Geomechanics Course Baker Hughes 2007.pdf
This document was uploaded by user and they confirmed that they have the permission to share it. If you are author or own the copyright of this book, please report to us by using this DMCA report form. Report DMCA
Overview
Download & View Geomechanics Course Baker Hughes 2007.pdf as PDF for free.
More details
- Words: 51,783
- Pages: 671
Loading documents preview...
Introduction to Petroleum Geomechanics August 27 - 31, 2007 El Tigre, Venezuela
© 2005 Baker Hughes Incorporated All rights reserved. © 2000 Baker Hughes Incorporated All rights reserved.
Course Objectives
To provide a broad overview of the fundamentals of Geomechanics. To demonstrate the use of these fundamentals to address oil field problems associated with the drilling and production of hydrocarbon resources.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Course Outline 1. Introduction to Geomechanics what, why, where fundamentals 2. Rock Mechanical Property Characterization static versus dynamic Logging of Mechanical Properties (LMP) 3. In-situ Stress Characterization pore pressure estimation subsurface stresses – magnitude & direction 4. Geomechanics Applications wellbore stability sand/solid production hydraulic fracturing reservoir compaction © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Geomechanics Applications
© 2005 Baker Hughes Incorporated All rights reserved. © 2000 Baker Hughes Incorporated All rights reserved.
Outline • What is Geomechanics? • Why Geomechanics? • Geomechanics Applications • How to Apply Geomechanics? • Geomechanics Application Examples • The Value of Geomechanics
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
What is Geomechanics?
STRESS vs. STRENGTH ESF
U
Z ER
O
RES
IS T
EN C
IA
A branch of engineering mechanics concerned with the response of geologic materials to the force field of their physical environment.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
What is Geomechanics? (Rock Mechanics) • Theoretical and applied science of the mechanical behavior of geological materials. • A branch of mechanics concerned with the response of geological materials to the force field of their physical environment. • Used in civil, petroleum and mining engineering and any discipline dealing with geological material’s mechanical behavior. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
What is Petroleum Geomechanics? Science and knowledge about the mechanical behavior of reservoir and overburden formations during different phases of petroleum operations.
Petroleum geomechanics enables us to predict wellbore and reservoir deformations/failures and generate engineered solutions for optimal field developments.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Why Geomechanics? z
Today’s reservoirs are more difficult to access and develop: – “Brown-field” reservoirs approach depletion and many are compartmentalized – Onshore reservoirs are deeper and manifest high-pressure, high-temperature (HPHT) conditions – Offshore reservoirs are in deep water and at greater depth – Heavy oil recovery require high temperature operations
z
z
Geomechanics is a key enabling technology for exploring and exploiting today’s technically challenged reservoirs (tectonics, deepwater, HPHT, brown, heavy oil). Advanced technology is required to optimally drill, complete and produce these reservoirs.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Why Geomechanics? Total E&P Costs = $82 billion
• In 1997
Drilling Costs = $32 billion$6.4 • In 2002 2002 SPE-ATW on Real-time Wellbore Stability
B
Drilling costs related to borehole instability = $3.2 billion
All major operating companies agreed on 10 to 15 % of the drilling budget goes to wellbore stability issues !!
Geopressure and borehole stability problems are estimated to cost the industry $8 billions every year !!
• In 2004
Offshore Magazine - Dodson Jan.2004
………but missing production can be equally expensive!!
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Applications of Geomechanics $
NPV
) Borehole stability/well planning
Business Drivers
) Drilling efficiency enhancement
) Solid production/completion strategy ) Reservoir compaction/subsidence ) Hydraulic fracturing/stimulation
Reservoir Properties
) Cuttings re-injection/remediation ) Well placement in fractured reservoirs
Log/Core Measurements
© 2005 Baker Hughes Incorporated All rights reserved.
) Fully-coupled reservoir simulation
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Geomechanics Applications – Summary Borehole Integrity Management
Sand Control Solutions
Wellbore Stability Wellbore Strengthening
Screen Completion Screenless Completion
mud weight windows mud composition/formulation wellbore trajectory casing program
critical drawdown pressure oriented perforation selective perforation wellbore/perforation trajectory expandable screen gravel pack
Reservoir Management
Waste Management
Reservoir Compaction [production induced]
Drilling Waste (drilling fluids, cuttings) Production Waste (produced water, CO2)
stress-dependent rock properties pore volume compressibility well/completion integrity platform subsidence drive mechanism pressure maintenance time-lapsed seismics
cap rock integrity fault seal integrity fracture containment fracture morphology/geometry candidate well selection (geomechanics)
Production Enhancement
Complex Geology Environments
Productivity Improvement (well-based) Recovery Improvement (field-wide)
Fault Seal Integrity Critically Stressed Fracture
dynamic under-balanced perforation hydraulic fracturing stimulation flood directivity oriented perforation stress vs. permeability anisotropy
exploration strategy injection pressure production management (depressurization) well placement in fracture reservoir
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Values of Geomechanics – A Success Story
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Value of Geomechanics – Baker Hughes z z z z z z z z z
Generating pull through revenue Value boosting for logging technologies Help generating needs for quality formation data Improve client relationships Quality assurance Understanding market and technology needs/requirements Increase communication with sister divisions Generate direct revenues for BHI/BA Secure the client - measured by # tenders
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Fundamentals of Geomechanics © 2005 Baker Hughes Incorporated All rights reserved. © 2000 Baker Hughes Incorporated All rights reserved.
Outline z z z z z z z
Basic Concepts of Stress and Strain Principal Stresses Mohr’s Circle Elasticity and Elastic Parameters Failure Strength Parameters Failure Theories Effective Stress Concept
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Definitions and Terminology Stress and Strain ♦ Stress (σ or τ): Defines the force field to which a material is subjected. Stress is a tensor with three orthogonal principal directions in a three dimensional coordinate system. ♦ Strain (ε or γ): Defines the deformation of a material in a force (stress) field. Strain is also a tensor with three orthogonal principal directions in a three dimensional coordinate system.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Definitions and Terminology Stress (σ)
Units of pressure (or force/area), e.g., psi, MPa, bar, etc. c.s. area F
Stress on the plane σ = F/A
a
A
b
A’
σ = F/A’
c
A’’
σ = F/A’’
F
F
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Definitions and Terminology Strain (ε)
P
Δl
Δl Change in Dimension ε= = l Original Dimension
l
l
1
Un-deformed
Deformed
• Defines the deformation of a material in a stress field. • Relative change in material dimension.
Unit or dimensionless
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Definitions and Terminology Stress (σ)
Fp
• Normal Stress –normal or perpendicular –
σn= Fn/A
Fn F
(e.g., σx , σy, etc.)
• Shear Stress – parallel to the plane –
τ = Fp/A
(e.g., τxy, τxz, etc.)
• Stress & Strain – vector quantities (on a single plane) • Magnitude (amount) • Direction © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Definitions and Terminology 2D State of Stress 2 Normal stresses 2 Shear stresses
σy
4 comp.
For no rotation & translation:
τxy = τyx
(σ )2D
σyy
⎧σ xx ⎫ ⎪ ⎪ = ⎨σ yy ⎬ ⎪τ ⎪ ⎩ xy ⎭
τyx
τxy σxx
σx
τij = Shear stress acting on a plane perpendicular to i and in a direction parallel to j
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Definitions and Terminology σyy
General 3D State of Stress 3 Normal stresses 9 comp. 6 Shear stresses τxy = τyx τyz = τzy τzx = τxz
τyz τzy τzx
τyx
τxy
τxz
σxx
Stress Tensor: total 9 components, with 6 independents.
3 normal + 3 shear stresses © 2005 Baker Hughes Incorporated All rights reserved.
σzz
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Definitions and Terminology Stress Tensor (σ) =
σxx τxy τxz τyx σyy τyz τxz τzy σzz
=
2D System © 2005 Baker Hughes Incorporated All rights reserved.
σ1 σ4 σ5 σ4 σ2 σ6 σ5 σ6 σ3
σ11 σ12 σ13 = σ21 σ22 σ23 σ31 σ32 σ33
=
σ1 σ2 σ3 σ4 σ5 σ6
Efficiency….Data accuracy….People-oriented service
= σij = [σ]Τ
www.bakeratlasdirect.com
Definitions and Terminology Stress Transformation - 2D σy
For the equilibrium of the body:
∑ Fx = ∑ (σ • A )x = 0
∑ Fy = ∑ (σ • A )y = 0
y
τxy
σ
σx τxy
τxy θ
θ
x
τxy
σ=( τ=(
σx +σy 2
σy −σx 2
)+(
σx −σy 2
) cos 2θ + τ xy sin 2θ
σx
τ
σy
) sin 2θ + τ xy cos 2θ
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Definitions and Terminology Other expressions for normal stress on a plane: σ = σxx cos2θ + σyy sin2θ + τxy sin2θ σ = σxx cos2θ + σyy sin2θ + 2τxy sinθ cosθ
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Exercise Problems σyy
Given:
Y
σxx = 100 psi σyy = 60 psi τxy = 40 psi
τxy σ
σxx τxy
(note: sin30 = cos60 = -cos120 = 1/2 cos30 = sin60 = sin120 = √3/2)
τxy σxx
θ τ
θ
X
τxy σyy
Determine normal (σ) and shear stresses (τ) for: 1) θ = 30 degrees σ = 124.6, τ = 2.7 2) θ = 60 degrees σ = 104.6, τ = -37.3 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline 9 Basic
Concepts of Stress and Strain ÎPrincipal Stresses & Mohr’s Circle z Elasticity and Elastic Parameters z Failure Strength Parameters z Failure Theories z Effective Stress Concept
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Principal Stresses
σ1 σ2 σ3
σv σH σh
Normal stresses on planes where shear stress is zero σ1 > σ2 > σ3
σ1 = σ v
(Max. > Intermediate > Minimum)
Other Notations:
σ2 = σ H
σ3 = σ h
σH = σHmax σh = σhmin
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Definitions and Terminology Principal Stresses - 2D
τ=(
σy −σx 2
) sin 2θ + τ xy cos 2θ
2 τxy tan 2θ = σx - σy
σ1 = (
σx +σy 2
σ2 = (
σx +σy 2
=0
σy y
y’
θ1, θ2 are the solutions (θ2 = θ1 + 90) Mutually orthogonal
x’
τxy
σx τxy
σx
τ=0 θ1 τxy
)+(
σ x −σ y 2
) cos 2θ1 + τxy sin 2θ1
)+(
σ x −σ y 2
) cos 2θ2 + τ xy sin 2θ2
© 2005 Baker Hughes Incorporated All rights reserved.
τxy
σ
Efficiency….Data accuracy….People-oriented service
x
σy
www.bakeratlasdirect.com
Exercise Problem Stress Transformation – 2D σxx = 100 psi σyy = 60 psi τxy = 40 psi
σy y
τxy τxy
σ1
σx τxy
σx
τ=0 θ1 τxy
x
σy
Determine the directions of principal stress axes (θ1, θ2) and the magnitudes of principal θ1 = 31.7 deg, θ2 = 121.7 deg stresses (σ1, σ2): σ1 = 124.7 psi, σ2 = 35.3 psi
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Definitions and Terminology Principal Stresses (2D) σ1 =
σ2 =
σx + σy 2 σx + σy 2
2
⎛ σx − σy ⎞ ⎟⎟ + τ 2xy + ⎜⎜ ⎝ 2 ⎠ 2
⎛ σx − σy ⎞ ⎟⎟ + τ 2xy − ⎜⎜ ⎝ 2 ⎠
σ1 ≥ σ2
σ1 = Mean Stress + Max. Shear Stress σ2 = Mean Stress – Max. Shear Stress © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Definitions and Terminology Mohr Stress Circles and Principal Stress Calculations
Y σy τxy σx
Shear Stress, τ
σx
X
(σx−σy)/2
τxy
Max Shear Stress: Mean Stress: (σx+ σy)/2
Shear Stress: τxy
σy σ2
Normal Stress, σ
σx
σy
σ1
σ1 = Mean Stress + Max. Shear Stress σ2 = Mean Stress – Max. Shear Stress © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Definitions and Terminology
τ
Mohr Circles - Graphic Representation of 2D Stresses
( σ1 + σ 3 ) σ1 −σ 3 σn = + Cos 2θ
τ σ3
σ1 − σ 3
σn
© 2005 Baker Hughes Incorporated All rights reserved.
2
2
2θ
σ1
σ
2
( σ1 − σ 3 ) τ = Sin 2θ
⎛ σ1 + σ 3 ⎞ ,0 ⎟ ⎜ ⎝ 2 ⎠
Efficiency….Data accuracy….People-oriented service
2
θ = 530
www.bakeratlasdirect.com
Definitions and Terminology Principal Stresses – 3D - Eigen Values of the Stress Matrix (s)
σ x −σ τ xy τ xz τ xy σ y −σ τ yz = 0 , σ 3 − I1σ 2 − I 2σ − I3 = 0 τ xz τ yz σ z −σ where
σ x τ xy σ x τ xz σ y τ zy I1 = σ x + σ y + σ z , I 2 = + + τ xy σ y τ xz σ z τ zy σ z and
σ x τ xy τ xz I 3 = τ xy σ y τ zy τ xz τ zy σ z
© 2005 Baker Hughes Incorporated All rights reserved.
are the Stress Invariants
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Principal Stresses σv
In the case of a reservoir, σh
σ1 = σv = Vertical/Overburden stress σ2 = σH = Maximum horizontal stress
σH Stress Magnitude
σ3 = σh = Minimum horizontal stress Depth
σh σH © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
σv
www.bakeratlasdirect.com
Representation of A Stress State •
The state of stress AT A POINT in the reservoir can be represented by Mohr’s circle τ
σ3 © 2005 Baker Hughes Incorporated All rights reserved.
σ2
σ1
Efficiency….Data accuracy….People-oriented service
σ www.bakeratlasdirect.com
Outline 9 Basic
Concepts of Stress and Strain 9 Principal Stresses and Mohr’s Circle ÎElasticity and Elastic Parameters z Failure Strength Parameters z Failure Theories z Effective Stress Concept
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Elastic Properties
σ
Elastoplastic
Linear Elastic
Yield
Max. Stress = Failure Strength Re-loading
P
Unloading
δ1 E
Sample
1 εpl
© 2005 Baker Hughes Incorporated All rights reserved.
εel
ε1
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Elastic Properties Elastic Moduli – E and ν P
Measure: Axial Load (P) Deformations: δ1, δ3 Conf. Pres. σ2 = σ3
δ3
σ1 = P / area ε1 = δ1 / orig. length ε3 = 2*δ3 / orig. dia. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
δ1
Sample
www.bakeratlasdirect.com
Elastic Properties Co = σmax
dσ1 dε3
dε1
ε3
ε1
Ε = dσ1 / dε1 ν = −dε3/ dε1 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Elastic Properties Young’s Modulus & Poisson’s Ratio )Young’s Modulus:
E = Δσ1 / Δε1
Young’s modulus describes the stiffness of a material when it is under stress. The higher the Young’s modulus, the harder it is to deform the material. i.e. requires more stress to deform.
)Poisson’s Ratio:
0 < ν = - Δε3 / Δε1 < 0.5
Poisson’s ratio defines the relative strain in a direction not subjected to incremental stress and orthogonal to the direction of the incremental stress. A material with Poisson’s ratio of 0.5 is an incompressible material.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Types of Moduli Young’s modulus: E = dσ1 / dε1
Initial Tangential Secant 50% peak stress
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Initial Modulus σ
dσ
E = dσ / dε
dε
ε © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Tangential Modulus σ
dσ x
E = dσ / dε
dε
ε © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Secant Modulus σ
x
E = dσ / dε dσ
dε © 2005 Baker Hughes Incorporated All rights reserved.
ε Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Modulus at 50% Peak Stress σ σmax
E = dσ / dε
50 % σmax
dσ dε
ε © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Quiz Quiz-- Elastic Properties Given:
P
Orig. length = 2 inches Orig. Dia. = 1 inch
δ3
δ1
Ax. Deformation = 0.05 inch Rad. Deformation = 0.003 inch Load = 20,000 lbf
L
Sample
Find: E=? ν=?
d © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Quiz Solution Solution-- Elastic Properties Solution: σ1 = P / cross-sectional area Area = πd2/4 ε1 = δ1 / orig. length ε3 = 2*δ3 / orig. dia. Area = 3.1416*(1)2/4 = .785in2 σ1 = P / area = 25465 psi ε1 = 0.05 / 2 = 0.025 ε3 = 2*(-0.003) / 1 = -0.006 E = σ1 / ε1 = 25465/.025 = 1.02E+06 psi ν = -ε3 / ε1 = .006/.025 = 0.24
© 2005 Baker Hughes Incorporated All rights reserved.
P
δ3
L
Efficiency….Data accuracy….People-oriented service
δ1
Sample
d www.bakeratlasdirect.com
Stress -Strain Relations Stress-Strain Relations between Stress and Strain (isotropic) Uniaxial Loading:
E = Δσ1 / Δε1 = Δσy / Δεy
1 ε xx = (σ xx − νσ yy − νσ zz ) E 1 ε yy = (σ yy − νσ xx − νσ zz ) E 1 ε zz = (σ zz − νσ yy − νσ xx ) E σ xx + σ yy + σ zz ε v = ε xx + ε yy + ε zz = 3K τ xy τ yz τ zx , ε yz = , ε zx = ε xy = 2G 2G 2G © 2005 Baker Hughes Incorporated All rights reserved.
Y
τyx
σy τyz
τzy σz
τxz τzx
σx
τxy
Z
E and ν
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
X
Stress -Strain Relations Stress-Strain Relations between Stress and Strain (isotropic) Uniaxial Loading:
E = Δσ1 / Δε1 = Δσy / Δεy
σ xx = λε v + 2 G ε xx
Y
τyx
σ yy = λε v + 2 G ε yy
σy τyz
σ zz = λε v + 2 G ε zz τ xy = 2 G ε xy
τzy
τ yx = 2 G ε yx
σz
τxz τzx
σx
τxy
τ zx = 2 G ε zx ε v = ε xx + ε yy + ε zz = ε xy =
τ xy 2G
, ε yz =
© 2005 Baker Hughes Incorporated All rights reserved.
τ yz 2G
σ xx + σ yy + σ zz , ε zx
3K τ zx = 2G
Z
where λ, G, and K are functions of E and ν
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
X
Elastic Properties Relations between Different Elastic Parameters (isotropic material – 2 constants) Bulk Modulus Shear Modulus
Lame’s constant
E E G= , K= , 2(1 + ν ) 3(1 - 2ν ) Eν λ= (1 + ν )(1 − 2ν )
9KG 3K - 2G 2Gν E= , ν= , λ= 3K + G 2(3K + G) 1 − 2ν © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline 9 Basic
Concepts of Stress and Strain 9 Principal Stresses 9 Mohr’s Circle 9 Elasticity and Elastic Parameters ÎFailure Strength Parameters ÎFailure Theories z Effective Stress
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Strength Parameters Intrinsic properties that describe the failure behavior/response under load/force/stress. ) Compressive & tensile strengths (C & To)
Related Parameters: ) ) ) )
Angle of internal friction (α) Shear Strength (Si) Unconfined Compressive Strength (UCS) Confined Compressive Strength
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Strength Parameters Compressive Strength – from Triaxial Compression Test
Test Apparatus
Stress-Strain Curves
Axial Strain measurement
Axial Differential Stress
Axial Stress
Confining Pressure inlet Seal
Radial Strain measurement
© 2005 Baker Hughes Incorporated All rights reserved.
Confining Pressure outlet Pore Pressure control
Radial Strain
Efficiency….Data accuracy….People-oriented service
Axial Strain
www.bakeratlasdirect.com
Failure Strength Parameters Typical Stress-Strain Curve (Triaxial) Axial/Shear/Deviatoric Stress (σa- σc or σ1-σ3) Compressive Strength Increasing crack density Macro cracking - failure by joining microcracks
New microcracks
Δσa
Δσa
Linearly elastic
Δεr
Sliding on macrocracks
Δεa Closure of pre-existing cracks
Radial Strain εr (extension)
© 2005 Baker Hughes Incorporated All rights reserved.
Axial Strain εa (contraction)
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Differential stresses (σ1-σ3)
Failure Strength Parameters
σmax- Peak Strength Starting of the mechanical damage ~0.60σmax
Cohesion lost
Massive damage, shear plane development Sudden drop of stresses (brittle failure) Continuous damage
Elastic behavior σ−ε
Residual strength
Micro-fissures closing
Axial strain (εa) (after Dusseault, 2000)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Strength Parameters Different Types of Compression Tests • Unconfined (Uniaxial) Compression Test σa
σc
σc = 0
σa UCS = σamax
© 2005 Baker Hughes Incorporated All rights reserved.
• Confined Triaxial Compression Test σa
σc
σa C(σc) = σamax(σc)
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Strength Parameters Failure Envelope
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Theories Mohr Failure Envelope τ D C
B A
σ An empirical criterion of failure defined by the envelope to a series of Mohr’s circles: A- direct tension; B- Brazilian; C- unconfined compression; D- triaxial compression. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Theories Mohr – Coulomb Failure Criterion S i = Cohesion or initial shear strength
τ = S i + σ tan φ
φ = Internal Friction Angle
τ
φ
τ = S i + σ tan φ
Si
σ3 © 2005 Baker Hughes Incorporated All rights reserved.
UCS Efficiency….Data accuracy….People-oriented service
σ1
σ www.bakeratlasdirect.com
Failure Strength Parameters Mohr–Coulomb Failure Criterion τ = So + μσ = So + σ tan φ or σ1 = UCS + σ 3 tan 2 ( π4 + φ2 )
The relationships between So , μ , φ and UCS are: tan( π4 + φ2 ) = 1 + μ 2 + μ =
1 + sin φ , and 1 − sin φ
UCS = 2So tan( π4 + φ2 ), μ = tan φ UCS = Unconfined Compressive Strength, So = Cohesion or initial shear strength φ = Internal Friction Angle μ = Friction Coefficient = tanφ © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Strength Parameters Confining Pressure Effect
Axial Differential Stress
σc = 50 MPa
σc = 25 MPa
σc = 10 MPa σc = 5 MPa σc = 0
Radial Strain © 2005 Baker Hughes Incorporated All rights reserved.
Axial Strain
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Mechanics – Failure Modes σ
Ductile – high confining stress (σ (σ3)
σ0 Transitional Brittle – low confining stress (σ (σ3)
ε
After de Van der Pluijm y Marshak, 1997
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Confining Pressure Effects COMPRESSIVE STRENGTH 160
120
During Compaction Undisturbed Formation Strength During Production
80
depth = 5000 ft shale
40
During Drilling 0
0
2
4
6
8
10
12
14
16
18
20
CONFINING PRESSURE [Mpa] © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Strength Parameters Temperature Effect 25°C
σ1 - σ3 [kbars]
20 15 10 5 0
300°C 500°C 800°C
5
10
15
Strain [%] © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Strength Parameters Specimen Size Effect (after Bienawski and Van Heerden, 1975)
Compressive Strength [MPa]
140 Calcareous Iron Ore Jahns, 1966
120
Cedar City Quartz Diorite, Pratt et. all, 1972. Coal, Bienawski, 1968
100 80 60 40 20 0
© 2005 Baker Hughes Incorporated All rights reserved.
0.5
1 1.5 2 Specimen Length [m]
2.5
Efficiency….Data accuracy….People-oriented service
3
www.bakeratlasdirect.com
Failure Strength Parameters Fluid/Saturation Effect Dry
σ1 - σ3 [kbars]
50 Saturated, non-wetting phase fluid
40 30
Saturated, wetting phase fluid
20 10
5
10 15 20 25 Strain [%]
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Strength Parameters Other Types of Compression Tests • Hydrostatic Compression Test σa
σc
σc = σa
σa
= σc/εv εv = εa + 2*εr c = 1/K K
εc = 0
ν Δ σx ' Δ σy ' K0 = = = t Δσ z ' Δσ z ' 1 - ν t
For Bulk modulus/Compressibility
© 2005 Baker Hughes Incorporated All rights reserved.
• Uniaxial Strain (K0) Test σa
σa Field Conditions
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Strength Parameters
Tensile Strength )
Capacity of a material to support tensile stress. • Direct Tension Test To = σTmax
σT
σT
• Bending Test
• Brazilian Indirect Tension Test
P
To = 2Pmax/πtD © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline 9 Basic
Concepts of Stress and Strain 9 Principal Stresses 9 Mohr’s Circle 9 Elasticity and Elastic Parameters 9 Failure Theories 9 Failure Strength Parameters ÎEffective Stress
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effective Stress Concept If a load is applied to a rock, a portion of the load is imparted on the rock matrix and a portion on the pore fluid (counteracting). Pore pressure increases if rock permeability is sufficiently low
F
Total stress (σ) = F/A A = area of the plane Grain load increases
Matrix
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effective Stress Concept Mathematically, the effective stress (σ’) concept is written as: Total Stress (σ) = Stress on grains (σ’) + Stress on fluid (Pp) Stress on grains (σ’) = Total Stress (σ) - Pore Pressure (Pp)
σ’ = σ – Pp
Î
Terzaghi’s effective stress law
For constant Pp: σ ↑, σ’↑ (and vice versa) For constant σ: Pp ↑, σ’↓ For constant σ: Pp ↓ , σ’↑
© 2005 Baker Hughes Incorporated All rights reserved.
This is known as the Terzaghi’s effective stress. Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effective Stress Concept For most rocks, a change in total stress (or pore pressure) does not yield an identical change in effective stress. To account for this, Terzaghi’s effective stress was modified by Biot (1941) as:
σ’ = σ - αPp where α = Biot’s effective stress coefficient
0< α < 1 (rocks) α = 1 (soil)
For α = 1 → a given Pp increase (∆Pp) yields an equal reduction in σ’ (i.e., ∆Pp = ∆σ’) For α < 1 → a Pp increase gives an unequal reduction in σ’ (i.e., ∆Pp ≠ ∆σ’)
Upshot: Biot’s constant is a measure of the “efficiency” of the fluid in counteracting the applied stress. Note that Biot’s constant is stress dependent. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effective Stress Stress-- Example Given: Three cylinders of identical geometrical proportions with the properties shown below. Find: The effective stress (axial) for each sample under an identical load. 2”
4”
steel φ=0 k = 0 md Pp = N/A α = N/A
shale φ = 10% k = 10-9 md Pp = 3000 psi α = 0.5
sandstone φ = 25% k=1d Pp = 3000 psi α = 0.9
Note: φ = total porosity, k = permeability [Darcy or milliDarcy], Pp = pore pressure [psi], α = Biot’s constant © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effective Stress Stress-- Example 10,000 lbf
10,000 lbf
10,000 lbf
steel
shale
sandstone
Solution: Total stress (σ) = F/A = 10,000/πr2 = 10,000/π12 = 3183 psi © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effective Stress Stress-- Example
Solution (cont’d):
σ’ = σ - αPp steel
σ’ = σ – αPp = 3183 – 0 = 3183 psi © 2005 Baker Hughes Incorporated All rights reserved.
shale
σ’ = σ – αPp = 3183 – 0.5*3000 = 1683 psi Efficiency….Data accuracy….People-oriented service
sandstone
σ’ = σ – αPp = 3183 – 0.9*3000 = 483 psi www.bakeratlasdirect.com
Poro -elasticity Poro-elasticity Induced fluid pressure brings stress relief to the solid material (dilation) (poro-elasticity); similar to heating (thermoelasticity) Permeable material (or slow loading) – pore pressure dissipates – acts like solid material, without fluid Tight rock/faster loading – pore pressure rises within entrapped fluid, resulting in smaller than expected rock deformation Material appears stiffer: combined rock and fluid Time-dependent behavior © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Rock Mechanical Properties Characterization © 2000 Baker Hughes Incorporated All rights reserved.
Outline ÎMechanical
behavior under loading ÎStratigraphy and rock fabric z Dynamic rock mechanical properties z Logging of Mechanical Properties z Empirical correlations z Rock mechanics laboratory
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
2
www.bakeratlasdirect.com
Rock Mechanical Behaviors Under Stress Loading σ
Linear Elastic
Elastoplastic Yield
Max. Stress = Failure Strength Re-loading Unloading
ε
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
3
www.bakeratlasdirect.com
Mechanical behavioral Models
Linear-elastic model (no rupture) Elastic model with brittle rupture Non-linear elasticity (where E = f(σ)) Elastic, perfectly plastic Elastic with strain-weakening, then plastic Visco-elastic (shales, some rocks at high T) Visco-plastic (salt and other halides) ………… Choose the model that adequately describes the mechanical behavior as exhibited by the σ - ε curve.
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
4
www.bakeratlasdirect.com
Stratigraphy and Rock Fabric Petroleum geomechanics deals with wide variety of rocks ranging from clay-free reservoir sandstones through siltstones to mudstones and shales. In-situ mechanical properties depend on the interaction between intrinsic and extrinsic properties. Intrinsic properties include mineralogy and its distribution in the rock frames, grain size distribution and rock fabric such as bedding planes or fractures. Extrinsic properties are confining pressure, strain rate and temperature. 1. 2.
Plumb, R.A: ”Influence of composition and texture on the failure properties of elastic rocks”, Eurock 94. Plumb, R.A., Heron, S.L., and Olsen, M.P.: “Influence of composition and texture on compressive strength variations in the Travis Peak formation”, SPE 27458
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
5
www.bakeratlasdirect.com
Mechanical Classifications of Reservoir Rocks Three categories depending on the basis of the volume of clay minerals: • grain supported, Vclay < 15% • transitional supported, 15 % < Vclay < 35% • clay supported, Vclay > 35% External loads applied to grain supported rocks are carried by grain-to-grain contacts. In transitional supported rocks, loads are distributed more equally among detrital grains and clay minerals. In clay supported rocks, externally applied loads are borne entirely by clay minerals. 1. 2.
Plumb, R.A: ”Influence of composition and texture on the failure properties of elastic rocks”, Eurock 94. Plumb, R.A., Heron, S.L., and Olsen, M.P.: “Influence of composition and texture on compressive strength variations in the Travis Peak formation”, SPE 27458
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
6
www.bakeratlasdirect.com
Rock Mechanical Behavior Under Stress Loading
Unconfined compressive strength and average friction angle vs. Vgrain for rocks classified by their load bearing solid phase. Vgrain= 1-(φ+Vclay) 1. 2.
Plumb, R.A: ”Influence of composition and texture on the failure properties of elastic rocks”, Eurock 94. Plumb, R.A., Heron, S.L., and Olsen, M.P.: “Influence of composition and texture on compressive strength variations in the Travis Peak formation”, SPE 27458
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
7
www.bakeratlasdirect.com
Lithology vs. Acoustic Velocity
After Castagna & Batzle (1985)
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
8
www.bakeratlasdirect.com
Lithology vs. Acoustic Velocity
Vp/Vs
After Tatham and McCormack 1991
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
9
www.bakeratlasdirect.com
Outline 9 Mechanical
behavior under loading 9 Stratigraphy and rock fabric ÎDynamic rock mechanical properties z Logging of Mechanical Properties z Empirical correlations z Rock mechanics laboratory
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
10
www.bakeratlasdirect.com
Elastic Constants From Logs ⎡⎛ Δ t s ⎞ ⎤ ⎟⎟ − 2 ⎥ ⎢ ⎜⎜ ⎡⎛ 1 ⎢⎣ ⎝ Δ t c ⎠ ⎥⎦ = ; E D = 2 ⎢ ⎜⎜ 2 ⎡⎛ Δ t s ⎞ ⎤ ⎢⎣ ⎝ Δ t s ⎟⎟ − 1 ⎥ 2 ⎢ ⎜⎜ ⎢⎣ ⎝ Δ t c ⎠ ⎥⎦ 2
νD
⎤ ⎞ ⎟⎟ * (1 + ν D )ρ ⎥ ⎠ ⎥⎦ 2
ED and νD are dynamic moduli, ρ is bulk density. Δtc and Δts are compressional and shear slownesses.
From Acoustic Logs Other dynamic moduli (such as Bulk modulus, Shear modulus, and compressibilities) can then be calculated. © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
11
www.bakeratlasdirect.com
Dynamic Mechanical Properties –
Example Calculations
⎡ ⎛ Cp 2 C s ρ ⎢3⎜⎜ ⎢⎣ ⎝ C s 10 E D = 1.347 × 10 ⎡⎛ C p ⎞ 2 ⎟⎟ ⎢⎜⎜ ⎢⎣⎝ C s ⎠ DEPTH m 630.0216 630.174 630.3264 630.4788 630.6312 630.7836 630.936 631.0884 631.2408 © 2000 2005 Baker Hughes Incorporated All rights reserved.
DTC us/ft 150.865 152.576 150.976 146.855 144.915 142.951 142.545 142.337 143.286
⎤ ⎞ ⎟⎟ − 4⎥ ⎥⎦ ⎠ ⎤ − 1⎥ ⎥⎦ 2
DTS us/ft 447.784 484.607 486.765 467.886 440.522 395.599 382.763 370.373 381.956
⎡⎛ C p ⎞ 2 ⎤ ⎟⎟ − 2⎥ 0.5⎢⎜⎜ ⎢⎣⎝ C s ⎠ ⎥⎦ υD = ⎡⎛ C p ⎞ 2 ⎤ ⎟⎟ − 1⎥ ⎢⎜⎜ ⎢⎣⎝ C s ⎠ ⎥⎦
DEN g/cc 2.22 2.22 2.23 2.24 2.25 2.28 2.26 2.27 2.24
POIS-dyn
E-dyn psi
0.436 0.445 0.447 0.445 0.439 0.425 0.419 0.413 0.418
4.26E+05 3.66E+05 3.65E+05 3.96E+05 4.47E+05 5.56E+05 5.87E+05 6.27E+05 5.84E+05
Efficiency….Data accuracy….People-oriented service
12
www.bakeratlasdirect.com
Static vs. Dynamic Moduli In General: ED >> ES,
GD >> GS, νD > or < νS
12
Ed [106 psi]
10 8 6 4 2
0
2
(from Preston, 1976) © 2000 2005 Baker Hughes Incorporated All rights reserved.
4
6
8
10
12
E [106 Psi] Efficiency….Data accuracy….People-oriented service
13
www.bakeratlasdirect.com
Causes of Difference between Static and Dynamic Moduli ¾Dynamic Loading (as opposed to static) •
Low amplitude (low magnitude of load)
•
High-frequency (fast loading and unloading)
•
Low affected mass (few mm)
•
Non-destructive testing
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
14
www.bakeratlasdirect.com
Static vs. Dynamic F
ACOUSTIC EXPERIMENT
FREQUENCY (Hz)
104 − 106
10−2 − 10−5
BOREHOLE
10−4 − 10−9
EARTH
10−15
TIME
μs
s - DAYS
HRS -YRS
106 YRS
STRAIN RATE
s-1
10-5 s-1
10-9 s-1
10-14 s-1
mm3
cm3
AFFECTED MASS © 2000 2005 Baker Hughes Incorporated All rights reserved.
100-1000
Efficiency….Data accuracy….People-oriented service
m3
1013 m3 15
www.bakeratlasdirect.com
Causes of Difference between Static and Dynamic Moduli ¾In Dynamic Loading (opposed to static), the micro-mechanisms such as: • grain crushing grain contact parameters • pore collapse • crack sliding • dilatancy are not activated, leading to higher dynamic moduli than static’s equivalents.
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
16
www.bakeratlasdirect.com
Grain Contact Processes
Grain Crushing σ1
σ1
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Shear Sliding σ1
σ1 Efficiency….Data accuracy….People-oriented service
Pore Collapse σ1
σ1 17
www.bakeratlasdirect.com
Crack Processes CLOSING OLD CRACKS
σ1 OPENING NEW CRACKS
SLIDING OLD CRACKS FORMATION OF “WING CRACKS”
σ1
σ1
σ1 σ1
σ1 © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
18
www.bakeratlasdirect.com
Stress Field Sliding Crack TENSION
COMPRESSION
COMPRESSION
TENSION
CRACKS CLOSE CRACKS OPEN “WING” or “TAIL” CRACKS © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
19
www.bakeratlasdirect.com
Total Strain εTOTAL = ε STATIC
= ε MATRIX + ε OPEN CRACKS + ε GRAIN CONTACTS (crushing + pore collapse) + ε SLIDING CRACKS
εELASTIC = εDYNAMIC = εMATRIX + εOPEN CRACKS © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
20
www.bakeratlasdirect.com
Outline 9 Mechanical
behaviors under loading 9 Stratigraphy and rock fabrics 9 Dynamic rock mechanical properties ÎLogging of Mechanical Properties z Empirical correlations z Rock mechanics laboratory
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
21
www.bakeratlasdirect.com
Logging of Mechanical Properties
Logging of Mechanical Properties - E, ν, C….. The evaluation of rock mechanical properties from wireline logs is fundamental to engineering problems associated with wellbore stability, sand production and hydraulic fracturing. © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
Radial Strain
60 Stress [MPa]
22
www.bakeratlasdirect.com
LMP Porosity, Density, Sonic, ....
Strength
12 10 8
Stress (MPa)
Provides estimates for the constitutive parameters
6 4 2 0 -5
0
5
10
15
Strain (mStrain)
Simulates rock mechanical test on fictitious core
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
23
www.bakeratlasdirect.com
Technical Background Challenge: - Establish
a log interpretation routine that estimates rock strength from wireline logs
The approach: Consider the relations between dynamic moduli and static moduli
Input from logs
Leads to strength
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
24
www.bakeratlasdirect.com
Acoustic Behavior Model Idealized model of rock formation as seen by acoustic waves: Pore Space Crack 1. Rock Matrix 2. Solid Pores (spherical) – contributes to porosity, but stiff. 3. Flat Thin Cracks (three orthogonal directions) – provide crack density – does not contribute to porosity, but are compliant. All three contribute to acoustic properties of the material. © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
25
www.bakeratlasdirect.com
Acoustic Behavior Dynamic (Sije) and Static compliance (Sij) are related by:
Sii =
S + Pi e ii
3
1 − ∑ Fij
ε ij = Sijklσ kl
j =1
Sij = Sije − S jj ( Fji + D ji ),
i≠ j
where: Pi are the grain contact parameters Fij are the shear crack sliding parameters Dij are the dilatancy parameters This is the constitutive model developed by SINTEF using the micro-mechanics principles. © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
26
www.bakeratlasdirect.com
Logging of Mechanical Properties (LMP) Vsh
Log Inputs , Vss , Vw , Vhc , ρ , VP , VS
Ideal porous medium model “Effective medium theory” Strip fluid and assume dry frame only, calculate theoretical VP and VS 20 parameters (a1 , a2 , a3 , l1 , l2 , l3 ……….) - basic sand - basic shale - basic chalk
VP , VS from logs. Substitute fluid and determine VP , VS of dry frame Inequality is attributed to microcrack/grain contacts/pore distribution
Theoretical constitutive relations between stress and strain: - microcracks ε = f(σ , ρ , l1 , l2 , l3 , ϕ ……) - grain contacts ε = f(σ , ρ , a1 , a2 , a3 , d ……)
σa
Δ ε = C Δσ εr
εa
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Taking the inequality to extract proportionally the pre-determined parameters
ε = Cσ
Efficiency….Data accuracy….People-oriented service
27
www.bakeratlasdirect.com
Model Calibration Af3 Af0 Af1 Af2 a1 a2 b1 d1 d2 d3 d4 Eg Jg1 h1 n0 n1 PSRAT, RV p1 p2 p3 p4 p5 T0 Gs Ks s φc
Sliding crack coefficient Basic sliding crack coefficient Porosity impact on sliding crack coefficient Crack density impact on sliding crack coefficient General failure parameter General failure parameter Wing crack coefficient Compaction constant for dilatancy parameter Dilation constant for dilatancy parameter Porosity impact on dilatancy exponent Stress impact exponent Pore collapse parameter Porosity impact on pore collapse Grain rotation coefficient Basic crack density exponent Porosity impact on n Ratio between dry P- and S-wave velocity Porosity impact on grain contact mechanism Crack density impact on grain contact mechanism Stress impact on grain contact mechanism Stress history impact on grain contact mechanism Stabilizing parameter for grain contact mechanism Tensile strength parameter Shear modulus of solid material Bulk modulus of solid material Dilatancy parameter Critical porosity
© 2000 2005 Baker Hughes Incorporated All rights reserved.
% Calibration data for sandstone 1.8E-9 p1 1.1E-9 p2 0.31e-6 p3 1.67 p4 1.0E6 p5 0.05 n0 0.05 n1 5.0E6 T0 7.3e-3 Af0 1.7 Af1 0.0 Af2 1.0E6 S 3.0 b1 400.0 h1 3.25 d1 6.0 d2 0.2 d3 0.8 d4 200e6 a1 10 a2 0.0 Af3 0.45 phic 40.01e9 GS 35.01e9 KS 1.5 PSRAT 1000.0E9 JG1 4.3 EG
Efficiency….Data accuracy….People-oriented service
28
www.bakeratlasdirect.com
Logging of Mechanical Properties Log Inputs Dtc, Dts, Porosity, Lithology, Saturations Produces Virtual Core Sample
σa Produce StressStrain Curves
σr σa
Applying Virtual Stresses to the “Core Sample”
εr
εa
Static Mechanical Properties: Rock Strength, Elastic Moduli Poisson’s Ratio, Compressibilities © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
LMP Procedure The input data to LMP are obtained from: • logs (provided by the user for each well) • lithology dependent calibration data (built-in) Calibration data - determined from rock mechanical tests where both static and dynamic measurements are made. • The model numerically simulates loading in small steps • At each step, the model quantities are updated • Process is repeated until failure (stress/strain level is reached). © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
30
www.bakeratlasdirect.com
LMP Log input data Poor quality in => Poor results High Intermediate Low
Note: the resolution of LMP is limited by the resolution of the sonic log!
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Curve
Description
Unit
Column 1:
DEPTH
Measured depth
[m]
Column 2:
TVD
True vertical depth
[m]
Column 3:
VSS
Relative volume of sand or chalk
Column 4:
VSH
Relative volume of shale
Column 5:
VW
Relative volume of water
Column 6:
VH
Relative volume of hydrocarbons
Column 7:
KH
Bulk modulus of hydrocarbons
[GPa]
Column 8:
RHOH
Density of hydrocarbons
[g/ccm]
Column 9:
RHOB
Bulk density
[g/ccm]
Column 10: DTP
Compressional slowness
[us/ft]
Column 11: DTS
Shear slowness
[us/ft]
Column 12: SIGV
Vertical stress
[MPa]
Column 13: PPORE
Pore pressure
[MPa]
Column 14: SIGH
Horizontal stress
[MPa]
Column 15: LMP
Calibration data set
Efficiency….Data accuracy….People-oriented service
31
www.bakeratlasdirect.com
Sample of LMP Log input data
DEPTH
TVD
VSS
VSH
VW
VH
KH
2460.739 2460.820 2460.901 2460.983 2461.063 2461.145 2461.226 2461.307 2461.388 2461.469 2461.550 2461.631 2461.712 2461.793 2461.875 2461.956
2430.73 2431.82 2431.90 2431.98 2432.06 2432.14 2432.22 2432.30 2432.38 2432.46 2432.55 2432.63 2432.71 2432.79 2432.87 2432.95
0.678 0.682 0.680 0.683 0.682 0.681 0.681 0.682 0.669 0.672 0.672 0.687 0.688 0.689 0.657 0.631
0.005 0.000 0.002 0.000 0.000 0.000 0.000 0.000 0.017 0.018 0.017 0.000 0.001 0.000 0.035 0.066
0.015 0.015 0.015 0.015 0.014 0.014 0.014 0.014 0.014 0.013 0.015 0.013 0.012 0.012 0.012 0.012
0.302 0.303 0.303 0.302 0.304 0.305 0.305 0.304 0.300 0.297 0.296 0.300 0.299 0.299 0.296 0.291
0.670 0.670 0.670 0.670 0.670 0.670 0.670 0.670 0.670 0.670 0.670 0.670 0.670 0.670 0.670 0.670
© 2000 2005 Baker Hughes Incorporated All rights reserved.
RHOH RHOB DTP 0.800 0.800 0.800 0.800 0.800 0.800 0.800 0.800 0.800 0.800 0.800 0.800 0.800 0.800 0.800 0.800
2.010 2.009 2.008 2.009 2.008 2.006 2.006 2.008 2.016 2.025 2.022 2.018 2.023 2.021 2.028 2.039
DTS
97.870 181.68 101.28 183.67 106.57 187.14 111.09 192.10 114.28 196.99 115.32 200.13 114.35 200.58 113.55 199.64 114.14 199.09 115.27 198.68 114.98 198.05 113.35 197.84 112.87 199.07 114.05 202.95 115.19 206.40 114.95 205.64
Efficiency….Data accuracy….People-oriented service
SIGV PPORE SIGW LMP 36.179 36.181 36.183 36.184 36.186 36.187 36.189 36.191 36.192 36.194 36.195 36.197 36.199 36.200 36.202 36.203
24.11 24.11 24.11 24.1 8 24.18 24.19 24.12 24.12 24.12 24.12 24.12 24.12 24.12 24.12 24.12 24.12
24.15 24.11 24.11 24.11 24.11 24.11 24.12 24.12 24.12 24.12 24.12 24.12 24.12 24.12 24.12 24.12
12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12
32
www.bakeratlasdirect.com
Control Parameters for LMP Description CONFP C1 C2 CLIM PORFAC WD
Default value
Confining pressure Lower calibration mixing limit Upper calibration mixing limit Limit for use of empirical calibration Controls porosity correction Water depth
5 0.15 0.4 1 0 0
Low
High
0 0 0 0 0 0
200 1 1 1 1 1E6
Units MPa
m
LMP data = IJ z IJ = 1-9, single calibration table z IJ = 11-98, mix calibration from calibration table I and J – C = vI/(vI+vJ) • C <= C1 : Lithology I calibration is used • C >= C2 : Lithology J calibration is used • C1 < C < C2 : Calibration data for lithology I and J is linearly mixed • C > CLIM: Empirical formula © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
33
www.bakeratlasdirect.com
Sample of control parameters
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
34
www.bakeratlasdirect.com
LMP Procedure – Shale Porosity z
Porosity corrections in shaly formations – If only effective porosity is present (PORFAC=1)
Δφ p R =0.05 0.05 , clay ⋅V V
| Δφ Δφ= S =f f(V(V ), ) | Δφ T =0.50⋅.V5V, cl
p
p , satp , sat cl
p
f (V p ,sat ) < 0.05 0.05 < f (V p ,sat ) < 0.5 f (V p ,sat ) > 0.5
clay
f (V p ,sat ) = e0 + e1V p ,sat + e2V p2,sat + e3V p3,sat
Vclay= shale/clay volume
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
35
www.bakeratlasdirect.com
LMP Procedure – Strength Correlation Empirical correlation for strength of shale material if C > CLIM:
vss ⎛ vsh ⎞ DTSc = DTC ⎜ Rsh + Rss ⎟ vsh + vss ⎝ vsh + vss ⎠ −3 −5.0
UCS = 1.05 ⋅10 ( DTSc ⋅10 ) -3
Rsh and Rss are the tabulated
Vp Vs
ratios for shale and sandstone respectively.
Mason (1987) © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
36
www.bakeratlasdirect.com
LMP – Output Parameters ) ) ) ) ) ) ) ) )
Compressive strength Young’s modulus Poisson’s ratio Shear modulus Bulk modulus (triaxial) Bulk modulus (hydrostatic) Internal friction angle Cohesive strength Biot’s constant
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Compressive Strength Comparison: LMP vs. Lab (deepwater GoM ex. 1) LMP1
LMP2
LMP3
LMP4
Lab1
Lab2
Lab3
Lab4
GR
GR [API] 0
20
40
60
80
100
120
140
Depth
Curve colors Blue= conf. press. #1 = unconfined Pink = conf. press. #2 Yellow = conf. press. #3 Turquiose = conf. press. #4
0
5000
10000
15000
20000
25000
Compressive Strength [psi] © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
30000
35000
38
www.bakeratlasdirect.com
Compressive Strength Comparison: LMP vs. Lab (deepwater GoM ex. 2) LMP1
LMP2
LMP3
LMP4
Lab1
Lab2
Lab3
Lab4
GR
GR [API] 20
40
60
80
100
120
140
160
180
200
Depth
0
Curve colors Blue= conf. press. #1 = unconfined Pink = conf. press. #2 Yellow = conf. press. #3 Turquiose = conf. press. #4
0
5000
10000
15000
Compressive Strength [psi] © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
20000
25000
39
www.bakeratlasdirect.com
Young’s Modulus Comparison: LMP vs. Lab (deepwater GoM ex. 1) LMP1
LMP2
LMP3
LMP4
Lab1
Lab2
Lab3
Lab4
GR
GR [API] 0
20
40
60
80
100
120
140
160
Depth
Curve colors Blue= conf. press. #1 = unconfined Pink = conf. press. #2 Yellow = conf. press. #3 Turquiose = conf. press. #4
0
0.5
1
1.5
2
2.5
Young's Modulus [MMpsi] © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
3
3.5
4
40
www.bakeratlasdirect.com
Young’s Modulus Comparison: LMP vs. Lab (deepwater GoM ex. 2) LMP1
LMP2
LMP3
LMP4
Lab1
Lab2
Lab3
Lab4
GR
GR [API] 20
40
60
80
100
120
2.5
3
Depth
0
Curve colors Blue= conf. press. #1 = unconfined Pink = conf. press. #2 Yellow = conf. press. #3 Turquiose = conf. press. #4
0
0.5
1
1.5
2
Young's Modulus [MMpsi] © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
41
www.bakeratlasdirect.com
Strength Prediction
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
42
www.bakeratlasdirect.com
Young’s Modulus Prediction
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
43
www.bakeratlasdirect.com
MOHR CIRCLES σ1 = 2So tan α + σ3 tan 2 β π φ β= + 4 2 With two Mohr’s circles, we have two equations relating internal friction angle (Φ) and cohesion (So) with σ1 and σ3. Therefore, with known stress conditions we can solve for the two Mohr Coulomb parameters!
© 2000 2005 Baker Hughes Incorporated All rights reserved.
⎛ ⎡ σ 1 a − σ 1b 1 − φ = 2⎜ tan ⎢ ⎜ ⎣ σ 3a − σ 3b ⎝ So =
⎤ π⎞ ⎥ − ⎟⎟ ⎦ 4⎠
1 [(σ1a + σ1b ) − (σ3a + σ3b ) tan 2 β] 4 tan β
or So =
UCS 2 tan β
Efficiency….Data accuracy….People-oriented service
44
www.bakeratlasdirect.com
MOHR CIRCLES
Shear Stress [MPa]
30 Confining pressure is 10 MPa
Strength is 41 MPa Friction angle
20
10
0
0
10
20
30
40
50
Confining Pressure [MPa] © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
45
www.bakeratlasdirect.com
LMP - Rocktest Program that uses well logging data to determine the formation’s stress-strain behaviors as well as the axial and radial acoustic velocities, based on static elastic properties (complement to LMP). … as with LMP, Rocktest is based on the FORMEL model, which describes the collective micro-structural behaviors of rock constituents during stress loading.
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
46
www.bakeratlasdirect.com
LMP - Rocktest What do we need to run Rocktest? INPUT DATA Æ MD, TVD, Δtc, Δts, lithology, mineral volumes, bulk density, water and hydrocarbon saturations, σH, and σV . ¾
¾ CONTROL PARAMETERS Æ Mixing limits (C1 and C2), empirical limit (CLIM), Outputon filethe (OUTPTFIL), … asrelationship LMP, Rocktest is based Porosity correction control (PORFAC), confining FORMEL model, which describes thepressure (SIGC), and processing depth (TSTDEPTH), request collective micro-structural behaviors of for parameters listing (VERBOSE), water depth (WD), and rock constituents during stress loading. calibration table file names (LMPTAB).
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
47
www.bakeratlasdirect.com
Rocktest – Input Data Hydrocarbon Properties
Depth
DEPTH 4460 4460.152 4460.305 4460.457 4460.61 4460.762 4460.914 4461.067 4461.219 4461.372 4461.524 4461.676
TVD 2456.356 2456.427 2456.498 2456.569 2456.64 2456.711 2456.782 2456.853 2456.924 2456.995 2457.066 2457.137
VSA 0.999 0.999 0.999 0.999 0.9217 0.9264 0.9436 0.9822 0.9985 0.9723 0.8926 0.8014
VSH 0 0 0 0 0 0 0 0 0 0 0 0
VW 0.001 0.001 0.001 0.001 0.061 0.0567 0.05 0.0178 0.0015 0.0277 0.047 0.0489
Volumetrics
© 2000 2005 Baker Hughes Incorporated All rights reserved.
VOIL 0 0 0 0 0.0173 0.0169 0.0064 0 0 0 0.0604 0.1497
KOIL 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8
HCDE 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7
Acoustic Slowness
DEN 2.5535 2.5556 2.5527 2.5461 2.5415 2.5491 2.5814 2.6256 2.6486 2.593 2.4621 2.3579
DTC 77.8283 77.6383 73.4818 71.5991 67.9204 67.3749 68.064 68.2664 74.7734 65.0705 91.1018 92.6543
DTS 143.7192 139.924 136.8492 136.9608 135.5699 143.9718 138.9534 135.4932 132.7831 133.2914 140.8076 141.6646
Bulk Density
Efficiency….Data accuracy….People-oriented service
Calibration
SIGV 52.12252 52.12415 52.12578 52.1274 52.12903 52.13066 52.13229 52.13392 52.13554 52.13717 52.1388 52.14043
PP 35.71542 35.71645 35.71748 35.71851 35.71954 35.72057 35.72161 35.72264 35.72367 35.7247 35.72573 35.72677
SIGH 43.86157 43.86301 43.86445 43.86589 43.86733 43.86877 43.87022 43.87166 43.8731 43.87454 43.87598 43.87742
LMP 12 12 12 12 12 12 12 12 12 12 12 12
Stress Field
48
www.bakeratlasdirect.com
Rocktest – Output File Radial Strain mStrain 0 0.01187 0.02359 0.03517 0.04661 0.0579 0.06906 0.08009 0.091 0.10177 0.11243 0.12297 0.13339 0.14369
Axial Confining Axial Radial-P Axial-P Radial-S Axial-S Strain Pressure Stress Velocity Velocity Velocity Velocity mStrain MPa MPa m/s m/s m/s m/s -0.00394 0.05 0.05 2085.349 3147.419 1417.535 1694.329 0.00404 0.1 0.1 2093.867 3153.143 1421.319 1697.517 0.01193 0.15 0.15 2102.312 3158.791 1425.077 1700.675 0.01972 0.2 0.2 2110.682 3164.366 1428.807 1703.801 0.02742 0.25 0.25 2118.98 3169.869 1432.509 1706.896 0.03503 0.3 0.3 2127.203 3175.302 1436.183 1709.96 0.04255 0.35 0.35 2135.354 3180.665 1439.83 1712.995 0.04998 0.4 0.4 2143.431 3185.962 1443.449 1716 0.05733 0.45 0.45 2151.436 3191.193 1447.04 1718.976 0.0646 0.5 0.5 2159.369 3196.36 1450.603 1721.923 0.07179 0.55 0.55 2167.23 3201.463 1454.139 1724.841 0.07891 0.6 0.6 2175.019 3206.506 1457.646 1727.731 0.08594 0.65 0.65 2182.737 3211.488 1461.126 1730.594 0.09291 0.7 0.7 2190.385 3216.411 1464.578 1733.429
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
49
www.bakeratlasdirect.com
Rocktest – Output File 180 160 Radial
140
Axial
Stress (MPa)
120 100 80 60 40
hydrostatic state of stress
20 0 -6
-4
-2
0
2
4
6
8
10
12
Strain (mstrain)
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
50
www.bakeratlasdirect.com
LMP Capabilities z
z
z
z
z
Predicts static properties from logs @ any given confining pressure Generates complete stress-strain curves Only one available in market Used for drilling, completion and subsidence/compaction studies Independently validated using laboratory results
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
51
www.bakeratlasdirect.com
Outline 9 Mechanical
behaviors under loading 9 Stratigraphy and rock fabrics 9 Dynamic rock mechanical properties 9 Logging of Mechanical Properties ÎEmpirical correlations z Rock mechanics laboratory
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
52
www.bakeratlasdirect.com
Lacy’s (1997) Empirical Correlations* Dynamic Young’s Modulus: E d [10 6 psi ] = 0.265 * (Vp ) 2.04
E d [10 6 psi ] = 59100 /( Δt C ) 2.17
E d [10 6 psi ] = 11300ρ b / (Δt C ) 2
Vp = compressional velocity [km/s] Δtc = compressional slowness [μsec/ft] ρb = bulk density [g/cm3]
Conversion from dynamic to static Young’s moduli: E[10 6 psi ] = 0.018E d + 0.422E d 2
Unconfined Compressive Strength: UCS[ksi ] = 0.2787E 2 + 2.458E *Lacy’s (1997- SPE 38716) correlations were developed based on lab testing of over 600 samples of sandstones, shales, limestones and dolomites. © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
53
www.bakeratlasdirect.com
Lal’s (1999) Empirical Correlations* Internal Friction Angle and Cohesion: φ[radians] = sin −1 (Vp − 1) /(Vp + 1) So [MPa ] = 5(Vp - 1)/ (Vp )
Vp = compressional velocity [km/s]
Unconfined Compressive Strength: UCS = 2So tan(45 + φ/2)
*Lal’s (1999- SPE 54356) correlations were developed for shales ONLY. Caution should be exercised if applying this correlation to other lithologies! © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
54
www.bakeratlasdirect.com
Coates & Denoo’s (1981) Empirical Correlation Unconfined Compressive Strength: UCS [MPa ] = 1.9 ×10-20 ρ b Vp ((1 +ν d )/(1 -ν d )) 2 (1 - 2ν d )(1 + 0.78Vclay ) 2
4
Vp = compressional velocity [km/s] Vclay = clay volume [fraction] ρb = bulk density [kg/m3] νd = dynamic Poisson’s ratio
*Coates & Denoo’s (1981) correlation was developed for sandstones & shales ONLY. © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
55
www.bakeratlasdirect.com
Mason’s (1987) Empirical Correlation Unconfined Compressive Strength: UCS[psi ] = 1.2 * (1000/Δt s ) 4 + 60.5 * (1000/Δt s ) 2
Δts = shear slowness [μsec/ft]
If Δts is not available, use Δtc and Δts/ Δtc ratio (based on lithology) in the following expression: UCS[psi ] = 1.2 * (1000/ (Δt c * ratio )) + 60.5 * (1000/ (Δt c * ratio )) 4
2
Δtc = compressional slowness [μsec/ft] ratio = Δts/Δtc *Mason’s (1987- SPE 13256) correlations were developed using tables of rock properties from Wuerker (SPE 663). © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
56
www.bakeratlasdirect.com
Mason’s (1987) Empirical Correlation Lithology anhydrite basalt chalk chert clay claystone diabase diorite dolomite epidosite gabbro gneiss granite gypsum hornstone limestone (clean) limestone (silty) limestone (argillaceous) marble mudstone pyrite quartzite quartzite salt sandstone (clean) sandstone (silty) sandstone (argillaceous) shale siltstone © 2000 2005 Baker Hughes Incorporated All rights reserved.
DTS/DTC 2.45 1.55 2.45 1.60 3.20 1.90 1.70 1.75 1.80 1.70 1.60 1.80 1.70 2.45 1.85 1.90 2.10 2.30 1.80 1.85 1.70 1.55 1.50 2.15 1.60 1.70 1.85 1.75 1.80
For mixed lithologies, use: Δts/Δtc ratio (composite) = ratio1*V1 + ratio2*V2…..+ ration*Vn
Efficiency….Data accuracy….People-oriented service
57
www.bakeratlasdirect.com
UCS Empirical Correlations – (Sandstone)
After Chandong Chang 2004
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
58
www.bakeratlasdirect.com
UCS Empirical Correlations – (Shale)
After Chandong Chang 2004
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
59
www.bakeratlasdirect.com
Outline 9 Mechanical
behaviors under loading 9 Stratigraphy and rock fabrics 9 Dynamic rock mechanical properties 9 Logging of Mechanical Properties 9 Empirical correlations ÎRock mechanics laboratory
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
60
www.bakeratlasdirect.com
Triaxial Compression Tests Test Apparatus
Stress-Strain Curves
Axial Strain measurement
Axial Differential Stress
Axial Stress
Confining Pressure inlet
Seal Radial Strain measurement
Confining Pressure outlet Pore Pressure control
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Radial Strain
Efficiency….Data accuracy….People-oriented service
Axial Strain
61
www.bakeratlasdirect.com
Strength & Static Elastic Moduli F
STATIC LABORATORY TEST RESULTS
dx {
Axial Differential Stress Compressive Strength
UNDEFORMED
Linearly elastic
Poisson’s ratio (ν) = -Δεr/Δεa
Δσa
Δσa Δεr
Radial Strain εr (extension) © 2000 2005 Baker Hughes Incorporated All rights reserved.
DEFORMED
Δεa
Young’s Modulus (E) = Δσa/Δεa
Axial Strain εa (contraction)
Efficiency….Data accuracy….People-oriented service
62
www.bakeratlasdirect.com
Failure Strength Parameters Different Types of Compression Tests • Triaxial Compression Test (Unconfined Compressive Strength, UCS)
• Hole Collapse Test (Hole Collapse Strength, HCS) σc
σa
σc
σc
σc
σc
σa © 2000 2005 Baker Hughes Incorporated All rights reserved.
σc
Efficiency….Data accuracy….People-oriented service
63
www.bakeratlasdirect.com
Hollow Cylinder Test
Confining pressure
Also called a hole-collapse test. Picture of a failed specimen (Ref: Ewy et al., 2001, SPE 75328)
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
64
www.bakeratlasdirect.com
Hollow Cylinder Test σc
Typical Test Details:
1.5-inch diameter specimen σc 0.5-inch diameter hole through the center Length – 2 to 3 inches Cylindrical steel end caps σc Jacketed with a thin, heat-shrink teflon Interior of the 0.5-inch diameter hole left empty Confining pressure is applied all around
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
σc
65
www.bakeratlasdirect.com
Hollow Cylinder Test – A Test Result
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
66
www.bakeratlasdirect.com
Relating HCS to UCS σc
C1 = HCS * {( 2c ) cos( 13 )cos -1d }- 1.0833 c = .42361 +
11.4375
η
2.84375 +
76.7819
d= c{−22.8749 −
617 .625
η
© 2000 2005 Baker Hughes Incorporated All rights reserved.
σc
σc
σc SPE 75328
η
4 tan φ (9 − 7 sin φ ) η= (1 − sin φ ) 2
Di 1 = Do 3
HCS = Hole-Collapse Strength
} C1 = Modified Lade strength – from HCS c, d, = groups of terms, dimensionless η = Modified Lade friction parameter Φ = internal friction angle
Efficiency….Data accuracy….People-oriented service
67
www.bakeratlasdirect.com
Relating HCS to UCS HCS is related to UCS (from triaxial compression test):
S1 = nC1
σc
n ≤1 So = S1 tan φ φ UCS = 2So tan(45 + ) 2
σc
σc
S1 = Modified Lade strength parameter C1 = Modified Lade strength, includes all the strengthening effects (nonlinear deformations, nonconstant moduli, intermediate stress)
σc
n = factor to adjust strength downward for wellboresize holes
SPE 75328
So= Mohr-Coulomb cohesion
SPE 56862
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
68
www.bakeratlasdirect.com
Effects of Borehole Size on Rock Strength
(Hoek and Brown,1980)
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
69
www.bakeratlasdirect.com
Effects of Borehole Size on Rock Strength
(Ηerrick 1994) © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
70
www.bakeratlasdirect.com
In-Situ Stress Characterizations
Outline I. II. III. IV.
Introduction to subsurface stresses Overburden calculation Horizontal stress determination techniques Summary
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline I. II. III. IV.
Introduction to subsurface stresses Overburden calculation In-situ stress determination techniques Summary
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Subsurface Stresses Rocks in the subsurface are subjected to compressive stresses* due primarily to Gravity and Tectonic forces! x y
σv
z
σv = Overburden Stress σH = Max. Horizontal Stress σh = Min. Horizontal Stress σH
σh NOTE: σH > σh
These arise due to weight of overburden, confinement, tectonic forces, temperature, pore fluid pressure, diagenesis, etc.
Generally Accepted Assumptions: 1) The overburden is a principal stress which acts perpendicular to
the Earth’s surface. 2) 3 major principal stresses (σv, σH, σh) are orthogonal. 3) Rocks conform to the requirements of the Theory of Elasticity (linearly elastic, homogeneous continuum, etc.).
* The Geomechanics sign convention for stress is compression = positive, tension = negative © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Subsurface Stress Regimes* NORMAL FAULTING
σ1 = σv
•Tensile regions •High-angle faults
STRIKE-SLIP FAULTING
σ2 = σv
•Shearing regions •High-angle, lateral faults
σ3
σ3
σ3 = σv σ1
φf ≈ 60º
σ2 σ1
THRUST FAULTING
φf ≈ 30º
footwall *(after Anderson, 1951) © 2005 Baker Hughes Incorporated All rights reserved.
hanging wall
•Compressive regions •Low-angle faults
σ2
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stress Profiles Profiles-- example Note: In some cases, the horizontal stresses may exceed vertical stress at shallow depths.
Depth
σv
Stresses typically diverge with depth increase (unless an overpressured zone is encountered).
σH σh
However, at great depth the stresses converge until the stress contrast disappears as the stresses become hydrostatic (after Breckels and van Eeklen 1982).
MUD PRESSURE PORE PRESSURE Pressure/Stress © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stress Profile Variations Horizontal Stresses are sensitive to: • LITHOLOGY • MECHANICAL PROPERTIES • PORE PRESSURE
Note: Pore pressure is depicted in a separate track! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stress Determination Techniques In-situ Stress Measurement Techniques Method (Category)
Hydraulic
Relief
Jacking Strain recovery Borehole breakout
Others
Name Hydraulic Fracturing Sleeve Fracturing Hydraulic test on preexisting fractures (HTPF) Surface relief methods Undercoring Borehole relief methods (overcoring, slotting, etc.) Relief of large rock volumes Flat jack Curved jack
Measurement Location b b b
Advantages Measurements in existing holes, accurate, quick.
Limitations
Primary Usage
2D only HTPF requires many test on existing fractures
Oil Industry, geological survey
s c b
Inexpensive, highly developed technique
Difficult to install gages
Mining, civil, defense
Inexpensive, easy
gages susceptible to conditions
Civil
Suitable for great depths
Results may be unreliable (sensitive to several factors)
Oil industry, civil
Accurate, quick
Restricted to info on est. breakout width (reduces accuracy)
Oil industry, geological survey
s s s
Anelastic Strain Recovery (ASR) Differential Strain Curve Analysis (DSCA) Image log analysis
b
Oriented caliper analysis
b
c c
Fault slip analysis l Low cost Results give only a Earthquake focal Oil industry, geological l rough estimate mechanisms survey Geological structures l Low cost Acoustic methods b,c Easy Results unreliable Bulk density log Data not always b Easy Oil industry available to surface integration Key: b = borehole, c = core, l = large scale geological structures, s = surface rock measurements
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
Denotes topics to be covered here.
A summary of all of these methods can be found in Amadei and Stephannson (1997).
www.bakeratlasdirect.com
Outline I. II. III. IV.
Introduction to subsurface stresses Overburden calculation Commonly used stress determination techniques Summary
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Overburden ((σ σv) Calculation dw
z
σv = ∫0 ρw g dz + ∫dw ρb gdz = weight of overburden where
ρb = bulk density of sediments = ρmatrix (1-φp) + ρpf φ ρmatrix = density of rock matrix ρw = density of seawater ρpf = density of pore fluid
dw
φp = total porosity
sf
z ds
g = gravitational constant ds = vertical depth of sediments dw = depth of water
Depth of interest © 2005 Baker Hughes Incorporated All rights reserved.
z = true vertical depth = dw + ds sf = sea floor
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
σv Calculation However……….bulk density data is rarely available from surface to depth of interest!
Usually requires one (or more) of the following: • estimating bulk density in region above measured data • use of acoustic data which is transformed to bulk density data in region above measured data (when available) • use of empirical formulas (may be region specific) to estimate ρb or σv
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Useful Bulk Density ((ρ ρ b) Transformations 1. Gardner (1974) ⎛ 10 ⎞ ⎡ g ⎤ ⎟⎟ ρ b ⎢ 3 ⎥ = 0.23⎜⎜ ⎣ cm ⎦ ⎝ Δt c ⎠ 6
0.25
where Δtc= measured interval travel time of compressive wave [μs/ft]
2. Ludwig et al. (1970)
⎡ g ⎤ ρ b ⎢ 3 ⎥ = 1.27 Vp − 0.28Vp2 + 0.0232Vp3 ⎣ cm ⎦
3. Bellotti & Giacca (1978) ⎛ Δt c − Δt c ( mx ) ⎞ ⎡ g ⎤ ⎟ ρ b ⎢ 3 ⎥ = ρ mx − 1.228(ρ mx − ρ f )⎜⎜ ⎟ t t Δ + Δ ⎣ cm ⎦ ( ) c c f ⎠ ⎝
4. Miller ρ = ρ matrix (1 − φ ) + ρ wφ © 2005 Baker Hughes Incorporated All rights reserved.
where Vp= compressive acoustic velocity [km/s]
where ρmx = matrix density (assume 2.75 g/cm3), ρf = pore fluid density (assume 1.03 g/cm3), and Δtc is the measured interval transit time, Δtc(mx) is the matrix transit time (assume 53 μs/ft) and Δtc(f) is the pore fluid transit time (assume 200 μs/ft).
φ = porosity , fraction ρ w = Water Density → 1.03 g / cc
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
ρb Estimation - Example WL Dens
Gardner
Ludwig
2.8
2.7
Gardner and Ludwig yield different densities in the vicinity of the mudline!
2.6
Bulk Density [g/cc]
2.5
2.4
2.3
2.2
2.1
Trend matches well with WL dens in this region.
2.0
1.9
1.8
Trend does not match as well with WL dens in this region (appears to be depth shift issue) Depth Below Mudline
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
σv Calculation - Quiz What is the overburden pressure at point A, B,C and D? 1 ρw = 1.074 g/cm3
A B
2 ρb(avg) = 1.95 g/cm3
g/cm3
600 feet
1200 feet
4 ρb(avg) = 2.25 g/cm3
D
Weight block 1 = 0.052*8.33*1.074*1000 = 465 psi Weight block 2 = 0.052*8.33*1.95*600 = 507 psi Weight block 3 = 0.052*8.33*2.10*1200 = 1092 psi Weight block 4 = 0.052*8.33*2.25*2400 = 2340 psi
3 ρb(avg) = 2.1
C
1000 feet
2400 feet
Not to scale!
© 2005 Baker Hughes Incorporated All rights reserved.
Solution P [psi] = ρgd = 0.052*8.33*sg*d [ft]
At pt. A: p = weight block 1 = 465 psi (0.465 psi/ft) At pt. B: p = weight block 1+2 = 465 + 507 = 972 psi (0.61 psi/ft) At pt. C: p = weight block 1+2+3 = 465+507+1092 = 2064 psi (0.74 psi/ft) At pt. D: p = weight block 1+2+3+4 = 465+507+1092+2340 = 4404 psi (0.85 psi/ft)
NOTE: OBG increases with depth and gradually approaches 1.0 psi/ft! Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Water Depth Effect σv Profile
OBG decreases with increasing water depth!
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Salt Effect σv Profile
Water OBG in absence of salt layer! OBG reduced due to thick salt layer!
Salt
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Published σv Correlations Vertical Stress Formulation σv [psi] = 0.465dw + 1.13ds - 3188.36 (1-exp[-8.5e-5ds]) σv [MPa] = (1.9 ± 1.31) + (0.0339 ± 0.0067)d σv [MPa] = (0.942 ± 1.26) + (0.0266 ± 0.0028)d σv [MPa] = 0.027d σv [MPa] = 0.0265d σv [MPa] = 0.026d – 0.0324d σv [MPa] = (0.0266 ± 0.008)d OBG [psi/ft] = OBO + 2.46e-5d - 1.79e-9 d2 + 6.6e-14 d3 – 5.97e-19 d4 σv [MPa] = (0.0275 - 0.0284)d σv [MPa] = 0.0285d σv [MPa] = 0.027d σv [MPa] = (0.0275 - 0.0284)d σv [MPa] = 0.233 + 0.024d σv [ppg] = (8.5dw + (16.3+( ds /3125)0.6)ds) / d σv [ppg] = (8.55dw + 5.3ds1.1356) / d σv [MPa] = 9e-7ds2 + 0.0187ds + 0.0101dw
Location and Depth Range (where available) Coastline GoM (ft) World (0-2400 m) North America Land (0-1500 m) World Data (0-3000m) World Data (100-3000m) Can. shield (0-2200m) Can. shield (0-2000m) GoM (ft) KTB pilot hole (800-3000m) Can. shield (0-2300m) Japan (0-1200m) KTB pilot hole (0-9000m) So. Korea (0-850m) GoM (ft) GoM (ft) North Sea (m)
References Eaton (1969) Hegret (1974) Lindner & Halpern (1977) Brown & Hoek (1978) McGarr & Gay (1978) Herget (1987) Arjang (1987) Bryant (1989) Baumgarten et al. (1993) Hegret (1993) Sugawara & Obara (1993) Te Kamp et al. (1993) Lim & Lee (1995) Traugott (1997) Barker and Wood (1998) Svennekjaer & Bratli (1998)
Note: dw = water depth, ds = sediment depth (dbml), d = true vertical depth OBO = overburden offset (land=0.87, shallow water=0.85, deepwater=0.82)
NOTE: These should only be used as a last resort! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline I. II. III. IV.
Introduction to subsurface stresses Overburden calculation In-situ stress determination techniques Summary
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Typical Log -Based σh Estimation Log-Based Conventional Log-based Methods for Determining the Minimum Horizontal Stress (σh) Magnitude: • Uniaxial strain method (no horizontal strain and vertical stress is due to gravity alone) in a tectonically inactive basin (Anderson et al. 1973 and others):
σh = ν/(1-ν)(σV- αPp)+αPp
• Uniaxial strain method in a tectonically active basin (Gatens et al. 1990):
σh = ν/(1−ν)(σV- αPp)+αPp+ σT
where σT is an additional “tectonic” stress used for calibration from measured stress data such as LOT, DIF’s, etc. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Conventional Hydraulic Fracturing Hydraulic fracturing is a great source of information about in-situ stress, formation leak-off properties, and rock permeability (transmissivity).
