Porous Media Transport Phenomena

by Civan, Faruk

• ISBN13: 9780470649954
• ISBN10: 047064995X
• Edition: 1st
• Format: Hardcover
• Copyright: 2011-08-30
• Publisher: Wiley

Summary

This book covers the mass, momentum, and energy conservation equations, and their applications in engineered and natural porous media for general applications. This book is an important text for graduate courses in various disciplines involving fluids in porous materials and a useful reference book. It provides a multi-disciplinary approach to transport in porous media. This book covers general porous media applications including chapters on the effect of temperature and particle migration and provides emphasis in energy resources development. The material is presented in a uniform format with consistent SI units.

Author Biography

Faruk Civan is a Miller Chair Professor in the Mewbourne School of Petroleum and Geological Engineering at the University of Oklahoma. He has been teaching graduate courses on porous media for twenty five years, and has published over two hundred and seventy journal and conference papers, a book, and several book chapters.

Table of Contents

Preface	p. xv
About The author	p. xix
Overview	p. 1
Introduction	p. 1
Synopses of Topics Covered in Various Chapters	p. 3
Transport Properties Of Porous Media	p. 7
Introduction	p. 7
Permeability of Porous Media Based on the Bundle of Tortuous Leaky-Tube Model	p. 10
Pore Structure	p. 11
Equation of Permeability	p. 13
Derivation of the Equation of Permeability	p. 16
Pore Connectivity and Parametric Functions	p. 20
Data Analysis and Correlation Method	p. 24
Parametric Relationships of Typical Data	p. 26
Example 1: Synthetic Spheres	p. 26
Example 2: Dolomite	p. 26
Example 3: Berea Sandstone 27
Correlation of Typical Permeability Data	p. 29
Example 4: Synthetic Porous Media	p. 29
Example 5: Glass Bead and Sand Packs	p. 31
Example 6: Silty Soil	p. 33
Permeability of Porous Media Undergoing Alteration by Scale Deposition	p. 33
Permeability Alteration by Scale Deposition	p. 36
Permeability Alteration in Thin Porous Disk by Scale Deposition	p. 37
Data Analysis and Correlation Method	p. 38
Correlation of Scale Effect on Permeability	p. 39
Example 7: Scale Formation	p. 39
Example 8: Acid Dissolution	p. 40
Example 9: Wormhole Development	p. 42
Temperature Effect on Permeability	p. 44
The Modified Kozeny-Carman Equation	p. 46
The Vogel-Tammann-Fulcher (VTF) Equation	p. 49
Data Analysis and Correlation	p. 51
Example 10: Correlation Using the Modified Kozeny-Carman Equation	p. 51
Example 11: Correlation Using the VTF Equation	p. 52
Effects of Other Factors on Permeability	p. 54
Exercises	p. 54
Macroscopic Transport Equations	p. 57
Introduction	p. 57
Rev	p. 58
Volume-Averaging Rules	p. 59
Mass-Weighted Volume-Averaging Rule	p. 61
Surface Area Averaging Rules	p. 68
Applications of Volume and Surface Averaging Rules	p. 68
Double Decomposition for Turbulent Processes in Porous Media	p. 70
Tortuosity Effect	p. 73
Macroscopic Transport Equations by Control Volume Analysis	p. 74
Generalized Volume-Averaged Transport Equations	p. 76
Exercises	p. 76
Scaling And Correlation Of Transport In Porous Media	p. 79
Introduction	p. 79
Dimensional and Inspectional Analysis Methods	p. 81
Dimensional Analysis	p. 81
Inspectional Analysis	p. 82
Scaling	p. 84
Scaling as a Tool for Convenient Representation	p. 84
Scaling as a Tool for Minimum Parametric Representation	p. 84
Normalized Variables	p. 86
Scaling Criteria and Options for Porous Media Processes	p. 87
Scaling Immiscible Fluid Displacement in Laboratory Core Floods	p. 89
Exercises	p. 92
Fluid Motion In Porous Media	p. 97
Introduction	p. 97
Flow Potential	p. 98
Modification of Darcy's Law for Bulk- versus Fluid Volume Average Pressures	p. 99
Macroscopic Equation of Motion from the Control Volume Approach and Dimensional Analysis	p. 102
Modification of Darcy's Law for the Threshold Pressure Gradient	p. 105
Convenient Formulations of the Forchheimer Equation	p. 108
Determination of; the Parameters of the Forchheimer Equation	p. 111
Flow Demarcation Criteria	p. 115
Entropy Generation in Porous Media	p. 117
Flow through a Hydraulic Tube	p. 118
Flow through Porous Media	p. 120
