Flow in random porous media

Flow in a porous medium with a random hydraulic conductivity tensor (K) ove r bar (x) is analyzed when the mean conductivity tensor (K) over bar (x) is a non-constant function of position x. The results are a non-local express ion for the mean flux vector (q) over bar (x) in terms of the gradient of t he mean hydraulic head <(<phi>)over bar>(x), an integrodifferential equatio n for <(<phi>)over bar>(x), and expressions for the two point covariance fu nctions of q(x) and phi (x). When K(x) is a Gaussian random function, the j oint probability distribution of the functions q(x) and phi (x) is determin ed.