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Stochastic Methods for Flow in Porous Media : Coping with Uncertainties - Dongxiao Zhang

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Stochastic Methods for Flow in Porous Media

Coping with Uncertainties

By: Dongxiao Zhang

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Hardcover | 3 October 2001

At a Glance

Hardcover
368 Pages

Dimensions(cm)
24.77 x 17.78 x 2.54

Hardcover

RRP $194.95

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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.

* As never seen before:
* 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

Industry Reviews

"...presents a comprehensive treatment of stochastic methods for water flow in saturated aquifers and unsaturated soils in a very tutorial and accessible way." -You-Kuan Zhang, University of Iowa, in VADOSE ZONE JOURNAL, 2006, VOL. 5, NO. 3 Excerpt from the Foreword by Prof. Shlomo P. Neuman: "The hydrogeologic properties of natural rocks and soils exhibit spatial variations on a multiplicity of scales. Incorporating such scaling in geostatistical and stochastic analyses of hydrogeologic phenomena has become a major challenge. ...Students, teachers, researchers and practitioners concerned with hydrogeologic uncertainty analysis will find much in this book that is instructive, useful and timely." --Prof. Shlomo P. Neuman "Dongxiao has clearly put together an excellent intermediate/advanced text on subsurface flow problems, and I highly recommend it as a graduate level text and as a source of information for the researcher and consultant." -PURE AND APPLIED GEOPHYSICS "...a comprehensive and lucid scientific monograph devoted to uncertainty analysis for a wide range of groundwater flow problems." -JOURNAL OF HYDRAULIC RESEARCH "This work considers numerous stochastic methods used by researchers for flow description. The methods' positive and negative characteristics are compared and selected methods are shown in examples. ...includes problems at the end of each chapter, making it useful for students and teachers in the field, as well as researchers and practitioners." BULLETIN AMERICAN METEOROLOGICAL SOCIETY

