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

Abstract

Summary 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 timestep requires many iterations and small timestep sizes to converge. Because the selection of solution variables affects 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 the 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 natural- and 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 varying 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 timestep-size cuts (caused by the nonconvergence of the NR procedure, also known as backups) are reduced when using natural variables instead of mass variables. However, the improvement is relatively 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 effect of using different primary solution variables on problem nonlinearity and solver efficiency. With this method, the effect of interchanging primary solution variables on problem nonlinearity can be rapidly evaluated.

Smooth Formulation for Isothermal Compositional Simulation with Improved Nonlinear Convergence

“…This approach has the advantage of avoiding the need for variable substitution, since the equations and unknowns are the same for any phase state. Numerical behaviors of nonlinear formulations were investigated and compared in some recent studies (Voskov and Tchelepi 2012;Alpak and Vink 2018).…”