Viscous Dissipation in Porous Media	p. 123
Generalized Darcy's Law by Control Volume Analysis	p. 124
General Formulation	p. 126
Simplified Equations of Motion for Porous Media Flow	p. 132
Equation of Motion for Non-Newtonian Fluids	p. 134
Frictional Drag for Non-Newtonian Fluids	p. 134
Modified Darcy's Law for Non-Newtonian Fluids	p. 135
	p. 137
Exercises	p. 138
Gas Transport In Tight Porous Media	p. 145
Introduction	p. 145
Gas Flow through a Capillary Hydraulic Tube	p. 146
Relationship between Transports Expressed on Different Bases	p. 147
The Mean Free Path of Molecules: FHS versus VHS	p. 149
The Knudsen Number	p. 150
Flow Regimes and Gas Transport at Isothermal Conditions	p. 152
Knudsen Regime	p. 154
Slip/Transition Regime	p. 156
Viscous Regime	p. 157
Adsorbed-Phase Diffusion	p. 158
Liquid Viscous or Capillary Condensate Flow	p. 159
Gas Transport at Nonisothermal Conditions	p. 159
Unified Hagen-Poiseuille-Type Equation for Apparent Gas Permeability	p. 160
The Rarefaction Coefficient Correlation	p. 161
The Apparent Gas Permeability Equation	p. 162
The Klinkenberg Gas Slippage Factor Correlation	p. 163
Single-Component Gas Flow	p. 165
Multicomponent Gas Flow	p. 166
Effect of Different Flow Regimes in a Capillary Flow Path and the Extended Klinkenberg Equation	p. 168
Effect of Pore Size Distribution on Gas Flow through Porous Media	p. 170
Exercises	p. 174
Fluid Transport Through Porous Media	p. 177
Introduction	p. 177
Coupling Single-Phase Mass and Momentum Balance Equations	p. 178
Cylindrical Leaky-Tank Reservoir Model Including the Non-Darcy Effect	p. 179
Coupling Two-Phase Mass and Momentum Balance Equations for Immiscible Displacement	p. 186
Macroscopic Equation of Continuity	p. 186
Application to Oil/Water Systems	p. 187
Pressure and Saturation Formulation	p. 188
Saturation Formulation	p. 189
Boundary Conditions	p. 190
One-Dimensional Linear Displacement	p. 190
Numerical Solution of Incompressible Two-Phase Fluid Displacement Including the Capillary Pressure Effect	p. 191
Fractional Flow Formulation	p. 192
The Buckley-Leverett Analytic Solution Neglecting the Capillary Pressure Effect	p. 193
Convenient Formulation	p. 194
Unit End-Point Mobility Ratio Formulation	p. 195
Example 1	p. 196
Example 2	p. 198
Potential Flow Problems in Porous Media	p. 200
Principle of Superposition	p. 200
Principle of Imaging	p. 202
Basic Method of Images	p. 202
Expanded Method of Images	p. 205
Streamline/Stream Tube Formulation and Front Tracking	p. 205
Basic Formulation	p. 206
Finite Analytic Representation of Wells in Porous Media	p. 211
Streamline Formulation of Immiscible Displacement in Uuconfined Reservoirs	p. 213
Streamline Formulation of Immiscible Displacement Neglecting Capillary Pressure Effects in Confined Reservoirs	p. 214
Exercises	p. 218
Parameters Of Fluid Transfer In Porous Media	p. 227
Introduction	p. 227
Wettability and Wettability Index	p. 230
Capillary Pressure	p. 231
Work of Fluid Displacement	p. 234
Temperature Effect on Wettability-Related Properties of Porous Media	p. 235
Direct Methods for the Determination of Porous Media Flow Functions and Parameters	p. 238
Direct Interpretation Methods for the Unsteady-State Core Tests	p. 238
Basic Relationships	p. 238
Solution Neglecting the Capillary End Effect for Constant Fluid Properties	p. 242
Inferring Function and Function Derivative Values from Average Function Values	p. 245
Relationships for Processing Experimental Data	p. 247
Applications	p. 251
The et al. Formulae for the Direct Determination of Relative Permeability from Unsteady-State Fluid Displacements	p. 251
Determination of Relative Permeability under Variable Pressure and Rate Conditions	p. 253
Determination of Relative Permeability under Constant Pressure Conditions	p. 256
Determination of Relative Permeability under Constant Rate Conditions	p. 257
Applications for Data Analysis	p. 257
Indirect Methods for the Determination of Porous Media Flow Functions and Parameters	p. 259
Indirect Method for Interpretation of the Steady-State Core Tests	p. 260
Unsteady-State Core Test History Matching Method for the Unique and Simultaneous Determination of Relative Permeability and Capillary Pressure	p. 261
