A Hybrid Physics-Constrained DNN Framework for Long-Term Cumulative Oil Production Forecasting

Accurate long-term forecasting of cumulative oil production (Np) is essential for effective reservoir management, reserves estimation, and field development planning. However, traditional decline curve analysis (DCA) methods suffer from limited extrapolation capability, while purely traditional artificial intelligence (AI) models often produce physically inconsistent cumulative production trends when applied beyond the training period. In this study, a hybrid physics-constrained deep learning framework is proposed to improve long-term cumulative oil production forecasting. The developed approach integrates a deep neural network (DNN) with a physically motivated monotonicity constraint to enforce realistic cumulative production behavior during extrapolation. Furthermore, a multi-branch model (MBM) architecture is introduced to address the practical challenge of unavailable future input variables by independently predicting the required production parameters and supplying them to the main forecasting model, rather than relying on fixed or scenario-based assumptions. The proposed framework was evaluated using real production data from an Iraqi oil reservoir and benchmarked against conventional DCA methods, including exponential, harmonic, and hyperbolic models. The results demonstrate that the physics-constrained DNN significantly outperforms traditional approaches in long-term forecasting, achieving a symmetric mean absolute percentage error (sMAPE) of 4.38% and a coefficient of determination (R²) of 0.87 over the testing period. Unlike classical DCA and unconstrained AI models, the proposed method preserves stable and physically consistent cumulative production trends, particularly over extended extrapolation horizons. Overall, this study highlights the importance of incorporating physical constraints into AI-based production forecasting models and provides a robust and practical tool for long-term reservoir performance prediction.