Misuse Eos Dca Upscaling

7/2/2017

On the Misuse of Equations of State, Upscaling & Decline Curve Analysis Tarek Ahmed, PhD, P.E. Emeritus Professor of Petroleum Engineering Tarek Ahmed & Associates Ltd 25326 Metzler Creek Drive Houston, Texas 77389 [email protected] www.TarekAhmedAssociates.com

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How Do you Define Experience? 1) 2) 3) 4)

5 years 10 Years 15 Years 20 Years

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On Equations of State

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The van der Waals’ EOS Ideal EOS:

p

RT V

p

ai   a

R 2 Tci2 pci

RT a  2 Vb V

& bi  b

R Tci pci

November 23, 1837 – March 8, 1923 Dutch 1910 Nobel Prize in Physics

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Equations of State

[

p ]T , p ,V  0 & V c c c

[

2 p ]T , p ,V  0 V 2 c c c

p = prepulsive - pattractive EOS idea vdW

prepulsive

pattractive

ai

bi

αi (T)

0

0

0

-

-

RT V RT V b

a V

2

a

R 2 Tc2 pc

b

R Tc pc

RK

RT V b

a V (V  b ) T

a

R 2 Tc2.5 pc

b

R Tc pc

SRK

RT V b

a  (T ) V (V  b )

a

R 2 Tc2 pc

b

R Tc pc

f(T,Tc,ω)

RT V b

a  (T ) V ( V  b )  b (V  b )

a

R 2 Tc2 pc

b

R Tc pc

f(T,Tc,ω)

PR

-

© 2006Tarek Ahmed & Associates, Ltd. All Rights Reserved.

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Numerous Applications of: PV=ZnRT

Imagine: A grid block in the reservoir:

Ki 

yi xi

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Equations of State “Why Tuning ?”

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Two Major Problems with Any EOS 1. The Plus-Fraction & Lumped Components 2. The Methane Problem [

p ]T , p ,V  0 & V c c c ai   a

R 2 Tci2 pci

[

2 p ]T , p ,V  0 V 2 c c c

& bi  b

R Tci pci

The Cn+ critical& other properties: Tc, Pc;…etc.

ac 7    a

R 2 (Tc2 ) c 7  ( pc ) c 7 

& bc 7   b

R (Tc ) c 7  ( pc ) c 7 

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[

p ]T , p ,V  0 & V c c c

ac 7    a

R 2 (Tc2 ) c 7  ( pc ) c 7 

[

2 p ]T , p ,V  0 V 2 c c c

& bc 7   b

R (Tc ) c 7  ( pc ) c 7 

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Experimental PVT Data 1. 2. 3. 4. 5. 6. 7. 8. 9.

Saturation Pressure Separator Test Constant Volume Depletion Test “CVD” Differential Expansion Test “DE” Constant Composition Expansion “CCE” Swelling Tests Slim-Tube Test Minimum Miscibility Pressure …etc.

© 2006Tarek Ahmed & Associates, Ltd. All Rights Reserved.

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Tuning of EOS Minimize one of the following two objective functions: W  exp  pred i i i min F ( pc , Tc ,  , BIC , c)    exp i i   W  exp  pred i i i min F ( a , b ,  , BIC , c)    exp i i  

       

Where: Wi = Weight factor Ψi = PVT data, e.g. pb, pd, Bo,…etc Ωa= EOS parameter Ωb= EOS parameter ω= Acentric factor

© 2006Tarek Ahmed & Associates, Ltd. All Rights Reserved.

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Tuning Strategy W  exp  pred i i i min F ( pc , Tc ,  , BIC , c)    exp i i  

   

1. Conduct several SENSITIVITY RUNS to evaluate the impact of individually shifting EOS parameters, i.e. pc,Tc, ω, Ωa, Ωb,…etc., on the predicted PVT Data. This step might reveal that changing pc has no significant impact on the results as compare with adjusting Tc. 2. Proper Selection of the experimental data to match 3. Proper Assigning the Weight Factors “Wi” to Experimental Data

© 2006Tarek Ahmed & Associates, Ltd. All Rights Reserved.

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Mis-selection of Experimental Data to Match W  exp  pred i i i min F ( pc , Tc ,  , BIC , c)    exp  i  i 

   

Assiging Weight on Experimental PVT Data: 1. 2. 3. 4. 5. 6. 7. 8.

