Geological entropy and solute transport in heterogeneous porous media

We propose a novel approach to link solute transport behavior to the physical heterogeneity of the aquifer, which we fully characterize with two measurable parameters: the variance of the log K values (sigma(2)(Y)), and a new indicator (H-R) that integrates multiple properties of the K field into a global measure of spatial disorder or geological entropy. From the results of a detailed numerical experiment considering solute transport in K fields representing realistic distributions of hydrofacies in alluvial aquifers, we identify empirical relationship between the two parameters and the first three central moments of the distributions of arrival times of solute particles at a selected control plane. The analysis of experimental data indicates that the mean and the variance of the solutes arrival times tend to increase with spatial disorder (i.e., H-R increasing), while highly skewed distributions are observed in more orderly structures (i.e., H-R decreasing) or at higher sigma(2)(Y). We found that simple closed-form empirical expressions of the bivariate dependency of skewness on H-R and sigma(2)(Y) can be used to predict the emergence of non-Fickian transport in K fields considering a range of structures and heterogeneity levels, some of which based on documented real aquifers. The accuracy of these predictions and in general the results from this study indicate that a description of the global variability and structure of the K field in terms of variance and geological entropy offers a valid and broadly applicable approach for the interpretation and prediction of transport in heterogeneous porous media.