Abstract
The effective (single-phase) permeability of an (infinite) heterogeneous porous medium is studied using a formalism of Green's functions. We give formal expressions for it in the form of a series expansion involving the ‘microscopic’ random-permeability field many-body correlation functions of higher and higher order. The particular case of a log-normal medium of infinite extent is studied using field-theoretical methods. Using partial series resummation techniques, we derivea formula up to all orders in the local correlations which was first reckoned by many authors by means of a first-order calculation. The formula — which remains an approximation — works whatever the dimensionality of the space, and gives the following simple estimate for the effective permeability in 3 D:K eff=〈k 1/3〉3. The method is general and the approximations can be systematically improved on when more complex situations are studied.
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