UNIQUAC equation, vapor-liquid

To illustrate calculations for a binary system containing a supercritical, condensable component. Figure 12 shows isobaric equilibria for ethane-n-heptane. Using the virial equation for vapor-phase fugacity coefficients, and the UNIQUAC equation for liquid-phase activity coefficients, calculated results give an excellent representation of the data of Kay (1938). In this case,the total pressure is not large and therefore, the mixture is at all times remote from critical conditions. For this binary system, the particular method of calculation used here would not be successful at appreciably higher pressures. 

An adequate prediction of multicomponent vapor-liquid equilibria requires an accurate description of the phase equilibria for the binary systems. We have reduced a large body of binary data including a variety of systems containing, for example, alcohols, ethers, ketones, organic acids, water, and hydrocarbons with the UNIQUAC equation. Experience has shown it to do as well as any of the other common models. V7hen all types of mixtures are considered, including partially miscible systems, the... 

Since we make the simplifying assumption that the partial molar volumes are functions only of temperature, we assume that, for our purposes, pressure has no effect on liquid-liquid equilibria. Therefore, in Equation (23), pressure is not a variable. The activity coefficients depend only on temperature and composition. As for vapor-liquid equilibria, the activity coefficients used here are given by the UNIQUAC equation. Equation (15). ... 

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. 

Outlined below are the steps required for of a X T.E calciilation of vapor-phase composition and pressure, given the liquid-phase composition and temperature. A choice must be made of an equation of state. Only the Soave/Redlich/Kwong and Peng/Robinson equations, as represented by Eqs. (4-230) and (4-231), are considered here. These two equations usually give comparable results. A choice must also be made of a two-parameter correlating expression to represent the liquid-phase composition dependence of for each pq binaiy. The Wilson, NRTL (with a fixed), and UNIQUAC equations are of general applicabihty for binary systems, the Margules and van Laar equations may also be used. The equation selected depends on evidence of its suitability to the particular system treated. Reasonable estimates of the parameters in the equation must also be known at the temperature of interest. These parameters are directly related to infinite-dilution values of the activity coefficients for each pq binaiy. 

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. 

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... 

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. 

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... 

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. 

Local-composition equations for g arc resdily extended to multicomponent mixtures. The multicomponent expressions contain parameters obtainable in principle from binary data only they provide descriptions of g of acceptable accuracy for many engineering calculations of multicomponent vapor-liquid equilibria at subcriiical conditions. Listed below are the multicomponent versions of the Wilson. NRTL. aed UNIQUAC equations. 

Figure 10.3-12 Vapor-liquid equilibria of the acetone-water binary mixture predicted using the combination of the Peng-Robinson equation of state, the Wong-Sandler mixing rule, and the UNIQUAC activity coefficient model with parameters obtained from the predictive UNIFAC model at 25°C. ...

Abrams and Prausnitz found that for vapor-liquid systems, the UNIQUAC equation is as accurate as the Wilson equation. However, an important advantage of the UNIQUAC equation lies in its applicability to liquid-liquid systems, as discussed in Section 5.8. Abrams and Prausnitz also give a one-parameter form of the UNIQUAC equation. The methods previously described can be used to determine UNIQUAC parameters from infinite-dilution activity coefficients or from azeotropic or other single-point data. 

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