Porous media transport phenomena

POROUS MEDIA TRANSPORT PHENOMENA......Page 5
CONTENTS......Page 9
PREFACE......Page 17
ABOUT THE AUTHOR......Page 21
1.1 INTRODUCTION......Page 23
1.2 SYNOPSES OF TOPICS COVERED IN VARIOUS CHAPTERS......Page 25
2.1 INTRODUCTION......Page 29
2.2 PERMEABILITY OF POROUS MEDIA BASED ON THE BUNDLE OF TORTUOUS LEAKY-TUBE MODEL......Page 32
2.2.1 Pore Structure......Page 33
2.2.2 Equation of Permeability......Page 35
2.2.3 Derivation of the Equation of Permeability......Page 38
2.2.4 Pore Connectivity and Parametric Functions......Page 42
2.2.5 Data Analysis and Correlation Method......Page 46
2.2.6.2 Example 2: Dolomite......Page 48
2.2.6.3 Example 3: Berea Sandstone......Page 49
2.2.7.1 Example 4: Synthetic Porous Media......Page 51
2.2.7.2 Example 5: Glass Bead and Sand Packs......Page 53
2.3 PERMEABILITY OF POROUS MEDIA UNDERGOING ALTERATION BY SCALE DEPOSITION......Page 55
2.3.1 Permeability Alteration by Scale Deposition......Page 58
2.3.2 Permeability Alteration in Thin Porous Disk by Scale Deposition......Page 59
2.3.3 Data Analysis and Correlation Method......Page 60
2.3.4.1 Example 7: Scale Formation......Page 61
2.3.4.2 Example 8: Acid Dissolution......Page 62
2.3.4.3 Example 9: Wormhole Development......Page 64
2.4 TEMPERATURE EFFECT ON PERMEABILITY......Page 66
2.4.1 The Modified Kozeny–Carman Equation......Page 68
2.4.2 The Vogel–Tammann–Fulcher (VTF) Equation......Page 71
2.4.3.1 Example 10: Correlation Using the Modified Kozeny–Carman Equation......Page 73
2.4.3.2 Example 11: Correlation Using the VTF Equation......Page 74
2.6 EXERCISES......Page 76
3.1 INTRODUCTION......Page 79
3.2 REV......Page 80
3.3 VOLUME-AVERAGING RULES......Page 81
3.4 MASS-WEIGHTED VOLUME-AVERAGING RULE......Page 89
3.6 APPLICATIONS OF VOLUME AND SURFACE AVERAGING RULES......Page 90
3.7 DOUBLE DECOMPOSITION FOR TURBULENT PROCESSES IN POROUS MEDIA......Page 92
3.8 TORTUOSITY EFFECT......Page 95
3.9 MACROSCOPIC TRANSPORT EQUATIONS BY CONTROL VOLUME ANALYSIS......Page 96
3.11 EXERCISES......Page 98
4.1 INTRODUCTION......Page 101
4.2.1 Dimensional Analysis......Page 103
4.2.2 Inspectional Analysis......Page 104
4.3.2 Scaling as a Tool for Minimum Parametric Representation......Page 106
4.3.3 Normalized Variables......Page 108
4.3.4 Scaling Criteria and Options for Porous Media Processes......Page 109
4.3.5 Scaling Immiscible Fluid Displacement in Laboratory Core Floods......Page 111
4.4 EXERCISES......Page 114
5.1 INTRODUCTION......Page 119
5.2 FLOW POTENTIAL......Page 120
5.3 MODIFICATION OF DARCY’S LAW FOR BULK-VERSUS FLUID VOLUME AVERAGE PRESSURES......Page 121
5.4 MACROSCOPIC EQUATION OF MOTION FROM THE CONTROL VOLUME APPROACH AND DIMENSIONAL ANALYSIS......Page 124
5.5 MODIFICATION OF DARCY’S LAW FOR THE THRESHOLD PRESSURE GRADIENT......Page 127
5.6 CONVENIENT FORMULATIONS OF THE FORCHHEIMER EQUATION......Page 130
5.7 DETERMINATION OF THE PARAMETERS OF THE FORCHHEIMER EQUATION......Page 133
5.8 FLOW DEMARCATION CRITERIA......Page 137
