Porous media transport phenomena

Title:

Personal Author:

Civan, Faruk

Publication Information:

Hoboken, NJ. : Wiley, c2011.

Physical Description:

xx, 463 p. : ill. ; 25 cm.

ISBN:

9780470649954

General Note:

Machine generated contents note: Preface.Chapter 1 Overview.1. Introduction.2. Synopses of Topics Covered in Various Chapters.Chapter 2 Transport Properties of Porous Media.1. Introduction.2. Permeability of Porous Media Based on the Bundle of Tortuous Leaky Tubes Model.3. Permeability of Porous Media Undergoing Alteration by Scale Deposition.4. Temperature Effect on Permeability.5. Effects of Other Factors on Permeability.6. Exercises.Chapter 3 Macroscopic Transport Equations.1. Introductiion.2. Representative Elementary Volume.4. Mass-Weighted Volume Averaging Rule.5. Surface-Area Averaging Rules.6. Applications of Volume and Surface Averaging Rules.7. Double-decomposition for Turbulent Processes in Porous Media.8. Tortuosity Effect.9. Macroscopic Transport Equations by Control Volume Analysis.10. Generalized Volume-Averaged Transport Equations.11. Exercises.Chapter 4 Scaling and Correlation of Transport in Porous Media.1. Introduction.2. Dimensional and Inspectional Analyses Methods.3. Scaling.4.Exercises.Chapter 5 Fluid Motion in Porous Media.1. Introduction.2. Flow Potential.3. Modification of Darcy's Law for Bulk- vs. Fluid-Volume Average Pressures.4. Macroscopic Equation of Motion from the Control Volume Approach and Dimensional Analysis.5. Modification of Darcy's Law for the Threshold Pressure Gradient.6. Convenient Formulations of the Forchheimer Equation.7. Determination of the Parameters of the Forchheimer Equation.8. Flow Demarcation Criteria.9. Entropy Generation in Porous Media.10. Viscous Dissipation in Porous Media.11. Generalized Darcy's Law of Control Volume Analysis.12. Equation of Motion for Non-Newtonian Fluids.13. Exercises.Chapter 6 Gas Transport in Tight Porous Media.1. Introduction.2. Gas Flow through a Capillary Hydraulic Tube.3. Relationship between Transports Expressed on Different Bases.4. The Mean-Free-Path of Molecules: Fixed Vs. Variable Cross-Section Hard Sphere.5. The Knudsen Number.6. Flow Regimes and Gas Transport at Isothermal Conditions.7. Gas Transport at Nonisothermal Conditions.8. Unified Hagen-Poiseuille-Type Equation for Apparent Gas Permeability.9. Single-Component Gas Flow.10. Multi-Component Gas Flow.11. Effect of Different Flow Regimes Flow Path-Extended Klinkenberg Equation.12. Effect of Pore-Size Distribution on Gas Flow through Porous Media.13. Exercises.Chapter 7 Fluid Transport through Porous Media.1. Introduction.2. Coupling Single-Phase Mass and Momentum Balance Equations.3. Cylindrical Leaky-Tank Reservoir Model Including the Non-Darcy Effect.4. Coupling Two-Phase Mass and Momentum Balance Equations for Immiscible Displacement.5. Potential Flow Problems in Porous Media.6. Streamline/Streamtube Formulation and Front Tracking.7. Exercises.Chapter 8 Parameters of Fluid Transfer in Porous Media.1. Introduction.2. Wettability and Wettability Index.3. Capillary Pressure.4. Work of Fluid Displacement.5. Temperature Effect on Wettability Related Properties of Porous Media.6. Direct Methods for Determination of Porous Media Flow Functions and Parameters.7. Indirect Methods for Determination of Porous Media Flow Functions and Parameters.8. Exercises.Chapter 9 Mass, Momentum, and Energy Transport in Porous Media.1. Introduction.2. Dispersive Transport of Species in Heterogeneous and Anisotropic Porous Media.3. General Multi-Phase Fully-Compositional Non-Isothermal Mixture Model.4. Formulation of Source/Sink Terms in Conservation Equations.5. Isothermal Black-Oil Model of a Nonvolatile Oil System.6. Isothermal Limited-Compositional Model of a Volatile Oil System.7. Flow of Gas and Vaporizing-Water Phases in the Near-Wellbore Region. 8. Flow of Condensate and Gas-Phase Containing Non-Condensable Gas Species in the Near-Wellbore Region.9. Shape-Averaged Formulations.10. Conductive Heat Transfer with Phase Change.11. Simultaneous Phase Transition and Transport in Porous Media.12. Modeling Non-Isothermal Hydrocarbon Fluid Flow Considering Expansion/Compression and Joule Thomson Effects.13. Exercises.Chapter 10. Suspended Particulate Transport in Porous Media.1. Introduction.2. Deep-Bed Filtration under Non-Isothermal Conditions.3. Cake Filtration over an Effective Filter.4. Exercises.Chapter 11. Transport in Heterogeneous Porous Media.1. Introduction.2. Transport Units and Transport in Heterogeneous Porous Media.3. Models for Transport in Fissured/Fractured Porous Media.4. Species Transport in Fractured Porous Media.5. Immiscible Displacement in Naturally-Fractured Porous Media.6. Method of Weighted Sums (Quadrature) Numerical Solutions.7. Finite-Difference Numerical Solution.8. Exercises.References.

