EFFECTIVE HYDRAULIC CONDUCTIVITY OF BOUNDED, STRONGLY HETEROGENEOUS POROUS-MEDIA

We develop analytical expressions for the effective hydraulic conducti vity K-e of a three-dimensional, heterogeneous porous medium in the pr esence of randomly prescribed head and flux boundaries. The log hydrau lic conductivity Y forms a Gaussian, statistically homogeneous and ani sotropic random field with an exponential autocovariance. By effective hydraulic conductivity of a finite volume in such a field, we mean th e ensemble mean (expected value) of all random equivalent conductiviti es that one could associate with a similar volume under uniform mean f low. We start by deriving a first-order approximation of an exact expr ession developed in 1993 by Neuman and Orr. We then generalize this to strongly heterogeneous media by invoking the Landau-Lifshitz conjectu re. Upon evaluating our expressions, we find that K-e decreases rapidl y from the arithmetic mean K-A toward an asymptotic value as distance between the prescribed head boundaries increases from zero to about ei ght integral scales of Y. The more heterogeneous is the medium, the la rger Is K-e relative to its asymptote at any given separation distance . Our theory compares well with published results of spatially power-a veraged expressions and with a first-order expression developed intuit ively by Kitanidis in 1990.