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 first volume in the three-volume series focuses on fluids in equilibrium in the pore space; interfaces, the equilibrium of solutions and freezing in porous media; and gives experimental investigations of capillary behavior and porometry, and sorption and porometry.
Jean-Fran ois Da an is a retired and voluntary researcher at LTHE (Laboratoire d' tude des Transferts en Hydrologie et Environnement) in Grenoble, France, having worked there as a lecturer for nearly 30 years before his retirement. His main fields of research include porous media, pore structure characterization: mercury porosimetry and the application of percolation theory. He is the co-author of the XDQ (Xu Ke, Quenard, Da an) model.
Foreword ix Nomenclature xiii Introduction xvii Chapter 1. Fluids in Equilibrium in the Pore Space: Capillary Behavior 1 1.1. The pore space and its representation 1 1.1.1. Complexity of the pore space 1 1.1.2. Description of the microstructure 2 1.1.3. Porometric distribution: representation through cylindrical pores 3 1.2. Capillary pressureGL and interfacial mechanical equilibrium: Laplace s law 4 1.2.1. Two-phase occupation of the pore space 4 1.2.2. Capillarity: wetting and interfacial tension 5 1.2.3. Laplace s law: capillary pressure 6 1.2.4. Saturation: retention curves 9 1.2.5. Fluids and cohesion of granular media 11 1.3. Liquid vapor thermodynamic equilibrium: Kelvin s law 14 1.3.1. The capillary couple of volatile liquid inert gas 14 1.3.2. Partial pressure of vapor: Kelvin s law 15 1.3.3. Sorption isotherms: the capillary domain and the adsorption domain 17 1.3.4. State variables and contingent variables 18 Chapter 2. Interfaces, Equilibrium of Solutions and Freezing in Porous Media: Thermodynamic Aspects 21 2.1. Interfaces and adsorption 22 2.1.1. Interfacial films 22 2.1.2. Capillary interface 23 2.1.3. Wetting and adsorption films 25 2.1.4. Intersection of the interfaces and wetting angles 28 2.1.5. Thermodynamics of interface and adsorption 29 2.2. Solutions in porous media: capillary potential and osmotic potential 40 2.2.1. Mechanical and thermodynamic equilibrium of solutions 40 2.2.2. Osmotic barriers 43 2.3. Freezing of the interstitial liquid 44 2.3.1. Mechanical and thermodynamic equilibrium 44 2.3.2. The freezing process: thermoporometry 46 2.4. Appendix: thermodynamic points of reference 48 2.4.1. Pressure in fluids 49 2.4.2. Principles of thermodynamics and state functions 55 2.4.3. Diphasic equilibrium of a pure body 59 2.4.4. Thermodynamics of mixtures 61 2.4.5. Expression of state functions 63 Chapter 3. Capillary Behavior and Porometry: Experimental Investigation 69 3.1. Retention curves 69 3.1.1. Retention curves and morphology of the pore space 69 3.1.2. Displacements of immiscible liquids 79 3.1.3. The liquid gas couple 86 3.1.4. The van Genuchten Form 86 3.1.5. Orders of magnitude 88 3.1.6. The case of deformable materials 89 3.2. Metrology of capillarity 90 3.2.1. Measurement of capillary pressure: tensiometer 90 3.2.2. Measuring saturation 92 3.2.3. Choice and treatment of the samples 101 3.3. Experimental determination and interpretation of retention curves 109 3.3.1. Open air drainage and imbibition 109 3.3.2. (Richards) pressure plate 113 3.3.3. Mercury porometry 116 3.3.4. Pore space and interstitial fluids imaging 121 3.4. Appendices and exercises 123 3.4.1. Hydrostatics and retention curves 123 3.4.2. Retention curves of a material with rough porometry 124 3.4.3. Dripping and centrifugation 126 3.4.4. Porometric distributions and in situ hydrostatic equilibrium 131 3.4.5. Capillary barrier 135 3.4.6. The fate of the entrained air during imbibition 137 3.4.7. Nucleation during drainage 141 3.4.8. Basic principles of percolation theory 144 Chapter 4. Sorption and Porometry: Experimental Investigations 151 4.1. Sorption metrology 151 4.1.1. Measurement of the saturation rate of vapor 152 4.1.2. Controlling the saturation rate of the vapor. Experimental determination of the sorption isotherms 156 4.2. Sorption isotherms interpretation 160 4.2.1. Capillary behavior and adsorption 160 4.2.2. Pure adsorption: BET interpretation and the specific surface 162 4.2.3. Capillary condensation: BJH interpretation 165 4.3. Thermal effects, adsorption heat and osmotic effects 169 4.3.1. The influence of temperature 169 4.3.2. Adsorption heat 170 4.3.3. Influence of dissolved species 170 4.4. Appendices and exercises 171 4.4.1. Oven drying of a hygroscopic material: simplified study 171 4.4.2. Balancing kinetics in an osmotic-conditioning chamber 174 4.4.3. BJH porometry 175 4.4.4. Mercury porometry and BJH model 176 4.4.5. Determination of the adsorption heat 180 Glossary 185 Bibliography 189 Index 193 Summary of other Volumes in the Series 195