Several hydraulic fracturing methods available: • Pump-in / decline tests (LOT, XLOT, mini-fracs) • Step-rate injection tests • Pump-in / flow-back tests Most hydraulic fracturing methods assume the following: • Rock is linearly elastic
• Borehole is vertical (within ~ 30º→ parallel to a major principal stress axis) • Overburden stress acts vertically downward and is the maximum in-situ stress (σ1) • Induced hydraulic fractures are vertical © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Fracture Orientation - Normal Stress Field Fracture plane is vertical and parallel to the strike of the fault!
re Fractu pl ane
σ1 = σv
σ2 = σH
σ3 = σh
Hydraulic fracture slide modified from Dusseault (2003)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Fracture Orientation – Strikeslip Faulting
tur c a Fr
la ep
ne
Fracture plane is vertical and sub-parallel (25º-30º) to the strike of the fault!
Hydraulic fracture
σ2 = σv σ3 = σh σ1 = σH © 2005 Baker Hughes Incorporated All rights reserved.
slide modified from Dusseault (2003) Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Fracture Orientation – Thrust Faulting
Hydraulic fracture F
ne a l p re u t c a r
φ Fracture plane is horizontal! σ3 = σv
σ1 = σH
σ2 = σh slide modified from Dusseault (2003)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Conventional Hydraulic Fracturing Tests Summary HF Test Method
Pump-in / decline type tests
HF Test Name
Applications
Test Specifications
LOT / XLOT
test cement/rock integrity, determine max. safe MW, stress measurement
Flow rate: 0.25-2.0 BPM Volume pumped: 10-20 bbls Interval length tested: 10-20'
Mini-frac / Microfrac
Pump -in / decline
Formation Type
Test Application
any
during drilling
stress measurement and Flow rate: 0.25-25 gpm Volume pumped: 0.5-2.5 bbls Interval leakoff coefficient length tested: 3-15' estimation
permeable
prior to hyd. frac.
stress measurement and leakoff coefficient estimation
Flow rate: 5-25 BPM Volume pumped: 50-100 bbls Interval length tested: 20-50'
permeable
prior to hyd. frac.
low perm.
prior to hyd. frac.
Pump-in/flow back
Pump-in/flow back
stress measurement
Q inj.: 1-10 BPM Q flowback= (1/6 - 1/4) Q inj Volume pumped: 2-5 bbls Interval length tested: 10-20'
Step rate
Step rate
stress measurement
Q inj: 0.25-20 BPM Volume pumped: 10-80 bbls Interval length tested: >50'
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
large interval (several prior to hyd. frac. formations)
www.bakeratlasdirect.com
L eak O ff T est Leak Off Test For the driller, the primary objectives of a LOT are: Test the integrity of the casing cement job near the casing shoe Determine the maximum MW that can be withstood by the formation before initiating a hydraulic fracture
For the geomechanical engineer, the primary objective of a LOT is: Create a “small” hydraulically-induced fracture in the rock for stress estimation LOT – pressure up to formation breakdown XLOT – same as LOT but continue pumping after formation breakdown to propagate the fracture © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Typical Single Cycle XLOT
σh
σH cement formation breakdown
shut-in frac prop frac. closure press.
Flow rate
Rathole typically 10 – 20 feet!
Pressure
LOP
Flow rate (Q) typically between 0.25 – 1.0 BPM (constant throughout test) Time
Flow rate © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
Press.
www.bakeratlasdirect.com
Typical LOT Pressure Response 1000
0.50
800
Pressure (psi)
0.45
Pressure Pump rate
0.40
700
0.35
600
0.30
500
0.25
400
0.20
Note the constant pump rate!
300
0.15
200
0.10
100
0.05
0
0.00 0
1
2
3
4
5
6
7
Pump Rate (bbls/min.)
900
8
Volume Pumped (bbls)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Critical Points of Typical LOT Pressure Response 1000
0.50
LOP
800
Pressure (psi)
0.45
Pressure Pump rate
0.40
700
0.35
600
0.30
500
0.25
400
0.20
300
0.15
200
0.10
100
0.05
0
Pump Rate (bbls/min.)
900
0.00 0
1
2
3
4
5
6
7
8
Volume Pumped (bbls)
Leak-off pressure (LOP) – point where the slope of the curve starts to decrease, deviating from the the best fit straight line at the beginning of the test. This represents the point at which micro-fractures are forming near the wellbore. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Critical Points of Typical LOT Pressure Response 0.50
Pb
900 800
Pressure (psi)
0.45
Pressure Pump rate
0.40
700
0.35
600
0.30
500
0.25
400
0.20
300
0.15
200
0.10
100
0.05
0
Pump Rate (bbls/min.)
1000
0.00 0
1
2
3
4
5
6
7
8
Volume Pumped (bbls)
Breakdown pressure (Pb) – the highest pressure achieved during the test, corresponding to the formation of a major fracture and large fluid losses. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Critical Points of Typical LOT Pressure Response 1000
0.50
Stop pumping after pressure decrease observed!
Pressure (psi)
800
0.45
Pressure Pump rate
ISIP
0.40
700
0.35
600
0.30
500
0.25
400
0.20
300
0.15
200
0.10
100
0.05
0
Pump Rate (bbls/min.)
900
0.00 0
1
2
3
4
5
6
7
8
Volume Pumped (bbls)
Instantaneous shut-in pressure (ISIP)- first point after the pumps are stopped. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Critical Points of Typical LOT Pressure Response 1000
0.50
800 700
Pressure (psi)
0.45
Pressure Pump rate
0.40 0.35
Closure stress
600
0.30
500
0.25
400
0.20
300
0.15
200
0.10
100
0.05
0
Pump Rate (bbls/min.)
900
0.00 0
1
2
3
4
5
6
7
8
Volume Pumped (bbls)
Closure stress- first point after the slope of the curve starts to decrease just beyond the short linear behavior observed after ISIP © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Summary of Critical Points of Typical LOT Pressure Response 0.50
Pb
900
LOP
800
ISIP
Pressure (psi)
700
0.45
Pressure Pump rate
0.40 0.35
Closure stress
600
0.30
500
0.25
400
0.20
300
0.15
200
0.10
100
0.05
0
Pump Rate (bbls/min.)
1000
0.00 0
1
2
3
4
5
6
7
8
Volume Pumped (bbls)
NOTE: Closure stress < both ISIP and LOP. Rule of thumb: LOP is 5 - 10% > than the closure stress. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Problems encountered during analysis of LOT results Shallow well in the GOM: 300
End of pumping LOP
250
Perhaps a high permeability zone was contacted (and plugged after some time?) Æ better re-test !!!
Pressure (psi)
200
150
Min. closure stress
100
50
0 0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Volume (BBLS)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Problems encountered during analysis of LOT results (cont’d) Well in the GOM: 1600
End of pumping
LOP
1400
Pressure (psi)
1200
Min. closure stress ???
1000
Slope shows a permanent decrease in slope below 700 psi. However, this value is too small to be reliable Æ Possible channel being contacted ÆBest option: RE-TEST !!!
800
600
400 0
1
2
3
4
5
6
7
8
Min. closure stress ???
9
10
11
12
Volume (BBLS)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
2 Cycle XLOT Pressure
From Perkins and Kern : Pb1- Pb2 = To Pb1
ISIP = σ C +
pump is shut-in!
πγ E 2 (1 − ν 2 ) L
Pb2 Pprop ISIP1
well is re-pressurized 1st PRESSURE CYCLE
Note: γ is the fracture surface energy.
ISIP2
time
2nd PRESSURE CYCLE
As # pressure cycles increase, the length of the induced fractures grows and the second term becomes less important!
Normally, the value of ISIP tends to decrease asymptotically with the number of pressure cycles !!! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
XLOT XLOT-- Field Example 51
From Perkins and Kern : 50
ISIP = σ C + 49
ISIP decreases with subsequent cycles until stabilization at the 5th & 6th cycles (i.e., fracture length increases).
48 IS IP (M pa )
πγE 2 (1 − ν 2 ) L
47
46
45
44
43 0
1
2
3
4
5
6
7
LOT Cycle
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
σH Estimation from LOT & XLOT For a vertical hole in a normally-stressed environment, fracture initiation occurs when the effective tangential stress (σ’θθ) exceeds the tensile strength (To) of the rock (i.e, σ’θθ ≤ To). For the case of an impermeable rock, this is expressed mathematically as:
Pb = 3 σh - σH – αPp + To Obtained from LOT Biot’s constant obtained from LMP (or assumed to be unity)
Tensile strength assumed to be zero or estimated as 121 UCS (from LMP). If XLOT, To = Pb1-Pb2. Pore pressure obtained from RCI data or estimated from log data
This represents an upper bound of breakdown pressure!
Solving for σH yields: 0 (pre-existing fractures)
σH = 3σh - Pb – αPp + To Note: For the case of a pre-existing fracture, tensile strength is zero! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
σH Estimation from LOT & XLOT For a permeable rock, the expression is:
3σ h - σ H - 2η pp + To Pb = 2(1 - η) in which
This represents a lower bound of breakdown pressure!
α (1 − 2ν ) η= 2(1 - ν ) Solving for σH yields: σH = 3σh - Pb 2(1-η) – 2ηPp + To
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Properly Designed LOT/XLOT In order to fully utilize LOT/XLOT data for stress determination, the following guidelines should be followed while conducting a LOT/XLOT:
Record downhole pressure Record flow rate vs time Record cumulative fluid volume pumped Record sequence of events during the LOT/XLOT (e.g., report leaks, report unnecessary shut-ins, etc.) Maintain constant flow rate during test Maintain constant fluid viscosity Report mud weight, type, and temperature used during the test Report TVD and length of rathole Conduct multiple cycles XLOT to obtain the tensile strength (To) and ensure accurate σh estimations © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
F ormation IIntegrity ntegrity T est Formation Test
9 Test objective is to test the integrity of the cement and fracture pressure of the formation below the shoe to a pre-determined amount. 9 The procedure is similar to a LOT except the formation usually is not fractured or broken down (unless accidentally because the fracturing pressure is less than anticipated).
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
FIT- Field Example 3000
Point of deviation from linearity gives the leakoff pressure (LOP)
2500
Pressure (psi)
2000
1500
1000
σh ≈ 0.9-0.95 LOP*
500
0 0
10
20
30
40
50
60
70
80
Time (minutes) *from
© 2005 Baker Hughes Incorporated All rights reserved.
Breckels and van Eeklen (1982) Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
FIT- Field Example 4500 4000
Stopped pumping!
3500
Pressure (psi)
3000 2500 2000 1500
Since the pumps were turned off prior to an observed LOP, this test is useless!
1000 500 0 0
5
10
15
20
25
30
35
40
45
Volume Pumped (bbls)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mini -frac Tests Mini-frac Mini-fracs are a special kind of pump-in/decline test designed to measure the closure stress and estimate the leakoff coefficient in a thin interval just prior to a hydraulic fracturing job!
Typical operational conditions:
packers
Interval of interest
• Flow rate: 0.25 - 25 gpm • Volume injected: 0.5-2.5 bbls • Interval length: 5 – 15’ • Several cycles are conducted to ensure repeatable results • Normally use low viscosity fracturing fluid Zone between packers is pressured and a hydraulic fracture is initiated, propagated, and closed. The pressure response during these phases is recorded and analyzed to determine closure stress and leak-off coefficient!
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
RCI Straddle Packer Assembly for Stress Test – micro -frac test micro-frac
Straddle Packer (Dual Packer) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Additional Methods for LOT/minifrac Pressure Analyses Using normal Cartesian plots for pressure decline analysis can sometimes be difficult Æ ISIP/Closure Stress is not clear! BHP
Where is the ISIP/σc ?
BHP Shut-in time (min) ISIP/ σc
Using pressure vs. √time plots is an additional tool for ISIP/Closure Stress identification.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
√Shut-in time (√min)
www.bakeratlasdirect.com
Additional Methods for LOT/minifrac Pressure Analyses
Δ pressure (Δp), psi
Semi-log plots are also used; however, they may also be confusing Æ Semi-log plots for wells A and B show two points with slope change each; which one represents the closure pressure on each case?
time (t), sec from McLennan and Roegiers (1982)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Additional Methods for LOT/minifrac Pressure Analyses From well testing we know that the linear flow regime (representing the fracture) is characterized by a 0.5 slope in a log-log plot. Thus, replotting the data from wells A and B… Æ The moment when the fracture closes would be represented by the end of the linear flow regime !!!
End of linear regime
End of linear regime
from McLennan and Roegiers (1982)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Additional Methods for LOT/minifrac Pressure Analyses We can always use the pressure derivative as an additional diagnosis tool… the end of a plateau (at dp/dt ~ 0.5 ) in the derivative marks the value of closure stress! (d log Δp) / (d log Δt) = 0.25…finite conductivity fracture = 0.5…infinite conductivity fracture = 1.0…wellbore storage
( Jones & Sargeant, 1993 ) Note: If skin is present, the derivative will simply stabilize at a slightly lower value. ICFF Æ Infinite Conductivity Fracture Flow. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pump-in/Decline Tests Procedure is similar to microfrac (i.e., initiate, propagate and close a hydraulic fracture) but this test is much larger: • higher flow rate (up to 20 BPM) • higher fluid viscosity • larger injected volume (up to 100 bbls) Measure the average closure stress over a whole interval (that is why it needs higher values of rate and injected volume!) ISIP should not be used for closure stress estimation Æ use a more robust P vs t analysis Impractical for low permeability rocks (it would take too long!!!)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Typical Pump-in/decline Test
Bottomhole Pressure
Stop pumping
σC is inferred from the change of slope!
dP =
dP =
ϕeμCt xf b
CH p E H2
k
a
c
pre-closure post-closure √ Shut-in time (√Δt)
2
NOTE: This plot is used to ascertain the minimum hor. stress after the fracture has formed and propagated! k=permeability, xf=fracture length, φpe=effective porosity, μ=fluid viscosity, C=fluid loss coefficient, Ct=Cb=total comp., Hp=propped fracture height, and H=fracture height.
a) This can occur when contacting a soft (low E), high permeability formation where the rate of pressure decline can actually increase upon fracture closure. b) This is the typical case of fracture closure accompanied by decreased leak-off. c) Theoretically, no slope change may occur making it difficult to identify σc. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Bottomhole Pressure
Limitations of Pump-in/decline Tests σC ??? σC ???
According to Gulrajani and Nolte (2000), the change of slope in the decline analysis may be due to any of the following: • • • • • •
√ time (pump shut-in)
• •
fracture closure fracture height receding from bounding layers transition from fracture extension to recession reservoir linear flow reservoir radial flow postclosure consolidation of filter cake and fracture irregularities typical of a radial fracture (or nearly contained) in a moderate to high permeability, high fluid loss formation possible initial fracture height containment, followed by fracture growth into higher stress shale
Upshot: Shut-in test should be used in conjunction with other tests as results may be unreliable! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pump-in/decline Tests cont’d However……..As a quality control check the following plot can be used to verify the fracture closure!
Bottomhole Pressure
Stop pumping (Δt ≈0)
σcl must be above the start of the pseudoradial flow
Pres ? @ Horner time = 1 (i.e., Δt →∞)
Log Horner time
⎛ t p + Δt ⎞ ⎟ ⎜ ⎜ Δt ⎟ ⎠ ⎝
*
*Note: tp denotes the pumping time and Δt denotes shut-in time © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pump-in/flowback Tests Test is usually carried out just prior to a hydraulic fracturing job to obtain σc Test involves inducing a hydraulic fracture, injection into the fracture followed by a constant flow-back rate Flow-back rate to be used during testing must initially be estimated Normally intended for low permeability formations The pressure response during flow-back differs during fracture closing and after the fracture has closed resulting in a slope change in the pressure versus time plot Typical operational parameters: • Injection rate (Qinj): 1-10 BPM • Volume pumped: 2-5 Bbls 1 1 • Qflowback = 6 to 4 Qinj
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pump-in/flowback Tests q too low (re-test)
A B
σcl
Ide al
“lazy S” shape
BHP
BHP
Ideal Test Result
C
q too high (re-test)
pump-in
pump-in
√ time (pump Shut-in)
√ time (pump Shut-in)
A Æ Pw > σcl
fracture open Kfr infinite
B Æ Pw ~ σcl
fracture closing near wellbore Kfr finite
C Æ Pw < σcl
fracture closing far from the wellbore Kfr very small
Note: Kfr = fracture conductivity (k*wfr) where k is the fracture permeability and wfr is the average fracture width © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Step Rate Tests • Objective is to measure the closure pressure in “gross” completion intervals (i.e., several formations being tested simultaneously Æhfr > 50 ft) • Performed with higher fluid viscosity, higher flow rates, and larger cumulative volumes than micro-frac tests Q
Pressure
Rate / Pressure
p pext σcl
Pext ≈ σ cl + 100 or 200 psi Shut-in time (min)
Inj. Rate
• Each rate step should have the same hold time (typically 2 to 3 min) • 0.25 bpm < Flow rate < 20 bpm © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stress Determination Techniques • Hydraulic (active) measurements • Strain recovery ¾ASR ¾DSCA
• Log-based • Other methods
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Strain Recovery Methods Once a rock core is physically removed from its in-situ position, the rock deforms (relaxes). Elastic strain occurs immediately upon unloading followed by longerterm anelastic strain. σ3
in-situ rock
εmin Stress Unloading σ1
Differential expansion creates micro-cracks perpendicular to the maximum principal stress direction (Nur & Simmons, 1970)!
εmax
Field measurements (see for example Warpinski and Teufel, 1989) have indicated that the greatest expansion occurs in the direction of maximum principal stress (σ1) and the least expansion occurs in the direction of minimum principal stress (σ3)! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Strain Recovery Methods Anelastic Strain Recovery (ASR)
Differential Strain Curve Analysis (DSCA)
Objective: Record strain due to stress unloading as soon as the core is retrieved.
Objective: Record induced strain due to hydrostatic loading of a previously unloaded core sample. εmin σc σc
εmin
εmax
Strain gages (at least 6) are placed on a core sample immediately upon core retrieval to measure strain relief. The recorded strain values are then used in a constitutive model to determine the magnitude of the in-situ stresses. © 2005 Baker Hughes Incorporated All rights reserved.
εmax σc
εmax σc
Strain gages are placed on core sample after unloading from the in-situ stress conditions. The core is then hydrostatically loaded and the recorded strain values are then used in a constitutive model to determine the magnitude of the in-situ stresses.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Typical ASR Equipment
Strain gages
NOTE: Stringent core handling procedures must be followed to prevent core de-hydration, thermal strains, etc. as well as to ensure precise core orientation!
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Generalized ASR Measurements
Strain (ε)
ε0
Instantaneous elastic strain at instant of coring
Elastic limit Anelastic strain prior to core retrieval
ε1 ε2
recorded strain
t0
Time sample cored
t1
Sample strain gaged
t2
End of measurements
ε0 − ε1
Component of elastic and anelastic strain relaxation (prior to recording)
ε1 − ε2
Component of anelastic strain relaxation (recorded)
Viscous (time-dependant strain continues) t0 t1
t2
© 2005 Baker Hughes Incorporated All rights reserved.
Time Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
ASR ASR-- Field Example 250
core cutting and retrieval
core strain recording
strain unchanged
εv
Strain (ε) [microstrain]
200
εH
NOTE:
150
100
εh
After 40 hours the strain no longer changes!
50
0 0
5
10
(from Teufel & Warpinski 1984) © 2005 Baker Hughes Incorporated All rights reserved.
15
20
25
30
35
40
45
50
Time [hours]
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
ASR Constitutive Models Two common models (Blanton’s-1983 & Warpinski and Teufel-1989) are used to describe the constitutive behavior of rock during rock unloading. These models are excellent for obtaining stress directions but are not as efficient at determining the in-situ stress magnitudes.
The assumptions applied in the two models are as follows*: • Principal stress directions coincide with the principal strain directions obtained from the strain data • The magnitude of the overburden is known • The rock is isotropic and homogeneous (i.e., no micro-cracks exist in-situ) • The borehole is vertical • The rock follows linearly viscoelastic behavior (time-dependant) • Unloading of stresses is instantaneous upon cutting of the core • Poisson’s ratio and Biot’s pore pressure constant remain unchanged during relaxation • Creep (anelastic relaxation) follows an exponential behavior • Bulk modulus of the rock is not viscoelastic *Note: assumptions common to both models are depicted in black, assumptions specific to Blanton’s model are shown in red while assumptions specific to Warpinski and Teufel are depicted in blue. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Blanton’s ASR Model Blanton’s model* was derived on the basis that the two horizontal stresses can be calculated from elastic expressions using the changes in the principal strains for a given time Increment. Mathematically, the expressions are:
(1−ν)ΔεH + ν(Δεh + Δεv) + αPp σH = (σv + αPp) (1−ν)Δεv + ν(Δεh + ΔεH) (1−ν)Δεh + ν(ΔεH + Δεv) + αPp σh = (σv + αPp) (1−ν)Δεv + ν(Δεh + ΔεH) where Δεi is the change in principal strain with respect to a given time increment in the ith direction, ν is Poisson’s ratio, α is Biot’s constant, Pp is the pore pressure and σv is the vertical (overburden) stress. *from Blanton (1983) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Differential Strain Curve Analysis (DSCA) Objective: Hydrostatically load the rock sample and record the resulting strain.
Y
2
X
1
10 3
45º
9
5
12 8
6
7 Position of the 12 strain gages used in a typical DSCA test (after Strickland and Ren, 1980). A 9 gage test can also be conducted. © 2005 Baker Hughes Incorporated All rights reserved.
4
11
Lab Methodology
1) 1.5-2” cubical sample is prepared from an oriented whole core and the surfaces are ground smooth, cleaned and covered with a silicon jacket to prevent pore fluid invasion. 2) Sample is strain gaged (rosette pattern of 0º, 45º, 90º so that directional deformation can be measured). 3) Sample is hydrostatically loaded (σ1=σ2=σ3) and unloaded beyond the estimated in-situ level (3 cycles). 4) Recorded strain data are used to calculate the microcrack closure strain and subsequently infer stress direction and magnitudes (assuming differential strains are directly related to in-situ stress).
Z
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pressure vs Volumetric Strain
Hydrostatic Confining Pressure (σc)
Linear elastic response
For homogeneous, isotropic rock:
ΔV K = σc V Typical DSCA response
For microfractured rock (Walsh, 1965):
ΔV = C σ + η(σ ) b c c V
Volumetric Strain,
© 2005 Baker Hughes Incorporated All rights reserved.
where K is the bulk modulus of the rock, V is the original sample volume, ΔV is the change in sample volume and σc is the confining pressure.
ΔV V
where η represents microcrack porosity (as function of pressure) and Cb is the intrinsic rock compressibility ( K1 ).
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pressure vs Volumetric Strain
Confining Pressure (σc)
For microfractured rock (Walsh, 1965): Linear elastic portion (microcracks closed)
ΔV = C b σ c + η( σ c ) V
pc
microcrack porosity
ηo
Critical crack pressure (pc) (pressure above which all microcracks have closed) © 2005 Baker Hughes Incorporated All rights reserved.
Cbpc
ΔV Volumetric Strain, V
Note: ηo = initial microcrack porosity Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Typical DSCA Plot Measured strain (ε) from the 1, 2, 3, and 10 gages on the X-Y face of the sample. microcrack closure
Y ε 10 3
2
X
1
45º
9 12
crack strain
rock strain from compressibility
4
5 8
6
3 2 1 10
11
7
Z
© 2005 Baker Hughes Incorporated All rights reserved.
σc Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
DSCA Data Analysis In DSCA, the data is used to determine the crack strain tensor within the linear portion of the strain-pressure curve prior to crack closure (Strickland and Ren, 1980).
The microcrack closure strain [ηi(p)] at a given conf. pressure (σc) in the ith direction is calculated as the difference between the measured average strain [εi(σc)] and the bulk rock compressibility [Cb σc]. Mathematically, this is written as: ηi(σc) = εi(σc) – Cb σc. The analysis is usually done by determining the crack strain tensor over Obtained from lab testing a pressure range or: ηij(σc) = εij(σc) + ηo(pc) – Cb σc The principal crack closure strains (ηp1, ηp2, ηp3) and their orientation are then obtained. It is assumed that these directions correspond to the principal stress directions! © 2005 Baker Hughes Incorporated All rights reserved.
Note: ηo(pc) = initial microcrack porosity Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
DSCA Data Analysis According to Ren and Roegiers (1983), for isotropic media the stresses can then be obtained from the following expressions:
σ1 ησc1 (1 − ν ) + ν(ησ c 2 + ησc 3 ) = σ3 ησc 3 (1 − ν ) + ν(ησc1 + ησc 2 )
σ 2 ησc 2 (1 − ν ) + ν(ησ c1 + ησc 3 ) = σ3 ησc 3 (1 − ν ) + ν(ησc1 + ησc 2 )
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stress Determination Techniques • Hydraulic (active) measurements • Strain recovery • Log-based ¾Borehole breakouts ¾Tensile fractures
• Other methods
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
σH Estimation using Breakouts σH Breakouts
σh Breakout width, w (degrees)
NOTE: Breakouts form when the maximum effective tangential stress exceeds the rock strength. Breakouts always form in the direction of the minimum in-plane stress (σh in the case of a vertical hole)! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Breakouts from Image Logs Breakout location (with respect to Earth Coordinate System) Breakouts
Breakout width (w)
Upshot: Breakout location and breakout width are recorded from image logs and used to estimate the maximum horizontal stress (σH)! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
σH Estimation using Breakouts Breakouts form when the compressive stress exceeds the compressive strength of the rock! According to Mohr-Coulomb, this occurs when: σ’1=UCS + σ’3 tan2(π/4+φ/2) where σ’1 is the maximum effective principal stress acting on the wellbore wall, σ’3 is the minimum effective principal stress and φ is the internal friction angle.
For a vertical well with anisotropic horizontal stresses, the effective tangential stress, σ’θθ for an impermeable borehole wall is given by: σ’θθ =σH+σh-2(σH-σh)cos2θ -Pw- αPp NOTE: If Pw ↓, σ’θθ ↑ and vice versa
Upshot: σ’θθ becomes highly compressive as wellbore pressure is decreased! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Borehole Breakout Calculations Calculations-BIAS
When stress exceeds the confined strength, breakouts form!
breakout width
breakout width
Requires knowledge of breakout location, breakout width and minimum horizontal stress orientation! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
σH Estimation using Breakouts In a vertical well at the wellbore wall, breakouts typically occur when:
σ’1 = σ’θθ and σ’3 = σ’rr where σ’rr = Pw - αPp
Substituting the expressions for σ’1 and σ’3 into the Mohr-Coulomb criterion yields: σH+σh-2(σH-σh)cos2θ -Pw- αPp > UCS+(Pw-αPp) tan2θ(π/4+φ/2)
For a given breakout width (w) at a given depth one has: σH+σh-2(σH-σh)cos2(90-w/2) -Pw- αPp =UCS+(Pw−αPp) tan2(π/4+φ/2) Estimated from log-based expressions Estimated from image logs © 2005 Baker Hughes Incorporated All rights reserved.
Estimated from LMP
Known from driller
Efficiency….Data accuracy….People-oriented service
Estimated from Pp prediction analysis www.bakeratlasdirect.com
Borehole Stress & Breakout (vertical well) Re-arranging gives:
σH =
C + Pw + αPp − σ h [1 − 2 cos w ] 1 + 2 cos w
where C = UCS + (Pw - α Pp) tan2(π/4 + φ/2) = confined compressive strength and w = breakout width [degrees]
The maximum horizontal stress (σH) profile can then be estimated by:
σH = x*σh or y + σh where x = σH/σh at the depth of breakout and y = σH – σh at the depth of breakout.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Breakouts from Caliper Logs Common Borehole Geometries In-gauge hole
bit size
tool
key seating
breakout
washout
tool
pipe abrasion
tool
missed breakout
NOTE: The calipers indicate hole elongation (E-W) but the hole is actually washed out! Thus, breakout direction is potentially inaccurate.
tool
tool
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
Breakout missed due to lack of pad coverage in large hole.
www.bakeratlasdirect.com
Breakout ID: Caliper Logs Plumb and Hickman (1985) Criteria* 1) 2) 3) 4)
Tool rotation ceases in the zone of elongation. Differential caliper is greater than 6 mm. Smaller caliper readings should be close to bit size. If smaller caliper reading is slightly greater than bit size, it should exhibit less variation than the larger caliper. 5) Height of the elongated zone should be greater than the pad length. 6) The direction of elongation should not consistently coincide with the azimuth of the high side of the hole in non-vertical wellbores. This may indicate key seating! NOTE: These criteria give only a rough estimate of borehole breakout location and therefore exact breakout width is very difficult to ascertain! *These criteria were originally developed for a 4-arm caliper device but can also be applied to 6-arm calipers! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Breakout Characterizations
9 Borehole geometry can be described combining information from 6-arm caliper (breakout length) and acoustic image log (breakout size) 9 The breakout characteristics are useful in describing in-situ stresses as well as calibrating the geomechanical models © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Log -Based Stress Determination Log-Based Alternative Methods for Determination of Minimum & Maximum Horizontal Stress Magnitudes (Strain Method): •Assume the vertical stress causes constant horizontal strains, isothermal case (Prats, 1981 and Warpinski & Smith, 1989):
σh = ν/(1-ν)(σV- αPp) + αPp +(εh+νεH)E/(1-ν2) σH = ν/(1-ν)(σV- αPp) + αPp +(εH+νεh)E/(1-ν2) •Assume the vertical stress causes constant horizontal strains, non-isothermal case (Blanton & Olson, 1997):
σh = ν/(1-ν)(σV- αPp) + αPp +(εh+νεH + A)E/(1-ν2) σH = ν/(1-ν)(σV- αPp) + αPp +(εH+νεh + A)E/(1-ν2) In which A = (1+ν)ατ∆Τ is a temperature term where αt is the thermal expansion coefficient of the rock and ∆T is the temperature at a particular depth minus the ambient surface temperature (ºF ). Typical values of αt are (Clark, 1966): 5.56 E-6/ºF (sandstone), 5.00 E6/ºF (shale) and 4.44 E-6/ºF (carbonates). © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Calibration to Breakout, Vertical Well (isothermal case) Breakout width measured at two depths, A & B: A
σHA+σhA-2(σHA-σhA)cos2(90-wA/2)–PwA- αΑPpA =sA σHA = νΑ/(1-νΑ)(σVA- αΑPpA)+αΑPpA+(εH+νεh)EA/(1-νΑ2) σhA= νΑ/(1-νΑ)(σVA- αΑPpA)+αΑPpA+(εh+νεH)EA/(1-νΑ2)
B
not valid in σResults HB+σ hB-2(σ HB-σhB)cos2(90-wB/2)–PwB- αΒPpB =sB
σHB = νΒ/(1-νΒ)(σVB- αΒPpB)+αΒPpB+(εH+νεh)EB/(1-νΒ2) σhB= νΒ/(1-νΒ)(σVB- αΒPpB)+αΒPpB+(εh+νεH)EB/(1-νΒ2)
Solve equations for εH & εh to calculate complete stress profile! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
σh Methods Comparison If no lateral strain:
If constant tectonic stress:
If constant lateral strain:
(conventional-uncalibrated)
(conventional- calibrated)
(strain method)
σh = ν/(1-ν)(σV- αPp)+αPp
σh = ν/(1-ν)(σV- αPp)+αPp+ΔσT
σh = Minimum horizontal stress magnitude ν = Poisson’s ratio (isotropic) σV = Vertical stress magnitude α = Biot’s coefficient © 2005 Baker Hughes Incorporated All rights reserved.
σh = ν/(1-ν)(σV- αPp)+αPp+ +εhE/(1-ν2)
Pp = Pore pressure εh = Horizontal strain E = Young’s Modulus
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Conventional vs Strain Method Example
ss
ss
Calibration point
Strain method provides a better match with the measured stress data!
sh ss sh ss sh
From Blanton & Olson (1997) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stress Determination Techniques • Hydraulic (active) measurements • Log-based ¾Borehole breakouts ¾Tensile fractures
• Other methods ¾ Stress Maps ¾ Acoustic methods (Kaiser effect, DWVA, shear wave anisotropy)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
World Stress Map Http:///www-gpi.physik.uni-karlshruhe.de/wsm/maps/
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
In -situ Shear Wave Splitting In-situ • Stress anisotropy causes splitting of the shear waves (faster and slower shear waves traveling at different speeds). The S-wave velocities and directions can be measured using Baker Atlas’ XMAC© acoustic anisotropy tool. • The azimuth of maximum attenuation of Swaves propagated vertically through a specimen is obtained and plotted to determine the maximum in-plane normal stress.
NOTE: Formation anisotropy can be caused by: • Unequal principal stresses • Oriented fractures and/or pores • Structural layering as in shales
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Acoustic (shear wave) Anisotropy
Shear wave map indicates high degree of anisotropy in the N-S direction. This indicates the possible maximum horizontal stress direction!
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Acoustic Velocity Analysis • Due to anisotropic stress removal, microcrack formation takes place in the direction perpendicular to the maximum in-plane stress (σH for the case of a vertical wellbore). • The test is usually performed on vertical cores. • There is no critical time to perform the test (as is the case in ASR). Therefore testing can be conducted on old cores. • Tests can be conducted under any stress/pore pressure conditions (higher stresses cause pores to close resulting in an increase in acoustic velocity). • The orientation of the minimum compressional and shear wave velocities is perpendicular to the microcrack orientation whereas the maximum velocities occur parallel to microcracks. σH VP(max), Vs(max), A(min) (Min. Attenuation)
VP(min), Vs(min), A(max) (Max. Attenuation) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
σh, VPmax
P-wave
receiver
σH, VPmin
transmitter
Typical P -Wave Velocity Test P-Wave P-wave is measured diametrically along azimuthal increments
P-wave Velocity (m/sec)
P-wave Anisotropy 5200 5000 4800 4600 4400 4200 4000 0
© 2005 Baker Hughes Incorporated All rights reserved.
σH direction
90
σh 180 direction Azimuth (degrees)
270
Efficiency….Data accuracy….People-oriented service
360
www.bakeratlasdirect.com
Typical S -Wave Velocity Test S-Wave S-wave Amplitude 5200
S-wave
S-wave Amplitude
transmitter
receiver
5000 4800 4600 4400 4200 4000 0
σH direction 90σh direction 180
270
360
Azimuth (degrees) σH, VSmin
σh, VSmax
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
The Kaiser Effect • A rock sample will yield acoustic signals (sub- audible noises) when
subjected to loading in the laboratory. The Kaiser effect occurs when the rate of acoustic signals drastically increases. This occurs when the applied stress surpasses the load previously experienced by the rock (Kaiser, 1953). • In the lab, a core is subjected to a sequence of stresses. In the first
cycle of loading, a high-frequency sound burst is emitted. However, in subsequent cycles, there is an absence of these emissions until the previous maximum stress is surpassed.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
AE (Acoustic Emission) Activity
The Kaiser Effect σi
σmax = Maximum Burial Stress in Direction i
NOTE: Some rocks lose their memory of previous loading in as little as a few days (Holcomb, 1993).
σi
Upshot: Kaiser effect may yield erroneous results!
σmax © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
σi www.bakeratlasdirect.com
Published σH and σh Correlations Horizontal Stress Formulation σH [MPa] = 4.6 + 0.025d σh [MPa] = 1.4 + 0.018d σh = 0.197d1.145 (d ≤11500 ft) σh = 1.167d – 4596 (d > 11500 ft) ΚH = 0.98 + 250/d Κh = 0.65 + 440/d ΚH = 1.46 + 357/d Κh = 1.10 + 167/d σH [MPa] = 15 + 0.028d σh [MPa] = 6 + 0.012d σH [MPa] = 8.8 + 0.0422d σh [MPa] = 3.64 + 0.0276d σH [MPa] = 30.4 + 0.023d σh [MPa] = 16.0 + 0.011d σH [MPa] = 9.1 + 0.0724d σh [MPa] = 5.3 + 0.0542d σH [MPa] = 2.8 + 0.0399d σh [MPa] = 2.2 + 0.0240d σH [MPa] = 15.83 + 0.0302d σh [MPa] = 6.52 + 0.01572d
Location and Depth Range
References
Michigan Basin (0-5000m)
Haimson (1977)
Gulf of Mexico (all depths- ft)
Breckels & van Eekelen (1982)
World Data (500-3000m)
Rummel (1986)
Canadian Shield (0-2200m)
Hegret (1987)
Cornwall, UK (0-2000m)
Pine & Kwakwa (1989)
Canadian Shield (0-2000m)
Arjang (1989)
KTB pilot hole (800-3000m)
Baumgarten et al. (1993)
Fennoscandia: (0-1000m)
Hast (in Stephansson 1993)
Fennoscandia: (0-9000m)
Stephansson (1993)
KTB pilot hole (0-9000m)
Te Kamp et al. (1993)
Note: KH = σH/σv and Kh = σh/σv
NOTE: These should only be used as a last resort! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline I. II. III. IV.
Introduction to subsurface stresses Overburden calculation Commonly used stress determination techniques Summary
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
In -situ Stress Workflow In-situ Analyze data/ Daily drill reports Calculate overburden stress Pore pressure estimation
Determine rock mechanical properties (LMP)
© 2005 Baker Hughes Incorporated All rights reserved.
Calculate minimum horizontal stress (σh) magnitude and direction. Calibrate using stress measurement techniques.
Conduct geomechanical analysis – borehole stability, sand production, hydraulic fracturing, etc.
Calculate maximum horizontal stress (σH) magnitude and direction. Fine tune using borehole image logs and other field/drilling observations. Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
In -situ Stress Puzzle In-situ Active
Passive
)Mini-Frac )LOT/ELOT )FMT/RCI
)Breakouts )Fractures )Acoustic Anisotropy
Integration
BIAS Existing Inf.
Core Based
)History )Stress maps )Geology
)DSA )ASR )Kaiser effect
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
All info must be integrated to build a consistent in-situ stress model!!!!
www.bakeratlasdirect.com
In-Situ Stress Regimes
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Pressure Characterizations
Outline I. Why pore pressure prediction is important II. Basics of abnormal pore pressure III. Pore pressure determination methods
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Why is Pore Pressure Est. Important? > 40% of trouble time attributed to Geomechanics/Pressure related incidences. These account for 24-27% of total drilling costs.* 0.8% 21.4% Directional Completion Cement Squeeze 11.4%
Chemical Problems Wait on Weather
3.0%
5.2%
Geomechanics/ Pressurerelated incidences
Casing or Wellhead Failure Rig Failure
9.0% 42.3%
Other Stuck Pipe Twist Off
12.8% 13.4%
Kick Lost Circulation
2.8% 0.7% 2.7%
2.6%
Sloughing Shale Wellbore Instability Shallow Water Flow Gas Flow
0.3%
9.4% 5.0%
*Data taken from Dodson et al. (2004). Data illustrates incidences from 549 GoM shelf wells (<600 ft water depth) drilled from 1993-2002. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
What is a Shallow Water Flow? Shallow Water Flows (SWF): Water/debris flow along the outside of structural casing to the seafloor.
Causes of SWF 1.
riser
2.
ρwater
3. 4.
ρmud sand
Geopressured sands within conductor intervals: Excessive sand pressures cause SWF’s prior to installation of riser and BOP- no closed system to contain geopressure! Induced fractures: Mud pressure at the casing shoe exceeds the formation tensile strength and induces a hydraulic fracture, resulting in a conduit of fluid flow to the seafloor. Induced storage: Permeable formations are “charged” by excessive MW resulting in flowback once circulation is ceased. Transmission of geopressure through cement channels: Poor cement jobs provide a conduit of fluid flow. This is typically time-delayed as there is more time required to flow through the cement channels.
Ramifications of SWF 1. 2.
Flowing water may cause deterioration of the structural support of the well leading to casing buckling and/or collapse. Loss of well control.
Thus, there is a need to predict SWF in advance! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Typical GoM PP Profiles Deepwater formations often encounter abnormal pressures directly below the mud-line; which can lead to a much narrower MW window. Shelf
Deepwater
PRESSURE
SWF (shallow water flow)
re tu ac Fr
(li th os ta tic )
e ur
Pore Pressure (Pp)
re su es
re ssu Pre tic sta dro Hy
GEO PRESSURE
© 2005 Baker Hughes Incorporated All rights reserved.
Pr es su re
r op Ge
Zone
σ’ = σ - Pp
s es Pr
Tran sitio n
re su res cP
Pore Pressure (Pp)
ur de n
re tu ac Fr
Stress (σ’)
ti sta dro Hy
e ur
DEPTH
σ’ = σ - Pp
s es Pr
Effective
O ve rb
DEPTH
O ve rb ur de n
PRESSURE
Effective Stress (σ’)
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Typical DW GoM Casing Program 4000
6000
Depth [feet-tvdrkb]
8000
10000
hydrostatic
12000
Planned MW
14000 PPG
FG
16000 8
9
10
11
12
13
14
15
16
17
18
Equivalent Mud Weight [lbs/gal]
Note: PPG = pore pressure gradient, FG = fracture gradient © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Unexpected Overpressured Zone 4000
6000
Depth [feet-tvdrkb]
8000
Planned MW
10000
hydrostatic
12000
potential kick zone or spalling shale (Pp>Pw)
14000 PPG
FG
16000 8
9
10
11
12
13
14
15
16
17
18
Equivalent Mud Weight [lbs/gal]
Note: PPG = pore pressure gradient, FG = fracture gradient © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Unexpected Depleted Zone 4000
6000
Fracturing in depleted zone (and possibly losses!)
Depth [feet-tvdrkb]
8000
hydrostatic
10000
12000
14000 PPG
FG
16000 8
9
10
11
12
13
14
15
16
17
18
Equivalent Mud Weight [lbs/gal]
Note: PPG = pore pressure gradient, FG = fracture gradient © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline I. Why pore pressure prediction is important II. Basics of abnormal pore pressure III. Pore pressure determination methods
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Pressure: The Basics
Pressure Normally (hydrostatic) Pressured Reservoirs
Depth
¾
hyd
c tati ros
lith os tat ic
Rocks which have pore pressures equal to a continuous column of water from surface to depth of interest (typically 8.3-8.9 PPG range).
under pressure
over pressure
© 2005 Baker Hughes Incorporated All rights reserved.
Abnormally Pressured Reservoirs ¾
Rocks which have pore pressures significantly greater than hydrostatic (overpressured) or less than hydrostatic (underpressured).
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Pressure: The Basics Normal Compaction Behavior Fluid pressure
Sea level
True vertical depth, m
Sedimentation
Water is expelled due to the compaction of sediments grain
Hydrostatic pressure
© 2005 Baker Hughes Incorporated All rights reserved.
Fluid
The column is supported by the grain to grain contact.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mechanisms of Overpressure Causal mechanisms of overpressure include the following: Æ Stress-related (pore volume reduction) • Disequilibrium compaction (vertical stress loading without fluid pressure dissipation) • Tectonic (lateral) stress loading (faulting, salt dome emplacement) Æ Fluid volume increase (pore volume expansion) • Increased temperature (pore fluid expansion) • Water release due to mineral transformation (smectite to illite transformation) • Hydrocarbon cracking These are the most likely mechanisms to result in large • Hydrocarbon generation from kerogen Æ
Fluid movement and buoyancy
scale overpressure (Swarbrick & Osborne, 1998)
• Osmosis (brine concentration contrasts across semi-perm membranes) • Hydraulic head (increased potentiometric head from highlands) • Buoyancy due to density contrasts between fluid type (oil, gas, water)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mechanisms of Overpressure Fluid pressure
Sea level
True vertical depth, m
Hydrostatic pressure
Compaction in an undrained condition
Part of the Overburden is supported by the pore fluid. Overpressure
• Fast sedimentation • Low permeability (clay sediments) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mechanisms of Overpressure
Overburden
Normal Compaction 1 - 1.07 sg Overpressure top 1.19 - 1.68 sg
Under Compaction
Under Compaction + Other Mechanisms
Overpressure
> 1.80 sg Fluid expansion
Bowers GL, 2001 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mechanisms of Overpressure 0.9
Pressure vs. Temperature for GoM Wells (Timko &Fertl, 1971)
Pp Gradient (psi/ft)
0.8
0.7
0.6
0.5
0.4
0.3 60
100
140
180
240
280
320
360
Temperature (oF) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mechanisms of Overpressure Relationship between Porosity – Depth and Pore Pressure 0
0.25
0.50
0.75
Porosity-Depth Relationships Normal compaction line for sandstone
1.0
Porosity
mud
clay
Normal compaction line for clay and shale
mudstone
shale
Overpressure effect on porosity 4-8 km
Depth © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mechanisms of Overpressure Pressure Overburden stress
Depth
Overpressure top
Effective stress Pore pressure Normal hydrostatic pressure
© 2005 Baker Hughes Incorporated All rights reserved.
Overpressure
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mechanisms of Overpressure Buoyancy Effect Gas or oil Sand
za
za= 2000 ft zb= 3000 ft
Sealed Fault
ρg= 0.12 psi/ft
zb Oil - Water contact (or Gas) Water Formation Sand
PB = 0.465 (psi/ft) * 3000 ft = 1395 psi PA = PB – (Zb –Za)*ρg* g PA = 1395 psi – (1000 ft)*0.12 psi/ft = 1275 psi PP Gradient = 1275psi/2000 ft = 0.638 psi/ft © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mechanisms of Overpressure Artesian System PP = 0.465 psi/ft * (10000-2000) ft = 3720 psi GPP = 3720 psi /2000 ft = 1.86 psi/ft
Z=10,000 ft
Z=2,000 ft
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mechanisms of Underpressure Underpressure is caused by: Æ Rock & fluid property change due to uplifting • Reduction in temperature (leading to reduction in pressure via fluid shrinkage) • Rock dilatancy (due to lower temperature and stress) • Groundwater discharge (accompanied by a lower permeability recharge zone) • Gas solubility (gas exsolves out of solution at a greater rate than gas generation to due decrease temp. and pressure at uplifted stage) • Osmotic flow (via semi-perm membrane)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mechanisms of Underpressure PP = 0.465 psi/ft * 7000 ft = 3255 psi GPP = 3255 psi /10000 ft = 0.33 psi/ft
Z=10000 ft
Z=7000 ft
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline I. Why pore pressure prediction is important II. Basics of pore pressure III. Pore pressure determination methods
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Pressure Prediction Process Calculate overburden Calculate PP using several techniques • Eaton (res/sonic/Dxc/cond) • Bryant (res) • Alixant (if geothermal gradient known) • Others
Evaluate secondary parameters (gas/geology/torque/drag/fill etc.)
Review possible effects of tectonics/ other mechanisms (faults/dipping beds/salt)
Techniques should agree within 0.5 PPG!
© 2005 Baker Hughes Incorporated All rights reserved.
Fine tune and calibrate PP models
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pressure Prediction Process Data Use all the data sources available, both primary and secondary. No one data source, alone, gives an accurate pressure prediction.
• Seismic (velocity/Δt) • Wireline (res / sonic / den / gam / calip) • MWD (res / gamma / sonic / density) • RCI (measured reservoir pressures) • Mud logs (gas / cuttings / lithology) • Fluids (mud density / hole cleaning) • IADC (wellbore stability/problems)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Pressure indicators
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
PP Determination Techniques Pore pressure (PP) determination methods can be broadly categorized into two general methods: 1. Direct Methods- Methods which directly relate the amount of pore pressure divergence from its normal trendline to the pore pressure gradient at a given depth.
2. Effective Stress Methods- Methods which are based on Terzaghi’s (1943) effective stress principle: compaction of porous material is controlled by the difference between total confining pressure and the pore fluid pressure.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Direct Methods Methods-- example Published examples of Hottman & Johnson Overlays Constructed for Various Regions For a given resistivity ratio, the 1.0
PPG is estimated based on regional curves
South China Sea
0.9 Vicksburg
0.8 Frio
0.7
Niger Delta Basin Gulf Coast
PPG=0.65 psi/ft
Wilcox
South China Sea
0.6
Frio Wilcox
Pore Pressure Gradient [psi/ft]
Pore Pressure Gradient [psi/ft]
1.0
0.5
0.9 Gulf Coast
0.8
Vicksburg
Niger Delta Basin
0.7
0.6 Wyoming Sedimentary Basin
0.5 Wyoming Sedimentary Basin
0.4 1
2
5 Log Rn/Ro
10
0.4 0
10
20
(data taken from Owolabi et. al, 1990)
30
40
50
60
70
80
Δto - Δtn
Rn & Ro are the “normal” and observed resistivity and Δtn & Δto are the “normal” and observed interval transit times.
NOTE: Since each region has a different signature, the overlay method is region specific. Additionally, it is necessary to construct new curves for new regions or whenever new geological horizons are encountered (Matthews & Kelly, 1967)! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effective Stress Methods Effective stress methods are generally categorized into the following: Vertical Effective Stress Methods- These methods assume that normally pressured and overpressured sections which exhibit identical properties are subjected to the same effective stress. Horizontal Effective Stress Methods- These methods are used to calculate the effective stress from the difference between observed and normal trend parameters at a given depth. Other Effective Stress Methods- These methods represent all other published methods that are used to obtain the relationship between compaction and effective stress. NOTE: These are the methods that will be examined in detail for the remainder of this session! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effective Stress Methods S = total stress σ = effective stress Overburden Stress
Pressure Required to Keep Water & Rock Grains from Squashing Out Horizontally
SV
=
SV = P + σV Sh = P + σh = P + K σV © 2005 Baker Hughes Incorporated All rights reserved.
σh
P
Sh
Total Stress
σV
P
Pore Pressure
+
Effective Stress
σh K= = Effective Stress Ratio; σV “K” increases with ductility.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effective Stress Methods Vertical Effective Stress Velocity (Km/s)
Pressure (Mpa)
Velocity (Km/s)
Depth (m)
Normal Trend
Compaction Trend
Effective Stress (Mpa)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effective Stress Methods Vertical Effective Stress – Equivalent Depth Foster & Whalen(1966) Dt
The effective stress in A and B are considered to be equal (since the state of compaction is equivalent) Zeq
A
Depth
PB = S B − (S A − PNA ) Z
B
where: P S
= Pore pressure (psi) = Overburden
σ = Effective stress © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effective Stress Methods Vertical Effective Stress – Equivalent Depth Traugott (1997) Dt
This method uses the mean stress Î (σ + σ h + σ H ) σM = 3
A
Depth
Zeq
⎛ 1 + 2K A ⎞ ⎟⎟( S A − PNA ) PB = S B − ⎜⎜ ⎝ 1 + 2K B ⎠ where :
Z
B
P S
= Pore Pressure (psi) = Overburden
K
= Vertical Effective stress = σh=σH/σ
σ © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effective Stress Methods Horizontal Effective Stress Velocity (Km/s)
Pressure (Mpa)
Velocity (Km/s)
Depth (m)
Eq. Eaton
Normal Trend
Effective Stress (Mpa)
S = total stress σ = effective stress © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effective Stress Methods Horizontal Effective Stress: Eaton’s Method (1975) ⎛V σ = σ N ⎜⎜ ⎝ VN
⎞ ⎟⎟ ⎠
3
⎛ Δt N ⎞ σ =σN⎜ ⎟ ⎝ Δt ⎠ ⎛ R σ = σ N ⎜⎜ ⎝ RN
⎛ V ( D) ⎞ ⎟⎟ Pp ( D) = S ( D) − (S ( D) − PN ( D) )⎜⎜ ⎝ VN ( D ) ⎠
3
1.2
⎞ ⎟⎟ ⎠
⎛ Dxc σ = σ N ⎜⎜ ⎝ DxcN
3
where :
1.2
⎞ ⎟⎟ ⎠
© 2005 Baker Hughes Incorporated All rights reserved.
P S D PN VN
= Current Pore Pressure = Overburden = Current Depth = Normal Pore Pressure = Normal Compaction Velocity
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effective Stress Methods Other Effective Stress: Bower’s Method (1995) Based on acoustic/velocity data using a modified equivalent depth type method that calculates effective stress along Bower’s derived curved trend line. This method is useful for correcting for unloading by manipulating several variables. © 2005 Baker Hughes Incorporated All rights reserved.
V
Concept of Virgin Curve
VMAX
Sub-Compaction σMAX
σ
Normal Compaction • Power trend of Compaction
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effective Stress Methods Other Effective Stress: Bower’s Method (1995) U
⎛ σA ⎞ ⎟⎟ σ B = σ max ⎜⎜ ⎝ σ max ⎠ where : A
= Equivalent depth σA = Effective stress at equivalent depth σmax = Effective stress at Vmax Vmax = Maximum velocity U = Calibration parameters (local data)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effective Stress Methods Other Effective Stress: Bower’s Method (1995)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effective Stress Methods Other Effective Stress: Bower’s Method (1995)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Table of PPP Methods PPP Approach Method Type
Name
PP Indicator
Crossplots
Hottman and Johnson (1965)
Acoustic/Resistivity
Overlays
Pennebaker (1968)
Acoustic/Resistivity
Equivalent Depth
Acoustic/Resistivity
Mean Stress Equivalent Depth
Acoustic/Resistivity
Bellotti and Giacca (1978)
Acoustic
Expression(s) X=
Direct
Effective Stress
Vertical
Hart and Flemings (1995)
Acoustic
Bryant (1989)
Resistivity
Alixant and Desbrandes (1991)
Resistivity
Rn Ro
X = Δt o − Δ t n
X=
Δto Δtn
P(b ) = σ v (b ) − (σ v (a ) − Pn (a ) ) ⎛ 1 + 2 K (a ) ⎞ ⎟ (σ P(b ) = σ v (b ) − ⎜ − Pn (a ) ) ⎜ 1 + 2 K ⎟ v (a ) (b ) ⎠ ⎝
σ' =
(Vo − Vm i n )B Vm at − A (Vo − Vmi n )
⎛ ⎜ φo 1 ⎜ σ ' = ln ⎜ 1 η ⎜ X V ⎛ ⎞ o ⎜1−⎜ ⎟ ⎜ ⎝ Vmat ⎠ ⎝
φ=
Rw Ro
w=
φ (1 − φ)
σ = σ max (1 − φ )
α
'
σ ' = 10
[ri − w ] / l c
⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠
Symbols: σv is the overburden stress, P is the pore pressure, V is acoustic velocity, R is resistivity, Δt is interval transit time and σ' is the effective stress. Subscripts: a is parameter at the “normal pressure”, b is parameter at the depth of interest, n is parameter at “normal pressure”, o is the observed parameter, mat is the matrix, min is the minimum and max is the maximum.
X is value used estimate the PPG (Y-axis) in overlay plots A & B are local calibration parameters
α is a calibration parameters (usually taken to be 7.35) ri and lc are local calibration parameters
φo & η are calibration parameters (X is typically taken to be 2.19) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Table of PPP Methods PPP Approach
Method Type
Name
PP Indicator
Expression(s) ⎛ Δt σ = σ n ⎜⎜ n ⎝ Δto
⎞ ⎟⎟ ⎠
3
⎛C σ = σ n ⎜⎜ n ⎝ Co
⎞ ⎟⎟ ⎠
1 .2
'
Eaton (1975)
acoustic/resistivity/ conductivity/D exponent
'
Horizontal
Weakley (1989)
acoustic
⎛R σ = σ n ⎜⎜ o ⎝ Rn '
⎞ ⎟⎟ ⎠
1.2
⎛d ⎞ σ ' = σ n ⎜⎜ xco ⎟⎟ ⎝ d xcn ⎠
⎛ σ − Pm log ⎜⎜ v ⎝ σ v − Pn N = ⎛V ⎞ log ⎜⎜ m ⎟⎟ ⎝ Vn ⎠
1.2
⎞ ⎟⎟ ⎠
σ ' = σ n 10 − b (φ − φ n )
Effective Stress Rasmus and Gray Stephens (1991)
resistivity
Bowers (1995)
acoustic
Holbrook (1987)
resistivity
Other
1
⎛ 1 V ⎞m φ − φ n = ⎜⎜ − c l ⎟⎟ ⎝ R o R cl ⎠
σ (b )
'
⎛ σ = σ max ⎜⎜ (a ) ⎝ σ max
⎞ ⎟⎟ ⎠
U
σ ' = A (1 − φ )
B
Symbols: σ is stress, σ' is the effective stress, P is the pore pressure, V is the lithology volume, R is resistivity, C is conductivity, dx is “drilling exponent”, Δt is interval transit time and φ is total porosity. Subscripts: a is parameter at the “normal pressure”, b is parameter at the depth of interest, n is the parameter at the “normal pressure”, o is the observed parameter, mat is matrix, min is minimum, max is maximum and v is vertical.
This method calculates Eaton’s (1975) N exponent m and b are local calibration factors
© 2005 Baker Hughes Incorporated All rights reserved.
σmax=σ′max (max. vel.) & U is a local calibration factor (3.13 for GoM) A & B are end-member parameters which vary based on lithology
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Resistivity Measurements Advantages
Limitations
¾ Resistivity data is often acquired from surface down to total depth
¾ Poorly defined normal trend in deep water environments
¾ Ability to use multiple trend-line and effective stress pressure prediction methods
¾ False indication of pressure due to pore water salinity change, proximity to salt and closeness to faults ¾ Temperature effects on measurement (resistivity decreases with increasing temperature) ¾ Resistivity response dependent on vertical resolution, depth of investigation and borehole rugosity
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Acoustic Measurement Advantages
Limitations
¾ Low sensitivity to hole size, formation temperature and pore water salinity
¾ Not run from surface to total depth in most wells
¾ Small effect of measurement around salt
¾ Lithology dependent, shale rich environments with no hydrocarbon influence work best
¾ Ability to calibrate with seismic-based predictions
¾ Variability in exponent in geologic areas
¾ Generally obtain good agreement with measured pore pressure data (e.g., RCI data) ¾ DTS shear data tends to show improved response in isolated pressured zones ¾ Ability to calculate bulk density and porosity from which overburden and pore pressure is derived
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Trend Line -based PP Prediction Line-based Step 1: Pick shale points Shale Point Guidelines
Shale picks denoted by red lines
• Pick shales at least 10-30 feet thick • Silty/limey shales should be avoided • Avoid picks within 10 feet of a sand • Shallow resistivity picks could be affected by the freshening of pore water
Note: It is necessary to select shale points because the PPP is valid only in the shale sections.
• Temperature correct resistivities, especially at shallow depths • Shales around salts may be too low of values • Geologic age boundaries and unconformities may shift trends • Hydrocarbon zones can affect the resistivity and/or acoustic readings © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Trend Line -based PP Prediction Line-based Step 2: Placement of Normal Trend Line (NTL) The trend line is defined by two points along the normal compaction trend, prior to entering the top of overpressure.
Inconsistent placement and slope of the NTL leads to errors in the predicted pore pressure!
NTL Slope is affected by: • Depositional rate • Age of the sediments • Thickness • Silt / lime content Potential overpressure zone
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
NTL Adjustments Shifting of the NTL is sometimes required to calibrate the pore pressure model when noncompaction related pressure mechanisms such as the presence of salt, faulting, unconformities or dipping beds are encountered. The shift should retain the same NTL slope!
NOTE: If a NTL shift is needed, verify from the company geologist/ geophysicist that tectonic-related mechanisms are present to support the shift.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Resistivity PP Prediction -example Prediction-example z
z
z
Due to the close proximity of salt, a shift of the normal trend line (NTL) was needed. In real-time, the actual degree of NTL shift needed is difficult without some sort of calibration or using some other data source such as acoustic data or measured pressure (such as TesTrak). Confidence in analysis is low if unable to compare with other types of analysis in this particular geologic environment (salt).
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Acoustic PP Prediction Prediction-- example
z
z z
z
In this case, no acoustic NTL shift was need to account for salinity changes, which was required by resistivity. Good agreement with wireline pressure tests. In areas of possible salinity water changes (around salt), using the acoustic improves the accuracy of the pore pressure & fracture gradient (PPFG) analysis. Reduced risk and increased safety with an accurate PPFG analysis
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
PP Adjustments z
z
z
Resistivity is affected by salinity changes much greater than acoustic. This gives an unrealistic indication of pore pressure. Adjustments to the RES NTL must be made to account for this effect, degree of shift must be calibrated with another PP source. No NTL adjustments for DTC, resulting in less error in PP.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Centroid Effects
After Eigill Nysaether Trindheim 2006 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Centroid Effects – lateral transfer Pressure
Large pressure in the reservoir that the Shale
Depth
Starting of Overpressure Zone
Increase Pressure Line of Overpressure
Hydrostatic
Tilt Res erv
oir
Lithostatic
After R. Swarbrick CSEG 2002
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Centroid Effects – fracturing potential
After Heppard and Traugott
© 2005 Baker Hughes Incorporated All rights reserved.
The equivalent mud weight increases toward the crest while decreases in the bounding shale which therefore also has a corresponding decrease in hydraulic fracture pressure. A well drilled directly at the structural crest of a trap can lose returns into the seal with the mud pumps on and have flow from the reservoir with the pumps off. Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Summarizing Pore Pressure ¾ Pore pressure prediction requires a complete formation evaluation analysis from “surface to total depth” to provide an accurate pressure prediction. ¾ Log response must be carefully analyzed for geological, structural, borehole and formation effects on measurements. ¾ Ability to use multiple effective stress pressure prediction methods is required to accurately predict PP. ¾ The use of multiple trend-lines may be necessary in geologically complex regions ¾ Seismic calibration of the acoustic data can enhance pre-drill models for real-time prediction. ¾ Real-time resistivity and acoustic can be used to continuously update the PP model as well as to provide “ahead of the bit” predictions.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Wellbore Stability Basics © 2005 Baker Hughes Incorporated All rights reserved.
Outline I. II. III. IV. V.
Stress distribution around a circular borehole Failure modes and failure criteria Mud weight window Stress polygon Borehole strengthening
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stress Concentration σh
σH
σH σh
When a well is drilled in a formation, stressed solid materials is removed and replaced with a fluid under pressure. Since the well fluid pressure normally does not match exactly the stress which the removed solid exerted, there will be an alteration in the stress state of the formation around the well. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
The Need for a 3D Stress Analysis Around A Borehole Multilateral Configurations
Dual
Stacked
Trilateral Fork
Herringbone
Backbone and Rib
Radial
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stresses Around A Borehole Coordinate Systems Z
Z βb
Xs
X
τbyz τbxy
τYX
X (North)
rock property
zb (borehole axis-down) Deeper Depth σbzz
τbyz
τZX
σXX
X
σ
xb (hole bottom)
τXY
αr
Z (down)
σZZ
τXZ
Y
zb (borehole down)
τZY
σbyy
σYY Y (East)
τYZ
Yr
Xr
βr
borehole
Stress Transformation Z (down)
Xb
αb
αs far-field stress
Z
Y
Y
X
Zr
Yb
Ys
βs
(Anisotropic Materials)
Zb
Zs
τbxz
σbzz τbyz τbxz
θ σθθ
xb (bottom of hole) τbxy
τbxz τbxy σbxx
σzz
a
τbxz
yb σrr
τbyz τbxy
σbyy
σbxx
Shallower Depth
Y (East)
yb
(Stress Components)
© 2005 Baker Hughes Incorporated All rights reserved.
X (North)
(Local Coordinate)
Efficiency….Data accuracy….People-oriented service
(Cylindrical Coordinate) www.bakeratlasdirect.com
Stresses Around the Borehole Due Dueto tothe thecylindrical cylindricalshape shapeof ofthe thestructure, structure,aacylindrical cylindricalcoordinate coordinatesystem system is often selected as the working coordinate system. The total stress-field is often selected as the working coordinate system. The total stress-field around aroundaawellbore wellboreof ofarbitrary arbitraryorientation orientationis isthus thusdefined definedby byσσrrrr’,’,σσθθθθ’,’,σσzzzz’,’,ττrθrθ, , ττrz, ,and andττθz :: rz
θz
(σbxx + σbyy ) ⎛ a 2 ⎞ (σbxx − σbyy ) ⎛ ⎛ a2 a4 ⎞ a2 a4 ⎞ a2 σ rr = ⎜ 1 − 2 ÷+ ⎜ 1 − 4 2 + 3 4 ÷ cos 2θ + τbxy ⎜ 1 − 4 2 + 3 4 ÷ sin 2θ + Pmud 2 r r ⎠ r r ⎠ r 2 2 ⎝ r ⎠ ⎝ ⎝ (σbxx + σbyy ) ⎛ a 2 ⎞ (σbxx − σbyy ) ⎛ ⎛ a4 ⎞ a4 ⎞ a2 σθθ = ⎜1 + 2 ÷ − ⎜1 + 3 4 ÷ cos 2θ − τbxy ⎜ 1 + 3 4 ÷ sin 2θ 1− Pmud 2 r ⎠ r ⎠ r 2 2 ⎝ r ⎠ ⎝ ⎝ a2 a2 σ zz = σbzz − 2υ (σbxx − σbyy ) 2 cos 2θ − 4υτbxy 2 sin 2θ r r ⎡ (σbxx − σ by ) ⎤⎛ a2 a4 ⎞ sin 2θ + τbxy cos 2θ ⎥⎜ 1 + 2 2 − 3 4 ÷ τ rθ = ⎢ y 2 r r ⎠ ⎣ ⎦⎝ ⎛ a2 ⎞ τrz = τbyz sinθ + τbxz cosθ ⎜ 1 − 2 ÷ ⎝ r ⎠
[
[
]
⎛ ⎝
]
τθz = − τbxy sinθ + τbyz cosθ ⎜1 +
z’ y’ O ’
β
x’ 2 α
a ⎞ ÷ r2 ⎠ 2
3 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stresses Around the Borehole At Atthe theborehole boreholewall, wall,the theeffective effectivestress stresscomponents: components: η = Biot' s constant − ηP rr mud pore ) − 2(σ ) cos 2θ − 4τ sin 2θ − P σ ' = (σ +σ −σ − ηP bxx byy bxx byy bxy mud pore θθ ) cos 2θ − 4υτ sin 2θ − ηP σ' = σ − 2υ (σ −σ 1 zz bzz bxx byy bxy pore τ =0 rθ z’ y’ τ =0 rz O sinθ + τ cosθ ) τ = 2( −τ bxz byz θz ’
σ' = P
β
x’ 2
The effective Principal Stresses at the borehole wall are: α
σ 1' , 2 =
σ θθ' + σ zz' 2
±
© 2005 Baker Hughes Incorporated All rights reserved.
(σ
'
θθ
− σ zz' 4
)
2
+ 4τ θ2z
σ ' = Pmud − ηPpore 3
Efficiency….Data accuracy….People-oriented service
3 www.bakeratlasdirect.com
Stresses Around the Borehole Pw = Pmud , Pp = Ppore σv
For the special case of a vertical well and in the principal stress directions (θ1, θ2):
σ
' 1, 3
=σ
θ2 θθ θ1 '
r
and if σ bxx = σ H , σ byy = σ h
σ
1
= 3σ H − σ h − pw − Pp
σ ' = 3σ h − σ H − pw − Pp 3
© 2005 Baker Hughes Incorporated All rights reserved.
σH
θ
The maximum tangential stress (σ1) occurs at θ = 90° & 270°→ cos (2θ) = -1
'
θ
z z’
σ rr = pw σ θθ = σ H ( 1 − 2 Cos 2θ ) + σ h (1 + 2 Cos 2θ ) − pw σ zz = 0 τ rθ = τ rz = τ θ z = 0
The minimum tangential stress (σ3) occurs at θ = 0° and 180°→ cos (2θ) = 1
σh
x’
r
y’
σh
σH
IfIfmax maxhoop hoopstress stressisistoo toohigh high(compression), (compression), the rock may fail in shear !!! the rock may fail in shear !!! IfIfmin minhoop hoopstress stressisistoo toolow low(tension), (tension), the rock may fail in tension !!! the rock may fail in tension !!!
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stresses Around the Borehole For the special case of a horizontal well drilled parallel to the maximum horizontal stress … σv
If σv > σh
σv σh
z’
σ ' = 3σ v − σ h − pw − Pp ( Along σ h ) 1
σ ' = 3σ h − σ v − pw − Pp ( Along σ v ) 3
If σh > σv y’
σH
x’
© 2005 Baker Hughes Incorporated All rights reserved.
σh
σ ' = 3σ h − σ v − pw − Pp ( Along σ v ) 1
σ ' = 3σ v − σ h − pw − Pp ( Along σ h ) 3
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stresses Around the Borehole For the special case of a horizontal well drilled parallel to the minimum horizontal stress … σv
If σv > σH
σv
σH
σ ' = 3σ v − σ H − pw − Pp ( Along σ H ) 1
σ ' = 3σ H − σ v − pw − Pp ( Along σ v ) 3
z’
If σH > σv
σ ' = 3σ H − σ v − pw − Pp ( Along σ v ) 1
σ ' = 3σ v − σ H − pw − Pp ( Along σ H ) 3
σH
x’
© 2005 Baker Hughes Incorporated All rights reserved.
y’
σh
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stresses Around the Borehole
σh
Numerical Example σh = 3500 psi σH = 5000 psi Pw = Pp = 3000 psi
A Pw
θ B
σH
At A: σ’θ = 3(5000) – (3500) – 3000 – 3000 = 5500 psi (+) At B: σ’θ = 3(3500) – (5000) – 3000 – 3000 = -500 psi (-) At A: σ’θ = 5500 psi (compressive) – breakout, shear failure At B: σ’θ = -500 psi (tensile) – hydraulic fracturing
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline I. II. III. IV. V.
Stress distribution around a circular borehole Failure modes and failure criteria Mud weight window Stress polygon Borehole strengthening
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Typical Borehole Failure Modes For a vertical well … If the mud weight becomes excessive, it may induce hydraulic fracturing (tensile failure) of the rock!
σH
tensile failure
Pw Note: These are the most common types of wellbore failure!
© 2005 Baker Hughes Incorporated All rights reserved.
σh
active shear failure
Efficiency….Data accuracy….People-oriented service
If the mud weight is too low, lack of wellbore support could induce rock compressive (active shear) failure!
www.bakeratlasdirect.com
Other Borehole Failure Modes For a vertical well …
If the mud weight becomes excessive, passive shear failure may occur! In most cases, passive shear failure is preceeded by hydraulic fracturing (tensile failure)!
σH
passive shear failure
Pw
Note: The location of spalling may occur anywhere along the wellbore!
σh
© 2005 Baker Hughes Incorporated All rights reserved.
radial tensile failure (σrr = pw – pp ≤ To)
Efficiency….Data accuracy….People-oriented service
If the mud weight is insufficient (resulting in underbalanced situation) and rock permeability is low, radial tensile failure (i.e., spalling or sloughing) may occur! www.bakeratlasdirect.com
Evidence of Borehole Failure resistivity image
acoustic image
STAR Image Borehole Breakout 180º What is the maximum hole deviation that we can use breakout to deduce the stress orientation with some degree of certainty?
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
Breakout direction corresponds to the orientation of σh in a vertical well
www.bakeratlasdirect.com
Shear/Compressive Failure Modes Breakout (onion peeled failure) – Type A σ θ > σ z > σr
σHmax
Toric failure – Type B
σHmin
σ z > σ θ > σr Helical shear failure – Type C σ z > σ r > σθ
© 2005 Baker Hughes Incorporated All rights reserved.
σθ = hoop stress σz = axial stress σr = radial stress
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Shear/Compressive Failure Modes
Wide breakout – commonly called breakout
Shallow knockout – the circumferential coverage is small and could be caused with a vertical fracture
High angle enchelon – makes highangle fractures that cover up to a quarter of the borehole circumference
Narrow breakout – the annular coverage is typically less than 300
σθ > σ z > σ r
σ z > σθ > σ r
σ z > σ r > σθ
σ r > σ z > σθ
Rezmer-Cooper, Bratton and Krabbe (2000) – SPE 59225 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Shear/Compressive Failure Modes
Rezmer-Cooper, Bratton and Krabbe (2000) – SPE 59225 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Shear/Compressive Failure Modes
Low angle enchelon
σθ > σ r > σ z
Deep knockout – occurs in the vertical plane, but is centered at the azimuth of the maximu horizontal stress
σ r > σθ > σ z
Rezmer-Cooper, Bratton and Krabbe (2000) – SPE 59225 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Modes – Breakout - INSUFFICIENT wellbore pressure (lack of support) - big difference between the in-situ stresses - low formation strength
σσθθ(max) = 3σ – σ – P – P (max) = 3σHH – σhh – Pww – PPP
Tangential stress acting at the borehole wall
If σH >> σh , the resultant tangential stress will be very high, which can potentially destabilize the borehole.
22(45°+φ/2) σσθθ(max) = UCS + (P – αP ) tan = UCS + (P w – αP p ) tan (45°+φ/2) (max) w p
Comparison of tangential stress (load) and rock strength Æ M-C failure criterion
From the equations, we can see that raising the mud weight has two beneficial effects: reduce the tangential stress increase the effective strength. These effects (in addition to controlling wellbore trajectory) effectively maintain borehole stability. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Modes – Breakout Compressive strength
Azimuthal Maximum Tangential Stress Distribution Compared with Rock Compressive Strength
σHmax=8000 psi @NS σhmin=6500 psi @EW σv=10000 psi @ Vert Pp = 4600 psi, UCS=8500 psi Mud Weight = 11.0 ppg
180
-175 -165-170 -160 -155 -150 12000 -145 -140 -135 -130 9000 -125
175 170 165
160
155
150 145 140 135 130 125
-120
Borehole Deviation = 0, Azimuth = 0
120
-115
115
6000
-110
110
-105
105 3000
100
Strength
95
drill//sH,Max_Tan Stress
-95 -90
0
90
-85
85
-80
80
-75
10000
-100
75
-70
N
70
-65
65
Compressive -55 stress -50
-60
6500
60 55 50
-45
45 -40
00 80
40 -35
35 -30
-25
-20
-15 -10
-5
5
10 15
20
25
30
0
Borehole Low-Side
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Modes – Breakout Compressive strength
Azimuthal Maximum Tangential Stress Distribution Compared with Rock Compressive Strength
σHmax=8000 psi @NS σhmin=6500 psi @EW σv=10000 psi @ Vert Pp = 4600 psi, UCS=8500 psi Mud Weight = 11.0 ppg
180
-175 -165-170 -160 -155 -150 12000 -145 -140 -135 -130 9000 -125
175 170 165
160
155
150 145 140 135 130 125
-120
Borehole Deviation = 60, Azimuth = 0
120
-115
115
6000
-110
110
-105
105 3000
100
Strength
95
drill//sH,Max_Tan Stress
-95 -90
0
90
-85
85
-80
80
-75
10000
-100
75
-70
N
70
-65 -60 -55 -50 -45
65
Compressive stress
6500
60 55 50 45
-40
00 80
40 -35
35 -30
-25
-20
-15 -10
-5
5
10 15
20
25
30
0
Borehole Low-Side
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Modes – Breakout Azimuthal Maximum Tangential Stress Distribution Compared with Rock Compressive Strength
Compressive strength
σHmax=8000 psi @NS σhmin=6500 psi @EW σv=10000 psi @ Vert Pp = 4600 psi, UCS=8500 psi Mud Weight = 11.0 ppg
180
-175 -165-170 -160 -155 -150 12000 -145 -140 -135 -130 9000 -125
175 170 165
160
155
150 145 140 135 130 125
-120
Borehole Deviation = 90, Azimuth = 0
120
-115
115
6000
-110
110
-105
105 3000
-100
100
Strength
95
drill//sH,Max_Tan Stress
-95 -90
0
90 85
-80
10000
-85
80
-75
75
-70
N
70
-65
65
Compressive stress
-60 -55 -50 -45
6500
60 55 50 45
-40
00 80
40 -35
35 -30
-25
-20
-15 -10
-5
5
10 15
20
25
30
0
Borehole Low-Side
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Modes – Breakout Major breakouts Problems: Ê high volume of solids due to rock spalling/caving Ê poor hole cleaning (more critical in inclined wells) Ê stuck pipe Ê high torque and drag Remedies: Ê increase wellbore fluid density Ê increase the sealing capacity of drilling fluid Ê minimize surge and swab pressure
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Modes – Breakout Small breakouts Problems: minor breakout is a restricted zone of shear failure wellbore is stabilized without experiencing borehole instability related problems the width and direction of breakouts are used for in-situ stress characterization Remedy: use controlled breakout concept to enhance drilling and completion efficiency
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Modes – Controlled Breakout Azimuthal Maximum Tangential Stress Distribution Compared with Rock Compressive Strength no breakout!
