A Physics-Informed Neural Network Model for Reservoir Seepage in Porous Media Based on Darcy’s Law

Purely data-driven machine-learning methods are currently limited by weak physical interpretability; meanwhile, the sparsity of well-site data in oil and gas fields further degrades the prediction performance of deep learning models for reservoir seepage simulation. To overcome this bottleneck, this study embeds Darcy’s law-based seepage equations as physical constraints into the loss function of a deep learning framework, thereby constructing a physics-informed neural network (PINN) for seepage flow in porous media of oil and gas reservoirs. Numerical simulations are performed in heterogeneous porous media to compare the predictive performance of the proposed PINN against conventional purely data-driven approaches, via evaluation metrics including the coefficient of determination (R2) and root mean square error (RMSE). The results show that both models achieve comparable predictive accuracy with sufficient training samples. In contrast, the PINN retains high predictive accuracy even with a reduced number of samples, and it delivers prominent superiority under conditions of sparse well data and strong reservoir heterogeneity. This study clarifies the applicable scenarios of the two aforementioned methods (physics-informed neural networks and purely data-driven machine-learning models) for fluid flow simulation in porous media and provides a solid theoretical and technical foundation for the accurate prediction of reservoir seepage fields and the optimization of oil and gas reservoir development. This work also offers a validated physics-constrained deep learning framework to guide the deployment of intelligent algorithms in practical subsurface flow engineering.