

τ Yp

µ

τ

µp ϒ˙

ϒ˙ τ = µϒ˙

n' K'

τ = Y p + µ pϒ˙ Yp →0

˙ logϒ 1.0

τ = K'ϒ˙ n n'

→0

Newtonian

Newtonian

µp = µ

K' = µ

Fig. 5.20 - Models for Fluid Flow.

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Fluid Viscosity

A Newtonian type fluid has a linear relationship between the variables with a slope equal to viscosity, i.e., water, brines, and oils. A Bingham Plastic type fluid differs from a Newtonian fluid by a non-zero stress (i.e., Plastic Yield Value) at zero shear rate. The slope of the line is termed the Plastic Viscosity (not equal to apparent viscosity). The initial work on these fluids was done by Bingham on paints and printer's ink - zero flow (shear rate) on vertical surfaces (shear stress). This fluid model is used in the industry for drilling muds and cements. The Power Law fluid model is commonly used for representing frac fluids and predicts a straight line on a log-log plot with the slope denoted as n' (generally < 1) and termed the Power Law Exponent or Flow Behavior Index (n' = 1, Newtonian; n' > 1 shear thickening; n' < 1, shear thinning). The stress at a shear rate of unity is denoted as K' and is termed the Consistency Index. This model does not predict a yield value (no flow with stress, e.g., can form a stationary lip when poured, remains as a glob on the table). The K' and n' values of real fluids change with increasing time and temperature (generally K' decreases and n tends toward unity) and depend on their flow history. Most service companies attempt to account for downhole flow conditioning in some manner when testing crosslinked fluids. Although the power law is the primary model used for fracturing fluids, it does not account for other aspects of flow behavior exhibited by many fluid systems, such as nonhomogeneous flow, e.g., slip or particle migration, or viscoelasticity. These factors can influence rheological scale-up and proppant transport and are presently the subject of research. All fracturing simulators treat frac fluids as if they were homogeneous power-law fluids. Fig. 5.21 defines and gives an example of apparent viscosity for a power law fluid. The example shows a realistic case for fracturing fluids. Different service companies have reported viscosity at different shear rates (i.e., 170 sec-1 or 511 sec-1). The rate in a fracture can be 40/sec. The example shows that the same fluid can be reported by one company to have 100 cp (at 170 sec-1), another to have 58 cp (at 511 sec-1) and the fluid may have 206 cp (at 40 sec-1) in the fracture. Therefore, in selecting fluids it is important to know what shear rate the data represents. Table 5.2 shows a typical rheological data set presented by service companies for use in fracture design and/or analysis. Fluid Entry Conditions and Temperature Considerations The viscosity of some fracturing fluids, can be very sensitive to their flow and thermal histories. Fluids often encounter intense flow energies while being pumped downhole, ranging from 0.2 hp/ft3 to 8 hp/ft3. Delayed crosslinked gels are formulated to start crosslinking after the gel enters the fracture and starts to heat up to avoid degradation of the crosslinks during high energy flow condition. Foams and oil-base gels, on the other hand, may actually achieve better viscosities after subjected to high-energy flow conditions. Thus, the viscosity of the frac fluid as it enters the fracture is frac-fluid system dependent and is influenced by flow and thermal conditions. December 1995

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• Example

τ

Power Law: Given: n' = .5 µa = 100 cp, =170 sec-1

τ1

Find: K', µa at 40 and 511 sec-1 K' = 100 x (170).5/ 4.8 x 104 = 0.27 µa (511) = (170/511).5 x 100 = 58 cp µa (40) = (170/40).5 x 100 = 206 cp

µa ϒ1

• •

µ

τ

a

= ---˙1- ( Depends on ϒ˙ ) ϒ

• Find: K',

µ a at 40 and 511 sec-1

For Power Law Model 4 4.8 × 10 K' µ a = -------------------------ϒϒ ˙ (1 – n)

K' = 100 x (170).5 / 4,8 x 104 =. .027 µ a (511) =

( -------- )

µa

= cp

µ a (40) =

( -------- )

K'

= lb – sec /ft

ϒ

= 1/sec, sec

n'

2

170 0.5 x = 58 cp 511

170 0.5 x 100 = 206 cp 40

–1

Fig. 5.21 - Effect of Shear Rate on Power-Law Viscosity.

An entry temperature and corresponding wellbore n' and K' values are required to calculate the entry viscosity of the frac fluid. As the fluid flows down the wellbore it acquires heat from the reservoir and from conversion of flow energy to heat. As an estimate for fluid heat up for water-base fluids and CO2 foams at typical fracturing flow rates, one can use 10°F temperature increases at 7000 ft, 10,350 ft, 12,900 ft, 15,120 ft, and 16,780 ft. Thus, if pumping to 13,000 ft, one might expect the fluid entry temperature to be about 30°F higher than surface temperature. If pumping oil-base gels, the fluid heats up roughly 25°F at each of the above depths because of their smaller heat capacities (e.g., 0.4 Btu/lbm -°F vs. 1.0 for water). As the fracturing fluid flows down the fracture it continues to heat to reservoir static bottomhole temperature (BHT). Some fracturing design programs assume a bilinear temperature variation based on the Perkins and Kern width model as shown in Fig. 5.22. The temperature increases linearly from the entry temperature to the reservoir temperature during the first one-quarter of the current fracture wing length and remains constant for the remaining three-fourths of the wing. More advanced programs calculate the fluid-temperature profile down the fracture using calculated or assumed heat-transfer coefficients and material heat capacities. The resulting temperature profiles are sensitive to fluid heat capacity and may vary significantly from Fig. 5.23.

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Fluid Viscosity

Table 5.2 - Typical Service Company Rheology Data (DS - 1984). Temp

Time

Viscosity (cp)

Fluid

( ° F)

(hr)

n'

K'

170 sec-1

511 sec -1

YF440 YF440 YF440 YF440 YF440

225 225 225 225 225

1 2 4 6 8

0.600 0.657 0.746 0.808 0.848

0.095 0.052 0.017 0.0065 0.0027

582 426 225 116 60

375 293 167 94 50

YF440 YF440 YF440 YF440 YF440 YF440

260 260 260 260 260 260

1 2 3 4 5 6

0.640 0.697 0.745 0.786 0.820 0.849

0.036 0.023 0.014 0.0091 0.0057 0.0036

272 230 186 145 109 079

183 165 141 114 89 67

YF450 YF450 YF450 YF450 YF450

260 260 260 260 260

1 2 4 6 8

0.600 0.657 0.746 0.808 0.848

0.056 0.035 0.016 0.0081 0.0047

342 289 205 145 103

221 197 157 117 87

YF450 YF450 YF450 YF450 YF450

285 285 285 285 285

1 2 4 6 8

0.640 0.697 0.786 0.849 0.888

0.030 0.018 0.0068 0.0029 0.0014

228 178 108 65 39

152 130 86 54 33

YF460 YF460 YF460 YF460 YF460

260 260 260 260 260

1 2 4 6 8

0.580 0.637 0.726 0.788 0.828

0.091 0.055 0.023 0.011 0.0058

502 409 270 177 115

317 273 199 140 95

YF460 YF460 YF460 YF460 YF460

285 285 285 285 285

1 2 4 6 8

0.600 0.657 0.746 0.808 0.848

0.057 0.033 0.013 0.0056 0.0027

350 274 166 100 59

225 186 127 81 50

Fig. 5.22 - A Bilinear Temperature Variation Down the Fracture.

As alluded to previously, the entry viscosity of the fluid depends on the type of fracturing fluid as well as on the fluid and thermal histories at the surface and down the wellbore. Not all fluids have maximum viscosities at the entry temperature. Some gelled oil systems, and most all delayed orga-

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Design of Pseudo 3-D Hydraulic Fracturing Treatments

Fig. 5.23 - Typical Gel Viscosity Trends with Time at Temperature.

nometallic crosslinked gels show viscosities to increase as the fluid heats to reservoir temperature. After attaining reservoir temperature, an eventual decline in viscosity will be observed. Fig. 5.23 shows typical viscosity trends for various fracturing fluids as a function of time at temperature. The first point at 0 hours is the entry point and in this case it takes 1.3 hours to attain BHT. Note that these viscosity trends are at different BHT. Reservoir Temperatures Reservoir temperature is a very important variable since the viscosity of the fluid will vary significantly depending on the amount of time the fluid has been at reservoir temperature (TR on Fig. 5.22). Therefore, it is best to get a measured BHT. Notice - It is not the maximum log temperature shown on the open hole logs. That value is much too low. The difference between 250°F and 270°F can be significant. Reservoir temperature should be determined by running a static temperature log in the well to be fractured. This log can be run with a cement bond log. The well must be at static conditions for the log to yield the temperature that we are interested in. It is suggested that the well be allowed to sit idle, with no downhole operations of any kind, for at least 1 week prior to running the static temperature log. After a number of such logs are run (5-10 wells) in a given field, the static bottom hole temperatures measured can be plotted against depth to mid pay to determine a static temperature gradient. Static temperature is expressed as T static = (T gradient (°F/ft) * Depth (ft)) +

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Fluid Viscosity

Ambient surface temperature. Once sufficient data has been obtained to determine this gradient, the calculated static temperature can be used on future frac designs. Note from Table 5.2 that for a YF400-5 fluid, a 25°F error in temperature (285°F vs. 260°F) results in only 2/3 the desired viscosity at 1 hr (228 cp vs. 342 cp) and only 1/2 the desired viscosity at 4 hr (108 cp vs. 205 cp). Get the most accurate BHT possible! Effect of Proppant on Viscosity When proppant is mixed into a fracturing fluid, the effect is an increase in apparent viscosity. Recent experiments indicate that both K' and n' are changed when proppant is added to uncrosslinked fluids, but there is no consensus on the best correlations to use on crosslinked fracturing fluids. The proppant effect on K' for the slurry can be approximated by: K ' slurry = K ' fluid × ( C k )

n'

with Ck = (1 - Cv /Cm)-2.5

Slurry / Fluid Viscosity

Here Cv is the proppant volume fraction and Cm is the maximum possible proppant volume fraction set to 0.6. This expression for K'slurry is supported by a limited amount of unpublished laboratory data. Fig. 5.23 shows the effect of proppant concentration on slurry viscosity as developed by Amoco and GRI, respectively.

Pnet = E' [µQL]1/4 Η

RI

G

101

CO

O AM

100

0

2

4 6 8 10 12 Sand Concentration, lb/gal

14

zlkb02.038

Fig. 5.24 - Effect of Proppant on Slurry Viscosity

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Design of Pseudo 3-D Hydraulic Fracturing Treatments

Summary For Fluid Viscosity Fluid viscosity is critical for the successful execution of pressure controlled treatments. Sufficient viscosity is required for proppant transport, while excessive viscosity will proportionally reduce the fracture penetration prior to the fluid pressure reaching the formation's pressure capacity (i.e., inefficient fracture extension). For proppant transport, crosslinked gels are preferred over noncrosslinked gels. Studies show substantial reduction (e.g., 78%) in proppant fall rates through crosslinked gels, under shear, compared to noncrosslinked gels with the same apparent viscosity. The fall rate through foams and emulsions are also believed to be less than indicated by the apparent viscosity. Another consideration is particle concentration which increases slurry viscosity and retards particle fall. The effect of increased slurry viscosity due to proppant concentration is important for pressure controlled designs and requires the base fluid's viscosity to be reduced as proppant concentration increases. Also, the apparent viscosity for non-Newtonian fluids depends on the shear rate with lower rates producing higher apparent viscosities. Generally, the shear rate in the fracture is lower than the 170 sec-1 normally used to characterize fluids. The above considerations can significantly reduce the viscosity requirement over that indicated by a direct use of Stokes Law. An example, illustrated in Fig. 5.3, show that if proppant fall were to be limited to 10 ft in four hours, a direct application of Stokes Law would require a viscosity of 1500 cp for 20-40 mesh sand. Assume that under fracturing conditions the crosslink effect would retard fall only by 50% in contrast to the 78% for ambient and laboratory conditions. In addition, assume the slurry dehydrates from a low proppant concentration as it enters the fracture to 10 lbm/gal, Fig. 5.3, at the end of the treatment. For these conditions, the effect of hindered settling would be equivalent to a multiple of 3.2 in the time-averaged value of viscosity. If the reference viscosity is at 170 sec-1, the shear rate in the fracture is 40 sec-1 and the fluid can be characterized by the power law with n = 0.6, the apparent viscosity would be 1.8 times greater in the fracture than for the reference. If, during the time in the fracture and at reservoir temperature, the fluid viscosity reduces by a factor of 10 with a log-viscosity vs. time relationship, the average value of viscosity would be 4.3 times the final value. Combining these factors (2 x 3.2 x 1.8 x 4.3) results in a multiple of 50, as shown in Table 5.3, and for the fluid considered, sufficient viscosity would be achieved if it had a final viscosity of 1500/50 = 30 cp at the end of the treatment. Furthermore, this estimate may be conservative since a reduction of the crosslink effect was used, the fluid does not experience reservoir temperature for a portion of the fracture length, and suspended particles are transported in the center portion of the channel (for viscoelastic fluids), where the shear rate is lower and the apparent viscosity higher than the channel average. Consequently, the viscosity requirements for proppant transport can be grossly overestimated and a reference value of 100 to 150 cp can provide significant transport.

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Fluid Viscosity

Table 5.3 - Why Low Viscosity Fluids Work.

Sufficient Viscosity (µ = 1500cp) 1) X-L FLUID (HARRINGTON-HANNAH

β = 0.22; USE 0.5 10 (ppg)

2) HINDERED SETTLING: 1 3) µ 40 = µ 170 4)

 170 ---------  40 

µ i = 10 x µ f

0.4

; (n' = 0.6)

(e.g. 500

50)

0.3

1.8 OR 0.55

0.23

0.5 x 0.3 x 0.55 x 0.23 = 0.019 x 1500 = 28 cp (FINAL µ )

The next chapter, Chap. 6, gives more background for selecting specific fluids and additives to achieve the desired viscosities throughout a treatment.

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Design of Pseudo 3-D Hydraulic Fracturing Treatments

5.4 Treatment Pumping There are numerous parameters of some importance to hydraulic fracturing design and interpretation. The remainder of this chapter is devoted to the most critical of these. Fracture Radius The term radius implies one wing of the fracture or the fracture’s half length and is equivalent to the reservoir notation xf. However, xf is the apparent productive length and may be smaller than the design value of hydraulic fracture length as shown in Fig. 5.25. If the production is in bilinear flow, the productive length is increasing with time, or if the conductivity is very low, (i.e., FCD < 1), the productive length may be much larger than the apparent productive length, xf.

Fracture Length = ?

Pay

Propped Length

Productive Length

Hydraulic Length

Fig. 5.25 - What is Fracture Length?

Consequently, the design radius should be larger than the desired productive length, xf, because of the above discussion and for a safety margin. If the created fracture length is too small, a refrac may be required, and there is some question if refracing can effectively increase the propped length. Ideally, a calibration for each field should be made to determine the relationship between design radius and productive length, xf. Pump Rate The consideration for pump rate has many facets and some fiction. Although pump rate increases net pressure in the fracture, and hence, the potential for height growth, normally the significant effect on height believed by some in the industry is more fiction than fact. If height growth is critical, reducing rate toward the end of the treatment will accomplish the required necessary reduction in net pressure and will facilitate the surface handling of the higher sand concentrations. Some of the considerations for rate are discussed below. Hydraulic Fracturing Theory Manual

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Treatment Pumping

Fluid Volume: As shown on Fig. 5.26, the pump rate affects all three volume terms of the continuity equation, i.e., pump time, fluid loss time, and fracture volume (width). Increasing pump rate increases the volume of fluid stored in the fracture (increased p, w) and decreases the volume lost (less fluid loss time). As a result, pump rate affects fluid volume required for a given length. The examples indicate that the balancing point is for fluid efficiency of about 0.6-0.7. For treatments with higher efficiencies, increasing rate will store more volume than is saved in fluid loss, while for lower efficiencies the opposite occurs. Rate becomes most important for very low efficiency. As efficiency goes to zero, the volume required for a given length is inversely proportional to rate, i.e., doubling rate reduces the required volume by one-half. The increase in volume for high efficiency is generally not a consideration because the extra stored fluid will increase the fracture length after shut-in, i.e., free extension will occur until the tip screens out. Increased pump rate will significantly increase friction-loss pressures in the tubulars (and in the perforations if inadequate number and size) and result in a small, but potentially critical, increase in net fracture pressure, as shown in Fig. 5.27. The increase in friction pressures also can dramatically increase horsepower requirements if friction-loss is a significant portion of the total surface pressure. For cases where horsepower and pressure capacities of tubulars are an important consideration, these considerations for rate become important.

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Design of Pseudo 3-D Hydraulic Fracturing Treatments

Transport and Viscosity:

Pump Rate and Time VOL

IN

=

VOL

LOST

+ VOL FRAC → Qt =  

8/3 π

 H CL  p

t

+ WHL =

( µQL ) =

VOL ------- IN Q

1/4

∼ρ

  log VOL  FOR FIXED L LOST  log Q  = 0.82 × LOST 1, FRAC 2 = 1.11 × FRAC 1 FRAC

FLUID LOSS & VOLUME REQ’MENTS 1) Q

2

=

1.5

× Q 1 → LOST 2

CAN SHOW VOL 2) Q

2

=

2/3Q

LOST

1

2

-18% VOL

IN

> if

=

1.22

+11%

FRAC ------------------ = VOL

eff

IN

× LOST 1 ;

FRAC

2

> 62%

=

+22% 3 ) eff

→0

VOL

0.90

× FRAC 1

-10%

∼ 1/Q IN Fig. 5.26 - Effect of Rate on Volume.

Pump Rate and Time SURFACE AND NET FRAC PRESSURES SP - CLOSURE - HEAD + FRICTION + p 1.75 F∼Q ( TURBULENT )

2

=

1.5

× Q1 → F2 =

2.0

× F 1 ;HHP F = 2

+100% 2 )Q

2

=

1/4

HHPF ∼ Q2.75

HHP - SP x Q 1 )Q

∼ ( µQL )

2/3Q

1

→ F2 =

0.49

× F 1 ;HHP F =

-51%

2

3.0

× HHP F

+200% 0.33

× HHP F -67%

;p 1

;p 1

2

=

1.11

× p1

+11%

2

=

0.90

× p1

-10%

MAY BE CRITICAL TO HEIGHT CONFINEMENT

Fig. 5.27 - Effect of Rate on Pressures.

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Treatment Pumping

Increasing pump rate will increase proppant transport distance (per fall distance) by an amount approximately proportional to the pump rate increase (as shown by the examples in Fig. 5.28.) (Note that transport distance is independent of height.)

Pump Rate and Time PROPPANT TRANSPORT

V1

H V2 D

V

1 --DH = ---V

V

2

D --H

=

1

FLUID VELOCITY 3/4

Q Q Q - ∼ ------------------= -----∼ ---------1/4 1/4 HW Hµ H ( µQ )

or ; V

2

=

FALL RATE

∼ -µ1

3/4 3/4

µ ----------------∼Q H

1 )Q

2

=

1.5

(D indep. of H)

× Q1 → D2 =

1.35

× D 1 ( same µ ) ; µ 2 =

0.79

-21% µ

+35% D 2 )Q

2

=

2/3Q

1

→ D2 =

.74 D

1 -26% D

× µ 1 ( same D )

µ = 1.28µ , 2 +28%µ & 1.5 > µ ENDURANCE

Fig. 5.28 - Effect of Rate on Transport and Viscosity Requirements.

The examples also indicate that increasing pump rate can reduce the fluid viscosity requirements. These reduced requirements result from both the lower ultimate viscosity for proppant transport needed and from the smaller residence times which reduce the initial viscosities required to allow for time degradation. This can be very significant for large jobs in hot zones. However, high pump rates down “small tubulars” (i.e., high friction pressures) may cause significant fluid degradation for some fluid systems. These systems are nondelayed crosslinked systems with metallic bonding (e.g., Titinate). Guidelines for these systems which will not result in significant degradation are:

December 1995

Tubulars

Maximum Rate (bpm)

2-3/8

7

2-7/8

12

3-1/2

15

4-1/2

28

5-1/2

40

7

65

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Design of Pseudo 3-D Hydraulic Fracturing Treatments

For these degradable systems, pumping down the annulus can cause significant degradation at very low rates due to the effect of the tool joints. Degradation is not a consideration for fluids which rebuild their crosslink, i.e., borate crosslinker, or fluids which benefit from shear, i.e., foams or emulsions. High pump rates can actually improve the quality of foams and polyemulsion fluids. Summary for Pump Rate: Pump rate has far reaching effects on many aspects of a fracture treatment, and these different aspects (Fig. 5.29) should be weighed o arrive at the optimum rate for a given treatment. Pump Rate and Time Summary I. VOLUME REQUIREMENTS REDUCE VOLUME: a) EFF > 60 - 70%; DECREASE RATE b) EFF < 60 - 70%; INCREASE RATE c) EFF → 0; VOL ∼ 1/Q II. PROPPANT TRANSPORT INCREASING RATE WILL: a) BETTER TRANSPORT b) REDUCE µ REQUIREMENTS c) REDUCE TIME ENDURANCE FOR FLUID III. PRESSURES DECREASING RATE WILL: a) LESS PRESSURE FOR TUBULARS b) LESS HHP c) REDUCE NET FRAC PRESS.

Fig. 5.29 - Considerations for Rate.

Depth The depth to mid point of perforations is used in the wellbore hydraulics equation to estimate surface pressure. At the present time it is considered to be true vertical depth for hydrostatic calculations. Friction Pressure The pressure loss associated with the flow of fracturing fluid and proppant through tubulars. Generally the values to be entered are estimated for the fluid system in units of psi/100 ft.

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Treatment Pumping

The following table shows an example of data obtained from various fracturing service companies' literature, measured at 20 bpm. Once the type of frac fluid and tubular size has been determined, the base friction value from the service company for the required fluid system can be entered. Table 5.4 - Turbulent Friction Pressures at 20 bpm (psi/100 ft). Fluid Dowell YF-400

2-3/8 2-7/8 3-1/2 4-1/2 5-1/2 2-3/8:4-1/2

2-3/8:5-1/2

2-7/8:5-1/2

80

40

14

4.5

Halliburton Versagel 1500

120

55

27

9.0

4.0

47

13

25

Western Apollo 20-40

120

55

20

5.5

2.5

33

8

13

Polyemulsion

370

145

55

20.0

8.0

90

28

40

Water

460

165

60

15.0

5.5

100

20

35

K

= The constant that can range from about 1/4 to 1/3. Normally, K = 1/3 for sandstones

OB = Overburden pressure - generally 1 psi per foot of depth P

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= Reservoir pressure

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Design of Pseudo 3-D Hydraulic Fracturing Treatments

Apollo Gel 20 30 40 A

1000

B

C

D

E

500

F

GH I

J K

Friction Pressure - psi/1000 ft

L

M

N

100

50

10 1

5

10

50

100

Injection Rate - BPM H - 2 3/8 in x 5 1/2 in, 15.5 lb annulus I - 4 1/2 in, 9.5 lb casing J - 5 1/2 in, 15.5 lb casing K - 2 7/8 in, 7 in, 23 lb annulus L - 2 3/8 in x 7 in, 23 lb annulus M - 7 in, 23 lb casing N - 7 5/8 in, 29.7 lb casing

A - 1 1/4 in, 2.4 lb tubing B - 2 3/8 in, 4.7 lb tubing C - 2 7/8 in, 6.5 lb tubing D - 2 3/8 in, 4 1/2 in, 9.5 annulus E - 3 1/2 in, 9.3 lb tubing F - 2 7/8 in, 5 1/2 in, 15.5 lb annulus G - 4 in, 11 lb tubing

Fig. 5.30 - Example Friction Pressure Data for”Base Friction.”

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References

5.5 References 1. Warpinski, N. R., Schmidt, R. A., and Northrop, D. A.: “In-Situ Stresses: The Predominant Influence on Hydraulic Fracture Containment,” JPT (March 1982), 653-64. 2. Kry, R. and Gronseth, M.: “In-Situ Stresses and Hydraulic Fracturing in the Deep Basin,” paper 82-3321 presented at the 1982 Petroleum Soc. of CIM Annual Meeting, Calgary, Alta., June 6-9. 3. Hubbert, M. K. and Willis, D. G.: “Mechanics of Hydraulic Fracturing,” Trans., AIME (1957) 210, 153-66. 4. Harrington, L. J., Hannah, R. R., and Williams, D.: “Dynamic Experiments on Proppant Settling in Crosslinked Fracturing Fluids,” paper SPE 8342 presented at the 1979 SPE Annual Technical Conference and Exhibition, Las Vegas, Sept. 23-26.

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Design of Pseudo 3-D Hydraulic Fracturing Treatments

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Chapter

6

Fluid Selection and Scheduling

6.1 Fluid Selection Fluid Classification Service companies offer fracturing fluids which can be categorized as either water-base or hydrocarbon-base depending on the nature of their continuous phase. Fracturing fluids can be grouped into the following classes: Water-Base Fracturing Fluid Systems • Slick Water: Small amounts of polymer in water for turbulent friction pressure reduction • Uncrosslinked Polymer Solutions: Guar, HPG, CMHPG, CMHEC, HEC, xanthan, polyacrylamide, secondary gelling system • Crosslinked Polymer Solutions (Gels): Polymers crosslinked with titanium, zirconium, boron, aluminum, or antimony 1. batch mixed (an emulsion if hydrocarbon fluid-loss additive is used) 1. continuous mixed (1/2 vol% hydrocarbon emulsion up to 5 vol% if liquid fluid loss additive is used) 1. energized with up to 50% N2 or CO2 • Polymer Emulsion: Approximately 33% aqueous polymer solution as the external phase with 67% hydrocarbon internal phase • Aqueous Foams: N2, CO2, or 45%-CO2/25%-N2 in water, polymer solution, or gels with 65 - 85% gas internal phase

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Fluid Selection and Scheduling

Hydrocarbon-Base Fracturing Fluid Systems • Slick Hydrocarbon: Diesel, kerosene, or crude with small amounts of synthetic polymer for reducing turbulent friction pressures • Crosslinked Hydrocarbons: Diesel, kerosene, or crude crosslinked with phosphate acid ester and aluminum, or fatty acid and caustic 1. batch mixed 1. continuous mixed 1. energized with up to 50% N2 or CO2 • Hydrocarbon Foams: N2 or CO2 in diesel, kerosene, or crude oil with 65% - 85% gas internal phase • Gelled Methanol [with or without CO2 up to 75 vol% (single phase w/CO2)]: Methanol in water-base polymer solutions- up to 25 vol% with guar, 60 vol% with HPG, and 100 vol% with dimethylacrylamide or hydroxypropylcellulose (can also be crosslinked). Within any of the above classes of fracturing fluids, the engineer is confronted with a list of mysterious sounding fluid system names (e.g. Saturn II, Water Frac, Versagel-HT, YF550-HT, YF-GO III, Polyemulsion, etc.), and associated with each, an equally cryptic list of trade-name chemical components and additives. As an example, the components for Versagel-HT (referenced on page 6.7) include WG-11, Cl-18, K-34, and HYG-3 with possible additives of GEL-STA, SP Breaker, WAC-12L, CLA-STA, SEM-7, EnWaR-288, BE-3, ABF, etc. To select the “best” fluid system for a particular hydraulic fracturing treatment, the engineer must consider various criteria. The next section will discuss these criteria.

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July 1999

Fluid Selection Criteria

Fluid Selection Criteria Probably the first criteria that an engineer considers when selecting a fracturing fluid are of a subjective nature including regional history and tradition, personal experience, service company performance, and service company advice. In addition to these criteria, the engineer should consider specific factors concerning the formation to be fractured, the fracture desired, and the properties of the fracturing fluid. These criteria can be grouped into the following categories: • Safety and Environmental Compatibility • Compatibility with Formation, Formation Fluids, and Additives • Simple Preparation and Quality Control • Low Pumping Pressure • Appropriate Viscosity (for desired geometry and proppant transport) • Low Fluid Loss • Good Flow Back and Cleanup (for high fracture conductivity) • Economics The following sections will discuss each of these. Table 6.1 gives qualitative ratings for selection criteria for various types of fracturing fluids.

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6-3

Hydraulic Fracturing Theory Manual

Viscosity

6

Compatibility

Fluid System

Prop Pack KfW

Low Pump Pres.

PropTransport

6-4

Cost

Safety and Environ.

Prep. and QC

Stable

Life

Linear Gel HPG/Guar (<130 - 150°F)

4

5

3

3

3

5

5

5

Linear HEC Gel(<180°F)

5

5

3

3

1

4

5

4

Borate X-Link(<180°F)

4

3

3

3

4

4

5

4

Delay Borate X-Link(160 - 280°F)

4

5

3

3

4

4

4

3

Delay metallic X-Link(180 - 220°F)

5

2

3

3

4

4

4

3

3

5

3

3

3

4

4

4

3

4

2

4

4

3

3

4

4

4

3

1

4

4

?

5

5

5

5(*)

2

2

2

5

1

4

4

4

5

5

5

5(*)

2

2

2

Lease Crude

4

3

2

3

3

5

5

4

2

3

2

2

Gelled Oil

2

4

4

4

4

3

5

4

4

3

2

2

Polymer Emulsion

4

2

4

4

5

4

4

4

5(*)

3

2

3

Gelled Methanol

3

4

4

5

5

1

5

4

4

2

1

Breaking

Formation /Fluid

Reservoir Pressure

Fluid Loss

3

5

3

3

3

3

4

3

4

3

5

5

4

4

4

5

2

4

5

4

Delay Metalic X-Link(220 - 280°F)

3

4

5

Delay Metalic X-Link(280 - 350°F)

3

4

Nitrogen Foam(<5000 ft)

5

CO2 Foam(5000 - 1000 ft)

1 - BAD 5 - Excellent (*) - Good loss control for permeability < 1md (+/-)

Fluid Selection and Scheduling

Hydraulic Fracturing Theory Manual

Table 6.1 - Qualitative Fluid Selection (courtesy of NSI).

July 1999

Fluid Selection Criteria

Safety and Environmental Compatibility Safety is a primary consideration in the selection of fracturing fluids. Hydrocarbon-base fluids have the inherent risks associated with flammable or combustible materials. It is advisable to use one which has a flash point (the minimum temperature at which a liquid gives off a vapor sufficient to form an ignitable mixture with the air near the surface of the liquid or within the vessel used) higher than expected ambient temperatures. Flash points of some commonly used hydrocarbons are shown in Table 6.2. Table 6.2 - Flash Points of Some Commonly Used Hydrocarbons. Hydrocarbon

Flash Point

Gasoline (60 Octane)

- 45 ° F

Condensate

< 32 ° F

Toluene

40 ° F

FRAC OIL (GOODFARE)

45 ° F

Methanol

52 ° F

FRAC OIL (KAYBOB)

83 ° F

FRAC OIL (EDSON)

85 ° F

Diesel No. 1

100 ° F

Diesel No. 2

125 ° F

40 ° API Crude Oil

It is easy to see why diesel No. 2 is so popular. In Canada FRAC OIL and methanol are used frequently, perhaps partly because of colder weather which makes their use more safe. Special precautions are used when pumping flammable liquids such as brass hammers (to avoid sparks) when tightening surface tubing, tarpaulins to cover surface hoses to protect personnel from spraying hydrocarbons, spark arrestors, and the prohibition of smoking.1 Foamed fluids, which can be hydrocarbon or water-base, are even more dangerous because of the expansion energies of leaking foams. There are varying degrees of toxicity associated with fracturing fluid components such as methanol, FRAC-OIL, biocides, surfactants and crosslinkers. Breathing apparatus is required for blender operators and anyone exposed to methanol vapors which can do irreversible brain damage. Oxidizers, such as ammonium and sodium persulfate should not be allowed to contact fuel sources. Corrosive acidic and basic additives should be handled with care. Material Safety Data (MSD) sheets should be reviewed for all chemicals on location. The recent emphasis on environmental awareness has limited the use of some additive such as certain extremely toxic biocides and crosslinkers (e.g. chromium-base). Service companies are supJuly 1999

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6

Fluid Selection and Scheduling

posedly knowledgeable about environmentally acceptable frac fluid systems. Consult your Amoco environmental representative if in doubt. Compatibility with Formation, Formation Fluids, and Chemical Additives A primary consideration in the selection of a fracturing fluid system is its compatibility with the formation, the formation fluids, and the chemical additives specified for the particular fluid system. A fracturing fluid may damage a reservoir to various degrees. Ideally, core flow tests should be done to evaluate the sensitivity of a particular rock to the fracturing fluid. If a reservoir has swelling or migrating clays, the engineer should use adequate clay control additives when using water-base fluids or should use an oil-base system. Certain salts such as KCl or ammonium chloride are effective to some extent in stabilizing swelling clays such as illite and montmorillonite by replacing exchangeable cations in the clays which can cause expansion of the stacked clay platelets when exposed to fresh water. Modified polyamines can reduce clay swelling and clay migration by adsorbing on clay particles and “locking” them into place. Cationic polymeric clay stabilizers adsorb on to clay particles even more strongly but they have the potential of plugging pore throats (because of their relatively large size) and can change the wettability of the formation. Clay control additives, other than 1% KCl, are generally not recommended for tight formation gas plays for this reason. 1% KCl is adequate for clay control in fluids with pH as high as 10. For higher permeability formations (where more conductive fractures are required) core tests should be performed to assess the effectiveness of the prescribed clay stabilizers. Water in fracturing fluids can actually dissolve the cementing material in some formations causing the release of damaging fines and consolidation problems. Again, core flooding tests should be conducted to evaluate this possibility. The ionic nature of the components in a fracturing fluid system have the potential of changing the wettability of formations. Ionic surfactants have ionic water soluble ends and nonionic hydrocarbon or fluorocarbon tails which are oil soluble. Sandstone formations, which are usually water wet and negatively charged, will adsorb cationic surfactants and will thus become oil wet because of their oil-soluble tail. Limestone formations, which usually are water-wet and positively charged, will adsorb anionic surfactants and become oil wet. Since water-wet formations promote movement of oil through the rock, anionic surfactants should be used in sandstone formations, and cationic surfactants should be used in limestone formations. For heterogeneous formations, e.g. sandy limes, nonionic surfactants should be used. If surfactants do not improve fluid recovery they should not be used unless they are required for foam or emulsion stabilization. Another consideration is the introduction of anaerobic bacteria (i.e. sulfate reducing bacteria such as Desulfovibrio) into the formation which can produced hydrogen sulfide and can turn the well sour. This is particularly a concern in wells less than 170°F. The fracturing fluid water should be Hydraulic Fracturing Theory Manual

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Fluid Selection Criteria

treated with an environmentally acceptable biocide. Thus, even in continuous mix operations, the use of biocides should be considered. In very hot wells, the possibility of bacterial contamination in the cooler regions of the wellbore exists. When using water-base fluids, sometimes problems with water blocks occur. These can be mitigated by using fluorocarbon surfactants and/or methanol which have especially good surface tension lowering qualities. Water with reduced surface tension has lower capillary pressure and is more easily displaced from pore throats through the rock matrix. Fracturing fluid compatibility with the reservoir fluids is likewise important. Water-base fluids can form emulsions with crudes or induce scaling with insitu water, e.g. CO3-- in sodium or potassium carbonate buffers can form CaCO3 scale by reacting with CA++ in the formation water. Oil-base fluids can induce sludging with crudes such as asphaltene or paraffin precipitation. The fracturing fluid system should be mixed with the reservoir fluids prior to specifying the treatment to check for incompatibilities, preferably at reservoir temperature and pressure. Fluorocarbon surfactants should be used in dry gas wells where there is no danger of forming oil-water emulsions. API RP392 describes a procedure conducted at ambient pressure, that tests for emulsion and precipitation potential. The compatibility of the fracturing fluid with its additives should be checked at location by performing pilot tests before pumping. Sometimes incompatible additives can be brought on location such as certain surfactants and biocides which can interfere with crosslinking. Some surfactants, e.g. foams, may adsorb on silica surfaces, such as sand or silica flour and cause the foam to break. Methanol is incompatible with guar at concentrations higher than 20 wt%. Most enzyme breakers will not work when used at pH higher than 8.5 or at temperatures greater than 120°F. Methanol should not be used with breakers since it renders them useless unless very large concentrations are used. Resin-coated proppants can interact with fluid additives. Some resin coatings can adsorb breaker and crosslinker, and can lower fluid pH. Some encapsulated breaker are not compatible with resin coated sands if the oxidizer breaker is released before the resin cures. For hydrocarbonbase fluids, the effect of additives on the value of the recovered fluid after flow back should be considered. Simple Preparation and Quality Control A fracturing fluid composition should be kept as simple as possible since every component and additive adds to the burden of monitoring chemical quality, proper chemical addition, and mixing - not to mention adding to the total expense. However, referring to the Versagel-HT system mentioned on page 6.2, chemical additives are needed for a variety of good reasons. Viscosifiers, such as HPG (WG-11), are polymers for thickening water; buffers, such as K-34 (sodium bicarbonate) and HYG-3 (fumaric acid), are used to adjust the pH for hydration, crosslinking, and thermal stability; salt (KCl) or cationic polymers (e.g. CLA-STA) are used to prevent clay swelling and clay migration; a liquid hydrocarbon fluid loss agent (WAC-12L) or 3 - 5 vol% diesel are used to reduce July 1999

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water loss to the formation; chemicals, such as SP Breaker (sodium persulfate), are used to enhance polymer degradation; GEL-STA (sodium thiosulfate) is used to enhance polymer high-temperature stability; surfactants are used for better load recovery (EnWar-288), to aid in preventing oil-water emulsions in the reservoir (LOSURF-251 nonemulsifier), and for emulsifying hydrocarbon in water (SEM-7); biocides are used to prevent biodegradation of the fracturing gel and to prevent contamination of the well; etc. Service companies should be able to justify the use of every fluid component and additive which they specify. The fluid system should be easy to mix, with the polymer readily dispersed and hydrated. HPG was developed in part to give better dispersibility and hydrating properties than guar. In the late 1980’s, advances in fluid formulations, equipment control, and fluid property monitoring have made continuous mixed fluid systems more popular. Continuous mixed water-base and hydrocarbon-base gels and foams are attractive because of reduced costs resulting from reductions in onsite time and fluid waste. A sample of frac fluid should be mixed before the treatment using all onsite chemical additives to test for proper hydration, crosslinking, and additive incompatibilities. After noting the fluid’s temperature and pH, viscosities of uncrosslinked gels should be checked with the Model 35 Fann viscometer or equivalent. Qualitative checks on water-base gel crosslinking can be made using vortex closure tests (e.g. 100 ml sample in a 250 ml beaker stirred at 450 rpm) and visually observing the crosslink strength by pouring the gel from the cup. Today’s delayed crosslinked systems have to be heated somewhat to initiate crosslinking. Usually crosslinking begins between 90°F and 140°F. Hydrocarbon gel viscosities can be checked using the Fann 35 or equivalent noting that mixing intensity can effect extent and degree of crosslinking. Hydrocarbon gels are difficult to prepare and require close quality control.1 The gellant and activator must be pilot mixed on location with the particular hydrocarbon to determine the proper amounts of gellant and activator. Too little activator will yield no viscosity and too much will give gel degradation (activator is a base, e.g. sodium aluminate, which can also serve as a breaker). The phosphate ester gellant must be added to the hydrocarbon before the activator. If the activator and gellant are added together, a precipitant will result. When the ester is uniformly distributed, the activator is added. Sometimes, the fluid has to be circulated at the highest rate possible for 20 minutes to form the gel. Gelation can be stopped by contaminants in the tanks such as residual surfactants, treating chemicals, or water. Improved continuous mixed hydrocarbon gel systems are making preparation easier. Gel quality control of continuous-mix jobs is possible if the service company has reliable real-time pH and viscometer instrumentation on their preblenders. Onsite rheological testing of foamed systems is not possible. However, the foaming potential and halflife can be checked by putting the liquid with all its additives into a Waring blender about 1 inch above the impeller and mixing at maximum rate to entrain air. The time it takes for 1/2 the solvent to return to its original state (drain) is the halflife.1 Foams with foaming agents have Hydraulic Fracturing Theory Manual

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Fluid Selection Criteria

halflives of 3-4 minutes, stabilized foams have halflives of 20-30 minutes, and crosslinked foams have halflives over an hour. For every type of fracturing fluid, proper additive metering and carrier vessel cleanliness are essential aspects of quality control. In the 1990’s, chemical addition is automated so that complex systems, such as binary foams, can be successfully pumped. Quality control of fracturing materials will be discussed in more detail in Chap. 11 of this manual. Low Pumping Pressure Most fracturing fluids have the desirable property of being drag-reducing (giving lower friction pressure than the solvent alone) when pumped under turbulent conditions. Fig. 6.1 shows friction pressures in 3-1/2 inch tubing (3.00 inch ID) for various solvents and the effect of Halliburton friction reducers. Water-base friction reducers are high-molecular weight polymers, e.g. polyacrylamide, and oil-base friction reducers are hydrocarbon soluble polymers (e.g. certain synthetic cationic polymers such as polyisodecylmethacrylate). The friction pressures of water, diesel, and 40oAPI oil are of similar magnitude. When friction reducers are added, the friction pressures are lowered by a factor of two to four. Note that adding more friction reducer does not always give more friction pressure reduction (e.g., FR-30 at < 15 BPM at 2 and 8 lb). Also shown in Fig. 6.1 are friction pressures for 40 lb/1000 HPG solution and a gelled diesel fracturing fluid. These give friction pressure reductions similar to when using drag reducers. High molecular weight polymers have a critical concentration where the maximum in friction pressure reduction is achieved. Friction pressures for various types of fracturing fluids are shown in Fig. 6.2 compared with water for flow in 3-1/2 inch tubing (3.00 inch ID). Polyemulsion (i.e., polymer emulsion) gives the highest friction pressure, even greater than water. There is some variation in reported friction pressures by different service companies, the largest being for borate gels and foams. Today, special formulations of delayed borate crosslinked gels are available which significantly lower friction pressures. Friction pressure can cause a significant increase in wellhead pressure and horsepower requirement and is an important consideration in design. Water-base solutions and gels formulated with high-molecular weight polymers, e.g., guar, guar derivatives, cellulose derivatives, and polyacrylamide derivatives, are all drag reducing. For overpressured reservoirs (i.e. those with reservoir pressures greater than hydrostatic water pressure at that depth), either water-base fluids with hydrostatic gradients of 0.438 psi/ft for 2% KCl fluids or hydrocarbon-base fluids with gradients ranging from 0.343 psi/ft for methanol to 0.379 psi/ft for 30°API crude can be flowed back with natural pressure. For underpressured reservoirs, lower density hydrocarbon-base fluids, energized fluids, or foamed fluids can be used to assist flow back. Nitrogen foams at typical treatment pressures and temperatures can have gradients less than 0.2 psi/ft. In addition, foams, by their composition of > 65 vol% gas, only require about 1/3 as much liquid load return. CO2 foams can have gradients greater than

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Water Diesel (Western) 40 deg API Oil (Western) 2 lb FR-30 Slick Water (Halliburton) 8lb FR-30 Slick Water (Halliburton) 1 gal FR-7A Slick Diesel (Halliburton) 2 gal FR-7A Slick Diesel (Halliburton)

Down 3 1/2 in tubing (3 in ID) Fric1 Data

40 lb HPG soln. (WG-1d Gelled Diesel 8/3 (Halliburton)

Fig. 6.1 - Friction Pressures for Friction Reducers.

Water Polyemulsion w/40 lb WG-11 (Halliburton) 40 lb HPG-Borate (BJ Services) 40 lb HPG-Borate (D-S) 40 lb HPG-Titanium (BJ Services) 40 lb HPG-delayed TI (Halliburton) 40 lb HPG soln. (WG-11) Gelled Diesel 8/3 (Hallibruton) 70 Qual. D-S Stabil. Foam 70 Qual. -40 lb HPG Foam (Hallib. correl.)

Down 3 1/2 in. tubing (3 in. ID) Fric2 Data

Fig. 6.2 - Friction Pressures: Various Frac Fluids.

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Fluid Selection Criteria

0.2 psi/ft at typical treating pressures and temperatures. However, the solubility of CO2 in fluids is generally high compared to nitrogen (see Fig. 6.32), and can give added flow back assistance as it comes out of solution. When using less dense fluid, however, one must consider the higher surface treating pressures required since up to 0.25 psi/ft hydrostatic head pressure can be lost relative to a water-base fluid. Higher treating pressures can reduce the maximum allowable pump rates and/or increase pumping horsepower (cost). Appropriate Viscosity Fracturing fluids are formulated to give sufficient viscosity to create wide fractures to prevent “pinch outs” and to give sufficient width to create a conductive proppant pack. Widths sufficient to prevent pinch outs are approximately equal to 2.5 times the maximum proppant diameter (e.g. about 0.1 inch for 20-40 sand). Lower widths can conduct slurry if the fluid flow rate and viscosity are high enough. Fracture width is generally not a strong function of viscosity (e.g. width ∝ µ 1 / 4 for the PKN model with a Newtonian fluid). Excessive fluid viscosity can increase the fracturing pressure to the point where natural fractures open up giving additional fluid loss or the fracture can break through confining zones and grow height. These conditions can lead to “screen outs.” Fluid viscosities should be sufficient for adequate proppant transport. This is a rather ambiguous criteria, however, since proppant has been pumped with very low viscosity fluids including slick water. Even nitrogen gas has been used successfully to pump 20/40-mesh sand in the Devonian shale when pumped at high rates. Generally speaking, however, larger quantities of fracturing fluid can be pumped away at the higher viscosities. This may be a result of better proppant transport and/or higher fracture pressures creating wider and higher fractures. When using thin fluids to transport proppant, such as slick water or uncrosslinked polymer solutions at elevated temperatures, it is probable that a settled bank forms along the bottom of the fracture. Research by Biot and Medlin3 and Medlin, Sexton, and Zumwalt4 indicates that the formation of an equilibrium bank (a settled bank of constant height above which all proppant is transported) may not apply to field scale fractures although equilibrium banks have been observed in laboratory-scale slot flow devices. They believe that for thin fluids, proppant transport results primarily from viscous drag where the suspension has nearly uniform proppant concentration. As the suspension flows down the fracture, a relatively clear fluid layer forms at the top of the fracture as proppant from the suspension falls to the settled bank. At any horizontal position x , down the frac1 ture, the clear-fluid height above the slurry top is given by: x1

Z1 =

∫ ( vt /U ) dx ≅ (for constant settling rates) vt x1 /U

;

o

where U is the average fracture fluid velocity and vt is the terminal settling velocity of a particle. July 1999

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Medlin et al. set forth the criteria that when vt /U is less than 0.1, suspension transport occurs. When 0.1 0.9, proppant will not be picked up. Values of vt depend on the particle size and density and on the rheological nature of the fluid. For instance at room temperature under static conditions, 20/40-mesh sand can settle in water at a rate of 1.7 ft/sec; in a 40 lb/1,000 gal HPG solution at 0.005 ft/sec; in a borate gel at 0.0007 ft/sec; and in titanium gels at 0 ft/sec. Under fracturing conditions, effective settling velocities of flowing slurries are not well defined at this time. For viscosities greater than 50 cp at 170 1/s, we will assume that the proppant is flowing as a suspension with settling rate defined using some correlation relating the particle drag coefficient, CD, to the generalized particle Reynolds number, N'Rep. These dimensionless groups are defined as: CD

4 g dp ρp – ρ - --------------= --------------2 ρ 3v t

;

′ N Rep

n′ 2 – n′

n′ 2 – n′

d p vt ρ 0.695 d p v t ρ = ----------------------= ---------------------------------------n′ – 1 K′ 3 K′ (in Oil-Field Units)

where g is the acceleration of gravity, dp is the particle diameter (inches), ρp is2the particle density (lbm/gal), ρ is the fluid density (lbm/gal), K' is the consistency index (lbf-sn'/ft ), and vt is terminal particle velocity (ft/sec). N'Rep has been written using an effective particle shear rate such as:5 γ˙ p = 3 v t /d p = 36 v t /d p (in oil-field units). The actual shear rate on a particle surface settling in a power-law fluid can not be calculated explicitly, and thus γ˙ p has been defined differently by various authors. If the relation of CD to N'Rep is given, then vt can be solved. For instance, for laminar settling (Stokes Settling), d p vt ρ 24 C D = ------------ , Where N Rep = ----------------= Newtonian particle Reynolds no., N Rep µ and if this is assumed to apply to Non-Newtonian fluids, then the following relation is derived using the expression for N'Rep: n′ + 1

g d p (ρ p – ρ) v t = --------------------------------------n′ – 1 18 K′ (3)

1/n′

in oil-field units: n′ + 1

d p (ρ p – ρ) = --------------------------------n′ 9.626 ( 36 ) K′ Hydraulic Fracturing Theory Manual

1/n′

, for N ′ Rep < 2.0 .

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Fluid Selection Criteria

If the calculated vt, does not give a N'Rep less than 2., then the higher Reynolds number correlations can be used.5 For 2 < N'Rep < 500, CD = 18.5/N'Rep0.6; and for 500 < N'Rep < 200,000, CD = 0.44. Thus, this can involve a trial and error approach. Shah6 developed a method using empirically generated correlation constants which avoids trial and error. Note that the above are relationships for single particle settling. As proppant concentration increases, the particles may clump and give accelerated settling. Above a certain proppant concentration, however, i.e. 4 lb/gal liquid, the separation between proppant particles becomes small enough where hindered settling starts to reduce the settling velocity. Hindered settling can be treated by increasing the K' to reflect an increase in the effective viscosity of the continuous medium. Novotny7 performed static settling tests in simulated fractures using concentrated proppant slurries in polyacrylamide solution and found the hindered settling velocity, vh, to be related to proppant concentration as ppg v h = 1 – ---------------------ppg + ρ p

5.5

vt ,

where ppg is the lbm proppant/gal liquid, and ρp is the proppant density in lbm proppant/gal proppant (e.g. 22.1 for sand). Thus, for ppg = 8, and vt = 0.005 ft/sec, vh would be 0.0009 ft/sec. For a fracture flow velocity, U, of 0.56 ft/sec, (40 BPM down a 50 ft high by 0.25 inch wide two-wing fracture) this would give vh /U equal to 0.0016, which according to Medlin’s criteria would give suspension flow. The clear fluid layer at the fracture top after 1000 ft would only be 1.6 ft. This of course is a rough estimate of settling. The settling properties of flowing suspensions are not yet well established. The viscosity is affected by temperature and time and should be accounted for in fracturing design since this can affect fracture width and proppant transport as stated above. There are high and low temperature versions of water-base crosslinked and uncrosslinked gels, of hydrocarbon-base crosslinked gels, and foams. Polyemulsion is usually restricted to temperatures less than 250°F. High temperature stabilizers, such as sodium thiosulfate or methanol, are used above 200°F to retard oxidative hydrolysis of water-base polymers. At pH less than 6., the sodium thiosulfate stabilizer is not effective in some cases. There can be a large variation of high temperature behavior for similar gel systems. For example in Fig. 6.3, various service company high temperature gels are compared at 265°F. All the gels were tested by Amoco using the Amoco procedure for testing organometallic crosslinked gels. It is apparent that high temperature stability is a function of pH and type of polymer, buffer, and crosslinker. In some cases, service companies reported viscosities to be up to six times greater than those measured in Amoco’s lab (e.g. those for the Saturn I, Apollo I, Gemini III DXL, and Titan XL gels). The discrepancy is the result of many factors including conditioning method, viscometer bob, viscometer procedure, and calculation method. At this time we feel our procedure gives the

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most realistic data. As of 1991, the API is still a couple of years away from approving a recommended practice for testing organometallic crosslinked gels.

40 lb Versagel HT, HPG-Ti, pH 8.32 40 lb Ultra Frac RXL, Guar-Zr Lactate, pH 7.9 40 lb Saturn II, HPG-Zr, 2 gal XLD, pH 9.0 40 lb Pur-Gel III, CMHPG-ZrNH4C1, pH 6.56 40 lb Titan XL, CMHPG-Zr AL acetate, pH 5.2 40 lb Gemini III DXL, CMHPG-Zr-Al, pH 6.-5.6 40 lb MY-T-Gel HT, Guar-Ti, pH 8.7-7.9 40 lb Saturn I, Guar-Zr, pH 9.5-9.0 40 lb Appollo I, Guar-Ti, pH 7.3-5.8

All Delayed Crosslinked Except Gemini II DXL Gel. Conditioned at 0.8 hp/ft3 for 5 min to simulate 40 BPM down 5 1/2" casing All contain 10 lb stabilizer and no breaker.

t6399-08 DATA

Fig. 6.3 - Ti and Zr Continuous-Mix Gels at 265 ° F.

Low Fluid Loss Fracturing fluid systems offer varying degrees of fluid loss control. Water-base fluids with polymer give fluid loss control by building filter cake as the fluid leaks off in formations having permeability less than 5-10 md. In higher permeability formations, a particulate fluid loss additive (preferably a degradable product, 100 mesh sand, or silica flour) should be used to prevent the polymer from flowing into the pores. This is especially true for naturally fractured reservoirs where the natural fractures provide the bulk of the permeability. Particulate fluid loss additives should be used only in the pad to avoid damaging the fracture conductivity. The gel filter cake has permeability on the order of 1x10-6 md and thus can significantly lower fluid loss. Crosslinked gels give fluid loss control roughly the same as uncrosslinked gels at the same polymer loading. Fluids with internal phases can have additional fluid loss control when used in low permeability reservoirs ( < 1. md). This is true when the internal phase is a hydrocarbon, such as is the case when diesel fluid loss additive is used. Aromatic hydrocarbons with surfactants which yield microemulsions are also used but to a lesser extent. Generally speaking 3% diesel gives about 80% of the fluid loss reduction possible with hydrocarbon fluid loss additives. Accordingly, polyemulsion (i.e., polymer emulsion), with 67% hydrocarbon internal phase, gives the lowest values of wall building Hydraulic Fracturing Theory Manual

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Fluid Selection Criteria

fluid loss coefficient, Cw. Typical values for polyemulsion are < 0.0007 ft min< for permeability < 25 md using guar or < 0.0015 ft min for permeability < 2 md using HEC. The dispersed hydrocarbon acts to reduce the permeability to water in the polymer filter cake by relative permeability effects. At permeabilities greater than 5 - 10 md, the hydrocarbon can penetrate pore throats and the use of particulate fluid loss additive is also advisable. Cw generally decreases with increasing polymer loading, except when using hydrocarbon fluid loss additive, in which case it is almost independent of polymer concentration. Fig. 6.4 and Fig. 6.5 show Cw as a function of fluid-loss additive type and concentration, and polymer concentration.8

0.01

Legend Polymer-resin Mix Silica Flour

Cw (ft/min1/2)

Polymer-Silica-Clay Mix Diesel (1-10 md)

0.001

0.0004 0

10

20

30

40

50

Fluid Loss Additive Concentration (lb or gal/Mgal)

Fig. 6.4 - Wall-Building Coefficient vs. Fluid-Loss Additive Type and Concentration at 125 ° F.

Foams with gas internal phases can give fluid loss control comparable to gels with hydrocarbon when the liquid external phase of the foam is stabilized with polymer. Foam Cw’s are also dependent on formation permeability. Fig. 6.6 shows D-S fluid loss coefficient values vs permeability for some of their foams at 150°F. Oil-base gels exhibit similar fluid loss behavior in that the volume of fluid leaked off is proportional to the square root of time. It is not clear at this time what kind of mechanism is responsible for this, i.e. “polymer” build up, pore throat plugging, or gell invasion. Most oil-base fluids use some form of non-oil-soluble fluid loss additive. At reservoir permeabilities less than 0.1 md, the total fluid loss coefficient, CT, starts to become influenced by leakoff resistance in the reservoir rock. Reservoir-leakoff resistance is influenced by the fracturing fluid filtrate and the formation fluids, the porosity of the reservoir, the compressibility of the formation fluids and the leakoff-driving pressure (the fracturing pressure minus the reservoir pressure), as well as the reservoir permeability. Increasing the leakoff driving pressure from July 1999

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0.005

Legend 0 lb Silica Flour/Mgal

0.004

25 lb Silica Flour/Mgal 50 lb Silica Flour/Mgal 100 lb Silica Flour/Mgal

Cw (ft/min1/2)

0.003

0.002

0.001 0

30

40

50

60

70

80

90

100

Gelling Agent Concentration (lb/Mgal) Fig. 6.5 - Wall-building Coefficient vs. Gelling Agent Concentration for Linear Gels at 125 ° F Through 0.1- to 100-md Cores.

Fig. 6.6 - Fluid-Loss Coefficient for a 55-75 Quality Foam at 150 ° F.

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500 to 2000 psi can increase CT by a factor of 3. At a reservoir permeability less than 0.0001 md, the reservoir resistance dominates leakoff and the fluid leakoff properties, (Cw), no longer are important. Little added fluid-loss reduction is gained by using fluid loss additives. Most fracturing simulators consider reservoir effects when calculating fluid loss. For naturally fractured reservoirs, it is of primary importance not to allow polymer to leak off into and plug the natural fractures which can be the primary source of permeability. Fluid loss additives should be considered which prevent polymer from entering the natural fractures (particulate agents) and which reduce the leakoff of the filtrate (hydrocarbon fluid loss additive). In the case of naturally fractured reservoirs, Cw again will control fluid loss. Fig. 6.7 shows calculated CT as a function of reservoir permeability for an East Texas Cotton Valley well with leakoff driving pressure and diesel concentration as parameters for cases with and without natural fractures.9 In this figure, particulate fluid loss additive is assumed necessary to seal natural fractures so that a filter cake can form. Experimental tests have shown silica flour to be necessary to stop leakoff into smaller natural fractures (i.e., 10 to 20 microns).8

Legend 5000 psi, w/o diesel 5000 psi, 3% diesel 2000 psi, w/o diesel 2000 psi, 3% diesel 1000 psi, w/o diesel 1000 psi, 3% diesel 500 psi, w/o diesel 500 psi, 3% diesel CW w/o diesel CW w/ 3% diesel

With Natural Fractures: 500 - 5000 psi (No diesel)

psi With Natural Fractures: 500 - 5000 psi (3% diesel)

psi

Fig. 6.7 - Calculated Total Fluid Loss Coefficient vs. Permeability ETCV at 275 ° F and 5000 psi Reservoir Pressure. Leakoff Driving Pressure as a Parameter; With and W/O 3% Diesel

The spurt loss of a fluid, which can be defined as the fluid loss/area before the formation of a filter cake, can be significant in naturally fractured reservoirs as well as reservoirs with permeabilities greater than 1. md. Spurt values increase strongly with reservoir permeability and leakoff-driving pressure and are affected by factors which affect fluid flow in reservoirs such as filtrate viscosities (and thus temperature) and compressibility effects. Spurt values in excess of 1 gal/100 ft2 can be July 1999

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expected for reservoirs with permeability greater than 10 md. Lab measurements show spurt values are affected by fluid loss additive and polymer type, as well as permeability. Fig. 6.8 - Fig. 6.11 show the effects of fluid loss additive type and concentration, and polymer concentration on spurt vs. permeability values.8

Fig. 6.8 - Spurt Loss vs. Permeability for Linear HPG Gels in Water at 125 ° F.

The preceding discussion dealt with fluid loss behavior of static fluids. Fluid loss can also be affected by fluid flow in the fracture. For uncrosslinked polymer solutions, Cw is independent of shear rate up to 300 1/s, but Cw for crosslinked gels can increase with shear rate. Leakoff driving pressure can affect the functional form of fluid loss. Fluid loss can increase from being proportional to t to proportional to t as the leakoff-driving pressure decreases from 1000 to 0 psi. Laboratory tests have shown that flowing proppant does not change the dynamically measured Cw for proppant concentrations up to 5 ppg.10 Dynamic fluid loss is a new technical concern which is not considered in all fracturing simulators. Good Flow Back and Cleanup The objective of hydraulic fracturing is to create a conductive fracture which requires a permeable proppant pack and permeable fracture face. To achieve this, the fracturing fluid must be removed from the formation. As discussed above, it is essential to prevent polymer from invading the rock matrix and natural fractures. Good fluid loss control can accomplish this. However, the leaked off filtrate must be removed. Producing the well will help remove load water but in some cases emulHydraulic Fracturing Theory Manual

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Fluid Selection Criteria

Fig. 6.9 - Spurt Loss vs. Permeability and Additive for 40 lbm Complexed HPG Fluids at 125 ° F.

Fig. 6.10 - Spurt Loss vs. Permeability and Gel Concentration For Complexed HPG Fluids at 125 ° F.

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Fig. 6.11 - Spurt Loss vs. Permeability and Additive for Gelled Diesel at 125 ° F.

sions, scales, or water blocks will form. Methods described in the “Compatibility With Formation, Formation Fluids, and Chemical Additives” section starting on page 6.6 can be used to reduce the severity of these problems when using water-base fluids. If these are not effective, hydrocarbon base fluids or foams should be considered. Gel breakers oxidize the polymer backbone enabling the polymer to be flowed back out of the fracture. Ammonium or sodium persulfate are commonly used at high temperatures > 150°F or lower temperatures with an activator. Enzyme breakers such as hemicellulose are used at temperatures less than 120°F and pH < 8.5. Western Company claims to have an enzyme breaker which is effective to pH 10. In 1991, service companies began offering encapsulated or crushable breakers designed to release the oxidizer after pumping has stopped. Cellulose polymers or synthetic polymers (e.g. polyacrylamide) leave negligible residue upon breaking! However, these broken polymers can damage the rock matrix, apparently by adsorbing on pore surfaces. Water-base fluids using guar or guar-derivatives, leave insoluble residue after breaking, that can occupy from 1 - 3 vol% of the original fluid volume. This residue has been shown to damage fracture conductivity. If the residue is dried, it loses more than 98% of its original volume and, therefore, would no longer be a problem. However, most reservoirs are wet to some degree, and this residue, which is not mobile,11 can permanently damage proppant packs. In addition, the effective polymer concentration is increased considerably by leakoff after shutin during

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Fluid Selection Criteria

fracture closing. For instance, the pounds of polymer per gallon of proppant pack pore space, (Cp)eff is: ρ p ( 1-φ p )C p ( C p ) eff = ------------------------------- , Cs φ p where ρp is the proppant density (lbm/gal proppant), φ p is the proppant pack porosity, Cp is the polymer concentration before closure (at shutin) in lbm/gal, and Cs is the pounds of proppant/gal of liquid in the fracture at shutin. For example, if at shutin Cs is 8 lbm proppant/gal liquid and Cp is 0.04 lbm HPG/ gal liquid, for sand proppant with a density of 22.1 lbm/gal proppant and a proppant pack porosity of 0.35, the effective polymer concentration after fracture closure would be 0.205 lbm HPG/gal liquid. It would concentrate over 5 times. In addition to this, there is polymer already deposited on the fracture wall before shutin which will contribute to the residue. Using a model based on the Kozeny equation12 for permeability which accounts for polymer residue from leak off during and after shutin, Fig. 6.12 and Fig. 6.13 can be derived which show the normalized impaired proppant pack permeability, k'/k, as a function of CT and Vrf for a position in the fracture with a width of 1/4 inch, and a fracture age of 60 minutes. Vrf is defined as gal of residue/gal of fluid. Shown in these figures are two hypothetical extremes. The first is where all the residue concentrates at the fracture wall, (effectively reduces the fracture width--the most optimistic case) and the second is where the residue is uniformly distributed--the most pessimistic case. Studies13 have shown that residue tends to concentrate near the wall, so, the optimistic values are probably more realistic. However, extreme permeability impairment can occur when Cs is less than 5 ppg at typical fracture widths and leakoff rates, as shown in Fig. 6.12 and Fig. 6.13. The preceding impairment discussion assumes that all the polymer breaks. In reality, using conventional breaker loadings, this is probably not the case since solid breaker (e.g. sodium persulfate) does not concentrate with the residue (it leaks off) and enzyme breakers are frequently destroyed by temperature, high pH, and chemical additives. This realization has spawned the new generations of crushable and controlled release breakers which can be used at much higher concentrations than before and which will accumulate with the polymer. Thus, it is now possible to achieve almost complete polymer breaks. These new types of breakers are even being used at temperatures above 275°F to maximize breaking, especially of high pH fluids. They also may be useful in breaking methanol gels which are very stable and require high breaker loadings. Some kinds of encapsulated breakers are incompatible with resin coated sands and can release varying amounts of breaker prematurely, e.g., 5% during a 3 hr treatment.14 Encapsulated breakers are used very aggressively in the pad stage (e.g., 7 lb/1,000 gal)14 with the concentration reduced somewhat during later proppant stages. Sometimes conventional breaker is added at the final stages of the treatment to enhance near wellbore cleanup. The benefit of adding large amounts (greater than 2 lb/1,000 gal) of conventional breaker is suspect. Tests have shown July 1999

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Fig. 6.12 - Gel Residue Flow Impairment - Fluid Loss During & After Pumping; Residue Uniformly Distributed or All on Wall.

Fig. 6.13 - Gel Residue Flow Impairment - Fluid Loss During & After Pumping; Residue Uniformly Distributed or All on Wall.

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that a frac fluid with 2 lb/1,000 gal breaker can be broken prematurely before it gets down to the fracture. Fewer problems with fracture conductivity impairment result when using hydrocarbon-base fluids or foams, as long as they break properly. Hydrocarbon gels are broken with base additive. At lower temperatures, e.g. < 120°F, breaking hydrocarbon gels can be a problem. Foams break when the liquid drains (half life), when the surfactant adsorbs onto the rock, and/or when the polymer in the liquid phase breaks. Flow back with foams has the added advantage of the nitrogen or CO2 expansion. Polymer emulsions break when the polymer in the continuous phase breaks and/or the surfactant adsorbs onto the rock. Economics After narrowing the list of possible fracturing fluid systems, the engineer should compare their relative costs. The costs of the base fluid and additives should be tallied along with disposal costs. For hydrocarbon-base fluids and polymer emulsion, the value of recovered hydrocarbon should be subtracted. In the past, hydrocarbon fluid and foam treatments were considerably more expensive because of the added safety, equipment, and implementation costs. However, presently their costs are becoming more comparable to water-base systems. Pumping cost is also a function of fluid type through the effect on friction pressure and hydrostatic gradient. See Table 6.3 for typical fracturing chemical and hydraulic horsepower prices (ca. 1992). In addition to the cost of materials and pumping, one should consider the net present value of post-frac production. This is a function of the fracture geometry and conductivity which are both affected by the fluid system through the fluid rheology, proppant transport, leakoff, and gel damage. Making this evaluation is best done using an integrated design package including a fracturing simulator, production simulator, and economic optimization program. See Chap. 9 of this manual for information on economic optimization.

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Description of Fracturing-Fluid Types In the preceding section, various types of fracturing fluids were discussed with regards to fluid system selection criteria. In this next section, types of fracturing fluids will be described in more detail and some flow-behavior data will be included. Water-Base Polymer Solutions Water-base polymer solutions are prepared primarily from naturally occurring water-soluble polymers or their chemical derivatives, although there is limited use of the more expensive synthetic products. The term “gelling agent” for water is synonymous with the term “water soluble polymer;” however, only the latter properly describes the material. The family of “natural” water soluble polymers consists of vegetable products, such as cellulose (although it is not water soluble, many of its derivations are), starch, alginates and natural gums. Also included in this list of natural gelling agents are animal products such as gelatin, glue and casein. Synthetic products fall into two major categories: modified natural products and completely synthetic products. The modified natural products are starch, natural gum or cellulose molecules which are modified with various chemical side chain substitutions. Some completely synthetic products are polyalcohols, polyacids, polyethers, and polyamides, made from a variety of synthetic monomers. Natural and synthetic water soluble polymers are listed in Table 6.4. The water soluble polymers most commonly used in fracturing fluids include guar gum and two of its derivations, hydroxypropyl guar (HPG) and carboxymethyl hydroxypropyl guar (CMHPG) whose chemical formuli are shown in Fig. 6.14 and Fig. 6.15. Other types of water soluble polymers used for fracturing fluids include cellulose derivatives, the most common of which are hydroxyethyl cellulose (HEC) and carboxymethyl cellulose (CMHEC). HEC and CMHEC leave no residue when broken, but are more expensive than the guar-based polymers. HEC cannot be crosslinked, but CMHEC can. Polyacrylamides are often used as friction reducers although recently some companies have started using various forms of crosslinked polyacrylamide. Although the large family of water soluble polymers has been reduced to a relatively few that are commercially important, the interaction between these various polymers, the ability to crosslink them and the possibilities of adding other materials to alter the physical properties make the choice of fracturing fluid difficult at times. Table 6.5 lists the primary types of water-soluble polymers used in fracturing today. Most service companies have the guar-based polymers available as “polymer concentrates” for continuous mix application. The rheology of uncrosslinked polymer solutions is easily measured. Resulting viscosities decrease with shear rate and show power law behavior at shear rate greater than 10 1/s. Fig. 6.16 shows HPG solution viscosity behavior as a function of shear rate at different temperature. Hydraulic Fracturing Theory Manual

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Fig. 6.17 and Fig. 6.18 show power law parameters for Halliburton’s HPG (WG-11) solutions at various concentrations as a function of temperature. Fast-Crosslinking Water-Base Gels Water-base fracturing fluids were originally crosslinked using fast crosslinking chemical formulations of organo titanates and zirconates, boron, aluminum, and antimony. Of these, the titanates and zirconates are not often used anymore without some kind of crosslinking delayer since high flow energy conditions down the tubular goods irreversibly degrade covalent Ti and Zr crosslinks,15 as shown in Fig. 6.19. Boron, aluminum, and antimony form relatively weak hydrogen bonds that can reform if broken by shear, and their gels can regain viscosity in the fracture. Fig. 6.20 shows Halliburton data for their borate crosslinked Boragel at 225 ° F. Guar, HPG, and CMHPG are the most commonly crosslinked fracturing polymers. CMHPG can be crosslinked by aluminum and/or organic-zirconates because of its dual crosslinked functionality (see Fig. 6.21). Titanate and zirconate crosslinkers are used at temperatures above 180 ° F because of their high temperature stability. Refer to Table 6.6 for pH and temperature ranges for crosslinkers. Notably, the use of boric acid and borax is limited to temperatures less than 225 ° F. Slowly solubilizing naturally occurring borate ores, such as Colemanite or Ulexite can be used at higher concentrations, avoiding gel overcrosslinking at the surface but providing more boron at downhole temperatures giving adequate viscosities to 275 ° F. Recently, B.J. Services developed an organo-complexed borate crosslinker (OCB) which they claim is effective to 300 ° F.16 Specialty fracturing fluids include residue-free crosslinked cellulosic derivatives, such as CMHEC. These residue-free crosslinked fracturing systems are useful in water injection well stimulations, tertiary recovery projects, and conventional treatments where residue free fluids are needed. In the mid 1980s, service companies introduced the use of polymer (gel) concentrates which could be continuously mixed during the treatment, rather than batch mixed the day before. This provides both the service company and operating company with cost and time savings. However, close monitoring of fluid streams and quality must be maintained during pumping. Typically, a polymer concentrate is prepared by mixing the polymer (e.g. guar, HPG, or CMHPG) in diesel at concentrations of up to 5 lbm/gal diesel. Suspension stabilizers are used to keep the polymer dispersed. When added to the mix water, the polymer in the gel concentrate hydrates rapidly and crosslinks down the wellbore or in the fracture. This produces a gel with hydrocarbon (e.g. diesel) as a dispersed phase usually at a concentration near 0.5 vol%. Delayed Crosslinked Fluids In the mid 1980s, “delayed crosslinked” fracturing fluids became very popular. This type of fluid system has evolved due to evidence of significant viscosity degradation at high shear levels (as shown in Fig. 6.19) with conventional titanate and zirconate crosslinked fracturing fluids. The July 1999

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basic idea behind delayed crosslinked frac fluids is to retard the crosslinking reaction until the fluids exit the very high shear regime occurring within the treating string, allowing crosslinking to occur under relatively low shear conditions within the fracture. Crosslinking under this much less severe shear regime results in a much higher in-situ viscosity with lower polymer concentrations. There is some confusion as to whether delayed crosslinkers are time or temperature activated. Crosslinking is a chemical reaction; therefore, chemical reaction kinetics apply. This infers that the crosslinking rate (change in viscosity or molecular weight with time) is a function of concentration of reactants, and temperature, as well as some sort of an effective activation energy. The ideal delayed crosslinked fluid would undergo minimal crosslinking within the treating string but quickly become crosslinked as soon as it left the perforations and entered the formation. This is not likely to occur, unless there was a rapid and significant temperature change at the fracture entrance (physically improbable due to heat transfer and subsequent temperature equilibration). Practically, a sort of balancing act may be required. It is desirable to maximize in-situ fluid viscosity as near the wellbore as possible to maintain adequate proppant transport in order to minimize excessive proppant banking that can cover the lower perforations, thereby increasing the potential for a near-wellbore screenout. This objective is weighed against the original objective of delayed crosslinked frac fluids--increased fracture viscosity by not crosslinking within the treating string. The practical solution may come by allowing a certain degree of “sacrificial” crosslinking to occur within the treating string such that the reaction is proceeding as the fluid enters the fracture, enhancing proppant transport early near the wellbore, and accepting loss of some “long term viscosity” potential. In order to do this, variables such as treating string residence time and specific flow energy, base fluid temperature, gel pH, polymer concentration, and heat-up rate within the fracture need to be known or estimated. Service companies also have developed dual-crosslinker systems (e.g. boron-delayed Ti or aluminum-delayed Zr) which provide viscosity at the wellbore as the boron and aluminum crosslinks reheal. Later in the fracture, as the gel heats up, the Ti and Zr crosslink under low shear and give good viscosity at high temperature. Generally, full delay of crosslinking is desired throughout the pad volume with progressively less delay as proppant is added and the fracture is cooled down. High temperature delayed crosslinked frac fluids are not designed to be used below 200 ° F. They may not break completely at lower temperatures or their crosslinkers may not react rapidly enough with cooled formations to provide adequate near-wellbore proppant transport. Fig. 6.22 shows Halliburton’s n' and K' data for their delayed crosslinked Versagel HT at 250 ° F. Fig. 6.3 shows the viscosity behavior at 265 ° F of Versagel HT compared to other service company organometallic delayed-crosslinked gels formulated with 40 lbm/1,000 gal of various polymers, as determined by Amoco.

