Physics-Informed Ensemble Machine Learning for Predicting Metal-Oxide Proppant Settling in Tortuous Hydraulic Fractures

Hydraulic fracturing has revolutionized hydrocarbon extraction from unconventional reservoirs, but optimizing proppant transport and settling remains a significant challenge due to complex fluid-particle interactions and fracture dynamics. Conventional computational fluid dynamics (CFD) and discrete element method (DEM) simulations provide insights but are computationally expensive and often fail to generalize across different geological formations. In this study, we introduce a stacked ensemble learning framework that integrates multiple machine learning models to enhance the predictive accuracy of proppant settling rates (PSR). The proposed framework combines Random Forest (RF), Gradient Boosting (GBR), Extreme Gradient Boosting (XGB), Extra Trees Regressor (ETR), and Support Vector Regression (SVR) as base learners, with a RidgeCV meta-learner to optimize predictions. Feature engineering plays a crucial role in improving model performance, incorporating log transformations, polynomial interactions, and permutation-based feature selection to capture nonlinear dependencies between fracture parameters and proppant properties. Model evaluation metrics, including mean absolute error (MAE = 50.45), mean squared error (MSE = 4225.18), root mean squared error (RMSE = 65.00), and coefficient of determination (R\(^2\) = 0.9984), demonstrate the framework’s robustness and high predictive accuracy. Additionally, statistical analyses such as T-tests (p < 0.0001) and ANOVA (F = 411182.77, p < 0.0001) confirm the significance of salient fracture and proppant parameters. Compared to conventional methods, the proposed approach reduces computational time while improving generalization across varying hydraulic fracturing conditions. This research bridges the gap between physics-based modeling and data-driven approaches by providing a scalable, interpretable, and computationally efficient solution for real-time proppant transport optimization in petroleum engineering.