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1. Stresses in the Subsurface
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Advanced Geomechanics - Class Notes
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Advanced Geomechanics - Class Notes
Contents
1
. Stresses in the Subsurface
1
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1
Scalar, vector, and tensor variables in the subsurface
1
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2
Cauchy's equilibrium equation and vertical stress
1
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3
Principal stresses and subsurface stress regimes
1
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4
Stress invariants and stress path
1
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5
WP1: Subsurface Stresses, Stress Tensor and Invariants
1
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5
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1
Exercise 1: Reading a stress log
1
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5
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2
Exercise 2: Computing total vertical stress
1
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6
Stress projection on a plane: normal and shear stress
1
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7
The geographical coordinate system
1
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8
WP2: 3D Stress Projection on Fractures and Faults
1
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8
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1
Exercise 1: Verification of critically stressed fractures intersecting a wellbore
1
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8
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2
Exercise 2: Verification of fault reactivation and available injection pressure window
2
. Continuum mechanics
2
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1
Equations needed to solve a continuum mechanics problem
2
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2
Kinematic equations
2
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2
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1
One-dimensional case
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2
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2
Three-dimensional case
2
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3
Constitutive equations
2
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3
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1
Linear elasticity
2
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3
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2
Stiffness matrix reduction to orthotropic elasticity
2
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3
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3
Stiffness matrix for vertical transverse isotropic elasticity
2
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3
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4
Stiffness matrix for isotropic elasticity
2
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4
1D subsurface mechanical models
2
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4
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1
Uniaxial strain case
2
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4
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2
Triaxial strain case
2
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4
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3
Parameters for Mechanical Earth Models
2
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5
Parameters for VTI MEM
2
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5
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1
Laboratory measurements
2
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5
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2
Anisotropy evaluation and models
2
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6
WP3: Horizontal Stresses Computed with Linear Elasticity
2
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6
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1
Exercise 1: One-dimensional mechanical Earth model (MEM)
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7
Navier's equation
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7
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1
Derivation
2
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7
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2
Analytical and numerical solutions
2
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7
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3
Weak formulation
2
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7
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4
Using FreeFem++ to solve equation of linear elasticity - by Igor Shovkun
2
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7
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5
Exercise 2: Vertical transverse isotropic elastic properties
2
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7
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6
Exercise 3: Displacement Field and Strain Field
2
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8
WP4: Solution of Navier's Equation for the Stress Field
2
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8
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1
Exercise 1: Stresses around a wellbore
2
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8
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2
Exercise 2: Stresses around a planar fracture
3
. Thermo-hydro-chemo-mechanical coupled processes in porous media
3
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1
Strain partition in the porous solid
3
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2
Free energy of the porous solid and poro-elastic equations
3
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3
Measurement of poro-elastic parameters
3
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4
Drained and undrained problems
3
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4
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1
Drained solution of in-situ stress and stress change with depletion
3
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5
Undrained problems
3
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5
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1
Diffusivity equation
3
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5
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2
Examples of undrained response in the subsurface
3
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5
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3
Undrained loading parameters
3
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6
WP5: Poroelasticity
3
.
6
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1
Exercise 1: Biot coefficient determination
3
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6
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2
Exercise 2: Depletion stress path
3
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7
Thermo-elasticity
3
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7
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1
Applications
3
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7
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2
Constitutive equations
3
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7
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3
Thermal-stress under uniaxial-strain condition
3
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7
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4
Thermal-stress in wellbores
3
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7
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5
Diffusivity equation for thermo-elasticity
3
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7
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6
Thermo-poroelasticity
3
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8
Chemo-mechanics
3
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8
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1
General constitutive equation
3
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8
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2
Changes of brine salinity in shales
3
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8
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3
Adsorption-induced deformation
3
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9
WP6: Applications of Thermoelasticity
3
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9
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1
Exercise 1: Thermal stress around a wellbore
3
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9
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2
Exercise 2: Thermal stress in a reservoir
4
. Inelasticity
4
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1
Examples of inelasticity in the subsurface
4
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2
The yield surface
4
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2
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1
Tresca
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2
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2
Von Mises
4
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2
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3
Mohr-Coulomb and Drucker-Prager
4
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2
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4
Lade
4
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2
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5
Mogi
4
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3
Plastic strains
4
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4
WP7: Rock Failure and Application to Wellbore Stability
4
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4
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1
Exercise 1: Determination of shear and tensile strength
4
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4
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2
Exercise 2: Shear and tensile failure in vertical and deviated wellbores
4
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5
Critical state soil mechanics
4
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5
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1
Yield surface and the critical state line
4
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5
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2
Calculation of elastic and plastic strains
4
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6
Brittle to ductile transition
4
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7
Special cases for changes in the yield surface
4
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8
Visco-elasticity and Visco-plasticity
4
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9
WP8: Soft Sediment Constitutive Models
4
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9
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1
Exercise 1: Compressibility of mudrocks
4
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9
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2
Exercise 2: Cam-clay model
4
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10
Suggested Reading
5
. Mechanics of fluid driven fractures
5
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1
Fracture initiation in a wellbore
5
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1
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1
Fracture injection/shut-in tests
5
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1
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2
Ideal orientation of hydraulic fractures
5
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2
Coupled fluid-driven fracture propagation
5
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2
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1
Overview
5
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2
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2
Linear elastic fracture mechanics
5
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2
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3
PKN solution and other cases
5
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2
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4
Fluid-driven fractures in porous media
5
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3
Hydraulic fracturing in tight formations
5
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3
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1
Design: Pads, wellbores, stages and clusters
5
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3
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2
Fracture interference and interaction
5
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3
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3
Typical hydraulic fracturing parameters
5
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3
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4
Fracture swarms
5
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3
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5
Monitoring: microseismicity and fiber optics
5
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4
WP9: Hydraulic Fracturing
5
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4
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1
Stress shadows and interference
5
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4
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2
Coupled hydraulic fracturing modeling
5
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5
Suggested reading
6
. Final Project
6
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1
Final Project Guidelines
7
. Appendix
7
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1
WP10: Laboratory Static and Dynamic Young Modulus
