Self-similar approximants of the permeability in heterogeneous porous media from moment equation expansions

We use a mathematical technique, the self-similar functional renormalization, to construct formulas for the average conductivity that apply for large heterogeneity, based on perturbative expansions in powers of a small parameter, usually the log-variance sigma(2)(Y) of the local conductivity. Using perturbation expansions up to third order and fourth order in sigma(2)(Y) obtained from the moment equation approach, we construct the general functional dependence of the scalar hydraulic conductivity in the regime where sigma(2)(Y) is of order 1 and larger than 1. Comparison with available numerical simulations show that the proposed method provides reasonable improvements over available expansions.