#### Date of Award

Spring 1971

#### Document Type

Dissertation

#### Degree Name

Doctor of Engineering Science in Chemical Engineering

#### Department

Chemical Engineering and Chemistry

#### First Advisor

Dimitrios P. Tassios

#### Second Advisor

Richard Clyde Parker

#### Third Advisor

Hung T. Chen

#### Fourth Advisor

Teddy Greenstein

#### Fifth Advisor

Leonard Salzarulo

#### Abstract

An extensive study of local mole fraction equations aimed at obtaining a two parameter expression for the Excess Free Energy of miscible and immiscible systems has been undertaken.

Initially our approach was to modify existing equations by substituting those parameters reflecting interaction between like molecules by the pure component energies of vaporization. This resulted in a one parameter modification of the three parameter Wilson equation, which correlates data poorly and a two parameter modification of the NRTL equation which correlates binary miscible data with fair accuracy. A modification of the Scatchard-Hildebrand equation, where mole fractions are substituted by local mole fractions yields also a fairly good correlation for binary miscible systems.

The most significant result, however, was obtained when it was found that the substitution a =-1, in the NRTL equation, results in an improved correlation for the excess free energy of mixing and consequently for the activity coefficients. A study of partially miscible systems, 5 binaries and 7 ternaries, shows that the new two parameter expression predicts binary vapor-liquid equilibrium from mutual solubility data and ternary liquid-liquid equilibrium from binary data with better accuracy than the NRTL equation with the value of α set according to the rules of Renon and Prausnitz. In predicting binary immiscible behavior from vapor-liquid equilibrium data, both equations offer practically the same accuracy. A similar study conducted on miscible systems, 55 binaries and 11 ternaries, shows that both equations correlate binary data and predict ternary vaporliquid equilibrium, from binary data, with about the same accuracy.

The importance of this finding is that now it becomes possible to use the NRTL equation, without the uncertainty involved in making the right choice fora, for predicting vapor-liquid and liquid-liquid equilibrium from either mutual solubility or azeotropic data. This modification, therefore, combines in a. single expression the advantages of both the Wilson and NRTL equations.

Considering that a value of α = -1 is inconsistent with Renon's derivation of the NRTL equation, a new model is proposed in which a distinction is made between bound and free molecules in a cell. Equating the ratio of local mole fractions of free molecules, what we call Effective Mole Fractions, to fugacities, leads to the desired two constant expression hereafter referred to as the LEMF equation.

During the course of this study a computational technique for the prediction of ternary liquid-liquid equilibria was developed. This technique makes use of a Fortran subroutine for function minimization to find the composition of phases in equilibrium.

Another result of this study was the finding that more than one set of Parameters can be obtained, for either the NRTL or LEMF equation, depending on the initial values chosen to initiate the search. From a study of this phenomena we concluded that a 0-0 set of initial values generally yields the best set of binary parameters.

#### Recommended Citation

Marina, Jose Mario, "Local mole fraction equations for the excess free energy of mixing" (1971). *Dissertations*. 1355.

https://digitalcommons.njit.edu/dissertations/1355