A new algorithm for rachford-rice for multiphase compositional simulation

Flash calculations for use in compositional simulation are more difficult and time-consuming as the number of equilibrium phases increases beyond two. Because of its complexity, many simulators do not even attempt to incorporate three or more hydrocarbon phases, even though such cases are important in many low-temperature gasfloods or for high temperatures where hydrocarbons can partition into water. Multiphase flash algorithms typically use successive substitution (SS) followed by Newton's method. For N_p-phase flash calculations, (N_p-1) Rachford-Rice (RR) equations are solved in every iteration step in SS and, depending on the choice of independent variables, in Newton's method. Solution of RR equations determines both compositions and amounts of phases for a fixed overall composition and set of K-values. A robust algorithm for RR is critical to obtain convergence in multiphase compositional simulation and has not been satisfactorily developed, unlike the traditional two-phase flash. In this paper, we develop an algorithm for RR equations for multiphase compositional simulation that is guaranteed to converge to the correct solution independent of the number of phases for both positive and negative flash calculations. We derive a function whose gradient vector consists of RR equations. This correct solution to the RR equations is formulated as a minimization of the nonmonotonic convex function using the independent variables of (N_p-1) phase mole fractions. The key to obtaining a robust algorithm is that we specify nonnegative constraints for the resulting equilibrium phase compositions, which are described by a very small region with no poles. The minimization uses Newton's direction with a line-search technique to exhibit superlinear convergence. We show a case in which a previously developed method cannot converge while our algorithm rapidly converges in a few iterations. We implement the algorithm both in a standalone flash code and in UTCOMP (Chang et al. 1990), a multiphase compositional simulator, and show that the algorithm is guaranteed to converge when a multiphase region exists as indicated by stability analysis.