1 - Dispersion in stratified soils with fractal permeability distribution

Summary

ABSTRACT Stochastic analysis of flow and transport in 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 process in porous media. Dispersion in perfectly stratified media with fractal distribution of permeability along the vertical was analyzed. Results were obtained for the transient and asymptotic longitudinal dispersivities. The results show that the macroscopic asymptotic dispersivity depends strongly on the fractal dimension of vertical permeability distribution. Macroscopic dispersivity was found to be problem-scale dependent in development and asymptotic phases.

INTRODUCTION

The impact of heterogeneities on flow and mass transport in groundwater has been investigated for some two decades. Usually this type of investigation is performed using a stochastic, as opposed to deterministic, framework. This choice is not based on the assumption that the flow process itself is stochastic, but rather on the recognition of the fact that the deterministic description of the parameter distributions would be impractical, if not impossible.

Initial research in this area did not consider the spatial structure of flow properties, assuming that either they behaved like the white noise process (lack of spatial correlation), or had a layered structure in the direction parallel or perpendicular to the flow (perfect correlation in one direction). The next step was to consider spatial correlation of flow properties.