Physics-informed graph neural network for predicting fluid flow in porous media

With the rapid development of deep learning neural networks, new solutions have emerged for addressing fluid flow problems in porous media. Combining data-driven approaches with physical constraints has become a hot research direction, with physics-informed neural networks (PINNs) being the most popular hybrid model. PINNs have gained widespread attention in subsurface fluid flow simulations due to their low computational resource requirements, fast training speeds, strong generalization capabilities, and broad applicability. Despite success in homogeneous settings, standard PINNs face challenges in accurately calculating flux between irregular Eulerian cells with disparate properties and capturing global field influences on local cells. This limits their suitability for heterogeneous reservoirs and the irregular Eulerian grids frequently used in reservoir. To address these challenges, this study proposes a physics-informed graph neural network (PIGNN) model. The PIGNN model treats the entire field as a whole, integrating information from neighboring grids and physical laws into the solution for the target grid, thereby improving the accuracy of solving partial differential equations in heterogeneous and Eulerian irregular grids. The optimized model was applied to pressure field prediction in a spatially heterogeneous reservoir, achieving an average L₂ error and R² score of 6.710 × 10⁻⁴ and 0.998, respectively, which confirms the effectiveness of model. Compared to the conventional PINN model, the average L₂ error was reduced by 76.93%, the average R² score increased by 3.56%. Moreover, evaluating robustness, training the PIGNN model using only 54% and 76% of the original data yielded average relative L₂ error reductions of 58.63% and 56.22%, respectively, compared to the PINN model. These results confirm the superior performance of this approach compared to PINN.