Abstract:

"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"-- Provided by publisher.

Subject Term:

Porous materials

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Summary

The book that makes transport in porous media accessible to students and researchers alike

Porous Media Transport Phenomena covers the general theories behind flow and transport in porous media--a solid permeated by a network of pores filled with fluid--which encompasses rocks, biological tissues, ceramics, and much more. Designed for use in graduate courses in various disciplines involving fluids in porous materials, and as a reference for practitioners in the field, the text includes exercises and practical applications while avoiding the complex math found in other books, allowing the reader to focus on the central elements of the topic.

Covering general porous media applications, including the effects of temperature and particle migration, and placing an emphasis on energy resource development, the book provides an overview of mass, momentum, and energy conservation equations, and their applications in engineered and natural porous media for general applications. Offering a multidisciplinary approach to transport in porous media, material is presented in a uniform format with consistent SI units.

An indispensable resource on an extremely wide and varied topic drawn from numerous engineering fields, Porous Media Transport Phenomena includes a solutions manual for all exercises found in the book, additional questions for study purposes, and PowerPoint slides that follow the order of the text.

Author Notes

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.

Preface	p. xv
About The author	p. xix
Chapter 1 Overview	p. 1
1.1 Introduction	p. 1
1.2 Synopses of Topics Covered in Various Chapters	p. 3
Chapter 2 Transport Properties Of Porous Media	p. 7
2.1 Introduction	p. 7
2.2 Permeability of Porous Media Based on the Bundle of Tortuous Leaky-Tube Model	p. 10
2.2.1 Pore Structure	p. 11
2.2.2 Equation of Permeability	p. 13
2.2.3 Derivation of the Equation of Permeability	p. 16
2.2.4 Pore Connectivity and Parametric Functions	p. 20
2.2.5 Data Analysis and Correlation Method	p. 24
2.2.6 Parametric Relationships of Typical Data	p. 26
2.2.6.1 Example 1: Synthetic Spheres	p. 26
2.2.6.2 Example 2: Dolomite	p. 26
2.2.6.3 Example 3: Berea Sandstone 27
2.2.7 Correlation of Typical Permeability Data	p. 29
2.2.7.1 Example 4: Synthetic Porous Media	p. 29
2.2.7.2 Example 5: Glass Bead and Sand Packs	p. 31
2.2.7.3 Example 6: Silty Soil	p. 33
2.3 Permeability of Porous Media Undergoing Alteration by Scale Deposition	p. 33
2.3.1 Permeability Alteration by Scale Deposition	p. 36
2.3.2 Permeability Alteration in Thin Porous Disk by Scale Deposition	p. 37
2.3.3 Data Analysis and Correlation Method	p. 38
2.3.4 Correlation of Scale Effect on Permeability	p. 39
2.3.4.1 Example 7: Scale Formation	p. 39
2.3.4.2 Example 8: Acid Dissolution	p. 40
2.3.4.3 Example 9: Wormhole Development	p. 42
2.4 Temperature Effect on Permeability	p. 44
2.4.1 The Modified Kozeny-Carman Equation	p. 46
2.4.2 The Vogel-Tammann-Fulcher (VTF) Equation	p. 49
2.4.3 Data Analysis and Correlation	p. 51
2.4.3.1 Example 10: Correlation Using the Modified Kozeny-Carman Equation	p. 51
2.4.3.2 Example 11: Correlation Using the VTF Equation	p. 52
2.5 Effects of Other Factors on Permeability	p. 54
2.6 Exercises	p. 54
Chapter 3 Macroscopic Transport Equations	p. 57
3.1 Introduction	p. 57
3.2 Rev	p. 58
3.3 Volume-Averaging Rules	p. 59
3.4 Mass-Weighted Volume-Averaging Rule	p. 61
3.5 Surface Area Averaging Rules	p. 68
