Explainable Physics-Guided Machine Learning for Discrepancy Modeling and Enhanced Permeability Prediction in Legacy Wells

Physics-based models for permeability prediction are essential for ensuring physically consistent reservoir characterization, yet they often fail to capture the full complexity of real geological systems. This study applies an explainable physics-informed machine learning (PIML) framework for discrepancy modeling to a legacy well dataset from a carbonate formation in southern Iraq. The dataset, originally comprising more than 2,400 samples from 10 wells, was heavily contaminated with incorrectly imputed or interpolated core permeability values. Through a rigorous zonation-based cleaning process, 1,130 high-quality samples were retained for modeling. A baseline physics model, built using well log–derived porosity and a porosity–permeability transform, was combined with a machine learning (ML) discrepancy model trained on three physics-informed features: neutron porosity (NPHI), the gamma ray/ bulk density (GR/RHOB) ratio, and depth. Three ML algorithms, Random Forest, XGBoost, and CatBoost, were evaluated, with five-fold cross-validation employed to ensure robustness. The discrepancy model effectively captured systematic biases in the physical model's predictions. When integrated into the boosted-ML frameworks, it delivered substantially higher permeability prediction performance, reducing root mean squared error (RMSE) by 56% and improving the adjusted coefficient of determination (adjusted R2) from −0.27 to 0.76 compared to the original physical model. These results demonstrate the strong potential of discrepancy-based ML-enhancement methodologies for improving permeability prediction in legacy well datasets. Explainable AI analysis using Shapley additive explanations (SHAP) to determine feature influence identified measured depth as the most influential predictor. Compaction effects not captured by the original physical model, GR/RHOB and NPHI also exerted substantial influence on the PIML permeability predictions. These findings not only improve permeability prediction performance but also reveal missing physics in the baseline model, enabling targeted refinement of physical relationships. This work highlights the feasibility and value of applying discrepancy-based PIML to noisy, incomplete legacy datasets, bridging the gap between empirical ML corrections and physically consistent modeling.