Self-similar approximants of the permeability in heterogeneous porous media from moment equation expansions期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	Simon Gluzman Didier Sornette

Affiliation:	(1) Institute of Geophysics and Planetary Physics, University of California Los Angeles, Los Angeles, CA 90095-1567, USA;(2) Present address: 3000 Bathurst St, Apt 606, Toronto, ON, Canada, M6B 3B4;(3) Department of Earth and Space Sciences, UCLA, Los Angeles, CA, USA;(4) Laboratoire de Physique de la Matière Condensée, CNRS UMR 6622, Université de Nice-Sophia Antipolis, 06108 Nice Cedex 2, France;(5) Department of Management, Technology and Economics, ETH Zurich, Kreuzplatz 5, Zurich, 8032, Switzerland

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 expansions.

Keywords:	Hydraulic permeability Heterogeneous porous media Moment equation expansions Renormalization Self-similarity
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