Mathematical Modeling of Rock Pore Geometry and Mineralization: Applications of Persistent Homology and Random Walk

Abstract

Mathematical methods used to model heterogeneous pore geometry of natural rocks and their temporal evolution (mineralization processes) are explored. Recent development of X-ray microcomputed tomography enables high-resolution (micrometers) pore geometry of rock to be obtained. Nevertheless, exploring the complex spatial distribution of pore bodies, and relating this information to hydraulic and elastic properties, remains a challenge. In this study, persistent homology is first applied to describe heterogeneous rock pores, which captures the appearance and disappearance of topological features. The persistence diagram derived from this analysis shows the characteristic features of rock pore. Next, random walk is used to model rock mineralization processes. The results show that rock pore evolution is successfully modeled using random walk by defining the probability of mineral precipitation and dispersion degree in each grid cell of a modeled rock body. The mineralization parameter can be flexibly changed and a short computation time used when using random walk; this approach may thus be practical when simulating rock evolution processes such as long-term chemical reactions in a reservoir.