Vapor-liquid equilibria for refrigerant mixtures modeled by an equation of state;are studied. Phase behavior calculated by the Soave-Redlich-Kwong (SRK) equation with a single adjustable binary interaction parameter is compared with experimental data for binary refrigerant mixtures, two with a supercritical component and one that exhibits azeotropic behavior. It is shown that the SRK equation gives an adequate description of the-phase envelope for binary refrigerant systems. The complex domain trust region methods of Lucia and co-workers (Lucia and Xu, 1992; Lucia et al., 1993) are applied to fixed vapor, isothermal flash model equations, with particular attention to root finding and root assignment at the equation of state (EOS) level of the calculations, and convergence in the retrograde and azeotropic regions of the phase diagram. Rules far assigning roots to the vapor and liquid phases in the case where all roots to the EOS are complex-valued are proposed and shown to yield correct results, even in retrograde regions. Convergence of the flash model equations is also studied. It is shown that the complex domain trust region algorithms outperform Newton’s method in singular regions of the phase diagram (i.e., at near azeotropic conditions and in the retrograde loop), primarily due to the eigenvalue-eigenvector decomposition strategy given in Sridhar and Lucia (1995). A variety of geometric figures are used to illustrate salient points.