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Delayed crosslinked borate gel systems are also available. Delayed borate gel systems were developed to reduce the relatively high friction pressures of borate crosslinked gels (e.g., the BJ borate gel in Fig. 6.2) and to provide high viscosities to 275 ° F. Crosslinking can be delayed by the use of delayed pH-control additives or by using slowly solubilizing borate ores. Polymer Emulsion Fluid The polymer emulsion fluid is a very efficient (i.e., low fluid loss) and relative clean fluid capable of achieving deep fracture penetrations. The fluid is normally prepared by emulsifying 2/3 hydrocarbon as the internal phase in 1/3 aqueous polymer solution. Emulsifier concentration is normally 2-8 gals/1000 gals of total fluid. The upper temperature limit is usually set at 260 ° F (based on field experience). Sand carrying capability is a function of viscosity and pump rate. Polymer emulsion is an ideal pad fluid--both low viscosity and fluid loss. The main disadvantages are safety and very high friction-pressure which can limit treating rates (see Fig. 6.2). As for foams discussed below, the viscosity is developed by a high volume fraction of internal phase (i.e., hydrocarbon). This is analogous to the increase in slurry viscosity when high proppant concentrations (internal phase) are added. The effect of internal diesel oil phase is shown in Fig. 6.23. When mixing proppant into polymer emulsion, the proppant effectively adds to the internal-phase volume fraction with a subsequent viscosity increase and, if in turbulent flow, an increase in friction pressure. The latter is responsible for “friction-outs” where pumping must be stopped because of excessively high well-head treating pressures.17 To avoid this, polymer emulsions should be pumped using the “constant internal phase” philosophy where the emulsion quality is reduced as proppant is added to maintain a nearly constant viscosity. Table 6.7 shows how the emulsion quality is varied as proppant concentration is increased to maintain constant internal phase volume fraction and constant viscosity.17 There is little difference in the two approaches which implies that maintaining constant internal phase is a convenient means of maintaining viscosity. Too much proppant can cause the emulsion to break, e.g. when the total internal phase approaches 0.85. Fig. 6.24 shows the shear thinning behavior of polymer emulsion as a function of temperature for a 0.67 quality fluid17 and Fig. 6.25 shows the effect of increasing the polymer concentration in the water phase.18 Fig. 6.26 shows the effect of temperature and quality on viscosity at 511 1/s for Western Co. diesel oil /0.57 wt% guar emulsions. Polymer emulsion viscosity is also dependent on mixing energy, where viscosity increases with increasing energy input. Fig. 6.27 shows the effect of emulsion droplet size on emulsion viscosity. Viscosity doubles as droplet-size decreases by 50%. Thus, field mixing method can effect viscosity significantly.17 Foamed Frac Fluids Foamed Fracturing Fluids consist of 55-85% by volume of gas dispersed in a suitable water-base or hydrocarbon-base liquid. Advantages of foams include: less liquid introduced into the formaJuly 1999

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tion, quicker fluid recovery due to gas expansion, less formation damage from invasion of foreign liquids or additives, and good proppant transport due to yield stresses retarding proppant settling. A typical composition of a foamed fracturing fluid is 70%, by total foam volume, of gaseous nitrogen, carbon dioxide, or 50%/20% CO2 /N2 (a binary foam) as microscopic bubbles in water containing 1-6 gallons of a surface tension reducing surfactant (foamer), 40 pounds of HPG per 1000 gallons of liquid, and a breaker, if appropriate. The viscosity of [foam increases exponentially above approximately 55 quality (percent dispersed gas volume to total foam volume) until an unstable condition is attained around 95 quality. Not only are rheological properties of foams very dependent upon foam quality, but they also depend upon the viscosity of the constituent fluids, bubble size, and size distribution (foam texture). The smaller the bubble and the larger the fraction of these small bubbles, i.e., the finer the texture, the higher the viscosity and stability of the foam at a given quality. Fig. 6.28 and Fig. 6.29 show n', K', and viscosity data for nitrogen foams as a function of temperature and/or shear rate with quality and HPG concentration as parameters.15 Fig. 6.30 shows the effect of shearing time on bubble size diameters.15 Fig. 6.2 shows some reported friction pressure data for foams and Fig. 6.31 gives the friction pressure of Dowell Schlumberger’s stabilized foam in 2 7/8 inch tubing. Texture depends upon the conditions under which the foam was generated. High shear conditions, such that intimate liquid-gas contact can occur, enhances the generation of fine foam texture. Increasing the viscosity of the aqueous phase via polymers also increases foam viscosity and stability. This is thought to occur by retarding the rate at which bubbles coalesce, as well as increasing the resistance to bubbles slipping past one another. The foam composition, amount of energy input during the generation of the foam, as well as foam quality, may have a dramatic effect upon the resultant rheological properties. Typically, without polymer, foams follow a Bingham plastic rheological model. With the addition of polymer, powerlaw properties are introduced. Increasingly finer foam texture and higher polymer concentrations result in increased non-Newtonian flow behavior. (See Chap. 5 of this manual for a discussion of rheological models.) There are questions to be answered about the feasibility of using foams for long-term, high temperature, fracturing applications. There are limited data to verify that under typically low fracture shear rates and for extended periods of time at high temperatures, foams retain sufficient viscosity to ensure continued leakoff control, and sufficient proppant transport capabilities to make them truly competitive with conventional fracturing fluids. This is particularly a concern after pumping has stopped and flow near the wellbore almost ceases. It may be advisable to crosslink the last stage of a foam job to give better wellbore stability. Disadvantages of foam are higher treating pressures (for nitrogen foams) due to reduced head, and low proppant concentrations because of the low fraction of water. This can be overcome by reducing the quality as higher sand concentra-

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tions are required. As in the case of polymer emulsions, constant internal phase during proppant addition maintains the foam viscosity approximately constant.19 Western Company has recently developed the use of binary foam composed of 50% CO2/20% N2 which they claim gives better well cleanup than pure CO2 foams. Fig. 6.32 shows the solubility of CO2 and N2 in water,20 andFig. 6.33 shows the viscosity of a 60 lbm CO2 foam vs. a 50 lbm binary foam.20 Foams are difficult to characterize because of their sensitivity to preparation techniques and test conditions. There are no long-term foam data available where the foam was not circulated through a pump (and perhaps restabilized). STIM-LAB testing has also indicated that foam stability is sensitive to silica flour. Apparently, surfactant may adsorb onto the silica surface. The same may also be true to some extent when using sand proppant. Gelled Hydrocarbons Gelled hydrocarbons were the first fluids used in hydraulic fracturing. In 1947, Stanolind Oil pumped four stages of gelled gasoline followed by a gasoline flush down a well in the Hugoton Field. Aqueous frac fluids were avoided until 1957, when it was found that clay control additives, such as KCl, were effective in water sensitive formations. The earliest gelled hydrocarbons were napalm-type fluids of aluminum octoate, and later in the 1950s, fatty-acid soaps composed of caustic and tall oil fatty acids were successfully used.21 These gels usually provided adequate viscosity to 150 ° F. In 1970, high-temperature gelled-hydrocarbon systems composed of aluminum crosslinked orthophosphate esters were introduced, eventually leading to systems that are thermally stable to 350 ° F. The reaction of the ester and base (e.g., sodium aluminate) forms an association complex throughout the hydrocarbon which increases its viscosity (see Fig. 6.34). The resulting “gel” is shear thinning (n' typically lower than 0.25) and is capable of rehealing after seeing high shear conditions. In fact, in preparing these gels, high shear conditions are required to form the association complex. Hydrocarbons such as kerosene, diesel, and FRAC-OILTM are often used to prepare these gels. If the produced crude has high enough gravity, e.g., > 35 ° (0.85 g/cm3), it can also be gelled.21 Use of the produced crude is advantageous since it can reduce fluid incompatibility problems. The primary advantages of gelled hydrocarbons are low damage to water sensitive formations and low damage to proppant packs if the gel breaks properly. The disadvantages include the fire hazards associated with pumping hydrocarbons, higher pumping pressures resulting from sometimes higher friction pressures and lower specific gravity (less head), more fluid loss, sensitivities to polar contaminates such as water, difficult quality control and mixing, and higher initial cost. The viscosity of hydrocarbon gels appears less sensitive to temperature than water-base gels. This is true when measured at higher shear rates. However, the low-shear (< 100 sec-1) viscosity may be reduced significantly as temperature increases, and low-shear viscosities control proppant transJuly 1999

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port. Unlike water base fluids, the viscosity of hydrocarbon gels increases with pressure (e.g., 6%/1000 psi) giving an additional viscosity edge over published data which are generally obtained at pressures less than 1000 psi. These trends are seen in Fig. 6.35. Table 6.8 shows the results of a comparative evaluation of Halliburton’s continuous mix MY-T-OIL IV and batch mixed MY-T-OIL II using FRAC-OIL 200 and crude. Viscosities at 158 ° F (70 ° C) are a function of gellant, activator, and breaker concentrations. Table 6.9 gives data for Western Company’s MAXI-0-74 gel. Gelled Methanol In 1974, aqueous polymer solutions with up to 25% methanol in guar solutions and up to 60% in HPG solutions started being used in water-sensitive formations. The maximum amount of methanol is limited by precipitation of the polymer. Some polymers, such as hydroxypropylcellulose can viscosify 100% methanol. In 1987 crosslinked forms of methanol became available, e.g. through BJ Services. These methanol gels can be used with CO2, which is generally soluble in methanol at all concentrations, forming a single phase. Methanol gels are suited for water sensitive formations because of lower water concentration. Methanol reduces surface tension which aids load recovery and the removal of water blocks. These gels also have low fluid loss, low friction pressure and, when used with CO2, give energized flowback. Disadvantages include high cost, high flammability, toxic vapors, and large amounts of breaker needed to break the polymer (methanol is a high temperature stabilizer). In water-sensitive formations, gelled oils or diesel are generally preferred over gelled methanol.20 Rheological Testing Of Fracturing Fluids A Fann Model 50C rotational (Couette) viscometer is generally used to test the rheological properties of fracturing fluids. The Fann Model 50C can test fluids at pressures up to 1000 psi and to a temperature of 400 ° F. Rotation of the “cup” imparts shear on the fluid and the resulting stress is measured as the torque transmitted to the bob. The apparent viscosity is simply the ratio of the shear stress and the associated shear rate. The addition of polymer to water results in a nonlinear relationship between the shear rate and shear stress, i.e., converts a Newtonian fluid into a non-Newtonian fluid. These non-Newtonian fluids are usually described by “power-law” or pseudo-plastic type rheological models, and use n' and K' parameters to mathematically describe the relationship between shear stress and shear rate. (Refer to Chap. 5 of this manual for a discussion of these models.) One of the major problems in testing crosslinked fracturing fluids results from an effect occurring under shear conditions known as “normal forces,” [which tends to force fluid samples up the stationary bob shaft resulting in measuring inaccuracies. It is possible to test organometallic crosslinked gels (i.e., titanium and zirconium gels) because they eventually “fragment” into dispersions which stay in the test-gap. Borate gels, however, only partially fill the test gap and resultant data are suspect. Tubular data are preferable for borate gels and foams. Because Hydraulic Fracturing Theory Manual

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crosslinked fracturing-fluids rheology is affected by preparation technique, shear conditions, instrument geometry, temperature, and time; meaningful, or even reproducible results are difficult to obtain. To further complicate matters, there is no standardized laboratory test for measuring fracturing fluid viscosity. This implies that some of the data currently in the literature and used by service and production company personnel are not directly comparable, let alone physically representative of actual conditions of application. Currently, the API Committee on Well Completion Fluids has a subcommittee investigating the possibility of developing a standardized testing technique for crosslinked frac fluids. Such an API recommended procedure is not expected before 1993 and is not expected to be applicable to borate crosslinked gels. Amoco has issued a recommended test procedure for determining the rheology of titanium and zirconium gels (report F90-P-73).22 This procedure conditions the fluid in a bench-top mixer to simulate downhole pumping in casing and tubing before pumping the gel to the Fann 50C. Special shear ramps are performed to check for slip flow, which can give anomalously low viscosities. Test procedures which subject the fluid to simulated field mixing and turbulent down-hole flow conditions before pumping into the Fann viscometer are preferred by Amoco, because of flow- and thermal-history sensitivities of some fluids. Halliburton conditions its fluids by circulating through a small loop using a Jabsco gear pump at a high flow rate for four minutes to simulate flow down shallow wells and for ten minutes for flow down a deep well. DS conditions its gels by flowing through capillary tubing at nominal shear rates matched to field nominal shear rates (2.5 minutes at 675 sec-1 for the shallow well case and for five minutes at 1350 sec-1 for the deep well case). However, the DS technique does not simulate turbulence, because capillary flow occurs at low Reynolds numbers. It also does not match flowing energies. The Amoco method mentioned above matches volumetric flow energy and achieves turbulence using a specially designed bench top mixing device. The API will probably standardize testing using the DS capillary method of conditioning. However, test data run using any form of conditioning is preferable to the old RP39 method which uses no fluid conditioning. Service Company Trade Names Most service companies consider their fracturing products as proprietary, providing only limited information regarding chemical components, concentrations, mixing techniques, testing techniques, data reduction, etc. Service companies usually designate their different fracturing fluids by digital codes, Latin words, planetary bodies or other relevant titles. The fracturing fluids for all the service companies are quite similar. One of the most commonly used fracturing fluids for treatments are crosslinked HPG systems frequently containing 5% hydrocarbon. Table 6.10 gives typical components for the titantium crosslinked HPG systems. As an example of service company fluid system nomenclature, consider Halliburton’s Versagel system. Versagel is the trade name of Halliburton's conventionally crosslinked HPG-titanate fracJuly 1999

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turing fluid. Halliburton has devised a four-digit designation associated with a Versagel fluid, e.g., Versagel 1400. The first digit of the Versagel designation indicates the use of a base polymer, either WG-11 (HPG) or WG-12 (HPG with internal breaker). The second digit of the four-digit Versagel designation is the polymer concentration of the base gel in 10's of pounds polymer per 1,000 gallons water. The third digit indicates the use of delayed hydration polymer, either HPG or HEC. The HP guar is designated as WG-14, and HEC is designated WG-17. The last digit is the secondary gelling agent polymer concentration in 10's of pounds per 1,000 gallons. Five percent hydrocarbon can be added to Versagel for leakoff control. More frequently, the delayed crosslinked Versagel HT is used, especially if fluid shear degradation is anticipated (as is almost always the case). CL-18 (delay organo-metallic) as well as CL-11 (titanate) are used to modulate the extent of initial crosslinking. The percentages of either constituent will vary depending upon mix water, pH, temperature, treating string, residence time, etc. Some of Halliburton's HPG systems (as of 1989) are given in the cross reference (Table 6.11). Dowell Schlumberger also has a coding system for some of its water-base crosslinked gels. These gels are labeled as “YF” for “wide frac” and have a three integer suffix. The first integer implies both the polymer type and the crosslinker. If odd, it is a guar system, whereas if even, it is HPG. This first integer is set to 1 or 2 if borate is the crosslinker (1 means a borate crosslinked guar and 2 a borate crosslinked HPG). Likewise, 3 and 4 refer to titanium systems and 5 and 6 refer to their delayed zirconium gels. For their borate gel, they add the letter “D” to denote whether it is delayed. The next two integers refer to the polymer concentration in lb/Mgal. For example, YF-140D is a delayed crosslinked borate guar gel at a concentration of 40 lb/Mgal. In 1991 Western Company changed their water-base crosslinked fluid naming system. Gels are now referred to by a name that corresponds to the crosslinker type followed by a roman numeral designation for the polymer type. Titanium, aluminum, zirconium, and borate gel systems are referred to as APOLLO, GEMINI, SATURN, and VIKING respectively. Guar, HPG, CMHPG, and CMHEC are indicated by I, II, III, IV respectively. Generally, service company fluid trade names give little information about the nature or indicated application of the fracturing fluid. Looking at the fluid cross reference (Table 6.11), it can be seen that there are some exceptions. The most simple system, water with friction reducer (< 0.12 wt% polyacrylamide) is given names such as Aqua Frac, Water Frac, and Slick Water. Some of the CMHEC systems are given names like Kleen Gel or Krystal Frac XL which refer to the low residue (essentially zero) of the CMHEC when it breaks. Some gelled oil systems are aptly named MY-T-OIL or YF-GO III. Halliburton’s new high temperature system (to 370 ° F) is called Thermagel (a high pH zirconium crosslinked CMHPG). Halliburton adds a suffix to some of its systems’ names referring to maximum intended temperature. Their “LT” designation implies maximum intended use of 125 ° F, i.e., low temperature. “HT” refers to intended high temperature use up to 300 ° F. Hydraulic Fracturing Theory Manual

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The cross reference (Table 6.11) provides a method for getting a general idea of generically similar systems for different service companies. However, the exact chemical formulations may differ. Some service companies, especially the “big four” take pride in their special formulations, which according to their own testing, can give superior performance. Sometimes, however, the “superior performance” may be a result of the particular test method used to evaluate it, rather than a superior composition.

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6.2 Fluid Scheduling After a fluid type is selected, the engineer must decide what composition of the fluid to pump at the various stages of the fracturing treatment, i.e. the fluid schedule. The fluid composition must yield enough viscosity for adequate fracture width and proppant transport without generating excessive viscosity resulting in breaking out of zone and excessive height growth. Also, the effect of fluid composition on fluid loss and fracture conductivity must be considered. At this time, the viscosity guideline (discussed in Section 5.3 of this manual) will be used for fluid scheduling. This guideline states that if a “neat” (proppant-free) fluid can maintain at least 50 cp at 170 1/s shear rate during its lifetime in the fracture, then it is probable that adequate proppant transport will result. This statement is based on the assumption that the effective viscosity acting to reduce proppant settling is increased by the presence of proppant and by shear rates typically lower than 170 1/s in the fracture. In addition, at times earlier than the total fluid exposure time in the fracture, viscosity is usually greater since the fluid has had less exposure to degrading thermal effects. Field experience has shown that fluids meeting this viscosity guideline can successfully transport proppant. Whether this transport proceeds via perfect proppant transport, slow settling, or an equilibrium banking process is presently the subject of research. Fracturing design simulators require a knowledge of the viscosity of a fluid element at a given time and position in the fracture. The fluid-element rheology is a function of exposure time at bottomhole temperature (BHT). However, the fluid-element exposure time is a function of the fracture geometry and leakoff which are in turn functions of the fluid rheology and composition (as well as the fracturing model used --PKN, GDK, etc.). Thus, the engineer does not know before the simulation, what BHT exposure time each fluid stage is going to experience. Therefore, optimal scheduling of fluids with the “appropriate” viscosity is an iterative process. The following are two approaches to fluid scheduling. The first uses a given fluid system with known rheology (n', and K' as functions of time at temperature) and the second constrains the rheology of the fluid element in the fracture to be between 200 cp and 50 cp. The first technique is more suited for smaller treatments (less than three hours), whereas the second method is useful for larger treatments. Fluid Scheduling Given the Fluid Rheology Fluid scheduling given the rheology of a particular fluid system is appropriate for smaller jobs using only one fluid stage. The following method of fluid scheduling will assume that the engineer is designing for a particular fracture length and height with a desired maximum slurry proppant concentration, given the pump rate. In this case, a fluid system is selected which gives viscosities greater than 50 cp at 170 1/s for the estimated pump time, and which will permit pumping at surface pressures within wellhead pressure constraints. If the simulator does not have an estimating routine for the fluid volume (and therefore pump time), the engineer can make a rough estimate by dividing the desired fracture volume by the pump rate and the expected fluid efficiency. If the averHydraulic Fracturing Theory Manual

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age fracture width and fluid efficiency are not known, values of 0.25 inches and 0.4 respectively can be assumed as starting values. The values of n' and K' at fracture entry temperature and at time at bottomhole temperature are entered into the simulator. Also, a value of Cw for the fluid system or a total fluid loss coefficient, CT, representative of the particular fluid system in a particular reservoir (ideally obtained from minifrac testing) are input. The simulator is then run. If the desired fracture geometry and conductivity are not attained, the design engineer must examine the simulator results and adjust the fluid system accordingly. For example if the job screens out prematurely, a new fluid could be chosen which gives more viscosity; a fluid-loss additive could be added to lower the fluid loss coefficient; or the maximum proppant concentration could be reduced. If the resulting conductivity is too small, the engineer could try a more viscous fluid which would give wider fracture widths (if height growth is not a problem); a cleaner fluid which gives less conductivity impairment; or a larger maximum slurry proppant concentration. If the calculated pump time is substantially less than the viscous life of the fluid (the time at bottomhole temperature during which the fluid viscosity at 170 1/s exceeds 50 cp), the engineer may try repeating the simulation with a less viscous fluid. This is particularly desirable when pumping water base gels where less polymer means less fluid expense and better ultimate conductivities at a given fracture proppant concentration. This method of fluid scheduling is essentially a trial and error approach, involving more or less iterations depending on the engineer’s familiarity with the particular fracturing simulator and the formation. The next method is more suited for jobs where multiple fluid types or stages are utilized. Fluid Scheduling Using Constrained Rheology For treatments where different fluid stages are utilized in order to maintain more uniform viscosities in the fracture (e.g. between 200 and 50 cp at 170 1/s) and to minimize polymer loadings, the following method can be used if the fracturing simulator can calculate fluid-element time at temperature vs. volume pumped. As in the previous fluid scheduling method, the engineer wishes to create a fracture having a particular length and height with a desired maximum slurry proppant concentration using a given pump rate. The maximum pump rate is constrained by wellhead pressure limitations. In this case the engineer can enter the viscosities of the fluid as it enters the fracture and when it first reaches bottomhole temperature as 200 cp at 170 1/s. An n' of 0.75 and a K' of 0.01508 lbf-sn' /ft2 corresponding to 200 cp can be assumed. The remaining viscosities at times greater than or equal to 1 hour can be set to 50 cp at 170 1/s with n' of 0.75 and K' of 0.003771. A total fluid loss coefficient, CT, representative of the type of formation being fractured (e.g. 0.001 ft/ min for permeability less than 0.1 md, 0.0025 ft/ min for permeabilities between 0.1 and 5.0 md, or 0.005 ft/ min for permeabilities greater than 5 md) can be input. If the simulator predicts a screen out, the engineer can increase the viscosities at appropriate time-at-temperatures or perhaps use a lower fluid loss coefficient.

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After the desired fracture length and fracture conductivity have been calculated by the simulator, the engineer can schedule a fluid system. Fig. 6.36 shows the fluid-element time at temperature vs. volume pumped calculated by a simulator using an assumed constant viscosity, such as recommended above (i.e. 200 cp initially and 50 cp thereafter). The engineer then uses the rheological data for the selected fluid system (e.g. the X-CEL gel system in Fig. 6.37) to mark the times at temperature corresponding to when the particular fluid reaches 50 cp. These times are then marked off on the ordinate of Fig. 6.36 and extended horizontally to intersect the time-at-temperature curve. The fluid volumes corresponding to the intersection points define the stages of various polymer loading for the fluid system. Fig. 6.36 shows the resulting gel schedule marked off on the abscissa. The pad consists of 20,000 gal of a 50 lb crosslinked gel plus 60,000 gal of a stabilized 50 lb crosslinked gel (X50S). The X50S gel continues for another 40,000 gal up to the 4 ppg proppant stage. Then 40,000 gal of crosslinked 50 lb gel followed by 30,000 gal of crosslinked 40 lb gel and 50,000 gal of crosslinked 30 lb gel complete the pumping of proppant through the 10 ppg stage. The middle sand stages on Fig. 6.36 have been reduced below the theoretical to account for additional slurry dehydration. Using the specified gel schedule, the engineer inputs the rheology for the selected fluid system (n' and K' as functions of time at temperature) plus the Cw appropriate for each stage and reruns the simulator. If the simulated results meet the engineer’s specifications of length and conductivity, then the design is completed. If not, the engineer must make appropriate rheology, fluid loss, and/or maximum slurry proppant concentration modifications. For a class problem, plot the data in Table 6.12 on the semilog graph paper in Fig. 6.38 to create an exposure time plot similar to Fig. 6.37. Also, indicate the optimum time exposures for each of the fluid stages. Warning: The testing of crosslinked gels is very difficult, with highly varying results from test to test. Some service company data result from gels that were conditioned to simulate the flow history down the tubular goods before testing on the viscometer. Viscosities of conditioned gels can be substantially different from those of unconditioned gels. Also, if breakers are required for a fluid system (e.g. for temperatures less than 250°F), they should be added to all proppant laden portions of the fluid. Breakers can significantly lower a fluid’s viscosity while pumping, and therefore, the viscosity vs time at temperature plots (e.g. Fig. 6.37) should be adjusted accordingly. Encapsulated breakers are now available which slow and/or delay the release of the breaker to avoid premature viscosity breaking and to allow high breaker concentrations for better gel breaking. The uncertainty in some of the data can be overcome by comparing similar systems for different companies and using field experience. Fig. 6.39 - Fig. 6.41 provide guidelines for three common fluid systems. These guidelines include the comparisons with various companies and have been

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successfully applied in the field. Guidelines include the use of viscosity stabilizers at higher temperatures and longer exposure times. The use of stabilizers allows higher viscosity to be maintained without using additional polymer. Another guideline, which has been successfully applied, is for pad fluids. This guideline is shown on Fig. 6.42 and was based on gel stability at high temperatures for an effective wall cake to control fluid loss. However, this guideline may be too conservative for the high temperature fluid systems currently available. Also, recent data for fluids with 5% hydrocarbon (generally used during pad or first half of treatment with X-L gel and low k) indicate that polymer loading may not significantly affect fluid loss. These reservations concerning Fig. 6.42 should be evaluated if fluid schedules are developed which differ from the guideline.

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PROPPANT AND FLUID SCHEDULING PROBLEM

Using the prior guidelines for fluid scheduling and the example plot of simulator results shown in Fig. 6.43 develop a complete fluid and proppant schedule assuming the fluid system is Western's APOLLO II/APOLLO II H system (Fig. 6.41). Assume the results in Fig. 6.43 are calculated assuming the minimum viscosity requirements discussed previously. Since frac tanks are generally 500 BBLS (20,000 gals), fluids should be selected in 20,000 gallon increments or another increment which is convenient for the tank size actually used.

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References

6.3 References 1. Ely, J. W.: Stimulation Treatment Handbook, An Engineer’s Guide to Quality Control, PennWell Publishing Co., Tulsa, OK (1985). 2. RP 39, Recommended Practice for Standard Procedures for the Evaluation of Hydraulic Fracturing Fluids,” API, Dallas (1983). 3. Biot, M.A. and Medlin, W.L.: “Theory of Sand Transport in Thin Fluids,” paper SPE 14468 presented at the 1985 SPE Annual Technical Conference and Exhibition, Las Vegas, Sept. 22-25. 4. Medlin, W.L., Sexton, J.H., and Zumwalt, G.L.: “Sand Transport Experiments in Thin Fluids,” paper SPE 14469 presented at the 1985 SPE Annual Technical Conference and Exhibition, Las Vegas, Sept. 22-25. 5. Daneshy, Ali: “Proppant Transport,” Monograph Series, SPE, Richardson, TX (1989) 12, vii, 210-22. 6. Shah, S. N.: “Proppant Settling Correlations for Non-Newtonian Fluids Under Static and Dynamic Conditions,” SPEJ (April 1982) 164-70. 7. Novotny, E.J.: “Proppant Transport,” paper SPE 6813 presented at the 1977 SPE Annual Technical Conference and Exhibition, Denver, Oct. 9-12. 8. Penny, G.S. and Conway, M.W.: “Fluid Leakoff,” Monograph Series, SPE, Richardson, TX (1989) 12, vii, 147-76. 9. Cameron, J.R.: “Fluid Loss Testing on East Texas Cotton Valley Sand Cores to Determine the Effects of Diesel and Polymer Concentration; With Consideration on Design Values of Spurt Loss and the Overall Fluid-Loss Coefficient,” Amoco Production Company Report F88-P-21 (July, 1987). 10. McGowan, J.M. and McDaniel, B.W.: “The Effects of Fluid Preconditioning and Test Cell Design on the Measurement of Dynamic Fluid Loss Data,” paper SPE 18212 presented at the 1988 SPE Annual Technical Conference and Exhibition, Houston, October 2-5. 11. Cooke, C.E., Jr.: “Effect of Fracturing Fluids on Fracture Conductivity,” JPT (Oct. 1975) 1273-82; Trans., AIME, 259. 12. Cameron, J.R.: “Vol% Residue of HPG Vs. Guar in Borate Crosslinked Gels and Flow Impairment Models Based on Vol% Residue and Fracturing Design Parameters,” Amoco Production Company Report F90-P-41 (Feb. 1990). 13. Penny, G.S.: “Evaluation of the Effects of Environmental Conditions and Fracturing Fluids on the Long-Term Conductivity of Proppants,” paper SPE 16900 presented at the 1987 SPE Annual Technical Conference and Exhibition, Dallas, Sept. 27-30. 14. Small, J., et. al.: “Improving Fracture Conductivities with a Delayed Breaker System: A Case History,” paper SPE 21497 presented at the 1991 SPE Gas Technology Symposium, Houston, Jan. 23-25. 15. Cameron, J.R. and Prud’homme, R.K.: “Fracturing-Fluid Flow Behavior,” Monograph Series, SPE, Richardson, TX (1989) 12, vii, 177-209.

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16. Brannon, H.D. and Ault, M.G.: “New Delayed Borate-Crosslinked Fluid Provides Improved Fracture conductivity in High-Temperature Applications,” paper SPE 22838 presented at the 1991 SPE Annual Technical Conference and Exhibition, Dallas, Oct. 6-9. 17. Roodhart, L.P. and Davies, D.R.: “Polymer Emulsion: The revival of a Fracturing Fluid,” paper SPE 16413 presented at the 1987 SPE/DOE Low Permeability Reservoirs Symposium, Denver (May 18-19). 18. Sinclair, A.R., Terry, W.M., and Kiel, O.M.: “Polymer Emulsion Fracturing,” JPT (July 1974) 731-38. 19. Harris, P.C., Klebenow, D.E., and Kundert, D.P.: “Constant Internal Phase Design Improves Stimulation Results,” paper SPE 17532 presented at the 1988 SPE Rocky Mountain Regional Meeting, Casper, WY, May 11-13. 20. Western Binary Foam System, Technical Manual, 1990. 21. Ely, J.W.: “Fracturing Fluids and Additives,” Monograph Series, SPE, Richardson, TX (1989) 12, vii, 131-146. 22. Cameron, J.R. and Gardner, D.C.: “Suggested Amoco Procedure for Testing Titanium and Zirconium Crosslinked Gels,” Amoco Production Company Report F90-P-73 (Oct. 1990).

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Table 6.3 - Smith Energy Services Fracturing Services & Products.

EQUIPMENT ZONE A

ZONE B

2.48

2.48

4.20 4.66 5.25 6.35 7.61 9.35 11.18 12.65 14.65 15.50 17.20 *P.O.R.

3.65 3.99 4.43 5.38 6.30 7.56 8.98 10.49 12.16 13.02 14.70 *P.O.R.

MILEAGE 33000

All units excluding sand and chemical delivery from the nearest SES operating point, one way, per unit, per mile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

FRACTURING PRESSURE (psi) Per HHP, four hours or less 33010 33015 33020 33025 33030 33035 33040 33045 33050 33055 33060 33065

0 to 5,000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5,001 to 6,000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6,001 to 7,000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7,001 to 8,000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8,001 to 9,000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9,001 to 10,000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10,001 to 11,000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11,001 to 12,000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12,001 to 13,000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13,001 to 14,000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14,001 to 14,500 . . . . . . . . . . . . . . . . . . . . . . . . . . . . Over 14,500. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

FRACTURING PUMP EQUIPMENT Based on hydraulic horsepower, ordered or used, whichever is greater, calculations are carried to the nearest BPM obtained while pumping the combined volume of fluid and solids. The average injection rate and average injection pressure to the nearest 100 psi and measured at the surface during fluid injection. Any abnormal fluctuations in pressure of short duration, such as high breakdown pressure are excluded. Minimum pressure used in this calculation will be 800 psi. HHP ordered is defined as the HHP required to provided the specific injection rate at specified injection pressures as calculated from the formula below:

HHP

BPM ( average ) × psi ( average ) = ------------------------------------------------------------------40.8

* Priced on Request

CHEMICAL ADDITIVES

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Table 6.3 - Smith Energy Services Fracturing Services & Products.

ZONE A

ZONE B

33.83 55.31 32.23 16.50 6.48 52.80

33.83 55.31 32.23 16.50 6.48 52.80

4.13 3.08 2.75 18.98 14.19 55.79

4.13 3.08 2.75 18.98 14.19 55.79

113.30 39.60 14.85

113.30 39.60 14.85

1.90 .43 2.40 1.95 2.68 1.12 1.18 *P.O.R.

1.90 .43 2.40 1.95 2.68 1.12 1.18 *P.O.R.

BACTERIA CONTROL 34000 34010 34020 34030 34031 34033

BCS-1; per gallon . . . . . . . . . . . . . . . . . . . . . . . . . . . BCS-2; per gallon . . . . . . . . . . . . . . . . . . . . . . . . . . . BCS-3; per gallon . . . . . . . . . . . . . . . . . . . . . . . . . . . BCS-4; (Dryocide), per pound. . . . . . . . . . . . . . . . . . BCS-5; sodium hypochlorite, per gallon . . . . . . . . . . BCS-7; (X-CIDE 600), per pound . . . . . . . . . . . . . . .

BREAKERS FOR GEL SYSTEMS 34040 34050 34051 34060 34961 34062 34070 34074 34077

OXB-3; oil gel, per pound . . . . . . . . . . . . . . . . . . . . . WCB-1; water gel, per pound . . . . . . . . . . . . . . . . . . WCB-2; water gel, per pound . . . . . . . . . . . . . . . . . . WCB-LT; breaker aid, water gel, per gallon . . . . . . . WCB-LTA; breaker aid, water gel, per gallon . . . . . . WCB-ACT; breaker activator, water gel, per gallon WEB-2; water enzyme breaker, per half gallon container . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . EWB-1; encapsulated breaker, per pound** . . . . . . . DWB-1; delayed breaker, per pound . . . . . . . . . . . . **Dowell Schlumberger License Fee Applies

BUFFERS 34080 34090 34100 34110 34120 34130 34140 34145

BW-1; per pound . . . . . . . . . . . . . . . . . . . . . . . . . . . . BW-3; per pound . . . . . . . . . . . . . . . . . . . . . . . . . . . . BW-4; per pound . . . . . . . . . . . . . . . . . . . . . . . . . . . . BW-5; per pound . . . . . . . . . . . . . . . . . . . . . . . . . . . . BW-6; per pound . . . . . . . . . . . . . . . . . . . . . . . . . . . . BW-9; per pound . . . . . . . . . . . . . . . . . . . . . . . . . . . . BW-10; ammonium chloride, per pound . . . . . . . . . . AA-11; caustic soda, per pound . . . . . . . . . . . . . . . .

* Priced on Request

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Table 6.3 - Smith Energy Services Fracturing Services & Products.

CHEMICAL ADDITIVES ZONE A

ZONE B

34.28 *P.O.R. 24.75 24.75 26.90 *P.O.R.

34.28 *P.O.R. 24.75 24.75 26.90 *P.O.R.

40.99 45.00 70.06 31.71 34.00 16.17 24.23 32.38 51.81 30.96 47.85

40.99 45.00 70.06 31.71 34.00 16.17 24.23 32.38 51.81 30.96 47.85

29.70 4.99 *P.O.R.

29.70 4.99 *P.O.R.

CLAY CONTROL CHEMICALS 34150 34155 34156 34160 34170 34175

CCC-3; per gallon . . . . . . . . . . . . . . . . . . . . . . . . . . . CCC-4; CLAYLOKR, per gallon**. . . . . . . . . . . . . . . . CCC-5; clay control alternative, per gallon . . . . . . . . KCI; potassium chloride, per cwt . . . . . . . . . . . . . . . . LPA-1; per gallon. . . . . . . . . . . . . . . . . . . . . . . . . . . . BRN-1; brine water, per barrel. . . . . . . . . . . . . . . . . .

** Chevron License Fee Applies CROSSLINKERS 34180 34189 34190 34200 34210 34220 34230 34240 34245 34250 34251 34252 34253 34254

CX-1; aqueous gel, per gallon . . . . . . . . . . . . . . . . . . CX-4; low temperature, low pH, per gallon . . . . . . . . CX-5; low pH, per gallon . . . . . . . . . . . . . . . . . . . . . . CX-6; cold water, per gallon . . . . . . . . . . . . . . . . . . . CX-12; brine water, per gallon. . . . . . . . . . . . . . . . . . CX-13; high pH, per gallon . . . . . . . . . . . . . . . . . . . . CX-14; high temp., per gallon . . . . . . . . . . . . . . . . . . CX-15; high temp., per gallon . . . . . . . . . . . . . . . . . . CX-16; aqueous gel, per gallon . . . . . . . . . . . . . . . . . CX-91; aqueous gel, per gallon . . . . . . . . . . . . . . . . . CDA-2; crosslink delay additive, per gallon . . . . . . . . CX-DB2; high temperature delayed borate crosslinker, per gallon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . DBX-1; delayed borate crosslinker, per gallon . . . . . RM-18; high pH boric acid, per pound. . . . . . . . . . . .

* Priced on Request

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CHEMICAL ADDITIVES ZONE A

ZONE B

.20 2.82 2.11 .20 4.22 3.45

.20 2.82 2.11 .20 4.22 3.45

30.15 30.15

30.15 30.15

36.00 28.14

36.00 28.14

6.60 2.48 .61 3.85 18.15

6.60 2.48 .61 3.85 18.15

12.97 .60

12.97 .60

DIVERTING AGENTS 34255 34260 34270 34280 34290 34300

DA-1; rock salt, course, per pound . . . . . . . . . . . . . . DA-2; naphthalene, per pound . . . . . . . . . . . . . . . . . DA-3; benzoic acid flakes, per pound . . . . . . . . . . . . DA-4; rock salt, graded, per pound . . . . . . . . . . . . . . DA-5; wax beads, per pound. . . . . . . . . . . . . . . . . . . DA-6; paraformaldehyde flakes, per pound. . . . . . . .

EMULSION PREVENTION SURFACTANTS 6-56

34310 34320

EPS-4; per gallon . . . . . . . . . . . . . . . . . . . . . . . . . . . EPS-9; per gallon . . . . . . . . . . . . . . . . . . . . . . . . . . .

EMULSIFIERS 34330 34340

PEM-1; water external, per gallon . . . . . . . . . . . . . . . PEM-3; 5% hydrocarbon systems, per gallon . . . . . .

FLUID LOSS ADDITIVES 34350 34360 34370 34380 34390 34395 34396

OFL-1; (Adomite Mark II) per pound . . . . . . . . . . . . . WFL-1; (Adomite Aqua) per pound . . . . . . . . . . . . . . WFL-2; per pound . . . . . . . . . . . . . . . . . . . . . . . . . . . WFL-3; (Adomite Regain), per pound . . . . . . . . . . . . WFL-4; per gallon . . . . . . . . . . . . . . . . . . . . . . . . . . . WFL-5; (Adomite Regain) diesel based slurry per gallon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . WFL-6; cornstarch, per pound. . . . . . . . . . . . . . . . . .

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DEFOAMING AND FOAMING AGENTS

Fluid Selection and Scheduling

Hydraulic Fracturing Theory Manual

Table 6.3 - Smith Energy Services Fracturing Services & Products.

July 1999

Table 6.3 - Smith Energy Services Fracturing Services & Products.

34410 34420 34430

AGD-2; defoamer, per gallon . . . . . . . . . . . . . . . . . . FAA-1; (Adofoam BF-1), foaming agent for fresh water and brines, per gallon. . . . . . . . . . . . . . . . . . . . . . FAA-2; foaming agent for fresh water, brine, and acid, per gallon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

63.06

63.06

31.50

31.50

21.05

21.05

ZONE A

ZONE B

23.28 8.25 26.24 32.25

23.28 8.25 26.24 32.25

42.90 15.29 51.15 51.00

42.90 15.29 51.15 51.00

6-57

* Priced on Request

CHEMICAL ADDITIVES

FRICTION REDUCERS OFR-1; oil friction reducer, per gallon . . . . . . . . . . . . WFR-1; water friction reducer, per pound . . . . . . . . . WFR-2; water/acid friction reducer, per gallon . . . . . WFR-3; water/acid friction reducer, per gallon . . . . .

GELLING AGENTS - OIL 34460 34470 34480 34490

OGA-1; per gallon . . . . . . . . . . . . . . . . . . . . . . . . . . . OGA-2; complexer, per gallon. . . . . . . . . . . . . . . . . . OGA-3; per gallon . . . . . . . . . . . . . . . . . . . . . . . . . . . OGA-4; high temp., per gallon. . . . . . . . . . . . . . . . . .

DIESEL FUEL

References

Hydraulic Fracturing Theory Manual

34440 34445 34450 34451

DIE-1; number one diesel, per gallon . . . . . . . . . . . . DIE-2; number two diesel, per gallon . . . . . . . . . . . .

6-58

*P.O.R. *P.O.R.

*P.O.R. *P.O.R.

6.17 6.10 5.17 4.57 20.35 27.50 27.50

6.17 6.10 6.17 4.57 20.35 27.50 27.50

23.87

23.87

26.16

26.16

1.90

1.90

GELLING AGENTS - WATER 34500 34510 34520 34530 34550 34560 34565 34567 34568

WGA-2; HPG, per pound. . . . . . . . . . . . . . . . . . . . . . WGA-4; CMHEC, per pound . . . . . . . . . . . . . . . . . . . WGA-5; CMHPG, per pound . . . . . . . . . . . . . . . . . . . WGA-6; premium guar, per pound . . . . . . . . . . . . . . CMG-1; Continuous Mix Gel - Guar, per gallon . . . . CMG-2; Continuous Mix Gel - HPG, per gallon. . . . . CMG-3; Continuous Mix Gel - CMHPG, per gallon. CMG-4; Environmentally Safe Continuous Mix Gel Guar, per gallon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . CMG-5; Environmentally Safe Continuous Mix Gel HPG, per gallon. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

GEL STABILIZING AGENTS 34570

HTS-2; high temperature, per pound. . . . . . . . . . . . .

* Priced on Request

CHEMICAL ADDITIVES

Fluid Selection and Scheduling

34495 34496

6

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Table 6.3 - Smith Energy Services Fracturing Services & Products.

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July 1999

Table 6.3 - Smith Energy Services Fracturing Services & Products.

ZONE A

ZONE B

55.83 52.25 64.76

55.83 52.25 64.76

20.79

20.79

35.97 21.71 18.22 26.40 46.70 28.17 31.37 32.31

35.97 21.71 18.22 26.40 46.70 28.17 31.37 32.31

.91 125.00

.91 125.00

.91 125.00

.91 125.00

5.50 121.00 11.00

5.50 121.00 11.00

SURFACTANTS 34580 34585 34590 34591 34598

6-59

34600 34610 34620 34622 34630 34640 34650

FRS-1; fluid recovery surfactant, per gallon . . . . . . . FRS-2; fluid recovery surfactant, per gallon . . . . . . . FRS-3; fluid recovery surfactant, per gallon . . . . . . . FRS-4; fluid recovery surfactant, non-fluorocarbon, per gallon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . MCFRS;methanecoalfluidrecoverysurfactant,pergallon SAA-1; per gallon . . . . . . . . . . . . . . . . . . . . . . . . . . . SAA-2; per gallon . . . . . . . . . . . . . . . . . . . . . . . . . . . SAA-3; per gallon . . . . . . . . . . . . . . . . . . . . . . . . . . . SAA-4; per gallon . . . . . . . . . . . . . . . . . . . . . . . . . . . SAA-7; per gallon . . . . . . . . . . . . . . . . . . . . . . . . . . . SAA-8; per gallon . . . . . . . . . . . . . . . . . . . . . . . . . . . USS-N; per gallon . . . . . . . . . . . . . . . . . . . . . . . . . . .

CHEMICAL DELIVERY For chemical delivery to location, per ton mile . . . . . Minimum delivery charge for all chemicals . . . . . . . .

CHEMICAL RETURN 34666 34667

For chemical return from location, per ton mile . . . . . Minimum return charge . . . . . . . . . . . . . . . . . . . . . . .

CHEMICAL HANDLING CHARGE Handling charge for chemicals furnished by customer 34670 34680 34681

Dry chemicals, per cwt . . . . . . . . . . . . . . . . . . . . . . . Liquid chemicals, per 55 gallon drum . . . . . . . . . . . . Liquid chemicals, per 5 gallon container . . . . . . . . . .

References

Hydraulic Fracturing Theory Manual

34660 34665

6

CHEMICALS NOT INCLUDED IN PRICE LIST 34999

Chemicals not included in Smith Energy Services’ price list . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

* Priced on Request

*P.O.R.

*P.O.R.

Fluid Selection and Scheduling

Hydraulic Fracturing Theory Manual

Table 6.3 - Smith Energy Services Fracturing Services & Products.

6-60 July 1999

July 1999

Table 6.4 - Water Soluble Polymers. NATURAL ANIMAL ORIGIN

BACTERIA ORIGIN

GELATIN GLUE CASEIN CHITIN

BIOPLOYMERS XANTHAN

VEGETABLE ORIGIN

6-61

CELLULOSE STARCH SEED GUMS GUAR GUM* LOCUST BEAN GUM QUINCE, FLAX & OKRA GUM TAMARIND PLANT EXUDATES GUM ARABIC GUM GHATTI GUM KARAYA GUM TRAGACANTH SEQWEED EXTRACTS AGAR ALGIN CARRAGEENAN PLANT EXTRACTS LARCH ARABINOGALACTAN PECTIN

SYNTHETIC SYNTHETIC PRODUCTS

CARBOXYMETHYCELLULOSE (CMC)*

POLYVINYL ALCOHOL

ETHYCELLULOSE

POLYVINYLPYRROLIDONE

HYDROXYETHYLCELLULOSE (HEC)*

POLYVINYLMETHYL ETHER

CARBOXYMETHYL HYDROXYETHYL CELLULOSE (CMHEC)*

POLYACRYLIC ACIDS & SALT

ETHYLHYDROXYETHYLCELLULOSE

POLYACRYLAMIDES*

METHYLCELLULOSE

ETHYLENE OXIDE POLYMERS

STARCH AMYLOSE

References

Hydraulic Fracturing Theory Manual

MODIFIED NATURAL PRODUCTS

ANIMAL ORIGIN

BACTERIA ORIGIN

VEGETABLE ORIGIN

STARCH AMYLODPECTIN STARCH DEXTRINS STARCH HYDROXYETHYL ETHERS HYDROXYPROPYL GUAR (HPG)* CARBOXYMETHYL HYDROXYPROPYL GUAR (CMHPG)* HYDROXYETHY GUAR * PRIMARY GELLING AGENTS FOR HYDRAULIC FRACTURING FLUIDS.

6-62

y A High Molecular Weight Carbohydrate Polymer (Polysaccharide) Guar Gum Molecule

July 1999

Fig. 6.14 - Where Guar Comes From.

Fluid Selection and Scheduling

NATURAL

6

Hydraulic Fracturing Theory Manual

Table 6.4 - Water Soluble Polymers.

July 1999

Double Purified Splits

Guar Pods

Single Purified Splits

Guar Seeds

Fig. 6.14 - Where Guar Comes From. 6-63 Hydroxypropyl Guar (Generalized Structure)

References

Hydraulic Fracturing Theory Manual

Fig. 6.15 - Principal Guar Derivatives.,

Table 6.5 - Primary Gelling Agents for Fracturing. Water Soluble Polymers Guar Gum HPG CMHPG Cellulose Derivatives HEC CMC CMHEC Polyacrylamides

Fluid Selection and Scheduling

6-64

Fig. 6.15 - Principal Guar Derivatives.,

6

Hydraulic Fracturing Theory Manual

Carboxymethyl Hydroxypropyl Guar (Generalized Structure)

July 1999

July 1999 6-65

Fig. 6.16 - HPG Solution: Effect of Shear Rate & Temperature.

References

Hydraulic Fracturing Theory Manual

Fig. 6.17 - Flow Behavior Index (n') vs. Temperature of Halliburton’s HPG Solution.

Fig. 6.18 - Consistency Index (K'a) vs. Temperature of Halliburton’s HPG solution.

6 Fluid Selection and Scheduling

Hydraulic Fracturing Theory Manual

6-66

July 1999

July 1999 6-67 Fig. 6.19 - Comparison of 40-lbm/1,000-gal Hpg Gels Crosslinked with Titanium Acetyl Acetonate Subjected to Various Turbulent Flow and Temperature Histories.

References

Hydraulic Fracturing Theory Manual

6

Fluid Selection and Scheduling

Hydraulic Fracturing Theory Manual

6-68

July 1999

References

July 1999

6-69

Hydraulic Fracturing Theory Manual

6

Fluid Selection and Scheduling

Fig. 6.20 - Viscosity of Halliburton’s Boragel (Borate Crosslinked Guar) as a Function of Time at 225 ° F.

Hydraulic Fracturing Theory Manual

6-70

July 1999

References

Table 6.6 - Useful Crosslinkers for Guar and Guar Derivatives. Crosslinking Guar

Crosslinker

pH Range of Fluid

Effective Temperature Region

Borate

8-10

60 ° F - 275 ° F maximum

Antimony

2-3.5

140 ° F maximum

Titanate

7-8 or higher

300 ° F +

Zirconium

7-8 or higher

350 ° F +

Aluminum

4-8

160 ° F maximum

Zirconium

<1 (acids)

<100 ° F

°

Crosslinking Through COOH Groups (CMHPG)

Crosslinking Through cis OH Groups

Fig. 6.21 - Generalized Crosslinking Scheme.

July 1999

6-71

Hydraulic Fracturing Theory Manual

6

Fluid Selection and Scheduling

Flow Behavior Index (n') vs. Time Versagel HT Fluids 1.0

D

0.8

n'

B C A

0.6 Versagel HT - 250 deg F 0.4

A B C D

WG-11 MEOH GEL-STA 40 5 10 40 5 0 40 0 10 40 0 0

0.2 0

1

2

3

4

5

6

Time (hr) Consistency Index (K'a) vs. Time

1.0

0.1

K'a A C 0.01

B D

0.001 0

1

2

3

4

5

6

Time (hr)

Fig. 6.22 - Power Law Data for Halliburton’s Versagel HT Fluid 250 ° F.

Hydraulic Fracturing Theory Manual

6-72

July 1999

References

Fig. 6.23 - Effect of Internal Phase on Polymer Emulsion Viscosity.

July 1999

6-73

Hydraulic Fracturing Theory Manual

6

Fluid Selection and Scheduling

Table 6.7 - Comparison Of “Constant-Internal-Phase” Concept With “Constant-Viscosity-Concept” For Two Polymer Emulsion Slurries With The Same Polymer Loading. Constant Viscosity

Constant Internal Phase

Proppant Loading (lb/gal)

Emulsion Quality (-)

Slurry Viscosity (mPa.s)

Emulsion Quality (-)

Slurry Viscosity (mPa.s)

0

0.70

266

0.70

266

2

0.67

266

0.67

266

4

0.66

266

0.65

254

6

0.64

266

0.62

236

8

0.62

266

0.59

228

10

0.59

266

0.56

228

12

0.56

266

0.54

244

Constant Viscosity

Constant Internal Phase

Proppant Loading (lb/gal)

Emulsion Quality (-)

Slurry Viscosity (mPa.s)

Emulsion Quality (-)

Slurry Viscosity (mPa.s)

0

0.67

197

0.67

197

2

0.63

197

0.64

205

4

0.61

197

0.61

197

6

0.59

197

0.58

191

8

0.56

197

0.55

191

10

0.52

197

0.52

197

12

0.48

197

0.50

200

Hydraulic Fracturing Theory Manual

6-74

July 1999

References

= 176° F

Fig. 6.24 - Flow Curves of a 0.67 Quality Emulsion at Various Temperatures.

1000

(Viscosity, cp @ 511 sec-1)

75 80 70

100

60 50

10 70

Fig. 6.25 - The Effect of Shear Rate on Polymer Emulsion Viscosity.

July 1999

80 75 70

60 50

90

110

130

150

170

Temperature (°F)

190

210

Fig. 6.26 - Viscosity vs. Temperature for Western Super K-Frac (Polyemulsion).

6-75

Hydraulic Fracturing Theory Manual

6

Fluid Selection and Scheduling

Fig. 6.27 - Plot of Viscosity of a 0.67 Quality Emulsion Vs. Mean Droplet Size.

Hydraulic Fracturing Theory Manual

6-76

July 1999

References

Fig. 6.28 - Power-law Data for a Water/N2 Foam Stabilized With 40 lbm Thickener/1,000 Gal Water.

Fig. 6.29 - Effect of HPG Concentration (lbm/1,000 gal) on the Viscosity of a 0.70-Quality Foam.

July 1999

6-77

Hydraulic Fracturing Theory Manual

6

Fluid Selection and Scheduling

Fig. 6.30 - Effect of Shear History on the Texture of an Aqueous/N2 Foam.

Friction Pressure - psi per 1000 ft

Foam Friction Pressure Pipe Data: 2 7/8 in. OD EUE tubing - 6.5 lb per ft 1000 900 800 700

1000 900 800 700

600

600

500

500

400

400

300

300

Foam Quality 200

200

0.85 0.80 100 90 80 70

100 90 80 70

0.75

60

60

0.70

50

50

40

40

0.65

30

20

30

20

0.60

0.55 10 1

2

3

4

5

6 7 8 9 10

20

30

10 40 50 60 70 80 90 100

Flow Rate - BPM

Fig. 6.31 - Friction Pressure for Dowell Schlumberger’s Stabilized Foam. Hydraulic Fracturing Theory Manual

6-78

July 1999

References

Fig. 6.32 - Comparison of the Solubility of Carbon Dioxide and Nitrogen in Water.

Fig. 6.33 - 70 Quality: CO2 Foam Vs. Binary Foam.

July 1999

6-79

Hydraulic Fracturing Theory Manual

6

Fluid Selection and Scheduling

Association Complex ... Reversible to shear but sensitive to polar contaminates

Fig. 6.34 - Aluminum Orthophosphate Ester Hydrocarbon Gel.

Fig. 6.35 - Pressure Effect on a Partially Gelled Diesel at Ambient Temperature and at 180 ° F [data by J. R. Cameron, courtesy Amoco Production Co. Research, Tulsa, OK (1986)].

Hydraulic Fracturing Theory Manual

6-80

July 1999

References

Table 6.8 - MY-T-OIL II & MY-T-OIL IV Comparative Evaluation (cp) Viscosity @ 170 1/s

MY-T-OIL IV (Continuous-Mix System) (L/m3) FDP-5445A

(L/m3) FDP-5445B

(Kg/m3) K-34

Crude Oil

6

6

0.4

Crude Oil

6

6

0.35

Hydrocarbon

Hours at Temp

Initial

Final

Initial

Final

Initial

Final

70

24

263

51

0.093

0.407

0.577

0.0223

70

19.6

329

76

0.098

0.33

0.707

0.0488

Temp

°C

(cp) Viscosity @ 170 1/s

MY-T-OIL II (Batch System)

Hydrocarbon

(L/M3) MO-55A

L/m(L/M3) MO-56

(Kg/m3) K-34

(1bf-secn'/ft2 K'

n'

Temp

°C

(1bf-secn'/ft2 K'

n'

Hours at Temp

Initial

Final

Initial

Final

Initial

Final

Crude Oil

13

4

3.5

71

2.5

302

215

0.13

0.11

0.550

0.433

Crude Oil

12

3.6

3.4

70

2.2

91

60

0.19

0.20

0.120

0.0751

Frac Oil 200

7

2.4

2.0

71

2.2

102

81

0.25

0.12

0.102

0.150

Frac oil 200

8

2.7

3.0

70

2.2

155

81

0.19

0.13

0.289

0.149

MO-55A and FDP-5445A are gellants MO-56 and FDP-5445B are activators K-34 is sodium bicarbonate breaker “initial” values are at 0 time at temperature and final values are at total hours at temperature

July 1999

6-81

Hydraulic Fracturing Theory Manual

6

Fluid Selection and Scheduling

Table 6.9 - Power-Law Rheology as a Function of Temperature, Western Maxi-0-74 Gelled Oil System.

Maxi-0-74 Gel

Temperature °F

Time

n'

K'

Viscosity 170 sec-1

8 gal1 8 gal1 8 gal1 8 gal1 8 gal1 8 gal1 8 gal1

80 120 140 160 180 200 220

Initial Initial Initial Initial Initial Initial Initial

.28 .26 .25 .25 .26 .28 .36

.15 .15 .15 .14 .13 .094 .048

178 161 153 142 139 112 86

8 gal2 8 gal2 8 gal2 8 gal2 8 gal2 8 ga2 8 gal2

80 120 140 160 180 200 220

Initial Initial Initial Initial Initial Initial Initial

.28 .23 .20 .19 .22 .27 .30

.12 .13 .14 .14 .12 .08 .035

142 119 110 105 105 90 46

1. Gal/1000 of gellant in kerosene. 2. Gal/1000 of gellant in No. 2 Diesel.

Table 6.10 - Typical Chemical Components of Organo-Metallic Crosslinked Frac Fluids. POLYMER:

30-60 #/1000 gal, 0.4 m.s. HPG

BUFFERING AGENTS: Example:

Weak acid and/or salt Fumeric acid/sodium bicarbonate or sodium carbonate Sulfamic acid/sodium bicarbonate or sodium carbonate Acetic acid or anhydride/sodium acetate pH: 5-7 or 8-10 stability requirements

CROSSLINKER:

Titanium chelates of acetyl acetonate (TiAA), triethanol amine (TiTE), lactic acid (TiLA), or TiTE/TiAA. TiTE + water (slower react.)

STABILIZER:

Alcohol (5-10% MeOH, sod. thiosulfate (10-20 #/1000 gal)

BREAKER:

Enzymatic, cellulose (<140 ° F), oxidative, persulfates (>140 ° F)

ADDITIVES:

Hydraulic Fracturing Theory Manual

Surfactants: non-emuls., surface tension reduct.; Clay Control: KCl (1-2%), cationic polymers, polyamines.

6-82

July 1999

References

Table 6.11 - Competitive Cross Reference of Similar Additives. Composition

BJ Services

Dowell Schlumberger

NOWSCO LTD

Halliburton

Smith

Western

Water Based Gel Systems Water and Friction reducer

Aqua Frac

River Frac

Friction Reducer

Available

Slick Water

Water Frac

Gelled water

Gelled Water Aqua Frac

Water Frac WF-100 (guar) WF-200 (HPG)

Gelled Water

Water Frac

Gelled Water WGA-6 WGA-7

Gelled Water

Gelled water with a fluid loss additive

Gelled water plus FLA

Redifrac

Gelled water & Fluid Loss

Water Frac plus FLA Logel 100 & FLA

Gelled Water with FL Additive

(Maxi-Pad) (Westpad A) available

Low residue gelled water (HPG)

GW-8 GW-32

WF200

LSR-1NB

WG-11, 12, HYG-5, WG-20

WGA-2 WGA-8

J-12 (J-16) J-20

No residue gelled water (HEC)

GW-21

YFHC

HEC

Hygel 100,300 & 500, LOGEL 100 WG-17, WG-21

WGA-3

Plus Gel (J-5) J-6

GWX-7 GWX-9

VIKING II VIKING II DHT APOLLO II SATURN II LT SATURN II

GWX-7 LT, GWX-7 HT GWX-9

VIKING I VIKING I DHT APOLLO I

Crosslinked Gel Systems Crosslinked HPG

Crosslinked guar system additive

Terra Frac T (Titanate)

YF-400 (Titanate) Delayed Available YF-200 YF-200D YF-600-HT (Zirconium delayed)

Ultravis LPW

Ultra Frac Terra Frac

YF-100 YF100D (Delayed) 100 - Borate YF-300 (Titanate) YF-500-HT (Zirconate Delayed)

Hy Vis

Thin prepad with buoyant diverting agent to control upward growth

Invertafrac

Oil prepad with a polymer coated sand diverting agent to control downward and water encroachment

Divertafrac

Versagel Versagel LT Versagel HT Hybor Gel

MY-T-GEL MY-T-GEL LT MY-T-GEL HT Hybor Gel KO Gel Thrifty Gel

Available

Crosslinked HPG with 3-5% hydrocarbon for fluid loss

Terra Frac-D

Stratafrac II Service (Available with most systems)

Ultravis LPW +5% Diesel

Versagel plus Diesel

GDX-7

APOLLO II H SATURN II H

Crosslinked HPG with high temperature stabilizers

Terra Frac RXL II

YF400 YF600-HT

ThermoVis

Versagel HT

GWX-7HT

Saturn Gel

Crosslinked CMHEC

Krystal Frac RXL Krystal Frac Krystal Frac-D (5% Diesel)

HyClean

Kleen Gel

Available

APOLLO IV LPH

July 1999

XL

6-83

Hydraulic Fracturing Theory Manual

6

Fluid Selection and Scheduling

Table 6.11 - Competitive Cross Reference of Similar Additives. Composition

BJ Services

Crosslinked CMHEC for high temperature

Super Krystal Frac

Crosslinked guar or HPG with Borate

Ultra Frac

Dowell Schlumberger

NOWSCO LTD

Halliburton

Smith

Kleen Gel II YF-100 (guar) YF-200 (HPG)

HyVis

Western WZ-100018 Gel

GWX-9 Guar or HPG

VIKING II VIKING II DHT VIKING I VIKING I DHT

PurGel II, &III ACIDGEL Frac ACIDGEL Frac II Versage LT KleenGel, MY-T-GEL LT KlexenGel II Alcogel I MY-T-Oil I, II, &III LOGEL 100 HYGEL 100 & 300

GWX-4LT GWX-4HT

SATURN II LT

Boragel Hybor Gel

CO2 compatible fracturing fluid

Krystal Frac (CMHEC) Super Terra Frac

YFLPH (HPG)

Economical, low residue cross-linked system

Terra Frac T (Low pH system)

YF-LPH

Ultravis LPW

Pur-Gel

WGA-5 GWX-5

APOLLO I

Controllable delayed crosslink HPG system

Terra Frac RXL II

YF-600-HT

Ultravis H-T

Versagel HT & CL-18 Hybor Gel

GWX-7

SATURN II APOLLO II

Controllable delayed crosslinked high temperature system

BJ-Titan RXL SpectraFrac G

YF600-HT (HPG) YF500-HT (Guar)

Thermo-Vis

Thermagel Pur-Gel III (CMHPG)

GWX-7HT

SATURN II APOLLO II

Alcohol Water Systems Gelled water - alcohol system Crosslinked water-alcohol system

Alcogel I & II Alcogel IV Metho Frac (G-8)

Alcohol Waterfrac (J-160)

Ultravis LPW

WZ-100013 Gel

Alcogel II-X

Available

WZ-100013 Gel

Crude Frac

Sandoil

Available

Oil Frac

Oil Systems Oil without viscosifier

Available

Gelled Oil

Oil Based Ultra Frac

Petrogel

Hycar 2000

Viso-O-Frac V-O-Gel

Gelled Oil

Low Friction Frac

Crosslinked gelled oil for medium temperature

Allo Frac

YF-GO III

HLG-1 HLG-5

My-T-Oil II

PGO-1

Maxi-0-74 Gel

Crosslinked gelled oil for higher temperatures

Allo Frac HT

YF-GO IV

My-T-Oil III

PGO-1

Maxi-0-86 HT Gel

Water external emulsion developed by Exxon

Polyemulsion

Super Sand Frac K-1

Super Emulsifrac

WEP-1

Super K-Frac

Continuous crosslinked gelled oil

Hydraulic Fracturing Theory Manual

Polyemulsion

YF-GO III

My-T-Oil IV

6-84

July 1999

References

Table 6.11 - Competitive Cross Reference of Similar Additives. Composition

BJ Services

Dowell Schlumberger

NOWSCO LTD

Halliburton

Smith

Western

Foamed Systems Water and nitrogen foam with or without gel

Aquafoam

Foamfrac Stabilized Foam Soulution (SFS)

Foam Frac

Foamfrac AquaFoam

Foam Frac

West-Foam, N2

Acid and nitrogen foam

Etching foam

Available

Foamed Acid

Available

FAS-1

West-Foam, N2

Hydrocarbon and Nitrogen foam

Available

Available

Foamed Hydrocarbon Frac

N10 Frac

Foamed Oil

Petro Foam

NOWFOAM followed by a gelled fluid

Combo Frac

Methanol and nitrogen foam

Foamed Alcohol

AlcoFoam

Foamed Methanol

Available

Poly-CO2

C-O-TWO Frac Pur-Gel II Pur-Gel III

CDM-1 GWX-4LT GWX-4HT

WestFoam, CO2

Water and CO2 foam

Available

Available

Available

Water and 50% CO2/20% N2

Binary Foam System

Crosslinked gelled water foam

Super foam

Available

GWX-4LT GWS-4HT

Available

WG-19 WG-22a WG-23

WGA-6

J-2, J-4

Water Base Polymers Powdered guar gum polymer. Delayed hydration, designed for batch mix applications. Powdered guar gum polymer. Rapid hydrating, designed for continuous mix applications. Contains internal breaker.

GW-27

J111, J424 J877

GW-5

J133

G-308WB

WG-6

J-4 (no breaker)

J457 Powered Hydroxypropylguar gum. Delayed hydration polymer, designed for batch mix applications. No internal breaker.

GW-32

J347 J362 J456 J876

Powdered hydroxyproplyguar viscosifier. Rapid hydrating, designed for continuous mix applications. Contains internal breaker.

GW-8 GW-30

(80% HPG) J348 (Sea Water)

Powdered hydroxyethylcelluloseviscosifier. Delayed Hydration polymer. Designed for use as a secondary gel or batch mix application.

AG-21R

J164

LSR-1NB

WG-11

WG-12

HEC

J-12 (J-18) J-20

(J-16) J-20 (J-10)

WGA-3

J-6

WG-17

Chemically modified HEC for use in crosslinked fluid. No internal breaker.

WG-21

Powdered hydroxypropylguar for delayed hydration used as a secondary gel in high temperature applications.

HYG-5

July 1999

WGA-2 WGA-8

6-85

Hydraulic Fracturing Theory Manual

6

Fluid Selection and Scheduling

Table 6.11 - Competitive Cross Reference of Similar Additives. Composition

BJ Services

Dowell Schlumberger

Powdered carboxymethylcellulose viscosifier. Rapid hydration, designed for both batch and continuous mix applications.

G25

Powdered carboxymethylhydroxy-ethylcellulose viscosifier. Designed for rapid hydration. Can be used both batch and continuous applications.

GW-28 GW-29 GW-34 GW-36 GW-44

J-365

Powdered xanthate polymer Designed for viscosifying 15% or lower strength hydrochloric acids. Can be batch mixed or mixed continuously.

AG-26

J360 J312

A proprietary blend of chemically modified low residue guar polymers. Delayed hydration mixture designed for batch mix applications. No internal breakers.

NOWSCO LTD

Halliburton

Smith

Western (J-8)

WG-15

J424

J-271

WG-19

G-317

WGA-4

J-13

AGA-1

J-15

WGA-6

J-4

MGA-1

WZ-100313

Chemically modified natural polymer for up to 80% methanol.

GW-20 GW-25 GW-35

Chemically modified natural polymer for gelling 100% methanol

GW-55

LSR-5

WG-20

MGA-1

Available

Chemically modified natural polymer CMHPG

GW-44 GW-36

G-313

WG-18

WGA-5

WZ-499579

Liquid Viscosifier for acid

AG-11

J429-J425

SGA-HT

AGS-1 AGA-1, AGA-2 AGA-4, AGA-5

Acigel

Liquid viscosifier for acid up to 15%

AG-12

J425 (15-28%) M33

SGA

AGS-1 AGA-1 AGA-2 AGA-4 AGA-5

Acigel Lt (low temp)

CMG-1

J-4L

DSGA Liquid

Continuous Mix Gel Concentrates HPG with KCl in aqueous slurry

LGC-I

Guar with KCl in aqueous slurry

LGC-II

HPG without KCl in aqueous slurry

LGC-III

Guar in diesel slurry

LFC-1

LSG

LGC-IV

Guar and Ammonium chloride in diesel slurry HPG in diesel slurry

LGC-IV M LFC-2 LFC-2A LFC-2B

Hydraulic Fracturing Theory Manual

LSG

LGC-V

6-86

J-4L CMG-2

J-20L

July 1999

References

Table 6.11 - Competitive Cross Reference of Similar Additives. Composition CMHPG in diesel slurry

BJ Services

Dowell Schlumberger

NOWSCO LTD

LFC-3

Halliburton LGC-VI

CMHEC in diesel slurry

Smith CMG-3

LGC-VII

Western J-22L Available

Friction Reducers Liquid anionic polyacrylamide friction reducer for water

FRA-12 FRW-11

J313 (Water Brine)

Liquid cationic polyacrylamide friction reducer for acids, brines & fresh water.

FRA-10

J321

F-657

FRC-26LC

WFR-2

FR-28LC

AGA-2, AGA-4 AGA-5, AFR-1

FR-20 FR-28 (Hard Water)

Powdered anionic friction reducer for acid, brines and fresh water.

J166 (Water, Brine)

FR-20

(FR-16) (FR-2, Water)

Powdered cationic friction reducer for acid, brines and fresh water.

J120 (Acid)

FR-30

(FR-6)

Liquid friction reducer for hydro-carbons

J257

F-100

FRO-18 Requires Activator

FR-5 FR-7 Requires Activator

OFR-1

FR-5AW

WAC-9

WFL-2

F-11

WAC-11D

AFL-2

Frac Seal M

Fluid Loss Selectively graded fine mesh silica flour used in water, oil and acid

FLC-8

J84 J418

Silica Flour

Combination of graded oil soluble resin and degradable low mole- cular weight polymers. Non-damaging fluid loss additive used in water and acid

FLC-1

J238

100 mesh benzoic acid used in water, acid or foam fracturing treatments.

