Euler-Poincaré Characteristic and Invasion Percolation for Critical Radius Determination: A Systematic Comparison in Synthetic Porous Structures
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Resumen
La determinación del radio crítico (Rc) en medios porosos es esencial para la estimación de permeabilidad mediante modelos analíticos. Este estudio presenta la primera comparación sistemática del método de la Característica de Euler-Poincaré (EPC) y el algoritmo de Percolación por Invasión basado en cola de prioridad (QBIP) utilizando cuatro estructuras porosas sintéticas (SPS) con geometría y topología controladas para determinar Rc . QBIP demostró aplicabilidad universal, determinando Rc = 0.09 – 0.15 μm en todas las SPS. EPC requirió conectividad inicial negativa para su aplicación; valores positivos impidieron la identificación del cruce por cero, y aunque el criterio de derivada detectó transiciones en la distribución de tamaño de poro (PSD), estas no corresponden a umbrales de percolación en estructuras desconectadas. Las desviaciones respecto a las modas de diseño variaron entre 0 –70% para EPC y 6.7– 50% para QBIP; ningún criterio fue uniformemente superior. A pesar de que las operaciones morfológicas alteraron la PSD inicial para lograr la porosidad objetivo en la generación de SPS, ambos métodos identificaron Rc dentro del mismo orden de magnitud que las modas de diseño (0.10 – 0.15 μm). Estos hallazgos demuestran que EPC y QBIP proporcionan perspectivas complementarias: EPC revela transiciones topológicas mientras QBIP captura la física de invasión, permitiendo la caracterización geométrica, topológica y capilar de medios porosos. Este enfoque dual proporciona criterios cuantitativos para la selección del método basados en la conectividad de la muestra y permite la validación cruzada para reducir la incertidumbre en la determinación de Rc para su uso en modelos analíticos de permeabilidad.
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