180 -175 -165-170 8000 -160 -155 -150 7000 -145 -140 6000 -135 -130 5000 -125 -120
175 170 165
160
180
155
-165-170 -160 -155 -150 -145 -140 -135 -130 -125
150 145 140 135 130 125
-120
120
4000
-115 3000
-105
110 105
2000
-100
100 1000
-95 -90
65
-60
-25
-20
-15 -10
-5
5 0
10 15
20
25
30
105
2000
100 95
85
-85
85
80
-80
80
90
0
-75
75
-70
70
MW = 11 ppg
-65
65
-60
60
-55 -50 -45
45
-30
110
1000
40 35
115
-100
55
-35
120
3000
-105
50 -40
5000 4000
-110
60
-55 -50 -45
145 140 135 130 125
6000
-95
70
MW = 12 ppg
-65
150
-90
75
-70
155
90
-85
-75
160
7000
95
0
-80
175 170 165
-115
115
-110
-175 8000
70° “allowed” breakout!
55 50 45 -40
Confined Strength Max Tang Stress
40 -35
35 -30
-25
-20
-15 -10
-5
5
10 15
20
25
30
0
Lower MW can be used if breakout is allowed to form! NOTE: Due to wellbore cleaning issues, the max. allowable breakout size in deviated boreholes is less than in vertical ones !!! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Shear Failure Criteria σ1 = UCS + σ3 tan 2 ( π4 + φ2 )
Mohr-Coulomb
2 3 sin φ A = Drucker Prager 3 − sin φ J2 =
[
J 2 = A × J1ef + B
1 (σ rr − σθθ )2 + (σθθ − σ zz )2 + (σ zz − σ rr )2 6 + σ 2rθ + σ θ2z + σ 2rz
Modified Lade
]
J1ef =
B=
2 3 cos φ 3 − sin φ
σ rr + σθθ + σ zz − p( r , t ) 3
'' 3 1
I = 27 + η '' I3
I ' '1 = (σ 1 + S1 − p0 ) + (σ 2 + S1 − p0 ) + (σ 3 + S1 − p0 )
I 3 = (σ 1 + S1 − p0 ) ⋅ (σ 2 + S1 − p0 ) ⋅ (σ 3 + S1 − p0 ) p0 : pore pressure S o: Mohr − Coulomb cohesion
© 2005 Baker Hughes Incorporated All rights reserved.
S1 =
S0 , η = 4 tan 2 φ (9 − 7 sin φ )(1 − sin φ ) tan φ
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Shear Failure Criteria Intermediate principle stress has no influence on rock strength
Mohr - Coulomb
Overestimate the effect of intermediate principle stress on rock strength
Drucker - Prager
Less conservative than Mohrcoulomb. More conservative than DruckrPrager (predicts greater strengthening effect from σ2).
© 2005 Baker Hughes Incorporated All rights reserved.
Major Stress, σ1 (psi)
Initial strengthening from increasing σ2, then decrease in strength.
Drucker - Prager
Modified Lade Mohr-Coulomb Intermediate Stress, σ2 (psi)
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effect of Failure Criteria on Critical Mud Weights (CMW) 13
Critical Mud Weight (ppg)
12
Mohr - Coulomb
CMW increases with increasing of inclination due to in-situ stress anisotropy
Modified Lade
11
10 9
Drucker - Prager
8
7 0
10
20
30
40
50
60
70
80
90
M-C predicts highest CMW, DP lowest CMW, and M-L is in the middle at the same inclination.
Well Inclination (degrees)
Ewy - SPE 47251 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Tensile Failure Modes
Cylindrical – concentric with the borehole, and is not visible on a wellbore image
σ r' < 0 Pw − Pp < −to
Horizontal
σ 3' < −to
Vertical
σ 3' < −to
Rezmer-Cooper, Bratton and Krabbe (2000) – SPE 59225 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Modes - Tension • Tensile fracture (vertical) - triggered by excessive wellbore pressure - big issue when having a big difference between the in-situ stresses acting normal to the borehole axis - fracture traces are diametrically opposed - fractures may extend long distances along the wellbore
σσ’’θθmin = 3σ – σ – P – P min = 3σhh – σHH – Pww – PPP
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Modes – Tension … ((ctd.) ctd.) Petal fractures: hydraulically-induced fractures that form ahead of the bit. Normally found in relatively stiff formations; probably caused by a combination of high mud weight and high weight-on-bit. Centerline fractures: Hydraulically-induced features that connect previously formed petal fractures
Hydraulic fractures: Used as a reservoir-stimulation and management method. Could be planned (for stimulation purposes) or accidental (i.e. drilling-induced fractures).
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Evidence of Borehole Failure
Drilling Induced Fractures (hydraulically induced)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Evidence of Borehole Failure IMAGE LOG
CORE PHOTOGRAPH Petal Fracture
Petal Centerline fracture
Breakout © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
180° www.bakeratlasdirect.com
Failure Modes – Tension … ((ctd.) ctd.) Drilling Induced Fractures Problems: Ê lost circulation - sudden loss of drilling fluid Ê similar fluid loss gradient across the field Ê losses occur when breakdown pressure > fracture gradient (fracture propagation pressure) Remedies: Ê decrease wellbore fluid gradient Ê increase the sealing capacity of drilling fluid
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline I. II. III. IV. V.
Stress distribution around a circular borehole Failure modes and failure criteria Mud weight window Stress polygon Borehole strengthening
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mud Weight Window - Definition of Terms )
Fracture initiation pressure is the wellbore pressure above which the initiation of hydraulically-induced fractures will take place.
)
Breakdown pressure is the wellbore pressure at which the formation of major hydraulically-induced fractures is expected to take place.
)
Fracture gradient is the wellbore pressure gradient above which the propagation of pre-existing fractures will take place.
)
Minimum mud weight @ breakout size is the mud weight below which the formation of breakouts of specific size (width in degrees) will take place.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pressure
For Clarification Purposes …
Pbreakdown
T0
Preopening
Ppropagation Frac.Grad. = σ3
time 1st PRESSURE CYCLE © 2005 Baker Hughes Incorporated All rights reserved.
2nd PRESSURE CYCLE Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mud Weight Window SHEAR FAILURE
IDEAL MW
TENSILE FAILURE
REAL LIFE MW
Excessive BO
Minor BO
In-gage hole Minor Losses
Excessive Losses
σ3 σ2
Pw
Pw
Low Pore Pressure © 2005 Baker Hughes Incorporated All rights reserved.
Pw
Pw
Mud Weight Scale
Pw
High
σ3 (magnitude)
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mud Weight Window … (ctd.) SHEAR FAILURE
IDEAL MW
TENSILE FAILURE
REAL LIFE MW
Æ Mud weight range defined by the breakout limit (lower bound) and the fracture propagation limit (upper bound).
Excessive BO
Minor BO
In-gage hole Minor Losses
Excessive Losses
σ3 σ2
Pw
Pw
Low Pore Pressure
Pw
Pw
Mud Weight Scale
Pw
High σ3 (magnitude)
ÆThe breakout limit is the minimum mud weight that could be used without exceeding the maximum allowable breakout size. Also defined by the Pp if the formation is sufficiently strong Æ The fracture propagation limit or fracture gradient is equal to the magnitude of the closure stress (minimum principal stress, σ3) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mud Weight Window … (ctd.) TUNE - Well 30/9-11-H
EMW (sg) 1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2,000
2.9
3
Balder FM
2,200
ROGALAND GRP
Fracture gradient, i.e. σ3
2,400
Mud window
2,600
SHETLAND GRP
2,800
3,000
Pore pressure
Depth, MD (m)
3,200 Viking
3,400
Breakdown Pressure
3,600
3,800 BRENT
4,000
4,200
MW for allowing 0, 30 and 60 degree breakouts
4,400
4,600
4,800
5,000 0
10
20
Pp MW (Breakout =0 deg) MW (Breakout =90 deg)
© 2005 Baker Hughes Incorporated All rights reserved.
30
40
50
FG MW (Breakout =30 deg) Breakdown
60
70
80
90
OBG MW (Breakout =60 deg) Inclination (deg)
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mud Weight Window The curves of pore pressure and fracture gradient are very important as they also define the casing setting depths: 8 0
8
Equivalent mud density (lb/gal) Equivalent mud density (lb/gal) 10 12 14 16 18 10 12 14 16 18
20 20
0
2,000 2,000
Csg. setting depth
4,000 4,000
(Data from Bourgoyne et al., 1991)
Depth (ft) Depth (ft)
6,000 6,000
8,000 8,000
10,000 10,000
Csg. setting depth
12,000 12,000
14,000 14,000
Pp Pp FG PpFG + 0.5 Pp- 0.5 + 0.5 FG FG - 0.5
Target
16,000 16,000
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mud Weight Contour Plot N 45
E
45
45 , 5 4
N 90
90, 90
0 270
90
N
N 0
E
45
E 180
© 2005 Baker Hughes Incorporated All rights reserved.
E
90
Efficiency….Data accuracy….People-oriented service
0, 0
www.bakeratlasdirect.com
Outline I. II. III. IV. V.
Stress distribution around a circular borehole Failure modes and failure criteria Mud weight window Stress polygon Borehole strengthening
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Evidence of Borehole Failure STAR Image - Drilling Induced Fracture (tensile feature) & Breakout (shear failure)
Breakout
Fracture
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Maximum Horizontal Stress (σH)
Stress Polygon
RF
f (μ) =
σh=σH SS
(μ
+1 + μ
)
2
σ1 − pp = f (μ ) σ 3 − pp
NF
Mohr’s Diagram
σv
Stress Polygon Bounding of horizontal stresses through the Frictional Theory. 1 ⎡ 2 ⎤ σ 1 = Co + σ 3 ⎢ χ + 1 2 + χ ⎥ ⎣ ⎦
)
© 2005 Baker Hughes Incorporated All rights reserved.
2
χ = tan φ φ = angle of internal friction
Shear Stress (τ)
Minimum Horizontal Stress (σh)
(
2
n ictio r F μ=
ient c i f f oe al C
Normal Stress (σ)
Co = uniaxial compressive strength
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stress Polygon
Breakdown line: (Tensile failure)
σ H = 3σ h − Po − Pb + To
σ
σ
σ
V >line: H , max > hfailure) , min Breakout (Compressible ⎡ C f + Pw + αPo ⎤ σ h [1 + 2 cos(2ϕ )] − Normal⎥Faulted ( ) [1 − 2 cos(2ϕ )] − 1 2 cos 2 ϕ ⎣ ⎦
σH = ⎢
In-situ stress regime
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stress Polygon
σ H ,max > σ V > σ h ,min Strike-Slip Faulted In-situ stress regime
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stress Polygon
σ H ,max > σ h,min > σ V Reverse or inverse In-situ stress regime
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Coefficient of Friction
Byerlee (1978)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stress Polygon Horizontal Stress Estimation
Maximum horizontal Stress (σH)
Induced fractures (extensional failure)
σ H = 3σ h − Po − Pb + To Breakout (Shear failure) ⎡ C f + Pw + αPo ⎤ σ h [1 + 2 cos(2ϕ )] σH = ⎢ ⎥− ( ) [1 − 2 cos(2ϕ )] − 1 2 cos 2 ϕ ⎣ ⎦
RI RF
RT
σh=σH
RN SS
By superposition of: Frictional theory Extensional failure Shear failure
NF
Knowledge of σh Î LOT, XLOT
σv Minimum Horizontal Stress (σh) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stress Polygon Bounding the horizontal stresses by using stress polygon and failure mechanism. North Sea Case: Breakout Induced Fractures The strength (UCS) of this zone is determined by LMP.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stress Polygon – Constraining the Horizontal Stresses
Pp=0.74 psi/ft Pmud=1.83 sg UCS= 3790 Psi θb=32°
∇σ
h
≅ 0 . 82
UC
© 2005 Baker Hughes Incorporated All rights reserved.
⇒
σ σ
H
= 1 . 17
h
0 psi 9 7 3 S=
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stress Polygon – Horizontal DIF Stress Calibration
DIF and breakout
No stress features
SPE 105808 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline I. II. III. IV. V.
Stress distribution around a circular borehole Failure modes and failure criteria Mud weight window Stress polygon Borehole strengthening
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Implications on a GoM Drilling Program Typical GoM Casing Profile
Including mud heating
frac gradient
“New” frac gradient is expanded due to heating. Therefore, the safe MW window is increased! “old” frac gradient
pore pressure
Requires 5 casing seats to reach TD
© 2005 Baker Hughes Incorporated All rights reserved.
pore pressure
$
$
driller
Requires only 4 casing seats to reach TD
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Borehole Strengthening
) Controlled ) Fracture ) Internal
Breakout
Linking and Plugging
Mud Cake
) Temperature
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Borehole Breakout – Lab Observation
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Borehole Strengthening – Breakout Normalized Strength, σ H/Co
3 2.5 2 1.5 1
Small Blk
0.5 Large Blk 0 Breakout
• Experiments have been conducted to examine “excavation strength” of circular and “broken out” geometry under same stress conditions - Breakout geometry has up to 40% higher strength than a circular geometry.
Circular
Excavation Geometry
Table 1. Strength of Breakout and Circular Excavations (Reference 28) K max K max Co σH σH (MPa) σH Co (MPa) Shape Co BK 1 BK 2 BKavg CR BK CR
Small Blocks (27.9cm × 27.9cm × 27.9cm) 19.24 2.80 >6 19.24 2.76 >6 19.24 2.78 >6 19.24 2.03 2.5 Large Blocks (100cm × 100cm × 105cm) 37.24 19.24 1.94 >6 27.93 19.24 1.45 2.5
53.79 53.10 53.45 38.97
16.80 16.56 16.68 5.06 11.61 3.63
σH - Maximum applied far field stress at on set of excavation failure. Co - Unconfined compressive strength of tested material. Kmax - Maximum stress concentration on each excavation shape. BK - abbreviation for breakout CR – abbreviation for circular geometry © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stress Variations with Breakout x
a
σ1
2 0 .7
b
x
P O IN T a
4 8 .3
S E C T IO N I
x
S E C T IO N II
c
S E C T IO N III x d e x
-6 .9 -3 4 .5
σ3 1
5
P O IN T c
P O IN T b
σ1
4 8 .3
4 8 .3
σ1
x
2 0 .7
x
2 0 .7
σ3
-6 .9
-6 .9
-3 4 .5
-3 4 .5
5
10
5
σ1
7 5 .8
STAGE A
4 8 .3
STAGE B
1
(c )
(d )
σ1
STAG E B x
σ3
-6 .9 -3 4 .5
STAGE B P O IN T d
x
STAGE A
4 8 .3 x
σ3
2 0 .7
© 2005 Baker Hughes Incorporated All rights reserved.
5
(e )
10
x
P O IN T e
-6 .9 1
10
7 5 .8
x
x
2 0 .7
x
σ3 STAGE A
1
10
(b )
(a )
1
5
Efficiency….Data accuracy….People-oriented service
(f)
10
www.bakeratlasdirect.com
Controlled Breakout - Summary Experimental and numerical studies have shown that boreholes with breakout geometry are more stable than circular boreholes, especially in high stress environments. Utilizing breakout concept helps to increase the choice of drilling directions in highly inclined boreholes, decrease mud weights and, hence, reduce formation damage and lost circulation. May need to increase the drilling fluid lifting capacity for effective hole cleaning.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Controlled Breakout - Application Mud MudWeight, Weight,PPG PPG 8.5 8.5
10 10
10.5 10.5
11 11
11.5 11.5
12 12
40 40
50 50
60 60
70 70
12.5 12.5
13 13
Frac-Propagation Frac-Propagation
1200 1200
Breakout=0deg. deg. Breakout=0
1500 1500 1600 1600
BoreholeDeviation Deviation Borehole
1700 1700 1800 1800 1900 1900 2000 2000
TrueVertical VerticalDepth Depth(Sub (SubSea), Sea),meter meter True
1400 1400
Breakout=60deg. deg. Breakout=60
1300 1300
SPE 64620 – Technology Applied to Extend the Drilling Reach of a Platform Workover Rig CADE 2003-005 – Wellbore Stability (Geomechanics) Modeling and Drilling Optimization Practices Reduce Drilling Cost – Terra Nova Project
9.5 9.5
1100 1100
1000 1000
SPE 47282 – Integrated Borehole Stability Analysis – Against Tradition
99
0
0
10 10
20 20
30 30
80 80
90 90
Borehole BoreholeDeviation Deviationfrom fromVertical, Vertical,degree degree
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Borehole Strengthening - Fracture )
Fracture Link-up Pressure •
•
According to Weng [SPE 26597] and Ito et al. [SPE 57007], if multiple fractures are induced, there is a critical pressure, Plink, above which the fractures will link up. If the mud pressure is less than Plink, no serious mud loss will occur.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Borehole Strengthening - Fracture )
Fracture Link-up Pressure •
If
σ norm f σ para →
•
If
σ para f σ norm
ω f = ω crit
Pw = σ norm ( Pw )
−0.72 ⎡ ⎤ − σ σ ⎧ para norm ⎫ −1 = sin ⎢0.57⎨ ⎬ ⎥ ⎢⎣ ⎩ Pw − σ norm ⎭ ⎥⎦
σpara
ωf=fracture inclination angle. Substitute ωf for ωcrit and solve for Pw
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
σnorm
www.bakeratlasdirect.com
Borehole Strengthening - Fracture Fracture Propagating Pressure According to Ito et al. [SPE 57007], after fractures linked up and if the mud pressure is not sufficient to propagate the fracture, no serious mud loss will occur. For plugged penny shape fracture:
•
•
p grow σ minh
1=
p pore σ minh
⎛c ⎞ 1−⎜ 1 ⎟ ⎝c⎠
⎛c ⎞ 1− 1−⎜ 1 ⎟ ⎝c⎠
2
2
4.0 3.5 3.0 P g ro w /σ m in h
)
Ppore/Sminh=0.0
Ppore/Sminh=0.2
Ppore/Sminh=0.4
Ppore/Sminh=0.6
Ppore/Sminh=0.8
Ppore/Sminh=1.0
2.5 2.0 1.5 1.0 0.5
c1 c1
0.0
c
0.7
0.75
0.8
0.85
0.9
0.95
1
c1/c
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Borehole Strengthening - Fracture )
Fracture Propagating Pressure According to Fuh et al. [SPE 24599] and Morita et al. [SPE 20409]: • Fluid leaks off into formation during fracture propagation and mud is concentrated during leak-off. • Dehydrated mud bridges near fracture tip, increases the fracture propagation pressure.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Wellbore “Strengthening” – Stress Cage Imagine the case of a fractured block that is kept loaded between two fixed (i.e. zero displacement) plates Æ constant stress across the rock (along red dotted lines) Now imagine that the fracture is forced (and kept) open Æ The compressive stress magnitude is increased near the edge of the rock where the fracture is. The wider the fracture, the more difficult it becomes to further open the crack In a well, the tangential stress around the borehole will increase; therefore, increasing the closure stress (i.e. the effective fracture gradient) of the formation (Fuh et al., 1992; Alberty and McLean, 2004; Dupriest, 2005)
Zone of increased closure stress (actual shape may differ)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stress Cage – Solution Concept
After Mark Alberty (2005) © 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Wellbore “Strengthening” – Stress Cage … (ctd.) Ê Wellbore initially stable, no
PW
fractures
σC
Ê Fracture is created; as fluid enters the crack, bridging particles and mud cake block the fracture entrance (PW > Pf > σC)
PW
Pf
σC
Ê After blocking has occurred, the fluid within the fracture is leaked off; thus, allowing the fracture to close (PW > Pf ~ σC2) Æ As a final result, the effective closure pressure acting on the rock is increased!!! (σC < σC2) © 2005 Baker Hughes Incorporated All rights reserved.
PW
σC2
Efficiency….Data accuracy….People-oriented service
σC2 www.bakeratlasdirect.com
Wellbore “Strengthening” – Stress Cage … (ctd.) Ê In low permeability rocks, the blocking “bridge” needs to be completely impermeable. Low leak-off WILL NOT reduce the fluid pressure within the fracture; thus, creating the conditions for further fracture extension (VERY UNSUCCESSFUL)
PW
Ê In permeable rocks (k > 1 md), even a partially permeable “bridge” may effectively arrest fracture growth. Leak-off will dissipate any fluid pressure increment in the fracture, reducing the possibility of experiencing additional fracture extension (EXTREMELY SUCCESSFUL)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
PW
www.bakeratlasdirect.com
Wellbore “Strengthening” – Stress cage … (ctd.) Design Procedure (Alberty and McLean, 2004)
Determine the fracture gradient increment goal Based on this goal, and using the rock mechanical properties and in-situ stress, calculate the fracture aperture needed at the borehole (normally a finite elements model is used for this purpose)
Determine particle size distribution and concentration of the solids used for wellbore strengthening. Solids such as calcium carbonate (stress support) and graphite (hydraulic seal) are commonly used.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Wellbore “Strengthening” – Stress cage … (ctd.) Highlights:
8 Very limited success in low permeability rocks (e.g. shales) Æ may be due to time dependent, to early response to loading (Wilson, 2005), and also to low leak-off rates.
8 Extremely successful in permeable (k > 1 md), soft formations 8 Failure to obtain good results in tectonic environments (e.g. strike-slip, inverse)
9 Proven technology in non-tectonic environments (when applied to permeable rocks)
9 Easy design and relatively standard job application
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Internal mud cake – Physical Model
1
2
σθ = σθ + σθ
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
σ r2 = Pw σ θ2 =
Po R22 − Pw R12 R22 − R12
+
(Po − Pw )R22
(R
2 2
− R12
)
www.bakeratlasdirect.com
DS is composed deformable colloidal particles that bridges at the borehole interface of lowpermeability sandstone formations Successful bridging requires proper characterizations of grain and pore throat sizes Under high differential pressure, DS is forced to penetrate into the face of the sand This forced ”packing” together with the deformable characteristics of the sealant provides a better internal mudcake sealing © 2005 Baker Hughes Incorporated All rights reserved.
Depth
Internal mud cake – Deformable Solid
0.1
Efficiency….Data accuracy….People-oriented service
1.0
10.0
100.0
Sand Particle Size microns
www.bakeratlasdirect.com
Internal Mud Cake – Effect of Stiffness Ratio
Tangential stress (psi)
30000 25000 20000 15000 10000 5000 0 0.75
1.00
1.25
1.50
1.75
2.00
2.25
E1/E2
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Borehole Strengthening – Internal Mud Cake
Altering the mechanical characteristics of the near wellbore region. Developing high tangential stresses in the near wellbore region by particulate plugging and bridging. Fracture-resistance enhancement is a function of stiffness contras and pressure differential. Successes in low-perm sands in South Texas: SPE 92266, SPE 103816, Petrotech 1002.
Rw Ri
Pmud Ppore
r © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Wellbore “Strengthening” – Breakdown Pressure Models Idealized near wellbore pore pressure profiles for different geomechanics models (comparison of pressure profile and breakdown pressures, Pbd) Æ from Benaissa et al. (2005) pwb Permeable wall, no cake
Pbd1
pp
pwb
Impermeable wall, external cake
Pbd2
pp rw
r
pwb Impermeable wall, internal cake
pp r w ri
© 2005 Baker Hughes Incorporated All rights reserved.
Pbd3
rw Mud losses
r No losses
Pbd1
r Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Wellbore “Strengthening” – Field Case (South Texas) From Benaissa et al. (2005) Pre s s ure /Stre s s Gradie nt (ppg)
0.0
10.0
20.0
Pressure/Stress Gradient (ppg)
30.0
0.0
6,000
5.0
10.0
25.0
30.0
6,500
8,000
7,000
9,000 7,500
10,000
TVD (ft)
TVD (ft)
20.0
6,000
7,000
11,000
8,000 8,500
12,000
NO
S E S S LO
9,000
13,000
9,500
14,000 15,000
15.0
PP MW sigmh Breakdow n Pres.-Permeable Wall Breakdow n Pres.-Impermeable Wall Breakdow n Pres.-Impermeable Internal Cake
© 2005 Baker Hughes Incorporated All rights reserved.
10,000
PP MW Breakdown Pres.-Permeable Wall Breakdown Pres.-Impermeable Wall Breakdown Pres.-Impermeable Internal Cake
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Borehole Strengthening – Effect of Temperature
Pressure (psi)
Temp Dependant LOT Tests 2900 2700 2500 2300 2100 1900 1700 1500 0
10
20
30
40
50
60
70
Pump Strokes
SPE 87217 © 2005 Baker Hughes Incorporated All rights reserved.
92 F
133 F
153 F
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Special Topics in Wellbore Stability
Outline ÎDrilling
through laminated formation z Drilling in and near salt bodies z Drilling through faults z Drilling through shale z Mud temperature effects on wellbore stability z Cavings analysis
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds Some rocks (mainly shales) show strength anisotropy, i.e. they tend to be “stronger” or “weaker” in a given direction. Thus, the relative angle between the bedding plane and the wellbore axis (also called angle of attack) may define the mechanical behavior of the formation while being drilled (and afterwards too !!!) .
δ
lane p g n i d Bed
Angle of attack
This situation has been found in the field, where previously “stable” formations became troublesome when drilled at lower attack angles (e.g., SPE 1721, 30464, 47285 & 53940).
© 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … ((ctd.) ctd.) Depending upon the reservoir structural geology, the angle of attack (hence, the rock mechanical properties) may change along the well trajectory; even for vertical wells. Two wells with the same trajectory drilled through the same formations, may encounter dramatically different rock mechanical properties.
The same formations may behave differently when reentered at a different angle of attack.
In addition, the in-situ stress field may also change along the reservoir structure… but this point will be covered later. © 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … ((ctd.) ctd.) When wells are drilled near faults (with some degree of folding along the fault) the same situation may occur …
Even vertical wells may be unstable when drilled near a fault.
The same formations may behave differently when reentered at a different angle of attack.
NOTE : It is not uncommon to find that the in-situ stress on each side of the fault is different !!! © 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … ((ctd.) ctd.) Rock Anisotropy: … but how dramatic is the variation in the mechanical properties of the rock as function of the angle between bedding and loading?
β
Laboratory measurements on Green River Shale, Colorado (McLamore and Gray, 1967) Diff. ~ 40%
In this old paper, compression is taken as negative. Thus, the axial (larger) stress is called σ3. © 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … ((ctd.) ctd.) Rock Anisotropy … (ctd.): … likewise, the magnitudes of tensile strength and Young’s modulus also change with orientation …
β
Laboratory measurements on Green River Shale, Colorado (McLamore and Gray, 1967)
Diff. ~ 67%
In this old paper, compression is taken as negative. Thus, the extensional stress is called σ1 throughout a series of Efficiency….Data accuracy….People-oriented service Brazilian tests. All rights reserved. © 2002 Baker Hughes Incorporated
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … ((ctd.) ctd.) Rock Anisotropy … (ctd.): More examples from around the world … Draupne shale, North Sea (Økland and Cook, 1998)
σ c =500 psi
14,000 12,000
Compressive strength (psi) with
10,000 8,000 6,000
Canadian shale
4,000 2,000 0 0
15
30
45
60
75
90
σ 1 orientation relative to bedding (deg)
© 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … stability considerations Stresses around borehole • isotropic and homogeneous • anisotropic and homogeneous Failure criteria (Mohr Coulomb) • weak (bedding) plane • native strength Wellbore trajectory δ • angle of attack
© 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … stability considerations
(Non-laminated)
(Laminated) Økland & Cook proposed a conceptual model consisting of two successive phenomena: 1. The failure criterion for bedding plane slip is met in the corners of the borehole 2. An exposed bedding– parallel sliver in the floor Økland, D., and Cook, J.M.: “Bedding-Related Borehole Instability in High-Angle Wells”, paper SPE 47285 presented at or ceiling of the EUROCK, Trondheim, Norway; 1998. horizontal borehole buckles into the borehole. The beam Upshot: Ignoring anisotropy can be fractures in the middle and breaks off at the detrimental to the stability of the borehole. endpoints.
SPE 53940 © 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … stability considerations …stability
Models of roof behavior in horizontally layered rock. (a) and (b) show the deflection and cracking in the case of a thinner beam beneath a thicker beam. (c) and (d) show the deflection and failure in the opposite case – thick beneath thin. (after Goodman 1989). © 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … stability considerations …stability Critical Mud Weigh, ppg
12 11.5 11 10.5 10 9.5 9 0
10
20
30
40
50
60
70
80
90
Attack Angles, degrees
“Both field experience and laboratory evidence …indicate that hole instability … is not a problem when drilling normal to bedding, or even parallel to bedding, but becomes very serious when the hole is … nearly parallel to bedding.” Oakland and Cook, 1998 © 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … stability considerations …stability
Critical Mud Weight, ppg
12.5 12 11.5 11 down-dip up-dip
10.5
Cross-dip
10 0
10
20
30
40
50
60
70
80
90
Inclination, degrees
“up-dip well are predicted to be stable with mud weights of around 11.5 ppg….” (Willson et al., 1999, P.4) © 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … stability considerations …stability
SPE 79846 © 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … stability considerations …stability 18
Crossdip
Minimum MW (ppg)
17
16
15
Downdip 14
13
0
30
45
66
12
Updip 11 0
30
60
Bedding Plane Dip = 70o Bedding Plane Dip Direction = 1250
© 2002 Baker Hughes Incorporated All rights reserved.
90
120
150
180
210
240
270
300
330
360
Wellbore Azimuth (degrees)
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … stability considerations …stability
Isotropic Strength
© 2002 Baker Hughes Incorporated All rights reserved.
Anisotropic Strength
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … stability considerations …stability Combined isotropic and anisotropic strength models, considering only the critical mud weights for initiation of shear failure mode (MohrCoulomb failure criterion).
TVD, ft 8239 BIOT 0.95
OBG, psi/ft 1.1 COHE, psi 1000
SHG, psi/ft
ShG, psi/ft
1.04 FRIC, deg
PPG, psi/ft 0.95
COHEW, psi
35.49
© 2002 Baker Hughes Incorporated All rights reserved.
20
SH DIR., deg
0.51 FRICW, deg 20
45 DIP DIR., deg 125
POIS 0.19 DIP, deg 70
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … ((ctd.) ctd.) Stress Perturbation : • The presence of geological structures (e.g. folds, faults, etc.) may create local alterations of the far-field in-situ stress, i.e. the stress field near faults / folds may be different from the regional in-situ stress field. In-situ stress field at the bottom of the syncline
Far-field insitu stress
In-situ stress field at the top of the anticline … Image redrawn from Billings (1956) © 2002 Baker Hughes Incorporated All rights reserved.
Not necessarily equal
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … ((ctd.) ctd.) Stress Perturbation … (ctd.): Zone where tensile stress appears as a consequence of folding (plastic rock Æ layer thinning due to deformation)
Zone where additional compressive stress occurs as a consequence of folding (plastic rock Æ layer thickening due to deformation)
If the formations are brittle (i.e. no plastic deformation occurs before failure) … Æ Tension fractures or small gravity faults might form on the convex side, while small thrust faults form on the concave side
Æ Under certain interlayer friction conditions, the rocks on the concave side may be crumpled
… Images redrawn from Billings (1956) © 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … ((ctd.) ctd.) Stress Perturbation … (ctd.):
Depth
rigid layer low stiffness layer
Vertical Stress/γZ
anticline
syncline
ρgh
The rigid formation holds most of the overburden load and directs the load down the limb of the fold. On the other hand, the low stiffness layer cannot sustain the same amount of loading (see AA’ and BB’)
(Modified from Goodman, 1989) © 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … ((ctd.) ctd.) Stress Perturbation … (ctd.): Before a fault is created, both blocks are affected by the same stress field. However, during fault displacement, one of the fault blocks moves; releasing strain energy (i.e. decreasing its stress). On the other hand, the stress in the “static” block remains unchanged.
Fault
“Static” block affected by the pre-faulting stress field
“Moving” block, releases some strain energy thereby decreasing its stress magnitude
IMPORTANT !!! Æ A well being drilled across a fault may encounter a dramatically different stress fields on each side of it (therefore avoid extrapolating stress magnitudes/directions across faults). © 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … ((ctd.) ctd.) Main issues: • Rock mechanical anisotropy (mainly in shales) due to the fact that beds are drilled by using a wide range of attack angles. The same bed may be re-entered at different attack angles, even by the same well. • As highly inclined beds are associated with geological structures such as folds and faults, there is a potential for finding local stress perturbation. These stress alterations may occur near faults and across folding structures. • Given the occurrence of stress perturbation, it is NOT recommended to extrapolate neither the direction nor the magnitude of the stress field across faults. The same situation occurs for wells located at different locations within a folding structure. © 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline Drilling through laminated formation ÎDrilling in and near salt bodies z Drilling through faults z Drilling through shale z Mud temperature effects on wellbore stability z Cavings analysis z
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Characteristics of Salt ¾
Salt is highly soluble and may be chemically sensitive to the water phase of drilling mud Ö Hole enlargement may occur Ö Insoluble layers (typically carbonates or anhydrite) may result in the formation of ledges Ö Dissolved salts in the mud affect efficiency of polymers, flocculates fresh water muds (creating a viscosity increase and subsequent hole cleaning issues), reduces filter cake quality and results in an overall increase in torque and drag
¾
Salt is a viscoplastic substance
Ö Salt cannot tolerate shear stress (i.e., σ1 = σ2 = σ3 = σsalt ~ σv) and will creep (deform) indefinitely with time until deviatoric stresses vanish
¾
Salt has a high thermal conductivity Ö Temperature gradients between rock and drilling mud may result in thermallyactivated creep.
¾
Pure salt is nearly impermeable (k < 10-10 Darcy’s) Ö Pore pressure effects are negligible within salt
¾
Salt intrusions increase the geological complexity Ö Significant alterations of the stress/PP fields in the vicinity of salt structures
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Salt Behavior During Lab Testing
Shear stress [τ]
At low temperature conditions Salt behaves in brittle manner like transition zone Salt behaves in plastic manner most other rocks at high stress, σ at low stress, σ φ ~ 0º
NOTE: Salt creep is the dominant mechanism of wellbore instability during drilling!
φ ~35º
σ′3
Co ~ 1000psi
σ′1
Normal stress [σ′] To ~ 200 psi
UCS
© 2005 Baker Hughes Incorporated All rights reserved.
Upshot: as σ increases, the salt behaves plastically!
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Creep Test Results: Metal vs Salt Strain
Metal will eventually rupture! Tertiary creep Secondary creep
Primary creep
NOTE: difference in behavior is usually attributed to: small salt porosity, solution- Salt does not rupture precipitation within the pore spaces, etc. (creeps indefinitely)! Metal Salt
elastic strain
Time © 2005 Baker Hughes Incorporated All rights reserved.
Upshot: salt behavior upon loading is very complex!
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Salt Creep Calculation In practice, it is common to employ the following simple creep law (Carter & Hansen, 1983): −n
ε salt = Aσ ⋅ e
−B
T Thermal effects
Effect of stresses
These are the most important factors affecting salt creep!
where σ is the deviatoric stress, A is a salt constant, B is a temperature exponent, n is the stress exponent and T is temperature. Temperature (T) Salt Constant (A) Degree F psi-1 sec-1 200 9.58E-14 250 1.15E-13 300 1.52E-13 350 1.33E-13 400 1.81E-13 450 1.82E-13
Temperature Exponent (B) degree K 8000 8000 8000 8000 8000 6000
Stress Exponent (n) 4.5 4.4 4.4 4.5 4.9 5.5
Data from Barker et al. 1992 for U.S. Gulf Coast salt formations © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Common Drilling Problems in Salt BHA stuck on ledges while POOH or RIH
BHA squeezed while POOH
solution washout Salt creep
BHA stuck while RIH due to washout
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
BHA squeezed while RIH after tripping www.bakeratlasdirect.com
Warning Signs of Drilling Salt The presence of salt across the shakers A lack of cuttings (indicating salt is dissolving into the mud) An increase in the chloride concentration in the mud An increase in the rate of penetration Increasing torque and drag (hole closure)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Overburden Stress near Salt Diapirs far-field well
tangent well
Vertical Stress
center well
Depth
σv increases at the flank of the salt.
bed dip angles ~70-80º
target
σv is reduced within the salt (stresses become isotropic!). bed dip angles ~30º
Tangent
Upshot: σv stress arching occurs along with a possible rotation (deviation from vertical) of the overburden stress along the flanks of the salt. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
Center
Far Field
Data taken from Fredrich et. al. 2003
www.bakeratlasdirect.com
Horizontal Stress near Salt Diapirs Horizontal Stress
far-field well
tangent well
center well
Depth
σh increases in the salt to ensure stress isotropy
σh is slightly reduced at the at the flank of the salt.
Upshot: σh increases within the salt to reach equilibrium with the vertical stress. σh is reduced at the flank of the salt. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
Tangent
Center
Far Field
Data taken from Fredrich et. al. 2003
www.bakeratlasdirect.com
Shear (von Mises Mises)) Stress near Salt Diapirs σ VM =
far-field well
[
1 (σ1 − σ 2 )2 + (σ 2 − σ 3 )2 + (σ1 − σ 3 )2 2 tangent well center well
]
von Mises Stress
Depth
σVM increases substantially at the flank of the salt.
σVM is zero within the salt.
Upshot: σVM stress increases substantially along the flanks of the salt. σVM is zero within the salt (salt cannot tolerate shear stress). © 2005 Baker Hughes Incorporated All rights reserved.
Data taken from Fredrich et. al. 2003
Efficiency….Data accuracy….People-oriented service
Tangent
Center
Far Field
www.bakeratlasdirect.com
Stress Directions Near Diapir
σh
Salt
σH
Stress directions around the salt dome are deflected due to the presence of the salt! (after Dusseault, 2003) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Overburden Stress near Salt Sheets far-field well
tangent well
center well Tangent
Center
Far Field
Vertical Stress
σv increases at the flank of the salt.
~2000 m Depth
Salt sheet
σv is unaltered within the salt.
Upshot: Some small stress arching occurs along the flanks of the salt. σv is not altered within the salt sheet. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
Data taken from Fredrich et. al. 2003
www.bakeratlasdirect.com
Horizontal Stress near Salt Sheets Tangent
far-field well
center well
tangent well
Center
Far Field
Horizontal Stress
Salt sheet
~2000 m
Depth
σh increases in the salt to ensure stress isotropy
Upshot: σh increases dramatically within the salt sheet (since σv does not decrease to create stress isotropy). Data taken from Fredrich et. al. 2003 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Shear Stress Near Salt Sheets Tangent
Center
Far Field
von Mises Stress
tangent well
center well
Salt sheet
~2000 m
Depth
far-field well
σVM is zero within the salt.
Upshot: σVM stress increases substantially along the flanks of the salt. σVM is zero within the salt sheet (as is the case for the salt diapir). © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
Data taken from Fredrich et. al. 2003
www.bakeratlasdirect.com
Potential Through Through-- and Near Salt Geomechanical Hazards
Ref.: Wilson and Fredrich (2005) - SPE 95621 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling Through vs. Around Salt Drilling Through Salt Pro's Allows use of a central platform.
Con's
Drilling Around (close to) Salt Pro's
Con's Rocks near salt bodies are under the More cost effective than Shallow gas hazards are often encountered. influence of complex & elevated stress, drilling through salt. resulting in many drilling difficulties. Sour gas often encountered directly below Uncertainty in salt body shape may lead cap rock (e.g., anhydrite). This requires use to accidental drilling into the salt. of sour grade casing. High MW needed to control salt mechanics. Highly dipping formations near the flanks This necessitates the need to set casing of the salt result in anisotropic upon exiting the salt. mechanical failure. Careful monitoring of mud chemistry is May require several platforms to access crucial to mitigate salt dissolution. all HC pools. PP and fracturing pressure are often Directional control can be difficult in salt. unknown just above and below the salt. The formation of ledges within the salt may result in stuck pipes/wellbore obstructions. PP and fracturing pressure are often unknown just above and below the salt. Rubble zones are often encountered prior to entry into salt and upon exit out of salt. Temperature control is needed so that static temp does not exceed 200 deg F (excessive salt creep initiation). Under-reaming is often necessary. Cementing is often difficult in salt due to hole rugosity, cement contamination, etc. Specially designed casing must be used. Is usually more costly relative to drilling next to salts method.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline Drilling through laminated formation z Drilling in and near salt bodies ÎDrilling through faults z Drilling through shale z Mud temperature effects on wellbore stability z Cavings analysis z
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling Through Faults Rubble Zone: The region near a fault in which the rock has experienced brittle failure resulting in many fragmented (brecciated) rock pieces. If the rock fragments are cemented, the fractures are impermeable (and vice versa).
Formations are also thinned and dragged near the fault (leading to a bed dip change). Rubble zone occurs in the vicinity of the fault! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling Through Faults A vertical well will intersect more rubble zone as well as intersecting the tilted formation at a low angle of attack. Therefore the well will be more susceptible to instability!
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling Through Faults Many wellpaths are designed to intersect the fault normally (~90º). The well does not intersect as much rubble zone and increases the angle of attack. This tends to increase the stability of the well in the vicinity of the fault!
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Fault Reactivation
¾ If the fault is permeable, the effective normal stress acting on the fault will be reduced due to fluid infiltration (causing slippage along the fault) ¾ lubricating effects by drilling fluid infiltration may also cause slippage along the fault ¾ leads to stuck pipe, excessive reaming, high torque and drag, etc. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stress Rotation Near Faults The orientation of the principal stresses is deflected by the presence of a pre-existing fault!
from Bell (1990)
Upshot: optimum drilling direction may change near the fault! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Location of the Cusiana field
Angle between vertical and σ1 direction
Stress Rotation Near Faults Faults-Cusiana Field Example σ1 is horizontal
(foot wall)
σ1 direction becomes vertical!
σ1 is vertical on the footwall side of the fault.
(hanging wall)
Horizontal distance along top of reservoir
Cross-section of the Cusiana field from Charlez et al., 1998. © 2005 Baker Hughes Incorporated All rights reserved.
Upshot: stress rotation occurs near the fault!
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Fractured ((Rubbelized) Rubbelized) Zones If the fractures are impermeable… Fragmented (rubbelized) rock mass near a fault.
If the fractures are permeable… de-stabilized block
wellbore
Increasing MW will provide additional support to the wellbore (in terms of collapse) © 2005 Baker Hughes Incorporated All rights reserved.
wellbore
Increasing MW will increase instability as the fluid penetrates the fractures reducing the confining pressure effect and allowing the block to fall into the well
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Problems Drilling Through Faults Faults-- Summary Stress rotations are possible in the vicinity of faults Ö The optimum drilling direction may be rotated relative to far field optimum direction
Damage (rubbelized) zones may be present near the fault Ö Rubbelized rock fragments with cohesion will be stabilized by increasing the MW Ö Rubbelized rock fragments without cohesion are permeable and therefore increasing MW tends to de-stabilize the wellbore Ö Naturally fissile rock (i.e., thinly bedded shale) is particularly susceptible to being rubbelized due to faulting Ö It is desirable to intersect the fault plane at a right angle to minimize the length of drilled section through the damage zone (to reduce WBS incidences)
Bedding dip direction and angles (due to bedding deformation) may change in the vicinity of the fault Ö Fault drag causes formation dips and angles to change Ö Failure along weak planes may occur as the wellbore becomes sub-parallel to bedding planes.
Fault reactivation Ö Fluid penetration into the fault may allow movement along the fault plane resulting in stuck pipe, excessive reaming, high torque and drag, etc. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline Drilling through laminated formation z Drilling in and near salt bodies z Drilling through faults ÎDrilling through shale z Mud temperature effects on wellbore stability z Cavings analysis z
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through shales Some characteristics of shale formations: ¾
Lamination
strength anisotropy (previously discussed)
¾
Clay content
¾
Extremely low permeability
¾
In tectonic environments
reactive - swelling, weakening pore pressure storage micro-fractured
Due to these unique characteristics, shale tends to be more susceptible to failures and accounts for about 75% of borehole instability problems.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Driving Forces At Shale/Drilling Mud Interface NOTE: One or all of these potentials may exist at a given moment in the subsurface. For low perm rocks, the chemical and thermal gradients tend to dominate. ¾ Hydraulic
gradient ¾ Electro-chemical gradient ¾ Thermal gradient
µwsh µwm Tw
where po
= far-field pore pressure
pw
= wellbore pressure
µwsh
= water activity of shale pore fluid
µwm
= water activity of drilling mud
Tf
= formation temperature
Tw
= drilling fluid temperature
© 2005 Baker Hughes Incorporated All rights reserved.
pw
po
Tf
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Swelling Properties - Pierre I Shale after Exposure into NaCl Solutions awshale = 0.98
0.7
aw=1 Deioned water aw=0.95 NaCl aw=0.85 NaCl aw=0.75 NaCl
0.6
Swelling Percentage (%)
Additional swelling occurs via chemical osmosis for the case of deioned water (aw=1 > awshale)
0.5 chemical osmosis
Causal Mechanisms
0.4 0.3
1.
0.2
De-watering occurs after capillary effects due to chemical osmosis (if aw NaCl < awshale)
0.1 0 capillary effects
2.
Capillary action acts quickly resulting in most of the total swelling within minutes After capillary action, chemical osmosis affects swelling secondarily
-0.1 1 from Zhang et al., 2004
© 2005 Baker Hughes Incorporated All rights reserved.
10
100
Time, Minutes
1000
10000
NOTE: Pierre 1 shale is retrieved from a surface outcrop!
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Swelling Behavior - Pierre I Shale Immersed into Simulated Pore Fluid
Swelling Percentage (%)
0.5
0.4
NOTE: This slide illustrates the effects of capillary pressure only!
0.3
0.2
Most swelling occurs as a result of capillary effects!
0.1
0 1 from Zhang et al., 2004
© 2005 Baker Hughes Incorporated All rights reserved.
10
100
1000
10000
T im e, M inutes Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Corrected Swelling Behavior - Pierre I Shale Immersed into NaCl Solutions 0.1
Swelling Percentage (%)
0
Ion movement
-0.1
NOTE: This slide illustrates the effects of chemical osmosis only (i.e., capillary effects have been removed)!
-0.2 -0.3 water movement
-0.4
aw=1 Deioned water aw=0.95 NaCl aw=0.85 NaCl aw=0.75 NaCl
-0.5 -0.6 1 from Zhang et al., 2004
© 2005 Baker Hughes Incorporated All rights reserved.
10
100
1000
10000
Time, Minutes Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effects of Water Activity on Strength of Pierre I Shale Deviatoric Strength, psi
10000 9000
De-watering of the shale leads to an increase in the compressive strength of the shale!
8000 7000 6000
NaCl CaCl2 KCl
5000 4000 0.75
0.8
from Zhang (2005)
© 2005 Baker Hughes Incorporated All rights reserved.
Native Shale
0.85
0.9
0.95
1
Water Activity
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effects of Water and Ions Movements z
The flux of water into shale: - Increases pore pressure - Alters the shale’s strength (Chenevert, 1970) - Shale swelling (Chenevert, 1970)
z
The exchange of ions: - changes the ionic concentration of pore fluid, which could affect the shale matrix mechanical properties and could result in cohesion degradation and cementing bonds weakening and thus reduces the overall rock strength (Ghassemi et. al. (2001), Fam and Dusseault (1998).
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
FORMATION PRESSURE (psi)
Chemical Instability – Pore Pressure Penetration 150 140 130 120 110 100 90 80 70 60 50 40 30 20
BOREHOLE: 195 PSI CONFINING: 315 PSI TEMPERATURE: 158F (70C) CORE: PIERRE II (E Bedding)
2% Sea salt 20% KCl, Neat
20% KCl non-Cloud Point Gylcol
Pmud-Ppore = 125 psi 20% KCl Cloud Point Gylcol
20% NaCl PHPA
Aluminum Chemistry PHPA, freshwater
Aluminum Chemistry PHPA, 20% NaCl 0
10
© 2005 Baker Hughes Incorporated All rights reserved.
20 30 40 50 HOURS
60
70
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Pressure Profiles Pore pressure caused by hydraulic and chemical potentials can be Pp(Lomba nRT K II ∂Cs K I et al., calculated∂as 2 2000):
∂t
−
cf
∇ P−
D eff c f
∂t
=0
Pp = Pore pressure [=] m/L-t2 KI = A parameter related to permeability [=] L3-t/m
n
= Number of molars of constituent of dissociating solute [=] amount R = Ideal gas constant [=] m-L2/t2-amount-T
T = Formation temperature [=] T K II = A parameter related to membrane efficiency [=] L3-t/m
Cs = Pore fluid solute concentration [=] mol/L3 D eff = Effective solute diffusion coefficient [=] L2/t
cf
= Fluid compressibility [=] t/m
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Pressure Distribution As A Function of Time ((σ σHH ≠ σhh) Due To Chemical Osmosis Typical GoM shale, k = 10-9 Darcy, considering only chemical effects
Osmotically-Induced Pore Pressure, MPa
4.0 3.5 t = 10 days t = 1 day
3.0
t = 0.1 day t = 0.001 day
2.5 2.0
μwmud - μwshale = 0.2
1.5 1.0 0.5 0 1
2
Borehole wall © 2005 Baker Hughes Incorporated All rights reserved.
3
4
5
6
7
8
9
10
from Wolfe (2002) r/a Efficiency….Data accuracy….People-oriented service www.bakeratlasdirect.com
Pore Pressure in shales Due to the extremely low permeability, shale tends to have higher pore pressure. This high pore pressure can be attributed to: • depositional environments (native pressure) • pore pressure transmission (osmotic / hydraulic effects) • stress/mechanical loading (poro-elastic effect) • thermal potential
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Pressure Distribution Around A Vertical Well As A Function of Time ((σ σHH ≠ σhh) 15
15
At the instant of drilling (t=0.001 day), there is a pressure increase inside the rock (near the wall).
Pore Pressure ( MPa )
14
13
14
13 t = 1 day t = 0.1 day
12
t = 0.001 day
11
θ = 90°
12 11 Far-field pore pressure 10
pw = 14 MPa
10
9 1
2
Borehole wall
3
4
5
6
7
8
9
9 10
r/a
Upshot: failure may be initiated inside the rock! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Pressure Distribution Around A Vertical Well As A Function of Time ((σ σHH ≠ σhh) Typical GoM shale, k = 10-9 Darcy, no chemical or thermal effects, in the direction of σH 14 θ = 0°
pw = 14 MPa
Pore pressure ( MPa )
12
10
Just after drilling (t=0.001 day), there is a pressure decrease inside the rock (near the wall).
Far-field pore pressure
t = 1 day
8
t = 0.1 day t = 0.001 day
6 1
Borehole wall © 2005 Baker Hughes Incorporated All rights reserved.
2
3 r/a
4
5
from Wolfe (2002) Efficiency….Data accuracy….People-oriented service www.bakeratlasdirect.com
Pore Pressure Distribution Around A Vertical Wellbore ((σ σ H ≠ σ h) Typical GoM shale, k = 10-9 Darcy, t = 0.001 day, no chemical or thermal effects circumferential flow develops at small time
0
15
330
30 14
mud pressure
wellbore 300
13
60
12
σh
11 270
90 10
far-field pore pressure 9 240
120
8 7
150
210
PP in region of low compressive stress from Wolfe (2002) © 2005 Baker Hughes Incorporated All rights reserved.
180
σH
PP in region of high compressive stress
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Pressure Distribution Around A Vertical Wellbore ((σ σ H ≠ σ h) Typical GoM shale, k = 10-9 Darcy, t = 10 days, no chemical or thermal effects 0
As time passes, the pore pressure distribution becomes symmetric!
14.5
30
330
14
300
60
mud pressure
13.5 13
σh
270
90
12.5 12 11.5
240
120 11 210
150 180
from Wolfe (2002) © 2005 Baker Hughes Incorporated All rights reserved.
σH
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through shales The rise in pore pressure has three detrimental effects: loss of mud hydrostatic support fracturing of formation decrease the effective normal stress (fissile shale)
Loss of mud hydrostatic support: From the equations below, although the increase in pore pressure will tend to decrease the effective tangential stress, the reduction of effective strength is more pronounced. This is particularly true in cases where there is a substantial decrease in UCS due to strength degradation and/or when the internal friction angle is high.
σ θθ' = 3σ H − σ h − Pw − αPp C f = UCS + ( Pw − αPp ) tan (45 + 2
© 2005 Baker Hughes Incorporated All rights reserved.
0
β 2
)
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through shales Formation Fracturing When the pore pressure in shale has risen to a level where the difference between the mud weight and pore pressure exceeds the tensile strength, radial fracturing will take place resulting in splintery cavings.
Pw − αPp = −to
Pw
rock chip
excessive pressure gradient (Pp>Pw) causes sloughing shale
wellbore
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Reduction of Effective Normal Stress – Fissile Shale
Shear Stress
Drilling through shales f ailu re line
cri ti cally s tress ed fract ure
n on -critically str essed fr actur e
In fissile shale, when fluid penetration has taken place, the reduction in effective normal stress as well the lubricating effect of infiltrated drilling fluid tend to promote weak plane slippage.
© 2005 Baker Hughes Incorporated All rights reserved.
σ 3’
σ1 ’
Norm al Stress
σn’ = σn - Po τcritical = μσn’
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling Through Shale
fractured (rubbelized) zones/micro-fractured shale
If the fractures are impermeable… Fragmented (rubbelized) rock mass near a fault.
If the fractures are permeable… de-stabilized block
wellbore
Increasing MW will provide additional support to the wellbore (in terms of collapse)
© 2005 Baker Hughes Incorporated All rights reserved.
wellbore
Increasing MW will increase instability as the fluid penetrates the fractures reducing the confining pressure effect and allowing the block to fall into the well
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling Through Shale
fractured (rubbelized) zones/micro-fractured shale Contrarily to conventional treatment of borehole instability, increasing mud weight when drilling through micro-fractured formations has two detrimental effects: Fluid penetration promoted by high mud weight reduces the mud hydrostatic support thus decreases the formation bulk strength Fluid penetration also provide lubrication to the fractured surfaces The key to successful drilling in microfractured (and fissile) shale is therefore to minimize fluid penetration or pressure transmission. This can be achieved by either decreasing the drilling fluid gradient or eliminating fluid loss by creating an impermeable internal mud cake. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling Through Shale pore pressure rise
The key to maintain borehole stability when drilling through shale is to minimize pore pressure rise. This can be achieved by controlling pore pressure transmission (including fluid penetration), avoiding abrupt mechanical loading and limiting formation heating. For high native pore pressure, increase the mud weight is effective in controlling splintery or ‘popping’ shale phenomenon. It is interesting to note that high (native) pore pressure shale and fluid filled microfractured shale has similar acoustic responses, however, the treatment for borehole stability problems is different! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Alternating Sand-Shale Sequences Typically, losses and tight hole occur in the sandier units while wellbore enlargements occur in the shalier units. Plausible reasons are: stresses in shale are higher (lithology - Poisson’s ratio) shale tends to have higher pore pressure (native or induced) the bulk strength of shale may have been reduced by microfracturing (and further reduced by fluid infiltration) shale is laminated (fissile) and possesses weak planes chemical effects may have weakened the inherent strength (reactive) …………. The key to successful drilling in alternating sand-shale sequences is to design a mud system that will not (create and) propagate the fractures in the sands, but this mud weight could be too low to completely eliminate breakouts. This can be achieved by utilizing the concept of borehole strengthening. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline Drilling through laminated formation z Drilling in and near salt bodies z Drilling through faults z Drilling through shale ÎMud temperature effects on wellbore stability z Cavings analysis z
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Temperature Effects on Borehole Consider a hollow cylinder (i.e., rock) with no porosity (φ = 0) at temperature (Tr) filled with a fluid at temperature (Tf).
Tf
Tr
Tf ≠ Tr
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Temperature Effects on Borehole Cont ’d Cont’d If Tf > Tr (i.e., wellbore heating)
Tr
σh
Tf
•
Higher borehole temperatures (from hot drilling fluid) will cause the rock to try to expand.
shear failure (breakouts)
•
The rock (downhole) cannot expand outward (due to confining effect of surrounding rock) or radially (due to the wellbore fluid pressure).
•
This leads to a higher tangential stress, which will increase the rock’s resistance to hydraulic fracturing but also increase the potential for shear failure (breakouts).
Tf
If Tf < Tr (i.e., wellbore cooling)
Tr
σh hyd. frac.
© 2005 Baker Hughes Incorporated All rights reserved.
•
Lower borehole temperatures (from cool drilling fluid) will cause the rock to try to shrink.
•
This leads to a reduction in the tangential stress, which will increase the propensity of hydraulic fracturing as well as reduce the potential for shear failure.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Cooling Effects on Borehole Example ~ 1050 psi tensile stress develops on the wellbore wall during circulation! circulating
Gradual cooling due to circulation leads to additional tensile stress
© 2005 Baker Hughes Incorporated All rights reserved.
tensile stress is reduced upon stopping circulation! not circulating
Gradual heating (from contact with hot rocks) as circulation is ceased reduces the tensile stress
from Tang and Lou (1998- SPE 39505) Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Production Field Data This chart shows how the injection pressure dropped 400 psi (on a fractured water disposal well) when the temperature dropped 17º F!
Perkins and Gonzalez (1981) also noted that injecting large volumes of cool fluid during the hydraulic fracturing process can greatly reduce the fracturing pressure!
from Schmidt et al. (1999- SPE 52738) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mud Heating Effects on LOTGoM Example
Instances of cooling exactly coincided with the occurrence of mud losses (i.e., hydraulic fracturing)!
from Gonzalez et al. (2004- SPE 87217) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Thermally -induced Pore Pressure Distribution Thermally-induced in Low Permeability, Porous Media Typical GoM shale, k = 10-9 Darcy, permeable wall, considering only heat conduction
Thermally-Induced Pore Pressure ( MPa )
This10 extreme pressure pulse can lead to spalling (i.e., circumferential tensile failure).
t = 10 days t = 1 day
8
t = 0.1 day t = 0.001 day
Heating combined with low permeability leads to the generation of a pressure wave that migrates into the formation with time! ΔT = +50°C
6
4
NOTE: This type of behavior is absent in high permeability rock because the pore pressure can diffuse instantaneously. In low permeability rocks, this requires that the entire region near the wellbore be analyzed for failure (i.e., not just the wellbore wall)!
2
0 1
Borehole wall © 2005 Baker Hughes Incorporated All rights reserved.
2
3
4
5
from Wolfe (2002) r/a Efficiency….Data accuracy….People-oriented service www.bakeratlasdirect.com
Thermal Effects on Safe MW Window Thermal loading affects breakdown pressure more than the collapse pressure! Typical GoM shale, k = 10-9 Darcy, permeable wall, normal stress environment σv from Yu et al. (2001) from Yu et al. (2001)
σH σh
Heating increases both the collapse and breakdown pressure whereas cooling leads to a reduction in collapse and breakdown pressure! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Thermal Effects on Safe MW Window Typical GoM shale, k = 10-9 Darcy, permeable wall, normal stress environment Collapse Stress Fracturing Stress
collapse
stable
stable fracture Cooling reduces the collapse pressure instantaneously. However, with time the potential for collapse increases. Heating produces the opposite effect. figures taken from Li et al. (1996) © 2005 Baker Hughes Incorporated All rights reserved.
Both heating and cooling reduces the fracture pressure instantaneously (here the stresses are evaluated inside the rock too). However, with time the potential for fracturing drastically decreases while heating but further increases while cooling.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Thermal & Time Effects on Safe MW Window Typical GoM shale, k = 10-9 Darcy, permeable wall, strike-slip environment, r 3000
2500
3000
Dashed lines represent small time (t = 0.001 day), Solid lines represent large time (t = 1 day)
Heating (or 2500 cooling) shifts the MW window
ΔT = +50°C
tensile failure
ΔT = -50°C
=a
Mud Weight, Kg/m
3
ΔT = 0°C
2000
2000
1500
1500
σv
Safe Operating Zone
Heating instantaneously increases the potential for collapse, which reduces with time.
1000
500 active shear failure
0 Cooling is initially beneficial 0 10 in terms of collapse but20 with time the benefits are reduced! © 2005 Baker Hughes Incorporated All rights reserved.
30
40
50
60
70
Borehole Inclination, β°
Efficiency….Data accuracy….People-oriented service
80
1000
500
σH 0 90
σh from Wolfe (2002)
www.bakeratlasdirect.com
Summary of Thermal Effects
permeable rock (thermoelastic)
low permeable rock (porothermoelastic)
Heating
Heating causes additional compressive stresses to develop in the rock. This increases the potential for shear failure but restricts the development of hydraulic fractures. Since pore pressure build up does not occur due to high permeability, time importance is lessened.
Heating yields an instantaneous increase in shear failure potential due to substantial pore pressure buildup inside the rock as a result of the differences between the thermal expansion coefficient of the rock and pore fluid. The pressure build up is short-lived and the potential for shear failure gradually decreases with time. Heating also greatly reduces the fracturing pressure due to a significant pore pressure build-up inside the rock.
Cooling
Cooling creates tensile stresses and therefore hydraulic fracturing is more likely (shear failure potential is simultaneously reduced). Pore pressure diffusion effects are irrelevant due to high permeability of the rock.
Cooling instantaneously reduces the breakdown pressure, which increases with time. It also quickly reduces the potential for shear failure, which will gradually increase with time.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline Drilling through laminated formation z Drilling in and near salt bodies z Drilling through faults z Drilling through shale z Mud temperature effects on wellbore stability ÎCavings analysis z
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Cavings Analysis Cavings analysis can provide information on: ¾ The mode of wellbore failure ¾ Wellbore cleaning issues ¾ Remedial actions required to stabilize the wellbore
Drill marks
Cavings/cuttings characteristics: ¾ Cuttings usually contain “bit marks” and are usually distinguished from cavings on this basis ¾ Cavings are typically 0.5-2 inches in size but may be as large as 4-5 inches ¾ Cavings are generally categorized into three types: → Angular → Splintery → Tabular © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Angular Cavings Angular cavings are characterized by curved, rough surfaces resulting from shear failure along the borehole wall. - fresh surfaces indicate borehole breakout is presently occurring - old surfaces indicate that shear failure occurred previously (e.g., rubble zone)
σθθ Excessive σθθ leads to shear failure
Pw
curved and rough failure surface
wellbore
Remedial Action(s) -Increase MW (do not exceed FG) -Closely monitor ECD & control tripping speeds -Effective hole cleaning measures should be implemented -Select optimum well trajectory to avoid shear failure © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Angular Cavings rough, curved surfaces
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Splintery Cavings Splintery cavings are characterized by long, thin, concave surfaces resulting from radial spalling due to drilling underbalanced in low permeability rocks (i.e., σ’r
Pw
rock chip
excessive pressure gradient (Pp>Pw) causes sloughing shale
wellbore
Remedial Action(s) -Increase MW -Reduce penetration rate -Monitor ECD & reduce tripping speed (swabbing) © 2005 Baker Hughes Incorporated All rights reserved.
curved and concave (splintery) failure surface
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Splintery Cavings long, thin, concave surfaces
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Tabular Cavings Tabular cavings are characterized by smooth, flat surfaces that are parallel to subparallel. These typically result from failure along bedding planes or cleavages in pre-existing fractures/joints sets. bedding plane failure - May yield square-shaped hole - Image logs often show enhanced enlargement on one side of the hole only! failure along pre-existing fractures
de-stabilized block
Remedial Action(s)
flat, parallel surfaces corner failure
picture taken from Økland and Cook (1998)
-Implement effective fluid loss measures (to plug conductive fractures) -Reduce drillstring vibrations as well as swab & surge (i.e., tripping speed) -Minimize instances of back reaming © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Tabular Cavings flat, parallel, old surfaces
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Wellbore Stability Case Study
© 2000 Baker Hughes Incorporated All rights reserved.
Application examples ÎCase
Study I
– Open-hole stability analysis of horizontal wells under production scenarios z
Case Study II – Wellbore integrity assessment during under-balanced drilling
z
Case Study III – Drilling through inclined laminated formations
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Case Study I Open -hole stability analysis of horizontal Open-hole wells under production scenarios Objective: To investigate the stability of horizontal wellbores under several production scenarios in order to select a suitable completion strategy which guarantees borehole integrity during the productive life of the field. Reference: SPE 105332 © 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
ST-2: Drilled Horizontally (W-side) ST-3: Horizontally Planned (E-side) H-2: Horizontally Planned (W-side)
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Formation mechanical properties characterizations GEOMECHANICS
Rock Mechanical Property Model
In-situ Stress & Pore Pressure Models
Laboratory testing on core samples (Discrete (discrete data) (Triaxial (triaxial tests, tests, acoustic acoustic measurements, measurements, hollow hollow cylinder cylinder test) test) Log-based dynamic mechanical properties (Elastic (elastic moduli and Poisson’s ratio) Empirical correlations for rock strength (Lacy, Lal, Coates-Denoo, Deere-Miller, etc) Log-based static mechanical properties (Micromechanical (micromechanics approach) approach) © 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Logging of Mechanical Properties (LMP)
(micro -mechanics approach) (micro-mechanics Log Inputs DTP, DTS, Porosity, Lithology, Saturations, ZDEN, Fluids Properties, Stresses Produces Virtual Core Sample
σa
Produce StressStrain Curves
σr σa
Applying Virtual Stresses to the “Core Sample”
εr
εa
Static Mechanical Properties: Rock Strength, Elastic Moduli Poisson’s Ratio, Biot’s Constant, Poisson’ Cohesion, Internal Friction Angle © 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Log -based static mechanical Log-based properties z
The Micromechanics Model provides a continuous representation of static mechanical properties at different confining conditions
Mohr-Coulomb failure envelope © 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
In -situ stress & pore pressure In-situ characterizations GEOMECHANICS
Rock Mechanical Property Model
In-situ Stress & Pore Pressure Models
Vertical Vertical/overburden Stress (Overburden stress Stress) (formation Formation density density integration integration throughout throughout the the lithology lithology column) column Magnitude of the Minimum minimum Horizontal horizontal Stress stress (Active (active measurement of the fracture closure pressure) Magnitude Magnitude of the Maximum of the maximum Horizontal horizontal Stress (Back-analysis stress calculation (back-analysis from afrom borehole evidence shearoforshear tensile or failure tensile evidence) failure) Horizontal Horizontal Stress stress Orientation orientation (breakout (Breakout or or induced Induced fractures) fractures) Pore Pore Pressure pressure Profile profile (Pressure (pressure data points, acoustic Acoustic logs) logs) © 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
In -situ stress analysis In-situ In-Situ stress tensor ⎡σ xx τ xy τ xz ⎤ ⎡σ H 0 0 ⎤ ⎢ ⎥ σ = ⎢τ xy σ yy τ yz ⎥ = ⎢⎢ 0 σ h 0 ⎥⎥ ⎢τ xz τ yz σ zz ⎥ ⎣ ⎦ xyz ⎢⎣ 0 0 σ v ⎥⎦ X 'Y 'Z '
Density log
dw
sf
Vertical stress (overburden)
σ v = ρ w gd w +
∫
ρ b (z )gdz
TD
sf
z ds
Depth of interest
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
In -situ stress analysis In-situ
σ1
In-Situ stress tensor ⎡σ xx τ xy τ xz ⎤ ⎡σ H ⎢ ⎥ σ = ⎢τ xy σ yy τ yz ⎥ = ⎢⎢ 0 ⎢ τ xz τ yz σ zz ⎥ ⎣ ⎦ xyz ⎢⎣ 0
0
σh 0
0⎤ 0 ⎥⎥ σ v ⎥⎦ X 'Y 'Z '
σ h ,min =
σh,min 0.914 psi/ft
ν 1 −ν
(σ
v
− αPp ) + αPp +
Fracture closure pressure from a minifrac test performed in an offset West-side well.
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
φf ˜ 60º
σ2
Minimum Horizontal Stress Uniaxial strain compaction process
σ3
• ν , α from the mechanical property model • Pp from reservoir pressure data
Eα t E νE ΔT + Δ ε + Δε y x 2 2 1 −ν 1 −ν 1 −ν Thermal induced stress
Lateral strains and tectonic effects
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
In -situ stress analysis In-situ In-Situ stress tensor
⎡σ xx τ xy τ xz ⎤ ⎡σ H ⎢ ⎥ σ = ⎢τ xy σ yy τ yz ⎥ = ⎢⎢ 0 ⎢ τ xz τ yz σ zz ⎥ ⎣ ⎦ xyz ⎢⎣ 0
0
σh 0
0⎤ 0 ⎥⎥ σ v ⎥⎦ X 'Y 'Z '
Maximum Horizontal stress • Back-analysis using breakout size measurement • Breakdown pressure – minifrac
Fracture closure line: (minifrac) z
σh,min = 0.914 psi/ft at 13,134 ft. Breakdown line: (tensile failure)
z
Mud losses reported with MW = 18.7 ppg (0.971 psi/ft) at 12,572 ft. Breakout line: (compressive failure)
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
In -situ stress analysis In-situ In-Situ stress tensor ⎡σ xx τ xy τ xz ⎤ ⎡σ H ⎢ ⎥ σ = ⎢τ xy σ yy τ yz ⎥ = ⎢⎢ 0 ⎢ τ xz τ yz σ zz ⎥ ⎣ ⎦ xyz ⎢⎣ 0
0
σh 0
0⎤ 0 ⎥⎥ σ v ⎥⎦ X 'Y 'Z '
Direction of the horizontal stresses • Breakouts and hydraulically induced fractures identified on borehole image logs • Regional stress regime
Hydraulically Induced Fractures Borehole Breakouts
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
In -situ stress analysis - summary In-situ W-2
Normal faulted stress regime, but very close to a strike-slip stress regime
σv ≥ σH > σh
W-2
Maximum horizontal Stress direction: East-side: N35E West-side: N45E
σh,min
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
W-6
σH,max
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Wellbore stability basics
[σ ]x' y ' z ' = [Q]T [σ ]XYZ [R] (East)
Wellbore Coordinate System
Earth Coordinate System
(North)
Zs
Z
Ys
βs
Xs
Y αs X
(Down)
far-field stress
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Wellbore stability basics
Y
X
East
North
Z
Earth Coordinate System
Down
Shear failure modes: z
z
z
Breakout shear failure
σ 'θθ > σ ' z ' z ' > σ 'rr
Borehole Coordinate System
y’
Toric shear failure
σ ' z ' z ' > σ 'θθ > σ 'rr
Helical shear failure
σ ' z ' z ' > σ 'rr > σ 'θθ © 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
σz’z’
Efficiency….Data accuracy….People-oriented service
z’
Drilling direction
x’
σrr Low-side borehole
Cylindrical Coordinate System
σθθ
Cartesian to Cylindrical Stress tensor transformation www.bakeratlasdirect.com
Wellbore stability basics Azimuthal Maximum Tangential Stress Distribution Compared with Rock Compressive Strength 180
Effective compressive -165-170-175 -160 -155 strength -150
175 170 165
160
155
12000
-145 -140 -135 -130 -125
C f = UCS + ( Pw − αPp ) tan 2 (450 +
β 2
)
150 145 140 135 130 125
9000
-120
120
-115
115
6000
-110
110
-105
105 3000
-100
100
-95
95 0
-90
90
-85
85
-80
80
-75
75
-70
70
-65
65
Compressive stress
-60
60
-55 -50 -45
55 50 45 -40
40 -35
35 -30
-25
-20
-15 -10
-5
5
10 15
20
25
30
0
Borehole Low-Side © 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Horizontal borehole stability predictions (multiple drawdown)
ΔPdrawdown = Pr − Pwf
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
Increasing Drawdown condition, DP
ST-2
www.bakeratlasdirect.com
Reservoir depletion – effects on in-situ stresses Δσ h =
In-situ stress path during reservoir depletion 1.2
Cleary & Geertsma (1978)
1.1
Stress gradient, [psi/ft]
α (1 − 2ν ) ΔP (1 − ν ) p
1.0 0.9 0.8 0.7
Initial reservoir Pressure
0.6 0.5
σh
Intermediate Pressure
σh
Abandonment Pressure
Overburden stress Maximum horizontal stress Minimum horizontal stress
0.4 10000
9000
8000
7000
6000
5000
4000
3000
Reservoir pressure, [psi]
Overburden stress, σv
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Horizontal borehole stability predictions (reservoir depletion) Reservoir pressure depletion
ST-2
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Horizontal borehole stability predictions (reservoir depletion) ST-2
Initial reservoir Pressure
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Intermediate Pressure
Efficiency….Data accuracy….People-oriented service
Abandonment Pressure
www.bakeratlasdirect.com
Case study I – concluding remarks z
z
z
Borehole stability analysis requires both mechanical property characterization and in-situ stress tensor estimation. Stability predictions of horizontal wellbores under open-hole production scenarios helped to define well completion/production strategy: – Safeguard well integrity during the productive live of reservoir – Early remediation advice: completion & production strategy decisions – Strength degradation when acid treatments are planned. The maximum drawdown for a stable horizontal borehole reduces with reservoir depletion.
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Application examples z
Case Study I – Open-hole stability analysis of horizontal wells under production scenarios
ÎCase Study II – Wellbore integrity assessment during under-balanced drilling z
Case Study III – Drilling through inclined laminated formations
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Case Study II Wellbore integrity assessment - under -balanced drilling under-balanced Objective: Assess the degree of instability with underbalance condition. Establish maximum under-balance for given rock strength and in-situ stress characteristics.
