Topological data analysis and 3D printing technologies for flow in fracture networks

Detailed characterization of flow and transport processes within complex fracture networks remains many challenges.The fluid flow is mainly controlled by the fracture structures. Fractures have complex shapes (e.g., roughness), and their intersections and connectivities with other fractures also lead to complex flow. We aim at quantifying the complex fracture structures by topological data analysis and finding interaction between the structure and flow with 3D fracture network models. We use persistent homology, which is a tool for evaluating complex and multi-scale features in the geometry and is usually used to analyze connected components, holes/tunnels, and voids in data of any dimension. We also conduct flow experiment using synthetic fracture network models created by a 3D printer. 3D printer technologies allow us to control any shapes of structures. Our study clarifies relationships between the geometries that can be detected by persistent homology and hydraulic properties obtained from the fracture network models.