Das / Mukherjee / Muralidhar Modeling Transport Phenomena in Porous Media with Applications

1. Auflage 2018
ISBN: 978-3-319-69866-3
Verlag: Springer Nature Switzerland
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 250 Seiten

Reihe: Mechanical Engineering Series

This book is an ensemble of six major chapters, an introduction, and a closure on modeling transport phenomena in porous media with applications. Two of the six chapters explain the underlying theories, whereas the rest focus on new applications. Porous media transport is essentially a multi-scale process. Accordingly, the related theory described in the second and third chapters covers both continuum- and meso-scale phenomena. Examining the continuum formulation imparts rigor to the empirical porous media models, while the mesoscopic model focuses on the physical processes within the pores. Porous media models are discussed in the context of a few important engineering applications. These include biomedical problems, gas hydrate reservoirs, regenerators, and fuel cells. The discussion reveals the strengths and weaknesses of existing models as well as future research directions.

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.

Autoren/Hrsg.

Das, Malay K.

Mukherjee, Partha P.

Muralidhar, K.

Inhaltsverzeichnis

1;Preface;6
2;Contents;8
3;1 Introduction;13
3.1;1.1 Physical Mechanisms;14
3.2;1.2 Representative Elementary Volume;14
3.3;1.3 Mathematical Modeling of Fluid Flow;16
3.4;1.4 Darcy’s Law;18
3.5;1.5 Microscale Phenomena;20
3.6;1.6 Applications;20
3.7;1.7 Terminology;21
3.8;1.8 Closure;22
3.9;Bibliography;23
3.10;Modeling Flow and Transport in Porous Media;23
3.11;Multiphase Flow in Porous Media;24
3.12;Biomedical Modeling in Porous Media;24
3.13;Numerical Techniques in Porous Media;25
3.14;Experiments in Porous Media;25
3.15;Hierarchical Modeling;25
3.16;Turbulent Flow;26
4;2 Equations Governing Flow and Transport in Porous Media;27
4.1;2.1 Darcy’s Law;27
4.1.1;2.1.1 Cartesian and Cylindrical Coordinate Systems;30
4.1.2;2.1.2 Inhomogeneous Media;31
4.1.3;2.1.3 Anisotropic Media;32
4.1.4;2.1.4 Compressible Flow;33
4.1.5;2.1.5 Effect of Gravity;35
4.2;2.2 Brinkman-Corrected Darcy’s Law;35
4.3;2.3 Forschheimer-Extended Darcy’s Law;37
4.4;2.4 Non-darcy Model of Flow;39
4.4.1;2.4.1 Non-dimensionalization;42
4.4.2;2.4.2 Special Cases;43
4.4.3;2.4.3 Compressible Flow;44
4.4.4;2.4.4 Turbulent Flow;45
4.5;2.5 Energy Equation;47
4.5.1;2.5.1 Thermal Non-equilibrium Model;51
4.5.2;2.5.2 Compressible Flow;53
4.6;2.6 Unsaturated Porous Medium;54
4.6.1;2.6.1 Oil–Water Flow;57
4.6.2;2.6.2 Multiphase Multicomponent Flow;61
4.7;2.7 Mass Transfer;63
4.8;2.8 Combined Heat and Mass Transfer;65
4.9;2.9 Flow, Heat, and Mass Transfer;67
4.10;2.10 Nanoscale Porous Media;69
4.11;2.11 Multiscale Porous Media;70
4.12;2.12 Closure;71
4.13;References;72
5;3 Mesoscale Interactions of Transport Phenomena in Polymer Electrolyte Fuel Cells;76
5.1;3.1 Introduction;76
5.2;3.2 Description of Charge Transport in Porous Media;79
5.2.1;3.2.1 Special Considerations;82
5.3;3.3 Mesoscale Models in Porous Media;83
5.4;3.4 Microstructure Generation;84
5.5;3.5 Lattice Boltzmann Modeling;84
5.5.1;3.5.1 Methodology;87
5.5.2;3.5.2 Representative Highlights;89
5.6;3.6 Electrochemistry-Coupled Direct Numerical Simulation;92
5.6.1;3.6.1 Methodology;94
5.6.2;3.6.2 Representative Results;95
5.7;3.7 Summary and Outlook;100
5.8;Acknowledgements;101
5.9;References;101
6;4 Porous Media Applications: Electrochemical Systems;104
6.1;4.1 Introduction;104
6.2;4.2 Thermodynamic, Kinetic, and Transport Behavior of Li-Ion Battery Materials;106
6.2.1;4.2.1 Open Circuit Potential;107
6.2.2;4.2.2 Entropic Coefficient;107
6.2.3;4.2.3 Cell Capacity and C-Rate;109
6.2.4;4.2.4 Intercalation Kinetics;111
6.2.5;4.2.5 Electrolyte Transport Properties;111
6.3;4.3 Modeling Isothermal Operation of a Li-Ion Cell;113
6.3.1;4.3.1 Macrohomogeneous Description;115