FLC-1

J227 (Particulate)

Available

Available

Flakes-DA-3

Available

100 mesh sand used in water, oil and acid

100 mesh sand

FLA100 S100

100 mesh sand

100 mesh sand

100 mesh sand

100 mesh sand

100 mesh oil soluble resin used water and acid

FLC-2

FLA10005

FL-30

OSR-100

AFL-3

FracSeal

100 mesh salt

100 mesh sand

DA-4 AFL-2

100 mesh salt

WAC-10

AFL-4

Aquaseal 2

WAC-12L FLD-1

WFL-4

Aquaseal L

Available

Fluid loss additive for water and oil Proprietary liquid fluid loss solution

FLC-15 FLC-17

J-451

Fluid loss additive used in water and oil (Adomite Aqua)

Adomite Aqua

J110

Adomite Aqua

Adomite Aqua

WFL-1

Available

Fluid loss additive used in oil base fluids (Adomite Mark II)

Adomite Mark II

J126

Adomite Mark II

Adomite Mark II

OFL-1

Adomite Mark II

WLC-4

WFL-3

Aquaseal WS

Fluid loss additive. Powdered fully degradable fluid loss additive for water base fluid used 120 - 350 ° F

July 1999

B1

6-87

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6

Fluid Selection and Scheduling

Table 6.11 - Competitive Cross Reference of Similar Additives. Composition

BJ Services

Dowell Schlumberger

NOWSCO LTD

Halliburton

Fluid Loss Additives - Acid

Liquid fluid loss additives for use in oil wells with water based fluids from 80-300 ° F (diesel or other hydrocarbon)

Smith

Western

AFL-1 AFL-2 AFL-3 AFL-4 WFR-2 Available

Available

Available

Solid fluid loss additive and gel breaker for use in water based fluids at 150-200 ° F.

Available

Available

Available

OPTIFLO C

Breakers Enzyme breaker for guar, guar derivatives and cellulose derivatives

GBW-10

J134

Breaker F

GWV-3 GBW-30

WEB-2

B-11, B-11L

Oxidizer breaker for guar, guar derivatives and cellulose derivatives

GBW-5

J218

Breaker S

SP Breaker

WCB-1

B-5

High temperature oxidizer breaker for guar, guar derivatives and cellulose

GBW-5

Breaker T

HT Breaker

B-9

Acid breaker for guar, guar derivatives and cellulose derivatives

GBA-1

Breaker H

MYF-5

P-4

Low temperature breaker activator for borate systems

GBW-10

Low temperature oil breaker

GBO-1

Breaker for phosphate ester oil gels

GBO-3

J318-J466

J318, YF 60 II J-295 YF60 II III J603 YF60 III

Gel breaker and filter cake degrader. Treatment follows water based fracturing fluids. Used from 80-270 ° F.

B-12

Breaker MO HL Breaker

OXB-3

B-20, B-23

Breaker MO II K34

OXB-3

B-15 B-16 B-25

Breaker VLT

OXB-3

B-20

Breaker VH

OXB-3

B-23

OXB-3

(B-14)

K-34

OXB-3

Sodium Bicarbonate, B-25

Optikleen

Oil breaker - Low Temperature

Y3, M3

Oil breaker - High Temperature Oil breaker

J318 (YF-GO II)

Breaker for phosphate ester gels

WCB-LT

GBO-6

Breaker 3700

J295 (YF-GO II, IV J-603, J860, GO III

Diverting Agents Oil soluble resin in aqueous solution

FLC-11

J237

L-12

Matriseal-0

AFL-1

ASP-530

Graded rock salt

Rock Salt Salt-Trimix

J66

Rock Salt

TBA-110

DA-4

Westblock, S-6

Hydraulic Fracturing Theory Manual

6-88

July 1999

References

Table 6.11 - Competitive Cross Reference of Similar Additives. Composition Flake Benzoic Acid

BJ Services Benzoic Acid Super Flake Regular

Dowell Schlumberger J227A

NOWSCO LTD Benzoic Acid

Nonaqueous solution

Halliburton TLC-80

Smith DA-3

Matriseal - OWG

Polymer coated sand which swells upon water contact

Western Westblock 3X &4 Available

S41 (Divertifrac)

Oil soluble graded napthalene

Moth Balls

J116

TLC-15

Diverting agent used in acid

FLC-18

(Concentrate) (Solution)

Matriseal 0 Matriseal OSR-100 TBA-350 TLC-80 TBA-100 Matriseal OWG TLC-155

Water soluble diverting agent

FLC-18

J363, J175 (Acid & Water), J187 (Fracturing)

TBA-110 TLC-80

Inorganic diverting material which is buoyant

DA-2

J423 (invertafrac)

S-3

Cenospheres

Polymer Plugs Guar or hydroxypropylguar system

Protectozone WL 300, 500

Hydroxyethylcellulose system linear or crosslinked

Protectozone WC 500, 750

Crosslinked hydroxypropylguar system

Protectozone WH 500, 700 (not crosslinked)

P5-Plug

Crosslinked guar or hydroxy-propylguar system

Temblok 80, 90, 100

Gel Block WX

Temblok 75 120

Available

Temblok 40 50, 60

TDA-1, High Friction Gel

Temblok 40 50, 60

Available

Emulsifiers Oil external emulsifier for HCl and HCl-organic mixtures

E

U74 (D.A.D. acid), U60 (Super Sand Frac), U80

DL-22

AF-61

AAE-1

E-9

Emulsifier for polyemulsion

E-2, E-5

U78A (not for diesel)

WS-50

SEM-5 SEM-6 SEM-7

PEM-1

Wellaid 266

Emulsifier for polyemulsion and CO2 emulsion or CO2 foams.

FAW-16

U78E

EF-10

SEM-5, ACO-1 SEM-7 HC-2 AQF-1 AQF-2 AQF-4

(E-15), E-16 PEM-1 FAA-2

Clay Stabilizers

July 1999

6-89

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Fluid Selection and Scheduling

Table 6.11 - Competitive Cross Reference of Similar Additives. Composition

BJ Services

Dowell Schlumberger

Cationic polymer for stabilizing clays

Claytrol5

L53 (W-Winterized) L42

Cationic clay stabilizer

Claytrol 3 Claytrol 4 Claylok SM

M38W

NOWSCO LTD CSA-6

Halliburton

Smith

Western

Cla Sta II Cla Sta 0 Cla Sta FS Cla Sta XP

CCC-3

Claymaster 4

ClayFix II

CCC-4 Claylok Sm

Claylok SM* WK-1 (Multi-use product) LT-22

SuperFlo II

FRS-2 FRS-3 USS-N

Flo Back 10 FS-2

EnWaR-288

FRS-1

(FS-1)

EPS-4, EPS-5 EPS-9, SAA-2, SAA-8

Aqua Flow Nine 40

SAA-5

Aqua Flow

SAA-3

F-Flow, Parasol D Wellaid 215

EPS-4, EPS5, EPS-9, SAA-2 SAA-8

Nine 40, Aqua Flow

SAA-3, SAA-7

LT-5

SAA-3

F-Flow Parasol D, LT-31, Corexit 7652

EPS-4, EPS-5 EPS-9 SAA-2, SAA-8

Aqua Flow LT-17 Nine 40

*All Companies’ have KCl *SM Service Mark of Chevron Research Company

Surfactants Nonionic fluorosurfactant for water and acid systems

Inflow50

F-75N

Cationic fluorosurfactant for water and acid systems

Inflo 45 Inflo 100

TEA-380

WS-70

Nonemulsifiers Nonionic nonemulsifier

W53

Nonionic nonemulsifier for oil

3N, 1N

Anionic nonemulsifier for oil

HD10-60 HD10-70

Nonionic nonemulsifier

Anionic nonemulsifier

F38

J-10

Anionic nonemulsifier for oil and dispersible in water

W31 (Freflow D) K224

Hyflo IV Anionic Nonionic mixture Oil soluble

Nonionic nonemulsifier for water and acid

NE-4 NE-15 NE-18 S100 S200 S400 S600

Hydraulic Fracturing Theory Manual

F40 EZEPlo, W39

W5-6 One

6-90

LOSURF-251 259, 300, 357 Pen-5, LOSURF 0

July 1999

References

Table 6.11 - Competitive Cross Reference of Similar Additives. Composition

BJ Services

Anionic nonemulsifier

NE-10 NE-31 NE-32 S-500

Cationic nonemulsifier for water and acid

NE-1 NE-7 NE-2 NE-6 NE-9 NE-11 NE-12 NE-13 NE-20 NE-21 NE-22

Nonionic fluorosurfactant for water and acid

Inflo50

Nonionic surfactant and nonemulsifier for water and acid

D-4

Dowell Schlumberger F78, M38 W22, W27, W39, M38W

NOWSCO LTD

Halliburton

Smith

Western

DL-22

TRI-S Fracflo II MorFlo II

SAA-3 SAA-7

LT-5, AS-2 LT-25, LT-31, F-Flow, Parasol D

AI-170

Cationic N Compounds

SAA-4 SAA-1 EPS-1 EPS-3 EPS-6

I-5, LT-22 LT-17, WK-1 F-Flow, Parasol D

Superflo

USS-N

FS-2 (FS-F)

Pen-5 Also foaming agent for acid

EPS-4, EPS-5 EPS-9, SAA-8

LT-21

Fracflow, 3N

SAA-7

LT-5, LT-25

USS-N

(FS-F) FS-2

SSS-2

LT-21

LPA-1

(CS-3), MR-1

AS-5, AS-6 AS-7, AS-8

SPS-1

AS-2, LT-31

Caustic Soda

Caustic Soda

Caustic Soda (G-5,G-6)

CW-1

BW-6

Buffer 1

Fumaric Acid

HYG-3

BW-2

Buffer 2

L6 L36

Formic Acid

MYF-2L

Formic Acid

WTI-25 WTI-26

M3

Nowplix 6P

K-35

Sodium Carbonate

Sodium Carbonate, Buffer 4

F75N (nonionic) marketed as Ezeflo F75

F40

Anionic nonemulsifier for water and acid

DL-26

Nonionic fluorosurfactant for water and acid

Fines Suspender Fines suspending agent for acid. Also functions as nonemulsifier

SS-100

Cationic fines suspendor

HC-2

F78

Anti-Sludge Agent Anti-sludge agent for acid

W35 (W50)

DL-22 DL-26

pH Control Strong base

D-2

J465, M2, U28 U28, J-221 (2% caustic)

Caustic Soda

Weak organic acid Weak organic acid Synergistic additive for extending inhibition times at elevated temperature Strong base

July 1999

D-2

6-91

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6

Fluid Selection and Scheduling

Table 6.11 - Competitive Cross Reference of Similar Additives. Composition

BJ Services

Dowell Schlumberger

NOWSCO LTD

Halliburton

Smith

Western

Buffers (proprietary)

BF-1, BF-5 BF-2 BF-3 BF-4

M47

BA-10, BA-20 BA-30 BA-40

BW-1, BW-5 BW-7, BW-10

Buffer 1 Buffer 2 Buffer 4

Strong base

Ammonium Hydroxide 30%, 50%

M11

Ammonium Hydroxide

Ammonium Hydroxide

Ammonium Hydroxide

M-223

K-34

Sodium Bicarbonate

Sodium Bicarbonate

U43

BA-2

Sulfamic

P-4

Powdered weak base Sulfamic Acid

Sulfamic

Crosslinkers Proprietary crosslinking control agent

XLW-3

CLM

Proprietary crosslinking control agent

XLA-Saturn XLD-Saturn

Proprietary crosslinking agent (Sb)

AKXL

MYF-10

WZ-100470

Proprietary crosslinking agent (Ti)

XLW-39

(J352)

ATX-25

CL-11 CL-18

CX-1, CS-91, CS-6

CL-9, T.I.C., CL-12

Proprietary crosslinking agent (Borate)

XLW-1, XLW-2

L10 (Powder)

BXL-1W

CL-22

CS-13 (liquid)

(2-C, Powder), CL-2

Proprietary crosslinking agent Zr

XLW-52

J366, J367 (Activator) J444 (Temp. Activated)

2R-XL

CL-24 CL-15 CL-21 CL-23

CX-7, CX-14 CX11A, CS-15 CX-16

CL-14, CL-14W CL-11

Proprietary crosslinking agent AL

XLW-6

CAX

CL-19

CX-5

Available

HC-2, AQF-1 AQF-2, AQF-4

FAA-1 FAA-2 SNF-1 SNF-4

Foamex, LT-30 Frac Foam 1

Howco Suds

FAA-1, FAA-2 SNF-4, SNF-7

Adofoam BF-1

Pen-5

FAA-1, FAA-2 SNF-4, SNF-1

LT-30

TRI-S

FAA-1 FAA-2

Foamex

Foamers Foaming Agent

FAW-12

F78

Foaming Agent

Adofoam

F52, 1

5F-1

Foaming Agent Foaming agent for water and brine

FAW-16

F52.1 (Water, Brine, Acid)

Foaming agent for water and acids

FAW-9

F78 (Foamer and Fines Suspender)

Foamer for hydrocarbons

FAO-25

Foaming agent for oil and condensates

FAO-25

Hydraulic Fracturing Theory Manual

SF-2

SF-3

6-92

AQF-1, SGA-1, Pen-5

FAA-2

FS-2 (FS-F)

OFA-2

SNF-1

Petro Foam 1

OFA-2

SNF-1

Petro Foam 1

July 1999

References

Table 6.11 - Competitive Cross Reference of Similar Additives. Composition

BJ Services

Dowell Schlumberger

NOWSCO LTD

Halliburton

Smith

Western

Foaming agent for water and methanol

FAW-20

SF-8

ACO-1

SNF-4

Frac Foam 1

Foaming agent for 100% methanol and methanol water mixtures

FAW-20

SF-8

ACO-1

SNF-4

Available

Scale Inhibitors Scale Inhibitor

ScaleTrol 4

L47, L49

P-300

Phosphonate Scale Inhib.

GSI-1

P-9

Scale Inhibitor

ScaleTrol 6

L50

SST-245

Phosphonate Scale Inhib.

GSI-1

P-8

Scale Inhibitor

ScaleTrol 8

L45

Phosphonate LP-60 Scale Inhib.

GSI-1

Ultra Sol II

Scale Inhibitor

X-4

LP-55

GSI-1, GSI-2 GSI-3

P-7

Scale Inhibitor

X-6

Similar to LP-55

GSI-2, GSI-1 GSI-3

P-2, P-3

July 1999

L35

6-93

Hydraulic Fracturing Theory Manual

6

Fluid Selection and Scheduling

Table 6.11 - Competitive Cross Reference of Similar Additives. Composition

BJ Services

Dowell Schlumberger

NOWSCO LTD

Halliburton

Smith

Western

Gel Stabilizer Liquid stabilizer for high temperature

Methanol

K46

Methanol

Methanol, Liquid Gel-Sta

Methanol

Methanol

Powdered stabilizer for high temperatures

GS-1 GS-2 GS-3

J353

GS-1

Gel-Sta

HTS-2 HTS-2

Gel Master

AGD-2

DF-11 AF-11 AF-11L

RFP-1

DF-1

Stabilizer

J59

Defoamer Defoamer for aqueous fluids

D-37L AntiFoamer-1

Defoamer for oil base fluids

D47, (Cold Water)

AFA-Z

J291

Oil Gelling Additives Liquid viscosifier for soap type gels

G-20

U27, U28 & U34

Powdered viscosifier for conventional oil gels

VI-10

G-5, G-6

HYCAR-2000

MO-33, VO-15

G-17 (G-30)

Liquid viscosifier for phosphate ester gels

GO-23,24

J452

HLG-1 HLG-5

MO-55, MO-65

OGA-1 OGA-3 OGA-4

Maxioil Maxioil HT

Liquid activator for phosphate ester gels

GO-53

J453 J602 J601L

HLG-2

MO-56, MO-66, and MO-67

OGA-2

Maxioil Activator

High Temperature oil gelling agent

MO-HT B

Maxioil XHT

Biocides Bactericide

X-Cide 102

M123 (Solid)

X-cide 102W

BCS-2 BCS-3 BCS-4

Frac Cide 10, Frac Cide 2

BE-3

BCS-1

Frac Cide 20

Biocide

X-Cide 207

Bactericide

Adocide

M155

Adocide

Adocide

Adocide

Biocide

Adomall

M76

Adomall

Adomall

Adomall

Biocide

X-cide 207

M-275

BE-4

Frac Cide 2, Frac Cide 20 Dryocide

a. Especially for use in oil base slurry.

Hydraulic Fracturing Theory Manual

6-94

July 1999

References

x40

Fig. 6.36 - Simulator Results of Fluid-Element Time at Temperature vs. Volume Pumped.

Fig. 6.37 - Viscosity vs. Time-at-Temperature for Various Polymer Concentrations. Fluid

Time Range (Min.)

X30

0 - 12 (Use for Temp < Reserv.)

X30+ X40+ X50+ X60+

July 1999

6-95

Hydraulic Fracturing Theory Manual

6

Fluid Selection and Scheduling

Table 6.12 - Selecting Polymer Loading to Achieve Desired Viscosity. Super Gel System

Time, Hours

K'

n'

Viscosity at 170 sec-1

X20

0 .25

.00108 .00017

.95 1.0

40 8

X30

0 .25 5

.00812 .00355 .00376

.85 .95 1.0

180 38 18

X30SGS

0 .25 .5 .75 1.0 1.5

.02262 .00700 .00339 .00188 .00111 .00049

.75 .80 .85 .90 .93 .97

300 120 74 54 37 20

X40SGS

0 .5 1.0 1.5 2.0

.05294 .01146 .00320 .00111 .00051

.65 .75 .85 .93 .97

420 152 71 37 21

X50SGS

0 .5 1 1.5 2 2.5 3 3.5

.06932 .02194 .00905 .00496 .00311 .00240 .00178 .00122

.65 .7 .75 .8 .85 .87 .90 .95

550 225 120 85 69 59 51 45

X60SGS

0 .5 1 1.5 2 2.5 3 3.5

.08823 .03130 .01486 .00875 .00564 .00428 .00342 .00286

.65 .7 .75 .8 .85 .87 .89 .90

700 321 197 150 125 105 93 82

Hydraulic Fracturing Theory Manual

6-96

July 1999

References

Fig. 6.38 - Class Example of Selecting Optimum Fluid for Time at Temperature.

July 1999

6-97

Hydraulic Fracturing Theory Manual

6

Fluid Selection and Scheduling

Fig. 6.39 - Dowell YF-400 Fluids (Sand Laden).

Fig. 6.40 - Halliburton Versagel Fluids (Sand Laden).

Hydraulic Fracturing Theory Manual

6-98

July 1999

References

Fig. 6.41 - Western Company APOLLO II/APOLLO II H Fluids.

Fig. 6.42 - Guidelines for Pad Fluids.

July 1999

6-99

Hydraulic Fracturing Theory Manual

6

Fluid Selection and Scheduling

Fig. 6.43 - Scheduling Example.

Hydraulic Fracturing Theory Manual

6-100

July 1999

References

Stage

M-Gal

PPG

Fluid

Additives

1 2 3 4 5 6 7 8 9 10

July 1999

6-101

Hydraulic Fracturing Theory Manual

6

Fluid Selection and Scheduling

Hydraulic Fracturing Theory Manual

6-102

July 1999

Chapter

7

Proppants and Fracture Conductivity

7.1 Overview The selection of a proppant for use in hydraulic fracturing is an economic decision requiring technical input. The purpose of this chapter is to provide the engineer with the technical capabilities to make good economic decisions with respect to fracture design. This chapter is broken into several sections. First, the sources of the available fracture sands and commercial proppants are discussed. In addition, the size and quality of these materials is reviewed to provide the engineer with the technical information required to make proppant decisions for fracture design. Next, the critical factors which affect fracture conductivity are reviewed. Factors such as closure stress, size, concentration, strength, shape, and gel residue effects can impact fracture conductivity and ultimately, well performance. Finally, the economic aspects of proppants and/or fracture conductivity will be reviewed.

March 1995

7-1

Hydraulic Fracturing Theory Manual

7

Proppants and Fracture Conductivity

7.2 Introduction Historically, fracture stimulations have been performed for two reasons; to overcome the detrimental effects of wellbore damage and/or to stimulate the well’s performance. The former reason has been typically applied to wells in moderate to high permeability reservoirs and generally resulted in the creation of short fractures. The latter generally resulted in the creation of long fractures in wells in low permeability reservoirs. The success or failure of fracturing in either case depended on whether or not the created fracture had adequate flow capacity so that the reservoir fluids flowed to the fracture and then to the wellbore.1,2 If the flow capacity of the fracture was large by comparison to the reservoir flow capacity, tremendous performance improvements would be realized. The purpose of the proppant is to keep the walls of the fracture propped apart so that a conductive path to the wellbore is retained after pumping has stopped and fluid pressure has dropped below that required to hold the fracture open. Ideally, the proppant will provide large enough flow capacity to make negligible pressure losses in the fracture during fluid production. In practice, this ideal might not be achieved because the selection of a proppant involves many compromises imposed by economic and practical considerations. The propped fracture must have a conductivity at least high enough to eliminate most of the radial flow path that exists in an unfractured well and to allow linear flow from the reservoir into the fracture. This requires relatively unimpeded linear flow within the fracture to the wellbore. To accomplish this, the proppant must enable the propped fracture to have a permeability several orders of magnitude larger than that of the reservoir rock.

Hydraulic Fracturing Theory Manual

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March 1995

Effect of Fracture Conductivity on Well Productivity

7.3 Effect of Fracture Conductivity on Well Productivity Historically, steady state performance predictions have been used by the industry to determine the effect of fracture conductivity on well productivity. However, there are limitations to the steady state analysis of fracturing which must be considered. One such limitation is that steady state analyses exclude the economic benefits of unsteady state flow, rate acceleration, and the time value of money. In addition, the effective wellbore radius concept is used in the steady state analysis, therefore, the analysis is subject to the limitations of this concept. However, steady state techniques of Prats provide a useful method of comparing the impact of fracture conductivity on the fracturing process.

Steady State Folds of Increase

Figure 7.1 is a plot of steady state folds of increase versus fracture half length for a 40 acre drainage area. This plot shows the productivity improvement associated with a 1000 md-ft fracture versus an unstimulated well in a reservoir with permeabilities of 1 and 10 md. This figure clearly indicates that there is no economic benefit associated with increasing fracture length beyond one hundred feet in a 10 md reservoir while in a 1 md reservoir there is some economic benefit associated with an increased fracture length. Figures 7.2 and 7.3 show similar plots for 2000 md-ft and 3000 md-ft fractures, respectively. Analysis of these figures indicates that, for any fracture length, increases in fracture conductivity result in increased productivity. In a 10 md reservoir, for example, a productivity improvement of 2.2 could be realized by creating a fracture of half length 100 ft and conductivity of 1000 md-ft. A 2.6-fold increase could be realized by creating a fracture of the same length with a 2000 md-ft conductivity. Creation of a 3000 md-ft fracture would result in a 2.7 fold production increase over an unstimulated well. Thus, increasing fracture conductivity from 1000 md-ft to 3000 md-ft would result in an additional 23% production increase without significantly increasing the treatment cost. It is this concept that underlies the importance of fracture conductivity to fracturing. Performance improvements can be realized by improving conductivity at little or not cost.

Fig. 7.1 March 1995

7-3

Hydraulic Fracturing Theory Manual

Proppants and Fracture Conductivity

Steady State Folds of Increase

7

Steady State Folds of Increase

Fig. 7.2

Fig. 7.3

Hydraulic Fracturing Theory Manual

7-4

March 1995

Commercial Proppants

7.4 Commercial Proppants Historical Perspective One of the first proppants used in the early days of hydraulic fracturing during the late 1940s was sand dredged from the Arkansas River. Initially, the sand was not cleaned and screened as today’s standards require, but as the need became evident, steps were taken to process the sand more thoroughly. During the mid-1950s, sand from the Saint Peter sandstone formation near Ottawa, Illinois, entered the market. As the need for a more economical and readily available fracturing sand grew, mines were opened near Brady, Texas, in 1958, and production from the Hickory sandstone formation began to be marketed. This sand, as well as most other high-quality sand used today, is mined from consolidated sandstone formations. The mining process includes crushing, screening, and washing to separate the sandstone matrix into its individual sand grains. A wide range of particle sizes is found in the deposits. Typically, only 20 to 30% of such deposits is found to be in a size range useful for hydraulic fracturing applications. The explosive growth of the hydraulic fracturing industry from the mid-1970s to the early 1980s created shortages of fracturing sand. Supplies from the Saint Peter sandstone of Illinois were supplemented by high-quality material from the Jordan, Ironton, and Galesville sandstones of Minnesota and Wisconsin. Similarly, sand from the Bidahochi formation in Arizona and aeolian dune sand of Colorado augmented proppant production from the Hickory sandstone in Texas. Finally, new sand-processing plants were constructed in Minnesota and Wisconsin specifically to produce fracturing sand and to replace plants designed to supply sand for other applications. Table 7.1 highlights general information on available fracturing proppants. Figure 7.4 shows a plot of permeability versus stress for various 20/40 mesh proppants. As shown, the intermediate and high strength proppants generally have greater retained permeabilities at higher stress levels than the sands. The subsequent sections will describe the physical properties of commercially available proppants with the importance of these properties described in more detail in Section 7.5. Commercial Fracturing Sand Brady-Type Sand This rounded quartz sand, also known as brown or Texas sand, is mined from the Hickory sandstone in central Texas near the town of Brady. The Hickory sandstone was deposited during the Upper Cambrian Age some 500 million years ago. The color of this sand results from small amounts of iron oxide contamination in the crystal structure. Color variation has no bearing on the strength of this sand or on any other sand discussed here. As mined, the sand is polycrystalline; i. e., each whole grain is composed of more than one quartz crystal bonded together, leaving cleavage planes in the whole grain. In terms of fines generated, March 1995

7-5

Hydraulic Fracturing Theory Manual

7

Proppants and Fracture Conductivity

Fig. 7.4 - Plot of all Proppants and Stress.

Hydraulic Fracturing Theory Manual

7-6

March 1995

Commercial Proppants

the API crush resistance test typically yields from <50 to as much as 85% of the API permissible fines. The deposit yields acceptable fracturing sand in the 20/40 mesh size range and larger. Production in sizes smaller than 20/40 mesh is not sized to meet API recommendations. Typical physical properties, fracture permeability, and pack-width data for this sand are presented in Table 7.1. Table 7.1 Typical Physical Properties of Brady-Type Fracturing Sand* API Mesh Size API Property Particle diameter range, µm

Recommended Limits Standard

6/12**

8/16

12/20

16/30

20/40

3350 to 1700

2360 to 1180

1700 to 850

1180 to 600

850 to 425

Sieve analysis, wt% retained Top sieve Between primary sieves Second and sixth sieves Pan

0.0 95.7 4.2 0.1

0.0 93.1 6.6 0.3

0.0 91.0 8.5 0.5

0.0 98.5 1.0 0.5

0.1 91.6 8.0 0.4

100.0

100.0

100.0

100.0

100.0

0.6 minimum 0.6 minimum

0.7 0.7

0.7 0.7

0.7 0.8

0.7 0.8

0.6 0.7

3.0 maximum

0.4

1.0

1.0

0.8

0.8

20 17.9 2000 22.1 95.5 <1.0

95 13.4 2000 22.1 98.0 <1.0

120 15.5 3000 22.1 99.9 <1.0

45 8.3 3000 22.1 101.1 0.0

115 11.4 4000 22.1 100.5 0.0

0.1 maximum 90.0 minimum 1.0 maximum

Total Krumbein shape factor Roundness Sphericity 12/3 HCI/HF solubility, 30 minutes at 150° F, wt% Silt and fine particle, FTU† Crush resistance, % fines generated at closure stress, psi Particle density, lbm/gal 3 Bulk density, lbm/ft Clustering, wt%

250 maximum Variable with size 22.11 maximum 105.0 maximum 1.0 maximum

* All tests performed according to Reference 11 or 12. Sources include Saint Peter, Jordan, Galesville, and Ironton sandstones. Values shown are averages of multiple production samples over a 4-year period. ** Available in limited quantities on special order only. † FTU = formazine turbidity units.

The Bidahochi formation sand is mined from shallow, lightly consolidated lenses in eastern Arizona. It was deposited during the Pliocene or Tertiary Age some 6 million years ago. This sand contains grains of chert, which is stronger than quartz, along with rose and smoky quartz. Fracturing sand from this formation is available in limited quantities in 12/20, 20/40, and 40/70 mesh only. The aeolian dune sand is mined in central Colorado from shallow, lightly consolidated lenses. This sand was deposited during the Holocene Age less that 1 million years ago. The large sizes, 6/12 through 12/20 mesh, are as high in quality as those from the Hickory formation, but the small sizes, 16/30 through 70/140 mesh, contain so much feldspar that they produce excessive fines in the API crush resistance test.

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Ottawa-Type Sand This well-rounded, very pure quartz sand exceeds API recommendations. In terms of fines generated, the API crush resistance test typically yields less than half of the maximum acceptable fines on this sand. The sand also is monocrystalline. Crushed particles are primarily large chipped grains rather than individual quartz crystals. Color variation is widespread in this sand, but has no impact on its performance characteristics as a proppant. For the most part, the sand is well processed and of high quality for fracturing applications. Typical physical properties, permeability, and packwidth data of this sand are presented in Table 7.2. Table 7.2 Typical Physical Properties of Ottawa-Type Fracturing Sand* API Mesh Size API Property Particle diameter range, µm

Recommended Limits Standard

12/20**

16/30

20/40

30/50

40/70

70/140

1700 to 850

1180 to 600

850 to 425

600 to 300

425 to 212

212 to 160

Sieve analysis, wt% retained Top sieve Between primary sieves Second and sixth sieves Pan

0.1 maximum 90.0 minimum

0.0 93.2 6.6 0.2

0.0 97.9 2.1 0.0

0.0 91.5 8.0 0.5

0.0 93.1 6.5 0.4

0.1 91.8 7.6 0.6

0.1 90.0 9.1 0.8

100.0

100.0

100.0

100.0

100.0

100.0

0.6 minimum 0.6 minimum

0.7 0.7

0.7 0.7

0.7 0.8

0.7 0.8

0.7 0.7

0.6 0.7

3.0 maximum

1.5

1.0

1.0

0.9

1.2

2.5

68 5.4 3000 22.1 95.5 0.0

110 1.6 3000 22.1 98.6 0.0

80 4.0 4000 22.1 102.7 0.0

60 3.3 4000 22.1 103.0 0.0

40 3.4 5000 22.1 102.7 0.0

130 2.5 5000 22.1 103.0 0.0

1.0 maximum

Total Krumbein shape factor Roundness Sphericity 12/3 HCI/HF solubility, 30 minutes at 150° F, wt% Silt and fine particle, FTU Crush resistance, % fines generated at closure stress, psi Particle density, lbm/gal 3 Bulk density, lbm/ft Clustering, wt%

250 maximum Variable with size 22.11 maximum 105.0 maximum 1.0 maximum

* All tests performed according to Reference 11 or 12. Sources include Saint Peter, Jordan, Galesville, and Ironton sandstones. Values shown are averages of multiple production samples over a 4-year period. ** Available in limited quantities on special order only.

The Saint Peter sandstone, commonly known as Ottawa sand, was deposited in the Ottawa district of Illinois during the Middle Ordovician Age some 460 million years ago. This sand is available in 20/40 mesh and smaller sizes only. Color variation runs from white through gray-white to pale yellow. The Jordan sandstone was deposited in south central Minnesota and western Wisconsin during the Upper Cambrian Age some 500 million years ago. Jordan fracturing sand is available only in

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Commercial Proppants

12/20 mesh and smaller sizes. The color varies from white through gray-white to pale yellow to brown. The Galesville and Ironton sandstones were deposited in south central Minnesota and western Wisconsin during the Upper Cambrian Age some 500 million years ago. Ironton fracturing sand is available in 12/20 mesh and smaller; the Galesville sand is available in 20/40 mesh and smaller sizes only. Its color varies from white to light tan. Efforts to Improve on Fracturing Sand Because of the well-recognized limitations of fracturing sand, especially at high stress levels, efforts have been made to find a different proppant with improved performance characteristics. Many of the deficiencies of sand relate to its brittle failure from point loading under high stress levels. Likewise, much effort has concentrated on materials as iron shot, aluminum pellets, quenched-glass beads, walnut hulls, plastic beads, and a vast array of high-strength and deformable particles were manufactured in the 1960s and evaluated as potential proppants. With the single exception of glass beads, none survived until the early 1970s because each of these proppants failed to achieve the desired results in actual field applications. With the drilling of deeper wells, the shortcomings of glass beads and quartzitic materials as proppants became apparent. Such materials are weakened by hot formation brines and tend to fail catastrophically under high closure stress. These factors accelerated the search for improved materials, and in the mid-1970s, a high-strength ceramic proppant, sintered bauxite, was introduced. The inertness and strength of sintered bauxite are caused by its major constituent, corundum, a form of aluminum oxide. Although expensive, sintered bauxite retains permeability under very high stress and severe reservoir conditions better than any other proppant available today. The expense of sintered bauxite motivated efforts to find less costly, but useful substitutes. Under development at the same time as sintered bauxite, curable resin-coated sand was the first such product to find application. Research and development on other ceramic proppants during the early 1980s produced a less expensive proppant containing mullite, another form of aluminum oxide, in addition to corundum. It has helped to bridge the cost-performance gap between sand and bauxite. Because of its lower cost and high performance, this material has enjoyed widespread use since its introduction. Improved Commercial Proppants Sintered Bauxite As previously described, sintered bauxite is an inert, high-strength ceramic proppant. Patented by Cooke et al., this high-density proppant is produced by the same manufacturing techniques as refractory ceramics and metal-working abrasive grits. The raw material is primarily high-alumina bauxite ore from South America. The ore is first ground to a particle size less than 15 µm, shaped into small ceramic pellets using water and a binder, and, after drying and screening, fired in a kiln March 1995

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to bind the edges of the individual particles that make up each pellet. After the sintering process, the color of the product varies from black to brown or gray. Typical physical properties, pack permeability, and width data for this proppant are presented in Table 7.3. Table 7.3 Typical Physical Properties of Sintered Bauxite - High-Strength, Sintered Ceramic Proppant17* API Mesh Size API Property Particle diameter range, µm

Recommended Limits Standard

12/20

16/20

20/40

40/70

1700 to 850

1180 to 600

850 to 425

452 to 212

Sieve analysis, wt% retained Top sieve Between primary sieves Second and sixth sieves Pan

0.1 maximum 90.0 minimum

0.0 96.3 3.7 0.0

0.0 95.3 4.7 0.0

0.0 94.0 6.0 0.0

0.0 95.4 4.6 0.0

100.0

100.0

100.0

100.0

0.7 minimum 0.7 minimum

0.8 0.9

0.8 0.9

0.8 0.9

0.8 0.9

7.5 maximum

2.0

2.0

2.0

2.0

250 maximum Variable with size and stress

80

100

100

120

5.4 10.6 16.8 22.5 30.88 140.0 <1.0

6.4 12.2 18.0 23.2 30.88 140.0 0.0

2.6 4.3 6.8 10.7 30.88 140.0 0.0

1.7 3.0 5.2 7.3 30.88 140.0 0.0

1.0 maximum

Total Krumbein shape factor Roundness Sphericity 12/3 HCI/HF solubility, 30 minutes at 150° F, wt% Silt and fine particle, FTU Crush resistance, % fines generated at 7500 psi at 10,000 psi at 12,500 psi at 15,000 psi Particle density, lbm/gal 3 Bulk density, lbm/ft Clustering, wt%

28.4 maximum 140.0 maximum 1.0 maximum

* All tests performed according to Reference 11 or 12. Values shown are averages of multiple production samples over a 4-year period.

Sintered bauxite draws its strength from the unique manufacturing process and from the materials present in the bauxite ore. Corundum, the major component of sintered bauxite, is one of the hardest materials known to man. It measures 9 on Moh’s hardness scale. For comparison, quartz is 7 and diamond is 10. When crushed, bauxite does not shatter as completely as the sands; it simply splits into large pieces that are still capable of providing flow capacity. This crush resistance is caused partially by sintered bauxite’s elastic properties, which allow slight deformation before failure under high stresses. The first sintered bauxite proppants were angular in shape, which could cause increased abrasion and failure of pumping equipment, treating lines, wellhead equipment, and chokes. Process improvements have produced a material with roundness and sphericity values better than the best fracturing sand and, thus, less abrasive than its predecessor. This proppant has become the standard against which all other proppants are measured.

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Commercial Proppants

Intermediate-Density Proppant Even though this material is often called “intermediate-strength proppant,” a more appropriate term is “intermediate-density proppant (IDP).” The strength of this type of proppant is much closer to that of sintered bauxite than to sand. While neither as strong nor as inert as sintered bauxite, this material has an advantage over sintered bauxite in that it has a lower density (approaching that of sand) than bauxite. The moderate density of these proppants makes them easier to transport and place in the fracture than the denser sintered bauxite. The search for a more economical replacement of sintered bauxite revealed that high-alumina, domestic bauxitic ores could be used to produce a high-performance, sintered proppant with properties approaching those of sintered bauxite. In addition to corundum, this proppant contains mullite, a less-dense mixed form of aluminum oxide. The result is a dark brown to tan proppant of lower bulk density and lower specific gravity than bauxite. This new material is produced by manufacturing techniques similar to those used for sintered bauxite. Typical physical properties, pack permeability, and width data for this proppant are presented in Table 7.4. Table 7.4 Typical Physical Properties of High-Strength, Intermediate-Density, Sintered Ceramic Proppant17* API Mesh Size API Property Particle diameter range, µm

Recommended Limits Standard

12/20

16/20

20/40

40/70**

1700 to 850

1180 to 600

850 to 425

452 to 212

Sieve analysis, wt% retained Top sieve Between primary sieves Second and sixth sieves Pan

0.1 maximum 90.0 minimum

0.0 98.0 2.0 0.0

0.0 92.4 7.6 0.0

0.0 93.7 6.3 0.0

0.0 95.2 4.8 0.0

100.0

100.0

100.0

100.0

0.7 minimum 0.7 minimum

0.8 0.8

0.8 0.8

0.8 0.9

0.7 0.9

7.5 maximum

4.5

4.8

6.2

5.0

250 maximum Variable with size and stress

100

100

100

120

6.4 13.6 19.3 26.9 26.29 113.0 <1.0

10.3 19.4 27.4 33.9 25.95 107.0 <1.0

3.2 6.0 9.8 14.3 25.62 106.0 <1.0

1.4 2.7 4.6 7.4 26.12 113.0 <1.0

1.0 maximum

Total Krumbein shape factor Roundness Sphericity 12/3 HCI/HF solubility, 30 minutes at 150° F, wt% Silt and fine particle, FTU Crush resistance, % fines generated at 7500 psi at 10,000 psi at 12,500 psi at 15,000 psi Particle density, lbm/gal 3 Bulk density, lbm/ft Clustering, wt%

28.4 maximum 114.0 maximum 1.0 maximum

* All tests performed according to Reference 11 or 12. Values shown are averages of multiple production samples over a 4-year period. ** Currently available in limited quantities on special order only.

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While the durability and strength of intermediate-density proppant are somewhat less than those of sintered bauxite, performance is virtually equivalent in all but the deepest and hottest wells. At high stress levels, the proppant breaks into large particles capable of providing good flow capacity. The proppant particles have good resistance to corrosion by hot formation brines; their roundness and sphericity are better than those of the best fracturing sands, while their bulk density is only slightly higher. Despite higher cost, intermediate-density proppants may replace sand at intermediate well depths because of their improved performance. Within the next few years a variety of sources may be developed to make this material widely available at lower costs. Resin-Coated Proppants The most commonly available resin-coated proppants are resin-coated sands. These low-density, intermediate-strength proppants are available in two forms: curable and precured resin-coated Ottawa-type fracturing sands. Both are manufactured by a process similar to that used to produce coated sand for the foundry industry. Curable resin-coated sand was originally patented by Graham et al., for use in gravel-packing operations. Precured resin-coated sand became available in 1982, about 7 years after the first curable product was used in fracturing operations. The emergence of a high-quality, curable resin-coated sand, along with the availability of a precured type, has led to a wide variety of fracturing applications. Although this proppant is not as strong nor as tough as the ceramic proppants, it is a significant improvement over uncoated sand. The plastic coating distributes point loads over a wider area on the sand grain and retards brittle failure. As such, the product is useful at higher stress levels (e. g., in deeper wells) than conventional fracturing sand. The major application of the curable resin-coated sand is as a tail-in material to retain the sand in producing zones that will not retain ordinary fracturing sand. The curable coating bonds the sand grains together after they are in place in the fracture. This in-situ consolidation often prevents proppant flowback, subsequent productivity loss, and damage to well equipment. Because of the consolidated nature of the proppant pack formed with resin-coated sand, compressive or tensile strength is often used as the critical physical property to describe resin-coated sand rather than its crush resistance. Typical physical properties, pack permeabilities, and width data for curable resincoated sand are presented in Table 7.5.. A curable resin coating can also be applied to proppants other than sand, and such materials as sintered bauxite, intermediate-density proppant, and zirconia have all been coated and used in fracturing treatments. The use of a curable resin coating in these applications is largely the same as with sand - to prevent proppant flowback. The major application of precured resin-coated sand is to enhance the performance of sand at high stress levels. This proppant is produced by heat curing the coating during the manufacturing process rather than allowing curing to occur after the resin-coated sand has been pumped into place.

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Commercial Proppants

Table 7.5 Typical Physical Properties of Curable Resin-Coated Sand - Low-Density, Intermediate-Strength Proppant17* API Mesh Size API Property Particle diameter range, µm

Recommended Limits Standard

12/20**

16/30

20/40

1700 to 850

1180 to 600

850 to 425

Sieve analysis, wt% retained Top sieve Between primary sieves Second and sixth sieves Pan

0.1 maximum 90.0 minimum

0.0 95.5 4.3 0.2

0.0 98.0 2.0 0.0

0.0 94.4 5.6 0.0

100.0

100.0

100.0

0.7 minimum 0.7 minimum

0.8 0.9

0.8 0.9

0.8 0.8

7.5 maximum

0.5

0.6

0.5

Variable with size

1400

2000

2800

Variable with size 3.6 to 4.4 98.0 minimum 0.5 maximum 21.7 maximum 100.0 maximum 0.5 maximum

180.0 3.7 99.5 0.2 21.3 96.0 <1.0

220.0 4.0 99.0 0.3 21.2 95.5 <1.0

270.0 3.8 98.5 0.2 21.3 96.0 <1.0

1.0 maximum

Total Krumbein shape factor Roundness Sphericity 12/3 HCI/HF solubility, wt% 30 minutes at 150° F, wt% Compressive strength, after 100 hours at 195°F, psi Tensile strength after 3 minutes at 450°F, psi Resin content, wt% Coating Continuity, count % Uncoated particles, wt% Particle density, lbm/gal 3 Bulk density, lbm/ft Clustering, wt%

* All tests performed according to Reference 11 or 12. Values shown are averages of multiple production samples over a 4-year period. ** Currently available in limited quantities on special order only.

The resin coating also encapsulates the sand grains, thus, preventing the migration of crushed fines during fluid production. It has also been shown to be resistant to destruction by hot formation brines and crude oils at temperatures up to 300°F [150°C]. At low stress levels, the performance of this material is not materially different from that of sand. At higher stress levels, however, performance of the resin-coated sand is improved considerably over the original uncoated sand. Table 7.6 shows typical physical properties of this material.

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Table 7.6 Typical Physical Properties of Precured Resin-Coated Fracturing Sand Low-Density, Intermediate-Strength Proppant17* API Mesh Size API Property Particle diameter range, µm

Recommended Limits Standard

12/20**

16/30

20/40

1700 to 850

1180 to 600

850 to 425

Sieve analysis, wt% retained Top sieve Between primary sieves Second and sixth sieves Pan

0.1 maximum 90.0 minimum

0.0 96.4 3.5 0.0

0.0 98.0 2.0 0.0

0.0 93.7 6.3 0.0

100.0

100.0

100.0

0.7 minimum 0.7 minimum

0.8 0.9

0.8 0.9

0.8 0.9

30 minutes at 150° F, wt%

7.5 maximum

0.3

0.3

0.4

Silt and fine particle, FTU Crush resistance, % fines generated at 7500 psi at 10,000 psi at 12,500 psi at 15,000 psi Resin content, wt% Coating Continuity, count % Uncoated particles, wt% Particle density, lbm/gal 3 Bulk density, lbm/ft Clustering, wt%

250 maximum

40

40

50

----11.2 --------3.7 99.5 0.2 21.2 97.4 <1.0

3.0 7.0 24.3 39.6 3.9 99.0 0.3 21.3 98.0 <1.0

0.8 3.0 7.2 11.2 4.2 99.7 0.2 21.3 98.6 <1.0

1.0 maximum

Total Krumbein shape factor Roundness Sphericity 12/3 HCI/HF solubility,

Variable with size and stress

3.6 to 4.4 98.0 minimum 0.5 maximum 21.7 maximum 100.0 maximum 1.0 maximum

* All tests performed according to Reference 11 or 12. Values shown are averages of multiple production samples over a 4-year period. ** Currently available in limited quantities on special order only.

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Factors Affecting Fracture Conductivity

7.5 Factors Affecting Fracture Conductivity This section discusses five factors that significantly affect the fracture flow capacity developed with proppants used in hydraulic fracturing. These factors can be readily evaluated in the laboratory, and their effect on fracture conductivity is relatively well established. Other factors to be discussed later, have not been evaluated routinely; therefore, their effects are less well known. Closure Stress The stress transmitted from the earth to the proppant during fracture closure causes crushing of the proppant, reducing particle size and increasing surface area of the proppant, both of which reduce permeability of the propped fracture. In addition to crushing, the stress applied to the proppant pack serves to compact the particle bed, to reduce its porosity, and to reduce its permeability further. The last effect occurs even at relatively low stress levels when breakage is not important. Cycling of stress, as would occur with periodic shut-ins of a well, also reduces fracture conductivity irreversibly. Closure stress may also cause proppant particles to embed into the walls of a soft formation, thus, decreasing fracture width and conductivity further. An example of how closure stress affects permeability of different proppant materials can be seen by comparing the permeability data for sand to sintered bauxite. Figure 7.5 shows a plot of permeability versus stress for 20/40 mesh Hickory sand and Bauxite. As shown, Bauxite is clearly less affected than sand within the stress levels tested. The stress a proppant sees will depend on the overburden stress, the reservoir pressure, the bottomhole flowing pressure, the ability of the vertical stress to be transmitted to the horizontal direction (related to Poisson’s ratio), tectonic stress (such as nearby mountain ranges) and to some extent, the fracture geometry (usually a small contribution). A prefrac well test called a “stress test” is the best method of estimating the stress on proppant. Or it can be estimated by the following equation: Stress = k ( OB – Pr ) + Pr – Pf + Pt where k = ratio of horizontal stress to vertical stress (k = (r/1-r)), OB = overburden stress (approximately 1 psi/ft of depth), Pr = reservoir pressure, Pf = fluid pressure in the fracture and Pt = stress due to tectonics (usually unknown and omitted). A few observations can be made by studying this equation. First, as the reservoir pressure is depleted, the stress on the proppant decreases. Second, as the well is drawn down further (Pf becomes smaller at the wellbore), the stress on the proppant will increase. Also, since Pf increases as one moves down the fracture (away from the wellbore), the maximum stress that a proppant will see is early in the life of a well near the wellbore, assuming Pf does not change with time. Proppant Particle Size The permeability of a proppant is controlled largely by the proppant particle size, as can be seen in Figure 7.6. This figure shows a plot of permeability versus stress for 20/40, 16/30, 12/20, and March 1995

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Fig. 7.5 - 20/40 Mesh Hickory versus Sintered Bauxite.

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Factors Affecting Fracture Conductivity

8/16 Hickory sand. As shown, the larger mesh proppants - e. g., 8/16 mesh - provide a greater conductivity at lower stress levels than the more commonly used smaller sizes, such as 20/40 mesh. As stress levels increase and particles are crushed, these differences in conductivity decrease because particle size distribution, porosity, and surface areas become similar despite initial particle-size differences. At this point, other factors often play a more dominating role in proppant size selection than conductivity considerations. Consideration of proppant size is important in the design of fracturing treatments because a minimum fracture width is needed to allow the proppant to enter the fracture. The generally accepted values for this so-called admittance criterion require fracture widths in the range of two to three times the largest grain diameter. An admittance criterion based on twice the largest grain diameter requires fracture widths of 0.187, 0.066, and 0.033 in. for 8/16, 20/40, and 40/70 mesh proppants, respectively. The largest of these values may be difficult to achieve in very deep wells with formations having high bottomhole fracturing pressures and usually requires the use of smaller proppant for successful completion of the fracturing treatment. Additionally, it should be thoroughly understood that proppant transport must be considered during the selection of the size of the propping agent. Even though a 12/20 mesh proppant may be much more conductive than a 20/40 mesh proppant, the smaller proppant is much easier to transport deeply into a fracture than the larger proppant. Proppant Concentration The term “proppant concentration” refers to the amount of proppant per unit area of fracture wall (measured on one side only). In customary units, it is expressed in pounds of proppant per square foot of one wall of the fracture. If proppant settles to the bottom of a vertical fracture as it enters, the concentration will be determined by the width of the fracture at the time of entry (i. e., during pumping). If the proppant is suspended in the fracturing fluid until the fracture closes, concentration will be determined by both the width during pumping and the concentration of proppant in the fluid. Fracture conductivity increases with increasing concentration of proppant in the fracture. Figure 7.7 shows a plot of fracture conductivity versus proppant concentration developed for 20/40 Ottawa sand at an in-situ stress of 5000 psi. Proppant Strength The strength of proppants is of major concern in the design of propped fractures. Historically, this strength has been expressed in terms of the load required to crush a single grain of proppant divided by the diameter squared of its contact area at the point of crushing. Another test, the API crush resistance test, was designed to determine the relative strength of proppants in packs and has been tested and adopted by API for testing sands to be used in hydraulic

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Proppants and Fracture Conductivity

Fig. 7.6 - 20/40, 16/30, 12/20, 8/16 HIckory.

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Fig. 7.7 - 20/40 Ottawa Showing Effect of Concentration on Conductivity.

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fracturing. The API test uses an apparatus for imposing a sustained load on a proppant pack. The degree of size reduction sustained by the proppant is taken as an inverse measure of proppant strength. The API crush resistance test is a more complex measure of strength than that described above for single particles. The values obtained are influenced by grain shape, particle-size distribution, packing arrangement, and other attributes of the particle pack. Although these factors are thought to make the test more representative of proppant performance under field conditions than the singleparticle test, sensitivity of the measurement to several pack attributes makes the test more difficult to reproduce, and small variations in results (e. g., 2 or 3%) are considered insignificant in critical comparisons. Figure 7.8 shows the relationship of closure stress to flow capacity of various proppants, which is determined primarily by proppant strength. This figure shows that Hickory sand has greater permeability at low stress compared to Ottawa sand. This effect results from the fact that Hickory sand has a larger sand distribution (20/30 mesh particles predominate) as compared to Jordan sand, as well as the fact that Hickory sand is more angular. These attributes result in Hickory sand providing greater permeability than Jordan sand up to nearly 5000 psi stress.

Effect of Proppant Type on Flow Capacity Sintered Bauxite

1,000 600 400

Intermediate Density Sintered Ceramic Proppant Zirconia

Permeability, ko, darcy

Sintered Bauxiye

200 100 60 40 20 10 6 4

Frac Sand Ottawa Type

Precured ResinCoated Sand

Frac Sand Brady Type

2 1 0

4 2 6 8 10 12 Closure Stress, psi in 1000's

14

Fig. 7.8 - All Proppants (non-Ultrafrac).

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Factors Affecting Fracture Conductivity

Above 5000 psi [34.5 MPa] closure stress, some of the largest grains break into smaller particles. Thus, at higher stresses, Ottawa sand, which had not broken as much as Brady sand, is seen to have the higher proppant-pack permeability. While the conductivity measurements on which these results are based are very sensitive to proppant-pack attributes and difficult to reproduce, the comparison cited is from measurements made in the same laboratory and therefore are as comparable as current measurement techniques permit. Proppant Grain Shape Roundness and sphericity are proppant particle properties that affect performance. Their importance depends somewhat on the stress level at which the proppant is to be used. Because the surface stresses are more uniform, a well-rounded, spherical particle is capable of carrying higher loads without crushing than a less-rounded particle. Therefore, at high stress levels, a high degree of roundness and sphericity contribute to higher proppant particle does not pack as well as a well-rounded particle and, thus, has more porosity and correspondingly greater permeability. An example of this phenomenon was described previously. Hickory sand, which is somewhat more angular than Ottawa sand, has slightly better flow capacity below about 5000 psi [34.5 MPa] than Ottawa sand, although the more rounded Ottawa sand is superior in proppantpack permeability at higher stress levels.

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Proppants and Fracture Conductivity

7.6 Other Factors Affecting Fracture Conductivity This section discusses five additional factors which typically have an adverse effect on fracture conductivity. The full effect of these factors on future treatment design is yet to be determined. Embedment If proppant particles penetrate the walls of the fracture, the effective width of the fracture, and thereby the conductivity, is decreased. Not only is the width of the fracture decreased by embedment, but fine particles are generated by failure of the formation rock. These fine particles may also contribute to the loss of fracture conductivity. An attempt to assess the severity of embedment has been made by ball-point penetrometer tests of formation rock. These tests are not as important as was earlier thought because in most modern fracture designs the proppant pack is many particles thick in the fracture. The intrusion of the proppant into the fracture wall represents only a small fraction of the proppant-to-proppant interaction. However, in soft formations such as North Sea Chalks, proppant embedment can be significant and fracture designs are modified to increase fracture width and minimize the detrimental effects of its occurrence. Fracturing-Fluid Residues The pore space of proppants packed in a fracture is sometimes decreased by the deposition of a residue from water-based fracturing fluids. Such residue may cause a drastic decrease in fracture conductivity under certain conditions. The problem is most pronounced when the volume of residue from the polymer is higher, when the concentration of proppant in the closed fracture is lower, and when stress on the fracture is higher which causes lower porosity. Figures 7.9 and 7.10 show pictures of the residue from borate and zirconate crosslinked fluid systems, respectively. These figures show the proppant pack damage that occurs due to residue and also indicate that this damage is minimized by using borate crosslinkers. The most common residue is a product of the degradation of water-soluble polymers used to build viscosity in fracturing fluids. Service companies have devoted much effort to reducing polymer residues in fracturing fluids. Recent research has focused on developing more efficient thickeners with more soluble degradation products. Some of the detrimental effects of residue deposition can be alleviated by minimizing polymer concentrations, using higher proppant concentrations in fluids that suspend the proppant, using foam or emulsion fluids, and avoiding conditions of extreme proppant crushing. STIMLAB has developed a program “PREDICTK” (available from EPTG Fracture Applications Team) which tabulates available data comparing retained permeabilities after breaking and cleanup of various generic fracturing-fluid types. The data are presented as retention factors that can be applied to API-type short-term permeability data to obtain a usable value of proppant-pack flow capacity. The retained permeability includes the effects of time, temperature, and fluid residues.

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Fig. 7.9 - Borate Crosslinked Fluid System.

Inspection of this program reveals a direct comparison of the effects of increasing gellant loading for a titanate cross-linked hydroxypropyl guar gum (HPG) type fluid. Increasing gellant from 40 to 50 lbm/1000 gal [4793 to 5991 b/m3] decreases retained permeability by an additional 15%. Further reduction is encountered by a gellant increase from 50 to 60 lbm/1000 gal [5991 to 7190 g/m3] of about 15%. Another comparison of fluid effects, i. e., guar gum vs HPG, shows little difference in retained permeability. Virtually no difference is seen between titanate cross-linked fluids and those linked with zirconates. Fracture closure, fluid leakoff, and viscosity breaking processes have a dramatic effect on cleanup and regained permeability of the proppant pack. Breaking times of 2, 10, and 24 hours are compared for a generic cross-linked fluid. Slow and fast breaks are compared for gelled oil. The trend is the same: more rapid breaks tend to be more effective in terms of regained permeability. In a comparison of the damaging effects of different types of generic fracturing fluids, one type stands out as being the least damaging: foam fracturing fluids. These fluids, composed mainly of March 1995

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Proppants and Fracture Conductivity

Fig. 7.10 - Zirconate Crosslinked Fluid

a gas and minor amounts of gelled water, permit a proppant pack to regain 70 to 90% of its potential flow capacity. Fines Movement The fine particles created by grain failure at higher stress levels lead to lower proppant-pack permeability. The particle-size distributions resulting from such crushed particles have been investigated by several authors and their effects on fracture conductivity reported. Fine particles have been shown to migrate through the propped fracture and to plug the pore throats, thereby reducing fracture conductivity. The long-term decreased permeability of sand proppant reported may be caused at the least partially by movement of preexisting fines with continued flow through the sand. Non-Darcy Flow For non-Darcy flow, the pressure drop in the fracture can be expressed by

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Other Factors Affecting Fracture Conductivity

∆p ⁄ ∆L f = µv ⁄ k f + ( β ) ( ρ )v

2

(7.1)

where ∆p

=

pressure,

∆Lf

=

length of proppant pack in direction of flow,

µ

=

viscosity,

v

=

velocity,

kf

=

permeability,

β

=

turbulence factor, and

ρ

=

fluid density.

The second term of the equation, with coefficient β, expresses the increased pressure gradient as a result of deviations from Darcy’s law. Values of β have been measured for a variety of sand sizes at different values of stress. Non-Darcy effects can substantially reduce the effective fracture conductivity in high-flow-rate gas wells. This reduction in conductivity will decrease the well’s PI and can complicate the analysis of pressure-transient tests. To analyze wells properly where non-Darcy flow affects the pressure distribution in and around the fracture, a reservoir simulator that includes non-Darcy flow must be used by the analyst.

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Proppants and Fracture Conductivity

7.7 Economic Proppant Selection Successful hydraulic fracturing requires the integration of technical proppant data with economics to allow the development and implementation of an optimum fracture design. To facilitate this optimization effort, the Fracture Applications Team of the Exploration and Production Technology Group (EPTG) has developed a fracture optimization tool, ULTRAFRAC. The critical factors affecting fracture conductivity, described in the previous section, such as closure stress, proppant size, proppant concentration, strength, embedment, fracturing-fluid residues can each be reviewed both from a technical and economic perspective with ULTRAFRAC. For aid in the use of this program, please contact Larry K. Britt (8-422-3958) or Sandra Dougherty (8-422-3332) for assistance.

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Chapter

8

Fracture Treating Pressure Analysis

8.1 Introduction To Fracturing Pressure Analysis Hydraulic fracturing, as with other drilling, completion, and reservoir behavior problems, is complicated by the fact that processes cannot be directly observed. For describing reservoir behavior, this deficiency has been overcome by the development over the past 50 years of analyses based on wellbore pressure and flow rate. But, only in the last few years has similar analyses for fracturing been introduced and successfully applied. History Shortly after the introduction of hydraulic fracturing and its acceptance by the industry, the importance of fracturing pressure data was recognized, as evidenced by a quotation from Godbey and Hodges1 “By obtaining the actual pressure on the formation during a fracture treatment, and if the inherent tectonic stresses are known, it should be possible to determine the type of fracture created.” Later, fracturing pressure and the relation between pressure and in-situ stresses were inherently included in pioneering model development work of Khristianovic and Zheltov,2 Perkins and Kern,3 and Geertsma and de Klerk4 during the 1950s and 1960s. However, it was still several years later before the analysis of fracturing pressure data started to become an accepted industry practice. In 1978, Amoco Production Company initiated a coordinated program of field data collection5 and analysis to improve the understanding of the mechanics of the fracturing process. Much of this understanding had not changed since the early 1960s and was being severely tested by ever larger and more expensive treatments. A series of papers at the annual meeting of SPE in 1979 presented results from this program, including a paper by Nolte and Smith6 which first introduced a basis for the interpretation of pressure behavior during a fracture treatment, and one by Nolte7 for interpreting pressure decline after the treatment. The paper by Nolte and Smith presented a means for inferring periods of confined-height extension, uncontrolled height growth, and, more importantly, identification of a “critical pressure.” When a treatment reaches the critical pressure, fracture extension is reduced significantly and a pressure (screenout) condition or undesired fracture height growth can follow. Nolte and Smith demonstrated in the paper that a log-log plot of net fracturing pressure (above closure stress) vs.

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Fracture Treating Pressure Analysis

treating time could be used to identify periods of unrestricted extension, confined height, excessive height growth, and restricted penetration. This plot and technique has been used extensively since its introduction by both operators and service companies to determine fracture characteristics and geometry, and as an evaluation tool for optimizing treatment designs. Nolte7 also presented analyses permitting some of the parameters that quantify a fracture and the fracturing process to be estimated from the pressure decline following fracturing. At the time this work was presented, there was no direct or simple procedure for evaluating the basic parameters controlling a fracture treatment. Procedures were presented for quantifying fluid loss coefficient, fracture length and width, fluid efficiency, and time for the fracture to close from the fracturing pressure decline. The “minifrac” procedure was introduced for obtaining these parameters for use in designing the actual fracture treatment. The analysis procedures from these two papers6,7 have been used extensively by the industry to evaluate fracture treatments related to tight gas massive hydraulic fracturing,8-10 waterflood wells,11 moderate permeability oil wells,12 and geothermal formations.13 The work by Nolte and Smith was extended to include analysis for determining proppant and fluid schedules from the fluid efficiency when little or no information is available,14 e.g., wildcat area. In addition, theoretical work has extended the analyses to cover the three popular 2-D fracture geometry models,15 to cover more complex geometries involving fracture height growth,16 and to consider such phenomena as pressure dependent fluid loss.17 In recent years, the service companies have built computer treatment monitoring vehicles for use on-site in collecting and analyzing fracturing pressure data using the analysis techniques presented by Nolte and Smith.18 Similarity to Pressure Transient Analysis Analysis of fracturing pressure response is analogous to pressure transient analysis in reservoir engineering. In both cases the pressure response resulting from fluid flow in rock can be interpreted using basic principles to provide insights into a complicated physical process and provide the basis for rational decision making. In both cases the same basic principles apply - continuity of flow (e.g., mass balance), fluid flow resistance (for fracturing, width squared is equivalent to permeability in porous media), and system compressibility. Another important parallel is that, although the principles remain the same for all applications, each application in a new area is different and requires additional data collection and the participation of experienced personnel. However, an important difference is that pressure analysis of reservoirs is a mature discipline while the application to fracturing is still in its infancy. Fig. 8.1 shows the first recording of bottomhole pressure during and after a fracture treatment. The analogy to transient pressures in reservoirs can be seen in the figure with increasing pressure during injection and the pressure falloff or decline after shutdown. The figure also shows that during the first half of the treatment, the pressure was increasing, while during the last half of the treat-

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Introduction To Fracturing Pressure Analysis

ment, the pressure remained essentially constant, e.g., a critical pressure was reached. This period might be interpreted that the increasing pressure indicates extension at essentially constant height, with subsequent increasing height during the constant pressure period. During the treatment, the rock was confining fluid at a pressure up to 1400 psi above the in-situ rock stress of the target formation. During the initial portion of the decline (41-44 hours), the fracture is closing due to fluid loss with the rate of loss proportional to the rate of pressure decline. The increased rate of pressure decline after 44 hours is due to the increasing stiffness of the fracture closing on the proppant at the wellbore. This time is significant for two reasons -- the propped width can be inferred from the net pressure, and the well could be backflowed with minimum proppant production. Beyond 44 hours, the fracture is essentially closed on proppant and the pressure decline reflects reservoir parameters as pressure declines back to initial conditions. At 56 hours, pressure has decayed back to initial reservoir pressure.

Bottomhole Treating Pressure (BHTP) (psi) 9000

Fracture Treatment

8000

Pressure Decline Fracture Transient Reservoir Closing Press. Near Wellbore

Pe Net Fracture Pressure = Pbh-Dc

(50MPc) 7000

•

Frac. Closes on Prop at Well,

Pe∝ Propped Width

Pressure From Bottomhole Bomb Inferred Pressure

Closure Press, Pc = Horiz. Rock Stress

6000

Reservoir Press.

5000 38

40

42

44 46 Clock Time (hrs)

48

50

56

58

Fig. 8.1 - Example of Fracturing Related Pressures.

The following discussion presents the basis for and examples of fracturing pressure analysis and design. Also included are procedures for the successful field application of this technology.

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Fracture Treating Pressure Analysis

8.2 Fracture Closure Stress Fracturing pressure analysis is based entirely on interpreting the “net fracturing pressure,” e.g., treating pressure above the minimum in-situ stress (the fracture closure pressure or closure stress) of the target formation. Thus an accurate knowledge of closure stress is essential to the technology. The term “closure pressure” is defined as the fluid pressure required to initiate the opening of an existing fracture. This pressure is equal to, and counteracts, the stress in the rock perpendicular to the fracture. Since the fracture preferentially opens perpendicular to the minimum in-situ stress, since any other direction would require a higher pressure, closure pressure equals the minimum in-situ stress. In the analysis of bottomhole treating pressure while fracturing, closure pressure is analogous to the flowing bottomhole pressure measured during well tests, e.g., it is a base pressure above which pressure analysis is performed. Closure pressure is equal to or less than the breakdown pressure required to initiate a fracture and less than the pressure required to extend an existing fracture (fracture extension pressure or fracture parting pressure). An upper bound for closure pressure might be estimated from the initial shut-in pressure (ISIP) after a small volume acid or prepad injection. An upper bound can also be found from the breakpoint on a step-rate injection test (fracture parting pressure or fracture extension pressure). However, for quantitative analysis, a more definitive value is needed. While other methods such as logs and core analysis, Chap. 10, exist to measure or estimate in-situ fracture closure stress, the only definitive data for pressure analysis comes from some type of injection test, e.g., we must hydraulically fracture the rock in order to measure the data needed for hydraulic fracturing pressure analysis. For measuring closure stress, three basic types of tests are used: (1) pump-in/decline tests, (2) step-rate injection tests (used to measure fracture extension pressure), and (3) pump-in/flowback tests. Microfrac Tests Microfrac tests are a special type of pump-in/decline test used to measure closure stress in a small, discrete zone. The test may be conducted in open-hole sections by isolating the test interval with inflatable packers; however, for most commercial fracturing cases, testing is conducted by perforating a short (1 to 2 ft) interval of casing, typically at 4 to 6 shots per foot with a 60 or 90 ° perforation phasing. These types of stress tests are discussed thoroughly by Warpinski19 and McLennan,20 and an ideal test might appear as seen in Fig. 8.2. Tests typically might consist of injecting 20 gallons of water at 5 gpm, the basic theory being that, after injecting a small volume (e.g., the term microfrac) of low viscosity fluid at a low rate, the ISIP (instantaneous shut-in pressure) will be a very close approximation to the actual closure pressure. In fact, where a clear ISIP exists as idealized in Fig. 8.2, or seen for real data in Fig. 8.3, selecting closure pressure as equal to the ISIP may be an acceptable approximation. However, as emphasized by Warpinski,19 tests must be repeated several Hydraulic Fracturing Theory Manual

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Fracture Closure Stress

times in order to ensure that the value is repeatable. Generally, multiple repeat tests tend to reduce any influence of rock strength since the fracture is no longer being extended but only reopened. This will tend to make an ISIP more definitive and easier to pick, and, if the value is also repeatable, then a good value for closure stress has probably been found.

First Cycle Initial Breakdown (Pb ) 1

Second Cycle

Bottomhole Pressure

Secondary Breakdown Pressure (Pb2) Propagation Pressure Propagation Pressure

Shut-in Pressure (Ps ) 1

Shut-in Pressure (Ps ) 1

Time

Fig. 8.2 - Ideal Microfrac Stress Test.

Bottomhole Pressure (psig)

7500.000

6750.000

ISIP

6000.000

5250.000

4500.000

3750.000

3000.000 0.0000

2.500

5.000

7.500

10.000 12.500 15.000 17.500 20.000 22.500 25.000

Time (minutes)

Fig. 8.3 - Microfrac Stress Test with “Clear” ISIP.

However, it should be realized that the instantaneous shut-in pressure is always an upper bound for closure pressure since a fracture cannot shut instantly when pumping is stopped. Therefore, picking an ISIP value and making use of this value must be done with care. Also in some instances, a definitive ISIP is never realized and other analysis methods must be used to determine fracture closure pressure. The most common analysis procedure, and the procedure recommended here, is to plot pressure vs. the square root of shut-in time. A change in slope indicates a drastic change in the linear flow behavior, and is taken to indicate the fracture closing. For example, Fig. 8.4 shows a cased hole July 1993

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Fracture Treating Pressure Analysis

microfrac stress test conducted in the Mesaverde formation of the Rocky Mountains - and clearly no definitive ISIP can be picked. However, plotting the pressure falloff vs. square root of shut-in time shows a definitive change in slope, and closure pressure is chosen as identified in the figure. For this Mesaverde well, closure stress was measured by Warpinski21 in several intervals, and this data was reanalyzed as discussed by Miller and Smith22 using the “reservoir type” analysis of plotting pressure vs. the square root of shut-in time. As seen in Fig. 8.5, agreement between the two analysis methods was nearly perfect. Thus, picking an ISIP value does give a good value for closure stress. However, in many cases an ISIP could not be identified, whereas the square root plot gave a definitive value and in virtually every case, the “reservoir type,” square root plot analysis yielded a more subjective, definitive analysis.

Fig. 8.4 - Bottomhole Pressure, Square Root Time and Elapsed Time Since Shut-In.

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Root Time Analysis (psi/foot)

Fracture Closure Stress

1.1 1

0.9

0.8 0.7 0.7

0.8

0.9

1

1.1

ISIP “Pick” (psi/foot) Fig. 8.5 - Comparison of ISIP vs. Root Time Analysis of “Microfrac” Stress Tests.

Pump-In/Decline Test As discussed on page 8.4, microfrac tests are a special class of pump-in/decline tests used to measure stress in small, discrete formation intervals, and these “micro” tests typically use small volumes of water injected at rates measured in gallons per minute. However, often it is more practical for commercial fracturing applications to measure the closure stress over the entire intended completion interval. The basic test procedure is, of course, identical to a microfrac type test; however, volumes are now measured in barrels and injection rate in bpm. For example, a typical test might involve injecting 50 barrels of water at 20 bpm. The important, indeed critical, point is that the injected volume and injection rate must be guaranteed to be sufficient to create and/or open a hydraulic fracture. For this reason, it is often desirable to proceed the actual stress test with a step-rate injection test as discussed on page 8.10. For a pump-in/decline test, closure pressure is determined by injecting a volume of fluid at a rate sufficient to create a fracture; then shutting in the well and allowing pressure to naturally decline to below closure pressure (e.g., allow the fracture to close). For testing an entire completion interval, this type of test is most useful in moderate to high permeability formations, where closure occurs reasonably quickly. For very low permeability zones, e.g., “tight” reservoirs, closure time may be so long that closure becomes difficult to identify. For these cases, pump-in/flowback tests may be preferable as discussed on page 8.9. Testing is usually conducted with the base fluid being used to prepare the fracturing fluid, e.g., KCl water, diesel, produced formation fluid, etc. The pump-in portion of the test is performed at the fracturing rate, and in most cases consists of 50 to 100 barrels of fluid. While a pump-in/decline test over an entire completion interval may be procedurally similar to the microfrac tests discussed July 1993

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Fracture Treating Pressure Analysis

earlier, a simple ISIP cannot be used to approximate closure pressure. Because of the larger volumes and higher rates needed to ensure that the completion interval is fractured, the injection pressure can easily be several hundred psi above closure pressure; thus, special analysis is mandatory in order to identify fracture closure.

Bottomhole Pressure

Since the test is, hopefully, being conducted in a porous, permeable formation, the first analysis is to plot a Horner plot of the pressure decline as seen in Fig. 8.6. For this plot, pressure is plotted on the “y” axis on a linear scale, and “Horner time,” [tp+ts]/ts, is plotted on the “x” axis on a logarithmic scale. If a semilog straight line is starting to develop as seen in Fig. 8.6, and if this line extrapolates to a reasonable value for reservoir pressure, then radial or pseudoradial flow may be affecting the pressure decline behavior. In order for this pseudoradial flow to start developing, the fracture must already be closed, thus pressure data falling on the semilog straight line is excluded from the closure stress analysis. Next, the pressure falloff (prior to the point where pseudoradial flow may be starting to affect the decline) is plotted vs. the square root of shut-in time as idealized in Fig. 8.7. Initially, pressure should decline on a straight line indicating linear flow in the formation. The point where the fracture closes should cause a drastic change in the flow system and a distinct change in slope on the square root plot. Note, however, that the change in slope may be either “up” or “down,” depending on the relationship of the fracture's variables and those of the reservoir. This implies a theoretical possibility that no change in slope may occur. Thus this analysis method should be treated with caution. In particular, this type of problem is most likely to occur in low permeability formations where closure time is extended. In such situations, the pump-in/flowback test, discussed below, should be utilized.

PUMP IN

SHUT-IN DECLINE

POSSIBILITIES

t s (Shut-In Time)

Fig. 8.6 - Illustrative Horner Plot for Shut-In Decline Test.

