AVERAGE FLOW IN HETEROGENEOUS MEDIA OF TRENDING HYDRAULIC CONDUCTIVITY

In this paper, we present a solution of the flow problem in heterogene ous, non-stationary media, where the non-stationarity is manifested as a linear trend in the mean log-conductivity, The flow problem is pose d in a stochastic framework, and our goal is to define an average flow equation and to derive the relationship between the mean gradient and the mean flux. For a stationary medium, such an approach would amount to the definition of the effective conductivity tensor, but in the pr esent case, since due to the specific boundary condition the coefficie nt proportionality between the mean gradient and the mean flux depends on the angle between the trend and the mean gradient, we refer to it as the tensor of equivalent conductivity. We derive this tensor for on e-, two- and three-dimensional flow equations.