Sta. Rosa
San Joaquinaco
Mar Cariberibe Sta. Ana
Goal: Provide inputs for establishing hole cleaning, ECD, drag-and-torque, and fluid volume trends. Optimize under-balanced drilling operations. Reduce drilling cost and maximize production. © 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Sucre
Sucre
Anzoá Anzoátegui Delta Amacuro
Monagas
El Toco
Anaco UE Gas / Condensado
Reference: SPE/IADC 99165
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Assembly of experience base
Considerable wellbore instability related problems in the Merecure and San Juan formations. The occurrence of lost circulation along side with pack-off, reaming, tight hole, over-pull and cavings.
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
• Combined information from more recent pressure measurements in sands. • Normal pressure gradient in shales.
8.0 6.0 4.0 2.0
EMW (ppg)
9900
9800
9700
9600
9500
9400
9300
9200
9100
9000
8900
8800
8700
8600
8500
8400
8300
8200
8100
8000
7900
7800
7700
0.0
PP
DIF
Medida
Perd Circ.
10.0
12.0
MW Usado
14.0
NewPP
16.0
Pore pressure model
M easured D epth (ft) © 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
In -situ stress characterizations In-situ
A
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Model calibrations – breakout and drilling induced fracture Sv DIF
Min MW Lost Circ.
Frac. Grad. MW Used
Max MW LOT/FIT
PP
Observed BO
5
10
15
20
0
25
9000
9000
9100
9100
9200
9200
Measured Depth (feet)
M e a su re d D e p th (ft)
9500
Caliper
20
40
60
80
100
120
140
160
180
200
9300
9300
9400
Predicted BO
Breakouts (degrees)
EMW (ppg) 0
Washouts
9400
9500
9600 9600
9700
Breakouts
9700
9800 9800
80deg
9900 0 9900
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
2
4
6
8
10
12
14
16
Caliper (inches)
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mud weight window
SHEAR FAILURE
IDEAL MW
TENSILE FAILURE
REAL LIFE MW
Excessive BO
Mud weight window Merecure © 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
σ2
Minor BO
Pw
Pw
Low Pore Pressure
In-gauge Minor Losses hole
Pw
Pw
Mud Weight Scale
Excessive Losses
σ3 Pw
High σ3 (magnitude)
Mud weight window Vidoño and San Juan
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Breakout expected Mud Weight Ave. breakout width in Merecure (degrees) Ave. breakout width in San Juan (degrees)
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
10 ppg
8 ppg
6 ppg
4 ppg
2.7
10.6
15.5
21.3
7.8
28.1
34.8
41.9
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mud losses – conventional vs. under -balanced drilling under-balanced Merecure
San Juan
12000
Merecure = 8 ppg (ΔP= - 900 psi) San Juan = 7 ppg (ΔP= - 1500 psi)
10000
Bbls
8000 6000 4000 2000
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
G-92
Avg.
JM-221
JM-220
JMN-216
JMN-215
JMN-214
JMN-205
JMN-204
JM-193
JM-190
0
www.bakeratlasdirect.com
Drilling time and cost saving 6-1/2” Hole - Conventional W ell
Es tim ate d
Re al
Cle an
days
K$.
days
K$.
days
K$.
G-91 / JI-X
14
677.0
9.0
886.6
9.0
886.6
G-93 / JI-O
20
1,221.2
11.8
591.8
11.8
591.8
JM -214 / JI-G
18
20.7
1,186.4
18.1
1,082.0
JM -215 /JI-B
20
1,242.7
29.6
1,596.7
17.8
644.7
JM -216 / JI-F
18
959.9
33.5
2,074.1
20.0
1,531.9
JM -220 / JJ-C
14
793.7
21.9
928.1
19.7
779.9
JM -221 / JI-Z
24
654.8
19.1
995.5
17.8
938.3
JM -225 / JI-J
18
793.9
14.1
778.5
11.8
650.6
JM -227 / JI-N
21
867.6
16.4
800.8
16.4
800.8
18.6
901.3
19.6
1093.2
15.8
878.5
Ave rage
6-1/2” Hole – Under Balance W ell G-92 / JI-H JM-229 / JJ-E JM-230 / JJ-G JM-233 / JJ-F JM-235 / JH-X Average
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Rig GW-61 GW-67 GW-60 PD-719 GW-68
Estimated days K$.
- 4 days
- 4.7 days
Real days K$.
Clean days K$.
- 183.2 K$
6 7 7 7 13
158.3 814.8 730.0 466.6
7.4 24.0 22.4 14.8 9.5
507.8 1,664.6 1,304.0 545.1 580.6
6.6 11.9 17.2 10.8 9.0
471.9 998.9 1,057.7 387.5698 560.6
8.0
542.4
15.6
920.4
11.1
695.3
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling time and cost saving 6-1/2" Hole
Actual trend
30 20
Conventional
Avg. UB
*JM -235
*JM -233
New Technologie Estimeted
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
*JM -230
*JM -229
*G -92
Average
JM -227
JM -225
JM -221
JM -220
JM -216
JM -215
JM -214
0
G-93
10 G-91
Tim e (days
40
Efficiency….Data accuracy….People-oriented service
Real
Clean
www.bakeratlasdirect.com
Case study II – concluding remarks z
z
z
z z
A geomechanical model was developed and calibrated with respect to the field data, wireline logs, breakout simulation and DIF. Underbalance mud weights were recommended based on the results of the geomechanical modeling. Lost circulations have successfully been avoided following the implementation of underbalance mud weight recommendations. Drilling rates were tripled in comparison with the conventional methods (8-1/2” and 6-1/2” holes). A total saving in time of 60 rig days, and in cost of more than $1MM have been realized, in prevention of fluid losses, in the 5 wells drilled so far following the underbalance mud weight implementations.
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Case Study III Drilling through inclined laminated formations Objective: Assess the degree of instability when drilling through inclined laminated formations Establish the optimum mud weight and wellbore trajectory to minimize borehole instability.
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Some background information…… z “traditional” well design (intersect zone “A” vertically)
– All wells drilled from drill centers – 3 critical zones (A,B,C) • Zone “A”: recently encountered wellbore instability while drilling high angle wells • Zone “B”: lost circulation issues
“Advanced” well design (intersect zone “A” at high angle)
Tertiary
zone “A”
z
zone “B” zone “C”
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Subsea development
Zone “C”: very weak, anisotropic shale (keep hole near vertical) – Initial 2 wells in field→ used WBM (shale reactivity issues) – SBM used to date – Most HA wells in past had significant WBS issues (no WBS analysis available on past failed wellbores!!)
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Some background information…… “traditional” well design (intersect zone “A” vertically)
z
– Directional – S-shape – 300 – 450 tangent angle – Drop tangent angle to 100 in zone “C” and reservoir
“Advanced” well design (intersect zone “A” at high angle)
Tertiary z zone “A”
Traditional Well Design ~ 25 wells
Advanced Well Design – 3 wells – Extended Reach – S-shape – Build to 600 to 700 through upper shales – Hold ~3000m tangent – Drop tangent angle to 100 in zone “C” and reservoir
zone “B” zone “C”
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Well #1 – traditional well design z Planned
pilot hole:
– Seismic tie-in – Formation evaluation – Geomechanical model update – 45° hole drilled thru zones “B” and “C” z Planned
hole
Tertiary
zone “A”
Production
– Kick off in shale (zone “C”) above target reservoir – KOP near fault – Horizontal completion © 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
zone “B”
production hole zone “C”
pilot hole
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Well #1 – pilot hole z
z
z
z z
z
Well drilled thru zones A,B,C with no significant problems initially Then……after approximately 1 day an abundance of “angular” and “splintery” cavings was observed. Wellsite geologist indicated cavings are from zone “C”. Mud weight was increased to combat the problems (high PP and/or low UCS??) Continued drilling ahead Approximately 2 days later, hole collapsed → left BHA in hole (no logs!) Sidetrack required
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Well #1 – sidetrack 1 (2nd pilot hole) • • •
•
•
Sidetrack drilled parallel to original hole with higher MW. Drilled beyond zone “C” with little problems. To address hole cleaning issues, several hours of circulating and rotating performed within zone “C”. Shortly thereafter, abundance of “tabular” and “blocky” cavings was observed. It was decided to POOH & sidetrack.
Tertiary
2nd pilot hole planned production hole
initial pilot hole © 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Well #1 – sidetrack 2 (final production hole) z
Well ST2 drilled nearly vertical thru zone “C” with no problems – Fault was avoided within zone “C” – Minimal “angular” cavings present – Shift in bedding dip from 10° to 55°→ two pilots drilled nearly parallel to bedding
Tertiary
final production hole
planned production hole
initial pilot hole
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Well #1 – stable mud weight simulations Anisotropic Case PetroCanada-Anisotropic Case 0 330 Anisotropic
Isotropic
75
12.5
30
12
60
Field Mud Weight
300
12
11
11.5 60
45
11
30
10.5
15
10
270
9.5
90
9 8.5
Mud Weight, ppg
10
240
8
120
7.5 9
7 210
150 180
8
Isotropic Case PetroCanada-Isotropic Case
7
0 330
6
75
7.29
30
7.19
60 300
7.09
60
45
6.99
30
5
15
0
10
20
30
40
50
60
70
80
6.89
90 270
Well Inclination, deg.
90
6.79 6.69 6.59
Formation dip & dip direction = Wellbore azimuth = 1150 © 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
550,
1080
Efficiency….Data accuracy….People-oriented service
240
120
6.5 6.4
210
150 180
www.bakeratlasdirect.com
Well #2 – extended reach drilling (ERD) • • • • •
Drilled beyond zone “A” with little problems. POOH, several significant tight spots observed in zone “A”. These were not present in all previous wells (which were drilled with < 60° inclination). Abundance of “angular” & “tabular” cavings were observed several days after drilling. It was speculated that roof collapse-type failure was beginning.
“Advanced” well design (intersect zone “A” at high angle)
Tertiary
zone “A”
zone “B” zone “C”
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Well #2 – stable mud weight simulations
Wireline Data 2 wk
LWD real-time 2 wk
LWD real-time initial
MW used
Formation dip & dip direction = 150, 1080 Wellbore azimuth = 1150 The attack angle in this case is referred to the bedding plane. © 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Well #2 – drilling fluid penetration Wireline Data Wireline Data 2 wk
LWD real-time 2 wk
LWD real-time
LWD real-time initial
LWD real-time initial
Confirms fluid penetration along weak planes in shale with time!
Slight invasion measured 2 weeks later © 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
No invasion measured while drilling
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Case study III – concluding remarks z
z
z
z
Early recognition of bedding plane characteristics is critical to optimizing the “attack angle” and the mud weight when drilling through inclined laminated formations. Increased mud weight to account for additional pressure to stabilize anisotropic formation can exacerbate wellbore instability due to fluid penetration. Mud additives must be added to minimize fluid leak-off. The geometry of cavings provides a means to characterize the failure mode and must be accurately monitored. Four (4) ERD wells have been drilled to date with nearly zero non-productive times (NPT).
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Hydraulic Fracturing Rock Mechanics Considerations
© 2005 Baker Hughes Incorporated All rights reserved.
Outline ¾ Background ¾ Effects of in-situ stress on fracture orientation and propagation ¾ Effects of closure stress, bed thickness and rock mechanical properties on fracture containment ¾ Pressure analysis during hydraulic fracturing ¾ Special cases in hydraulic fracturing ¾ Reservoir connectivity
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Background – Creating a hydraulic fracture During a hydraulic fracturing job, fluid is injected at a relatively high pressure into the formation inducing a TENSILE fracture
σc Upper Bounding Layer
Closure stress contrast is, perhaps, the most important parameter affecting fracture containment
Pay Zone
Lower Bounding Layer
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Background – Hydraulic fracturing applications Reservoir stimulation Æ Enhancement of well productivity / injectivity of hydrocarbon reservoirs Reservoir management Æ Access to naturally fractured zones, increase of drainage efficiency, injection / production of fluids in thermal energy projects Stress measurement Æ Minifrac, LOT, XLOT Waste management Æ Massive waste injection, drill cuttings reinjection Sand management Æ Frac-packs in poorly consolidated formations and sanding-prone rocks
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Importance of in-situ stress in hydraulic fracturing
Direction Æ Controls fracture orientation (dip and azimuth); horizontal vs. vertical Magnitude Æ Determines the fluid injection pressure; thus, the choice of tubular and pumps Stress contrast Æ Dominant role in fracture containment; thus, controls fracture geometry
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Origin and magnitude of in-situ stresses
σ
In-situ stress due to overburden + tectonics At a large scale, fractures open and propagate along the path of least resistance ÆALWAYS NORMAL to σ3
σh min Depth
σH max
© 2005 Baker Hughes Incorporated All rights reserved.
σv
Due to the weight of the overlying rock: Æ σv ~ 1.0 psi/ft (normally) Æ σh min ~ 0.7 psi/ft (normally)
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Background - Fracture classifications s3
s1 s1
s1 mode I opening Induced: Petal Centerline Hydraulic Natural: Joint Vein
closing
mode II
mode III
Induced: Compaction band (experiments)
Induced: Shear fractures/faults, initial breakout, reactivated joints/faults.
Natural: Compaction band (sand) Stylolite (carbonates)
Natural: Normal/reverse/strike slip - bedding plane deformation bands (cataclastic faults).
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Fracture orientation - Normal stress field Normal regime Æ σv > σHmax > σhmin Hydraulically-induced fracture is vertical
σ1 = σv Fault
σ2 = σHmax σ3 = σhmin
φ
(Redrawn from Dusseault, 2004) © 2005 Baker Hughes Incorporated All rights reserved.
re u t c a r F pl ane
Efficiency….Data accuracy….People-oriented service
Hydraulic fracture www.bakeratlasdirect.com
Fracture orientation – Strike slip regime Strike-slip regime Æ σHmax > σv > σhmin Hydraulically-induced fracture is vertical
σ2 = σv σ3 = σhmin
σ1 = σHmax
ctu a r F
re
n p la
(Redrawn from Dusseault, 2004) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
e
Hydraulic fracture www.bakeratlasdirect.com
Fracture orientation – Thrust regime Thrust regime Æ σHmax > σhmin > σv Hydraulically-induced fracture is horizontal (Redrawn from Dusseault, 2004)
Hydraulic fracture
ne a l p re u t c Fra
σ3 = σv σ1 = σHmax
σ2 = σhmin
© 2005 Baker Hughes Incorporated All rights reserved.
φ
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Bottom hole pressure
Fracturing process - Minifrac Breakdown pressure Tensile strength Re-opening pressure ISIP
σC
Flow rate Flow rate
time
ISIP is only an UPPER BOUND for the value of closure stress Æ ISIP > σc !!! (Most people assume they are equal) The fracture initiation at breakdown pressure may be defined as (Hubbert and Willis, 1957):
Pb = 3 σ h − σ H + T0 − p p © 2005 Baker Hughes Incorporated All rights reserved.
Æ assumes the rock to be impervious (i.e. negligible fluid leak-off) and linear-elastic.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
In-situ stress - closure The magnitude of the net pressure determines fracture propagation Æ Pnet = Pf – σc
The LARGER the magnitude of σc , the more DIFFICULT it is to open the fracture !!!
p pf
σ3 = σC © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline ¾ Background ¾ Effects of in-situ stress on fracture orientation and propagation ¾ Effects of closure stress, formation thickness and rock mechanical properties on fracture containment ¾ Pressure analysis during hydraulic fracturing ¾ Special cases in hydraulic fracturing ¾ Reservoir connectivity © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effect of stress contrast on fracture containment
Closure stress contrast is the single most important parameter controlling fracture propagation !!! - Stress differences between the target formation and the adjacent layers determine fracture height containment characteristics Æ contained vs. “run-away” fractures - Other parameters such as rock mechanical properties contrast, flow rate, fluid viscosity although important have less effect on fracture propagation
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effect of stress contrast on fracture containment … (continued) Stress profile, Mesaverde Group, Rifle, Colorado (after Warpinski et al., 1985)
Normally, σsand < σshale
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effect of stress contrast on fracture containment … (continued) σh =
ν 1 −ν
[σ V − α PP ] + α PP
In general, ν coal > ν shale > ν sand
In non-tectonic environments, generally, σ3 Coal > σ3 Shales > σ3 Sands
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Hydraulic fractures in the laboratory σz = 3000 psi σy = 1300 psi (coming out of the picture plane)
σx = 1050 psi
Haimson and Fairhurst, 1969 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
300 psi
300 psi
Effect of stress contrast on fracture containment … (continued)
400 psi
400 psi
Photographs of hydraulically induced fractures in tuff samples (taken from Warpinski et al., 1982) The same fracture height containment behavior has been observed in the field (Smith et al., 1982; Warpinski et al., 1982) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Hydraulic fractures in the field WELDED TUFF
FRACTURE
Mineback experiments (Warpinski et al., 1982)
ASH FALL TUFF
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effect of stress contrast on fracture containment … (continued) σc2 hs2
σc1
2a
h
hs2
σc2
Fracture profile
Width profile
σc2 σc1
hs2
σσc2 <<σσc3 c2 c3 Æ Æhhs2 >>hhs3
2a h
s2
σc3
hs3 Fracture profile
Width profile
The ellipses shown here are a GROSS APPROXIMATION of the actual fracture geometry. In reality, fracture shape is much more irregular !!! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
s3
Effect of stress contrast on fracture containment … (continued) Fracture height propagation – (Example from Warpinski and Smith, 1989): Stress (psi)
2500 1200 1500 1000 1250 1700
2000
Fracture height propagation is slowed down by the presence of a layer with σ3=1700 psi Fracture height propagation rate is increased noticeably due to the presence of a low stress horizon ( σ3=1200 psi ) Fracture height propagation rate is decreased dramatically due to the presence of a high stress barrier ( σ3=2500 psi )
¾
ALL the equations shown above NEGLECT the effect of pressure losses due to vertical flow Æ Thus, their results tend to be overly conservative !!! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effect of stress contrast on fracture containment … (continued) Further injection will create additional height but almost negligible length increment
σc1
Pressure
σc2 h
σc2
σc1
ΔP time
ΔP Due to additional pressure losses, it becomes easier to grow height than to extend the fracture length
Behavior of the pressure vs. time curve allows for quality control and geometry confirmation !!! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effect of formation thickness on fracture containment Values of net pressures for creating a 700 ft fracture under the following conditions: Q=30 bpm, μ=150 cp, C=0.001 ft√min, Xf=700 ft (data generated by using Stimplan® from NSI Technologies, 2005)
Net pressure (psi)
10000
Pnet 2 = P – σC2 E= E= E= E=
6 *10 e6 psi 4 *10 e6 psi 2 *10 e6 psi 1 *10 e6 psi
Pnet 1 = P – σC1 Pnet 2 = P – σC2
1000
ΔPnet = Pnet 1 – Pnet 2 = σ2 – σ1
100 10
100 Fracture height (ft)
1000
Æ For containment to occur, the net pressure in formation 1 should not exceed the value of the stress closure differential (σ2 – σ1)
Æ For a given fracture length, keeping a fracture within a thinner vertical interval requires more degree of confinement (because the value of Pnet becomes larger) than in the case of a thicker formation. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effect of formation thickness on fracture containment … (continued) ¾ When the thickness of a stress barrier is considered, the confining effect of that layer is effectively reduced (i.e. thin, high stress formations may not stop fracture height growth once certain pressure threshold is overcome) ¾ The “minimum” thickness of a stress barrier is a function of the thickness of the pay-zone, the stress differential, and the mechanical properties contrast between the two layers.
C A B
Horizon B is probably a better stress barrier than formation C !!! Æ B is a much thicker interval with slightly lower closure stress than C Æ Rule-of-thumb: In order to be effective, the stress barrier should be as thick as the treated formation (or thicker !!!)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effect of Young’s modulus contrast on fracture containment Young’s modulus contrast is also a factor affecting fracture height containment (although not as important as stress contrast) - E contrast may slow down the fracture height propagation rate; however, it is not a mechanism of arrest (i.e. it does not “stop” fracture height propagation) - If a fracture enters a stiffer formation, then its width will be reduced (i.e. it becomes increasingly difficult to open the fracture); thus, flow resistance will increase making further fracture propagation more difficult ÆIn the field, normally, Esh < Ess ; thus, the fracture would be more easily propagated in shales. However, this behaviour is contrary to the effect created by stress contrast STRESS CONTRAST IS MORE IMPORTANT !!! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effect of Young’s modulus contrast on fracture containment H
h
L
NOTE that (2L/h) / (H/h) is only slightly larger than 1 for the range of mechanical properties contrast expected in the field (with Δσc =0) Plot built based on the work by van Eekelen (1982)
Æ E2 / E1 values are normally less than 15; thus, mechanical properties contrast is expected to SLIGHTLY affect fracture propagation (i.e. the effect is not strong enough to stop the fracture height growth).
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Summary - effects of stress contrast, formation thickness and mech. prop. • In hydraulic fracturing, nature ALWAYS takes the path of least resistance • Closure stress contrast (i.e. ΔPnet ) is the single MOST IMPORTANT parameter controlling fracture propagation • Usually, closure stress in shales is higher than in sands; thus, they act as stress barriers • The thickness of the stress barrier is also important; a good stress barrier should be thicker than the treated formation • Young’s modulus contrast also affects the fracture height growth. However, its effect is not as important as the effect of stress contrast
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline ¾ Background ¾ Effects of in-situ stress on fracture orientation and propagation ¾ Effects of closure stress, rock mechanical properties and leak-off coefficient on fracture geometry ¾ Pressure analysis during hydraulic fracturing ¾ Special cases in hydraulic fracturing ¾ Reservoir connectivity © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pressure analysis during hydraulic fracturing Leak-off coefficient, fracture geometry (Xf, w), and efficiency
Bottom hole pressure
Shut-in
Fracture propagation diagnosis (containment)
Confirmation of Leak-off coefficient, and fracture geometry. Estimate of reservoir transmissivity (kh)
After closure
Closure stress
Injection
Fracture closing
Time © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pressure analysis during hydraulic fracturing - pumping in Assumptions Æ vertical fracture, with L >> H, constant flow rate and viscosity
Reasonable height containment, unrestricted extension
σ1
Stable height growth (shown here) OR increased fluid loss OR tip effect-dominated fracturing
Unstable height growth, injection becomes pointless (no length growth)
σ5 H0
σ3 σ5 σ7
Mode I
Mode II
Mode IV
Mode III occurs when there is a flow restriction in the fracture Æ slurry dehydration leading to screen-out, width reduction in higher stress zones
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pressure analysis during hydraulic fracturing - pumping in … (continued) Log P net
Nolte-Smith Plot (Nolte and Smith, 1981):
III e d Mo
1
Mode II eI
d Mo 1 1 to 8 4
slope = 0
<0
Mo de IV
(Smith, 2003)
⎡ E μqL ⎤ Pnet ≈ ⎢ P + tip ⎥ 2 4 ⎣ (1 − ν ) H ⎦
1/ 4
Log Pump time
MODE I : positive slope (1/8-1/4) Æ Confined height, unrestricted extension MODE II : slope ~ 0 Æ extension with accelerated height growth MODE III : slope ~ 1 Æ restricted growth MODE IV : slope < 0 Æ unstable / uncontrolled height growth © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pressure analysis during hydraulic fracturing - pumping in … (continued) L
MODE I: positive slope (1/8-1/4) V(x)
Æ PKN model based, confined height, unrestricted extension Æ fluid loss is linear flow-dominated, flow rate (q) and viscosity (μ) are assumed to be constant Æ coincides with the PKN growth model
x W(x, t)
W(0, t)
If the fluid is assumed to follow the Power Law (τ = K γn):
H
Pnet ∝ t e → high fluid loss : e = 1 /(4n + 4) → low fluid loss : e = 1 /(2n + 3)
→ high fluid loss, Newtonian, n = 1 : e = 1 / 8 → low fluid loss, Newtonian, n = 1 : e = 1 / 5 → high fluid loss, non − Newtonian, n = 0.5 : e = 1 / 6 → low fluid loss, non − Newtonian, n = 0.5 : e = 1 / 4 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pressure analysis during hydraulic fracturing - pumping in … (continued) ⎡ E μqL ⎤ + Pnet ≈ ⎢ P tip ⎥ 2 4 ⎣ (1 − ν ) H ⎦
MODE II: positive slope ~ 0
1/ 4
Less important for the case of low E rocks
P net
Æ stable height growth Æ increased fluid loss (probably due to the interception of natural fractures), higher risk of screen-out Æ may be indication of confined height with net pressure behavior dominated by tip effects (soft, low modulus formations) σ1 σ5
Mode II Mode IV
σ7
Mode II
σ5
Mode I
H0
σ3
Mode I
Mode IV
H /Ho © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pressure analysis during hydraulic fracturing - pumping in … (continued) MODE III: positive slope ~ 1 Æ flow restriction in the fracture (unit slope indicates storage of fluid, i.e. fracture “ballooning”) Æ may be caused by pad depletion with proppant at the fracture tip, slurry dehydration, excessive height growth, or proppant fallout (i.e. blockage)
σ4
Screenout created by late height growth !!! σ3
σ1
Rpinch
R pinch
q E (Δp / Δt ) = 1.8 (1 −ν 2 ) H 2
(Smith, 2003)
σ2 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pressure analysis during hydraulic fracturing - pumping in … (continued) MODE IV: negative slope (< 0) Æ near wellbore height growth Æ “run-away” fractures Æ slope is a function of the rate of unstable growth Æ in the case of complete lack of height containment, slope will be close to -1/8 (Smith, 2003)
σ1 σ5
Fracture growing vertically instead of extending laterally
σ3
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pressure analysis during hydraulic fracturing - pumping in … (continued) Example from the field (data taken from Nolte & Smith ,1981): 4000 4000
Case CaseAA
3500 3500 3000 3000 Pressure (psi) Pressure (psi)
2500 2500
Case CaseBB
2000 2000 1500 1500
Case CaseCC
1000 1000 500 500 0 0
0 0
© 2005 Baker Hughes Incorporated All rights reserved.
50 50
100 100
150 150
200 200 Time (min) Time (min)
250 250
300 300
Efficiency….Data accuracy….People-oriented service
350 350
400 400
www.bakeratlasdirect.com
Pressure analysis during hydraulic fracturing - pumping in … (continued) Using Nolte & Smith plot:
ΙΙΙ ΙΙ
Ι
Case CaseAA
ΙΙΙ
Case CaseBB
Ι Case CaseCC
Ι
© 2005 Baker Hughes Incorporated All rights reserved.
ΙΙ
Efficiency….Data accuracy….People-oriented service
ΙV
www.bakeratlasdirect.com
Outline ¾ Background ¾ Effects of in-situ stress on fracture orientation and propagation ¾ Effects of closure stress, rock mechanical properties and leak-off coefficient on fracture geometry ¾ Pressure analysis during hydraulic fracturing ¾ Special cases in hydraulic fracturing ¾ Reservoir connectivity © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Special cases in hydraulic fracturing Hydraulic fracturing of high permeability rocks - Extremely high values of leak-off - 3D fluid loss rather than Carter’s fluid loss (1D) - Possibility of having both tensile and shear failure
Hydraulic fracturing in deviated wells - Normal and shear stress created by well deviation - Possibility of fracture “turning” (i.e. non-planar fractures) - Proppant transport problems due to the presence of “turns” Æ higher screen-out risk !!!
Cuttings injection - Batch process - Possibility of creating several fractures in the same horizon - Environmental concerns due to fracture height growth © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Hydraulic fracture in high permeability rocks Objectives: - To bypass damaged formation zones (recovering productivity) - To reduce the possibility of sanding and solids production (by reducing fluid pressure gradients)
Characteristics: - High leak-off (i.e. low efficiency) fractures - Fractures tend to be a lot shorter and wider than in conventional fracturing © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Hydraulic fracture in high permeability rocks…… (continued) The area of flow in a fracpack is about two orders of magnitude larger than the area of flow in a gravel pack Gravel pack:
9.5 Ax = 2π r h = 2π h = 4.97 h 12
Frac & pack:
Ax = 4 L f h = 4 * 50h = 200h Æ Therefore, the fluid velocity in a gravel pack is about two orders of magnitude higher than in the case of fracpacks (i.e. considerably larger drag forces in gravel packs) Æ Possibility of using larger proppants in fracpacks due to lower sanding risk (i.e. potential for more production) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Hydraulic fracture in high permeability rocks…..(continued) Equivalent wellbore radius (rw eq) Æ producing from a stimulated well is like producing from an effectively larger un-stimulated well C fD =
where
Cf K Xf
=
K f wf K Xf
K : Reservoir permeability Kf : fracture permeability wf : fracture width Xf: fracture half-length
The values of CfD for high permeability fracturing tend to be < 0.5 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Hydraulic fracture in high permeability rocks……(continued) rw eq = 0.28
Cf k
=
k f wf k
In order to increase rw eqÆ kf or wf may be increased Æ Achieving larger fracture width may be difficult as the pressure demands rise and operational risk increases. Besides, theoretical studies have shown that fracture width is relatively insensitive to controllable job variables such as pump rate and viscosity (Nolte, 1979) Æ Increasing fracture permeability is easily accomplished by augmenting the size and concentration of the proppant being pumped
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Hydraulic fracturing in deviated wells Borehole deviation creates a completely different picture Æ STRESS field around the well and far-field stress are NOT EQUAL Æ FRACTURE ORIENTATION near to and far from the borehole are likely to be DIFFERENT (i.e. “turning” fractures) Æ Proppant transport issues (fluid can “turn” easily, but proppant cannot !), HIGHER RISK OF SCREEN-OUT
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Hydraulic fracturing in deviated wells…..(continued) It is important to notice that the fracture initiation plane may be inclined with respect to the borehole axis … and also that, after the fracture grows away from the wellbore, it will turn to follow the in-situ stress field !!! It has been observed that the degree of “fracture turning” (hence, of near wellbore friction) is less severe under the following conditions (Emanuele et al., 1998):
Low natural fracture density and competent cement bonding (less leak-off issues)
Overbalanced or extreme overbalanced perforating (probable hydrofrac during perforation)
Fracture initiated by pumping the fracturing fluid at very high rate (Weijers and de Pater, 1994), i.e. higher values of Pnet 3
⎛ E ⎞ μ ⎟⎟ τ C = ⎜⎜ ⎝ Pnet ⎠ E
where
τ C = characteristic time for fracture propagation E = plane strain Young ' s modulus
μ = fracturing fluid viscosity Pnet = net pressure = Pw − σ c
Shorter propagation time (i.e. faster failure) creates the potential for creating a “smooth” turning fracture (i.e. better wellbore-fracture hydraulic connectivity) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Hydraulic fracturing in deviated wells…..(continued) Depending upon the azimuth (i.e. orientation with respect to North) of the wellbore, the breakdown pressure may vary as follows (Yew and Li, 1988):
z’ θ γ
y’
x’
Fracture
20
60
30
0
Breakdown pressure , Pb (Ksi)
40
θ
16
90 Fracture position , θ (deg)
For α = 0º (North) and a given in-situ stress field
Fracture orientation , γ (deg)
60
12
Pb
8
Pb
γ γ
θ 10
40
70
90
Well inclination, β (deg)
20
0
60
30
Breakdown pressure , Pb (Ksi)
40
16
90 Fracture position , θ (deg)
For α = 45º (North-East) and a given in-situ stress field
Fracture orientation , γ (deg)
60
The Thebreakdown breakdownpressure pressuremay may increase/decrease increase/decreasedepending dependingupon upon the theorientation orientation(α) (α)and andinclination inclination(β) (β) of the wellbore where the fracture is of the wellbore where the fracture is initiated initiated
θ 12
Pb γ
8
10
40
70
90
Well inclination, β (deg)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Cuttings Injection
Batch injection of slurry (water + liquid waste + solid waste) into selected formations (sandstones / shales / carbonates)
Sources of solid waste Æ drill cuttings, contaminated soil
Sources of liquid waste Æ drilling mud, tank bottoms, produced water, human activity Cuttings injection started in the early 1980’s with small annulus volume injection in the GOM. It was later implemented in the North Sea, Alaska and elsewhere.
Two main issues: - Where does the waste go ? - How much waste can we safely dispose of?
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Cuttings Injection … (continued) Similar to hydraulic fracturing stimulation,
σc Upper Bounding Layer
However … Pay Zone
Lower Bounding Layer
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Cuttings Injection … (continued) Hydraulic fracturing Stimulation Volume (Bbls) Injection rate (BPM) Duration Fluid Type Viscosity (cP) Solids type Solids size(mesh) Concentration (% Vol)
1,000 – 5,000 10- 50 Min- Hours Polymeric gel 20-200 Proppant (sand/ceramics) 20/40 10-30
Cuttings / Waste injection 30,000 - Millions 0.5 – 20 Weeks – Years Slurry 2-20 Cuttings D90 < 300 microns Normally, < 15
But most importantly, INJECTION is a batch process while HYDRAULIC FRACTURING is continuous !!! The intermittent nature of waste injection tends to create several fracture rather than a single planar crack (as is the case of hydraulic fracturing).
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Cuttings Injection … (continued) Where does the injected waste go? Competent / low permeability formations:
σ3
Multiple fractures (disposal domain concept), roughly perpendicular to the direction of the minimum in-situ stress
Unconsolidated / high permeability formations:
σ3
© 2005 Baker Hughes Incorporated All rights reserved.
A “disaggregated” zone around the main fractures, the effect of in-situ stress is less evident Æ Much higher storage capacity
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Cuttings Injection … (continued) Microseismic mapping of fractures induced during waste injection (Moschovidis et al., 2000) Æ Wilcox sand (tight sand)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Cuttings Injection … (continued) Creation of multiple fractures Æ much lesser fracture height growth, and much higher volume can be safely disposed (Figure from Moschovidis et al., 2000) Originally, it was thought that the waste injection process should form a SINGLE fracture (red circle). However, tiltmeter mapping proved the existence of several fractures in the same rock interval (black ellipses) As a result, more waste material may be disposed of in the same interval (through a set of small fractures) than it was originally anticipated !!!
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Cuttings Injection … (continued) NOTE: A tiltmeter is a tool used to monitor changes in the inclination of a structure; in this case, the earth surface or a monitoring well.
Figure taken from Wolhart et al. (2001) Æ Measurements on a well tiltmeter as function of the hydraulic fracture inclination (α)
Microseismic mapping is based on the fact that when rock fails it emits “noise” that may be measured and located in space by geophones. Thus, allowing to pinpoint the tip location over time during a hydraulic fracturing job. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Cuttings Injection … (continued) Injection in unconsolidated formations Æ injection pressure remains almost unchanged throughout the disposal process (figure from Dusseault et al., 1998) cycle
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Cuttings Injection … (continued) Injection in competent, low permeability rocks Æ injection pressure tends to change throughout the disposal process (Figure from Moschovidis et al., 2000)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Cuttings Injection … (summary) ¾ Cuttings injection is a much larger scale process than hydraulic fracturing (years vs. hours, millions of barrels vs. thousands of gallons …) ¾ The cyclic nature of the cuttings injection process tends to create MORE THAN ONE MACRO-SCALE FRACTURE. Thus, augmenting the amount of waste than may disposed of in a given rock interval ¾ Injection of waste into low-permeability rock is a more difficult (hence more risky) operation, as the injection pressure tends to increase over time. This creates the possibility of extending the fracture vertically Æ undesirable effect that could jeopardize the waste containment ¾ The geometry and location of the fracture(s) may be monitored by using tiltmeters, microseismic mapping and tracers
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline ¾ Background ¾ Effects of in-situ stress on fracture orientation and propagation ¾ Effects of closure stress, rock mechanical properties and leak-off coefficient on fracture geometry ¾ Pressure analysis during hydraulic fracturing ¾ Special cases in hydraulic fracturing ¾ Reservoir connectivity © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Reservoir Connectivity σ h min
σ1
σ H max Fracture Wellbore
σ2
σ1 σ
σ
3
© 2005 Baker Hughes Incorporated All rights reserved.
σ3
σ3 σ2
2
σ1 Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Reservoir Connectivity Hydraulic fractures parallel to the direction of maximum permeability - low well deliverability
σh Vertical Well
kh kH
σH
Vertical Well
σ H kh
kH
σh
Hydraulic fractures perpendicular to the direction of maximum permeability - high well deliverability © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Reservoir Connectivity Horizontal well drilled perpendicular to the direction of maximum permeability - high well deliverability
σh
σ H kh
kh kH
σH
kH
σh
Horizontal well with multiple transverse hydraulic fractures - high well deliverability © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Reservoir Connectivity Waterflood/EOR Application - Sweep Efficiency Producing wells drilled perpendicular to fracture direction - good areal sweep efficiency
σh σH
producer © 2005 Baker Hughes Incorporated All rights reserved.
injector
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Reservoir Connectivity Waterflood/EOR Application - Sweep Efficiency Producing wells drilled parallel to fracture direction - poor areal sweep efficiency
σh σH
producer © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
injector www.bakeratlasdirect.com
Reservoir Connectivity Low Permeability Reservoir – Optimum Infill Drilling Locations
Well spacing ≈ fracture length → fracture orientation becomes critical
Good Drainage © 2005 Baker Hughes Incorporated All rights reserved.
Incomplete Drainage
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Reservoir Geomechanics
Outline
Î
Critically stressed fractures/faults
z
Reservoir compaction
z
Pore volume compressibility
z
Surface subsidence
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
E&P Business Drivers z
Well placement ¾ hydraulically conductive fractures (reservoir objective) ¾ fault sealing/re-activation (exploration/development objective) ¾ wellbore stability considerations (drilling objective)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Critically Stressed Fractures z
z
z
Critically stressed fracture analysis enables the identification of fractures which are optimally aligned to fail in the present day stress regime, and hence are most likely to be conduits to fluid flow. Several studies have demonstrated that fluid flow within fractured rocks occurs largely through critically stressed fractures (e.g. Barton et al, 1998; Hickman, 1998). That a fracture is critically stressed does not necessarily mean that it is open and permeable (although this is likely).
© 2005 Baker Hughes Incorporated All rights reserved.
Vung Tau headland – FRACTURE DENSITY
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Critically Stressed Fractures z
Critically stressed fracture analysis consists of the following activities: – Natural fracture identification and characterization. – The far-field in-situ stress tensor is projected onto the fracture plane to give the normal and shear stresses acting on the plane. – These stresses are then plotted on a normalized Mohr-Coulomb diagram and compared to the fracture failure line defined by the friction coefficient of faults and fractures in the rock. – Finally, fractures are classified as critically stressed if the ratio of shear to normal stress exceeds the shear failure line.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Critically Stressed Fractures CSFA Workflows Far field stress tensor analysis
Poroelastic properties & friction coefficient
Natural Fracture Characterization r
σn
σ ij Critically Stressed Fracture Analysis
v
τ
Fracture plane
nˆ
Drilling trajectory recommendations Fracture reactivation, pressure maintenance © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Critically Stressed Fractures
A
B α
Natural Fracture characterization (dip angle & dip azimuth)
A
St rik e
+ B
Dip direction
In-situ stress tensor (magnitude & direction) ⎡σ xx τ xy τ xz ⎤ ⎡σ H ⎥ ⎢ σ = ⎢τ xy σ yy τ yz ⎥ = ⎢⎢ 0 ⎢ τ xz τ yz σ zz ⎥ ⎦ xyz ⎢⎣ 0 ⎣
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
0
σh 0
0⎤ 0 ⎥⎥ σ v ⎥⎦ X 'Y 'Z '
www.bakeratlasdirect.com
In -situ Stress Regimes In-situ σv
σv > σH > σ h
σ h min
σ H max σv
σH > σv > σ h
σ H max
σ h min σv
σH > σ h > σ v
© 2005 Baker Hughes Incorporated All rights reserved.
σ h min
Efficiency….Data accuracy….People-oriented service
σH
www.bakeratlasdirect.com
Stress Vector Projection into a Fracture Plane Up
Upper hemisphere A
x
B
nˆ North
α
West
East
St rik e
South
A
B
Dip direction Down
σ1 σ2
r
σ3 σ2
North
σn
σ
v
τ
West
σ1 © 2005 Baker Hughes Incorporated All rights reserved.
Upper hemisphere (Plan view) Efficiency….Data accuracy….People-oriented service
15
30
Dip
x
nˆ
σ3
0
45 60
75 90
East
Strike
South www.bakeratlasdirect.com
Normal & Shear Stresses on a Plane ¾
¾
Z Assume that XYZ coordinate system corresponds to the far-field stress directions, i.e., principal axes, and l, m, n are the C direction cosines of normal OP (define by the dip and dip direction). P
The normal stress on the plane:
σ =l σ +m σ +n σ 2
2
1
¾
2
2 2
2
2 3
B
O
The shear stress on the plane:
τ 2 = (σ 1 − σ 2 )2 l 2 m 2 + (σ 2 − σ 3 )2 m 2 n 2 + (σ 3 − σ 1 )2 n 2l 2
© 2005 Baker Hughes Incorporated All rights reserved.
(l,m,n)
Efficiency….Data accuracy….People-oriented service
A X
www.bakeratlasdirect.com
Y
Critically Stressed Fractures z
z
3D Mohr Circle plot shows resolved stresses on fractures Fractures above failure envelope may be more τ conductive to flow σv
criticallystressed stressedfractures fracturesabove above critically frictionalfailure failureenvelope envelope frictional stablefractures fractures stable belowfrictional frictional below failureenvelope envelope failure
© 2005 Baker Hughes Incorporated All rights reserved.
σ3 σv
Efficiency….Data accuracy….People-oriented service
σ2 σv
σ1 σv www.bakeratlasdirect.com
Critically Stressed Fractures
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Critically Stressed Fractures
(normal fault stress regime) σv>σH,max>σh,min σH,max
z
σH,max
z
In-situ stress tensor characterization Natural fracture identification r
σn
σ ij
v
τ
Fracture plane
nˆ
σh,min © 2005 Baker Hughes Incorporated All rights reserved.
σH,max
σv
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Critically Stressed Fractures
(strike -slip and reverse fault stress regimes) (strike-slip σH,max>σv>σh,min
© 2005 Baker Hughes Incorporated All rights reserved.
σH,max>σh,min>σv
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Exploiting Permeable Fractures 35
RD-8X
R D -8 x 3600
μ = 1.2
30
μ = 0.6
0
Mud Loss, bbl/hr M u d L o ss , b b l/h r 50
100
150
200
250
300
350
400
3650
20
15
3700
Shear Stress, MPa
25
10
0 0
5
10
15
20
25
30
35
40
45
50
55
M in _ D is c
M in o r
W id e
W id e -D is c
A lte re d
D IH F
V uggy
3750
MD, m
5
M u d L o ss
60
Normal Stress, MPa
3800
R D -1X : P LT lo g 13000 12000 11000
3850
10000 9000
bbl/d
8000 7000 6000
3900
5000 4000
0
0 .2
3000
0 .4
0 .6
D is co n tin u ity R e la tiv e A p e r tu r e
0 .8
2000 1000 0 3000
3020
3040
3060
3080
3100
3120
3140
3160
3180
3200
3220
3240
3260
3280
3300
3320
3340
3360
3380
3400
M D (m .BRT )
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
1
Critically Stressed Fractures
(drilling application)
Critically stressed fractures
Preferred horizontal well trajectory is E-W Fractures not under a critically stress state
σHmax direction N - S © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Critically Stressed Fractures
(well completion application)
Stratigraphy Open-hole logs Fracture orientation from core
Location of the CSF in the Lithology column
Rose-diagrams of cemented (red) and partially-cemented (cyan)/non-cemented (blue) fractures Fracture density of all fractures Rose-diagrams of critically stressed fractures Fracture density of critically stressed fractures Stress model
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
““Critically-Stressed” Critically-Stressed” Faults z
Shear Stress
z
Fault sealing capacity – fault reactivation during injection/production Critical pore pressure – estimate the ambient (excess/reduction) pore pressure a fault can maintain before slipping f ailu re line
τ − μ ( S n − Pp ) ≥ 0 rearranging gives: critical p
P
τ = Sn − μ
water depth earthquakes
cri ti cally s tress ed fract ure
n on -critically str essed fr actur e
σ 3’
© 2005 Baker Hughes Incorporated All rights reserved.
σ1 ’
Norm al Stress
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
““Critically-Stressed” Critically-Stressed” Faults
(normal fault stress regime)
Mohr diagram showing the effects of pore pressure/stress coupling during pore pressure depletion in a normal fault stress regime. A decreasing minimum horizontal stress leads to higher differential stress. Streit and Hillis (2002) – SPE 78226
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Pressure/Stress Coupling
ΔS h b= ΔPf b ~ 0.5 - 0.8
Streit and Hillis (2002) – SPE 78226 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Optimally vs. Non -Optimally Non-Optimally Oriented Faults
Mohr diagram showing the state of stress for the reactivation of cohesionless fault at an optimum fault angle (θ=45o -0.5tan-1μ) .
Mohr diagram showing the state of stress for the reactivation of cohesionless fault at an non-optimum fault angle (θ>45o).
Streit and Hillis (2002) – SPE 78226
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
Mohr diagram showing the state of stress for the reactivation of a cemented fault with cohesive strength. www.bakeratlasdirect.com
Critical Pore Pressure to cause Compressional Shear Failure Normal fault stress regime − 2C + (S v − S h )(1 − μ tan θ )sin 2θ ( S v − S h ) = 1− − Sv Sv 2μ Sv
Pf
Defining:
C = fault cohesive strength
Pf = Pfo − ΔPf S h = S ho − ΔS h
μ = coefficient of friction θ = fault angle Pfo = initial pore pressure S ho = initial minimum horizontal stress Sv = overburden stress
Streit and Hillis (2002) – SPE 78226 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Critical Pore Pressure to cause Compressional Shear Failure Normal fault stress regime Pf = Pfo −
2C − 2 μPfo + μS ho + S ho sin 2θ − 2μ + bμ + b sin 2θ + bμ cos 2θ
μS ho cos 2θ − S v sin 2θ + μS v 2(sin θ ) 2 + − 2μ + bμ + b sin 2θ + bμ cos 2θ
Streit and Hillis (2002) – SPE 78226 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Critical Pore Pressure to cause Fault Reactivation Ekofisk Field
μ = 0.6 C = 0 (cohesionless) © 2005 Baker Hughes Incorporated All rights reserved.
Streit and Hillis (2002) – SPE 78226
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Critical Pore Pressure to cause Fault Reactivation, f( μ) f(μ) Ekofisk Field
Streit and Hillis (2002) – SPE 78226 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Summary - CSF z
z
z
Accurate characterizations of in-situ stresses and natural fractures/faults are critical to the understanding of fractured reservoir performance and fault reactivation potential. Quantifications of critically-stressed fractures provide an ‘engineered’ approach to fractured reservoirs’ exploration and exploitation strategies. Predicting induced reservoir and fault failure (re-activation) is an essential requirement for the long term planning of hydrocarbon field depletion strategies.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline
z
Critically stressed fractures/faults
Î
Reservoir compaction
z
Pore volume compressibility
z
Surface subsidence
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Reservoir Compaction What is Reservoir Compaction? ) Initially, pore fluids and grains support the overburden. When produced, load is transferred to the grains and stress on rock grains (“effective stress”) increases. At low effective stress levels, elastic deformation take place while at higher effective stresses, grains undergo crushing resulting in irreversible compaction of reservoir layers. ) The phenomenon is called “pore collapse”.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Reservoir Compaction Ice tea
Rigid body movement, grain slippage, rotation and displacement, grain cracking and crushing, pore volume reduction © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Reservoir Compaction & Subsidence Surface Subsidence Overburden
Reservoir Sideburden
Sideburden
• • • • •
Pore pressure decline Effective stress increase Reservoir compaction Overburden load transfer Subsidence
Underburden
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Reservoir Compaction – Arching Effect figure from SPE 17852
• • • • •
Overburden load may not transfer completely (SPE 17852) Leading to reduction in load in the middle Called “arching effect” Especially in rigid (or less compliant) formations Leading to smaller compaction and subsidence in the middle than at the flanks
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Pressure Depletion Effects overburden stress fluid-filled pores
grains
Total Stress = Pore Pressure + Effective Stress Carried by the Grains
σ © 2005 Baker Hughes Incorporated All rights reserved.
=
p
+
σ’
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Pressure Depletion Effects overburden stress fluid-filled pores
grains
Total Stress = Pore Pressure + Effective Stress Carried by the Grains
Depletion = ΔP
σ © 2005 Baker Hughes Incorporated All rights reserved.
=
P
+
σ’
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Pressure Depletion Effects Overburden stress subsidence
compaction
Total Stress = Pore Pressure + Effective Stress Carried by the Grains
σ © 2005 Baker Hughes Incorporated All rights reserved.
=
p
+
Efficiency….Data accuracy….People-oriented service
σ’ www.bakeratlasdirect.com
Compaction At Low Effective Stress Levels:
Porosity Decrease
Pore Pressure Decrease Elastic or reversible
• “Elastic region” • Gradual porosity decrease • Low compressibility • Small displacements • Mostly reversible
At High Effective Stress Levels:
Post-pore collapse Pore Pore collapse collapse stress
Effective Stress Increase
© 2005 Baker Hughes Incorporated All rights reserved.
• “Pore collapse” region • Beyond certain “threshold stress” • Rapid porosity decrease • Increased compressibility • Large displacements • Irreversible or permanent
After Pore Collapse: • “Post-pore collapse” region • Material hardening • Decreasing compressibility
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Collapse Behavior
Compressibility Increase
Porosity Decrease
Pore Pressure Decrease pore collapse
• Compressibility is defined as change in volume for a given change in pressure • Sharp increase in compressibility • Large displacements • Irreversible or permanent
Effective Stress Increase
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Reservoir Compaction Compaction leads to: • • • • • • • • •
Reduction in permeability (pore throat closure) Increase in permeability due to fracturing/shearing Provides compaction drive energy Reduction in ultimate recovery Casing collapse/shear, esp. along faults Could trigger sand production Surface subsidence/Platform settlement Costly remedial measures Could also lead to well abandonment
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Case Histories (Compaction & Subsidence) ) Ekofisk field (North Sea) - Johnson et al., 1989 Total subsidence (Feb. 1989) ~ 14.4 ft Expected subsidence (in 2011) -- 20 ft
) Lagunillas Oil Field (Venezuela) – v.d. Knaap & v.d. Vlis, 1967 Coast of Lake Maracaibo, first produced 1926 Parts of shoreline permanently flooded by lake water (1929) 27 mi. concrete protection walls & dikes built to protect local population & installations Subsidence ~10 ft. by 1960 and 13.5 ft by 1976
) Wilmington Oil Field (California) - Allen & Mayuga, 1970 Oil field was discovered in 1932, production started 1941-42 Cumulative subsidence reached more than 29.5 ft. in 1968 Subsidence effectively stopped by water injection
) Offshore Sarawak (Malaysia) - van Ditzhuijzen & de Waal, 1984 Central Luconia gas fields, depletion caused pore collapse in limestones and dolomites Cumulative subsidence calculated at 8 to 20ft, based on location
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Reservoir Compaction Calculation
Elastic
Porosity Decrease
Reservoir Compaction
Pore Pressure Decrease
Plastic (Pore collapse)
Effective Stress
) Elastic compaction calculated using elastic equations for compressibility (bulk, grain and pore volume) - reversible ) Pore collapse compaction is more severe and larger compared to elastic – e.g., using trendline method - irreversible © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Reservoir Compaction Calculation compressibility = change in volume/orig. volume = change in height/orig. height pressure change (depletion) pressure change (depletion)
C pp ( u )
Δh / h = ΔP
(ΔP=pore pressure change)
Δh = compaction
h
Δ h = C pp ( u ) * Δ P * h © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Collapse Compaction Pore Pressure Decrease
Porosity Decrease
Trendline
Trendline behavior (Smits et al., 1988): • Divide reservoir into layers based on porosity and rock type • Establish a “trend line” for each of the formation rock types through lab tests • Estimate the expected drawdown (depletion) • Determine the increase in effective stress
Effective Stress Increase
• Estimate the change in porosity for the change in effective stress • Compaction in each layer is given by:
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Collapse Compaction Pore Pressure Decrease
Porosity Decrease
Trendline
(φ i − φ f ) Δh i = h i (100 − φ f )
Initial porosity, φi
n
Total = ∑ Δ h i i =1
Final porosity, φf
Initial eff. Collapse Final eff. stress stress stress
Effective Stress Increase
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Total Compaction
Total Compaction = Elastic Compaction (calculated from compressibility)
+ Pore Collapse Compaction (using trendline method)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline
z
Critically stressed fractures/faults
z
Reservoir compaction
Î
Pore volume compressibility
z
Surface subsidence
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Why are Compressibility Measurements Important? z z z z z z
Reserve estimation Reservoir pressure maintenance Reservoir drive assessment Production forecasting & history matching Reservoir compaction & subsidence predictions Permeability change prediction
© 2003 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Reservoir Compaction – Reservoir Stress Conditions •
•
•
Hydrostatic stress – isotropic state of stress does not replicate field boundary conditions; not realistic stress path; however, easiest to σc simulate in the laboratory Triaxial stress – anisotropic state of stress is more realistic but still does not replicate field boundary conditions; relatively easy to simulate in the laboratory Uniaxial strain - reservoir fluid production is associated with pore pressure reduction, constant overburden and zero lateral deformation; most realistic stress path; however, difficult to perform in the laboratory
© 2003 Baker Hughes Incorporated All rights reserved.
σa
σ c = σa
σa
σa
σc
σc
σa
εc = 0
σa
σa
www.bakeratlasdirect.com
Elastic Compressibilities z
Bulk compressibility, Cb
z
Pore volume compressibility, Cp
z
Grain compressibility, Cg
Obtained from elastic moduli: Young’s modulus (E) and Poisson’s ratio (ν)
Need to differentiate between: • hydrostatic (commonly performed in lab), and • uniaxial (more representative of field conditions) As well as between: • changing confining pressure and • changing pore pressure © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Compressibility – Definitions C bc
C pc
− 1 ⎛ ∂Vb ⎞ ⎜⎜ ⎟⎟ = Vb ⎝ ∂Pc ⎠ p
− 1 ⎛ ∂Vp ⎞ ⎜⎜ ⎟⎟ = Vp ⎝ ∂Pc ⎠ p
C gc = C gp
C bp p = cons tan t
C pp p = cons tan t
1 = Vb
⎛ ∂Vb ⎞ ⎜ ⎟ (bulk) ⎜ ∂P ⎟ ⎝ p ⎠ Pc=cons tan t
1 = Vp
⎛ ∂Vp ⎞ ⎜ ⎟ (pore) ⎜ ∂P ⎟ ⎝ p ⎠ Pc=cons tan t
⎡ ⎤ ⎞ ⎛ V ∂ ⎛ ⎞ V 1 ∂ p b 1 − ⎢ ⎟ ⎥ (grain) ⎜ ⎜ ⎟ = Cg = = ⎢ Vb ⎜⎝ ∂Pc ⎟⎠ p Vp ⎜⎝ ∂Pp ⎟⎠ ⎥ Pc ⎦ p ⎣ [Δ ( Pc − Pp ) = 0 ]
( from Zimmerman, 1991) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Bulk Compressibility, Cb z
Under changing pore pressure, Cbp
z
Under changing confining pressure, Cbc We need Cbp – replicates field conditions Most labs obtain Cbc
σc
PP
Note: Cxy means: x compressibility under changing y x: b (bulk), p (pore) or g (grain) y: p (pore pressure), c (confining pressure) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Volume Compressibility, Cp z z
Under changing pore pressure, Cpp Under changing confining pressure, Cpc We need Cpp– replicates field conditions Most labs obtain Cpc Also need to convert Cpp (hydrostatic/triaxial) to Cpp(u) (uniaxial) Relationships are available for these conversions.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Compressibility Relationships C bp = C bc − C gc
C pp =
C pc =
Pore © 2005 Baker Hughes Incorporated All rights reserved.
φ
C bc − (1 + φ )C gc
Bulk Grain
C bc − C gc
C pp ( u ) =
φ
C pp (1 + ν ) 3(1 − ν )
(hydrostatic)
(uniaxial strain)
(Zimmerman, 1991)
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Grain Compressibility, Cg z z z
Under changing pore pressure, Cgp Under changing confining pressure, Cgc But, Cgp = Cgc→ very small
Pc
Obtained using unjacketed sample or jacketed sample, ensuring Pore pressure = confining pressure Only grains deform, measuring Cg
Pc
Cg for quartz = 1.6*10-5 psi-1 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Compressibility Measurement z
Direct measurement (lab-based) – – – – – –
z
Time consuming Expensive Difficult to get cores Core damage and handling, etc. Limited labs equipped for this Limited personnel capabilities
In-Direct measurement (log-based) – – – – –
Time saving Economic Requires logs (usually available) Fairly accurate As a function of depletion and stress changes
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Compressibility Measurement z
Direct measurement (lab-based) – Hydrostatic Test (easy to perform, not preferred for isotropic stresses) – Triaxial Test (anisotropic stress conditions, easy to perform, preferred) – Uniaxial Strain (most preferred, simulates field conditions, but most difficult to perform) – As a compromise, compressibilities obtained using Triaxial Test and converted into uniaxial equivalent
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Hydrostatic Test σ
Radial
δ1
Volumetric
δ3/2
σ
Confining Pressure (psi)
1200
l
d
Axial
1000 800 600 400 200 0 0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
Strain
δ1 εv = ε1 + 2* ε3 ε1 = l δ3 K = σ C = 1 ε3 = b K εv d © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Triaxial Test σ1
Radial
Axial
16000 14000 Axial Stress (psi)
δ1 l
12000 10000 8000 6000 4000 2000 0 -0.006 -0.004 -0.002
d
σ1 E= ε1
0
0.002
0.004
0.006
0.008
0.01
0.012
Strain
δ3/2
ε3 ν=− ε1
E 1 K= Cb = 3(1− 2ν) K © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Uniaxial Strain Test σ1
Radial
σ3
l
d
δ3 = 0
A x ia l S t re s s ( p s i)
δ1
Axial
16000 14000 12000 10000 8000 6000 4000 2000 0 0
0.002
0.004
0.006
0.008
0.01
Strain
1 σ1 Cu = < Cb M= M ε1 (1 + ν) Cb Cu = (1 − ν) 3 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
0.012
Intelligent Triaxial Compression
Stress
— σc — Pp — σa E F
C
B Grain compressibility C Bulk modulus/compressibility
G H
B
A Pre-seating - secure jacket
D
D Young’s modulus, Poisson’s ratio E Compressive strength F Post-failure strain softening G Residual strength
A
H Unloading Time
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Intelligent Compaction/Drawdown Test design Stress
E D C B A
F
A Pre-seating - secure jacket G H — σc — Pp — σa
B Skempton’s constant B C Grain compressibility Cg D Bulk modulus K, bulk compressibility Cb
Strain
E Young’s modulus E, Poisson’s ratio ν F Creep/equilibration
— εa — εr
G Uniaxial strain drawdown, compaction, grain crashing, pore collapse Time
© 2005 Baker Hughes Incorporated All rights reserved.
H Unloading
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stress Loading History - Triaxial Compression at Uniaxial Strain Condition with Pore Pressure Depletion
8000 Total Axial
7000 6000
Effective Axial
5000
Confining
4000 3000 2000
Pore
1000 0 0
2
4
6
8
10
12
14
Time (hour)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Compressibility Determinations from Volumetric Strain - Stress Plot 0.016 0.014 0.012
Confining y = -3.5378E-07x + 1.3746E-02 2
R = 9.9436E-01 Axial Compaction Coefficient = 3.538 E-7 psi-1 Pore Volume Compressibility w/ Initial Porosity = 23.0%
0.01 0.008
Pore y = 2.432E-06x - 1.524E-03 2
R = 9.957E-01 Bulk Compressibility
-1
= 1.447 E-6 psi
-1
= 2.432 E-6 psi α = 0.96
0.006
y = 5.264E-06x - 1.404E-02
0.004
2
R = 9.992E-01 Initial Bulk Compressibility
y = 9.168E-08x + 3.838E-03
0.002
-1
2
5.264 E-6 psi α = 0.98
R = 9.306E-01 -1
Grain Compressibility = 9.168 E-8 psi
0 0
1000
2000
3000
4000
5000
6000
Stress, psi © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Compressibility Measurement – Log-based Approach Pore volume compressibility using LMP: Considers reservoir stress changes with depletion (pressuredependent PVC) Incorporates stress condition constraints that ensure deformations are within elastic bounds Considers stress anisotropy effects (hydrostatic vs. triaxial) Takes log input, commonly available Provides continuous profile with depth Cost-effective, time-saving (particularly when core is n.a.) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Logging of Mechanical Properties σa
Log Inputs
Produce StressStrain Curves
Δtc, Δts, Porosity, Lithology
σr Produces Virtual Core Sample
σa
Applying Virtual Stresses to the “Core Sample”
εr
εa
Static Mechanical Properties: Rock Strength, Elastic Moduli Poisson’s Ratio, Compressibilities © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Log Derived Compressibility – Simulated Hydrostatic Compression z z z z z
Process LMP Determine static bulk modulus (HC) Calculate bulk compressibility Assume grain compressibility (Cgc) from table Calculate pore volume compressibility (PVC)
∂σ c Kb = ∂ε v 1 C bc = Kb © 2005 Baker Hughes Incorporated All rights reserved.
C pp =
C bc − (1 + φ )C gc
Efficiency….Data accuracy….People-oriented service
φ www.bakeratlasdirect.com
Log Derived Compressibility – Elastic Moduli z z z z z
Process LMP - static elastic moduli Calculate bulk modulus Calculate bulk compressibility Assume grain compressibility (Cgc) from table Calculate pore volume compressibility (PVC)
E Kb = 3(1 − 2ν ) 1 C bc = Kb © 2005 Baker Hughes Incorporated All rights reserved.
C pp =
C bc − (1 + φ )C gc
Efficiency….Data accuracy….People-oriented service
φ www.bakeratlasdirect.com
Uniaxial Strain Condition z
Reservoir fluid production is associated with pore pressure reduction, constant overburden and zero lateral deformation (constrained by earth crust)
z
Convert hydrostatic pore volume compressibility [Cpp] into uniaxial strain ‘equivalent’ pore volume compressibility [Cpp(u)], using:
C pp ( u ) =
© 2005 Baker Hughes Incorporated All rights reserved.
C pp (1 + ν ) 3(1 − ν )
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
PV Comparison – LMP vs. Lab
L M P ( P P = 1 2 0 0 0 p s i) L M P ( P P = 4 0 0 0 p s i) L a b I D # 5 - 1 ( 1 2 8 0 0 - 1 0 9 9 0 p s i) L a b ID # 5 -1 (4 7 9 0 -2 8 0 5 ) L a b I D # 1 0 - 3 ( 1 2 8 0 0 - 1 0 6 2 5 p s i) L a b I D # 1 0 - 3 ( 6 4 2 0 - 4 8 2 0 p s i)
TVDRKB, ft
Comparison of LMP vs. labderived uniaxial pore volume compressibility, with depth, for two effective stress conditions
L a b I D # 1 8 - 5 ( 1 2 8 0 0 - 1 0 8 0 5 p s i) L a b I D # 1 8 - 5 ( 6 6 0 0 - 5 0 0 0 p s i)
1
2
3
4
E ffe c tiv e P o r e C o m p r e s s ib ility x 1 0
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
5 -6
psi
6
-1
www.bakeratlasdirect.com
Pore Pressure Depletion Effects (Elastic) Reservoir Depletion Analysis – –
–
–
Changes in in-situ stresses, caused by reservoir pressure depletion, can result in shear failure of the formation Shear failure causes weakly cemented rock to disaggregate, leading to low values of cohesive strength and critical drawdown pressure For reservoir management and workover planning purposes, it is, therefore, important to know the onset of formation shear failure associated with reservoir depletion Reservoir stress path analysis is required
© 2003 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Pressure Depletion Effects (Elastic) z Stress
Path – under uniaxial strain condition:
σ = σ + K o (σ − σ
Δσ h' νt Ko = = ' Δσ v 1 −ν t
' h
' ho
' v
' vo
)
z Reservoir
Failure – Mohr-Coulomb failure criterion
Ko is the stress path coefficient, are the effective σ ho' andσ zo' horizontal and vertical stresses, respectively, at the previous depletion stage and νt is the tangential Poisson’s ratio. © 2003 Baker Hughes Incorporated All rights reserved.
τ = S o + μσ = S o + σ tan φ or φ
σ = UCS + σ tan ( + 2 ) '
'
1
3
Efficiency….Data accuracy….People-oriented service
2 π 4
www.bakeratlasdirect.com
Uniaxial Strain PVC Variations with Depletions (Elastic)
Two general approaches: Constant stress path coefficient z Stress path coefficient as a function of effective horizontal and vertical stresses z
© 2003 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Uniaxial Strain PVC Variations with Depletions (Elastic) Constant Stress Path Coefficient 1.
Run LMP at initial reservoir confining condition.
2.
Calculate pore volume compressibility, Cpp, at triaxial stress condition (@ 50% peak stress) and convert to uniaxial strain equivalent, Cpp(u).
3.
At next pore pressure level, calculate the new horizontal stress using a constant stress path coefficient, Ko. Run LMP at the new confining stress condition.
4.
Repeat step 2.
5.
Continue step 3 until reservoir failure
Reference: SPE 95545 – Log-Based Pore Volume Compressibility Prediction – A Deepwater GoM Case Study (2005) © 2003 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Uniaxial Strain PVC Variations with Depletions (Elastic) Constant Stress Path Coefficient
*Discrepancy between lab and LMP derived PVC is probably due to different stress path coefficients and porosity values used in the computations. © 2000 Baker Hughes Incorporated All rights reserved. © 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Uniaxial Strain PVC Variations with Depletions (Elastic) Stress Path Coefficient = f(σh’, σv’) 1.
2.
3.
Run LMP at initial reservoir confining as well as several other confining pressure conditions expected to be experienced during reservoir depletion. Generate tangential Poisson’s ratio and Young’s modulus and plot these tangential elastic moduli as a function of axial stress at different confining pressures. At initial reservoir pressure condition, calculate the effective horizontal and vertical stresses. With these stress conditions (confining, axial) known, interpolate using plots generated in step 2 to obtain tangential Poisson’s ratio and Young’s modulus.
© 2003 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Uniaxial Strain PVC Variations with Depletions (Elastic) Stress Path Coefficient = f(σh’, σv’)
Reference: ARMA/USRMS 05-791 - Characterizing Pore Compressibility, Reservoir Compaction and Stress Path under Uniaxial Strain Condition for Nonlinear Elastic Rock (2005) © 2003 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Uniaxial Strain PVC Variations with Depletions (Elastic) Stress Path Coefficient = f(σh’, σv’)
Reference: ARMA/USRMS 05-791 - Characterizing Pore Compressibility, Reservoir Compaction and Stress Path under Uniaxial Strain Condition for Nonlinear Elastic Rock (2005) Efficiency….Data accuracy….People-oriented service www.bakeratlasdirect.com
© 2000 Baker Hughes Incorporated All rights reserved. © 2002 Baker Hughes Incorporated All rights reserved.
Uniaxial Strain PVC Variations with Depletions (Elastic) Stress Path Coefficient = f(σh’, σv’) 4.
Calculate stress path coefficient and uniaxial strain pore volume compressibility using: Δσ h' νt = Ko = ' Δσ v 1 −ν t
C pp (u ) 5.
6.
1 (1 + ν t )(1 − 2ν t ) ≈α φEt 1 −ν t
(neglect grain compressibility)
At next pore pressure level, calculate the effective vertical stress and assume an effective horizontal stress. With these stress conditions, interpolate using plots generated in step 2 to obtain tangential elastic moduli.
© 2000 Baker Hughes Incorporated All rights reserved. © 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Uniaxial Strain PVC Variations with Depletions (Elastic) Stress Path Coefficient = f(σh’, σv’) 7.
Calculate stress path coefficient and then effective horizontal stress using:
σ = σ + K o (σ − σ ' h
8.
9.
' ho
' v
' vo
)
Repeat step 6 until the effective horizontal stress converges. Calculate stress path coefficient and uniaxial pore volume compressibility as per step 4. Repeat steps 5, 6, 7 and 8 until reservoir failure.
© 2003 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Uniaxial Strain PVC Variations with Depletions (Elastic) Stress Path Coefficient = f(σh’, σv’)
Reference: ARMA/USRMS 05-791 - Characterizing Pore Compressibility, Reservoir Compaction and Stress Path under uniaxial Strain Condition for Nonlinear Elastic Rock (2005)
© 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Uniaxial Strain PVC Variations with Depletions (Elastic) Comparison of PVCs assuming different stress dependency elastic moduli
Reference: ARMA/USRMS 05-791 - Characterizing Pore Compressibility, Reservoir Compaction and Stress Path under uniaxial Strain Condition for Nonlinear Elastic Rock (2005) © 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
–Reservoir Reservoir Reservoir Compaction – Productivity Change (Elastic) Depletion-induced porosity & permeability change
φ = 1 − (1 − φo )e
ε z −ε zo
φo and εzo are porosity and vertical strain, respectively, at the previous depletion stage.
[ −γ ( p k = ko e
'
' − po
)]
p = '
σ v + 2σ h 3
− pp
ko is permeability measured at effective mean stress, po’, and γ =0.004 MPa-1 for a 20% porosity sandstone.
© 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Reservoir Compaction – Reservoir Productivity Change (Elastic) Depletion-induced porosity & permeability change q p' = 1.23 * + 0.00275 (damage/permeability criterion) * p p 2
2
⎡ p' ⎤ ⎡ q ⎤ ⎢ * ⎥ + ⎢ * ⎥ =1 ⎣p ⎦ ⎣p ⎦
(cap surface)
k = ko e [−γ ( p − po ) ] '
'
q p' = 1.81 * + 0.06 p* p
(for p ' / p * ≤ 0.175)
2
⎡ p' ⎤ q p' = −2.073⎢ * ⎥ + 2.536 * - 0.003 p* p ⎣p ⎦
(for p ' / p * ≥ 0.175)
1 ∂k ∂p ' − = 0.0049 + 0.0017 ∂q k o ∂q
q = σ v −σ h
p * = 6.435UCS
q and p* are the deviatoric stress and critical effective pressure for the onset of grain crushing under hydrostatic loading, respectively. Valid for 20% porosity rock. © 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
Reference: SPE 58717
www.bakeratlasdirect.com
Summary – Pore Volume
Compressibility •
•
•
We have presented a log-based method to compute uniaxial strain pore volume compressibility, stress path and permeability changes as a function of reservoir pressure depletion. The method is valid for reservoir pressures prior to the on-set of reservoir failure which can be estimated using a shear failure criterion such as the Mohr-Coulomb’s. Beyond shear failure, a constitutive law must be established to describe the mechanical behavior of rock deformation under stresses.
© 2000 Baker Hughes Incorporated All rights reserved. © 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline
z
Critically stressed fractures/faults
z
Reservoir compaction
z
Pore volume compressibility
Î
Surface subsidence
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Surface Subsidence Calculations z
Rigorous Methods – Reservoir and overburden heterogeneity – Non-uniform pressure distributions – Numerical methods (Finite Element, boundary element, etc.) – Fairly accurate, but time consuming and costly
z
Approximate Methods – – – – –
*Geertsma’s (1973) nucleus of strain model Smits and de-Waal (1985) Morita et al (1989) Not expensive or time consuming Approximate, use as a guideline
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Surface Subsidence Calculations z
Assumptions: – Reservoir experiences the full overburden load (true near the center of the reservoir) – Exceptions near flanks, arching effects, presence of anticlines, faults, etc. are ignored – No lateral deformation (uniaxial compaction) – Uniform pressure distribution in the reservoir – Rock mechanical properties are uniform – Overburden behaves in an elastic manner homogeneously
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Surface Subsidence Calculations z
Geertsma’s* nucleus of strain model (spherical) – Consider a contracting sphere within an infinite medium (inner sphere) – Displacement trend in the surrounding medium will be spherically symmetric, given by:
where
ro 2 u = uo 2 R
u = radial displacement at a point
u R
uo ro
u0 = displacement at the nucleus r0 = radius of nucleus of strain sphere R = radial distance from center of sphere to the point *from Geertsma 1973 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Geertsma’s Model (disk-shaped) Cb Cb u r (a ) = hΔ PB (ρ , η) u z (a ) = hΔ PA (ρ , η) 2 2 a D ρ = ;η = r r A = R ∫ J ( α R )J ( α a )e ∞
1
− Dα
0
dα
0
∞
A
B = R ∫ J 1 ( α R )J 1 ( α a )e − Dα dα 0
z
y
x
ur
a
(x,y,0)
D
B
uz (x’,y’,z’)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Surface Subsidence Calculations z
Geertsma’s nucleus of strain model –The nucleus of strain model does not guarantee the uniaxial strain nature of reservoir compaction –To overcome this, “imaging” concept is introduced, commonly used in reservoir engineering. surface
Zero displacement planes (“no- flow” boundary) nucleus of strain
© 2005 Baker Hughes Incorporated All rights reserved.
image nucleus
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Solved Example Problem: Calculate the maximum surface subsidence given the following: reservoir diameter = 4 km (r = 2 km) reservoir depth (D) = 2 km reservoir height (h) = 50 m compressibility: 6.0*10-5 bar-1 expected compaction: 2.5′ subsidence (S)
D = 2km compaction (C)
50m 4km 4km © 2005 Baker Hughes Incorporated All rights reserved.
4km
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Solved Example Solution: uz(a) = Cb/2 DP h A(r,h) cancel
S 0.5 * C b * ΔP * h * A s (ρ, η) A s (ρ, η) = = C 0.5 * C b * ΔP * h * A c (ρ, η) A c (ρ, η)
S 0.2929 + 4 * 0.0519 = = 0 .5 C 1.00
Contribution Point
Location(s)
a
D
ρ
η
A (from table)
Center, top of reservoir
1
0
0
0
0
1
Center, surface contribution from the reservoir
2
0
2
0
1.0
0.2929
Center, surface contribution from the 4 images
3
4
2
2.0
1.0
0.0519 * 4
subsidence (S)
D = 2km
3
compaction (C) 1
50m 2
3
4km
a = 4km 4km
3
3
S= surface subsidence, C= reservoir compaction © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Summary - Subsidence Surface subsidence should be estimated and considered in: – Platform design – Casing design – Reservoir management (injection, depletion rate, etc.) – Production life of the reservoir – Impact on surrounding structures and environment
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
© 2005 Baker Hughes Incorporated All rights reserved. © 2000 Baker Hughes Incorporated All rights reserved.
