This paper presents the development of a model enabling the analysis of rarefied gas flow through highly heterogeneous porous media. To capture the characteristics associated with the global- and the local-scale topology of the permeable phase in a typical porous medium, the heterogeneous multi-scale method, which is a flexible framework for constructing two-scale models, was employed. The rapid spatial variations associated with the local-scale topology are accounted for stochastically, by treating the permeability of different local-scale domains as a random variable. The results obtained with the present model show that an increase in the spatial variability in the heterogeneous topology of the porous medium significantly reduces the relevance of rarefaction effects. This clearly shows the necessity of considering a realistic description of the pore topology and questions the applicability of the results obtained for topologies exhibiting regular pore patterns. Although the present model is developed to study low Knudsen number flows, i.e. the slip-flow regime, the same development procedure could be readily adapted for other regimes as well.

中文翻译：

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高度非均质多孔介质中稀薄气体流动的随机两尺度模型

本文介绍了一种模型的开发，该模型能够分析通过高度异质多孔介质的稀薄气体流动。为了捕捉与典型多孔介质中渗透相的全局和局部尺度拓扑相关的特征，采用了异质多尺度方法，这是构建两尺度模型的灵活框架。通过将不同局部尺度域的渗透率视为随机变量，随机解释了与局部尺度拓扑相关的快速空间变化。使用本模型获得的结果表明，多孔介质异质拓扑结构中空间变异性的增加显着降低了稀疏效应的相关性。这清楚地表明了考虑对孔隙拓扑结构进行真实描述的必要性，并质疑所获得的结果对于呈现规则孔隙模式的拓扑结构的适用性。虽然本模型是为研究低克努森数流，即滑流状态而开发的，但同样的开发程序也可以很容易地适用于其他状态。