Stochastic Methods for Flow in Porous Media ：Coping with Uncertainties

Publication subTitle ：Coping with Uncertainties

Author： Zhang   Dongxiao  

Publisher： Elsevier Science‎

Publication year： 2001

E-ISBN: 9780080517773

P-ISBN(Paperback): 9780127796215

P-ISBN(Hardback):  9780127796215

Subject： O211 probability (probability theory, probability theory);P57 mineralogy

Language： ENG

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Description

Stochastic Methods for Flow in Porous Media: Coping with Uncertainties explores fluid flow in complex geologic environments. The parameterization of uncertainty into flow models is important for managing water resources, preserving subsurface water quality, storing energy and wastes, and improving the safety and economics of extracting subsurface mineral and energy resources.

This volume systematically introduces a number of stochastic methods used by researchers in the community in a tutorial way and presents methodologies for spatially and temporally stationary as well as nonstationary flows. The author compiles a number of well-known results and useful formulae and includes exercises at the end of each chapter.

  • Balanced viewpoint of several stochastic methods, including Greens' function, perturbative expansion, spectral, Feynman diagram, adjoint state, Monte Carlo simulation, and renormalization group methods
  • Tutorial style of presentation will facilitate use by readers without a prior in-depth knowledge of Stochastic processes
  • Practical examples throughout the text
  • Exercises at the end of each chapter reinforce specific concepts and techniques
  • For the reader who is interested in hands-on experience, a number of computer codes are included and discussed

Chapter

Front Cover

Stochastic Methods for Flow in Porous Media

Copyright Page

Contents

Forword

Preface

Chapter 1. Introduction

1.1 Stochastic Partial Differential Equations

1.2 Saturated Flow with Random Forcing Terms

1.3 Saturated Flow with Random Boundary Conditions

1.4 Saturated Flow with Random Coefficients

1.5 Unsaturated Flow in Random Media

1.6 Scope of the Book

1.7 Exercises

Chapter 2. Stochastic Variables and Processes

2.1 Real Random Variables

2.2 Jointly Distributed Random Variables

2.3 Stochastic Processes and Random Fields

2.4 Some Mathematical Tools

2.5 Exercises

Chapter 3. Steady-State Saturated Flow

3.1 Introduction

3.2 Perturbative Expansion Method

3.3 Green's Function Method

3.4 Numerical Solutions to the Moment Equations

3.5 Analytical Solutions to the Moment Equations

3.6 Spectral methods

3.7 Higher-Order Corrections

3.8 Space-State Method

3.9 Adomian Decomposition

3.10 Closure Approximations

3.11 Monte Carlo Simulation Method

3.12 Some Remarks

3.13 Exercises

Chapter 4. Transient Saturated Flow

4.1 Introduction

4.2 Moment Partial Differential Equations

4.3 Moment Integrodifferential Equations

4.4 Some Remarks

4.5 Exercises

Chapter 5. Unsaturated Flow

5.1 Introduction

5.2 Spatially Nonstationary Flow

5.3 Gravity-Dominated Flow

5.4 Kirchhoff Transformation

5.5 Transient Flow in Nonstationary Media

5.6 Exercises

Chapter 6. Two-Phase Flow

6.1 Introduction

6.2 Buckley-Leverett Displacement

6.3 Lagrangian Approach

6.4 Eulerian Approach

6.5 Exercises

Chapter 7. Flow in Fractured Porous Media

7.1 Introduction

7.2 Saturated Flow

7.3 Unsaturated Flow

7.4 Exercises

References

Index

Color Plate Section

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