A stochastic model of transport in three-dimensional porous media

Modeling of solute transport remains a key issue in the area of groundwater contamination. The fundamental processes of solute transport are advection and dispersion and an accurate description is needed for all modeling studies. The most common approach (advection-dispersion equation) considers an average advective flow rate and a Fickian-like dispersion. Here we propose a more accurate approach: advection is a function of the dispersive behavior of the solute and of medium characteristics. This method provides useful insight for the dispersion process in general. The aim of this article is to present the mathematical background of the random walk model and a simple numerical application.