Saturation Pressure Separator Test Constant Volume Depletion Test “CVD” Differential Expansion Test “DE” Constant Composition Expansion “CCE” Swelling Tests Slim-Tube Test Minimum Miscibility Pressure

© 2006Tarek Ahmed & Associates, Ltd. All Rights Reserved.

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Example 1: CCE & DE Laboratory Data 100 % oil

100 % oil

100 % Oil

90 % oil

Pb

Pi> Pb

P
Vt

Vsat

Vt

70% oil

60 % oil

P <
P <<
Vt

Vt

Hg

Vrel 

Vt VSat

Notice, reference volume is Vsat

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DE 11 data points

CCE 31 data points

Vrel 

(Vt ) p,T (V ) Psat ,T

Vrel 

(Vo ) p,T (V )14.7,60 o

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167 oF

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170 oF

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175 oF

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168 oF

© 2006Tarek Ahmed & Associates, Ltd. All Rights Reserved.

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Constant Composition Expansion CCE My Advise: ASSIGN WEIGHT FACTORS=0

Comment: Why using Vsat; why not Vi ?

Vrel 

Vt (error ) V  t The problem is the VSat (error ) VSat reference volume Vsat

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Example 2: Z-Factor Related Laboratory Data “CVD, CCE”

© 2006Tarek Ahmed & Associates, Ltd. All Rights Reserved.

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Matching Reported Gas Z-Factor

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Matching Reported Gas Density, Why !!!



p Ma ZRT

Perfect match; why? because you had a perfect match of Z-Factor

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Matching Gas Recovery Factor

RF is a function of Z-factor RF  1  [

p Zi ] Z pi

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“Lee-Gonzales Gas Viscosity”

Why matching results from a correlation?

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Defining Data Weight Factors

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Wi  iexp  ipred F (a, b,  , BIC )     iexp i  

   

Property

Z-Factor

Gas RF

Gas Density

Gas Viscosity

Vrel

Weight Factor

10

0

0

0

1

RF  1  [

g 

p Zi ] Z pi

( MW ) P Z RT

Lee-Gonzalez Method g=

  0.001494 M p Y  (9.4 + 0.02 M a ) T 1.5 a   exp  X  0.0209 + 0.0019 M a + T Z T    

Y = 1 .7 

197.2  0.002 M a T

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Challenges with Matching Differential Rs and Bo With EOS  Challenges associated with measuring the liquid volume at reference temperature and pressure, i.e. stock-tank.  EOS simulation might not replicate the final depletion point of the laboratory process.

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Eliminating the Stock-Tank Reference: To eliminate the propagation of errors and for better match with EOS; consider using the following conversions:

( Rs ) cum  Bo 

Bo Bob

Rsb  Rs Bob

Scf/bbl to eliminate the ST: Cumulative gas solubility is referenced to Bubble point volume

bbl/bbl to eliminate the ST: Dimensionless Bo is referenced to Bubble point volume

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Rs

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( Rs ) cum 

Rsb  Rs Bob

Pressure

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Bo

Bo 

Bo Bob

Pb

Pressure

© 2006Tarek Ahmed & Associates, Ltd. All Rights Reserved.

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An Alternative Approach Instead of: a, b, and m = f (pC, TC, ω)c7+ replace with : a, b, and m = f (MW, sp.gr)C7+

Molecular weight and specific gravity are measurable properties

© 2006Tarek Ahmed & Associates, Ltd. All Rights Reserved.

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SPE Reservoir Engineering Journal Paper # 18532 3

a or b  [  (ci D i )]  i 0

D

6 c c4  [  (ci  7i 4 )]  7 , D i 5  7

M 7

 7

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12

10

8

Modified EOS

LDO, %

Exp. Data

6

PVTSim WinProp 4

2

0 0

1000

2000

3000

4000

5000

Pressure

CVD for Gas 5

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4000

3500

3000

2500

Rsd; 2000 scf/STB

PVTSim WinProp Modified EOS

1500

Exp. Data

1000

500

0 0.00

1,000.00

2,000.00

3,000.00

4,000.00

5,000.00

Pressure

DE Rsd for Oil 2 at 176 oF

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Comment on Gas Cycling

© 2006Tarek Ahmed & Associates, Ltd. All Rights Reserved.

