Porous Media (eBook)

Front Cover 1
Porous Media: Geometry and Transports 6
Copyright Page 7
Table of Contents 8
Dedication 7
Preface 16
Chapter 1. Introduction 18
1.1 Definition and Purpose 18
1.2 General Review 19
1.3 Outline of the Book 22
References 25
Chapter 2. The Geometry of Porous Media 26
2.1 Introduction 26
2.2 Illustrative Examples of Porous Media 27
2.3 General Concepts 35
2.4 Major Structures and Models 46
2.5 Spatially Periodic Structures 47
2.6 Fractal Structures 52
2.7 Random Structures 56
2.8 Composite Structures 63
2.9 Reconstructed Porous Media 67
2.10 Formation and Structures of Some Geological Porous Media 69
References 70
Chapter 3. Transports in Porous Media 72
3.1 General 72
3.2 The Diffusion Equation 75
3.3 Equations for Fluid Motions 79
3.4 Convection-Diffusion Equation 89
3.5 Other Transports 91
3.6 General Problems of Transports in Porous Media 91
3.7 Resolution of Field Equations 94
References 97
Chapter 4. Spatially Periodic Structures 100
Section 4.A General Concepts 101
4.1 Characteristic Length Scales 101
4.2 Geometry of Spatially Periodic Media 103
4.3 Spatially Periodic Functions 113
Section 4.B Diffusion in Spatially Periodic Structures 121
4.4 Diffusion in an Infinite Spatially Periodic Medium 121
4.5 Diffusion by Asymptotic Analysis 138
4.6 Determination of the Macroscopic Diffusion Tensor 145
Section 4.C Flow in Spatially Periodic Structures 161
4.7 Stokes Flow in an Infinite Spatially Periodic Medium 161
4.8 Determination of the Permeability Tensor 175
4.9 Extension to Inertial Flows and Non-Newtonian Fluids 192
Section 4.D Taylor Dispersion in Spatially Periodic Structures 203
4.10 Taylor Dispersion by the Method of Moments 203
4.11 Taylor Dispersion by Asymptotic Analysis 223
Section 4.E Spatially Periodic Capillary Networks 235
4.12 Capillary Networks 235
4.13 Stokes Flow in Spatially Periodic Capillary Networks 247
4.14 Taylor Dispersion in Spatially Periodic Capillary Networks 255
References 264
Chapter 5. Deterministic Fractal Structures 270
Section 5.A General Concepts 270
5.1 Geometry of Fractals Sets 270
5.2 Examples of Fractals and Measurements of the Fractal Dimension 277
5.3 Mathematics of Fractals 286
5.4 Transports in Fractals 293
Section 5.B Fractal Capillary Networks 300
5.5 Convection and Conduction of Fractal Networks 300
5.6 Diffusion in Fractal Networks 326
5.7 Taylor Dispersion in Fractal Networks 333
5.8 Conduction and Convection in Apollonian Packings 343
Section 5.C Continuous Deterministic Fractals 358
5.9 Conduction in Continuous Deterministic Fractals 358
5.10 Convection in Continuous Deterministic Fractals 368
5.11 Taylor Dispersion in Continuous Deterministic Fractals 381
References 387
Chapter 6. Random Structures 392
Section 6.A General Concepts 392
6.1 Introduction 392
6.2 Geometry of Site and Bond Percolation 393
Section 6.B Random Networks 419
6.3 Conduction of Random Networks 419
6.4 Convection in Random Networks 441
6.5 Taylor Dispersion in Random Networks 445
Section 6.C Random Continua 451
6.6 Conduction in Random Continua 451
6.7 Convection in Random Continua 476
6.8 Taylor Dispersion in Random Continua 500
References 512
Chapter 7. Reconstructed Porous Media 520
7.1 Introduction 520
7.2 Reconstruction of Porous Media 522
7.3 Application 531
7.4 The Permeability of Reconstructed Porous Media 542
7.5 Formation Factor of Reconstructed Porous Media 551
References 554
Index 556