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 $σ_Y^2$ of the local conductivity. Using perturbation expansions up to third order and fourth order in $σ_Y^2$ obtained from the moment equation approach, we construct the general functional dependence of the transport variables in the regime where $σ_Y^2$ is of order 1 and larger than 1. Comparison with available numerical simulations give encouraging results and show that the proposed method provides significant improvements over available expansions.

Latex, 14 pages + 5 ps figures