Validation Of a Modified Normalized Skillings-Mack Fractal Dimension For Characterizing Pore Structure in Permo-Triassic Khuff Carbonate Reservoirs , Central Saudi Arabia

Abstract Carbonate reservoirs are characterized by complex pore systems and significant heterogeneity that strongly influence fluid flow and reservoir quality. In this study, carbonate samples were collected from surface exposures of the Permo–Triassic Khuff Formation in central Saudi Arabia to investigate the relationship between pore-network heterogeneity and reservoir properties using fractal analysis. Porosity and permeability measurements were obtained for all samples and ranged from 2.269 to 11.253% and from 0.264 to 3.445 mD, respectively. Two independent fractal approaches derived from capillary-pressure data were employed to characterize pore structure. The first method utilized the relationship between the logarithm of normalized pore radius, log10(R/Rmax), and log10(water saturation), whereas the second method employed the logarithm of the Modified Normalized Skillings-Mack parameter (MNSM) versus log10(water saturation). In both approaches, the fractal dimension was determined from the positive linear coefficient of a fitted quadratic equation according to Df = 2 + b. Calculated fractal dimensions ranged from 2.3584 to 2.8575 for the MNSM method and from 2.3628 to 2.8647 for the normalized pore-radius method, with mean values of 2.7038 and 2.7101, respectively. Representative samples with low, intermediate, and high pore-network complexity yielded fractal dimensions of approximately 2.36, 2.72, and 2.86. Statistical comparison of the two methods demonstrated excellent agreement, yielding a correlation coefficient of R = 1.0, a coefficient of determination of R ² = 1.0 , and a root mean square error ( RMSE) of 0.0063. Bland–Altman analysis further indicated a negligible mean bias and narrow limits of agreement, confirming the consistency of the two approaches. The results show that increasing fractal dimension is associated with improved pore connectivity and higher permeability, indicating that fractal geometry provides a reliable quantitative measure of pore-network heterogeneity. The near-perfect agreement between the MNSM and normalized pore-radius methods demonstrates that the Modified Normalized Skillings-Mack fractal dimension is a robust alternative parameter for characterizing pore structure and reservoir quality in Khuff carbonate reservoirs. The proposed approach provides an effective framework for evaluating carbonate reservoir heterogeneity and may contribute to improved reservoir characterization and flow-property prediction.