Scale-Dependent Subsurface Dispersion: A Fractal-Based Stochastic Model
Publication: Journal of Hydrologic Engineering
Volume 6, Issue 1
Abstract
A stochastic model that can simulate non-Fickian (scale-dependent) subsurface dispersion by imposing long-range correlation structure within a particle-based transport scheme is detailed here. The model uses increments from self-similar random fractal processes. These processes [fractional Brownian motions (FBMs)] are characterized by an index H, which is related to the correlation properties of the function. Temporally correlated FBMs that mimic the faster-than-Fickian growth observed in contaminant plumes in heterogeneous subsurface porous media are chosen. It is shown how FBMs can be incorporated within traditional Langevin-based formulations of the random-walk particle tracking models to describe mass displacements. A Fokker-Planck diffusion equation with a time-dependent tensor and its solution are presented to describe FBM anomalous dispersion. A relationship of the model's parameters to measurable porous media parameters is given.
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Information & Authors
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Published In
Journal of Hydrologic Engineering
Volume 6 • Issue 1 • January 2001
Pages: 34 - 42
History
Received: Feb 24, 1999
Published online: Jan 1, 2001
Published in print: Jan 2001
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