A Physics-Informed Spatial-Temporal Neural Network for Reservoir Simulation and Uncertainty Quantification

Surrogate models play a vital role in reducing computational complexity and time burden for reservoir simulations. However, traditional surrogate models suffer from limitations in autonomous temporal information learning and restrictions in generalization potential, which is due to a lack of integration with physical knowledge. In response to these challenges, a physics- informed spatial- temporal neural network (PI- STNN) is proposed in this work, which incorporates flow theory into the loss function and uniquely integrates a deep convolutional encoder- decoder (DCED) with a convolutional long short- term memory (ConvLSTM) network. To demonstrate the robustness and generalization capabilities of the PI- STNN model, its performance was compared against both a purely data- driven model with the same neural network architecture and the renowned Fourier neural operator (FNO) in a comprehensive analysis. Besides, by adopting a transfer learning strategy, the trained PI- STNN model was adapted to the fractured flow fields to investigate the impact of natural fractures on its prediction accuracy. The results indicate that the PI- STNN not only excels in comparison with the purely data- driven model but also demonstrates a competitive edge over the FNO in reservoir simulation. Especially in strongly heterogeneous flow fields with fractures, the PI- STNN can still maintain high prediction accuracy. Building on this prediction accuracy, the PI- STNN model further offers a distinct advantage in efficiently performing uncertainty quantification, enabling rapid and comprehensive analysis of investment decisions in oil and gas development.