UNIQUAC equation, vapor-liquid equilibrium

Figure 15 shows results for a difficult type I system methanol-n-heptane-benzene. In this example, the two-phase region is extremely small. The dashed line (a) shows predictions using the original UNIQUAC equation with q = q. This form of the UNIQUAC equation does not adequately fit the binary vapor-liquid equilibrium data for the methanol-benzene system and therefore the ternary predictions are grossly in error. The ternary prediction is much improved with the modified UNIQUAC equation (b) since this equation fits the methanol-benzene system much better. Further improvement (c) is obtained when a few ternary data are used to fix the binary parameters. 

These models are semiempirical and are based on the concept that intermolecular forces will cause nonrandom arrangement of molecules in the mixture. The models account for the arrangement of molecules of different sizes and the preferred orientation of molecules. In each case, the models are fitted to experimental binary vapor-liquid equilibrium data. This gives binary interaction parameters that can be used to predict multicomponent vapor-liquid equilibrium. In the case of the UNIQUAC equation, if experimentally determined vapor-liquid equilibrium data are not available, the Universal Quasi-chemical Functional Group Activity Coefficients (UNIFAC) method can be used to estimate UNIQUAC parameters from the molecular structures of the components in the mixture3. 

A model is needed to calculate liquid-liquid equilibrium for the activity coefficient from Equation 4.67. Both the NRTL and UNIQUAC equations can be used to predict liquid-liquid equilibrium. Note that the Wilson equation is not applicable to liquid-liquid equilibrium and, therefore, also not applicable to vapor-liquid-liquid equilibrium. Parameters from the NRTL and UNIQUAC equations can be correlated from vapor-liquid equilibrium data6 or liquid-liquid equilibrium data9,10. The UNIFAC method can be used to predict liquid-liquid equilibrium from the molecular structures of the components in the mixture3. 

Basically, DESIGNER can use different physical property packages that are easy to interchange with commercial flowsheet simulators. For the case considered, the vapor-liquid equilibrium description is based on the UNIQUAC model. The liquid-phase binary diffusivities are determined using the method of Tyn and Calus (see Ref. 72) for the diluted mixtures, corrected by the Vignes equation (57), to account for finite concentrations. The vapor-phase diffusion coefficients are assumed constant. The reaction kinetics parameters taken from Ref. 202 are implemented directly in the DESIGNER code. 

Equilibrium compositions of liquid phases at equilibrium are calculated by equating the component fugacities, similar to vapor-liquid equilibrium calculations, described in more detail in Chapter 2. The activity coefficients may be calculated by equations presented in Section 1.3.3, in particular the UNIQUAC and NRTL equations. The composition dependence of these equations is developed to the point where the same equation with the same constants can predict activity coefficients over wide ranges of composition, thus allowing it to predict two immiscible liquid phases at equilibrium. 

Using one of these activity coefficient equations it is possible to calculate liquid-liquid equihbrium (LLE) behavior of multicomponent hquid systems. Consider, for example, the ternary system of Figure 1. A system of overall composition A splits into two liquid phases B and C. The calculation of compositions of B and C is analogous to the flash ciculation of vapor-liquid equilibrium problems. By using the UNIQUAC equations to obtain the partition coefficients, Kj, this problem can be solved for any composition A of the overall system. The calculations are lengthy but computer programs for this purpose (2) have been published. In this paper simpler approximate methods for phase equilibrium problems of environmental interest is sought. For the moment it is sufficient to note that the activity coefficients provide the means of complete liquid-liquid equihbrium computations. 

Vapor-Liquid Equilibrium Data Collection (Gmehling et al., 1980). In this DECHEMA data bank, which is available both in more than 20 volumes and electronically, the data from a large fraction of the articles can be found easily. In addition, each set of data has been regressed to determine interaction coefficients for the binary pairs to be used to estimate liquid-phase activity coefficients for the NRTL, UNIQUAC, Wilson, etc., equations. This database is also accessible by process simulators. For example, with an appropriate license agreement, data for use in ASPEN PLUS can be retrieved from the DECHEMA database over the Internet. For nonideal mixtures, the extensive compilation of Gmehling (1994) of azeotropic data is very useful. 

This example involves vapor-liquid equilibrium (VLE) data for the design of a distillation tower to dehydrate ethanol. A portion of the T-x-y data for an ethanol-water mixture, measured at 1.013 bar (1 atm) using a Gillespie still (Rieder and Thompson, 1949), is shown in Figure 3.1a. Here, it is desired to use regression analysis to enable the UNIQUAC equation to represent the data accurately over the entire composition range. 

Here, a, a 2, and fl2i are the binary adjustable parameters estimated from experimental vapor-liquid equilibrium data. The adjustable energy parameters, a 2 and 21. are independent of composition and temperature. However, when the parameters are temperature-dependent, prediction ability of the NRTL model enhances. The Wilson, NRTL, and UNIQUAC equations are readily generalized to multicomponent mixtures. 

Table E13.7 shows the results obtained from six simulations, all with the same input specifications but with different thermodynamic options. The number of actual stages calculated ranges from 15 to 22 however, the results for two of the simulations (denoted n/a in the table) indicated that the minimum reflux ratio was greater than that specified. Without further information about the ability of the various models to correlate experimental vapor-liquid equilibrium data, a precise solution to the problem is not possible. However, the differences in the results obtained indicate that the choice of thermodynamic model is a crucial one. Of special concern here is the choice of correction of fugacities (denoted w/correction). These corrections are the first and last terms in Equation (13T). Note that these results were obtained using the CHEMCAD databank BIP values for the NRTE and UNIQUAC models. Different BIP values will yield different results.

Values of the activity coefficients are deduced from experimental data of vapor-liquid equilibria and correlated or extended by any one of several available equations. Values also may be calculated approximately from structural group contributions by methods called UNIFAC and ASOG. For more than two components, the correlating equations favored nowadays are the Wilson, the NRTL, and UNIQUAC, and for some applications a solubility parameter method. The fust and last of these are given in Table 13.2. Calculations from measured equilibrium compositions are made with the rearranged equation... 

The UNIQUAC equation developed by Abrams and Prausnitz is usually preferred to the NRTL equation in the computer-aided design of separation processes. It is suitable for miscible and immiscible systems, and so can be used for vapor-liquid and liquid-liquid systems. As with the Wilson and NRTL equations, the equilibrium compositions for a multicomponent mixture can be predicted from experimental data for the binary pairs that comprise the mixture. Also, in the absence of experimental data for... 

Activity coefficients are generally either determined from Equation 6.18a and Equation 6.18b using measured vapor- and liquid-equilibrium compositions or are estimated from the UNIQUAC equation mentioned earlier. A third method arises when the two components in question have low mutual solubilities, y values are then confined to the Henry s law regions near x = 0 and X = 1 (Eigure 6.19) and cease to exist outside those regions. This provides a way of calculating activity coefficients using classical chemical thermodynamics. 

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