An Entrogram-Based Approach to Describe Spatial Heterogeneity With Applications to Solute Transport in Porous Media

The recently introduced geological entropy concept evaluates spatial order/disorder in the structure of the hydraulic conductivity (K) field to explain and predict certain characteristics of transport behavior. This concept is expanded in this work by introducing a novel tool for spatial analysis called entrogram from which a metric called entropic scale (HS) can be calculated to measure the overall persistency of patterns of spatial association in a distributed field and to allow robust comparisons between different spatial structures. The entrogram and the entropic scale concepts are applied here to investigate the link between solute transport behavior and the spatial structure of K fields modeled as the distribution of three hydrofacies in alluvial aquifers. Accurate empirical relationships are found between HS and key transport quantities confirming the clear correlation between transport and the structure of the K field described in terms of its entropic scale. The entrogram analysis is also applied to continuous 2-D and 3-D fields having identical lognormal K distributions, but with different connectivity. Comparisons between the entrograms and the calculated HS values for these fields, as well as for their corresponding flow velocity distributions, shed light on the key differences among these structures in 2-D and in 3-D, which in turn explain their dissimilar impact on solute transport. The entrogram-based interpretation of the transport simulations seems to confirm that the geological entropy is a promising approach for predicting solute transport behavior simply from a description of the K field heterogeneity.