Prediction of Vapor-Liquid Equilibria

We are interested in comparing the effectiveness of the various equations of state in predicting the (p. V. T) properties. We will limit our comparisons to Tr > 1 since for Tr < 1 condensations to the liquid phase occur. Prediction of (vapor + liquid) equilibrium would be of interest, but these predictions present serious problems, since in some instances the equations of state do not converge for Tr< 1. 

A review is presented of techniques for the correlation and prediction of vapor-liquid equilibrium data in systems consisting of two volatile components and a salt dissolved in the liquid phase, and for the testing of such data for thermodynamic consistency. The complex interactions comprising salt effect in systems which in effect consist of a concentrated electrolyte in a mixed solvent composed of two liquid components, one or both of which may be polar, are discussed. The difficulties inherent in their characterization and quantitative treatment are described. Attempts to correlate, predict, and test data for thermodynamic consistency in such systems are reviewed under the following headings correlation at fixed liquid composition, extension to entire liquid composition range, prediction from pure-component properties, use of correlations based on the Gibbs-Duhem equation, and the recent special binary approach. 

The following is the prediction of vapor-liquid equilibrium composition when CaCl2 is added in 7.24 mol % to the ethyl acetate-ethanol system in which the liquid-phase composition of ethyl acetate is 0.502 in terms of mole fraction. 

The activity coefficient of a component in a mixture is a function of the temperature and the concentration of that component in the mixture. When the concentration of the component proaches zero, its activity coefficient approaches the limiting activity coefficient of th component in the mixture, or the activity coefficient at infinite dilution, y . The limiting activity coefficient is useful for several reasons. It is a strictly dilute solution property and can be used dir tly in nation 1 to determine the equilibrium compositions of dilute mixtures. Thus, there is no reason to extrapolate uilibrium data at mid-range concentrations to infinite dilution, a process which may introduce enormous errors. Limiting activity coefficients can also be used to obtain parameters for excess Gibbs energy expressions and thus be used to predict phase behavior over the entire composition range. This technique has been shown to be quite accurate in prediction of vapor-liquid equilibrium of both binary and multicomponent mixtures (5). 

Boukouvalas, C., Spiliotis, N., Coutsikos, P., and Tzouvaras, N., 1994. Prediction of vapor-liquid equilibrium with the LCVM model. A linear combination of the Huron-Vidal and Michelsen mixing rules coupled with the original UNIFAC and the t-mPR equation of state. Fluid Phase Eq., 92 75-106. 

With all these choices, and limited knowledge of your system, you will likely want to use the recommended options and make predictions of vapor-liquid equilibrium using Aspen Plus in order to compare those predictions with experimental data. Chapter 3 presented an example of such a comparison for the ethanol-water system. 

K. Kojima and T. Tochigi, Prediction of Vapor-Liquid Equilibrium by the ASOG Method, Elsevier, Amsterdam (1979). 

We now turn from the qualitative description of high-pressure phase equilibria and its measurement to the quantitative description, that is, to the correlation or prediction of vapor-liquid equilibrium for hydrocarbon (and light gas). systems, of which the ethane-propylene system is merely one example. Our interest will be only in systems describable by a single equation of state for both the vapor and liquid phases, as the case in which the liquid is described by an activity coefficient model was considered in the previous section. 

Urata, S., Takada, A., Murata, J., Hiaki, T., and Sekiya, A. (2002). Prediction of vapor-liquid equilibrium for binary systems containing HFEs by using artificial neural network. Fluid Phase Equilib 199, 63-78. 

Chao-Seader Correlation. Reference was made earlier to the well known and much used Chao-Seader correlation for the prediction of vapor-liquid equilibrium for principally hydrogen-hydrocarbon systems with small amounts of CO2, H2S, O2, N2, etc. The heart of the correlation consists of several equations to represent liquid fugacity. The other two constituents, the Scatchard-Hildebrand equation for activity coefficients and the Redllch-Kwong equation for the vapor-phase nonideality, were already well established. 

Stepanova and Velikovskii (1970) stated that deviation from ideal behavior is connected with fugacity and activity. A paper on the prediction of vapor-liquid equilibrium for polar-nonpolar binary systems by Finch and Van Winkle is mentioned here because of the terminology and the principles involved. The 12 systems examined comprised systems such as ethylbenzene-hexylene glycol, n-octane-cellosolve, toluene-phenol, and n-heptane-toluene. It was pointed out that whereas the Scatchard-Hildebrand theory has had some success in predicting the vapor-liquid equilibria for nonpolar binary systems, it has proved to be unsatisfactory in the quantitative prediction of such equilibria for polar-polar systems and for polar-nonpolar systems. 

Figure 14.11 Prediction of vapor-liquid equilibrium with the PR EoS for the system 2(1) - C (2) - nC4(3) at 260,270 and 280 K using k j = 0.0 for all pairs. (Data from Clark and Stead, 1988.)...

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. 

Although the methods developed here can be used to predict liquid-liquid equilibrium, the predictions will only be as good as the coefficients used in the activity coefficient model. Such predictions can be critical when designing liquid-liquid separation systems. When predicting liquid-liquid equilibrium, it is always better to use coefficients correlated from liquid-liquid equilibrium data, rather than coefficients based on the correlation of vapor-liquid equilibrium data. Equally well, when predicting vapor-liquid equilibrium, it is always better to use coefficients correlated to vapor-liquid equilibrium data, rather than coefficients based on the correlation of liquid-liquid equilibrium data. Also, when calculating liquid-liquid equilibrium with multicomponent systems, it is better to use multicomponent experimental data, rather than binary data. 

