Self-similar Approximants of the Permeability in Heterogeneous Porous Media from Moment Equation Expansions

Details Self-similar Approximants of the Permeability in Heterogeneous Porous Media from Moment Equation Expansions Self-similar Approximants of the Permeability in Heterogeneous Porous Media from Moment Equation Expansions

2002-11-25

arxiv.org/abs/cond-mat/0211565v1

Transport in Porous Media, 10.1007/s11242-007-9112-9 (2007)

Physics

Condensed Matter

Statistical Mechanics

Latex, 14 pages + 5 ps figures

Scientific paper

10.1007/s11242-007-9112-9

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 transport variables in the regime where $\sigma_Y^2$ 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.

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