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Mean Flow in composite porous media
Author(s) -
Winter C. L.,
Tartakovsky Daniel M.
Publication year - 2000
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/1999gl011030
Subject(s) - porous medium , disjoint sets , homogeneous , perturbation (astronomy) , porosity , probability distribution , hydraulic conductivity , mathematics , standard deviation , composite number , darcy's law , scale (ratio) , block (permutation group theory) , statistical physics , materials science , statistics , mathematical analysis , geology , geotechnical engineering , physics , geometry , soil science , combinatorics , algorithm , quantum mechanics , soil water
We develop probabilities and statistics for the parameters of Darcy flows through saturated porous media composed of units of different materials. Our probability model has two levels. On the local level, a porous medium is composed of disjoint, statistically homogeneous volumes (or blocks) each of which consists of a single type of material. On a larger scale, a porous medium is an arrangement of blocks whose extent and location are uncertain. Using this two‐scaled model, we derive general formulae for the probability distribution of hydraulic conductivity and its mean; then we develop general perturbation expansions for mean head. We express distributions and parameters in terms of mixtures of locally homogeneous block densities weighted by large‐scale block membership probabilities.