We study the abilities of pore network models of different complexities to determine the flow statistics and structural controls for single-phase flow in partially saturated porous media. The medium permeability and hydraulic tortuosity are the basic parameters for upscaling flow problems from the pore to the Darcy scale. They represent average flow properties. However, upscaling and predicting dispersion and anomalous solute transport from the pore to the continuum scale requires knowledge of the velocity distribution, not only its mean values. Considering four different network models of increasing complexity, we analyze the statistical and structural properties of the fluid-filled pore space that determines the flow statistics. We consider statistical network models based on regular lattices with the same statistical properties as the porous medium regarding coordination number and pore-size distribution. We consider regular lattices which are characterized by uniform coordination, and diluted lattices, and random lattices, which are characterized by a distribution of coordination numbers. Furthermore, we consider a detailed network model, which accounts for the spatial location of pores, their coordination numbers, and the sizes of pore bodies and throats. The flow behaviors estimated from these network models are compared to direct numerical single-phase flow simulations in the digitized images of a fully and partially saturated two-dimensional porous medium and different saturation degrees. We find that the statistical network models can capture the saturation dependence of permeability and tortuosity but are not able to reproduce velocity statistics of even the velocity range observed in the direct flow simulations. The detailed network models, in contrast, provide excellent estimates for all flow statistics. This indicates that the configuration and correlation of the fluid phase are crucial structural controls of the observed distribution of flow velocities.

中文翻译：

---

孔隙网络模型，用于确定部分饱和多孔介质中单相流的流动统计和结构控制


我们研究了不同复杂度的孔隙网络模型的能力，以确定部分饱和多孔介质中单相流的流动统计和结构控制。中等渗透率和水力弯曲度是将流动问题从孔隙上调到达西尺度的基本参数。它们表示平均流属性。然而，放大和预测分散和异常溶质从孔隙到连续介质尺度的传输需要了解速度分布，而不仅仅是其平均值。考虑到四种复杂性不断增加的不同网络模型，我们分析了决定流动统计的充满流体的孔隙空间的统计和结构特性。我们考虑基于规则晶格的统计网络模型，这些晶格在配位数和孔径分布方面与多孔介质具有相同的统计特性。我们考虑以均匀配位为特征的正晶格、稀晶格和以配位数分布为特征的随机晶格。此外，我们考虑了一个详细的网络模型，该模型解释了孔的空间位置、它们的配位数以及孔体和喉咙的大小。将从这些网络模型估计的流动行为与完全和部分饱和的二维多孔介质和不同饱和度的数字化图像中的直接数值单相流模拟进行比较。我们发现统计网络模型可以捕获磁导率和曲折度的饱和依赖性，但无法再现在直接流动模拟中观察到的速度范围的速度统计数据。 相比之下，详细的网络模型为所有流统计数据提供了出色的估计值。这表明，液相的构型和相关性是观察到的流速分布的关键结构控制。