Essentials of Multiphase Flow in Porous Media

ESSENTIALS OF MULTIPHASE FLOW AND TRANSPORT IN POROUS MEDIA......Page 4
CONTENTS......Page 10
Preface......Page 14
Acknowledgments......Page 16
1.1 Introduction......Page 18
1.2 Phases and Porous Media......Page 19
1.3 Grain and Pore Size Distributions......Page 23
1.4 The Concept of Saturation......Page 29
1.5 The Concept of Pressure......Page 30
1.6 Surface Tension Considerations......Page 33
1.7 Concept of Concentration......Page 47
1.9 Exercises......Page 49
Bibliography......Page 50
2.1 Introduction......Page 52
2.2 Microscale Mass Conservation......Page 55
2.3 Integral Forms of Mass Conservation......Page 56
2.4 Integral Theorems......Page 61
2.4.2 Transport Theorem......Page 62
2.5 Point Forms of Mass Conservation......Page 63
2.6 The Macroscale Perspective......Page 65
2.6.1 The Representative Elementary Volume......Page 66
2.6.2 Global and Local Coordinate Systems......Page 67
2.6.3 Macroscopic Variables......Page 70
2.6.4 Definitions of Macroscale Quantities......Page 73
2.6.5 Summary of Macroscale Quantities......Page 79
2.7 The Averaging Theorems......Page 80
2.7.1 Spatial Averaging Theorem......Page 81
2.7.2 Temporal Averaging Theorem......Page 83
2.8.1 Macroscale Point Forms......Page 84
2.8.2 Integral Forms......Page 88
2.9 Applications......Page 90
2.9.1 Integral Analysis......Page 91
2.9.2 Point Analysis......Page 93
2.11 Exercises......Page 96
Bibliography......Page 98
3.1 Introduction......Page 100
3.2 Darcy’s Experiments......Page 102
3.3 Fluid Properties......Page 105
3.4.1 Mass Fraction......Page 106
3.4.2 Mass Density and Pressure......Page 107
3.4.3 Fluid Viscosity......Page 109
3.5.1 Hydrostatic Force and Hydraulic Head......Page 110
3.5.2 Derivatives of Hydraulic Head......Page 114
3.6 Single-Phase Fluid Flow......Page 115
3.6.1 Darcy’s Law......Page 116
3.6.2 Hydraulic Conductivity and Permeability......Page 119
3.6.3 Derivation of Groundwater Flow Equation......Page 123
3.6.4 Recapitulation of the Derivation......Page 128
3.6.5 Initial and Boundary Conditions......Page 130
3.6.6 Two-Dimensional Flow......Page 133
3.7.1 Derivation of Flow Equations......Page 138
3.7.2 Observations on the p(c)-s(w) Relationship......Page 144
3.7.3 Formulas for the p(c)-s(w) Relationship......Page 152
3.7.4 Observations of the k(α)(rel)-s(w) Relationship......Page 160
3.7.5 Formulas for the k(α)(rel)-s(w) Relation......Page 163
3.7.6 Special Cases of Multiphase Flow......Page 166
3.8.1 Fractional Flow......Page 172
3.8.2 Derivation of the Buckley-Leverett Equation......Page 174
3.8.3 Solution of the Buckley-Leverett Equation......Page 175
3.9 Summary......Page 177
3.10 Exercises......Page 178
Bibliography......Page 179
4.1 Introduction......Page 182
4.2 Velocity in the Species Transport Equations......Page 184
4.2.1 Direct Approach......Page 185
4.2.2 Rigorous Approach......Page 186
4.2.3 Distribution Approach......Page 189
4.2.4 Summary......Page 192
4.3 Closure Relations for the Dispersion Vector......Page 193
4.4 Chemical Reaction Rates......Page 197
4.5 Interphase Transfer Terms......Page 199
4.5.1 Kinetic Formulation......Page 200
4.5.2 Equilibrium Formulation......Page 204
4.5.3 Summary: Kinetic vs. Equilibrium Formulations......Page 211
4.6 Initial and Boundary Conditions......Page 212
4.7 Conclusion......Page 213
4.8 Exercises......Page 214
Bibliography......Page 215
5.1 1-D Simulation of Air-Water Flow......Page 216
5.1.1 Drainage in a Homogeneous Soil......Page 218
5.1.2 Drainage in a Heterogeneous Soil......Page 222
5.1.3 Imbibition in Homogeneous Soil......Page 223
5.2 1-D Simulation of DNAPL-Water Flow......Page 224
5.2.2 Density Effect......Page 225
5.2.3 DNAPL Drainage in Homogeneous Soil......Page 226
5.2.4 Secondary Imbibition of DNAPL in Homogeneous Soil......Page 227
5.2.5 Secondary Drainage in Homogeneous Soil......Page 228
5.2.6 Primary Imbibition in Heterogeneous Soil......Page 229
5.3.1 DNAPL Descent into a Water-Saturated Reservoir......Page 230
5.4 Simulation of Multiphase Flow and Transport......Page 233
5.4.1 1-D Two-Phase Flow and Transport......Page 234
5.4.2 2-D Two-Phase Flow and Transport......Page 235
5.5 2-D Single-Phase Flow and Transport......Page 241
5.5.2 Effect of Inflow......Page 245
5.5.3 Impact of Well Discharge......Page 247
5.5.4 Effect of Adsorption......Page 248
5.5.5 Effect of a Low Transmissivity Region......Page 249
5.5.6 Effect of a High Transmissivity Region......Page 251
5.5.7 Effect of Rate of Reaction......Page 252
5.6 3-D Single-Phase Flow and Transport......Page 253
5.7 2-D Three-Phase Flow......Page 256
5.8 Summary......Page 261
Bibliography......Page 262
Select Symbols......Page 264
Index......Page 270