5.9 ENTROPY GENERATION IN POROUS MEDIA......Page 139
5.9.1 Flow through a Hydraulic Tube......Page 140
5.9.2 Flow through Porous Media......Page 142
5.10 VISCOUS DISSIPATION IN POROUS MEDIA......Page 145
5.11 GENERALIZED DARCY’S LAW BY CONTROL VOLUME ANALYSIS......Page 146
5.11.1 General Formulation......Page 148
5.11.2 Simplified Equations of Motion for Porous Media Flow......Page 154
5.12.1 Frictional Drag for Non-Newtonian Fluids......Page 156
5.12.2 Modified Darcy’s Law for Non-Newtonian Fluids......Page 157
5.12.3 Modified Forchheimer Equation for Non-Newtonian Fluids......Page 159
5.13 EXERCISES......Page 160
6.1 INTRODUCTION......Page 167
6.2 GAS FLOW THROUGH A CAPILLARY HYDRAULIC TUBE......Page 168
6.3 RELATIONSHIP BETWEEN TRANSPORTS EXPRESSED ON DIFFERENT BASES......Page 169
6.4 THE MEAN FREE PATH OF MOLECULES: FHS VERSUS VHS......Page 171
6.5 THE KNUDSEN NUMBER......Page 172
6.6 FLOW REGIMES AND GAS TRANSPORT AT ISOTHERMAL CONDITIONS......Page 174
6.6.1 Knudsen Regime......Page 176
6.6.2 Slip/Transition Regime......Page 178
6.6.3 Viscous Regime......Page 179
6.6.4 Adsorbed-Phase Diffusion......Page 180
6.7 GAS TRANSPORT AT NONISOTHERMAL CONDITIONS......Page 181
6.8 UNIFIED HAGEN–POISEUILLE-TYPE EQUATION FOR APPARENT GAS PERMEABILITY......Page 182
6.8.1 The Rarefaction Coefficient Correlation......Page 183
6.8.2 The Apparent Gas Permeability Equation......Page 184
6.8.3 The Klinkenberg Gas Slippage Factor Correlation......Page 185
6.9 SINGLE-COMPONENT GAS FLOW......Page 187
6.10 MULTICOMPONENT GAS FLOW......Page 188
6.11 EFFECT OF DIFFERENT FLOW REGIMES IN A CAPILLARY FLOW PATH AND THE EXTENDED KLINKENBERG EQUATION......Page 190
6.12 EFFECT OF PORE SIZE DISTRIBUTION ON GAS FLOW THROUGH POROUS MEDIA......Page 192
6.13 EXERCISES......Page 196
7.1 INTRODUCTION......Page 199
7.2 COUPLING SINGLE-PHASE MASS AND MOMENTUM BALANCE EQUATIONS......Page 200
7.3 CYLINDRICAL LEAKY-TANK RESERVOIR MODEL INCLUDING THE NON-DARCY EFFECT......Page 201
7.4.1 Macroscopic Equation of Continuity......Page 208
7.4.2 Application to Oil/Water Systems......Page 209
7.4.2.1 Pressure and Saturation Formulation......Page 210
7.4.2.2 Saturation Formulation......Page 211
7.4.3 One-Dimensional Linear Displacement......Page 212
7.4.4 Numerical Solution of Incompressible Two-Phase Fluid Displacement Including the Capillary Pressure Effect......Page 213
7.4.5 Fractional Flow Formulation......Page 214
7.4.6 The Buckley–Leverett Analytic Solution Neglecting the Capillary Pressure Effect......Page 215
7.4.7 Convenient Formulation......Page 216
7.4.8 Unit End-Point Mobility Ratio Formulation......Page 217
7.4.8.1 Example 1......Page 218
7.4.8.2 Example 2......Page 220
7.5.1 Principle of Superposition......Page 222
7.5.3 Basic Method of Images......Page 224
7.6 STREAMLINE/STREAM TUBE FORMULATION AND FRONT TRACKING......Page 227
7.6.1 Basic Formulation......Page 228
7.6.2 Finite Analytic Representation of Wells in Porous Media......Page 233
