Scale-dependent subsurface dispersion: A fractal-based stochastic model

A stochastic model that can simulate non-Fickian (scale-dependent) subsurfa ce dispersion by imposing long-range correlation structure within a particl e-based transport scheme is detailed here. The model uses increments from s elf-similar random fractal processes. These processes [fractional Brownian motions (FBMs)] are characterized by an index H, which is related to the co rrelation properties of the function. Temporally correlated FBMs that mimic the faster-than-Fickian growth observed in contaminant plumes in heterogen eous subsurface porous media are chosen. It is shown how FBMs can be incorp orated within traditional Langevin-based formulations of the random-walk pa rticle tracking models to describe mass displacements. A Fokker-Planck diff usion equation with a time-dependent tensor and its solution are presented to describe FBM anomalous dispersion. A relationship of the model's paramet ers to measurable porous media parameters is given.