Stochastic transport in heterogeneous media with multiple families of transport paths

We examine in detail a model for transport in heterogeneous solids and porous media which contain N distinct families of transport paths (with N≥2), recently proposed by the authors [Phys. Rev. Lett. 70, 2581 (1993)]. The model is relevant to transport in metals, polycrystals, porous catalysts, coalbed methane reservoirs, and geological systems with fractures and pores. We develop a number of exact results for the one-dimensional case and, more generally, study the behavior of its effective transport properties using an effective-medium approximation, which yields several exact results in one spatial dimension.