3.6 Applications of Volume and Surface Averaging Rules	p. 68
3.7 Double Decomposition for Turbulent Processes in Porous Media	p. 70
3.8 Tortuosity Effect	p. 73
3.9 Macroscopic Transport Equations by Control Volume Analysis	p. 74
3.10 Generalized Volume-Averaged Transport Equations	p. 76
3.11 Exercises	p. 76
Chapter 4 Scaling And Correlation Of Transport In Porous Media	p. 79
4.1 Introduction	p. 79
4.2 Dimensional and Inspectional Analysis Methods	p. 81
4.2.1 Dimensional Analysis	p. 81
4.2.2 Inspectional Analysis	p. 82
4.3 Scaling	p. 84
4.3.1 Scaling as a Tool for Convenient Representation	p. 84
4.3.2 Scaling as a Tool for Minimum Parametric Representation	p. 84
4.3.3 Normalized Variables	p. 86
4.3.4 Scaling Criteria and Options for Porous Media Processes	p. 87
4.3.5 Scaling Immiscible Fluid Displacement in Laboratory Core Floods	p. 89
4.4 Exercises	p. 92
Chapter 5 Fluid Motion In Porous Media	p. 97
5.1 Introduction	p. 97
5.2 Flow Potential	p. 98
5.3 Modification of Darcy's Law for Bulk- versus Fluid Volume Average Pressures	p. 99
5.4 Macroscopic Equation of Motion from the Control Volume Approach and Dimensional Analysis	p. 102
5.5 Modification of Darcy's Law for the Threshold Pressure Gradient	p. 105
5.6 Convenient Formulations of the Forchheimer Equation	p. 108
5.7 Determination of; the Parameters of the Forchheimer Equation	p. 111
5.8 Flow Demarcation Criteria	p. 115
5.9 Entropy Generation in Porous Media	p. 117
5.9.1 Flow through a Hydraulic Tube	p. 118
5.9.2 Flow through Porous Media	p. 120
5.10 Viscous Dissipation in Porous Media	p. 123
5.11 Generalized Darcy's Law by Control Volume Analysis	p. 124
5.11.1 General Formulation	p. 126
5.11.2 Simplified Equations of Motion for Porous Media Flow	p. 132
5.12 Equation of Motion for Non-Newtonian Fluids	p. 134
5.12.1 Frictional Drag for Non-Newtonian Fluids	p. 134
5.12.2 Modified Darcy's Law for Non-Newtonian Fluids	p. 135
5.12.3\|yModified Forchheimer Equation for Non-Newtonian Fluids p. 137
5.13 Exercises	p. 138
Chapter 6 Gas Transport In Tight Porous Media	p. 145
6.1 Introduction	p. 145
6.2 Gas Flow through a Capillary Hydraulic Tube	p. 146
6.3 Relationship between Transports Expressed on Different Bases	p. 147
6.4 The Mean Free Path of Molecules: FHS versus VHS	p. 149
6.5 The Knudsen Number	p. 150
6.6 Flow Regimes and Gas Transport at Isothermal Conditions	p. 152
6.6.1 Knudsen Regime	p. 154
6.6.2 Slip/Transition Regime	p. 156
6.6.3 Viscous Regime	p. 157
6.6.4 Adsorbed-Phase Diffusion	p. 158
6.6.5 Liquid Viscous or Capillary Condensate Flow	p. 159
6.7 Gas Transport at Nonisothermal Conditions	p. 159
6.8 Unified Hagen-Poiseuille-Type Equation for Apparent Gas Permeability	p. 160
6.8.1 The Rarefaction Coefficient Correlation	p. 161
6.8.2 The Apparent Gas Permeability Equation	p. 162
6.8.3 The Klinkenberg Gas Slippage Factor Correlation	p. 163
6.9 Single-Component Gas Flow	p. 165
6.10 Multicomponent Gas Flow	p. 166
6.11 Effect of Different Flow Regimes in a Capillary Flow Path and the Extended Klinkenberg Equation	p. 168
6.12 Effect of Pore Size Distribution on Gas Flow through Porous Media	p. 170
6.13 Exercises	p. 174
Chapter 7 Fluid Transport Through Porous Media	p. 177
7.1 Introduction	p. 177
7.2 Coupling Single-Phase Mass and Momentum Balance Equations	p. 178
7.3 Cylindrical Leaky-Tank Reservoir Model Including the Non-Darcy Effect	p. 179
7.4 Coupling Two-Phase Mass and Momentum Balance Equations for Immiscible Displacement	p. 186
7.4.1 Macroscopic Equation of Continuity	p. 186
7.4.2 Application to Oil/Water Systems	p. 187
7.4.2.1 Pressure and Saturation Formulation	p. 188
7.4.2.2 Saturation Formulation	p. 189
7.4.2.3 Boundary Conditions	p. 190
