Physics-Constrained Meta-Embedded Neural Network for Bottom-Hole Pressure Prediction in Radial Oil Flow Reservoirs

With the advancement of petroleum engineering, the increasing complexity of formations and unpredictable conditions make wellbore pressure prediction more challenging. Accurate bottom-hole pressure (BHP) prediction is crucial for the safe and stable development of oil and gas reservoirs. Solving the partial differential equations (PDEs) governing fluid flow is key to this prediction. As deep learning becomes widespread in scientific and engineering applications, physics-informed neural networks (PINNs) have emerged as powerful tools for solving PDEs. However, traditional PINNs face challenges such as insufficient fitting accuracy, large errors, and gradient explosion. This study introduces MetaPress, a novel physics-informed neural network structure, to address inaccurate formation pressure prediction. MetaPress incorporates a meta-learning-based embedding function that integrates spatial information into the input and forget gates of Long Short-Term Memory networks. This enables the model to capture complex spatiotemporal features of flow problems, improving its generalization and nonlinear modeling capabilities. Using the MetaPress architecture, we predicted BHP under single-phase flow conditions, achieving an error of less than 2% for L2. This approach offers a novel method for solving seepage equations and predicting BHP, providing new insights for subsequent studies on reservoir fluid flow processes.