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Nitrogen Injection % LDO

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Lean Injection

% LDO

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Understand the impact of: a) Gas injection volume on vaporizing LDO b) Gas Composition on vaporizing/reducing LDO c) Timing of gas cycling; delay suggests more heaving components to vaporize

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What is the impact of injecting gas in a PVT cell containg condensate? 1- LDO curve ! 2- dewpoint pressure !

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North Sea Gas-Condensate System Pd T Max LDO C1 C7+

= = = = =

6750 psi 280 oF 21.6% 73.19% 8.21%

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North Sea Gas Original Liquid Drop Out Curve.

Liquid Drop Out, %

25 20 15 10

5 0 0

2000

4000

6000

8000

Pressure, psig

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North Sea Gas - Methane Injection commencing at 4300 psig.

Liquid Drop Out, %

25 Original

20

500 scf/bbl

15

1000 scf/bbl

10

1500 scf/bbl 2000 scf/bbl

5 0

0

2000

4000

6000

8000

Pressure, psig

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Liquid Drop Out, %

Comparison of North Sea Injected gas at 3100 psig (500 scf/bbl).

30 25 20 15 10 5 0

Original LDO = 21.3%

Injected Gas

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Comparison of North Sea Injected gas at 1200 psig (500 scf/bbl).

Liquid Drop Out, %

Original LDO = 19.6% 40

20

0 Original

N2/CO2/C1

N2/C1

CO2/C1

N2/CO2

N2

CO2

C1

Injected Gas

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EOS must be tuned to match Hysis Simulation Data

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The Nameless Field Schematic of the Central Processing Facilities “CPF” injection gas line

Stripper Column (19 distillation trays)

80-250oc 55oc 1500 KPA

Oil Composition !!!

1st Stage

250oc 80oc 1300 KPA

2nd Stage

Stock-Tank

Boiler –Furnace (Tray-20) Gradual

changes in the temperature in the flow line

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Treatment of the Temperature Profile of the Distillation Column injection gas line

Temp profile is Described by single value of 150oc 150oc 700 KPA

55oc 1500 KPA

Oil Composition !!! 1st Stage 80oc 1300 KPA

Stripper Column

Stock-Tank

(19 distillation trays)

2nd Stage The study suggests that the current treatment of the Column in the FFM overestimates the liquid shrinkage; i.e. it underestimates STOIP and ST oil produced © 2006Tarek Ahmed & Associates, Ltd. All Rights Reserved.

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The Eagle Ford Example The Eagle Ford shale is one of the newest shale plays. Located in S. Texas, it extends over an area of about 20,000 square miles

6 Hydrocarbon Windows

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Industry Fluid Identification Standards System

CGR STB/MMscf

GOR SCF/STB

API

Dry Gas

-

> 100,000

-

Wet Gas

10-15

70,000100,000

> 60

Retrograde Gas

15-300

3,300-70,000

> 50

Near Critical

>300

> 3,300

> 50

Volatile Oil

-

1,000-3,300

> 45

Ordinary Oil

-

200-1,000

< 45

Low Shrinkage Oil

-

< 200

< 20

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C1+N2

A

A- Dry Gas B- Wet Gas C- Retrograde Gas D- Near Critical E- Volatile Oil F- Ordinary Oil G- Low Shrinkage Oil

D

C

B

E

F G C7+

C2-C6+CO2 © 2006 Tarek Ahmed & Associates, Ltd. All Rights Reserved.

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CGR ≠ Condensate Yield “Y” CGR  Y

Qo Qg Qo

Qg

The stream from a “Well” or “ PVT cell”

CGR 

Qstream

Qstream

Qo

Qstream  Veq QO  (Qg ) sep scf/day Y

Qo Veq Qo  Qg Hg

Y

CGR Veq CGR 1

Qo Qg

Veq  133,000

o Mo

; scf / STB

Y < CGR

© 2006Tarek Ahmed & Associates, Ltd. All Rights Reserved.

