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.
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Gluzman, S., Sornette, D. Self-similar approximants of the permeability in heterogeneous porous media from moment equation expansions. Transp Porous Med 71, 75–97 (2008). https://doi.org/10.1007/s11242-007-9112-9
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DOI: https://doi.org/10.1007/s11242-007-9112-9