Course Objectives
To provide a broad overview of the fundamentals of Geomechanics. To demonstrate the use of these fundamentals to address oil field problems associated with the drilling and production of hydrocarbon resources.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Course Outline 1. Introduction to Geomechanics what, why, where fundamentals 2. Rock Mechanical Property Characterization static versus dynamic Logging of Mechanical Properties (LMP) 3. In-situ Stress Characterization pore pressure estimation subsurface stresses – magnitude & direction 4. Geomechanics Applications wellbore stability sand/solid production hydraulic fracturing reservoir compaction © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Geomechanics Applications
© 2005 Baker Hughes Incorporated All rights reserved. © 2000 Baker Hughes Incorporated All rights reserved.
Outline • What is Geomechanics? • Why Geomechanics? • Geomechanics Applications • How to Apply Geomechanics? • Geomechanics Application Examples • The Value of Geomechanics
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
What is Geomechanics?
STRESS vs. STRENGTH ESF
U
Z ER
O
RES
IS T
EN C
IA
A branch of engineering mechanics concerned with the response of geologic materials to the force field of their physical environment.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
What is Geomechanics? (Rock Mechanics) • Theoretical and applied science of the mechanical behavior of geological materials. • A branch of mechanics concerned with the response of geological materials to the force field of their physical environment. • Used in civil, petroleum and mining engineering and any discipline dealing with geological material’s mechanical behavior. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
What is Petroleum Geomechanics? Science and knowledge about the mechanical behavior of reservoir and overburden formations during different phases of petroleum operations.
Petroleum geomechanics enables us to predict wellbore and reservoir deformations/failures and generate engineered solutions for optimal field developments.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Why Geomechanics? z
Today’s reservoirs are more difficult to access and develop: – “Brown-field” reservoirs approach depletion and many are compartmentalized – Onshore reservoirs are deeper and manifest high-pressure, high-temperature (HPHT) conditions – Offshore reservoirs are in deep water and at greater depth – Heavy oil recovery require high temperature operations
z
z
Geomechanics is a key enabling technology for exploring and exploiting today’s technically challenged reservoirs (tectonics, deepwater, HPHT, brown, heavy oil). Advanced technology is required to optimally drill, complete and produce these reservoirs.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Why Geomechanics? Total E&P Costs = $82 billion
• In 1997
Drilling Costs = $32 billion$6.4 • In 2002 2002 SPE-ATW on Real-time Wellbore Stability
B
Drilling costs related to borehole instability = $3.2 billion
All major operating companies agreed on 10 to 15 % of the drilling budget goes to wellbore stability issues !!
Geopressure and borehole stability problems are estimated to cost the industry $8 billions every year !!
• In 2004
Offshore Magazine - Dodson Jan.2004
………but missing production can be equally expensive!!
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Applications of Geomechanics $
NPV
) Borehole stability/well planning
Business Drivers
) Drilling efficiency enhancement
) Solid production/completion strategy ) Reservoir compaction/subsidence ) Hydraulic fracturing/stimulation
Reservoir Properties
) Cuttings re-injection/remediation ) Well placement in fractured reservoirs
Log/Core Measurements
© 2005 Baker Hughes Incorporated All rights reserved.
) Fully-coupled reservoir simulation
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Geomechanics Applications – Summary Borehole Integrity Management
Sand Control Solutions
Wellbore Stability Wellbore Strengthening
Screen Completion Screenless Completion
mud weight windows mud composition/formulation wellbore trajectory casing program
critical drawdown pressure oriented perforation selective perforation wellbore/perforation trajectory expandable screen gravel pack
Reservoir Management
Waste Management
Reservoir Compaction [production induced]
Drilling Waste (drilling fluids, cuttings) Production Waste (produced water, CO2)
stress-dependent rock properties pore volume compressibility well/completion integrity platform subsidence drive mechanism pressure maintenance time-lapsed seismics
cap rock integrity fault seal integrity fracture containment fracture morphology/geometry candidate well selection (geomechanics)
Production Enhancement
Complex Geology Environments
Productivity Improvement (well-based) Recovery Improvement (field-wide)
Fault Seal Integrity Critically Stressed Fracture
dynamic under-balanced perforation hydraulic fracturing stimulation flood directivity oriented perforation stress vs. permeability anisotropy
exploration strategy injection pressure production management (depressurization) well placement in fracture reservoir
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Values of Geomechanics – A Success Story
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Value of Geomechanics – Baker Hughes z z z z z z z z z
Generating pull through revenue Value boosting for logging technologies Help generating needs for quality formation data Improve client relationships Quality assurance Understanding market and technology needs/requirements Increase communication with sister divisions Generate direct revenues for BHI/BA Secure the client - measured by # tenders
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Fundamentals of Geomechanics © 2005 Baker Hughes Incorporated All rights reserved. © 2000 Baker Hughes Incorporated All rights reserved.
Outline z z z z z z z
Basic Concepts of Stress and Strain Principal Stresses Mohr’s Circle Elasticity and Elastic Parameters Failure Strength Parameters Failure Theories Effective Stress Concept
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Definitions and Terminology Stress and Strain ♦ Stress (σ or τ): Defines the force field to which a material is subjected. Stress is a tensor with three orthogonal principal directions in a three dimensional coordinate system. ♦ Strain (ε or γ): Defines the deformation of a material in a force (stress) field. Strain is also a tensor with three orthogonal principal directions in a three dimensional coordinate system.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Definitions and Terminology Stress (σ)
Units of pressure (or force/area), e.g., psi, MPa, bar, etc. c.s. area F
Stress on the plane σ = F/A
a
A
b
A’
σ = F/A’
c
A’’
σ = F/A’’
F
F
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Definitions and Terminology Strain (ε)
P
Δl
Δl Change in Dimension ε= = l Original Dimension
l
l
1
Un-deformed
Deformed
• Defines the deformation of a material in a stress field. • Relative change in material dimension.
Unit or dimensionless
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Definitions and Terminology Stress (σ)
Fp
• Normal Stress –normal or perpendicular –
σn= Fn/A
Fn F
(e.g., σx , σy, etc.)
• Shear Stress – parallel to the plane –
τ = Fp/A
(e.g., τxy, τxz, etc.)
• Stress & Strain – vector quantities (on a single plane) • Magnitude (amount) • Direction © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Definitions and Terminology 2D State of Stress 2 Normal stresses 2 Shear stresses
σy
4 comp.
For no rotation & translation:
τxy = τyx
(σ )2D
σyy
⎧σ xx ⎫ ⎪ ⎪ = ⎨σ yy ⎬ ⎪τ ⎪ ⎩ xy ⎭
τyx
τxy σxx
σx
τij = Shear stress acting on a plane perpendicular to i and in a direction parallel to j
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Definitions and Terminology σyy
General 3D State of Stress 3 Normal stresses 9 comp. 6 Shear stresses τxy = τyx τyz = τzy τzx = τxz
τyz τzy τzx
τyx
τxy
τxz
σxx
Stress Tensor: total 9 components, with 6 independents.
3 normal + 3 shear stresses © 2005 Baker Hughes Incorporated All rights reserved.
σzz
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Definitions and Terminology Stress Tensor (σ) =
σxx τxy τxz τyx σyy τyz τxz τzy σzz
=
2D System © 2005 Baker Hughes Incorporated All rights reserved.
σ1 σ4 σ5 σ4 σ2 σ6 σ5 σ6 σ3
σ11 σ12 σ13 = σ21 σ22 σ23 σ31 σ32 σ33
=
σ1 σ2 σ3 σ4 σ5 σ6
Efficiency….Data accuracy….People-oriented service
= σij = [σ]Τ
www.bakeratlasdirect.com
Definitions and Terminology Stress Transformation - 2D σy
For the equilibrium of the body:
∑ Fx = ∑ (σ • A )x = 0
∑ Fy = ∑ (σ • A )y = 0
y
τxy
σ
σx τxy
τxy θ
θ
x
τxy
σ=( τ=(
σx +σy 2
σy −σx 2
)+(
σx −σy 2
) cos 2θ + τ xy sin 2θ
σx
τ
σy
) sin 2θ + τ xy cos 2θ
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Definitions and Terminology Other expressions for normal stress on a plane: σ = σxx cos2θ + σyy sin2θ + τxy sin2θ σ = σxx cos2θ + σyy sin2θ + 2τxy sinθ cosθ
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Exercise Problems σyy
Given:
Y
σxx = 100 psi σyy = 60 psi τxy = 40 psi
τxy σ
σxx τxy
(note: sin30 = cos60 = -cos120 = 1/2 cos30 = sin60 = sin120 = √3/2)
τxy σxx
θ τ
θ
X
τxy σyy
Determine normal (σ) and shear stresses (τ) for: 1) θ = 30 degrees σ = 124.6, τ = 2.7 2) θ = 60 degrees σ = 104.6, τ = -37.3 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline 9 Basic
Concepts of Stress and Strain ÎPrincipal Stresses & Mohr’s Circle z Elasticity and Elastic Parameters z Failure Strength Parameters z Failure Theories z Effective Stress Concept
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Principal Stresses
σ1 σ2 σ3
σv σH σh
Normal stresses on planes where shear stress is zero σ1 > σ2 > σ3
σ1 = σ v
(Max. > Intermediate > Minimum)
Other Notations:
σ2 = σ H
σ3 = σ h
σH = σHmax σh = σhmin
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Definitions and Terminology Principal Stresses - 2D
τ=(
σy −σx 2
) sin 2θ + τ xy cos 2θ
2 τxy tan 2θ = σx - σy
σ1 = (
σx +σy 2
σ2 = (
σx +σy 2
=0
σy y
y’
θ1, θ2 are the solutions (θ2 = θ1 + 90) Mutually orthogonal
x’
τxy
σx τxy
σx
τ=0 θ1 τxy
)+(
σ x −σ y 2
) cos 2θ1 + τxy sin 2θ1
)+(
σ x −σ y 2
) cos 2θ2 + τ xy sin 2θ2
© 2005 Baker Hughes Incorporated All rights reserved.
τxy
σ
Efficiency….Data accuracy….People-oriented service
x
σy
www.bakeratlasdirect.com
Exercise Problem Stress Transformation – 2D σxx = 100 psi σyy = 60 psi τxy = 40 psi
σy y
τxy τxy
σ1
σx τxy
σx
τ=0 θ1 τxy
x
σy
Determine the directions of principal stress axes (θ1, θ2) and the magnitudes of principal θ1 = 31.7 deg, θ2 = 121.7 deg stresses (σ1, σ2): σ1 = 124.7 psi, σ2 = 35.3 psi
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Definitions and Terminology Principal Stresses (2D) σ1 =
σ2 =
σx + σy 2 σx + σy 2
2
⎛ σx − σy ⎞ ⎟⎟ + τ 2xy + ⎜⎜ ⎝ 2 ⎠ 2
⎛ σx − σy ⎞ ⎟⎟ + τ 2xy − ⎜⎜ ⎝ 2 ⎠
σ1 ≥ σ2
σ1 = Mean Stress + Max. Shear Stress σ2 = Mean Stress – Max. Shear Stress © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Definitions and Terminology Mohr Stress Circles and Principal Stress Calculations
Y σy τxy σx
Shear Stress, τ
σx
X
(σx−σy)/2
τxy
Max Shear Stress: Mean Stress: (σx+ σy)/2
Shear Stress: τxy
σy σ2
Normal Stress, σ
σx
σy
σ1
σ1 = Mean Stress + Max. Shear Stress σ2 = Mean Stress – Max. Shear Stress © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Definitions and Terminology
τ
Mohr Circles - Graphic Representation of 2D Stresses
( σ1 + σ 3 ) σ1 −σ 3 σn = + Cos 2θ
τ σ3
σ1 − σ 3
σn
© 2005 Baker Hughes Incorporated All rights reserved.
2
2
2θ
σ1
σ
2
( σ1 − σ 3 ) τ = Sin 2θ
⎛ σ1 + σ 3 ⎞ ,0 ⎟ ⎜ ⎝ 2 ⎠
Efficiency….Data accuracy….People-oriented service
2
θ = 530
www.bakeratlasdirect.com
Definitions and Terminology Principal Stresses – 3D - Eigen Values of the Stress Matrix (s)
σ x −σ τ xy τ xz τ xy σ y −σ τ yz = 0 , σ 3 − I1σ 2 − I 2σ − I3 = 0 τ xz τ yz σ z −σ where
σ x τ xy σ x τ xz σ y τ zy I1 = σ x + σ y + σ z , I 2 = + + τ xy σ y τ xz σ z τ zy σ z and
σ x τ xy τ xz I 3 = τ xy σ y τ zy τ xz τ zy σ z
© 2005 Baker Hughes Incorporated All rights reserved.
are the Stress Invariants
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Principal Stresses σv
In the case of a reservoir, σh
σ1 = σv = Vertical/Overburden stress σ2 = σH = Maximum horizontal stress
σH Stress Magnitude
σ3 = σh = Minimum horizontal stress Depth
σh σH © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
σv
www.bakeratlasdirect.com
Representation of A Stress State •
The state of stress AT A POINT in the reservoir can be represented by Mohr’s circle τ
σ3 © 2005 Baker Hughes Incorporated All rights reserved.
σ2
σ1
Efficiency….Data accuracy….People-oriented service
σ www.bakeratlasdirect.com
Outline 9 Basic
Concepts of Stress and Strain 9 Principal Stresses and Mohr’s Circle ÎElasticity and Elastic Parameters z Failure Strength Parameters z Failure Theories z Effective Stress Concept
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Elastic Properties
σ
Elastoplastic
Linear Elastic
Yield
Max. Stress = Failure Strength Re-loading
P
Unloading
δ1 E
Sample
1 εpl
© 2005 Baker Hughes Incorporated All rights reserved.
εel
ε1
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Elastic Properties Elastic Moduli – E and ν P
Measure: Axial Load (P) Deformations: δ1, δ3 Conf. Pres. σ2 = σ3
δ3
σ1 = P / area ε1 = δ1 / orig. length ε3 = 2*δ3 / orig. dia. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
δ1
Sample
www.bakeratlasdirect.com
Elastic Properties Co = σmax
dσ1 dε3
dε1
ε3
ε1
Ε = dσ1 / dε1 ν = −dε3/ dε1 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Elastic Properties Young’s Modulus & Poisson’s Ratio )Young’s Modulus:
E = Δσ1 / Δε1
Young’s modulus describes the stiffness of a material when it is under stress. The higher the Young’s modulus, the harder it is to deform the material. i.e. requires more stress to deform.
)Poisson’s Ratio:
0 < ν = - Δε3 / Δε1 < 0.5
Poisson’s ratio defines the relative strain in a direction not subjected to incremental stress and orthogonal to the direction of the incremental stress. A material with Poisson’s ratio of 0.5 is an incompressible material.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Types of Moduli Young’s modulus: E = dσ1 / dε1
Initial Tangential Secant 50% peak stress
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Initial Modulus σ
dσ
E = dσ / dε
dε
ε © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Tangential Modulus σ
dσ x
E = dσ / dε
dε
ε © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Secant Modulus σ
x
E = dσ / dε dσ
dε © 2005 Baker Hughes Incorporated All rights reserved.
ε Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Modulus at 50% Peak Stress σ σmax
E = dσ / dε
50 % σmax
dσ dε
ε © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Quiz Quiz-- Elastic Properties Given:
P
Orig. length = 2 inches Orig. Dia. = 1 inch
δ3
δ1
Ax. Deformation = 0.05 inch Rad. Deformation = 0.003 inch Load = 20,000 lbf
L
Sample
Find: E=? ν=?
d © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Quiz Solution Solution-- Elastic Properties Solution: σ1 = P / cross-sectional area Area = πd2/4 ε1 = δ1 / orig. length ε3 = 2*δ3 / orig. dia. Area = 3.1416*(1)2/4 = .785in2 σ1 = P / area = 25465 psi ε1 = 0.05 / 2 = 0.025 ε3 = 2*(-0.003) / 1 = -0.006 E = σ1 / ε1 = 25465/.025 = 1.02E+06 psi ν = -ε3 / ε1 = .006/.025 = 0.24
© 2005 Baker Hughes Incorporated All rights reserved.
P
δ3
L
Efficiency….Data accuracy….People-oriented service
δ1
Sample
d www.bakeratlasdirect.com
Stress -Strain Relations Stress-Strain Relations between Stress and Strain (isotropic) Uniaxial Loading:
E = Δσ1 / Δε1 = Δσy / Δεy
1 ε xx = (σ xx − νσ yy − νσ zz ) E 1 ε yy = (σ yy − νσ xx − νσ zz ) E 1 ε zz = (σ zz − νσ yy − νσ xx ) E σ xx + σ yy + σ zz ε v = ε xx + ε yy + ε zz = 3K τ xy τ yz τ zx , ε yz = , ε zx = ε xy = 2G 2G 2G © 2005 Baker Hughes Incorporated All rights reserved.
Y
τyx
σy τyz
τzy σz
τxz τzx
σx
τxy
Z
E and ν
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
X
Stress -Strain Relations Stress-Strain Relations between Stress and Strain (isotropic) Uniaxial Loading:
E = Δσ1 / Δε1 = Δσy / Δεy
σ xx = λε v + 2 G ε xx
Y
τyx
σ yy = λε v + 2 G ε yy
σy τyz
σ zz = λε v + 2 G ε zz τ xy = 2 G ε xy
τzy
τ yx = 2 G ε yx
σz
τxz τzx
σx
τxy
τ zx = 2 G ε zx ε v = ε xx + ε yy + ε zz = ε xy =
τ xy 2G
, ε yz =
© 2005 Baker Hughes Incorporated All rights reserved.
τ yz 2G
σ xx + σ yy + σ zz , ε zx
3K τ zx = 2G
Z
where λ, G, and K are functions of E and ν
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
X
Elastic Properties Relations between Different Elastic Parameters (isotropic material – 2 constants) Bulk Modulus Shear Modulus
Lame’s constant
E E G= , K= , 2(1 + ν ) 3(1 - 2ν ) Eν λ= (1 + ν )(1 − 2ν )
9KG 3K - 2G 2Gν E= , ν= , λ= 3K + G 2(3K + G) 1 − 2ν © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline 9 Basic
Concepts of Stress and Strain 9 Principal Stresses 9 Mohr’s Circle 9 Elasticity and Elastic Parameters ÎFailure Strength Parameters ÎFailure Theories z Effective Stress
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Strength Parameters Intrinsic properties that describe the failure behavior/response under load/force/stress. ) Compressive & tensile strengths (C & To)
Related Parameters: ) ) ) )
Angle of internal friction (α) Shear Strength (Si) Unconfined Compressive Strength (UCS) Confined Compressive Strength
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Strength Parameters Compressive Strength – from Triaxial Compression Test
Test Apparatus
Stress-Strain Curves
Axial Strain measurement
Axial Differential Stress
Axial Stress
Confining Pressure inlet Seal
Radial Strain measurement
© 2005 Baker Hughes Incorporated All rights reserved.
Confining Pressure outlet Pore Pressure control
Radial Strain
Efficiency….Data accuracy….People-oriented service
Axial Strain
www.bakeratlasdirect.com
Failure Strength Parameters Typical Stress-Strain Curve (Triaxial) Axial/Shear/Deviatoric Stress (σa- σc or σ1-σ3) Compressive Strength Increasing crack density Macro cracking - failure by joining microcracks
New microcracks
Δσa
Δσa
Linearly elastic
Δεr
Sliding on macrocracks
Δεa Closure of pre-existing cracks
Radial Strain εr (extension)
© 2005 Baker Hughes Incorporated All rights reserved.
Axial Strain εa (contraction)
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Differential stresses (σ1-σ3)
Failure Strength Parameters
σmax- Peak Strength Starting of the mechanical damage ~0.60σmax
Cohesion lost
Massive damage, shear plane development Sudden drop of stresses (brittle failure) Continuous damage
Elastic behavior σ−ε
Residual strength
Micro-fissures closing
Axial strain (εa) (after Dusseault, 2000)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Strength Parameters Different Types of Compression Tests • Unconfined (Uniaxial) Compression Test σa
σc
σc = 0
σa UCS = σamax
© 2005 Baker Hughes Incorporated All rights reserved.
• Confined Triaxial Compression Test σa
σc
σa C(σc) = σamax(σc)
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Strength Parameters Failure Envelope
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Theories Mohr Failure Envelope τ D C
B A
σ An empirical criterion of failure defined by the envelope to a series of Mohr’s circles: A- direct tension; B- Brazilian; C- unconfined compression; D- triaxial compression. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Theories Mohr – Coulomb Failure Criterion S i = Cohesion or initial shear strength
τ = S i + σ tan φ
φ = Internal Friction Angle
τ
φ
τ = S i + σ tan φ
Si
σ3 © 2005 Baker Hughes Incorporated All rights reserved.
UCS Efficiency….Data accuracy….People-oriented service
σ1
σ www.bakeratlasdirect.com
Failure Strength Parameters Mohr–Coulomb Failure Criterion τ = So + μσ = So + σ tan φ or σ1 = UCS + σ 3 tan 2 ( π4 + φ2 )
The relationships between So , μ , φ and UCS are: tan( π4 + φ2 ) = 1 + μ 2 + μ =
1 + sin φ , and 1 − sin φ
UCS = 2So tan( π4 + φ2 ), μ = tan φ UCS = Unconfined Compressive Strength, So = Cohesion or initial shear strength φ = Internal Friction Angle μ = Friction Coefficient = tanφ © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Strength Parameters Confining Pressure Effect
Axial Differential Stress
σc = 50 MPa
σc = 25 MPa
σc = 10 MPa σc = 5 MPa σc = 0
Radial Strain © 2005 Baker Hughes Incorporated All rights reserved.
Axial Strain
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Mechanics – Failure Modes σ
Ductile – high confining stress (σ (σ3)
σ0 Transitional Brittle – low confining stress (σ (σ3)
ε
After de Van der Pluijm y Marshak, 1997
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Confining Pressure Effects COMPRESSIVE STRENGTH 160
120
During Compaction Undisturbed Formation Strength During Production
80
depth = 5000 ft shale
40
During Drilling 0
0
2
4
6
8
10
12
14
16
18
20
CONFINING PRESSURE [Mpa] © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Strength Parameters Temperature Effect 25°C
σ1 - σ3 [kbars]
20 15 10 5 0
300°C 500°C 800°C
5
10
15
Strain [%] © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Strength Parameters Specimen Size Effect (after Bienawski and Van Heerden, 1975)
Compressive Strength [MPa]
140 Calcareous Iron Ore Jahns, 1966
120
Cedar City Quartz Diorite, Pratt et. all, 1972. Coal, Bienawski, 1968
100 80 60 40 20 0
© 2005 Baker Hughes Incorporated All rights reserved.
0.5
1 1.5 2 Specimen Length [m]
2.5
Efficiency….Data accuracy….People-oriented service
3
www.bakeratlasdirect.com
Failure Strength Parameters Fluid/Saturation Effect Dry
σ1 - σ3 [kbars]
50 Saturated, non-wetting phase fluid
40 30
Saturated, wetting phase fluid
20 10
5
10 15 20 25 Strain [%]
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Strength Parameters Other Types of Compression Tests • Hydrostatic Compression Test σa
σc
σc = σa
σa
= σc/εv εv = εa + 2*εr c = 1/K K
εc = 0
ν Δ σx ' Δ σy ' K0 = = = t Δσ z ' Δσ z ' 1 - ν t
For Bulk modulus/Compressibility
© 2005 Baker Hughes Incorporated All rights reserved.
• Uniaxial Strain (K0) Test σa
σa Field Conditions
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Strength Parameters
Tensile Strength )
Capacity of a material to support tensile stress. • Direct Tension Test To = σTmax
σT
σT
• Bending Test
• Brazilian Indirect Tension Test
P
To = 2Pmax/πtD © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline 9 Basic
Concepts of Stress and Strain 9 Principal Stresses 9 Mohr’s Circle 9 Elasticity and Elastic Parameters 9 Failure Theories 9 Failure Strength Parameters ÎEffective Stress
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effective Stress Concept If a load is applied to a rock, a portion of the load is imparted on the rock matrix and a portion on the pore fluid (counteracting). Pore pressure increases if rock permeability is sufficiently low
F
Total stress (σ) = F/A A = area of the plane Grain load increases
Matrix
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effective Stress Concept Mathematically, the effective stress (σ’) concept is written as: Total Stress (σ) = Stress on grains (σ’) + Stress on fluid (Pp) Stress on grains (σ’) = Total Stress (σ) - Pore Pressure (Pp)
σ’ = σ – Pp
Î
Terzaghi’s effective stress law
For constant Pp: σ ↑, σ’↑ (and vice versa) For constant σ: Pp ↑, σ’↓ For constant σ: Pp ↓ , σ’↑
© 2005 Baker Hughes Incorporated All rights reserved.
This is known as the Terzaghi’s effective stress. Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effective Stress Concept For most rocks, a change in total stress (or pore pressure) does not yield an identical change in effective stress. To account for this, Terzaghi’s effective stress was modified by Biot (1941) as:
σ’ = σ - αPp where α = Biot’s effective stress coefficient
0< α < 1 (rocks) α = 1 (soil)
For α = 1 → a given Pp increase (∆Pp) yields an equal reduction in σ’ (i.e., ∆Pp = ∆σ’) For α < 1 → a Pp increase gives an unequal reduction in σ’ (i.e., ∆Pp ≠ ∆σ’)
Upshot: Biot’s constant is a measure of the “efficiency” of the fluid in counteracting the applied stress. Note that Biot’s constant is stress dependent. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effective Stress Stress-- Example Given: Three cylinders of identical geometrical proportions with the properties shown below. Find: The effective stress (axial) for each sample under an identical load. 2”
4”
steel φ=0 k = 0 md Pp = N/A α = N/A
shale φ = 10% k = 10-9 md Pp = 3000 psi α = 0.5
sandstone φ = 25% k=1d Pp = 3000 psi α = 0.9
Note: φ = total porosity, k = permeability [Darcy or milliDarcy], Pp = pore pressure [psi], α = Biot’s constant © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effective Stress Stress-- Example 10,000 lbf
10,000 lbf
10,000 lbf
steel
shale
sandstone
Solution: Total stress (σ) = F/A = 10,000/πr2 = 10,000/π12 = 3183 psi © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effective Stress Stress-- Example
Solution (cont’d):
σ’ = σ - αPp steel
σ’ = σ – αPp = 3183 – 0 = 3183 psi © 2005 Baker Hughes Incorporated All rights reserved.
shale
σ’ = σ – αPp = 3183 – 0.5*3000 = 1683 psi Efficiency….Data accuracy….People-oriented service
sandstone
σ’ = σ – αPp = 3183 – 0.9*3000 = 483 psi www.bakeratlasdirect.com
Poro -elasticity Poro-elasticity Induced fluid pressure brings stress relief to the solid material (dilation) (poro-elasticity); similar to heating (thermoelasticity) Permeable material (or slow loading) – pore pressure dissipates – acts like solid material, without fluid Tight rock/faster loading – pore pressure rises within entrapped fluid, resulting in smaller than expected rock deformation Material appears stiffer: combined rock and fluid Time-dependent behavior © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Rock Mechanical Properties Characterization © 2000 Baker Hughes Incorporated All rights reserved.
Outline ÎMechanical
behavior under loading ÎStratigraphy and rock fabric z Dynamic rock mechanical properties z Logging of Mechanical Properties z Empirical correlations z Rock mechanics laboratory
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
2
www.bakeratlasdirect.com
Rock Mechanical Behaviors Under Stress Loading σ
Linear Elastic
Elastoplastic Yield
Max. Stress = Failure Strength Re-loading Unloading
ε
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
3
www.bakeratlasdirect.com
Mechanical behavioral Models
Linear-elastic model (no rupture) Elastic model with brittle rupture Non-linear elasticity (where E = f(σ)) Elastic, perfectly plastic Elastic with strain-weakening, then plastic Visco-elastic (shales, some rocks at high T) Visco-plastic (salt and other halides) ………… Choose the model that adequately describes the mechanical behavior as exhibited by the σ - ε curve.
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
4
www.bakeratlasdirect.com
Stratigraphy and Rock Fabric Petroleum geomechanics deals with wide variety of rocks ranging from clay-free reservoir sandstones through siltstones to mudstones and shales. In-situ mechanical properties depend on the interaction between intrinsic and extrinsic properties. Intrinsic properties include mineralogy and its distribution in the rock frames, grain size distribution and rock fabric such as bedding planes or fractures. Extrinsic properties are confining pressure, strain rate and temperature. 1. 2.
Plumb, R.A: ”Influence of composition and texture on the failure properties of elastic rocks”, Eurock 94. Plumb, R.A., Heron, S.L., and Olsen, M.P.: “Influence of composition and texture on compressive strength variations in the Travis Peak formation”, SPE 27458
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
5
www.bakeratlasdirect.com
Mechanical Classifications of Reservoir Rocks Three categories depending on the basis of the volume of clay minerals: • grain supported, Vclay < 15% • transitional supported, 15 % < Vclay < 35% • clay supported, Vclay > 35% External loads applied to grain supported rocks are carried by grain-to-grain contacts. In transitional supported rocks, loads are distributed more equally among detrital grains and clay minerals. In clay supported rocks, externally applied loads are borne entirely by clay minerals. 1. 2.
Plumb, R.A: ”Influence of composition and texture on the failure properties of elastic rocks”, Eurock 94. Plumb, R.A., Heron, S.L., and Olsen, M.P.: “Influence of composition and texture on compressive strength variations in the Travis Peak formation”, SPE 27458
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
6
www.bakeratlasdirect.com
Rock Mechanical Behavior Under Stress Loading
Unconfined compressive strength and average friction angle vs. Vgrain for rocks classified by their load bearing solid phase. Vgrain= 1-(φ+Vclay) 1. 2.
Plumb, R.A: ”Influence of composition and texture on the failure properties of elastic rocks”, Eurock 94. Plumb, R.A., Heron, S.L., and Olsen, M.P.: “Influence of composition and texture on compressive strength variations in the Travis Peak formation”, SPE 27458
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
7
www.bakeratlasdirect.com
Lithology vs. Acoustic Velocity
After Castagna & Batzle (1985)
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
8
www.bakeratlasdirect.com
Lithology vs. Acoustic Velocity
Vp/Vs
After Tatham and McCormack 1991
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
9
www.bakeratlasdirect.com
Outline 9 Mechanical
behavior under loading 9 Stratigraphy and rock fabric ÎDynamic rock mechanical properties z Logging of Mechanical Properties z Empirical correlations z Rock mechanics laboratory
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
10
www.bakeratlasdirect.com
Elastic Constants From Logs ⎡⎛ Δ t s ⎞ ⎤ ⎟⎟ − 2 ⎥ ⎢ ⎜⎜ ⎡⎛ 1 ⎢⎣ ⎝ Δ t c ⎠ ⎥⎦ = ; E D = 2 ⎢ ⎜⎜ 2 ⎡⎛ Δ t s ⎞ ⎤ ⎢⎣ ⎝ Δ t s ⎟⎟ − 1 ⎥ 2 ⎢ ⎜⎜ ⎢⎣ ⎝ Δ t c ⎠ ⎥⎦ 2
νD
⎤ ⎞ ⎟⎟ * (1 + ν D )ρ ⎥ ⎠ ⎥⎦ 2
ED and νD are dynamic moduli, ρ is bulk density. Δtc and Δts are compressional and shear slownesses.
From Acoustic Logs Other dynamic moduli (such as Bulk modulus, Shear modulus, and compressibilities) can then be calculated. © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
11
www.bakeratlasdirect.com
Dynamic Mechanical Properties –
Example Calculations
⎡ ⎛ Cp 2 C s ρ ⎢3⎜⎜ ⎢⎣ ⎝ C s 10 E D = 1.347 × 10 ⎡⎛ C p ⎞ 2 ⎟⎟ ⎢⎜⎜ ⎢⎣⎝ C s ⎠ DEPTH m 630.0216 630.174 630.3264 630.4788 630.6312 630.7836 630.936 631.0884 631.2408 © 2000 2005 Baker Hughes Incorporated All rights reserved.
DTC us/ft 150.865 152.576 150.976 146.855 144.915 142.951 142.545 142.337 143.286
⎤ ⎞ ⎟⎟ − 4⎥ ⎥⎦ ⎠ ⎤ − 1⎥ ⎥⎦ 2
DTS us/ft 447.784 484.607 486.765 467.886 440.522 395.599 382.763 370.373 381.956
⎡⎛ C p ⎞ 2 ⎤ ⎟⎟ − 2⎥ 0.5⎢⎜⎜ ⎢⎣⎝ C s ⎠ ⎥⎦ υD = ⎡⎛ C p ⎞ 2 ⎤ ⎟⎟ − 1⎥ ⎢⎜⎜ ⎢⎣⎝ C s ⎠ ⎥⎦
DEN g/cc 2.22 2.22 2.23 2.24 2.25 2.28 2.26 2.27 2.24
POIS-dyn
E-dyn psi
0.436 0.445 0.447 0.445 0.439 0.425 0.419 0.413 0.418
4.26E+05 3.66E+05 3.65E+05 3.96E+05 4.47E+05 5.56E+05 5.87E+05 6.27E+05 5.84E+05
Efficiency….Data accuracy….People-oriented service
12
www.bakeratlasdirect.com
Static vs. Dynamic Moduli In General: ED >> ES,
GD >> GS, νD > or < νS
12
Ed [106 psi]
10 8 6 4 2
0
2
(from Preston, 1976) © 2000 2005 Baker Hughes Incorporated All rights reserved.
4
6
8
10
12
E [106 Psi] Efficiency….Data accuracy….People-oriented service
13
www.bakeratlasdirect.com
Causes of Difference between Static and Dynamic Moduli ¾Dynamic Loading (as opposed to static) •
Low amplitude (low magnitude of load)
•
High-frequency (fast loading and unloading)
•
Low affected mass (few mm)
•
Non-destructive testing
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
14
www.bakeratlasdirect.com
Static vs. Dynamic F
ACOUSTIC EXPERIMENT
FREQUENCY (Hz)
104 − 106
10−2 − 10−5
BOREHOLE
10−4 − 10−9
EARTH
10−15
TIME
μs
s - DAYS
HRS -YRS
106 YRS
STRAIN RATE
s-1
10-5 s-1
10-9 s-1
10-14 s-1
mm3
cm3
AFFECTED MASS © 2000 2005 Baker Hughes Incorporated All rights reserved.
100-1000
Efficiency….Data accuracy….People-oriented service
m3
1013 m3 15
www.bakeratlasdirect.com
Causes of Difference between Static and Dynamic Moduli ¾In Dynamic Loading (opposed to static), the micro-mechanisms such as: • grain crushing grain contact parameters • pore collapse • crack sliding • dilatancy are not activated, leading to higher dynamic moduli than static’s equivalents.
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
16
www.bakeratlasdirect.com
Grain Contact Processes
Grain Crushing σ1
σ1
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Shear Sliding σ1
σ1 Efficiency….Data accuracy….People-oriented service
Pore Collapse σ1
σ1 17
www.bakeratlasdirect.com
Crack Processes CLOSING OLD CRACKS
σ1 OPENING NEW CRACKS
SLIDING OLD CRACKS FORMATION OF “WING CRACKS”
σ1
σ1
σ1 σ1
σ1 © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
18
www.bakeratlasdirect.com
Stress Field Sliding Crack TENSION
COMPRESSION
COMPRESSION
TENSION
CRACKS CLOSE CRACKS OPEN “WING” or “TAIL” CRACKS © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
19
www.bakeratlasdirect.com
Total Strain εTOTAL = ε STATIC
= ε MATRIX + ε OPEN CRACKS + ε GRAIN CONTACTS (crushing + pore collapse) + ε SLIDING CRACKS
εELASTIC = εDYNAMIC = εMATRIX + εOPEN CRACKS © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
20
www.bakeratlasdirect.com
Outline 9 Mechanical
behaviors under loading 9 Stratigraphy and rock fabrics 9 Dynamic rock mechanical properties ÎLogging of Mechanical Properties z Empirical correlations z Rock mechanics laboratory
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
21
www.bakeratlasdirect.com
Logging of Mechanical Properties
Logging of Mechanical Properties - E, ν, C….. The evaluation of rock mechanical properties from wireline logs is fundamental to engineering problems associated with wellbore stability, sand production and hydraulic fracturing. © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
Radial Strain
60 Stress [MPa]
22
www.bakeratlasdirect.com
LMP Porosity, Density, Sonic, ....
Strength
12 10 8
Stress (MPa)
Provides estimates for the constitutive parameters
6 4 2 0 -5
0
5
10
15
Strain (mStrain)
Simulates rock mechanical test on fictitious core
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
23
www.bakeratlasdirect.com
Technical Background Challenge: - Establish
a log interpretation routine that estimates rock strength from wireline logs
The approach: Consider the relations between dynamic moduli and static moduli
Input from logs
Leads to strength
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
24
www.bakeratlasdirect.com
Acoustic Behavior Model Idealized model of rock formation as seen by acoustic waves: Pore Space Crack 1. Rock Matrix 2. Solid Pores (spherical) – contributes to porosity, but stiff. 3. Flat Thin Cracks (three orthogonal directions) – provide crack density – does not contribute to porosity, but are compliant. All three contribute to acoustic properties of the material. © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
25
www.bakeratlasdirect.com
Acoustic Behavior Dynamic (Sije) and Static compliance (Sij) are related by:
Sii =
S + Pi e ii
3
1 − ∑ Fij
ε ij = Sijklσ kl
j =1
Sij = Sije − S jj ( Fji + D ji ),
i≠ j
where: Pi are the grain contact parameters Fij are the shear crack sliding parameters Dij are the dilatancy parameters This is the constitutive model developed by SINTEF using the micro-mechanics principles. © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
26
www.bakeratlasdirect.com
Logging of Mechanical Properties (LMP) Vsh
Log Inputs , Vss , Vw , Vhc , ρ , VP , VS
Ideal porous medium model “Effective medium theory” Strip fluid and assume dry frame only, calculate theoretical VP and VS 20 parameters (a1 , a2 , a3 , l1 , l2 , l3 ……….) - basic sand - basic shale - basic chalk
VP , VS from logs. Substitute fluid and determine VP , VS of dry frame Inequality is attributed to microcrack/grain contacts/pore distribution
Theoretical constitutive relations between stress and strain: - microcracks ε = f(σ , ρ , l1 , l2 , l3 , ϕ ……) - grain contacts ε = f(σ , ρ , a1 , a2 , a3 , d ……)
σa
Δ ε = C Δσ εr
εa
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Taking the inequality to extract proportionally the pre-determined parameters
ε = Cσ
Efficiency….Data accuracy….People-oriented service
27
www.bakeratlasdirect.com
Model Calibration Af3 Af0 Af1 Af2 a1 a2 b1 d1 d2 d3 d4 Eg Jg1 h1 n0 n1 PSRAT, RV p1 p2 p3 p4 p5 T0 Gs Ks s φc
Sliding crack coefficient Basic sliding crack coefficient Porosity impact on sliding crack coefficient Crack density impact on sliding crack coefficient General failure parameter General failure parameter Wing crack coefficient Compaction constant for dilatancy parameter Dilation constant for dilatancy parameter Porosity impact on dilatancy exponent Stress impact exponent Pore collapse parameter Porosity impact on pore collapse Grain rotation coefficient Basic crack density exponent Porosity impact on n Ratio between dry P- and S-wave velocity Porosity impact on grain contact mechanism Crack density impact on grain contact mechanism Stress impact on grain contact mechanism Stress history impact on grain contact mechanism Stabilizing parameter for grain contact mechanism Tensile strength parameter Shear modulus of solid material Bulk modulus of solid material Dilatancy parameter Critical porosity
© 2000 2005 Baker Hughes Incorporated All rights reserved.
% Calibration data for sandstone 1.8E-9 p1 1.1E-9 p2 0.31e-6 p3 1.67 p4 1.0E6 p5 0.05 n0 0.05 n1 5.0E6 T0 7.3e-3 Af0 1.7 Af1 0.0 Af2 1.0E6 S 3.0 b1 400.0 h1 3.25 d1 6.0 d2 0.2 d3 0.8 d4 200e6 a1 10 a2 0.0 Af3 0.45 phic 40.01e9 GS 35.01e9 KS 1.5 PSRAT 1000.0E9 JG1 4.3 EG
Efficiency….Data accuracy….People-oriented service
28
www.bakeratlasdirect.com
Logging of Mechanical Properties Log Inputs Dtc, Dts, Porosity, Lithology, Saturations Produces Virtual Core Sample
σa Produce StressStrain Curves
σr σa
Applying Virtual Stresses to the “Core Sample”
εr
εa
Static Mechanical Properties: Rock Strength, Elastic Moduli Poisson’s Ratio, Compressibilities © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
LMP Procedure The input data to LMP are obtained from: • logs (provided by the user for each well) • lithology dependent calibration data (built-in) Calibration data - determined from rock mechanical tests where both static and dynamic measurements are made. • The model numerically simulates loading in small steps • At each step, the model quantities are updated • Process is repeated until failure (stress/strain level is reached). © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
30
www.bakeratlasdirect.com
LMP Log input data Poor quality in => Poor results High Intermediate Low
Note: the resolution of LMP is limited by the resolution of the sonic log!
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Curve
Description
Unit
Column 1:
DEPTH
Measured depth
[m]
Column 2:
TVD
True vertical depth
[m]
Column 3:
VSS
Relative volume of sand or chalk
Column 4:
VSH
Relative volume of shale
Column 5:
VW
Relative volume of water
Column 6:
VH
Relative volume of hydrocarbons
Column 7:
KH
Bulk modulus of hydrocarbons
[GPa]
Column 8:
RHOH
Density of hydrocarbons
[g/ccm]
Column 9:
RHOB
Bulk density
[g/ccm]
Column 10: DTP
Compressional slowness
[us/ft]
Column 11: DTS
Shear slowness
[us/ft]
Column 12: SIGV
Vertical stress
[MPa]
Column 13: PPORE
Pore pressure
[MPa]
Column 14: SIGH
Horizontal stress
[MPa]
Column 15: LMP
Calibration data set
Efficiency….Data accuracy….People-oriented service
31
www.bakeratlasdirect.com
Sample of LMP Log input data
DEPTH
TVD
VSS
VSH
VW
VH
KH
2460.739 2460.820 2460.901 2460.983 2461.063 2461.145 2461.226 2461.307 2461.388 2461.469 2461.550 2461.631 2461.712 2461.793 2461.875 2461.956
2430.73 2431.82 2431.90 2431.98 2432.06 2432.14 2432.22 2432.30 2432.38 2432.46 2432.55 2432.63 2432.71 2432.79 2432.87 2432.95
0.678 0.682 0.680 0.683 0.682 0.681 0.681 0.682 0.669 0.672 0.672 0.687 0.688 0.689 0.657 0.631
0.005 0.000 0.002 0.000 0.000 0.000 0.000 0.000 0.017 0.018 0.017 0.000 0.001 0.000 0.035 0.066
0.015 0.015 0.015 0.015 0.014 0.014 0.014 0.014 0.014 0.013 0.015 0.013 0.012 0.012 0.012 0.012
0.302 0.303 0.303 0.302 0.304 0.305 0.305 0.304 0.300 0.297 0.296 0.300 0.299 0.299 0.296 0.291
0.670 0.670 0.670 0.670 0.670 0.670 0.670 0.670 0.670 0.670 0.670 0.670 0.670 0.670 0.670 0.670
© 2000 2005 Baker Hughes Incorporated All rights reserved.
RHOH RHOB DTP 0.800 0.800 0.800 0.800 0.800 0.800 0.800 0.800 0.800 0.800 0.800 0.800 0.800 0.800 0.800 0.800
2.010 2.009 2.008 2.009 2.008 2.006 2.006 2.008 2.016 2.025 2.022 2.018 2.023 2.021 2.028 2.039
DTS
97.870 181.68 101.28 183.67 106.57 187.14 111.09 192.10 114.28 196.99 115.32 200.13 114.35 200.58 113.55 199.64 114.14 199.09 115.27 198.68 114.98 198.05 113.35 197.84 112.87 199.07 114.05 202.95 115.19 206.40 114.95 205.64
Efficiency….Data accuracy….People-oriented service
SIGV PPORE SIGW LMP 36.179 36.181 36.183 36.184 36.186 36.187 36.189 36.191 36.192 36.194 36.195 36.197 36.199 36.200 36.202 36.203
24.11 24.11 24.11 24.1 8 24.18 24.19 24.12 24.12 24.12 24.12 24.12 24.12 24.12 24.12 24.12 24.12
24.15 24.11 24.11 24.11 24.11 24.11 24.12 24.12 24.12 24.12 24.12 24.12 24.12 24.12 24.12 24.12
12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12
32
www.bakeratlasdirect.com
Control Parameters for LMP Description CONFP C1 C2 CLIM PORFAC WD
Default value
Confining pressure Lower calibration mixing limit Upper calibration mixing limit Limit for use of empirical calibration Controls porosity correction Water depth
5 0.15 0.4 1 0 0
Low
High
0 0 0 0 0 0
200 1 1 1 1 1E6
Units MPa
m
LMP data = IJ z IJ = 1-9, single calibration table z IJ = 11-98, mix calibration from calibration table I and J – C = vI/(vI+vJ) • C <= C1 : Lithology I calibration is used • C >= C2 : Lithology J calibration is used • C1 < C < C2 : Calibration data for lithology I and J is linearly mixed • C > CLIM: Empirical formula © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
33
www.bakeratlasdirect.com
Sample of control parameters
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
34
www.bakeratlasdirect.com
LMP Procedure – Shale Porosity z
Porosity corrections in shaly formations – If only effective porosity is present (PORFAC=1)
Δφ p R =0.05 0.05 , clay ⋅V V
| Δφ Δφ= S =f f(V(V ), ) | Δφ T =0.50⋅.V5V, cl
p
p , satp , sat cl
p
f (V p ,sat ) < 0.05 0.05 < f (V p ,sat ) < 0.5 f (V p ,sat ) > 0.5
clay
f (V p ,sat ) = e0 + e1V p ,sat + e2V p2,sat + e3V p3,sat
Vclay= shale/clay volume
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
35
www.bakeratlasdirect.com
LMP Procedure – Strength Correlation Empirical correlation for strength of shale material if C > CLIM:
vss ⎛ vsh ⎞ DTSc = DTC ⎜ Rsh + Rss ⎟ vsh + vss ⎝ vsh + vss ⎠ −3 −5.0
UCS = 1.05 ⋅10 ( DTSc ⋅10 ) -3
Rsh and Rss are the tabulated
Vp Vs
ratios for shale and sandstone respectively.
Mason (1987) © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
36
www.bakeratlasdirect.com
LMP – Output Parameters ) ) ) ) ) ) ) ) )
Compressive strength Young’s modulus Poisson’s ratio Shear modulus Bulk modulus (triaxial) Bulk modulus (hydrostatic) Internal friction angle Cohesive strength Biot’s constant
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Compressive Strength Comparison: LMP vs. Lab (deepwater GoM ex. 1) LMP1
LMP2
LMP3
LMP4
Lab1
Lab2
Lab3
Lab4
GR
GR [API] 0
20
40
60
80
100
120
140
Depth
Curve colors Blue= conf. press. #1 = unconfined Pink = conf. press. #2 Yellow = conf. press. #3 Turquiose = conf. press. #4
0
5000
10000
15000
20000
25000
Compressive Strength [psi] © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
30000
35000
38
www.bakeratlasdirect.com
Compressive Strength Comparison: LMP vs. Lab (deepwater GoM ex. 2) LMP1
LMP2
LMP3
LMP4
Lab1
Lab2
Lab3
Lab4
GR
GR [API] 20
40
60
80
100
120
140
160
180
200
Depth
0
Curve colors Blue= conf. press. #1 = unconfined Pink = conf. press. #2 Yellow = conf. press. #3 Turquiose = conf. press. #4
0
5000
10000
15000
Compressive Strength [psi] © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
20000
25000
39
www.bakeratlasdirect.com
Young’s Modulus Comparison: LMP vs. Lab (deepwater GoM ex. 1) LMP1
LMP2
LMP3
LMP4
Lab1
Lab2
Lab3
Lab4
GR
GR [API] 0
20
40
60
80
100
120
140
160
Depth
Curve colors Blue= conf. press. #1 = unconfined Pink = conf. press. #2 Yellow = conf. press. #3 Turquiose = conf. press. #4
0
0.5
1
1.5
2
2.5
Young's Modulus [MMpsi] © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
3
3.5
4
40
www.bakeratlasdirect.com
Young’s Modulus Comparison: LMP vs. Lab (deepwater GoM ex. 2) LMP1
LMP2
LMP3
LMP4
Lab1
Lab2
Lab3
Lab4
GR
GR [API] 20
40
60
80
100
120
2.5
3
Depth
0
Curve colors Blue= conf. press. #1 = unconfined Pink = conf. press. #2 Yellow = conf. press. #3 Turquiose = conf. press. #4
0
0.5
1
1.5
2
Young's Modulus [MMpsi] © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
41
www.bakeratlasdirect.com
Strength Prediction
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
42
www.bakeratlasdirect.com
Young’s Modulus Prediction
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
43
www.bakeratlasdirect.com
MOHR CIRCLES σ1 = 2So tan α + σ3 tan 2 β π φ β= + 4 2 With two Mohr’s circles, we have two equations relating internal friction angle (Φ) and cohesion (So) with σ1 and σ3. Therefore, with known stress conditions we can solve for the two Mohr Coulomb parameters!
© 2000 2005 Baker Hughes Incorporated All rights reserved.
⎛ ⎡ σ 1 a − σ 1b 1 − φ = 2⎜ tan ⎢ ⎜ ⎣ σ 3a − σ 3b ⎝ So =
⎤ π⎞ ⎥ − ⎟⎟ ⎦ 4⎠
1 [(σ1a + σ1b ) − (σ3a + σ3b ) tan 2 β] 4 tan β
or So =
UCS 2 tan β
Efficiency….Data accuracy….People-oriented service
44
www.bakeratlasdirect.com
MOHR CIRCLES
Shear Stress [MPa]
30 Confining pressure is 10 MPa
Strength is 41 MPa Friction angle
20
10
0
0
10
20
30
40
50
Confining Pressure [MPa] © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
45
www.bakeratlasdirect.com
LMP - Rocktest Program that uses well logging data to determine the formation’s stress-strain behaviors as well as the axial and radial acoustic velocities, based on static elastic properties (complement to LMP). … as with LMP, Rocktest is based on the FORMEL model, which describes the collective micro-structural behaviors of rock constituents during stress loading.
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
46
www.bakeratlasdirect.com
LMP - Rocktest What do we need to run Rocktest? INPUT DATA Æ MD, TVD, Δtc, Δts, lithology, mineral volumes, bulk density, water and hydrocarbon saturations, σH, and σV . ¾
¾ CONTROL PARAMETERS Æ Mixing limits (C1 and C2), empirical limit (CLIM), Outputon filethe (OUTPTFIL), … asrelationship LMP, Rocktest is based Porosity correction control (PORFAC), confining FORMEL model, which describes thepressure (SIGC), and processing depth (TSTDEPTH), request collective micro-structural behaviors of for parameters listing (VERBOSE), water depth (WD), and rock constituents during stress loading. calibration table file names (LMPTAB).
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
47
www.bakeratlasdirect.com
Rocktest – Input Data Hydrocarbon Properties
Depth
DEPTH 4460 4460.152 4460.305 4460.457 4460.61 4460.762 4460.914 4461.067 4461.219 4461.372 4461.524 4461.676
TVD 2456.356 2456.427 2456.498 2456.569 2456.64 2456.711 2456.782 2456.853 2456.924 2456.995 2457.066 2457.137
VSA 0.999 0.999 0.999 0.999 0.9217 0.9264 0.9436 0.9822 0.9985 0.9723 0.8926 0.8014
VSH 0 0 0 0 0 0 0 0 0 0 0 0
VW 0.001 0.001 0.001 0.001 0.061 0.0567 0.05 0.0178 0.0015 0.0277 0.047 0.0489
Volumetrics
© 2000 2005 Baker Hughes Incorporated All rights reserved.
VOIL 0 0 0 0 0.0173 0.0169 0.0064 0 0 0 0.0604 0.1497
KOIL 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8
HCDE 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7
Acoustic Slowness
DEN 2.5535 2.5556 2.5527 2.5461 2.5415 2.5491 2.5814 2.6256 2.6486 2.593 2.4621 2.3579
DTC 77.8283 77.6383 73.4818 71.5991 67.9204 67.3749 68.064 68.2664 74.7734 65.0705 91.1018 92.6543
DTS 143.7192 139.924 136.8492 136.9608 135.5699 143.9718 138.9534 135.4932 132.7831 133.2914 140.8076 141.6646
Bulk Density
Efficiency….Data accuracy….People-oriented service
Calibration
SIGV 52.12252 52.12415 52.12578 52.1274 52.12903 52.13066 52.13229 52.13392 52.13554 52.13717 52.1388 52.14043
PP 35.71542 35.71645 35.71748 35.71851 35.71954 35.72057 35.72161 35.72264 35.72367 35.7247 35.72573 35.72677
SIGH 43.86157 43.86301 43.86445 43.86589 43.86733 43.86877 43.87022 43.87166 43.8731 43.87454 43.87598 43.87742
LMP 12 12 12 12 12 12 12 12 12 12 12 12
Stress Field
48
www.bakeratlasdirect.com
Rocktest – Output File Radial Strain mStrain 0 0.01187 0.02359 0.03517 0.04661 0.0579 0.06906 0.08009 0.091 0.10177 0.11243 0.12297 0.13339 0.14369
Axial Confining Axial Radial-P Axial-P Radial-S Axial-S Strain Pressure Stress Velocity Velocity Velocity Velocity mStrain MPa MPa m/s m/s m/s m/s -0.00394 0.05 0.05 2085.349 3147.419 1417.535 1694.329 0.00404 0.1 0.1 2093.867 3153.143 1421.319 1697.517 0.01193 0.15 0.15 2102.312 3158.791 1425.077 1700.675 0.01972 0.2 0.2 2110.682 3164.366 1428.807 1703.801 0.02742 0.25 0.25 2118.98 3169.869 1432.509 1706.896 0.03503 0.3 0.3 2127.203 3175.302 1436.183 1709.96 0.04255 0.35 0.35 2135.354 3180.665 1439.83 1712.995 0.04998 0.4 0.4 2143.431 3185.962 1443.449 1716 0.05733 0.45 0.45 2151.436 3191.193 1447.04 1718.976 0.0646 0.5 0.5 2159.369 3196.36 1450.603 1721.923 0.07179 0.55 0.55 2167.23 3201.463 1454.139 1724.841 0.07891 0.6 0.6 2175.019 3206.506 1457.646 1727.731 0.08594 0.65 0.65 2182.737 3211.488 1461.126 1730.594 0.09291 0.7 0.7 2190.385 3216.411 1464.578 1733.429
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
49
www.bakeratlasdirect.com
Rocktest – Output File 180 160 Radial
140
Axial
Stress (MPa)
120 100 80 60 40
hydrostatic state of stress
20 0 -6
-4
-2
0
2
4
6
8
10
12
Strain (mstrain)
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
50
www.bakeratlasdirect.com
LMP Capabilities z
z
z
z
z
Predicts static properties from logs @ any given confining pressure Generates complete stress-strain curves Only one available in market Used for drilling, completion and subsidence/compaction studies Independently validated using laboratory results
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
51
www.bakeratlasdirect.com
Outline 9 Mechanical
behaviors under loading 9 Stratigraphy and rock fabrics 9 Dynamic rock mechanical properties 9 Logging of Mechanical Properties ÎEmpirical correlations z Rock mechanics laboratory
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
52
www.bakeratlasdirect.com
Lacy’s (1997) Empirical Correlations* Dynamic Young’s Modulus: E d [10 6 psi ] = 0.265 * (Vp ) 2.04
E d [10 6 psi ] = 59100 /( Δt C ) 2.17
E d [10 6 psi ] = 11300ρ b / (Δt C ) 2
Vp = compressional velocity [km/s] Δtc = compressional slowness [μsec/ft] ρb = bulk density [g/cm3]
Conversion from dynamic to static Young’s moduli: E[10 6 psi ] = 0.018E d + 0.422E d 2
Unconfined Compressive Strength: UCS[ksi ] = 0.2787E 2 + 2.458E *Lacy’s (1997- SPE 38716) correlations were developed based on lab testing of over 600 samples of sandstones, shales, limestones and dolomites. © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
53
www.bakeratlasdirect.com
Lal’s (1999) Empirical Correlations* Internal Friction Angle and Cohesion: φ[radians] = sin −1 (Vp − 1) /(Vp + 1) So [MPa ] = 5(Vp - 1)/ (Vp )
Vp = compressional velocity [km/s]
Unconfined Compressive Strength: UCS = 2So tan(45 + φ/2)
*Lal’s (1999- SPE 54356) correlations were developed for shales ONLY. Caution should be exercised if applying this correlation to other lithologies! © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
54
www.bakeratlasdirect.com
Coates & Denoo’s (1981) Empirical Correlation Unconfined Compressive Strength: UCS [MPa ] = 1.9 ×10-20 ρ b Vp ((1 +ν d )/(1 -ν d )) 2 (1 - 2ν d )(1 + 0.78Vclay ) 2
4
Vp = compressional velocity [km/s] Vclay = clay volume [fraction] ρb = bulk density [kg/m3] νd = dynamic Poisson’s ratio
*Coates & Denoo’s (1981) correlation was developed for sandstones & shales ONLY. © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
55
www.bakeratlasdirect.com
Mason’s (1987) Empirical Correlation Unconfined Compressive Strength: UCS[psi ] = 1.2 * (1000/Δt s ) 4 + 60.5 * (1000/Δt s ) 2
Δts = shear slowness [μsec/ft]
If Δts is not available, use Δtc and Δts/ Δtc ratio (based on lithology) in the following expression: UCS[psi ] = 1.2 * (1000/ (Δt c * ratio )) + 60.5 * (1000/ (Δt c * ratio )) 4
2
Δtc = compressional slowness [μsec/ft] ratio = Δts/Δtc *Mason’s (1987- SPE 13256) correlations were developed using tables of rock properties from Wuerker (SPE 663). © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
56
www.bakeratlasdirect.com
Mason’s (1987) Empirical Correlation Lithology anhydrite basalt chalk chert clay claystone diabase diorite dolomite epidosite gabbro gneiss granite gypsum hornstone limestone (clean) limestone (silty) limestone (argillaceous) marble mudstone pyrite quartzite quartzite salt sandstone (clean) sandstone (silty) sandstone (argillaceous) shale siltstone © 2000 2005 Baker Hughes Incorporated All rights reserved.
DTS/DTC 2.45 1.55 2.45 1.60 3.20 1.90 1.70 1.75 1.80 1.70 1.60 1.80 1.70 2.45 1.85 1.90 2.10 2.30 1.80 1.85 1.70 1.55 1.50 2.15 1.60 1.70 1.85 1.75 1.80
For mixed lithologies, use: Δts/Δtc ratio (composite) = ratio1*V1 + ratio2*V2…..+ ration*Vn
Efficiency….Data accuracy….People-oriented service
57
www.bakeratlasdirect.com
UCS Empirical Correlations – (Sandstone)
After Chandong Chang 2004
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
58
www.bakeratlasdirect.com
UCS Empirical Correlations – (Shale)
After Chandong Chang 2004
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
59
www.bakeratlasdirect.com
Outline 9 Mechanical
behaviors under loading 9 Stratigraphy and rock fabrics 9 Dynamic rock mechanical properties 9 Logging of Mechanical Properties 9 Empirical correlations ÎRock mechanics laboratory
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
60
www.bakeratlasdirect.com
Triaxial Compression Tests Test Apparatus
Stress-Strain Curves
Axial Strain measurement
Axial Differential Stress
Axial Stress
Confining Pressure inlet
Seal Radial Strain measurement
Confining Pressure outlet Pore Pressure control
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Radial Strain
Efficiency….Data accuracy….People-oriented service
Axial Strain
61
www.bakeratlasdirect.com
Strength & Static Elastic Moduli F
STATIC LABORATORY TEST RESULTS
dx {
Axial Differential Stress Compressive Strength
UNDEFORMED
Linearly elastic
Poisson’s ratio (ν) = -Δεr/Δεa
Δσa
Δσa Δεr
Radial Strain εr (extension) © 2000 2005 Baker Hughes Incorporated All rights reserved.
DEFORMED
Δεa
Young’s Modulus (E) = Δσa/Δεa
Axial Strain εa (contraction)
Efficiency….Data accuracy….People-oriented service
62
www.bakeratlasdirect.com
Failure Strength Parameters Different Types of Compression Tests • Triaxial Compression Test (Unconfined Compressive Strength, UCS)
• Hole Collapse Test (Hole Collapse Strength, HCS) σc
σa
σc
σc
σc
σc
σa © 2000 2005 Baker Hughes Incorporated All rights reserved.
σc
Efficiency….Data accuracy….People-oriented service
63
www.bakeratlasdirect.com
Hollow Cylinder Test
Confining pressure
Also called a hole-collapse test. Picture of a failed specimen (Ref: Ewy et al., 2001, SPE 75328)
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
64
www.bakeratlasdirect.com
Hollow Cylinder Test σc
Typical Test Details:
1.5-inch diameter specimen σc 0.5-inch diameter hole through the center Length – 2 to 3 inches Cylindrical steel end caps σc Jacketed with a thin, heat-shrink teflon Interior of the 0.5-inch diameter hole left empty Confining pressure is applied all around
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
σc
65
www.bakeratlasdirect.com
Hollow Cylinder Test – A Test Result
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
66
www.bakeratlasdirect.com
Relating HCS to UCS σc
C1 = HCS * {( 2c ) cos( 13 )cos -1d }- 1.0833 c = .42361 +
11.4375
η
2.84375 +
76.7819
d= c{−22.8749 −
617 .625
η
© 2000 2005 Baker Hughes Incorporated All rights reserved.
σc
σc
σc SPE 75328
η
4 tan φ (9 − 7 sin φ ) η= (1 − sin φ ) 2
Di 1 = Do 3
HCS = Hole-Collapse Strength
} C1 = Modified Lade strength – from HCS c, d, = groups of terms, dimensionless η = Modified Lade friction parameter Φ = internal friction angle
Efficiency….Data accuracy….People-oriented service
67
www.bakeratlasdirect.com
Relating HCS to UCS HCS is related to UCS (from triaxial compression test):
S1 = nC1
σc
n ≤1 So = S1 tan φ φ UCS = 2So tan(45 + ) 2
σc
σc
S1 = Modified Lade strength parameter C1 = Modified Lade strength, includes all the strengthening effects (nonlinear deformations, nonconstant moduli, intermediate stress)
σc
n = factor to adjust strength downward for wellboresize holes
SPE 75328
So= Mohr-Coulomb cohesion
SPE 56862
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
68
www.bakeratlasdirect.com
Effects of Borehole Size on Rock Strength
(Hoek and Brown,1980)
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
69
www.bakeratlasdirect.com
Effects of Borehole Size on Rock Strength
(Ηerrick 1994) © 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
70
www.bakeratlasdirect.com
In-Situ Stress Characterizations
Outline I. II. III. IV.
Introduction to subsurface stresses Overburden calculation Horizontal stress determination techniques Summary
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline I. II. III. IV.
Introduction to subsurface stresses Overburden calculation In-situ stress determination techniques Summary
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Subsurface Stresses Rocks in the subsurface are subjected to compressive stresses* due primarily to Gravity and Tectonic forces! x y
σv
z
σv = Overburden Stress σH = Max. Horizontal Stress σh = Min. Horizontal Stress σH
σh NOTE: σH > σh
These arise due to weight of overburden, confinement, tectonic forces, temperature, pore fluid pressure, diagenesis, etc.
Generally Accepted Assumptions: 1) The overburden is a principal stress which acts perpendicular to
the Earth’s surface. 2) 3 major principal stresses (σv, σH, σh) are orthogonal. 3) Rocks conform to the requirements of the Theory of Elasticity (linearly elastic, homogeneous continuum, etc.).
* The Geomechanics sign convention for stress is compression = positive, tension = negative © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Subsurface Stress Regimes* NORMAL FAULTING
σ1 = σv
•Tensile regions •High-angle faults
STRIKE-SLIP FAULTING
σ2 = σv
•Shearing regions •High-angle, lateral faults
σ3
σ3
σ3 = σv σ1
φf ≈ 60º
σ2 σ1
THRUST FAULTING
φf ≈ 30º
footwall *(after Anderson, 1951) © 2005 Baker Hughes Incorporated All rights reserved.
hanging wall
•Compressive regions •Low-angle faults
σ2
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stress Profiles Profiles-- example Note: In some cases, the horizontal stresses may exceed vertical stress at shallow depths.
Depth
σv
Stresses typically diverge with depth increase (unless an overpressured zone is encountered).
σH σh
However, at great depth the stresses converge until the stress contrast disappears as the stresses become hydrostatic (after Breckels and van Eeklen 1982).
MUD PRESSURE PORE PRESSURE Pressure/Stress © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stress Profile Variations Horizontal Stresses are sensitive to: • LITHOLOGY • MECHANICAL PROPERTIES • PORE PRESSURE
Note: Pore pressure is depicted in a separate track! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stress Determination Techniques In-situ Stress Measurement Techniques Method (Category)
Hydraulic
Relief
Jacking Strain recovery Borehole breakout
Others
Name Hydraulic Fracturing Sleeve Fracturing Hydraulic test on preexisting fractures (HTPF) Surface relief methods Undercoring Borehole relief methods (overcoring, slotting, etc.) Relief of large rock volumes Flat jack Curved jack
Measurement Location b b b
Advantages Measurements in existing holes, accurate, quick.
Limitations
Primary Usage
2D only HTPF requires many test on existing fractures
Oil Industry, geological survey
s c b
Inexpensive, highly developed technique
Difficult to install gages
Mining, civil, defense
Inexpensive, easy
gages susceptible to conditions
Civil
Suitable for great depths
Results may be unreliable (sensitive to several factors)
Oil industry, civil
Accurate, quick
Restricted to info on est. breakout width (reduces accuracy)
Oil industry, geological survey
s s s
Anelastic Strain Recovery (ASR) Differential Strain Curve Analysis (DSCA) Image log analysis
b
Oriented caliper analysis
b
c c
Fault slip analysis l Low cost Results give only a Earthquake focal Oil industry, geological l rough estimate mechanisms survey Geological structures l Low cost Acoustic methods b,c Easy Results unreliable Bulk density log Data not always b Easy Oil industry available to surface integration Key: b = borehole, c = core, l = large scale geological structures, s = surface rock measurements
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
Denotes topics to be covered here.
A summary of all of these methods can be found in Amadei and Stephannson (1997).
www.bakeratlasdirect.com
Outline I. II. III. IV.
Introduction to subsurface stresses Overburden calculation Commonly used stress determination techniques Summary
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Overburden ((σ σv) Calculation dw
z
σv = ∫0 ρw g dz + ∫dw ρb gdz = weight of overburden where
ρb = bulk density of sediments = ρmatrix (1-φp) + ρpf φ ρmatrix = density of rock matrix ρw = density of seawater ρpf = density of pore fluid
dw
φp = total porosity
sf
z ds
g = gravitational constant ds = vertical depth of sediments dw = depth of water
Depth of interest © 2005 Baker Hughes Incorporated All rights reserved.
z = true vertical depth = dw + ds sf = sea floor
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
σv Calculation However……….bulk density data is rarely available from surface to depth of interest!
Usually requires one (or more) of the following: • estimating bulk density in region above measured data • use of acoustic data which is transformed to bulk density data in region above measured data (when available) • use of empirical formulas (may be region specific) to estimate ρb or σv
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Useful Bulk Density ((ρ ρ b) Transformations 1. Gardner (1974) ⎛ 10 ⎞ ⎡ g ⎤ ⎟⎟ ρ b ⎢ 3 ⎥ = 0.23⎜⎜ ⎣ cm ⎦ ⎝ Δt c ⎠ 6
0.25
where Δtc= measured interval travel time of compressive wave [μs/ft]
2. Ludwig et al. (1970)
⎡ g ⎤ ρ b ⎢ 3 ⎥ = 1.27 Vp − 0.28Vp2 + 0.0232Vp3 ⎣ cm ⎦
3. Bellotti & Giacca (1978) ⎛ Δt c − Δt c ( mx ) ⎞ ⎡ g ⎤ ⎟ ρ b ⎢ 3 ⎥ = ρ mx − 1.228(ρ mx − ρ f )⎜⎜ ⎟ t t Δ + Δ ⎣ cm ⎦ ( ) c c f ⎠ ⎝
4. Miller ρ = ρ matrix (1 − φ ) + ρ wφ © 2005 Baker Hughes Incorporated All rights reserved.
where Vp= compressive acoustic velocity [km/s]
where ρmx = matrix density (assume 2.75 g/cm3), ρf = pore fluid density (assume 1.03 g/cm3), and Δtc is the measured interval transit time, Δtc(mx) is the matrix transit time (assume 53 μs/ft) and Δtc(f) is the pore fluid transit time (assume 200 μs/ft).
φ = porosity , fraction ρ w = Water Density → 1.03 g / cc
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
ρb Estimation - Example WL Dens
Gardner
Ludwig
2.8
2.7
Gardner and Ludwig yield different densities in the vicinity of the mudline!
2.6
Bulk Density [g/cc]
2.5
2.4
2.3
2.2
2.1
Trend matches well with WL dens in this region.
2.0
1.9
1.8
Trend does not match as well with WL dens in this region (appears to be depth shift issue) Depth Below Mudline
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
σv Calculation - Quiz What is the overburden pressure at point A, B,C and D? 1 ρw = 1.074 g/cm3
A B
2 ρb(avg) = 1.95 g/cm3
g/cm3
600 feet
1200 feet
4 ρb(avg) = 2.25 g/cm3
D
Weight block 1 = 0.052*8.33*1.074*1000 = 465 psi Weight block 2 = 0.052*8.33*1.95*600 = 507 psi Weight block 3 = 0.052*8.33*2.10*1200 = 1092 psi Weight block 4 = 0.052*8.33*2.25*2400 = 2340 psi
3 ρb(avg) = 2.1
C
1000 feet
2400 feet
Not to scale!
© 2005 Baker Hughes Incorporated All rights reserved.
Solution P [psi] = ρgd = 0.052*8.33*sg*d [ft]
At pt. A: p = weight block 1 = 465 psi (0.465 psi/ft) At pt. B: p = weight block 1+2 = 465 + 507 = 972 psi (0.61 psi/ft) At pt. C: p = weight block 1+2+3 = 465+507+1092 = 2064 psi (0.74 psi/ft) At pt. D: p = weight block 1+2+3+4 = 465+507+1092+2340 = 4404 psi (0.85 psi/ft)
NOTE: OBG increases with depth and gradually approaches 1.0 psi/ft! Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Water Depth Effect σv Profile
OBG decreases with increasing water depth!
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Salt Effect σv Profile
Water OBG in absence of salt layer! OBG reduced due to thick salt layer!
Salt
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Published σv Correlations Vertical Stress Formulation σv [psi] = 0.465dw + 1.13ds - 3188.36 (1-exp[-8.5e-5ds]) σv [MPa] = (1.9 ± 1.31) + (0.0339 ± 0.0067)d σv [MPa] = (0.942 ± 1.26) + (0.0266 ± 0.0028)d σv [MPa] = 0.027d σv [MPa] = 0.0265d σv [MPa] = 0.026d – 0.0324d σv [MPa] = (0.0266 ± 0.008)d OBG [psi/ft] = OBO + 2.46e-5d - 1.79e-9 d2 + 6.6e-14 d3 – 5.97e-19 d4 σv [MPa] = (0.0275 - 0.0284)d σv [MPa] = 0.0285d σv [MPa] = 0.027d σv [MPa] = (0.0275 - 0.0284)d σv [MPa] = 0.233 + 0.024d σv [ppg] = (8.5dw + (16.3+( ds /3125)0.6)ds) / d σv [ppg] = (8.55dw + 5.3ds1.1356) / d σv [MPa] = 9e-7ds2 + 0.0187ds + 0.0101dw
Location and Depth Range (where available) Coastline GoM (ft) World (0-2400 m) North America Land (0-1500 m) World Data (0-3000m) World Data (100-3000m) Can. shield (0-2200m) Can. shield (0-2000m) GoM (ft) KTB pilot hole (800-3000m) Can. shield (0-2300m) Japan (0-1200m) KTB pilot hole (0-9000m) So. Korea (0-850m) GoM (ft) GoM (ft) North Sea (m)
References Eaton (1969) Hegret (1974) Lindner & Halpern (1977) Brown & Hoek (1978) McGarr & Gay (1978) Herget (1987) Arjang (1987) Bryant (1989) Baumgarten et al. (1993) Hegret (1993) Sugawara & Obara (1993) Te Kamp et al. (1993) Lim & Lee (1995) Traugott (1997) Barker and Wood (1998) Svennekjaer & Bratli (1998)
Note: dw = water depth, ds = sediment depth (dbml), d = true vertical depth OBO = overburden offset (land=0.87, shallow water=0.85, deepwater=0.82)
NOTE: These should only be used as a last resort! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline I. II. III. IV.
Introduction to subsurface stresses Overburden calculation In-situ stress determination techniques Summary
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Typical Log -Based σh Estimation Log-Based Conventional Log-based Methods for Determining the Minimum Horizontal Stress (σh) Magnitude: • Uniaxial strain method (no horizontal strain and vertical stress is due to gravity alone) in a tectonically inactive basin (Anderson et al. 1973 and others):
σh = ν/(1-ν)(σV- αPp)+αPp
• Uniaxial strain method in a tectonically active basin (Gatens et al. 1990):
σh = ν/(1−ν)(σV- αPp)+αPp+ σT
where σT is an additional “tectonic” stress used for calibration from measured stress data such as LOT, DIF’s, etc. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Conventional Hydraulic Fracturing Hydraulic fracturing is a great source of information about in-situ stress, formation leak-off properties, and rock permeability (transmissivity).
Several hydraulic fracturing methods available: • Pump-in / decline tests (LOT, XLOT, mini-fracs) • Step-rate injection tests • Pump-in / flow-back tests Most hydraulic fracturing methods assume the following: • Rock is linearly elastic
• Borehole is vertical (within ~ 30º→ parallel to a major principal stress axis) • Overburden stress acts vertically downward and is the maximum in-situ stress (σ1) • Induced hydraulic fractures are vertical © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Fracture Orientation - Normal Stress Field Fracture plane is vertical and parallel to the strike of the fault!
re Fractu pl ane
σ1 = σv
σ2 = σH
σ3 = σh
Hydraulic fracture slide modified from Dusseault (2003)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Fracture Orientation – Strikeslip Faulting
tur c a Fr
la ep
ne
Fracture plane is vertical and sub-parallel (25º-30º) to the strike of the fault!
