Prediction of azeotropic behaviour by the inversion of functions from the plane to the plane

• Published in: Canadian journal of chemical engineering 2015-05, Vol.93 (5), p.914-928
• Main Authors: Guedes, Aline L., Moura Neto, Francisco D., Platt, Gustavo M.
• Format: Article
• Language: English
• Subjects: Algebra; Azeotropes; double azeotropy; Dynamical systems; functions from the plane to the plane; Inversions; Mathematical analysis; Mathematical models; nonlinear algebraic systems; Nonlinear dynamics; Planes
• ISSN: 0008-4034; 1939-019X
• DOI: 10.1002/cjce.22152

Azeotropy is a thermodynamic phenomenon where liquid and vapour coexisting phases have the same composition. In binary mixtures, the azeotropy calculation is represented by a 2 × 2 nonlinear system of algebraic equations with temperature (or pressure) and one molar fraction as unknowns. On rare occasions, this nonlinear system exhibits two solutions, characterizing a double azeotrope. In this work, we calculate double azeotropes with a geometry‐based methodology: the numerical inversion of functions from the plane to the plane. We present results for two mixtures where the double azeotropy phenomenon occurs: the system benzene + hexafluorobenzene and the system 1,1,1,2,3,4,4,5,5,5‐decafluoropentane + oxolane. The persistence of double azeotropes across different pressures is made clear by this global geometric approach. Moreover the vanishing of the existence of a pair of azeotropes is explained by the coalescence of them in just one, as can be easily understood from a global geometric viewpoint presented of the nonlinear function involved. The results indicate that this methodology can be a powerful tool for a better understanding of nonlinear algebraic systems in phase coexistence problems.