  The problem of diffusion in a porous medium with a spatially varying porosity
is considered. The particular microstructure analyzed comprises a collection of
impenetrable spheres, though the methods developed are general. Two different
approaches for calculating the effective diffusion coefficient as a function of
the microstructure are presented. The first is a deterministic approach based
on the method of multiple scales; the second is a stochastic approach for small
volume fraction of spheres based on matched asymptotic expansions. We compare
the two approaches, and we show good agreement between them in a number of
example configurations.
