The Rachford-Rice equation: application to ternary diagram

Abstract

Ternary phase diagrams in liquid-liquid equilibrium, for the water-ethanol-ethyl acetate system, were calculated and the results presented in rectangular and triangular diagrams. Initially, the thermodynamical background and the conditions of equilibrium are presented, involving the equality of activities and the mass balance condition. From this system of equations, the Rachford-Rice equation is deduced, transforming the problem of eight equations into a problem of one equation with one unknown. The Non-Random-Two-Liquid model was adopted to calculate activity coefficients, but other models can be easily adapted. An algorithm is presented to calculate the equilibrium compositions of this ternary system, together with numerical results. The theoretical-experimental comparison is in fair agreement, showing the robustness and simplicity of the Rachford-Rice equations. The material presented here is accessible to undergraduate students.