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

Abstract

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 $$\sigma_{Y}^2$$ of the local conductivity. Using perturbation expansions up to third order and fourth order in $$\sigma_{Y}^2$$ obtained from the moment equation approach, we construct the general functional dependence of the scalar hydraulic conductivity in the regime where $$\sigma_{Y}^2$$ is of order 1 and larger than 1. Comparison with available numerical simulations show that the proposed method provides reasonable improvements over available expansion