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.