Essentials of Multiphase Flow and Transport

This book looks at the mathematical-physical rationale behind the equations that are currently used to describe the flow of fluid and transport of solutes in porous media. It presents a comprehensive approach to the development of appropriate equations without prior knowledge of continuum mechanics, mixture theory, or similar areas of expertise. The book carries the reader from the simplest of concepts to the final equations and then illustrates how the equations can be used to solve practical problems. This book will fill the need for a reference and text in the physics of flow in porous media at the advanced undergraduate-graduate level and can also be used as a professional reference.

George F. Pinder, PHD, is the Director of the Research Center for Groundwater Remediation Design and also a Professor of Civil and Environmental Engineering, Mathematics and Statistics, and Computer Science at the University of Vermont. He has served on the editorial board of numerous journals including the International Journal for Numerical Methods in Fluids. He has published extensively in the fields of groundwater flow and transport modeling and has written on the use of such models in combination with optimization methods in addressing problems of environmental optimal design.

William G. Gray, PHD, is a Professor of Environmental Sciences and Engineering at the University of North Carolina at Chapel Hill. He has over thirty years of research and teaching experience in environmental modeling and the physics of flow in porous media. He has published widely on various aspects of environmental modeling and simulation and has served as editor and on the editorial boards of leading journals in his field. He is a Fellow of the American Geophysical Union.

Preface	p. xi
Acknowledgments	p. xiii
Setting the Stage	p. 1
Introduction	p. 1
Phases and Porous Media	p. 2
Grain and Pore Size Distributions	p. 6
The Concept of Saturation	p. 12
The Concept of Pressure	p. 13
Surface Tension Considerations	p. 16
Concept of Concentration	p. 30
Summary	p. 32
Exercises	p. 32
Bibliography	p. 33
Mass Conservation Equations	p. 35
Introduction	p. 35
Microscale Mass Conservation	p. 38
Integral Forms of Mass Conservation	p. 39
Integral Theorems	p. 44
Divergence Theorem	p. 45
Transport Theorem	p. 45
Point Forms of Mass Conservation	p. 46
The Macroscale Perspective	p. 48
The Representative Elementary Volume	p. 49
Global and Local Coordinate Systems	p. 50
Macroscopic Variables	p. 53
Definitions of Macroscale Quantities	p. 56
Summary of Macroscale Quantities	p. 62
The Averaging Theorems	p. 63
Spatial Averaging Theorem	p. 64
Temporal Averaging Theorem	p. 66
Macroscale Mass Conservation	p. 67
Macroscale Point Forms	p. 67
Integral Forms	p. 71
Applications	p. 73
Integral Analysis	p. 74
Point Analysis	p. 76
Summary	p. 79
Exercises	p. 79
Bibliography	p. 81
Flow Equations	p. 83
Introduction	p. 83
Darcy's Experiments	p. 85
Fluid Properties	p. 88
Equations of State for Fluids	p. 89
Mass Fraction	p. 89
Mass Density and Pressure	p. 90
Fluid Viscosity	p. 92
Hydraulic Potential	p. 93
Hydrostatic Force and Hydraulic Head	p. 93
Derivatives of Hydraulic Head	p. 97
Single-Phase Fluid Flow	p. 98
Darcy's Law	p. 99
Hydraulic Conductivity and Permeability	p. 102
Derivation of Groundwater Flow Equation	p. 106
Recapitulation of the Derivation	p. 111
Initial and Boundary Conditions	p. 113
Two-Dimensional Flow	p. 116
Two-Phase Immiscible Flow	p. 121
Derivation of Flow Equations	p. 121
Observations on the p[superscript c]-s[superscript w] Relationship	p. 127
Formulas for the p[superscript c]-s[superscript w] Relationship	p. 135
Observations of the k[subscript rel superscript alpha]-s[superscript w] Relationship	p. 143
Formulas for the k[subscript rel superscript alpha]-s[superscript w] Relation	p. 146
Special Cases of Multiphase Flow	p. 149
The Buckley-Leverett Analysis	p. 155
Fractional Flow	p. 155
Derivation of the Buckley-Leverett Equation	p. 157
Solution of the Buckley-Leverett Equation	p. 158
Summary	p. 160
Exercises	p. 161
Bibliography	p. 162
Mass Transport Equations	p. 165
Introduction	p. 165
Velocity in the Species Transport Equations	p. 167
Direct Approach	p. 168
Rigorous Approach	p. 169
Distribution Approach	p. 172
Summary	p. 175
Closure Relations for the Dispersion Vector	p. 176
Chemical Reaction Rates	p. 180
Interphase Transfer Terms	p. 182
Kinetic Formulation	p. 183
Equilibrium Formulation	p. 187
Summary: Kinetic vs. Equilibrium Formulations	p. 194
Initial and Boundary Conditions	p. 195
Conclusion	p. 196
Exercises	p. 197
Bibliography	p. 198
Simulation	p. 199
1-D Simulation of Air-Water Flow	p. 199
Drainage in a Homogeneous Soil	p. 201
Drainage in a Heterogeneous Soil	p. 205
Imbibition in Homogeneous Soil	p. 206
1-D Simulation of DNAPL-Water Flow	p. 207
Primary DNAPL Imbibition in Homogeneous Soil	p. 208
Density Effect	p. 208
DNAPL Drainage in Homogeneous Soil	p. 209
Secondary Imbibition of DNAPL in Homogeneous Soil	p. 210
Secondary Drainage in Homogeneous Soil	p. 211
Primary Imbibition in Heterogeneous Soil	p. 212
2-D Simulation of DNAPL-Water Flow	p. 213
DNAPL Descent into a Water-Saturated Reservoir	p. 213
Simulation of Multiphase Flow and Transport	p. 216
1-D Two-Phase Flow and Transport	p. 217
2-D Two-Phase Flow and Transport	p. 218
2-D Single-Phase Flow and Transport	p. 224
Base Case	p. 228
Effect of Inflow	p. 228
Impact of Well Discharge	p. 230
Effect of Adsorption	p. 231
Effect of a Low Transmissivity Region	p. 232
Effect of a High Transmissivity Region	p. 234
Effect of Rate of Reaction	p. 235
3-D Single-Phase Flow and Transport	p. 236
2-D Three-Phase Flow	p. 239
Summary	p. 244
Bibliography	p. 245
Select Symbols	p. 247
Index	p. 253
Table of Contents provided by Ingram. All Rights Reserved.

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Essentials of Multiphase Flow and Transport in Porous Media

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