Suzuki Anna, Miyazawa Miyuki, Minto James M, Tsuji Takeshi, Obayashi Ippei, Hiraoka Yasuaki, Ito Takatoshi
Institute of Fluid Science, Tohoku University, Sendai, 980-8577, Japan.
Department of Civil and Environmental Engineering, University of Strathclyde, Glasgow, UK.
Sci Rep. 2021 Sep 9;11(1):17948. doi: 10.1038/s41598-021-97222-6.
Topological data analysis is an emerging concept of data analysis for characterizing shapes. A state-of-the-art tool in topological data analysis is persistent homology, which is expected to summarize quantified topological and geometric features. Although persistent homology is useful for revealing the topological and geometric information, it is difficult to interpret the parameters of persistent homology themselves and difficult to directly relate the parameters to physical properties. In this study, we focus on connectivity and apertures of flow channels detected from persistent homology analysis. We propose a method to estimate permeability in fracture networks from parameters of persistent homology. Synthetic 3D fracture network patterns and their direct flow simulations are used for the validation. The results suggest that the persistent homology can estimate fluid flow in fracture network based on the image data. This method can easily derive the flow phenomena based on the information of the structure.
拓扑数据分析是一种用于描述形状的新兴数据分析概念。拓扑数据分析中的一种先进工具是持久同调，它有望总结量化的拓扑和几何特征。尽管持久同调对于揭示拓扑和几何信息很有用，但难以解释持久同调自身的参数，也难以将这些参数直接与物理性质联系起来。在本研究中，我们关注从持久同调分析中检测到的流道的连通性和孔径。我们提出了一种从持久同调参数估计裂缝网络渗透率的方法。使用合成的三维裂缝网络模型及其直接流模拟进行验证。结果表明，持久同调可以基于图像数据估计裂缝网络中的流体流动。该方法可以根据结构信息轻松推导流动现象。