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On Decline Curves Analysis

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Traditional Decline Curve Analysis “Arps’ Decline Curve Methodology” Arps Decline Curve Analysis “DCA” has been the standard for evaluating the expected ultimate recovery “EUR” in conventional gas and oil wells since 1950’s. Arps’s equations were developed based on the assumptions that wells are producing under the Boundary Dominated Flow “BDF” and past well performance trend will continue in the future .

qt 

qi (1  bDi t ) 1 / b

The curvature of decline “b” in the production rate vs. time curve can be expressed mathematically by one of the following three hyperbolic family of equations: Exponential decline: Harmonic decline: Hyperbolic decline: PROBLEMS:

“b=0” “b=1” “01”

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The Misuse of Arps’ Equations o Arps’ equation has been often misused and applied to model the performance of oil and gas wells whose flow regimes are in a transient flow. Arps approach is strictly applicable ONLY when the well is under boundary-dominated flow conditions o When b >1; Arps ’decline curve approach will OVER ESTIMATE RESERVES

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Total Time Days 0- 365 0-730 0-1095 1825 3650 7300

b 2.93 3.00 3.02 2.96 2.59 1.9

Di Day-1 0.0164 0.0171 0.0173 0.0164 0.0114 0.0045

qi Mscf/day 2025 2030 2031 2023 1945 1675

qt 

qi (1  bDi t ) 1 / b

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When “b” > 1 and why? It is common in tight and oil and gas wells that the best fit to the production data requires values of “b” > 1, beyond the application limit of Arps’ equation. Main reasons that the best-fit to the observed data requires a value of b>1 is that: 1. The observed production data are collected under the unsteady-state (transient) flow regime 2. Production is commingled from multilayered formations that are hydraulically fractured with multiple stages. Lower permeability zones maybe in transient flow, while higher-permeability zones have established stabilized boundary-dominated flow.

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Modern DCA Methodologies 1) 2) 3) 4) 5) 6) 7)

Boundary Dominated “b” Modified Arp’s Method Duong’s Approach Logistic Growth Model Power Law Exponential Decline Simplified Stretched Exponential Production Decline Stretched Exponential Production Decline

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Which decline curve you should select?

© 2006Tarek Ahmed & Associates, Ltd. All Rights Reserved

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Recommended Approach A.

Regress and Match Cumulative Production; i.e. Gp or Np, NOT THE RATE

B.

Regress and Match ONLY 80% of Observed Data; keep the 20% for Validation

C.

Apply and Compare Different Methodologies to Provide with a Range of Answers

D.

Using a Sufficient Sample of Wells that Represent the Field and Develop Type Curves

E.

Express Results in Terms of P90, P50, and P10

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Boundary Dominated “b” Under boundary dominated flow, the best oil or gas flow rate equation is give by: 2 2  Qo or Qg  C  p r  pwf   

n

2 1 1 2  log  p r  pwf   log Qo  log C n   n

b

2 p   1   (2 n  1)   wf   2n   pi   

For a gas reservoir and based on the dependency of the parameter ‘b’ on fluid and production conditions, a model to estimate average “b” as a best approximation during boundary-dominated depletion as given by:     (  g c g ) i  m( pi )  m( pwf )  b  1   pi pwf 2 )   (  Z i Z wf  

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Logistic Growth Model: The logistic growth model “LGM” is a mathematical expression that used to forecast growth in numerous applications, e.g. model population growth.

Np 

( EUR ) t n at

EUR

n

N P ( EUR ) n a t n 1  qt  2 t a tn





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Doung’s Governing Equations





  a  1 m  q N P  oMax exp   1   t a  1 m  





 a  1 m  N P  qo  qoMax t  m exp  1   t t 1  m    qo Np qoMax

= oil orate = Cumulative oil = Maximum anticipated oil rate

Regression variables: 1) qoMax 2) a (recommended range 0.5< m <6) 3) m (recommended range 1.1< m <4)

© 2006 Tarek Ahmed & Associates Ltd. All Rights Reserved.

