THE EFFECTIVE PERMEABILITY OF A HETEROGENEOUS POROUS-MEDIUM

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 derive a 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) = [k1/3]3. The method is general and the approximations can be systematically improved on when more complex situations are studied.