Geological entropy and solute transport in heterogeneous porous media

Abstract

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 (r 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 r 2 Y. We found that simple closed-form empirical expressions of the bivariate dependency of skewness on H R and r 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.

The Parabolic Variational Inequalities for Variably Saturated Water Flow in Heterogeneous Fracture Networks

“…However, the value in case 1 with faster finger flow is much smaller than that in case 2 with a slower volume-averaged manner. The results are consistent with the conclusion of Bianchi and Pedretti [43] that fingering is more pronounced when the relative entropy is low. Therefore, in a way similar to the derivation of geological entropy indicators, it can be recognized that the relative entropy , which takes into account the spatial distributions of the heterogeneous fracture network including connectivity, extent and spacing, and aperture distribution, has significant effects on the development and propagation of preferential flow during heterogeneous seepage analysis.…”

“…It is found that the indicator is sensitive to the connectivity of the fracture networks. Furthermore, Bianchi and Pedretti [43] pointed out that is a global metric that integrates multiple properties of the spatial distribution of hydraulic conductivity.…”

“…In order to quantify the connectivity in these heterogeneous fracture networks with fracture geometrical properties, the concept of geological entropy [43] is employed to characterize the heterogeneity of these fracture networks rather than the fracture density (the number of fractures per unit area). Based on the theoretical and numerical study of the geological entropy in porous media, the related relationships yield …”

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

“…Because the Shannon entropy H can be seen as a measure of unpredictability, it has been extensively applied to quantify uncertainty, disorder, and randomness in a wide range of disciplines, including hydrogeology, geostatistics, and related fields (e.g., Chiogna et al, ; Journel & Deutsch, ; Kitanidis, ; Mays et al, ; Ye et al, ). In Bianchi and Pedretti (), numerical simulations of solute transport in generic alluvial aquifers with a wide range of heterogeneity ( between 1.7 and 28.0, mean lengths of the facies between 1 and 30 m) were performed to analyze the effect of spatial disorder on the first three spatial central temporal moments of the breakthrough curves (BTCs). Empirical expressions were subsequently developed to describe the correlation between H R and these moments.…”

Migration of chlorinated hydrocarbons in multilayer unconsolidated porous media: a case study from the Po Plain, Italy

“…In such a case, a detailed characterization of depositional facies is a valuable tool in order to identify and group together the geological and hydrogeological features of the system, possibly interacting with the contaminants (e.g. Bianchi and Pedretti 2017). For example, the occurrence in the stratigraphic architecture of organic-rich layers (such as peaty layers), could substantially affect the migration and degradation of contaminants, since the organic matter can sorb the contaminants and also act as electron donor in biodegradation reactions with potential production of hazardous metabolites (e.g.…”