Validation of a Modified Normalized Mann-Whitney Fractal Dimension Method for characterizing Permo-Tiassic Khuff Carbonate Reservoirs, Saudi Arabia

Abstract A comparison between fractal dimensions derived from the normalized pore-radius method and the modified normalized Mann–Whitney approach showed excellent agreement. The relationship is characterized by a near-perfect correlation (R² = 0.9999998), with an RMSE of 0.00213, an MAE of 0.00212, and a mean absolute percentage error of only 0.078%. These results demonstrate that the modified normalized Mann–Whitney method provides an accurate approximation of the pore-radius-based fractal dimension for the studied Khuff carbonate samples. A Bland–Altman analysis was performed to evaluate agreement between fractal dimensions derived from the normalized pore-radius method and the modified normalized Mann–Whitney approach. The mean difference (bias) was + 0.00212, indicating a slight systematic overestimation by the modified Mann–Whitney method. The standard deviation of the differences was 0.00023, yielding 95% limits of agreement ranging from 0.00168 to 0.00257. The narrow limits of agreement demonstrate excellent consistency between the two approaches and confirm that the modified normalized Mann–Whitney method provides a reliable approximation of the pore-radius-derived fractal dimension.