VARIATIONAL CALCULATION OF THE EFFECTIVE FLUID PERMEABILITY OF HETEROGENEOUS MEDIA

We evaluate the effective permeability of heterogenous media with Gaus sian local permeability disorder using the replica-variational approac h. We obtain integral equations that determine the effective permeabil ity kernel, and we study specific cases that admit analytical solution s. Specifically, in the case of homogeneous disorder we obtain a varia tional estimate for the uniform effective permeability. We compare the results of our analytical calculations with experimental and numerica l data. Finally, we model the behavior of the effective permeability i n the preasymptotic regime by means of momentum filters. Explicit fini te-size expressions are obtained in terms of a support function that i ncreases monotonically with the ratio of the support scale over the co rrelation length of the disorder. It is found that the asymptotic effe ctive permeability is approached at a slower rate than expected.