An approach to the subsurface transport in statistically inhomogeneous velocity fields

To solve the general case of dispersion in heterogeneous porous media, an application based on the first order stochastic analysis coupled with finite element method is proposed to evaluate the statistically non homogeneous Eulerian velocity field. In natural formations analyses the spatial nonstationarity of flow may derive from statistical nonhomogeneity of medium properties, spatial sinks and/or sources, finite boundaries and conditioning on measurements. These situations are commonly encountered and 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 can be utilized. While the impact of these simplifications was analyzed in some cases, e.g. by checking the influence of boundaries conditions on the velocity variance, only few attempts to found a general solution are given in literature. In the present note a numerical solution for the inhomogeneous velocity field like the one taking place in a bounded domain is obtained by first-order stochastic analysis and finite element method. In this general context the hydraulic properties of the media are not necessary statistically homogeneous and/or the hydraulic conductivity integral scale may be comparable with the domain extension, so that a significant portion of the flow field is affected by conditions imposed on the boundaries. A discussion on the results of some test cases in comparison with known literature solutions gives a measure of the capabilities of the proposed method.