Basic Constitutive Relations for Unsaturated Media

Abstract

The following sections describe how to find the hydraulic conductivity, air permeability, electrical conductivity, as well as solute and gas diffusion in porous media. The results are valid for the “upscaling” from the pore scale to the sample scale. The theoretical development and the parameters are consistent between the various phenomena and the results predict experiment. Several authors have considered whether the universal scaling of percolation transport coefficients should be seen in basic properties such as the hydraulic or electrical conductivities (Jerauld et al., 1984; Balberg, 1987; Hilfer, 1991; Berkowitz and Balberg, 1992, 1993; Golden et al., 1998; Golden, 2001) . One particular example that it is possible to explain is Archie's law (Archie, 1942) for the electrical conductivity, a result which has occupied the following researchers, among others (Adler et al., 1992; Bigalke, 2000; Binley et al., 2001, 2002; Thompson et al., 1987; Kuentz et al., 2000; Lemaitre. et al., 1988; Johnson and Schwartz, 1989; Le Ravalec et al., 1996; Mattisson and Knackstedt, 1987; Ruffet et al., 1991; Wong et al., 1984) . Rudolf Hilfer and colleagues have more recently also determined that percolation theory can be used to help interpret simulations of flow and conduction (Manwart and Hilfer, 2001) in simulated media (Manwart et al., 2000).