6.3.2;4.3.2 Comments on Mathematical Nature of Governing Equations and Solution;116
6.3.3;4.3.3 Results and Discussion;118
6.4;4.4 Importance of Thermal Effects and Its Influence on Electrochemical Operation;123
6.4.1;4.4.1 Energy Equation to Define Temperature Changes;124
6.4.2;4.4.2 Results and Discussion;126
6.5;4.5 Direct Numerical Simulation;126
6.5.1;4.5.1 Governing Equations;128
6.5.2;4.5.2 Microstructural Effects: Properties for Composite Electrodes;129
6.6;4.6 Summary and Outlook;132
6.7;Acknowledgements;132
6.8;References;132
7;5 Porous Media Applications: Biological Systems;134
7.1;5.1 Introduction;134
7.1.1;5.1.1 Aneurysm and the Treatment Options;134
7.1.2;5.1.2 Blood Flow in Coil-Embolized Aneurysm: Role of Modeling and Simulation;135
7.2;5.2 Analytical Solutions of Flow in a Channel and a Tube;136
7.2.1;5.2.1 Pulsatile Flow Through a Tube with Clear Media;136
7.2.2;5.2.2 Steady Flow Through a Channel Filled with Porous Media;138
7.2.3;5.2.3 Steady Flow Through a Tube Filled with Porous Media;138
7.2.4;5.2.4 Pulsatile Flow Through a Channel Filled with Porous Media;139
7.2.5;5.2.5 Pulsatile Flow Through a Tube Filled with Porous Media;140
7.3;5.3 Pulsatile Flow in a Porous Bulge;141
7.3.1;5.3.1 Governing Equations;142
7.3.2;5.3.2 Flow Parameters;143
7.3.3;5.3.3 Pulsatile Flow in a Porous Bulge: Numerical Solution;145
7.3.4;5.3.4 Validation of the Finite Volume Solver;145
7.3.5;5.3.5 Pulsatile Flow in a Bulge;150
7.3.6;5.3.6 Pulsatile Flow in a Patient-Specific Geometry;155
7.4;5.4 Rheology of Biological Fluids;158
7.4.1;5.4.1 Role of RBC in Blood Rheology;159
7.4.2;5.4.2 Realistic Blood Model;160
7.5;5.5 Closure;161
7.6;References;162
8;6 Oscillatory Flow in a Mesh-Type Regenerator;166
8.1;6.1 Introduction;167
8.1.1;6.1.1 Stirling Refrigerator;167
8.1.2;6.1.2 Regenerator;170
8.2;6.2 Thermodynamic and Transport Models;171
8.3;6.3 Transport Modeling of a Mesh-Type Regenerator;172
8.3.1;6.3.1 Thermal Non-Equilibrium;173
8.4;6.4 Non-Darcy Thermal Nonequilibrium Model;174
8.4.1;6.4.1 Flow Equations in One-Dimensional Unsteady Form;176
8.4.2;6.4.2 Specification of Model Parameters;179
8.4.3;6.4.3 Time Constant;183
8.4.4;6.4.4 Harmonic Analysis;184
8.4.5;6.4.5 Numerical Solution of the Energy Equation;188
8.5;6.5 Results and Discussion;189
8.5.1;6.5.1 Flow Behavior;190
8.5.2;6.5.2 Thermal Performance;197
8.5.3;6.5.3 Dynamic Steady State;197
8.5.4;6.5.4 Heat Losses;202
8.5.5;6.5.5 Coarse Mesh;203
8.5.6;6.5.6 Transient Response;204
8.6;6.6 Conclusions;207
8.7;References;208
9;7 Geological Systems, Methane Recovery, and CO2 Sequestration;211
9.1;7.1 Introduction;211
9.1.1;7.1.1 Gas Hydrate as an Energy Resource;212
9.1.2;7.1.2 Environmental Concerns and CO2 Sequestration;213
9.1.3;7.1.3 Nature of Marine Hydrate Reservoirs and CH4 Recovery;214
9.1.4;7.1.4 Role of Modeling and Simulation;215
9.2;7.2 Mathematical Modeling;216
9.2.1;7.2.1 Single-Phase Model;216
9.2.2;7.2.2 Governing Equations;217
9.2.3;7.2.3 Constitutive Relations;219
9.2.4;7.2.4 Initial and Boundary Conditions;220
9.3;7.3 Two-Phase Model;221
9.3.1;7.3.1 Governing Equations;221
9.3.2;7.3.2 Equilibrium Data for Hydrate Stability;224
9.3.3;7.3.3 Porosity and Absolute Permeability;224
9.3.4;7.3.4 Relative Permeability and Capillary Pressure;225
9.3.5;7.3.5 Gas Phase Viscosity;225
9.3.6;7.3.6 Specific Heat Capacities;226
9.3.7;7.3.7 Heat of Hydrate Formation;226
9.3.8;7.3.8 Equivalent Thermal Conductivity;227
9.3.9;7.3.9 Initial and Boundary Conditions;227
9.4;7.4 Results and Discussion;228
9.4.1;7.4.1 Evolution of Pressure and Temperature Profiles;228
9.4.2;7.4.2 Sensitivity Analysis;232
9.4.3;7.4.3 Multiphase Simulation;232
9.4.4;7.4.4 Evolution of Pressure and Temperature Profiles;233
9.4.5;7.4.5 Sensitivity Analysis: Thermal Conductivity;238
9.4.6;7.4.6 Sensitivity Analysis: Medium Porosity;240
9.5;7.5 Closure;243
9.6;References;243
10;8 Closure;246
11;Index;248