Robust Pediction of Double Retrograde Vaporization by Numerical Inversion of Functions

Abstract

Double retrograde vaporization is a thermodynamic phenomenon that occurs in mixtures formed by a solute with low volatility when compared to the solvent. Specially in high pressures, when the mixture reaches a temperature which is higher than the critical temperature of the pure solvent, the phase equilibriumcan exhibit four different solutions (dew point pressures and liquid phase compositions), characterizing a very unique behavior. Because of the difficulty in predictingliquid molar fractions and pressure in which this phenomenon occurs, it makes the problem areal challenge for the supercritical fluid and oil industry. The occurrence of this physical phenomenon will be illustrated in a binary system formed by ethane + limonene. Under certain conditions, the problem can be modelled through a 2 × 2 system of nonlinear algebraic equations. This fact makes it possible to predictthe phenomenon of double retrograde vaporization by numerical inversion of functions from a subset of the plane to the plane. This method canobtain all the solutions of the problem in a robust and efficient way, besides offering a basis for conducting a qualitative analysis of the function behavior.
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