Pore Geometry Characterization by Persistent Homology Theory

Rock pore geometry has heterogeneous characteristics and is scale dependent. This feature in a geological formation differs significantly from artificial materials and makes it difficult to predict hydrologic and elastic properties. To characterize pore heterogeneity, we propose an evaluation method that exploits the recently developed persistent homology theory. In the proposed method, complex pore geometry is first represented as sphere cloud data using a pore-network extraction method. Then, a persistence diagram (PD) is calculated from the point cloud, which represents the spatial distribution of pore bodies. A new parameter (distance index H) derived from the PD is proposed to characterize the degree of rock heterogeneity. Low H value indicates high heterogeneity. A new empirical equation using this index H is proposed to predict the effective elastic modulus of porous media. The results indicate that the proposed PD analysis is very efficient for extracting topological feature of pore geometry.