Fractal-Constrained Analytical Reconstruction of Capillary Pressure Curves and Log-Based Saturation Evaluation

Summary

Capillary pressure curves link reservoir pore structure to multiphase flow behavior and are fundamental for saturation evaluation. The Thomeer capillary pressure model quantitatively characterizes capillary pressure behavior using the displacement pressure Pd, maximum mercury-intrusion bulk volume (Bv)P∞, and pore-geometry factor G. However, existing approaches for inverting Thomeer parameters rely largely on empirical fitting, which limits their transferability. To overcome this limitation, we propose an analytical reconstruction method for Thomeer capillary pressure curves based on the validated fractal characteristics of the pore-throat structures and derives explicit analytical relationships between Thomeer parameters and routine petrophysical properties. The derivations indicate that (Bv)P∞ follows a linear scaling relationship with porosity φ; Pd is jointly constrained by fractal dimension D, permeability K, and porosity φ; and an explicit analytical expression for G is obtained by introducing the Swanson parameter. In application, the Levenberg-Marquardt optimization algorithm is adopted to extract Thomeer parameters for multimodal pore/throat systems. Validation using 154 carbonate core-plug mercury injection capillary pressure (MICP) measurements from the Middle East demonstrates reduced prediction errors, with the root mean square error (RMSE) of G decreasing from 0.0616 to 0.0505, and the mean absolute percentage error (MAPE) decreasing from 4.44% to 3.70%. The applicability of the workflow is further examined using additional carbonate and sandstone data sets provided in the Supplementary Material. In addition, the proposed framework is extended to complex capillary pressure curves that cannot be adequately reconstructed using a single-component Thomeer function. Building on this framework, continuous capillary-pressure curves are reconstructed along the evaluated well interval using log-interpreted φ and K. When coupled with the saturation/height function, the reconstructed curves enable continuous saturation evaluation along the evaluated interval.