A novel sequential-based hybrid approach incorporating physical modeling and deep learning for multiphase subsurface flow simulation

Multiphase subsurface flows are of great importance for both the sustainable utilization of resources and ecological protection. The simulation of multiphase flow is conventionally resolved using either physics-driven numerical discretization or data-driven machine learning strategy. Despite being perceived as distinct paradigms, their algorithmic-level synergy is expected to bring tremendous advantages. Within the implicit pressure and explicit saturation scheme, this study constructs deep learning model for pressure approximation using an ensemble of equal-probable permeability realizations and the corresponding pressure/velocity fields under randomized injection/production strategies. Specifically, this study proposes two network models, namely U-Net and Fourier Neural Operator, and empower them by physics-guided loss functions, which not only improve the training efficiency but also ensure the physical continuity of the velocity field and maintain the overall mass balance of the coupled system. Moreover, we advance the saturation front using a standard explicit solver under its strict stability condition. The results demonstrate that our hybrid approach performs strong adaptability and flexibility under different permeability and injection/production conditions enclosed in the model training set. For all test cases, we achieve less than 0.6% relative errors for both pressure and saturation solutions. More importantly, our well-trained hybrid solver only uses a fraction of second, which is several orders of magnitude faster than the traditional physics-driven numerical solvers. Our newly designed solution architecture provides a physically reliable technique for superfast multiphase subsurface flow field approximation, which is believed to be of great value for the challenging production optimization and uncertainty quantifications of subsurface resource utilizations.