Flow in Random Porous Media

Abstract

Flow in a porous medium with a random hydraulic conductivity tensor K(x) is analyzed when the mean conductivity tensor \(\overline K\)(x) is a non-constant function of position x. The results are a non-local expression for the mean flux vector \(\overline q\)(x) in terms of the gradient of the mean hydraulic head \(\overline \varphi\)(x), an integrodifferential equation for \(\overline \varphi\)(x), and expressions for the two point covariance functions of q(x) and ϕ(x). When K(x) is a Gaussian random function, the joint probability distribution of the functions q(x) and ϕ(x) is determined.