Global phase equilibrium calculations: Critical lines, critical end points and liquid–liquid–vapour equilibrium in binary mixtures

A general strategy for global phase equilibrium calculations (GPEC) in binary mixtures is presented in this work along with specific methods for calculation of the different parts involved. A Newton procedure using composition, temperature and volume as independent variables is used for calculation of critical lines. Each calculated point is analysed for stability by means of the tangent plane distance, and the occurrence of an unstable point is used to determine a critical endpoint (CEP). The critical endpoint, in turn, is used as the starting point for constructing the three-phase line. The equations for the critical endpoint, as well as for points on the three-phase line, are also solved using Newton's method with temperature, molar volume and composition as the independent variables.The different calculations are integrated into a general procedure that allows us to automatically trace critical lines, critical endpoints and three-phase lines for binary mixtures with phase diagrams of types from I to V without advance knowledge of the type of phase diagram. The procedure requires a thermodynamic model in the form of a pressure-explicit EOS but is not specific to a particular equation of state.