PetroMod*

Geomechanics

Thomas Hantschel, Michael Fuecker

Schlumberger, Technology Center Aachen

© 2012 Schlumberger. All rights reserved.

An asterisk is used throughout this presentation to denote a mark of

Schlumberger. Other company, product, and service names are the

properties of their respective owners.

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Subsurface Pressure Conditions

Bu

ria

l D

ep

th

Pressure

Lithostatic

Pressure

Hydrostatic

Pressure

Pore

Pressure

Fluidflow

Compaction

Zon

e o

f

Ove

rpre

ssu

re

hP

u

lP : Effective Overburden Pressure (MPa)

u : Excess Pore Pressure (MPa)

lP

hP

: Lithostatic Pressure (MPa)

: Hydrostatic Pressure (MPa)

eP

normal / hydrostatic

pressure

overpressure

Definition and Application

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Overpressure Model

Flow Term

ttt

uC

t

uCugrad

kdiv

cca

11

ke 1)(

Mechanical

Compaction

Chemical

Compaction

Overburden

Load

Pore Fluid

Expansion

RT

E

eT

0

)1(),(

V

p

C

1..Outflow: 2..Pore Pressure Decrease;

3..Compaction

1..Compaction: 2..Pore Pressure Increase;

3. Outflow

V

p

C

3D (Water) Flow

Rock Compaction

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log(mD)

impermeable

low permeable

moderate permeable

high permeable

50% Carb & 50% Marl35% Silt & 35% Shale & 30% Carb

70% Sand & 30 & Shale50% Sand & 50% Shale10% Sand & 80% Shale+10& CarbSandstone15% Sand & 85% ShaleSiltstone70%Sand & 30%ShaleShale33% Sand & 34% Shale+33%CarbSS(5) & SH(95)SaltBasement

Lithology

Permeability (vertical)

Overpressures

Example: Santos Basin

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Mpa

Lithostatic pressurein saltHigh overpressure

in dense shales

Shallow hydrostatic area

High overpressure below the salt

Moderate overpressurebelow salt windows

Overpressures

No overpressuregradient in sands

Example: Santos Basin

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100 my

20 my

Present Day

Overpressure

In MPa

Pore Pressure Prediction: Prospect in Gulf of Mexico

Basics: • Dynamic model acting on

geological time scales

• Based on permeability

controlled one phase fluid flow

equation

Advanced: • Calibration Methods

• Additional Effects: HC

Generation Pressure and

Aquathermal Pressuring

• Salt Tectonics

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Applications:

• Improved predictions of fracture

orientations and fault properties (seal

analysis)

• Descriptions of salt movements

• Better pore pressure predictions

3D stress tensor display

around salt domes the interactive Mohr Circle shows the

stress/strain relationships in any selected

cell in the model

Basin Scale Geomechanics (PetroMod GM: 2011.1)

• Dynamic model acting on geological time

scales

• Coupling of stress calculations with a basin

scale fluid simulator

• Adjustment of material parameters to larger

scale cells

• Plastic and failure effects, such as compaction

and fault movements

• Suitable boundary conditions.

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PetroMod 2011.1: Geomechanics

Calculate a basin-wide multidimensional stress field for better modeling of fracturing, salt

movement, faulting and lateral compaction caused by tectonics.

Approach 1: “Irreversible Poroelasticity”

Use linear elasticity methodology to calculate the 3D stresses. Only three material

properties are needed: bulk density, elasticity model, Poisson ratio.

Approach 2: Poroplasticity (PetroMod 2012)

The two failure effects of compaction and fracturing are described with plastic failure

curves (Yield surfaces) and subsequent hardening (or softening) behavior. The

methodology is very powerful and sophisticated, but many additional material parameters

are needed.

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PetroMod 2011 Geomechanics

Approach 1: “Irreversible Poroelasticity”

Use linear elasticity methodology to calculate the 3D stresses. Only three material

properties are needed: bulk density, elasticity model, Poisson ratio.

Material properties for this approach are either already available in petroleum systems

modeling, or in the case of the Poisson's ratio are within a limited range (usually about

0.35) with salt as an exception (approx. 0.48).

Benefits:

Directly coupled with petroleum system model data and process modeling (e,g,

pressures)

Access to all properties e.g. for basin scale compaction modeling

Extension of classical Terzaghi compaction modeling

Enables boundary conditions to be defined

Limitation:

Stress is not limited based on failure criteria, so the processes that result from

exceeding the failure criteria cannot be modeled … this will be covered in Development

Stage 2

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Poro-elasticity: The 3D Compaction Law

1. Elasticity described a (linear) relationship between Forces and Deformation

Stress (Forces)

Strain (Deformation)

e

Elasticity Module E

Poisson Ratio n (Shear Module G

Compressibility Module K)

2. Stress is Effective Stress = Total Stress – Pore Pressure

c)

Shear Effective Stress ’ t

Normal Effective Stress ’ n

b)

Deviator Effective Stress q

Mean Effective Stress ’

B

D

C

A

A

B

C

D

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Elastic Properties: irreversible poroelasticity

How to compute the Modulus of elasticity from compaction curve:

Decrease of porosity with compaction is irreversible, which will result in larger modulus of elasticity.