Hydraulic fracture
σ2 = σv σ3 = σh σ1 = σH © 2005 Baker Hughes Incorporated All rights reserved.
slide modified from Dusseault (2003) Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Fracture Orientation – Thrust Faulting
Hydraulic fracture F
ne a l p re u t c a r
φ Fracture plane is horizontal! σ3 = σv
σ1 = σH
σ2 = σh slide modified from Dusseault (2003)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Conventional Hydraulic Fracturing Tests Summary HF Test Method
Pump-in / decline type tests
HF Test Name
Applications
Test Specifications
LOT / XLOT
test cement/rock integrity, determine max. safe MW, stress measurement
Flow rate: 0.25-2.0 BPM Volume pumped: 10-20 bbls Interval length tested: 10-20'
Mini-frac / Microfrac
Pump -in / decline
Formation Type
Test Application
any
during drilling
stress measurement and Flow rate: 0.25-25 gpm Volume pumped: 0.5-2.5 bbls Interval leakoff coefficient length tested: 3-15' estimation
permeable
prior to hyd. frac.
stress measurement and leakoff coefficient estimation
Flow rate: 5-25 BPM Volume pumped: 50-100 bbls Interval length tested: 20-50'
permeable
prior to hyd. frac.
low perm.
prior to hyd. frac.
Pump-in/flow back
Pump-in/flow back
stress measurement
Q inj.: 1-10 BPM Q flowback= (1/6 - 1/4) Q inj Volume pumped: 2-5 bbls Interval length tested: 10-20'
Step rate
Step rate
stress measurement
Q inj: 0.25-20 BPM Volume pumped: 10-80 bbls Interval length tested: >50'
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
large interval (several prior to hyd. frac. formations)
www.bakeratlasdirect.com
L eak O ff T est Leak Off Test For the driller, the primary objectives of a LOT are: Test the integrity of the casing cement job near the casing shoe Determine the maximum MW that can be withstood by the formation before initiating a hydraulic fracture
For the geomechanical engineer, the primary objective of a LOT is: Create a “small” hydraulically-induced fracture in the rock for stress estimation LOT – pressure up to formation breakdown XLOT – same as LOT but continue pumping after formation breakdown to propagate the fracture © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Typical Single Cycle XLOT
σh
σH cement formation breakdown
shut-in frac prop frac. closure press.
Flow rate
Rathole typically 10 – 20 feet!
Pressure
LOP
Flow rate (Q) typically between 0.25 – 1.0 BPM (constant throughout test) Time
Flow rate © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
Press.
www.bakeratlasdirect.com
Typical LOT Pressure Response 1000
0.50
800
Pressure (psi)
0.45
Pressure Pump rate
0.40
700
0.35
600
0.30
500
0.25
400
0.20
Note the constant pump rate!
300
0.15
200
0.10
100
0.05
0
0.00 0
1
2
3
4
5
6
7
Pump Rate (bbls/min.)
900
8
Volume Pumped (bbls)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Critical Points of Typical LOT Pressure Response 1000
0.50
LOP
800
Pressure (psi)
0.45
Pressure Pump rate
0.40
700
0.35
600
0.30
500
0.25
400
0.20
300
0.15
200
0.10
100
0.05
0
Pump Rate (bbls/min.)
900
0.00 0
1
2
3
4
5
6
7
8
Volume Pumped (bbls)
Leak-off pressure (LOP) – point where the slope of the curve starts to decrease, deviating from the the best fit straight line at the beginning of the test. This represents the point at which micro-fractures are forming near the wellbore. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Critical Points of Typical LOT Pressure Response 0.50
Pb
900 800
Pressure (psi)
0.45
Pressure Pump rate
0.40
700
0.35
600
0.30
500
0.25
400
0.20
300
0.15
200
0.10
100
0.05
0
Pump Rate (bbls/min.)
1000
0.00 0
1
2
3
4
5
6
7
8
Volume Pumped (bbls)
Breakdown pressure (Pb) – the highest pressure achieved during the test, corresponding to the formation of a major fracture and large fluid losses. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Critical Points of Typical LOT Pressure Response 1000
0.50
Stop pumping after pressure decrease observed!
Pressure (psi)
800
0.45
Pressure Pump rate
ISIP
0.40
700
0.35
600
0.30
500
0.25
400
0.20
300
0.15
200
0.10
100
0.05
0
Pump Rate (bbls/min.)
900
0.00 0
1
2
3
4
5
6
7
8
Volume Pumped (bbls)
Instantaneous shut-in pressure (ISIP)- first point after the pumps are stopped. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Critical Points of Typical LOT Pressure Response 1000
0.50
800 700
Pressure (psi)
0.45
Pressure Pump rate
0.40 0.35
Closure stress
600
0.30
500
0.25
400
0.20
300
0.15
200
0.10
100
0.05
0
Pump Rate (bbls/min.)
900
0.00 0
1
2
3
4
5
6
7
8
Volume Pumped (bbls)
Closure stress- first point after the slope of the curve starts to decrease just beyond the short linear behavior observed after ISIP © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Summary of Critical Points of Typical LOT Pressure Response 0.50
Pb
900
LOP
800
ISIP
Pressure (psi)
700
0.45
Pressure Pump rate
0.40 0.35
Closure stress
600
0.30
500
0.25
400
0.20
300
0.15
200
0.10
100
0.05
0
Pump Rate (bbls/min.)
1000
0.00 0
1
2
3
4
5
6
7
8
Volume Pumped (bbls)
NOTE: Closure stress < both ISIP and LOP. Rule of thumb: LOP is 5 - 10% > than the closure stress. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Problems encountered during analysis of LOT results Shallow well in the GOM: 300
End of pumping LOP
250
Perhaps a high permeability zone was contacted (and plugged after some time?) Æ better re-test !!!
Pressure (psi)
200
150
Min. closure stress
100
50
0 0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Volume (BBLS)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Problems encountered during analysis of LOT results (cont’d) Well in the GOM: 1600
End of pumping
LOP
1400
Pressure (psi)
1200
Min. closure stress ???
1000
Slope shows a permanent decrease in slope below 700 psi. However, this value is too small to be reliable Æ Possible channel being contacted ÆBest option: RE-TEST !!!
800
600
400 0
1
2
3
4
5
6
7
8
Min. closure stress ???
9
10
11
12
Volume (BBLS)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
2 Cycle XLOT Pressure
From Perkins and Kern : Pb1- Pb2 = To Pb1
ISIP = σ C +
pump is shut-in!
πγ E 2 (1 − ν 2 ) L
Pb2 Pprop ISIP1
well is re-pressurized 1st PRESSURE CYCLE
Note: γ is the fracture surface energy.
ISIP2
time
2nd PRESSURE CYCLE
As # pressure cycles increase, the length of the induced fractures grows and the second term becomes less important!
Normally, the value of ISIP tends to decrease asymptotically with the number of pressure cycles !!! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
XLOT XLOT-- Field Example 51
From Perkins and Kern : 50
ISIP = σ C + 49
ISIP decreases with subsequent cycles until stabilization at the 5th & 6th cycles (i.e., fracture length increases).
48 IS IP (M pa )
πγE 2 (1 − ν 2 ) L
47
46
45
44
43 0
1
2
3
4
5
6
7
LOT Cycle
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
σH Estimation from LOT & XLOT For a vertical hole in a normally-stressed environment, fracture initiation occurs when the effective tangential stress (σ’θθ) exceeds the tensile strength (To) of the rock (i.e, σ’θθ ≤ To). For the case of an impermeable rock, this is expressed mathematically as:
Pb = 3 σh - σH – αPp + To Obtained from LOT Biot’s constant obtained from LMP (or assumed to be unity)
Tensile strength assumed to be zero or estimated as 121 UCS (from LMP). If XLOT, To = Pb1-Pb2. Pore pressure obtained from RCI data or estimated from log data
This represents an upper bound of breakdown pressure!
Solving for σH yields: 0 (pre-existing fractures)
σH = 3σh - Pb – αPp + To Note: For the case of a pre-existing fracture, tensile strength is zero! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
σH Estimation from LOT & XLOT For a permeable rock, the expression is:
3σ h - σ H - 2η pp + To Pb = 2(1 - η) in which
This represents a lower bound of breakdown pressure!
α (1 − 2ν ) η= 2(1 - ν ) Solving for σH yields: σH = 3σh - Pb 2(1-η) – 2ηPp + To
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Properly Designed LOT/XLOT In order to fully utilize LOT/XLOT data for stress determination, the following guidelines should be followed while conducting a LOT/XLOT:
Record downhole pressure Record flow rate vs time Record cumulative fluid volume pumped Record sequence of events during the LOT/XLOT (e.g., report leaks, report unnecessary shut-ins, etc.) Maintain constant flow rate during test Maintain constant fluid viscosity Report mud weight, type, and temperature used during the test Report TVD and length of rathole Conduct multiple cycles XLOT to obtain the tensile strength (To) and ensure accurate σh estimations © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
F ormation IIntegrity ntegrity T est Formation Test
9 Test objective is to test the integrity of the cement and fracture pressure of the formation below the shoe to a pre-determined amount. 9 The procedure is similar to a LOT except the formation usually is not fractured or broken down (unless accidentally because the fracturing pressure is less than anticipated).
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
FIT- Field Example 3000
Point of deviation from linearity gives the leakoff pressure (LOP)
2500
Pressure (psi)
2000
1500
1000
σh ≈ 0.9-0.95 LOP*
500
0 0
10
20
30
40
50
60
70
80
Time (minutes) *from
© 2005 Baker Hughes Incorporated All rights reserved.
Breckels and van Eeklen (1982) Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
FIT- Field Example 4500 4000
Stopped pumping!
3500
Pressure (psi)
3000 2500 2000 1500
Since the pumps were turned off prior to an observed LOP, this test is useless!
1000 500 0 0
5
10
15
20
25
30
35
40
45
Volume Pumped (bbls)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mini -frac Tests Mini-frac Mini-fracs are a special kind of pump-in/decline test designed to measure the closure stress and estimate the leakoff coefficient in a thin interval just prior to a hydraulic fracturing job!
Typical operational conditions:
packers
Interval of interest
• Flow rate: 0.25 - 25 gpm • Volume injected: 0.5-2.5 bbls • Interval length: 5 – 15’ • Several cycles are conducted to ensure repeatable results • Normally use low viscosity fracturing fluid Zone between packers is pressured and a hydraulic fracture is initiated, propagated, and closed. The pressure response during these phases is recorded and analyzed to determine closure stress and leak-off coefficient!
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
RCI Straddle Packer Assembly for Stress Test – micro -frac test micro-frac
Straddle Packer (Dual Packer) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Additional Methods for LOT/minifrac Pressure Analyses Using normal Cartesian plots for pressure decline analysis can sometimes be difficult Æ ISIP/Closure Stress is not clear! BHP
Where is the ISIP/σc ?
BHP Shut-in time (min) ISIP/ σc
Using pressure vs. √time plots is an additional tool for ISIP/Closure Stress identification.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
√Shut-in time (√min)
www.bakeratlasdirect.com
Additional Methods for LOT/minifrac Pressure Analyses
Δ pressure (Δp), psi
Semi-log plots are also used; however, they may also be confusing Æ Semi-log plots for wells A and B show two points with slope change each; which one represents the closure pressure on each case?
time (t), sec from McLennan and Roegiers (1982)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Additional Methods for LOT/minifrac Pressure Analyses From well testing we know that the linear flow regime (representing the fracture) is characterized by a 0.5 slope in a log-log plot. Thus, replotting the data from wells A and B… Æ The moment when the fracture closes would be represented by the end of the linear flow regime !!!
End of linear regime
End of linear regime
from McLennan and Roegiers (1982)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Additional Methods for LOT/minifrac Pressure Analyses We can always use the pressure derivative as an additional diagnosis tool… the end of a plateau (at dp/dt ~ 0.5 ) in the derivative marks the value of closure stress! (d log Δp) / (d log Δt) = 0.25…finite conductivity fracture = 0.5…infinite conductivity fracture = 1.0…wellbore storage
( Jones & Sargeant, 1993 ) Note: If skin is present, the derivative will simply stabilize at a slightly lower value. ICFF Æ Infinite Conductivity Fracture Flow. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pump-in/Decline Tests Procedure is similar to microfrac (i.e., initiate, propagate and close a hydraulic fracture) but this test is much larger: • higher flow rate (up to 20 BPM) • higher fluid viscosity • larger injected volume (up to 100 bbls) Measure the average closure stress over a whole interval (that is why it needs higher values of rate and injected volume!) ISIP should not be used for closure stress estimation Æ use a more robust P vs t analysis Impractical for low permeability rocks (it would take too long!!!)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Typical Pump-in/decline Test
Bottomhole Pressure
Stop pumping
σC is inferred from the change of slope!
dP =
dP =
ϕeμCt xf b
CH p E H2
k
a
c
pre-closure post-closure √ Shut-in time (√Δt)
2
NOTE: This plot is used to ascertain the minimum hor. stress after the fracture has formed and propagated! k=permeability, xf=fracture length, φpe=effective porosity, μ=fluid viscosity, C=fluid loss coefficient, Ct=Cb=total comp., Hp=propped fracture height, and H=fracture height.
a) This can occur when contacting a soft (low E), high permeability formation where the rate of pressure decline can actually increase upon fracture closure. b) This is the typical case of fracture closure accompanied by decreased leak-off. c) Theoretically, no slope change may occur making it difficult to identify σc. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Bottomhole Pressure
Limitations of Pump-in/decline Tests σC ??? σC ???
According to Gulrajani and Nolte (2000), the change of slope in the decline analysis may be due to any of the following: • • • • • •
√ time (pump shut-in)
• •
fracture closure fracture height receding from bounding layers transition from fracture extension to recession reservoir linear flow reservoir radial flow postclosure consolidation of filter cake and fracture irregularities typical of a radial fracture (or nearly contained) in a moderate to high permeability, high fluid loss formation possible initial fracture height containment, followed by fracture growth into higher stress shale
Upshot: Shut-in test should be used in conjunction with other tests as results may be unreliable! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pump-in/decline Tests cont’d However……..As a quality control check the following plot can be used to verify the fracture closure!
Bottomhole Pressure
Stop pumping (Δt ≈0)
σcl must be above the start of the pseudoradial flow
Pres ? @ Horner time = 1 (i.e., Δt →∞)
Log Horner time
⎛ t p + Δt ⎞ ⎟ ⎜ ⎜ Δt ⎟ ⎠ ⎝
*
*Note: tp denotes the pumping time and Δt denotes shut-in time © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pump-in/flowback Tests Test is usually carried out just prior to a hydraulic fracturing job to obtain σc Test involves inducing a hydraulic fracture, injection into the fracture followed by a constant flow-back rate Flow-back rate to be used during testing must initially be estimated Normally intended for low permeability formations The pressure response during flow-back differs during fracture closing and after the fracture has closed resulting in a slope change in the pressure versus time plot Typical operational parameters: • Injection rate (Qinj): 1-10 BPM • Volume pumped: 2-5 Bbls 1 1 • Qflowback = 6 to 4 Qinj
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pump-in/flowback Tests q too low (re-test)
A B
σcl
Ide al
“lazy S” shape
BHP
BHP
Ideal Test Result
C
q too high (re-test)
pump-in
pump-in
√ time (pump Shut-in)
√ time (pump Shut-in)
A Æ Pw > σcl
fracture open Kfr infinite
B Æ Pw ~ σcl
fracture closing near wellbore Kfr finite
C Æ Pw < σcl
fracture closing far from the wellbore Kfr very small
Note: Kfr = fracture conductivity (k*wfr) where k is the fracture permeability and wfr is the average fracture width © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Step Rate Tests • Objective is to measure the closure pressure in “gross” completion intervals (i.e., several formations being tested simultaneously Æhfr > 50 ft) • Performed with higher fluid viscosity, higher flow rates, and larger cumulative volumes than micro-frac tests Q
Pressure
Rate / Pressure
p pext σcl
Pext ≈ σ cl + 100 or 200 psi Shut-in time (min)
Inj. Rate
• Each rate step should have the same hold time (typically 2 to 3 min) • 0.25 bpm < Flow rate < 20 bpm © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stress Determination Techniques • Hydraulic (active) measurements • Strain recovery ¾ASR ¾DSCA
• Log-based • Other methods
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Strain Recovery Methods Once a rock core is physically removed from its in-situ position, the rock deforms (relaxes). Elastic strain occurs immediately upon unloading followed by longerterm anelastic strain. σ3
in-situ rock
εmin Stress Unloading σ1
Differential expansion creates micro-cracks perpendicular to the maximum principal stress direction (Nur & Simmons, 1970)!
εmax
Field measurements (see for example Warpinski and Teufel, 1989) have indicated that the greatest expansion occurs in the direction of maximum principal stress (σ1) and the least expansion occurs in the direction of minimum principal stress (σ3)! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Strain Recovery Methods Anelastic Strain Recovery (ASR)
Differential Strain Curve Analysis (DSCA)
Objective: Record strain due to stress unloading as soon as the core is retrieved.
Objective: Record induced strain due to hydrostatic loading of a previously unloaded core sample. εmin σc σc
εmin
εmax
Strain gages (at least 6) are placed on a core sample immediately upon core retrieval to measure strain relief. The recorded strain values are then used in a constitutive model to determine the magnitude of the in-situ stresses. © 2005 Baker Hughes Incorporated All rights reserved.
εmax σc
εmax σc
Strain gages are placed on core sample after unloading from the in-situ stress conditions. The core is then hydrostatically loaded and the recorded strain values are then used in a constitutive model to determine the magnitude of the in-situ stresses.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Typical ASR Equipment
Strain gages
NOTE: Stringent core handling procedures must be followed to prevent core de-hydration, thermal strains, etc. as well as to ensure precise core orientation!
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Generalized ASR Measurements
Strain (ε)
ε0
Instantaneous elastic strain at instant of coring
Elastic limit Anelastic strain prior to core retrieval
ε1 ε2
recorded strain
t0
Time sample cored
t1
Sample strain gaged
t2
End of measurements
ε0 − ε1
Component of elastic and anelastic strain relaxation (prior to recording)
ε1 − ε2
Component of anelastic strain relaxation (recorded)
Viscous (time-dependant strain continues) t0 t1
t2
© 2005 Baker Hughes Incorporated All rights reserved.
Time Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
ASR ASR-- Field Example 250
core cutting and retrieval
core strain recording
strain unchanged
εv
Strain (ε) [microstrain]
200
εH
NOTE:
150
100
εh
After 40 hours the strain no longer changes!
50
0 0
5
10
(from Teufel & Warpinski 1984) © 2005 Baker Hughes Incorporated All rights reserved.
15
20
25
30
35
40
45
50
Time [hours]
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
ASR Constitutive Models Two common models (Blanton’s-1983 & Warpinski and Teufel-1989) are used to describe the constitutive behavior of rock during rock unloading. These models are excellent for obtaining stress directions but are not as efficient at determining the in-situ stress magnitudes.
The assumptions applied in the two models are as follows*: • Principal stress directions coincide with the principal strain directions obtained from the strain data • The magnitude of the overburden is known • The rock is isotropic and homogeneous (i.e., no micro-cracks exist in-situ) • The borehole is vertical • The rock follows linearly viscoelastic behavior (time-dependant) • Unloading of stresses is instantaneous upon cutting of the core • Poisson’s ratio and Biot’s pore pressure constant remain unchanged during relaxation • Creep (anelastic relaxation) follows an exponential behavior • Bulk modulus of the rock is not viscoelastic *Note: assumptions common to both models are depicted in black, assumptions specific to Blanton’s model are shown in red while assumptions specific to Warpinski and Teufel are depicted in blue. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Blanton’s ASR Model Blanton’s model* was derived on the basis that the two horizontal stresses can be calculated from elastic expressions using the changes in the principal strains for a given time Increment. Mathematically, the expressions are:
(1−ν)ΔεH + ν(Δεh + Δεv) + αPp σH = (σv + αPp) (1−ν)Δεv + ν(Δεh + ΔεH) (1−ν)Δεh + ν(ΔεH + Δεv) + αPp σh = (σv + αPp) (1−ν)Δεv + ν(Δεh + ΔεH) where Δεi is the change in principal strain with respect to a given time increment in the ith direction, ν is Poisson’s ratio, α is Biot’s constant, Pp is the pore pressure and σv is the vertical (overburden) stress. *from Blanton (1983) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Differential Strain Curve Analysis (DSCA) Objective: Hydrostatically load the rock sample and record the resulting strain.
Y
2
X
1
10 3
45º
9
5
12 8
6
7 Position of the 12 strain gages used in a typical DSCA test (after Strickland and Ren, 1980). A 9 gage test can also be conducted. © 2005 Baker Hughes Incorporated All rights reserved.
4
11
Lab Methodology
1) 1.5-2” cubical sample is prepared from an oriented whole core and the surfaces are ground smooth, cleaned and covered with a silicon jacket to prevent pore fluid invasion. 2) Sample is strain gaged (rosette pattern of 0º, 45º, 90º so that directional deformation can be measured). 3) Sample is hydrostatically loaded (σ1=σ2=σ3) and unloaded beyond the estimated in-situ level (3 cycles). 4) Recorded strain data are used to calculate the microcrack closure strain and subsequently infer stress direction and magnitudes (assuming differential strains are directly related to in-situ stress).
Z
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pressure vs Volumetric Strain
Hydrostatic Confining Pressure (σc)
Linear elastic response
For homogeneous, isotropic rock:
ΔV K = σc V Typical DSCA response
For microfractured rock (Walsh, 1965):
ΔV = C σ + η(σ ) b c c V
Volumetric Strain,
© 2005 Baker Hughes Incorporated All rights reserved.
where K is the bulk modulus of the rock, V is the original sample volume, ΔV is the change in sample volume and σc is the confining pressure.
ΔV V
where η represents microcrack porosity (as function of pressure) and Cb is the intrinsic rock compressibility ( K1 ).
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pressure vs Volumetric Strain
Confining Pressure (σc)
For microfractured rock (Walsh, 1965): Linear elastic portion (microcracks closed)
ΔV = C b σ c + η( σ c ) V
pc
microcrack porosity
ηo
Critical crack pressure (pc) (pressure above which all microcracks have closed) © 2005 Baker Hughes Incorporated All rights reserved.
Cbpc
ΔV Volumetric Strain, V
Note: ηo = initial microcrack porosity Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Typical DSCA Plot Measured strain (ε) from the 1, 2, 3, and 10 gages on the X-Y face of the sample. microcrack closure
Y ε 10 3
2
X
1
45º
9 12
crack strain
rock strain from compressibility
4
5 8
6
3 2 1 10
11
7
Z
© 2005 Baker Hughes Incorporated All rights reserved.
σc Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
DSCA Data Analysis In DSCA, the data is used to determine the crack strain tensor within the linear portion of the strain-pressure curve prior to crack closure (Strickland and Ren, 1980).
The microcrack closure strain [ηi(p)] at a given conf. pressure (σc) in the ith direction is calculated as the difference between the measured average strain [εi(σc)] and the bulk rock compressibility [Cb σc]. Mathematically, this is written as: ηi(σc) = εi(σc) – Cb σc. The analysis is usually done by determining the crack strain tensor over Obtained from lab testing a pressure range or: ηij(σc) = εij(σc) + ηo(pc) – Cb σc The principal crack closure strains (ηp1, ηp2, ηp3) and their orientation are then obtained. It is assumed that these directions correspond to the principal stress directions! © 2005 Baker Hughes Incorporated All rights reserved.
Note: ηo(pc) = initial microcrack porosity Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
DSCA Data Analysis According to Ren and Roegiers (1983), for isotropic media the stresses can then be obtained from the following expressions:
σ1 ησc1 (1 − ν ) + ν(ησ c 2 + ησc 3 ) = σ3 ησc 3 (1 − ν ) + ν(ησc1 + ησc 2 )
σ 2 ησc 2 (1 − ν ) + ν(ησ c1 + ησc 3 ) = σ3 ησc 3 (1 − ν ) + ν(ησc1 + ησc 2 )
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stress Determination Techniques • Hydraulic (active) measurements • Strain recovery • Log-based ¾Borehole breakouts ¾Tensile fractures
• Other methods
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
σH Estimation using Breakouts σH Breakouts
σh Breakout width, w (degrees)
NOTE: Breakouts form when the maximum effective tangential stress exceeds the rock strength. Breakouts always form in the direction of the minimum in-plane stress (σh in the case of a vertical hole)! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Breakouts from Image Logs Breakout location (with respect to Earth Coordinate System) Breakouts
Breakout width (w)
Upshot: Breakout location and breakout width are recorded from image logs and used to estimate the maximum horizontal stress (σH)! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
σH Estimation using Breakouts Breakouts form when the compressive stress exceeds the compressive strength of the rock! According to Mohr-Coulomb, this occurs when: σ’1=UCS + σ’3 tan2(π/4+φ/2) where σ’1 is the maximum effective principal stress acting on the wellbore wall, σ’3 is the minimum effective principal stress and φ is the internal friction angle.
For a vertical well with anisotropic horizontal stresses, the effective tangential stress, σ’θθ for an impermeable borehole wall is given by: σ’θθ =σH+σh-2(σH-σh)cos2θ -Pw- αPp NOTE: If Pw ↓, σ’θθ ↑ and vice versa
Upshot: σ’θθ becomes highly compressive as wellbore pressure is decreased! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Borehole Breakout Calculations Calculations-BIAS
When stress exceeds the confined strength, breakouts form!
breakout width
breakout width
Requires knowledge of breakout location, breakout width and minimum horizontal stress orientation! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
σH Estimation using Breakouts In a vertical well at the wellbore wall, breakouts typically occur when:
σ’1 = σ’θθ and σ’3 = σ’rr where σ’rr = Pw - αPp
Substituting the expressions for σ’1 and σ’3 into the Mohr-Coulomb criterion yields: σH+σh-2(σH-σh)cos2θ -Pw- αPp > UCS+(Pw-αPp) tan2θ(π/4+φ/2)
For a given breakout width (w) at a given depth one has: σH+σh-2(σH-σh)cos2(90-w/2) -Pw- αPp =UCS+(Pw−αPp) tan2(π/4+φ/2) Estimated from log-based expressions Estimated from image logs © 2005 Baker Hughes Incorporated All rights reserved.
Estimated from LMP
Known from driller
Efficiency….Data accuracy….People-oriented service
Estimated from Pp prediction analysis www.bakeratlasdirect.com
Borehole Stress & Breakout (vertical well) Re-arranging gives:
σH =
C + Pw + αPp − σ h [1 − 2 cos w ] 1 + 2 cos w
where C = UCS + (Pw - α Pp) tan2(π/4 + φ/2) = confined compressive strength and w = breakout width [degrees]
The maximum horizontal stress (σH) profile can then be estimated by:
σH = x*σh or y + σh where x = σH/σh at the depth of breakout and y = σH – σh at the depth of breakout.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Breakouts from Caliper Logs Common Borehole Geometries In-gauge hole
bit size
tool
key seating
breakout
washout
tool
pipe abrasion
tool
missed breakout
NOTE: The calipers indicate hole elongation (E-W) but the hole is actually washed out! Thus, breakout direction is potentially inaccurate.
tool
tool
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
Breakout missed due to lack of pad coverage in large hole.
www.bakeratlasdirect.com
Breakout ID: Caliper Logs Plumb and Hickman (1985) Criteria* 1) 2) 3) 4)
Tool rotation ceases in the zone of elongation. Differential caliper is greater than 6 mm. Smaller caliper readings should be close to bit size. If smaller caliper reading is slightly greater than bit size, it should exhibit less variation than the larger caliper. 5) Height of the elongated zone should be greater than the pad length. 6) The direction of elongation should not consistently coincide with the azimuth of the high side of the hole in non-vertical wellbores. This may indicate key seating! NOTE: These criteria give only a rough estimate of borehole breakout location and therefore exact breakout width is very difficult to ascertain! *These criteria were originally developed for a 4-arm caliper device but can also be applied to 6-arm calipers! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Breakout Characterizations
9 Borehole geometry can be described combining information from 6-arm caliper (breakout length) and acoustic image log (breakout size) 9 The breakout characteristics are useful in describing in-situ stresses as well as calibrating the geomechanical models © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Log -Based Stress Determination Log-Based Alternative Methods for Determination of Minimum & Maximum Horizontal Stress Magnitudes (Strain Method): •Assume the vertical stress causes constant horizontal strains, isothermal case (Prats, 1981 and Warpinski & Smith, 1989):
σh = ν/(1-ν)(σV- αPp) + αPp +(εh+νεH)E/(1-ν2) σH = ν/(1-ν)(σV- αPp) + αPp +(εH+νεh)E/(1-ν2) •Assume the vertical stress causes constant horizontal strains, non-isothermal case (Blanton & Olson, 1997):
σh = ν/(1-ν)(σV- αPp) + αPp +(εh+νεH + A)E/(1-ν2) σH = ν/(1-ν)(σV- αPp) + αPp +(εH+νεh + A)E/(1-ν2) In which A = (1+ν)ατ∆Τ is a temperature term where αt is the thermal expansion coefficient of the rock and ∆T is the temperature at a particular depth minus the ambient surface temperature (ºF ). Typical values of αt are (Clark, 1966): 5.56 E-6/ºF (sandstone), 5.00 E6/ºF (shale) and 4.44 E-6/ºF (carbonates). © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Calibration to Breakout, Vertical Well (isothermal case) Breakout width measured at two depths, A & B: A
σHA+σhA-2(σHA-σhA)cos2(90-wA/2)–PwA- αΑPpA =sA σHA = νΑ/(1-νΑ)(σVA- αΑPpA)+αΑPpA+(εH+νεh)EA/(1-νΑ2) σhA= νΑ/(1-νΑ)(σVA- αΑPpA)+αΑPpA+(εh+νεH)EA/(1-νΑ2)
B
not valid in σResults HB+σ hB-2(σ HB-σhB)cos2(90-wB/2)–PwB- αΒPpB =sB
σHB = νΒ/(1-νΒ)(σVB- αΒPpB)+αΒPpB+(εH+νεh)EB/(1-νΒ2) σhB= νΒ/(1-νΒ)(σVB- αΒPpB)+αΒPpB+(εh+νεH)EB/(1-νΒ2)
Solve equations for εH & εh to calculate complete stress profile! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
σh Methods Comparison If no lateral strain:
If constant tectonic stress:
If constant lateral strain:
(conventional-uncalibrated)
(conventional- calibrated)
(strain method)
σh = ν/(1-ν)(σV- αPp)+αPp
σh = ν/(1-ν)(σV- αPp)+αPp+ΔσT
σh = Minimum horizontal stress magnitude ν = Poisson’s ratio (isotropic) σV = Vertical stress magnitude α = Biot’s coefficient © 2005 Baker Hughes Incorporated All rights reserved.
σh = ν/(1-ν)(σV- αPp)+αPp+ +εhE/(1-ν2)
Pp = Pore pressure εh = Horizontal strain E = Young’s Modulus
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Conventional vs Strain Method Example
ss
ss
Calibration point
Strain method provides a better match with the measured stress data!
sh ss sh ss sh
From Blanton & Olson (1997) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stress Determination Techniques • Hydraulic (active) measurements • Log-based ¾Borehole breakouts ¾Tensile fractures
• Other methods ¾ Stress Maps ¾ Acoustic methods (Kaiser effect, DWVA, shear wave anisotropy)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
World Stress Map Http:///www-gpi.physik.uni-karlshruhe.de/wsm/maps/
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
In -situ Shear Wave Splitting In-situ • Stress anisotropy causes splitting of the shear waves (faster and slower shear waves traveling at different speeds). The S-wave velocities and directions can be measured using Baker Atlas’ XMAC© acoustic anisotropy tool. • The azimuth of maximum attenuation of Swaves propagated vertically through a specimen is obtained and plotted to determine the maximum in-plane normal stress.
NOTE: Formation anisotropy can be caused by: • Unequal principal stresses • Oriented fractures and/or pores • Structural layering as in shales
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Acoustic (shear wave) Anisotropy
Shear wave map indicates high degree of anisotropy in the N-S direction. This indicates the possible maximum horizontal stress direction!
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Acoustic Velocity Analysis • Due to anisotropic stress removal, microcrack formation takes place in the direction perpendicular to the maximum in-plane stress (σH for the case of a vertical wellbore). • The test is usually performed on vertical cores. • There is no critical time to perform the test (as is the case in ASR). Therefore testing can be conducted on old cores. • Tests can be conducted under any stress/pore pressure conditions (higher stresses cause pores to close resulting in an increase in acoustic velocity). • The orientation of the minimum compressional and shear wave velocities is perpendicular to the microcrack orientation whereas the maximum velocities occur parallel to microcracks. σH VP(max), Vs(max), A(min) (Min. Attenuation)
VP(min), Vs(min), A(max) (Max. Attenuation) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
σh, VPmax
P-wave
receiver
σH, VPmin
transmitter
Typical P -Wave Velocity Test P-Wave P-wave is measured diametrically along azimuthal increments
P-wave Velocity (m/sec)
P-wave Anisotropy 5200 5000 4800 4600 4400 4200 4000 0
© 2005 Baker Hughes Incorporated All rights reserved.
σH direction
90
σh 180 direction Azimuth (degrees)
270
Efficiency….Data accuracy….People-oriented service
360
www.bakeratlasdirect.com
Typical S -Wave Velocity Test S-Wave S-wave Amplitude 5200
S-wave
S-wave Amplitude
transmitter
receiver
5000 4800 4600 4400 4200 4000 0
σH direction 90σh direction 180
270
360
Azimuth (degrees) σH, VSmin
σh, VSmax
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
The Kaiser Effect • A rock sample will yield acoustic signals (sub- audible noises) when
subjected to loading in the laboratory. The Kaiser effect occurs when the rate of acoustic signals drastically increases. This occurs when the applied stress surpasses the load previously experienced by the rock (Kaiser, 1953). • In the lab, a core is subjected to a sequence of stresses. In the first
cycle of loading, a high-frequency sound burst is emitted. However, in subsequent cycles, there is an absence of these emissions until the previous maximum stress is surpassed.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
AE (Acoustic Emission) Activity
The Kaiser Effect σi
σmax = Maximum Burial Stress in Direction i
NOTE: Some rocks lose their memory of previous loading in as little as a few days (Holcomb, 1993).
σi
Upshot: Kaiser effect may yield erroneous results!
σmax © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
σi www.bakeratlasdirect.com
Published σH and σh Correlations Horizontal Stress Formulation σH [MPa] = 4.6 + 0.025d σh [MPa] = 1.4 + 0.018d σh = 0.197d1.145 (d ≤11500 ft) σh = 1.167d – 4596 (d > 11500 ft) ΚH = 0.98 + 250/d Κh = 0.65 + 440/d ΚH = 1.46 + 357/d Κh = 1.10 + 167/d σH [MPa] = 15 + 0.028d σh [MPa] = 6 + 0.012d σH [MPa] = 8.8 + 0.0422d σh [MPa] = 3.64 + 0.0276d σH [MPa] = 30.4 + 0.023d σh [MPa] = 16.0 + 0.011d σH [MPa] = 9.1 + 0.0724d σh [MPa] = 5.3 + 0.0542d σH [MPa] = 2.8 + 0.0399d σh [MPa] = 2.2 + 0.0240d σH [MPa] = 15.83 + 0.0302d σh [MPa] = 6.52 + 0.01572d
Location and Depth Range
References
Michigan Basin (0-5000m)
Haimson (1977)
Gulf of Mexico (all depths- ft)
Breckels & van Eekelen (1982)
World Data (500-3000m)
Rummel (1986)
Canadian Shield (0-2200m)
Hegret (1987)
Cornwall, UK (0-2000m)
Pine & Kwakwa (1989)
Canadian Shield (0-2000m)
Arjang (1989)
KTB pilot hole (800-3000m)
Baumgarten et al. (1993)
Fennoscandia: (0-1000m)
Hast (in Stephansson 1993)
Fennoscandia: (0-9000m)
Stephansson (1993)
KTB pilot hole (0-9000m)
Te Kamp et al. (1993)
Note: KH = σH/σv and Kh = σh/σv
NOTE: These should only be used as a last resort! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline I. II. III. IV.
Introduction to subsurface stresses Overburden calculation Commonly used stress determination techniques Summary
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
In -situ Stress Workflow In-situ Analyze data/ Daily drill reports Calculate overburden stress Pore pressure estimation
Determine rock mechanical properties (LMP)
© 2005 Baker Hughes Incorporated All rights reserved.
Calculate minimum horizontal stress (σh) magnitude and direction. Calibrate using stress measurement techniques.
Conduct geomechanical analysis – borehole stability, sand production, hydraulic fracturing, etc.
Calculate maximum horizontal stress (σH) magnitude and direction. Fine tune using borehole image logs and other field/drilling observations. Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
In -situ Stress Puzzle In-situ Active
Passive
)Mini-Frac )LOT/ELOT )FMT/RCI
)Breakouts )Fractures )Acoustic Anisotropy
Integration
BIAS Existing Inf.
Core Based
)History )Stress maps )Geology
)DSA )ASR )Kaiser effect
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
All info must be integrated to build a consistent in-situ stress model!!!!
www.bakeratlasdirect.com
In-Situ Stress Regimes
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Pressure Characterizations
Outline I. Why pore pressure prediction is important II. Basics of abnormal pore pressure III. Pore pressure determination methods
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Why is Pore Pressure Est. Important? > 40% of trouble time attributed to Geomechanics/Pressure related incidences. These account for 24-27% of total drilling costs.* 0.8% 21.4% Directional Completion Cement Squeeze 11.4%
Chemical Problems Wait on Weather
3.0%
5.2%
Geomechanics/ Pressurerelated incidences
Casing or Wellhead Failure Rig Failure
9.0% 42.3%
Other Stuck Pipe Twist Off
12.8% 13.4%
Kick Lost Circulation
2.8% 0.7% 2.7%
2.6%
Sloughing Shale Wellbore Instability Shallow Water Flow Gas Flow
0.3%
9.4% 5.0%
*Data taken from Dodson et al. (2004). Data illustrates incidences from 549 GoM shelf wells (<600 ft water depth) drilled from 1993-2002. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
What is a Shallow Water Flow? Shallow Water Flows (SWF): Water/debris flow along the outside of structural casing to the seafloor.
Causes of SWF 1.
riser
2.
ρwater
3. 4.
ρmud sand
Geopressured sands within conductor intervals: Excessive sand pressures cause SWF’s prior to installation of riser and BOP- no closed system to contain geopressure! Induced fractures: Mud pressure at the casing shoe exceeds the formation tensile strength and induces a hydraulic fracture, resulting in a conduit of fluid flow to the seafloor. Induced storage: Permeable formations are “charged” by excessive MW resulting in flowback once circulation is ceased. Transmission of geopressure through cement channels: Poor cement jobs provide a conduit of fluid flow. This is typically time-delayed as there is more time required to flow through the cement channels.
Ramifications of SWF 1. 2.
Flowing water may cause deterioration of the structural support of the well leading to casing buckling and/or collapse. Loss of well control.
Thus, there is a need to predict SWF in advance! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Typical GoM PP Profiles Deepwater formations often encounter abnormal pressures directly below the mud-line; which can lead to a much narrower MW window. Shelf
Deepwater
PRESSURE
SWF (shallow water flow)
re tu ac Fr
(li th os ta tic )
e ur
Pore Pressure (Pp)
re su es
re ssu Pre tic sta dro Hy
GEO PRESSURE
© 2005 Baker Hughes Incorporated All rights reserved.
Pr es su re
r op Ge
Zone
σ’ = σ - Pp
s es Pr
Tran sitio n
re su res cP
Pore Pressure (Pp)
ur de n
re tu ac Fr
Stress (σ’)
ti sta dro Hy
e ur
DEPTH
σ’ = σ - Pp
s es Pr
Effective
O ve rb
DEPTH
O ve rb ur de n
PRESSURE
Effective Stress (σ’)
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Typical DW GoM Casing Program 4000
6000
Depth [feet-tvdrkb]
8000
10000
hydrostatic
12000
Planned MW
14000 PPG
FG
16000 8
9
10
11
12
13
14
15
16
17
18
Equivalent Mud Weight [lbs/gal]
Note: PPG = pore pressure gradient, FG = fracture gradient © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Unexpected Overpressured Zone 4000
6000
Depth [feet-tvdrkb]
8000
Planned MW
10000
hydrostatic
12000
potential kick zone or spalling shale (Pp>Pw)
14000 PPG
FG
16000 8
9
10
11
12
13
14
15
16
17
18
Equivalent Mud Weight [lbs/gal]
Note: PPG = pore pressure gradient, FG = fracture gradient © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Unexpected Depleted Zone 4000
6000
Fracturing in depleted zone (and possibly losses!)
Depth [feet-tvdrkb]
8000
hydrostatic
10000
12000
14000 PPG
FG
16000 8
9
10
11
12
13
14
15
16
17
18
Equivalent Mud Weight [lbs/gal]
Note: PPG = pore pressure gradient, FG = fracture gradient © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline I. Why pore pressure prediction is important II. Basics of abnormal pore pressure III. Pore pressure determination methods
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Pressure: The Basics
Pressure Normally (hydrostatic) Pressured Reservoirs
Depth
¾
hyd
c tati ros
lith os tat ic
Rocks which have pore pressures equal to a continuous column of water from surface to depth of interest (typically 8.3-8.9 PPG range).
under pressure
over pressure
© 2005 Baker Hughes Incorporated All rights reserved.
Abnormally Pressured Reservoirs ¾
Rocks which have pore pressures significantly greater than hydrostatic (overpressured) or less than hydrostatic (underpressured).
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Pressure: The Basics Normal Compaction Behavior Fluid pressure
Sea level
True vertical depth, m
Sedimentation
Water is expelled due to the compaction of sediments grain
Hydrostatic pressure
© 2005 Baker Hughes Incorporated All rights reserved.
Fluid
The column is supported by the grain to grain contact.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mechanisms of Overpressure Causal mechanisms of overpressure include the following: Æ Stress-related (pore volume reduction) • Disequilibrium compaction (vertical stress loading without fluid pressure dissipation) • Tectonic (lateral) stress loading (faulting, salt dome emplacement) Æ Fluid volume increase (pore volume expansion) • Increased temperature (pore fluid expansion) • Water release due to mineral transformation (smectite to illite transformation) • Hydrocarbon cracking These are the most likely mechanisms to result in large • Hydrocarbon generation from kerogen Æ
Fluid movement and buoyancy
scale overpressure (Swarbrick & Osborne, 1998)
• Osmosis (brine concentration contrasts across semi-perm membranes) • Hydraulic head (increased potentiometric head from highlands) • Buoyancy due to density contrasts between fluid type (oil, gas, water)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mechanisms of Overpressure Fluid pressure
Sea level
True vertical depth, m
Hydrostatic pressure
Compaction in an undrained condition
Part of the Overburden is supported by the pore fluid. Overpressure
• Fast sedimentation • Low permeability (clay sediments) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mechanisms of Overpressure
Overburden
Normal Compaction 1 - 1.07 sg Overpressure top 1.19 - 1.68 sg
Under Compaction
Under Compaction + Other Mechanisms
Overpressure
> 1.80 sg Fluid expansion
Bowers GL, 2001 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mechanisms of Overpressure 0.9
Pressure vs. Temperature for GoM Wells (Timko &Fertl, 1971)
Pp Gradient (psi/ft)
0.8
0.7
0.6
0.5
0.4
0.3 60
100
140
180
240
280
320
360
Temperature (oF) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mechanisms of Overpressure Relationship between Porosity – Depth and Pore Pressure 0
0.25
0.50
0.75
Porosity-Depth Relationships Normal compaction line for sandstone
1.0
Porosity
mud
clay
Normal compaction line for clay and shale
mudstone
shale
Overpressure effect on porosity 4-8 km
Depth © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mechanisms of Overpressure Pressure Overburden stress
Depth
Overpressure top
Effective stress Pore pressure Normal hydrostatic pressure
© 2005 Baker Hughes Incorporated All rights reserved.
Overpressure
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mechanisms of Overpressure Buoyancy Effect Gas or oil Sand
za
za= 2000 ft zb= 3000 ft
Sealed Fault
ρg= 0.12 psi/ft
zb Oil - Water contact (or Gas) Water Formation Sand
PB = 0.465 (psi/ft) * 3000 ft = 1395 psi PA = PB – (Zb –Za)*ρg* g PA = 1395 psi – (1000 ft)*0.12 psi/ft = 1275 psi PP Gradient = 1275psi/2000 ft = 0.638 psi/ft © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mechanisms of Overpressure Artesian System PP = 0.465 psi/ft * (10000-2000) ft = 3720 psi GPP = 3720 psi /2000 ft = 1.86 psi/ft
Z=10,000 ft
Z=2,000 ft
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mechanisms of Underpressure Underpressure is caused by: Æ Rock & fluid property change due to uplifting • Reduction in temperature (leading to reduction in pressure via fluid shrinkage) • Rock dilatancy (due to lower temperature and stress) • Groundwater discharge (accompanied by a lower permeability recharge zone) • Gas solubility (gas exsolves out of solution at a greater rate than gas generation to due decrease temp. and pressure at uplifted stage) • Osmotic flow (via semi-perm membrane)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mechanisms of Underpressure PP = 0.465 psi/ft * 7000 ft = 3255 psi GPP = 3255 psi /10000 ft = 0.33 psi/ft
Z=10000 ft
Z=7000 ft
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline I. Why pore pressure prediction is important II. Basics of pore pressure III. Pore pressure determination methods
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Pressure Prediction Process Calculate overburden Calculate PP using several techniques • Eaton (res/sonic/Dxc/cond) • Bryant (res) • Alixant (if geothermal gradient known) • Others
Evaluate secondary parameters (gas/geology/torque/drag/fill etc.)
Review possible effects of tectonics/ other mechanisms (faults/dipping beds/salt)
Techniques should agree within 0.5 PPG!
© 2005 Baker Hughes Incorporated All rights reserved.
Fine tune and calibrate PP models
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pressure Prediction Process Data Use all the data sources available, both primary and secondary. No one data source, alone, gives an accurate pressure prediction.
• Seismic (velocity/Δt) • Wireline (res / sonic / den / gam / calip) • MWD (res / gamma / sonic / density) • RCI (measured reservoir pressures) • Mud logs (gas / cuttings / lithology) • Fluids (mud density / hole cleaning) • IADC (wellbore stability/problems)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Pressure indicators
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
PP Determination Techniques Pore pressure (PP) determination methods can be broadly categorized into two general methods: 1. Direct Methods- Methods which directly relate the amount of pore pressure divergence from its normal trendline to the pore pressure gradient at a given depth.
2. Effective Stress Methods- Methods which are based on Terzaghi’s (1943) effective stress principle: compaction of porous material is controlled by the difference between total confining pressure and the pore fluid pressure.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Direct Methods Methods-- example Published examples of Hottman & Johnson Overlays Constructed for Various Regions For a given resistivity ratio, the 1.0
PPG is estimated based on regional curves
South China Sea
0.9 Vicksburg
0.8 Frio
0.7
Niger Delta Basin Gulf Coast
PPG=0.65 psi/ft
Wilcox
South China Sea
0.6
Frio Wilcox
Pore Pressure Gradient [psi/ft]
Pore Pressure Gradient [psi/ft]
1.0
0.5
0.9 Gulf Coast
0.8
Vicksburg
Niger Delta Basin
0.7
0.6 Wyoming Sedimentary Basin
0.5 Wyoming Sedimentary Basin
0.4 1
2
5 Log Rn/Ro
10
0.4 0
10
20
(data taken from Owolabi et. al, 1990)
30
40
50
60
70
80
Δto - Δtn
Rn & Ro are the “normal” and observed resistivity and Δtn & Δto are the “normal” and observed interval transit times.
NOTE: Since each region has a different signature, the overlay method is region specific. Additionally, it is necessary to construct new curves for new regions or whenever new geological horizons are encountered (Matthews & Kelly, 1967)! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effective Stress Methods Effective stress methods are generally categorized into the following: Vertical Effective Stress Methods- These methods assume that normally pressured and overpressured sections which exhibit identical properties are subjected to the same effective stress. Horizontal Effective Stress Methods- These methods are used to calculate the effective stress from the difference between observed and normal trend parameters at a given depth. Other Effective Stress Methods- These methods represent all other published methods that are used to obtain the relationship between compaction and effective stress. NOTE: These are the methods that will be examined in detail for the remainder of this session! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effective Stress Methods S = total stress σ = effective stress Overburden Stress
Pressure Required to Keep Water & Rock Grains from Squashing Out Horizontally
SV
=
SV = P + σV Sh = P + σh = P + K σV © 2005 Baker Hughes Incorporated All rights reserved.
σh
P
Sh
Total Stress
σV
P
Pore Pressure
+
Effective Stress
σh K= = Effective Stress Ratio; σV “K” increases with ductility.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effective Stress Methods Vertical Effective Stress Velocity (Km/s)
Pressure (Mpa)
Velocity (Km/s)
Depth (m)
Normal Trend
Compaction Trend
Effective Stress (Mpa)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effective Stress Methods Vertical Effective Stress – Equivalent Depth Foster & Whalen(1966) Dt
The effective stress in A and B are considered to be equal (since the state of compaction is equivalent) Zeq
A
Depth
PB = S B − (S A − PNA ) Z
B
where: P S
= Pore pressure (psi) = Overburden
σ = Effective stress © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effective Stress Methods Vertical Effective Stress – Equivalent Depth Traugott (1997) Dt
This method uses the mean stress Î (σ + σ h + σ H ) σM = 3
A
Depth
Zeq
⎛ 1 + 2K A ⎞ ⎟⎟( S A − PNA ) PB = S B − ⎜⎜ ⎝ 1 + 2K B ⎠ where :
Z
B
P S
= Pore Pressure (psi) = Overburden
K
= Vertical Effective stress = σh=σH/σ
σ © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effective Stress Methods Horizontal Effective Stress Velocity (Km/s)
Pressure (Mpa)
Velocity (Km/s)
Depth (m)
Eq. Eaton
Normal Trend
Effective Stress (Mpa)
S = total stress σ = effective stress © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effective Stress Methods Horizontal Effective Stress: Eaton’s Method (1975) ⎛V σ = σ N ⎜⎜ ⎝ VN
⎞ ⎟⎟ ⎠
3
⎛ Δt N ⎞ σ =σN⎜ ⎟ ⎝ Δt ⎠ ⎛ R σ = σ N ⎜⎜ ⎝ RN
⎛ V ( D) ⎞ ⎟⎟ Pp ( D) = S ( D) − (S ( D) − PN ( D) )⎜⎜ ⎝ VN ( D ) ⎠
3
1.2
⎞ ⎟⎟ ⎠
⎛ Dxc σ = σ N ⎜⎜ ⎝ DxcN
3
where :
1.2
⎞ ⎟⎟ ⎠
© 2005 Baker Hughes Incorporated All rights reserved.
P S D PN VN
= Current Pore Pressure = Overburden = Current Depth = Normal Pore Pressure = Normal Compaction Velocity
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effective Stress Methods Other Effective Stress: Bower’s Method (1995) Based on acoustic/velocity data using a modified equivalent depth type method that calculates effective stress along Bower’s derived curved trend line. This method is useful for correcting for unloading by manipulating several variables. © 2005 Baker Hughes Incorporated All rights reserved.
V
Concept of Virgin Curve
VMAX
Sub-Compaction σMAX
σ
Normal Compaction • Power trend of Compaction
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effective Stress Methods Other Effective Stress: Bower’s Method (1995) U
⎛ σA ⎞ ⎟⎟ σ B = σ max ⎜⎜ ⎝ σ max ⎠ where : A
= Equivalent depth σA = Effective stress at equivalent depth σmax = Effective stress at Vmax Vmax = Maximum velocity U = Calibration parameters (local data)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effective Stress Methods Other Effective Stress: Bower’s Method (1995)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effective Stress Methods Other Effective Stress: Bower’s Method (1995)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Table of PPP Methods PPP Approach Method Type
Name
PP Indicator
Crossplots
Hottman and Johnson (1965)
Acoustic/Resistivity
Overlays
Pennebaker (1968)
Acoustic/Resistivity
Equivalent Depth
Acoustic/Resistivity
Mean Stress Equivalent Depth
Acoustic/Resistivity
Bellotti and Giacca (1978)
Acoustic
Expression(s) X=
Direct
Effective Stress
Vertical
Hart and Flemings (1995)
Acoustic
Bryant (1989)
Resistivity
Alixant and Desbrandes (1991)
Resistivity
Rn Ro
X = Δt o − Δ t n
X=
Δto Δtn
P(b ) = σ v (b ) − (σ v (a ) − Pn (a ) ) ⎛ 1 + 2 K (a ) ⎞ ⎟ (σ P(b ) = σ v (b ) − ⎜ − Pn (a ) ) ⎜ 1 + 2 K ⎟ v (a ) (b ) ⎠ ⎝
σ' =
(Vo − Vm i n )B Vm at − A (Vo − Vmi n )
⎛ ⎜ φo 1 ⎜ σ ' = ln ⎜ 1 η ⎜ X V ⎛ ⎞ o ⎜1−⎜ ⎟ ⎜ ⎝ Vmat ⎠ ⎝
φ=
Rw Ro
w=
φ (1 − φ)
σ = σ max (1 − φ )
α
'
σ ' = 10
[ri − w ] / l c
⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠
Symbols: σv is the overburden stress, P is the pore pressure, V is acoustic velocity, R is resistivity, Δt is interval transit time and σ' is the effective stress. Subscripts: a is parameter at the “normal pressure”, b is parameter at the depth of interest, n is parameter at “normal pressure”, o is the observed parameter, mat is the matrix, min is the minimum and max is the maximum.
X is value used estimate the PPG (Y-axis) in overlay plots A & B are local calibration parameters
α is a calibration parameters (usually taken to be 7.35) ri and lc are local calibration parameters
φo & η are calibration parameters (X is typically taken to be 2.19) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Table of PPP Methods PPP Approach
Method Type
Name
PP Indicator
Expression(s) ⎛ Δt σ = σ n ⎜⎜ n ⎝ Δto
⎞ ⎟⎟ ⎠
3
⎛C σ = σ n ⎜⎜ n ⎝ Co
⎞ ⎟⎟ ⎠
1 .2
'
Eaton (1975)
acoustic/resistivity/ conductivity/D exponent
'
Horizontal
Weakley (1989)
acoustic
⎛R σ = σ n ⎜⎜ o ⎝ Rn '
⎞ ⎟⎟ ⎠
1.2
⎛d ⎞ σ ' = σ n ⎜⎜ xco ⎟⎟ ⎝ d xcn ⎠
⎛ σ − Pm log ⎜⎜ v ⎝ σ v − Pn N = ⎛V ⎞ log ⎜⎜ m ⎟⎟ ⎝ Vn ⎠
1.2
⎞ ⎟⎟ ⎠
σ ' = σ n 10 − b (φ − φ n )
Effective Stress Rasmus and Gray Stephens (1991)
resistivity
Bowers (1995)
acoustic
Holbrook (1987)
resistivity
Other
1
⎛ 1 V ⎞m φ − φ n = ⎜⎜ − c l ⎟⎟ ⎝ R o R cl ⎠
σ (b )
'
⎛ σ = σ max ⎜⎜ (a ) ⎝ σ max
⎞ ⎟⎟ ⎠
U
σ ' = A (1 − φ )
B
Symbols: σ is stress, σ' is the effective stress, P is the pore pressure, V is the lithology volume, R is resistivity, C is conductivity, dx is “drilling exponent”, Δt is interval transit time and φ is total porosity. Subscripts: a is parameter at the “normal pressure”, b is parameter at the depth of interest, n is the parameter at the “normal pressure”, o is the observed parameter, mat is matrix, min is minimum, max is maximum and v is vertical.
This method calculates Eaton’s (1975) N exponent m and b are local calibration factors
© 2005 Baker Hughes Incorporated All rights reserved.
σmax=σ′max (max. vel.) & U is a local calibration factor (3.13 for GoM) A & B are end-member parameters which vary based on lithology
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Resistivity Measurements Advantages
Limitations
¾ Resistivity data is often acquired from surface down to total depth
¾ Poorly defined normal trend in deep water environments
¾ Ability to use multiple trend-line and effective stress pressure prediction methods
¾ False indication of pressure due to pore water salinity change, proximity to salt and closeness to faults ¾ Temperature effects on measurement (resistivity decreases with increasing temperature) ¾ Resistivity response dependent on vertical resolution, depth of investigation and borehole rugosity
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Acoustic Measurement Advantages
Limitations
¾ Low sensitivity to hole size, formation temperature and pore water salinity
¾ Not run from surface to total depth in most wells
¾ Small effect of measurement around salt
¾ Lithology dependent, shale rich environments with no hydrocarbon influence work best
¾ Ability to calibrate with seismic-based predictions
¾ Variability in exponent in geologic areas
¾ Generally obtain good agreement with measured pore pressure data (e.g., RCI data) ¾ DTS shear data tends to show improved response in isolated pressured zones ¾ Ability to calculate bulk density and porosity from which overburden and pore pressure is derived
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Trend Line -based PP Prediction Line-based Step 1: Pick shale points Shale Point Guidelines
Shale picks denoted by red lines
• Pick shales at least 10-30 feet thick • Silty/limey shales should be avoided • Avoid picks within 10 feet of a sand • Shallow resistivity picks could be affected by the freshening of pore water
Note: It is necessary to select shale points because the PPP is valid only in the shale sections.
• Temperature correct resistivities, especially at shallow depths • Shales around salts may be too low of values • Geologic age boundaries and unconformities may shift trends • Hydrocarbon zones can affect the resistivity and/or acoustic readings © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Trend Line -based PP Prediction Line-based Step 2: Placement of Normal Trend Line (NTL) The trend line is defined by two points along the normal compaction trend, prior to entering the top of overpressure.
Inconsistent placement and slope of the NTL leads to errors in the predicted pore pressure!
NTL Slope is affected by: • Depositional rate • Age of the sediments • Thickness • Silt / lime content Potential overpressure zone
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
NTL Adjustments Shifting of the NTL is sometimes required to calibrate the pore pressure model when noncompaction related pressure mechanisms such as the presence of salt, faulting, unconformities or dipping beds are encountered. The shift should retain the same NTL slope!
NOTE: If a NTL shift is needed, verify from the company geologist/ geophysicist that tectonic-related mechanisms are present to support the shift.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Resistivity PP Prediction -example Prediction-example z
z
z
Due to the close proximity of salt, a shift of the normal trend line (NTL) was needed. In real-time, the actual degree of NTL shift needed is difficult without some sort of calibration or using some other data source such as acoustic data or measured pressure (such as TesTrak). Confidence in analysis is low if unable to compare with other types of analysis in this particular geologic environment (salt).
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Acoustic PP Prediction Prediction-- example
z
z z
z
In this case, no acoustic NTL shift was need to account for salinity changes, which was required by resistivity. Good agreement with wireline pressure tests. In areas of possible salinity water changes (around salt), using the acoustic improves the accuracy of the pore pressure & fracture gradient (PPFG) analysis. Reduced risk and increased safety with an accurate PPFG analysis
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
PP Adjustments z
z
z
Resistivity is affected by salinity changes much greater than acoustic. This gives an unrealistic indication of pore pressure. Adjustments to the RES NTL must be made to account for this effect, degree of shift must be calibrated with another PP source. No NTL adjustments for DTC, resulting in less error in PP.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Centroid Effects
After Eigill Nysaether Trindheim 2006 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Centroid Effects – lateral transfer Pressure
Large pressure in the reservoir that the Shale
Depth
Starting of Overpressure Zone
Increase Pressure Line of Overpressure
Hydrostatic
Tilt Res erv
oir
Lithostatic
After R. Swarbrick CSEG 2002
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Centroid Effects – fracturing potential
After Heppard and Traugott
© 2005 Baker Hughes Incorporated All rights reserved.
The equivalent mud weight increases toward the crest while decreases in the bounding shale which therefore also has a corresponding decrease in hydraulic fracture pressure. A well drilled directly at the structural crest of a trap can lose returns into the seal with the mud pumps on and have flow from the reservoir with the pumps off. Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Summarizing Pore Pressure ¾ Pore pressure prediction requires a complete formation evaluation analysis from “surface to total depth” to provide an accurate pressure prediction. ¾ Log response must be carefully analyzed for geological, structural, borehole and formation effects on measurements. ¾ Ability to use multiple effective stress pressure prediction methods is required to accurately predict PP. ¾ The use of multiple trend-lines may be necessary in geologically complex regions ¾ Seismic calibration of the acoustic data can enhance pre-drill models for real-time prediction. ¾ Real-time resistivity and acoustic can be used to continuously update the PP model as well as to provide “ahead of the bit” predictions.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Wellbore Stability Basics © 2005 Baker Hughes Incorporated All rights reserved.
Outline I. II. III. IV. V.
Stress distribution around a circular borehole Failure modes and failure criteria Mud weight window Stress polygon Borehole strengthening
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stress Concentration σh
σH
σH σh
When a well is drilled in a formation, stressed solid materials is removed and replaced with a fluid under pressure. Since the well fluid pressure normally does not match exactly the stress which the removed solid exerted, there will be an alteration in the stress state of the formation around the well. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
The Need for a 3D Stress Analysis Around A Borehole Multilateral Configurations
Dual
Stacked
Trilateral Fork
Herringbone
Backbone and Rib
Radial
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stresses Around A Borehole Coordinate Systems Z
Z βb
Xs
X
τbyz τbxy
τYX
X (North)
rock property
zb (borehole axis-down) Deeper Depth σbzz
τbyz
τZX
σXX
X
σ
xb (hole bottom)
τXY
αr
Z (down)
σZZ
τXZ
Y
zb (borehole down)
τZY
σbyy
σYY Y (East)
τYZ
Yr
Xr
βr
borehole
Stress Transformation Z (down)
Xb
αb
αs far-field stress
Z
Y
Y
X
Zr
Yb
Ys
βs
(Anisotropic Materials)
Zb
Zs
τbxz
σbzz τbyz τbxz
θ σθθ
xb (bottom of hole) τbxy
τbxz τbxy σbxx
σzz
a
τbxz
yb σrr
τbyz τbxy
σbyy
σbxx
Shallower Depth
Y (East)
yb
(Stress Components)
© 2005 Baker Hughes Incorporated All rights reserved.
X (North)
(Local Coordinate)
Efficiency….Data accuracy….People-oriented service
(Cylindrical Coordinate) www.bakeratlasdirect.com
Stresses Around the Borehole Due Dueto tothe thecylindrical cylindricalshape shapeof ofthe thestructure, structure,aacylindrical cylindricalcoordinate coordinatesystem system is often selected as the working coordinate system. The total stress-field is often selected as the working coordinate system. The total stress-field around aroundaawellbore wellboreof ofarbitrary arbitraryorientation orientationis isthus thusdefined definedby byσσrrrr’,’,σσθθθθ’,’,σσzzzz’,’,ττrθrθ, , ττrz, ,and andττθz :: rz
θz
(σbxx + σbyy ) ⎛ a 2 ⎞ (σbxx − σbyy ) ⎛ ⎛ a2 a4 ⎞ a2 a4 ⎞ a2 σ rr = ⎜ 1 − 2 ÷+ ⎜ 1 − 4 2 + 3 4 ÷ cos 2θ + τbxy ⎜ 1 − 4 2 + 3 4 ÷ sin 2θ + Pmud 2 r r ⎠ r r ⎠ r 2 2 ⎝ r ⎠ ⎝ ⎝ (σbxx + σbyy ) ⎛ a 2 ⎞ (σbxx − σbyy ) ⎛ ⎛ a4 ⎞ a4 ⎞ a2 σθθ = ⎜1 + 2 ÷ − ⎜1 + 3 4 ÷ cos 2θ − τbxy ⎜ 1 + 3 4 ÷ sin 2θ 1− Pmud 2 r ⎠ r ⎠ r 2 2 ⎝ r ⎠ ⎝ ⎝ a2 a2 σ zz = σbzz − 2υ (σbxx − σbyy ) 2 cos 2θ − 4υτbxy 2 sin 2θ r r ⎡ (σbxx − σ by ) ⎤⎛ a2 a4 ⎞ sin 2θ + τbxy cos 2θ ⎥⎜ 1 + 2 2 − 3 4 ÷ τ rθ = ⎢ y 2 r r ⎠ ⎣ ⎦⎝ ⎛ a2 ⎞ τrz = τbyz sinθ + τbxz cosθ ⎜ 1 − 2 ÷ ⎝ r ⎠
[
[
]
⎛ ⎝
]
τθz = − τbxy sinθ + τbyz cosθ ⎜1 +
z’ y’ O ’
β
x’ 2 α
a ⎞ ÷ r2 ⎠ 2
3 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stresses Around the Borehole At Atthe theborehole boreholewall, wall,the theeffective effectivestress stresscomponents: components: η = Biot' s constant − ηP rr mud pore ) − 2(σ ) cos 2θ − 4τ sin 2θ − P σ ' = (σ +σ −σ − ηP bxx byy bxx byy bxy mud pore θθ ) cos 2θ − 4υτ sin 2θ − ηP σ' = σ − 2υ (σ −σ 1 zz bzz bxx byy bxy pore τ =0 rθ z’ y’ τ =0 rz O sinθ + τ cosθ ) τ = 2( −τ bxz byz θz ’
σ' = P
β
x’ 2
The effective Principal Stresses at the borehole wall are: α
σ 1' , 2 =
σ θθ' + σ zz' 2
±
© 2005 Baker Hughes Incorporated All rights reserved.
(σ
'
θθ
− σ zz' 4
)
2
+ 4τ θ2z
σ ' = Pmud − ηPpore 3
Efficiency….Data accuracy….People-oriented service
3 www.bakeratlasdirect.com
Stresses Around the Borehole Pw = Pmud , Pp = Ppore σv
For the special case of a vertical well and in the principal stress directions (θ1, θ2):
σ
' 1, 3
=σ
θ2 θθ θ1 '
r
and if σ bxx = σ H , σ byy = σ h
σ
1
= 3σ H − σ h − pw − Pp
σ ' = 3σ h − σ H − pw − Pp 3
© 2005 Baker Hughes Incorporated All rights reserved.
σH
θ
The maximum tangential stress (σ1) occurs at θ = 90° & 270°→ cos (2θ) = -1
'
θ
z z’
σ rr = pw σ θθ = σ H ( 1 − 2 Cos 2θ ) + σ h (1 + 2 Cos 2θ ) − pw σ zz = 0 τ rθ = τ rz = τ θ z = 0
The minimum tangential stress (σ3) occurs at θ = 0° and 180°→ cos (2θ) = 1
σh
x’
r
y’
σh
σH
IfIfmax maxhoop hoopstress stressisistoo toohigh high(compression), (compression), the rock may fail in shear !!! the rock may fail in shear !!! IfIfmin minhoop hoopstress stressisistoo toolow low(tension), (tension), the rock may fail in tension !!! the rock may fail in tension !!!
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stresses Around the Borehole For the special case of a horizontal well drilled parallel to the maximum horizontal stress … σv
If σv > σh
σv σh
z’
σ ' = 3σ v − σ h − pw − Pp ( Along σ h ) 1
σ ' = 3σ h − σ v − pw − Pp ( Along σ v ) 3
If σh > σv y’
σH
x’
© 2005 Baker Hughes Incorporated All rights reserved.
σh
σ ' = 3σ h − σ v − pw − Pp ( Along σ v ) 1
σ ' = 3σ v − σ h − pw − Pp ( Along σ h ) 3
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stresses Around the Borehole For the special case of a horizontal well drilled parallel to the minimum horizontal stress … σv
If σv > σH
σv
σH
σ ' = 3σ v − σ H − pw − Pp ( Along σ H ) 1
σ ' = 3σ H − σ v − pw − Pp ( Along σ v ) 3
z’
If σH > σv
σ ' = 3σ H − σ v − pw − Pp ( Along σ v ) 1
σ ' = 3σ v − σ H − pw − Pp ( Along σ H ) 3
σH
x’
© 2005 Baker Hughes Incorporated All rights reserved.
y’
σh
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stresses Around the Borehole
σh
Numerical Example σh = 3500 psi σH = 5000 psi Pw = Pp = 3000 psi
A Pw
θ B
σH
At A: σ’θ = 3(5000) – (3500) – 3000 – 3000 = 5500 psi (+) At B: σ’θ = 3(3500) – (5000) – 3000 – 3000 = -500 psi (-) At A: σ’θ = 5500 psi (compressive) – breakout, shear failure At B: σ’θ = -500 psi (tensile) – hydraulic fracturing
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline I. II. III. IV. V.
Stress distribution around a circular borehole Failure modes and failure criteria Mud weight window Stress polygon Borehole strengthening
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Typical Borehole Failure Modes For a vertical well … If the mud weight becomes excessive, it may induce hydraulic fracturing (tensile failure) of the rock!
σH
tensile failure
Pw Note: These are the most common types of wellbore failure!
© 2005 Baker Hughes Incorporated All rights reserved.
σh
active shear failure
Efficiency….Data accuracy….People-oriented service
If the mud weight is too low, lack of wellbore support could induce rock compressive (active shear) failure!
www.bakeratlasdirect.com
Other Borehole Failure Modes For a vertical well …
If the mud weight becomes excessive, passive shear failure may occur! In most cases, passive shear failure is preceeded by hydraulic fracturing (tensile failure)!
σH
passive shear failure
Pw
Note: The location of spalling may occur anywhere along the wellbore!
σh
© 2005 Baker Hughes Incorporated All rights reserved.
radial tensile failure (σrr = pw – pp ≤ To)
Efficiency….Data accuracy….People-oriented service
If the mud weight is insufficient (resulting in underbalanced situation) and rock permeability is low, radial tensile failure (i.e., spalling or sloughing) may occur! www.bakeratlasdirect.com
Evidence of Borehole Failure resistivity image
acoustic image
STAR Image Borehole Breakout 180º What is the maximum hole deviation that we can use breakout to deduce the stress orientation with some degree of certainty?
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
Breakout direction corresponds to the orientation of σh in a vertical well
www.bakeratlasdirect.com
Shear/Compressive Failure Modes Breakout (onion peeled failure) – Type A σ θ > σ z > σr
σHmax
Toric failure – Type B
σHmin
σ z > σ θ > σr Helical shear failure – Type C σ z > σ r > σθ
© 2005 Baker Hughes Incorporated All rights reserved.
σθ = hoop stress σz = axial stress σr = radial stress
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Shear/Compressive Failure Modes
Wide breakout – commonly called breakout
Shallow knockout – the circumferential coverage is small and could be caused with a vertical fracture
High angle enchelon – makes highangle fractures that cover up to a quarter of the borehole circumference
Narrow breakout – the annular coverage is typically less than 300
σθ > σ z > σ r
σ z > σθ > σ r
σ z > σ r > σθ
σ r > σ z > σθ
Rezmer-Cooper, Bratton and Krabbe (2000) – SPE 59225 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Shear/Compressive Failure Modes
Rezmer-Cooper, Bratton and Krabbe (2000) – SPE 59225 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Shear/Compressive Failure Modes
Low angle enchelon
σθ > σ r > σ z
Deep knockout – occurs in the vertical plane, but is centered at the azimuth of the maximu horizontal stress
σ r > σθ > σ z
Rezmer-Cooper, Bratton and Krabbe (2000) – SPE 59225 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Modes – Breakout - INSUFFICIENT wellbore pressure (lack of support) - big difference between the in-situ stresses - low formation strength
σσθθ(max) = 3σ – σ – P – P (max) = 3σHH – σhh – Pww – PPP
Tangential stress acting at the borehole wall
If σH >> σh , the resultant tangential stress will be very high, which can potentially destabilize the borehole.
22(45°+φ/2) σσθθ(max) = UCS + (P – αP ) tan = UCS + (P w – αP p ) tan (45°+φ/2) (max) w p
Comparison of tangential stress (load) and rock strength Æ M-C failure criterion
From the equations, we can see that raising the mud weight has two beneficial effects: reduce the tangential stress increase the effective strength. These effects (in addition to controlling wellbore trajectory) effectively maintain borehole stability. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Modes – Breakout Compressive strength
Azimuthal Maximum Tangential Stress Distribution Compared with Rock Compressive Strength
σHmax=8000 psi @NS σhmin=6500 psi @EW σv=10000 psi @ Vert Pp = 4600 psi, UCS=8500 psi Mud Weight = 11.0 ppg
180
-175 -165-170 -160 -155 -150 12000 -145 -140 -135 -130 9000 -125
175 170 165
160
155
150 145 140 135 130 125
-120
Borehole Deviation = 0, Azimuth = 0
120
-115
115
6000
-110
110
-105
105 3000
100
Strength
95
drill//sH,Max_Tan Stress
-95 -90
0
90
-85
85
-80
80
-75
10000
-100
75
-70
N
70
-65
65
Compressive -55 stress -50
-60
6500
60 55 50
-45
45 -40
00 80
40 -35
35 -30
-25
-20
-15 -10
-5
5
10 15
20
25
30
0
Borehole Low-Side
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Modes – Breakout Compressive strength
Azimuthal Maximum Tangential Stress Distribution Compared with Rock Compressive Strength
σHmax=8000 psi @NS σhmin=6500 psi @EW σv=10000 psi @ Vert Pp = 4600 psi, UCS=8500 psi Mud Weight = 11.0 ppg
180
-175 -165-170 -160 -155 -150 12000 -145 -140 -135 -130 9000 -125
175 170 165
160
155
150 145 140 135 130 125
-120
Borehole Deviation = 60, Azimuth = 0
120
-115
115
6000
-110
110
-105
105 3000
100
Strength
95
drill//sH,Max_Tan Stress
-95 -90
0
90
-85
85
-80
80
-75
10000
-100
75
-70
N
70
-65 -60 -55 -50 -45
65
Compressive stress
6500
60 55 50 45
-40
00 80
40 -35
35 -30
-25
-20
-15 -10
-5
5
10 15
20
25
30
0
Borehole Low-Side
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Modes – Breakout Azimuthal Maximum Tangential Stress Distribution Compared with Rock Compressive Strength
Compressive strength
σHmax=8000 psi @NS σhmin=6500 psi @EW σv=10000 psi @ Vert Pp = 4600 psi, UCS=8500 psi Mud Weight = 11.0 ppg
180
-175 -165-170 -160 -155 -150 12000 -145 -140 -135 -130 9000 -125
175 170 165
160
155
150 145 140 135 130 125
-120
Borehole Deviation = 90, Azimuth = 0
120
-115
115
6000
-110
110
-105
105 3000
-100
100
Strength
95
drill//sH,Max_Tan Stress
-95 -90
0
90 85
-80
10000
-85
80
-75
75
-70
N
70
-65
65
Compressive stress
-60 -55 -50 -45
6500
60 55 50 45
-40
00 80
40 -35
35 -30
-25
-20
-15 -10
-5
5
10 15
20
25
30
0
Borehole Low-Side
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Modes – Breakout Major breakouts Problems: Ê high volume of solids due to rock spalling/caving Ê poor hole cleaning (more critical in inclined wells) Ê stuck pipe Ê high torque and drag Remedies: Ê increase wellbore fluid density Ê increase the sealing capacity of drilling fluid Ê minimize surge and swab pressure
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Modes – Breakout Small breakouts Problems: minor breakout is a restricted zone of shear failure wellbore is stabilized without experiencing borehole instability related problems the width and direction of breakouts are used for in-situ stress characterization Remedy: use controlled breakout concept to enhance drilling and completion efficiency
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Modes – Controlled Breakout Azimuthal Maximum Tangential Stress Distribution Compared with Rock Compressive Strength no breakout!