7.4.3 One-Dimensional Linear Displacement	p. 190
7.4.4 Numerical Solution of Incompressible Two-Phase Fluid Displacement Including the Capillary Pressure Effect	p. 191
7.4.5 Fractional Flow Formulation	p. 192
7.4.6 The Buckley-Leverett Analytic Solution Neglecting the Capillary Pressure Effect	p. 193
7.4.7 Convenient Formulation	p. 194
7.4.8 Unit End-Point Mobility Ratio Formulation	p. 195
7.4.8.1 Example 1	p. 196
7.4.8.2 Example 2	p. 198
7.5 Potential Flow Problems in Porous Media	p. 200
7.5.1 Principle of Superposition	p. 200
7.5.2 Principle of Imaging	p. 202
7.5.3 Basic Method of Images	p. 202
7.5.4 Expanded Method of Images	p. 205
7.6 Streamline/Stream Tube Formulation and Front Tracking	p. 205
7.6.1 Basic Formulation	p. 206
7.6.2 Finite Analytic Representation of Wells in Porous Media	p. 211
7.6.3 Streamline Formulation of Immiscible Displacement in Uuconfined Reservoirs	p. 213
7.6.4 Streamline Formulation of Immiscible Displacement Neglecting Capillary Pressure Effects in Confined Reservoirs	p. 214
7.7 Exercises	p. 218
Chapter 8 Parameters Of Fluid Transfer In Porous Media	p. 227
8.1 Introduction	p. 227
8.2 Wettability and Wettability Index	p. 230
8.3 Capillary Pressure	p. 231
8.4 Work of Fluid Displacement	p. 234
8.5 Temperature Effect on Wettability-Related Properties of Porous Media	p. 235
8.6 Direct Methods for the Determination of Porous Media Flow Functions and Parameters	p. 238
8.6.1 Direct Interpretation Methods for the Unsteady-State Core Tests	p. 238
8.6.1.1 Basic Relationships	p. 238
8.6.1.2 Solution Neglecting the Capillary End Effect for Constant Fluid Properties	p. 242
8.6.1.3 Inferring Function and Function Derivative Values from Average Function Values	p. 245
8.6.1.4 Relationships for Processing Experimental Data	p. 247
8.6.1.5 Applications	p. 251
8.6.2 The et al. Formulae for the Direct Determination of Relative Permeability from Unsteady-State Fluid Displacements	p. 251
8.6.2.1 Determination of Relative Permeability under Variable Pressure and Rate Conditions	p. 253
8.6.2.2 Determination of Relative Permeability under Constant Pressure Conditions	p. 256
8.6.2.3 Determination of Relative Permeability under Constant Rate Conditions	p. 257
8.6.2.4 Applications for Data Analysis	p. 257
8.7 Indirect Methods for the Determination of Porous Media Flow Functions and Parameters	p. 259
8.7.1 Indirect Method for Interpretation of the Steady-State Core Tests	p. 260
8.7.2 Unsteady-State Core Test History Matching Method for the Unique and Simultaneous Determination of Relative Permeability and Capillary Pressure	p. 261
8.7.2.1 Formulation of a Two-Phase Flow in Porous Media	p. 261
8.7.2.2 Representation of Flow Functions	p. 263
8.7.2.3 Parameter Estimation Using the Simulated Annealing Method	p. 265
8.7.2.4 Applications for Drainage Tests	p. 267
8.7.2.5 Applications for Imbibition Tests	p. 269
8.8 Exercises	p. 276
Chapter 9 Mass, Momentum, And Energy Transport In Porous Media	p. 281
9.1 Introduction	p. 281
9.2 Dispersive Transport of Species in Heterogeneous and Anisotropic Porous Media	p. 282
9.2.1 Molecular Diffusion	p. 283
9.2.2 Hydrodynamic Dispersion	p. 283
9.2.3 Advective/Convective Flux of Species	p. 285
9.2.4 Correlation of Dispersivity and Dispersion	p. 286
9.3 General Multiphase Fully Compositional Nonisothermal Mixture Model	p. 288
9.4 Formulation of Source/Sink Terms in Conservation Equations	p. 292
9.5 Isothermal Black Oil Model of a Nonvolatile Oil System	p. 295
9.6 Isothermal Limited Compositional Model of a Volatile Oil System	p. 298
9.7 Flow of Gas and Vaporizing Water Phases in the Near-Wellbore Region	p. 299