1

)1(3Tv CC

VCE

)21(3

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The Stress Tensor

mzzyzxz

yzmyyxy

xzxymxx

m

m

m

zzyzxz

yzyyxy

xzxyxx

00

00

00

Total stress tensor Mean stress tensor

(isotropic component)

Deviatoric stress tensor

(anisotropic component)

The stress tensor is symmetric

It is composed of an isotropic (mean stress) and anisotropic (deviatoric stress) component

It can be described by six independent components in 3d (three in 2d) with

– xx , yy , zz : normal stress components

– xy , yz , xz : shear stress components

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Definitions: Stress

Principal stresses

1, 2, 3; with 1 > 2 > 3

Axes orthogonal to each other

Mean stress (m = (1 2 3)/3)

Arithmetic mean (average) stress of the principle stresses

Deviatoric stress (dev = total – m)

Total stress minus mean stress

Differential stress (diff = 1 – 3) (simplified deviatoric stress)

Difference between the largest and the smallest principal stresses

Effective stress („ = – pf)

Total stress minus pore pressure (pf)

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The three principal stresses 1, 2, 3 are also a set of three stress

invariants (1 > 2 > 3)

Another set of stress invariants are:

Mean stress:

Deviatoric stress:

Lode angle:

q is especially important

to estimate the failure of a material

Stress Invariants

)(3

2tan

23

321

2

32

2

31

2

21 )()()(2

1 q

p~

q~

2

1

3

1 = 2 =3

)(3

1321 p

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Mohr and p/q diagrams

mzzyzxz

yzmyyxy

xzxymxx

m

m

m

zzyzxz

yzyyxy

xzxyxx

00

00

00

Total stress

tensor Mean stress tensor

(isotropic component)

p

Deviatoric stress tensor

(anisotropic component)

q

312

1 p 321

3

1 p

312

1 q 2

32

2

31

2

212

1 q

The p/q-diagram is a diagram in the deviatoric stress/mean stress plane

Visualization of points instead of circles

Parameters are derived from the principal stresses

2-dimensional 3-dimensional

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Mohr and p/q diagrams

312

1 p 321

3

1 p

312

1 q 2

32

2

31

2

212

1 q

The p/q-diagram is a diagram in the deviatoric stress/mean stress plane

visualization of points instead of circles

Parameters are derived from the principal stresses

2-dimensional 3-dimensional

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Mohr and p/q diagrams

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The Vertical Stress Distribution

Pressure: Lithostatic Stress zz

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Geomechanical Effects of Salt Bodies Poisson‟s ratio

ν=0.495 v=0.3

Horizontal Displacement

sxx εxx

Modulus of Elasticity

v=10 MPa

v=200 MPa

Vertical Stress

0 MPa

v=120 MPa

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Geomechanical Effects of Salt Bodies

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Campos Basin

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Total Vertical Stress versus Lithostatic Pressure

Szz p_lith

100 MPa

200MPa

0 MPa

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Lateral Stress Sxx

75 MPa

150MPa

0 MPa

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Seal Failure (and Fracture) Analysis in the Campos Basin

Salt Shale

10MPa 69MPa

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Development of fractures and fracture orientation

Fracture depends on differential stress τ≈ σ 1- σ 3

and mean effective stress σ‟=(σ 1+ σ 2+ σ 3)/3-pp

Ф≈30 ̊

Mohr-Coulomb criteria: Direction of fracture plane: σ 1

σ 2

Θ=90̊-2Ф

New Fracturing Risk Overlay

A user defined yield line determines fracturing risk using a

Drucker-Prager failure criterion

Information about failure is

provided by an overlay

eff

eff

Fractures Yield line

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Santa Barbara Model

Dynel 2D reconstruction

.. In accordance with Parra et all (2010) and structural restoration in accordance with Maerten (2010)

Fig. 6: Litho-Stratigraphy of the Section under Study

Fig. 5: Predicted Petroleum Systems at Present Day

Major hangingwall

Major footwall

0 150

300

Mean stress [MPa]

13my

present

65my

Fig. 10: Mean Stress Formation Through Geologic Time

0 150

300

Mean stress [MPa]

Fig. 11: Mean Stress

0 50

100

Deviatoric stress [MPa]

Fig. 12: Deviator Stress

0 50 200

Pore-pressure [MPa]

No compression Compression [MPa]

3

1

Fig. 13: Pressures and Stresses along a Well

Well

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Cumulative slip distribution along faults for

each restoration step.

Fault activity and development

through time

Mechanically Based Restoration with Dynel 2D

Fault Property Prediction in 2D

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Summary

The model encompasses:

Dynamic model acting on geological time scales

Coupling of stress calculations with a basin scale fluid simulator

Adjustment of material parameters to larger scale cells

Plastic and failure effects, such as compaction and fault movements

Suitable boundary conditions.

The model can be applied to

Improve predictions of fracture orientations and fault properties (seal analysis)

(Describe of salt movements)

Improve pore pressure predictions, especially for compression basins