Mean flow in composite porous media

We develop probabilities and statistics for the parameters of Darcy flows through saturated porous media composed of units of different materials. Our probability model has two levels. On the local level, a porous medium is composed of disjoint, statistically homogeneous volumes (or blocks) each of which consists of a single type of material. On a larger scale, a porous medium is an arrangement of blocks whose extent and location are uncertain. Using this two-scaled model, we derive general formulae for the probability distribution of hydraulic conductivity and its mean; then we develop general perturbation expansions for mean head. We express distributions and parameters in terms of mixtures of locally homogeneous block densities weighted by large-scale block membership probabilities.