Integrating optimization and machine learning for estimating water resistivity and saturation in shaley sand reservoirs

Abstract Accurate characterization of shaley-sand reservoirs remains a significant challenge in petroleum geophysics, where complex clay mineralogy often renders traditional evaluation methods unreliable. This study introduces an integrated, data-driven framework that synergizes numerical optimization and machine learning (ML) to accurately estimate formation water resistivity (R w ) and predict water saturation (S w ), overcoming the limitations of data scarcity. The workflow begins with rigorous preprocessing of well log data from 11 wells across the Norwegian North Sea and Egyptian Western Desert. First, we establish a robust, physically-constrained R w by evaluating four optimization algorithms. The Powell and Nelder-Mead algorithms emerged as superior, demonstrating the ability to recover the true Rw from log data with low error (1×10-4 RMSE) against measured samples rapidly. This optimized R w then serves as a high-quality "pseudo-core" label to generate a continuous S w log for training a comprehensive suite of ML models, including ensemble methods (Random Forest, CatBoost, XGBoost) and neural networks (ANNs, LSTM), to predict S w . The models demonstrated predictive accuracy, validated by a robust 5-fold cross-validation protocol. On the blind test wells, the top-performing models (LSTM, CatBoost , and XGBoost) achieved a coefficient of determination (R2) up to 0.944 with Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE) as low as 0.03 and 0.050 respectively. The automated fusion of optimization-derived physics with ML-driven prediction marks a transformative step toward more reliable, data-centric petrophysical workflows. This integrated framework offers a significant enhancement in reservoir characterization, providing a cost-effective and scalable methodology that reduces reliance on expensive core analyses and improves the accuracy of hydrocarbon-in-place estimations.