Cover image for Essentials of multiphase flow in porous media
Title:
Essentials of multiphase flow in porous media
Publication Information:
Haboken, NJ : Wiley, 2008
Physical Description:
xiii, 257 p. : ill ; 26 cm.
ISBN:
9780470317624

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30000010167526 TA418.9.P6 P56 2008 Open Access Book Book
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30000010191508 TA418.9.P6 P56 2008 Open Access Book Book
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Summary

Summary

Learn the fundamental concepts that underlie the physics of multiphase flow and transport in porous media with the information in Essentials of Multiphase Flow in Porous Media , which demonstrates the mathematical-physical ways to express and address multiphase flow problems. Find a logical, step-by-step introduction to everything from the simple concepts to the advanced equations useful for addressing real-world problems like infiltration, groundwater contamination, and movement of non-aqueous phase liquids. Discover and apply the governing equations for application to these and other problems in light of the physics that influence system behavior.


Author Notes

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
William G. Gray, PhD, is a Professor of Environmental Sciences and Engineering at the University of North Carolina at Chapel Hill


Table of Contents

Prefacep. xi
Acknowledgmentsp. xiii
1 Setting the Stagep. 1
1.1 Introductionp. 1
1.2 Phases and Porous Mediap. 2
1.3 Grain and Pore Size Distributionsp. 6
1.4 The Concept of Saturationp. 12
1.5 The Concept of Pressurep. 13
1.6 Surface Tension Considerationsp. 16
1.7 Concept of Concentrationp. 30
1.8 Summaryp. 32
1.9 Exercisesp. 32
Bibliographyp. 33
2 Mass Conservation Equationsp. 35
2.1 Introductionp. 35
2.2 Microscale Mass Conservationp. 38
2.3 Integral Forms of Mass Conservationp. 39
2.4 Integral Theoremsp. 44
2.4.1 Divergence Theoremp. 45
2.4.2 Transport Theoremp. 45
2.5 Point Forms of Mass Conservationp. 46
2.6 The Macroscale Perspectivep. 48
2.6.1 The Representative Elementary Volumep. 49
2.6.2 Global and Local Coordinate Systemsp. 50
2.6.3 Macroscopic Variablesp. 53
2.6.4 Definitions of Macroscale Quantitiesp. 56
2.6.5 Summary of Macroscale Quantitiesp. 62
2.7 The Averaging Theoremsp. 63
2.7.1 Spatial Averaging Theoremp. 64
2.7.2 Temporal Averaging Theoremp. 66
2.8 Macroscale Mass Conservationp. 67
2.8.1 Macroscale Point Formsp. 67
2.8.2 Integral Formsp. 71
2.9 Applicationsp. 73
2.9.1 Integral Analysisp. 74
2.9.2 Point Analysisp. 76
2.10 Summaryp. 79
2.11 Exercisesp. 79
Bibliographyp. 81
3 Flow Equationsp. 83
3.1 Introductionp. 83
3.2 Darcy's Experimentsp. 85
3.3 Fluid Propertiesp. 88
3.4 Equations of State for Fluidsp. 89
3.4.1 Mass Fractionp. 89
3.4.2 Mass Density and Pressurep. 90
3.4.3 Fluid Viscosityp. 92
3.5 Hydraulic Potentialp. 93
3.5.1 Hydrostatic Force and Hydraulic Headp. 93
3.5.2 Derivatives of Hydraulic Headp. 97
3.6 Single-Phase Fluid Flowp. 98
3.6.1 Darcy's Lawp. 99
3.6.2 Hydraulic Conductivity and Permeabilityp. 102
3.6.3 Derivation of Groundwater Flow Equationp. 106
3.6.4 Recapitulation of the Derivationp. 111
3.6.5 Initial and Boundary Conditionsp. 113
3.6.6 Two-Dimensional Flowp. 116
3.7 Two-Phase Immiscible Flowp. 121
3.7.1 Derivation of Flow Equationsp. 121
3.7.2 Observations on the p[superscript c]-s[superscript w] Relationshipp. 127
3.7.3 Formulas for the p[superscript c]-s[superscript w] Relationshipp. 135
3.7.4 Observations of the k[subscript rel superscript alpha]-s[superscript w] Relationshipp. 143
3.7.5 Formulas for the k[subscript rel superscript alpha]-s[superscript w] Relationp. 146
3.7.6 Special Cases of Multiphase Flowp. 149
3.8 The Buckley-Leverett Analysisp. 155
3.8.1 Fractional Flowp. 155
3.8.2 Derivation of the Buckley-Leverett Equationp. 157
3.8.3 Solution of the Buckley-Leverett Equationp. 158
3.9 Summaryp. 160
3.10 Exercisesp. 161
Bibliographyp. 162
4 Mass Transport Equationsp. 165
4.1 Introductionp. 165
4.2 Velocity in the Species Transport Equationsp. 167
4.2.1 Direct Approachp. 168
4.2.2 Rigorous Approachp. 169
4.2.3 Distribution Approachp. 172
4.2.4 Summaryp. 175
4.3 Closure Relations for the Dispersion Vectorp. 176
4.4 Chemical Reaction Ratesp. 180
4.5 Interphase Transfer Termsp. 182
4.5.1 Kinetic Formulationp. 183
4.5.2 Equilibrium Formulationp. 187
4.5.3 Summary: Kinetic vs. Equilibrium Formulationsp. 194
4.6 Initial and Boundary Conditionsp. 195
4.7 Conclusionp. 196
4.8 Exercisesp. 197
Bibliographyp. 198
5 Simulationp. 199
5.1 1-D Simulation of Air-Water Flowp. 199
5.1.1 Drainage in a Homogeneous Soilp. 201
5.1.2 Drainage in a Heterogeneous Soilp. 205
5.1.3 Imbibition in Homogeneous Soilp. 206
5.2 1-D Simulation of DNAPL-Water Flowp. 207
5.2.1 Primary DNAPL Imbibition in Homogeneous Soilp. 208
5.2.2 Density Effectp. 208
5.2.3 DNAPL Drainage in Homogeneous Soilp. 209
5.2.4 Secondary Imbibition of DNAPL in Homogeneous Soilp. 210
5.2.5 Secondary Drainage in Homogeneous Soilp. 211
5.2.6 Primary Imbibition in Heterogeneous Soilp. 212
5.3 2-D Simulation of DNAPL-Water Flowp. 213
5.3.1 DNAPL Descent into a Water-Saturated Reservoirp. 213
5.4 Simulation of Multiphase Flow and Transportp. 216
5.4.1 1-D Two-Phase Flow and Transportp. 217
5.4.2 2-D Two-Phase Flow and Transportp. 218
5.5 2-D Single-Phase Flow and Transportp. 224
5.5.1 Base Casep. 228
5.5.2 Effect of Inflowp. 228
5.5.3 Impact of Well Dischargep. 230
5.5.4 Effect of Adsorptionp. 231
5.5.5 Effect of a Low Transmissivity Regionp. 232
5.5.6 Effect of a High Transmissivity Regionp. 234
5.5.7 Effect of Rate of Reactionp. 235
5.6 3-D Single-Phase Flow and Transportp. 236
5.7 2-D Three-Phase Flowp. 239
5.8 Summaryp. 244
Bibliographyp. 245
Select Symbolsp. 247
Indexp. 253