Heterogeneous Multi-Rate mass transfer models in OPENFOAM®

We implement the Multi-Rate Mass Transfer (MRMT) model for mobile–immobile transport in porous media (Haggerty and Gorelick, 1995; Municchi and Icardi, 2019 [1]) within the open-source finite volume library OpenFOAM® (Foundation, 2014). Unlike other codes available in the literature (Geiger et al., 2011 [2]; Silva et al., 2009), we propose an implementation that can be applied to complex three-dimensional geometries and highly heterogeneous fields, where the parameters of the MRMT can arbitrarily vary in space. Furthermore, being built over the widely diffused OpenFOAM® library, it can be easily extended and included in other models, and run in parallel. We briefly describe the structure of the multiContinuumModels library that includes the formulation of the MRMT based on the works of Haggerty and Gorelick (1995) and Municchi and Icardi (2020a). The implementation is verified against benchmark solutions and tested on two- and three-dimensional random permeability fields. The role of various physical and numerical parameters, including the transfer rates, the heterogeneities, and the number of terms in the MRMT expansions, is investigated. Finally, we illustrate the significant role played by heterogeneity in the mass transfer when permeability and porosity are represented using Gaussian random fields.