Numerical evaluation of non homogeneous flow statistics in random porous media

Transport phenomena that take place in subsurface naturally heterogeneous formations are generally characterized by non stationary velocity fields. So that in field analyses the assumption of location independent statistics of flow is often violated to adapt real life cases to synthetic schemes where spatially stationary approaches that can be found in literature are utilized. In the note we discuss the spatial behaviour of 2-D velocity field covariances where the nonstationarity is due to the domain finite boundary. These results are obtained by a numerical solution based on the first order stochastic analysis coupled with finite element method and useful to handle different causes of the flow field statistical inhomogeneity. The discussion of results gives a measure of the ability of this method to reproduce the statistics of inhomogeneous velocity fields with a relatively limited amount of computer resources.