Graph Convolutional Networks for Simulating Multi-phase Flow and Transport in Porous Media
arxiv(2023)
摘要
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.
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