Saturation-Dependence of Dispersion in Porous Media

TL;DR

This paper introduces a saturation-dependent model for dispersion in porous media, incorporating percolation concepts, and compares predictions with experiments across different saturations, highlighting the importance of percolation models.

Contribution

It develops a new saturation-dependent dispersion model based on critical path analysis and percolation theory, improving predictions of solute transport in porous media.

Findings

Model accurately predicts dispersivity over ten orders of magnitude

Arrival time distributions depend more on percolation model applicability than saturation value

Experimental comparisons suggest percolation model choice is crucial for accurate predictions

Abstract

In this study, we develop a saturation-dependent treatment of dispersion in porous media using concepts from critical path analysis, cluster statistics of percolation, and fractal scaling of percolation clusters. We calculate spatial solute distributions as a function of time and calculate arrival time distributions as a function of system size. Our previous results correctly predict the range of observed dispersivity values over ten orders of magnitude in experimental length scale, but that theory contains no explicit dependence on porosity or relative saturation. This omission complicates comparisons with experimental results for dispersion, which are often conducted at saturation less than 1. We now make specific comparisons of our predictions for the arrival time distribution with experiments on a single column over a range of saturations. This comparison suggests that the most important predictor of such distributions as a function of saturation is not the value of the saturation per se, but the applicability of either random or invasion percolation models, depending on experimental conditions.