Abstract The modelling and simulation of the unsaturated flow or the flow of two immiscible fluid phases in a porous medium is challenging as this flow takes place through the pores of the medium, which form a highly complex domain. Next to the complexity of the domain, a major challenge is to account for the interface separating the fluids, or the unsaturated fluid from the inert filling part, as the location of this interface is not known a-priori. The evolution of this interface depends on the flow of both fluids and of the surface tension. Moreover, the surface tension may depend on the concentration of a surfactant dissolved in one fluid phase. In this work, such aspects are taken into account, and effective, Darcy-scale models are derived based on the known physics at the pore scale. In this sense a thin strip is used as the representation of a single pore in the porous medium. The Darcy-scale models are derived for various regimes, accounting for different pore-scale processes. Numerical examples show that the upscaled models are a good approximation of the transversal average of the solution to the pore-scale models, as the ratio of the width and the length of the pore approaches zero.

中文翻译：

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关于具有演化界面的两相流的放大孔隙尺度模型

摘要 多孔介质中不饱和流动或两种不混溶流体相流动的建模和模拟具有挑战性，因为这种流动是通过介质的孔隙发生的，这些孔隙形成了一个高度复杂的域。除了域的复杂性之外，一个主要挑战是考虑将流体或不饱和流体与惰性填充部分分离的界面，因为该界面的位置是先验未知的。该界面的演变取决于两种流体的流动和表面张力。此外，表面张力可能取决于溶解在一种流体相中的表面活性剂的浓度。在这项工作中，这些方面都被考虑在内，并且有效的达西尺度模型是基于孔隙尺度的已知物理学推导出来的。在这个意义上，薄带用作多孔介质中单个孔的表示。达西尺度模型是针对不同的状态推导出来的，说明了不同的孔隙尺度过程。数值例子表明，当孔隙的宽度和长度之比接近于零时，放大的模型是溶液对孔隙尺度模型的横向平均值的良好近似。