Pore Characterization of Organic-Rich Shales through Application of Topological Data Analysis and Persistent Homology

Abstract

This paper discusses pore characterization of organic-rich shales using 3D high-resolution imaging and a topological data analysis (TDA) framework. In particular, our focus is on persistent homology. Our data set contains four organic-rich shale samples (imaged at 10 nm3/voxel) and a Bentheimer sandstone as the anchor point for comparison. The analysis shows that pores larger than 12.4 nm have poor connectivity, and there is no evidence of a percolating path through any of the shale samples. In contrast, the Bentheimer sandstone shows remarkable differences from the shales in terms of pore connectivity. In terms of geometry, pores and grains in shale are shown to be highly nonconvex, while sandstone exhibits a more uniform and convex distribution of pore and grain size. Euler characteristics of the samples are also computed and discussed along with the pore network extracted on the segmented images. The results show all three methods have an agreement in the overall description of the pore space. However, persistent homology data reveal more information on the pore and grain phase as compared to the other methods. In the last section of the paper, we present an investigation of topological changes in the pore space as a function of pore radius. The analysis indicates most pores must be enlarged by ∼70–80 nm for the pore space to span into a connected network. The implication is that flow mainly occurs through independent channels in shales, as opposed to sandstone where many redundant flow pathways exist.

Investigating rough single fracture permeabilities with persistent homology

“…This method was already developed in the early 2000s (Edelsbrunner et al, 2000;Zomorodian and Carlsson, 2005) and is applied in various research fields such as materials science (Hiraoka et al, 2016), computer science (Choudhury et al, 2012) or biology (Chan et al, 2013). In geosciences, it has only been applied in the last decade with typical applications in the characterization of porous rocks and the determination of the permeability of such (Delgado-Friedrichs et al, 2014;Robins et al, 2016;Bizhani and Haeri Ardakani, 2021). Furthermore, the determination of hydro-elastic properties of porous media is possible with this method (Jiang et al, 2018).…”