This equation uncovers the relationship between volatility and relative volatility.

Apart from volatility, there is another important physical quantity used in special distillation processes, i.e. selectivity, defined as

Eq. (67) is different from Eq.(63) in that the term, , is omitted. As we know, this term is dependent of temperature. Evaluation for special distillation processes and the corresponding separating agents is frequently made at constant temperature. So sometimes selectivity can be regarded as the alternative to relative volatility. However, compared with relative volatility, selectivity as the evaluation index isn't complete in the vapor-liquid equilibrium where we can't judge whether relative volatility a,, is enough larger than unity. As a matter of fact, it is more appropriate to consider selectivity in the liquid-liquid equilibrium because at this time, P°

the term, , needn't to be concerned. But liquid-phase activity coefficient is indispensable and plays an important role in phase equilibrium calculation.

1.2. Liquid-phase activity coefficient in binary and multi-component mixtures

From the classic thermodynamics, we know that activity coefficient is introduced as the revision and judgment for non-ideality of the mixture. As the activity coefficient is equal to unity, it means that the interactions between dissimilar or same molecules are always identical and the mixture is in the ideal state; as the activity coefficient is away from unity, the mixture is in the non-ideal state. The concept of activity coefficient is often used for the liquid phase. The activity coefficient in the liquid phase must be determined so as to derive the equilibrium ratio Kt and relative volatility and thus establish the mathematics model of special distillation processes. The liquid-phase activity coefficient models are set up based on excess

Gibbs free energy. The relation of activity coefficient yj and excess Gibbs free energy Gh is given below:

The liquid-phase activity coefficient models are divided into two categories:

(1) The models are suitable for the non-polar systems, for instance, hydrocarbon mixture, isomers and homologues. Those include regular solution model, Flory-Huggins no-heat model.

(2) The models are suitable for the non-polar and/or polar systems. Those models are commonly used in predicting the liquid-phase activity coefficient, and include Margules equation, van Laar equation, Wilson equation, NRTL (nonrandom two liquid) equation, UNIQUAC (universal quasi-chemical) equation, UNIFAC (UNIQUAC Functional-group activity coefficients) equation and so on.

Among those, Wilson, NRTL, UNIQUAC and UNIFAC equations are the most widely used for binary and multi-component systems because of their flexibility, simplicity and ability to fit many polar and nonpolar systems. Besides, one outstanding advantage of those equations is that they can be readily extended to predict the activity coefficients of multi-component mixture from the corresponding binary-pair parameters. In fact, in special distillation processes, multi-component mixture is often involved.

The formulations of Wilson, NRTL and UNIQUAC equations are listed in Tables 1 and 2 for binary and multi-component mixtures, respectively. In some famous chemical engineering simulation software programs, such as ASPEN PLUS, PROII and so on, the formulations of those equations have been embraced and even the binary-pair parameters are able to be rewritten to meet various requirements. But is should be aware of the unit consistency. For instance, in Table 1 for Wilson equation, if the unit of Ân -An is cal mol"1, then R = 1.987 cal mol"1 K."1. Otherwise, if the unit of Al2 -Au is J mol"1, then R = 8.314 J mol"1 K"1.

RTlny,

Name

Equation

Wilson (two-parameter)

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