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Teaching

PGE 334 – Reservoir Geomechanics (Undergraduate)

This course reviews the fundamentals of structural geology, continuum mechanics, rock constitutive laws, and applications to fault stability, wellbore stability, hydraulic fracturing and reservoir geomechanics.

Course notes: Introduction to Energy Geomechanics

Homework and exercises: Problems in Introduction to Energy Geomechanics and exercises in Github

Lectures:

  • Fall 2020 (to be updated soon)
  • Spring 2020 (Youtube)
  • Fall 2019 (YouTube)
  • Spring 2019 (YouTube)
  • Fall 2018 (YouTube)

Table of Contents:

Week Lecture Homework and Laboratory
1 Introduction to the course

Applications of geomechanics

Homework 1:

Section 1.3 (all questions)

2-3  Vertical stress – lithostatic gradient

Pore pressure – effective stress

Overpressure

Horizontal stresses

HF-based measurement of least principal stress

Stress regimes

Homework 2

Section 2.4 (all questions)

Due 9/16

4 Stress equilibrium – stress tensor

Strain tensor

3D Hooke’s law, Young’s Modulus

Homework 3

Section 3.8 (Questions 1 and 2)

LAB 1: Young’s modulus UCS (during lecture)

5 Horizontal stress determination with linear elasticity

Constrained modulus and pore compressibility

Homework 4

Section 3.8 (Questions 3 to 5)

6 Generalized continuum mechanics problem

Anisotropy, visco-elasto-plasticity, and multiphysics problems: poro-thermo-chemo-mechanics

Rock failure: tensile and shear strength

Brazilian and triaxial tests

Mohr circle, Mohr-Coulomb failure criterion

Homework 5

Section 4.9 (all questions)

 

LAB 2: Tensile strength

7

 

Compression yield cap

Strength anisotropy and length-scale effects

Ductile VS Brittle failure

 

 

8

 

Fault mapping

Fault classification and ideal orientation

Homework 6

Section 5.6 (Questions 1 to 4)

LAB 3: Confined shear strength of rock

9 Stresses on faults and 3D Mohr circle

Fracture permeability and fault reactivation

Limits on stress field imposed by frictional strength of faults

Homework 7

Section 5.6 (Questions 5, 7, 8, and 9)

10 Wellbore stability

Near wellbore effects: Kirsch equations

Breakouts and tensile fractures

Wellbore breakdown pressure

Homework 8

Section 6.9 (Questions 1, and 2)

11 Mud window

Deviated wellbores

Homework 9

Section 6.9 (Questions 3, 4 and 5)

LAB 4: Wellbore tensile fractures and breakouts

12 Thermal stresses, shale swelling,  loss of mud support, and anisotropy
13 Hydraulic fractures in well testing

Leak-off test, Diagnostics fracture initiation test, Step rate test

The coupled fluid-driven fracture propagation problem

Homework 10

Section 7.6: (Questions 1 to 4)

14 Net pressure and fracture toughness

Hydraulic fracture design

KGD and PKN models

Hydraulic fracture containment

Homework 11

Section 7.6: (Questions 5 and 6)

15 Multistage hydraulic fracturing

Induced micro-seismicity

Homework 12

Section 7.6: (Questions 7 and 8)

16 Reservoir depletion and injection

Reservoir Compressibility

PGE 383 – Advanced Reservoir Geomechanics (Graduate)

This course explores the fundamentals of theoretical geomechanics. Topics include general theory of linear elasticity, plasticity, poromechanics and fracture mechanics. The theory is linked to problems of stability of deviated wellbores, hydraulic fracturing, reservoir depletion, and fault stability.

Homework and exercises: Github repository

Lectures:

  • Fall 2020 (to be updated soon)
  • Fall 2019 (YouTube)
  • Fall 2018 (YouTube)

Course Topics

  1. Review on continuum mechanics: Stresses at a point, principal stresses, Mohr circle, decomposition of the stress tensor and deviatoric stress tensor invariants.
  2. Problems in elasticity: Equilibrium, kinematic, and constitutive laws. Solution of the Navier equations for plane-strain problems. Wellbore problem: determination of in-situ stresses from sonic logs.
  3. Inelasticity: failure criteria (Coulomb, Griffith), plasticity-yield surface, post-peak behavior, creep, grain crushing.
  4. Mechanics of the saturated porous solid: Particle fluid interaction, poroelasticity, effective stress, drained and undrained loading, consolidation theory. Problems: overpressure and stress path during reservoir depletion.
  5. Mechanics of open mode fractures: Linear elastic fracture mechanics, PKN-KGD models, wellbore frac tests, hydraulic fracture propagation in heterogeneous media, stress interference in multistage fracturing, open mode fractures in unconsolidated sands. Problem: solve coupled PKN/KGD models.
  6. Mechanical properties of reservoir geomaterials: unconsolidated sands, shale, sandstone, limestone, evaporites, scales and effective properties, heterogeneity-spatial variability, stress-dependent permeability, laboratory methods and measurements.