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Foreword	p. ix
Preface	p. xiii
Introduction	p. 1
Stochastic Partial Differential Equations	p. 1
Saturated Flow with Random Forcing Terms	p. 4
Moment Differential Equations	p. 6
Moment Integral Equations	p. 7
Solutions of Statistical Moments	p. 9
Monte Carlo Simulation Method	p. 10
Saturated Flow with Random Boundary Conditions	p. 11
Direct Moment Method	p. 12
Direct PDF Method	p. 12
Discussion	p. 15
Saturated Flow with Random Coefficients	p. 16
Closure Approximation Method	p. 16
Perturbative Expansion Method	p. 19
Green's Function Method	p. 23
Solutions	p. 26
Discussion	p. 28
Unsaturated Flow in Random Media	p. 30
Moment Differential Equations	p. 30
Solutions and Discussion	p. 33
Scope of the Book	p. 35
Exercises	p. 37
Stochastic Variables and Processes	p. 40
Real Random Variables	p. 40
Continuous Random Variables	p. 41
Discrete Random Variables	p. 43
Functions of a Random Variable	p. 44
Statistical Moments	p. 45
Conditional Probability	p. 47
Characteristic Functions and Cumulants	p. 48
Jointly Distributed Random Variables	p. 49
Joint Distributions	p. 49
Marginal Distributions	p. 50
Functions of Random Variables	p. 51
Statistical Moments	p. 52
Independent Random Variables	p. 53
Conditional Probability and Expectation	p. 54
Joint Characteristic Functions	p. 56
Multivariate Normal and Lognormal Random Variables	p. 58
The Central Limit Theorem	p. 61
Stochastic Processes and Random Fields	p. 62
Statistics of Stochastic Processes	p. 62
Stationary Stochastic Processes	p. 66
Nonstationary Stochastic Processes	p. 72
Some Mathematical Tools	p. 82
Dirac Delta Functions	p. 82
Dirac Delta Representation of PDFs	p. 85
Stochastic Continuity and Differentiation	p. 86
Fourier Transform	p. 89
Laplace Transform	p. 92
Exercises	p. 93
Steady-State Saturated Flow	p. 95
Introduction	p. 95
Perturbative Expansion Method	p. 96
Moment Partial Differential Equations	p. 98
Green's Function Method	p. 101
Formal Integrodifferential Equations	p. 101
Perturbed Integrodifferential Equations	p. 107
Alternative Procedure	p. 109
Numerical Solutions to the Moment Equations	p. 111
Finite Differences	p. 111
Finite Elements	p. 114
Mixed Finite Elements	p. 118
Discussion	p. 121
Illustrative Examples	p. 122
Analytical Solutions to the Moment Equations	p. 133
Uniform Mean Flow in Stationary Media	p. 133
Flow Subject to Recharge	p. 145
Flow in Linearly Trending Media	p. 148
Convergent Flow	p. 151
Spectral methods	p. 156
Stationary Spectral Method	p. 156
Nonstationary Spectral Method	p. 161
Application to Flow in Semiconfined Aquifers	p. 165
Higher-Order Corrections	p. 168
Space-State Method	p. 173
Space-State Equations	p. 174
Adjoint State Equations	p. 175
Adomian Decomposition	p. 178
Neumann Series Expansion	p. 178
Discussion	p. 181
Closure Approximations	p. 182
Hierarchy Closure Approximation	p. 182
Cumulant Neglect Hypothesis	p. 186
Monte Carlo Simulation Method	p. 187
A Historical Review	p. 188
Methodology	p. 188
Discussion	p. 194
Some Remarks	p. 195
Application to Gas Flow	p. 195
Conditional Moment Equations	p. 197
Field Theoretic Methods	p. 199
Exercises	p. 201
Transient Saturated Flow	p. 203
Introduction	p. 203
Moment Partial Differential Equations	p. 204
Numerical Solution Strategies	p. 207
Illustrative Examples	p. 208
Moment Integrodifferential Equations	p. 212
Green's Function Representation	p. 213
Transient Effective Hydraulic Conductivity	p. 215
Some Remarks	p. 217
Adjoint State Equations	p. 217
Laplace-Transformed Moment Equations	p. 218
Quasi-Steady State Flow	p. 218
Exercises	p. 219
Unsaturated Flow	p. 221
Introduction	p. 221
Governing Equations	p. 221
Constitutive Relations	p. 222
Spatial Variabilities	p. 223
Spatially Nonstationary Flow	p. 224
Moment Partial Differential Equations	p. 224
Adjoint State Moment Equations	p. 235
Gravity-Dominated Flow	p. 239
Spectral Analysis	p. 240
Covariance Evaluation	p. 241
Kirchhoff Transformation	p. 242
Transient Flow in Nonstationary Media	p. 247
Moment Partial Differential Equations	p. 248
Discussion	p. 258
Exercises	p. 260
Two-Phase Flow	p. 262
Introduction	p. 262
Buckley-Leverett Displacement	p. 265
Moment Partial Differential Equations	p. 265
Statistical Moments of Apparent Velocity	p. 268
Solutions	p. 269
Lagrangian Approach	p. 272
One-Dimensional Flow	p. 272
Two-Dimensional Flow	p. 280
Summary and Discussion	p. 287
Eulerian Approach	p. 289
Moment Partial Differential Equations	p. 289
Unidirectional, Uniform Mean Flow	p. 293
Exercises	p. 295
Flow in Fractured Porous Media	p. 297
Introduction	p. 297
Discrete Network Models	p. 297
Dual-Porosity/Double-Permeability Models	p. 298
Saturated Flow	p. 299
Moment Partial Differential Equations	p. 301
Numerical Solutions	p. 306
Illustrative Examples	p. 307
Unsaturated Flow	p. 316
Moment Partial Differential Equations	p. 317
Exercises	p. 324
References	p. 326
Index	p. 339
Table of Contents provided by Syndetics. All Rights Reserved.

Stochastic Methods for Flow in Porous Media

Coping with Uncertainties

At a Glance

Hardcover

Industry Reviews

Shipping

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Defective items

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