Hydraulic Fracturing Theory Manual

Fig. 8.7 - Illustrative Root Time Analysis for Closure Stress.

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Fracture Closure Stress

Pump-In/Flowback Test For low permeability, “tight” formations, the time-to-close for a pump-in/decline test may be quite long, making identification of fracture closure (e.g., identifying two distinct slopes on a square root plot) difficult. For these cases, a pump-in/flowback test (PI/FB) may be used to accelerate fracture closure-- thus making closure pressure more identifiable.

Digital Readout

Flowback Line

2 inch Flowmeter Disposal Pit

Wellhead Gate Valve or Lo-Torque Valve

1 inch Flowmeter

Adjustable Choke or Gate Valve

Digital Readout

Fig. 8.8 - Flowback Manifold for PI/FB Stress Tests.

For a PI/FB test, the injection is immediately followed by a flowback at a constant rate, typically through a flowback manifold similar to that shown in Fig. 8.8. The constant flowback rate is maintained with an adjustable choke or valve and should be metered with a low-rate flowmeter. The primary purpose of the flowback is to flow back at a rate on the order of the rate at which fluid is leaking off to the formation. For this flowback rate, a characteristic reverse curvature occurs in the pressure decline at closure pressure as shown by the middle curve in Fig. 8.9. The proper or ideal flowback rate must be determined through trial and error, performing the first flowback at 1 to 2 bpm and changing the rate until the “S-shaped” character of the pressure decline is achieved. Once the desired rate is achieved, at least one additional PI/FB test should be performed to ensure repeatability. The principle behind a pump-in/flowback test is illustrated in Fig. 8.10. During the early stages of the flowback pressure decline (“A”), the fracture and formation are dominating behavior and the pressure decline is “normal.” When pressure declines equal closure pressure at the wellbore, the fracture begins to close in the near well region. However, this closure is over a limited distance and since even a closed fracture possesses significant permeability, there will be no sudden, drastic change in pressure decline behavior. Also, it should be noted that away from the well the fracture is still open; driving fluid to the wellbore and preventing any sudden increase in the rate of pressure decline. With further pressure drawdown in the wellbore, the effective stress (e.g., fracture closure stress minus pore pressure in the fracture) acting over the closed portion of the fracture increases, July 1993

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Bottomhole Pressure

8

Time

Fig. 8.9 - Illustrative PI/FB Stress Test Analysis (linear p vs. t plot).

decreasing the permeability of the closed fracture. This begins to reduce flow into the wellbore and the rate of pressure decline starts to accelerate as the flowback is increasingly coming from simply the pressurized fluid in the well. The acceleration of the rate of pressure decline (“B”) creates the characteristic “reverse curvature” behavior (“C”), and the point where this acceleration starts is identified as fracture closure pressure, e.g., the point where the fracture first begins to close at the wellbore. An additional analysis procedure for PI/FB tests is a derivative plot such as seen in Fig. 8.11. For this plot the change in pressure with respect to time, dP/dt, is plotted vs. time. Since closure is identified at the point where the rate of decline accelerates, closure would be identified with the maximum point on the derivative plot. For the example in the figure, the derivative is constant for a fairly long period time, e.g., pressure is declining linearly with time. In such a case, closure should probably be identified at the end of the constant derivative period, e.g., at the point where the rate of pressure decline begins to accelerate. For this case, it would probably be advisable to run an additional case with a higher flowback rate to achieve a more identifiable maximum on the derivative plot, and thus a more distinct value for closure pressure. Step-Rate Injection Test As mentioned previously, stress testing of a gross completion interval should generally be preceded by a step-rate injection test (SRT). This test will yield a value for the fracture extension pressure which is a good upper bound for closure pressure, typically being 100 to 200 psi about closure pressure. Also, by noting the rate where fracture extension begins, a minimum rate is determined for subsequent injection/decline or PI/FB tests. The SRT procedure is similar to that performed for reservoir flooding purposes. Fluid is pumped at incrementally increasing rates and the final injection pressure recorded for each rate is plotted vs. rate as seen in Fig. 8.12. A typical test may include rates ranging from 0.25 bpm to 20 bpm.

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Fracture Closure Stress

Flowback

Pressure Holding Frac Open k = Infinite

Leakoff

Pressure = Pc k = Finite

Pressure < Pc so frac is “stressed” k = very small

Fig. 8.10 - Pump-In/Flowback Test.

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Fracture Treating Pressure Analysis

a) Start Injection, 5 BPM b) Increase Injection to 7 BPM, Start 2 BPM Flowback c) Stop Injection, Maintain Constant Flowback at 2 BPM

Fig. 8.11 - Example PI/FB Test with Derivative.

The resultant pressures at each rate are plotted vs. rate and the breakpoint is identified as fracture extension pressure. For best results each rate should be maintained for a fixed period of time (typically 2 to 5 minutes). Also, because of the very low rates at the beginning of the test, the proper pumping equipment is required (e.g., low rate acid injection pump), equipped with a small ID flowmeter for accurate metering. Conventional fracture pumping units have a difficult time maintaining constant rates at less than 2 bpm.

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Fracture Closure Stress

Fig. 8.12 - Illustrative Step-Rate Injection Test. Table 8.1 - Summary

of Analysis Methods In-Situ Stress Tests

Microfrac Test (measure stress in small, discrete interval) Pick ISIP Plot Pressure vs. Square Root of Time Pump-In/Decline Test (stress in gross completion interval) Horner Plot (to identify any pseudoradial flow effects) Plot Pressure vs. Square Root of Shut-In Time (distinct change in slope identifies closure) Pump-In/Flowback Test (stress in gross completion interval) Plot Pressure vs. Time (reverse curvature identifies closure, looking for “broad” curvature down, NOT “wiggles”) Superimpose plot of dP/dt vs. time (maximum on derivative plot identifies closure “or end of flat derivative”) Step-Rate-Injection Test (measure extension pressure) Plot Pressure at End of Each Rate Step vs. Rate (“break” indicates start of fracture extension and sets a good upper bound for closure pressure)

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Fracture Treating Pressure Analysis

8.3 Bottomhole Treating Pressure Bottomhole pressure is the single parameter that can be measured during a fracturing treatment to interpret the fracturing process. All other parameters controlling fracture growth can be related to this pressure. Pressure in the fracture is a function of formation parameters and the fluid system used to create the fracture. If the pertinent rock and fluid properties can be defined, the behavior of bottomhole treating pressure (BHTP) while fracturing can provide valuable insight into fracture growth/geometry characteristics. The equation used to define fracturing pressure is E' 1/4 P net = ----- [ µQL ] H where net pressure, pnet, is the total fluid pressure minus closure pressure, and the closure pressure is equal to, and counteracts, the horizontal rock stress perpendicular to the fracture plane. Other parameters in the equation are rock modulus, E', which can be obtained from laboratory core data; fracturing fluid viscosity, µ; injection rate, Q; and created fracture height and length, H and L. This relation predicts that net pressure should increase with time as fracture length increases, provided fracture height is near constant or restricted. However, variations from this prediction of increasing pressure have been observed in numerous cases. The following discussion presents interpretation techniques to interpret and analyze these pressure variations to aid in defining the fracturing process for different situations. Nolte-Smith Log-Log Interpretation A log-log plot of net fracturing pressure vs. treating time has proven to be a powerful tool for interpreting the fracturing process. From pressure behavior observations during fracturing, Nolte and Smith6 presented four distinct pressure “modes,” as seen in Fig. 8.13, which permit the identification of periods of confined-height extension (Mode I), constant height growth (Mode II), restricted extension (Mode III), and uncontrolled height growth (Mode IV). These interpretations are based on combining historical work performed by Perkins & Kern3 and Nordgren,23 showing that net pressure is proportional to time raised to an exponent as seen in Fig. 8.14. For actual fluids used for fracturing, the exponent, e, can be bounded for cases of high and low fluid loss, and where the fluid’s non-Newtonian power law exponent, n, varies from 1 for a Newtonian fluid to n = 0.5 for a highly non-Newtonian fluid. For the Newtonian fluid with high fluid loss, the exponent, e, would equal 1/8. For a highly non-Newtonian fluid with low fluid loss, e would be 1/4. This defines the boundaries for Mode I fracture extension, as seen in Fig. 8.15, and the following discussion centers on the four characteristic slopes shown in Fig. 8.16.

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Bottomhole Treating Pressure

Fig. 8.13 - Nolte-Smith Plot Slope Interpretation.

Fig. 8.14 - Theoretical Basis for Fracturing Pressure Interpretation.

Mode I - A log-log net pressure to pump time slope of 1/8 to 1/4, as discussed above, implies that the fracture is propagating with confined height, unrestricted extension, that fluid loss is linear flow dominated, and that injection rate and fluid viscosity are reasonably constant. These assumptions comply with the Perkins and Kern fracture growth model. Fig. 8.16 shows the net treating pressure for three fracture treatments, the initial portion of each treatment indicating confined height, unrestricted extension (Mode I). Beyond this portion, though, the treating pressure deviates from the 1/8 to 1/4 slope, mentioned above - confined height, unrestricted extension, linear flow fluid loss, and constant rate and viscosity. For cases 1 and 3 in the figure, the slope is nearly flat, indicating near constant pressure which characterizes Mode II behavior.

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P≅t

e

n' is Non-Newtonian Fluid Power Law Exponent n' = 1 Newtonian Fluid

e High Loss Low Loss

1/2(2n'+2) 1/(2n'+3)

1/8 1/5

n' = 0.5 Very Non-Newtonian Fluid 1/6 1/4

Log Pnet

Nolte-Smith Plot

Slope: 1/8 to 1/4

Log Time

Fig. 8.15 - Nolte-Smith Slope Limits for Mode I (Restricted Height, Unrestricted Extension).

Fig. 8.16 - Example Nolte-Smith Plots with Different Characteristic Slopes.

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Bottomhole Treating Pressure

To analyze what may cause this flattening of the pressure - time slope, the continuity or mass balance equation can be examined; Q = q Loss + q Frac where qFrac is the rate of fluid storage in fracture volume (e.g., ∆w + ∆H + ∆L). Pressure is proportional to fracture width, thus the equation can be rewritten as Q = q Loss + K [ ∆P + ∆H + ∆L ] , where K is a constant. For the Mode I behavior, injection rate Q is constant, height is constant (∆H = 0), and qLoss increases with time as fracture area increases. Also, ∆P and ∆L are increasing with time. If ∆P goes to zero, then ql and/or ∆H must increase to honor the equation. As a result, more fluid is lost to the formation or stored in additional height. This leads into a discussion of Mode II behavior on a log-log net pressure vs. time plot. Mode II - A flat pressure:time slope indicates stable height growth or increased fluid loss which negates the predicted pressure increase. The potential for height increase is shown in Fig. 8.17, where the fracture penetrates a section of higher stress at a constant growth rate. As additional height is generated, the cross-sectional area of the fracture increases, thus reducing the flow velocity and frictional pressure drop down the fracture and reducing the normal pressure increase. If height growth continues and reaches a low stress zone, as seen in the figure, the pressure:time slope may become negative, indicating uncontrolled, rapid height growth (Mode IV). This type of behavior is discussed later on page 8.19. The other variable that can change besides ∆H, without violating the continuity equation is qLoss (fluid loss). One mechanism for a higher fluid loss rate would be opening of natural fissures intersected by the main fracture as shown in Fig. 8.18. The opening of natural fissures increases fracture volume and fluid loss area, and decreases the pressure in the fracture. When pressure declines below the stress holding the fissures closed, the fissures re-close. Pressure then increases slightly and the fissures reopen, etc. This opening-closing-opening of the fissures is like a pressure regulator, producing a constant pressure profile. Due to the increased fluid loss rate, Mode II will normally be followed by undesired behavior such as a screenout. Looking back at the continuity equation, if something occurs to stop fracture extension (i.e., ∆L = 0), then either ∆P or ∆H must increase. As shown in Fig. 8.18, increased fluid loss to natural fissures may dehydrate the slurry to the point that a proppant bridge forms in the fracture. If pumping continues, no additional fracture penetration will occur. If the fracture is contained, pressure must increase at a higher rate as seen in cases 1 and 2 on Fig. 8.16. If the fracture is not contained, the rate of height growth will increase and pressure will decrease with time as shown by case 3 of Fig. 8.16. In the case where the fracture is contained and the pressure increases, this rapid pressure increase is characteristic of Mode III behavior on the log-log Nolte-Smith plot, Fig. 8.21.

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Fracture Treating Pressure Analysis

Fig. 8.17 - Height vs. Net Pressure for Multizone Geology.

P+S<σ:I

P + S > σ : II Regulator

“Screenout”: III 1/1 Slope PV

Fig. 8.18 - Effect of Natural Fractures, Critical Pressure Causes Increased Fluid Loss.

Mode III - This behavior is characterized by a region of positive unit slope (i.e., 1:1 log-log slope), indicating a flow restriction in the fracture. This implies that the pressure is proportional to time or, more importantly, that the incremental pressure change is proportional to the incremental injected fluid volume. This 1:1 slope is similar to the same slope in Pressure Transient Analysis, indicating storage of fluid, in this case by swelling or ballooning the fracture. Common causes of this behavior are pad depletion where proppant reaches the fracture tip, slurry dehydration to natural fissures (discussed above), excessive height growth increasing fluid loss area, and/or proppant fallout due to poor gel quality. Fig. 8.19 shows how excessive height growth can cause slurry depletion resulting in a premature screenout. The fracture has grown through a shale section into a lower closure pressure sand. Due to the higher stress in the shale, the fracture width is less than in the sands forming a “pinch point” which will not allow sand to pass through, yet allows fluid to pass, dehydrating the slurry in the

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Bottomhole Treating Pressure

target interval. As the slurry dehydrates it forms a plug which will eventually bridge in the fracture. The approximate distance to the bridge can be calculated from:

Log

Width Top

Top

Fig. 8.19 - Example of Height Growth Directly Leading to Premature Screenout.

QE' R max = x f – max = 1.8 --------------------2 H ∆p/∆t where Q = pump rate (bpm), E' = modulus (psi), H = frac height (ft), and ∆p/∆t = rate of pressure increase (psi/min). This information can be useful in postanalysis and the design of future treatments. A near-wellbore bridge would likely be caused by natural fissures, height growth, or a high sand concentration slug; whereas a bridge some distance from the wellbore would more likely be due to pad depletion, or sand fallout due to poor gel quality. As noted previously on page 8.14, if fracture extension ceases and the fracture is not contained, then rapid, unstable height growth will occur as pumping continues and the pressure:time slope will become negative. This is Mode IV behavior as seen during case 3, Fig. 8.16. Mode IV - A negative slope can be interpreted as rapid height growth into a lower closure stress zone. Referring back to the continuity equation, discussed on page 8.17, a significant decrease in pressure must be accompanied by a significant increase in one or more of the other variables. A significant increase in fluid loss is possible from opening new fractures or fissures, but is not likely with decreasing pressure. An increase in length is not consistent with a decrease in pressure. The only change which is compatible with a decrease in pressure is an increase in height. The steepness of the negative slope would imply the rate of unstable growth. A high rate of growth would exhibit a steep slope, while a low negative slope would imply a low rate of growth. If the fracture grows into a much lower stress zone, the decrease July 1993

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in pressure will be rapid. If the fracture grows into a slightly lower stress zone the negative slope will be shallower. A negative slope observed from the beginning of the treatment indicates a lack of height confinement. In this case the fracture will grow radially and future treatments should be designed using a radial model. While the observed pressure behavior on the net pressure vs. time plot is primarily a function of fracture geometry, other parameters may interfere with interpretation. These parameters are shown in Fig. 8.20, clearly showing that an increase in rate or viscosity will increase net pressure. As a simple example of this, consider the plot in Fig. 8.21 for a gelled oil fracture treatment. The initial declining pressure indicates unconfined fracture height, and then after ± 9 minutes, pressure begins to increase. This might be interpreted as a change in fracture geometry but, for this simple case, this is simply the time when gelled fluid is on the perforations. After 4 or 5 minutes, the fracture is filled with this new, higher viscosity fluid, and pressure again begins to decline. Complete records of treating parameters must be kept, and what was happening during a job borne in mind when interpreting net pressure behavior.

“P & K” Confined Height Fracture

Unconfined Height “Penny” Shaped Fracture

Elasticity W

W

∼ ( µQ -EL- ) 1 / 4

1/4

P

∼ H--E P

- ( µQL ) 1 / 4 ∼ E-------H

W

Fluid Friction

Combining

W

∼ R--E P

∼ ( µQ R--E ) 1 / 4 3/4

P

- ( µQR ) 1 / 4 ∼ E-------R

Fig. 8.20 - Variables Affecting Fracture Pressure.

Critical Pressure As mentioned in the previous discussion on page 8.17, Mode II behavior on the net pressure vs. time plot is usually followed by some undesirable behavior such as excessive height growth or a screenout. For this reason, the net pressure where the pressure:time slope flattens is termed the critical pressure. For the case of height growth, critical pressure is roughly 70-80% of the differential closure stress between the initial zone and bounding beds. When natural fissures exist, critical Hydraulic Fracturing Theory Manual

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Net Pressure (psi)

Bottomhole Treating Pressure

Pump Time (minutes) Fig. 8.21 - Viscosity Effect of Nolte-Smith Plot.

pressure is approximately the net stress component (above closure pressure) acting normal to the plane of the fissures, holding the fissures closed. In fieldwide studies, critical pressure has been found to be reasonably constant. During the early development of a field, strategic wells should be monitored to determine the critical pressure, which can then be extrapolated to offset wells. Treatment designs can then be formulated to keep net treating pressure below the critical pressure, possibly by reducing viscosity or rate. If it is impossible to stay below critical pressure by these means, unconventional-type designs may possibly be developed to minimize height growth or screenout tendencies.

Summary of Nolte-Smith Slope Analysis Small (1/8 to 1/4) Positive Slope Continued height or restricted height growth Unrestricted extension “Normal” C/ time fluid loss Flat Slope - Constant Net Pressure CRITICAL Pressure Increased Height Growth Increased Fluid Loss Reduced Rate of Fracture Length Extension Rapidly Increasing Pressure - 1:1 Slope Restricted Fracture Extension, e.g., Screenout Negative Slope - Declining Net Pressure Unconfined Height Growth

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Fracture Treating Pressure Analysis

BHTP Measuring Techniques To perform a meaningful analysis of fracturing pressures requires direct measurement or a very accurate calculation of bottomhole treating pressure (BHTP) during the injection and pressure decline. The primary objective is to record the fluid pressure at the entrance to the fracture (e.g., just outside the perforations). While several companies have developed software for calculating BHTP from surface pressure, to date no technique has been developed to accurately account for all variables affecting friction pressures. In some cases of shallow wells, where injection was down large casing, these programs have given reasonable results. But, in deeper wells, and especially those where the fracture treatment was pumped down tubing, results have been erroneous and in many cases have led to incorrect decision making during the treatment. Three techniques which are recommended for measuring fracturing BHTP are seen in Fig. 8.22. The first configuration uses a tubing string with an open annulus and a surface pressure recording. The treatment is pumped down the tubing or casing, with the other side static. Pressures are measured on the static side and corrected for hydrostatic pressure to obtain BHTP. This configuration is applicable if the fracturing pressure is greater than the hydrostatic head on the static side, which is usually the case except in severely underpressured or depleted reservoirs. The second configuration involves running the pressure sensor inside a side-pocket mandrel, above a packer, with pressure transmitted to the surface via an electric line fastened to the outside of the tubing. The last technique is running a downhole recording pressure gauge inside a tail pipe below a perforated joint and packer. With this technique real-time access to the data is not possible. The data is accessed after the treatment, when the pressure recorder is retrieved. With the first two techniques, on-site computers can be used to manipulate and analyze the data for fracture treatment design or to make on-site judgmental decisions during the treatment. The following describes in more detail the procedures for using these three BHP measurement techniques: 1. Open-Ended Tubing - Run tubing (no packer) to within 100 ft of the perforations. Circulate out any gas so as to leave a liquid filled static column, whether this is on the tubing or annular side. Gas in the static column will reduce the hydrostatic head from which BHTP is calculated and reduce the accuracy of the true BHTP due to gas compression and expansion during the injection and shut-in periods. The density of the fluid used to circulate the hole should be measured periodically, so the hydrostatic head of the static column will be accurately known. During testing and the actual fracture treatment, both tubing and annular pressure should be recorded continuously. If injecting down the annulus, the tubing pressure will reflect bottomhole pressure and likewise, the annular pressure will reflect BHTP when injecting down tubing. 2. Surface Recorded BHP Gauge - A side pocket mandrel containing the pressure gauge is run above the packer. The wireline for the pressure gauge is strapped to the outside of the tubing as the string is run in the hole, and a port from the mandrel to the inside of the tubing allows transmission of pressure to the gauge. This type system is commercially available.

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Bottomhole Treating Pressure

Pt Pa Qt Qa

Q

Q

WIRELINE

PACKER MANDRIL PORT

SIDE POCKET MANDRIL Qt - 0

PERFORATED SUB (BLAST JOINT)

PRESSURE SENSOR

Pt - BHP-Pn or Qa - 0

PRESSURE BOMB SEATING NIPPLE NO-GO NIPPLE

PACKER

Pa- BHP-Pn

1

2

3

( )

(b)

( )

Fig. 8.22 - Well Configurations for Recording Bottomhole Treating Pressure.

3. BHTP Gauge Tail pipe Assembly - In this configuration, the pressure gauge is placed below a perforated joint and packer in a tail pipe assembly. The complete assembly from bottom to top would consist of a joint of tubing with a “NO-GO” nipple at the bottom, a seating nipple, a perforated sub, and a pup joint below the packer. The most reliable and least expensive way to prepare the perforated sub would be to drill the holes in a machine shop. This would ensure all holes are open, large, and properly spaced. The BHTP gauge would be run into the seating nipple on a slick line, and the treatment pumped down the tubing and out the perforated sub. After the treatment, the bomb could be retrieved with a slick line by latching into a fishing neck on top of the bomb or by pulling the tubing string. BHTP Measuring Devices During prefrac testing, a BHTP gauge can be run on wireline to just below the perforations. This procedure cannot be used on the main treatment, though, because of damage caused by the proppant to the wireline. Many wireline companies can supply quartz pressure gauges which have a pressure range of 0-12,000 psi, a resolution of 0.01 psi, and an operating temperature up to 300°F. This same type gauge can be run in the side pocket mandrel assembly in the previously discussed configuration #2. Accurate pressure measurements during prefrac testing and the actual fracture treatment are required for useful analysis and evaluation. For prefrac tests, i.e., closure pressure, minifrac, etc., pressure resolution to nearest 2 psi and 10 second data acquisition is normally adequate. For the main treatment pressures recorded to the nearest 5 psi, one data point every 20 to 30 seconds is sufficient. In-line pressure transducers normally supplied by the fracturing service companies have proven to be unreliable for this type work. Aside from the resolution of the transducers, they may

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Fracture Treating Pressure Analysis

not be accurately calibrated. Given adequate notice, however, service companies can usually obtain the precision-type transducers required.

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Pressure Decline Analysis

8.4 Pressure Decline Analysis Prior sections presented an analysis of injection pressure behavior during a fracture treatment, this behavior being a function of several variables, height, length, leakoff rate, etc., all of which change with time. However, shortly after pumping stops, the fracture stops growing and a simpler situation exists, e.g., Q, ∆H, and ∆L become zero in the continuity equation, 1 Q = q Loss + ( L p net CH ) ( ∆L/L + ∆ p net / p net + ∆C p /C p + ∆H /H ) ----∆t

(8.1)

leaving the rate of pressure decline, ∆pnet, proportional to the rate, qLoss. From pressure decline analysis, values for fluid efficiency and fluid loss coefficient can be determined as will be shown in this section. Note that while the equation above contains a term for changes in fluid compressibility, Cp, this effect will not be included in this discussion. In general, this is not a major factor for pressure decline analysis. The analysis of the pressure decline for fluid loss and fluid efficiency is then combined with the Nolte-Smith analysis of treating pressures (for fracture geometry) to give a complete description of the fracturing process. Note - neither analysis can truly stand alone, they are complementary and must be used together to describe the process. The pressure-volume, P-V, relationship of a fracture can be thought of as analogous to a fluid-filled elastic membrane (e.g., balloon) as depicted in Fig. 8.23. The fluid volume can be determined from the pressure in terms of the membrane's stiffness - fracture stiffness, S, being a function of fracture geometry and the elastic modulus of the formation(s). If the balloon develops a leak and the P-V-T relationship is known, then the rate of fluid, qLoss, can be determined from the rate of pressure decline. Since the fracture system is much simpler after shutdown (as opposed to during injection), e.g., only two variables changing with time P and V, it is possible to solve for these variables.

Fig. 8.23 - Volume Relationship of Fracture, Analogy to Balloon.

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Fracture Treating Pressure Analysis

Fracture Stiffness Fig. 8.24 shows equations used to describe fracture stiffness, S, for both a confined height fracture and a fracture with radial geometry. For both geometries, S is proportional to the crack opening modulus, E', and either fracture height, H, or fracture radius, R, or for a Geertsma fracture geometry, to fracture length, L. As shown in the figure for the confined height case, if the fracture grows into a bounding formation, the fracture stiffness, and thus pressure decline analysis is still primarily dependent on the initial fracture height.

Fig. 8.24 - Width/Pressure Relations for Two Common Fracture Geometries.

Knowing fracture stiffness, the fracture P-V relationship can be calculated from the expression dV A β ------- = --------- d p net /dt dt S

(8.2)

where dpnet is the change in average pressure in the fracture. Unfortunately, only wellbore pressure can be measured, and even though the fracture has stopped extending, fluid will continue to flow down the fracture and wellbore pressure will be higher than the average pressure in the fracture. Thus, a term β is defined which relates wellbore pressure to the average pressure in the fracture as p avg = β p well .

(8.3)

Fig. 8.25 provides graphs for determining β for a confined height fracture. For a radial fracture or a short Geertsma geometry fracture, β will be approximately 1. Since the rate of change in fluid volume, dV/dt, is equal to the fluid loss rate, qLoss, Eq. (8.2) can be rewritten as q Loss = – ( A β/S )d p net /dt

,

(8.4)

where qLoss is a volume loss term and thus, negative to the system.

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Pressure Decline Analysis

Fig. 8.25 - β Ratio of Average Pressure in Fracture to Wellbore Pressure, After Shut-In, for a Confined Height Fracture.

Fluid Loss Rate For most hydraulic fracturing situations, the rate of fluid loss is governed by linear flow into the reservoir, and expressed by the relationship C v Loss = --------------------------[t – τ(a)]

(8.5)

where vLoss is the fluid loss velocity over an incremental area of the fracture, da; C is the fluid loss coefficient; and τ(a) is the time when the area was created. The final relationship then between fracture stiffness, S, rate of pressure decline, and C, the fluid loss coefficient, will be termed ∆P* as discussed on page 8.30. Note, despite the similarity in terminology with a Horner plot P*, the ∆P* value for fracture pressure decline analysis has no relation to reservoir pressure. Instead, ∆P* is simply related to the rate of pressure decline following an injection at fracturing rate. Assuming linear flow or “Carter” type24 fluid loss, and referring back to Eq. (8.5), the total volume rate of fluid loss, qLoss, can be found from q Loss =

2Cda

∫ A -------------------------[t – τ(a)]

(8.6)

e.g., integrating the fluid loss velocity over the entire fracture area with the factor of 2 occurring since the fracture has two “sides.” Obviously, to reduce this to any usable form, the unknown, τ(a) (e.g., the time when each element of the fracture area was created) must be known. In general, of course, this is not a simple, or a known function, and if this is an important factor, then analysis of July 1993

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Fracture Treating Pressure Analysis

the fracturing pressure decline data will become of limited usefulness. However, while this function is not known, it can be bounded and these bounds can be used to test the importance. For example, as shown by Nordgren,23 Geertsma,4 and others, for very low fluid loss, fracture area will grow approximately linearly with time, A≈t ,

Low ( "0" )Loss

(8.7)

while for very high fluid loss, fracture area will grow with the square root of time A≈ t ,

High ( "∞" )Loss

(8.8)

Area

as illustrated in Fig. 8.26.

Time Fig. 8.26 - Fracture Growth with Time.

As an example, consider a low fluid loss case, A ≈ t, or a τ --- = ---A tp where A is the total fracture area created at the end of the pump time, tp, and 'a' is a small incremental fracture area that was created or opened at time τ, τ < tp. This gives a s = --- t p A or q Loss =

Hydraulic Fracturing Theory Manual

2Cda

∫ ----------------------------------[ t – ( A/a )t p ] 8-28

July 1993

Pressure Decline Analysis

which can be integrated from area=“0” to area = “A” to give the rate of fluid loss, qLoss, for times greater than (or equal to) tp. This integration gives 2 AC q Loss = -----------2 { t – t – t p } tp or 2 AC q Loss = -----------2 { ( 1 + δ ) – δ } tp where time, t, equals tp+ts (e.g., pump time + shut-in time) and δ = ts/tp. Similarly, for high fluid loss, Eqs. (8.6) and (8.8) can be integrated to give  2CA  –1 1 q Loss = -----------  sin ---------------------  tp  (1 + δ)  or, more generally, 2Cr p Af ( δ ) q Loss = --------------------------tp

(8.9)

where δ = t s /t p ( e.g., Shut-in Time/pump time ) and a new parameter, rp, has been added for cases where only a fraction of the fracture area is leakoff area. That is, rp is the ratio of permeable area opened by the fracture to total fracture area, Permeable Fracture Area r p = ------------------------------------------------------------ . Total Fracture Area The time behavior of the fluid loss rate is determined by f(δ) 1/2

1/2

f ( δ ) = 2 { ( 1 + δ ) – δ } – Low Fluid Loss –1 sin [ 1/ ( 1 + δ ) ] – High Fluid Loss and these two functions are plotted vs. dimensionless shut-in time, δ in Fig. 8.27. The similarity between the two time functions seen in the figure indicates that an EXACT knowledge of how the fracture grew with time is not necessary for the decline analysis - so long as the fracture was free to extend, e.g., no screenout condition occurred. For example, consider the dashed curve in Fig. 8.24, showing an ideal fracture area vs. time behavior for a treatment which screens out very early. For this case, fracture area stops increasing early during the pumping. Thus, during the presJuly 1993

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Fracture Treating Pressure Analysis

sure decline, all of the leakoff area is “old,” leading to lower than expected leakoff and application of the pressure decline analysis to the postpumping pressure behavior would calculate an erroneously low fluid loss coefficient. Finally, note that Fig. 8.27 does not indicate that there is no behavior difference between high and low fluid loss cases. Merely just that the exact time-rate-of-growth of the fracture while pumping is not a dominant factor, and that postfrac fluid loss rate (and thus pressure decline behavior) is a function of fluid loss coefficient, C, pump time, tp, and the total created fracture area, A.

Fig. 8.27 - Bounds on Rate of Fluid Loss Function (bounds are less than 10% different after shut-in time equal to 1/4 of pump time).

∆P* - Pressure Decline Analysis Going back to the basic pressure decline behavior Eq. (8.2) and combining this with the fluid loss rate from Eq. (8.9) gives 2 AC Aβ q Loss = ----------- r p f ( δ ) = – -------d p net /dt S tp

(8.10)

2CS – d p net /dt = ------------ r p f ( δ ) β tp

(8.11)

or

and this gives a definite relation between fracture stiffness, S, fluid loss coefficient, and postfrac pressure decline. If pressure decline were a linear function of time (e.g., dp/dt = constant), then the relation could be characterized with a simple “psi/minute.” For example, assume a case with a pump time, tp, of 20 minutes. If 10 minutes after pumping is stopped, e.g., ts = 10 or δ = 0.5, the rate of pressure decline, dp/dt was 5 psi/minute, then, from Fig. 8.25, f(δ) ≈ 1. If the fracture stiffness were known, then Eq. (8.11) could be solved for fluid loss coefficient. However, the behavior Hydraulic Fracturing Theory Manual

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Pressure Decline Analysis

is more complex than this, and a value, defined as ∆P*, will be used to describe the pressure decline behavior. Basically, ∆P* is a single value which characterizes the rate of pressure decline. A high value indicates a rapid pressure decline, which would usually correspond to high fluid loss, however, it might also correspond to a very stiff formation. Thus we see that ∆P* does not directly describe fluid loss, but rather it will be seen to specify a relation between several variables. Unfortunately, the rate of change of pressure, dpnet/dt, is hard to measure and use, making it convenient to integrate the pressure decline, dpnet/dt, to convert Eq. (8.11) into a pressure difference form. Clearly integrating dp/dt from time = to to time = to + ∆t dp

- dt ∫ – ----dt

= ∆p = p ( t=t o ) + p ( t o + ∆t )

gives a pressure difference ∆p ( δ o, δ ) = p ( δ o ) – p ( δ ) where to (or δo) is just a convenient “marker” time or starting time for calculating pressure differences. Simultaneously, the right hand side of Eq. (8.11) is integrated from to to a later time, t giving pCS ∆p ( δ o, δ ) = p ( δ o ) – p ( δ ) = ----------- r p t p G ( δ o, δ ) 2β where the “G function,” G(δo,δ), is defined as 4 G ( δ o, δ ) = --- { g ( δ ) – g ( δ o ) } π and arises from integrating the time function, f(δ), controlling the postfrac rate of fluid loss. For example, for the low fluid loss (high efficiency) limit, g(δ) is given by 4 3/2 3/2 g ( δ ) = --- { ( 1 + δ ) – δ } , 3 while, for the high fluid loss (low efficiency) limit, g ( δ ) = ( 1 + δ )sin

–1

1 --------------------- + δ (1 + δ)

Finally, redefining the variable group (πC rp t p S)/(2β) as ∆P* gives ∆p ( δ o, δ ) = ∆P* G ( δ o, δ ) ,

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(8.12)

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8

Fracture Treating Pressure Analysis

indicating that the variable ∆P* is simply a multiplier which best matches the actual pressure decline behavior to the theoretically perfect behavior defined by “G,” πCS ∆P* = ----------- r p t p . 2β Type Curve Analysis The actual value for ∆P* is found by creating theoretical type curves from the “G function” (as seen in Fig. 8.28) and then matching the actual data to these curves. This is illustrated in the following example.

Fig. 8.28 - Plot of G(δ,δo), Master Curves for Matching Pressure Differences.

Consider a case where a “minifrac” (e.g., a volume of fracturing fluid pumped without proppant) has been pumped down tubing while measuring surface annulus pressure. After shut in, the pressure decline is measured as seen in Fig. 8.29 and tabulated in the table below. The first step in any pressure decline analysis is to determine the fracture closure pressure and closure time. For the example here, it is assumed that pre-minifrac stress tests indicated a (surface equivalent) closure stress of 1500 psi. The minifrac pressure decline reaches this pressure after a shut-in time, ts, of about 26 minutes - giving a closure time, tc, of 26 minutes. This gives a dimensionless closure time, δc, of 1.3, with, since no proppant was pumped, the fracture being completely closed at “closure time.”

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Fig. 8.29 - Example, Minifrac Pressure Decline Data. Table 8.2 - Example Pressure Decline Data. Shut-in Time (min)

ts

0

Pressure (psi)

∆ P(to=4,t) ∆ P(to=10,t) ∆ P(to=20,t) (psi)

(psi)

(psi)

1658

2

1.4

1642

4

2.0

1625

6

2.47

1610

8

2.83

1595

30

10

3.16

1582

43

12

3.46

1569

56

13

14

3.74

1558

67

24

16

4.0

1544

81

38

18

4.24

1534

91

48

20

4.47

1525

100

57

22

4.69

1515

110

67

10

24

4.90

1507

75

18

26

5.10

1498

84

27

28

5.29

1493

89

32

30

5.48

1486

96

39

32

5.66

1481

101

44

34

5.83

1476

106

49

1625-1610 = 15 psi

26 Shut-in Time at Closure δ c = t c /t p = -------------------------------------------------------------- = ------ . 20 Pump Time

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In selecting the “start” times for the pressure difference analysis, all start times must be less than this dimensionless closure time since the analysis has no meaning for pressures below fracture closure pressure. Referring to the “type curve” of Fig. 8.28, one might select the “0.2,” the “0.5,” and the “1.0” curves, since the dimensionless start times, δo, for these curves all come prior to the dimensionless closure time of δc = 1.3. For the δo = 0.2 curve, the corresponding “real” start time is t o = δ o × t p = 0.2 × 20 = 4 minutes . e.g., dimensionless start time, δo, times pump time. Thus a column of pressure differences is created (as seen in Table 8.2) starting at a shut-in time of four minutes. Similarly, a column of pressure differences is created corresponding to a “real” start time of 10 minutes (to = δo x tp = 0.5 x 20) and to a “real” start time of 20 minutes. These pressure difference values are then plotted vs. shut-in-time (as three separate and independent curves) on log-log scales identical to the type curve scales as seen in Fig. 8.30, and the data is “matched” to the theoretical curve.

Fig. 8.30 - Type Curve Match for Example.

Note, however, that the theoretical type curves include two “sets” of curves: three “dashed” curves for dimensionless start times of δo = 0.05, 0.10, and 0.20; and “solid” curves for dimensionless start times of δo = 0.20, 0.50, 0.75, 1.0, and 2.0. The “early time,” “dashed” curves correspond to the low efficiency solution, while the “later time,” “solid” curves correspond to the high efficiency, e.g., low fluid loss, solution. Closure time, found by plotting the pressure decline vs. the Hydraulic Fracturing Theory Manual

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square-root of shut-in time, is used to determine which type curves to use. If the fracture closes at a dimensionless time less than 0.5 (δc < 0.5), e.g., a fracture closing in less than 30 minutes after a 1 hour pump time, then the high curves (dashed) should be used. For closure times greater than pump time, the low curves (solid) should be used. For cases which fall into the gray area in between these limits (e.g., maybe a closure time of 30 minutes after a pump time of 40 minutes) the curves which best match the “shape” of the data should be used, and/or one might interpolate between the two sets of theoretical type curves. 'G' Function Plot for ∆P* Eq. (8.12) showed a linear relation between the pressure decline “differences” and a function of shut-in time - the 'G' Function. As a special case for using this equation, a “start time,” δo, of “0” might be chosen, then Eq. (8.12) could be rewritten as ∆p ( 0, δ ) = ISIP – p ( δ ) = ∆P*G ( 0, δ ) where ISIP is the Instantaneous Shut-In Pressure. This leads to p ( δ ) = ISIP – ∆P*G ( 0, δ ) or ∆P* = – dp/dG . That is, the slope of a linear plot of the shut-in pressure decline vs. 'G' (as defined earlier) gives the “match pressure” ∆P*. Since this 'G' function is generally a complex function of the dimensionless shut-in time, d, the 'G' Function Plot is clearly most amenable to computer generated analysis. Also, in several cases the 'G' function has been found to work better for very high fluid loss cases where closure time is on the order of 20 to 30% of pump time or less. For cases with longer closure times, e.g., closure time 40% (or more) of pump time, the type curve approach discussed above often offers an easier analysis. For the previous example, the pressure decline data is plotted vs. 'G' in Fig. 8.31, where, as before, closure stress is assumed known from minifrac tests to be 1500 psi. (Actually, this would be a “surface equivalent” closure pressure, with “real” closure pressure equal to 4530 psi, e.g., 1500 plus the hydrostatic head of ±7000 ft of water.) At any rate, in the 'G' Function Plot, the slope of the data is taken just prior to closure pressure, though for this plot (which is an excellent example of a 'G' Plot) the slope is relatively constant from shut-in all the way down to fracture closure. Taking the slope of the indicated line shows a slope of -98 psi, which gives ∆P* = 98 psi, essentially perfect agreement with the earlier type curve match analysis.

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Fig. 8.31 - ‘G’ Function Plot.

This plot also shows a distinct slope change at a pressure of ±1500 psi, e.g., just at closure pressure and sometimes, a 'G' Function Plot can be used to determine fracture closure. The procedure is similar to a root-shut-in-time analysis for closure, a distinct slope change is taken to indicate a distinct fracture behavior change, e.g., the fracture closing. Again, as with 'G' Function Plot analysis in general, we have found this analysis procedure to be most useful in low efficiency (high fluid loss) environments - though clearly this example shows a very clear 'G' Function analysis for a case with closure time equal to 1.3 times pump time, e.g., δc = tc/tp = 1.3. A final note concerning 'G' Function Plots is - What 'G' Function should be used? For low efficiency (high fluid loss) cases where δc < 0.4 to 0.5, clearly the low efficiency function is correct. Similarly, for longer closure time cases with δc > 1, the high efficiency (low fluid loss) function as used for Fig. 8.31 is probably most correct. However, for the “gray” area between these limits, some distortion and error can be introduced by the lack of a purely applicable 'G' Function. In these cases, type curve analysis often proves superior by allowing easy, manual interpolation between the two limiting theoretical solutions. Fluid Efficiency Fluid efficiency is defined as the fracture volume (at the end of pumping, e.g., at time = tp) divided by the total slurry volume pumped (e.g., fluid, sand, everything). As an aid in Pressure Decline Analysis, the rate of pressure decline equation can be integrated to determine the volume of fluid lost between shut-in, tp, and the time at which the fracture closes, tp + tc. For a minifrac treatment, e.g., a small volume calibration treatment with no proppant, the volume lost between tp and tp+tc equals the volume of the fracture at tp. Dividing this volume by the total volume injected gives efficiency. Thus, a relationship between closure time and fluid efficiency exists as shown in Fig. 8.32.

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Fig. 8.32 - Efficiency vs. Dimensionless Closure Time.

The efficiency, ef, obtained from this figure is used to define a new variable, ρ, which is used in the type curve analysis and defined as ρ = V f /V L = e f / ( 1 – e f ), or e f = ρ/ ( 1 + ρ ), where Vf is fracture volume and VL is fluid loss volume during injection. ρ can also be determined directly from the type curve analysis in terms of the match pressure, ∆P*, and the net fracturing pressure at shut-in, ps (e.g., ISIP - closure pressure). ρ = π p s /4K g o ∆P* , g o = 1.57 – 0.238 × e f (within 5%,g o = 1.45 ), where Go is the pressure difference function at δ = 0 (discussed on page 8.31) and equal to 1.57-0.238 ef (within 5%, Go = 1.45), and K is a correction to the fluid loss coefficient which accounts for additional fluid loss only during pumping (e.g., spurt loss or opening of natural fissures during injection). However, K cannot (at this time) be determined from any analytical pressure decline analysis so should always be set equal to “1.” These “two” efficiency values supply a means of quality control for fracturing pressure decline analysis. First, efficiency is determined from the dimensionless time-to-close, δc and the graph in Fig. 8.32. Next, the loss ratio, ρ, is determined from the type curve match pressure, ∆P*, and the final net pressure, ps, as discussed above. This value for ρ is then used to calculate an efficiency July 1993

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from ef = ρ / (1 + ρ). These efficiency values should be within 2 to 3 “percentage units” of each other, e.g., 10% vs. 12% would be good agreement as would 90 vs. 92%. If the difference is greater than this, then one might initially check the analysis, choice of closure pressure, etc. If disagreement persists, then it may indicate a real discrepancy between actual fracture behavior, and the theoretical assumptions which form the basis for decline analysis. If the efficiency from time-to-close and the chart in Fig. 8.32 is less than the calculated efficiency (e.g., calculated from ∆P*), the discrepancy could be due to significant spurt loss and/or to fluid loss to natural fractures which are open during injection but which close (or are closing) during the pressure decline. Decline analysis cannot quantify this loss, but can indicate its existence and thus allow appropriate job changes (for example, possibly the inclusion of 100 mesh fluid loss additive to reduce any loss to natural fractures). In addition to this quality control procedure for the decline analysis, Section 8.6 presents a procedure for determining a fracture treatment design schedule based solely on fluid efficiency. Also, efficiency corrections are presented to account for proppant in the fracture at closure, so the pressure decline after an actual propped fracture treatment can be used in a type curve analysis to calculate fluid loss coefficient. Example/Guidelines The following will present some general guidelines for fracturing pressure decline analysis in the context of reviewing an actual field example. The pressure data is the same as that presented and discussed earlier in Fig. 8.29 and Table 8.2. Example - Pressure Decline Analysis: Prefrac tests were conducted on a 7000 ft deep oil bearing formation with a reservoir pressure of 3250 psi and a formation temperature of 240°F. The formation is a thick sand-shale sequence with 5-10 ft sandstone layers (porosity of 12 to 14%) interbedded with 1 to 3 ft thick layers of low porosity siltstones and anhydrites. From pump-in/flowback stress tests, surface closure pressure was found to be 1500 psi. The stress tests were followed by pumping a 20,000 gallon crosslinked gel minifrac (estimated viscosity of ±300 cp) in 20 minutes at an average rate of 24 bpm. At the end of pumping the ISIP was 1658 psi and the postminifrac pressure decline data was shown in Fig. 8.29 (listed in Table 8.2). Lab Tests show the sand to have a Young's modulus of 4 to 5 million psi; the siltstones, 6-8 million; and the anhydrite, 8-10 million. Based on a simple volume percentage, a modulus of 6 million psi is assumed to be representative of the formation. Before proceeding with the example, some general guidelines are given in Table 8.3, and these guidelines will be followed (essentially step-by-step) for analyzing this data and calculating a fluid loss coefficient. Hydraulic Fracturing Theory Manual

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Following the general guidelines, the first step is always to determine fracture closure pressure. For this case, closure pressure was known as 1500 psi from pre-minifrac stress tests and one might simply assume that the fracture closes when the pressure declines to this value. However, it is often a good procedure to conduct a closure stress analysis with the decline data itself. This is particularly appropriate since into a liquid saturated formation (remembering that this is an oil bearing formation) can locally increase pore pressure and thus locally increase closure pressure, e.g., fluid loss can generate what is often referred to as “back stress.” Since this is an oil zone, the pressure decline is first plotted vs. root shut-in time as seen in Fig. 8.33. This shows a distinct slope change at a pressure of 1500 psi, e.g., for this case the minifrac has not altered closure stress. Table 8.3 - Guidelines for Analysis. 1.

Must know when fracture closes (or closes on proppant) a. pressure = known closure pressure b. pressure vs.

t s plot (ts is shut-in time)

2.

Find dimensionless time-to-close δ c = Shut-in time-to-closure / pump-time (tc/tp)

3.

Select 2 or 3

4.

δ o values from master curves such that δ o < about 2/3 δ c Convert δ o to real shut-in time, to = ( δ o) x (tp)

5.

Find pressure differences for each to e.g., ∆ P(to,t) = p(to) - p(t), t > to

6.

Plot a data curve for each to e.g., plot ∆ P(to,t) vs. t on log-log paper with same scale as Master Curves

7.

Draw vertical line at t = tc do not use ∆ data for matching after fracture closure

8.

Draw vertical line at t = tp (shut-in time equal to pump time)

9.

Place transparency of Master over data with vertical “PUMP-TIME” line on Master aligned with vertical “t = tp“line on data

10.

Only moving master vertically, find best match for corresponding to curves - give most weight for greater to curves as these are least affected by any additional fracture extension - give more weight for longer times on each curve (but t < tc)

11.

After match, read

12.

Determine efficiency from

∆ P* (match pressure) from pressure difference scale on left

a. Find efficiency from

δ c and “time-to-close vs. efficiency” chart

b. Use ∆ P* from type curve match and net pressure at shut-in (ps = ISIP - closure pressure) to calculate ef. 13.

Compare ef (a) and (b) If similar within a 2-3 percentage units, proceed to determine and choose correct fracture model and then calculate other variables such as fluid loss coefficient, etc.

Pitfalls 1.

Using pressure data after fracture closed.

2.

Using equations for wrong fracture model.

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Fig. 8.33 - Example Pressure Decline Data - Closure.

This plot also shows closure after about 26 minutes (also see Table 8.2) giving a dimensionless closure time of Shut – In – Time – To – Closure δ c = ---------------------------------------------------------------------------------- = 26 / 20 = 1.3 , Pump Time and 2/3 of this value is about 0.9 - thus, referring to the type curves in Fig. 8.28, the 0.2, 0.5, and 1.0 curves might be chosen for analysis giving real “start” times for constructing the data curves of 0.2, 0.5, and 1.0 times the pump time of 20 minutes, or real start times of 4, 10, and 20 minutes as seen in Table 8.2. As an example, the reference time for calculating the pressure differences for matching the δo = 0.2 curve would be a shut-in time of 0.2 times 20 minutes or 4 minutes. All subsequent pressures are subtracted from the pressure at 4 minutes (1625 psi) to get the actual ∆p curve for comparison to the type curve. This same procedure is followed for the δo = 0.5 and 1.0 curves, giving three curves which are “best fit” matched to the master curves. The pressure differences are calculated as seen in Table 8.2 and then pressure difference is plotted on the “y” axis vs. shut-in time on the “x” axis of a log-log plot (with scales the same size as the master curves) which is then matched with the theoretical curves as seen in Fig. 8.30. This gives a match pressure of ∆P* = 100 psi, noting that since closure time is greater than pump time, the “solid” high efficiency (low fluid loss) curves are used to match the data. The dimensionless closure time of δc = 1.3 is then used with the efficiency chart, Fig. 8.32, to get a “time-to-close” efficiency of 47%. The match pressure of 100 psi along with the net pressure at shut-in, ps, of 158 psi (as seen in Fig. 8.33) is used to calculate efficiency as 3.142 × 158 ρ = π p s /4K G o ∆P* = -------------------------------------------- = 0.86 4 × 1 × 1.45 × 100

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where Go is assumed = 1.45, K = 1, and ef = ρ/ (1 + ρ) = 0.86 / 1.86 = 0.46. Note: If this calculated efficiency was significantly different from 50%, it would probably be best to use this first calculated efficiency to recalculate go = 1.57 - 0.238 * ef, and then use this new value of go to find a new efficiency. It is seldom worthwhile, however, to follow this iteration for more than one time through. This is clearly in excellent agreement with the “time-to-close” efficiency and thus the analysis can proceed with confidence, e.g., there is no indication of “unaccounted for” fluid loss. Note that up to this point, the analysis has been independent of fracture geometry, e.g., it made no difference whether the fracture was radial, confined height, etc. However, once the match pressure, ∆P*, and efficiency have been determined and the efficiency “checked,” then it is necessary to assume a fracture geometry in order to calculate a loss coefficient. For this example, one might initially expect no height confinement based on: (1) no discrete beds with sufficient thickness to contain a fracture, and (2) high modulus which leads to high treating pressures and thus increases any tendencies for height growth. While it is not conclusive, the low net pressure at shut-in of 160 psi reinforces this expectation since confined height fractures often have higher net treating pressures than this. Equations from Table 8.5 can then be used as seen below: First the radius of the fracture is found from 0.134 VG E' x f = ---------------------------------------------2πK∆P*g o ( 1 + ρ ) 6

1/3

( 0.134 ) ( 20, 000 ) ( 6 × 10 ) x f = ----------------------------------------------------------------------------( 2 ) ( 3.14 ) ( 1 ) ( 100 ) ( 1.45 ) ( 1.86 )

1/3

= 211 ft

and this radius is then used to calculate a fluid loss coefficient and fracture width p

p

6

C = [ ( ∆P*x f )/ ( r E' t ) ] = ( 100 ) ( 211 )/ ( 1 ) ( 6 × 10 ) ( 20 ) = 0.0008 ft/ min and 6

w = ( 6π p s x f )/E' = ( 6 ) ( 3.14 ) ( 158 ) ( 211 )/ ( 6 × 10 ) = 0.10 inches. Taking a look at this problem from a slightly different view, assume that postminifrac logs were available which gave indications of a gross fracture height of 350 to 400 ft. This value for ‘H' might then be used in the equations for a confined height fracture (e.g., a Perkins & Kern fracture geometry) as seen below,

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0.134 VG E' x f = -------------------------------------------------------24K∆P*β x g o ( 1 + ρ )H 6

( 0.134 ) ( 20, 000 ) ( 6 × 10 ) x f = ---------------------------------------------------------------------------------------------------------- = 163 ft . ( 4 ) ( 1 ) ( 100 ) ( 0.65 ) ( 1.45 ) ( 1.86 ) ( 375 × 375 ) However, it is immediately noted that this gives a tip-to-tip length of 326 ft which is less than the approximate fracture height of 350 to 400 ft; thus, the Perkins & Kern model would not be appropriate, and the calculations should move on to the radial model (as discussed on page 8.26) or to the Geertsma model calculations (which would be for a fracture with a tip-to-tip length less than the height). For this example, the radial model shows a predicted radius of 211 ft which would give a total, gross fracture height of H = 422 ft, and since this would be in fair agreement with the logs, a radial model would probably be the most appropriate geometry model for describing the test. It is important to note in these calculations that there are several uncertainties; in particular, the final result for fluid loss coefficient (the usual goal for the decline analysis) is strongly dependent on the value of modulus. If this value is not known from core analysis then the final result for 'C' becomes uncertain. In many cases, however, the final analysis can be improved through a procedure of pressure history matching as discussed in Section 8.3. Post-propped-Frac Pressure Decline Analysis Fracture pressure decline analysis as presented above assumes a minifrac test injection, where, at closure, a fracture will be completely closed. However, the same analysis is applicable to postpropped-fracture treatment pressure data, so long as two important points are remembered: 1. After a propped fracture treatment, fracture closure occurs when the fracture closes on proppant. However, at this point, of course, the fracture is not completely closed, but is held partially open by the proppant. Thus the time-to-close efficiency must be corrected as discussed below. 2. The pressure decline analysis assumes that the fracture was free to propagate during the injection period. When proppant is included in a real stimulation there is, of course, always the possibility that due to slurry dehydration and/or proppant reaching the fracture tip, fracture extension will be halted and a tip screenout will occur. This is usually evident from the net pressure behavior and if such a condition occurs, then normal decline analysis is no longer applicable. Note, however, that pressure history matching as discussed below can still be used to analyze the data with the time where the screenout starts (e.g., the beginning of the “unit” slope on a Nolte-Smith plot, Fig. 8.16) being a good marker for history matching analysis. The time-to-close expressions previously presented on page 8.35, assumed the fracture closed completely, e.g., no proppant. Similar analysis can be performed from the postfrac pressure decline Hydraulic Fracturing Theory Manual

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Table 8.4 - Pressure Decline Analysis Calculations. Perkins & Kern (Confined Height) Geometry

xf

1/2

0.134 VG E ' = -----------------------------------------------2 4 K ∆ P *β s g o ( 1 + ρ ) H

w

C

Geertsma deKlerk Geometry

=

[ 0.134 VG E ' ] = ---------------------------------------------8 K ∆ P *β g ( 1 + ρ ) H s o

xf

w

6πβ s p s H / E '

= ( ∆ P *β s H ) / ( r p E '

t p)

C

= =

12πβ s p s x f / E '

2∆ P *β s x f / r p t p E '

Radial Geometry (Unconfined Height Growth) 0.134 VG E ' = ---------------------------------------2π K ∆ P * g o ( 1 + ρ )

xf

w

C

1/3

= ( 6π p s x f ) / E '

= (∆P *x f )/(r pE '

t p)

NOMENCLATURE

βs

- See discussion on reverse side of table

K

- Correction factor for spurt loss, normally K = 1

C

- Fluid loss coefficient (ft/ min

E'

- “Plain Strain” Modulus = E / (1- υ 2) (psi) E - Young’s Modulus, υ - Poisson’s Ratio

ef

- Fluid efficiency = Fracture-volume-at-shut-in / Volume-injected

go

- Constant approximately = 1.45, (go = 1.57 - 0.238 ef)

Hp - Permeable or leakoff height (ft) H

- Gross fracture height (ft)

∆ P*- Pressure decline Type Curve Match Pressure (psi) Ps - Net pressure at shut-in (psi)

ρ

- “Loss Ratio” = Fracture-Volume-at-shut-in divided by Volume-lost-during-pumping = ef / (1-ef)

rp

- Ratio of permeable or leakoff area to total fracture area For P&K or Geertsma rp = Hp / H, for a radial geometry rp is more difficult to define and is normally set = 1

tp

- Injection time (minutes)

VG - Total Injected Volume in Gallons = Vp w

- Average fracture width (inches)

xf

- Fracture 1/2 length or penetration (ft) (Radius for Radial Geometry)

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Table 8.4 - Pressure Decline Analysis Calculations. βs - Average Pressure Correction Factor Pressure decline analysis is based on the average pressure in the fracture, but, unfortunately, the only value that can be monitored is wellbore pressure, which will tend to be slightly higher than the average pressure. The value for this correction factor is a function of fracture geometry and fluid rheology. Geertsma deKlerk Geometry For a fracture with this geometry, Daneshy showed in SPE publications that βp (the correction factor during pumping) is ± 0.85. After shut-in, the correction a f ctor will be higher than this, thus 0.85 < βs < 1.0. Typically, a value of 0.9 is used. Radial Geometry For a radial geometry (or “penny” shaped fracture), βs is near unity. For convenience in simplifying the preceding equations, βs was assigned a value of 2 β s = 3π /32 = 0.925 . Perkins & Kern Geometry Perkins & Kern Geometry For a confined height fracture, the correction factor can vary from 0.5 to 0.8, with a “typical” value of 0.65. The exact value for a particular case is a function of the non-Newtonian character of the injected fluid, and a function of how much viscosity degradation occurs along the fracture during pumping. The non-Newtonian nature of the fluid is characterized by the fluid’s non-Newtonian, n', and this parameter might vary between 0.5 (for very non-Newtonian fluids such as a Nitrogen foam) and 1.0 for an essentially Newtonian fluid such as a linear gel. The amount of viscosity degradation is qualitatively associated with “a,” where a=1 indicates no viscosity degradation along the fracture, a=1 indicates “moderate” viscosity degradation, and a=2 indicates “severe” viscosity degradation from the wellbore out to the fracture tip. The pressure correction factor is found from these two parameters by β s = ( 2 n ' + 2 )/ ( 2 n ' + 3 + a ) . Typical Values for this factor are given below: T(°F) Linear Gel Crosslink Gel Nitrogen Foam Gelled Oil

-

60-80 80-120 - 80-120 140-180 200-250 - 80-120 140-180 - 100-140 150-220

'n

a

βs

1 1 0.75 0.75 0.75 0.5 0.75 0.5 0.75

1 2 0 1 2 1 2 1 2

0.67 0.57 0.78 0.64 0.54 0.60 0.54 0.60 0.54

if the propped volume of the fracture is taken into account. If proppant is considered, the effective fracture volume that will close, Vf', can be written as V f ' = V f – V pr , where Vf is the total fracture volume created and Vpr is the volume of proppant including the porosity of the proppant. In terms of an apparent fluid efficiency, ef', e.g., the efficiency that would be calculated based on closure time and not corrected for the propped volume of the fracture, the actual fluid efficiency can be expressed as

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e f = 1 – ( 1 – f pr ) ( 1 – e f ' ) , where fpr is the volume fraction of proppant pumped (including proppant porosity) relative to the total slurry injected and defined as f pr = V pr /V p = W / ( ρ pr V p ( 1 – φ ) ) . W is the proppant weight, ρpr is the specific weight of the proppant material, e.g., 165 lb/ft3, 2.65 gm/cc, 22 lbs/gallon for sand, φ is the proppant porosity (typically on the order of 0.40 since this refers to a proppant pack with essentially “zero” stress), and Vp = Vfl+W/ρpr. For example, assume a fracture treatment containing 100,000 gallons of gel and 300,000 lbs of sand is pumped at a rate of 30 bpm. After the end of injection, the pressure decline is monitored and fracture closure is detected at tc = 45 minutes. The total volume injected is V p = 100, 000 gals + [ 300, 000 lbs/(22 lbs/gal) ] = 113, 636 gals . Substituting Vp into the equation for fpr, f pr = 300, 000 lbs/ [ ( 22 lbs/gal ) ( 113, 636 gals ) ( 1 – 0.40 ) ] = 0.179 . Total pump time was 113,636 gallons/(42 gal/bbl)/(30 bpm) = 90.2 minutes and with a closure time of tc = 45 minutes, the dimensionless time-to-close was δ c = 45/90.2 = 0.50 . This value of δc = 0.50 is used with the time-to-close/efficiency relation to give an “apparent efficiency” of 28%, e f ' = 0.28 . However, the actual efficiency must be greater than this since this “apparent efficiency” is based on closure on proppant, and, of course, the fracture is not completely closed at this point. The actual efficiency is then found from e f = 1 – ( 1 – f pr ) ( 1 – e f ' ) = – ( 1 – 0.179 ) ( 1 – 0.28 ) = 0.41 . to be equal to 41%. This efficiency of 0.41 is now used with the pressure decline data (prior to closure on proppant) to perform a type curve analysis using the same procedures discussed previously and outlined in Table 8.3.

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8.5 Pressure History Matching The most powerful method of interpreting/analyzing fracturing pressure data is via the history matching of actual net treating pressure (and pressure decline) data - generally with a numerical fracture simulator. Another method of looking at this is - Calibrating the Fracture Model for the particular formation being studied. Also, whether a numerical model is used, or the simple equations below are used, some simple pressure history matching can overcome the uncertainties involved in fracturing pressure analysis.

Pressure Decline (Fluid Loss; Sand Schedule)

Treating Pressures (Critical Pressure)

Simulator

Improved Designs

Fig. 8.34 - Pressure History Matching

These uncertainties mainly arise since there are essentially more variables than there are equations. The first of the two main equations can be represented by (from Section 8.3) E' 3/4 p net = ----- [ µQL ] H where the net treating pressure (and thus the value for ps used in the decline analysis) is mainly a function of the modulus of the formation and the gross or total fracture height, H. The second main “equation” is the pressure decline behavior which might be represented by the ∆P* value πCS ∆P* = ----------- r p t p . 2β where 'S' is the fracture stiffness which (for any fracture geometry) is primarily a function of fracture height and the formation modulus. Thus there are three main variables or unknowns, modulus, E, height, H, and fluid loss coefficient, C. The important point here is that since there are basically three unknowns and only two “equations,” these equations and any solution for them is interde-

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pendent. For example, simply solving the pressure decline equations for a loss coefficient gives no assurance that the answer is meaningful; i.e., is the modulus and fracture height used to calculate the fluid loss consistent with the net treating pressure. If these values are consistent, then the fluid loss coefficient determined from ∆P* will be a reasonable (though possibly still not unique) value. This history matching process is illustrated in Fig. 8.34. For an example, consider the data in Fig. 8.35. The Nolte-Smith plot of net treating pressure shows increasing pressure with a small positive slope, indicating a confined height fracture and a numerical model was used to history match this data and thus determine a height and modulus consistent with the actual treating pressure behavior (with the modulus also being consistent with published industry data). This height and modulus can then be used with some confidence to calculate a fluid loss coefficient from the decline analysis. At this point, however, the calculated value for 'C' might be different from the value used in the initial numerical modeling of the treating pressure, and if this difference is significant (e.g., greater than 20 to 30% difference), the modeling should be redone with the new value for 'C', modifying the height and/or modulus values as required. The new height and modulus would be used to calculate a revised fluid loss coefficient, e.g., one would iterate. Note, however, that it is very seldom necessary more than one time since the net treating pressure is relatively in- sensitive to a precise value for 'C'. Because of this relationship (that net pressure is relatively insensitive to fluid loss), the history matching should always begin with matching the net pressure, with the modulus and height thus determined then used to calculate a loss coefficient .

Fig. 8.35 - Case History of Pressure History Matching

With this history match, then, one has a set of three main variables (H, E, & C) which yield a good description of the minifrac test. These can then be used with some confidence to consider different July 1993

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treatment designs, larger/smaller volumes, etc. Note, however, that even though the three values may be “consistent” they are still not necessarily the correct values. External data is required to fully determine the problem. For example, core data for the modulus might make this a fully determined problem. For the case in Fig. 8.35, postfrac temperature logs showed a height in fair agreement with the history matching, making this a fully determined problem. Simple History Matching The use of a numerical model for pressure history matching offers many advantages including the ability to handle fairly complex geology, the ability to simulate the entire history of a test, and (possibly most important) the ability to proceed immediately to considering different treating schedules, treatment volumes, etc. Since these considerations are based on a set of data that has accurately described the “past,” one can simulate other treatment designs and arrive at an optimum treatment with some confidence. However, in many cases an appropriate model may not be available, but, rather than abandon history matching, it is often possible to use quite simple equations to gain some of the benefits achievable from detailed modeling and matching. In particular, for a confined height fracture (e.g., a case where the net treating pressure increases during a job as seen in Fig. 8.35), treating pressure is generally dominated by fluid flow considerations and can often be reasonably predicted (e.g., maybe within ±10%). For a confined height fracture, net pressure can be approximated by the following equation 3

p net

1/4

0.015 [ E µQx f ] = -------------------------------------------H

0.134 VG E x f = ------------------------------------------------------24K∆P*β s g o ( 1 + ρ )H

(8.13)

(8.14)

where µ is the average fluid viscosity (centipoise), 'VG' is the total fluid volume pumped in gallons, 'Q' is the pump rate in bpm, 'E' is the modulus in psi, xf is the fracture 1/2 length in feet, 'H' is the gross fracture height in feet, and ∆P*, ρ, etc., are determined from the pressure decline analysis as discussed earlier starting on page 8.30. For other geometries such as an unconfined, radial fracture or a case where the fracture is initially confined but then experiences significant height growth, rock mechanics considerations at the fracture tip begin to play a more dominant role, often precluding the use of such simple, analytical equations. However, such equations can be developed and may sometimes prove useful. For example, for a radial fracture, 3 1/4

p net

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0.0078 [ QµE ] = ----------------------------------------2/3 xf 8-48

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1/3 0.134 VG E' x f =  ---------------------------------------------- .  2πK∆P*g o ( 1 + ρ )

Simple History Matching Procedure & Example The suggested procedure for use of such equations is a type of single data point history matching. That is, ps, the final net pressure (e.g., ISIP minus closure pressure) is matched to determine a compatible set of 'H' and 'E' values to use in calculating fluid loss coefficient, 'C'. These values for modulus and height are then used in the pressure decline equations to recalculate the fracture 1/2 length, xf, and the loss coefficient. If these new values for penetration and 'C' are significantly different from the first values, it might be necessary to iterate one more time. However, as mentioned above, it is seldom necessary to iterate more than once. If the final height determined from this pressure matching is consistent with the geology and/or possibly other log indications of fracture height; or if the modulus is consistent with core data; then the final three major variables (E, H, and C) can be used with confidence. As an example, consider the minifrac studied earlier in Section 8.4, with some of the relevant data from that case listed in Table 8.5. Table 8.5 - Minifrac Analysis Data. Test Parameters

Volume=20,000 gallons Q = 24 bpm

tp = 20 minutes µ = 300 cp

Minifrac Analysis Parameters

K =1 DP* = 100 psi

ef = 0.46 ρ = 0.86

Pressure Decline Analysis Initial Results (Calculations for Radial Fracture Geometry)

E' xf C

= Assumed equal to 6x106 psi = Calculated as 211 ft = Calculated as 0.0008 ft/ minute

Using this data in the radial fracture geometry calculation for pnet gives a predicted net pressure at shut-in (e.g., ps) of 240 psi, somewhat greater than the actual measured value of ps = 158 psi. Remembering that the modulus was strictly an assumed value, one might then use a lower modulus, say 4x106 psi to calculate (still using the initial value for xf) a final net pressure of 178 psi, in fair agreement with the actual data. This new modulus is then used to revise the initial estimate of fracture radius (xf), with a new calculated value of xf = 185 ft, and a new calculated loss coefficient of 0.0010 ft/ minute . With this new fracture radius of 185 ft, and the new modulus of 4 million psi, the new calculated ps is 195 psi, which is still about 20% greater than the actual data, thus one more iteration might be in order with a modulus of maybe 3.5x106 psi. At the end of that final iteration, a set of the three major variables (H, E, and C) would be determined which are compatible with the minifrac data. In addition, since the calculated fracture radius of ±190 ft (which gives a July 1993

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gross fracture height at the wellbore of 380 ft) is consistent with fracture height logs, it is probable that these values are a very good solution to the actual in-situ conditions. Complex Geology Effects Pressure analysis might be considered “proven” for simple geologies, making it a practical tool for many (if not most) cases. In general, even, it might be stated that where the basic theory and analysis methods break down - the problems are related to some more complex geology. These geologic complexities can further be “categorized” into cases involving: (1) multiple formation layers and (2) natural fractures. In fact, the bulk of the problems in analyzing fracturing pressure data or in utilizing the results of such analysis can be traced to one of these complicating factors. The effect of natural fractures was discussed in Section 8.4, and this effect is often identifiable from a constant net pressing pressure on a Nolte-Smith plot (e.g., a “critical” pressure) and sometimes by comparing the type curve match efficiency with the efficiency derived directly from the time-to-close. The possible effects of multiple formation(s) layers is more difficult to categorize since such multi-layered geology can lead to gross distortions and changes with time of the basic fracture geometry. As an example, consider the case pictured in Fig. 8.36, where a hydraulic fracture was initiated in one zone, but then penetrated a barrier and “broke into” a zone with lower closure stress. During the remainder of the pumping, the lower stress zone will accept most of the injected fluid. That is the “main” fracture will not be in the zone where the fracture started. After shutdown, however, one might expect the barrier between these two zones to close rather quickly - isolating the perforated interval from the “main” fracture. Thus the pressure decline behavior will be dominated by the characteristics of the perforated zone, and may give little or no information concerning the redirection of the fracture geometry, or the characteristics of the lower stressed zone which accepted most of the injection. Possibly, though, such behavior may be inferred through an observation of some decline in the net treating pressure indicating the height growth combined with discrepancies between the ∆P* derived efficiency and the efficiency derived from the time-to-close. Another example of the effect of multiple layers might be seen in the “Big” pressure decline analysis problem. The problem as described and several parameters determined from the pressure decline analysis are included in table Table 8.6. Using the simple history match equations from page 8.48 (for a confined height, “Perkins & Kern” geometry since the net pressure for the minifrac increased indicating height confinement), 3

p net

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1/4

0.015 [ E µQx f ] = -------------------------------------------H

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(8.13)

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Fig. 8.36 - Fracture Going Out of Zone.

0.134 VG E x f = ------------------------------------------------------24K∆P*β s g o ( 1 + ρ )H

(8.14)

and the problem definition data from Table 8.6, one calculates a final net treating pressure (e.g., net pressure at shut-in) of 688 psi, 20% less than the actual value of about 860 psi. Since net pressure is most affected by fracture height and modulus, either the fracture height must be less than the gross zone thickness (e.g., less than 150 ft), or the modulus of the formation(s) must be greater than 7x106 psi, or “?”. Since it might be unexpected (but not impossible) for the fracture height to be less than the gross formation thickness, an initial approach to history matching this data would probably be to increase the modulus. Doing this shows, after a couple of iterations, a modulus of 9x106 psi giving a calculated final net pressure, ps, of 885 psi, in near perfect agreement with the actual data. The new calculated values for xf and 'C' are then 802 ft and 0.00075 ft/ minute , respectively.

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Table 8.6 - “Big” Pressure Analysis Problem.

Problem Definition Volume Pumped = VG = 38,000 gallons E = Modulus, estimated as 7 million psi Gross formation thickness = H = 150 ft Leakoff Height (= net height?) = 110 ft Rate = 35 bpm Pump Time = 25.5 minutes Fluid Viscosity estimated at 300 cp Pressure Decline Analysis Variables ∆P* = 260 psi Final Net Treating Pressure = ps = 860 psi Efficiency = 0.62 ρ = 0.62 / (1 - 0.62) = 1.63 Initial Calculations Fracture 1/2 Length = 624 ft C = 0.00095 ft/ minute Thus the pressure history matching gives a set of three major variables of H = 150 ft, E = 9x106 psi, and C = 0.00075 ft/ minute , which satisfy both the final net treating pressure of about 860 psi and the pressure decline behavior of ∆P* = 260 psi and efficiency = 62%. However, since core data indicated a modulus on the order of 7 million psi, what might explain the higher apparent stiffness of the formation(s)? A possible answer to this might be seen in Fig. 8.37, which illustrates the “geology” of the formation, showing that the 110 ft net height (out of the 150 ft gross section) is actually composed of two distinct sandstone layers with ±30 ft of shale separating the two zones. Since the increasing pressure behavior during the minifrac seems to indicate good height confinement (e.g., the over- and underlying shales having higher closure stress than the sands), it might be reasonable to assume that the “separating” shale might also be a barrier (e.g., have a higher closure stress) to fracture growth. Thus this shale would “pinch” the fracture width (as seen Fig. 8.37), causing the fracture to behave “stiffer” than a simple, 150 ft high fracture, thus explaining the need for an unusually high modulus if the basic pressure analysis methods are to be used. Given this more complex geology, a fracture simulator capable of treating multiple formation layers might be used to history match the actual data, as seen in Fig. 8.38 for the treating pressure behavior. Once the model is successfully set up to “history match the past,” it can then, of course, be used with some confidence to design future jobs. Or, in fact, where the dominant effect of the “multiple zones” is to just stiffen the fracture, a simple “Perkins & Kern” type procedure might be used for frac design by using the artificially high modulus value to account for the effect of the shale layer on fracture width. Hydraulic Fracturing Theory Manual

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Fig. 8.37 - Actual Fracture Geometry - Pressure Decline Analysis Problem.

