Learning CO$_2$ plume migration in faulted reservoirs with Graph Neural
  Networks
Xin Ju François P. Hamon Gege Wen Rayan Kanfar Mauricio Araya-Polo Hamdi A. Tchelepi
Deep-learning-based surrogate models provide an efficient complement to
numerical simulations for subsurface flow problems such as CO$_2$ geological
storage. Accurately capturing the impact of faults on CO$_2$ plume migration
remains a challenge for many existing deep learning surrogate models based on
Convolutional Neural Networks (CNNs) or Neural Operators. We address this
challenge with a graph-based neural model leveraging recent developments in the
field of Graph Neural Networks (GNNs). Our model combines graph-based
convolution Long-Short-Term-Memory (GConvLSTM) with a one-step GNN model,
MeshGraphNet (MGN), to operate on complex unstructured meshes and limit
temporal error accumulation. We demonstrate that our approach can accurately
predict the temporal evolution of gas saturation and pore pressure in a
synthetic reservoir with impermeable faults. Our results exhibit a better
accuracy and a reduced temporal error accumulation compared to the standard MGN
model. We also show the excellent generalizability of our algorithm to mesh
configurations, boundary conditions, and heterogeneous permeability fields not
included in the training set. This work highlights the potential of GNN-based
methods to accurately and rapidly model subsurface flow with complex faults and
fractures.