Calculation of the effective permeability of a randomly inhomogeneous porous medium

The effective permeability of a porous medium is calculated nonperturbatively. An exact expression for the permeability in terms of a double path integral is derived on the assumption that the permeability obeys a log-normal distribution function. Path integration is carried out in general form in the large-scale limit. The result confirms the well-known conjecture that the effective permeability is independent of the structure of the correlation function, but it disagrees with the hypothesis that the effective permeability depends exponentially on the variance. Zh. éksp. Teor. Fiz. 112, 313–324 (July 1997)