Physics-informed neural network-based petroleum reservoir simulation with sparse data using domain decomposition

Recent advances in deep learning have expanded new possibilities for fluid flow simulation in petroleum reservoirs. However, the predominant approach in existing research is to train neural networks using high-fidelity numerical simulation data. This presents a significant challenge because the sole source of authentic wellbore production data for training is sparse. In response to this challenge, this work introduces a novel architecture called physics-informed neural network based on domain decomposition (PINN-DD), aiming to effectively utilize the sparse production data of wells for reservoir simulation with large-scale systems. To harness the capabilities of physics-informed neural networks (PINNs) in handling small-scale spatial-temporal domain while addressing the challenges of large-scale systems with sparse labeled data, the computational domain is divided into two distinct sub-domains: the well-containing and the well-free sub-domain. Moreover, the two sub-domains and the interface are rigorously constrained by the governing equations, data matching, and boundary conditions. The accuracy of the proposed method is evaluated on two problems, and its performance is compared against state-of-the-art PINNs through numerical analysis as a benchmark. The results demonstrate the superiority of PINN-DD in handling large-scale reservoir simulation with limited data and show its potential to outperform conventional PINNs in such scenarios.