Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Minimization of Gibbs free energy Using activity coefficient models and nonlinear equation solution techniques is commonly applied to phase stability problems. However, when conventional techniques, Such as the Newton-Raphson method, are employed, serious convergence problems may arise. Due to the existence Of Multiple solutions, several problem can be found in modeling, liquid-liquid equilibrium of multicomponent systerns, which are highly dependent oil the initial guess. In this Nvork phase stability analysis of liquid-liquid equilibrium is investigated using the NRTL model. For this purpose, two distinct stochastic numerical algorithms are employed to minimize the tangent plane distance of Gibbs free energy: a subdivision algorithm that can find all roots of nonlinear equations for liquid-liquid stability analysis and the Simulated Annealing method. Results obtained in this work for the two stochastic algorithms are compared with those of the Interval Newton method from the literature. Several different binary and multicomponent systerns from the literature were successfully investigated.253571583CENPES/PETROBRASFAPERGSConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)