Macrodispersion in generalized sub-Gaussian randomly heterogeneous porous media

In this work, we explore the implications of modeling the logarithm of hydraulic conductivity, Y , as a Generalized Sub-Gaussian (GSG) field on the features of conservative solute transport in randomly het-erogeneous, three-dimensional porous media. Hydro-geological properties are often viewed as Gaussian random fields. Nevertheless, the GSG model enables us to capture documented non-Gaussian traits that are not explained through classical Gaussian models. Our formulation yields lead-(or first-) order analytical solutions for key statistical moments of flow and transport variables. These include flow velocities, hydraulic head, and macrodispersion coefficients, as obtained across GSG log-conductivity fields. The analytical model is based on a first-order spectral theory, which constrains the rigorous validity of our results to small values of log-conductivity variance (sigma(2)(Y) << 1 ). Analytical results are then compared against detailed numerical estimates obtained through a Monte Carlo scheme encompassing various levels of domain heterogeneity. An asymptotic Fickian transport regime is attained at late times in both Gaussian and GSG Y fields. Convergence to such regime is slower for GSG as compared to Gaussian fields. This suggests a strong impact of the heterogeneity structure on non-Fickian pre-asymptotic behaviors of the kind documented in the literature. The quality of the comparison between analytical and numerical results deteriorates with increasing sigma(2)(Y) . Otherwise, our lead-order solutions frame macrodispersion coefficients in appropriate orders of magnitude also for values of sigma(2)(Y) up to approximately 1.7, which are consistent with the spatial variability of Y across a single geological unit. In this sense, our analytical approach enables one to obtain prior information on solute plume evolution and to grasp the effects of non-Gaussian medium heterogeneity while favoring simplicity. Our findings also enhance the current level of under-standing of the nature of mass transfer across heterogeneous media characterized by complex variability structures which cannot be reconciled with classical Gaussian scenarios. (C) 2022 Elsevier Ltd. All rights reserved.

Automated summary

In this work, the implications of modeling the logarithm of hydraulic conductivity as a Generalized Sub-Gaussian (GSG) field on solute transport in heterogeneous porous media are explored. Analytical solutions for flow and transport variables are derived and compared with numerical estimates. The results show that the convergence to a Fickian transport regime is slower for the GSG field compared to the Gaussian field, and the quality of the comparison between analytical and numerical results deteriorates with increasing variance of the logarithm of hydraulic conductivity.