Learning multi-phase flow and transport in fractured porous media with auto-regressive and recurrent graph neural networks

TL;DR

This paper introduces graph neural network architectures to efficiently model multi-phase flow and transport in fractured porous media, offering a scalable alternative to traditional mesh-based methods with promising accuracy and generalization capabilities.

Contribution

The study develops and evaluates autoregressive and recurrent GNN models for simulating flow and transport in fractured media, demonstrating their effectiveness and superior long-term prediction performance.

Findings

Both GNNs generalize well to unseen fracture networks.

Recurrent GNN outperforms GNN in long sequence predictions.

Two-stage training mitigates error accumulation in autoregressive models.

Abstract

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.