The Saturation Dependence of Dispersion From Percolation Theory.

We have previously shown that the dispersion of solutes in porous media can be predicted using a formulation based on concepts from critical path analysis, cluster statistics of percolation, and fractal scaling of percolation clusters. We calculated spatial solute distributions at an instant in time and arrival time distributions as a function of system size. One notable result was the correct prediction of the range of observed dispersivity values over ten orders of magnitude of experimental length scales. Our existing calculations did not account explicitly for the effects of variable saturation and arbitrary porosity. Now that we have incorporated these variables explicitly we can also compare predictions of arrival time distributions with experiment under arbitrary conditions. Such comparisons have shown that the most important predictor of such distributions is the character of the percolation model required, i.e., whether one should use random or invasion percolation. Invasion percolation is appropriate when, for example, a wetting fluid does not displace all the defending fluid, leaving entrapped air. We have been able to use the theoretical construction to identify those experiments where entrapped air has an influence on the arrival time distribution.