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.

Uncertainty quantification of well-log interpretation is essential to derisking subsurface exploration and development decision-making by providing possible scenarios for reservoir property distribution, fluid flow behaviors, and hydrocarbon potential. Well-log interpretation offers crucial insights into permeability variations, reservoir compartmentalization, mineral composition, and fluid mobility. Inherent uncertainties, such as those arising from geological heterogeneity, limited sampling, and non-uniform distribution of rock properties, can lead to inaccuracies that compromise petrophysical interpretation and formation evaluation. However, traditional data-driven well-log interpretation methods, which map well logs to formation properties based on core measurements, are primarily deterministic and fail to quantify uncertainty accurately. By leveraging deep learning and generative models, we introduce a probabilistic approach that significantly improves permeability estimation and uncertainty quantification. Our methodology integrates co-kriging techniques with Conditional Generative Adversarial Networks (cGANs) and Conditional Variational Autoencoders (cVAEs), establishing a quantitative relationship between kriged core, well-log data and permeability. Our approach enhances petrophysical property uncertainty estimations based on geostatistics by establishing a quantitative relationship between kriged estimates and flow-related properties. Training features are constructed using collocated co-kriging, capturing the cross-correlation between well logs (input features) and core data (output formation properties). Core bulk density, calculated from grain density, is kriged to well-log resolution to enable porosity estimation, while permeability is similarly kriged. A low-pass filter is then applied to smooth the kriged core bulk density, permeability, and estimated porosity, ensuring more accurate interpretations. The results reveal that cGANs and cVAEs consistently produce lower uncertainty estimates compared to traditional machine learning models. High-permeability zones exhibit lower uncertainty (approximately 3–5%), while low-permeability zones show higher uncertainty (10–15%). Traditional deep learning models tend to overestimate uncertainty, whereas generative models provide more reliable estimates. Additionally, applying kriged permeability data improves uncertainty estimations, further reducing uncertainty to 3% in high-permeability zones and 10% in low-permeability zones. To ensure broad applicability, the methods were tested on datasets from both carbonate and clastic reservoirs. In carbonate formations, prior classification steps are necessary to achieve accurate permeability predictions. The interpretation workflow improves permeability estimation accuracy and enhances uncertainty quantification across conventional and unconventional reservoirs. Additionally, this method is adaptable for CO₂ injection and H₂ storage wells, demonstrating versatility across various reservoir types.

Permeability estimation from mercury injection capillary pressure (MICP) data remains challenging in heterogeneous and low-permeability rocks because conventional empirical methods often rely on single-point pore-throat descriptors. This study presents a data-driven workflow that integrates generalized extreme-value (GEV) CDF-PDF fitting, petrophysical rock classification, and machine-learning models to estimate permeability from MICP-derived parameters and porosity. We analyzed 199 samples from 7 hydrocarbon fields, incorporating MICP and routine core analysis (RCA) data spanning marine mud, tight gas, carbonate, and sandstone formations. Parametric fitting was performed using Thomeer’s method, Gaussian cumulative distribution and its probability distribution function (CDF-PDF), and generalized extreme-value (GEV) CDF-PDF. Optimized fitting parameters from GEV, including location (μ), scale (σ_gev), entry pressure (P_e) equivalent and weighting constraints, served as inputs for machine-learning methods to estimate permeability. Ridge regression, random forests, and artificial neural networks (ANNs) were applied to estimate logarithmic permeability from porosity and optimized parameters and benchmarked against Swanson’s method. The GEV CDF-PDF method achieved the strongest correlation with permeability, with an R² of 95%. Incorporating Gaussian Mixture Modeling (GMM) with k-Means + + initialization enhanced the accuracy of the estimation. Ridge regression and random forests improved to 81%, while ANNs achieved 89%. In contrast, Swanson’s method consistently overestimated permeability in tight rocks. The universal method developed in this paper exhibits robust applicability and computational efficiency, yielding permeability estimations in under one minute of CPU time on standard hardware. Nonlinear machine-learning methods with regularization and ANN, combined with prior classification, are recommended for improved accuracy. Ensuring diverse training datasets and high-quality MICP and RCA data is essential to maximize reliability of results as well as accurate permeability estimation across varied rock types.