Fig. 8.38 - Nolte-Smith History Match, Pressure Decline Analysis “Big” Problem.

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The above two brief examples have illustrated the extreme range of effects that multiple formation layers can have on fracture pressure analysis - from the case of the frac growing totally out of zone and almost invalidating the analysis methods; to a case where the basic analysis methods are fine, but a slightly artificial modulus must be used in order to accurately describe the fracture width. In general, it is this extreme range of effects that makes general statements about the effects of complex geology difficult or impossible to make. However, while multiple formation layers clearly create problems, two recent studies (Warpinski25 and Miller and Smith22) have shown that the combination of pressure decline analysis with numerical modeling/history matching provides a useful, powerful tool for analysis of such complex geologic cases.

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8.6 Proppant/Fluid Schedule From Pressure Decline While the ultimate goal of a well stimulation treatment is to increase production using the most cost effective procedures and materials, the actual, final “product” from the treatment design and analysis consists of pumping schedules specifying volumes, proppant addition concentrations (as seen in Fig. 8.39), and specifying in-situ time-temperature history for the injected fluid (as seen in Fig. 8.40 for use in selecting and specifying materials). The pressure analysis procedure discussed in this chapter have concentrated on measuring or determining the physical variables which govern fracture growth, e.g., in-situ stresses, modulus, fluid loss coefficient, etc. With these variables properly measured, it becomes possible, through the use of a numerical fracture model, to develop pumping schedules for achieving the desired goals. However, in some conditions existing wellbore limitations, or time/budget constraints may not allow adequate time or data collection for measuring the individual variables governing fracture behavior. However, it will be shown and discussed below (following Nolte14) that the final “products” (e.g., pumping schedules) are a strong function of a single variable, the fluid efficiency for the treatment. If this single value can be determined from a prefrac injection test (or from experience gained on previous treatments in the area) then a pumping schedule can be determined directly from this one value, e.g., efficiency is essentially a “state variable” for the propped fracturing process. Note however, that the efficiency derived schedule is developed from a preselected total treatment volume - with no direct consideration of fracture length, fracture conductivity, etc. (e.g., no direct consideration of creating the best or most cost effective stimulation for a particular formation).

Fig. 8.39 - Treatment Schedule, Proppant Addition Concentrations.

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Fig. 8.40 - Treatment Schedule, Fluid Temperature History.

Advantages of an Efficiency Derived Schedule 1. Allows development of an “optimum” pumping schedule based on a direct measurement of fluid efficiency for the particular well and formation being treated. 2. The analysis requires relatively simple data collection and can generally be done from surface pressure information. Also, the analysis can be completed in a short time making it an ideal procedure for field use. 3. Final pumping schedule is not significantly affected by actual fracture geometry, thus efficiency procedures can be used in formations (such as coal seams for one example) where actual fracture geometry may be very complex. Also, this “independence” from fracture geometry makes the procedure ideal for initial treatments in a new, “wildcat” area. Disadvantages of an Efficiency Derived Schedule 1. Prefrac injection must use same fluid as planned for the stimulation and must be pumped at the same rate as will be used for the actual propped fracture treatment. 2. Efficiency procedure assumes no knowledge of actual fracture geometry, thus the pre-selected treatment volumes used as a basis for developing the final pumping schedule may be insufficient for achieving required production, or the volumes may be excessive, incurring additional costs and unnecessarily increasing the risks associated with completion operations. The information generally needed for a stimulation are: (1) the fluid volume to be injected, (2) the injection rate, (3) the proppant addition schedule, (4) the resulting propped fracture width and length, and (5) the amount of time that fluids will be exposed to reservoir temperature. This expo-

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sure time is needed for selecting the required fluid system along with the amount and type of fluid additives. For a new area, the volume limitations may be determined from budget constraints, or, for a more developed area, volumes may be specified based on the requirements to achieve a relative change in fracture length (or conductivity) from that achieved by prior treatments. Finally, pump rate is often prescribed based on horsepower limitations or pressure limit constraints of the wellhead and/or tubulars. While, as mentioned above, the efficiency procedure gives no information on propped fracture length or width, it does give the final ingredient, that being the required pad volume and proppant addition schedule. While lack of knowledge of final propped fracture dimensions precludes any quantitative development of the treatment design in terms of postfrac production; determining the required pad volume and pumping schedule still remains the most difficult and critical to obtain of any of the necessary information. As an example, consider the final fracture conductivity distribution pictured in Fig. 8.41. This is the results of a numerical simulation for a case which (purposefully) included an excess pad volume. As seen in the figure, at shut-down (e.g., at the end of pumping) the propped fracture 1/2 length is on the order of 500 ft, which was the design length. However, due to the excess pad volume, the created length is nearly twice as long. Since the area of high fluid loss is located near the fracture tip, fluid continues to flow from the wellbore region of the fracture out toward the fracture tip after shutdown. This “afterflow” results in a proppant redistribution leaving a relatively (undesirable) low fracture conductivity in the near well area - reducing future production rates. Another example of the critical need for pad volume/proppant schedule information is, of course, the case of inadequate pad volume. This will result in the slurry portions of a treatment dehydrating and “screening out,” reducing the propped fracture length and possibly forcing remedial wellbore cleanout operations. Thus, even for fixed treatment volume, either too much, or too little pad volume is detrimental to final postfrac results. Determining Fracture Fluid Efficiency As discussed in Section 8.3, the fluid efficiency for a treatment can be determined by measuring the time-to-close after a fracturing rate injection. Thus the most direct way to measure fluid efficiency for use in an efficiency design is to conduct a prefrac “calibration treatment” or “minifrac test.” This is the most common method when using the efficiency design techniques, and data collection and analyses for such prefrac testing are thoroughly discussed in earlier sections and will not be repeated here. However, an alternate method may be available when earlier propped fracture treatments have been performed in the area, and where formation properties such as thickness and permeability do not change radically from well-to-well. As an example, consider the ideal Nolte-Smith net pressure plot in Fig. 8.42, and assume this is a field measured curve from an offset propped fracture stimulation. At a pump time of 20 minutes, proppant is on the formation (e.g., pad was pumped for twenty minutes) and one hour later (e.g., at a pump time of ±80 minutes) pressure starts to increase indicating that fracture growth has stopped. Probably this job would have been pumped to compleJuly 1993

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Fig. 8.41 - Fracture Conductivity Redistribution Resulting from Excess Pad Volume.

tion, since pressure only increases by ±500 psi after the start of the “screenout,” with this relatively small increase possibly not even being noted in normal surface pumping records. However, unless this screenout was a planned occurrence, it is probable that fracture length is much less than desired. While unfortunate for this well, the information can aid in future treatment designs by simply noting the pad percentage at the start of the pressure increase.

Fig. 8.42 - Use of Field Data to Determine Fluid Efficiency.

For this case, pressure starts increasing after ±80 minutes, with a pad pump time of 20 minutes thus pad percentage for the “first part of the job” was 25%. For future treatments, the pad percentage should be increased in volume to at least equal 25% of the total pump time. More accurately, since pad percentage is related to job size, the pad percentage of 25% could be used to “back out” Hydraulic Fracturing Theory Manual

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a fluid efficiency. The fluid efficiency thus measured for the first 80 minutes of the job is then used to calculate an expected fluid efficiency for a larger treatment (as discussed below), and this expected efficiency for the total job is used to determine the new, required pad percentage and pad volume. Pad Volume Once an efficiency (or expected efficiency) has been determined for a proposed treatment, the required pad percentage for the job is found from the simple relation 2

f p = (1 – e f ) + f c

(8.15)

where ef is the expected efficiency for the treatment, fp is the required pad fraction for the treatment, and fC is a “correction” term. In developing this, consider the curve shown in Fig. 8.43. This curve illustrates fracture area growing with time (or volume). Further, consider that at some time, ftp (where tp is the total pump time and f is a fraction) a switch is made from pumping pad to pumping proppant laden slurry. Thus, the initial fracture area created (e.g., the small element of fracture created just as pumping starts) is exposed to fluid loss for the entire pump time tp, with this fluid loss coming out of the pad from time '0' to time ftp, with subsequent fluid loss coming out of, and serving to dehydrate, the proppant laden slurry.

Fig. 8.43 - Variables for Determining Pad Percentage.

Similarly, one might consider some later element of the created fracture area, da, which is created at time = τ (e.g., before that time it did not exist since the fracture had not reached that point) and has a total exposure time to fluid loss of η = (tp - τ). For some fraction of that total exposure time (τ < tp), fluid loss from this increment of the fracture area will come from the pad volume. After that point, the slurry “front” passes and subsequent fluid loss out of that element of the fracture July 1993

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area will be coming out of the slurry. Assume then, that this point in time where the slurry front passes an element of fracture area is similar for each element of the fracture. Then for some incremental area, da, total fluid loss exposure time is τ. For a fraction of this total time, fη, fluid loss is from the pad while for the remainder of the exposure time, fluid loss is from slurry. The volume of fluid lost during a fraction, f, of each incremental fracture area's fluid exposure time, η, can then be found by integrating14 A fη

V Loss ( f ) = 2C

dη

∫ ∫ -------η da 0 0

=

f x V Loss

where VLoss is the total volume of fluid lost during the entire pump time. Thus the portion of fluid lost for a (constant) fraction of the fluid exposure time of each incremental area of the fracture is simply proportional to f . Also, if this assumption concerning the slurry “front” passing each element of the fracture is correct, then this simple curve (dashed line in Fig. 8.43) defines the perfect pad. That is, the slurry front reaches the fracture tip just as pumping stops, e.g., it neither reaches the tip prematurely leading to proppant bridging (a screenout), nor does it fail to reach the tip, leaving a portion of the fracture without proppant or allowing harmful “afterflow” proppant redistribution during fracture closure. Clearly then this is a possible curve for the optimum pad volume, and based on this curve, the desired fraction, f = fp, is readily found. As discussed above, the volume of fluid lost during a fraction, f, of each fracture elements' fluid exposure time, equals f x VLoss, where VLoss is the total loss volume during the treatment. For the ideal pad then this fractional lost volume exactly equals the pad volume giving f p xV p =

f xV Los

where Vp is the total volume injected during the entire pump time tp. Since efficiency, ef, is defined as fracture volume at the end of pumping divided by the total volume injected, then VLoss, must equal V Loss = ( 1 – e f )xV p and the ideal, theoretical pad fraction is given by 2

f p = (1 – e f ) .

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However, reviewing the dashed (“slurry front propagation”) curve in Fig. 8.43 shows a vertical slope at the beginning, e.g., implying an initially infinite velocity for the slurry front. This is clearly an impossibility, and leads to a correction factor,14 fC, as shown in Fig. 8.44.

Fig. 8.44 - Correction Factor for Pad.

Thus, more generally, the ideal pad percentage, fp, is given by 2

f p = (1 – e f ) + f C where fC = 0.05,

efficiency, ef, > = 0.20,

= ef/4,

(8.13)

efficiency < 0.20

.

Using this (somewhat in reverse) with the ideal case shown in Fig. 8.42 where the pad percentage (prior to start of screenout) was 0.25 gives an efficiency on the order of 2

2

0.25 = ( 1 – e f ) + 0.05, ( 1 – e f ) = 0.20 e f = ± 0.55 for the first 80 minutes pumping of that job. (Note that in this case, the final efficiency is greater than 0.20, thus the initial estimate of fC = 0.05 was correct, otherwise it would have been necessary to iterate on the correction term in order to find the actual efficiency.) Of course, while the dashed curve in Fig. 8.43 represents the general character of an ideal pad stage, the assumption that each incremental fracture area element is exposed to pad fluid loss and slurry fluid loss in the same ratio (e.g., 'f' is a constant for each incremental element of the fracture) is not proven. As one “proof,” or at least justification, for this assumption, pad percentage and proppant addition schedules (as discussed in the following section) arising from the efficiency analysis are compared to schedules developed from computer models in Fig. 8.45. This shows actual treatment schedules from three separate areas, representing fluid efficiencies ranging from 18 to 70%. The low loss, high efficiency example is for a tight gas field in Colorado where height July 1993

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confinement was virtually perfect; the middle curve comes from treatment histories from a gas field in East Texas where some height growth generally occurred; and the third, high fluid loss example, was for fracturing in a thick, moderate permeability, carbonate formation in the North Sea. In each case, computer model designs were based on extensive data collection programs and field experience, and, in each case, the final proppant schedule is seen to be quite accurately determined by fluid efficiency alone.

Fig. 8.45 - Comparison with Computer Models.

Proppant Addition Schedule The average proppant concentration, cavg, for a treatment is c avg = W /V p

(8.16)

where W is the total weight of the proppant and Vp is the total slurry volume (fluid plus proppant) injected. Note here that this definition of proppant concentration differs from the normal field usage of pounds-of-proppant per gallon-or-fluid. Additionally, cf is defined as the final, maximum proppant concentration pumped during a treatment, and due to fluid loss, cf must be greater than cavg. One possible design goal for a propped fracture stimulation is to, at the end of pumping, have a uniform proppant concentration, equal to cf, from the wellbore to the fracture tip. This will generate a fracture with reasonably uniform conductivity along the fracture length (assuming a single type of proppant is used) and will maintain fairly uniform slurry viscosity throughout the fracture. In terms of the fracture volume at the end of pumping, V = ef x Vp, this final proppant concentration can be written as c f = W /V = W / ( e f V p ) . Hydraulic Fracturing Theory Manual

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Combining this with the definition of average concentration gives c D – avg = c avg /c f = e f , where cD-avg is a “normalized” value for average concentration. Similarly, a normalized concentration at any point in time during the treatment is defined by c D = c/c f , and, for convenience a new “time scale” is defined, ξ, where the new time scale starts at “0” when proppant is started and reaches a value of “1” at the end of the job as illustrated in Fig. 8.46.

Fig. 8.46 - Time Scale, ξ, for Determining Proppant Addition Schedule.

ξ = ( t – f t p )/ ( t p – f t p ) . In terms of this new time scale, certain fixed values for the normalized proppant schedule, cD, can be stated c D ( ξ ) = 0 ( ξ < = 0 ), cD ( ξ ) = 1 ( ξ < = 1 ) c D – avg = e f . Assuming a function for the proppant schedule of the form cD ( ξ ) = ξ

∈

(0 < =ξ < = 1)

the exponent, ∈, can be evaluated from the above limits on the function, cD, given above July 1993

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or after incorporating a “correction” factor discussed on page 8.62 for the pad volume calculations ∈ = 1 – e f – f C /e f . Thus a “dimensionless” or “normalized” proppant addition schedule is defined by c D ( ξ ) = ξ ε ( 0 < = ξ < = 1 ) , ∈ = 1 – e f – f C /e f ,

(8.17)

and since this function satisfies the numerical end points for a proppant schedule as stated above, satisfies the relation for the final average proppant concentration, and also provides a monotonically increasing schedule as commonly utilized in practice - it is expected to be a reasonable approximation to an ideal schedule. As seen in Fig. 8.45, again for three cases covering a range of conditions and fluid efficiency, this simple relation does indeed provide an acceptable pumping schedule. Effect of Treatment Volume In an example considered in the discussion of Fig. 8.42, from the pad pump time of 20 minutes and the time when a screenout started at 80 minutes (pad fraction, fp, of 0.25), it was found that the fluid efficiency for the first 80 minutes of pumping was ±55%. Also, a minimum design criteria for future treatments in that formation was to use a pad volume equal to 25% of the total volume to be pumped. However, this fluid efficiency of 55% is applicable for the first 80 minutes of the job and, in general, fluid efficiency is a function of job size and will tend to decrease as pumping time gets longer and longer. Thus for a job requiring a total pump time of about 2 hours as shown in Fig. 8.42, the expected efficiency would be somewhat lower than 55% and the required pad percentage would be somewhat greater than 25%. Fluid efficiency is related to pump time (e.g., volume and rate), fluid loss coefficient, C, and to the fluid loss area, or rp, the ratio of loss area to total fracture area. While these are the primary variables governing efficiency, it is also slightly affected by fracture geometry (e.g., confined height vs. radial fracture growth) and fluid rheology. For a general case there is no analytical solution for fluid efficiency, however, as with the other fracturing pressure decline analyses discussed earlier, it is possible to place certain bounds. For example, for efficiency approaching “0” (e.g., very high fluid loss), fluid efficiency is proportional to time raised to a power14 e f ≈ t**

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– ( 2n + 1 )/ ( 4n + 4 ) – n / ( 2n + 2 ) – ( 5n + 2 )/ ( 82 + 8 )

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where 'n' is the power law exponent for a non-Newtonian fluid. 'n' generally ranges between 0.5 and 1 for common fracturing fluids, and using n = 0.75 (a typical value for crosslink gels) gives Geometry – 0.357 "PK" e f ≈ t** – 0.214 "GdK" Geometry . – 0.411 "Radial" Geometry While the range between these various possible fracture geometries is possibly significant in some cases, it is noted that the values above are for the limited case of very high fluid loss. As efficiency approaches “1” (e.g., no fluid loss), then the fracture geometry does not effect efficiency, and, in the above form, efficiency is proportional to time raised to the “0” power, e.g., 0

e f ≈ t = constant = 1 . Interpolating between these limits gives a ratio of efficiencies between two different pump times (t2 and t1) as ( e f 2 /e f 1 ) = ( t 2 /t 1 ) **

– 0.357 ( 1 – e f 1 ) – 0.214 ( 1 – e f 1 ) – 0.411 ( 1 – e f 1 )

"PK" Geometry "GdK" Geometry , "Radial" Geometry

but, generally, acceptable accuracy is obtained by simplifying the above ratio to a single relationship ( e f 2 /e f 1 ) = ( t 2 /t 1 )

–( 1 – e1 ) ⁄ 3

(8.18)

Example As an example, consider a case where a “minifrac” test was pumped. The test consisted of a crosslinked gel identical to the fluid planned for use during the propped fracture treatment. The test used 25,000 gallons (595 barrels) pumped at 25 bpm with a total pump time, tp, of 23.8 minutes. Fracture closure was observed 28.6 minutes after shut-in, e.g., tc = 28.6 minutes. This gives a dimensionless closure time of δ c = t c /t p = 28.6/23.8 = 1.20 And, from Fig. 8.32, δc of 1.20 gives ef = 0.45 (45). Find Actual Job “Expected” Efficiency Now assume that it is desired to pump an actual propped fracture treatment with a total slurry volume of 100,000 gallons and a final proppant concentration of 8 ppg (pounds of proppant per fluid gallon). The actual treatment will also be pumped at 25 bpm, and it is important to note here that July 1993

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while the minifrac efficiency can be corrected for the larger volume, it cannot be corrected for rate changes, thus in order to use simply the efficiency from the minifrac, the propped stimulation treatment must be pumped at the same rate. This gives [using Eq. (8.18)] an expected efficiency for the actual treatment of – ( 1 – 0.45/3 )

e f 2 /0.45 = ( 4/1 ) – 0.18 e f 2 = ( 0.45 ) ( 4 ) = 0.35 = 35% . Treatment Pad Percentage The actual treatment pad percentage is then found from Eq. (8.15) 2

f p = ( 1 – 0.35 ) + 0.05 = 0.47 , and since the total expected treatment volume is 100,000 gallons, the pad stage should consist of 47,000 gallons. Proppant Addition Schedule The “proppant schedule exponent,” ε, is then found from ε = 1 – e f – f C /e f = 1 – 0.35 – 0.05/0.35 = 0.51 and the dimensionless proppant schedule is given by c D ( ξ ) = ξ ε (0 < = ξ < = 1),ε = 0.51, and this equation is used to construct the simple table shown in Table 8.7, where the slurry volumes shown are “arbitrarily” selected points which will be used to construct a curve of prop concentration vs. slurry volume. It is particularly important to note that the calculations are conducted in terms of slurry volume and slurry concentration, e.g., pounds of proppant per slurry gallon, so a conversion is necessary to the more common industry terminology of “ppg” (pounds of proppant per fluid gallon). These conversions from ppg (pounds of proppant per fluid gallon - Cfl) to pounds of proppant per slurry gallon (Csl) have been made using the formulae C sl = ( C fl × S.G. × 8.33 )/ ( C fl + S.G. × 8.33 ) and C fl = ( S.G. × 8.33 )/(S.G. × 8.33 /C sl – 1 ) .

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Proppant/Fluid Schedule From Pressure Decline

Table 8.7 - Application of Proppant Addition Schedule. Total Treatment Volume - 100,000 Slurry Gallons Pump Rate - 25 bpm Proppant is sand - S.G. = 2.65 Max Proppant Concentration is 8 ppg (5.87 pounds per slurry gallon) Slurry Volume (gallons)

ξ

47,000

0.0

59,720

0.24

72,970 86,750 100,000

Pounds of Prop per Slurry Gal

PPG (lbs of prop per fluid gal)

0.0

0

0.0

0.48

0.48x5.87 = 2.82

3.5

0.49

0.70

4.10

5.2

0.75

0.86

5.05

6.6

1.0

1.0

5.87

8.0

cD

Finally, these calculated points might be plotted as shown in Fig. 8.47, and a smooth curve connecting the points constructed - with this curve then describing the ideal proppant addition schedule. This curve might then be the final job input for a computer controlled “ramp” type treatment, or the curve might be subdivided into discrete stages as seen by the dashed line in the figure, with these discrete stages then being used for job control.

8 Eff, Mini-Frac = 0.45 Expected Eff, Main Frac = 0.40 Rate = 25 BPM

7 6 PPG

5 4 3 2 1 0

20

40 60 80 Slurry Volume (M-gallons)

100

Fig. 8.47 - Treatment Schedule from Efficiency.

Time/Temperature History The efficiency can also be used to determine an approximate time-temperature history for the treatment as illustrated in Fig. 8.40 as discussed by Nolte, in his paper “Determination of Proppant and Fluid Schedules from Fracturing Pressure Decline.”14

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8.7 Nomenclature A

Total Fracture Area created after pumping for tp minutes (ft2)

C

Fluid Loss Coefficient (ft/ minute )

∆P

Pressure Difference (psi)

∆P*

Match pressure for pressure decline analysis (psi)

δ

Dimensionless Shut-In Time, δ = ts/tp

δc

Dimensionless Closure Time, δc = tc/tp

ef

Fracture Fluid Efficiency = Fracture Volume at Shut-In (V)/Total Volume Pumped (Vp)

E

Young's Modulus of Formation (psi), Typical Values - 2x106 psi to 8x106 psi

E'

Crack Opening Modulus = E/(1-υ2) (psi)

f

Fraction

fp

Pad Fraction or Pad Percentage

fpr

Proppant Fraction of Job, Vpr/Vp

H

Total or Gross Fracture Height (ft)

Hp

Permeable or Leakoff Height (ft)

pc

Fracture Closure Pressure (psi)

pnet

Net Fracturing Pressure (e.g., bottomhole treating pressure just outside the perforations minus fracture closure pressure) (psi)

ps

Net Pressure at Shut-In (e.g., ISIP - pc)

φ

Porosity of Proppant Pack (typically on the order of 0.40)

Q

Total Injection Rate (barrels/minute, bpm)

qLoss

Fluid Loss Rate (bpm)

rp

Ratio of permeable or leakoff area to total fracture area for P&K or Geertsma rp = Hp/ H; for a radial geometry rp is more difficult to define and is normally set = 1

ρ

Loss Ratio = efficiency/(1 - efficiency)

ρpr

Specific Gravity of Proppant (e.g., 2.65 gm/cc or 22 lb gal for sand)

S

Fracture “Stiffness” for Pressure Decline Analysis

tc

Closure Time, e.g., Shut-In Time to Fracture Closure (minutes)

tp

Pump Time (minutes)

ts

Shut-In Time (e.g., incremental time since pumping stopped) (minutes)

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Nomenclature

τ

Time when an incremental element of fracture area is first exposed to fluid loss

V

Fracture Volume (ft3)

VLoss Total Fluid Loss Volume During Pumping (ft3) Vp

Total Slurry Volume Pumped (ft3)

Vpr

Total Proppant Volume Pumped (ft3), including porosity of proppant

Vfl

Total Fluid Volume Pumped (ft3)

δ

Dimensionless Shut-In Time, ts/tp or (t-tp)/tp

W

Total weight of proppant pumped (pounds)

υ

Poisson's Ratio for Formation (dimensionless), Typical Values - 0.15 to 0.25

µ

Fluid Viscosity (centipoise)

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8.8 References 1. Godbey, J. K. and Hodges, H. D.: “Pressure Measurements During Fracturing Operations,” Trans., AIME, (1958) 213, 65-69. 2. Khristianovic, S. A. and Zheltov, Y. P.: “Formation of Vertical Fractures by Means of Highly Viscous Liquid,” Proc. Fourth World Pet. Cong., Rome (1955) Sec. II, 579-86. 3. Perkins, T. K. Jr. and Kern, L. R.: “Widths of Hydraulic Fractures,” JPT (Sept. 1961) 937-49; Trans., AIME 222. 4. Geertsma, J. and de Klerk, F.: “A Rapid Method of Predicting Width and Extent of Hydraulic Induced Fractures,” JPT (Dec. 1969) 1571-81; Trans., AIME 246. 5. Veatch, R. W. and Crowell, R. F.: “Joint Research/Operations Programs Accelerate Massive Hydraulic Fracturing Technology,” JPT (Dec. 1982), 2763-75. 6. Nolte, K. G. and Smith, M. G.: “Interpretation of Fracturing Pressures,” JPT (Sept. 1981), 1767-75. 7. Nolte, K. G.: “Determination of Fracture Parameters from Fracturing Pressure Decline,” paper SPE 8341, presented at the 1979 SPE Annual Technical Conference and Exhibition, Las Vegas, Sept. 23-26. 8. Schlottman, B. W., Miller, W. K. II, and Leuders, R. K.: “Massive Hydraulic Fracture Design for the East Texas Cotton Valley Sands,” paper SPE 10133, presented at the 1981 SPE Annual Technical Conference and Exhibition, San Antonio, Oct. 4-7. 9. Elbel, J. L. et al.: “Stimulation Study of Cottage Grove Formation,” JPT (July 1984) 1199-1205. 10. Dobkins, T. A.: “Procedures, Results, and Benefits of Detailed Fracture Treatment Analysis,” paper SPE 10130, presented at the 1981 SPE Annual Technical Conference and Exhibition, San Antonio, Oct. 4-7. 11. Smith, M. B.: “Stimulation Design for Short, Precise Hydraulic Fractures” SPEJ (June 1985) 371-79. 12. Smith, M. B., Miller, W. K. II, and Haga, J.: “Tip Screenout Fracturing: A Technique for Soft, Unstable Formations,” SPEFE (Feb. 1987) 95-103; Trans., AIME, 283. 13. Morris, C. W. and Sinclair, R. A.: “Evaluation of Bottomhole Treatment Pressure for Geothermal Well Hydraulic Fracture Stimulation,” JPT (May 1984) 829-36. 14. Nolte, K. G.: “Determination of Proppant and Fluid Schedules From Fracturing-Pressure Decline,” SPEPE (July 1986) 255-65; Trans., AIME, 281. 15. Nolte, K. G.: “A General Analysis of Fracturing Pressure Decline With Application to Three Models,” SPEFE, (Dec. 1986) 571-83. 16. Martins, J. P. and Harper, T. R.: “Mini-frac Pressure Decline Analysis for Fractures Evolving From Long Perforated Intervals and Unaffected by Confining Strata,” paper SPE 13869 presented at the 1985 SPE/DOE Low-Permeability Gas Reservoirs Symposium, Denver, May 19-22. 17. Castillo, J. L.: “Modified Fracture Pressure Decline Analysis Including Pressure-Dependent Leakoff,” paper SPE 16417, presented at the 1987 SPE/DOE Low-Permeability Gas Reservoirs Symposium,.Denver, May 18-19.

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References

18. Cooper, G. D., Nelson, S. G., and Schopper, M. D.: “Comparison of Methods for Determining In-Situ Leakoff Rate Based on Analysis With an On-Site Computer,” paper SPE 13223 presented at the 1984 SPE Annual Technical Conference and Exhibition, Houston, Sept. 16-19. 19. Warpinski, N. R.: “Investigation of the Accuracy and Reliability of In Situ Stress Measurements Using Hydraulic Fracturing in Perforated, Cased Holes,” Proc., 24th U.S. Symposium on Rock Mechanics, College Station, TX, (June 1983) 773-86. 20. McLennan, J. D. and Rogiers, J. C.: “How Instantaneous are Instantaneous Shut-In Pressures,” paper SPE 11064, presented at the 1982 Annual Meeting of SPE, New Orleans, Louisiana, Sept. 26-29. 21. Warpinski, N. R. and Teufel, L. W.: “In-Situ Stresses in Low Permeability, Nonmarine Rocks,” JPT, April, 1989. 22. Miller, W. K. II and Smith, M. B.: “Reanalysis of the MWX-Fracture Stimulation Data from the Paludal Zone of the Mesaverde Formation,” paper SPE 19772, presented at 1989 Annual Fall Meeting of SPE, San Antonio, Texas, Oct. 8-11. 23. Nordgren, R. P.: “Propagation of a Vertical Hydraulic Fracture,” SPEJ (Aug. 1972) 306-14; Trans., AIME, 253. 24. Carter, R. D.: Appendix I to paper by C. C. Howard and C. R. Fast, “Optimum Fluid Characteristics for Fracture Extension,” presented at the 1957 ASME Spring Meeting, Mid-Continent District, Div. of Production, Tulsa, OK, April. 25. Warpinski, N. R.: “Dual Leakoff Behavior in Hydraulic Fracturing of Tight, Lenticular Gas Sands,” SPE Production Engineering (August 1990) 243.

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References

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Chapter

9

Economic Optimization of Hydraulic Fracture Treatments

9.1 Introduction “After 40 years of growth in income, we are now in a period where there will be little growth. We have to continue to rationalize both staff and assets to reduce our operations to the size required for expected level of (future) investment and to reduce costs so that cash flow can be maximized. The fat, lazy days are over. We must continue to become leaner and meaner. We must improve our efficiency.” This is the charge made by the authors of a paper entitled “Petroleum ReinvestmentIs there a future for our Industry?” Doom and gloom or a challenge to be overcome? These statements bring home the importance of properly maximizing cash flow in the management of our oil and gas properties and emphasize the need to focus on immediate opportunities to bring about revenue improvement. Well stimulation, either by acidizing or through hydraulic fracture stimulation, is one method available to generate, virtually overnight, improved production revenues that will assist in our accomplishing this goal. Well stimulation, however, is a business decision that can just as easily result in an investment loss if not properly understood and applied. Amoco Corporation has traditionally reinvested over 50% of it's total earnings in Amoco Production Company (APC) for the sole purpose of developing reserves and the resulting production of oil and gas. Over the last decade, APC has developed and applied hydraulic fracture stimulation technology worldwide, an investment that today provides over 50% of all oil and gas produced in our domestic U.S., Canadian and North Sea operations. Price declines in recent years have made it increasingly difficult to justify investment in drilling, completing and stimulating wells. Low prices have been compounded by an increased incidence of poor economic returns and project cost overruns, as summarized in Table 9.1, suggesting better risk management procedures must be included as a part of economic analysis and stimulation optimization. This section addresses the methods to follow and the pitfalls to avoid when maximizing revenue from the implementation of hydraulic fracture treatments. Table 9.1 - Average of Gulf of Mexico Projects to 1988.1

August 1992

Production:

-10%

Reserves

-9%

Project Time

+29%

Project Cost:

+33%

Present Worth

-88%

9-1

Hydraulic Fracturing Theory Manual

Introduction

Economic optimization of a well stimulation treatment requires that the designer carefully balance a large number of parameters describing the reservoir, including its fluid and rock properties, with the inflow performance and associated cost of providing a man-made flow conduit that will produce the largest production increase at the least incremental cost. There are usually many solutions to this problem because the different stimulation materials and their associated costs can be combined in many ways to produce an optimum. The challenge facing us today is to consider all materials and sensitivities, and their associated risks, to arrive at the true “optimum,” a task that is by no means trivial and is best suited to today’s computer technology. Amoco Production Research has developed an integrated fracture, reservoir, and economics program called ULTRAFRAC. This program allows the user to assess the economic benefits and sensitivities of the fracturing process. The following sections are some of the more important considerations to be evaluated when optimizing stimulation treatments.

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Economic Optimization of Hydraulic Fracture Treatments

9.2 General Economic Criteria Provided that cash inflows may be reinvested in projects yielding some positive rate of return, there is a benefit associated with receiving cash inflows as early as possible, and delaying expenditures as long as possible. This is just a restatement that funds have time value. The magnitude and timing of project net cash flows are important yardsticks by which to measure project performance. Similar considerations are valid with associated costs of production. Amoco evaluates investment projects on the basis of several standards. The most important of these will be discussed in this section, and the merits and shortcomings of each will be outlined. As the discussion proceeds, it will become clear that no single measure is sufficient to adequately analyze a project and that an evaluation utilizing a variety of measures is desirable. The measures used within Amoco are defined as follows: 1. Net Present Worth or Value (PW or PV) The sum of all future cash flows discounted to the initial time, at a stated discount rate. 2. Incremental Present Worth or Value of the Fracture (INCPVF) The Net Present Value of a fracture case less the present value of the unfractured case. 3. Fracture Incremental Present Worth or Value (FINCPV) The Net Present Value of a fracture case less the present value of the preceding case. Used to show diminishing returns. 4. Profitability Index (PI) The [continuous] compound interest rate whose discount factors make the present worth of a project’s net cash flows equal to zero. 5. Discounted Return on Investment (DROI) The ratio of a project’s net present worth to the present worth of the total investments discounted at a stated rate. (The denominator is calculated after tax and overhead and includes investment tax credits and the after-tax effect of depreciation.) In ULTRAFRAC, DROI includes capital expenses such as well costs in addition to fracturing costs. 6. Fracture Discounted Return on Investment (FDROI) FDROI is defined as above only capital costs such as well costs are excluded. Only the AFIT (After Federal Income Tax) fracturing costs are used in this economic analysis. 7. Incremental Discounted Return on Investment (INCDROI) INCDROI is defined as the ratio of the incremental present worth of the fracture cases to the incremental cost to achieve the additional length. As a result, a DROI cutoff, consistent with Business Unit budgeting, can be used to aid in determining the optimum fracture treatment. 8. Payout (PO) The time for the cumulative undiscounted cash flow of a project to reach zero.

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General Economic Criteria

The Present Worth Concept A concept which lies at the foundation of economic evaluation procedures is present worth, also called present value (PV). While these two expressions are interchangeable and all of Amoco’s other subsidiaries use the term present value, the term present worth is normally used within Amoco Production. Present worth is abbreviated in this text as PWi, where i is the interest rate. The principle is that a dollar of income is worth more to an investor, or a firm, if received now rather than at some time in the future. This is because the dollar can be invested at some positive percentage rate of return (interest rate) during the intervening time. For example, a dollar received now would, at 5% annual interest, be worth $1.05 after one year. Hence, to be indifferent between accepting a dollar now or a certain sum of money one year in the future, that sum of money would have to be $1.05 (assuming 5% return is the highest return available to investors). The future worth (FW) of a dollar after one year at 5% is calculated as follows: FW = 1.00 (1 + .05) = 1.05

After two years, if the interest were left in the account, the future worth would be: FW = 1.00 (1 + .05) (1 + .05) = 1.00 (1.05)2 = 1.1025

Present worth is the value that, when invested at the given interest rate, will yield the given future worth after the applicable number of periods. Using the previous example of $1.05 received after a year, the present worth is $1.00 (since it would grow to the future worth of $1.05 when invested at 5% for one year). Another way to think of present worth is the value in current dollars you would require to make you indifferent between receiving that amount or the future worth. The relationship of present and future worth can be stated generally as, FW = PW (1 + i)n

(2.1)

where FW = future worth, PW = present worth, i = interest rate (assumed constant), and n= number of periods over which the interest rate applies. In general terms, present worth is found by solving Eq. (2.1) for PW. PW = FW

1 -----------------n(1 + i)

(2.2)

The quantity 1 -----------------n(1 + i) August 1992

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Economic Optimization of Hydraulic Fracture Treatments

is known as a discount factor. The form of present worth discussed so far is known as end-of-period discrete (or periodic) discounting. If one assumes that the time period over which compounding occurs is infinitesimally short, the result is continuous discounting, the type employed Amoco. With continuous discounting, the present worth is determined as follows: FW PW = -------e ni

(2.3)

where PW = present worth, FW = future worth, e = Exponential Function, i = Interest Rate (assumed constant) and n = number of periods over which the interest rate applies The use of tables and computer programs simplifies the calculation of the discount factor 1/eni. If more than one future amount, occurring at different times, is being discounted, it is necessary to alter the equation to account for multiple cash flows. Eq. (2.4) illustrates the case of n cash flows, each assumed to occur at year end. PW = C o + C 1 ( DF 1 ) + C 2 ( DF 2 ) + ... + C n ( DF n )

(2.4)

where C0, C1, ..., Cn = annual point-in-time cash flows for years 1 through n and DF1, DF2, ..., DFn = associated continuous discount factors for years 1 through n. The discussion of present worth thus far has centered around cash flows which occur at a point in time. More frequently, however, cash flows occur uniformly throughout a period, rather than at year end. An example of a uniform cash flow is revenue from an oil well. The oil is not all produced on December 31, 19xx; therefore end-of-year discounting is not appropriate. An example of a situation tailored to use end-of-period discounting might be annuity payments received at year end for several years. Table 9.2 summarizes the types of discounting and cash flows which exist and the applicable discount factor tables, which are included, along with brief instructions, in a separate section of this manual. Only the continuous form of discounting is utilized by Amoco and all future references to discounting will be to that form. Table 9.2 - Summary of Discounting and Cash Flows. Type of Discounting

Cash Flow

Applicable Table

1. Discrete

Point-in-time Uniform

Not applicable Not applicable

2. Continuous

Point-in-time Uniform

9.3 9.4

Annual continuous discount factors, the type normally used by Amoco, for point-in-time cash flows are listed in Table 9.3, and factors for uniform cash flows are listed in Table 9.4. Examples Hydraulic Fracturing Theory Manual

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General Economic Criteria

of present worth calculations for both uniform and point-in-time cash flows are also provided. For anything other than the simplest of examples, computer programs such as ULTRAFRAC and GEM handle the calculations. Table 9.4 also shows an example of present worth calculation. The annual $75 M project net cash flow streams are assumed to result from a $100 M investment. Discounted cash flows are obtained by multiplying the annual net cash flows by the appropriate discount factors. The present worth of the project is the sum of the discounted cash flows. Present worth has been calculated at 15% discount rate for point-in-time and uniform cash flows. Table 9.3 Calculation of Present Worth Using Continuous Discount Factors (Amoco). Point-in-time Cash Flows

Year

Net Cash Flow ($M)

Discount Factors @ 15%

Discounted Cash Flow ($M

0

-100

-

-100

1

75

.8607

64.6

2

75

.7408

55.6

3

75

.6376

47.8 68.0

= PW15 (Point-in-Time)

Table 9.4 - Calculation of Present Worth Using Uniform Discount Factors. Uniform Cash Flows

Year

Net Cash Flow ($M)

Discount Factors @ 15%

Discounted Cash Flow ($M

0

-100

-

-100

0-1

75

.9286

69.6

1-2

75

.7993

59.9

2-3

75

.6879

51.6 81.1

= PW15 (Uniform)

The significance of present worth is that, provided an investor has other investment opportunities at the stated discount rate, he would be indifferent to accepting $81.1 M now or accepting the undiscounted uniform cash flows over the three years of project life. In fact, the value of a firm is frequently said to be the present worth of all of its cash flows from its various projects. Present worth is helpful in ranking projects of the same size as illustrated by Table 9.5: In examining these projects, it is clear that an investor would favor project A over B, because Project B for the same investment ($1,000 M) yields $100 M less per year over the three-year August 1992

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Economic Optimization of Hydraulic Fracture Treatments

Table 9.5 - Project Ranking Using Present Worth Concept. Annual Cash Flows Year

Project A

Project B

Project C

0

-1,000

-1,000

-1,000

1

500

400

600

2

500

400

600

3

500

400

300

Total

500

200

500

PW13

163

-70

193

PW15

120

-104

152

project life. Project A and Project C, however, each return a total of $500 M, and the concept of present worth aids in differentiating between them. Project C is preferred because it returns more of its cash earlier which leads to its having a higher present worth (the incoming cash can be reinvested). This once again emphasizes that both the timing and magnitude of investments have to be considered. It is interesting to note that Project B, while returning all of its investment, still has a negative present value at both 13% and 15% discount rates. If this firm’s cost of capital is 13%, it would undertake all projects with a PW13 > 0, accepting project A and C but rejecting B. However, if the firm were capital constrained, it would rank the projects in order of economic attractiveness and choose those which maximize the value of the firm within the imposed constraints. Amoco has set a minimum investment criterion that those projects accepted must have a positive PW15. Subject to the size of Amoco’s investment budget and manpower constraints, those projects should be selected which maximize the present worth of the total package of projects available. Profitability Index Profitability Index (PI) is defined as that [continuous] compound interest rate whose discount factors make the present worth of a project’s net cash flows equal to zero. PI is also referred to as the project’s internal rate of return. The PI may also be thought of as the discount rate which sets the sum of the discounted annual cash inflows equal to the sum of the discounted annual cash outlays. Investments normally occur at the commencement of a project, followed by a number of years of cash inflows. Where this pattern is substantially altered, there may be multiple PI’s, which is a serious limitation to the use of this technique.

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General Economic Criteria

An example may be helpful in explaining PI. Suppose a firm is offered a project with annual endof-year point-in-time cash flows of $100 M for five years after an initial (time “zero”) investment of $350 M. The calculation of PI for such a project is shown in Table 9.6. Table 9.6 - Calculation of Profitability Index. Present Worth @ 12%

Present Worth @ 14%

Time (years)

Cash Flow ($M)

Discount Factors

Present Value

Discount Factors

Present Value

0

-350

-

-350.0

-

-350.0

1

100

.8869

88.7

.8694

86.9

2

100

.7866

78.7

.7558

75.6

3

100

.6977

69.8

.6570

65.7

4

100

.6188

69.9

.5712

57.1

5

100

.5488

54.9

.4966

59.7

+4.0

-15.0

Recall that the PI is that discount rate which sets the present worth of the project equal to zero. Therefore, by interpolation, 4 PI = ------ x ( 14% – 12% ) + 12% 19 PI = 12.4 approximately

Once the PI is calculated for a proposed project, it should be compared to the established standard. In the current environment for Amoco, the minimum standard is 15 PI (or PW 15 ≥ 0 ). Projects which yield less than a 15 PI should not generally be accepted. However, other considerations, such as an interrelationship with more profitable opportunities, may lead to their acceptance. Should Amoco’s supply of projects returning at least 15 PI dwindle to the point where the available monies exceed the investment requirements for such projects, the minimum PI standard would presumably be lowered, but never less than the cost of capital. Investors would prefer that Amoco pay out the excess funds as dividends if they can earn higher return than can be realized by plowing the funds back into Amoco’s operations. Amoco might also choose to invest the funds elsewhere within the consolidated corporation if projects in other lines of business could yield a higher PI. Discounted Return on Investment (includes Fracture Discounted Return on Investment) Discounted Return on Investment (DROI) is the ratio of a project’s net present worth to the present worth of the total investments (after tax and overhead and including investment tax credits and the after-tax effects of depreciation), discounted at some rate. The denominator is calculated as follows:

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Economic Optimization of Hydraulic Fracture Treatments

Discounted PW of Cash Investment, After Tax = + (Capitalized Part of Investment), discounted at i percent + 0.5 (Expensed Part of Investment), discounted at i percent + 0.5 (0.2 x Investment), discounted at i percent - 0.5 (Depreciation), discounted at i percent - (Investment Tax Credit), discounted at i percent where 0.5 = Tax Rate and 0.2 x Investment = Overhead DROI is a measure of capital efficiency which may be viewed as the amount of after-tax present worth generated per dollar of discounted investment. It is only used within Amoco Production’s domestic operations. Differing fiscal regimes in foreign countries make it difficult to define the denominator of the expression on a consistent basis, so the measure is not useful to any subsidiary having operations outside the United States. To understand how DROI is useful in economic evaluations, it may be worthwhile first to review other evaluation criteria, and the circumstances under which they are useful. Some of their shortcomings will illustrate the utility of DROI. When considering two mutually exclusive projects with the same investment, the one with the higher present worth should be accepted. Likewise, when considering an entire collection of potential projects with different investment requirements (such as during budget preparation), the present worth of the total package should be maximized. The decision as to which projects to include and which to reject is complicated by the fact that not all projects offering a given present value require an equal capital investment. DROI is a useful tool for dealing with this problem, as illustrated by the following group, in Table 9.7, of potential projects available to a firm: Table 9.7 - Utility of DROI in Project Ranking.

Project

Current Year Investment ($MM)

After-tax PW15 Investment ($MM)

PI

PW15 ($MM)

DROI15*

A

12

6

21

9

1.50

B

8

4

17

5

1.25

C

4

2

18

4

2.00

D

6

3

19

2

0.67

E

2

1

16

3

3.00

F

2

1

20

2

2.00

G

8

4

14

-2

-.50

* Assumes these are after-tax numbers and that no overhead, tax credits, or depreciation credits exist.

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General Economic Criteria

Assume that this year’s capital budget allows $20 MM of expenditures. Since the projects returning at least 15 PI exceed the available funds, some projects must be foregone. Under these conditions, the firm should rank its projects in such a way as to maximize the present worth of the package of projects. Ranking these projects on the basis of the highest PW15 results in Projects A and B being selected with a combined PW15 of $14 MM. Ranking these projects on the basis of PI results in the selection of projects A, F, and D with a combined PW15 of 9 + 2 + 2 = $13 MM for the total $20 MM investment. Ranking on the basis of highest DROI15 yields projects E, C, F, and A for a combined PW15 of 3 + 4 + 2 + 9 = $18 MM for the $20 MM investment, which is consistent with the goal of maximizing PW15 of the package of projects given the spending limitations. The PW method of ranking fails in the situation described above because of the different investments required to yield a given present worth. The PI method also fails to rank projects since it implies an ability to reinvest cash thrown off by a project at the PI rate. Since this is not generally the case, the PI method does not compare projects on a consistent basis. In summary, DROI is of use in ranking projects of different investment magnitudes. It takes into account the time value of money and it also measure a project’s susceptibility to risk. In the above example, a DROI15 of 1.50 is the minimum which would be accepted. Amoco in fact has no rigid minimum DROI criterion. In general, where a 15 PI is Amoco’s minimum investment standard, a DROI15 would be determined and used to rank the available investment projects. A DROI15 equal to zero will indicate that the 15 PI standard has been met. While DROI provides a consistent method of ranking projects, other factors such as payout, ROI, and maximum cash out-of-pocket may be considered depending upon the investment climate. Payout Payout (PO) is defined as the length of time taken for the cumulative cash flow of a project to reach zero. For some projects payout provides a rough measure of risk, by indicating how long the investment capital is exposed. Amoco has no specific payout time criterion. When neither present worth, PI nor DROI distinguishes between two mutually exclusive projects, the one with the shorter payout is generally preferred. The major shortcoming of the payout standard is that it fails to account for the timing of cash flows, or to recognize cash flows after payout. If, for example, most of the project life occurs after payout, later cash flows are not considered by the payout criterion. Table 9.8 summarizes a comparison of two projects which have identical payouts but differ in present worth and illustrates how the timing of cash flow is ignored by payout. When used in combination with PI and present worth, payout does serve a useful purpose. Not only does it indicate how long investment capital is at risk, but it also functions as a rough measure of liquidity. For instance, if Amoco’s management decided that all available capital was to be needed next year for a major expenditure, e.g., a large acquisition, then payout time could be the determining factor in ranking economically qualified projects.

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Table 9.8 - Pitfalls of Optimizing Using Payout. Net Cash Flow Year

Project A

Project B

0

-$2000

-$2000

1

1500

1000

2

500

1000

3

1000

1000

PW15 =

$ 299

$ 240

PI

=

23.3

21.0

PO

=

2.0 years

2.0 years

Return on Investment Return on Investment (ROI) is defined as the ratio of the undiscounted cumulative net cash flow of a project to the total investments (after tax and overhead and including investment and depreciation tax credits). The ROI calculation is performed in the same manner as the DROI calculation (shown on page 9-8) with the exception that all values are undiscounted in the ROI equation. When comparing project with similar cash flow patterns, such as a number of individual development drilling wells, ROI, in combination with payout, can provide an indication of project attractiveness. Like payout, however, ROI does not account for the time value of money. This is illustrated by the two projects in Table 9.9 which are identical with regard to ROI. When evaluated on a present worth basis, which accounts for the time value of money, Project B is clearly preferred. Another characteristic of ROI, which may be misleading, is that the measure increases dramatically with an increase in project life. The example in Table 9.10 clearly demonstrates this effect for five projects, each of which shows a 15 PI on a single $1,000 time zero investment. The cash return is the total amount of cash to be returned to the investor at the end of the project. All five projects are equally attractive assuming the ability to reinvest the cash in similar 15 PI opportunities over the lives of the projects. Amoco has no minimum ROI standard, for reasons which are apparent from the above example. The high ROI, long-life project does have the advantage that the company does not have to go out and find a 15% reinvestment opportunity quite as soon, but as long as it is assumed that such opportunity can be found, there is no need for a minimum ROI. Requiring minimum ROIs indicates that the company does not have the ability to find reinvestment opportunities. As a result, ROI is not included in ULTRAFRAC.

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General Economic Criteria

Table 9.9 - Pitfalls of Optimizing Using ROI. Year

Project A

Project B

0

-200

-200

1

100

150

2

100

150

3

150

100

4

150

100

Total

300

300

ROI

1.5

1.5

PW15

138.1

158.9

Table 9.10 - ROI and Project Life Relationship. Project Life (years)

Cash Return ($)

PI

1

1,162

15

0.16

5

2,117

15

1.12

10

4,482

15

3.48

20

20,089

15

19.09

50

1,808,042

15

1,807.04

ROI

Incremental Economics The PI standard should be employed to qualify projects for acceptance, but not to select between mutually exclusive projects, i.e., projects such that either Project A or Project B may be undertaken, but not both. Incremental economics should be run in this case. If both projects return positive cash flows, there is an opportunity cost in opting for one over the other. Hence, the benefit to the firm, in terms of increased cash flow, is the difference (or increment) between the two cash flows. An importance use of incremental economics is shown by the example below (Table 9.11). The two alternatives represent the options of developing or dropping a certain lease. Note that because Alternative A generates tax benefits with no cash expenditures, the resulting PI is infinite. Examining either mutually exclusive option in isolation can result in an incorrect decision. In the example, while Alternative A provides a positive PW15 due to the benefit of being able to write off

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Table 9.11 - Incremental Economics. Alternative A (Drop)

Alternative B (Develop)

PI

∞

19

PW15 ($MM)

3

3.5

the asset on current taxes, it is less than the PW15 of Alternative B. On the other hand, deciding on Alternative B means foregoing the option of dropping the lease (an opportunity cost). The net benefit to Amoco of developing would not be $3.5 MM, but rather $0.5 million. When considering development of a lease, it is important to examine the drop alternative since doing nothing is generally a poor alternative. Dropping the lease at least has the advantage of tax write-offs. A development vs. drop analysis is ideally handled by incremental economics, as in the above example. On occasion, the alternatives may both have negative (but different) PW15’s, but an incremental PW for one alternative over the other will always be positive. Mutual exclusivity frequently gives rise to multiple PIs since the cumulative incremental cash flow may have several sign reversals. In that case, the PW vs. discount rate profile would cross the horizontal axis (PW=0) more than once (Table 9.12). The following example illustrates this situation. Table 9.12 - Illustration of Multiple or Dual PI. Investment Annual Cash Flows Project A (M$)

Project B (M$)

Incremental (B)-(A)

Cumulative Incremental

0

-400

-500

-100

-100

0-1

75

150

75

-25

1-2

100

150

50

25

2-3

100

150

50

75

3-4

125

150

25

100

4-5

100

150

50

150

5-6

50

0

-50

100

6-7

50

0

-50

50

7-8

25

0

-25

25

8-9

25

0

-25

0

9-10

20

0

-20

-20

Total

270

250

-20

-20

Year

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General Economic Criteria

The incremental cash flow in this case represents the benefit to the firm of selection Project B over A. The cash flow of Project A becomes an opportunity cost which is subtracted from Project B to determine the incremental cash flow. The present worth profile would be of the general shape shown on Fig. 9.1. Points C and D indicate the discount rates for which the present worth is zero (definition of PI).

Fig. 9.1 - Present Worth Profile.

This type of present worth profile is typical of most incremental projects. To avoid the problem of multiple PIs, the present worth of the incremental cash flow stream (B-A) at the marginal reinvestment rate should be examined. A positive PW15 would imply acceptance of Project B. Sometimes the incremental cash flow approach is hard to apply. On some of the more complicated scenarios which arise, the correct incremental cash flow stream is difficult to identify. However, the importance of choosing the correct project alternatives and properly defining the problem cannot be overstressed. Failure to do so may lead to a decision which does not maximize the present worth of the total cash flows and, hence, of the corporation. Present Worth Vs. the Profitability Index The present worth concept is theoretically superior to PI for several reasons, and should be relied upon more heavily than PI. PI may lead to an incorrect ranking decision because of the implicit assumption that project proceeds can be reinvested at the PI rate. Present worth, on the other hand, assumes reinvestment at the discount rate used in its calculation. While PI serves to qualify an investment, it does not provide the correct solution when ranking projects under capital rationing or when choosing among mutually exclusive alternatives. The project offering the higher PW15 should instead be selected in a mutually exclusive situation, since we are concerned with maximizing the present value of the cash flow from projects as the means by which to maximize the value of the firm. August 1992

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Situations in which present worth and PI may rank mutually exclusive projects differently occur when the investment cost of one is larger than another, or when the timing of the projects’ cash flows differs. Examples of mutually exclusive projects include the farm-out vs. drill decision and the choice of 40-acre spacing vs. 20-acre spacing in the same field. An example where PW and PI give different rankings to projects with dissimilar investments is illustrated in Table 9.13. Project A calls for the investment of $100 and yields $150 after one year. Its PI would be 40.6 with continuous discounting (point-in-time cash flow) and its PW15 would be $29. Project B, in contrast, would require a $1 million investment and provide $1.25 million at the end of a year. Its PI is only 22.4 but its PW15 is $75,884. The two methods rank the projects differently, as the PI of A is greater than the PI of B, but the PW15 of B is greater than the PW15 of A. Obviously, you would prefer project B as it returns significantly more than the present worth. Table 9.13 - Comparison of PW vs. PI for Ranking. Annual Cash Flows ($) Year

Project A

Project B

0

-100

-1,000,000

1

150

1,250,000

PI

40.6

PW15

29

22.4 75,884

An example of projects differing in the timing of their cash flows is shown Table 9.14. In ranking Project C and Project D on the basis of PI, Project C would appear to be the better option. However, a closer examination reveals that Project D has the higher PW15. Table 9.14 - Timing of Cash Flow. Annual Cash Flows (M$) Year

Project C

Project D

0

-25,000

-25,000

0-1

15,000

0

1-2

15,000

30,000

2-3

15,000

25,000

3-4

15,000

10,000

PI =

53

45

PW15 =

20,120

22,098

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General Economic Criteria

Fig. 9.2 is a plot of present worth vs. discount rate for two mutually exclusive projects such as the 40-or 20-acre spacing alternatives, which shows the curves crossing at some positive PW. Note that the particular discount rate at which the decision is made (15% in this example) determines the selection. At the intersection of the two curves one would be indifferent between 40- and 20acre spacing.

Fig. 9.2 - Present Worth Profiles.

PI causes problems in reaching a decision when multiple (Dual PI) solutions occur, as shown in the previous example. PI is defined as the intersection of the PW profile with the horizontal axis. Note that in that example (Fig. 9.1), the profile has two points of intersection with the axis. In Dual PI projects, PI should not be used as a ranking criterion. In this example, it is more appropriate to utilize present worth and Discounted Return on Invement in the ranking process. Why then use PI at all? There are several advantages to the PI method. One advantage is that it can be compared directly with the cost of capital and anticipated rate of return. A second advantage is that, unlike the PW method, PI abstracts from the size of a project. A PW15 of $50,000 can be obtained on a $10 million investment as well as on an original outlay of $25,000. Accordingly, it is possible to distinguish these two different sized projects on the basis of PI, but not on the basis of present worth. A third advantage, and not an insignificant one, is Amoco management’s familiarity with PI. If management has a basic familiarity with the method, they can feel more confident in their decision-making process. Despite these advantages, it is important to be aware of the shortcomings of PI, as well as those of each of the other investment criteria.

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Yet-to-Spend (Point Forward Evaluation) Vs. Full-Cycle Economics As has been noted, timing is a very critical variable in making effective economic evaluation decision. The present value of a dollar of revenue received at some future date is considerably less than if it were available now. Ideally, one would prefer to receive all revenues immediately, and delay all expense as long as possible Timing enters into economic analysis in yet another way. The time of the analysis relative to the life of the project must be established. Most of the discussion of investment decision-making so far has centered around the timing and magnitude of cash flows produced by a project as viewed at the present time. Fig. 9.3 indicates the cash flows and the point at which the analysis is undertaken (time zero) for such a project. Note that the analysis and initial investment occur at time zero, with cash flows received later in the project life.

500

600

800

600

1

2

3

4

0 Project Life

-1,000 Fig. 9.3 - Point Forward Evaluation.

Not all analyses are conducted before the initial investment is made. In the case of a develop vs. drop decision on a well proposal, a reanalysis may be required after a considerable investment outlay has already occurred. Perhaps estimates of reserves have fallen or operating costs have soared. Fig. 9.4 illustrates a well reassessment made after the initial investment spending occurred at time t = -2. In this case, how should the economics be calculated?

200

200

500

600

800

600

-1

0

1

2

3

4

-2 Project Life

-1,000 Fig. 9.4 - Full Cycle Evaluation.

The original investment of $1,000 represents a sunk cost and the $200 received at time t = -1 is a benefit already received. No current decision can affect past expenditures, and conversely, no past spending should be considered in a yet-to-spend decision. One qualifier to this statement exists.

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General Economic Criteria

Past spending, or sunk cost, may affect future economic decisions via an impact on future taxes. Such effects must be considered in a yet-to-spend analysis. The rationale of yet-to-spend economics, which evaluate only current and prospective cash flows and disregard sunk costs, can best be illustrated Table 9.15. Assume that $500,000 (after tax) is spent on exploration in a certain area and that two fields are found. The fields are subsequently developed at a cost of $600,000 per field (after tax). One field is projected to have an operating cash flow, after all operating costs, royalties, and local and federal taxes, of $2,000,000, and a PW15 of $560,000. The second field, of poorer quality, will have an operating cash flow of only $800,000 with a PW15 of $80,000. A yet-to-spend evaluation would show that both fields have positive PW15’s and PI’s of 15 or better. Accordingly, both would be developed. Table 9.15 - Rationale of Point Forward Economics. Point Forward Economics

Operating Cash Flow Development Cost Net cash Flow on Development

Development PW15

Field A

Field B

Total

$2,000,000

$800,000

$2,800,000

600,000

600,000

1,200,000

$1,400,000

$200,000

$1,600,000

$ 560,000

$ 80,000

$

640,000

If the sunk exploration costs ($250,000 per field) were considered when deciding whether or not to develop the discoveries, the net cash flow and PW15 would differ, and the decision would differ. Table 9.16 - Full Cycle Economics Full-Cycle Economics Field A

Field B

Total

$2,000,000

$800,000

$2,800,000

Development Cost

600,000

600,000

1,200,000

Sunk Cost

250,000

250,000

500,000

Net Cash Flow

1,150,000

- 50,000

1,100,000

PW15 Including Sunk Costs

$310,000

$-170,000

$140,000

Operating Cash Flow

In fact, Field B would not be developed, and all the exploration costs would have to be assigned to Field A. In this event, an analysis of the full-cycle economics shown as Table 9.16 of developing Field A (including all sunk and anticipated cash flows over the life of a project) would show a final net cash flow of $900,000 ($2,000,000 less $600,000 development cost and $500,000 total explo-

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Economic Optimization of Hydraulic Fracture Treatments

ration cost) and a PW15 of $60,000 ($310,000 less Field B’s $250,000 share of the exploration cost at time zero). This answer is incorrect because by developing Field B, the total full-cycle net cash flow would be $1,100,000, with a PW15 of $140,000, which is greater than that of developing Field A only. Thus the analysis which considers sunk costs leads to an incorrect investment decision. It must be remembered that past expenditures may have a substantial effect on the future tax consequences. Previous costs may affect depreciation, cost depletion, and the gain or loss resulting from sale or abandonment of the original project. As a result, future tax liabilities would be altered. In analyzing future investments or other alternatives, considerations must be given to the cash effects of the future tax consequences. Although sunk costs should be disregarded in a yet-to-spend investment decision, except as to the resulting future tax consequences, they should be considered in compiling a PIA. PIA’s will be discussed in detail in Section IV.

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Elements Of Fracturing Treatment Costs

9.3 Elements Of Fracturing Treatment Costs Fracturing treatment costs are primarily comprised of pumping and blending charges, and material costs for fracturing fluids, fluid additives, and propping agents. In some cases associated activities such as well pulling costs, tubular rentals, etc., contribute significantly to the total treatment costs. Some of the types of costs associated with fracturing treatments from stimulation service companies and other associated contractors and suppliers are presented. Stimulation Service Company Costs Treatment costs usually include the following service company cost components. Fracturing Pumping Equipment: Pump truck costs base minimum charges for all trucks except pressure multiplier pumps, per well, for a period up to 4 hours continuous service, on location, per hydraulic horsepower ordered. Prices are based on pumping pressure, and hydraulic horsepower pumping charges increase with pumping pressure increment increases. Other costs include additional pumping time over 4 hours, nonpumping service time, minimum pump truck charges and standby pumping equipment. Propping Agent Pumping Charge: These charges apply when propping agents are pumped with any fluid and are in addition to the fracturing pump truck charges. Prices per unit weight (usually 100 lbs (CWT)) are based on the type and size of the proppant. Pressure Multiplier Pumps: These are usually required for pumping pressures in the 10,000 20,000 psi range. Charges include pressure multiplier pump base charges, per well, for up to 4 hours continuous service on location, per hydraulic horsepower ordered. Prices are based on pumping pressure. Other costs include additional pumping time over 4 hours, nonpumping service time, minimum charges, standby unit charges, and propping agent pumping charges. Blender Services: Base charges for continuous proportioning and mixing of propping agent and fracturing fluid, based on average injection rate, first 4 hours or fraction, per well. Other costs include blender services time over four hours, based on pumping rate, nonpumping blender time; blender standby; other blender and equipment charges such as paddle mixers, densitometers, etc. Slurry Concentration Handling Service: These charges apply when propping agents are pumped with any fluid and are in addition to blender charges and propping agent pumping charges. Prices depend on propping agent concentration. Auxiliary Stimulation Equipment: These items include sand handling equipment, radioactive material for tagging sand, wellhead protective injection equipment (tree-savers, etc.), manifolds, nitrogen, CO2 equipment, flow meters, fracturing support units, special equipment (tanks, transfer pumps, valves, wellheads), ball sealer equipment, treating connections left on location, sand concentrators, etc.

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9.4 References. 1. Campbell, J. M.,”Analysis and Management of Petroleum Invests, Risk, Taxes and Time.” 2. Prats, M.: “Effect of Vertical Fractures on Reservoir Behavior - Incompressible Fluid Case,” SPEJ (June 1961) 105-18;Trans., AIME, 222. 3. McGuire, W. J. and Sikora, V. J.: “the Effect of Vertical Fractures on Well Productivity,” Trans., AIME (1960) 219, 401-04. 4. Tinsley, J.M. et al.: “Vertical Fracture Height - Its Effect on Steady-State Production Increase,” JPT (May 1969) 633-38; Trans., AIME, 246. 5. Elkins, L.E.: “Western Tight Sands Major Research Requirements,” Proc., Gas Research Inst./American Gas Assn./U. S. DOE Intl. Gas Research Conference, Chicago (June 9-12, 1980). 6. Petroleum Production Handbook, T. C. Frick (ed.), SPE, Richardson, TX (1962) Chap. 38. 7. Guerrero, E. T.: Practical Reservoir Engineering, The Petroleum Publishing Co., Tulsa, OK (1968) 72-75.

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References.

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Chapter

10

Special Topics

This chapter is divided into two sections: 10.1

Fracturing Tests starting on page 10-3 and

10.2

TerraFrac starting on page 10-29.

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Special Topics

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Fracturing Tests

10.1Fracturing Tests Introduction The success of a fracture stimulation depends on the accuracy of the design theory, an understanding of the propagation or growth of hydraulic fractures, and the accuracy of design parameters. Many field and laboratory tests are available which allow a more accurate approximation of fracturing parameters. This section covers the more widely used tests; providing a description of the test procedures and in some cases interpretation guidelines. Descriptions are included for core tests, prefrac logs, perforation and permeability determination, bottomhole treating pressure measurements, closure stress tests, minifracs, postfrac logs, and fracture azimuth determination. Core Tests to Determine Mechanical Rock Properties and Fluid Loss Coefficient Fluid Loss Coefficient Core can be analyzed to determine elastic modulus, Poisson's Ratio, and fluid loss coefficient for use in fracture stimulation design. Core analysis is currently the best technique available for obtaining elastic rock properties. Full diameter cores should be cut through the interval of interest, including both the pay zone and adjacent formations, with coring of adjacent formations of sufficient thickness to obtain representative samples. In many cases, a gradation occurs from one bed to another; such as shale grading into a sandstone forming a siltstone transition bed. In a case such as this, mechanical properties tests performed on the transition core would not be representative of the adjacent shale formation. When available, open hole logs from an offset well should be used to determine the required coring interval. Core for rock properties tests should have a minimum diameter of 2-1/2 inches, since the tests utilize a 3/4-inch diameter by 1.5-inch long plug which is cut perpendicular to the long axis of the core. The core should be peel-sealed on location. Peel-sealing the core prevents dehydration of the samples, which provides a more accurate measure of elastic and mechanical properties at in-situ conditions. Transporting the core back to a warehouse for peel-sealing allows excessive dehydration of samples. Past attempts to designate specific portions of the core interval to be peel-sealed have led to confusion, and critical portions of the core have sometimes been left unsealed. Unless personnel familiar with the selection of samples for the specific tests can be on location during the entire coring operation, it is recommended that all of the core be sealed on-site and shipped to the Amoco Research Department or outside laboratory for analysis. The core facility handling the samples should be advised that the core is to be shipped straight to the Research Department or laboratory with no whole-core or plug analysis to be performed. Routine core analysis can be performed after samples have been collected for mechanical properties tests. As discussed in Chap. 4, core is analyzed by triaxial stress-strain tests to yield modulus of elasticity (E). The test is performed by applying a hydraulic pressure to the core plug, then loading it axially September 1992

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Special Topics

and measuring the displacement or strain (ε). In determining modulus for fracturing calculations, the applied hydraulic pressure is normally set equal to the mean effective stress (σ) acting on the reservoir rock, i.e., the confining stress. An additional stress is then applied which is representative of the net pressure above confining pressure required to open a fracture. E is then determined from the resultant stress strain curve as E = σ/ε. Fig. 10.1 shows stress strain curves for a sandstone under several confining stresses to illustrate the sensitivity of E to confining stress. Care must be taken to estimate the confining stress correctly.

Confining Stress, psi 7,500

30,000

3,000 24,000

18,000 Stress (σ) psi

0

12,000

6,000

0 0.00

0.20

0.40

0.60

0.80

STRAIN (ε) - Percent

1.00 E-02

Example: At a confining stress of 7500 psi, E =σ/ε = 24,000 / 0.0047 = 5.1 x 106 psi

Fig. 10.1 - Modulus of Elasticity.

Poisson's ratio (γ) is also determined in the laboratory in a triaxial stress test. γ is the ratio of lateral expansion to longitudinal contraction for a rock under a uniaxial stress condition. The ratio of the measured lateral strain to the axial strain is γ. Fig. 10.2 shows an example of strain data and the calculation of γ. Cores are also used to perform static fluid loss tests to determine a fluid loss coefficient. An explanation of the testing procedure and interpretation and use of the results is covered in the section on fluid loss.

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Fracturing Tests

30,000

24,000 LATERAL 18,000 STRESS (s ) psi 12,000

AXIAL

6,000

0 -1.00 -0.80 -0.60 -0.40 -0.20 -0.00 0.20 0.40 0.60 0.80 1.00 E-02 STRAIN (e) - Percent Example: Poisson’s Ratio (g) = - elat. / eaxial = -(-0.0008 / 0.0047) = 0.17

Fig. 10.2 - Poisson’s Ratio.

Prefrac Logging Program As a minimum, the standard suite of open-hole logs should be run for determination of reservoir characteristics and lithology. This should include gamma ray and/or spontaneous potential, neutron porosity and density logs, and resistivity logs. Several special logs can be run to collect data specifically related to fracturing. Borehole Geometry Log Borehole geometry logs measure hole eccentricity or ellipticity and its orientation, and therefore must be run in open-hole. It has been noted in some fields that wellbore washouts create elliptical cross sections, with the long axis of these noncircular sections sharing a common azimuth. In cases where the minimum hole diameter is equal to bit diameter, such washouts or spalls have been termed “breakouts” and have been reported on from many different areas.1-3 These should not be confused with common washouts or key seats as illustrated by Fig. 10.3. It has been theorized that breakouts are caused by shear failure induced by a stress concentration around the wellbore as a result of (1) unequal horizontal stress and (2) appreciable shear strength of the rock.5 Unequal stresses will cause a preferential stress concentration on the side of the wellbore perpendicular to the maximum stress direction, and if the shear strength is high enough, breakout will be limited to this region. In such a case, the breakout will develop with the long axis of the elliptical borehole perpendicular to the expected azimuth of hydraulic fractures.

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Special Topics

Fig. 10.3 - Borehole Geometry Log.4

Because alternative interpretations exist for breakouts, it should be emphasized that care must be taken in utilizing this type of data to determine fracture azimuth. Although it may not be a good technique as a primary indicator of azimuth, borehole ellipticity could serve as a powerful tool for extrapolating data where more comprehensive azimuth measurements have been made. Long Spaced Digital Sonic Log (LSDS) The Digital Sonic Log has shown to have application in the estimation of vertical in-situ closure stress distribution.6 This data is critical in defining the differential closure stresses between beds Hydraulic Fracturing Theory Manual

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September 1992

Fracturing Tests

for determining fracture height growth parameters. These logs measure shear and compressional sonic velocities, which may be used to calculate dynamic elastic rock properties, and theoretical closure stress in a given horizon.7 The stresses thus calculated should be calibrated to actual in-situ stresses by measuring the in-situ closure stress in 3-4 zones in the wellbore, and shifting the calculated stresses to match in-situ stresses. Both Amoco and Schlumberger have developed a Digital Sonic Log, both of which have been used successfully in this technique. This log is run routinely by both Amoco and Schlumberger. Schlumberger charges only slightly more for their Long Spaced Sonic Log than for the standard Borehole Compensated Sonic Log. The Long Spaced Sonic Log yields as good or better porosity measurements as the Borehole Compensated Sonic, and yields information regarding stress profiles as described above, along with a qualitative indication of natural fractures. Downhole Television and Borehole Televiewer One of the most reliable methods for determining fracture azimuth is with downhole television. The tool is a downhole closed circuit television developed by Amoco, which directly views the borehole wall making interpretation very simple. The disadvantages to using this tool are its depth limitations, openhole requirements, and the need to deliver visibly clean fluid to the bottom of the wellbore.8 While TV logging cannot be done on a routine basis, it offers a reliable method of determining fracture azimuth at the wellbore, and supplies additional data about fracture width, height, etc., as part of the process. The Borehole Televiewer (BHTV) is a “sonic” type tool, introduced by Zemanek et al.,9 which in principal should be an excellent fracture identification tool. However, the tool has not always performed up to its potential. The tool consists of a crystal which emits high frequency sonic pulses, then receives and records the reflection of these pulses from the borehole wall - with the lack of any reflection possibly indicating the existence of a fracture. One problem in using this tool is that borehole ellipticity and/or wellbore deviation creates blind areas due to decentralization of the tool.10 Also, at this time, fracture width cannot be defined with this logging method. Cement Bond Log A cement bond log should be run in all wells to be fractured to determine the integrity of the cement bond. Should poor bonding exist through the pay and adjacent beds, these zones should be cement squeezed to afford a hydraulic seal between zones of potentially lower closure stress than the pay. Channeling behind pipe would tend to aggravate any height growth problems that may exist and could introduce discrepancies in data to be collected later that may make any results obtained meaningless. Poor cement behind casing further aggravates the problems of casing rupture due to poor quality casing or joints and can affect temperature behavior on postfrac temperature surveys.