A method of prediction of the salt effect of vapor-liquid equilibrium relationships in the methanol-ethyl acetate-calcium chloride system at atmospheric pressure is described. From the determined solubilities it is assumed that methanol forms a preferential solvate of CaCl296CH OH. The preferential solvation number was calculated from the observed values of the salt effect in 14 systems, as a result of which the solvation number showed a linear relationship with respect to the concentration of solvent. With the use of the linear relation the salt effect can be determined from the solvation number of pure solvent and the vapor-liquid equilibrium relations obtained without adding a salt. 

Until recently the ability to predict the vapor-liquid equilibrium of electrolyte systems was limited and only empirical or approximate methods using experimental data, such as that by Van Krevelen (7) for the ammonia-hydrogen sulfide-water system, were used to design sour water strippers. Recently several advances in the prediction and correlation of thermodynamic properties of electrolyte systems have been published by Pitzer (5), Meissner (4), and Bromley ). Edwards, Newman, and Prausnitz (2) established a similar framework for weak electrolyte systems. 

The Non-Random, Two Liquid Equation was used in an attempt to develop a method for predicting isobaric vapor-liquid equilibrium data for multicomponent systems of water and simple alcohols—i.e., ethanol, 1-propanol, 2-methyl-l-propanol (2-butanol), and 3-methyl-l-butanol (isoamyl alcohol). Methods were developed to obtain binary equilibrium data indirectly from boiling point measurements. The binary data were used in the Non-Random, Two Liquid Equation to predict vapor-liquid equilibrium data for the ternary mixtures, water-ethanol-l-propanol, water-ethanol-2-methyl-1-propanol, and water-ethanol-3-methyl-l-butanol. Equilibrium data for these systems are reported. 

For azeotropic distillation especially the systems are non-ideal which makes calculating vapor-liquid equilibrium properties more difficult than, for example, in distillation of mixtures of simple hydrocarbons. Work predicting the vapor-liquid equilibrium properties of ternary mixtures of... 

The direct measurement of vapor-liquid equilibrium data for partially miscible mixtures such as 3-methyl-l-butanol-water is difficult, and although stills have been designed for this purpose (9, 10), the data was indirectly obtained from measurements of pressure, P, temperature, t, and liquid composition, x. It was also felt that a test of the validity of the NRTL equation in predicting the VLE data for the ternary mixtures would be the successful prediction of the boiling point. This eliminates the complicated analytical procedures necessary in the direct measurement of ternary VLE data. 

Gmehhug aud Oukeu (Vapor-Liquid Equilibrium Data Collection, DECHEMA, Fraukfurt, Germauy 1979) have reported a large col-lectiou of vapor-liquid equilibrium data aloug with correlatious of the resultiug activity coefficieuts. This cau be used to predict liquid-liquid equilibrium partitiou ratios as showu iu Example 1. 

Perry et al. (1997) give a useful summary of solubility data. Liquid-liquid equilibrium (LLE) compositions can be predicted from vapor-liquid equilibrium data, but the predictions are seldom accurate enough for use in the design of liquid-liquid extraction processes. 

For vapors, use the equation of state selected for predicting the vapor-liquid equilibrium. For liquids, use the same equation if it is suitable for estimating liquid density. 

Figure 8 faj Comparison of vapor-liquid equilibrium predictions from COSMO-SAC, UNI-FAC and modified UNIFAC models for water( 1) -h 1,4-dioxane(2) mixtures at temperatures 308.15 and 323.15 K, and (b) vapor-liquid equilibrium prediction from COSMO-SAC for benzene(l)/n-methylformamide(2) at temperatures of 318.15 and 328.15 K... 

Prediction of solubility is also receiving more attention, mostly limited to academic research. In comparison to the vapor-Equid equilibrium situation, which has built an extensive database for reliable prediction (Reid et al. 1977), prediction of solid-liquid equilibrium remains in its early stage (Kolaret al. 2002). However, this field is developing rapidly, and its fuUire potential cannot be overlooked (Tung et al. 2007). 

While the Redlich-Kwong equation is said to give volumetric and thermal properties of pure components and of mixtures with good accuracy, the vapor-liquid-equilibrium data predicted by this equation often gives poor results.59 To improve this equation for the prediction of vapor-liqnid-equilibrium data, Soave59 proposed the following modified form of the Redlich-Kwong equation of state... 

This value is 31.3% lower than the experimental value. This result indicates that the assumption of temperature independence of (A,y-A,() and ViJvjL is not valid. When temperature dependence is taken into account, predictions are improved. For best accuracy, however, Nagata and Yamada" showed that Wilson parameters should be determined by simultaneous fit of vapor-liquid equilibrium and heat of mixing data. 

To predict the vapor-liquid equilibrium (VLE) of these simulations, the NRTL-HOC property model, which uses the Hayden-O Connell equation of state as the vapor-phase model and the NRTL for the liquid phase, was employed (Aspen Technology, 2009). 

Vrabec et al. [41] predicted the vapor-liquid equilibrium of the mixture CO2 + C2H6 for three different isotherms. The azeotropic behavior of this mixture was predicted using the Lorentz-Berthelot combining mle (12), i.e., relying exclusively on pure substance models without considering any experimental binary data. The quality of the predicted data is clearly superior to the Peng-Robinson EOS with the... 

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