Analytical expression and its application of Rayleigh fractionation for ternary mixtures

Abstract

The Rayleigh equation is an important fundamental equation in distillation, isotope separation, hydrology and many other fields. However, it is only applicable to binary systems. In this work, analytical expressions are derived describing the composition of the residual liquid in Rayleigh fractionation for ternary systems with constant relative volatilities. The expressions are in the form of parameter equations, and the range of the parameter is analyzed from a mathematical perspective. Two methods for calculating the compositions of the residual liquid and the distillate are presented. The analytical equations are verified by calculating the liquid compositions for multi-stage flash cascades. The compositions of the streams involved in Rayleigh fractionation are investigated with the analytical equations and the results are compared with those in an equilibrium flash process. It indicates that Rayleigh fractionation achieves a better degree of separation than equilibrium flash. The physical significance of the parameter in the equations is interpreted based on the residue curve. Finally, an example is given to show that the analytical expressions produce results with better precision compared to applying numerical methods directly on the system of differential equations. The analytical equations for ternary mixtures are expected to cast some new light on other fields involving Rayleigh fractionation and to promote the development of many disciplines.