180 -175 -165-170 8000 -160 -155 -150 7000 -145 -140 6000 -135 -130 5000 -125 -120
175 170 165
160
180
155
-165-170 -160 -155 -150 -145 -140 -135 -130 -125
150 145 140 135 130 125
-120
120
4000
-115 3000
-105
110 105
2000
-100
100 1000
-95 -90
65
-60
-25
-20
-15 -10
-5
5 0
10 15
20
25
30
105
2000
100 95
85
-85
85
80
-80
80
90
0
-75
75
-70
70
MW = 11 ppg
-65
65
-60
60
-55 -50 -45
45
-30
110
1000
40 35
115
-100
55
-35
120
3000
-105
50 -40
5000 4000
-110
60
-55 -50 -45
145 140 135 130 125
6000
-95
70
MW = 12 ppg
-65
150
-90
75
-70
155
90
-85
-75
160
7000
95
0
-80
175 170 165
-115
115
-110
-175 8000
70° “allowed” breakout!
55 50 45 -40
Confined Strength Max Tang Stress
40 -35
35 -30
-25
-20
-15 -10
-5
5
10 15
20
25
30
0
Lower MW can be used if breakout is allowed to form! NOTE: Due to wellbore cleaning issues, the max. allowable breakout size in deviated boreholes is less than in vertical ones !!! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Shear Failure Criteria σ1 = UCS + σ3 tan 2 ( π4 + φ2 )
Mohr-Coulomb
2 3 sin φ A = Drucker Prager 3 − sin φ J2 =
[
J 2 = A × J1ef + B
1 (σ rr − σθθ )2 + (σθθ − σ zz )2 + (σ zz − σ rr )2 6 + σ 2rθ + σ θ2z + σ 2rz
Modified Lade
]
J1ef =
B=
2 3 cos φ 3 − sin φ
σ rr + σθθ + σ zz − p( r , t ) 3
'' 3 1
I = 27 + η '' I3
I ' '1 = (σ 1 + S1 − p0 ) + (σ 2 + S1 − p0 ) + (σ 3 + S1 − p0 )
I 3 = (σ 1 + S1 − p0 ) ⋅ (σ 2 + S1 − p0 ) ⋅ (σ 3 + S1 − p0 ) p0 : pore pressure S o: Mohr − Coulomb cohesion
© 2005 Baker Hughes Incorporated All rights reserved.
S1 =
S0 , η = 4 tan 2 φ (9 − 7 sin φ )(1 − sin φ ) tan φ
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Shear Failure Criteria Intermediate principle stress has no influence on rock strength
Mohr - Coulomb
Overestimate the effect of intermediate principle stress on rock strength
Drucker - Prager
Less conservative than Mohrcoulomb. More conservative than DruckrPrager (predicts greater strengthening effect from σ2).
© 2005 Baker Hughes Incorporated All rights reserved.
Major Stress, σ1 (psi)
Initial strengthening from increasing σ2, then decrease in strength.
Drucker - Prager
Modified Lade Mohr-Coulomb Intermediate Stress, σ2 (psi)
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effect of Failure Criteria on Critical Mud Weights (CMW) 13
Critical Mud Weight (ppg)
12
Mohr - Coulomb
CMW increases with increasing of inclination due to in-situ stress anisotropy
Modified Lade
11
10 9
Drucker - Prager
8
7 0
10
20
30
40
50
60
70
80
90
M-C predicts highest CMW, DP lowest CMW, and M-L is in the middle at the same inclination.
Well Inclination (degrees)
Ewy - SPE 47251 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Tensile Failure Modes
Cylindrical – concentric with the borehole, and is not visible on a wellbore image
σ r' < 0 Pw − Pp < −to
Horizontal
σ 3' < −to
Vertical
σ 3' < −to
Rezmer-Cooper, Bratton and Krabbe (2000) – SPE 59225 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Modes - Tension • Tensile fracture (vertical) - triggered by excessive wellbore pressure - big issue when having a big difference between the in-situ stresses acting normal to the borehole axis - fracture traces are diametrically opposed - fractures may extend long distances along the wellbore
σσ’’θθmin = 3σ – σ – P – P min = 3σhh – σHH – Pww – PPP
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Failure Modes – Tension … ((ctd.) ctd.) Petal fractures: hydraulically-induced fractures that form ahead of the bit. Normally found in relatively stiff formations; probably caused by a combination of high mud weight and high weight-on-bit. Centerline fractures: Hydraulically-induced features that connect previously formed petal fractures
Hydraulic fractures: Used as a reservoir-stimulation and management method. Could be planned (for stimulation purposes) or accidental (i.e. drilling-induced fractures).
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Evidence of Borehole Failure
Drilling Induced Fractures (hydraulically induced)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Evidence of Borehole Failure IMAGE LOG
CORE PHOTOGRAPH Petal Fracture
Petal Centerline fracture
Breakout © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
180° www.bakeratlasdirect.com
Failure Modes – Tension … ((ctd.) ctd.) Drilling Induced Fractures Problems: Ê lost circulation - sudden loss of drilling fluid Ê similar fluid loss gradient across the field Ê losses occur when breakdown pressure > fracture gradient (fracture propagation pressure) Remedies: Ê decrease wellbore fluid gradient Ê increase the sealing capacity of drilling fluid
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline I. II. III. IV. V.
Stress distribution around a circular borehole Failure modes and failure criteria Mud weight window Stress polygon Borehole strengthening
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mud Weight Window - Definition of Terms )
Fracture initiation pressure is the wellbore pressure above which the initiation of hydraulically-induced fractures will take place.
)
Breakdown pressure is the wellbore pressure at which the formation of major hydraulically-induced fractures is expected to take place.
)
Fracture gradient is the wellbore pressure gradient above which the propagation of pre-existing fractures will take place.
)
Minimum mud weight @ breakout size is the mud weight below which the formation of breakouts of specific size (width in degrees) will take place.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pressure
For Clarification Purposes …
Pbreakdown
T0
Preopening
Ppropagation Frac.Grad. = σ3
time 1st PRESSURE CYCLE © 2005 Baker Hughes Incorporated All rights reserved.
2nd PRESSURE CYCLE Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mud Weight Window SHEAR FAILURE
IDEAL MW
TENSILE FAILURE
REAL LIFE MW
Excessive BO
Minor BO
In-gage hole Minor Losses
Excessive Losses
σ3 σ2
Pw
Pw
Low Pore Pressure © 2005 Baker Hughes Incorporated All rights reserved.
Pw
Pw
Mud Weight Scale
Pw
High
σ3 (magnitude)
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mud Weight Window … (ctd.) SHEAR FAILURE
IDEAL MW
TENSILE FAILURE
REAL LIFE MW
Æ Mud weight range defined by the breakout limit (lower bound) and the fracture propagation limit (upper bound).
Excessive BO
Minor BO
In-gage hole Minor Losses
Excessive Losses
σ3 σ2
Pw
Pw
Low Pore Pressure
Pw
Pw
Mud Weight Scale
Pw
High σ3 (magnitude)
ÆThe breakout limit is the minimum mud weight that could be used without exceeding the maximum allowable breakout size. Also defined by the Pp if the formation is sufficiently strong Æ The fracture propagation limit or fracture gradient is equal to the magnitude of the closure stress (minimum principal stress, σ3) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mud Weight Window … (ctd.) TUNE - Well 30/9-11-H
EMW (sg) 1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2,000
2.9
3
Balder FM
2,200
ROGALAND GRP
Fracture gradient, i.e. σ3
2,400
Mud window
2,600
SHETLAND GRP
2,800
3,000
Pore pressure
Depth, MD (m)
3,200 Viking
3,400
Breakdown Pressure
3,600
3,800 BRENT
4,000
4,200
MW for allowing 0, 30 and 60 degree breakouts
4,400
4,600
4,800
5,000 0
10
20
Pp MW (Breakout =0 deg) MW (Breakout =90 deg)
© 2005 Baker Hughes Incorporated All rights reserved.
30
40
50
FG MW (Breakout =30 deg) Breakdown
60
70
80
90
OBG MW (Breakout =60 deg) Inclination (deg)
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mud Weight Window The curves of pore pressure and fracture gradient are very important as they also define the casing setting depths: 8 0
8
Equivalent mud density (lb/gal) Equivalent mud density (lb/gal) 10 12 14 16 18 10 12 14 16 18
20 20
0
2,000 2,000
Csg. setting depth
4,000 4,000
(Data from Bourgoyne et al., 1991)
Depth (ft) Depth (ft)
6,000 6,000
8,000 8,000
10,000 10,000
Csg. setting depth
12,000 12,000
14,000 14,000
Pp Pp FG PpFG + 0.5 Pp- 0.5 + 0.5 FG FG - 0.5
Target
16,000 16,000
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mud Weight Contour Plot N 45
E
45
45 , 5 4
N 90
90, 90
0 270
90
N
N 0
E
45
E 180
© 2005 Baker Hughes Incorporated All rights reserved.
E
90
Efficiency….Data accuracy….People-oriented service
0, 0
www.bakeratlasdirect.com
Outline I. II. III. IV. V.
Stress distribution around a circular borehole Failure modes and failure criteria Mud weight window Stress polygon Borehole strengthening
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Evidence of Borehole Failure STAR Image - Drilling Induced Fracture (tensile feature) & Breakout (shear failure)
Breakout
Fracture
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Maximum Horizontal Stress (σH)
Stress Polygon
RF
f (μ) =
σh=σH SS
(μ
+1 + μ
)
2
σ1 − pp = f (μ ) σ 3 − pp
NF
Mohr’s Diagram
σv
Stress Polygon Bounding of horizontal stresses through the Frictional Theory. 1 ⎡ 2 ⎤ σ 1 = Co + σ 3 ⎢ χ + 1 2 + χ ⎥ ⎣ ⎦
)
© 2005 Baker Hughes Incorporated All rights reserved.
2
χ = tan φ φ = angle of internal friction
Shear Stress (τ)
Minimum Horizontal Stress (σh)
(
2
n ictio r F μ=
ient c i f f oe al C
Normal Stress (σ)
Co = uniaxial compressive strength
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stress Polygon
Breakdown line: (Tensile failure)
σ H = 3σ h − Po − Pb + To
σ
σ
σ
V >line: H , max > hfailure) , min Breakout (Compressible ⎡ C f + Pw + αPo ⎤ σ h [1 + 2 cos(2ϕ )] − Normal⎥Faulted ( ) [1 − 2 cos(2ϕ )] − 1 2 cos 2 ϕ ⎣ ⎦
σH = ⎢
In-situ stress regime
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stress Polygon
σ H ,max > σ V > σ h ,min Strike-Slip Faulted In-situ stress regime
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stress Polygon
σ H ,max > σ h,min > σ V Reverse or inverse In-situ stress regime
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Coefficient of Friction
Byerlee (1978)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stress Polygon Horizontal Stress Estimation
Maximum horizontal Stress (σH)
Induced fractures (extensional failure)
σ H = 3σ h − Po − Pb + To Breakout (Shear failure) ⎡ C f + Pw + αPo ⎤ σ h [1 + 2 cos(2ϕ )] σH = ⎢ ⎥− ( ) [1 − 2 cos(2ϕ )] − 1 2 cos 2 ϕ ⎣ ⎦
RI RF
RT
σh=σH
RN SS
By superposition of: Frictional theory Extensional failure Shear failure
NF
Knowledge of σh Î LOT, XLOT
σv Minimum Horizontal Stress (σh) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stress Polygon Bounding the horizontal stresses by using stress polygon and failure mechanism. North Sea Case: Breakout Induced Fractures The strength (UCS) of this zone is determined by LMP.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stress Polygon – Constraining the Horizontal Stresses
Pp=0.74 psi/ft Pmud=1.83 sg UCS= 3790 Psi θb=32°
∇σ
h
≅ 0 . 82
UC
© 2005 Baker Hughes Incorporated All rights reserved.
⇒
σ σ
H
= 1 . 17
h
0 psi 9 7 3 S=
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stress Polygon – Horizontal DIF Stress Calibration
DIF and breakout
No stress features
SPE 105808 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline I. II. III. IV. V.
Stress distribution around a circular borehole Failure modes and failure criteria Mud weight window Stress polygon Borehole strengthening
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Implications on a GoM Drilling Program Typical GoM Casing Profile
Including mud heating
frac gradient
“New” frac gradient is expanded due to heating. Therefore, the safe MW window is increased! “old” frac gradient
pore pressure
Requires 5 casing seats to reach TD
© 2005 Baker Hughes Incorporated All rights reserved.
pore pressure
$
$
driller
Requires only 4 casing seats to reach TD
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Borehole Strengthening
) Controlled ) Fracture ) Internal
Breakout
Linking and Plugging
Mud Cake
) Temperature
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Borehole Breakout – Lab Observation
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Borehole Strengthening – Breakout Normalized Strength, σ H/Co
3 2.5 2 1.5 1
Small Blk
0.5 Large Blk 0 Breakout
• Experiments have been conducted to examine “excavation strength” of circular and “broken out” geometry under same stress conditions - Breakout geometry has up to 40% higher strength than a circular geometry.
Circular
Excavation Geometry
Table 1. Strength of Breakout and Circular Excavations (Reference 28) K max K max Co σH σH (MPa) σH Co (MPa) Shape Co BK 1 BK 2 BKavg CR BK CR
Small Blocks (27.9cm × 27.9cm × 27.9cm) 19.24 2.80 >6 19.24 2.76 >6 19.24 2.78 >6 19.24 2.03 2.5 Large Blocks (100cm × 100cm × 105cm) 37.24 19.24 1.94 >6 27.93 19.24 1.45 2.5
53.79 53.10 53.45 38.97
16.80 16.56 16.68 5.06 11.61 3.63
σH - Maximum applied far field stress at on set of excavation failure. Co - Unconfined compressive strength of tested material. Kmax - Maximum stress concentration on each excavation shape. BK - abbreviation for breakout CR – abbreviation for circular geometry © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stress Variations with Breakout x
a
σ1
2 0 .7
b
x
P O IN T a
4 8 .3
S E C T IO N I
x
S E C T IO N II
c
S E C T IO N III x d e x
-6 .9 -3 4 .5
σ3 1
5
P O IN T c
P O IN T b
σ1
4 8 .3
4 8 .3
σ1
x
2 0 .7
x
2 0 .7
σ3
-6 .9
-6 .9
-3 4 .5
-3 4 .5
5
10
5
σ1
7 5 .8
STAGE A
4 8 .3
STAGE B
1
(c )
(d )
σ1
STAG E B x
σ3
-6 .9 -3 4 .5
STAGE B P O IN T d
x
STAGE A
4 8 .3 x
σ3
2 0 .7
© 2005 Baker Hughes Incorporated All rights reserved.
5
(e )
10
x
P O IN T e
-6 .9 1
10
7 5 .8
x
x
2 0 .7
x
σ3 STAGE A
1
10
(b )
(a )
1
5
Efficiency….Data accuracy….People-oriented service
(f)
10
www.bakeratlasdirect.com
Controlled Breakout - Summary Experimental and numerical studies have shown that boreholes with breakout geometry are more stable than circular boreholes, especially in high stress environments. Utilizing breakout concept helps to increase the choice of drilling directions in highly inclined boreholes, decrease mud weights and, hence, reduce formation damage and lost circulation. May need to increase the drilling fluid lifting capacity for effective hole cleaning.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Controlled Breakout - Application Mud MudWeight, Weight,PPG PPG 8.5 8.5
10 10
10.5 10.5
11 11
11.5 11.5
12 12
40 40
50 50
60 60
70 70
12.5 12.5
13 13
Frac-Propagation Frac-Propagation
1200 1200
Breakout=0deg. deg. Breakout=0
1500 1500 1600 1600
BoreholeDeviation Deviation Borehole
1700 1700 1800 1800 1900 1900 2000 2000
TrueVertical VerticalDepth Depth(Sub (SubSea), Sea),meter meter True
1400 1400
Breakout=60deg. deg. Breakout=60
1300 1300
SPE 64620 – Technology Applied to Extend the Drilling Reach of a Platform Workover Rig CADE 2003-005 – Wellbore Stability (Geomechanics) Modeling and Drilling Optimization Practices Reduce Drilling Cost – Terra Nova Project
9.5 9.5
1100 1100
1000 1000
SPE 47282 – Integrated Borehole Stability Analysis – Against Tradition
99
0
0
10 10
20 20
30 30
80 80
90 90
Borehole BoreholeDeviation Deviationfrom fromVertical, Vertical,degree degree
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Borehole Strengthening - Fracture )
Fracture Link-up Pressure •
•
According to Weng [SPE 26597] and Ito et al. [SPE 57007], if multiple fractures are induced, there is a critical pressure, Plink, above which the fractures will link up. If the mud pressure is less than Plink, no serious mud loss will occur.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Borehole Strengthening - Fracture )
Fracture Link-up Pressure •
If
σ norm f σ para →
•
If
σ para f σ norm
ω f = ω crit
Pw = σ norm ( Pw )
−0.72 ⎡ ⎤ − σ σ ⎧ para norm ⎫ −1 = sin ⎢0.57⎨ ⎬ ⎥ ⎢⎣ ⎩ Pw − σ norm ⎭ ⎥⎦
σpara
ωf=fracture inclination angle. Substitute ωf for ωcrit and solve for Pw
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
σnorm
www.bakeratlasdirect.com
Borehole Strengthening - Fracture Fracture Propagating Pressure According to Ito et al. [SPE 57007], after fractures linked up and if the mud pressure is not sufficient to propagate the fracture, no serious mud loss will occur. For plugged penny shape fracture:
•
•
p grow σ minh
1=
p pore σ minh
⎛c ⎞ 1−⎜ 1 ⎟ ⎝c⎠
⎛c ⎞ 1− 1−⎜ 1 ⎟ ⎝c⎠
2
2
4.0 3.5 3.0 P g ro w /σ m in h
)
Ppore/Sminh=0.0
Ppore/Sminh=0.2
Ppore/Sminh=0.4
Ppore/Sminh=0.6
Ppore/Sminh=0.8
Ppore/Sminh=1.0
2.5 2.0 1.5 1.0 0.5
c1 c1
0.0
c
0.7
0.75
0.8
0.85
0.9
0.95
1
c1/c
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Borehole Strengthening - Fracture )
Fracture Propagating Pressure According to Fuh et al. [SPE 24599] and Morita et al. [SPE 20409]: • Fluid leaks off into formation during fracture propagation and mud is concentrated during leak-off. • Dehydrated mud bridges near fracture tip, increases the fracture propagation pressure.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Wellbore “Strengthening” – Stress Cage Imagine the case of a fractured block that is kept loaded between two fixed (i.e. zero displacement) plates Æ constant stress across the rock (along red dotted lines) Now imagine that the fracture is forced (and kept) open Æ The compressive stress magnitude is increased near the edge of the rock where the fracture is. The wider the fracture, the more difficult it becomes to further open the crack In a well, the tangential stress around the borehole will increase; therefore, increasing the closure stress (i.e. the effective fracture gradient) of the formation (Fuh et al., 1992; Alberty and McLean, 2004; Dupriest, 2005)
Zone of increased closure stress (actual shape may differ)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stress Cage – Solution Concept
After Mark Alberty (2005) © 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Wellbore “Strengthening” – Stress Cage … (ctd.) Ê Wellbore initially stable, no
PW
fractures
σC
Ê Fracture is created; as fluid enters the crack, bridging particles and mud cake block the fracture entrance (PW > Pf > σC)
PW
Pf
σC
Ê After blocking has occurred, the fluid within the fracture is leaked off; thus, allowing the fracture to close (PW > Pf ~ σC2) Æ As a final result, the effective closure pressure acting on the rock is increased!!! (σC < σC2) © 2005 Baker Hughes Incorporated All rights reserved.
PW
σC2
Efficiency….Data accuracy….People-oriented service
σC2 www.bakeratlasdirect.com
Wellbore “Strengthening” – Stress Cage … (ctd.) Ê In low permeability rocks, the blocking “bridge” needs to be completely impermeable. Low leak-off WILL NOT reduce the fluid pressure within the fracture; thus, creating the conditions for further fracture extension (VERY UNSUCCESSFUL)
PW
Ê In permeable rocks (k > 1 md), even a partially permeable “bridge” may effectively arrest fracture growth. Leak-off will dissipate any fluid pressure increment in the fracture, reducing the possibility of experiencing additional fracture extension (EXTREMELY SUCCESSFUL)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
PW
www.bakeratlasdirect.com
Wellbore “Strengthening” – Stress cage … (ctd.) Design Procedure (Alberty and McLean, 2004)
Determine the fracture gradient increment goal Based on this goal, and using the rock mechanical properties and in-situ stress, calculate the fracture aperture needed at the borehole (normally a finite elements model is used for this purpose)
Determine particle size distribution and concentration of the solids used for wellbore strengthening. Solids such as calcium carbonate (stress support) and graphite (hydraulic seal) are commonly used.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Wellbore “Strengthening” – Stress cage … (ctd.) Highlights:
8 Very limited success in low permeability rocks (e.g. shales) Æ may be due to time dependent, to early response to loading (Wilson, 2005), and also to low leak-off rates.
8 Extremely successful in permeable (k > 1 md), soft formations 8 Failure to obtain good results in tectonic environments (e.g. strike-slip, inverse)
9 Proven technology in non-tectonic environments (when applied to permeable rocks)
9 Easy design and relatively standard job application
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Internal mud cake – Physical Model
1
2
σθ = σθ + σθ
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
σ r2 = Pw σ θ2 =
Po R22 − Pw R12 R22 − R12
+
(Po − Pw )R22
(R
2 2
− R12
)
www.bakeratlasdirect.com
DS is composed deformable colloidal particles that bridges at the borehole interface of lowpermeability sandstone formations Successful bridging requires proper characterizations of grain and pore throat sizes Under high differential pressure, DS is forced to penetrate into the face of the sand This forced ”packing” together with the deformable characteristics of the sealant provides a better internal mudcake sealing © 2005 Baker Hughes Incorporated All rights reserved.
Depth
Internal mud cake – Deformable Solid
0.1
Efficiency….Data accuracy….People-oriented service
1.0
10.0
100.0
Sand Particle Size microns
www.bakeratlasdirect.com
Internal Mud Cake – Effect of Stiffness Ratio
Tangential stress (psi)
30000 25000 20000 15000 10000 5000 0 0.75
1.00
1.25
1.50
1.75
2.00
2.25
E1/E2
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Borehole Strengthening – Internal Mud Cake
Altering the mechanical characteristics of the near wellbore region. Developing high tangential stresses in the near wellbore region by particulate plugging and bridging. Fracture-resistance enhancement is a function of stiffness contras and pressure differential. Successes in low-perm sands in South Texas: SPE 92266, SPE 103816, Petrotech 1002.
Rw Ri
Pmud Ppore
r © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Wellbore “Strengthening” – Breakdown Pressure Models Idealized near wellbore pore pressure profiles for different geomechanics models (comparison of pressure profile and breakdown pressures, Pbd) Æ from Benaissa et al. (2005) pwb Permeable wall, no cake
Pbd1
pp
pwb
Impermeable wall, external cake
Pbd2
pp rw
r
pwb Impermeable wall, internal cake
pp r w ri
© 2005 Baker Hughes Incorporated All rights reserved.
Pbd3
rw Mud losses
r No losses
Pbd1
r Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Wellbore “Strengthening” – Field Case (South Texas) From Benaissa et al. (2005) Pre s s ure /Stre s s Gradie nt (ppg)
0.0
10.0
20.0
Pressure/Stress Gradient (ppg)
30.0
0.0
6,000
5.0
10.0
25.0
30.0
6,500
8,000
7,000
9,000 7,500
10,000
TVD (ft)
TVD (ft)
20.0
6,000
7,000
11,000
8,000 8,500
12,000
NO
S E S S LO
9,000
13,000
9,500
14,000 15,000
15.0
PP MW sigmh Breakdow n Pres.-Permeable Wall Breakdow n Pres.-Impermeable Wall Breakdow n Pres.-Impermeable Internal Cake
© 2005 Baker Hughes Incorporated All rights reserved.
10,000
PP MW Breakdown Pres.-Permeable Wall Breakdown Pres.-Impermeable Wall Breakdown Pres.-Impermeable Internal Cake
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Borehole Strengthening – Effect of Temperature
Pressure (psi)
Temp Dependant LOT Tests 2900 2700 2500 2300 2100 1900 1700 1500 0
10
20
30
40
50
60
70
Pump Strokes
SPE 87217 © 2005 Baker Hughes Incorporated All rights reserved.
92 F
133 F
153 F
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Special Topics in Wellbore Stability
Outline ÎDrilling
through laminated formation z Drilling in and near salt bodies z Drilling through faults z Drilling through shale z Mud temperature effects on wellbore stability z Cavings analysis
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds Some rocks (mainly shales) show strength anisotropy, i.e. they tend to be “stronger” or “weaker” in a given direction. Thus, the relative angle between the bedding plane and the wellbore axis (also called angle of attack) may define the mechanical behavior of the formation while being drilled (and afterwards too !!!) .
δ
lane p g n i d Bed
Angle of attack
This situation has been found in the field, where previously “stable” formations became troublesome when drilled at lower attack angles (e.g., SPE 1721, 30464, 47285 & 53940).
© 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … ((ctd.) ctd.) Depending upon the reservoir structural geology, the angle of attack (hence, the rock mechanical properties) may change along the well trajectory; even for vertical wells. Two wells with the same trajectory drilled through the same formations, may encounter dramatically different rock mechanical properties.
The same formations may behave differently when reentered at a different angle of attack.
In addition, the in-situ stress field may also change along the reservoir structure… but this point will be covered later. © 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … ((ctd.) ctd.) When wells are drilled near faults (with some degree of folding along the fault) the same situation may occur …
Even vertical wells may be unstable when drilled near a fault.
The same formations may behave differently when reentered at a different angle of attack.
NOTE : It is not uncommon to find that the in-situ stress on each side of the fault is different !!! © 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … ((ctd.) ctd.) Rock Anisotropy: … but how dramatic is the variation in the mechanical properties of the rock as function of the angle between bedding and loading?
β
Laboratory measurements on Green River Shale, Colorado (McLamore and Gray, 1967) Diff. ~ 40%
In this old paper, compression is taken as negative. Thus, the axial (larger) stress is called σ3. © 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … ((ctd.) ctd.) Rock Anisotropy … (ctd.): … likewise, the magnitudes of tensile strength and Young’s modulus also change with orientation …
β
Laboratory measurements on Green River Shale, Colorado (McLamore and Gray, 1967)
Diff. ~ 67%
In this old paper, compression is taken as negative. Thus, the extensional stress is called σ1 throughout a series of Efficiency….Data accuracy….People-oriented service Brazilian tests. All rights reserved. © 2002 Baker Hughes Incorporated
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … ((ctd.) ctd.) Rock Anisotropy … (ctd.): More examples from around the world … Draupne shale, North Sea (Økland and Cook, 1998)
σ c =500 psi
14,000 12,000
Compressive strength (psi) with
10,000 8,000 6,000
Canadian shale
4,000 2,000 0 0
15
30
45
60
75
90
σ 1 orientation relative to bedding (deg)
© 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … stability considerations Stresses around borehole • isotropic and homogeneous • anisotropic and homogeneous Failure criteria (Mohr Coulomb) • weak (bedding) plane • native strength Wellbore trajectory δ • angle of attack
© 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … stability considerations
(Non-laminated)
(Laminated) Økland & Cook proposed a conceptual model consisting of two successive phenomena: 1. The failure criterion for bedding plane slip is met in the corners of the borehole 2. An exposed bedding– parallel sliver in the floor Økland, D., and Cook, J.M.: “Bedding-Related Borehole Instability in High-Angle Wells”, paper SPE 47285 presented at or ceiling of the EUROCK, Trondheim, Norway; 1998. horizontal borehole buckles into the borehole. The beam Upshot: Ignoring anisotropy can be fractures in the middle and breaks off at the detrimental to the stability of the borehole. endpoints.
SPE 53940 © 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … stability considerations …stability
Models of roof behavior in horizontally layered rock. (a) and (b) show the deflection and cracking in the case of a thinner beam beneath a thicker beam. (c) and (d) show the deflection and failure in the opposite case – thick beneath thin. (after Goodman 1989). © 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … stability considerations …stability Critical Mud Weigh, ppg
12 11.5 11 10.5 10 9.5 9 0
10
20
30
40
50
60
70
80
90
Attack Angles, degrees
“Both field experience and laboratory evidence …indicate that hole instability … is not a problem when drilling normal to bedding, or even parallel to bedding, but becomes very serious when the hole is … nearly parallel to bedding.” Oakland and Cook, 1998 © 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … stability considerations …stability
Critical Mud Weight, ppg
12.5 12 11.5 11 down-dip up-dip
10.5
Cross-dip
10 0
10
20
30
40
50
60
70
80
90
Inclination, degrees
“up-dip well are predicted to be stable with mud weights of around 11.5 ppg….” (Willson et al., 1999, P.4) © 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … stability considerations …stability
SPE 79846 © 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … stability considerations …stability 18
Crossdip
Minimum MW (ppg)
17
16
15
Downdip 14
13
0
30
45
66
12
Updip 11 0
30
60
Bedding Plane Dip = 70o Bedding Plane Dip Direction = 1250
© 2002 Baker Hughes Incorporated All rights reserved.
90
120
150
180
210
240
270
300
330
360
Wellbore Azimuth (degrees)
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … stability considerations …stability
Isotropic Strength
© 2002 Baker Hughes Incorporated All rights reserved.
Anisotropic Strength
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … stability considerations …stability Combined isotropic and anisotropic strength models, considering only the critical mud weights for initiation of shear failure mode (MohrCoulomb failure criterion).
TVD, ft 8239 BIOT 0.95
OBG, psi/ft 1.1 COHE, psi 1000
SHG, psi/ft
ShG, psi/ft
1.04 FRIC, deg
PPG, psi/ft 0.95
COHEW, psi
35.49
© 2002 Baker Hughes Incorporated All rights reserved.
20
SH DIR., deg
0.51 FRICW, deg 20
45 DIP DIR., deg 125
POIS 0.19 DIP, deg 70
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … ((ctd.) ctd.) Stress Perturbation : • The presence of geological structures (e.g. folds, faults, etc.) may create local alterations of the far-field in-situ stress, i.e. the stress field near faults / folds may be different from the regional in-situ stress field. In-situ stress field at the bottom of the syncline
Far-field insitu stress
In-situ stress field at the top of the anticline … Image redrawn from Billings (1956) © 2002 Baker Hughes Incorporated All rights reserved.
Not necessarily equal
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … ((ctd.) ctd.) Stress Perturbation … (ctd.): Zone where tensile stress appears as a consequence of folding (plastic rock Æ layer thinning due to deformation)
Zone where additional compressive stress occurs as a consequence of folding (plastic rock Æ layer thickening due to deformation)
If the formations are brittle (i.e. no plastic deformation occurs before failure) … Æ Tension fractures or small gravity faults might form on the convex side, while small thrust faults form on the concave side
Æ Under certain interlayer friction conditions, the rocks on the concave side may be crumpled
… Images redrawn from Billings (1956) © 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … ((ctd.) ctd.) Stress Perturbation … (ctd.):
Depth
rigid layer low stiffness layer
Vertical Stress/γZ
anticline
syncline
ρgh
The rigid formation holds most of the overburden load and directs the load down the limb of the fold. On the other hand, the low stiffness layer cannot sustain the same amount of loading (see AA’ and BB’)
(Modified from Goodman, 1989) © 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … ((ctd.) ctd.) Stress Perturbation … (ctd.): Before a fault is created, both blocks are affected by the same stress field. However, during fault displacement, one of the fault blocks moves; releasing strain energy (i.e. decreasing its stress). On the other hand, the stress in the “static” block remains unchanged.
Fault
“Static” block affected by the pre-faulting stress field
“Moving” block, releases some strain energy thereby decreasing its stress magnitude
IMPORTANT !!! Æ A well being drilled across a fault may encounter a dramatically different stress fields on each side of it (therefore avoid extrapolating stress magnitudes/directions across faults). © 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through highly -inclined highly-inclined beds … ((ctd.) ctd.) Main issues: • Rock mechanical anisotropy (mainly in shales) due to the fact that beds are drilled by using a wide range of attack angles. The same bed may be re-entered at different attack angles, even by the same well. • As highly inclined beds are associated with geological structures such as folds and faults, there is a potential for finding local stress perturbation. These stress alterations may occur near faults and across folding structures. • Given the occurrence of stress perturbation, it is NOT recommended to extrapolate neither the direction nor the magnitude of the stress field across faults. The same situation occurs for wells located at different locations within a folding structure. © 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline Drilling through laminated formation ÎDrilling in and near salt bodies z Drilling through faults z Drilling through shale z Mud temperature effects on wellbore stability z Cavings analysis z
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Characteristics of Salt ¾
Salt is highly soluble and may be chemically sensitive to the water phase of drilling mud Ö Hole enlargement may occur Ö Insoluble layers (typically carbonates or anhydrite) may result in the formation of ledges Ö Dissolved salts in the mud affect efficiency of polymers, flocculates fresh water muds (creating a viscosity increase and subsequent hole cleaning issues), reduces filter cake quality and results in an overall increase in torque and drag
¾
Salt is a viscoplastic substance
Ö Salt cannot tolerate shear stress (i.e., σ1 = σ2 = σ3 = σsalt ~ σv) and will creep (deform) indefinitely with time until deviatoric stresses vanish
¾
Salt has a high thermal conductivity Ö Temperature gradients between rock and drilling mud may result in thermallyactivated creep.
¾
Pure salt is nearly impermeable (k < 10-10 Darcy’s) Ö Pore pressure effects are negligible within salt
¾
Salt intrusions increase the geological complexity Ö Significant alterations of the stress/PP fields in the vicinity of salt structures
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Salt Behavior During Lab Testing
Shear stress [τ]
At low temperature conditions Salt behaves in brittle manner like transition zone Salt behaves in plastic manner most other rocks at high stress, σ at low stress, σ φ ~ 0º
NOTE: Salt creep is the dominant mechanism of wellbore instability during drilling!
φ ~35º
σ′3
Co ~ 1000psi
σ′1
Normal stress [σ′] To ~ 200 psi
UCS
© 2005 Baker Hughes Incorporated All rights reserved.
Upshot: as σ increases, the salt behaves plastically!
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Creep Test Results: Metal vs Salt Strain
Metal will eventually rupture! Tertiary creep Secondary creep
Primary creep
NOTE: difference in behavior is usually attributed to: small salt porosity, solution- Salt does not rupture precipitation within the pore spaces, etc. (creeps indefinitely)! Metal Salt
elastic strain
Time © 2005 Baker Hughes Incorporated All rights reserved.
Upshot: salt behavior upon loading is very complex!
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Salt Creep Calculation In practice, it is common to employ the following simple creep law (Carter & Hansen, 1983): −n
ε salt = Aσ ⋅ e
−B
T Thermal effects
Effect of stresses
These are the most important factors affecting salt creep!
where σ is the deviatoric stress, A is a salt constant, B is a temperature exponent, n is the stress exponent and T is temperature. Temperature (T) Salt Constant (A) Degree F psi-1 sec-1 200 9.58E-14 250 1.15E-13 300 1.52E-13 350 1.33E-13 400 1.81E-13 450 1.82E-13
Temperature Exponent (B) degree K 8000 8000 8000 8000 8000 6000
Stress Exponent (n) 4.5 4.4 4.4 4.5 4.9 5.5
Data from Barker et al. 1992 for U.S. Gulf Coast salt formations © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Common Drilling Problems in Salt BHA stuck on ledges while POOH or RIH
BHA squeezed while POOH
solution washout Salt creep
BHA stuck while RIH due to washout
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
BHA squeezed while RIH after tripping www.bakeratlasdirect.com
Warning Signs of Drilling Salt The presence of salt across the shakers A lack of cuttings (indicating salt is dissolving into the mud) An increase in the chloride concentration in the mud An increase in the rate of penetration Increasing torque and drag (hole closure)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Overburden Stress near Salt Diapirs far-field well
tangent well
Vertical Stress
center well
Depth
σv increases at the flank of the salt.
bed dip angles ~70-80º
target
σv is reduced within the salt (stresses become isotropic!). bed dip angles ~30º
Tangent
Upshot: σv stress arching occurs along with a possible rotation (deviation from vertical) of the overburden stress along the flanks of the salt. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
Center
Far Field
Data taken from Fredrich et. al. 2003
www.bakeratlasdirect.com
Horizontal Stress near Salt Diapirs Horizontal Stress
far-field well
tangent well
center well
Depth
σh increases in the salt to ensure stress isotropy
σh is slightly reduced at the at the flank of the salt.
Upshot: σh increases within the salt to reach equilibrium with the vertical stress. σh is reduced at the flank of the salt. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
Tangent
Center
Far Field
Data taken from Fredrich et. al. 2003
www.bakeratlasdirect.com
Shear (von Mises Mises)) Stress near Salt Diapirs σ VM =
far-field well
[
1 (σ1 − σ 2 )2 + (σ 2 − σ 3 )2 + (σ1 − σ 3 )2 2 tangent well center well
]
von Mises Stress
Depth
σVM increases substantially at the flank of the salt.
σVM is zero within the salt.
Upshot: σVM stress increases substantially along the flanks of the salt. σVM is zero within the salt (salt cannot tolerate shear stress). © 2005 Baker Hughes Incorporated All rights reserved.
Data taken from Fredrich et. al. 2003
Efficiency….Data accuracy….People-oriented service
Tangent
Center
Far Field
www.bakeratlasdirect.com
Stress Directions Near Diapir
σh
Salt
σH
Stress directions around the salt dome are deflected due to the presence of the salt! (after Dusseault, 2003) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Overburden Stress near Salt Sheets far-field well
tangent well
center well Tangent
Center
Far Field
Vertical Stress
σv increases at the flank of the salt.
~2000 m Depth
Salt sheet
σv is unaltered within the salt.
Upshot: Some small stress arching occurs along the flanks of the salt. σv is not altered within the salt sheet. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
Data taken from Fredrich et. al. 2003
www.bakeratlasdirect.com
Horizontal Stress near Salt Sheets Tangent
far-field well
center well
tangent well
Center
Far Field
Horizontal Stress
Salt sheet
~2000 m
Depth
σh increases in the salt to ensure stress isotropy
Upshot: σh increases dramatically within the salt sheet (since σv does not decrease to create stress isotropy). Data taken from Fredrich et. al. 2003 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Shear Stress Near Salt Sheets Tangent
Center
Far Field
von Mises Stress
tangent well
center well
Salt sheet
~2000 m
Depth
far-field well
σVM is zero within the salt.
Upshot: σVM stress increases substantially along the flanks of the salt. σVM is zero within the salt sheet (as is the case for the salt diapir). © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
Data taken from Fredrich et. al. 2003
www.bakeratlasdirect.com
Potential Through Through-- and Near Salt Geomechanical Hazards
Ref.: Wilson and Fredrich (2005) - SPE 95621 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling Through vs. Around Salt Drilling Through Salt Pro's Allows use of a central platform.
Con's
Drilling Around (close to) Salt Pro's
Con's Rocks near salt bodies are under the More cost effective than Shallow gas hazards are often encountered. influence of complex & elevated stress, drilling through salt. resulting in many drilling difficulties. Sour gas often encountered directly below Uncertainty in salt body shape may lead cap rock (e.g., anhydrite). This requires use to accidental drilling into the salt. of sour grade casing. High MW needed to control salt mechanics. Highly dipping formations near the flanks This necessitates the need to set casing of the salt result in anisotropic upon exiting the salt. mechanical failure. Careful monitoring of mud chemistry is May require several platforms to access crucial to mitigate salt dissolution. all HC pools. PP and fracturing pressure are often Directional control can be difficult in salt. unknown just above and below the salt. The formation of ledges within the salt may result in stuck pipes/wellbore obstructions. PP and fracturing pressure are often unknown just above and below the salt. Rubble zones are often encountered prior to entry into salt and upon exit out of salt. Temperature control is needed so that static temp does not exceed 200 deg F (excessive salt creep initiation). Under-reaming is often necessary. Cementing is often difficult in salt due to hole rugosity, cement contamination, etc. Specially designed casing must be used. Is usually more costly relative to drilling next to salts method.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline Drilling through laminated formation z Drilling in and near salt bodies ÎDrilling through faults z Drilling through shale z Mud temperature effects on wellbore stability z Cavings analysis z
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling Through Faults Rubble Zone: The region near a fault in which the rock has experienced brittle failure resulting in many fragmented (brecciated) rock pieces. If the rock fragments are cemented, the fractures are impermeable (and vice versa).
Formations are also thinned and dragged near the fault (leading to a bed dip change). Rubble zone occurs in the vicinity of the fault! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling Through Faults A vertical well will intersect more rubble zone as well as intersecting the tilted formation at a low angle of attack. Therefore the well will be more susceptible to instability!
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling Through Faults Many wellpaths are designed to intersect the fault normally (~90º). The well does not intersect as much rubble zone and increases the angle of attack. This tends to increase the stability of the well in the vicinity of the fault!
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Fault Reactivation
¾ If the fault is permeable, the effective normal stress acting on the fault will be reduced due to fluid infiltration (causing slippage along the fault) ¾ lubricating effects by drilling fluid infiltration may also cause slippage along the fault ¾ leads to stuck pipe, excessive reaming, high torque and drag, etc. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stress Rotation Near Faults The orientation of the principal stresses is deflected by the presence of a pre-existing fault!
from Bell (1990)
Upshot: optimum drilling direction may change near the fault! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Location of the Cusiana field
Angle between vertical and σ1 direction
Stress Rotation Near Faults Faults-Cusiana Field Example σ1 is horizontal
(foot wall)
σ1 direction becomes vertical!
σ1 is vertical on the footwall side of the fault.
(hanging wall)
Horizontal distance along top of reservoir
Cross-section of the Cusiana field from Charlez et al., 1998. © 2005 Baker Hughes Incorporated All rights reserved.
Upshot: stress rotation occurs near the fault!
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Fractured ((Rubbelized) Rubbelized) Zones If the fractures are impermeable… Fragmented (rubbelized) rock mass near a fault.
If the fractures are permeable… de-stabilized block
wellbore
Increasing MW will provide additional support to the wellbore (in terms of collapse) © 2005 Baker Hughes Incorporated All rights reserved.
wellbore
Increasing MW will increase instability as the fluid penetrates the fractures reducing the confining pressure effect and allowing the block to fall into the well
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Problems Drilling Through Faults Faults-- Summary Stress rotations are possible in the vicinity of faults Ö The optimum drilling direction may be rotated relative to far field optimum direction
Damage (rubbelized) zones may be present near the fault Ö Rubbelized rock fragments with cohesion will be stabilized by increasing the MW Ö Rubbelized rock fragments without cohesion are permeable and therefore increasing MW tends to de-stabilize the wellbore Ö Naturally fissile rock (i.e., thinly bedded shale) is particularly susceptible to being rubbelized due to faulting Ö It is desirable to intersect the fault plane at a right angle to minimize the length of drilled section through the damage zone (to reduce WBS incidences)
Bedding dip direction and angles (due to bedding deformation) may change in the vicinity of the fault Ö Fault drag causes formation dips and angles to change Ö Failure along weak planes may occur as the wellbore becomes sub-parallel to bedding planes.
Fault reactivation Ö Fluid penetration into the fault may allow movement along the fault plane resulting in stuck pipe, excessive reaming, high torque and drag, etc. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline Drilling through laminated formation z Drilling in and near salt bodies z Drilling through faults ÎDrilling through shale z Mud temperature effects on wellbore stability z Cavings analysis z
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through shales Some characteristics of shale formations: ¾
Lamination
strength anisotropy (previously discussed)
¾
Clay content
¾
Extremely low permeability
¾
In tectonic environments
reactive - swelling, weakening pore pressure storage micro-fractured
Due to these unique characteristics, shale tends to be more susceptible to failures and accounts for about 75% of borehole instability problems.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Driving Forces At Shale/Drilling Mud Interface NOTE: One or all of these potentials may exist at a given moment in the subsurface. For low perm rocks, the chemical and thermal gradients tend to dominate. ¾ Hydraulic
gradient ¾ Electro-chemical gradient ¾ Thermal gradient
µwsh µwm Tw
where po
= far-field pore pressure
pw
= wellbore pressure
µwsh
= water activity of shale pore fluid
µwm
= water activity of drilling mud
Tf
= formation temperature
Tw
= drilling fluid temperature
© 2005 Baker Hughes Incorporated All rights reserved.
pw
po
Tf
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Swelling Properties - Pierre I Shale after Exposure into NaCl Solutions awshale = 0.98
0.7
aw=1 Deioned water aw=0.95 NaCl aw=0.85 NaCl aw=0.75 NaCl
0.6
Swelling Percentage (%)
Additional swelling occurs via chemical osmosis for the case of deioned water (aw=1 > awshale)
0.5 chemical osmosis
Causal Mechanisms
0.4 0.3
1.
0.2
De-watering occurs after capillary effects due to chemical osmosis (if aw NaCl < awshale)
0.1 0 capillary effects
2.
Capillary action acts quickly resulting in most of the total swelling within minutes After capillary action, chemical osmosis affects swelling secondarily
-0.1 1 from Zhang et al., 2004
© 2005 Baker Hughes Incorporated All rights reserved.
10
100
Time, Minutes
1000
10000
NOTE: Pierre 1 shale is retrieved from a surface outcrop!
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Swelling Behavior - Pierre I Shale Immersed into Simulated Pore Fluid
Swelling Percentage (%)
0.5
0.4
NOTE: This slide illustrates the effects of capillary pressure only!
0.3
0.2
Most swelling occurs as a result of capillary effects!
0.1
0 1 from Zhang et al., 2004
© 2005 Baker Hughes Incorporated All rights reserved.
10
100
1000
10000
T im e, M inutes Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Corrected Swelling Behavior - Pierre I Shale Immersed into NaCl Solutions 0.1
Swelling Percentage (%)
0
Ion movement
-0.1
NOTE: This slide illustrates the effects of chemical osmosis only (i.e., capillary effects have been removed)!
-0.2 -0.3 water movement
-0.4
aw=1 Deioned water aw=0.95 NaCl aw=0.85 NaCl aw=0.75 NaCl
-0.5 -0.6 1 from Zhang et al., 2004
© 2005 Baker Hughes Incorporated All rights reserved.
10
100
1000
10000
Time, Minutes Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effects of Water Activity on Strength of Pierre I Shale Deviatoric Strength, psi
10000 9000
De-watering of the shale leads to an increase in the compressive strength of the shale!
8000 7000 6000
NaCl CaCl2 KCl
5000 4000 0.75
0.8
from Zhang (2005)
© 2005 Baker Hughes Incorporated All rights reserved.
Native Shale
0.85
0.9
0.95
1
Water Activity
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effects of Water and Ions Movements z
The flux of water into shale: - Increases pore pressure - Alters the shale’s strength (Chenevert, 1970) - Shale swelling (Chenevert, 1970)
z
The exchange of ions: - changes the ionic concentration of pore fluid, which could affect the shale matrix mechanical properties and could result in cohesion degradation and cementing bonds weakening and thus reduces the overall rock strength (Ghassemi et. al. (2001), Fam and Dusseault (1998).
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
FORMATION PRESSURE (psi)
Chemical Instability – Pore Pressure Penetration 150 140 130 120 110 100 90 80 70 60 50 40 30 20
BOREHOLE: 195 PSI CONFINING: 315 PSI TEMPERATURE: 158F (70C) CORE: PIERRE II (E Bedding)
2% Sea salt 20% KCl, Neat
20% KCl non-Cloud Point Gylcol
Pmud-Ppore = 125 psi 20% KCl Cloud Point Gylcol
20% NaCl PHPA
Aluminum Chemistry PHPA, freshwater
Aluminum Chemistry PHPA, 20% NaCl 0
10
© 2005 Baker Hughes Incorporated All rights reserved.
20 30 40 50 HOURS
60
70
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Pressure Profiles Pore pressure caused by hydraulic and chemical potentials can be Pp(Lomba nRT K II ∂Cs K I et al., calculated∂as 2 2000):
∂t
−
cf
∇ P−
D eff c f
∂t
=0
Pp = Pore pressure [=] m/L-t2 KI = A parameter related to permeability [=] L3-t/m
n
= Number of molars of constituent of dissociating solute [=] amount R = Ideal gas constant [=] m-L2/t2-amount-T
T = Formation temperature [=] T K II = A parameter related to membrane efficiency [=] L3-t/m
Cs = Pore fluid solute concentration [=] mol/L3 D eff = Effective solute diffusion coefficient [=] L2/t
cf
= Fluid compressibility [=] t/m
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Pressure Distribution As A Function of Time ((σ σHH ≠ σhh) Due To Chemical Osmosis Typical GoM shale, k = 10-9 Darcy, considering only chemical effects
Osmotically-Induced Pore Pressure, MPa
4.0 3.5 t = 10 days t = 1 day
3.0
t = 0.1 day t = 0.001 day
2.5 2.0
μwmud - μwshale = 0.2
1.5 1.0 0.5 0 1
2
Borehole wall © 2005 Baker Hughes Incorporated All rights reserved.
3
4
5
6
7
8
9
10
from Wolfe (2002) r/a Efficiency….Data accuracy….People-oriented service www.bakeratlasdirect.com
Pore Pressure in shales Due to the extremely low permeability, shale tends to have higher pore pressure. This high pore pressure can be attributed to: • depositional environments (native pressure) • pore pressure transmission (osmotic / hydraulic effects) • stress/mechanical loading (poro-elastic effect) • thermal potential
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Pressure Distribution Around A Vertical Well As A Function of Time ((σ σHH ≠ σhh) 15
15
At the instant of drilling (t=0.001 day), there is a pressure increase inside the rock (near the wall).
Pore Pressure ( MPa )
14
13
14
13 t = 1 day t = 0.1 day
12
t = 0.001 day
11
θ = 90°
12 11 Far-field pore pressure 10
pw = 14 MPa
10
9 1
2
Borehole wall
3
4
5
6
7
8
9
9 10
r/a
Upshot: failure may be initiated inside the rock! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Pressure Distribution Around A Vertical Well As A Function of Time ((σ σHH ≠ σhh) Typical GoM shale, k = 10-9 Darcy, no chemical or thermal effects, in the direction of σH 14 θ = 0°
pw = 14 MPa
Pore pressure ( MPa )
12
10
Just after drilling (t=0.001 day), there is a pressure decrease inside the rock (near the wall).
Far-field pore pressure
t = 1 day
8
t = 0.1 day t = 0.001 day
6 1
Borehole wall © 2005 Baker Hughes Incorporated All rights reserved.
2
3 r/a
4
5
from Wolfe (2002) Efficiency….Data accuracy….People-oriented service www.bakeratlasdirect.com
Pore Pressure Distribution Around A Vertical Wellbore ((σ σ H ≠ σ h) Typical GoM shale, k = 10-9 Darcy, t = 0.001 day, no chemical or thermal effects circumferential flow develops at small time
0
15
330
30 14
mud pressure
wellbore 300
13
60
12
σh
11 270
90 10
far-field pore pressure 9 240
120
8 7
150
210
PP in region of low compressive stress from Wolfe (2002) © 2005 Baker Hughes Incorporated All rights reserved.
180
σH
PP in region of high compressive stress
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Pressure Distribution Around A Vertical Wellbore ((σ σ H ≠ σ h) Typical GoM shale, k = 10-9 Darcy, t = 10 days, no chemical or thermal effects 0
As time passes, the pore pressure distribution becomes symmetric!
14.5
30
330
14
300
60
mud pressure
13.5 13
σh
270
90
12.5 12 11.5
240
120 11 210
150 180
from Wolfe (2002) © 2005 Baker Hughes Incorporated All rights reserved.
σH
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through shales The rise in pore pressure has three detrimental effects: loss of mud hydrostatic support fracturing of formation decrease the effective normal stress (fissile shale)
Loss of mud hydrostatic support: From the equations below, although the increase in pore pressure will tend to decrease the effective tangential stress, the reduction of effective strength is more pronounced. This is particularly true in cases where there is a substantial decrease in UCS due to strength degradation and/or when the internal friction angle is high.
σ θθ' = 3σ H − σ h − Pw − αPp C f = UCS + ( Pw − αPp ) tan (45 + 2
© 2005 Baker Hughes Incorporated All rights reserved.
0
β 2
)
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling through shales Formation Fracturing When the pore pressure in shale has risen to a level where the difference between the mud weight and pore pressure exceeds the tensile strength, radial fracturing will take place resulting in splintery cavings.
Pw − αPp = −to
Pw
rock chip
excessive pressure gradient (Pp>Pw) causes sloughing shale
wellbore
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Reduction of Effective Normal Stress – Fissile Shale
Shear Stress
Drilling through shales f ailu re line
cri ti cally s tress ed fract ure
n on -critically str essed fr actur e
In fissile shale, when fluid penetration has taken place, the reduction in effective normal stress as well the lubricating effect of infiltrated drilling fluid tend to promote weak plane slippage.
© 2005 Baker Hughes Incorporated All rights reserved.
σ 3’
σ1 ’
Norm al Stress
σn’ = σn - Po τcritical = μσn’
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling Through Shale
fractured (rubbelized) zones/micro-fractured shale
If the fractures are impermeable… Fragmented (rubbelized) rock mass near a fault.
If the fractures are permeable… de-stabilized block
wellbore
Increasing MW will provide additional support to the wellbore (in terms of collapse)
© 2005 Baker Hughes Incorporated All rights reserved.
wellbore
Increasing MW will increase instability as the fluid penetrates the fractures reducing the confining pressure effect and allowing the block to fall into the well
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling Through Shale
fractured (rubbelized) zones/micro-fractured shale Contrarily to conventional treatment of borehole instability, increasing mud weight when drilling through micro-fractured formations has two detrimental effects: Fluid penetration promoted by high mud weight reduces the mud hydrostatic support thus decreases the formation bulk strength Fluid penetration also provide lubrication to the fractured surfaces The key to successful drilling in microfractured (and fissile) shale is therefore to minimize fluid penetration or pressure transmission. This can be achieved by either decreasing the drilling fluid gradient or eliminating fluid loss by creating an impermeable internal mud cake. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling Through Shale pore pressure rise
The key to maintain borehole stability when drilling through shale is to minimize pore pressure rise. This can be achieved by controlling pore pressure transmission (including fluid penetration), avoiding abrupt mechanical loading and limiting formation heating. For high native pore pressure, increase the mud weight is effective in controlling splintery or ‘popping’ shale phenomenon. It is interesting to note that high (native) pore pressure shale and fluid filled microfractured shale has similar acoustic responses, however, the treatment for borehole stability problems is different! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Alternating Sand-Shale Sequences Typically, losses and tight hole occur in the sandier units while wellbore enlargements occur in the shalier units. Plausible reasons are: stresses in shale are higher (lithology - Poisson’s ratio) shale tends to have higher pore pressure (native or induced) the bulk strength of shale may have been reduced by microfracturing (and further reduced by fluid infiltration) shale is laminated (fissile) and possesses weak planes chemical effects may have weakened the inherent strength (reactive) …………. The key to successful drilling in alternating sand-shale sequences is to design a mud system that will not (create and) propagate the fractures in the sands, but this mud weight could be too low to completely eliminate breakouts. This can be achieved by utilizing the concept of borehole strengthening. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline Drilling through laminated formation z Drilling in and near salt bodies z Drilling through faults z Drilling through shale ÎMud temperature effects on wellbore stability z Cavings analysis z
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Temperature Effects on Borehole Consider a hollow cylinder (i.e., rock) with no porosity (φ = 0) at temperature (Tr) filled with a fluid at temperature (Tf).
Tf
Tr
Tf ≠ Tr
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Temperature Effects on Borehole Cont ’d Cont’d If Tf > Tr (i.e., wellbore heating)
Tr
σh
Tf
•
Higher borehole temperatures (from hot drilling fluid) will cause the rock to try to expand.
shear failure (breakouts)
•
The rock (downhole) cannot expand outward (due to confining effect of surrounding rock) or radially (due to the wellbore fluid pressure).
•
This leads to a higher tangential stress, which will increase the rock’s resistance to hydraulic fracturing but also increase the potential for shear failure (breakouts).
Tf
If Tf < Tr (i.e., wellbore cooling)
Tr
σh hyd. frac.
© 2005 Baker Hughes Incorporated All rights reserved.
•
Lower borehole temperatures (from cool drilling fluid) will cause the rock to try to shrink.
•
This leads to a reduction in the tangential stress, which will increase the propensity of hydraulic fracturing as well as reduce the potential for shear failure.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Cooling Effects on Borehole Example ~ 1050 psi tensile stress develops on the wellbore wall during circulation! circulating
Gradual cooling due to circulation leads to additional tensile stress
© 2005 Baker Hughes Incorporated All rights reserved.
tensile stress is reduced upon stopping circulation! not circulating
Gradual heating (from contact with hot rocks) as circulation is ceased reduces the tensile stress
from Tang and Lou (1998- SPE 39505) Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Production Field Data This chart shows how the injection pressure dropped 400 psi (on a fractured water disposal well) when the temperature dropped 17º F!
Perkins and Gonzalez (1981) also noted that injecting large volumes of cool fluid during the hydraulic fracturing process can greatly reduce the fracturing pressure!
from Schmidt et al. (1999- SPE 52738) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mud Heating Effects on LOTGoM Example
Instances of cooling exactly coincided with the occurrence of mud losses (i.e., hydraulic fracturing)!
from Gonzalez et al. (2004- SPE 87217) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Thermally -induced Pore Pressure Distribution Thermally-induced in Low Permeability, Porous Media Typical GoM shale, k = 10-9 Darcy, permeable wall, considering only heat conduction
Thermally-Induced Pore Pressure ( MPa )
This10 extreme pressure pulse can lead to spalling (i.e., circumferential tensile failure).
t = 10 days t = 1 day
8
t = 0.1 day t = 0.001 day
Heating combined with low permeability leads to the generation of a pressure wave that migrates into the formation with time! ΔT = +50°C
6
4
NOTE: This type of behavior is absent in high permeability rock because the pore pressure can diffuse instantaneously. In low permeability rocks, this requires that the entire region near the wellbore be analyzed for failure (i.e., not just the wellbore wall)!
2
0 1
Borehole wall © 2005 Baker Hughes Incorporated All rights reserved.
2
3
4
5
from Wolfe (2002) r/a Efficiency….Data accuracy….People-oriented service www.bakeratlasdirect.com
Thermal Effects on Safe MW Window Thermal loading affects breakdown pressure more than the collapse pressure! Typical GoM shale, k = 10-9 Darcy, permeable wall, normal stress environment σv from Yu et al. (2001) from Yu et al. (2001)
σH σh
Heating increases both the collapse and breakdown pressure whereas cooling leads to a reduction in collapse and breakdown pressure! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Thermal Effects on Safe MW Window Typical GoM shale, k = 10-9 Darcy, permeable wall, normal stress environment Collapse Stress Fracturing Stress
collapse
stable
stable fracture Cooling reduces the collapse pressure instantaneously. However, with time the potential for collapse increases. Heating produces the opposite effect. figures taken from Li et al. (1996) © 2005 Baker Hughes Incorporated All rights reserved.
Both heating and cooling reduces the fracture pressure instantaneously (here the stresses are evaluated inside the rock too). However, with time the potential for fracturing drastically decreases while heating but further increases while cooling.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Thermal & Time Effects on Safe MW Window Typical GoM shale, k = 10-9 Darcy, permeable wall, strike-slip environment, r 3000
2500
3000
Dashed lines represent small time (t = 0.001 day), Solid lines represent large time (t = 1 day)
Heating (or 2500 cooling) shifts the MW window
ΔT = +50°C
tensile failure
ΔT = -50°C
=a
Mud Weight, Kg/m
3
ΔT = 0°C
2000
2000
1500
1500
σv
Safe Operating Zone
Heating instantaneously increases the potential for collapse, which reduces with time.
1000
500 active shear failure
0 Cooling is initially beneficial 0 10 in terms of collapse but20 with time the benefits are reduced! © 2005 Baker Hughes Incorporated All rights reserved.
30
40
50
60
70
Borehole Inclination, β°
Efficiency….Data accuracy….People-oriented service
80
1000
500
σH 0 90
σh from Wolfe (2002)
www.bakeratlasdirect.com
Summary of Thermal Effects
permeable rock (thermoelastic)
low permeable rock (porothermoelastic)
Heating
Heating causes additional compressive stresses to develop in the rock. This increases the potential for shear failure but restricts the development of hydraulic fractures. Since pore pressure build up does not occur due to high permeability, time importance is lessened.
Heating yields an instantaneous increase in shear failure potential due to substantial pore pressure buildup inside the rock as a result of the differences between the thermal expansion coefficient of the rock and pore fluid. The pressure build up is short-lived and the potential for shear failure gradually decreases with time. Heating also greatly reduces the fracturing pressure due to a significant pore pressure build-up inside the rock.
Cooling
Cooling creates tensile stresses and therefore hydraulic fracturing is more likely (shear failure potential is simultaneously reduced). Pore pressure diffusion effects are irrelevant due to high permeability of the rock.
Cooling instantaneously reduces the breakdown pressure, which increases with time. It also quickly reduces the potential for shear failure, which will gradually increase with time.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline Drilling through laminated formation z Drilling in and near salt bodies z Drilling through faults z Drilling through shale z Mud temperature effects on wellbore stability ÎCavings analysis z
© 2000 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Cavings Analysis Cavings analysis can provide information on: ¾ The mode of wellbore failure ¾ Wellbore cleaning issues ¾ Remedial actions required to stabilize the wellbore
Drill marks
Cavings/cuttings characteristics: ¾ Cuttings usually contain “bit marks” and are usually distinguished from cavings on this basis ¾ Cavings are typically 0.5-2 inches in size but may be as large as 4-5 inches ¾ Cavings are generally categorized into three types: → Angular → Splintery → Tabular © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Angular Cavings Angular cavings are characterized by curved, rough surfaces resulting from shear failure along the borehole wall. - fresh surfaces indicate borehole breakout is presently occurring - old surfaces indicate that shear failure occurred previously (e.g., rubble zone)
σθθ Excessive σθθ leads to shear failure
Pw
curved and rough failure surface
wellbore
Remedial Action(s) -Increase MW (do not exceed FG) -Closely monitor ECD & control tripping speeds -Effective hole cleaning measures should be implemented -Select optimum well trajectory to avoid shear failure © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Angular Cavings rough, curved surfaces
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Splintery Cavings Splintery cavings are characterized by long, thin, concave surfaces resulting from radial spalling due to drilling underbalanced in low permeability rocks (i.e., σ’r
Pw
rock chip
excessive pressure gradient (Pp>Pw) causes sloughing shale
wellbore
Remedial Action(s) -Increase MW -Reduce penetration rate -Monitor ECD & reduce tripping speed (swabbing) © 2005 Baker Hughes Incorporated All rights reserved.
curved and concave (splintery) failure surface
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Splintery Cavings long, thin, concave surfaces
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Tabular Cavings Tabular cavings are characterized by smooth, flat surfaces that are parallel to subparallel. These typically result from failure along bedding planes or cleavages in pre-existing fractures/joints sets. bedding plane failure - May yield square-shaped hole - Image logs often show enhanced enlargement on one side of the hole only! failure along pre-existing fractures
de-stabilized block
Remedial Action(s)
flat, parallel surfaces corner failure
picture taken from Økland and Cook (1998)
-Implement effective fluid loss measures (to plug conductive fractures) -Reduce drillstring vibrations as well as swab & surge (i.e., tripping speed) -Minimize instances of back reaming © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Tabular Cavings flat, parallel, old surfaces
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Wellbore Stability Case Study
© 2000 Baker Hughes Incorporated All rights reserved.
Application examples ÎCase
Study I
– Open-hole stability analysis of horizontal wells under production scenarios z
Case Study II – Wellbore integrity assessment during under-balanced drilling
z
Case Study III – Drilling through inclined laminated formations
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Case Study I Open -hole stability analysis of horizontal Open-hole wells under production scenarios Objective: To investigate the stability of horizontal wellbores under several production scenarios in order to select a suitable completion strategy which guarantees borehole integrity during the productive life of the field. Reference: SPE 105332 © 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
ST-2: Drilled Horizontally (W-side) ST-3: Horizontally Planned (E-side) H-2: Horizontally Planned (W-side)
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Formation mechanical properties characterizations GEOMECHANICS
Rock Mechanical Property Model
In-situ Stress & Pore Pressure Models
Laboratory testing on core samples (Discrete (discrete data) (Triaxial (triaxial tests, tests, acoustic acoustic measurements, measurements, hollow hollow cylinder cylinder test) test) Log-based dynamic mechanical properties (Elastic (elastic moduli and Poisson’s ratio) Empirical correlations for rock strength (Lacy, Lal, Coates-Denoo, Deere-Miller, etc) Log-based static mechanical properties (Micromechanical (micromechanics approach) approach) © 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Logging of Mechanical Properties (LMP)
(micro -mechanics approach) (micro-mechanics Log Inputs DTP, DTS, Porosity, Lithology, Saturations, ZDEN, Fluids Properties, Stresses Produces Virtual Core Sample
σa
Produce StressStrain Curves
σr σa
Applying Virtual Stresses to the “Core Sample”
εr
εa
Static Mechanical Properties: Rock Strength, Elastic Moduli Poisson’s Ratio, Biot’s Constant, Poisson’ Cohesion, Internal Friction Angle © 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Log -based static mechanical Log-based properties z
The Micromechanics Model provides a continuous representation of static mechanical properties at different confining conditions
Mohr-Coulomb failure envelope © 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
In -situ stress & pore pressure In-situ characterizations GEOMECHANICS
Rock Mechanical Property Model
In-situ Stress & Pore Pressure Models
Vertical Vertical/overburden Stress (Overburden stress Stress) (formation Formation density density integration integration throughout throughout the the lithology lithology column) column Magnitude of the Minimum minimum Horizontal horizontal Stress stress (Active (active measurement of the fracture closure pressure) Magnitude Magnitude of the Maximum of the maximum Horizontal horizontal Stress (Back-analysis stress calculation (back-analysis from afrom borehole evidence shearoforshear tensile or failure tensile evidence) failure) Horizontal Horizontal Stress stress Orientation orientation (breakout (Breakout or or induced Induced fractures) fractures) Pore Pore Pressure pressure Profile profile (Pressure (pressure data points, acoustic Acoustic logs) logs) © 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
In -situ stress analysis In-situ In-Situ stress tensor ⎡σ xx τ xy τ xz ⎤ ⎡σ H 0 0 ⎤ ⎢ ⎥ σ = ⎢τ xy σ yy τ yz ⎥ = ⎢⎢ 0 σ h 0 ⎥⎥ ⎢τ xz τ yz σ zz ⎥ ⎣ ⎦ xyz ⎢⎣ 0 0 σ v ⎥⎦ X 'Y 'Z '
Density log
dw
sf
Vertical stress (overburden)
σ v = ρ w gd w +
∫
ρ b (z )gdz
TD
sf
z ds
Depth of interest
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
In -situ stress analysis In-situ
σ1
In-Situ stress tensor ⎡σ xx τ xy τ xz ⎤ ⎡σ H ⎢ ⎥ σ = ⎢τ xy σ yy τ yz ⎥ = ⎢⎢ 0 ⎢ τ xz τ yz σ zz ⎥ ⎣ ⎦ xyz ⎢⎣ 0
0
σh 0
0⎤ 0 ⎥⎥ σ v ⎥⎦ X 'Y 'Z '
σ h ,min =
σh,min 0.914 psi/ft
ν 1 −ν
(σ
v
− αPp ) + αPp +
Fracture closure pressure from a minifrac test performed in an offset West-side well.
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
φf ˜ 60º
σ2
Minimum Horizontal Stress Uniaxial strain compaction process
σ3
• ν , α from the mechanical property model • Pp from reservoir pressure data
Eα t E νE ΔT + Δ ε + Δε y x 2 2 1 −ν 1 −ν 1 −ν Thermal induced stress
Lateral strains and tectonic effects
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
In -situ stress analysis In-situ In-Situ stress tensor
⎡σ xx τ xy τ xz ⎤ ⎡σ H ⎢ ⎥ σ = ⎢τ xy σ yy τ yz ⎥ = ⎢⎢ 0 ⎢ τ xz τ yz σ zz ⎥ ⎣ ⎦ xyz ⎢⎣ 0
0
σh 0
0⎤ 0 ⎥⎥ σ v ⎥⎦ X 'Y 'Z '
Maximum Horizontal stress • Back-analysis using breakout size measurement • Breakdown pressure – minifrac
Fracture closure line: (minifrac) z
σh,min = 0.914 psi/ft at 13,134 ft. Breakdown line: (tensile failure)
z
Mud losses reported with MW = 18.7 ppg (0.971 psi/ft) at 12,572 ft. Breakout line: (compressive failure)
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
In -situ stress analysis In-situ In-Situ stress tensor ⎡σ xx τ xy τ xz ⎤ ⎡σ H ⎢ ⎥ σ = ⎢τ xy σ yy τ yz ⎥ = ⎢⎢ 0 ⎢ τ xz τ yz σ zz ⎥ ⎣ ⎦ xyz ⎢⎣ 0
0
σh 0
0⎤ 0 ⎥⎥ σ v ⎥⎦ X 'Y 'Z '
Direction of the horizontal stresses • Breakouts and hydraulically induced fractures identified on borehole image logs • Regional stress regime
Hydraulically Induced Fractures Borehole Breakouts
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
In -situ stress analysis - summary In-situ W-2
Normal faulted stress regime, but very close to a strike-slip stress regime
σv ≥ σH > σh
W-2
Maximum horizontal Stress direction: East-side: N35E West-side: N45E
σh,min
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
W-6
σH,max
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Wellbore stability basics
[σ ]x' y ' z ' = [Q]T [σ ]XYZ [R] (East)
Wellbore Coordinate System
Earth Coordinate System
(North)
Zs
Z
Ys
βs
Xs
Y αs X
(Down)
far-field stress
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Wellbore stability basics
Y
X
East
North
Z
Earth Coordinate System
Down
Shear failure modes: z
z
z
Breakout shear failure
σ 'θθ > σ ' z ' z ' > σ 'rr
Borehole Coordinate System
y’
Toric shear failure
σ ' z ' z ' > σ 'θθ > σ 'rr
Helical shear failure
σ ' z ' z ' > σ 'rr > σ 'θθ © 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
σz’z’
Efficiency….Data accuracy….People-oriented service
z’
Drilling direction
x’
σrr Low-side borehole
Cylindrical Coordinate System
σθθ
Cartesian to Cylindrical Stress tensor transformation www.bakeratlasdirect.com
Wellbore stability basics Azimuthal Maximum Tangential Stress Distribution Compared with Rock Compressive Strength 180
Effective compressive -165-170-175 -160 -155 strength -150
175 170 165
160
155
12000
-145 -140 -135 -130 -125
C f = UCS + ( Pw − αPp ) tan 2 (450 +
β 2
)
150 145 140 135 130 125
9000
-120
120
-115
115
6000
-110
110
-105
105 3000
-100
100
-95
95 0
-90
90
-85
85
-80
80
-75
75
-70
70
-65
65
Compressive stress
-60
60
-55 -50 -45
55 50 45 -40
40 -35
35 -30
-25
-20
-15 -10
-5
5
10 15
20
25
30
0
Borehole Low-Side © 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Horizontal borehole stability predictions (multiple drawdown)
ΔPdrawdown = Pr − Pwf
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
Increasing Drawdown condition, DP
ST-2
www.bakeratlasdirect.com
Reservoir depletion – effects on in-situ stresses Δσ h =
In-situ stress path during reservoir depletion 1.2
Cleary & Geertsma (1978)
1.1
Stress gradient, [psi/ft]
α (1 − 2ν ) ΔP (1 − ν ) p
1.0 0.9 0.8 0.7
Initial reservoir Pressure
0.6 0.5
σh
Intermediate Pressure
σh
Abandonment Pressure
Overburden stress Maximum horizontal stress Minimum horizontal stress
0.4 10000
9000
8000
7000
6000
5000
4000
3000
Reservoir pressure, [psi]
Overburden stress, σv
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Horizontal borehole stability predictions (reservoir depletion) Reservoir pressure depletion
ST-2
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Horizontal borehole stability predictions (reservoir depletion) ST-2
Initial reservoir Pressure
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Intermediate Pressure
Efficiency….Data accuracy….People-oriented service
Abandonment Pressure
www.bakeratlasdirect.com
Case study I – concluding remarks z
z
z
Borehole stability analysis requires both mechanical property characterization and in-situ stress tensor estimation. Stability predictions of horizontal wellbores under open-hole production scenarios helped to define well completion/production strategy: – Safeguard well integrity during the productive live of reservoir – Early remediation advice: completion & production strategy decisions – Strength degradation when acid treatments are planned. The maximum drawdown for a stable horizontal borehole reduces with reservoir depletion.
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Application examples z
Case Study I – Open-hole stability analysis of horizontal wells under production scenarios
ÎCase Study II – Wellbore integrity assessment during under-balanced drilling z
Case Study III – Drilling through inclined laminated formations
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Case Study II Wellbore integrity assessment - under -balanced drilling under-balanced Objective: Assess the degree of instability with underbalance condition. Establish maximum under-balance for given rock strength and in-situ stress characteristics.
Sta. Rosa
San Joaquinaco
Mar Cariberibe Sta. Ana
Goal: Provide inputs for establishing hole cleaning, ECD, drag-and-torque, and fluid volume trends. Optimize under-balanced drilling operations. Reduce drilling cost and maximize production. © 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Sucre
Sucre
Anzoá Anzoátegui Delta Amacuro
Monagas
El Toco
Anaco UE Gas / Condensado
Reference: SPE/IADC 99165
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Assembly of experience base
Considerable wellbore instability related problems in the Merecure and San Juan formations. The occurrence of lost circulation along side with pack-off, reaming, tight hole, over-pull and cavings.
