Estimating Relative Permeability from Multimodal Capillary Pressure and Vice Versa: Machine Learning vs. Brooks-Corey/Burdine Methods

Summary Saturation-dependent relative permeability (Rel Perm) and capillary pressure (Pc) functions are fundamental for modeling multiphase flow in porous media, yet their laboratory measurements are technically challenging. Traditional Brooks-Corey (Brooks and Corey 1966) and Burdine (Burdine 1953) parametric approaches require iterative curve fitting and assume unimodal throat-size distributions, limiting their applicability in spatially heterogeneous formations. To overcome these challenges, we develop a unified data-driven framework that (1) fits generalized extreme value (GEV) distributions to both mercury injection capillary pressure (MICP) and two-phase Rel Perm curves to extract key optimization parameters, and (2) uses the GEV-derived features to train four machine learning (ML) models—k-nearest neighbors, random forest (RF), extreme gradient boosting, and artificial neural network (ANN)—for direct interconversion between Pc and Rel Perm. We apply our method to 13 paired laboratory MICP measurements and two-phase Rel Perm data sets from heterogeneous, bimodal-pore/throat rocks. Samples are classified, within the ML workflow, by their GEV-derived parameter sets, and in the traditional workflow by pore-throat distribution shape and the logarithm of permeability to porosity [ln (K/ϕ)] ratio. The ML model performance is benchmarked against a modified Brooks-Corey capillary pressure model coupled with Burdine’s classical Rel Perm equations. Accuracy is evaluated via the coefficient of determination (R2) and computational efficiency via runtime per sample. The ML models consistently achieve R2 = 92–95% and a 30–50% reduction in error relative to the conventional approach, with the greatest improvements for samples exhibiting pronounced multimodal pore-/throat-size distributions. Moreover, once trained, each ML predictor delivers subsecond curve estimations, compared with minutes of iterative fitting in the Brooks-Corey/Burdine workflow. While our framework relies on high-quality paired MICP and Rel Perm measurements, it markedly enhances both predictive accuracy and computational speed. In summary, the GEV-parameterized, ML-driven interconversion strategy offers a fast, robust alternative to classical Burdine-based predictions, readily scaling to large special core analysis (SCAL) data sets and improving confidence in reservoir simulation workflows.