Application of generalised effective-medium theory to transport in porous media

Abstract

Abstract. The use of effective-medium treatments to estimate bulk properties pertaining to transport (of, for example, fluids, heat, particles or electricity) through random composite media (such as reservoir rocks), is widespread. This is because they are relatively simple, often reasonably accurate (on occasion, remarkably so) and in many cases yield closed-form expressions for the properties concerned. However, the single-bond effective-medium treatment (EMT) of random resistor networks that has been used to determine transport coefficients for various transport problems in pore networks is limited to some special isotropic networks with nearest-neighbour connections. We demonstrate here that transport through two different fracture system models, with stress-induced anisotropy, can be treated using an EMT originally applied to anisotropic resistor networks. The main purpose of the present contribution, however, is to present a new, more general effective medium formalism applicable to networks of arbitrary topology. This new generalised EMT is used to obtain a new criterion for percolation of an arbitrary conducting network under random dilution. A specific application to unsaturated flow through a pore network with nearest-and next-nearest-neighbour connections is also given.

Measurement and approximate critical path analysis of the pore‐scale‐induced anisotropy factor of an unsaturated porous medium

“…This feature of anisotropic pore networks, changing to a more isotropic network just before they cease to conduct, is a universal property of anisotropic systems approaching their percolation threshold. This phenomenon was demonstrated by calculations of conductivities of artificial anisotropic networks [Skal, 1987;Harris, 1990 (4) with/x being the dynamic viscosity of the water. The different exponents of the pore widths, 1 for electrical conductivity and 3 for viscous permeability, reflect the greater sensitivity of the permeability to the directional distributions of the pore widths.…”

“…This feature of anisotropic pore networks, changing to a more isotropic network just before they cease to conduct, is a universal property of anisotropic systems approaching their percolation threshold. This phenomenon was demonstrated by calculations of conductivities of artificial anisotropic networks [Skal, 1987;Harris, 1990 The anisotropy factors of the three mica packings (A •) are presented in Figure 5. Since the anisotropy factor is the ratio of the two measured conductivities, it is more sensitive to experimental errors and other difficulties.…”

“…The calculation of the transport parameters of anisotropic capillary networks can be carried out by direct solution of the resulting set of linear equations [Bear et al, 1987;Friedman and Seaton, 1996] or by approximate methods. Bernasconi [1974], Harris [1990Harris [ , 1992, and Toledo et al [1992], for example, have extended the effective medium approximation of Kirkpatrick [1973] to anisotropic networks. In addition to calculating the directional conductivities of anisotropic networks, concepts of percolation theory [Skal, 1987;Skal and Grebnev, 1992 Figure 1.…”

Relations and Links Between Soil Mechanics, Porous Media Physics, Physiochemical Theory, and Effective Medium Theory

“…However, it is also possible to find deformation gradient-effective stress links, based on the effective medium theory. For the reader not used to the terminology, Effective Medium Theory (EMT) is a way to describe the macroscopic properties of a composite material from some sort of averaging of the multiple values of the constituents of this composite (e.g., [2][3][4][5]). The properties of the system are calculated from constituents' properties knowing the volume fraction of the constituents and geometrical details.…”

Modelling moisture distribution and isothermal transfer in a heterogeneous porous material

“…Effective mean theory (EMT) dates back to Maxwell in the nineteenth century. Kirkpatrick (1973), proposed a general formalism for the theory and more recent studies related to EMT may be found in Koplik (1982), King (1989), David et al (1990) and Harris (1990Harris ( , 1993.…”