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
• Combined information from more recent pressure measurements in sands. • Normal pressure gradient in shales.
8.0 6.0 4.0 2.0
EMW (ppg)
9900
9800
9700
9600
9500
9400
9300
9200
9100
9000
8900
8800
8700
8600
8500
8400
8300
8200
8100
8000
7900
7800
7700
0.0
PP
DIF
Medida
Perd Circ.
10.0
12.0
MW Usado
14.0
NewPP
16.0
Pore pressure model
M easured D epth (ft) © 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
In -situ stress characterizations In-situ
A
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Model calibrations – breakout and drilling induced fracture Sv DIF
Min MW Lost Circ.
Frac. Grad. MW Used
Max MW LOT/FIT
PP
Observed BO
5
10
15
20
0
25
9000
9000
9100
9100
9200
9200
Measured Depth (feet)
M e a su re d D e p th (ft)
9500
Caliper
20
40
60
80
100
120
140
160
180
200
9300
9300
9400
Predicted BO
Breakouts (degrees)
EMW (ppg) 0
Washouts
9400
9500
9600 9600
9700
Breakouts
9700
9800 9800
80deg
9900 0 9900
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
2
4
6
8
10
12
14
16
Caliper (inches)
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mud weight window
SHEAR FAILURE
IDEAL MW
TENSILE FAILURE
REAL LIFE MW
Excessive BO
Mud weight window Merecure © 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
σ2
Minor BO
Pw
Pw
Low Pore Pressure
In-gauge Minor Losses hole
Pw
Pw
Mud Weight Scale
Excessive Losses
σ3 Pw
High σ3 (magnitude)
Mud weight window Vidoño and San Juan
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Breakout expected Mud Weight Ave. breakout width in Merecure (degrees) Ave. breakout width in San Juan (degrees)
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
10 ppg
8 ppg
6 ppg
4 ppg
2.7
10.6
15.5
21.3
7.8
28.1
34.8
41.9
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Mud losses – conventional vs. under -balanced drilling under-balanced Merecure
San Juan
12000
Merecure = 8 ppg (ΔP= - 900 psi) San Juan = 7 ppg (ΔP= - 1500 psi)
10000
Bbls
8000 6000 4000 2000
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
G-92
Avg.
JM-221
JM-220
JMN-216
JMN-215
JMN-214
JMN-205
JMN-204
JM-193
JM-190
0
www.bakeratlasdirect.com
Drilling time and cost saving 6-1/2” Hole - Conventional W ell
Es tim ate d
Re al
Cle an
days
K$.
days
K$.
days
K$.
G-91 / JI-X
14
677.0
9.0
886.6
9.0
886.6
G-93 / JI-O
20
1,221.2
11.8
591.8
11.8
591.8
JM -214 / JI-G
18
20.7
1,186.4
18.1
1,082.0
JM -215 /JI-B
20
1,242.7
29.6
1,596.7
17.8
644.7
JM -216 / JI-F
18
959.9
33.5
2,074.1
20.0
1,531.9
JM -220 / JJ-C
14
793.7
21.9
928.1
19.7
779.9
JM -221 / JI-Z
24
654.8
19.1
995.5
17.8
938.3
JM -225 / JI-J
18
793.9
14.1
778.5
11.8
650.6
JM -227 / JI-N
21
867.6
16.4
800.8
16.4
800.8
18.6
901.3
19.6
1093.2
15.8
878.5
Ave rage
6-1/2” Hole – Under Balance W ell G-92 / JI-H JM-229 / JJ-E JM-230 / JJ-G JM-233 / JJ-F JM-235 / JH-X Average
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Rig GW-61 GW-67 GW-60 PD-719 GW-68
Estimated days K$.
- 4 days
- 4.7 days
Real days K$.
Clean days K$.
- 183.2 K$
6 7 7 7 13
158.3 814.8 730.0 466.6
7.4 24.0 22.4 14.8 9.5
507.8 1,664.6 1,304.0 545.1 580.6
6.6 11.9 17.2 10.8 9.0
471.9 998.9 1,057.7 387.5698 560.6
8.0
542.4
15.6
920.4
11.1
695.3
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Drilling time and cost saving 6-1/2" Hole
Actual trend
30 20
Conventional
Avg. UB
*JM -235
*JM -233
New Technologie Estimeted
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
*JM -230
*JM -229
*G -92
Average
JM -227
JM -225
JM -221
JM -220
JM -216
JM -215
JM -214
0
G-93
10 G-91
Tim e (days
40
Efficiency….Data accuracy….People-oriented service
Real
Clean
www.bakeratlasdirect.com
Case study II – concluding remarks z
z
z
z z
A geomechanical model was developed and calibrated with respect to the field data, wireline logs, breakout simulation and DIF. Underbalance mud weights were recommended based on the results of the geomechanical modeling. Lost circulations have successfully been avoided following the implementation of underbalance mud weight recommendations. Drilling rates were tripled in comparison with the conventional methods (8-1/2” and 6-1/2” holes). A total saving in time of 60 rig days, and in cost of more than $1MM have been realized, in prevention of fluid losses, in the 5 wells drilled so far following the underbalance mud weight implementations.
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Case Study III Drilling through inclined laminated formations Objective: Assess the degree of instability when drilling through inclined laminated formations Establish the optimum mud weight and wellbore trajectory to minimize borehole instability.
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Some background information…… z “traditional” well design (intersect zone “A” vertically)
– All wells drilled from drill centers – 3 critical zones (A,B,C) • Zone “A”: recently encountered wellbore instability while drilling high angle wells • Zone “B”: lost circulation issues
“Advanced” well design (intersect zone “A” at high angle)
Tertiary
zone “A”
z
zone “B” zone “C”
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Subsea development
Zone “C”: very weak, anisotropic shale (keep hole near vertical) – Initial 2 wells in field→ used WBM (shale reactivity issues) – SBM used to date – Most HA wells in past had significant WBS issues (no WBS analysis available on past failed wellbores!!)
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Some background information…… “traditional” well design (intersect zone “A” vertically)
z
– Directional – S-shape – 300 – 450 tangent angle – Drop tangent angle to 100 in zone “C” and reservoir
“Advanced” well design (intersect zone “A” at high angle)
Tertiary z zone “A”
Traditional Well Design ~ 25 wells
Advanced Well Design – 3 wells – Extended Reach – S-shape – Build to 600 to 700 through upper shales – Hold ~3000m tangent – Drop tangent angle to 100 in zone “C” and reservoir
zone “B” zone “C”
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Well #1 – traditional well design z Planned
pilot hole:
– Seismic tie-in – Formation evaluation – Geomechanical model update – 45° hole drilled thru zones “B” and “C” z Planned
hole
Tertiary
zone “A”
Production
– Kick off in shale (zone “C”) above target reservoir – KOP near fault – Horizontal completion © 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
zone “B”
production hole zone “C”
pilot hole
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Well #1 – pilot hole z
z
z
z z
z
Well drilled thru zones A,B,C with no significant problems initially Then……after approximately 1 day an abundance of “angular” and “splintery” cavings was observed. Wellsite geologist indicated cavings are from zone “C”. Mud weight was increased to combat the problems (high PP and/or low UCS??) Continued drilling ahead Approximately 2 days later, hole collapsed → left BHA in hole (no logs!) Sidetrack required
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Well #1 – sidetrack 1 (2nd pilot hole) • • •
•
•
Sidetrack drilled parallel to original hole with higher MW. Drilled beyond zone “C” with little problems. To address hole cleaning issues, several hours of circulating and rotating performed within zone “C”. Shortly thereafter, abundance of “tabular” and “blocky” cavings was observed. It was decided to POOH & sidetrack.
Tertiary
2nd pilot hole planned production hole
initial pilot hole © 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Well #1 – sidetrack 2 (final production hole) z
Well ST2 drilled nearly vertical thru zone “C” with no problems – Fault was avoided within zone “C” – Minimal “angular” cavings present – Shift in bedding dip from 10° to 55°→ two pilots drilled nearly parallel to bedding
Tertiary
final production hole
planned production hole
initial pilot hole
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Well #1 – stable mud weight simulations Anisotropic Case PetroCanada-Anisotropic Case 0 330 Anisotropic
Isotropic
75
12.5
30
12
60
Field Mud Weight
300
12
11
11.5 60
45
11
30
10.5
15
10
270
9.5
90
9 8.5
Mud Weight, ppg
10
240
8
120
7.5 9
7 210
150 180
8
Isotropic Case PetroCanada-Isotropic Case
7
0 330
6
75
7.29
30
7.19
60 300
7.09
60
45
6.99
30
5
15
0
10
20
30
40
50
60
70
80
6.89
90 270
Well Inclination, deg.
90
6.79 6.69 6.59
Formation dip & dip direction = Wellbore azimuth = 1150 © 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
550,
1080
Efficiency….Data accuracy….People-oriented service
240
120
6.5 6.4
210
150 180
www.bakeratlasdirect.com
Well #2 – extended reach drilling (ERD) • • • • •
Drilled beyond zone “A” with little problems. POOH, several significant tight spots observed in zone “A”. These were not present in all previous wells (which were drilled with < 60° inclination). Abundance of “angular” & “tabular” cavings were observed several days after drilling. It was speculated that roof collapse-type failure was beginning.
“Advanced” well design (intersect zone “A” at high angle)
Tertiary
zone “A”
zone “B” zone “C”
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Well #2 – stable mud weight simulations
Wireline Data 2 wk
LWD real-time 2 wk
LWD real-time initial
MW used
Formation dip & dip direction = 150, 1080 Wellbore azimuth = 1150 The attack angle in this case is referred to the bedding plane. © 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Well #2 – drilling fluid penetration Wireline Data Wireline Data 2 wk
LWD real-time 2 wk
LWD real-time
LWD real-time initial
LWD real-time initial
Confirms fluid penetration along weak planes in shale with time!
Slight invasion measured 2 weeks later © 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
No invasion measured while drilling
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Case study III – concluding remarks z
z
z
z
Early recognition of bedding plane characteristics is critical to optimizing the “attack angle” and the mud weight when drilling through inclined laminated formations. Increased mud weight to account for additional pressure to stabilize anisotropic formation can exacerbate wellbore instability due to fluid penetration. Mud additives must be added to minimize fluid leak-off. The geometry of cavings provides a means to characterize the failure mode and must be accurately monitored. Four (4) ERD wells have been drilled to date with nearly zero non-productive times (NPT).
© 2000 Baker Hughes Incorporated All rights reserved. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Hydraulic Fracturing Rock Mechanics Considerations
© 2005 Baker Hughes Incorporated All rights reserved.
Outline ¾ Background ¾ Effects of in-situ stress on fracture orientation and propagation ¾ Effects of closure stress, bed thickness and rock mechanical properties on fracture containment ¾ Pressure analysis during hydraulic fracturing ¾ Special cases in hydraulic fracturing ¾ Reservoir connectivity
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Background – Creating a hydraulic fracture During a hydraulic fracturing job, fluid is injected at a relatively high pressure into the formation inducing a TENSILE fracture
σc Upper Bounding Layer
Closure stress contrast is, perhaps, the most important parameter affecting fracture containment
Pay Zone
Lower Bounding Layer
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Background – Hydraulic fracturing applications Reservoir stimulation Æ Enhancement of well productivity / injectivity of hydrocarbon reservoirs Reservoir management Æ Access to naturally fractured zones, increase of drainage efficiency, injection / production of fluids in thermal energy projects Stress measurement Æ Minifrac, LOT, XLOT Waste management Æ Massive waste injection, drill cuttings reinjection Sand management Æ Frac-packs in poorly consolidated formations and sanding-prone rocks
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Importance of in-situ stress in hydraulic fracturing
Direction Æ Controls fracture orientation (dip and azimuth); horizontal vs. vertical Magnitude Æ Determines the fluid injection pressure; thus, the choice of tubular and pumps Stress contrast Æ Dominant role in fracture containment; thus, controls fracture geometry
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Origin and magnitude of in-situ stresses
σ
In-situ stress due to overburden + tectonics At a large scale, fractures open and propagate along the path of least resistance ÆALWAYS NORMAL to σ3
σh min Depth
σH max
© 2005 Baker Hughes Incorporated All rights reserved.
σv
Due to the weight of the overlying rock: Æ σv ~ 1.0 psi/ft (normally) Æ σh min ~ 0.7 psi/ft (normally)
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Background - Fracture classifications s3
s1 s1
s1 mode I opening Induced: Petal Centerline Hydraulic Natural: Joint Vein
closing
mode II
mode III
Induced: Compaction band (experiments)
Induced: Shear fractures/faults, initial breakout, reactivated joints/faults.
Natural: Compaction band (sand) Stylolite (carbonates)
Natural: Normal/reverse/strike slip - bedding plane deformation bands (cataclastic faults).
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Fracture orientation - Normal stress field Normal regime Æ σv > σHmax > σhmin Hydraulically-induced fracture is vertical
σ1 = σv Fault
σ2 = σHmax σ3 = σhmin
φ
(Redrawn from Dusseault, 2004) © 2005 Baker Hughes Incorporated All rights reserved.
re u t c a r F pl ane
Efficiency….Data accuracy….People-oriented service
Hydraulic fracture www.bakeratlasdirect.com
Fracture orientation – Strike slip regime Strike-slip regime Æ σHmax > σv > σhmin Hydraulically-induced fracture is vertical
σ2 = σv σ3 = σhmin
σ1 = σHmax
ctu a r F
re
n p la
(Redrawn from Dusseault, 2004) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
e
Hydraulic fracture www.bakeratlasdirect.com
Fracture orientation – Thrust regime Thrust regime Æ σHmax > σhmin > σv Hydraulically-induced fracture is horizontal (Redrawn from Dusseault, 2004)
Hydraulic fracture
ne a l p re u t c Fra
σ3 = σv σ1 = σHmax
σ2 = σhmin
© 2005 Baker Hughes Incorporated All rights reserved.
φ
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Bottom hole pressure
Fracturing process - Minifrac Breakdown pressure Tensile strength Re-opening pressure ISIP
σC
Flow rate Flow rate
time
ISIP is only an UPPER BOUND for the value of closure stress Æ ISIP > σc !!! (Most people assume they are equal) The fracture initiation at breakdown pressure may be defined as (Hubbert and Willis, 1957):
Pb = 3 σ h − σ H + T0 − p p © 2005 Baker Hughes Incorporated All rights reserved.
Æ assumes the rock to be impervious (i.e. negligible fluid leak-off) and linear-elastic.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
In-situ stress - closure The magnitude of the net pressure determines fracture propagation Æ Pnet = Pf – σc
The LARGER the magnitude of σc , the more DIFFICULT it is to open the fracture !!!
p pf
σ3 = σC © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline ¾ Background ¾ Effects of in-situ stress on fracture orientation and propagation ¾ Effects of closure stress, formation thickness and rock mechanical properties on fracture containment ¾ Pressure analysis during hydraulic fracturing ¾ Special cases in hydraulic fracturing ¾ Reservoir connectivity © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effect of stress contrast on fracture containment
Closure stress contrast is the single most important parameter controlling fracture propagation !!! - Stress differences between the target formation and the adjacent layers determine fracture height containment characteristics Æ contained vs. “run-away” fractures - Other parameters such as rock mechanical properties contrast, flow rate, fluid viscosity although important have less effect on fracture propagation
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effect of stress contrast on fracture containment … (continued) Stress profile, Mesaverde Group, Rifle, Colorado (after Warpinski et al., 1985)
Normally, σsand < σshale
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effect of stress contrast on fracture containment … (continued) σh =
ν 1 −ν
[σ V − α PP ] + α PP
In general, ν coal > ν shale > ν sand
In non-tectonic environments, generally, σ3 Coal > σ3 Shales > σ3 Sands
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Hydraulic fractures in the laboratory σz = 3000 psi σy = 1300 psi (coming out of the picture plane)
σx = 1050 psi
Haimson and Fairhurst, 1969 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
300 psi
300 psi
Effect of stress contrast on fracture containment … (continued)
400 psi
400 psi
Photographs of hydraulically induced fractures in tuff samples (taken from Warpinski et al., 1982) The same fracture height containment behavior has been observed in the field (Smith et al., 1982; Warpinski et al., 1982) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Hydraulic fractures in the field WELDED TUFF
FRACTURE
Mineback experiments (Warpinski et al., 1982)
ASH FALL TUFF
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effect of stress contrast on fracture containment … (continued) σc2 hs2
σc1
2a
h
hs2
σc2
Fracture profile
Width profile
σc2 σc1
hs2
σσc2 <<σσc3 c2 c3 Æ Æhhs2 >>hhs3
2a h
s2
σc3
hs3 Fracture profile
Width profile
The ellipses shown here are a GROSS APPROXIMATION of the actual fracture geometry. In reality, fracture shape is much more irregular !!! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
s3
Effect of stress contrast on fracture containment … (continued) Fracture height propagation – (Example from Warpinski and Smith, 1989): Stress (psi)
2500 1200 1500 1000 1250 1700
2000
Fracture height propagation is slowed down by the presence of a layer with σ3=1700 psi Fracture height propagation rate is increased noticeably due to the presence of a low stress horizon ( σ3=1200 psi ) Fracture height propagation rate is decreased dramatically due to the presence of a high stress barrier ( σ3=2500 psi )
¾
ALL the equations shown above NEGLECT the effect of pressure losses due to vertical flow Æ Thus, their results tend to be overly conservative !!! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effect of stress contrast on fracture containment … (continued) Further injection will create additional height but almost negligible length increment
σc1
Pressure
σc2 h
σc2
σc1
ΔP time
ΔP Due to additional pressure losses, it becomes easier to grow height than to extend the fracture length
Behavior of the pressure vs. time curve allows for quality control and geometry confirmation !!! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effect of formation thickness on fracture containment Values of net pressures for creating a 700 ft fracture under the following conditions: Q=30 bpm, μ=150 cp, C=0.001 ft√min, Xf=700 ft (data generated by using Stimplan® from NSI Technologies, 2005)
Net pressure (psi)
10000
Pnet 2 = P – σC2 E= E= E= E=
6 *10 e6 psi 4 *10 e6 psi 2 *10 e6 psi 1 *10 e6 psi
Pnet 1 = P – σC1 Pnet 2 = P – σC2
1000
ΔPnet = Pnet 1 – Pnet 2 = σ2 – σ1
100 10
100 Fracture height (ft)
1000
Æ For containment to occur, the net pressure in formation 1 should not exceed the value of the stress closure differential (σ2 – σ1)
Æ For a given fracture length, keeping a fracture within a thinner vertical interval requires more degree of confinement (because the value of Pnet becomes larger) than in the case of a thicker formation. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effect of formation thickness on fracture containment … (continued) ¾ When the thickness of a stress barrier is considered, the confining effect of that layer is effectively reduced (i.e. thin, high stress formations may not stop fracture height growth once certain pressure threshold is overcome) ¾ The “minimum” thickness of a stress barrier is a function of the thickness of the pay-zone, the stress differential, and the mechanical properties contrast between the two layers.
C A B
Horizon B is probably a better stress barrier than formation C !!! Æ B is a much thicker interval with slightly lower closure stress than C Æ Rule-of-thumb: In order to be effective, the stress barrier should be as thick as the treated formation (or thicker !!!)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effect of Young’s modulus contrast on fracture containment Young’s modulus contrast is also a factor affecting fracture height containment (although not as important as stress contrast) - E contrast may slow down the fracture height propagation rate; however, it is not a mechanism of arrest (i.e. it does not “stop” fracture height propagation) - If a fracture enters a stiffer formation, then its width will be reduced (i.e. it becomes increasingly difficult to open the fracture); thus, flow resistance will increase making further fracture propagation more difficult ÆIn the field, normally, Esh < Ess ; thus, the fracture would be more easily propagated in shales. However, this behaviour is contrary to the effect created by stress contrast STRESS CONTRAST IS MORE IMPORTANT !!! © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Effect of Young’s modulus contrast on fracture containment H
h
L
NOTE that (2L/h) / (H/h) is only slightly larger than 1 for the range of mechanical properties contrast expected in the field (with Δσc =0) Plot built based on the work by van Eekelen (1982)
Æ E2 / E1 values are normally less than 15; thus, mechanical properties contrast is expected to SLIGHTLY affect fracture propagation (i.e. the effect is not strong enough to stop the fracture height growth).
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Summary - effects of stress contrast, formation thickness and mech. prop. • In hydraulic fracturing, nature ALWAYS takes the path of least resistance • Closure stress contrast (i.e. ΔPnet ) is the single MOST IMPORTANT parameter controlling fracture propagation • Usually, closure stress in shales is higher than in sands; thus, they act as stress barriers • The thickness of the stress barrier is also important; a good stress barrier should be thicker than the treated formation • Young’s modulus contrast also affects the fracture height growth. However, its effect is not as important as the effect of stress contrast
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline ¾ Background ¾ Effects of in-situ stress on fracture orientation and propagation ¾ Effects of closure stress, rock mechanical properties and leak-off coefficient on fracture geometry ¾ Pressure analysis during hydraulic fracturing ¾ Special cases in hydraulic fracturing ¾ Reservoir connectivity © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pressure analysis during hydraulic fracturing Leak-off coefficient, fracture geometry (Xf, w), and efficiency
Bottom hole pressure
Shut-in
Fracture propagation diagnosis (containment)
Confirmation of Leak-off coefficient, and fracture geometry. Estimate of reservoir transmissivity (kh)
After closure
Closure stress
Injection
Fracture closing
Time © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pressure analysis during hydraulic fracturing - pumping in Assumptions Æ vertical fracture, with L >> H, constant flow rate and viscosity
Reasonable height containment, unrestricted extension
σ1
Stable height growth (shown here) OR increased fluid loss OR tip effect-dominated fracturing
Unstable height growth, injection becomes pointless (no length growth)
σ5 H0
σ3 σ5 σ7
Mode I
Mode II
Mode IV
Mode III occurs when there is a flow restriction in the fracture Æ slurry dehydration leading to screen-out, width reduction in higher stress zones
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pressure analysis during hydraulic fracturing - pumping in … (continued) Log P net
Nolte-Smith Plot (Nolte and Smith, 1981):
III e d Mo
1
Mode II eI
d Mo 1 1 to 8 4
slope = 0
<0
Mo de IV
(Smith, 2003)
⎡ E μqL ⎤ Pnet ≈ ⎢ P + tip ⎥ 2 4 ⎣ (1 − ν ) H ⎦
1/ 4
Log Pump time
MODE I : positive slope (1/8-1/4) Æ Confined height, unrestricted extension MODE II : slope ~ 0 Æ extension with accelerated height growth MODE III : slope ~ 1 Æ restricted growth MODE IV : slope < 0 Æ unstable / uncontrolled height growth © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pressure analysis during hydraulic fracturing - pumping in … (continued) L
MODE I: positive slope (1/8-1/4) V(x)
Æ PKN model based, confined height, unrestricted extension Æ fluid loss is linear flow-dominated, flow rate (q) and viscosity (μ) are assumed to be constant Æ coincides with the PKN growth model
x W(x, t)
W(0, t)
If the fluid is assumed to follow the Power Law (τ = K γn):
H
Pnet ∝ t e → high fluid loss : e = 1 /(4n + 4) → low fluid loss : e = 1 /(2n + 3)
→ high fluid loss, Newtonian, n = 1 : e = 1 / 8 → low fluid loss, Newtonian, n = 1 : e = 1 / 5 → high fluid loss, non − Newtonian, n = 0.5 : e = 1 / 6 → low fluid loss, non − Newtonian, n = 0.5 : e = 1 / 4 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pressure analysis during hydraulic fracturing - pumping in … (continued) ⎡ E μqL ⎤ + Pnet ≈ ⎢ P tip ⎥ 2 4 ⎣ (1 − ν ) H ⎦
MODE II: positive slope ~ 0
1/ 4
Less important for the case of low E rocks
P net
Æ stable height growth Æ increased fluid loss (probably due to the interception of natural fractures), higher risk of screen-out Æ may be indication of confined height with net pressure behavior dominated by tip effects (soft, low modulus formations) σ1 σ5
Mode II Mode IV
σ7
Mode II
σ5
Mode I
H0
σ3
Mode I
Mode IV
H /Ho © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pressure analysis during hydraulic fracturing - pumping in … (continued) MODE III: positive slope ~ 1 Æ flow restriction in the fracture (unit slope indicates storage of fluid, i.e. fracture “ballooning”) Æ may be caused by pad depletion with proppant at the fracture tip, slurry dehydration, excessive height growth, or proppant fallout (i.e. blockage)
σ4
Screenout created by late height growth !!! σ3
σ1
Rpinch
R pinch
q E (Δp / Δt ) = 1.8 (1 −ν 2 ) H 2
(Smith, 2003)
σ2 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pressure analysis during hydraulic fracturing - pumping in … (continued) MODE IV: negative slope (< 0) Æ near wellbore height growth Æ “run-away” fractures Æ slope is a function of the rate of unstable growth Æ in the case of complete lack of height containment, slope will be close to -1/8 (Smith, 2003)
σ1 σ5
Fracture growing vertically instead of extending laterally
σ3
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pressure analysis during hydraulic fracturing - pumping in … (continued) Example from the field (data taken from Nolte & Smith ,1981): 4000 4000
Case CaseAA
3500 3500 3000 3000 Pressure (psi) Pressure (psi)
2500 2500
Case CaseBB
2000 2000 1500 1500
Case CaseCC
1000 1000 500 500 0 0
0 0
© 2005 Baker Hughes Incorporated All rights reserved.
50 50
100 100
150 150
200 200 Time (min) Time (min)
250 250
300 300
Efficiency….Data accuracy….People-oriented service
350 350
400 400
www.bakeratlasdirect.com
Pressure analysis during hydraulic fracturing - pumping in … (continued) Using Nolte & Smith plot:
ΙΙΙ ΙΙ
Ι
Case CaseAA
ΙΙΙ
Case CaseBB
Ι Case CaseCC
Ι
© 2005 Baker Hughes Incorporated All rights reserved.
ΙΙ
Efficiency….Data accuracy….People-oriented service
ΙV
www.bakeratlasdirect.com
Outline ¾ Background ¾ Effects of in-situ stress on fracture orientation and propagation ¾ Effects of closure stress, rock mechanical properties and leak-off coefficient on fracture geometry ¾ Pressure analysis during hydraulic fracturing ¾ Special cases in hydraulic fracturing ¾ Reservoir connectivity © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Special cases in hydraulic fracturing Hydraulic fracturing of high permeability rocks - Extremely high values of leak-off - 3D fluid loss rather than Carter’s fluid loss (1D) - Possibility of having both tensile and shear failure
Hydraulic fracturing in deviated wells - Normal and shear stress created by well deviation - Possibility of fracture “turning” (i.e. non-planar fractures) - Proppant transport problems due to the presence of “turns” Æ higher screen-out risk !!!
Cuttings injection - Batch process - Possibility of creating several fractures in the same horizon - Environmental concerns due to fracture height growth © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Hydraulic fracture in high permeability rocks Objectives: - To bypass damaged formation zones (recovering productivity) - To reduce the possibility of sanding and solids production (by reducing fluid pressure gradients)
Characteristics: - High leak-off (i.e. low efficiency) fractures - Fractures tend to be a lot shorter and wider than in conventional fracturing © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Hydraulic fracture in high permeability rocks…… (continued) The area of flow in a fracpack is about two orders of magnitude larger than the area of flow in a gravel pack Gravel pack:
9.5 Ax = 2π r h = 2π h = 4.97 h 12
Frac & pack:
Ax = 4 L f h = 4 * 50h = 200h Æ Therefore, the fluid velocity in a gravel pack is about two orders of magnitude higher than in the case of fracpacks (i.e. considerably larger drag forces in gravel packs) Æ Possibility of using larger proppants in fracpacks due to lower sanding risk (i.e. potential for more production) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Hydraulic fracture in high permeability rocks…..(continued) Equivalent wellbore radius (rw eq) Æ producing from a stimulated well is like producing from an effectively larger un-stimulated well C fD =
where
Cf K Xf
=
K f wf K Xf
K : Reservoir permeability Kf : fracture permeability wf : fracture width Xf: fracture half-length
The values of CfD for high permeability fracturing tend to be < 0.5 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Hydraulic fracture in high permeability rocks……(continued) rw eq = 0.28
Cf k
=
k f wf k
In order to increase rw eqÆ kf or wf may be increased Æ Achieving larger fracture width may be difficult as the pressure demands rise and operational risk increases. Besides, theoretical studies have shown that fracture width is relatively insensitive to controllable job variables such as pump rate and viscosity (Nolte, 1979) Æ Increasing fracture permeability is easily accomplished by augmenting the size and concentration of the proppant being pumped
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Hydraulic fracturing in deviated wells Borehole deviation creates a completely different picture Æ STRESS field around the well and far-field stress are NOT EQUAL Æ FRACTURE ORIENTATION near to and far from the borehole are likely to be DIFFERENT (i.e. “turning” fractures) Æ Proppant transport issues (fluid can “turn” easily, but proppant cannot !), HIGHER RISK OF SCREEN-OUT
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Hydraulic fracturing in deviated wells…..(continued) It is important to notice that the fracture initiation plane may be inclined with respect to the borehole axis … and also that, after the fracture grows away from the wellbore, it will turn to follow the in-situ stress field !!! It has been observed that the degree of “fracture turning” (hence, of near wellbore friction) is less severe under the following conditions (Emanuele et al., 1998):
Low natural fracture density and competent cement bonding (less leak-off issues)
Overbalanced or extreme overbalanced perforating (probable hydrofrac during perforation)
Fracture initiated by pumping the fracturing fluid at very high rate (Weijers and de Pater, 1994), i.e. higher values of Pnet 3
⎛ E ⎞ μ ⎟⎟ τ C = ⎜⎜ ⎝ Pnet ⎠ E
where
τ C = characteristic time for fracture propagation E = plane strain Young ' s modulus
μ = fracturing fluid viscosity Pnet = net pressure = Pw − σ c
Shorter propagation time (i.e. faster failure) creates the potential for creating a “smooth” turning fracture (i.e. better wellbore-fracture hydraulic connectivity) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Hydraulic fracturing in deviated wells…..(continued) Depending upon the azimuth (i.e. orientation with respect to North) of the wellbore, the breakdown pressure may vary as follows (Yew and Li, 1988):
z’ θ γ
y’
x’
Fracture
20
60
30
0
Breakdown pressure , Pb (Ksi)
40
θ
16
90 Fracture position , θ (deg)
For α = 0º (North) and a given in-situ stress field
Fracture orientation , γ (deg)
60
12
Pb
8
Pb
γ γ
θ 10
40
70
90
Well inclination, β (deg)
20
0
60
30
Breakdown pressure , Pb (Ksi)
40
16
90 Fracture position , θ (deg)
For α = 45º (North-East) and a given in-situ stress field
Fracture orientation , γ (deg)
60
The Thebreakdown breakdownpressure pressuremay may increase/decrease increase/decreasedepending dependingupon upon the theorientation orientation(α) (α)and andinclination inclination(β) (β) of the wellbore where the fracture is of the wellbore where the fracture is initiated initiated
θ 12
Pb γ
8
10
40
70
90
Well inclination, β (deg)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Cuttings Injection
Batch injection of slurry (water + liquid waste + solid waste) into selected formations (sandstones / shales / carbonates)
Sources of solid waste Æ drill cuttings, contaminated soil
Sources of liquid waste Æ drilling mud, tank bottoms, produced water, human activity Cuttings injection started in the early 1980’s with small annulus volume injection in the GOM. It was later implemented in the North Sea, Alaska and elsewhere.
Two main issues: - Where does the waste go ? - How much waste can we safely dispose of?
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Cuttings Injection … (continued) Similar to hydraulic fracturing stimulation,
σc Upper Bounding Layer
However … Pay Zone
Lower Bounding Layer
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Cuttings Injection … (continued) Hydraulic fracturing Stimulation Volume (Bbls) Injection rate (BPM) Duration Fluid Type Viscosity (cP) Solids type Solids size(mesh) Concentration (% Vol)
1,000 – 5,000 10- 50 Min- Hours Polymeric gel 20-200 Proppant (sand/ceramics) 20/40 10-30
Cuttings / Waste injection 30,000 - Millions 0.5 – 20 Weeks – Years Slurry 2-20 Cuttings D90 < 300 microns Normally, < 15
But most importantly, INJECTION is a batch process while HYDRAULIC FRACTURING is continuous !!! The intermittent nature of waste injection tends to create several fracture rather than a single planar crack (as is the case of hydraulic fracturing).
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Cuttings Injection … (continued) Where does the injected waste go? Competent / low permeability formations:
σ3
Multiple fractures (disposal domain concept), roughly perpendicular to the direction of the minimum in-situ stress
Unconsolidated / high permeability formations:
σ3
© 2005 Baker Hughes Incorporated All rights reserved.
A “disaggregated” zone around the main fractures, the effect of in-situ stress is less evident Æ Much higher storage capacity
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Cuttings Injection … (continued) Microseismic mapping of fractures induced during waste injection (Moschovidis et al., 2000) Æ Wilcox sand (tight sand)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Cuttings Injection … (continued) Creation of multiple fractures Æ much lesser fracture height growth, and much higher volume can be safely disposed (Figure from Moschovidis et al., 2000) Originally, it was thought that the waste injection process should form a SINGLE fracture (red circle). However, tiltmeter mapping proved the existence of several fractures in the same rock interval (black ellipses) As a result, more waste material may be disposed of in the same interval (through a set of small fractures) than it was originally anticipated !!!
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Cuttings Injection … (continued) NOTE: A tiltmeter is a tool used to monitor changes in the inclination of a structure; in this case, the earth surface or a monitoring well.
Figure taken from Wolhart et al. (2001) Æ Measurements on a well tiltmeter as function of the hydraulic fracture inclination (α)
Microseismic mapping is based on the fact that when rock fails it emits “noise” that may be measured and located in space by geophones. Thus, allowing to pinpoint the tip location over time during a hydraulic fracturing job. © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Cuttings Injection … (continued) Injection in unconsolidated formations Æ injection pressure remains almost unchanged throughout the disposal process (figure from Dusseault et al., 1998) cycle
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Cuttings Injection … (continued) Injection in competent, low permeability rocks Æ injection pressure tends to change throughout the disposal process (Figure from Moschovidis et al., 2000)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Cuttings Injection … (summary) ¾ Cuttings injection is a much larger scale process than hydraulic fracturing (years vs. hours, millions of barrels vs. thousands of gallons …) ¾ The cyclic nature of the cuttings injection process tends to create MORE THAN ONE MACRO-SCALE FRACTURE. Thus, augmenting the amount of waste than may disposed of in a given rock interval ¾ Injection of waste into low-permeability rock is a more difficult (hence more risky) operation, as the injection pressure tends to increase over time. This creates the possibility of extending the fracture vertically Æ undesirable effect that could jeopardize the waste containment ¾ The geometry and location of the fracture(s) may be monitored by using tiltmeters, microseismic mapping and tracers
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline ¾ Background ¾ Effects of in-situ stress on fracture orientation and propagation ¾ Effects of closure stress, rock mechanical properties and leak-off coefficient on fracture geometry ¾ Pressure analysis during hydraulic fracturing ¾ Special cases in hydraulic fracturing ¾ Reservoir connectivity © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Reservoir Connectivity σ h min
σ1
σ H max Fracture Wellbore
σ2
σ1 σ
σ
3
© 2005 Baker Hughes Incorporated All rights reserved.
σ3
σ3 σ2
2
σ1 Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Reservoir Connectivity Hydraulic fractures parallel to the direction of maximum permeability - low well deliverability
σh Vertical Well
kh kH
σH
Vertical Well
σ H kh
kH
σh
Hydraulic fractures perpendicular to the direction of maximum permeability - high well deliverability © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Reservoir Connectivity Horizontal well drilled perpendicular to the direction of maximum permeability - high well deliverability
σh
σ H kh
kh kH
σH
kH
σh
Horizontal well with multiple transverse hydraulic fractures - high well deliverability © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Reservoir Connectivity Waterflood/EOR Application - Sweep Efficiency Producing wells drilled perpendicular to fracture direction - good areal sweep efficiency
σh σH
producer © 2005 Baker Hughes Incorporated All rights reserved.
injector
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Reservoir Connectivity Waterflood/EOR Application - Sweep Efficiency Producing wells drilled parallel to fracture direction - poor areal sweep efficiency
σh σH
producer © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
injector www.bakeratlasdirect.com
Reservoir Connectivity Low Permeability Reservoir – Optimum Infill Drilling Locations
Well spacing ≈ fracture length → fracture orientation becomes critical
Good Drainage © 2005 Baker Hughes Incorporated All rights reserved.
Incomplete Drainage
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Reservoir Geomechanics
Outline
Î
Critically stressed fractures/faults
z
Reservoir compaction
z
Pore volume compressibility
z
Surface subsidence
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
E&P Business Drivers z
Well placement ¾ hydraulically conductive fractures (reservoir objective) ¾ fault sealing/re-activation (exploration/development objective) ¾ wellbore stability considerations (drilling objective)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Critically Stressed Fractures z
z
z
Critically stressed fracture analysis enables the identification of fractures which are optimally aligned to fail in the present day stress regime, and hence are most likely to be conduits to fluid flow. Several studies have demonstrated that fluid flow within fractured rocks occurs largely through critically stressed fractures (e.g. Barton et al, 1998; Hickman, 1998). That a fracture is critically stressed does not necessarily mean that it is open and permeable (although this is likely).
© 2005 Baker Hughes Incorporated All rights reserved.
Vung Tau headland – FRACTURE DENSITY
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Critically Stressed Fractures z
Critically stressed fracture analysis consists of the following activities: – Natural fracture identification and characterization. – The far-field in-situ stress tensor is projected onto the fracture plane to give the normal and shear stresses acting on the plane. – These stresses are then plotted on a normalized Mohr-Coulomb diagram and compared to the fracture failure line defined by the friction coefficient of faults and fractures in the rock. – Finally, fractures are classified as critically stressed if the ratio of shear to normal stress exceeds the shear failure line.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Critically Stressed Fractures CSFA Workflows Far field stress tensor analysis
Poroelastic properties & friction coefficient
Natural Fracture Characterization r
σn
σ ij Critically Stressed Fracture Analysis
v
τ
Fracture plane
nˆ
Drilling trajectory recommendations Fracture reactivation, pressure maintenance © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Critically Stressed Fractures
A
B α
Natural Fracture characterization (dip angle & dip azimuth)
A
St rik e
+ B
Dip direction
In-situ stress tensor (magnitude & direction) ⎡σ xx τ xy τ xz ⎤ ⎡σ H ⎥ ⎢ σ = ⎢τ xy σ yy τ yz ⎥ = ⎢⎢ 0 ⎢ τ xz τ yz σ zz ⎥ ⎦ xyz ⎢⎣ 0 ⎣
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
0
σh 0
0⎤ 0 ⎥⎥ σ v ⎥⎦ X 'Y 'Z '
www.bakeratlasdirect.com
In -situ Stress Regimes In-situ σv
σv > σH > σ h
σ h min
σ H max σv
σH > σv > σ h
σ H max
σ h min σv
σH > σ h > σ v
© 2005 Baker Hughes Incorporated All rights reserved.
σ h min
Efficiency….Data accuracy….People-oriented service
σH
www.bakeratlasdirect.com
Stress Vector Projection into a Fracture Plane Up
Upper hemisphere A
x
B
nˆ North
α
West
East
St rik e
South
A
B
Dip direction Down
σ1 σ2
r
σ3 σ2
North
σn
σ
v
τ
West
σ1 © 2005 Baker Hughes Incorporated All rights reserved.
Upper hemisphere (Plan view) Efficiency….Data accuracy….People-oriented service
15
30
Dip
x
nˆ
σ3
0
45 60
75 90
East
Strike
South www.bakeratlasdirect.com
Normal & Shear Stresses on a Plane ¾
¾
Z Assume that XYZ coordinate system corresponds to the far-field stress directions, i.e., principal axes, and l, m, n are the C direction cosines of normal OP (define by the dip and dip direction). P
The normal stress on the plane:
σ =l σ +m σ +n σ 2
2
1
¾
2
2 2
2
2 3
B
O
The shear stress on the plane:
τ 2 = (σ 1 − σ 2 )2 l 2 m 2 + (σ 2 − σ 3 )2 m 2 n 2 + (σ 3 − σ 1 )2 n 2l 2
© 2005 Baker Hughes Incorporated All rights reserved.
(l,m,n)
Efficiency….Data accuracy….People-oriented service
A X
www.bakeratlasdirect.com
Y
Critically Stressed Fractures z
z
3D Mohr Circle plot shows resolved stresses on fractures Fractures above failure envelope may be more τ conductive to flow σv
criticallystressed stressedfractures fracturesabove above critically frictionalfailure failureenvelope envelope frictional stablefractures fractures stable belowfrictional frictional below failureenvelope envelope failure
© 2005 Baker Hughes Incorporated All rights reserved.
σ3 σv
Efficiency….Data accuracy….People-oriented service
σ2 σv
σ1 σv www.bakeratlasdirect.com
Critically Stressed Fractures
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Critically Stressed Fractures
(normal fault stress regime) σv>σH,max>σh,min σH,max
z
σH,max
z
In-situ stress tensor characterization Natural fracture identification r
σn
σ ij
v
τ
Fracture plane
nˆ
σh,min © 2005 Baker Hughes Incorporated All rights reserved.
σH,max
σv
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Critically Stressed Fractures
(strike -slip and reverse fault stress regimes) (strike-slip σH,max>σv>σh,min
© 2005 Baker Hughes Incorporated All rights reserved.
σH,max>σh,min>σv
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Exploiting Permeable Fractures 35
RD-8X
R D -8 x 3600
μ = 1.2
30
μ = 0.6
0
Mud Loss, bbl/hr M u d L o ss , b b l/h r 50
100
150
200
250
300
350
400
3650
20
15
3700
Shear Stress, MPa
25
10
0 0
5
10
15
20
25
30
35
40
45
50
55
M in _ D is c
M in o r
W id e
W id e -D is c
A lte re d
D IH F
V uggy
3750
MD, m
5
M u d L o ss
60
Normal Stress, MPa
3800
R D -1X : P LT lo g 13000 12000 11000
3850
10000 9000
bbl/d
8000 7000 6000
3900
5000 4000
0
0 .2
3000
0 .4
0 .6
D is co n tin u ity R e la tiv e A p e r tu r e
0 .8
2000 1000 0 3000
3020
3040
3060
3080
3100
3120
3140
3160
3180
3200
3220
3240
3260
3280
3300
3320
3340
3360
3380
3400
M D (m .BRT )
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
1
Critically Stressed Fractures
(drilling application)
Critically stressed fractures
Preferred horizontal well trajectory is E-W Fractures not under a critically stress state
σHmax direction N - S © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Critically Stressed Fractures
(well completion application)
Stratigraphy Open-hole logs Fracture orientation from core
Location of the CSF in the Lithology column
Rose-diagrams of cemented (red) and partially-cemented (cyan)/non-cemented (blue) fractures Fracture density of all fractures Rose-diagrams of critically stressed fractures Fracture density of critically stressed fractures Stress model
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
““Critically-Stressed” Critically-Stressed” Faults z
Shear Stress
z
Fault sealing capacity – fault reactivation during injection/production Critical pore pressure – estimate the ambient (excess/reduction) pore pressure a fault can maintain before slipping f ailu re line
τ − μ ( S n − Pp ) ≥ 0 rearranging gives: critical p
P
τ = Sn − μ
water depth earthquakes
cri ti cally s tress ed fract ure
n on -critically str essed fr actur e
σ 3’
© 2005 Baker Hughes Incorporated All rights reserved.
σ1 ’
Norm al Stress
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
““Critically-Stressed” Critically-Stressed” Faults
(normal fault stress regime)
Mohr diagram showing the effects of pore pressure/stress coupling during pore pressure depletion in a normal fault stress regime. A decreasing minimum horizontal stress leads to higher differential stress. Streit and Hillis (2002) – SPE 78226
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Pressure/Stress Coupling
ΔS h b= ΔPf b ~ 0.5 - 0.8
Streit and Hillis (2002) – SPE 78226 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Optimally vs. Non -Optimally Non-Optimally Oriented Faults
Mohr diagram showing the state of stress for the reactivation of cohesionless fault at an optimum fault angle (θ=45o -0.5tan-1μ) .
Mohr diagram showing the state of stress for the reactivation of cohesionless fault at an non-optimum fault angle (θ>45o).
Streit and Hillis (2002) – SPE 78226
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
Mohr diagram showing the state of stress for the reactivation of a cemented fault with cohesive strength. www.bakeratlasdirect.com
Critical Pore Pressure to cause Compressional Shear Failure Normal fault stress regime − 2C + (S v − S h )(1 − μ tan θ )sin 2θ ( S v − S h ) = 1− − Sv Sv 2μ Sv
Pf
Defining:
C = fault cohesive strength
Pf = Pfo − ΔPf S h = S ho − ΔS h
μ = coefficient of friction θ = fault angle Pfo = initial pore pressure S ho = initial minimum horizontal stress Sv = overburden stress
Streit and Hillis (2002) – SPE 78226 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Critical Pore Pressure to cause Compressional Shear Failure Normal fault stress regime Pf = Pfo −
2C − 2 μPfo + μS ho + S ho sin 2θ − 2μ + bμ + b sin 2θ + bμ cos 2θ
μS ho cos 2θ − S v sin 2θ + μS v 2(sin θ ) 2 + − 2μ + bμ + b sin 2θ + bμ cos 2θ
Streit and Hillis (2002) – SPE 78226 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Critical Pore Pressure to cause Fault Reactivation Ekofisk Field
μ = 0.6 C = 0 (cohesionless) © 2005 Baker Hughes Incorporated All rights reserved.
Streit and Hillis (2002) – SPE 78226
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Critical Pore Pressure to cause Fault Reactivation, f( μ) f(μ) Ekofisk Field
Streit and Hillis (2002) – SPE 78226 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Summary - CSF z
z
z
Accurate characterizations of in-situ stresses and natural fractures/faults are critical to the understanding of fractured reservoir performance and fault reactivation potential. Quantifications of critically-stressed fractures provide an ‘engineered’ approach to fractured reservoirs’ exploration and exploitation strategies. Predicting induced reservoir and fault failure (re-activation) is an essential requirement for the long term planning of hydrocarbon field depletion strategies.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline
z
Critically stressed fractures/faults
Î
Reservoir compaction
z
Pore volume compressibility
z
Surface subsidence
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Reservoir Compaction What is Reservoir Compaction? ) Initially, pore fluids and grains support the overburden. When produced, load is transferred to the grains and stress on rock grains (“effective stress”) increases. At low effective stress levels, elastic deformation take place while at higher effective stresses, grains undergo crushing resulting in irreversible compaction of reservoir layers. ) The phenomenon is called “pore collapse”.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Reservoir Compaction Ice tea
Rigid body movement, grain slippage, rotation and displacement, grain cracking and crushing, pore volume reduction © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Reservoir Compaction & Subsidence Surface Subsidence Overburden
Reservoir Sideburden
Sideburden
• • • • •
Pore pressure decline Effective stress increase Reservoir compaction Overburden load transfer Subsidence
Underburden
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Reservoir Compaction – Arching Effect figure from SPE 17852
• • • • •
Overburden load may not transfer completely (SPE 17852) Leading to reduction in load in the middle Called “arching effect” Especially in rigid (or less compliant) formations Leading to smaller compaction and subsidence in the middle than at the flanks
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Pressure Depletion Effects overburden stress fluid-filled pores
grains
Total Stress = Pore Pressure + Effective Stress Carried by the Grains
σ © 2005 Baker Hughes Incorporated All rights reserved.
=
p
+
σ’
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Pressure Depletion Effects overburden stress fluid-filled pores
grains
Total Stress = Pore Pressure + Effective Stress Carried by the Grains
Depletion = ΔP
σ © 2005 Baker Hughes Incorporated All rights reserved.
=
P
+
σ’
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Pressure Depletion Effects Overburden stress subsidence
compaction
Total Stress = Pore Pressure + Effective Stress Carried by the Grains
σ © 2005 Baker Hughes Incorporated All rights reserved.
=
p
+
Efficiency….Data accuracy….People-oriented service
σ’ www.bakeratlasdirect.com
Compaction At Low Effective Stress Levels:
Porosity Decrease
Pore Pressure Decrease Elastic or reversible
• “Elastic region” • Gradual porosity decrease • Low compressibility • Small displacements • Mostly reversible
At High Effective Stress Levels:
Post-pore collapse Pore Pore collapse collapse stress
Effective Stress Increase
© 2005 Baker Hughes Incorporated All rights reserved.
• “Pore collapse” region • Beyond certain “threshold stress” • Rapid porosity decrease • Increased compressibility • Large displacements • Irreversible or permanent
After Pore Collapse: • “Post-pore collapse” region • Material hardening • Decreasing compressibility
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Collapse Behavior
Compressibility Increase
Porosity Decrease
Pore Pressure Decrease pore collapse
• Compressibility is defined as change in volume for a given change in pressure • Sharp increase in compressibility • Large displacements • Irreversible or permanent
Effective Stress Increase
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Reservoir Compaction Compaction leads to: • • • • • • • • •
Reduction in permeability (pore throat closure) Increase in permeability due to fracturing/shearing Provides compaction drive energy Reduction in ultimate recovery Casing collapse/shear, esp. along faults Could trigger sand production Surface subsidence/Platform settlement Costly remedial measures Could also lead to well abandonment
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Case Histories (Compaction & Subsidence) ) Ekofisk field (North Sea) - Johnson et al., 1989 Total subsidence (Feb. 1989) ~ 14.4 ft Expected subsidence (in 2011) -- 20 ft
) Lagunillas Oil Field (Venezuela) – v.d. Knaap & v.d. Vlis, 1967 Coast of Lake Maracaibo, first produced 1926 Parts of shoreline permanently flooded by lake water (1929) 27 mi. concrete protection walls & dikes built to protect local population & installations Subsidence ~10 ft. by 1960 and 13.5 ft by 1976
) Wilmington Oil Field (California) - Allen & Mayuga, 1970 Oil field was discovered in 1932, production started 1941-42 Cumulative subsidence reached more than 29.5 ft. in 1968 Subsidence effectively stopped by water injection
) Offshore Sarawak (Malaysia) - van Ditzhuijzen & de Waal, 1984 Central Luconia gas fields, depletion caused pore collapse in limestones and dolomites Cumulative subsidence calculated at 8 to 20ft, based on location
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Reservoir Compaction Calculation
Elastic
Porosity Decrease
Reservoir Compaction
Pore Pressure Decrease
Plastic (Pore collapse)
Effective Stress
) Elastic compaction calculated using elastic equations for compressibility (bulk, grain and pore volume) - reversible ) Pore collapse compaction is more severe and larger compared to elastic – e.g., using trendline method - irreversible © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Reservoir Compaction Calculation compressibility = change in volume/orig. volume = change in height/orig. height pressure change (depletion) pressure change (depletion)
C pp ( u )
Δh / h = ΔP
(ΔP=pore pressure change)
Δh = compaction
h
Δ h = C pp ( u ) * Δ P * h © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Collapse Compaction Pore Pressure Decrease
Porosity Decrease
Trendline
Trendline behavior (Smits et al., 1988): • Divide reservoir into layers based on porosity and rock type • Establish a “trend line” for each of the formation rock types through lab tests • Estimate the expected drawdown (depletion) • Determine the increase in effective stress
Effective Stress Increase
• Estimate the change in porosity for the change in effective stress • Compaction in each layer is given by:
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Collapse Compaction Pore Pressure Decrease
Porosity Decrease
Trendline
(φ i − φ f ) Δh i = h i (100 − φ f )
Initial porosity, φi
n
Total = ∑ Δ h i i =1
Final porosity, φf
Initial eff. Collapse Final eff. stress stress stress
Effective Stress Increase
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Total Compaction
Total Compaction = Elastic Compaction (calculated from compressibility)
+ Pore Collapse Compaction (using trendline method)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline
z
Critically stressed fractures/faults
z
Reservoir compaction
Î
Pore volume compressibility
z
Surface subsidence
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Why are Compressibility Measurements Important? z z z z z z
Reserve estimation Reservoir pressure maintenance Reservoir drive assessment Production forecasting & history matching Reservoir compaction & subsidence predictions Permeability change prediction
© 2003 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Reservoir Compaction – Reservoir Stress Conditions •
•
•
Hydrostatic stress – isotropic state of stress does not replicate field boundary conditions; not realistic stress path; however, easiest to σc simulate in the laboratory Triaxial stress – anisotropic state of stress is more realistic but still does not replicate field boundary conditions; relatively easy to simulate in the laboratory Uniaxial strain - reservoir fluid production is associated with pore pressure reduction, constant overburden and zero lateral deformation; most realistic stress path; however, difficult to perform in the laboratory
© 2003 Baker Hughes Incorporated All rights reserved.
σa
σ c = σa
σa
σa
σc
σc
σa
εc = 0
σa
σa
www.bakeratlasdirect.com
Elastic Compressibilities z
Bulk compressibility, Cb
z
Pore volume compressibility, Cp
z
Grain compressibility, Cg
Obtained from elastic moduli: Young’s modulus (E) and Poisson’s ratio (ν)
Need to differentiate between: • hydrostatic (commonly performed in lab), and • uniaxial (more representative of field conditions) As well as between: • changing confining pressure and • changing pore pressure © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Compressibility – Definitions C bc
C pc
− 1 ⎛ ∂Vb ⎞ ⎜⎜ ⎟⎟ = Vb ⎝ ∂Pc ⎠ p
− 1 ⎛ ∂Vp ⎞ ⎜⎜ ⎟⎟ = Vp ⎝ ∂Pc ⎠ p
C gc = C gp
C bp p = cons tan t
C pp p = cons tan t
1 = Vb
⎛ ∂Vb ⎞ ⎜ ⎟ (bulk) ⎜ ∂P ⎟ ⎝ p ⎠ Pc=cons tan t
1 = Vp
⎛ ∂Vp ⎞ ⎜ ⎟ (pore) ⎜ ∂P ⎟ ⎝ p ⎠ Pc=cons tan t
⎡ ⎤ ⎞ ⎛ V ∂ ⎛ ⎞ V 1 ∂ p b 1 − ⎢ ⎟ ⎥ (grain) ⎜ ⎜ ⎟ = Cg = = ⎢ Vb ⎜⎝ ∂Pc ⎟⎠ p Vp ⎜⎝ ∂Pp ⎟⎠ ⎥ Pc ⎦ p ⎣ [Δ ( Pc − Pp ) = 0 ]
( from Zimmerman, 1991) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Bulk Compressibility, Cb z
Under changing pore pressure, Cbp
z
Under changing confining pressure, Cbc We need Cbp – replicates field conditions Most labs obtain Cbc
σc
PP
Note: Cxy means: x compressibility under changing y x: b (bulk), p (pore) or g (grain) y: p (pore pressure), c (confining pressure) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Volume Compressibility, Cp z z
Under changing pore pressure, Cpp Under changing confining pressure, Cpc We need Cpp– replicates field conditions Most labs obtain Cpc Also need to convert Cpp (hydrostatic/triaxial) to Cpp(u) (uniaxial) Relationships are available for these conversions.
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Compressibility Relationships C bp = C bc − C gc
C pp =
C pc =
Pore © 2005 Baker Hughes Incorporated All rights reserved.
φ
C bc − (1 + φ )C gc
Bulk Grain
C bc − C gc
C pp ( u ) =
φ
C pp (1 + ν ) 3(1 − ν )
(hydrostatic)
(uniaxial strain)
(Zimmerman, 1991)
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Grain Compressibility, Cg z z z
Under changing pore pressure, Cgp Under changing confining pressure, Cgc But, Cgp = Cgc→ very small
Pc
Obtained using unjacketed sample or jacketed sample, ensuring Pore pressure = confining pressure Only grains deform, measuring Cg
Pc
Cg for quartz = 1.6*10-5 psi-1 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Compressibility Measurement z
Direct measurement (lab-based) – – – – – –
z
Time consuming Expensive Difficult to get cores Core damage and handling, etc. Limited labs equipped for this Limited personnel capabilities
In-Direct measurement (log-based) – – – – –
Time saving Economic Requires logs (usually available) Fairly accurate As a function of depletion and stress changes
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Compressibility Measurement z
Direct measurement (lab-based) – Hydrostatic Test (easy to perform, not preferred for isotropic stresses) – Triaxial Test (anisotropic stress conditions, easy to perform, preferred) – Uniaxial Strain (most preferred, simulates field conditions, but most difficult to perform) – As a compromise, compressibilities obtained using Triaxial Test and converted into uniaxial equivalent
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Hydrostatic Test σ
Radial
δ1
Volumetric
δ3/2
σ
Confining Pressure (psi)
1200
l
d
Axial
1000 800 600 400 200 0 0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
Strain
δ1 εv = ε1 + 2* ε3 ε1 = l δ3 K = σ C = 1 ε3 = b K εv d © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Triaxial Test σ1
Radial
Axial
16000 14000 Axial Stress (psi)
δ1 l
12000 10000 8000 6000 4000 2000 0 -0.006 -0.004 -0.002
d
σ1 E= ε1
0
0.002
0.004
0.006
0.008
0.01
0.012
Strain
δ3/2
ε3 ν=− ε1
E 1 K= Cb = 3(1− 2ν) K © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Uniaxial Strain Test σ1
Radial
σ3
l
d
δ3 = 0
A x ia l S t re s s ( p s i)
δ1
Axial
16000 14000 12000 10000 8000 6000 4000 2000 0 0
0.002
0.004
0.006
0.008
0.01
Strain
1 σ1 Cu = < Cb M= M ε1 (1 + ν) Cb Cu = (1 − ν) 3 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
0.012
Intelligent Triaxial Compression
Stress
— σc — Pp — σa E F
C
B Grain compressibility C Bulk modulus/compressibility
G H
B
A Pre-seating - secure jacket
D
D Young’s modulus, Poisson’s ratio E Compressive strength F Post-failure strain softening G Residual strength
A
H Unloading Time
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Intelligent Compaction/Drawdown Test design Stress
E D C B A
F
A Pre-seating - secure jacket G H — σc — Pp — σa
B Skempton’s constant B C Grain compressibility Cg D Bulk modulus K, bulk compressibility Cb
Strain
E Young’s modulus E, Poisson’s ratio ν F Creep/equilibration
— εa — εr
G Uniaxial strain drawdown, compaction, grain crashing, pore collapse Time
© 2005 Baker Hughes Incorporated All rights reserved.
H Unloading
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Stress Loading History - Triaxial Compression at Uniaxial Strain Condition with Pore Pressure Depletion
8000 Total Axial
7000 6000
Effective Axial
5000
Confining
4000 3000 2000
Pore
1000 0 0
2
4
6
8
10
12
14
Time (hour)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Compressibility Determinations from Volumetric Strain - Stress Plot 0.016 0.014 0.012
Confining y = -3.5378E-07x + 1.3746E-02 2
R = 9.9436E-01 Axial Compaction Coefficient = 3.538 E-7 psi-1 Pore Volume Compressibility w/ Initial Porosity = 23.0%
0.01 0.008
Pore y = 2.432E-06x - 1.524E-03 2
R = 9.957E-01 Bulk Compressibility
-1
= 1.447 E-6 psi
-1
= 2.432 E-6 psi α = 0.96
0.006
y = 5.264E-06x - 1.404E-02
0.004
2
R = 9.992E-01 Initial Bulk Compressibility
y = 9.168E-08x + 3.838E-03
0.002
-1
2
5.264 E-6 psi α = 0.98
R = 9.306E-01 -1
Grain Compressibility = 9.168 E-8 psi
0 0
1000
2000
3000
4000
5000
6000
Stress, psi © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Compressibility Measurement – Log-based Approach Pore volume compressibility using LMP: Considers reservoir stress changes with depletion (pressuredependent PVC) Incorporates stress condition constraints that ensure deformations are within elastic bounds Considers stress anisotropy effects (hydrostatic vs. triaxial) Takes log input, commonly available Provides continuous profile with depth Cost-effective, time-saving (particularly when core is n.a.) © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Logging of Mechanical Properties σa
Log Inputs
Produce StressStrain Curves
Δtc, Δts, Porosity, Lithology
σr Produces Virtual Core Sample
σa
Applying Virtual Stresses to the “Core Sample”
εr
εa
Static Mechanical Properties: Rock Strength, Elastic Moduli Poisson’s Ratio, Compressibilities © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Log Derived Compressibility – Simulated Hydrostatic Compression z z z z z
Process LMP Determine static bulk modulus (HC) Calculate bulk compressibility Assume grain compressibility (Cgc) from table Calculate pore volume compressibility (PVC)
∂σ c Kb = ∂ε v 1 C bc = Kb © 2005 Baker Hughes Incorporated All rights reserved.
C pp =
C bc − (1 + φ )C gc
Efficiency….Data accuracy….People-oriented service
φ www.bakeratlasdirect.com
Log Derived Compressibility – Elastic Moduli z z z z z
Process LMP - static elastic moduli Calculate bulk modulus Calculate bulk compressibility Assume grain compressibility (Cgc) from table Calculate pore volume compressibility (PVC)
E Kb = 3(1 − 2ν ) 1 C bc = Kb © 2005 Baker Hughes Incorporated All rights reserved.
C pp =
C bc − (1 + φ )C gc
Efficiency….Data accuracy….People-oriented service
φ www.bakeratlasdirect.com
Uniaxial Strain Condition z
Reservoir fluid production is associated with pore pressure reduction, constant overburden and zero lateral deformation (constrained by earth crust)
z
Convert hydrostatic pore volume compressibility [Cpp] into uniaxial strain ‘equivalent’ pore volume compressibility [Cpp(u)], using:
C pp ( u ) =
© 2005 Baker Hughes Incorporated All rights reserved.
C pp (1 + ν ) 3(1 − ν )
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
PV Comparison – LMP vs. Lab
L M P ( P P = 1 2 0 0 0 p s i) L M P ( P P = 4 0 0 0 p s i) L a b I D # 5 - 1 ( 1 2 8 0 0 - 1 0 9 9 0 p s i) L a b ID # 5 -1 (4 7 9 0 -2 8 0 5 ) L a b I D # 1 0 - 3 ( 1 2 8 0 0 - 1 0 6 2 5 p s i) L a b I D # 1 0 - 3 ( 6 4 2 0 - 4 8 2 0 p s i)
TVDRKB, ft
Comparison of LMP vs. labderived uniaxial pore volume compressibility, with depth, for two effective stress conditions
L a b I D # 1 8 - 5 ( 1 2 8 0 0 - 1 0 8 0 5 p s i) L a b I D # 1 8 - 5 ( 6 6 0 0 - 5 0 0 0 p s i)
1
2
3
4
E ffe c tiv e P o r e C o m p r e s s ib ility x 1 0
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
5 -6
psi
6
-1
www.bakeratlasdirect.com
Pore Pressure Depletion Effects (Elastic) Reservoir Depletion Analysis – –
–
–
Changes in in-situ stresses, caused by reservoir pressure depletion, can result in shear failure of the formation Shear failure causes weakly cemented rock to disaggregate, leading to low values of cohesive strength and critical drawdown pressure For reservoir management and workover planning purposes, it is, therefore, important to know the onset of formation shear failure associated with reservoir depletion Reservoir stress path analysis is required
© 2003 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Pore Pressure Depletion Effects (Elastic) z Stress
Path – under uniaxial strain condition:
σ = σ + K o (σ − σ
Δσ h' νt Ko = = ' Δσ v 1 −ν t
' h
' ho
' v
' vo
)
z Reservoir
Failure – Mohr-Coulomb failure criterion
Ko is the stress path coefficient, are the effective σ ho' andσ zo' horizontal and vertical stresses, respectively, at the previous depletion stage and νt is the tangential Poisson’s ratio. © 2003 Baker Hughes Incorporated All rights reserved.
τ = S o + μσ = S o + σ tan φ or φ
σ = UCS + σ tan ( + 2 ) '
'
1
3
Efficiency….Data accuracy….People-oriented service
2 π 4
www.bakeratlasdirect.com
Uniaxial Strain PVC Variations with Depletions (Elastic)
Two general approaches: Constant stress path coefficient z Stress path coefficient as a function of effective horizontal and vertical stresses z
© 2003 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Uniaxial Strain PVC Variations with Depletions (Elastic) Constant Stress Path Coefficient 1.
Run LMP at initial reservoir confining condition.
2.
Calculate pore volume compressibility, Cpp, at triaxial stress condition (@ 50% peak stress) and convert to uniaxial strain equivalent, Cpp(u).
3.
At next pore pressure level, calculate the new horizontal stress using a constant stress path coefficient, Ko. Run LMP at the new confining stress condition.
4.
Repeat step 2.
5.
Continue step 3 until reservoir failure
Reference: SPE 95545 – Log-Based Pore Volume Compressibility Prediction – A Deepwater GoM Case Study (2005) © 2003 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Uniaxial Strain PVC Variations with Depletions (Elastic) Constant Stress Path Coefficient
*Discrepancy between lab and LMP derived PVC is probably due to different stress path coefficients and porosity values used in the computations. © 2000 Baker Hughes Incorporated All rights reserved. © 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Uniaxial Strain PVC Variations with Depletions (Elastic) Stress Path Coefficient = f(σh’, σv’) 1.
2.
3.
Run LMP at initial reservoir confining as well as several other confining pressure conditions expected to be experienced during reservoir depletion. Generate tangential Poisson’s ratio and Young’s modulus and plot these tangential elastic moduli as a function of axial stress at different confining pressures. At initial reservoir pressure condition, calculate the effective horizontal and vertical stresses. With these stress conditions (confining, axial) known, interpolate using plots generated in step 2 to obtain tangential Poisson’s ratio and Young’s modulus.
© 2003 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Uniaxial Strain PVC Variations with Depletions (Elastic) Stress Path Coefficient = f(σh’, σv’)
Reference: ARMA/USRMS 05-791 - Characterizing Pore Compressibility, Reservoir Compaction and Stress Path under Uniaxial Strain Condition for Nonlinear Elastic Rock (2005) © 2003 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Uniaxial Strain PVC Variations with Depletions (Elastic) Stress Path Coefficient = f(σh’, σv’)
Reference: ARMA/USRMS 05-791 - Characterizing Pore Compressibility, Reservoir Compaction and Stress Path under Uniaxial Strain Condition for Nonlinear Elastic Rock (2005) Efficiency….Data accuracy….People-oriented service www.bakeratlasdirect.com
© 2000 Baker Hughes Incorporated All rights reserved. © 2002 Baker Hughes Incorporated All rights reserved.
Uniaxial Strain PVC Variations with Depletions (Elastic) Stress Path Coefficient = f(σh’, σv’) 4.
Calculate stress path coefficient and uniaxial strain pore volume compressibility using: Δσ h' νt = Ko = ' Δσ v 1 −ν t
C pp (u ) 5.
6.
1 (1 + ν t )(1 − 2ν t ) ≈α φEt 1 −ν t
(neglect grain compressibility)
At next pore pressure level, calculate the effective vertical stress and assume an effective horizontal stress. With these stress conditions, interpolate using plots generated in step 2 to obtain tangential elastic moduli.
© 2000 Baker Hughes Incorporated All rights reserved. © 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Uniaxial Strain PVC Variations with Depletions (Elastic) Stress Path Coefficient = f(σh’, σv’) 7.
Calculate stress path coefficient and then effective horizontal stress using:
σ = σ + K o (σ − σ ' h
8.
9.
' ho
' v
' vo
)
Repeat step 6 until the effective horizontal stress converges. Calculate stress path coefficient and uniaxial pore volume compressibility as per step 4. Repeat steps 5, 6, 7 and 8 until reservoir failure.
© 2003 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Uniaxial Strain PVC Variations with Depletions (Elastic) Stress Path Coefficient = f(σh’, σv’)
Reference: ARMA/USRMS 05-791 - Characterizing Pore Compressibility, Reservoir Compaction and Stress Path under uniaxial Strain Condition for Nonlinear Elastic Rock (2005)
© 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Uniaxial Strain PVC Variations with Depletions (Elastic) Comparison of PVCs assuming different stress dependency elastic moduli
Reference: ARMA/USRMS 05-791 - Characterizing Pore Compressibility, Reservoir Compaction and Stress Path under uniaxial Strain Condition for Nonlinear Elastic Rock (2005) © 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
–Reservoir Reservoir Reservoir Compaction – Productivity Change (Elastic) Depletion-induced porosity & permeability change
φ = 1 − (1 − φo )e
ε z −ε zo
φo and εzo are porosity and vertical strain, respectively, at the previous depletion stage.
[ −γ ( p k = ko e
'
' − po
)]
p = '
σ v + 2σ h 3
− pp
ko is permeability measured at effective mean stress, po’, and γ =0.004 MPa-1 for a 20% porosity sandstone.
© 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Reservoir Compaction – Reservoir Productivity Change (Elastic) Depletion-induced porosity & permeability change q p' = 1.23 * + 0.00275 (damage/permeability criterion) * p p 2
2
⎡ p' ⎤ ⎡ q ⎤ ⎢ * ⎥ + ⎢ * ⎥ =1 ⎣p ⎦ ⎣p ⎦
(cap surface)
k = ko e [−γ ( p − po ) ] '
'
q p' = 1.81 * + 0.06 p* p
(for p ' / p * ≤ 0.175)
2
⎡ p' ⎤ q p' = −2.073⎢ * ⎥ + 2.536 * - 0.003 p* p ⎣p ⎦
(for p ' / p * ≥ 0.175)
1 ∂k ∂p ' − = 0.0049 + 0.0017 ∂q k o ∂q
q = σ v −σ h
p * = 6.435UCS
q and p* are the deviatoric stress and critical effective pressure for the onset of grain crushing under hydrostatic loading, respectively. Valid for 20% porosity rock. © 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
Reference: SPE 58717
www.bakeratlasdirect.com
Summary – Pore Volume
Compressibility •
•
•
We have presented a log-based method to compute uniaxial strain pore volume compressibility, stress path and permeability changes as a function of reservoir pressure depletion. The method is valid for reservoir pressures prior to the on-set of reservoir failure which can be estimated using a shear failure criterion such as the Mohr-Coulomb’s. Beyond shear failure, a constitutive law must be established to describe the mechanical behavior of rock deformation under stresses.
© 2000 Baker Hughes Incorporated All rights reserved. © 2002 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Outline
z
Critically stressed fractures/faults
z
Reservoir compaction
z
Pore volume compressibility
Î
Surface subsidence
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Surface Subsidence Calculations z
Rigorous Methods – Reservoir and overburden heterogeneity – Non-uniform pressure distributions – Numerical methods (Finite Element, boundary element, etc.) – Fairly accurate, but time consuming and costly
z
Approximate Methods – – – – –
*Geertsma’s (1973) nucleus of strain model Smits and de-Waal (1985) Morita et al (1989) Not expensive or time consuming Approximate, use as a guideline
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Surface Subsidence Calculations z
Assumptions: – Reservoir experiences the full overburden load (true near the center of the reservoir) – Exceptions near flanks, arching effects, presence of anticlines, faults, etc. are ignored – No lateral deformation (uniaxial compaction) – Uniform pressure distribution in the reservoir – Rock mechanical properties are uniform – Overburden behaves in an elastic manner homogeneously
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Surface Subsidence Calculations z
Geertsma’s* nucleus of strain model (spherical) – Consider a contracting sphere within an infinite medium (inner sphere) – Displacement trend in the surrounding medium will be spherically symmetric, given by:
where
ro 2 u = uo 2 R
u = radial displacement at a point
u R
uo ro
u0 = displacement at the nucleus r0 = radius of nucleus of strain sphere R = radial distance from center of sphere to the point *from Geertsma 1973 © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Geertsma’s Model (disk-shaped) Cb Cb u r (a ) = hΔ PB (ρ , η) u z (a ) = hΔ PA (ρ , η) 2 2 a D ρ = ;η = r r A = R ∫ J ( α R )J ( α a )e ∞
1
− Dα
0
dα
0
∞
A
B = R ∫ J 1 ( α R )J 1 ( α a )e − Dα dα 0
z
y
x
ur
a
(x,y,0)
D
B
uz (x’,y’,z’)
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Surface Subsidence Calculations z
Geertsma’s nucleus of strain model –The nucleus of strain model does not guarantee the uniaxial strain nature of reservoir compaction –To overcome this, “imaging” concept is introduced, commonly used in reservoir engineering. surface
Zero displacement planes (“no- flow” boundary) nucleus of strain
© 2005 Baker Hughes Incorporated All rights reserved.
image nucleus
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Solved Example Problem: Calculate the maximum surface subsidence given the following: reservoir diameter = 4 km (r = 2 km) reservoir depth (D) = 2 km reservoir height (h) = 50 m compressibility: 6.0*10-5 bar-1 expected compaction: 2.5′ subsidence (S)
D = 2km compaction (C)
50m 4km 4km © 2005 Baker Hughes Incorporated All rights reserved.
4km
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Solved Example Solution: uz(a) = Cb/2 DP h A(r,h) cancel
S 0.5 * C b * ΔP * h * A s (ρ, η) A s (ρ, η) = = C 0.5 * C b * ΔP * h * A c (ρ, η) A c (ρ, η)
S 0.2929 + 4 * 0.0519 = = 0 .5 C 1.00
Contribution Point
Location(s)
a
D
ρ
η
A (from table)
Center, top of reservoir
1
0
0
0
0
1
Center, surface contribution from the reservoir
2
0
2
0
1.0
0.2929
Center, surface contribution from the 4 images
3
4
2
2.0
1.0
0.0519 * 4
subsidence (S)
D = 2km
3
compaction (C) 1
50m 2
3
4km
a = 4km 4km
3
3
S= surface subsidence, C= reservoir compaction © 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Summary - Subsidence Surface subsidence should be estimated and considered in: – Platform design – Casing design – Reservoir management (injection, depletion rate, etc.) – Production life of the reservoir – Impact on surrounding structures and environment
© 2005 Baker Hughes Incorporated All rights reserved.
Efficiency….Data accuracy….People-oriented service
www.bakeratlasdirect.com
Related Documents
Geomechanics Course Baker Hughes 2007.pdf
January 2021 2
Baker Hughes
January 2021 2
Baker Hughes Presentation
January 2021 1
7. Baker Hughes - Technologies
January 2021 3
6 - Baker Hughes - Glen Benge
January 2021 0
13 - Baker Hughes - Kennedy En
January 2021 0More Documents from "Specule"