Gibbs Energy of Mixing Function: Topological Analysis in Azeotropic Systems

Abstract

Thermodynamic models have been used for decades to formulate the activity coefficients of the components of non-ideal liquid mixtures in phase equilibrium calculations. Additionally, the use of topological analysis and constrains have been applied with success in the characterization and simultaneous correlation of complex phase equilibrium including condensed phases: Liquid-Liquid, Liquid-Solid, Liquid-Liquid-Solid and Liquid-Liquid-Hydrated Solid. In a recent paper, we presented the results of a systematic topological study of the Gibbs energy of mixing (gM) as a function of composition and showed that the NRTL model exhibits “gaps” or regions where solutions of the NRTL model for miscible binaries do not exist. But what is more important is that the gaps themselves are responsible for the poor correlation of the LLE and VLE data of many systems. On the other hand, the Perry Handbook of Chemical Engineering presents 125 possible theoretical types of ternary systems regarding the distillation boundaries for systems involving up to three binary azeotropes and one ternary azeotrope. The schematic maps for the distillation boundaries are presented, stating that: “residue curves can be constructed from experimental data or can be calculated analytically if equations-of-state or activity-coefficient expressions are available…”. Nevertheless, an initial analysis of these maps reveals that there are many of these theoretical VLE behaviors that equations as Wilson or NRTL cannot predict. Thus, the objective of the present paper is to analyze the topology of the Gibbs energy of mixing and the behavior of its composition derivatives, in relation to the corresponding VL and LL phase equilibrium conditions such as the minor common tangent plane, and the existence and characteristics of azeotropic points and distillation boundaries.