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Special Topics

Temperature Logs Base Temperature Logs: A base temperature log is run to determine geothermal gradient and static bottomhole temperature. To obtain a valid static temperature survey, the well should have been shut-in for at least one week prior to logging. Temperature disturbances caused by circulating the well during clean-out operations, etc., require approximately 3-5 days to dissipate, depending upon individual well conditions. Preperforation Cold Water Circulation Temperature Surveys: This technique is used to identify zones in the wellbore which are apt to exhibit temperature anomalies on postfracturing temperature surveys due to thermal conductivity and/or wellbore effects, such as shown in Fig. 10.4 and Fig. 10.5. These anomalies often are confusing and misleading and often complicate temperature log interpretation for fracture height determination.

8800

9000

PRE FRAC PROFILE

THERMAL CONDUCTIVITY EFFECTS

2790 PRE FRAC TEMP LOG

STATIC LOG

9600

9800

THERMAL CONDUCTIVITY EFFECTS FRACTURE TOP FLUID MOVEMENT EFFECTS

2670

9400

10000

2710

9200

HOLE DEPTH (METERS)

2750

9000

POST FRAC PROFILE HOLE DEPTH (ft)

9400

POST FRAC LOG

8800

9200

HOLE DEPTH (ft)

2830

8600

PROFILES SEPARATE

FRACTURE TOP

PERFS 10200 PERFS 10400 175

2630

9600

200

225

TEMPERATURE ( F)

250

°

180

200

82

93

220 240 TEMPERATURE 103

116

260

°F

126

°C

Fig. 10.4 - Example of Cold Water Circulation Test.

Many anomalies are usually present on postfracturing temperature surveys but may not all be indicative of the presence of a fracture. This technique provides a method to “subtract out” the nonfracture related anomalies to improve the accuracy of postfrac temperature log interpretation. The procedure for obtaining these surveys is as follows:

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Fracturing Tests

TEMPERATURE ° F

HOLE DEPTH (ft)

4300 4400 4500

75

80

85

90

95

100

105

110

115

110

115

INJECTION TIME 2100 150 DAYS DAYS INJECTION CURVE 48 HR SI

4600

11” DIA HOLE

4700 4800

INJECTION ZONE

4900

TEMPERATURE °F 75 4300

80

85

90

95

100

105

4400 4500

HOURS SHUT-IN 3 12 48 INJECTION CURVE

4600 14” DIA HOLE

4700

4800

CEMENT

INJECTION ZONE

4900

Fig. 10.5 - Effect of Wellbore & Completion.11

1. Run static temperature log over interval to be fractured [approximately 1,000 ft above pay to Plug Back Total Depth (PBTD)] at 20-30 ft/min. 2. Run tubing open-ended to 20-25 ft above PBTD. 3. Circulate water down tubing and up the annulus at maximum possible rate within pressure limitations for at least 3-4 hours. Friction reducer may be added to the water to reduce pumping pressure. The water may be recirculated if a significant temperature differential exists between reservoir temperature and the outlet temperature of the water at the surface. Cold water should be added to the inlet stream when the outlet temperature rises by 25% of the initial reservoir: inlet temperature differential. 4. Trip in with temperature tool to 1,000 ft above the pay interval.

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5. Log downward at a speed of 20-30 ft/min. 6. Pull tool to 1,000 ft above pay. 7. Repeat logging runs every 30-45 minutes until temperature anomalies are well developed, usually 3-5 logging runs. This technique has shown more success in some areas than others. Still, in new areas, the test may be run to verify whether it shows potential to increase the accuracy of postfrac temperature log interpretation. Perforating and Permeability Determination The interval to be stimulated should be perforated with a casing gun at a minimum density of four shots per expected bpm fracturing injection rate, using guns with 90° or 120° phasing. Perforating with many large holes will reduce perforation friction pressure and excessive shear on the frac fluids. Perforating out of phase decreases the likelihood of the perforation being oriented in a line at a high angle to the fracture azimuth, as shown in Fig. 10.6, and therefore reduces friction pressure and shear between the wellbore and fracture. This method of perforating also affords a better flow path to the wellbore during bottomhole pressure buildup and may reduce the need to acidize the zone to attain an adequate flow rate for obtaining a buildup. If possible, do not stimulate or breakdown the perforations prior to flow testing.

Narrow Gap

Vertical Fracture

min Cement max Fig. 10.6 - The Effect of Zero Degree Phasing Perforations on a Fracture Treatment.

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Fracturing Tests

Better results are obtained in the minifrac and fracture treatment analysis if only one pay zone is perforated. The analysis of net pressure is complicated by fracturing multiple zones at the same time, particularly if the zones are separated by sufficient thicknesses of confining beds to allow the propagation of two or more fractures at the same time. When closure stress tests are performed in shales to measure the closure stress of bounding layers, experience has indicated that high density perforating with large charges could compress the shale around the perforation tunnel. This added stress to the rock has made breakdown impossible in some cases. Little is known at this time about the best method for perforating shales for stress testing and further field research testing is required in this area. A bottomhole pressure buildup test should be run to determine formation flow capacity. The formation permeability is used to determine optimum fracture length, to set limits on the fluid loss coefficient to be used for designing the fracture stimulation, for improving the accuracy of postfracturing performance prediction, and for analyzing postfrac buildup tests for fracture length and conductivity. Bottomhole Treating Pressure Measurement Three tests require the measurement of BottomHole Treating Pressure (BHTP): closure stress tests to establish the base fracturing pressure, minifracs to determine the mechanics of fracture growth and to estimate fluid loss coefficient, and fracture stimulation BHTP analysis to determine the mechanics of fracture growth and to evaluate the treatment. In all cases, the pressure data needed is the pressure at the perforations to eliminate tubing friction pressure as a factor. To date, a “foolproof” technique has not been developed to accurately account for all variables affecting friction pressure to allow the subtraction of friction pressure from surface treating pressures to yield BHTP. Extensive work has been performed in this area by the industry, but at best the results are only reliable about 50% of the time. Three techniques are recommended for measuring BHTP.12 Fig. 10.7 shows wellbore schematics for executing these procedures. The first requires running tubing open-ended (without a packer) and pumping down either the tubing or annulus. The other side is then static, and pressures at the surface on the static side are a direct reflection of BHTP, corrected for hydrostatic pressure. The second technique involves the use of a surface readout pressure gauge mounted in a side pocket mandrel, strapping the electric line to the outside of the tubing. The third technique employs a downhole recording pressure bomb placed into a simple mandrel below a packer. With this technique, actual BHTP are recorded, but the data cannot be accessed until after the treatment. For the two procedures where BHTP is measured in real-time, the stimulation service companies can provide on-site computer vans which facilitate quick manipulation of the prefrac test and/or main treatment data for plotting to make on-site judgmental decisions.

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Special Topics

Pt Pa Qt Qa

Q

Q

WIRELINE

PACKER MANDRIL PORT

SIDE POCKET MANDRIL Qt - 0

PERFORATED SUB (BLAST JOINT)

PRESSURE SENSOR

Pt - BHP-Pn or Qa - 0

PRESSURE BOMB SEATING NIPPLE NO-GO NIPPLE

PACKER

Pa- BHP-Pn

(a) Open-ended Tubing

(b) Downhole Recorder With Surface Readout

(c) Downhole Pressure Measurement

Fig. 10.7 - BHTP Measurement.

Procedure for Measurement of Static Pressure Tubing/Annulus Run tubing open ended (without packer) to within 100 ft of the perforations. When pumping begins, tubing and annular pressure will be continuously recorded. If pumping down the tubing, the annular pressure is a direct reflection of BHP, with a correction for hydrostatic head. Any gas on the static side (tubing or annulus) should be circulated out of the hole so that the pressure at the surface will reflect true bottomhole treating pressures. Gas bubbles in the static fluid column will (1) alter the hydrostatic head of the fluid and (2) dampen the pressure response being transmitted through the fluid as the gas compresses and expands with changing pressure. Collect four water samples for determination of specific gravity at one-third points (beginning, one-third, two-thirds, and end) of the total volume used to load and circulate the hole. Since BHTP must be corrected for hydrostatic head to derive bottomhole closure stress, an accurate fluid density determination is desirable. Procedure for Recording Downhole with Surface Readout Prior to running tubing for any of the BHTP tests, a side pocket mandrel is placed in the tubing string just above the packer. A port from the side pocket mandrel to the inside of the tubing allows measurement of pressure by a pressure gauge in the mandrel. The wireline for the pressure gauge is strapped to the tubing as the string is run in the hole. The wireline is connected to the pressure bomb through an electrical port which is an integral part of the side pocket mandrel.

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September 1992

Fracturing Tests

Procedure for Downhole Pressure Measurement Prior to running tubing and packer a special mandrel must be constructed in which to set a pressure bomb. The mandrel consists of (from bottom to top) a joint of tubing with a “NO-GO” nipple at the bottom, a seating nipple, a perforated sub (usually a blast joint) and a pup joint for tailpipe. A downhole recording pressure bomb is set into the seating nipple with a slick line, and the treatment pumped down tubing and out the perforated sub. Pressures at the bottom of the string are then measured by the bomb. To ensure the mandrel assembly does not cause increased fluid shear during the treatment, (1) the perforated subs should be prepared such that the perforation area is adequate to yield near zero perforation friction, and (2) the outside diameter of the assembly should not exceed the outer diameter of the tubing to provide adequate annular space between the assembly and casing. Probably the easiest and least expensive way to prepare the perforated sub is to have the holes drilled in a machine shop. This ensures all holes are open, large and properly spaced. After the fracture treatment, the pressure bomb may be retrieved with a slick line by latching onto a fishing neck on top of the bomb or by pulling the tubing string. Pressure Measurement Devices A number of service companies are equipped to accurately record treating pressures. Accurate pressure measurements are a must. The minimum pressure/time resolution for minifrac and fracture treatment analysis is pressure to the nearest 10 psi and data acquisition once per minute. For closure stress tests, pressure resolution to the nearest 1 psi and 10 sec data acquisition is usually adequate. Fracturing service company pressure transducers have proven to be too unreliable for this type of work. Aside from the resolution of the transducers, fracturing company equipment is often not accurately calibrated and is prone to failure. In cases where highly accurate pressure devices have been used to independently monitor the same pressures as the service companies, the two pressure recordings commonly differed by 100-500 psi. This level of accuracy is generally unacceptable for this type of analysis. Closure Stress Tests Closure stress is measured to determine the minimum pressure necessary to sustain a fracture, to allow determination of net fracture pressure during a minifrac and fracture stimulation, and to evaluate proppant strength requirements. In the analysis of bottomhole treating pressures while fracturing, closure pressure is analogous to the flowing bottomhole pressure measured in pressure transient tests; i.e., it is a base pressure above which pressure analysis is performed. Closure stress is determined by pumping a volume of fluid at a rate sufficient to create a fracture, and then allowing the fracture to close either by shutting-in the well and allowing pressure to decline to below closure pressure, or by flowing the well back until pressure is reduced to below cloSeptember 1992

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Special Topics

TIME

“BOTTOMHOLE” PRESS. AT STEP END

INJECTION RATE

sure pressure.12 In either case, closure pressure is identified by a change in the pressure decline characteristics as the fracture closes. Either test should be preceded by a step-rate test to determine extension pressure, which should be within about 100 psi of closure pressure. The step-rate test will also assure that a fracture exists before the closure test is attempted. Fig. 10.8 shows a typical step-rate test plot. The time step at each rate should be constant, e.g., 2 minute intervals.

“FRACTURE EXTENION PRESS”

INJECTION RATE

Fig. 10.8 - Step-Rate Test.

To create the fracture requires that a sufficient volume of fluid be pumped at a sufficient rate. In practically all cases, pumping for 10-20 minutes at 10 bpm has proven to be adequate; but, depending on the results of the step-rate test, these guidelines may be altered. In low permeability, low leakoff formations 50 bbls at 5 bpm may be sufficient. Any fluid, which is compatible with the formation rock and fluids, may be used for the tests. Generally whatever base fluid is to be used for the fracture stimulation is used for the closure stress test: produced formation water, 2% KCl water, etc. Determination of closure pressure from shut-in pressure declines is operationally very simple. The well is left shut-in until pressure declines to a point at which closure pressure can be identified as shown in Fig. 10.9. This method of determining closure pressure is most appropriate for high permeability formations which close quickly. In this type formation, closure would occur almost instantly during a flowback test making identification of closure pressure difficult. The data, during a shut-in decline test, should be plotted real-time, if possible, to determine the length of shut-in time. The decline data can also be plotted on a Horner type plot, Fig. 10.9, to identify radial flow and, thus, ensure the fracture has closed.13 Also, this plot can be used to estimate the near wellbore reservoir pressure, p*. To ascertain the length of shut-in time may require a “trial” test, followed by subsequent tests. The number of tests performed will depend on the agreement of closure pressures picked. If good agreement is evident, only 2-3 tests may be required. It has been noted that in liquid filled reservoirs closure pressure increases with each subsequent test due to an increase in pore pressure. When this occurs, the earlier test results are probably most representative of for-

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September 1992

Fracturing Tests

“BOTTOMHOLE” PRESS

“BOTTOMHOLE” PRESS

mation closure and should be used to calculate net pressure during the minifrac and fracture treatment.

SHUT-IN DECLINE

CLOSURE PRESSURE

POSSIBILITIES

START RADIAL P*

tsi or ti + tsi

LOG (tsi +ti) / tsi

tsi = SHUT-IN TIME

tsi = SHUT-IN TIME

ti = INJECTION TIME INTO FRACTURE

ti = INJECTION TIME = INTO FRACTURE

Fig. 10.9 - Pump-In/Shut-In Decline.

Fig. 10.10 - Pump-In/Shut-In Decline.

“BOTTOMHOLE” PRESS

Closure stress determination from flowback pressures is only slightly more complicated than a shut-in decline test and is more conducive for low to moderate permeability formations, which would require extensive monitoring periods during a shut-in decline test. The flowback rate is determined by the fluid loss characteristics of the formation and the surface pressure; the purpose of the flowback being to flow back at a rate on the order of the rate at which fluid is being lost to the formation. For this flow back rate, a characteristic reverse curvature occurs in the pressure decline at closure pressure as shown on Curve “b” in Fig. 10.11. A suggested initial flowback rate is 1-2 bpm. The proper flowback rate is usually determined by trial and error on the first tests, flowing back at different rates until the correct flow back rate is found and a good test is obtained.

PUMP IN / FLOWBACK

a - RATE TOO LOW b - CORRECT RATE FOR pc - CLOSURE PRESS AT CURVATURE REVERSAL FROM (+) TO (-)

a pc

b

c - RATE TOO HIGH

c TIME

Fig. 10.11 - Pump-In/Flowback.

To control the flowback rate, a manifold similar to that shown in Fig. 10.12 is required. An adjustable choke, gate valve, or automatic constant flow regulator (e.g., manufactured by Oilmaster - seSeptember 1992

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Special Topics

rial no. 280-390) should be installed downstream of a 1-inch and/or 2-inch flowmeter(s). When selecting a flowmeter for measuring the flowback rate, one must keep in mind the rate range of the meter used. Service companies tend to recommend, and will usually supply, a 2-inch turbine meter. Experience has shown that it is difficult to impossible to measure flowback rates of 1-2 bpm with meters of this size. The best choice seems to be a 1-1.5 inch turbine meter with digital readout in bpm. Digital readout boxes, showing flowback rate, should be positioned near the valve or choke for ease, accuracy, and quickness of adjustment. To minimize the adjustment of this valve or choke from test to test, a full opening gate valve or Lo-Torque valve should also be placed between the wellhead and flowmeter(s). This valve can be used to open and close the flowback system without having to fully close the valve downstream of the flowmeter(s).

DIGITAL READOUT 2” FLOWMETER FLOWBACK LINE

DISPOSAL PIT

WELLHEAD GATE VALVE OR LO-TORQUE VALVE

1” FLOWMETER

ADJUSTABLE CHOKE OR GATE VALUE

DIGITAL READOUT

Fig. 10.12 - Pump-In/Flowback.

The following procedure is recommended for closure stress tests in low to moderate permeability formations: 1. Since real-time data is necessary, either open-ended tubing or a downhole pressure recorder with a surface readout is required to obtain BHP. In some cases, surface pressures may be sufficient. Pressures and rates should be monitored and recorded continuously throughout the tests. 2. Perform step-rate test to determine “extension pressure” and the minimum injection rate required to fracture the formation. Utilize the step-rate test as a pump-in/flowback test, flowing the well back at a constant rate of 2 bpm. Note: In latter portion of pump-in, the injection rate should be increased by an equivalent rate to the planned flowback rate. At the same time, the flowback manifold should be opened and the flowback rate set prior to shutting down injection. The shutdown should be slow, i.e., in 10-15 seconds be pumping at 0.5 bpm, then shutdown completely. This will prevent “fluid hammer” effects in the wellbore, which could distort test results. 3. Flowback at a constant rate until the BHP approaches reservoir pressure. To keep the flowback rate constant will require constant adjustment to the valve as the surface pressure decreases.

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September 1992

Fracturing Tests

4. Based on the required injection rate, perform pump-in/flowback test by injecting fluid for a minimum of 10 minutes, e.g., if rate = 5 bpm, pump 50 bbls. Flowback using procedure in Steps 2 and 3 above. Constant flowback rate may have to be increased or decreased from the 2 bpm in Step 2 depending on the results from Step 3. Fig. 10.11 shows examples of too high and too low flowback rates. 5. Repeat Step 4 until a repeatable closure pressure is established. 6. Perform pump-in/shut-in decline using the same volume and rate determined above. Record pressure decline until pressure falls well below the closure pressure determined above. Do not flowback during this step. Note: In formations with relatively high permeability (>0.1 md), acid ISIPs may closely approximate closure stress, if the acid jobs are small, pump rates are low (yet high enough to create a fracture), and nitrogen or CO2 are not mixed with the acid.14 This will yield a first estimate of closure stress in most cases and will set an upper limit for closure stress. Minifracs Minifracs or “Calibration Treatments” are pumped to obtain information on the mechanics of fracture propagation during the small treatment (net fracture pressures, height growth or confinement, etc.), and to collect data for determination of fracture geometry, time for the fracture to close, and fluid loss coefficient.15 This test consists of pumping a relatively small volume of fluid, i.e., 10-20% of the main fracture treatment depending on its size, using the main treatment fluid system and pumping at the expected main treatment injection rate. During and after the minifrac, BHTP and the shut-in pressure decline is monitored and recorded. The following procedure is recommended to perform the minifrac: 1. Batch mix the required amount of fracturing fluid. Batch mixing is required for gel consistency and to minimize friction pressure variations throughout the test. 2. One of the BHP measurement techniques described previously on page 10-11 should be used for measuring pumping and shut-in decline pressures. Tubing pressure and casing pressure should be recorded by the fracturing service company. In addition, the wellhead should be rigged with a lubricator as described under Temperature Profiles. 3. Pump minifrac at expected main treatment rate (constant rate throughout test). Record all pressures and rates continuously throughout the job. 4. Shut down and record pressure decline for as long as required until the pressure bleeds off to well below the closure stress value previously determined by the closure stress test. Fracture geometry can be evaluated from a Nolte-Smith Log-Log plot of net fracturing pressure (BHTP - closure pressure) vs. pump time as discussed previously in Chap 8. Design parameters, including the fluid loss coefficient, can be determined using the pressure decline analysis which is also presented in the Fracturing Pressure Analysis Section. September 1992

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Special Topics

Postfrac Logging Program Temperature Decay Profiles Temperature decay profile surveys should be run as soon as possible after a minifrac without interfering with the collection of pressure decline data. If bottomhole pressure is measured via a static tubing string, the lubricator can be rigged up on the wellhead ahead of time, and the closure stress tests and minifrac can be pumped through a wing valve or T-connection below the lubricator. The temperature tool is run in the lubricator before the job and isolated from the wellbore with a valve while pumping. If a wireline pressure gauge is run during the prefrac tests, the pressure decline data collection should be completed and the pressure gauge removed prior to installing and running the temperature tool. If bottomhole pressure is measured via a static open-ended tubing string, the temperature tool should not be run until after the pressure decline since running the tool will distort the pressure data. A minimum of three logging runs should be made at intervals of 45 minutes from the start of each run. No backflow from the well should be allowed prior to or during temperature profiling. The logs should be run from several hundred ft above the pay interval to several hundred ft below the fracture bottom or plug back Total Depth (TD), logging down at a speed of about 20 ft/minute. It is the Amoco engineer's responsibility to see that the logging company records the necessary data on the log heading, including fluid type and volume pumped, total pump time, times minifrac started and ended, and fluid surface temperature. This same procedure also applies to temperature decay profile surveys run after the main fracture treatment. Postfrac Temperature Log Interpretation After a minifrac or fracture treatment, heat transfer will occur above the treated zone by radial heat conduction, while over the fracture faces, heat transfer will be by linear flow. Ideally, across these two areas temperature will recover at different rates following the end of pumping, causing a temperature anomaly to develop which identifies the fractured zone. Unfortunately, this ideal situation rarely occurs, making misinterpretation of postfrac temperature logs all too common. As discussed earlier on page 10-8, a static base temperature log and cold water circulation survey may be run to determine the temperature gradient and identify anomalies caused by formation changes, the wellbore, and the completion. Fig. 10.13 shows the conductivity effects from different formations on both pre and postfrac logs.11 Fig. 10.5, shown previously, shows how a washout behind casing will create a cool anomaly which may be interpreted as a fractured zone. On the other hand, a washout completely filled with cement will insulate the wellbore and create a “hot nose” on the log. Also, a change in tubular diameter, such as the bottom of tubing or casing can cause an Hydraulic Fracturing Theory Manual

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September 1992

Fracturing Tests

“offset” in the log. All of the above anomalies can be detected with the base temperature log and subtracted out of the postfrac log interpretation.

2690

8800

9200

THERMAL CONDUCTIVITY EFFECTS

POST FRAC TEMP LOG

2750

PRE FRAC PROFILE STATIC LOG

2810

TOP? 3720

2870

POST FRAC PROFILE

9600

2930

9800

2990

10000

3050 FRACTURE TOP

HOLE DEPTH (ft)

HOLE DEPTH (ft)

9400

HOLE DEPTH (meters)

12200

GR

HOLE DEPTH (meters)

9000

TOP

SP

12300

TOP?

3750

PROFILES SEPARATE 3110

10200 PERFS

PERFS 10400 175

200

80

93

225 250 TEMPERATURE 108 121

3170 F 275

°

135

190

°C

88

Fig. 10.13 - Pre and Postfrac Temperature Logs Showing Thermal Conductivity Effects.

200 TEMPERATURE 93

210 98

°F °C

Fig. 10.14 - Temperature Log Showing Warm Anomaly Above Treatment Zone.

Fig. 10.14 shows a warm anomaly or “hot nose” above the fractured zone and the obvious problems associated with picking the fracture top.11 It has been theorized that this is caused by fluid movement after shut-in and that the “hot nose” is part of the fracture height. Temperature crossovers are often seen below the perforated interval from one logging run to another. Below the perforations, the wellbore is filled with stagnant, hot fluid; and any downward fracture growth will place cooler fluid outside the casing than inside. Thus, heat flow will be in the opposite direction from that across and above the fractured zone and the wellbore may cool down with time. This often results in a temperature “crossover,” as seen in Fig. 10.15, which can be a good indicator of the bottom of the created fracture. Since temperature logs are shallow investigative tools, they only see the fracture at or near the wellbore. If the created fracture is not vertical, but dipping at an angle somewhere between true vertical and true horizontal, temperature logs will not provide a meaningful interpretation of the fractured interval as illustrated in Fig. 10.16. This same problem occurs when the fracture is vertical and the wellbore is deviated. Thus, under these circumstances temperature logs are, at best, poor indicators of fracture growth. September 1992

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Special Topics

GR

TEMP LOG #1 TOP #4

4

1

Fig. 10.15 - Crossover Below Perfs.

Vertical Fracture Straight Wellbore

Fracture Communication With Wellbore

Dipping Fracture Or Deviated Wellbore

Fig. 10.16 - Fracture - Wellbore Communication.

In a well which “goes on vacuum” after a stimulation, the falling fluid level will continually carry warm fluid down into the fractured zone, obscuring the temperature anomaly. This is possible in injection well stimulations and on pumping wells with low reservoir pressure. In such cases, the fluid level should be allowed to stabilize prior to running the logs.

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September 1992

Fracturing Tests

Postfrac Gamma Ray Logs In addition to temperature logging, postfrac gamma ray logs are often run to evaluate fracture height. Fracturing proppant is tagged with radioactive-traced proppant, the tracer concentrations, shown in Table 9.1, have proven to give good results:16 Table 9.1 - Tracer Concentrations. Tracer

Half-Life

Recommended Concentration

Iodine 131

8 days

2 mc/10,000 lbs

Iridium 192

74 days

1 mc/10,000 lbs

Scandium 46

85 days

0.5 mc/10,000 lbs

Noting the variation in half-lives, a postfrac gamma ray log should be run early in the half-life of the tracer used. Also, for the most definitive results with regard to fracture height, the tagged material should be added throughout the stimulation. One advantage of gamma-ray over temperature logs is that they do not need to be run immediately after a stimulation, allowing wellbore fill below perforations to be removed before logging. However, the other restrictions on the temperature logs apply equally to radioactivity logs - that is they are shallow investigative tools (shallower, even, than temperature logs), the response is proportional to fracture width, and the wellbore and completion can effect the resultant log profile. Thus while the two logs are often used in combination, the potential exists for them to confirm one another and still not yield reliable results. One disadvantage of radioactivity logs is their inability to distinguish between a fracture and a small channel behind casing. The temperature response due to a small amount of flow in a channel or annular space behind casing may not alter the radial flow heat conduction around unfractured portions of the wellbore and does not affect the temperature logs. However, any material deposited in a channel is indistinguishable from tagged material in a fracture. Fig. 10.17a shows a good example of pre and postfrac gamma ray logs.11 The radioactive material indicates the top and bottom of the fracture and correlates well with the postfrac temperature log. A second example, shown in Fig. 10.17b, utilized radioactive material in only the later pact of the fracture treatment, thus radioactive material showed up only through a portion of the fracture.11 In this same figure, radioactive material shows up across the “hot nose” indicating this to be, in fact, part of the fracture height. Fracture Azimuth Determination Currently, the four most common techniques available for determining fracture azimuth include tiltmeters, borehole geophones, oriented core, and borehole geometry. The two most widely acSeptember 1992

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Special Topics

(a)

(b)

9200

POST FRAC GAMMA RAY 9100 SP

POST FRAC TEMP PROFILE BASE GR

9400

POST FRAC GAMMA RAY

HOLE DEPTH (ft)

HOLE DEPTH (ft)

9300

POST FRAC TEMP PROFILE

2780

WARM NOSE

RADIOACTIVE SAND IN WARM NOSE

9200

2810

9300

2840

9400

2870

9500

2900

HOLE DEPTH (meters)

10

FRAC ZONE 9500 PERFS

9600

Fig. 10.17 - Comparison of Postfrac Gamma-Ray and Temperature Logs.

cepted techniques are tiltmeters and geophones, with increasing acceptance of oriented core analysis generated through recent consistent results from strain relaxation measurements. Tiltmeters Tiltmeters are highly sophisticated, extremely accurate bi-axial instruments which utilize “bubble” sensors to measure the change in angle of a surface. These devices were originally developed to aim intercontinental missiles, and were later employed by the U.S. Geological Survey for use in the study of earth movements associated with earthquakes and volcanic activity. The use of tiltmeters to monitor hydraulic fractures, at depths up to 10,000 ft, is based on the assumption that the earth will respond in a “more or less” elastic manner to deformations caused by opening a hydraulic fracture. In that case, the surface of the earth will deform in a predictable manner and measurements of this deformation can be interpreted to obtain data with respect to fracture geometry.17,18,19 Fig. 10.18 illustrates surface deformations associated with fractures of several orientations. A typical tiltmeter array consists of 12-16 instruments evenly spaced radially around the well, at a distance of about 0.4 times the depth of the zone to be fractured. Each instrument is installed in a shallow cased hole, usually 10 to 20 ft deep, and packed into position using sand to insulate the device from surface weather and noise effects. The tiltmeter instruments are capable of measuring changes in tilt of a surface with accuracy on the order of 1 x 10-7 radians. Due to the sensitivity of the measurements, changes in the level of the earth's crust due to solid earth tides cause changes in the surface angle which are orders of magniHydraulic Fracturing Theory Manual

10-22

September 1992

Fracturing Tests

DIP = 90°

DIP = 60°

DIP = 30°

DIP = 0°

Fig. 10.18 - Surface Tiltmeter Monitoring.

tude greater than the fracture treatment. Fortunately, the period of the fracture event is much shorter than the “tidal noise” and can be separated by post-analysis using frequency domain filtering and/or tidal filtering. The residual from this filtering is then used to measure the tilt signal related to hydraulic fracturing. The signals from both channels of a tiltmeter are combined to form a tilt vector which embodies direction and magnitude of the tilt measured at that site. Fig. 10.19 shows the recorded response for one channel from a single site. To analyze the data, observed tilts are compared with theoretical values for many possible combinations of fracture azimuth and dip; and thus, the azimuth and dip are determined which produce the least error. An example shown in Fig. 10.20 shows theoretical tilt responses for vertical and horizontal fractures and Fig. 10.21 shows a least error fit for observed vs. theoretical data. Just as the pattern, or direction of the tilt vectors is related primarily to the fracture azimuth and dip, the magnitude of the vectors is principally a function of fracture volume. Recent work has been performed which combines fracturing pressure analysis with tilt vector magnitude to place bounds on created fracture dimensions for wells shallower than 4000 ft, as seen in Fig. 10.22.

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Special Topics

VOL1 1.7670

CHANNEL 9 - RAW DATA

1.7537 1.7404 1.7270 1.7137

Tilt Signal

1.7004 1.6871 1.6738 1.6604 1.6471 1.6338 317.51 317.53 317.55 317.56 317.58 317.59 317.61 317.62 317.64 11:12:11:58:05 TO 11:12:15:40:31 READING ARE FROM CHANNEL 9 PROJ: 84-28 TOTAL OF 217 POINTS PLOTTED STARTING TIME IS 11:12:11:58:05 ENDING TIME IS 11:12:15:40:31 STARTING TIME IN JULIAN UNIT IS 317.49867 ENDING TIME IN JULIAN UNIT IS 317.65314

Fig. 10.19 - Typical Tiltmeter Record for a Hydraulic Fracture.

Because extensive site preparation is required to install the tiltmeter array and a site “aging” period is required, scheduling should begin far in advance of the hydraulic fracture treatment. Site preparation should begin a minimum of three weeks prior to the treatment. District personnel involved in this testing should work closely with the Research Department in setting up and executing these tests. Borehole Geophones Borehole geophones measure the sonic energy, or noise, produced while a formation is being fractured.21-,25 A set of three geophones is typically installed in the wellbore on a single conductor wireline prior to the well being fractured. Since a wireline is in the hole while fracturing, the treatment is usually a small gelled-water minifrac without proppant. One geophone is vertical and the other two are horizontal. The orientation of the geophone tool is determined using surface shots set off in strategically located sites in an array with a radius equal to the depth of the tool. A minimum of

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Fracturing Tests

VERTICAL FRACTURE (mirror symmetry relative to the strike of the fracture) HORIZONTAL FRACTURE (radial symmetry relative to the wellbore)

Fig. 10.20 - Theoretical Tilt Vectors.

Theoretical Observed

Well B

DIP = 50

AZIMUTH=29

Fig. 10.21 - Observed vs. Theoretical.

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Special Topics

R = 330 ft Error in Fil (%)

R = 1000 ft

R = 570 ft Fracture Volume Fig. 10.22 - Fracture Dimensions.

four shots are detonated, one at a time, using dynamite. The sites are 20 ft deep and located at equal intervals of 45°. The recorded arrival time of the shock wave indicates the direction of the source with respect to the geophones. Fracture azimuth is determined by analyzing the arrival times of sonic waves being propagated through the formation as the rock cracks and the fracture extends in length. The variation in arrival times between the three geophones is analyzed to determine the direction of the source of the sonic waves (the tip of the fracture) from the wellbore. Fig. 10.23 shows an example of the type of results obtained. Oriented Core Analysis The use of oriented cores to predict fracture azimuth has been suggested for many years.3,5 The chief advantage of core analysis for fracture azimuth is its ease of application. During routine coring operations, the additional work required to orient and analyze the core is small compared to other azimuth measuring procedures. Also, since most coring is done early in the life of the field, the azimuth data collection is very timely. The biggest disadvantage to common oriented core analysis is the fact that this is an indirect measurement, and it is difficult to be certain that the answer is correct. The most successful core analysis, which has only recently gained acceptance, is the direct on-site measurement of strain relaxation.26

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Fracturing Tests

N

Y

SIGNAL AMPLITUDE

X W

E

Z Time Typical microseismic event recorded on three orthogonally mounted seismic detectors. The time marks are 0.017 sec. apart. S Polarization of “single-phase” events recorded with downhole three-axis geophone package.

Fig. 10.23 - Borehole Geophones.

The indirect oriented coring process uses a shoe on the bottom of the core barrel with three knives to cut grooves in the core. One of these is the reference groove at a known orientation to an azimuth lug attached to the inner core barrel. An orientation tool is mounted above the core barrel such that the orientation lug is visible when the tool photographs the compass. The correction between the reference knife and the orientation lug can be pre-set in the shop, but a preferred technique is to hoist the barrel in the derrick and use an optical aligning device to determine their relative orientation; this is then recorded for future calculations.27 Since this tying of orientation to depth is indirect, the biggest sources of error come from incomplete core recovery, breaks in core, or a spiraling reference groove. The technique of direct on-site measurement of strain relaxation from cores to determine fracture azimuth is based on laboratory observations that the stress-strain behavior of rocks is not purely elastic, but is a function of loading rate and time.28 In such a case, strains stored in the rock by the in-situ stresses will not be released instantly when the core is cut, but will relax over many hours. If the core can be recovered and instrumented during this time, the orientation of stresses can be determined by measuring relaxation in different directions. The strain relaxation process involves selecting several core samples as soon as possible after the core reaches the surface. The samples should be selected from intact core sections to ensure good orientation data, then removed to a reasonably constant temperature environment, sealed to prevent moisture evaporation, and then tested by attaching the deformation gauges to the sample to record strain relaxation (and temperature) data from 12 to 24 hours. These measurements are then used to calculate the orientation of the in-situ stresses.29 Fig. 10.24 shows typical data taken from strain relaxation measurements on a shale sample.30

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Special Topics

STRAIN

A

Elastic Strain

B C'

to t1

Time-Dependent Strain Det1 - t2 C t2

TIME Core Recovered and Instrumented at C' Fig. 10.24 - Strain Relaxation.

The strain relaxation technique has proven accurate in several tests where azimuth was also measured with other procedures.21,26,31,32 These include tests in a volcanic tuff in Nevada; a low permeability Mesa Verde Sandstone; a low permeability gas sand in the Cotton Valley Formation; and a high porosity, high permeability sandstone in Oklahoma. Borehole Geometry The geometry of the borehole (ellipticity) may be affected by the stresses in the earth in the near wellbore region. The fracture azimuth is also affected by these stresses. 1-5 Therefore, a simple correlation might be made between borehole ellipticity and azimuth if conclusive supporting data can be obtained. As discussed earlier on page 10-5, borehole ellipticity measurements in two different areas indicate that fracture azimuth is either parallel to or perpendicular to the long axis of the borehole. By combining the results of the azimuth measurements discussed above with borehole geometry, a correlation might be made for a given field which would greatly simplify fracture azimuth determination. Borehole geometry must be obtained in open-hole, and can be measured with a Borehole Geometry Log as previously discussed on page 10-5, or from the oriented caliper incorporated into the Dipmeter Log. The Dipmeter Log yields information useful in geologic interpretation, whereas the Borehole Geometry Log describes only the orientation and dimensions of the borehole.

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Introduction To TerraFrac

10.2Introduction To TerraFrac TerraFrac is a three dimensional fracturing simulator that is probably the most advanced commercially available hydraulic fracturing simulator presently available. It has been in use by TRC since 1983 to address nonstandard fracture design problems. Fracturing design problems in wells in the Valhall Field in the North Sea, as well as exploration wells all over the world, have been successfully addressed using the TerraFrac Simulator. TerraFrac is installed on the IBM mainframe computer at the Research Center; however it is not yet released for general use because of the complexity and time-consuming requirements of data input, code execution, and the requirement of output analysis. The code is still undergoing development and possesses very advanced capabilities such as thermal and poroelastic effects. It can also be applied in fracture designs where the fracture may migrate considerably up or down from the point of initiation, to study the effects of perforation placement on resulting fracture geometry. TerraFrac solves the fracturing problem, in a general sense, i.e., it determines the fracture geometry as part of the solution process. A three-dimensional simulator is a simulator that can predict fracture shape (width and height at any point along the fracture’s length). However, this is a numerically demanding problem which is strongly nonlinear because of the coupling required between the fluid pressure distribution in the fracture with the stiffness of the opening fracture. The solution of the problem may lead to fracture shapes that are complex, like the one at the top of Fig. 10.25, which are relatively realistic even though they employ certain simplifying assumptions, e.g., planar fractures. The schematics in the lower part of Fig. 10.25 represent the simplest models which are still used throughout the industry for simulating fracture treatment design. These are idealistic versions of what may be happening downhole. There is a category of fracturing simulators of intermediate complexity referred to as pseudo three-dimensional simulators. These simulators can also predict the shape of the fracture, however they still apply some simplifying assumptions on fracture propagation derived from the simplest models. The majority of practical fracture design simulators (e.g., STIMPLAN, MFRAC, FRAC-HT, etc.) fall in this category and are widely used because of their computational efficiency. However, they do not replace the need for a 3-D simulator, especially when estimation of fracture shape is crucial, e.g., for fractures near water bearing zones in the absence of strong confining barriers, unconventional location of the perforations within adjacent layers to the pay zone, etc. Therefore, depending on the fracture design problem, the engineer has a wide range of tools to use and obtain the proper solution, the most important of which is sound judgment and understanding of the governing physical phenomena. General Description of the TerraFrac Simulator The TerraFrac simulator assumes that the fracture is planar and symmetric with respect to the well-

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Special Topics

Actual?

R

wf Penny

Area of Largest Flow Resistance

xf

Approximately Ellipitical Share of Fracture hf xf wf wf

Perkins & Kern

Geertsma & deKlerk

Fig. 10.25 - Models to Better Simulate “Actual” Fracture Behavior.

bore. It determines fracture geometry from the solution of a complex nonlinear interaction problem of: • 3-D Rock Deformation assuming Elastic Layered Formation; • Fluid flow in the Fracture with Proppant and Thermal Effects on Rheology; • Fracture Propagation using Linear Fracture Mechanics; • Leakoff; • Simplified (One Dimensional) Thermo-poroelastic Effects; • etc. In this sense TerraFrac is a fully three-dimensional fracturing model. However, it is not the “ultimate” model! Our desire is for a “super” simulator which can determine the shape of nonplanar fractures and account for other phenomena such as formation nonlinearity (plasticity) rigorous Hydraulic Fracturing Theory Manual

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Introduction To TerraFrac

modeling of the formation-fracture interaction (coupled thermo-poroelastic interaction of the reservoir and the propagating fracture), etc. Although much work has been done in these areas, this type of simulation capability is not yet available. A short account of how the model works is as follows: TerraFrac determines the shape of the fracture in an iterative way. It starts from an assumed fracture shape which is small relative to the fracture dimensions after the treatment has ended. An initial pressure distribution is also assumed. It is recommended to start the simulation with a small penny shaped fracture at the center of the perforations. If the perforation interval is large with varying closure stresses, one would probably choose to initiate the fracture at a point where the closure stress is minimized. The fluid pressure is assumed (handled internally) initially to be constant. The fracture width is dependent on fluid pressure distribution and fracture shape, and can be calculated from an elastic 3-D rock deformation solution. TerraFrac has the capability to calculate fracture width for a general shaped fracture with arbitrary fluid pressure distribution. The widths from this solution stage are used to solve the fluid flow problem in the plane of the fracture. The fracturing fluid is assumed to behave like a power law fluid in laminar flow between parallel plates. The widths determined from the elastic solution are used as the distance between the parallel plates. The fluid pressure distribution can be calculated by satisfying the momentum and continuity equations with appropriate conditions at the boundaries. Then the fracture widths can be derived using this pressure distribution from the elastic solution. In this way, an iteration can be performed to derive the pressures and widths which are mutually consistent. The tendency of the fracture to propagate can be quantified using the closure stress profile, elastic constants, toughness, the fluid pressure distribution, and the pre-existing fracture shape. A Critical Fracture Width is calculated internally (Fracture Propagation Criterion), and, if the width of the fracture at some given distance behind the front exceeds the critical fracture width, the fracture propagates. The distance of propagation is calculated from a combination of mass balance enforcement and the amount by which the widths near the front exceed the critical fracture width. During the propagation, leakoff is assumed to occur according to Carter's model. The enforcement of the continuity equation dominates the propagation and is given priority. In this sense, the fracture Propagation Criterion is satisfied within broad tolerances, while continuity near the fracture front is satisfied more accurately. Input To Terrafrac The downhole schematic of Fracturing Configuration of Fig. 10.26 gives a pictorial definition of the input to TerraFrac. For each formation layer, it is required to define reservoir (porosity, permeability, thermal conductivity), and elastic (modulus, Poisson’s ratio, toughness) properties. Input relative to model discretization, convergence limits, input, output, and plotting are also required. The model uses a combination of finite element and boundary element methods to solve

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Special Topics

Fig. 10.26 - Schematic of the Hydraulic Fracturing Configuration.

the coupled elastic-fluid flow problems. The fracture’s boundary is subdivided into quadrilaterals which are further subdivided into four triangles. All calculations are performed on the triangles in terms of the pressures and widths at the nodes. A typical plot of the mesh is shown on Fig. 10.28. A detailed explanation of the input and the numerical techniques employed are beyond the scope of this manual. Note that the original TerraFrac formulation required the elastic properties to be uniform in all layers; however, an approximate way to account for the first order effects of modulus changes from layer to layer has been recently implemented by TerraTek and has been installed on our IBM mainframe computer. Terrafrac Simulation Runs Confined Fracture Growth The TerraFrac model can be applied for confined fracture growth. However, it should be remembered that confined fracture growth is not the target of the TerraFrac capabilities. For confined fracture growth, Perkins and Kern (PKN) type model programs are much more efficient than TerraFrac. The confined height example of Fig. 10.27 was devised to demonstrate the influence of leakoff and closure stress gradient during the initial stages of fracture evolution. Furthermore, it acquaints the reader with typical plots of the TerraFrac results produced by the plotting postprocessor developed Hydraulic Fracturing Theory Manual

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Introduction To TerraFrac

by the Frac Group. The mesh used for this analysis is shown on Fig. 10.28.

Depth-Feet -7900 C = 0.0

LAYER 1

LAYER 2

0.848 psi/ft

C = 0.0025 ft/min

-8000 LAYER 3

C = 0.0025 ft/min

LAYER 4

C = 0.0005 ft/min

-8100

C = 0.0

LAYER 5

-8200 7200

7300 7400 7500 CLOSURE PRESSURE - PSI

7600 CLOSURE STRESS

FORMATION PROPERTIES

1-2

E = 1.26x106 psi υ = 0.35

2-3 3-4

FLUID VISCOSITY µ = 90 cp

4-5

PUMPING RATE Q = 16 bbl/min

PERFORATIONS

Fig. 10.27 - TerraFrac Example (Demo 2).

The fracture shape evolution gives an appreciation of the delicate balance of the in-situ parameters and their influence on fracture shape. Note that steep closure stress gradients push the fracture growth upwards, while low leakoff zones encourage fracture growth in them. This is clearly demonstrated in Fig. 10.29 which shows fracture evolution until the fracture reaches the lower confining layer (layer 5). The fracture was initiated as a penny shaped fracture of 20 ft radius at 8025 ft depth. The fracture initially propagates as a penny in layer 3. Later, the small leakoff of layer 4 is attracting the fracture more than the closure stress gradient of 0.848 psi/ft of layer 2 and the fracture grows downwards until it reaches layer 5. The remainder of the fracture evolution is shown in Fig. 10.30. The fracture, being confined below, grows upwards until it reaches layer 1. From then on, we have confined fracture growth and the TerraFrac analysis does not offer anything additional to a PKN program analysis. September 1992

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Hydraulic Fracturing Theory Manual

Special Topics

Y (FEET)

10

X (FEET)

Y (FEET)

Fig. 10.28 - Step 50 Fracture Grid.

X (FEET) Fig. 10.29 - Fracture Evolution Steps 0-40.

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Y (FEET)

Introduction To TerraFrac

X (FEET) Fig. 10.30 - Fracture Evolution Steps 41-80.

Fig. 10.31 shows the plot of the step number vs. injected volume. From this plot we see that a great amount of steps (and computing time) is spent during the initial propagation stages. During the first 40 steps only 23 barrels of treatment volume were injected. Consequently, a small amount of injected volume propagates the fracture rapidly to a confined mode of fracture extension; therefore, a PKN analysis is essentially applicable for the entire fracturing propagation process. Fig. 10.32, Fig. 10.33, and Fig. 10.34 show plots of the evolution of leakoff volume, fracture volume, fracture width, and fracture dimensions. Fig. 10.35 shows the variation of fluid pressure during the fracture treatment. The “kinks” in the pressure are due to numerical reasons and should be smoothed out (see next paragraph). The maximum pressure reflects the slightly increasing pressure trend of confined fracture extension. The pressure at the perforations (depths are plotted with reference to the center of perforations referred to as 0.0 ft) shows this increasing tendency to a lesser degree. Note that hydrostatic head in the fracture forces the maximum pressure to occur below the perforations. Fig. 10.36 and Fig. 10.37 show the error distributions of the iteration scheme. Comparing these figures with Fig. 10.35, we see that the pressure distribution is sensitive to these errors. This is expected due to the strong nonlinearity of the problem. Consequently, despite the stringent convergence error of 1%, the TerraFrac user should be able to distinguish real behavior from spurious numerical behavior of the solution. This is valid especially for pressures which are the most sensitive.

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Special Topics

REFERENCE DEPTH (ft): 8.025000E+03 REFERENCE PRESSURE (psi): 7.300000E+03 100

STEP NUMBER

80

60

40

20

0

800 200 400 600 TOTAL VOLUME INJECTED (bbl)

0

1000

STEP NUMBER

Fig. 10.31 - Evolution of Leakoff Volume, Fracture Volume, Fracture Width, and Fracture Dimensions.

REFERENCE DEPTH (ft): 8.025000E+03 REFERENCE PRESSURE (psi): 7.300000E+03 800

BARRELS

600

400

200

0

0

200

400

600

800

TOTAL VOLUME INJECTED (bbl)

1000 TOT. FRACTURE VOL (bbl) TOT. LEAKOFF VOL (bbl)

Fig. 10.32 - Evolution of Leakoff Volume, Fracture Volume, Fracture Width, and Fracture Dimensions.

Hydraulic Fracturing Theory Manual

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Introduction To TerraFrac

REFERENCE DEPTH (ft): 8.025000E+03 REFERENCE PRESSURE (psi): 7.300000E+03 0.30

0.25

INCHES

0.20

0.15 0.10

0.05 0.00

0

200 400 600 800 TOTAL VOLUME INJECTED (bbl)

1000

MAX FRAC WIDTH (in) WIDTH (in) AT 0.0000C+00 ft

Fig. 10.33 - Evolution of Leakoff Volume, Fracture Volume, Fracture Width, and Fracture Dimensions.

Fig. 10.38 shows the efficiency of the treatment. We see that the efficiency of the treatment drops to approximately 20% while 80% of the volume injected leaks into the formation. Unconfined Fracture Growth Two examples of unconfined fracture growth are briefly discussed in this section. They were taken from a real case analysis of fracturing treatment for the Upper Hod formation of the 2/8A-17 well in Valhall. These examples illustrate the capabilities offered by TerraFrac and the opportunity it offers to enhance understanding of the fracturing process for complicated in-situ conditions. Fig. 10.39 shows the two closure stress profiles considered; they were derived from our best estimates of the in-situ conditions. Case A represents the base case; case B has a 200 psi lower closure stress in the Tor relative to case A (due to reduced reservoir pressure after production) and a 50 psi higher closure stress in the “Dense zone” to account for its higher confining capacity. The perforations are located directly below the dense zone. A constant 15 bbl/min pumping rate and a 90 cp downhole viscosity fracturing fluid were assumed. The reservoir pressure was taken as 6275 psi. Completion experience in Valhall has established that the Tor should not be directly perforated because it produces solids and plugs the well. The Upper Hod is perforated instead. Upper Hod treatments have the dual purpose of stimulating the poorer Hod formation and communicating with the “rich” Tor formation. Fracture height growth is not confined and fracture shapes may be complex dependent on the in-situ conditions. It has been the practice to design such fracture treatments as September 1992

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Special Topics

REFERENCE DEPTH (ft): 8.025000E+03 REFERENCE PRESSURE (psi): 7.300000E+03 600

500

400

FEET

300

200

100

0

0

200 400 600 800 1000 TOTAL VOLUME INJECTED (bbl) MAX FRAC LENGTH (ft) MAX FRAC HEIGHT (ft) MAX HEIGHT ABOVE CNTR (ft) MAX DEPTH BELOW CNTR (ft)

Fig. 10.34 - Evolution of Leakoff Volume, Fracture Volume, Fracture Width, and Fracture Dimensions.

REFERENCE DEPTH (ft): 8.025000E+03 REFERENCE PRESSURE (psi): 7.300000E+03 350 300

PSI

250

200

150 100

50

0

200 400 600 TOTAL VOLUME INJECTED (bbl)

800

1000 MAX PRESSURE (psi) PRES (psi) AT 0.0000F+00 ft

Fig. 10.35 - Variation of Fluid Pressure During the Fracture Treatment. Hydraulic Fracturing Theory Manual

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Introduction To TerraFrac

REFERENCE DEPTH (ft): 8.025000E+03 REFERENCE PRESSURE (psi): 7.300000E+03

CONVERGENCE ERROR (%)

1

0.8

0.6

0.4

0.2 0

200 400 600 800 TOTAL VOLUME INJECTED (bbl)

1000

CONVERGENCE ERROR (%)

Fig. 10.36 - Error Distributions of the Iteration Scheme.

“penny” shaped fractures for lack of a better alternative. However, using TerraFrac we can determine fracture shape and study the effects of closure stress profile, actual closure stress gradient, leakoff variation, and position of perforations. It is this capability that makes the TerraFrac simulator so useful for Valhall field and other fields where no significant confining barriers exist. Fig. 10.40 shows the fracture evolution for case A. The fracture was initiated (for both A and B cases) as a small penny (of 10 ft radius) located at the center of the perforations, which is the origin of the Y-axis. Note that in case A the fracture essentially remains approximately a penny, although some confinement can be observed at the shale-Tor interface. Fig. 10.41 shows the fracture evolution for case B. For this case the shape is drastically different. It grows mainly in the Tor where closure stress is low. The lower part of the fracture simply connects the perforations. This type of behavior can only be quantified by numerical simulation and represents a delicate balance of the in-situ values of closure stress, closure gradients, and leakoff as well as the location of the perforations and fluid rheology. Fig. 10.42 compares the fracture width profiles along the wellbore for both A and B cases. In case A, the maximum fracture width occurs close to the perforations (the origin of the Y-axis). In case B, the fracture grows “unsymmetrical” with respect to the perforations and a pinching point develops. Width pinching near the perforations may cause a screen-out during the early stages of the treatment. September 1992

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Special Topics

REFERENCE DEPTH (ft): 8.025000E+03 REFERENCE PRESSURE (psi): 7.300000E+03 12 10 8

PERCENT

6 4 2 0 -2 -4

TOTAL VOLUME INJECTED (bbl) 200

400

600 800 STEP VOLUME. BAL. ERROR (%) TOTAL VOLUME BAL. ERROR (%) CONVERGENCE ERROR (%)

Fig. 10.37 - Error Distributions of the Iteration Scheme.

Fig. 10.43 shows the fracture width history for both cases. The maximum fracture width and the fracture width at the perforations (i.e., at 0.0 ft) are plotted vs. the total injected volume. In case A, we see no significant difference between these two values, both of which increase with the volume of the fracturing treatment. In case B, the max width occurs in Tor and increases with the volume injected as expected. However, the width at the perforations initially increases (while the fracture is still a penny) and subsequently decreases at about 200 bbl, to remain constant at approximately 0.10 inches for the remaining of the treatment. This pinching effect may be the reason for premature screen-out. For such a case, an increased pad volume does not diminish the danger of screen-out. More viscous fluid and small proppant may be required to pump the fracturing treatment successfully. Note that the width at perforations can actually decrease during pumping of the treatment, especially when unconfined nonsymmetric fracture growth occurs. The width history plot may by used to estimate the volumes of the pad and the total volume of the treatment, so that proppant is introduced when the fracture attains sufficient width. The maximum proppant size may also be estimated. For example, case B allows a 20/40 proppant to be pumped with a maximum proppant diameter of 0.0331 inches. The character of the pumping pressure behavior for the two cases is also different as shown in Fig. 10.44. These pressure histories are sufficiently smooth to represent real pressure behavior. The maximum pressure and the pressure at the perforations are plotted vs. the total injected volume. Note that the pressures plotted are in addition to the reference pressure of 7084 psi. Due to Hydraulic Fracturing Theory Manual

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Introduction To TerraFrac

REFERENCE DEPTH (ft): 8.025000E+03 REFERENCE PRESSURE (psi): 7.300000E+03 1

0.8

0.6

0.4

0.2

0

0

200 400 600 800 TOTAL VOLUME INJECTED (bbl)

1000

TOTAL FRAC VOL/VOL INJ STEP LEAK VOL/INJ VOL

Fig. 10.38 - Efficiency of Treatment.

hydrostatic pressure the maximum pressure occurs below the perforations. Case A demonstrates a typical pressure decrease during pumping which is characteristic of unconfined fracture growth of a penny shaped fracture. Case B shows a complicated pressure behavior at the early pumping stages. This is due to the presence of the pressure barrier in the dense zone which temporarily confines the fracture. In some cases the pressure plot may be used as a closure stress diagnostic tool by comparing the simulated pressure with the actual pumping pressure during a minifrac test. Fig. 10.45 shows the evolution of the fracture dimensions. Maximum fracture length, fracture height above perforations, fracture depth below perforations, and maximum fracture height are plotted vs. the total volume injected. In case A, the fracture propagates in both the horizontal and vertical directions. In case B, the fracture is essentially confined height-wise and grows length-wise in the Tor formation. An estimate of the total fracture treatment volume may be made from this plot, based on the desired dimensions of the fracture. Summary TerraFrac is be a valuable simulation tool both for research and design of hydraulic fractures. 1. It can be used to determine the fracture shape for given in-situ and pumping conditions.

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Special Topics

-8200

0.75 psi/ft

C=0

SHALE TOR

0.68 psi/ft

C=0.005 ft/ min

-8300

DEPTH (ft)

0.66 psi/ft

C=0.002 ft/ min

DENSE ZONE

-8400

PERFORATIONS U. HOD

0.64 psi/ft C=0.002 ft/ min

-8500

0.64 psi/ft L. HOD

C=0.002 ft/ min

-8600 6700

6800

6900

7000

7100

7200

CLOSURE PRESSURE (psi)

FORMATION PROP. E = 1.26 X 106 psia ν = 0.4 FLUID VISCOSITY µ = 90 cp PUMPING RATE Q = 15 bbl/min

CLOSURE STRESS A CLOSURE STRESS B

Fig. 10.39 - Valhall A-17 Cases A and B.

2. It can be used to study the effect of the location of the perforations and the associated problems of width pinching. 3. It may be used to diagnose in-situ closure stress features by comparing the actual minifrac pressure with simulated pressure. It is possible, however, to make some overall proppant scheduling judgements using the history plots. For example, the proppant volume at screen-out conditions should be less than the fracture volume at any instant, and this leads to an upper limit for proppant loading per fluid gallon.

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Introduction To TerraFrac

150

570 bbl

75

TOR

346 bbl 201 bbl

50 Y FEET

SHALE

1338 bbl 896 bbl

125 100

25

DENSE ZONE

0

113 bbl

-25 -50 -75

U HOD

-100 -125 -150 0

50

100 150 200 X FEET

250

300

Fig. 10.40 - Fracture Evolution A17A.

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Special Topics

Y FEET

10

140 120 100 80 60 40 20 0 -20 -40 -60 -80

SHALE 631 bbl 442 bbl 298 bbl 128 bbl TOR DENSE ZONE

U HOD 138 bbl 87 bbl 40

0

160

200

SHALE 1424 bbl 1012 bbl 751 bbl

TOR

Y FEET

175 150 125 100 75 50 25 0 -25 -50 -75 -100

80 120 X FEET

DENSE ZONE

U HOD

50

0

100 150 X FEET

200

250

Fig. 10.41 - Fracture Evolution A17B.

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Introduction To TerraFrac

A17A

150 125

1338 bbl

Y FEET

100 75 50 25 0 -25 -50 -75 -100 -125 -150 0.00

0.05

0.10

0.15

0.20

WF IN

A17B 140 120

631 bbl

100 80

Y FEET

60 40 20 0 -20 -40 -60 -80 0.00

0.05

0.10

0.15

0.20

0.25

WF IN

Fig. 10.42 - Fracture Width at the Wellbore.

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Special Topics

A17A

0.25

INCHES

0.20

0.15

0.10

0.05

0.00 0

500

1000

1500

2000

TOTAL VOLUME INJECTED (bbl)

A17B

0.30 0.25

INCHES

0.20 0.15 0.10 0.05 0.00

0

1200 1600 400 800 TOTAL VOLUME INJECTED (bbl)

MAX FRAC WIDTH (in) X WIDTH (in) AT 0.0000E+00 ft

Fig. 10.43 - Fracture Width, A17A and A17B.

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Introduction To TerraFrac

AMOCO REPORT NO. A17A 500 REFERENCE DEPTH (ft): 8.366000E+03

400 300 PSI

REFERENCE PRESSURE (psi): 7.084000E+03

200

100 0

0

1000 1500 500 TOTAL VOLUME INJECTED (bbl)

2000

AMOCO REPORT NO. A17B

500 400

PSI

300 200 100 0 MAX PRESSURE (psi) X PRES (psi) AT 0.0000E+00 ft

-100 0

1600 400 800 1200 TOTAL VOLUME INJECTED (bbl)

Fig. 10.44 - Pumping Pressure.

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Special Topics

A17A

400

FEET

300

200

100

0 0

500

1000

1500

2000

TOTAL VOLUME INJECTED (bbl)

A17B

600

FEET

400

200 MAX FRAC LENGTH (ft) X

MAX FRAC HEIGHT (ft) MAX HEIGHT ABOVE CNTR (ft)

X

MAX DEPTH BELOW CNTR (ft)

0 0

1600 400 800 1200 TOTAL VOLUME INJECTED (bbl)

Fig. 10.45 - Fracture Dimensions.

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References

10.3References 1. Gough, D. I. and Bell, J. S.: “Stress Orientations from Oil Well Fractures in Alberta and Texas,” Cdn. J. Earth Sci. (1981) 18, 638. 2. Thorpe, R. and Springer, J.: “Relationship Between Borehole Elongation and In Situ Stress Orientation at the Nevada Test Site,” paper presented at the 1982 U.S. Rock Mechanics Symposium, Berkley, CA, Aug. 25-27. 3. Babcock, E. A.: “Measurement of Subsurface Fractures from Dipmeter Logs,” AAPG Bull. (July 1978) 62, 1111. 4. Brown, R. O., Forgotson, J. M., and Forgotson, J. M. Jr.: “Predicting the Orientation of Hydraulically Created Fractures in the Cotton Valley Formation of East Texas,” paper SPE 9269 presented at the 1980 SPE Technical Conference and Exhibition, Dallas, TX, Sept. 21-24. 5. Bell, J. S. and Gough, D. I.: “Northeast-Southwest Compressive Stress in Alberta: Evidence from Oil Wells,” Earth and Planetary Sci. Letters, 45, 475-82. 6. Dutton, R. E., Nolte, K. G., and Smith, M. G.: “Use of the Long-Spaced-Digital-Sonic Log to Determine Relationships of Fracturing Pressure and Fracture Height for Wells in the East Texas, Cotton Valley Tight Gas Play,” Amoco Production Company Report F82-P-12 (February 15, 1982). 7. Beaudoin, G. J.: “Interpretation and Use of 3-D Sonic Data: A Preliminary Study,” Amoco Production Company Report F80-E-13 (September 1980). 8. Smith, M. G., Rosenberg, R. J., and Bowen, J. F.: “Fracture Width: Design vs. Measurement,” paper SPE 10965, presented at the 1982 SPE Annual Technical Conference and Exhibition, New Orleans, Sept. 26-29. 9. Zamenek, J. et al.: “The Borehole Televiewer - A New Logging Concept for Fracture Location and Other Types of Borehole Inspection,” JPT (June 1969) 762-74; Trans., AIME, 246. 10. Bredehoeft, J. D., et al.: “Hydraulic Fracturing to Determine the Regional In Situ Stress Field, Piceance Basin, Colorado,” Bull., GSA (Feb. 1976) 87, 250-58. 11. Dobkins, T. A.: “Improved Methods To Determine Hydraulic Fracture Height,” JPT (April 1981) 719-26. 12. Nolte, K. G.: “Fracture Design Considerations Based on Pressure Analysis,” paper SPE 10911 presented at the 1982 SPE Cotton Valley Symposium, Tyler, TX, May 20. 13. Nolte, K. G.: “Analysis of Pump-In/Shut-In Tests for Closure Pressure,” Amoco Document. 14. Rosepiler, J. M.: “Determination of Principal Stresses and Confinement of Hydraulic Fractures in Cotton Valley,” paper SPE 8405 presented at the 1979 SPE Annual Technical Conference and Exhibition, Las Vegas, Sept. 23-26. 15. Nolte, K. G.: “Determination of Fracture Parameters from Fracturing Pressure Decline,” paper SPE 8341 presented at the 1979 SPE Annual Technical Conference and Exhibition, Las Vegas, Sept. 23-26. 16. Heidt, J. H., Nolte, K. G., and Smith, M. B.: “Fracturing Field Research Programs,” unpublished Amoco Research document, September 1981.

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Special Topics

17. Wood, M. D., Pollard, D. D., and Raleigh, C. B.: “Determination of In-Situ Geometry of Hydraulically Generated Fractures Using Tiltmeters,” paper SPE 6091 presented at the 1976 SPE Annual Technical Conference and Exhibition, New Orleans, Oct. 3-6. 18. Wood, W. D.: “Method of Determining Change in the Subsurface Structure Due to Application of Fluid Pressure to the Earth,” U.S. Patent No. 4,272,696, (1981). 19. Davis, P. M.: “Surface Deformation Associated with Dipping Hydrofracture,” J. Geophysical Res. (1983) 881, No. 87, 5826. 20. Pollard, P. O. and Holzhausen, G.: “On the Mechanical Interaction Between a Fluid-Filled Fracture and the Earth Surface,” Tectonophysics (1979) 53I, 27. 21. Lacy, L. L.: “Comparison of Hydraulic-Fracture Orientation Techniques,” SPEFE (March 1987) 66-76; Trans., AIME, 283. 22. Schuster, C. L.: “Detection Within the Wellbore of Seismic Signals Created by Hydraulic Fracturing,” paper SPE 7448 presented at the 1978 SPE Annual Technical Conference and Exhibition, Houston, Oct. 1-3. 23. Pearson, C.: “The Relationship Between Microseismicity and High Pore Pressure During Hydraulic Stimulation Experiments in Low Permeability Granite Rock,” J. Geophysical Res. (Sept. 1981) 86, 7855-64. 24. Albright, J. N. and Pearson, C. F.: “Acoustic Emissions as a Tool for Hydraulic Fracture Location: Experience at the Fenton Hill Hot Dry Rock Site,” SPEJ (Aug. 1982) 523-30. 25. Dobecki, T. L.: “Hydraulic Fracture Orientation by Use of Passive Borehole Seismics,” paper SPE 12110 presented at the 1983 SPE Annual Technical Conference and Exhibition, San Francisco, Oct. 5-8. 26. Teufel, L. W.: “Prediction of Hydraulic Fracture Azimuth from Anelastic Strain Recovery Measurements of Oriented Core,” Proc., 23rd U.S. National Rock Mechanics Symposium (1982) 238-46. 27. Rowley, D. S., Burk, C. A., and Manual, T.: “Oriented Cores,” Christensen Technical Report, Christensen Diamond Products (Feb. 1981). 28. Robertson, E. C.: Viscoelasticity of Rocks in State of Stress in the Earth’s Crust, W. Judd (ed.), (1964) 181-224. 29. Blanton, T. L.: “The Relation Between Recovery Deformation and In-Situ Stress Magnitudes,” paper SPE 11624 presented at the 1983 SPE/DOE Low-Permeability Gas Reservoirs Symposium, Denver, March 14-16. 30. Blanton, T. L. and Teufel, L. W.: “A Field Test of the Strain Recovery Method of Stress Determination in Devonian Shales,” paper SPE 12304 presented at the 1983 SPE Eastern Regional Meeting, Champion, PA, Nov. 9-11. 31. Teufel, L. W. et al.: “Determination of Hydraulic Fracture Azimuth by Geophysical, Geological, and Oriented-Core Methods at the Multiwell Experiment Site, Rifle, Colorado,” paper SPE 13226 presented at the 1984 Annual Technical Conference and Exhibition, Houston, Sept. 16-19. 32. Smith, M. B., Ren, N. K., Sorrels, G. G., and Teufel, L. W.: “A Comprehensive Fracture Diagnostic Experiment. Part II. Comparison of Seven Fracture Azimuth Measurements,” paper SPE 13894 presented at the 1985 Symposium on Low-Permeability, Denver, May.

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Chapter

11

Fracture Stimulation Guidelines and Quality Control

11.1 Perforating Proper selection and execution of a perforating program is essential to the success of a fracture treatment completion. Consideration must be given to perforation diameter, shot density, phasing, location and length of the perforation interval, and, in some special cases, perforation orientation. While most of that presented in this section applies to both vertical and deviated wellbores, parts also deal specifically with perforation patterns and procedures for deviated or horizontal well fracturing. Hole Diameter Perforation hole diameter directly affects the proppant size and maximum concentration that can be pumped during a fracturing treatment. Perforations must be large enough relative to the maximum proppant diameter to prevent bridging. Fig. 11.1 shows the minimum recommended perforation size necessary to inject various size proppants at different concentrations. For example, to pump 20/40 mesh sand at 10 ppg, a minimum perforation diameter of 0.20 in. is recommended. “RULE-OF-THUMB”: Perforation diameter should be at least six times the maximum proppant diameter to prevent bridging. Another consideration in perforation sizing is fracturing fluid degradation. If perforation diameter is too small, high shear-rates in the perforation tunnel can irreversibly destroy gel structure. This will result in a reduction in the gel’s ability to carry proppant and a screenout can ensue. Entry hole diameter can be affected by several variables, including •

casing grade

•

stand-off of the perforation gun with the casing,

•

charge design (big hole versus deep penetrating),

•

charge alignment, and

•

casing thickness.

API charges are tested in casing from K-55 to L-80. When using P-110 and harder casing, the entrance hole size will be reduced by as much as 20%.

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Figure 11.1 Minimum Perforation Diameter v. Proppant Size and Concentration.

The “ideal” stand-off to obtain maximum performance from a perforating gun is approximately 1/ 4 in. to 3/4 in., depending on gun size and charge design. If stand-off is significantly greater than this, hole diameter and penetration will be reduced. Also, if the jet charges do not exit the port plugs of the gun through the near center of the plug, perforation performance can be dramatically reduced. Following a perforation job, all guns should be inspected to determine what percent of charges fired and any misalighned firing through the port plugs. Table 11.1 provides a very approximate chart of gun type/size, casing/tubing size, and weight charge versus perforation entry hole diameter. These diameters were generated by various service companies using the API recommended cement target. Results from different service companies can vary dramatically; thus, this chart should only be used as a rough reference. When determining the most appropriate perforating gun and weight charge, the service company should be consulted to obtain the most recent data and recommendations. Hydraulic Fracturing Theory Manual

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Perforating

Table 11.1 - Approximate Chart of Gun and Casing/Tubing Sizes Versus Charge Size and Entry Hole Diameter for Various Type Perforating Guns. Gun OD (in.)

Casing OD (in.)

Entry Hole Diameter (in.)

Charge Wt. (grams)

Hollow Steel Carrier

3-1/8 3-3/8 3-5/8 4 4

4-1/2 4-1/2 4-1/2 5-1/2 7

0.31-0.39 0.38 0.40 0.34-0.50 0.38-0.46

10 14 10 10-22.7 19-22.7

Expendable Retrievable Carrier

1 1-1/4 1-11/16 1-11/16 1-11/16 2-1/8 2-1/8 2-1/8

4-1/2 2-3/8 2-3/8 2-7/8 5-1/2 2-7/8 5-1/2 7

0.15 0.30 0.36 0.38 0.27 0.43 0.33-0.49 0.32-0.44

2 5 13 13 13 22.7 22.7 22.7

Expendable

1-1/4 1-11/16 1-11/16 1-11/16 2-1/8 2-1/8 2-1/8 3-3/4 3-3/4 3-3/4

2-3/8 2-7/8 4-1/2 5-1/2 2-7/8 5-1/2 7 4-1/2 5-1/2 7

0.30 0.36 0.51 0.30 0.44 0.41 0.42 0.66 0.67 0.71

5 13 13.5 13 22.7 22.7 22.7 90 90 90

Gun Type

NOTE: Entry hole diameters generated with API Concrete Target test.

Number of Perforations In addition to perforation size, the number of holes open affects the injection rate at which a fracture treatment can be pumped. To determine the number of perforations required for a specific treatment design, the following equation can be used ( P pf ) ( d pf ) 4 ( α ) 2 i pf = -------------------------------------0.2369 ( ρ )

1/2

(11.1)

where, i pf is the specific injection rate per perforation (bpm/perf), P pf is perforation friction (psi), dpf is perforation diameter (in.), α is the perforation coefficient (usually 0.9), and ρ is the maximum fracturing fluid (slurry) density (lbs/gal). α is an efficiency number that corrects for the fact that all perforations are not perfectly circular or smooth orifices. Assuming minimal perforation friction, a value of 100 psi is normally used in the equation. July 1999

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11 While Eq. (11.1) can be used to calculate the minimum number of holes required for desired treatment parameters, normally some holes may be plugged, some charges may have misfired, and/or the holes may be substandard due to misaligned firing or poor gun stand-off. The following is recommended to compensate for this: “RULE-OF-THUMB”: Either a perforation coefficient of 0.5 should be used in Eq. (11.1) or the number of holes, determined with a coefficient of 0.9, should be doubled to insure that enough, good quality holes are open for the treatment. If a well has already been perforated before the fracture treatment design is formulated, which is usually the case; Eq. (11.1) can be used to determine the maximum injection rate through the available perforations or decide if additional perforations are required. An example of this is shown in Table 11.2 for a well that was perforated and tested and found to have much higher permeability and skin than anticipated. Initially, the well was shot 2 spf over the 20 ft pay interval with a hole diameter of 0.38 in. From testing, the well appeared to have a permeability of 200 md and a skin of +20. Based on fracture modeling, a treatment rate of 40 bpm was desired, limited by the workstring, and to obtain good conductivity through the damaged region, a maximum proppant concentration of 10 ppg 20/40 mesh sand was required. As seen in Table 11.2, the minimum number of perforations required for this treatment was about 110 or 70 more than available. Thus, the well had to be either reperforated prior to fracturing or the maximum injection rate reduced to 1520 bpm, the later probably not feasible given the expected high fluid leak-off. Perforation Phasing When perforating for a fracture treatment smaller phasing angles are better, i.e., 90 or 120° phasing better than 180 or 360° (same as 0°) phasing. As shown in Fig. 11.2, if enough of the perforations are not in the near direction of the preferred fracture azimuth, the fracture must traverse around the outside of the cement to reach this orientation. Since the fracture will propagate perpendicular to the least principle stress, the portion of the fracture which travels around the wellbore will be subjected to higher stress, resulting in a narrower width or “pinch-point”. This causes a high fluid shear environment and can result in fluid degradation and proppant bridging and an ensuing screenout. This type environment is the most common cause of “tortuosity” or a tortuous fracture path caused by some near-wellbore restriction such as described above. Most cases of tortuosity can be cured with proper perforating to insure good communication between the wellbore and main fracture body. This will also, typically, result in reduced treating pressures (lower HHP costs) and better post-frac performance. Perforating for Deviated/Horizontal Well Fracturing There is nothing good about the effect of well deviation on fracturing, and, when possible, this should be avoided. However, many situations exist where fracturing deviated wells is either desirable or dictated by other concerns. One example might be multiple completions from long reach wells, with another being workover or recompletion operations in existing wellbores. Perforation

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Perforating

Table 11.2 - Example Calculation of Number of Perforations Required or Maximum Rate Obtainable for Fracturing Treatment Design.