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Stretched –Exponential –Production-Decline “SEPD”  t qt  qi exp     

  

n

 & Np  

qi  n

  1  1  t       ,   n     n 

  

n 

   

Gamma Function Г(x+1):

  1 1 139 571  ( x  1)  x x e x 2  x 1     2 3 4   12 x 288 x 51840 x 2488320 x 

For example, Г(5) is expressed as Г(4+1) which means x=4

Incomplete Gamma Function Г(g,h)):

 g  1 ( g  1) ( g  2) ( g  1) ( g  2) ( g  3)   1  h   h2 h3  ( g , h)  h g 1 e  h     ( g  1) ( g  2) ( g  3) ( g  4)  h4  

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On Sector Modeling & Upscaling

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Nameless Field

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Nameless Field Upper TAGI Formation , Described by Four Zones 1) U4: 10 Fine scale layers 1 coarse scale Layer 2) U3: 15 Fine scale layers 2 coarse scale layers 3) U2: 5 Fine scale layers 1 coarse scale layer 4) U1: 23 Fine scale layers 3 coarse scale layers Middle TAGI Formation , Described by Two Zones 1) M2: 5 Fine scale layers 1 coarse scale Layer 2) M1: 35 Fine scale layers 5 coarse scale layers Lower TAGI Formation, Described by Three Zones 1) L3: 20 Fine scale layers 1 coarse scale Layer 2) L2: 20 Fine scale layers 1 coarse scale layers 3) L1: 40 Fine scale layers 4 coarse scale layers 173 Fine Scale Layers

19 Coarse Scale Layers

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Three Major Issues in Upscaling 1)Zonation (Optimum Number of Layers) 2)Averaging Technique 3)Downscaling !

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Upscaling Permeability, Porosity,…etc. A.

Power Average

B.

Arithmetic (Volumetric) Average

C.

Root-Mean-Square “RMS” Average

D.

Tensor Averaging

E.

Renormalization

Which averaging methodology should we use?

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Why not 15? Why Not 30?

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Upper TAGI Formation , Described by Four Zones 1) U4: 10 Fine scale layers 1 coarse scale Layer 2) U3: 15 Fine scale layers 2 coarse scale layers 3) U2: 5 Fine scale layers 1 coarse scale layer 4) U1: 23 Fine scale layers3 coarse scale layers 23 layers

3 layers

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Upper TAGI Formation , Described by Four Zones 1) U4: 10 Fine scale layers 1 coarse scale Layer 2) U3: 15 Fine scale layers2 coarse scale layers 3) U2: 5 Fine scale layers 1 coarse scale layer 4) U1: 23 Fine scale layers 3 coarse scale layers 15 layers

2 layers

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Sector Modeling

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Identifying Problem Layers per Zone

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Combined Performance of the Lower TAGI Formation 6Layers Coarse System vs. 80 Layers Fine System

Water cut vs. time

Cumulative oil vs. time

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VERDICT 1)19 Layers are Not Sufficient, Downscaling 2)New Geological Model

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On Relative Permeability

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Reservoir Simulation

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Simulator 1) TA 2) TAREK

(this is the driver program) (The simulator)

Three Files are needed to run the simulator: TA.dat (Initialization File) TA.Sim TA.out

(Simulation File) (Output File) Be SURE to use Notepad when you open TA.dat & TA.sim (Remember that PLEASE)

© 2006Tarek Ahmed & Associates, Ltd. All Rights Reserved

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STEPS TO RUN THE MODEL Step 1:

Step 2:

a)

Click on the application file: TA

a)

Click on the application file: TA

b)

Select: Initialization Run

b)

Select: Simulation Run

c)

Follow instruction and answer all questions and “CLICK ON THE ENTER KEY TO CLOSE”

c)

Follow instruction and answer all questions and “CLICK ON THE ENTER KEY TO CLOSE”

d)

At the end of step (C); Open TA.dat with Notepad and Enter Missing Reservoir Data.

d)

Open: TA.sim with Notepad; this file contains wells info

e)

Save and close the file

e)

Save and close the file

f)

f)

Click on the application file : “Tarek” (this is a MUST STEP); simulator WILL NOT RUN WITHOUT THIS STEP

Click on: Tarek.exe to run the simulator (this is a MUST STEP)

g)

Results of the run are given in TA.OUT as well as other files

do not go to step 2 until you: a) answers all questions b) close the software by pressing the <ENTER> key c) Open TA.dat with Notepad and enter missing data d) Clicking on Tarek.exe e) Observed the reported OOIP or OGIP f) If you did not see OOIP or OGIP, something wrong in TA.dat

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Initialization File: TA.dat ! !

3) Reservoir Model Grid Dimensions ********************************** 100 100 10 ! x,y, and z blocks

! !

