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Statistical Inference Over Persistent Homology Predicts Fluid Flow in Porous Media
Author(s) -
Moon Chul,
Mitchell Scott A.,
Heath Jason E.,
Andrew Matthew
Publication year - 2019
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2019wr025171
Subject(s) - persistent homology , tortuosity , similarity (geometry) , homogeneity (statistics) , mathematics , porous medium , computer science , artificial intelligence , pattern recognition (psychology) , image (mathematics) , statistical physics , algorithm , porosity , geology , statistics , physics , geotechnical engineering
We statistically infer fluid flow and transport properties of porous materials based on their geometry and connectivity, without the need for detailed We summarize structure by persistent homology and then determines the similarity of structures using image analysis and statistics. Longer term, this may enable quick and automated categorization of rocks into known archetypes. We first compute persistent homology of binarized 3D images of material subvolume samples. The persistence parameter is the signed Euclidean distance from inferred material interfaces, which captures the distribution of sizes of pores and grains. Each persistence diagram is converted into an image vector. We infer structural similarity by calculating image similarity. For each image vector, we compute principal components to extract features. We fit statistical models to features estimates material permeability, tortuosity, and anisotropy. We develop a Structural SIMilarity index to determine statistical representative elementary volumes.