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

Abstract

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 Â 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 þ hexafluorobenzene and the system 1,1,1,2,3,4,4,5,5,5decafluoropentane þ 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.Keywords: double azeotropy, functions from the plane to the plane, nonlinear algebraic systems

Evaluation of a New Multimodal Optimization Algorithm in Fluid Phase Equilibrium Problems

“…The azeotropic coordinates for the system HFC4130mee (1) + THF (2) at 35 kPa are ( 1 , ) = (0, 0924, 309, 45) (Azeotrope 1) and ( 2 , ) = (0, 255, 309, 57) (with T in Kelvin), as reported by Guedes, Moura Neto, and Platt (2015). As previously described as detailed by several authors (Segura et al, 2005;Guedes et al, 2015), two azeotropes appear at this pressure. We observed that the values for the azeotropic temperatures are extremely close, which can be a challenge for the algorithm.…”

How do you write and present research well? 10—State the uncertainty, but not too precisely

“…Factors that influence Guedes et al [3] Pure Temperature 315.71827 K 315.7 K Lu et al [4] Pure Pressure 101 325 Pa 101 kPa Kianinejad et al [5] Pure Porosity 52.47 % 52 % Abdelaziz et al [6] Pure Length 2.655 m 2.65 m Jeon et al [7] Analytical Surface area 163.9 m 2 · g −1 160 m 2 · g −1 Lin et al [8] Analytical EDS analysis 40.09 wt% 0.40 g · g −1 Jia et al [9] Analytical Viscosity 5.875 cP 5.9 cP Ma et al [10] Derived Selectivity 63.3 63 Vedoy and Soares [11] Derived Solids recovered 25.97 % 26 % Esmailpour et al [12] Derived Air density 0.921 02 kg · m −3 0.92 kg · m −3 Verma et al [13] Derived COD 1000.00 mg · L 1 .00 g · L Moradi et al [14] Derived Activation energy 36.314 kJ · mol…”

Geometrical Tools for Teaching Azeotropy Using Simplified Thermodynamic Models

“…Missen [8] described an algebraic method devoted to the calculation of azeotropic coordinates for some common excess Gibbs free energy models. Guedes et al [9] analyzed-with a geometric approach, using the concept of functions from the plane to the plane-the existence of double azeotropy in two binary systems. Libotte et al [10] used geometrical concepts to explain the double retrograde vaporization phenomenon (another author rare and nonlinear thermodynamic phenomenon, which can occur in mixtures close to the critical point).…”

“…The focus of this work is essentially different from that employed by Guedes et al [9], which used some complex mathematical tools (such as homotopy-continuation methods) and highly nonlinear thermodynamic models, making it technically more difficult to demonstrate in elementary terms the basic geometric ideas involved in the azeotropy calculations. The azeotropy phenomenon in binary mixtures can be characterized by a nonlinear application of R 2 to R 2 , which motivates us to present some geometric notions on quadratic maps in the plane in Section 2.…”