关键词: 油气人工智能, 物理信息约束, 数值模拟, 渗流方程, 试井分析

Abstract: The application of artificial intelligence in oil and gas development has been progressively expanding and demonstrates considerable potential in reservoir numerical simulation. Flow partial differential equations (PDEs) serve as the core tool for reservoir numerical simulation. However, due to the complex computational mechanisms and high computational cost of PDEs, obtaining efficient and accurate solutions to PDEs is the key to intelligent reservoir numerical simulation. In recent years, driven by the rapid development of artificial intelligence technologies in the oil and gas industry, deep learning models, particularly convolutional neural networks (CNNs), have emerged as a novel paradigm for solving flow equations owing to their powerful capability in capturing and representing spatially distributed data. Consequently, a Physical-Informed Laplace Convolutional Neural Network (PILCNN) is proposed for solving the flow equation. By integrating a Laplace convolution operator into the conventional CNN architecture, the proposed method enables the accurate extraction of local features within flow fields. Meanwhile, the loss function is formulated via the finite volume method (FVM) to enforce physical constraints during neural network training, thereby facilitating the solution of flow equations. The proposed method is validated under four common scenarios in oil and gas reservoirs, including homogeneous reservoirs, heterogeneous reservoirs, reservoirs with mixed fault boundaries, and variable-rate production conditions. The results indicate that PILCNN achieves mean relative errors (MRE) as low as 0.009.7% and 0.005.9% in predicting homogeneous and heterogeneous cases, respectively, showing excellent agreement with the reference solutions. In addition, PILCNN exhibits robust stability when applied to mixed boundary and variable-rate production problems. Furthermore, four groups of parameter sensitivity analyses are conducted by varying permeability, boundary distance, wellbore storage coefficient, and skin factor. The results show that PILCNN maintains reliable solution stability under different parameter configurations. Comparative training experiments are performed among the Physics-Informed Convolutional Neural Network (PICNN), Physics-Informed Residual Neural Network (PIResNet) and Physics-Informed Neural Network (PIetNN). PILCNN demonstrates preferable performance throughout the entire training process.

Key words: artificial intelligence in oil and gas, physics-informed, numerical simulation, flow equation, well testing analysis