Inferring fracture forming processes by characterizing fracture network patterns with persistent homology

H Shimizu,A Okamoto,T Ito,I Obayashi,A Suzuki,T Tsuji,Y Hiraoka,M Miyazawa,P.K Kang

doi:10.1016/j.cageo.2020.104550

Abstract

Persistent homology is a mathematical method to quantify topological features of shapes, such as connectivity. This study applied persistent homology to analyze fracture network patterns in rocks. We show that persistent homology can detect paths connecting from one boundary to the other boundary constituting fractures, which is useful for understanding relationships between fracture patterns and flow phenomena. In addition, complex fracture network patterns so-called mesh textures in serpentine were analyzed by persistent homology. In previous studies, fracture network patterns for different flow conditions were generated by a hydraulic–chemical–mechanical simulation and classified based on additional data and on expert's experience and knowledge. In this study, image analysis based on persistent homology alone was able to characterize fracture patterns. Similarities and differences of fracture network patterns between natural serpentinite and simulation were quantified and discussed. The data-driven approach combining with the persistent homology analysis helps to infer fracture forming processes in rocks. The results of persistent homology analysis provide critical topological information that cannot be obtained by geometric analysis of image data only.

Highlights

Fracture network patterns are thought to result from dynamic interactions among fluid flows, reactions, and geomechanical deformation in the subsurface
We show that persistent homology can detect paths connecting from one boundary to the other boundary constituting fractures, which is useful for understanding relationships between fracture patterns and flow phenomena
We show an example using persistent homology for a data-driven approach combining numerical simulation to explore the possibility of fracture characterization by Persistent homology (PH) analysis

Summary

Introduction

Fracture network patterns are thought to result from dynamic interactions among fluid flows, reactions, and geomechanical deformation in the subsurface. PH can be a powerful and practical tool for characterizing porous structures and predicting hydrological–elastic properties from structural images It may be useful for investigating fracture network patterns in rocks, this approach has yet to be tested and applied. One of the advantages in PH is to detect topological features from any shapes of fracture network patterns in image data automatically It would accelerate our understanding of physical phenomena in fractured rocks if we can obtain useful information of topological features in fracture patterns and find relationship between the structure patterns and physical phenomena such as flow and transport. We proposed a data-driven approach based on the PH analysis to provide practical structure information and to infer fracture forming processes in rocks.

Concept of persistent homology

Description of fracture structures using PH parameters

Concluding remarks

Computer code availability