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Equilibrium and Transfer in Porous Media 2: Transfer Laws

Equilibrium and Transfer in Porous Media 2: Transfer Laws

Jean-François Daïan

ISBN: 978-1-118-93126-4

Apr 2014

240 pages



A porous medium is composed of a solid matrix and its geometrical complement: the pore space. This pore space can be occupied by one or more fluids. The understanding of transport phenomena in porous media is a challenging intellectual task.  This book provides a detailed analysis of the aspects required for the understanding of many experimental techniques in the field of porous media transport phenomena. It is aimed at students
or engineers who may not be looking specifically to become theoreticians in porous media, but wish to integrate knowledge of porous media with their previous scientific culture, or who may have encountered them when dealing with a technological problem.  While avoiding the details of the more mathematical and abstract developments of the theories of macroscopization, the author gives as accurate and rigorous an idea as possible of the methods used to establish the major laws of macroscopic behavior in porous media. He also illustrates the constitutive laws and equations by demonstrating some of their classical applications. Priority is to put forward the constitutive laws in concrete circumstances without going into technical detail.

This second volume in the three-volume series focuses on transport and transfer from homogeneous phases to porous media, and isothermal transport in the pore space.

Nomenclature vii

Chapter 1. Transport and Transfer: from Homogeneous Phases to Porous Media 1

1.1. Transfer phenomena: complementary approaches 1

1.1.1. Transfer processes and couplings 1

1.1.2. Continuums and molecular aspect 3

1.2. Usual formulations for homogeneous phases 6

1.2.1. FLOW of a viscous fluid 6

1.2.2. Isothermal diffusion 8

1.2.3. Thermal conduction. Fourier’s law 12

1.3. Transfers in porous media, macroscopization 13

1.3.1. General approach of macroscopization   14

1.3.2. Fundamental concepts of macroscopization 17

1.3.3. Conditions of validity of macroscopization 20

1.3.4. Obtaining the macroscopic transfer laws 25

1.4. Porous media: elementary balances and transfer laws 28

1.4.1. Rules of play 28

1.4.2. Filtration of a fluid saturating the pore space: Darcy’s law 32

1.4.3. Isothermal molecular diffusion in the gaseous or liquid phase saturating the pore space   36

1.4.4. Thermal conduction in a composite medium 40

1.5. Appendices   41

1.5.1. Mechanics and thermodynamics of homogeneous phases: the continuum approach 41

1.5.2. Thermodynamic balances. Overview of the thermodynamics of irreversible processes (TIP) 49

1.5.3. Transfers in porous media: the TIP approach 56

1.5.4. Three examples of macroscopization by spatial averaging 62

1.5.5. Inertial flows: the Dupuit-Forchheimer law 72

1.5.6. Transfer of dissolved matter. Hydrodynamic dispersion  76

1.5.7. Composites and mixing laws 79

1.5.8. Transfers and percolation theory 85

1.5.9. Viscous stress. Poiseuille’s law 88

1.5.10. A look at non-equilibrium transfers 90

Chapter 2. Isothermal Transport in the Pore Space  99

2.1. Laws of transport in the pore space occupied by one or two phases: additional points   99

2.1.1. Diffusion and filtration in porous media occupied by two immiscible fluids. 100

2.1.2. Porometric distribution and transport in the gaseous phase Knudsen and Klinkenberg effects 106

2.1.3. Transport with phase-change isothermal transport of a volatile liquid   115

2.2. A classification of Isothermal transport processes constitutive equations boundary conditions 123

2.2.1. General definitions vocabulary  123

2.2.2. Filtration under an isobaric atmosphere of a capillary liquid, which may be volatile 129

2.2.3. Filtration of a volatile liquid and of its pure vapor 139

2.2.4. Linearized constitutive equations 141

2.2.5. Transport of a gas or a non-condensible gaseous component   142

2.2.6. Transport in porous media of matter dissolved in the liquid phase 144

2.2.7. Other isothermal transport processes 147

2.3. Appendices and exercises 147

2.3.1. Two-phase filtration macroscopization   147

2.3.2. Transport in the gaseous phase and kinetic theory of gases 149

2.3.3. Isothermal transport of a volatile liquid: proportion of each of the PHASEs 162

2.3.4. Isothermal transport of a volatile liquid: illumination of the effective medium theory (EMT) 173

2.3.5. Illumination of the self-consistent theory (SCT) 180

2.3.6. Percolation theory, conductivity, permeability 192

Glossary 195

Bibliography 203

Index 207

Summary of other Volumes in the Series 209