# 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 {alpha}-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.

- Authors:

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

- Sponsoring Org.:
- Earth Sciences Division

- OSTI Identifier:
- 971505

- Report Number(s):
- LBNL-2325E

Journal ID: ISSN 1539-1663; VZJAAB; TRN: US201004%%184

- DOE Contract Number:
- DE-AC02-05CH11231

- Resource Type:
- Journal Article

- Journal Name:
- Vadose Zone Journal

- Additional Journal Information:
- Journal Volume: 7; Journal Issue: 4; Related Information: Journal Publication Date: 2008; Journal ID: ISSN 1539-1663

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 54; 58; ALGORITHMS; AQUIFERS; ASYMMETRY; DIFFUSION; DIFFUSION EQUATIONS; DISTRIBUTION FUNCTIONS; FRACTALS; SOLUTES; TRANSPORT

### Citation Formats

```
Semenov, V N, Korotkin, I A, Pruess, K, Goloviznin, V M, and Sorokovikova, O S.
```*Stochastic models of solute transport in highly heterogeneous geologic media*. United States: N. p., 2009.
Web.

```
Semenov, V N, Korotkin, I A, Pruess, K, Goloviznin, V M, & Sorokovikova, O S.
```*Stochastic models of solute transport in highly heterogeneous geologic media*. United States.

```
Semenov, V N, Korotkin, I A, Pruess, K, Goloviznin, V M, and Sorokovikova, O S. Tue .
"Stochastic models of solute transport in highly heterogeneous geologic media". United States. https://www.osti.gov/servlets/purl/971505.
```

```
@article{osti_971505,
```

title = {Stochastic models of solute transport in highly heterogeneous geologic media},

author = {Semenov, V N and Korotkin, I A and Pruess, K and Goloviznin, V M and Sorokovikova, O S},

abstractNote = {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 {alpha}-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.},

doi = {},

journal = {Vadose Zone Journal},

issn = {1539-1663},

number = 4,

volume = 7,

place = {United States},

year = {2009},

month = {9}

}