Statistical Inference Over Persistent Homology Predicts Fluid Flow in Porous Media. Issue 11 (21st November 2019)

• Record Type: Journal Article
• Authors: Moon, Chul; Mitchell, Scott A.; Heath, Jason E.; Andrew, Matthew
• Is Part Of: Water resources research. Volume 55:Issue 11(2019)
• Page Start: 9592
• Page End: 9603
• Publication Date: 2019-11-21
• Subjects: Fluid Flow -- Persistent Homology -- REV -- Statistical Inference -- LASSO -- Principal Component Analysis; Hydrology -- Periodicals; 333.91
• DOI: 10.1029/2019WR025171
• Languages: English
• ISSNs: 0043-1397

Abstract

Abstract: 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. Key Points: Statistical inference of persistent homology over 3D rock images predicts constitutive behaviors. Principal component analysis and a penalized regression model computes structural characteristics of sample volumes. Output is consistent with established sREV sizes, and fluid flow and transport properties, but requires low computational cost.