Learning multi-phase flow and transport in fractured porous media with auto-regressive and recurrent graph neural networks
This work addresses computational inefficiencies in subsurface flow simulations for geoscience and engineering applications, presenting an incremental improvement using deep learning on existing discretization methods.
The authors tackled the challenge of modeling multi-phase flow and transport in fractured porous media, which is computationally expensive with traditional methods, by proposing graph neural networks (GNNs) and recurrent GNNs that generalize well to unseen fracture realizations, with the recurrent GNN showing superior accuracy in long-sequence predictions.
In the past three decades, a wide array of computational methodologies and simulation frameworks has emerged to address the complexities of modeling multi-phase flow and transport processes in fractured porous media. The conformal mesh approaches which explicitly align the computational grid with fracture surfaces are considered by many to be the most accurate. However, such methods require excessive fine-scale meshing, rendering them impractical for large or complex fracture networks. In this work, we propose to learn the complex multi-phase flow and transport dynamics in fractured porous media with graph neural networks (GNN). GNNs are well suited for this task due to the unstructured topology of the computation grid resulting from the Embedded Discrete Fracture Model (EDFM) discretization. We propose two deep learning architectures, a GNN and a recurrent GNN. Both networks follow a two-stage training strategy: an autoregressive one step roll-out, followed by a fine-tuning step where the model is supervised using the whole ground-truth sequence. We demonstrate that the two-stage training approach is effective in mitigating error accumulation during autoregressive model rollouts in the testing phase. Our findings indicate that both GNNs generalize well to unseen fracture realizations, with comparable performance in forecasting saturation sequences, and slightly better performance for the recurrent GNN in predicting pressure sequences. While the second stage of training proved to be beneficial for the GNN model, its impact on the recurrent GNN model was less pronounced. Finally, the performance of both GNNs for temporal extrapolation is tested. The recurrent GNN significantly outperformed the GNN in terms of accuracy, thereby underscoring its superior capability in predicting long sequences.