Approximate Statistical Moments of Darcy Flows in Composite Porous Media

Larry Winter

Mathematical Modeling and Analysis Group
Theoretical Division
Los Alamos National Lab

I'll develop probabilities and statistics for the parameters of Darcy flows through saturated porous media composed of units of different materials. The probability model has two levels. On the local level, a porous medium is composed of disjoint, statistically homogeneous blocks, each of which consists of a single type of material. On a larger scale, a porous medium is an arrangement of heterogeneous blocks whose extent and location are defined by uncertain boundaries. Using this two-scaled model, I'll give general formulas for the probability distribution of hydraulic conductivity and for its mean, and then develop perturbation expansions for mean and covariance of head in multiple dimensions. Distributions and parameters turn out to be mixtures of locally homogeneous block distributions weighted by large-scale boundary probabilities.