Modeling Transport Phenomena in Porous Media with Applications (eBook)

Malay K. Das is an Associate Professor in the Department of Mechanical Engineering, Indian Institute of Technology Kanpur, India; Partha P. Mukherjee is an Associate Professor the Department of Mechanical Engineering, Purdue University, USA; and K. Muralidhar is a Professor in the Department of Mechanical Engineering, Indian Institute of Technology Kanpur, India.

Preface 6
Contents 8
1 Introduction 13
1.1 Physical Mechanisms 14
1.2 Representative Elementary Volume 14
1.3 Mathematical Modeling of Fluid Flow 16
1.4 Darcy’s Law 18
1.5 Microscale Phenomena 20
1.6 Applications 20
1.7 Terminology 21
1.8 Closure 22
Bibliography 23
Modeling Flow and Transport in Porous Media 23
Multiphase Flow in Porous Media 24
Biomedical Modeling in Porous Media 24
Numerical Techniques in Porous Media 25
Experiments in Porous Media 25
Hierarchical Modeling 25
Turbulent Flow 26
2 Equations Governing Flow and Transport in Porous Media 27
2.1 Darcy’s Law 27
2.1.1 Cartesian and Cylindrical Coordinate Systems 30
2.1.2 Inhomogeneous Media 31
2.1.3 Anisotropic Media 32
2.1.4 Compressible Flow 33
2.1.5 Effect of Gravity 35
2.2 Brinkman-Corrected Darcy’s Law 35
2.3 Forschheimer-Extended Darcy’s Law 37
2.4 Non-darcy Model of Flow 39
2.4.1 Non-dimensionalization 42
2.4.2 Special Cases 43
2.4.3 Compressible Flow 44
2.4.4 Turbulent Flow 45
2.5 Energy Equation 47
2.5.1 Thermal Non-equilibrium Model 51
2.5.2 Compressible Flow 53
2.6 Unsaturated Porous Medium 54
2.6.1 Oil–Water Flow 57
2.6.2 Multiphase Multicomponent Flow 61
2.7 Mass Transfer 63
2.8 Combined Heat and Mass Transfer 65
2.9 Flow, Heat, and Mass Transfer 67
2.10 Nanoscale Porous Media 69
2.11 Multiscale Porous Media 70
2.12 Closure 71
References 72
3 Mesoscale Interactions of Transport Phenomena in Polymer Electrolyte Fuel Cells 76
3.1 Introduction 76
3.2 Description of Charge Transport in Porous Media 79
3.2.1 Special Considerations 82
3.3 Mesoscale Models in Porous Media 83
3.4 Microstructure Generation 84
3.5 Lattice Boltzmann Modeling 84
3.5.1 Methodology 87
3.5.2 Representative Highlights 89
3.6 Electrochemistry-Coupled Direct Numerical Simulation 92
3.6.1 Methodology 94
3.6.2 Representative Results 95
3.7 Summary and Outlook 100
Acknowledgements 101
References 101
4 Porous Media Applications: Electrochemical Systems 104
4.1 Introduction 104
4.2 Thermodynamic, Kinetic, and Transport Behavior of Li-Ion Battery Materials 106
4.2.1 Open Circuit Potential 107
4.2.2 Entropic Coefficient 107
4.2.3 Cell Capacity and C-Rate 109
4.2.4 Intercalation Kinetics 111
4.2.5 Electrolyte Transport Properties 111
4.3 Modeling Isothermal Operation of a Li-Ion Cell 113
4.3.1 Macrohomogeneous Description 115
4.3.2 Comments on Mathematical Nature of Governing Equations and Solution 116
4.3.3 Results and Discussion 118
4.4 Importance of Thermal Effects and Its Influence on Electrochemical Operation 123
4.4.1 Energy Equation to Define Temperature Changes 124
4.4.2 Results and Discussion 126
4.5 Direct Numerical Simulation 126
4.5.1 Governing Equations 128