7.6.3 Streamline Formulation of Immiscible Displacement in Unconfined Reservoirs......Page 235
7.6.4 Streamline Formulation of Immiscible Displacement Neglecting Capillary Pressure Effects in Confined Reservoirs......Page 236
7.7 EXERCISES......Page 240
8.1 INTRODUCTION......Page 249
8.2 WETTABILITY AND WETTABILITY INDEX......Page 252
8.3 CAPILLARY PRESSURE......Page 253
8.4 WORK OF FLUID DISPLACEMENT......Page 256
8.5 TEMPERATURE EFFECT ON WETTABILITY-RELATED PROPERTIES OF POROUS MEDIA......Page 257
8.6.1.1 Basic Relationships......Page 260
8.6.1.2 Solution Neglecting the Capillary End Effect for Constant Fluid Properties......Page 264
8.6.1.3 Inferring Function and Function Derivative Values from Average Function Values......Page 267
8.6.1.4 Relationships for Processing Experimental Data......Page 269
8.6.2 Tóth et al. Formulae for the Direct Determination of Relative Permeability from Unsteady-State Fluid Displacements......Page 273
8.6.2.1 Determination of Relative Permeability under Variable Pressure and Rate Conditions......Page 275
8.6.2.2 Determination of Relative Permeability under Constant Pressure Conditions......Page 278
8.6.2.4 Applications for Data Analysis......Page 279
8.7 INDIRECT METHODS FOR THE DETERMINATION OF POROUS MEDIA FLOW FUNCTIONS AND PARAMETERS......Page 281
8.7.1 Indirect Method for Interpretation of the Steady-State Core Tests......Page 282
8.7.2.1 Formulation of a Two-Phase Flow in Porous Media......Page 283
8.7.2.2 Representation of Flow Functions......Page 285
8.7.2.3 Parameter Estimation Using the Simulated Annealing Method......Page 287
8.7.2.4 Applications for Drainage Tests......Page 289
8.7.2.5 Applications for Imbibition Tests......Page 291
8.8 EXERCISES......Page 298
9.1 INTRODUCTION......Page 303
9.2 DISPERSIVE TRANSPORT OF SPECIES IN HETEROGENEOUS AND ANISOTROPIC POROUS MEDIA......Page 304
9.2.2 Hydrodynamic Dispersion......Page 305
9.2.3 Advective/Convective Flux of Species......Page 307
9.2.4 Correlation of Dispersivity and Dispersion......Page 308
9.3 GENERAL MULTIPHASE FULLY COMPOSITIONAL NONISOTHERMAL MIXTURE MODEL......Page 310
9.4 FORMULATION OF SOURCE/SINK TERMS IN CONSERVATION EQUATIONS......Page 314
9.5 ISOTHERMAL BLACK OIL MODEL OF A NONVOLATILE OIL SYSTEM......Page 317
9.6 ISOTHERMAL LIMITED COMPOSITIONAL MODEL OF A VOLATILE OIL SYSTEM......Page 320
9.7 FLOW OF GAS AND VAPORIZING WATER PHASES IN THE NEAR-WELLBORE REGION......Page 321
9.8 FLOW OF CONDENSATE AND GAS PHASE CONTAINING NONCONDENSABLE GAS SPECIES IN THE NEAR-WELLBORE REGION......Page 323
9.9.1 Thickness-Averaged Formulation......Page 327
9.9.2 Cross-Sectional Area-Averaged Formulation......Page 328
9.10 CONDUCTIVE HEAT TRANSFER WITH PHASE CHANGE......Page 329
9.10.1 Unfrozen Water in Freezing and Thawing Soils: Kinetics and Correlation......Page 331
9.10.2 Kinetics of Freezing/Thawing Phase Change and Correlation Method......Page 333
9.10.3 Representation of the Unfrozen Water Content for Instantaneous Phase Change......Page 339
