Validation of a Modified Normalized Particle Swarm Optimization Model for Characterizing Pore Structure in Permo–Triassic Khuff Carbonate Reservoirs, Central Saudi Arabia

Abstract Carbonate reservoirs commonly exhibit highly heterogeneous pore systems that exert a major control on reservoir quality and fluid-flow behavior. Quantitative characterization of pore-network complexity is therefore essential for understanding permeability variations and predicting reservoir performance. In this study, a modified normalized particle swarm optimization (MNPSO) approach was validated for characterizing pore-structure heterogeneity in carbonate samples collected from surface exposures of the Khartam Member of the Permo–Triassic Khuff Formation in central Saudi Arabia. Porosity and permeability measurements were obtained for all samples, and pore-network heterogeneity was investigated using two independent capillary-pressure-derived fractal methods. The first method employed the relationship between normalized pore radius, Log10(R/RMAX), and water saturation, whereas the second method utilized the modified normalized particle swarm optimization parameter (MNPSO) as a function of water saturation. For both approaches, fractal dimensions were determined from the positive linear coefficient of fitted quadratic expressions. The calculated fractal dimensions ranged from approximately 2.36 to 2.86, indicating substantial variability in pore-network complexity among the investigated carbonate samples. The results reveal a strong positive relationship between fractal dimension and permeability, demonstrating that increasing pore-network complexity is associated with improved pore connectivity and enhanced fluid-flow pathways. Samples characterized by low fractal dimensions exhibited relatively poor pore connectivity and low permeability, whereas samples with higher fractal dimensions displayed more interconnected pore systems and higher permeability values. Comparison of the two fractal approaches showed excellent agreement, with a coefficient of determination (R²) of 0.99988 and a regression slope of 0.9881, indicating that the MNPSO-based method produces fractal-dimension estimates that are nearly identical to those derived from the conventional normalized pore-radius approach. The results confirm that the MNPSO fractal model provides a reliable and robust tool for evaluating pore-network heterogeneity in carbonate reservoirs. The strong correlation between fractal dimension and permeability further suggests that capillary-pressure-derived fractal parameters can serve as practical indicators of reservoir quality and fluid-flow performance in Khuff carbonate reservoirs and comparable carbonate systems worldwide.