A Localized Variable Switching Method for Mass-Variable Based Reservoir Simulators

Abstract

Abstract Field-scale simulations of complex processes, often suffer from long simulation times. One of the main reasons is that the Newton-Raphson (NR) process used to solve each simulation time step requires many iterations and small time-step sizes to converge. Since the selection of solution variables impacts the nonlinearity of the equations, it is attractive to have a practical method to rapidly explore the use of alternative primary variables in general-purpose reservoir simulators. Many reservoir simulators use pressure, saturations, and temperature in each gridblock as primary solution variables, which are referred to as natural variables. There is also a class of reservoir simulators that uses pressure, total component masses (or moles), and internal energy in each gridblock as primary variables. These simulators are referred to as mass-variable based reservoir simulators. For a given choice of primary variables, most simulators have dedicated, highly optimized procedures to compute the required derivatives and chain rules required to build the Jacobian matrix. Hence, it is usually not possible to switch between mass and natural variables. In this work, however, we establish a link at the numerical solution level between naturaland mass-variable formulations and design a novel (nonlinear) block-local method that transforms mass-variable shifts (computed at each NR iteration) into equivalent natural variable shifts. We demonstrate on a number of simulation models of various complexity that, by use of the proposed approach, a mass-variable based flow simulator can still effectively use natural variables, where the change of variables can be made locally per gridblock. Results indicate that in some models the total number of NR iterations, linear solver (LS) iterations, and backups are reduced when using natural variables, instead of mass variables. However, the improvement is fairly modest and not generally observed. Our findings also signify that, depending on the specific characteristics of the simulation problem at hand, mass-variable based simulators may perform comparably or outperform natural-variable based simulators. The proposed variable switching method can be used effectively to evaluate the impact of using different primary solution variables on problem nonlinearity and solver efficiency. With this method, the impact of interchanging primary solution variables on problem nonlinearity can be rapidly evaluated.