4) x-direction Grid Block Lengths ********************************* Each time you see

! Warning Warning Warning The Warning message; ! ^^^^^^^^^^^^^^^^^^^^^^^^^^^ you must enter some data ! Please, enter below the x-direction grid dimension (length) ! for each grid block. 100 values MUST BE entered : ! ************************************************* 100*300 You enter the data ! !

5) y-direction Grid Block Lengths *********************************

! Warning Warning Warning ! ^^^^^^^^^^^^^^^^^^^^^^^^^^^ ! Please, enter below the y-direction grid dimension (length) ! for each grid block. 100 values MUST BE entered : ! ************************************************* You enter the data 100*300 © 2006 Tarek Ahmed & Associates Ltd. All Rights Reserved.

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Open the Following Files with EXCEL to Make Plots (e.g. GasRec.dat, FieldQg.dat,…etc) File Name -------------------------1) Summary.dat 2) DailyQ.dat 3) OilRec.dat 4) GasRec.dat 5) FieldQg.dat 6) WellQw.dat 7) GasQ.dat 8) WellQg.dat 9) Pmap.dat 10) Sgmap.dat 11) Swmap.dat 12) Layers.dat 13) LayerRate.dat

Contents --------------------------------------------> History Matching info.& Well data > Field Daily Flow Rates > Field Oil Recovery Factor > Field Gas Recovery Factor > Field Monthly Flow Rates > Well Monthly Water Flow Rates > Field Total Daily Gas Flow Rate > Monthly Gas Flow Rates/well > Pressure Map > Gas Saturation Map > Water Saturation Map > Performance of layers, cross flow,…etc > Production/injection rate/layer © 2006Tarek Ahmed & Associates, Ltd. All Rights Reserved

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The Big Saigon Gas Field  Grid dimensions=

30 x 30 x 3

 Reservoir dimensions=

∆X=300 ft, ∆Y=300 ft, ∆Z=20 ft

 Initial # of wells=

3 wells

 Depth to top=

5000 ft

 Start date=

Jan 1, 1990

 Total Thickness =

100 ft

 Temperature

200 oF

 Initial Pressure

4000 psi @ 5020 ft

 Sgi=

0.70

 Simulation time=

7200 days

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The Texas Oil Field  Grid dimensions=

30 x 30 x 5

 Reservoir dimensions=

∆X=300 ft, ∆Y=300 ft, ∆Z=20 ft

 Initial # of wells=

8 wells

 Depth to top=

5000 ft

 Start date=

Jan 1, 1990

 Total Thickness =

100 ft

 Soi=

0.70

 Simulation time=

7200 days

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Initial Pressure =4500 psia 35o API Temperature 200 oF Gas gravity=0.75 GOR=500 scf/STB Model will calculate Pb Pressure at 5020 ft =4500 psi Minimum Pwf = 300 psi

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Layer 1

Layer 2

Layer 3

Layer 4

Layer 5

Kx, md

20

15

35

12

10

Ky, md

15

12

30

10

5

Kz, md

1.7

1.3

3.0

1.0

0.7

ᶲ

0.25

0.20

0.30

0.15

0.12

h, ft

20

20

20

20

20

∆Z, ft

20

20

20

20

20

y-direction (rows)

30 1

1

1

x-direction (columns)

30 Δz=20 ft Δz=20 ft Δz=20 ft

100 ft

Δz=20 ft

Δz=20 ft 5

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Objectives: 1) Maximize Oil Recovery 2) Open Summary.dat to exam the performance of each layer and where the injected water is going 3) Important that you open Sgmap.dat , Swmap.dat & Pmap.dat with Excel 4) Open with Excel: Oilrec.dat to to plot RF & average P vs. time 5) Open with Excel: WellQg.dat, WellQo.dat & WellQw.dat to plot well rates vs. time 6) Open with Excel: WellGOR.dat & WellWOR.dat to plot well rates vs. time 7) Compare Water Injection with Gas Injection 8) Balance Production-Injection rate “VRR” 9) Drill Horizontal injectors /producers and:  test completion in Layer 1,2,3,4, and 5  Effect of horizontal well orientation  document the difference in RF 10) Stimulate Wells 11) Miscible Displacement 12) Document your Team Results Graphically 13) Team Presentation

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