Convex Envelope Method for determining liquid multi-phase equilibria in systems with arbitrary number of components  

The determination of liquid phase equilibria plays an important role in chemical process simulation. This work presents a generalization of an approach called the convex envelope method (CEM), which constructs all liquid phase equilibria over the whole composition space for a given system with an arbitrary number of components. For this matter, the composition space is discretized and the convex envelope of the Gibbs energy graph is computed. Employing the tangent plane criterion, all liquid phase equilibria can be determined in a robust way. The generalized CEM is described within a mathematical framework and it is shown to work numerically with various examples of up to six components from the literature.