Accurate long-term forecasting of cumulative oil production (Np) is critical for effective reservoir management, reserve estimation, and field development planning. However, existing decline curve analysis (DCA) techniques have limited extrapolation capability, while data-driven artificial intelligence (AI) models tend to produce physically unreasonable cumulative production profiles when extrapolated beyond the data range. Specifically, conventional AI-based forecasting models may display unreasonable long-term forecasting characteristics because of their inability to leverage basic knowledge of reservoir physics. This paper presents a new physics-constrained deep learning model to improve long-term cumulative oil production forecasting and overcome the existing limitations and challenges. The proposed model combines a deep neural network (DNN) with a physically inspired monotonicity constraint to provide reasonable cumulative production profiles during extrapolation. Furthermore, a multi-branch model (MBM) architecture is also presented to address the problem of unavailability of future input data by independently forecasting the necessary production parameters (instead of using fixed or scenario-specific values) and then passing them to the primary forecasting model. The proposed framework was tested using actual production data from an Iraqi oil reservoir and compared with traditional DCA methods such as exponential, harmonic, and hyperbolic models, as well as AI models that include traditional DNNs, TCNs, and LSTMs. The results show that the physics-constrained DNN performs much better than traditional methods in long-term forecasting, with a symmetric mean absolute percentage error (sMAPE) of 4.38% and a coefficient of determination (R2) of 87% on the testing data. In contrast to traditional DCA methods and unconstrained AI models, the new method ensures stable and physically sound cumulative production behavior, especially in terms of extended extrapolation intervals. The main novelty of this research effort is the enforcement of physical consistency on a DNN-based cumulative production forecasting model, which improves the stability of long-term predictions and alleviates extrapolation uncertainties in a realistic field environment. The new method offers reservoir engineers a useful and applicable tool for long-term cumulative production forecasting.
Mohamed et al. (Thu,) studied this question.