Non-Fickian Transport in Heterogeneous Saturated Porous Media

Abstract

Existing theories of flow and contaminant transport in aquifers are either based on Monte Carlo simulations or small perturbation solutions of the governing stochastic partial differential equations, which limit the applications to cases of small variances in the physical parameters. In most cases the “smallness” is a subjective statement from the modeler or is forced by considering the logarithm of the random quantities. This article constitutes a preliminary attempt to reanalyze the problem of flow and contaminant transport in a hypothetical heterogeneous aquifer without the usual assumptions of small perturbation, logarithmic transformation, a specific probability law, and disregard for the underlying hydrologic problem. Statistical properties of the pore velocity are derived from the inherent ground water flow problem; a non-Fickian dispersion equation is derived by assuming two scales, a small and a large one; and a solution of the dispersion equation is obtained. A general analytic procedure, the decomposition method is used in the solution of the flow and dispersion equations. Finally, some comparisons with existing results are presented.