Topological Invariants in the Pore Morphology Method

TL;DR

This paper presents a topological approach to analyze pore morphology in porous media, identifying invariants like percolation threshold and residual saturation that characterize flow properties independently of geometric details.

Contribution

It introduces a novel topological framework for pore network analysis, emphasizing invariants that capture essential connectivity features and universal scaling behavior.

Findings

Percolation threshold acts as a topological phase transition.

Residual saturation is a key topological invariant.

Universal scaling exponents indicate topological universality classes.

Abstract

This study introduces a pore morphology algorithm that emphasizes the central role of topology in multiphase flow through porous media. Analysis of drainage in lattice-based pore networks identifies two key quantities, the percolation threshold and residual saturation, as topological invariants. These descriptors, which are based solely on connectivity rather than geometric details, capture the essential structure of the network. The percolation threshold is interpreted as a topological phase transition, marking the transition from global connectivity of the defending fluid to isolated clusters of trapped fluid. The universality of scaling exponents across different lattice geometries reveals the existence of topological universality classes, where systems with equivalent connectivity display identical critical behavior. This topological framework underscores the robustness of the identified invariants and provides a general basis for upscaling pore-scale processes in complex media.