Contaminant spreading in stratified soils with fractal permeability distribution

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Abstract
Stochastic analysis of flow and transport in the subsurface usually assumes that the soil permeability is a stationary, homogeneous stochastic process with a finite variance. Some field data suggest, however, that the permeability distributions may have a fractal character with long‐range correlations. It is of interest to investigate how the fractal character of permeability distribution influences the spreading and mixing process in porous media. The results of our analysis of this problem for perfectly stratified media with fractal distribution of permeability along the vertical are presented. Results were obtained for the transient and asymptotic dispersivities in the longitudinal direction. The results show that the macroscopic asymptotic dispersivity depends strongly on the fractal dimension of vertical permeability distribution. Specifically, the higher the fractal dimension, the lower the value of macroscopic dispersivity. The macroscopic dispersivity was found to be problem‐scale dependent in transient (development) and asymptotic phases. Variance of fluctuation of concentration was also analyzed and found to be dependent on the fractal dimension. In this case, the higher fractal dimension results in more mixing of pore water and therefore smoother (smaller σα2) concentration distribution.