Features of transport in non-Gaussian random porous systems

Abstract

The goal of this work is to employ a semi-analytical framework to investigate key features associated with the transport behavior of an inert solute in non-Gaussian random fields. We focus our analysis on the transport dynamics of a solute plume through a porous medium characterized by spatially heterogeneous non-Gaussian log-conductivity fields, Y. We rest on a stochastic Lagrangian framework to provide semi-analytical formulations to evaluate the statistical moments and cumulative distribution function (CDF) of solute concentration. The heterogeneous structure of the log-conductivity field is modeled as a Generalized Sub-Gaussian process. This model has been shown to capture non-Gaussian and scale-dependent features displayed by several variables, including key parameters of porous media. Our results suggest that the effects of non-Gaussianity in Y on solute concentration statistics are more pronounced at locations near the solute source zone and at early times. The impact of the analyzed non-Gaussian nature of the field of Y is also significant at the lower tails of the distribution. We also explore conditions under which when the concentration CDF in Generalized Sub-Gaussian Y fields can be approximated by the widely used beta distribution. Furthermore, the methodology used in this work is an alternative to the commonly used numerical Monte Carlo method and can be employed as a benchmark tool in computational stochastic mass transport problems in porous media.