Formulation of a Two-Phase Flow in Porous Media	p. 261
Representation of Flow Functions	p. 263
Parameter Estimation Using the Simulated Annealing Method	p. 265
Applications for Drainage Tests	p. 267
Applications for Imbibition Tests	p. 269
Exercises	p. 276
Mass, Momentum, And Energy Transport In Porous Media	p. 281
Introduction	p. 281
Dispersive Transport of Species in Heterogeneous and Anisotropic Porous Media	p. 282
Molecular Diffusion	p. 283
Hydrodynamic Dispersion	p. 283
Advective/Convective Flux of Species	p. 285
Correlation of Dispersivity and Dispersion	p. 286
General Multiphase Fully Compositional Nonisothermal Mixture Model	p. 288
Formulation of Source/Sink Terms in Conservation Equations	p. 292
Isothermal Black Oil Model of a Nonvolatile Oil System	p. 295
Isothermal Limited Compositional Model of a Volatile Oil System	p. 298
Flow of Gas and Vaporizing Water Phases in the Near-Wellbore Region	p. 299
Flow of Condensate and Gas Phase Containing Noncondensable Gas Species in the Near-Wellbore Region	p. 301
Shape-Averaged Formulations	p. 305
Thickness-Averaged Formulation	p. 305
Cross-Sectional Area-Averaged Formulation	p. 306
Conductive Heat Transfer with Phase Change	p. 307
Unfrozen Water in Freezing and Thawing Soils: Kinetics and Correlation	p. 309
Kinetics of Freezing/Thawing Phase Change and Correlation Method	p. 311
Representation of the Unfrozen Water Content for Instantaneous Phase Change	p. 317
Apparent Heat Capacity Formulation for Heat Transfer with Phase Change	p. 318
Enthalpy Formulation of Conduction Heat Transfer with Phase Change at a Fixed Temperature	p. 322
Thermal Regimes for Freezing and Thawing of Moist Soils: Gradual versus Fixed Temperature Phase Change	p. 326
Simultaneous Phase Transition and Transport in Porous Media Containing Gas Hydrates	p. 328
Modeling Nonisothermal Hydrocarbon Fluid Flow Considering Expansion/Compression and Joule-Thomson Effects	p. 338
Model Considerations and Assumptions	p. 339
Temperature and Pressure Dependency of Properties	p. 339
Mixture Properties	p. 341
Equations of Conservations	p. 342
Applications	p. 345
Exercises	p. 346
Suspended Particulate Transport In Porous Media	p. 353
Introduction	p. 353
Deep-Bed Filtration under Nonisothermal Conditions	p. 355
Concentration of Fine Particles Migrating within the Carrier Fluid	p. 356
Concentration of Fine Particles Deposited inside the Pores of the Porous Matrix	p. 359
Variation of Temperature in the System of Porous Matrix and Flowing Fluid	p. 359
Initial Filter Coefficient	p. 361
Filter Coefficient Dependence on Particle Retention Mechanisms and Temperature Variation	p. 363
Permeability Alteration by Particle Retention and Thermal Deformation	p. 365
Applications	p. 366
Cake Filtration over an Effective Filter	p. 370
Exercises	p. 379
Transport In Heterogeneous Porous Media	p. 383
Introduction	p. 383
Transport Units and Transport in Heterogeneous Porous Media	p. 385
Transport Units	p. 385
Sugar Cube Model of Naturally Fractured Porous Media	p. 386
Models for Transport in Fissured/Fractured Porous Media	p. 388
Analytical Matrix-Fracture Interchange Transfer Functions	p. 388
Pseudo-Steady-State Condition and Constant Fracture Fluid Pressure over the Matrix Block: The Warren-Root Lump-Parameter Model	p. 390
Transient-State Condition and Constant Fracture Fluid Pressure over the Matrix Block	p. 391
Single-Phase Transient Pressure Model of de Swaan for Naturally Fractured Reservoirs	p. 392
Species Transport in Fractured Porous Media	p. 394
Immiscible Displacement in Naturally Fractured Porous Media	p. 396
Correlation of the Matrix to-Fracture Oil Transfer	p. 397
Formulation of the Fracture Flow Equation	p. 402
Exact Analytical Solution Using the Unit End-Point Mobility Approximation	p. 404
Asymptotic Analytical Solutions Using the Unit End-Point Mobility Approximation	p. 405
Formulation	p. 406
Small-Time Approximation	p. 407
Approximation for Large Time	p. 408
Method of Weighted Sum (Quadrature) Numerical Solutions	p. 410
Formulation	p. 411
Quadrature Solution	p. 413
Finite Difference Numerical Solution	p. 415
Formulation	p. 416
Numerical Solutions	p. 418
Exercises	p. 425
References	p. 429
Index	p. 455
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