Methods and systems for accelerating nonlinear solving in numerical reservoir simulation

Abstract

Systems and methods are disclosed. The method includes obtaining a reservoir model (216) and a production schedule. The method also includes determining a first set of parameters at a first time from the reservoir model (216) and the production schedule, predicting a second set of parameters at a second, later time using the first set of parameters, including primary variables for determining values of mass, flux, and well terms. The predicting includes, for each computational cell (218) in the reservoir model (216), determining a primary variable update and a residual using the first set of parameters, determining updated flux and well terms, predicting the second set of parameters from the updated flux and well terms, assigning the second set of parameters to the first set of parameters, and determining a predicted location of unproduced hydrocarbons from the second set of parameters.