Convex envelope method for the determination of fluid phase diagrams

In this work a new method – the convex envelope method (CEM) – for the reliable determination of fluid phase diagrams is presented. The method yields the entire phase equilibrium diagram and does not rely on the determination of individual equilibria. Formally, the CEM is based on the original idea of Gibbs interpreting all globally stable equilibrium states as those belonging to the convex envelope of the Gibbs energy over the composition space. In this work, the continuous Gibbs energy surface is approximated by an appropriate set of points. This allows a mathematically clear reformulation of the original problem as convex hull determination for a discrete set of Gibbs energy points and thus the continuous Gibbs energy surface itself. The CEM is quite generally formulated for any system with arbitrary coexisting (fluid and solid) phases. In this work it is applied to systems with multiple liquid phases only, since liquid multi-phase equilibrium diagrams are extremely important in practice for extraction and decanter design. The implementation of CEM relies on a numerical construction of the convex hull which determines the accuracy of the results. The CEM can be easily integrated in short-cut methods for analysis of separation methods based on liquid phase splitting. Therefore, the CEM is explained for the application to liquid multi-phase equilibria and validated with available experimental data and rigorous decanter simulations for several systems with complex phase behavior.