The flow mechanisms of shale oil are inherently complex, characterized by diverse occurrence states. Establishing a robust production forecasting model is essential for thoroughly evaluating well deliverability and the efficacy of reservoir stimulation. While conventional analytical techniques, numerical reservoir simulation, and production decline analysis constitute standard practice, they often struggle to balance computational efficiency with predictive fidelity. Intelligent algorithms offer superior precision in short-term forecasting following extensive data training; however, they frequently exhibit poor generalization and underfitting during long-term performance projections. Consequently, integrating domain-specific production decline theory as physical constraints represents a strategic pathway to enhance the robustness of data-driven frameworks. In this study, the ordinary differential equation (ODE) governing the Duong decline model was derived and embedded into a deep neural network (DNN) architecture. Concurrently, Bayesian optimization was employed to fine-tune both the ODE parameters and the DNN hyperparameters, culminating in the development of a Bayesian-optimized physics-informed neural network (PINN). To validate the model, production data from shale oil wells in the Jimsar Sag were analyzed to evaluate predictive performance. The results demonstrate that Bayesian optimization reduces errors by directly using cumulative oil production as the fitting target for decline model parameter optimization, while also accurately capturing data characteristics. Compared with the traditional decline analysis method, the prediction ability of the Duong decline model optimized by Bayesian is improved by about 68.5% on average. Regarding network architecture and hyperparameter tuning, Bayesian optimization leverages surrogate models and acquisition functions to systematically identify optimal configurations. While its impact on long short-term memory (LSTM) networks proved marginal, it substantially enhanced DNN and PINN performance, yielding an average improvement of roughly 53.1% for the PINN. Under physical constraints, the Bayesian-PINN outperformed standalone DNN and harmonic decline models in future long-term forecasting by approximately 61.7% and 21.4%, respectively. Notably, the predictive superiority of the PINN becomes increasingly pronounced as the forecast horizon extends. This integration of production decline laws with deep learning feature extraction provides a robust technical foundation for the digital transformation of oilfield operations.
Hu et al. (Thu,) studied this question.