Prediction of Multicomponent VLE Behavior

Analytical expressions for the activity coefficient as a function of composition and temperature will then be developed, so that extrapolation from a limited number of experimental measurements can be achieved. We will see, for example, that a single measurement in a binary VLE system is sufficient to provide a reasonably accurate description of the whole composition range or, that binary VLE data alone can be successfully used for the prediction of multicomponent VLE behavior. 

Correlation of binary vapor-liquid equilibrium data, and prediction of multicomponent VLE behavior from binary ones, using this single-parameter expression is discussed by this author (1969 1971) and by Hankinson et al (1972). Typical multicomponent predictions are shown in Figure 13.12. In general, the results obtained are reliable and close to those obtained by the two-parameter expression, even for four- and five-com-... 

Thesame models provide reliable predictions of multicomponent VLE behavior from binary data. The accuracy becomes somewhat poorer, however, for srongly nonideal systems. 

This means that the Wilson equation based on the local composition concept allows the prediction of the VLE behavior of multicomponent systems from binary data. 

Silverman examined next the effect of this variation in parameter values from the different models on the quality of the multicomponent predictions. To this purpose, he used experimental data for 247 binaries in the prediction of the VLE behavior of 73 multicomponent systems with the Wilson equation. 

The real test, of course, for these EoS with polar systems will be in their ability to predict multicomponent VLE behavior from binary data. This, in turn, may depend more on the mixing rules than on the EoS... 

In addition, several equations of state have been developed to predict the VLE behavior of a subcritical liquid mixture with a supercritical component. These theoretical models are of current research interest. In addition, several approaches have been formulated to extend the analysis to multicomponent systems utilizing concepts of continuous thermodynamics(9. 101. 

The principle of distillation is the use of differences in volatiHties of the components to be separated. Distillation processes are usually carried out in countercurrent mode in multistage units. The differences that can be obtained in concentrations of the components in the vapor and liquid phases are determined by the vapor-liquid equihbrium (VLE). Until the 1970s reliable data for vapor-liquid equilibria could only be obtained by measurement, which, for a mixture containing more than two components, required a large number of time-consuming measurements. Advances in chemical thermodynamics have resulted in methods activity coefficient models (g models or equations of state) for the calculation of the phase-equihbrium behavior of multicomponent mixtures on the basis of binary subsystems. In the case that no information about the binary subsystems is available, predictive methods (group contribution methods) are available to allow estimation of the required phase equilibria. 

Local composition models, as suggested by the expressions for the activity coefficient in multicomponent systems, provide description of multi-component VLE behavior using binary parameters only. These parameters, in turn, can be evaluated from the corresponding binary data and, consequently, multicomponent VLE information - that is very scarce in the literature - can be predicted. The Wohl-type models, on the other hand, require at least ternary parameters, as Eq. 13.11.1 indicates. 

The goal of a subctitical VLE calculation is to quantitatively predict or correlnte the various kinds of behavior illustrated by Fig. 1.5-1 or by its iso baric or multicomponent coimlerparta. The basis for the calculation is phase-equilibrium formulation of Section 1.2-5, whare liquid-phase fogaciries are elimienled in favor of liquid-phase activity coefficients, aed vapor-pbase fugaciries in favor of vapor-phase fugacity coefficients. Raoult s Law standard states are chosen (tor all components in the liquid phase hence, (fTf- = f > and Eq. (1.2-63) becomes... 

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