Macroscale three-dimensional modeling of fluid flow in a thin porous layer under unsaturated conditions is a challenging task. One major issue is that such layers do not satisfy the representative elementary volume length-scale requirement. Recently, a new approach, called reduced continua model (RCM), has been developed to describe multiphase fluid flow in a stack of thin porous layers. In that approach, flow equations are formulated in terms of thickness-averaged variables and properties. In this work, we have performed a set of experiments, where a wet $$260\hbox {-}\upmu \hbox {m}$$260-μm-thin porous layer was placed on top of a dry layer of the same material. We measured the change of average saturation with time using a single-sided low-field nuclear magnetic resonance device known as NMR-MOUSE. We have employed both RCM and the traditional Richards equation-based models to simulate our experimental results. We found that the traditional unsaturated flow model cannot simulate experimental results satisfactorily. Very close agreement was obtained by including the dynamic capillary term as postulated by Hassanizadeh and Gray in the traditional equations. The reduced continua model was found to be in good agreement with the experimental result without adding dynamic capillarity term. Moreover, the computational effort needed for RCM simulations was one order of magnitude less than that of traditional models.

中文翻译：

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薄亲水纤维层中液体再分布的连续尺度建模

在非饱和条件下对薄多孔层中的流体流动进行宏观三维建模是一项具有挑战性的任务。一个主要问题是这样的层不满足代表性的基本体积长度尺度要求。最近，已开发出一种称为简化连续模型 (RCM) 的新方法来描述薄多孔层堆叠中的多相流体流动。在这种方法中，流动方程是根据厚度平均变量和特性来制定的。在这项工作中，我们进行了一组实验，其中将湿 $$260\hbox {-}\upmu \hbox {m}$$260-μm 薄多孔层放置在相同材料的干层顶部。我们使用称为 NMR-MOUSE 的单侧低场核磁共振设备测量了平均饱和度随时间的变化。我们采用了 RCM 和传统的基于理查兹方程的模型来模拟我们的实验结果。我们发现传统的非饱和流动模型不能令人满意地模拟实验结果。通过在传统方程中包含 Hassanizadeh 和 Gray 假设的动态毛细管项，获得了非常接近的一致性。发现简化的连续模型与实验结果非常吻合，无需添加动态毛细管项。此外，RCM 模拟所需的计算工作量比传统模型少一个数量级。通过在传统方程中包含 Hassanizadeh 和 Gray 假设的动态毛细管项，获得了非常接近的一致性。发现简化的连续模型与实验结果非常吻合，无需添加动态毛细管项。此外，RCM 模拟所需的计算工作量比传统模型少一个数量级。通过在传统方程中包含 Hassanizadeh 和 Gray 假设的动态毛细管项，获得了非常接近的一致性。发现简化的连续模型与实验结果非常吻合，无需添加动态毛细管项。此外，RCM 模拟所需的计算工作量比传统模型少一个数量级。