Computing the effective permeability of log-normal permeability fields using renormalization methods

Abstract We consider the computation of the equivalent permeability K eff of a heterogeneous porous medium. The logarithm of local permeabilities is a stationary isotropic gaussian random function, characterized by its covariance function ρ r . Using a renormalization group analysis, we compute the equivalent permeability K eff Γ as a function of the wave vector cut-off Γ . Finally, using a mean-field approximation, we obtain a very simple differential equation linking the equivalent permeability to the power spectrum of the permeability fluctuations. After integration over the whole wave vectors, K eff is expressed as a power averaging formulae, which was conjectured by Landau and Lifshitz.