Euler-Poincaré Characteristic and Invasion Percolation for Critical Radius Determination: A Systematic Comparison in Synthetic Porous Structures

Critical radius (Rc ) determination in porous media is essential for permeability estimation through analytical models. This study presents the first systematic comparison of the Euler-Poincaré Characteristic (EPC) method and queue-based Invasion Percolation (QBIP) algorithm using four synthetic porous structures (SPS) with controlled geometry and topology to determine Rc . QBIP demonstrated universal applicability, determining Rc = 0.09 – 0.15 μm across all SPS. EPC required negative initial connectivity for its application; positive values prevented zero-crossing identification, and while the derivative criterion detected pore size distribution (PSD) transitions, these do not correspond to percolation thresholds in disconnected structures. Deviations from design modal radii ranged from 0 – 70% for EPC and 6.7 – 50% for QBIP; no single criterion was uniformly superior. Despite morphological operations altering the initial PSD to accomplish the target porosity in SPS generation, both methods identified Rc within the same order of magnitude as the design modes (0.10 – 0.15 μm). These findings demonstrate that EPC and QBIP provide complementary insights: EPC reveals topological transitions while QBIP captures invasion physics, enabling geometric, topological, and capillary characterization of porous media. This dual-method approach provides quantitative criteria for the selection of the method based on sample connectivity and enables cross-validation to reduce uncertainty in Rc determination for use in analytical permeability models.