Abstract
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.
Highlights
Topological data analysis is an emerging concept of data analysis for characterizing shapes
Fluid flow processes are ubiquitous in the world, and most are governed by the geometry and nature of the surrounding structures
The porosity–permeability correlation has been studied extensively in the literature to estimate permeability using porosity[2,3]. This Kozeny–Carman equation provides a relationship between structure and flow
Summary
Topological data analysis is an emerging concept of data analysis for characterizing shapes. The results suggest that the persistent homology can estimate fluid flow in fracture network based on the image data. This method can derive the flow phenomena based on the information of the structure. It is attracting attention to understand flow behaviors in complex fracture networks in developments of natural resources, as in the case of shale gas and geothermal developments It has been a long-term scientific challenge to predict flow behavior of porous media from structural properties. The Hagen–Poiseuille equation is a physical law that describe a steady laminar flow of a viscous, incompressible, and Newtonian fluid through a circular tube of constant radius, r This is an exact solution for the flow, can be derived from the (Navier–) Stokes equations, and is another way of expressing the relationship between structure and flow. Since the flow rate is proportional to the cube of the fracture aperture, this relationship between flow and aperture is well-known as the “cubic law” 4–7
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