### Cite Details

E. K. Paleologos, S.P. Neuman and D. M. Tartakovsky, "Effective hydraulic conductivity of bounded, strongly
heterogeneous porous media", *Water Resour. Res.*, vol. 32, no. 5, pp. 1333-1341, 1996

### Abstract

We develop analytical expressions for the effective
hydraulic conductivity *K*_{e} of a three-dimensional,
heterogeneous porous medium in the presence of randomly
prescribed head and flux boundaries. The log hydraulic
conductivity *Y* forms a Gaussian, statistically
homogeneous and anisotropic random field with an exponential
autocovariance. By effective hydraulic conductivity of a finite
volume in such a field, we mean the ensemble mean (expected
value) of all random equivalent conductivities that one could
associate with a similar volume under uniform mean flow. We
start by deriving a first-order approximation of an exact
expression developed in 1993 by Neuman and Orr. We then
generalize this to strongly heterogeneous media by invoking the
Landau-Lifshitz conjecture. Upon evaluating our expressions, we
find that *K*_{e} decreases rapidly from the arithmetic
mean *K*_{A} toward an asymptotic value as distance
between the prescribed head boundaries increases from zero to
about eight integral scales of *Y*. The more heterogeneous is the
medium, the larger is *K*_{e} relative to its asymptote
at any given separation distance. Our theory compares well with
published results of spatially power-averaged expressions and
with a first-order expression developed intuitively by Kitanidis
in 1990.

### BibTeX Entry

@article{paleologos-1996-effective,

author = {E. K. Paleologos and S.P. Neuman and D. M. Tartakovsky},

title = {Effective hydraulic conductivity of bounded, strongly
heterogeneous porous media},

year = {1996},

urlpdf = {http://maeresearch.ucsd.edu/Tartakovsky/Papers/paleologos-1996-effective.pdf},

journal = {Water Resour. Res.},

volume = {32},

number = {5},

pages = {1333-1341}

}