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.

本研究在开源有限体积库OpenFOAM®（基金会，2014）中实现了针对多孔介质内可动-不动质输运的多速率传质（Multi-Rate Mass Transfer, MRMT）模型（Haggerty与Gorelick，1995；Municchi与Icardi，2019 [1]）。与现有文献中已发表的其他代码（Geiger等，2011 [2]；Silva等，2009）不同，本研究提出的实现方案可适配复杂三维几何构型与高度非均质性场域，且MRMT模型的参数可在空间中任意分布。此外，由于该实现基于当前广泛使用的OpenFOAM®库构建，因此可便捷扩展并集成至其他模型，同时支持并行运行。本研究简要阐述了multiContinuumModels库的结构框架，该库包含基于Haggerty与Gorelick（1995）以及Municchi与Icardi（2020a）的研究成果所建立的MRMT模型公式。该实现方案通过与基准解对标完成验证，并在二维及三维随机渗透率场中开展了测试。研究同时探讨了各类物理与数值参数的影响规律，包括传质速率、非均质性程度以及MRMT展开式中的项数。最后，本研究展示了当渗透率与孔隙度采用高斯随机场表征时，非均质性对传质过程所起到的显著调控作用。