Calculation Of Critical Lines Of Ternary Systems

G.O. PISONI; S.B. RODRIGUEZ-REARTES; M. CISMONDI; M.S. ZABALOY

San Petersburgo

Simposio; 25rd European Symposium on Applied Thermodynamics (ESAT 2011); 2011

St.Petersburg State Univ., Russian Acad. Sci., the Mendeleev Russian Chem. Soc.

The phase diagrams corresponding to the fluid phase equilibria of ternary systems may be quite complex, especially when wide ranges of conditions are considered. It is often necessary to describe such phase diagrams with the help of thermodynamic models. It is desirable to have available a calculation tool able to generate ternary phase diagrams in an automated way. Such calculation tool should be robust, it should account for all situations of practical interest and it should be applicable over wide ranges of conditions. The software to be developed should have available a number of subroutines for calculating equilibrium hyperlines which characterize the phase behavior of ternary systems, e.g., critical, three-phase and azeotropic lines at specified temperature or pressure. Similarly, once the values for the model parameters have been set, for a given ternary system, it is necessary to compute certain set of univariant lines. Such lines make possible to build a map, in the pressure/temperature plane, which characterizes the phase equilibria over a wide range of conditions. An example of a ternary univariant hyperline is a line of four-phase equilibria. Another example of a ternary univariant hyperline is the one which connects critical end points, where a ternary critical phase is at equilibrium with a ternary non-critical fluid phase. We focus in this work on the robust calculation of ternary critical hyperlines obtained after specifying a degree of freedom, such as temperature. We consider models of the equation of state (EOS) type and use them in wide ranges of conditions. We carry out the calculations using numerical continuation methods (NCMs), which make possible to minimize the user intervention during the computation of a complete hyperline. The present work builds on previous developments which were limited to binary systems. NCMs can deal with highly non-linear hyperlines. NCMs cleverly minimize the possibility of lack of convergence. However, NCMs have not been sufficiently exploited in the field of phase equilibrium thermodynamics. To the best of our knowledge, NCMs have not been previously used for computing ternary critical hyperlines. This is done in the present work. The non-linear system of equations corresponding to the critical conditions of a fluid mixture has been considered in the literature in a number of alternative ways. In this work, we discuss the relative convenience of the available approaches from the standpoint of the features of the present work, i.e., focus on ternary systems and computation through NCMs.