 Table of contents

Week of Lecture Literature Project
1 Introduction to geomechanics in Petroleum Engineering Espinoza, Ch. 1 –
2 Review Continuum Mechanics: stresses at a point, principal stresses, equilibrium equations, vertical stress. Stress projection on a plane. Stress plotting: Mohr’s circle, stress path, p-q space, I1-J2 space Fjaer Ch. 1.1

Zoback Ch. 1

Malvern Ch. 2, 3, 4 Jaeger et al. Ch. 2

Espinoza, Ch. 3, 5

(1) Stress tensor profile along a vertical wellbore
3 Elasticity: strains, kinematic equations, constitutive equations Fjaer Ch. 1.2

Jaeger Ch. 5

Espinoza, Ch. 3

(2) Shear and normal stresses on fractures along a wellbore
4 Linear elasticity, solution for horizontal stresses with tectonic strains, constrained modulus Fjaer Ch. 1.2

Jaeger Ch. 5

Espinoza, Ch. 3

(3) Horizontal stress determination with linear elasticity
5 Elastic anisotropy: material parameters of VTI solids. Elasticity: Navier’s equation LEIS, Analytical and numerical solutions. Fjaer Ch. 4

Jaeger Ch. 8

Zoback Ch. 6/10

Espinoza, Ch. 3

(4) Stress field around  wellbores and fractures: analytical and numerical solution
6 Finite Element Method, stresses around wellbores (Kirsch solution) and fractures

 

Fjaer Ch. 4

Jaeger Ch. 8

Zoback Ch. 6/10

Espinoza, Ch. 6

(4) (continued)
7 Poroelasticity: The porous solid, Biot’s coefficient, Biot’s effective stress, drained loading: depletion stress path, Fjaer Ch. 1.6

Coussy Ch. 4

Jaeger Ch. 7

(5) Determination of Biot’s coefficient and reservoir stress-path during depletion: CMG verification
8 Undrained loading: consolidation and disequilibrium compaction, Skempton’s coefficient Fjaer Ch. 1.6

Coussy Ch. 4

Jaeger Ch. 7

9 Thermo-elasticity and visco-elasticity: Thermal stresses around the wellbore and in the reservoir. Long-term reservoir compaction.

Chemo-mechanical coupled processes.

Fjaer Ch. 1.5, 1.9

Coussy Ch. 4

Jaeger Ch. 7.8

Jaeger Ch. 9.8-11

Zoback Ch.3 (end)

10 Inelasticity: fracture modes, shear yield stress: Tresca, von Mises, Drucker Prager, Mohr-Coulomb criterion, the triaxial test. Fjaer Ch. 2.1, 2.5

Jaeger Ch. 4

Espinoza, Ch. 4

(6) Rock failure and wellbore stability
11 Inelasticity: beyond the yield point, post-peak behavior, flow rule and hardening, critical state soil mechanics, strain-softening and strain-hardening geomaterials, shear-enhanced compaction (compression cap), oedometer test Fjaer Ch. 2.8

Jaeger Ch. 9

(7) Constitutive models for soft rocks: reservoir ovepressure
12 Mechanics of fluid-driven open mode fractures: tensile strength, breakdown pressure, ideal open-mode fracture propagation, fracture containment Fjaer Ch. 11

Espinoza, Ch. 7

Final Project: paper abstract due
13

 

Mechanics of fluid-driven open mode fractures: LEFM, Griffith criterion, fracture toughness, the coupled fluid-driven fracture propagation problem: PKN-KGD models, fracture propagation regimes Fjaer Ch. 11

Espinoza, Ch. 7

(8) Stress shadows in multistage hydraulic fracturing
14 Mechanics of fluid-driven open mode fractures: microseismicity, open-mode fractures in unconsolidated sediments, multistage hydraulic fracturing design. Valko and Economides
15 Mechanics of elastic wave propagation, frequency and wavelength, dynamic to static transforms Fjaer Ch. 5 (9) Laboratory dynamic to static transforms

– Fjaer, et al. “Petroleum Related Rock Mechanics”

– Jaeger, Cook and Zimmerman, “Fundamentals of Rock Mechanics”

– Malvern, “Introduction to the Mechanics of a Continuous Medium”

– Zoback, “Reservoir Geomechanics”

– Coussy, “Mechanics and Physics of Porous Solids”

– Valko and Economides, “Hydraulic Fracture Mechanics”

– Espinoza, “Introduction to Energy Geomechanics” <https://dnicolasespinoza.github.io/ (Links to an external site.)>

 

PGE 373L – Petroleum and Geosystems Engineering Design

There are two equally important goals in this class:
(1) The solution of engineering design problems based on actual field data.
(2) To develop and demonstrate satisfactory written and oral report preparation and delivery skills.

PGE 424 – Petrophysics

This course reviews fundamentals of the physics of rocks, including the measurement of diverse physical properties. The interpretation of measurements and relationship between physical properties is used to assess subsurface resources and processes.

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D. Nicolas Espinoza

espinoza@austin.utexas.edu

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