ABSTRACT
In this chapter, we present a novel methodology for modeling ˆuid imbibition in brous porous media. The modeling methodology is based on obtaining mathematical expressions for the variation of a medium’s capillary pressure and relative permeability with saturation, via 3-D numerical simulations conducted on scales comparable to the dimensions of the constituting bers. This information is then used in Richards’ equation for twophase ˆow in porous media to predict the rate of ˆuid absorption in a brous
CONTENTS
6.1 Virtual Three-Dimensional Fibrous Media ........................................... 132 6.1.1 Imaged Fibrous Structures ........................................................... 132 6.1.2 Modeled Fibrous Structures ......................................................... 133
6.2 Modeling Capillary Pressure in 3-D Fibrous Media ............................ 135 6.2.1 Full-Morphology Approach ......................................................... 136 6.2.2 Effects of Microstructural Parameters on Capillary Pressure ........................................................................................... 138
6.3 Modeling Permeability in 3-D Fibrous Media ....................................... 141 6.3.1 FM-Stokes Simulation Method.................................................... 141 6.3.2 Analytic Expressions for Saturated and Relative
Permeability .................................................................................... 142 6.4 Bimodal Fibrous Media ............................................................................. 145
6.4.1 Modeled Bimodal Fibrous Geometries ....................................... 145 6.4.2 Effect of Bimodality on Capillary Pressure and Permeability .................................................................................... 146
6.5 Richards’ Equation of Two-Phase Flows in Porous Media .................. 148 6.5.1 Richards’ Equation versus the Lucas-Washburn Equation .... 148 6.5.2 Effect of Media’s Microstructure on Absorption ...................... 152
6.6 Summary ..................................................................................................... 154 Nomenclature ...................................................................................................... 155
Greek Letters ............................................................................................... 156 Abbreviations ............................................................................................. 156
References ............................................................................................................. 156
material as a function of time and space. A peculiar feature of the simulation method presented here is the possibility of isolating different microstructural parameters of the medium ( ber diameter, ber orientation, etc.) and studying their inˆuence on the rate of ˆuid absorption.
