A Multigrid Graph U-Net Framework for Simulating Multiphase Flow in Heterogeneous Porous Media

TL;DR

This paper introduces a novel Graph U-Net framework, AMG-GU, for simulating multi-phase flow in heterogeneous porous media, overcoming grid limitations of CNNs and achieving high accuracy and generalization in complex geological scenarios.

Contribution

The paper develops a multigrid Graph U-Net model, AMG-GU, that effectively models multi-phase flow in heterogeneous porous media using a graph coarsening strategy inspired by AMG, improving accuracy and generalization.

Findings

High accuracy in pressure and saturation predictions in 3D heterogeneous cases

Significant outperforming of single-level baseline models

Strong generalization to unseen configurations

Abstract

Numerical simulation of multi-phase fluid dynamics in porous media is critical to a variety of geoscience applications. Data-driven surrogate models using Convolutional Neural Networks (CNNs) have shown promise but are constrained to regular Cartesian grids and struggle with unstructured meshes necessary for accurately modeling complex geological features in subsurface simulations. To tackle this difficulty, we build surrogate models based on Graph Neural Networks (GNNs) to approximate space-time solutions of multi-phase flow and transport processes. Particularly, a novel Graph U-Net framework, referred to as AMG-GU, is developed to enable hierarchical graph learning for the parabolic pressure component of the coupled partial differential equation (PDE) system. Drawing inspiration from aggregation-type Algebraic Multigrid (AMG), we propose a graph coarsening strategy adapted to heterogeneous PDE coefficients, achieving an effective graph pooling operation. Results of three-dimensional heterogeneous test cases demonstrate that the multi-level surrogates predict pressure and saturation dynamics with high accuracy, significantly outperforming the single-level baseline. Our Graph U-Net model exhibits great generalization capability to unseen model configurations.