9.8 Flow of Condensate and Gas Phase Containing Noncondensable Gas Species in the Near-Wellbore Region	p. 301
9.9 Shape-Averaged Formulations	p. 305
9.9.1 Thickness-Averaged Formulation	p. 305
9.9.2 Cross-Sectional Area-Averaged Formulation	p. 306
9.10 Conductive Heat Transfer with Phase Change	p. 307
9.10.1 Unfrozen Water in Freezing and Thawing Soils: Kinetics and Correlation	p. 309
9.10.2 Kinetics of Freezing/Thawing Phase Change and Correlation Method	p. 311
9.10.3 Representation of the Unfrozen Water Content for Instantaneous Phase Change	p. 317
9.10.4 Apparent Heat Capacity Formulation for Heat Transfer with Phase Change	p. 318
9.10.5 Enthalpy Formulation of Conduction Heat Transfer with Phase Change at a Fixed Temperature	p. 322
9.10.6 Thermal Regimes for Freezing and Thawing of Moist Soils: Gradual versus Fixed Temperature Phase Change	p. 326
9.11 Simultaneous Phase Transition and Transport in Porous Media Containing Gas Hydrates	p. 328
9.12 Modeling Nonisothermal Hydrocarbon Fluid Flow Considering Expansion/Compression and Joule-Thomson Effects	p. 338
9.12.1 Model Considerations and Assumptions	p. 339
9.12.2 Temperature and Pressure Dependency of Properties	p. 339
9.12.3 Mixture Properties	p. 341
9.12.4 Equations of Conservations	p. 342
9.12.5 Applications	p. 345
9.13 Exercises	p. 346
Chapter 10 Suspended Particulate Transport In Porous Media	p. 353
10.1 Introduction	p. 353
10.2 Deep-Bed Filtration under Nonisothermal Conditions	p. 355
10.2.1 Concentration of Fine Particles Migrating within the Carrier Fluid	p. 356
10.2.2 Concentration of Fine Particles Deposited inside the Pores of the Porous Matrix	p. 359
10.2.3 Variation of Temperature in the System of Porous Matrix and Flowing Fluid	p. 359
10.2.4 Initial Filter Coefficient	p. 361
10.2.5 Filter Coefficient Dependence on Particle Retention Mechanisms and Temperature Variation	p. 363
10.2.6 Permeability Alteration by Particle Retention and Thermal Deformation	p. 365
10.2.7 Applications	p. 366
10.3 Cake Filtration over an Effective Filter	p. 370
10.4 Exercises	p. 379
Chapter 11 Transport In Heterogeneous Porous Media	p. 383
11.1 Introduction	p. 383
11.2 Transport Units and Transport in Heterogeneous Porous Media	p. 385
11.2.1 Transport Units	p. 385
11.2.2 Sugar Cube Model of Naturally Fractured Porous Media	p. 386
11.3 Models for Transport in Fissured/Fractured Porous Media	p. 388
11.3.1 Analytical Matrix-Fracture Interchange Transfer Functions	p. 388
11.3.2 Pseudo-Steady-State Condition and Constant Fracture Fluid Pressure over the Matrix Block: The Warren-Root Lump-Parameter Model	p. 390
11.3.3 Transient-State Condition and Constant Fracture Fluid Pressure over the Matrix Block	p. 391
11.3.4 Single-Phase Transient Pressure Model of de Swaan for Naturally Fractured Reservoirs	p. 392
11.4 Species Transport in Fractured Porous Media	p. 394
11.5 Immiscible Displacement in Naturally Fractured Porous Media	p. 396
11.5.1 Correlation of the Matrix to-Fracture Oil Transfer	p. 397
11.5.2 Formulation of the Fracture Flow Equation	p. 402
11.5.3 Exact Analytical Solution Using the Unit End-Point Mobility Approximation	p. 404
11.5.4 Asymptotic Analytical Solutions Using the Unit End-Point Mobility Approximation	p. 405
11.5.4.1 Formulation	p. 406
11.5.4.2 Small-Time Approximation	p. 407
11.5.4.3 Approximation for Large Time	p. 408
11.6 Method of Weighted Sum (Quadrature) Numerical Solutions	p. 410
11.6.1 Formulation	p. 411
11.6.2 Quadrature Solution	p. 413
11.7 Finite Difference Numerical Solution	p. 415
11.7.1 Formulation	p. 416
11.7.2 Numerical Solutions	p. 418
11.8 Exercises	p. 425
References	p. 429
Index	p. 455

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