4.5.2 Microstructural Effects: Properties for Composite Electrodes 129
4.6 Summary and Outlook 132
Acknowledgements 132
References 132
5 Porous Media Applications: Biological Systems 134
5.1 Introduction 134
5.1.1 Aneurysm and the Treatment Options 134
5.1.2 Blood Flow in Coil-Embolized Aneurysm: Role of Modeling and Simulation 135
5.2 Analytical Solutions of Flow in a Channel and a Tube 136
5.2.1 Pulsatile Flow Through a Tube with Clear Media 136
5.2.2 Steady Flow Through a Channel Filled with Porous Media 138
5.2.3 Steady Flow Through a Tube Filled with Porous Media 138
5.2.4 Pulsatile Flow Through a Channel Filled with Porous Media 139
5.2.5 Pulsatile Flow Through a Tube Filled with Porous Media 140
5.3 Pulsatile Flow in a Porous Bulge 141
5.3.1 Governing Equations 142
5.3.2 Flow Parameters 143
5.3.3 Pulsatile Flow in a Porous Bulge: Numerical Solution 145
5.3.4 Validation of the Finite Volume Solver 145
5.3.5 Pulsatile Flow in a Bulge 150
5.3.6 Pulsatile Flow in a Patient-Specific Geometry 155
5.4 Rheology of Biological Fluids 158
5.4.1 Role of RBC in Blood Rheology 159
5.4.2 Realistic Blood Model 160
5.5 Closure 161
References 162
6 Oscillatory Flow in a Mesh-Type Regenerator 166
6.1 Introduction 167
6.1.1 Stirling Refrigerator 167
6.1.2 Regenerator 170
6.2 Thermodynamic and Transport Models 171
6.3 Transport Modeling of a Mesh-Type Regenerator 172
6.3.1 Thermal Non-Equilibrium 173
6.4 Non-Darcy Thermal Nonequilibrium Model 174
6.4.1 Flow Equations in One-Dimensional Unsteady Form 176
6.4.2 Specification of Model Parameters 179
6.4.3 Time Constant 183
6.4.4 Harmonic Analysis 184
6.4.5 Numerical Solution of the Energy Equation 188
6.5 Results and Discussion 189
6.5.1 Flow Behavior 190
6.5.2 Thermal Performance 197
6.5.3 Dynamic Steady State 197
6.5.4 Heat Losses 202
6.5.5 Coarse Mesh 203
6.5.6 Transient Response 204
6.6 Conclusions 207
References 208
7 Geological Systems, Methane Recovery, and CO2 Sequestration 211
7.1 Introduction 211
7.1.1 Gas Hydrate as an Energy Resource 212
7.1.2 Environmental Concerns and CO2 Sequestration 213
7.1.3 Nature of Marine Hydrate Reservoirs and CH4 Recovery 214
7.1.4 Role of Modeling and Simulation 215
7.2 Mathematical Modeling 216
7.2.1 Single-Phase Model 216
7.2.2 Governing Equations 217
7.2.3 Constitutive Relations 219
7.2.4 Initial and Boundary Conditions 220
7.3 Two-Phase Model 221
7.3.1 Governing Equations 221
7.3.2 Equilibrium Data for Hydrate Stability 224
7.3.3 Porosity and Absolute Permeability 224
7.3.4 Relative Permeability and Capillary Pressure 225
7.3.5 Gas Phase Viscosity 225
7.3.6 Specific Heat Capacities 226
7.3.7 Heat of Hydrate Formation 226
7.3.8 Equivalent Thermal Conductivity 227
7.3.9 Initial and Boundary Conditions 227
7.4 Results and Discussion 228
7.4.1 Evolution of Pressure and Temperature Profiles 228
7.4.2 Sensitivity Analysis 232
7.4.3 Multiphase Simulation 232
7.4.4 Evolution of Pressure and Temperature Profiles 233
7.4.5 Sensitivity Analysis: Thermal Conductivity 238
7.4.6 Sensitivity Analysis: Medium Porosity 240
7.5 Closure 243
References 243
8 Closure 246
Index 248