Determine the number of perforations required to inject at 40 bpm or the maximum injection rate possible with the existing 40, 0.38 in. holes. Assume a perforation friction of 100 psi. The maximum planned slurry design is 14.59 lbs/gal. 1. To safely inject at 40 bpm: ( P pf ) ( d pf ) 4 ( α ) 2 i pf = -------------------------------------0.2369 ( ρ )

1/2

( 100 ) ( 0.38 ) 4 ( 0.9 ) 2 i pf = ----------------------------------------------( 0.2369 ) ( 14.59 )

1/2

i pf = 0.7 bpm/perf holes required = (40 bpm/0.7) x 2 = 114 holes Using α = 0.5, instead of 0.9, in the above eq.: i pf = 0.39 bpm/perf holes required = 103 holes * REPERFING REQUIRED TO ADD ABOUT 70 MORE HOLES! 2. Maximum rate achievable without perforating: (0.39 bpm/perf)(40 perfs) = 16 bpm patterns can play a dominant role in fracturing from non-vertical wellbores. To better understand this, the following briefly describes possible fracture to wellbore patterns in deviated wells. While current “state-of-the-art” does not allow complete quantification of the effects of well deviation on fracturing, it is clear that these effects are related to two angles: (1) the well deviation from vertical, α, (assuming a vertical fracture) and (2) the difference in direction between the wellbore and the preferred fracture azimuth, β, as shown in Fig. 11.3. Best communication will exist when these two angles are minimized. Basically, there are five possible patterns of wellbore to fracture communication for deviated wells (and vertical fractures). First is when the wellbore is parallel to the maximum horizontal stress direction, i.e., parallel to the preferred fracture azimuth, and the fracture follows the wellbore. This is the only “good” scenario and fracture behavior can be expected to be similar to behavior for a vertical well. The remaining four patterns are illustrated in Fig. 11.4, and in order of increasing “badness”, include (1) a single fracture along the wellbore turning gradually to the preferred orientation, (2) a single fracture parallel with the well but then July 1999

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Fig. 11.2 - Effect of Perforation Phasing on Fracture - Wellbore Communication.

turning sharply to follow the preferred azimuth, (3) a single fracture crossing the well, and (4) multiple fractures crossing the well. In each of these cases, high “apparent” downhole friction may be caused by near-wellbore fracture width restrictions (tortuosity). For the “most” awful case, i.e., multiple fractures crossing the wellbore, a small clustered group of perforations is often used as shown in Fig. 11.5, though this may not totally eliminate multiple fractures. To totally eliminate the possibility of multiple fractures, a single “plane” of perforations is desired, or even better a “notched” casing using abrasive techniques. Some perforation patterns may maximize the chances of creating the preferred single fracture along the wellbore. In particular, two “lines” of perforations (0-180° phasing), properly oriented, with a minimum spacing between holes, should maximize the chances of this occurring. The fracture, though, may then still have to turn to follow the preferred azimuth. Any real calculation of an “optimal” perfo-

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Perforating

Fig. 11.3 - “Wellbore Orientation with Respect to Hydraulic Fracture.

Fig. 11.4 - “Bad” to “Awful” Patterns of Wellbore to Fracture Communication for Deviated Wells (and Vertical Fractures).

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11 rating pattern for deviated or horizontal wells requires extensive knowledge of the in in-situ stresses.

Fig. 11.5 - Perforation Patterns for Deviated Well Fracture.

Over-Pressured Perforating Another procedure first introduced in Prudhoe Bay, is the combination of “in-line” perforations with super over-pressure perforating. ARCO has shown that a rapidly propagating fracture turns much more slowly and smoothly to follow its preferred direction than a hydraulic fracture propagating at a “normal” speed. The following perforation procedure is followed: (1) a small volume of water is placed in the bottom of the well, (2) the perforation guns are then positioned and the remainder of the well filled with nitrogen at relatively low pressure, (3) water is then injected into the top of the well to compress the gas and increase bottomhole pressure to a level far beyond the fracture closure stress, and (4) the perforating guns are fired, opening perforations in the pipe and creating and rapidly propagating a fracture (downhole injection rates on the order of 100’s of bpm have been measured during the initial breakdown following perforating). Since the fracture is being created with pressure greater that the “other” in-situ stresses, a fracture can open and propagate at unfavorable angles. This high pressure, combined with dynamic effects of rapid propagation cause a smooth, slow turning to the favorable fracture orientation, e.g., case “1” in Fig. 11.4. Thus, in principal, this procedure should produce the “least non-ideal” deviated well Hydraulic Fracturing Theory Manual

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Perforating

fracture, though of course for certain combinations of wellbore orientation and in-situ stresses, the same procedure could cause the very undesirable, multiple, crossing fractures, with the critical conditions where this might occur again being related to the differences in the three directional insitu stresses. Since the directions and magnitudes of all in-situ stresses is usually not known, determining the proper conditions for this type of completion becomes subject to field “experiments”. Other Considerations The location and length of the perforated interval needs to also be considered under certain circumstances. For example, if a large pay zone is bounded above by a zone of similar stress, it may be more conducive to perforate only the lower half of the pay to obtain more complete vertical coverage. With the entire pay perforated, the fracture would tend to initiate in the top half and might grow more in an upward direction and place a large portion of the treatment in non-pay. Similar perforating strategy might also be appropriate when an oil-water or gas-oil contact is in the near proximity to the pay zone.

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11 11.2 WELLBORE CONFIGURATION The three most common wellbore configurations used to pump fracture treatments (Fig. 11.6) are •

down production casing,

•

down tubing with a packer, and

•

down open-ended tubing.

Performing a fracture treatment down casing can be quite beneficial, this configuration allowing higher injection rates and lower surface treating pressures and, in turn, requiring less fluid and hydraulic horsepower to perform the treatment. In certain situations, though, it may be necessary to pump down tubing with a packer to isolate the annulus, i.e., when the casing is not strong enough to withstand fracturing pressure or shallower perforations exist. The third configuration, i.e., pumping down open-ended tubing, allows fracturing BHP to be obtained via the open annulus and this can be a very valuable tool in determine fracturing behavior, especially on early wells in a development program. The disadvantages to this configuration, however, are that the casing must be strong enough to withstand fracturing pressure and pumping down tubing lowers the injection rate and/or increases the surface treating pressure. This and alternative methods of measuring fracturing BHP are presented later. First, though, the following discusses the pressure limitations of each configuration and briefly how to determine them.

Fig. 11.6 - Common Wellbore Configurations for Hydraulic Fracture Treatments.

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WELLBORE CONFIGURATION

Fracturing Down Casing Fracture treatment conditions should be considered in the casing design, when possible. When fracturing down casing, one must design the treatment to keep the surface treating pressure below the “burst pressure” of the casing. The worst conditions will occur if the treatment screens-out and surface pressure reaches a predetermined maximum value. One can either design a casing string to withstand the expected maximum surface treating pressure under screenout conditions or limit the maximum surface pressure if the casing has already been set. Treating pressure conditions can be calculated by the equation p s = BHTP – p h + p f + p pf

(11.2)

where, BHTP is the expected bottomhole fracturing pressure, p h is hydrostatic pressure, p f is pipe friction, and p pf is perforation friction. While p h and p f are easily calculated or data exists, often times BHTP and p pf are unknown at onset of a treatment. In an exploratory or new development well, a minifrac may be in order to determine these values, along with in-situ stress and fluid leakoff data. Casing burst values can be found in most service company or casing design handbooks. To determine a safe surface treating pressure, a burst safety factor of 1.1 is recommended for fairly new casing. For older casing, this should be increased. Assuming a 2000 psi “sudden” increase in pressure if a screenout occurs, the design treating pressure should not exceed the safety factor reduced casing burst pressure minus 2000 psi. Pop-offs or pressure relief valve should always be installed on the injection line(s) and set/tested to just below the predetermined maximum surface treating pressure. Fracturing Down Tubing with a Packer As for a casing treatment, the maximum allowable surface fracturing pressure for this configuration must be determined from the burst pressure of the tubing string. With this setup where the annulus is isolated, backside or annulus pressure can be held to allow increased maximum surface treating pressure. In addition to the burst pressure of the tubing, other factors must also be considered; including forces on the packer when the tubing is anchored in the packer, and tubing movement when a locator seal assembly is used. When the tubing is latched or anchored in the packer, disallowing tubing movement, forces on the packer should be calculated to select a packer strong enough to withstand these forces. Tubing pressure will cause an upward-acting force below the packer, and the annular pressure will cause a downward-acting force above the packer. This can be computed by the equation F a = [ ( A p – Ao ) po ] – [ ( A p – Ai ) pi ]

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11-11

(11.3)

Hydraulic Fracturing Theory Manual

11 where A p is the area of the packer bore, A o is the area based on the tubing OD, A i is the area based on the tubing ID, p o is the annular pressure at the packer, and p i is the injection pressure at the packer. The injection pressure, p i , should be calculated based on the maximum allowable surface treating pressure under screenout conditions with the maximum slurry density in the tubing. When a locator seal assembly is used, allowing tubing movement, the forces and length changes on the tubing must be calculated to determine the length of seals to run and slack-off when landing the tubing. The four different effects that cause these forces and length changes are 1. piston effect, 2. buckling effect, 3. ballooning effect, and 4. temperature effect. The first three are caused by pressure changes and the last by temperature changes in the wellbore. Table 11.3 includes the equations used to calculate these to determine the length of seals required and tubing slack-off for fracturing conditions. Again, screenout conditions need to always be considered in designing the tubing/packer configuration. Fracturing Down Open-Ended Tubing When designing this type configuration for a fracture treatment, the burst pressure for both the casing and tubing must be considered. Since this configuration is normally used to obtain BHTP via the live annulus, no additional pressure is applied on the annulus side at the surface. Thus, the maximum surface treating pressure should be limited to keep the surface annulus pressure below the safety factor reduced casing burst. Since the tubing burst will normally be greater than the casing, this configuration will not allow as high a treating pressures as would be possible with a packer and the annulus isolated. This configuration also allows pumping of a fracture treatment down the annulus and monitoring the BHTP on the tubing side. When pumping down the annulus, a blast joint should be used at the top of the tubing string to prevent erosion. Again, the maximum surface treating pressure should not exceed the safety factor reduced burst pressure of the casing. Also, screenout conditions should always be considered in determining the maximum treating pressure and pressure relief valves set to just below this pressure on all injection lines. Methods of Obtaining Fracturing BHP Several methods exist to obtain BHTP during a fracturing treatment, including •

open-ended tubing,

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Table 11.3 Tubing Forces and Length Changes

Nomenclature

PISTON EFFECT: F1

= [ ( Ap – Ao ) dpo ] – [ ( Ap – Ai ) dpi ]

(11.4)

(F 1)(L) = ----------------( E ) ( As )

(11.5)

dL1

HELICAL BUCKLING:

dL2

=

0

(11.6)

( dr **2 ) ( Ap**2 ) ( dpi – dpo ) **2 = ------------------------------------------------------------8EI ( Ws + Wi – Wo )

(11.7)

F2

BALLOONING EFFECT:

– ( dpi ) ( Ai ) ]

(11.8)

R**2 ( dpo – dpi ) 0.2L - -------------------------------= -------------------1.0 × 10**7 R**2 – 1

(11.9)

F3

11-13

dLm

0.6 [ ( dpo ) ( Ao )

=

TEMPERATURE EFFECT: F4 dL4

207 ( As ) ( dT )

(11.10)

0.0000069 ( L ) ( dT )

(11.11)

=

=

dLm

( Fm ) ( L ) ( dr **2 ) ( Fm**2 ) = ------------------ + ---------------------------------------( E ) ( As ) 8EI ( Ws + Wi – Wo )

(11.12)

TOTAL EFFECT:

= F 1 + F 3 + F 4 + Fm = dL1 + dL2 + dL2 + dL3 + dL4 + dLm Fp

dLt

(11.13) (11.14)

ACTUAL FORCE: Fa

= [ ( Ap – Ao ) po ] – [ ( Ap – Ai ) pi ]

(11.15)

= = = = = = = = = = = = = = = = = = = = = = = = = = =

area based on tubing ID, in**2 [cm**2] area basing on tubing OD, in**2 [cm**2] area of packer bore, in**2 [cm**2] area of steel in pipe body, in**2 [cm**2] Young’s modulus for steel, 30x10**6 psi [207x10**6 kPa] actual force, lbf [N] mechanical force, lbf [N] total force at packer, lbf [N] piston force, lbf [N] helical force, lbf [N] ballooning force, lbf [N] temperature force, lbf [N] moment of inertia, in**4 [cm**4] length of tubing or casing, in. [cm] length change due to mechanical force, in. [cm] total length change due to changes in pres. & temp., in. [cm] length change due to piston force, in. [cm] length change due to buckling, in. [cm] length change due to ballooning force, in. [cm] length change due to temperature force, in. [cm] change in pressure in tubing at packer, psi [kPa] change in pressure in annulus at packer, psi [kPa] clearance between casing ID and tubing OD, in. [cm] change in average temperature, deg F [deg C] weight of fluid inside tubing, lbm/in. [kg/cm] weight of fluid in annulus displaced by tubing, lbm/in. [kg/cm] weight of steel, lbm/in. [kg/cm]

WELLBORE CONFIGURATION

Hydraulic Fracturing Theory Manual

SLACKOFF EFFECT:

Ai Ao Ap As E Fa Fm Fp F1 F2 F3 F4 I L dLm dLt dL1 dL2 dL3 dL4 dpi dpo dr dT Wi Wo Ws

11 •

gauges in a tail-pipe below a perforated joint below the packer,

•

placing gauges in the rat-hole, and

•

through a telemetry acquisition system.

To obtain fracturing BHP with open-ended tubing, the annulus must be kept full of a known density fluid and the annulus surface pressure measured. The main advantage of this system is that can be monitored real-time. To insure that the annulus is full of the same density fluid, the wellbore should be circulated prior to the fracture treatment and the density of the fluid measured. Gauges are often times placed in a nipple in a tail-pipe configuration below a perforated tubing joint below the packer. This is a good method for obtaining fracturing BHP when the annulus must be isolated. While proppant may fall down around the gauges, making retrieval with wireline difficult, the data can still be retrieved by pulling the tubing string. When possible, a fishing neck should be installed on top of the gauges and the location of the gauge landing nipple placed so that the fishing neck extends into the perforated joint. Proppant is less likely to pack around the fishing neck, making wireline retrieval of the gauges more likely. Gauges can be placed in the rathole, but this requires going in and washing out proppant settled from the under-flush to retrieve them. A recent advance in BHTP measurement during a fracturing treatment is a telemetry acquisition system patented by Real Time Diagnostics, Inc. A sensor placed in the bottom of the well detects pressure and temperature and transmits this data to the surface in the form of electromagnetic waves. A receiver at the surface captures, interprets, and records the data. The advantages of this system are (1) that is acquired nearly real-time to make informed decisions during the fracture treatment and (2) that it allows the treatment to be pumped down casing at higher rates with often times less fluid. The only disadvantage would be possible difficulty in retrieval of the bottomhole sensor. Measurement of fracturing BHP can be a valuable tool in evaluating fracturing behavior, especially on early development wells in an area. The best method of retrieving this data must be determined as a function of the wellbore configuration and the requirements of the treatment. Considerations for Frac-Pack Completions In addition to the forces placed on the workstring and packer during a fracturing treatment, other things must be considered when fracturing through gravel-pack tools. Typically, frac-packs are pumped through multi-positional gravel-pack tools upgraded to allow for high-pressure, highrate injections. Normally, the tools have three positions, including squeeze, circulate, and reverse as shown in Fig. 11.7. When injecting into the formation, the tool is in the squeeze position and the fracturing slurry exits the workstring through ports in the tool. Most tools have either two or three ports, sized and positioned to allow for a large flow area to prevent tool erosion. The port

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WELLBORE CONFIGURATION

size and number have to be considered when determining the design injection rate to prevent tool erosion and shear-thinning of the fracturing fluid. The diameter of the tool ports must also be large enough to prevent proppant bridging and eventual treatment screenout in the gravel-pack tool. The previous section discussed proppant bridging in perforations and the same applies here. Depending on the number and port diameter, the design maximum proppant concentration may have to be limited. Another consideration deals with the blank pipe normally used to extend from the top joint of screen to the bottom of the gravel-pack tool assembly. This must be of a sufficiently high enough grade to withstand maximum collapse forces during a frac-pack operation. This needs to be determined under screenout conditions.

Fig. 11.7 - Multi-Positional Gravel-Pack Tool Commonly Used for Frac-Packs

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11 11.3 PRE-TREATMENT PLANNING Pre-treatment planning encompasses many aspects including data collection, preliminary treatment design, preparation of the frac “brief”, and service company/operator interaction. The success or failure of most treatments can be traced to (1) the availability and judicious use of data necessary to optimize the treatment design, and (2) improper planning by and interaction between the service company and operator. Data Collection Requirements With respect to data requirements, three technical areas need to be addressed, these being well potential, fracture geometry, and treatment fluids and proppants. Proper evaluation of each of these areas requires the knowledge of various rock and fluid properties. In practice, it is not possible or economical to collect data from every desirable source. In general, optimization of the data gathering should be done on the basis of whether the well is early or late in a development program. In an initial development well, effort should be made to fully understand the well from all perspectives. However, knowledge gained from exploratory or early development wells can be applied to subsequent wells in a localized area provided there is a good understanding of the local geology. Formation Flow Potential. To justify a stimulation treatment, the formation flow potential from fracturing must first be critically evaluated. The important data and parameters that fall into this category include •

porosity (logs),

•

water saturation (logs),

•

permeability (logs/core),

•

petrographic description of minerals (core),

•

reservoir pressure (pressure transient testing), and

•

gas/oil, water/oil contacts (logs).

In an early development well these would need to be measured or determined directly. In later development wells, though, it might be possible to extract reasonable estimates from offset wells. This again would depend, to a great degree, on the spacing of the wells, the complexity of the localized geology, and the number and behavior of previous treatments in the area. Fracture Geometry. After it has been established that a fracture stimulation will provide sufficient economic recovery, certain data and parameters are required to ascertain what size treatment is required to optimize recovery. For fracture length, width, and height determination, the following data is required.

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PRE-TREATMENT PLANNING

•

minimum horizontal stress (pre-frac injection testing),

•

Young's modulus (core),

•

overburden stress (integrate density log),

•

pore pressure (pressure transient testing),

•

reservoir temperature (logs, static measurement),

•

an estimate of fluid leak-off properties (core, minifrac injection), and

•

treatment fluid injection rates, viscosity, and proppant density.

Again, the extent to which this data is collected should depend on when the well is drilled in a development program, the availability of data from previous wells, the complexity of geology, and the number and behavior of previous treatments. For example, injection/decline tests and minifracs may only be required on a select few wells early in a development program to ascertain formation stresses and leak-off. Also, overburden stress and Young's modulus values should only be required on early wells, unless the geology varies significantly from one area to another in the development region. Treatment Fluid and Proppant Evaluation. The areas that need to be addressed when optimizing treatment fluid and proppant requirements are •

ability of the fluid to carry the proppant the desired distance out in the fracture,

•

fluid loss control,

•

minimum impairment to proppant-pack conductivity by the fluid, and

•

the strength and size of the proppant to provide the necessary fracture

conductivity.

Laboratory testing by the service company may be required early in the life of a development program to choose the most appropriate fluid and proppant. Preliminary Treatment Design Using the available data, a “preliminary” treatment design should be formulated at this point to aid in pre-treatment planning. While this might not be the final design pumped, this will provide estimates of treatment requirements including •

fluid/chemical/proppant amounts,

•

on-site storage,

•

equipment,

•

location sizing, and

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11 •

personnel requirements.

The expected treatment schedule should be reviewed by the service company at the earliest possible date to insure that these requirements can be met. Often times, in remote areas, chemicals or proppant may have to be ordered weeks or even months in advance. Also, additional equipment may have to be brought in from other areas or scheduled. Frac “Brief” Procedure To aid in pre-frac planning and treatment execution a fracturing procedure should be prepared either by the operator or jointly by the operator and service company for each treatment and should include at a minimum the following: •

pertinent wellbore information including casing/tubing depth, size, weight, and grade; packer type and depth; plug-back TD; perforation interval; and perforation size, density, and phasing.

•

pertinent reservoir information including formation name and type, reservoir pressure, and reservoir temperature.

•

treatment pump schedule including stage volumes, rates, proppant concentrations, fluid and proppant types, special chemical addition, e.g., breaker scheduling, and displacement fluid and volume.

•

pressure requirements including maximum allowable surface pressure (tubing/casing) and anticipated treating pressure.

•

maximum HHP requirements.

•

standby equipment requirements.

Service Co./Operator Interaction In an “Alliance” environment, more responsibility for designing, setting-up, executing, and evaluating fracture treatments has been placed with the service company partner. There are certain areas, however, where the operator and service company need to interact to help insure a successful treatment. The first obvious area is in the design phase. The operator will need to furnish the service company with all available well and reservoir data. If sufficient data is not available, both parties should discuss and determine what additional data is required and how it can be most cost-

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PRE-TREATMENT PLANNING

effectively acquired. Regardless which party takes on the bulk of responsibility for the design, all designs should be reviewed by the other partner to insure there are no differences or questions before proceeding to the field. When prepared, the frac “brief” should also be reviewed and approved by both parties since, ultimately, safety issues are still the responsibility of Amoco. Once the design and procedure have been prepared, under the alliance arrangement it is the service company's responsibility to implement the treatment. This includes making sure the location size is adequate, that adequate storage tanks are provided, and that sufficient fluid, chemicals, proppant, equipment, and personnel are available to fulfill the requirements of the treatment. Certain phases of this will require interaction with the operator representative, e.g., enlargement or grading of the location. During the treatment it is the ultimate responsibility of the service company to insure that the materials pumped meet design specifications and that proper quality control procedures have been implemented to insure this. Periodically, the service company should be called upon to demonstrate to the operator the quality of the fluids and proppants on-site. It is also the service company's responsibility to see that the treatment is pumped as close to design as possible, adhering to safe practices as dictated by both parties. An operator representative should be present for the pre-treatment safety meeting and treatment execution and should be allowed to interject comments or make changes to the treatment if deemed necessary to insure completion of the treatment or to prevent an unsafe situation. Post-treatment appraisal should include both parties. Any deviations from the design and problems encountered with equipment or fluids should be documented and contingencies formulated to help prevent reoccurrences.

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11 11.4 FRACTURING FLUID QC Several types of fracturing fluids are available for use on today's fracturing treatments, including water-based fluids, oil-based fluids, alcohol-based fluids, emulsion fluids, and foam-based fluids. It is important that the design engineer choose the best fluid to achieve successful and the most cost-effective stimulation of his/her well. While this is a design issue, it is also the first step in a proper fluid quality control program. Compatibility of the fracturing fluid with the formation material/fluids is essential to prevent such things as clay swelling and pore throat plugging, the creation of emulsions and/or sludging of crude oil, the degradation of matrix cementation, etc. An ideal fracturing fluid should have certain physical and chemical properties that include: •

Compatibility with the formation materials/fluids.

•

Sufficient viscosity to develop the necessary fracture width and transport desired distance into the fracture.

•

An efficient (i.e., low fluid loss) fluid to minimize the amount of fluid required.

•

Easy to remove from the formation with minimal damage to the formation and proppant pack.

•

Low friction pressure in the tubulars.

•

Easy preparation of the fluid and quality control in the field.

proppants the

Choosing a fracturing fluid will require compatibility testing by the service company with formation core/fluids and rheology testing with the actual base (source) mixing fluid. In a new area or formation, where no historical data exists, these tests should always be performed. Starting with this step, a proper fluids quality control program should include the following: •

Choosing the appropriate gel system and familiarity with this system.

•

Base fluid and gel rheology testing.

•

Base fluid delivery, filtration, and storage on-location.

•

Gel pilot testing on-location.

•

Final gel preparation.

•

Sampling.

Since most treatment today are performed with water-based, oil-based, or foam-based fracturing fluids, the following focuses on quality control measures for these.

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FRACTURING FLUID QC

Base Mixing Fluid Prior to moving any equipment on location for a fracturing treatment, the service company should be confident that the base mixing fluid will be compatible with the formation and the chosen gel system. In a new area and/or formation, where there are significant changes to job size, and/or the source water changes, the base mixing fluid should always be tested by the service company in the lab and a base set of rheology values generated. At the other end of the spectrum, where a particular water source has been tested and used routinely with success, this is not necessary on every treatment; but, should still be periodically spot checked. When a water-based gel is used, it is imperative that a fresh, clean water be used and that the service company check the ion content and bacteria count. Certain ions, bacteria, and other foreign materials can interfere with the proper building of a quality fracturing fluid. One example of this is a source water used in Australia where the natural borate content is high and causes a weak crosslink of the base gel if the pH is lowered. This was discovered through laboratory testing and prevented a potentially nasty situation, i.e., crosslinking of the base gel in the frac tanks. Instead these jobs are successfully pumped by adding the pH reducing chemicals on-the-fly. Table 11.4 is an example form for testing the base mixing water. The three most important components of a base mixing water are the iron content, pH, and bacteria count. For most waterbased gel systems, the total iron content should be less than 25 mg/liter. Excess iron can reduce the temperature stability of the gel as well as causing the gel to be more shear-sensitive when crosslinked. Excessive iron is usually introduced into the system through rusty frac tanks or transports delivering the water to location. The pH of the base mixing water should be in the 6 to 8 range. A pH higher than 8 can cause poor gel hydration and a ph less than 6 can cause gel lumping and “fish eyes”. It is desirable to start with a base mixing water pH close to a 7. A pH buffer, acid, or base can be used to bring the pH into this desired range. One of the more common sources of gelation problems is bacterial contamination of the base water. Certain types of bacteria thrive on gel as a food source, destroying the gel structure by bacterial enzymes. Sulfate reducing bacteria are most common, converting sulfates in the fluid and reservoir to sulfide, a detrimental formation blocking agent. This type of bacteria is characterized by a blackening of the water and a strong hydrogen sulfide odor. Bacteria presence is most common during summer months when temperatures exceed 80°F. During hot periods, bacteria growth accelerates in stagnant water such as that stored in frac tanks for an extended period (as little as a few days). As a preventative, bactericide should always be added to the frac tanks prior to filling. This measure is more effective and less expensive than combating the bacteria after it has flourished. If the water becomes contaminated, dispose of the water, re-clean the tanks, and re-fill with bactericide treated water. Adding bactericide to a contaminated tank will not solve the problem. This will only kill the bacteria, but the bodies and enzymes will remain.

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11 Table 11.4 - Sample Form for Testing Base Mixing Water for Hydraulic Fracturing

WATER QUALITY TEST Date: _________________________________________________________________ Water Source: __________________________________________________________ Company/Person Testing: ________________________________________________ TESTS: Temperature SG Corrected to 60 deg F pH Total Iron Ferrous Iron (Fe+2) Ferric Iron (Fe+3) Total Phosphorous (PO4-3) Sulfite (SO3-2) Sulfate (SO4-2) Calcium-Magnesium Hard (CaCO3) Total Reducing Agents Total Bacteria Count Aerobic Anaerobic Boron

Recom’d Level

Conc. ppm, mg/l

40-100 deg F <1.038 6-8 <20 ppm

<5 ppm

<1000 ppm 0 ppm <10**5 ppm

In many cases, the water should be filtered through a 10 micron filtering system. While this is more costly and time consuming, it can prevent much larger costs incurred if the gel cannot be properly mixed and has to be disposed of. When city water is routinely used, filtering should not be required. The service company/operator must make sure, though, that the source water delivered to location is the same as that requested and not contaminated in transit. Visual inspection of the water in the frac tanks should be a routine step prior to mixing any gel. This may help detect contaminants in the water and, possibly, the improper filtration of the water. When oil is the base fluid, usually lease crude or diesel, compatibility/stability tests should be performed with the gel system chemicals (preferably those to be used during the treatment). Most systems will not gel as easily with crudes having an API gravity of 30° or higher. Also, some diesels may contain detrimental components. The content of diesel will vary with supplier, refinery, and seasonal changes. Special additives are included in extreme cold regions to prevent diesel freezing and these can be detrimental to the gelling and gel breakage process. Oil-based fluids are more difficult to mix than water-based gels and by knowing the properties of the oil and performing early pilot tests, the first step has been taken to insure the fluid can be prepared on-site with the least amount of difficulty.

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FRACTURING FLUID QC Table 11.5 - Testing of Base Mixing Fluids for Hydraulic Fracturing

BASE MIXING FLUID •

Obtain 3 Samples from Source - Composition / Compatibility Testing (Svc Co.)

WATER-BASE FLUID:

•

•

•

Iron Content <20 mg Fe/liter - Reduce Temp. Stab. of Gel - Transports / Frac Tanks pH between 6.0-8.0 - >8.0 Poor Gel Hydration - <6.0 Lumping or “Fish-Eyes” Bacteria - Most Common Above 80 deg F - Will Destroy Gel Structure - Hydrogen Sulfide Odor

OIL-BASE FLUID:

• • • •

Lease Crude or Diesel deg API Gravity or Lower Best Diesel Content Change with Supplier, Refinery, and Seasonal Change Compatibility Test is a Must

Transport and Storage of Fluid All transports bringing the base mixing fluid and all frac tanks used for storage on location should be very clean and free of rust and other chemical contaminants. Transports and frac tanks should be thoroughly drained, steam cleaned, and flushed with clean water prior to loading the mixing fluid. If oil or diesel is to be shipped and stored, all water must be removed prior to filling. Less than 1% water in a gelled-oil system can cause severe gelation problems. If frac tanks are showing signs of excessive rust and wear, the valves do not operate freely, and/or the tanks are not thoroughly clean they should be rejected. This will require an inspection by the service company and/or operator. Ultimate care should be taken to insure that the transport and on-site storage of the base-mixing fluids results in a clean fluid to start with in mixing the fracturing fluid. Of all the quality control measures, this is one of the most important to preventing gelation problems. “Prevention far exceeds the cure.”

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11 Quality Controlling Water-Based Gels Water-based fluids can be broken into two categories, i.e., linear and crosslinked gels. Linear gel is water thickened with a viscosifier, the more common viscosifiers being guar, hydroxypropal guar (HPG), hydroxyethylcellulose (HEC), and carboxymethyl HPG (CMHPG). With linear gels the only means of increasing the viscosity is to increase the polymer loading. Crosslinked fluids on the other hand start with a linear gel and a borate or metal (zirconate or titinate) crosslinker is added which ties or bonds the polymer molecules together, resulting in a pseudoplastic fluid with much higher viscosity than obtainable with simple linear gel systems. Quality control procedures for linear gels are fairly straight forward and include checking the following: •

Base gel viscosity.

•

pH of the fluid.

•

Consistency and appearance of the gel.

•

Breakage of the fluid.

Prior to mixing any gel in the frac tanks, pilot tests should first be performed with the basemixing water from each tank. Minimum equipment requirements to perform these tests, which should be supplied by the service company, include: •

Fann 35 viscometer.

•

Properly calibrated scale.

•

pH meter.

•

Thermometer.

•

Waring blender or similar mixing devise.

•

Heat bath capable of reaching 180-200°F.

All pilot tests should be performed using samples of the chemicals supplied on-location for the treatment. The following procedure should be followed and all phases recorded: •

Visually check the base water for signs of bacteria or contaminants.

•

Measure the pH of the base mixing water.

•

Mix the gel sample to include all chemicals planned for the treatment, including the breaker.

•

Measure the temperature and pH of the final gel sample.

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FRACTURING FLUID QC

•

Measure the viscosity of the gel, taking Fann readings at 100, 300, and 600 rpms.

•

Immerse the gel sample in the heat bath.

•

Measure and record the viscosity of the fluid in the heat bath every 30 minutes or so to determine viscosity degradation for use in the design model and to evaluate breakage of the fluid. (At a minimum, the fluid should be heated and sufficient breaker added to insure that the breaker on-site works.)

Fig. 11.1 and Fig. 11.2 are Fann viscometer readings for various linear HPG gel loadings and temperatures at a shear-rate of 511 sec-1 (corresponds to Fann 35 - 300 rpm reading). The same are provided for linear HEC gel in Fig. 11.3 and Fig. 11.4 . These can be used as a guide in checking the initial gel viscosity at surface temperature. Some tolerance should be allowed, i.e., a few cp either side of the values shown in the plots, since there will be some variance in the mixing of each tank, e.g., for a 50 lb HPG gel loading an acceptable range of Fann readings at 70°F might be 45-53 cp. If the gel viscosity falls much outside this range, another sample should be caught from the tank and re-checked. If it is still outside this range, then corrective measures must be taken to bring it into spec if it can not be used in the tail-end of the treatment when the formation is coolest

Fig. 11.8 - Hydroxypropylguar (HPG) - Fann Viscosity v. Polymer Concentration in 2% KCI Water @ 60°F.

When performing break tests, it is usually necessary to mix several samples with different breaker concentrations to determine the final breaker loading. The breaker loading should be tailored so that the maximum effective loading is added throughout the treatment to insure

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11

Fig. 11-9 - Hydroxpropylguar (HPG) - Fann Viscosity v. Temperature for Various Polymer Loadings in 2% KCI Water.

eventual complete degradation of the gel. When the expected BHT exceeds the achievable temperature of field heat baths, the breaker scheduling will have to be determined in the laboratory (also required when go into a new area or formation or where significant changes are made to the treatment size and/or the fracturing fluid or water source is changed). Different breaker concentrations may be required for different fluid systems. Also, the reservoir BHT will dictate the amount of breaker that can be added so the gel degrades in the time required. Two general types of breakers are available for use, i.e., raw (oxidizing or enzyme) breaker and encapsulated (delayed) breaker. It has been shown in industry studies that up to a point more breaker is better from the standpoint of degrading the gel filter-cake formed on the fracture walls and removing the gel residue from the proppant pack. A “rough rule-of-thumb” is to design the breaker schedule so the pad fluid is completely broken in twice the expected pump time and the tail-end fluid is broken in about an hour after shutdown. For example, as shown in Table 11.3, on a 1-hour or less treatment, sufficient breaker should be added to the pad to break the fluid in approximately 2 hours and the breaker schedule increased so the tail-end fluid breaks within 1 hour after shut-down. Depending on the reservoir temperature and gel loading, only encapsulated (delayed) breaker may be required in the pad, whereas in the later stages the raw breaker concentration may be increased and the encapsulated breaker concentration decreased. When feasible, the breaker schedule should be

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FRACTURING FLUID QC

Fig. 11.10 - Hydroxyethlcellulose (HEC) - Fann Viscosity v. Polymer Concentration in 2% KCI Water @ 60°F.

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11

Fig. 11.11 - Hydroxyethylcellulose (HEC) - Fann Viscosity v. Temperature for Various Polymer Loadings in 2% KCI Water.

designed/evaluated on-site based on pilot test ing with the actual mix fluid and breaker stock provided for the treatment. Ineffective batches of breaker have been known to exist! Table 11.6 - Sample Fracture Treatment Schedule with Raw and Encapsulated Breaker Ramps.

Fluid Type

Fluid Vol (gals)

Raw Brkr (#/Mgal)

Enc. Brkr (#/Mgal)

Prop Conc (ppg)

Rate (bpm)

30# Borate XL

3500

0.0

5.0

0.0

20.0

30# Borate XL

500

0.0

5.0

1.0

20.0

30# Borate XL

300

0.5

4.0

2.0

20.0

30# Borate XL

300

0.5

4.0

3.0

20.0

30# Borate XL

300

1.0

3.0

4.0

20.0

30# Borate XL

300

2.0

3.0

5.0

20.0

30# Borate XL

300

3.0

2.0

6.0

20.0

30# Borate XL

400

4.0

2.0

7.0

20.0

30# Borate XL

600

5.0

2.0

8.0

20.0

Note: Raw breaker ramped up and encapsulated breaker ramped down based on field-generated lab tests in heat bath at expected BHT.

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Quality control procedures for crosslinked gels are much the same as for linear gels with the exception of checking the ability of the fluid to crosslink, it's crosslinked consistency, and crosslink time. The same procedures as above should be followed to prepare and test the base linear gel prior to crosslinking. Crosslinked gel systems generally fall in one of two categories, i.e., instantaneous crosslink and delayed crosslink. The crosslink time can be controlled by a number of methods. Some companies control crosslinking by adjusting pH, others vary crosslink time by changing the crosslinker concentration or by blending crosslinkers, while still others use retarders or accelerators to control the time to crosslink without changing the crosslinker or pH. Again, pilot testing is very important in determining if the gel is properly crosslinking and how long it takes to crosslink. Generally, the best way to test this is to obtain a sample of the crosslinker on-site and observe the crosslinking of the linear gel in a blender. The speed of the blender should be set just high enough so a vortex forms in the center of the linear gel sample. The crosslink time is then measured from the time the crosslinker is added until the vortex closes and a mushroom forms on top of the sample - this termed the “Vortex closure time”. For instantaneous crosslink systems, the gel should form a bonded structure very quick. For a delayed system, though, this may take some time, depending on the temperature and pH of the fluid. When testing a delayed crosslinked gel, it is best to heat the base gel to the expected average wellbore temperature during the treatment to perform the pilot tests. The delay time for the crosslink is determined by the expected residence time in the pipe, i.e., the gel should ideally be crosslinking just outside the perforations. This will minimize pipe friction pressure and minimize the shear on the gel before it enters the fracture. A good crosslinked gel should exhibit a strong bonding with a smooth texture that can be lipped out of the sample container and returned as a whole unit. If a gel is under-crosslinked it will exhibit a weak, slimy, runny appearance absent of strong bonding. At the other end of the spectrum an over-crosslinked gel will exhibit a chunky, rough, “brittle” appearance. This type fluid, while viscous in appearance will have poor temperature stability. If crosslinking problems occur, several things can be investigated including: •

The crosslinker itself. Catch another sample from a different drum on-site.

•

The pH of the fluid if the crosslinker is being controlled by pH.

•

The crosslinker concentration.

In special cases where the gel simply will not crosslink properly, it may be due to contaminants in the base gel. This, however, can be prevented if proper laboratory and pilot testing (including

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11 crosslinking) is performed prior to mixing the tanks of gel. If crosslinking is a problem in only one tank and sufficient excess is available or can be mixed, then that particular tank may have to be utilized as prepad or flush or disposed of. Do not pump any gel as part of the main treatment that is suspect. Again, as for the linear gel systems, breaker scheduling is very important for crosslinked gel systems. There is nothing worse than pumping a crosslinked gel into a reservoir that might not break. Undoubtedly many wells have been ruined this way. If possible, breaker tests should be performed in a heat bath on-site to determine the optimum breaker schedule. If the reservoir temperature exceeds 200°F, the upper limit for most conventional heat baths, then extensive laboratory testing should be performed by the service company with the actual mixing water and preferably the chemicals from the treatment stock to determine the best breaker schedule for the desired time period. When utilizing resin-coated proppants, these can have a dramatic affect on the crosslink and break time of crosslinked gel systems. Some of the crosslinker and breaker are neutralized by the resin, requiring that additional amounts of these chemicals be added to achieve the same gel. Again, this requires extensive testing by the service company to determine the adjustments required. This is generally a hard thing to quantify and impossible to determine on-site. A new encapsulated curable resin-coated proppant has just recently been introduced on the market which still bonds in the fracture with closure stress yet is inert to fracturing fluids and chemicals. If it proves to work as advertised, it should eliminate the problems associated with the interaction with crosslink gel chemicals and breakers. All pilot test results done on-site should be recorded on a form similar to Table 11.7. Quality Controlling Oil-Based Gels Some formations, although these are few and far apart, simply do not lend themselves to waterbased fracturing. These might have large quantities of swelling or migrating clays, imbibe large amounts of water, and/or the rock matrix structure is weakened by water. In these cases, oil-based gel may be the preferred fracturing fluid. Due to difficulties in properly mixing and quality controlling this system, in addition to the safety hazards, gelled-oil should only be used as a last resort after careful reservoir and laboratory evaluation. Most gelled-oil are made up of the following components: • • • • • •

Lease crude or diesel as the base fluid. Gelling agent. Activator additive. pH control additive. Breaker. Fluid loss additive.

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Table 11.7- Fracturing Fluid Quality Control Form.

Well / Field:________________________________

Date:_________________

Location:

Tested By: ___________

Tank No.

________________________________

Gel Type / Conc.

Gauge / Pump Volume

Fluid Temp.

Vis. @ 300 rpm

pH

XL Time

Break Time

Appearance

Most crude oil from 28°F API and higher can be gelled with this system; however, the particular crude must be tested for gelation prior to a decision being made on its use. Testing should also be performed with each diesel source to determine its suitability. The content of diesel may vary with supplier, refinery, and seasonal changes. Special additives included to prevent diesel freezing can have a detrimental affect on the gelation and breakage of a gelled-oil system. The concentration of gelling agent (aluminum phosphate) is the controlling factor in determining the viscosity of the gel. This concentration will depend on the desired viscosity at BHT. Typical viscosities achievable with this system are 50-300 cp (170 sec-1) at 80-190°F and 50-150 cp at 200-250°F. The activator (sodium aluminate or other base) is normally held to a constant ratio with the amount of gelling agent, e.g., if 8 gals/Mgals gelling agent is used, 3 gals/Mgals of actiJuly 1999

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11 vator is added; with 6 gals/Mgals of gelling agent the activator concentration is around 2.3 gals/Mgals. The concentration of pH control additive is dependent on the pH of the particular oil. Lab testing, through trial and error, is required to determine the correct concentration of pH control additive. In lab testing the gelling agent and activator are added first and then the pH control added drop wise until gel viscosity is observed. Breakers used for gelled oil systems include sodium bicarbonate (baking soda) and slaked lime or calcium hydroxide. The sodium bicarbonate is used on most treatments unless the BHT is very low or a short break time is desired. Typical concentrations of breaker range from 1075 lbs/1000 Mgals depending on the BHT, pump time, and the desired break time. As noted for the water-based gel systems, it is preferable to add as much breaker as lab tests indicate possible while still maintaining sufficient viscosity to safely complete the treatment. Cases have been sited where no or an insufficient amount of breaker were added and the gel did not break, causing the treatment to be ineffective and plugging of the formation. In a gelled-oil system, the sodium bicarbonate breaker also acts as a fluid loss agent, this being in a free flowing powder form. Other additives such as Adomite Aqua and silica flour can be used, however, these are not recommended unless absolutely necessary. On-site quality control test procedures for gelled-oil systems should include the following: •

Roll each frac tank of oil thoroughly.

•

Sample the base oil from each tank.

•

Add the gelling agent and activator to the sample(s) at the prescribed concentrations recommended by the service company and previous lab testing.

•

Determine the amount of pH control additive by adding drop-wise until viscosity develops.

•

Test the viscosity of the fluid with a Fann 35 viscometer. If the viscosity is within the desired range, proceed with the next step. If it is too high or too low, prepare another sample, adjusting the gelling agent and activator concentration and going through the pH additive test again. Continue to retest until the desired viscosity is obtained or the best gel obtainable is achieved.

•

After the gelling agent, activator, and pH additive concentrations have been fine-tuned, mix several more samples with varying concentrations of breaker and immerse these in a heat bath to monitor the gel degradation and break time. The gel should have sufficient viscosity to complete the treatment safely and then break back to less than 10 cp at a Fann 300 rpm reading. An example of the results of this type testing are shown in Fig. 11.12. In this case, it was determined that 40 lbs/Mgals of breaker was optimum for completing the short pump time treatment and getting a good break within a reasonable time after the treatment.

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These tests should be performed for each tank of oil as some may react differently than others requiring slight alterations to the chemical additive combination.

Fig. 11.12 - Results of Field Break Test for Oil-Base Gel, Using a Fann 35 Viscometer and Heat Bath to Determine Optimum Breaker Concentration.

Safety precautions associated with handling gelled-oils include: •

Wearing rubber gloves and safety goggles when handling all chemicals. Some are and some alkaline and can cause severe burning.

acidic

•

Take the necessary precautions associated with a highly flammable fluid, i.e., ground the blending and pumping equipment, no smoking on location, use of shrouds on high pressure discharge lines, and proper fire fighting equipment.

Quality Controlling Foam Fracturing Fluids Foam fracturing fluids are sometimes an alternative to oil-based gels to minimize the amount of fluid placed on the formation. Their most common application, though, is in fracturing underpressured reservoirs where the entrained gas in the fluid results in improved and rapid cleanup. Virtually any liquid can be foamed, including methanol, methanol/water mixtures, hydrocarbons, and water. The most commonly used system is comprised of a 20-40 lb/Mgal linear water-based gel and 65-80% CO2 or N2, i.e., a 65-80 quality foam. This means that 65-80% less water is used as compared to conventional treatments. The advantages of using CO2 over nitrogen as the gas phase

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11 is (1) that CO2 can be pumped as a liquid, it not turning into its gas phase until reaching reservoir conditions, and this resulting in lower treating pressures and (2) the liquid CO2 is soluble in water, thus as it turns into a gas in the reservoir it will not dissipate into the formation as might be the case with a less soluble gas such as nitrogen. The use of nitrogen, though, can be considerably cheaper when the expected treating pressures are low. Some of the disadvantages of using foam fracturing fluid are (1) that job execution must be precise - small variations in water or gas mixing rates can cause loss of foam stability and (2) downhole proppant concentrations are generally limited to about 8 ppg since all of the proppant must be added to the liquid phase which comprises only about 1/4 of the total foam fluid. Since most foam treatments use a water-based linear gel for the liquid phase, the same quality control procedures outlined previously for this type gel should be applied here. Generally, these would again include checking the base gel viscosity, pH, and temperature to make sure the gel meets design specifications. Little can be done in regard to quality controlling the gas phase, aside from checking to make sure sufficient quantity is on-site to conduct the desired treatment. Because foam fracturing treatments are more complex to perform than single-phase treatments, it is important that the service company treater and engineer fully understand the surface proppant schedule and liquid/gas rates to obtain the desired concentrations and rate downhole. A plan should be carefully laid out with a table such as shown in Table 11.8 for all to follow during the treatment. Table 11.8 - Sample Schedule Prepared for Constant Clean Side and Nitrogen-Rate Foam Fracture Treatment. FOAM FRAC PUMPING SCHEDULE Proppant

Slurry Volume

Pumping Rate

Foam Volume, gal

Liquid Volume, gal

Foam, ppg

Liquid, ppg

Total lb

Foam, gal

Blend, gal

Nitrogen, scfm

Liquid, bbl/min

Sand,* bbl/min

Total bbl/min

Time, min:sec

35,000 25,000 30,000 12,500 10,000 7,500 1,800 TOTALS: 121,800

10,500 7,500 9,000 3,750 3,000 2,250 540

0.0 1.0 2.0 3.0 4.0 5.0 0.0

0.0 3.3 6.7 10.0 13.3 16.7 0.0

0 25,000 60,000 37,500 40,000 37,500 0

35,000 26,130 32,712 14,195 11,808 9,195 1,800

10,500 8,630 11,712 5,445 4,808 3,945 540

13,820 13,820 13,820 13,820 13,820 13,820 13,820

4.5 4.5 4.5 4.5 4.5 4.5 4.5

0.0 0.7 1.4 2.0 2.7 3.4 0.0

15.0 15.7 16.4 17.0 17.7 18.4 15.0

55:33 39:37 47:29 19:53 15:53 11:54 2:51

200,000

130,840

45,570

36,540

Foam quality: 0.70 Total Nitrogen required:

193:10

2,669,563 scf (calculated as scf/min x total time) 2,671,480 scf (calculated as total bbl nitrogen x scf/bbl space)

*Rate of sand, bbl/min = ppg x bbl/min x 0.0452

Additional Fluid Quality Control Measures •

Inventory all chemicals and fluids/gas on location at the earliest possible time to make sure the right materials in the right amounts are available for the treatment.

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•

Perform pilot tests as soon as possible on-site to insure that the available chemicals all work and that the base mixing fluid is not contaminated.

•

Take tank dips before and after the treatment to help in evaluating the accuracy of metering during the treatment and to access what was actually pumped.

•

Set up a sampling program during the treatment to determine that the system is acting as pilot testing predicted it would. On a relatively small treatment, this might include catching 1-2 samples during the pad and 2-4 samples during the proppant stages. On a larger treatment, with a pump time of several hours, several samples should be caught during the pad and, preferably, one sample per proppant stage. In the most severe case on a crosslinked gel treatment, where the gel is not properly crosslinking and this can be detected before proppant is started, the treatment should be aborted and the problem remedied before a reattempt of the treatment.

•

Immerse half of the treatment samples in a heat bath to determine the gel break time and to determine the earliest possible time at which the well can be flowed back. The remaining samples should be retained for a period of time after the treatment until the well has cleaned up. Also, if gelation problems occur during the treatment, these samples may help determine the cause.

•

Record all phases of the gel pilot testing, inventory, mixing, and results of treatment sampling.

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11 11.5 PROPPANT QC The selection and quality of a proppant agent is very important to the outcome of a fracturing treatment. Production increase is a function of fracture conductivity, and fracture conductivity is directly related to the insitu proppant characteristics and confining (closure) stress on the proppant. Factors affecting fracture conductivity include: •

Closure stress and proppant strength.

•

Proppant particle size.

•

Proppant concentration.

•

Proppant grain shape - roundness/sphericity.

•

Amount of fines generated.

Many of these variables can be controlled to varying degrees through proper quality control practices. Closure Stress and Proppant Strength The stress transmitted from the earth to the proppant pack at fracture closure can cause proppant crushing and embedment of the proppant into softer formation, both of which reduce the effective fracture conductivity. In selecting a proppant it is very important to know the approximate stress, the stress on proppant being equivalent to the closure stress minus the bottomhole flowing pressure. The maximum potential for proppant damage will usually occur early in the life of a well when the reservoir and closure pressures are high and the BHFP is low. Fig. 11.13 illustrates the affect closure stress has on several types of proppants, showing that at higher stresses, higher strength proppants will be required to provide adequate fracture conductivity. If closure stress is unknown, this parameter should be measured through injection/decline testing. A list of currently available proppants and their recommended stress limitations are shown in Table 11.9, including sand, intermediate-strength, high-strength, and resin-coated proppants. Industry studies over the past 10-15 years have shown that when proppants are subjected to stress and temperature for longer periods of time, conductivity decays with most of this decay occurring over the first 100 hours. Fig. 11.14 shows examples of this for several different type proppants. In designing the fracture treatment, long-term conductivity data should be obtained from the service company and used instead of the more typically published short-term data. Proppant Particle Size Proppant particle size selection is a design consideration and dependent on the stress level, desired conductivity, and proppant transport (i.e., achievable fracture width). In most cases, either 20/40, Hydraulic Fracturing Theory Manual

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Fig. 11.13 - Effect of Proppant Type on Proppant-Pack Permeability (Conductivity). Relative Performance of Various Proppant is Demonstrated for 20/40 Mesh Size. Table 11.9 - Fracturing Proppant List Proppant

Manufacture

Specific Gravity

Application

AcFrac CR-5000

Acme Borden

2.59

Curable resin coated white sand. Less resin than AcFrac CR. Closure stress to 6,000 psi.

AcFrac CR

Acme Borden

2.59

Curable resin coated white sand for flowback control. Closure stress to 8,000 psi.

AcFrac CR-100

Acme Borden

-

July 1999

Limitations/ Alternative

Curable resin coated 100 mesh sand.

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11 Table 11.9 - Fracturing Proppant List (Continued) Proppant

Manufacture

Specific Gravity

Application

Super TF

Santrol

2.60

Low cost low resin content (2%) for bonding and flowback control. A true 20/40 mesh white sand. Closure stresses up to 6,000 psi.

Super LC

Santrol

2.60

Low cost low resin content (2%) for bonding and flowback control. White sand. Closure stresses up to 6,000 psi.

Super DC

Santrol

2.57

Dual-coat, half-cured and half-uncured resin coated white sand for strength and flowback control. 4% resin. Closure stresses up to 8,000 psi.

Super HS

Santrol

2.54

High strength, dual-coat, resin coated white sand for strength and flowback control. 5% resin. Closure stresses up to 8,000 psi.

Tempered TF

Santrol

2.60

Identical to Super series except precured rather than curable.

Tempered LC

Santrol

2.60

Identical to Super series except precured rather than curable.

Tempered DC

Santrol

2.57

Identical to Super series except precured rather than curable.

Tempered HS

Santrol

2.54

Identical to Super series except precured rather than curable.

EconoFlex

Santrol

2.55

Resin coated EconoProp ceramic proppant. Closure stresses to 14,000 psi

2.65

Used to prop open created fracture to conduct hydrocarbons to the wellbore. Closure pressure to 4,500 psi. Ranked 1st among sands.

White Sand

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Limitations/ Alternative

Low closure stress.

PROPPANT QC

Table 11.9 - Fracturing Proppant List (Continued) Proppant

Manufacture

Specific Gravity

Application

EconoProp

Carbo Ceramics

2.65

Economical intermediate strength ceramic proppant. Closure stress 3,000 to 8,000 psi.

Lower closure application. Only offered in 20/40 mesh. Competes with LWP 1.

Carbo-Lite

Carbo Ceramics

2.73

Intermediate strength ceramic proppant. Closure stress 4,000 to 9,000 psi.

Competes with LWP Plus.

Carbo-Prop HC

Carbo Ceramics

3.17

Intermediate strength bauxite. Closure stress up to 15,000 psi.

Competes with InterProp Plus.

Carbo ISP-1

Carbo Ceramics

3.16

Intermediate strength bauxite. Closure stress up to 15,000 psi. Less expensive than Carbo-Prop HC. Broader size distribution.

20/40 mesh only. Competes with InterProp 1.

LWP 1

Norton-Alcoa

2.64

Economical intermediate strength ceramic proppant. Closure stress 3,000 to 8,000 psi.

Lower closure application. Only offered in 20/40 mesh. Competes with EconoProp.

LWP Plus

Norton-Alcoa

2.60

Intermediate strength ceramic proppant. Closure stress 4,000 to 9,000 psi.

Competes with Carbo-Lite.

InterProp Plus

Norton-Alcoa

3.15

Intermediate strength bauxite. Closure stress up to 15,000 psi.

Competes with Carbo-Prop HC.

InterProp 1

Norton-Alcoa

3.15

Intermediate strength bauxite. Closure stress up to 15,000 psi. Less expensive than InterProp Plus and Carbo-Prop HC. Broader size distribution.

Competes with Carbo ISP-1.

InterProp 1 RCP

Norton-Alcoa

3.06

Same as above with resin coating for flowback control.

Same as above.

UltraProp Plus

Norton-Alcoa

3.49

High strength bauxite. Closure stress up to 20,000 psi.

Expensive.

AcFrac SB ULTRA

Acme Borden

2.56

Partially cured white sand, requires stress for bonding. For flowback control and strength. Will not set up in wellbore in screenout. Closure stress to 8,000 psi.

More compatible with oxidizing breakers.

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Limitations/ Alternative

Hydraulic Fracturing Theory Manual

11 Table 11.9 - Fracturing Proppant List (Continued) Proppant

Manufacture

Specific Gravity

Application

Limitations/ Alternative

AcFrac Black (PRB)

Acme Borden

2.55

Precured white sand designed for strength during closure. Closure stress to 8,000 psi.

AcFrac PR-5000

Acme Borden

2.59

Precured white sand designed for strength during closure. Closure stress to 8,000 psi.

Brown Sand

2.65

Brady sand. Used to prop open created fracture to conduct hydrocarbons to the wellbore. Closure pressure to 4,500 psi. Ranked 2nd among sands.

Low closure stress.

Colorado Sand

2.65

Used to prop open created fracture to conduct hydrocarbons to the wellbore. Closure pressure to 4,500 psi. Ranked 3rd among sands.

Does not meet a number of API RP56 guidelines.

Arizona Sand

2.70

Used to prop open created fracture to conduct hydrocarbons to the wellbore. Closure pressure to 4,500 psi. Ranked 4th among sands.

Does not meet a number of API RP56 guidelines.

Sinter Ball

3.60

Sintered bauxite from Brazil. Used for high closure pressure conditions too extreme for ceramics.

Exxon license fee required for wells deeper than 7,150 feet.

16/20, or 12/20 mesh proppant is used. Particle size distribution can have a measurable affect on fracture conductivity. For example, as shown in Fig. 11.15, one sand having 90% of the grains falling between the designated 20/40 mesh sieve screen sizes, as compared to another having only 60% of the grains within the required range, will exhibit much higher conductivity and the contrast will increase as the closure stress increases. Testing of proppant size distribution requires a sieve analysis and should be routinely performed as a quality control practice on most fracture treatments. The American Petroleum Institute (API) provides several publications detailing tests for sands and intermediate- and high-strength proppants. Shown in Table 11.10 is an excerpt from API RP 56 showing the range of various frac sands (6/12 to 70/140) and the nest of sieve screens recommended for testing. A minimum of 90% of the tested sand sample (also generally applies to other proppant types) should fall between the designated sieve sizes correlative to the indicated mesh size, i.e., 6/12, 12/20, 20/40, etc. Not over Hydraulic Fracturing Theory Manual

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PROPPANT QC

Fig. 11.14 - Example of Long-Term Permeability (Conductivity) Data for Various 20/40 Mesh Proppants Tested @ 275°F and a Proppant Concentration of 2 lbm/sq. ft.

0.1% of the total proppant sample should be larger than the largest sieve screen mesh and not over 1.0% should be smaller than the smallest sieve screen mesh. Proppant Grain Shape Proppant particle “roundness” and “sphericity” are measures of grain shape. Roundness is a measure of the relative sharpness of grain corners or grain curvature and sphericity is a measure of how close a proppant grain approaches the shape of a sphere. Because the surface stresses are more uniform, a well-rounded, spherical particle is capable of carrying higher loads without crushing. Therefore, at higher stress levels, a higher degree of roundness and sphericity contribute to higher proppant-pack conductivity. A visual comparator, shown in Fig. 11.16 from API RP 56, is the most widely used method of determining grain shape. For sands, the API recommends a minimum sphericity of 0.6 and a minimum roundness of 0.6 (1.0 being a perfect sphere). For intermediate- and high- strength proppants a minimum sphericity and roundness of 0.7 is recommended.

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11

Fig. 11.15 - Effect of Proppant Particle Size Distribution on Fracture Conductivity for 20/40 Mesh Sand at Proppant Stresses of 5,000-10,000 psi.

Fig. 11.17 shows the effect on fracture conductivity for two sands at stresses of 5000 and 10,000 psi, one exceeding API specs and other falling below the recommended roundness/sphericity. From this, it is obvious that the rounder, more spherical proppant results in much higher conductivity, i.e., 61% higher at 5000 psi and 300% higher at 10,000 psi stress. Proppants routinely used and/or new proppants being considered for use should be subjected to grain shape testing under a microscope by the service company and/or operator. Proppant Fines The presence of silts, clays, and other fine particles in the proppant can also reduce fracture conductivity. Fine particles can be detected through an API recommended turbidity test on-site. The recommended procedure for this test is: •

Using a black marking pen, record the proppant sample identification on one side of a clear glass 4-ounce prescription bottle (100 ml in 10 ml increments) in characters approximately 1/2” high.

•

Place the proppant sample in the container and fill to the 20 ml mark, gently tapping and leveling the sand and further fill to bring to but not exceed the 20 ml mark.

•

Add turbidity-free water (distilled water, if available) to the 100 ml mark.

•

Cap the bottle and shake vigorously for 10 seconds.

•

Hold the bottle at arm's length toward a moderate light source with the side of the bottle with the identification mark facing the light source.

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Table 11.10 - Recommended API Proppant Specifications for Frac Sand and Manufactured Proppants.

Recommended Mesh Size Requirements A minimum of 90% of the tested sample should fall between the designated sieve size. Not more than 0.1% of the tested sample should be larger than the first sieve size. Not over 1% should be smaller than the last sieve size. Recognized Proppant Mesh Sizes Frac Sand Size Designation

USA Sievesa Required for Testing

+ 6/12

+ 8/16

* 12/20

+ 16/30

* 20/40

+ 30/50

* 40/70

+ 70/140

4

6

8

12

16

20

30

50

6

8

12

16

20

30

40

70

8

12

16

20

30

40

50

100

10

14

18

25

35

45

60

120

12

16

20

30

40

50

70

140

16

20

30

40

50

70

100

200

Pan

Pan

Pan

Pan

Pan

Pan

Pan

Pan

* Primary Mesh Size + Alternate Mesh Size a USA Sieve Series as defined in ASTM E 11-70 Frac Sand

Manufactured

Roundness:

0.6 value or greater

0.7 value or greater

Sphericity:

0.6 value or greater

0.7 value or greater

Turbidity:

250 FTU or less

not specified

Silica:

greater than 98% by weight

not specified

Hydrochloric acid solubility - less than 0.3%. 12% hydrochloric - 3% hydrofluoric acid solubility - 6/12 through 30/40 mesh - 2.0% maximum allowable, 40/70 through 60/140 mesh - 3.0% maximum allowable percentage.

Hydrochloric acid solubility - not specified. 12% hydrochloric - 3% hydrofluoric - not specified.

Acid Solubility

Interpretation •

If the sample ID can be read through the water phase, the proppant and suitable for use.

•

If the sample ID can not be read, the proppant sample should be judged dirty and unsuitable for use.

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should be judged clean

Hydraulic Fracturing Theory Manual

11

Fig. 11.16 - Chart for Visual Estimation of Roundness and Sphericity for Proppants Used in Hydraulic Fracturing (from Krumbein and Sloss, 1955).

Fig. 11.17 - Effect of Proppant Roundness and Sphericity on Fracture Conductivity for 20/40 Mesh Sand at Proppant Stresses of 5,000-10,000 psi.

•

If the sample ID can be read but with some difficulty, let the sample stand for 10 minutes and repeat the test. If the ID still cannot be read, the sample should be judged unsuitable for use.

The most suitable time to perform the turbidity test is when the proppant bins or trucks are loaded in order to get a representative sample from a moving stream. Also, performing the test at

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this early time in the operation will allow for corrective measures to be taken if necessary without undue delay to the treatment. Proppant fines can also be generated in the fracture if the proppant strength is not high enough to withstand formation stresses. Crush resistance testing should be performed periodically on routinely used proppants and all new proppants being considered for use, using the recommended procedure in API RP 56. Testing of this nature can be performed by the service company, the Amoco Tulsa Technology Center, or by commercial core laboratories. Table 11.11 includes the recommended test cell loads and maximum allowable fines for frac sand. Table 11.11 - Stress to be Applied and Suggested Maximum Fines for Frac and Sand Crush Resistance Tests (API RP 56).

Mesh Size

Load on Cell* (lb force)

Stress on Sand (psi)

Suggested Max. Fines (% by weight)

6/12

6,283

2,000

20

8/16

6,283

2,000

18

12/20

9,425

3,000

16

16/30

9,425

3,000

14

20/40

12,566

4,000

14

30/50

12,566

4,000

10

40/70

15,708

5,000

8

70/140

15,708

5,000

6

NOTE: Indicated loads are for cells with a 2” diameter piston. For cells of other sizes, the cell load should be adjusted by the factor: (diam. of cell, in./2)**2. Additional Proppant Quality Control Measures •

Obtain weight tickets from the service company on the amounts and types of proppant delivered and loaded on location.

•

If using more than one type or size of proppant on a treatment, know where each proppant is loaded in the proppant storage bins on location and discuss with the frac operator in what order these are to be run.

•

Catch samples of the proppant during various stages of the treatment and label these according to size/type proppant and when they were caught.

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11 11.6 TREATMENT EXECUTION Successful execution of a fracturing treatment requires good lines of communication, following safe working practices, and having contingencies in place for mechanical and/or abnormal pressure behavior problems. Lines of Authority and Communication •

The operator should have only one person in charge of communicating changes or decisions to the service company.

•

Key personnel from the operator and service co. should have a final review meeting to go over the treatment pump schedule, maximum treating pressures, lines of authority, contingency plans in case of mechanical/pressure problems, and safety issues.

•

Service co. should supply properly working radios and headsets to all personnel at key equipment focal points, i.e., blender, pumps, sand delivery, frac tanks, valve operator, and frac operator in control van.

•

Prior to pressure testing, the service co. should perform a radio check to make sure all radios and headsets are fully functional. If an insufficient number of “working” radios are not available, the treatment should not be performed until this is remedied.

Safety Meeting The safety meeting should be conducted by the frac operator with all personnel on-site and should include the following: •

An outline of the job procedure.

•

Maximum treating pressures and rate.

•

Pressure testing.

•

Operator responsibilities.

•

Operator safety gear, including safety glasses, hard hats, safety boots, and proper clothing.

•

Chemical hazards.

•

Location and use of fire extinguishers, eye wash facilities, first aid kits, and other safety equipment.

•

Other emergency procedures, including fire, leaks, other accidents.

•

Smoking restrictions.

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•

Normal and emergency shut-down procedures.

•

A sign-up list of all personnel on-location during the treatment.

•

A designated safe assembly area in case of an emergency situation.

Pressure Testing Prior to every fracture treatment, all injection lines and valves should be pressure tested and “popoffs” or pressure relief valves set. All lines should be properly staked and all personnel not directly involved in the pressure test should move well clear of the area surrounding the lines, wellhead, and fracturing equipment. All lines should be tested to just above the determined maximum treating pressure set by the operator, with this pressure being held and recorded for a minimum of 5 minutes. If treating down tubing, with the plan to hold back-pressure on the annulus, both tubing and annulus lines must be tested. All leaks should be eliminated prior to proceeding with the treatment. Pressure relief valves should always be installed on injection lines and set and tested to just below the determined maximum treating pressure. Treating Problems Oftentimes, treating problems arise during the job that must be dealt with, the most common be equipment failures, gel not properly crosslinking, proppant delivery problems, and abnormal pressures. These can be very disruptive to the successful completion of a treatment if proper planning and contingencies have not been put in place. Some of the more common problems are as follows: •

Blender failure due to mechanical problem - In most cases, it is advisable to have a standby blender rigged-up and operational. While blender failures are rare, the cost of standby is minimal compared to the costs that might be incurred if the treatment has to be prematurely aborted. Hoses should be run from the standby to the frac tank manifold, the standby blender tub filled with gel, and sufficient chemicals installed on this blender to complete the job if need be. Also, when a standby blender is installed, provisions need to be made to change the sand delivery over to this second blender. On small treatments, where leak-off is expected to be high, fracture closure time may not allow sufficient time to switch to a standby blender. If this is the case, a standby serves no purpose.

•

Sanding-up” the blender tub - This is caused when fluid cannot be transferred to the blender at a fast enough rate, blender operator error (i.e., letting tub fluid level get too low), and/or the proppant feed rate into the tub is too high. If this occurs, switch immediately to the standby blender and resume the treatment. If no provision has been made for a standby, the treatment may have to be terminated. With a single blender, opening multiple fluid tanks may increase the feed rate to the blender. If problems are encountered early in the treatment in

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11 sucking fluid fast enough from the tanks at the desired injection rate, and a standby blender is available; then both blenders may have to be employed to keep up with the rate. This, though, takes careful planning. •

Inadequate fluid transfer from tanks to blender - This can be caused by the inability of the centrifugal pump on the suction side of the blender to draw fluid from the tanks, especially those a significant distance from the blender; partially closed valves; and/or plugged or kinked suction hoses. Adequate suction lines of proper sizing must be installed to achieve the desired rate. On extremely large treatments, transfer blenders may be required to transfer fluid from remote tanks to the primary blender.

•

Proppant delivery system failure - This is usually the weak link on any treatment. On smaller treatments, there is seldom any way to provide backup for the proppant delivery system. If this fails, the treatment should be flushed. On larger treatments, however, dual-belt proppant conveyor systems are available, which allow the treatment to be continued if one belt bogs down or the hydraulics on one side fail. It is important that the proppant delivery system used be capable of delivering the desired pounds per minute with adequate safety margin.

•

Pump failures - This is one of the more common occurrences and should be dealt with by having adequate standby. The amount of standby is usually determined by the nature of the treatment. Long, high-pressure treatments, where an abrasive proppant such as bauxite is pumped, should have a minimum of 100% standby. On other treatments, 50% standby is usually sufficient.

•

Inaccurate metering - Flowmeters, densimeters, and pressure transducers can sometimes fail. It is advisable to have at least two of each type meter/gauge in the main injection line. All should be properly calibrated prior to the treatment, and early in the treatment, they should be checked against other gauging methods, e.g., the flowmeter checked against tank dips and the densimeter checked against sand screw RPM's. Prior to and immediately following the treatment, the fluid, chemicals, and proppant should be inventoried to determine what was pumped and how this compares with the treatment metering.

•

Loss of power or electronics to treatment van - This can present a very dangerous situation if not dealt with properly. A proper contingency plan is required to avoid this. This would include good communication with the operators and material gaugers - the volume and rate obtained from the tank gaugers, the sand concentration determined from the blender sand screw RPM's, and the pressure monitored on the pump trucks.

Fluctuations in treating pressure can often signal quality control problems. Pressure changes can be caused by mechanical problems, a change in gel properties, varying proppant concentration, and formation responses. •

Abnormal pressures from wellbore conditions - The more common pressure problems caused by wellbore conditions are excessive pipe or perforation friction, and downhole equipment failures or leaks. An ISIP early in the treatment or during pre-frac testing can detect

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TREATMENT EXECUTION

whether or not pipe and/or perforation friction is a problem. Without bottomhole pressure data, though, it can be difficult to tell the difference between perforation friction and excessive pipe friction due to improperly mixed frac fluids. One common reason for excessive pipe friction on crosslinked gel treatments is that the fluid is crosslinking too quick or the crosslinker addition is incorrect. Also, different tanks of base gel may result in slightly different crosslinked gel frictions. This should be checked as a first line of action. If the fluid mixing is not a problem and the treating pressure is excessively high, the treatment should be aborted. Re-design of the treatment at a lower rate may be required or the well re-perforated or an acid ball-out performed. Proper pre-frac testing with BHP, including a gel minifrac, can usually detect these types of problems so they can be remedied prior to performing the treatment. When the treatment is pumped down tubing, below a packer, positive annulus pressure should always be held to immediately detect any communication through a tubing leak or packer failure. If this occurs, the treatment should be terminated. •

Abnormal pressures from formation response - The two most common abnormal pressure responses caused by the formation are usually a result of fracturing out of zone or pressuring out (screening-out). If the fracture grows out of zone into a lower stressed interval, a sudden drop in pressure may be apparent. This, however, is often hard to detect at the surface due to changing friction and hydrostatic pressures. Pressure increases preceding a screenout may serve as an early warning signal to flush the treatment. Often, though, this is also masked by the changing friction and hydrostatic pressures and it is not until a complete screenout occurs that it is apparent at the surface. The service companies have developed means of calculating BHTP from surface pressure and friction correlations to use in detecting downhole pressure changes. Due to the oftentimes inaccuracy of these correlations, though, the calculated BHTP can be misleading and has resulted in premature flushing of treatments when, in fact, the rising pressures were nothing more than poor gel quality and increased friction pressure. As a rule-of-thumb, calculated BHTP's can not be relied on and should not be used to make real-time decisions during a fracturing treatment. The only time when they may provide valuable information is when pumping down large tubing or casing where friction is not a factor and the proppant stages are large enough that the pipe contains all one slurry.

