Computational Methods in Subsurface Flow

Computational Methods in Subsurface Flow explores the application of all of the commonly encountered computational methods to subsurface problems. Among the problems considered in this book are groundwater flow and contaminant transport; moisture movement in variably saturated soils; land subsidence and similar flow and deformation processes in soil and rock mechanics; and oil and geothermal reservoir engineering. This book is organized into 10 chapters and begins with an introduction to partial differential and various solution approaches used in subsurface flow. The discussion then shifts to the fundamental theory of the finite element method, with emphasis on the Galerkin finite element method and how it can be used to solve a wide range of subsurface problems. The subjects treated range from simple problems of saturated groundwater flow to more complex ones of moisture movement and multiphase flow in petroleum reservoirs. The chapters that follow focus on fluid flow and mechanical deformation of conventional and fractured porous media; point and subdomain collocation techniques and the boundary element technique; and the applications of finite difference techniques to single- and multiphase flow and solute transport. The final chapter is devoted to other alternative numerical methods that are based on combinations of the standard finite difference approach and classical mathematics. This book is intended for senior undergraduate and graduate students in geoscience and engineering, as well as for professional groundwater hydrologists, engineers, and research scientists who want to solve or model subsurface problems using numerical techniques.

Preface

1. Introduction

1.1 Purpose and Scope

1.2 Introduction to Partial Differential Equations

1.3 Partial Differential Equations in Subsurface Flow

1.4 Solution Methodology

1.5 Computational Methods in Subsurface Flow

References

2. The Finite Element Method

2.1 General

2.2 Basic Concepts in Finite Element Analysis

2.3 Solution of Discrete Problems

2.4 Solution of Steady-State Continuum Problems

2.5 Solution of Time Dependent Continuum Problems

References

3. Element Families and Interpolation Functions

3.1 General

3.2 Polynomial Series

3.3 One-Dimensional Elements

3.4 Two-Dimensional Elements

3.5 Three-Dimensional Elements

3.6 Numerical Integration

References

4. Finite Element Simulation of Isothermal Flow in Porous Media

4.1 Introduction

4.2 General Governing Equations for Saturated Flow

4.3 Saturated Groundwater

4.4 Single-Phase Oil and Gas Reservoir Simulation

4.5 Governing Equations for Variably Saturated Flow

4.6 Iterative Methods for Solving Nonlinear Equations

4.7 Fluid Flow in Variably Saturated Media

4.8 Concluding Remarks

References

5. Finite Element Simulation of Solute and Energy Transport in Porous Media

5.1 Introduction

5.2 Mass Transport in Single-Phase Flow

5.3 Mass Transport in Multiphase Flow

5.4 Energy Transport in Single-Phase Flow

5.5 Energy Transport in Multiphase Flow

5.6 Finite Element Simulation of Mass and Energy Transport in Single-Phase Flow

5.7 Finite Element Simulation of Mass and Energy Transport in Multiphase Flow

5.8 Conclusions

References

6. Finite Element Simulation of Fluid Flow and Deformation in Unfractured and Fractured Porous Media

6.1 Introduction

6.2 Fluid Flow and Deformation in an Unfractured Porous Medium

6.3 Discrete Fracture Flow Deformation Model

6.4 Double-Porosity Flow Models

6.5 Double-Porosity Flow Deformation Model

6.6 Summary

References

7. Alternative Finite Element Techniques and Applications

7.1 Introduction

7.2 The Point Collocation Technique

7.3 The Subdomain Collocation Technique

7.4 Boundary Element Method

References

8. The Finite Difference Method

8.1 Introduction

8.2 Stability of Finite Difference Approximations

8.3 Consistency and Convergence of Finite Difference

Approximations

References

9. Finite Difference Simulation of Single and Multiphase Isothermal Fluid Flow and Solute Transport

9.1 Simulation of Single-Phase Flow

9.2 Simulation of Multiphase Flow

9.3 Simulation of Single-Phase Species Transport

9.4 Simulation of Multiphase Species Transport

9.5 Summary

References

10. Alternative Finite Difference Methods

10.1 Introduction

10.2 Finite Difference Methods by Transformations

10.3 Methods of Characteristics

References

Index