Graph Convolutional Networks for Simulating Multi-phase Flow and Transport in Porous Media
This work addresses a domain-specific problem for energy and environmental applications by enabling efficient simulation on unstructured meshes, representing an incremental improvement over existing CNN-based methods.
The authors tackled the challenge of simulating multi-phase flow in porous media on irregular meshes by developing a Graph Convolutional Network (GCN) surrogate model, achieving high accuracy and stability in predicting pressure and saturation states for 2D heterogeneous test cases.
Numerical simulation of multi-phase fluid dynamics in porous media is critical for many energy and environmental applications in Earth's subsurface. Data-driven surrogate modeling provides computationally inexpensive alternatives to high-fidelity numerical simulators. While the commonly used convolutional neural networks (CNNs) are powerful in approximating partial differential equation solutions, it remains challenging for CNNs to handle irregular and unstructured simulation meshes. However, simulation models for Earth's subsurface often involve unstructured meshes with complex mesh geometries, which limits the application of CNNs. To address this challenge, we construct surrogate models based on Graph Convolutional Networks (GCNs) to approximate the spatial-temporal solutions of multi-phase flow and transport processes in porous media. We propose a new GCN architecture suited to the hyperbolic character of the coupled PDE system, to better capture transport dynamics. Results of 2D heterogeneous test cases show that our surrogates predict the evolutions of pressure and saturation states with high accuracy, and the predicted rollouts remain stable for multiple timesteps. Moreover, the GCN-based models generalize well to irregular domain geometries and unstructured meshes that are unseen in the training dataset.