Learning and predicting dynamics of compositional multiphase mixtures using Graph Neural Networks

In this paper, we investigate the time evolution of compositional multiphase flows in porous media using Graph Neural Networks (GNN). A recent approach to this problem is the unified formulation introduced by Lauser et al. (2011) [2], which incorporates the complementarity conditions. The advantage of this formulation is its ability to automatically handle the appearance and disappearance of phases. To solve the system of equations numerically, Ben Gharbia and Flauraud (2019) [13] employed the Newton-min method. More recently, Vu et al. (2021) [14] proposed a new strategy called NPIPM (NonParametric Interior-Point Method). However, these existing methods still face challenges, particularly with convergence when using large time steps during iterations. Inspired by the relationships between a cell and its neighborhood cells in the mesh when applying the finite volume method (FVM) to solve the problem, we recognize that these connections can be represented as a graph of nodes and edges in a Graph Neural Network. This GNN approach provides a promising framework for predicting long-term phenomena in porous media flows, especially when integrated into a hybrid algorithm along with other numerical solvers.