We implement the Multi-Rate Mass Transfer (MRMT) model for mobile-immobile transport in porous media within the open-source finite volume library \textsc{OpenFOAM}\reg \citep{Foundation2014}. Unlike other codes available in the literature [Geiger, S., Dentz, M., Neuweiler, I., SPE Reservoir Characterisation and Simulation Conference and Exhibition (2011); Silva, O., Carrera, J., Dentz, M., Kumar, S., Alcolea, A., Willmann, M., Hydrology and Earth System Sciences 13, (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\reg library, it can be easily extended and included in other models, and run in parallel. We briefly describe the structure of the library that includes the formulation of the MRMT based on the works of [Haggerty, R., Gorelick, S.M., Water Resources Research 31, (1995)] and [F. Municchi and M. Icardi Phys. Rev. Research 2, 013041, (2020)]. 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.

中文翻译：

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OpenFOAM® 中的异构多速率传质模型

我们在开源有限体积库 \textsc{OpenFOAM}\reg \citep{Foundation2014} 中实现了多孔介质中移动-固定传输的多速率传质 (MRMT) 模型。与文献中的其他代码不同 [Geiger, S., Dentz, M., Neuweiler, I., SPE Reservoir Characterization and Simulation Conference and Exhibition (2011); Silva, O., Carrera, J., Dentz, M., Kumar, S., Alcolea, A., Willmann, M., Hydrology and Earth System Sciences 13, (2009)]，我们提出了一个可以应用的实施方案复杂的三维几何形状和高度异质的场，其中 MRMT 的参数可以在空间中任意变化。此外，它基于广泛传播的 OpenFOAM\reg 库构建，可以轻松扩展并包含在其他模型中，并并行运行。我们根据 [Haggerty, R., Gorelick, SM, Water Resources Research 31, (1995)] 和 [F. Municchi 和 M. Icardi Phys。Rev. Research 2, 013041, (2020)]。该实施针对基准解决方案进行了验证，并在二维和三维随机渗透率场上进行了测试。研究了各种物理和数值参数的作用，包括传输速率、异质性和 MRMT 扩展中的项数。最后，我们说明了当渗透率和孔隙度使用高斯随机场表示时，非均质性在传质中所起的重要作用。Municchi 和 M. Icardi Phys。Rev. Research 2, 013041, (2020)]。该实施针对基准解决方案进行了验证，并在二维和三维随机渗透场上进行了测试。研究了各种物理和数值参数的作用，包括传输速率、异质性和 MRMT 扩展中的项数。最后，我们说明了当渗透率和孔隙率使用高斯随机场表示时，非均质性在传质中所起的重要作用。Municchi 和 M. Icardi Phys。Rev. Research 2, 013041, (2020)]。该实施针对基准解决方案进行了验证，并在二维和三维随机渗透场上进行了测试。研究了各种物理和数值参数的作用，包括传输速率、异质性和 MRMT 扩展中的项数。最后，我们说明了当渗透率和孔隙率使用高斯随机场表示时，非均质性在传质中所起的重要作用。并研究了 MRMT 扩展中的项数。最后，我们说明了当渗透率和孔隙率使用高斯随机场表示时，非均质性在传质中所起的重要作用。并研究了 MRMT 扩展中的项数。最后，我们说明了当渗透率和孔隙率使用高斯随机场表示时，非均质性在传质中所起的重要作用。