Hybrid Physics-Informed Dynamic Productivity Index (HPD-PI) Model for Oil Reservoir Production Forecasting

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Abstract
Accurate prediction of reservoir production remains a critical challenge due to the complex interplay of multiphase flow behavior, temporal dynamics, and reservoir heterogeneity. This study proposes a Hybrid Physics-Informed Dynamic Productivity Index (HPD-PI) model that integrates classical inflow performance relationships with data-driven temporal features to enhance production forecasting. The model extends the conventional productivity index formulation by incorporating water-cut and gas-oil ratio corrections, dynamic production trends, and temporal memory through lagged production terms. A comprehensive dataset comprising production, pressure, and multiphase-flow parameters was used to evaluate the proposed approach. A baseline Random Forest model was first developed for comparison, achieving a coefficient of determination (R 2 ) of 0.8138. However, analysis revealed that the model was predominantly driven by temporal dependencies with limited physical interpretability. In contrast, the proposed Hybrid HPD-PI model achieved superior performance, with an R 2 of 0.9466, root mean square error (RMSE) of 71.01, and mean absolute error (MAE) of 38.78. The improvement is attributed to the integration of temporal memory, multiphase flow corrections, and dynamic behavior within a physically consistent framework. The results demonstrate that the hybrid model effectively captures both short-term fluctuations and long-term production trends while maintaining interpretability. The study highlights the importance of combining physical principles with data-driven techniques for robust reservoir modeling. The proposed HPD-PI framework provides a reliable tool for production forecasting, reservoir management, and decision-making, with potential applicability to a wide range of reservoir systems.

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