Flow Path Resistance in Heterogeneous Porous Media Recast into a Graph-Theory Problem
Flow Path Resistance in Heterogeneous Porous Media Recast into a Graph-Theory Problem
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非均质多孔介质中的流路阻力重新转化为图论问题
DOI：
10.1007/s11242-021-01671-6
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发表时间：
2021
影响因子：
2.7
通讯作者：
Morales, V. L.
中科院分区：
文献类型：
--
作者：
Kanavas, Z.;Pérez-Reche, F. J.;Arns, F.;Morales, V. L.
这项工作的目的是从非均质多孔介质中地下孔隙结构的特征来描述流动的空间分布。使用数千个多分散颗粒介质的二维样本来(1)通过直接数值模拟获得速度场，以及(2)将孔隙网络概念化为每个样本中的图形。对流场的分析使我们能够区分优先流区和停滞区，并量化流动的沟道化程度。然后，根据相应孔洞的几何属性对图的边进行加权，以找到每个样本的阻力最小的路径。优先流动路径和预测的最小阻力路径之间的重叠决定了单个样本的准确性。采用进化算法来确定最适合的加权方案(这里是通道的弧长与孔喉比)，该方案在最大化整个数据集的精度的同时最小化过度参数。最后，分析了相邻边的结构相似性，解释了优先流在孔隙网络中的空间分布。我们发现优先流子网络中的连通边高度相似，而停滞流子网络中的连通边不相似。这些区域之间的相似性差异随着流动通道化而增加，这解释了对局部流动的结构性限制。与计算量大的直接数值模拟相比，该框架可用于快速表征多孔介质的非均质性。文章重点介绍了一种流动通道的定量评估方法，它将孔隙尺度的流场区分为优先流区和停滞区。仅根据结构数据，就可以利用孔隙网络的几何和拓扑来预测快速流动路径的空间分布。孔隙网络的局部无序为流动分离到优先滞流区提供了结构约束，并提供了速度对比的信息。
This work aims to describe the spatial distribution of flow from characteristics of the underlying pore structure in heterogeneous porous media. Thousands of two-dimensional samples of polydispersed granular media are used to (1) obtain the velocity field via direct numerical simulations, and (2) conceptualize the pore network as a graph in each sample. Analysis of the flow field allows us to distinguish preferential from stagnant flow regions and to quantify how channelized the flow is. Then, the graph’s edges are weighted by geometric attributes of their corresponding pores to find the path of minimum resistance of each sample. Overlap between the preferential flow paths and the predicted minimum resistance path determines the accuracy in individual samples. An evolutionary algorithm is employed to determine the “fittest” weighting scheme (here, the channel’s arc length to pore throat ratio) that maximizes accuracy across the entire dataset while minimizing over-parameterization. Finally, the structural similarity of neighboring edges is analyzed to explain the spatial arrangement of preferential flow within the pore network. We find that connected edges within the preferential flow subnetwork are highly similar, while those within the stagnant flow subnetwork are dissimilar. The contrast in similarity between these regions increases with flow channelization, explaining the structural constraints to local flow. The proposed framework may be used for fast characterization of porous media heterogeneity relative to computationally expensive direct numerical simulations.Article HighlightsA quantitative assessment of flow channeling is proposed that distinguishes pore-scale flow fields into preferential and stagnant flow regions.Geometry and topology of the pore network are used to predict the spatial distribution of fast flow paths from structural data alone.Local disorder of pore networks provides structural constraints for flow separation into preferential v stagnant regions and informs on their velocity contrast.
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