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SPECIAL SECTION: NONCLASSICAL TRANSPORT

Stochastic Models of Solute Transport in Highly Heterogeneous Geologic Media

^a Russian Academy of Sciences, Nuclear Safety Institute, 52 Bolshaya Tul'skaya St., 115191 Moscow, Russia
^b Earth Sciences Division, Lawrence Berkeley National Lab., Berkeley, CA 94720
^* Corresponding authors (gol{at}ibrae.ac.ru, K_Pruess{at}lbl.gov).

Received 6 September 2007.

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 -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.

Abbreviations: FADE, fractional-order advection–dispersion equation • MADE, macrodispersion experiment

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