A PARAMETER-BASED APPROACH FOR 2-PHASE-EQUILIBRIUM PREDICTION WITH CUBIC EQUATIONS OF STATE

A parameter-based approach for two-phase-equilibrium prediction that u ses the two-parameter Peng-Robinson equation of state (EOS) has been d eveloped. This approach takes advantage of the special mathematical fo rms of the ideal mixing and excess parts of the Gibb's free energy to reduce the N-C-component equilibrium problem to a minimization problem in three or four variables, depending on whether binary interaction c oefficients (BIC's) are zero or nonzero. The Gibb's free energy is min imized in two steps. The ideal mixing term is minimized first subject to certain constraints that include the mixing rules for the EOS param eters. A second minimization is performed over the total Gibb's free e nergy with the Lagrange multipliers from the first minimization as a r educed set of variables in place of the usual component-related variab les. The new approach has been applied to develop parameter-based vers ions of the Newton-Raphson and trust-region methods for performing fla sh calculations as well as the phase-stability test to handle the tran sition from one to two phases. These methods have been implemented in computer programs and tested on phase-behavior problems taken from the petroleum literature. In the case of zero BIC's, the reduction in the number of variables produces substantial reduction in computational c ost compared with component-based methods, especially as the number of components increases, while convergence behavior is essentially uncha nged. For the nonzero BIC case, however, a practical implementation re quires the introduction of approximations that compromise convergence and offset the lower cost per iteration.