An improved method to determine phase boundaries for multicomponent mixtures is described. This technique uses procedures based upon Gibbs minimization that lead to a more efficient algorithm that can also converge closer to the mixtures' critical points than other algorithms (e.g., K-value method). Moreover, all the curves reported correspond to stable points according to the stability analysis suggested by Michelsen that implies minimization of the tangent plane distance function. Several examples compare the efficiency of this technique to commercial programs that often fail at certain conditions around the critical point, cricondenbar, and/or cricondentherm.