Stochastic Models of Solute Transport in Highly Heterogeneous Geologic Media

Abstract

A stochastic model of anomalous diffusion was developed in which transport occurs by random motion of Brownian particles, described by distribution functions of random displacements with heavy (power‐law) tails. One variant of an effective algorithm for random function generation with a power‐law asymptotic and arbitrary factor of asymmetry is proposed that is based on the Gnedenko–Levy limit theorem and makes it possible to reproduce all known Levy α‐stable fractal processes. A two‐dimensional stochastic random walk algorithm has been developed that approximates anomalous diffusion with streamline‐dependent and space‐dependent parameters. The motivation for introducing such a type of dispersion model is the observed fact that tracers in natural aquifers spread at different super‐Fickian rates in different directions. For this and other important cases, stochastic random walk models are the only known way to solve the so‐called multiscaling fractional order diffusion equation with space‐dependent parameters. Some comparisons of model results and field experiments are presented.