Flushing the Treatment Special attention should be given the flush procedure to avoid over-flushing the proppant away from the wellbore. Flush should be initiated from a near-wellhead densimeter, to avoid major discrepancies in the treatment line volume. Using this method, the flush volume can be calculated by adding (1) the wellbore volume to the top perforation to (2) the volume from the near-WH densimeter to the wellhead, and subtracting (3) the desired under-displacement. Flowmeters are usually only accurate to within 5% and this should be used as a “rule-of-thumb” in determining the under-displacement, unless the flush volume is relatively small to begin with. All treatments December 1995

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11 should always be under-flushed by at least 2 bbls unless the 5% rule dictates more. When calculating the flush volume, several people should go through this exercise to insure there are no mistakes. The flush counter should be immediately zeroed at the time the proppant concentration from the wellhead densimeter starts to fall off from the maximum slurry concentration. This will generally result in leaving the maximum proppant concentration in the fracture at the wellbore. Performing the flush this way, though, will also result in a “tail-off” of proppant left in the wellbore above the point of flushing, this tail-off being that in the lines and blender tub behind the wellhead densimeter. If adequate rat-hole is not available to accommodate this, the wellbore may have to be cleaned out. Another method to prevent some of the proppant tail-off is to by-pass the blender tub. While this prevents the blender contents from being pumped into the well, there are certain problems that can occur in switching to the by-pass, the most common of these being a loss of prime on the pumps. While this method is attractive, it is not recommended. It is not advisable to flush Foam fracturing treatments with foam. To accurately determine a foam flush volume, the bottomhole conditions (temperature and pressure) must be accurately known and this is seldom the case. After a foam fracturing treatment, the reservoir should be charged up enough to unload a column of water, provided the flowback is initiated in a timely fashion. When to Flowback Following a non-foam type fracturing treatment, the well should remain shut-in long enough for the fracture to close and the tail-end gel to fully break. If closure time is expected to be short, this can be monitored from surface pressure in the frac control van. In tighter reservoirs, the shutin time may be as much as 24 hours. Samples caught during the treatment, should be placed in a heat-bath immediately after the treatment to monitor the break time. Depending on the size of treatment, it will take some time for the reservoir in the proximity of the fracture to recover to original BHT. This needs to be taken into consideration to allow some safety margin prior to initiating flowback. Where a foam fracturing treatment has been performed, the primary objective is usually to flow the well back in a relatively short time frame to aid in cleanup from under-pressured reservoirs. Typically, this is done within 1-2 hours following the treatment and, in most cases, this is sufficient time for the foam to degrade, i.e., foam half-life generally less than 1 hour. Initiating flowback immediately after a non-foam type treatment, i.e., “forced closure”, is not recommended. During flowback, the fracture will try to close in the near-wellbore region and, if the proppant is still suspended in viscous fluid, much of the proppant in this region of the fracture may be pulled back into the wellbore. If this happens, as suspected, the result could be poorer near-wellbore fracture communication. Only in cases where the closure time is very long and proppant may tend to settle beneath the primary pay zone, should forced closure even be considered. Hydraulic Fracturing Theory Manual

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11.7 POST-FRAC LOGGING Post-frac logs are often run to help in evaluating whether or not model-predicted fracture geometry was obtained. These independent measurements, when coupled with pressure analysis and postfrac modeling, can help to verify and/or modify the calculation procedure for future treatments in an area. The two most common post-frac logging tools are the temperature and gamma-ray logs. While both are shallow investigative tools and can have interpretation problems, they can provide valuable information when run correctly in a proper environment. Temperature Logs Post-frac temperature logs are the most common method of measuring fracture height due to their operational ease of use. They are easy to run, can be run in cased- or open-hole, and have minimal impact on operations since the well is typically shut-in for several hours after a stimulation. Procedure. The most reliable procedure for running post-frac temperature logs is to first run a base (pre-fracture) log to determine the undisturbed temperature gradient of the formations, then two to three additional logs following the fracture treatment as shown in Fig. 11.18. The best results are obtained by logging down, so the temperature sensor is always entering undisturbed fluid, at a speed of 20-30 fpm. The best time to obtain the base log is prior to any other completion phase, e.g., perforating, running tubing, etc. This, however, might not always be possible or cost-effective and the next best method is to run the base log the day before the fracture treatment. The post-frac logs should be run shortly (1-3 hours) after the treatment and multiple passes made with a minimum of 3/4 to 1 hour between logging starts. No flowback from the well should be allowed prior to logging, but if this is necessary, it is usually possible to obtain a good log by allowing a couple of hours for the temperature to re-stabilize following the flow back. In the case of an under-pressured reservoir where the fluid level might continue to fall after the treatment, the fluid level should be allowed to nearly stabilize prior to running the post-frac logs. When To Log. Post-frac temperature logs are typically run when there is a question about the degree of fracture height containment that occurred as compared to model predictions. Fracture height determination is generally more applicable when stimulating low permeability zones, where the objective is to achieve long fracture half-lengths. In particular, in new areas with wells having virgin reservoir pressure where little is known of the boundary stresses, it is usually appropriate to conduct a minifrac and run post-minifrac logs to “calibrate” the model stress profile for final design determination. Temperature logs may then also be run after the main treatment to confirm or verify model predictions. In moderate to high permeability zones usually the main objective is to by-pass near-wellbore damage and fracture height is not as critical. For these type zones, though, temperature logs might still be appropriate following a minifrac if the objective is to stay out of alternative pay zones or water-bearing intervals in close proximity to the target zone. Also, when fracturing thick intervals of moderate to high permeability, where multiple layers exist with varying permeabilities and stresses, temperature logs might be appropriate following a minifrac and/or treatment to evaluate how much of the interval was treated.

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11

Fig. 11.18 - Base and Post-Fracture Temperature Logs: Runs #1 - 8 hrs after Injection and Run #2 18 hrs after Injection.

Limitations. Ideal logs, such as shown in Fig. 11.18, are rare and may be in error when they do occur. To help in evaluating when temperature logs should be run and how best to interpret them, it is important to understand their limitations. The two primary factors affecting temperature log interpretation are the created fracture width and wellbore conditions. Low-stress and/or lowmodulus zones can have significantly greater fracture width and will accept the majority of fluid. This results in more cooling across this region(s) and the largest temperature anomaly. This is both a strength and weakness: a strength because the log is indicating where the bulk of fluid went and a weakness because the larger anomaly can mask height growth into higher stress/modulus zones, leading to misinterpretation of fracture height and geometry. Wellbore conditions can also affect temperature log interpretation, these including placement of the downhole assembly and wellbore deviation. Pumping down tubing will create a temperature anomaly immediately below the tubing because of the difference in radial heat flow rates for a tubing/casing configuration compared with fluid flow just inside the casing. •

When post-frac temperature logging is planned, the tubing/packer/tail-pipe assembly should be positioned far enough above the highest point of expected fracture growth to prevent interpretation problems.

Wellbore deviation can also significantly impact temperature log interpretation. Generally, where the wellbore is vertical and the fracture grows vertically, there is complete communication of the fracture along the wellbore. However, when the fracture grows vertically from a deviated wellbore or a non-vertical fracture grows from a vertical wellbore, the fracture will (in most cases) leave the wellbore. And, because the temperature tool is a very shallow investigative tool, it will not identify Hydraulic Fracturing Theory Manual

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POST-FRAC LOGGING

that portion of the fracture not in direct contact with the wellbore. Thus, in situations such as this, temperature logs have limited application. •

Temperature logs have very little to no application in deviated well fracturing, unless they are used to determine whether vertical or horizontal fracturing is occurring. Even for this application, their interpretation may be questionable.

Interpretation. While temperature logs, when used as a stand-alone tool, can be difficult to interpret, they can yield valuable information when interpreted correctly. Several analysis techniques have been developed to aid in this. One of these is a cold-water circulating test to assist in analysis. This involves circulating down tubing and up the annulus to cool the wellbore without creating a fracture. Post-circulation logs then indicate perturbations caused by thermal conductivity changes and wellbore effects, such as washouts. Post-frac logs can then be compared to this prefrac log to identify fluid movement outside the pipe and thus the presence of fracture height growth. An example of this is shown in Fig. 11.19. For the particular case of a “warm nose” above perforations, further evidence of the correctness of this interpretation was given by comparing post-frac temperature and gamma-ray logs, as shown in Fig. 11.20.

Fig. 11.19 - Example of Post-Cold-Water-Circulation Test Log with Post-Fracture Log.

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11

Fig. 11.20 - Comparison of Post-Fracture Temperature Log and Post-Fracture Gamma-Ray Log.

Running of multiple post-frac logs also improves the temperature log interpretation. Fig. 11.21 shows an example where the temperature profile changed with later logs, giving a much easier interpretation. Downward fracture growth is difficult to determine with a temperature log. Typically, at the conclusion of a fracture treatment, the wellbore fluid below the perforated interval is very near static reservoir temperature. Thus, the temperature log will show a sharp break at this point and this is often misconstrued as the fracture bottom when, in fact, this is only indicating stagnant fluid in the rathole. If the fracture has grown downward, the fluid outside the wellbore will be cooler than that inside the rathole and post-fracture cooling below the perforated interval may be observed, resulting in a “temperature cross-over” as shown in Fig. 11.22. This is a clear indication of downward fracture growth and the point of cross-over is interpreted as the fracture bottom. Gamma-Ray Logs Gamma-ray logs are another common method of measuring fracture height. These are conducted by inducing artificial radioactivity in the fracture by including tagged proppant or tagged liquid in the normal fracturing proppant or fluid, followed by post-treatment gamma-ray logs. One advantage of gamma-ray logs over temperature logs is that they need not be run immediately after stimulation, allowing wellbore fill below perforations to be cleaned out before logging. The other restrictions on temperature logs, however, apply equally to radioactive logs, i.e., they are shalHydraulic Fracturing Theory Manual

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Fig. 11.21 - Example of Temperature Profile Changing with Time, Later Log Showing a “Clearer” Interpretation.

low investigative tools (shallower even than temperature logs) and the response is proportional to fracture width. Thus, while the two logs are often used in combination, the potential exists for them to confirm one another and still not yield totally reliable results. Procedure. Radioactive materials are added to the fracturing slurry stream with proper injection and metering equipment supplied by the radioactive tracer company. Both high-pressure and lowpressure equipment is available for adding the radioactive material either upstream or downstream of the high pressure pumps. As mentioned earlier, tracers can be added either in a solid (proppant) form or a liquid form. Zero-wash tracers, patented by ProTechnics, should be used whenever possible. This minimizes the residual radioactive material left in the wellbore and eases the interpretation of post-frac gamma-ray logs. Table 11.12 lists the available types of tracers, their recommended application, the more commonly used isotopes, mesh sizes for solid tracers, and crush resistance limitations. Typically, for a fracturing treatment, proppant embedded with Sc-46 (Scandium), Sb-124 (Antimony), and/or Ir-192 (Iridium) are used as solid tracers. These same isotopes can also be used in liquid form. Typical tracer concentrations are 0.15-0.8 mCi per 1000 gals of fluid or pounds of proppant, depending on the gamma-ray tool size planned for use. For a 1-11/16 in. tool, the recommended concentration is 0.35-0.8 mCi/1000 gals or lbs and for a 3-5/8 in. tool, it is 0.15-0.30 mCi/1000 gals or lbs. The types and concentrations of isotopes used is dependent on the program objectives and the time before post-frac logs will be run, some iso-

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Fig. 11.22 - Example of Temperature Crossover Below Perforations.

topes having longer half-lifes than others, i.e., Au-198 (gold) - 3 days, Sb-124 - 60 days, Ir-192 74 days, and Sc-46 - 84 days. The tracer service company should be consulted to obtain recommendations for a specific application. A proper gamma-ray logging program for fracture treatment evaluation should always include a pre-treatment log to identify naturally occurring isotopes in formation layers and to provide a base log for comparison to the post-frac log. Comparing these two greatly enhances the interpretation of post-frac logs. Spectral gamma-ray tools are available for use in distinquishing multiple isotope tracing. Application. Some of the more common applications of tracer logs are: •

Minimum fracture height. Radioactive tracers can identify the minimum height of the medium pumped - either hydraulic height (liquid tracers) or propped height (proppant tracers). In many cases, this minimum height may be equal to or very close to the created height; but,

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Table 11.12 - General Description and Properties of ProTechnic’s Patented ZERO WASH Tracer Products.

SOLIDS ZERO WASH -- Intermediate strength ceramic bead embedded with Sc-46 (2.65 s.g.), Sb-124 (2.60 s.g.), or Ir-192 (2.64 s.g.). Color: Various shades of gray. Mesh Size: 40/70 (will not flow through 20/40 or 12/20 sand pack). 16 through 80 mesh available. Crush Strength: >8000 psi

•

PTI-ZW

•

PTI-ZWLD

•

PTI-LZW

ZERO WASH LD -- low density ceramic bead that is embedded with Sc-46 (1.29 s.g.), Sb-124 (1.48 s.g.), or Ir-192 (1.34 s.g.). Designed for acidizing applications and low matrix injection rates. Color: Dark green to brown. Mesh Size: 40/70 (will not flow through 20/40 or 12/20 sand pack). 30 through 100 mesh available. Crush Strength: <2000 psi LIQUID ZERO WASH -- Resin micro embedded with Sc-46 (3.17 s.g.) or Sb-124 (4.17 s.g.). Designed to emulate a fluid. Color: Ranges from light brown to white. Mesh Size: 5-50 microns Crush Strength: N/A

Custom irradiated High Volume Zero Wash products are available by special order. LIQUIDS Most tracers can be made both oil and water soluble. Specific chemical additives can be used to balance the pH of the fluid to enhance adsorption on the formation or to reduce “plating out” on tubulars. TRACER CONCENTRATION GUIDELINES MINI-TOOL (1-11/16”) Water Based Fluids: Acids:

0.35 - 0.80 mCi/1000 gals or lbs 0.50 - 1.50 mCi/1000 gals or lbs

LARGE TOOL (3-5/8”) Water Based Fluids: Acids:

December 1995

0.15 - 0.30 mCi/1000 gals or lbs 0.40 - 1.25 mCi/1000 gals or lbs

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11 in other cases, due to width restrictions in higher stress layers, this height may be considerably less than the actual created height. •

Proppant distribution at the wellbore. By placing multiple tracers staggered throughout a fracturing treatment, it may be possible to determine whether proppant in an interval was placed early or late in the treatment, i.e., are all perforation sets effectively propped at the wellbore. Fig. 11.23 shows an example of this type application. In this treatment, Sb-124 (medium shading) was used in the first 18,000 lbs (1-3 ppg), Sc-46 (white) in the middle 30,000 lbs (4-6 ppg), and Ir-192 (dark shading) in the last 48,000 lbs (6 ppg). From this log, the lower perforated interval took only the lower concentration slurry, while the higher concentration slurry went primarily in the upper sets of perforations.

•

Proppant settling. The effects of proppant settling to the lower part of the perforated interval or out of the desired zone can be seen with radioactive logs.

•

Staging efficiency. In many cases, the need to separate a fracture treatment into multiple stages is apparent from tracer analysis. There may be a larger stress or pore pressure contrast between layers than assumed causing inefficient stimulation in a single stage treatment. Conversely, multiple stage treatments may be determined to be unnecessary with tracer analysis. Fig. 11.24 shows an example where very little proppant was placed in the upper three sets of perforations with the initial treatment and post-frac performance was disappointing. A second treatment (refrac) was performed after isolating the bottom perforations with a bridge plug. As shown from the second log, after the refrac which was tagged with a different isotope than used on the first treatment, the upper sets of perforations were stimulated. Post-frac performance doubled.

When Applicable to Run. Table 11.13 lists some of the more common circumstances under which tracer logs might have an application in helping to define fracture treatment effectiveness.

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Fig. 11.23 - Example Gamma-Ray Log Where Three Isotopes Were Used to Tag Proppant - Sb-124 (1-3 ppg), Sc-46 (4-6 ppg), and Ir-192 (6 ppg). Note Bottom Zone - Lower Concentrations Only, with High Concentration in Top Zone Only.

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Fig. 11.24 - Example Gamma-Ray Logs Where (1) the Initial Fracture Treatment Only Propped the Bottom Zone and (2) Successful Propping of the Upper Zones with a Second Treatment.

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Table 11.13 - Some Criteria for Tracer Addition and Gamma-Ray Logging.

•

If, Due to Size of Gross Interval, Total Zone Coverage is in Doubt.

•

If Stress Contrast Between Zone and Barrier is < an Amount That Might Allow Growth Out of Zone.

•

If Limited Entry Perforating is Used.

•

If These are Multiple Perforation Sets.

•

If the Perforated Intervals is Within the Vicinity of an Undesirable (Gas/Oil/Water), Fluid Contrast in the Reservoir.

•

If the Permeability Varies by a Factor of Some Significant Percentage or More Per Stage.

•

If Specialty Proppants are “Tailed In.”

•

If the Well has Questionable Cement Quality or Casing Integrity.

•

If You Are Using Diversion in Completion.

•

If Stress Contrast is > Some Significant Pressure Psi Between Perforated Layers.

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School Problems FRAC School Problem No. 1

Use the Quick Worksheet to complete the following table. Cost M$

Slurry Vol (mhsld)

Net Pressure

Average Width

Fluid Efficiency

FCD

FOI

xf = 250 xf = 500

*

xf = 750 H = 50' H = 100'

*

H = 150' C = .005 C = .0015

*

C = .0025 Q = 20 Q = 35

*

Q = 40 E=4 E=8

*

E = 12 April 1994

P-1

Hydraulic Fracturing Theory Manual

School Problems

FRAC School Problem No. 2 Evaluation of a recompletion to a moderate permeability gas sand. Abstract The Workshop No 2. was drilled as an infill producing well to a deeper horizon. Repeat Formation Test (RFT) pressure data and dipmeter log, however, indicate the planned completion interval is in a fault block already being depleted by at least two offset wells. As a result, plans are being made to complete a porous and permeable gas sand at 5300 ft. This sand has been seen in a number of wells in the area and appears to be fairly continuous over at least an entire section. Because the sand is in a known regulatory horizon, it will be completed as a development well. Purpose This problem illustrates the benefits associated with the application of fracture pressure analysis techniques to the design and optimization of fracture stimulations. The techniques utilized include the analysis of closure stress, step rate, flowback, and minifrac tests. Analysis of this data will be used to develop an understanding of the fracture characteristics. This will be done through building an ULTRAFRAC data file and history matching minifrac data. Once the fracture is characterized, ULTRAFRAC will be run in DESIGN Mode to determine the optimum treatment design for the new horizon in the well in question. Description A calculated log section over the potential completion shown in Fig. P.1 highlights the pay sand. In addition, a Long-Spaced-Digital-Sonic (LSDS) log over the section showed the sand to have a compressional wave sonic travel time of approximately 65 micro-seconds per foot. Fig. P.2 shows a plot of acoustic travel time vs. Young’s Modulus, E, for various rock types. Use this figure to formulate initial estimates. The maximum bottomhole temperature recorded over the sand interval was 170 ° F. Reservoir pressure in the sand is unknown, though, the deeper target sands have been found to be normally pressured (e.g., 0.433 psi/ft of depth). The interval in question was drilled with 9.5 lb/gal mud with no significant gas shows. Assuming a normal pressure gradient indicates a reservoir pore pressure of 2295 psi at 5300 ft. The well was completed in 5.5 inch casing with 2 7/8 inch tubing landed at 5130 ft. The well was perforated with 2 shots/ft and produced for 24 hours at a rate of 520 mscfd. The production stream was dry gas. A build up test was run but bottomhole pressure gauge failure precluded the build up interpretation. Surface pressure data indicated fairly stable wellhead pressure of 1200 psi. Some core data exists from a nearby exploration well which indicated the interval in question was a clean sandstone with a porosity between 11.2 and 14.7%. Core permeability tests showed permeability to air (no confining stress) of 0.44 to 0.55 md. Generally, core permeability is reduced by a factor of approximately 5 to represent in-situ gas permeability. Hydraulic Fracturing Theory Manual

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FRAC School Problem No. 2

Fig. P.1 - Log Section.

April 1994

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Acoustic Travel Time microseconds/ft

School Problems

Sand Dolomite Lime

E x 106 - psi

Fig. P.2 - Young’s Modulus (E) vs. Acoustic Travel Time.

Production plans include compression which will allow a surface producing pressure of 100 psi with a flowing bottomhole pressure of approximately 450 psi. The Gas Marketing Business Unit indicates that it will cost nearly 0.15 $/mcf to transport the gas to the delivery point. Annual operating costs are $6,000 per well in the area. Because of the limited rock property data a series of injection flowback tests were conducted to determine formation closure pressure. During these tests, bottomhole treatment pressure was measured with a gauge set at 5375 ft. The closure stress tests were conducted with 2% KCl water with friction reducer. This data is used to find the fracture closure stress, and possibly to give an estimate of reservoir pressure. Reservoir fluid data assuming a gas gravity of 0.65, a reservoir pressure of 2295 psi, and 170 degrees is calculated in the fluid property section of ULTRAFRAC to be: •

Gas Viscosity:

0.0174 cp

•

Z-Factor:

0.85696

•

Gas Compressibility:

455.6 x 10-6 psi-1

The closure stress tests consisted of: A. Pumpin/Shutin Test An injection/shutin pressure decline test conducted by injecting 25 bbl of KCl water at 10 bpm (tp = 2.5 minutes) and then recording the pressure decline as shown in Fig. P.3. Fig. P.4 shows a plot of pressure vs. horner log time extrapolated to give a rough approximation of reservoir pressure.

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P-4

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FRAC School Problem No. 2

Injection/Decline Test 4250.000

4000.000

Pws psia

3750.000

3500.000

psi

Closure Pressure = 3250.000

3000.000

2750.000 0.0000

0.5000

1.000

1.500

2.000

2.500

3.000

3.500

4.000

4.500

5.00

SQRT [dt] (min**0.5)

Fig. P.3 - Pressure Decline Analysis. File: PROBLEM.FRA Company: Well: Field:

Test Date: Test Type: Perforations, Top: Bottom:

Extrap. p# 2271.921

Plot Horner Plot as QC for Shut-OIn Decline Analysis 4250.000

Pws psia

4000.000

3750.000

3500.000

3250.000 Start of Pseudo-Radial Flow Effects 3000.000 P* = Reservoir Pressure = 2280 psi 2750.000 1.00

10.00

Log [(tp + dt)/dt]

Fig. P.4 - Pseudo-Pressure Estimation.

April 1994

P-5

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B. Step Rate Inject Test A step rate injection test was then performed immediately following the pressure decline. the step rate test consisted of pumping KCl water at rates of 0.5, 1, 2, 3,4, 5, 7, 10, 12, and 15 bpm for two minutes at each rate. The rates and pressures at the end of each two minute step are shown in Fig. P.5. 4500

Bottomhole Press (psig)

4000

3500

3000

Extension Pressure =

psi

2500

2000 0

5

10

15

20

Inj Rate (bpm)

Fig. P.5 - Step-Rate Injection Test.

C. Pumpin/Flowback Test At the end of the step rate test the rate was increased to 17 bpm, the well was then flowed back at a rate of 2 bpm. The resulting pressure decline is shown in Fig. P.6. D. Minifrac Test A gel minifrac was pumped by injecting 38,000 gallons of 40 lb/1000 gals crosslinked frac fluid down tubing at an average rate of 35 bpm (injection time approximately 25.5 minutes), and then flushing the well with 2% KCl water. Analysis of the pumping decline data is used to calculate the fluid loss coefficient. The minifrac data both injection and pressure decline are shown in Fig. P.7. A plot of net pressure versus time for the minifrac injection period is shown in Fig. P.8.

Hydraulic Fracturing Theory Manual

P-6

April 1994

FRAC School Problem No. 2

File: PROBLEM.FRA Company: Well: Field:

Test Date: Test Type: Perforations, Top: Bottom:

Clos Time Tc.: 6.874 Clos press Pc.: 3434.801

4200.000

Pressure psia

4000.000

3800.000

3600.000

3400.000

3200.000 3000.000 30.000 32.000 34.000 36.000 38.000 40.000 42.000 44.000 46.000 48.000 50.000 Clock Time (minutes)

Fig. P.6 - Pumpin Flowback Test.

Fig. P.7 - Minifrac Pressure Data.

April 1994

P-7

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Fig. P.8 - Nolte-Smith Net Pressure Plot.

Hydraulic Fracturing Theory Manual

P-8

April 1994

FRAC School Problem No. 2

Procedure: Step 1:

Update economic and reservoir data.

Step 2:

Develop geomechanical input from porosity and sonic log data.

Step 3:

Evaluate injection/decline, step rate test, and pumpin flowback test data for closure pressure.

Step 4:

Input closure pressure data into geomechanical panel.

Step 5:

Evaluate minifrac test for fluid efficiency and leakoff coefficient.

Step 6:

Enter leakoff into ULTRAFRAC.

Step 7:

Enter Framode in Analysis and enter minifrac volume of 38,000 gallons.

Step 8:

Save file.

Step 9:

Enter Quick Worksheet and history match net pressure, P*, and efficiency by altering fluid loss coefficient and Young’s Modulus.

Step 10: Once history match obtained with Quick Worksheet, execute fracture model and match net pressure data. Step 11: Once matched, change FRACMODE to design and conduct an optimization study. Note both optimum length and conductivity.

April 1994

P-9

Hydraulic Fracturing Theory Manual

School Problems

Workshop Problem 3 Understanding the reservoir response to fracturing through the evaluation of a Tight Gas Well. Abstract The Nowayds No. 1 was drilled as a 640 acre location in the East Texas Cotton Valley Field. Conventional fracture stimulations in the Cotton Valley have consisted of 415,000 gallons of 40 lb crosslinked frac fluid and 1 MMlb of 20/40 sand. A service company representative showed up one Monday morning recommending a significantly larger fracture treatment using carbo prop plus. This problem illustrates the importance of understanding the reservoir response to hydraulic fracturing (i.e., the importance of FCD). The problem also highlights the benefits of optimizing fracture treatments in the East Texas Cotton Valley. Description The Cotton Valley Sand Formation is upper Jurassic in age and is bounded by the Bossier Shale below and the Travis Peak Formation above. The formation is approximately 1,400 ft thick and is typically found at depths ranging from 8,000 to 10,800 ft and covers nearly all of Panola, Rusk, and Harrison Counties in East Texas. The Cotton Valley is basically a transgressive-regressive marine sequence. The Taylor Zone, the lowermost sand member in the Cotton Valley is an offshore bar-shoreface transition and consists of a series of small bars and shales. The Taylor Sand is nearly 250 ft in gross thickness in the Nowayds No. 1. Above the Taylor interval lies 200 ft of shale which generally confines a 2,500 ft fracture. The Taylor sand, in the Cotton Valley trend, has an average permeability of approximately 0.005 md. Buildup tests in the vicinity of the Nowayds No. 1 indicated an average reservoir pressure of 4,300 psi. Production from the Taylor is a dry gas at about 265°F. Table P.1 summarizes treatment and design data important to this analysis, while Table P.2 shows a conventional pump schedule used in this area. Average porosity and water saturation for the Taylor Sand is 6% and 55%, respectively. Fig. P.1 shows a log section of the Nowayds No. 1. Fig. P.2 shows plots of net pressure during a fracture treatment performed in offset wells using the conventional treatment design. Fig. P.3 shows a dimensionless closure time to injection time plot to be used in this analysis to determine fluid efficiency. Objective Your job is to compare the conventional Cotton Valley treatment design (Table P.1.) to the service company recommendation shown in Table P.3. Develop an ULTRAFRAC data set and evaluate the two designs in the ANALYSIS Mode. Compare and contrast the economic results of the two treatments. How do these results compare to your optimum design (DESIGN Mode).

Hydraulic Fracturing Theory Manual

P-10

April 1994

Workshop Problem 3

Procedure: Step 1:

Using the default file in the ULTRAFRAC database, Table P.1 and Figure P.1, update the geomechanical data, calculate leakoff, set fracmode to analysis and input conventional schedule.

Step 2:

Save file.

Step 3:

Execute Fracture Simulation.

Step 4:

Look at fracture output and determine fluid efficiency.

Step 5:

Compare efficiency to that determined from analysis of Figure P.3 and Table P.1.

Step 6:

Modify leakoff and rerun trying to match efficiency, repeat until matched.

Step 7:

Save file.

Step 8:

Print/Save Fracture output and economic summary output.

Step 9:

Modify schedule (Table P.3) and save as.

Step 10: Execute fracture simulation. Step 11: Compare results. Step 12: Set Fracmode to design. Step 13: Run and determine optimum (optional) fracture length and conductivity.

April 1994

P-11

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School Problems

Table P.2 - Conventional/Schedule

Table P.1 - Data for Example Well Analysis Treatment Volume (MGALS)

360

Treatment Rate (bpm)

75

Treatment Time (min.)

178

Closure Time (min.)

356

Fluid Type Reservoir Depth (ft)

Crosslink 10000

Temperature (°F)

265

Permeability, (md)

.005

Fracture Height (ft)

300

Fluid-Loss Height (ft)

280

Formation Modulus (106 psi)

8

Proppant Concentration (lbs/gal)

9

Hydraulic Fracturing Theory Manual

P-12

Sand lbs/gal

Stage

Volume

Pad

72,000

1

31,200

1

2

4,875

2

3

12,000

3

4

28,000

4

5

35,000

5

6

40,000

6

7

42,000

7

8

50,000

8

9

45,000

9

April 1994

Workshop Problem 3

April 1994

P-13

Hydraulic Fracturing Theory Manual

School Problems

Table P.3 - Pumping Schedule Recommended by Service Company Job Description Information Stage Name

Pump Rate bbl/min

Fluid Name

Stage Field Vol gal

Prop Conc lb/gal

Pad 4 PPA 6 PPA 8 PPA 10 PPA 12 PPA 12 PPA/R Flush

75 75 75 75 75 75 75 75

YF540HT YF540HT YF540HT YF540HT YF540HT YF540HT YF540HT WF120

90000 30000 34000 31600 29600 69400 10000 9482

0 4 6 8 10 12 12 0

Proppant Type and Mesh ISP 20/40 ISP 20/40 ISP 20/40 ISP 20/40 ISP 20/40 ISP 20/40 ISP 20/40

Job Totals Fluids

Prop

44500 gal of WF120 359000 gal of YF540HT

2390000 lb of 20/40 ISP

Hydraulic Fracturing Theory Manual

P-14

April 1994

Workshop Problem 4

Workshop Problem 4 Application of fracture optimization to a multilayer reservoir, North Cowden Unit, Ector County, Texas. Abstract Fracture treatment optimization techniques have been developed using Long-Spaced-DigitalSonic (LSDS) logs, pumpin-flowback, pumpin-shutin, minifrac, and downhole treating pressure data. These analysis techniques have been successfully applied to massive hydraulic fracturing (MHF) of tight gas wells and short highly conductive fractures in moderate permeability reservoirs alike. Purpose This problem illustrates the application of fracture analysis techniques to a moderate permeability reservoir. These techniques will be used to develop an ULTRAFRAC data set and identify large zonal variations in rock properties and pore pressure which result from the complex carbonate geology. The inclusion of geologic factors in fracture treatment design and their resulting effects on fracture geometry will be highlighted. Geologic Setting The North Cowden Unit produces from the Permian Age Grayburg Formation at an average depth of 4,300 ft. The Grayburg, which is bounded by the Queen and San Andres Formations, consists of varying percentages of dolomite, anhydrite, and sand as shown in Figure P.11. Gross pay thickness is 450 ft with a net pay thickness of approximately 200 ft. The average porosity is 9% and permeability ranges from 0.1 to 50 md with an average of 2 md the average water saturation is 50%. The Grayburg Formation is informally subdivided into nine zones. Zones that are primarily sand are identified as S-1 through S-3. Figure P.12 shows a CNL/FDC typelog of the Grayburg sequence with an additional S-4 interval, which is present in portions of the field. The Grayburg Formation exhibits a great diversity of carbonate lithologies ranging from supratidal mudstones to fusulinid wackestones representing subtidal conditions. Interfingered with these carbonates are terrigeneous felspathic quartzarenites. The carbonates and sands have been extensively dolomitized with all sediments having varying degrees of anhydrite infilling and/or anhydrite pore filling and cementation. Although there is a lack of any distinct trend, localized areas of relatively high pore volume and flow capacity do exist and generally correspond to sand development areas, most notable the S-2 horizon as shown in the velocity profile, Figure P.13. Description The North Cowden Unit was in the early stages of an extensive infield development program designed to densify from 80 acre to 40 acre development. One hundred and fifty infield producing wells have been identified for drilling at a capital investment of $250 M per well with an additional April 1994

P-15

Hydraulic Fracturing Theory Manual

School Problems

$50,000 per well to complete. The North Cowden Unit budget for 1992 totals $15 MM (i.e., drill and complete 50 wells). The production engineer, while reviewing historical NCU performance, found that NCU producers did not perform as well as their offset competitors. It was also determined that treatments in the Unit consistently exhibited increasing net pressure during stimulations (see Figure P.14) which was inconsistent with the presumed radial fracture propagation. An ivnestigation of NCU fracture treatment designs showed that, historically, 30,000 gallons of 30# crosslinked gelled water and 30,000 lbs of 8/12 mesh sand were pumped down 2-7/8 inch tubing at rates of 15 bpm as shown in Table P.4. Prefrac production rates average 150 BOPD x 150 BWPD with a 6% production decline. The economic limit is 5 BOPD. Additional data available includes a long-spaced-digital-sonic log from a nearby well in the field which was used to determine Young’s Modulus and Poisson’s Ratio on a foot by foot basis as shown in Figure P.15. Table P.5 shows the comparison of LSDS derived rock properties to physical core measurements. Further in-situ test data available includes closure test data from the S-2 and D-2 horizons. Analysis of these test are included as Figure P.16 and Figure P.17, respectively. Figure P.18 shows a dimensionless pressure match of post-frac pressure decline data which indicates a D-5 horizon fluid leakoff coefficient of 0.00025. The sand intervals in the unit should be expected to have an even higher fluid loss coefficient. Also shown for completeness (Figure P.19 - Figure P.21) are net pressure plots of stimulations conducted in the D-2, S-2, and D-5 intervals, respectively. The production engineer was charged with evaluating this treatment schedule to ensure that it was the optimum treatment design to maximize the present value of the infield development program. Hydraulic Fracturing Theory Manual

P-16

April 1994

Workshop Problem 4

April 1994

P-17

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Hydraulic Fracturing Theory Manual

P-18

April 1994

Workshop Problem 4

Table P.4 - Conventional NCU Fracture Stimulation Design Pump 30,000 gallons of 30 lb/m gal. crosslinked gelled water and 30,000 lb of 8/12 mesh sand 10,000 gallons pad 2,000 gallons w/ 1/2 lb/gal 8/12 sand 4,000 gallons w/ 1 lb/gal 8/12 sand+ 6,000 gallons w/ 1-1/2 lb/gal 8/12 sand 8,000 gallons w/ 2 lb/gal 8/12 sand Flush

Table P.5 - Comparison of Young’s Modulus Zone

April 1994

Core (10° psi)

LSDS (10° psi)

D-1

8.01 9.02

D-2

8.84

9.00

D-3

6.36 7.31

9.25 9.25

S-2

4.77 4.54

5.00 5.00

D-4

7.99 9.75

9.5 9.5

S-3

9.08

10.0

P-19

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Hydraulic Fracturing Theory Manual

P-20

April 1994

Workshop Problem 4

April 1994

P-21

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School Problems

Hydraulic Fracturing Theory Manual

P-22

April 1994

Workshop Problem No. 5

Workshop Problem No. 5 Fracture design in a moderate permeability reservoir in the North Sea. Abstract The NS25 was drilled and completed as a horizontal well. Production from the 5000 ft horizontal section averages 500 BOPD well below expectations. In addition, the well produced slugs of chalk (formation). Wellbore stability is reasoned to be the cause for the under performance of the lateral section. Therefore, to minimize both proppant or formation flowback problems resin coated proppants are used in fracture stimulations. To aid in the design and execution of the fracture stimulation, a minifrac was conducted utilizing 56,000 gallons of a water based crosslinked borate system pumped at 35 BPM which is the maximum achievable rate from the stimulation vessel. This problem illustrates the benefits of utilizing minifrac data to design treatments at the well site. This will be accomplished by first analyzing the minifrac data and then utilizing design techniques captured in an EXCEL spreadsheet program to design and implement a treatment. Description The NS25 produces from the TOR Formation as shown in Figure 1. The Tor, as shown, is some 75 ft thick in the NS25. Rock properties testing has indicated that the chalk formation has a Young’s modulus of 500,000 psi and a poisson’s ratio of 0.3. Because of the softness of the chalk, the resistance to the creation of a fracture is great and as a result, fracture toughness is on the order of 15,000. The reservoir is normally pressured and has a permeability of 10 md and a porosity of 30%. The stimulation vessel from which the fracture stimulation was to be performed was fully loaded with 1 million pounds of resin coated proppant and 329,000 gallons of 30# crosslinked borate fracturing fluid. In additional to conventional land based materials costs an additional $300,000 boat service charge is required to stimulate this well. Objective: Your job is to utilize the results of the minifrac test to optimally place all of the fluid and proppant loaded on the boat. Secondly, test this design with ULTRAFRAC and determine the fracture length and conductivity of the fracture stimulation. Also note the in-situ pounds per square foot of proppant in the fracture. Finally, utilize this information to determine the post-frac production rate and payout of the stimulation.

April 1994

P-23

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Hydraulic Fracturing Theory Manual

P-24

April 1994

Workshop Problem No. 5

April 1994

P-25

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Hydraulic Fracturing Theory Manual

P-26

April 1994

Workshop Problem No. 5

April 1994

P-27

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Hydraulic Fracturing Theory Manual

P-28

April 1994

Workshop Problem No. 5

Procedure: Step 1:

Interpret the minifrac test and determine fluid efficiency, closure pressure, and closure time.

Step 2:

Build an ULTRAFRAC file by first adding the boat service charge to miscellaneous costs in the economic section.

Step 3:

From the log generate a geomechanical data set.

Step 4:

Estimate leakoff and check with respect to the minifrac analysis.

Step 5:

Simulate minifrac and match final pressure and fluid efficiency

Step 6:

In design mode, determine the optimum fracture length and conductivity.

Step 7:

In analysis mode, select optimum design schedule and execute fracture simulation to determine length, conductivity, and in-situ pounds per square foot.

Step 8:

Use Quick Worksheet or Prats curve to estimate Post-Frac Folds of Increase, FOI.

April 1994

P-29

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School Problems

Water Injection Well Problem 6 The El Marginalo Field is a mature waterflood of a sandstone reservoir located at a depth of 2200'. Injection rates have declined due to fillup, and from the development of positive skins from the injection of some unfiltered water. This skin is not removable by acid washes, and the decision has been made to fracture stimulate all injection wells. For tax purposes, this must be done quickly, so there is no time to field evaluate various stimulation procedures. Therefore, it is imperative to arrive at an optimum stimulation design quickly since almost a hundred wells are involved. A candidate well for the first stimulation has been selected. The well was shut in and the pressure falloff measured; three closure stress tests were run; then 200 bbl of fracturing fluid were injected down tubing with the surface annulus pressure measured during injection and during the pressure decline after injection (Note: Due to possible problems with old casing, all the stimulations must be pumped down tubing.) The data from these tests, along with some open hole logs are included as attachments. Also included is the present worth of increased injection. This was developed based on model runs for various fracture lengths and conductivities. The chart is the present worth of increased oil production only, and does not include the fracturing costs. Based on service company price books, stimulation costs should be about $1.00/gal for fluid, $0.08/lb for sand, and $2500.00 for mileage, workover rig time, etc. Your assignment - should you decide to accept it - is to design a stimulation program, in sufficient detail to allow field execution. Since there will be no time to evaluate long-term effectiveness of different procedures, the job should be designed to maximize the discounted return on investment (DROI). Also, fracture length should not interfere with reservoir sweep, since hydraulic fracture azimuth is totally unknown in this field. Pressure Falloff Test Reservoir Properties φ

= 0.15

, Residual Oil Saturation = 0.20

µ

= 1 (cp)

, C = 9 x 10-6 (1/psi)

BHST = 100°F Test Parameters rw = 0.40 (ft)

, Injection Rate = 280 BWPD

Injection Pressure = 1340 psi Average Reservoir Pressure = 700 psi: Hydraulic Fracturing Theory Manual

P-30

April 1994

Water Injection Well Problem 6

April 1994

P-31

Hydraulic Fracturing Theory Manual

School Problems

OPEN HOLE LOGS FOR WATER INJECTION WELL EXAMPLE

Hydraulic Fracturing Theory Manual

P-32

April 1994

Water Injection Well Problem 6

April 1994

P-33

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School Problems

“Mini-Frac” Pressure Data Data measured on static, open annulus while injecting down tubing. Pump time was 25 minutes, pumping 200 bbl at an average rate of 8 bpm (rate was reasonably constant). Time Since Pumping Started (min)

Pressure (psi)

0.5 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 10.0 12.0 15.0 17.0 20.0 22.0 24.0 25.0 Shut-in at 25.0 minutes 26.0 1 1 27.0 2 1.41 28.0 3 1.73 29.0 4 2.00 30.0 5 2.24 31.0 6 2.45 32.0 7 2.65 33.0 8 2.83 34.0 9 3.00 35.0 10 3.16 37.0 12 3.46 39.0 14 3.74 41.0 16 4.00 43.0 18 4.24 Hydraulic Fracturing Theory Manual

P-34

400 403 418 425 430 435 438 443 449 458 463 468 471 479 480 482 483 434 406 392 380 369 359 350 341 332 324 307 290 274 258 April 1994

Water Injection Well Problem 6

April 1994

P-35

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P-36

April 1994

Water Injection Well Problem 6

April 1994

P-37

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School Problems

CLOSURE STRESS TESTS FOR WATER INJECTION WELL EXAMPLE

280 250

250

Hydraulic Fracturing Theory Manual

P-38

April 1994

Tight Gas Problem 7

Tight Gas Problem 7 320 acre wells; 4-1/2 casing; frac orientation N 80 E Reservoir: Estimate 5-10 µ d; P = 3000 psi; φ = 0.10, Sw = 0.50 T = 260 °F Other Information 1. Open hole log (attached) 2. Calibration Treatment Decline (attached) 3. Offset BHTP (attached) 4. Well Cost $275M 5. Frac Costs: $0.75/gal; Sand: $0.06/lb; IDP: $0.60/lb

PW(15) Xf

Production Only kfw PW($MM)

1000 2000 3000 4000

100 100 100 100

0.40 0.63 0.79 0.91

1000 2000 3000 4000

300 300 300 300

0.45 0.75 0.99 1.10

1000 2000 3000 4000

1000 1000 1000 1000

0.46 0.80 1.09 1.25

Triaxial Lab Test Stress(psi) Strain(10-6in/in) 500 1000 1500 2000 2500 3000 3500 4000

125 255 385 520 630 810 980 1170

(From 2DMHF and GEM)

Prepare: Optimum Fracture Design with sufficient detail that an Experienced Field Foreman could execute the treatment with the results you expected.

April 1994

P-39

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School Problems

Hydraulic Fracturing Theory Manual

P-40

April 1994

Tight Gas Problem 7

TIGHT GAS WELL

April 1994

P-41

Hydraulic Fracturing Theory Manual

School Problems

BOTTOM-HOLE TREATING PRESSURES FOR WELLS OFFSETTING TIGHT GAS WELL

Hydraulic Fracturing Theory Manual

P-42

April 1994

Oil Well Problem 8

Oil Well Problem 8 Desperate Energy Co. is evaluating the drilling of a 160 acre spacing development well in the Hopeful Field to a total depth of 2610 meters (M). The target chalk formation of an offset well was found from 2500 M to 2565 M as shown on Attachment 1, and had an indicated porosity of 35% and an average oil saturation of 60%. Core obtained from the same well was subjected to lab tests which revealed the chalk to be water sensitive, very soft, and conducive to proppant embedment. A pressure buildup test from the offset is shown in Attachments 2 and 3. The cost of drilling and setting casing on this well is estimated to be $5 MM. Based on production from other ells in the field, the unstimulated, damaged PW(15) is estimated to be $2.5 MM. Desperate Energy management wants you, the engineer, to evaluate data and make a recommendation whether the well should be drilled and what the optimum fracture design would be. Conventional fracture treatment designs, provided by the service company for other wells in this field, have been unsuccessful in obtaining economic production rates. Unfortunately, the records for these treatments are not available. The wellbore configuration normally used in this field is shown in Attachment 1. Data from pre-frac tests performed on the offset are included in Attachments 4 and 6. Other Pertinent Information 1. The zones above and below the pay interval are also chalk. 2. Due to proppant embedment in the soft chalk, an in-situ proppant concentration of 2 lbs/sq ft must be achieved. 3. If a fracture treatment is performed, the cost for doing the treatment will be $3.50/slurry gal for gel “Ottawa” sand or $.25/slurry gal for gel + intermediate proppant. Equipment and pumping charges are figures in as part of the material costs. Pressure Build-Up Data from Offset Well Reservoir Properties C = 9 x 10-6 (1/psi) φ = 0.35 Net Pay = 200 (ft)

, µ = 2.0 (cp) , B = 1.1 (bbl/bbl)

Parameters rw = 0.40 (ft) Test Data Flow Time - 6 (hrs) , Rate = 582 BOPD Final Flowing Pressure (BHFP) = 2334 (psia)

April 1994

P-43

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School Problems

Results from Minifrac Treatment Injected 20,000 gals of 90 cp gel at an average injection rate of 7.94 BPM. Following injection, the shut-in BHP was monitored for 14 minutes. SI TIme (min) 0 1 2 3 4

BHP (psi) 7200 7194 7169 7157 7146

5 6 7 8 10 12 14

Hydraulic Fracturing Theory Manual

7136 7128 7121 7114 7100 7087 7074

P-44

April 1994

Oil Well Problem 8

April 1994

P-45

Hydraulic Fracturing Theory Manual

School Problems

Hydraulic Fracturing Theory Manual

P-46

April 1994

Oil Well Problem 8

OIL WELL PROBLEM ATTACHMENT 5

Net Treating Pressure During Minifrac (Time = 0 when gel on performations)

April 1994

P-47

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Hydraulic Fracturing Theory Manual

P-48

April 1994

Bili near FLow Problem 9

Bili near FLow Problem 9 An oil field, fully developed on 80 acres is being considered for a re-stimulation program. One well was fractured and a post-frac build up test run. Plotting the data on a log-log type curve showed a 1/4 slope, and a plot of build-up vs. fourth root of shut-in time is attached. Based on a qualitative examination of this plot, can any general recommendations be made about future stimulations?

Using the plot and the following reservoir properties, find fracture conductivity and length, Fcd, and steady-state folds of increase (FOI) resulting from this stimulation. Reservoir Properties k = 3.3 md µ = 3.0 cp

, ,

φ

= 0.10 h = 200 ft

Ct = 9 x 10-6 (1/psi) q = 290 BPD ,

, ,

B = 1.2

Calculations kfw = (eqn. 6, p. 11) xf = (eqns. 13-15, p. 16) (Note: These equations can be solved in several ways, one way is graphically, plotting both sides of the equation vs. length, since both sides are functions of xf.) Fcd = Steady-State FOI =

Based on extrapolating from 3 months production, it has been determined that the PW(15) of the increased production resulting from the stimulations is $390,500. The cost of the fracture job was $35,500. Calculate the discounted return on investment for this stimulation. DROI =

Fracture design calculations were done based on analysis of post-frac pressure data from the first well. These were used to develop a price table for changes in the stimulation design:

April 1994

P-49

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School Problems

(Costs in $1,000.00) xf = kfw

0.5 * base

base case

2 * base

0.5 * base

24

34

48

base case

25

35.5

51.5

2 * base

27

39

59

Using these prices and steady-state calculations for folds of increase (FOI), calculate the DROI for the various stimulation designs. Should a change in design be recommended? Should more cases be considered? DROI xf = kfw

0.5 * base

base case

2 * base

0.5 * base base case 2 * base

Hydraulic Fracturing Theory Manual

P-50

April 1994

Bili near FLow Problem 9

April 1994

P-51

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Hydraulic Fracturing Theory Manual

P-52

April 1994

Index A

Borate gels and foams 6-9 ores 6-34 Borehole geometry log 10-5 televiewer 10-7 Boron, aluminum and antimony 6-32 Bottomhole pressure 5-15 treating pressure 8-14, 8-22 Bounding beds 5-3, 5-4, 5-12, 5-13, 5-15 Breakdown pressure 8-4 Breaker(s) crushable 6-20 encapsulated 6-7, 6-20 enzyme 6-7, 6-20 gel 6-20 release, crushable and controlled 6-21

Accelerated settling 6-13 Acid Fracturing 3-22 Activator and gellant 6-8 Additive(s) chemical 6-7 clay control 6-6 diesel fluid loss 6-14 fluid loss 5-23 particulate fluid loss 6-14 Advantages foamed frac fluids 6-41 gelled hydrocarbons 6-48 methanol gels 6-49 polymer emulsion fluid 6-40 Aluminum antimony and boron 6-32 crosslinked orthophosphate esters 6-47 Anaerobic bacteria 6-6 Analysis of bilinear flow data 3-46 Anderson and Stahl 1-4 Anionic surfactants 6-6 Antimony, boron and aluminum 6-32 Apparent productive length 5-36 Appropriate viscosity 6-11 Aqueous fluids 1-4 foam 6-1 Auxiliary stimulation equipment 9-20 Axial strain 4-2, 4-3 stress 4-2 Azimuth 3-8

C Capacity finite 3-4 infinite 3-4 variable finite 3-4 Capillary tubing field nominal shear rates 6-51 nominal shear rates 6-51 Carboxymethyl cellulose (CMHEC) 6-30 hydroxypropyl guar (CMHPG) 6-30 Cationic polymeric clay stabilizers 6-6 surfactants 6-6 Cement bond log 10-7 Ceramic proppants 7-1 Chemical stabilizers 1-5 Clay control additives 6-6 swelling or migrating 6-6 Cleanup, flow back and 6-18 Closure pressure 5-13 stress 5-3, 5-4, 5-11, 5-13 differentials 5-15 profile 5-3 tests 5-14 Clump 6-13 CMHEC (carboxymethyl cellulose) 6-30 CMHPG (carboxymethyl hydroxypropyl guar) 6-30 CO2 foams 6-9 Cochran, Heck and Waters 1-4 Coding system Dowell Schlumberger 6-53

B Bacteria, anaerobic 6-6 Base temperature logs 10-8 Bedload, transport 6-12 BHTP gauge tailpipe assembly 8-23 measuring devices 8-23 measuring techniques 8-22 Bilinear flow 3-25, 3-27 data analysis 3-35 equations 3-28 graphs 3-41 Binary foam 6-43, 6-46 Bingham plastic fluid 5-29 Biocides 6-7 Blender 1-8 services 9-20 Blocks,water 6-7

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Hydraulic Fracturing Theory Manual

Index

D

Halliburton’s 6-52 Western Company 6-53 Cold water circulation temperature surveys 10-8 Compatibility formation, formation fluids and chemical additives 6-6 safety and environmental 6-5 Compression test 4-2, 4-3 Computer control console 1-9 Concentrates, polymer 6-30 Concentration, effective polymer 6-20 Conditions dynamic 4-2 quasi static 4-2 Conductivity of proppant 7-19 Consistency Index 5-29 Constant formation face pressure 3-29, 3-42, 3-44 rate 3-28, 3-41 internal phase 6-40 Continuity equation 2-1, 8-17, 8-19, 8-25 Continuous mixed fluid systems 6-8 proportioner 1-8 Controlling fracture height 5-2 Core bulging 4-2, 4-4 flow tests 6-6 tests 10-3 Cost(s) pumping 6-23 pumping hp 6-11 Criteria, fluid selection 6-3 Critical concentration 6-9 pressure 8-1, 8-20 strain energy release rate 4-7 stress intensity factor 4-7 Cross reference of similar additives 6-54 Crosslinked aluminum orthophosphate esters 6-47 delayed fluids 6-38 delayed systems 6-8 dual functionality 6-34 gels 6-14 hydrocarbon 6-2 ideal delayed fluid 6-38 polymer solutions (gels) 6-1 Crosslinking agents 1-5 fast 6-32 fast, water-base gels 6-32 Crushable breakers 6-20

Hydraulic Fracturing Theory Manual

Delayed crosslinked systems 6-8 Density log 10-5 Depth 5-40 Design package, integrated 6-23 Desired fracture half-lengths 1-12 Devonian shale 6-11 Diesel fluid loss additive 6-14 Dimensionless fracture capacity (FCD) 3-1 conductivity (FCD) 1-12 Disadvantages foamed frac fluids 6-46 gelled hydrocarbons 6-48 methanol gels 6-49 polymer emulsion fluid 6-40 Discounted return on investment (DROI) 9-3, 9-8 Dowell Schlumberger coding system 6-53 Downhole flow, turbulent conditions 6-51 television 10-7 Drag coefficient, particle 6-12 reducing 6-9 DROI (discounted return on investment) 9-3 Droplet-size 6-41 Dynamic conditions 4-2 fluid loss 6-18 moduli 4-2 modulus 4-5

E Economics 6-23 Effect of flow restrictions 3-37 wellbore storage 3-37 Effective particle shear rate 6-12 porosity 5-21 wellbore radius (r’w) 3-10 Elastic modulus 10-3 Elasticity equation 2-1 Emulsifying 6-8 Emulsions 6-7 Encapsulated breaker(s) 6-7, 6-20 Environmental and safety compatibility 6-5 Enzyme breakers 6-7, 6-20 Equation continuity 2-1 elasticity 2-1 fluid flow 2-1 Equilibrium bank(s) 6-11

I-54

Index

F

Foam(s) 6-15 aqueous 6-1 binary 6-43, 6-46 CO2 6-9 friction pressure data 6-43 hydrocarbon 6-2 hydrocarbon-base 6-23 nitrogen 6-9 viscosity data 6-43 texture 6-43 Foamed frac fluids advantages 6-41 disadvantages 6-46 Foaming potential 6-8 FOI (folds of increase) 1-12, 3-5, 3-10 Folds of increase (FOI) 1-12, 3-5, 3-10 Formation elastic properties 4-1 fluid 5-22 linear flow 3-27 permeability 3-1 wettability of 6-6 Frac Height variables affecting 5-15 Fracture 5-36 closure pressure 5-11 closure stress 8-4 determining fluid efficiency 8-58 discounted return on investment (FDROI) 9-3 early design 1-8 extension pressure 8-4 flow capacity 3-1, 3-2, 3-3 geometry 5-16 half-length 3-2, 5-36 height 5-1, 5-3, 5-15, 5-16 controlling 5-2 growth 5-1, 5-3 incremental present worth or value (FINCPV) 9-3 initial height 5-3 length 3-1, 5-16 linear flow 3-27 orientation 1-3, 3-8 radius 5-36 stiffness 8-26 stimulation critical factors to optimum 1-11 design 1-12 toughness 4-7 treatment 1-6 design 5-15 width 5-15, 5-16 Fracturing effect of modulus on 4-4 fluid(s) 1-4 compatibility with its additives 6-7

Fatty-acid soaps 6-47 FCD dimensionless fracture capacity 3-1 dimensionless fracture conductivity 1-12 FDROI (fracture discounted return on investment) 9-3 Filtrate 5-20 FINCPV (fracture incremental present worth or value) 9-3 Finite capacity 3-4 Flash points 6-5 Flow back and cleanup 6-18 behavior index 5-29 Fluid loss 6-14 addtives 5-23 coefficient 5-20, 10-3 foams 6-15 oil base gels 6-15 rate 8-27 test 5-22 Fluid(s) affected by fluid flow loss 6-18 aqueous 1-4 bingham plastic 5-29 classification 6-1 crosslinked delayed 6-38 degradation 5-39 description of fracturing types 6-30 dynamic loss 6-18 efficiency 5-37, 8-36, 8-44, 8-55 flow equation 2-1 foamed frac 6-41 hydrocarbon-base 6-23 ideal delayed crosslinked 6-38 low loss 6-14 napalm-type 6-47 optimal scheduling for 6-70 polymer emulsion 6-40 power law 5-29 pressure calculating 5-15 rheological testing of fracturing 6-49 scheduling 6-70 scheduling given the fluid rheology 6-70 scheduling using contained rheology 6-71 selection 6-1 selection criteria 6-3 viscosities, proppant transport 6-11 viscosity 5-27 volume 5-37 Fluid-element exposure time 6-70 rheology 6-70 time at temperature vs. volume pumped 6-72 Fluidized layer of sand 6-12 Fluorocarbon, surfactants 6-7

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Index

components, toxicity 6-5 costs 6-23 friction pressure 6-9 gelled diesel 6-9 pressure analysis 8-1 pumping equipment 9-20 stimulation treatments 1-1 Friction pressure 5-40 data for foams 6-43 fracturing fluids 6-9 various frac fluids 6-10 wellhead and horesepower requirements 6-9 reducers oil-base 6-9 water-base 6-9 Friction-loss pressures 5-37 Friction-outs 6-40 Full-cycle 9-18 economics 9-17

high-temperature 6-47 methanol 6-2, 6-48 Gradients, hydrostatic 6-9 Growth, fracture height 5-1 Guar gum 6-30 Guideline 6-73 pad fluids 6-74 viscosity 6-70

H Half-length 2-4, 5-36 Halflife 6-8 Halliburton coding system 6-52 Oil Well Cementing Company 1-2 Hardness 4-1 HEC (hydroxyethyl cellulose) 6-30 Height confinement 5-13, 5-14 growth 5-11, 5-12, 5-13, 5-15, 5-16 vertical growth 5-16 hhp prices and fracturing chemical 6-23 High temperature stability 6-13 stabilizers 6-13 Hindered settling 6-13 History matching 5-15 of hydraulic fracturing 1-1 Horizontal closure stress 4-3 Horner plot 8-8 Horsepower 5-37 requirements, friction and wellhead pressure 6-9 Howard and Fast 1-8 hp, pumping (cost) 6-11 HPG hydroxypropyl guar 6-30 solution viscosity behavior 6-32 Hugoton 1-2, 1-7 Hydraulic fracture treatments 1-1 fracturing developments 1-3 fracturing history 1-1 horsepower 1-6 Hydrocarbon Aromatic with surfactants 6-14 crosslinked 6-2 foams 6-2 gel viscosities 6-8 gelled 6-46 gels, viscosity 6-48 recovered, value of 6-23 slick 6-2 Hydrocarbon-base fluids or foams 6-23

G G function 8-35 Gamma ray log 5-13, 5-17, 5-18, 10-5 Gas-constant pressure 3-47 rate 3-47 GDK (Geertsma and de Klerk model) 2-4, 5-16 Gear pump, Jabsco 6-51 Geertsma and de Klerk model 2-4, 5-10, 5-16 Gel breakers 6-20 crosslinked 6-14 crosslinked polymer solutions 6-1 determining rheology of 6-51 fast-crosslinking water-base 6-32 filter cake 6-14 high temperature 6-13 oil base 6-15 organometallic crosslinked 6-13 polymer concentrates 6-37 quality control of continuous-mix jobs 6-8 stabilizers 1-5 systems, high temperature behavior 6-13 testing organometallic crosslinked 6-14 uncrosslinked 6-14 viscosities, hydrocarbon 6-8 viscosity uncrosslinked 6-8 Gelatin model 1-4 Gellant and activator 6-8 Gelled diesel fracturing fluid 6-9 hydrocarbons 6-46 advantages 6-48 disadvantages 6-48

Hydraulic Fracturing Theory Manual

I-56

Index

Log(s) base temperature 10-8 borehole geometry 10-5 cement bond 10-7 density 10-5 gamma ray 5-13, 5-17, 5-18, 10-5 long spaced digital sonic 10-6 LSDS 10-6 neutron porosity 10-5 resistivity 10-5 spontaneous potential 5-18, 10-5 static temperature 10-9 temperature 5-18 Long spaced digital sonic log (LSDS) 10-6 Low fluid loss 6-14 pumping pressure 6-9

fracturing fluid systems 6-2 Hydrostatic, gradients 6-9 Hydroxyethyl cellulose (HEC) 6-30 Hydroxypropyl guar (HPG) 6-30 Hydroxypropylcellulose 6-49

I INCDROI (incremental discounted return on investment) 9-3 INCPVF (incremental PW or value of the fracture) 9-3 Incremental discounted return on investment (INCDROI) 9-3 economics 9-12 present worth or value of the fracture(INCPVF) 9-3 Infinite bounding beds 5-3 capacity 3-4 thickness 5-3 Initial fracture height 5-3 In-situ closure stress 5-12 closure stress profile 5-15 stress 5-12 stress profile 5-13 stress tests 8-4 stresses 5-15 Insoluble residue 6-20 Integrated design package 6-23 Interface slip 5-11 Ionic surfactants 6-6 ISIP (instantaneous shut-in pressure) 8-4

M Mass balance equation 8-17 Massive hydraulic fracturing (MHF) 1-7 Material Safety Data (MSD) 6-5 Mechanical properties in fracturing 4-1 Methanol 1-5, 6-7 gelled 6-2, 6-48 gels advantages 6-49 disadvantages 6-49 used with CO2 6-49 viscosify 6-49 MHF (Massive hydraulic fracturing) 1-7 Microfrac 8-4 tests 8-4, 8-7 Minifrac 8-2 calibration treatments 1-10 Mixing, simulated field 6-51 Model 35 Fann viscometer 6-8 Models, Pseudo 3-D 5-16 Moduli dynamic 4-2 static 4-2 Modulus effect on fracturing 4-4 of elasticity 4-1, 4-3, 4-4, 10-3 plane strain 4-1 MSD (Material Safety Data) 6-5

J Jabsco gear pump 6-51 Jet mixer 1-7

K K (Geertsma and de Klerk model) 2-4 kfw (fracture flow capacity) 3-2 Khristianovic model 2-4 Perkins and Kern comparison of 2-5

L Lateral strain 4-2 Lateral strain 4-2, 4-3 Leakoff driving pressure 6-15, 6-18 resistance in the reservoir rock 6-15 Liquid-constant pressure 3-36 rate 3-35 Lithology changes 5-12 Load recovery 6-8

N Napalm 1-2 Napalm-type fluids 6-47 Net fracture pressure 5-3, 5-4, 5-15 fracturing pressure 4-4 present value of post-frac production 6-23

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Index

PO (payout) 9-3 Point forward evaluation 9-17 Points, flash 6-5 Poisson’s ratio 4-1, 4-3, 5-13, 10-3 Polyacrylamides 6-30 Polyemulsion, see polymer emulsion Polymer (gel) concentrates 6-37 concentrates 6-30 effective concentration 6-20 emulsion 6-1, 6-14, 6-23 fluid 6-40 fluid advantages 6-40 fluid disadvantages 6-40 viscosity 6-41 natural water soluble 6-30 solutions crosslinked (gels) 6-1 uncrosslinked 6-1 Pore pressure 5-11, 5-12, 5-13 variations 5-12 Power law exponent 5-29 fluid 5-29 Prefrac stress tests 1-10 Preparation and quality control 6-7 Present worth 1-1, 9-4, 9-14 Pressure bottomhole treating 8-14 closure 5-13 critical 8-1, 8-20 decline 8-2 decline analysis 8-25, 8-30 example/guidelines 8-38 post-propped-frac 8-42 differential 5-21 fracture closure 5-11 History Matching 8-46 leakoff driving 6-15, 6-18 multiplier pumps 9-20 net 5-16, 8-14 net fracture 5-3, 5-4 net fracturing 4-4 reservoir closure 5-13 Prices fracuring chemical and hhp 6-23 Problem proppant and fluid scheduling 6-78 Products modified natural 6-30 synthetic 6-30 Profitability index 9-7, 9-14 index (PI) 9-3 Propagation criterion 2-1 Proppant fall correction factor (PFCF) 7-26

present worth or value (PW or PV) 9-3 pressure 2-5, 5-11, 5-16, 8-14 Neutron porosity log 10-5 Newtonian fluid 5-29 Nitrogen foams 6-9 Nolte-Smith log-log interpretation 8-14 Nomenclature, service company fluid system 6-52 Non-darcy flow 7-29 Nonemulsifier 6-8 Nonionic surfactants 6-6 Nordgren 2-4

O Oil-base friction reducers 6-9 gels 6-15 Open-ended tubing 8-22 Organo titanates and zironates 6-32 Organometallic crosslinked gels 6-13 delayed-crosslinked gels 6-39 Orientation fracture 3-8 Overburden weight 5-11 Overpressured reservoirs 6-9

P Pad fluids guideline 6-74 volume 8-59 Pan American Petroleum Corporation 1-2 Particle clumping 6-13 drag coefficient 6-12 generalized, Reynolds 6-12 single settling 6-13 terminal settling velocity 6-11 Pay zone 5-3, 5-4, 5-13 Payout (PO) 9-3, 9-10 Perforating 10-10 Perkins and Kern model 2-4, 5-16 Khristianovic model comparison of 2-5 Permeability 5-20 formation 3-1 impaired proppant pack 6-21 of proppant 7-19 proppant 7-5 reservoir 3-2 pH 6-8 PI (profitability index) 9-3 Pilot tests 6-7 Pinch outs 6-11 PK (Perkins and Kern model) 2-4 PKN (Perkins and Kern model) 2-4, 5-16 Plane strain modulus 4-1

Hydraulic Fracturing Theory Manual

I-58

Index

and preparation 6-7 aspects of 6-9 gel continuous-mix jobs 6-8 Quasi static conditions 4-2

Proppant(s) 1-5 acid solubility 7-11 addition schedule 8-62, 8-66 and fluid scheduling problem 6-78 bulk and grain density 7-11 ceramic 7-1 concentrations 8-55 crush resistance 7-9 damage factor 7-23 design techniques 1-5 fluid schedule from pressure decline 8-55 hardness 7-4 high strength - see Proppant(s), ceramic impaired pack permeability 6-21 intermediate strength - see Proppant(s), ceramic long-term conductivity 7-20 permeability 7-5 PREDICTK 7-23 resin-coated 6-7, 7-1, 7-16 sand 7-1 sieve distribution - see size distribution single-grain test 7-4 size distribuiton 7-5 sphericity and roundness 7-4 stress 7-1 temperature effect on conductivity 7-21 transport 5-39 fluid viscosities 6-11 fluid viscosity 6-11 from viscous drag 6-11 using thin fluids 6-11 turbidity 7-13 volume fraction 5-33 Propping agent pumping charge 9-20 agents 1-5 Pseudo 3-D model 5-16 Pseudo-Radial Flow 3-27 Pump Jabsco gear 6-51 rate 5-36 time, estimated 6-70 Pump-in/decline test 8-4, 8-7 Pump-in/flowback test 8-9 Pumping cost 6-23 hp (cost) 6-11 PV (net present worth or value) 9-3 PW (net present worth or value) 9-3

R Radius 5-36 Recovery, load 6-8 Reservoir closure pressure 5-13 naturally fractured 6-14, 6-17 overpressured 6-9 permeability 3-2 rock leakoff resistance in 6-15 Temperatures 5-32 underpressured 6-9 Residue concentrates at the fracture wall 6-21 insoluble 6-20 uniformly distributed 6-21 Resin-coated proppant(s) 6-7, 7-1, 7-16 compressive strength 7-17 Resistivity log 10-5 Return on investment 9-11 Reynolds generalized particle 6-12 Rheological data 6-72 Rheology determining for titanium and zirconium gels 6-51 of uncrosslinked polymer solutions 6-30 Rock hardness 4-10

S Safety and environmental compatibility 6-5 Sand 7-1 fluid proportioner 1-8 Scaling 6-7 Scheduling fluid 6-70 given the fluid rheology 6-70 optimal for fluids 6-70 using contained rheology 6-71 Screen outs 6-11 Secant Modulus 4-3 Service company fluid system nomenclature 6-52 trade names 6-52 Settling hindered 6-13 single particle 6-13 Stokes 6-12 terminal, velocity of a particle 6-11 velocities 6-12 Shear rate 5-27 Silica flour 6-14, 6-17

Q Qualitative checks on water-base gel crosslinking 6-8 Quality 6-43 control

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Index

Simple history matching 8-48 Simulated field mixing 6-51 Slick hydrocarbon 6-2 water 6-1, 6-11 Slip flow 6-51 Slurry concentration handling service 9-20 Solutions polymer crosslinked (gels) 6-1 polymer uncrosslinked 6-1 Spontaneous potential log 10-5 potential logs 5-18 Spurt loss 5-20, 6-17 SRT (step-rate injection test) 8-10 Stability of foam 6-43 Stabilizers cationic polymeric clay 6-6 chemical 1-5 gel 1-5 high temperature 6-13 viscosity guideline 6-74 Stanolind Oil and Gas Corporation 1-2 Static moduli 4-2 temperature log 10-9 temperature gradient 5-32 Step-rate injection test (SRT) 8-10 Stokes Law, Proppant Transport 7-26 settling 6-12 Strain axial 4-2, 4-3 critical enery release rate 4-7 lateral 4-2, 4-3 volumetric 4-2, 4-3 Stress axial 4-2 closure 5-3, 5-11, 5-13, 5-15 critical intensity factor 4-7 differential 5-3 horizontal closure 4-3 in-situ 5-12, 5-15 closure 5-12 closure profile 5-15 profile 5-15 proppant 7-1 vertical 5-11 Surface recorded BHP gauge 8-22 treating pressures 1-7, 6-11 Surfactants 1-4, 6-8 anionic 6-6 aromatic hydrocarbons with 6-14

Hydraulic Fracturing Theory Manual

cationic 6-6 fluorocarbon 6-7 ionic 6-6 nonionic 6-6 Suspension flows 6-11 transport 6-12 Synthetic products 6-30 water soluble polymers 6-30 Systems delayed crosslinked 6-8 dual crosslinker 6-38 fluid, continuous mixed 6-8 hydrocarbon-base fracturing fluid 6-2 water-base fracturing fluid 6-1

T Tangent modulus 4-3 Temperature and time, viscosity affected by 6-13 high gel system behavior 6-13 gelled-hydrocarbon 6-47 gels 6-13 logs 5-18 time at 6-72 TerraFrac 5-15 Test(s) closure stress 5-14 compression 4-2, 4-3 core 10-3 flow 6-6 fluid loss 5-22 in-situ stress 8-4 microfrac 8-4, 8-7 pilot 6-7 procedures 6-51 pump-in/decline 8-4, 8-7 pump-in/flowback 8-9 step-rate injection 8-10 triaxial stress-strain 10-3 vortex closure 6-8 Testing organometallic crosslinked gels 6-14 rheology, of fracturing fluids 6-49 Texture 6-43, 6-46 3-D models 5-15 Time at temperature 6-72 Time-temperature history 8-67 for fluid 8-55 Titanium, determining rheology of 6-51 Toxicity, fracturing fluid components 6-5 Trade names, service company 6-52

I-60

Index

fast crosslinking gels 6-32 fracturing fluid systems 6-1 friction reducers 6-9 Wellhead pressure, friction pressure and horsepower requirements 6-9 Western Company coding system 6-53 Wettability of formation 6-6 Width create conductive proppant pack 6-11 fracture 6-11 prevent pinch outs 6-11

Transient Reservoir Response 3-24 Transport bedload 6-12 suspension 6-12 Treatment pad percentage 8-66 volume, effect of 8-64 Triaxial stress-strain tests 10-3 Type curve(s) 8-32 analysis 8-32

U

Y

Uncrosslinked gels 6-14 polymer solutions 6-1 viscosity gels 6-8 Underpressured reservoirs 6-9

Yet-to-spend 9-17 Young’s modulus 4-1, 4-3

Z Zirconium, determining rheology of 6-51 Zironates and organo titanates 6-32

V Valhall chalk 4-3 Variable(s) affecting frac height 5-15 finite capacity 3-4 Vertical fracture width profile 5-16 stress 5-11 Viscometer, Model 35 Fann 6-8 Viscosify, methanol 6-49 Viscosity 6-39 affected by temperature and time 6-13 appropriate 6-11 data for nitrogen foams 6-43 effective 6-70 fluid, proppant transport 6-11 guideline 6-70 hydrocarbon gels 6-48 of foam 6-43 polymer emulsion 6-41 proppant transport 6-11 stabilizer guideline 6-74 sufficient to create wide fractures 6-11 Ti and Zr continuous-mix gels 6-14 uncrosslinked gels 6-8 Volumetric strain 4-2, 4-3 Vortex closure tests 6-8

W Wall building 5-23 effect 5-22 Water blocks 6-7 slick 6-1, 6-11 soluble polymers, natural 6-30 Water-base

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