Myron B. Allen, III - The Mathematics of Fluid Flow Through Porous Media

Myron B. Allen

University of Wyoming

This edition first published 2021

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Library of Congress Cataloging‐in‐Publication Data Applied for:

ISBN: 9781119663843

Cover Design: Wiley

Cover Image: © Myron B. Allen

To Professor George F. Pinder, who has lit the path for so many.

1 Cover

2 Title page The Mathematics of Fluid Flow Through Porous Media Myron B. Allen University of Wyoming

3 Copyright

4 Preface

5 1: Introduction1.1 Historical Setting 1.2 Partial Differential Equations (PDEs) 1.3 Dimensions and Units 1.4 Limitations in Scope

6 2: Mechanics 2.1 Kinematics of Simple Continua 2.2 Balance Laws for Simple Continua 2.3 Constitutive Relationships 2.4 Two Classic Problems in Fluid Mechanics 2.5 Multiconstituent Continua

7 3: Single‐fluid Flow Equations 3.1 Darcy's Law 3.2 Non‐Darcy Flows 3.3 The Single‐fluid Flow Equation 3.4 Potential Form of the Flow Equation 3.5 Areal Flow Equation 3.6 Variational Forms for Steady Flow 3.7 Flow in Anisotropic Porous Media

8 4: Single‐fluid Flow Problems 4.1 Steady Areal Flows with Wells 4.2 The Theis Model for Transient Flows 4.3 Boussinesq and Porous Medium Equations

9 5: Solute Transport 5.1 The Transport Equation 5.2 One‐Dimensional Advection 5.3 The Advection–Diffusion Equation 5.4 Transport with Adsorption

10 6: Multifluid Flows 6.1 Capillarity 6.2 Variably Saturated Flow 6.3 Two‐fluid Flows 6.4 The Buckley–Leverett Problem 6.5 Viscous Fingering 6.6 Three‐fluid Flows 6.7 Three‐fluid Fractional Flow Analysis

11 7: Flows With Mass Exchange 7.1 General Compositional Equations 7.2 Black‐oil Models 7.3 Compositional Flows in Porous Media 7.4 Fluid‐phase Thermodynamics

12 Appendix A: Dedicated Symbols

13 Appendix B: Useful Curvilinear Coordinates B.1 Polar Coordinates B.2 Cylindrical Coordinates B.3 Spherical Coordinates

14 Appendix C: The Buckingham Pi Theorem C.1 Physical Dimensions and Units C.2 The Buckingham Theorem

15 Appendix D: Surface Integrals D.1 Definition of a Surface Integral D.2 The Stokes Theorem D.3 A Corollary to the Stokes Theorem

16 Bibliography

17 Index

18 End User License Agreement

1 Chapter 3Table 3.1 Isotropic, anisotropic, homogeneous, and inhomogeneous permeability...

2 Chapter 7Table 7.1 Phases in a compositional model.Table 7.2 Derived quantities used in compositional modeling.Table 7.3 Partitioning of pseudospecies in a black‐oil model.Table 7.4 Molar quantities used in compositional reservoir modeling.

3 Appendix ATable A.1 Dedicated symbols for physical quantities.

1 Chapter 2 Figure 2.1 A reference configuration of a body, showing the referential coor... Figure 2.2 The deformation mapping the reference configuration onto the bo... Figure 2.3 Regions and occupied by a body in two reference configuration... Figure 2.4 Orthonormal basis vectors defining a Cartesian coordinate system.... Figure 2.5 A time‐independent region having oriented boundary and unit o... Figure 2.6 A region in three‐dimensional space with unit outward normal ve... Figure 2.7 A cube of material illustrating the interpretations of entries of... Figure 2.8 Coordinate system used to define the depth function . Figure 2.9 Geometry of the Stokes problem for slow fluid flow around a solid... Figure 2.10 Profile of flow through a thin circular cylinder having radius Figure 2.11 A reference configuration and the deformation at times and f... Figure 2.12 Sketch of a fluid‐saturated porous medium showing three possible... Figure 2.13 Conceptual plot of REV‐averaged volume fraction versus radius of...