Hybrid Newton method for the acceleration of well event handling in the simulation of CO2 storage using supervised learning

Abstract

Geological storage of CO₂ is an essential instrument for efficient Carbon Capture and Storage policies. Numerical simulations provide the solution to the multi-phase flow equations that model the behavior of the CO₂ injection site. However, numerical simulations of fluid flow in porous media are computationally demanding: it can take up to several hours on a HPC cluster in order to simulate one injection scenario for a large CO₂ reservoir if we want to accurately model the complex physical processes involved. This becomes a limiting issue when performing a large number of simulations, e.g. in the process of ‘history matching’. Well events, such as opening and closure, cause important numerical difficulties due to their instant impact on the pressure and saturation unknowns. This often forces a drastic reduction of the time step size to be able to solve the non-linear system of equations resulting from the discretization of the continuous mathematical model. However, these specific well events in a simulation have a relatively similar impact across space and time. We propose a proof of concept methodology to alleviate the impact of well events during the numerical simulation of CO₂ storage in the underground by using a machine-learning based non-linear preconditioning. We complement the standard fully implicit solver by predicting an initialization of Newton’s method directly in the domain of quadratic convergence using supervised learning. More specifically, we replace the initialization in pressure by a linear approximation obtained through an implicit solver and we use a Fourier Neural Operator (FNO) to predict the saturation initialization. Furthermore, we present an open-source Python framework for conducting reservoir simulations and integrating machine-learning models. We apply our methodology to two test cases derived from a realistic CO₂ storage in saline aquifer benchmark. We reduce the required number of Newton iterations to handle a well opening by 53% for the first test case, i.e required number of linear system to solve and by 38% for the second test case.