9.10.4 Apparent Heat Capacity Formulation for Heat Transfer with Phase Change......Page 340
9.10.5 Enthalpy Formulation of Conduction Heat Transfer with Phase Change at a Fixed Temperature......Page 344
9.10.6 Thermal Regimes for Freezing and Thawing of Moist Soils: Gradual versus Fixed Temperature Phase Change......Page 348
9.11 SIMULTANEOUS PHASE TRANSITION AND TRANSPORT IN POROUS MEDIA CONTAINING GAS HYDRATES......Page 350
9.12 MODELING NONISOTHERMAL HYDROCARBON FLUID FLOW CONSIDERING EXPANSION/COMPRESSION AND JOULE–THOMSON EFFECTS......Page 360
9.12.2 Temperature and Pressure Dependency of Properties......Page 361
9.12.3 Mixture Properties......Page 363
9.12.4 Equations of Conservations......Page 364
9.12.5 Applications......Page 367
9.13 EXERCISES......Page 368
10.1 INTRODUCTION......Page 375
10.2 DEEP-BED FILTRATION UNDER NONISOTHERMAL CONDITIONS......Page 377
10.2.1 Concentration of Fine Particles Migrating within the Carrier Fluid......Page 378
10.2.3 Variation of Temperature in the System of Porous Matrix and Flowing Fluid......Page 381
10.2.4 Initial Filter Coefficient......Page 383
10.2.5 Filter Coefficient Dependence on Particle Retention Mechanisms and Temperature Variation......Page 385
10.2.6 Permeability Alteration by Particle Retention and Thermal Deformation......Page 387
10.2.7 Applications......Page 388
10.3 CAKE FILTRATION OVER AN EFFECTIVE FILTER......Page 392
10.4 EXERCISES......Page 401
11.1 INTRODUCTION......Page 405
11.2.1 Transport Units......Page 407
11.2.2 Sugar Cube Model of Naturally Fractured Porous Media......Page 408
11.3.1 Analytical Matrix–Fracture Interchange Transfer Functions......Page 410
11.3.2 Pseudo-Steady-State Condition and Constant Fracture Fluid Pressure over the Matrix Block: The Warren–Root Lump-Parameter Model......Page 412
11.3.3 Transient-State Condition and Constant Fracture Fluid Pressure over the Matrix Block......Page 413
11.3.4 Single-Phase Transient Pressure Model of de Swaan for Naturally Fractured Reservoirs......Page 414
11.4 SPECIES TRANSPORT IN FRACTURED POROUS MEDIA......Page 416
11.5 IMMISCIBLE DISPLACEMENT IN NATURALLY FRACTURED POROUS MEDIA......Page 418
11.5.1 Correlation of the Matrix-to-Fracture Oil Transfer......Page 419
11.5.2 Formulation of the Fracture Flow Equation......Page 424
11.5.3 Exact Analytical Solution Using the Unit End-Point Mobility Approximation......Page 426
11.5.4 Asymptotic Analytical Solutions Using the Unit End-Point Mobility Approximation......Page 427
11.5.4.1 Formulation......Page 428
11.5.4.2 Small-Time Approximation......Page 429
11.5.4.3 Approximation for Large Time......Page 430
11.6 METHOD OF WEIGHTED SUM (QUADRATURE) NUMERICAL SOLUTIONS......Page 432
11.6.1 Formulation......Page 433
11.6.2 Quadrature Solution......Page 435
11.7 FINITE DIFFERENCE NUMERICAL SOLUTION......Page 437
11.7.1 Formulation......Page 438
11.7.2 Numerical Solutions......Page 440
11.8 EXERCISES......Page 447
REFERENCES......Page 451
INDEX......Page 477