Vapor-liquid equilibrium data prediction

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... 

The regular solution model approach is very similar to the UNIFAC model developed by Fredenslund et al. [23,24], where the interactions between molecules are estimated on the basis of the groups present in each molecule. Extensive tables of interaction parameters [24,25] for vapor-liquid equilibrium data prediction are weii deveioped, and the method has found applicability in the modeling of deodorizer performance [26],... 

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. 

Gmehhng and Onken (Vapor-Liquid Equilibrium Data Collection, DECHEMA, Frankfurt, Germany, 1979) have reported a large collection of vapor-liqnid equilibrium data along with correlations of the resulting activity coefficients. This can be used to predict liqnid-hqnid equilibrium partition ratios as shown in Example 1. 

It is essential to calculate, predict or experimentally determine vapor-liquid equilibrium data in order to adequately perform distillation calculations. These data need to relate composition, temperature, and system pressure. 

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. 

Care should be exercised in using the coefficients from Table 4.14 to predict two-liquid phase behavior under subcooled conditions. The coefficients in Table 4.14 were determined from vapor-liquid equilibrium data at saturated conditions. 

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. 

There is always uncertainty and inaccuracy with vapor-liquid equilibrium data and correlations. Any errors in this data could mean an incorrect prediction of the location and shape of the boundary. 

In the book, Vapor-Liquid Equilibrium Data Collection, Gmehling and colleagues (1981), nonlinear regression has been applied to develop several different vapor-liquid equilibria relations suitable for correlating numerous data systems. As an example, p versus xx data for the system water (1) and 1,4 dioxane (2) at 20.00°C are listed in Table El2.3. The Antoine equation coefficients for each component are also shown in Table E12.3. A12 and A21 were calculated by Gmehling and colleaques using the Nelder-Mead simplex method (see Section 6.1.4) to be 2.0656 and 1.6993, respectively. The vapor phase mole fractions, total pressure, and the deviation between predicted and experimental values of the total p... 

Figure 7 shows the predicted vapor-phase mole fractions of HC1 at 25°C as a function of the liquid-phase molality of HC1 for a constant NaCl molality of 3. Also included are predicted vapor-phase mole fractions of HC1 when the interaction parameter A23 is taken as zero. There are unfortunately no experimental vapor-liquid equilibrium data available for the HC1-NaCl-FLO system however, considering the excellent description of the liquid-phase activity coefficients and the low total pressures, it is expected that predicted mole fractions would be within 2-3% of the experimental values. 

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. 

Here, a, al2. and a21 are the binary parameters estimated from experimental vapor-liquid equilibrium data. The adjustable energy parameters, al2 and a2l, are usually assumed to be independent of composition and temperature. However, when the parameters are temperature dependent, prediction ability of the NRTL model enhances. Table 1.7 tabulates the temperature-dependent parameters of the NRTL model for some binary liquid mixtures. 

Prediction of Isobaric Vapor-Liquid Equilibrium Data for Mixtures of Water and Simple Alcohols... 

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. 

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. 

Ternary System. The values of all binary parameters used in predicting the ternary data are shown in Table IV. The predicted values of the vapor-liquid equilibrium data—i.e.9 the boiling point, and the composition of the vapor phase, y, for given values of the liquid composition, x, are presented in Tables V, VI, and VII. Also shown are the measured boiling points for the given values of the liquid composition. The RMSD value between the predicted and measured boiling points for the systems water-ethanol-l-propanol, water-ethanol-2-methyl-l-propanol, and water-ethanol-2-methyl-l-butanol are 0.23°C, 0.69°C, and 2.14°C. It seems therefore that since the NRTL equation successfully predicts temperature, the predicted values of y can be accepted confidently. 

Consistent vapor-liquid equilibrium data are necessary to design all types of rectification devices. However, many industrially important mixtures are nonideal, particularly in the liquid phase, and predicting their equilibrium properties from fundamental thermodynamics is not possible. Thus, the correlating of experimental x-y-t and x-y-P data has developed as an important branch of applied thermodynamics. 

Tpo obtain vapor-liquid equilibrium data for binary systems, it is now well established that under certain circumstances it can be more accurate and less time consuming to measure the boiling point, the total pressure, and the liquid composition and then use the Gibbs-Duhem relationship to predict vapor composition (I) rather than to measure it. The disadvantage is that there is no way of checking the thermodynamic consistency of the experimental data. 

A method to predict salt effect on vapor-liquid equilibrium in which salt is dissolved in a saturated state is introduced. In this method, salt effect is predicted by using preferential solvation numbers, the concentration of the salt, and the vapor-liquid equilibrium data for which salt is not involved. It is possible to predict salt effect completely without using actually measured data if the preferential solvation number can be predicted. Presently, however, it is impossible to completely predict preferential solvation number. Hence, the preferential solvation numbers are obtained through actual measurements, and these numbers are used for the prediction. If preferential solvation number can be predicted independently in the future, this method will be an extremely hopeful one. The salt effect prediction method is entirely in reverse sequence of that used to obtain preferential solvation number. Specifically, it is carried out in the following sequence. 

Gas solubility has been treated extensively (7). Alethods for the prediction of phase equilibria and actual solubility data have been given (8,9) and correlations of the equilibrium K values of hydrocarbons have been developed and compiled (10). Several good sources for experimental information on gas— and vapor—liquid equilibrium data of nonideal systems are also available (6,11,12). 

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. 

All of the necessary experimental data [Vf, H2,i, 7 2,3, and E (Margules parameter)] were taken from the original publications (indicated as footnotes to Table 1) or calculated using the data from Gmehling s vapor-liquid equilibrium data compilation. Figure 1 and Table 1 show that the present eq 25 is in much better agreement with experiment than Krichevsky s eq 1 and equations A2-3—5 from Appendix 2, which involve the Margules expression for the activity coefficient. The new eq 25 provides predictions that are comparable to those of an empirical correlation for aqueous mixtures of solvents, which involves three adjustable parameters. 

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. 

EPAR ATION and purification processes account for a large portion of the design, equipment, and operating costs of a chemical plant. Further, whether or not a mixture forms an azeotrope or two liquid phases may determine the process flowsheet for the separations section of a chemical plant. Most separation processes are contact operations such as distillation, gas absorption, gas stripping, and the like, the design of which requires the use of accurate vapor-liquid equilibrium data and correlating models or, in the absence of experimental data, of accurate predictive methods. Phase behavior, especially vapor-Uquid equilibria, is important in the design, development, and operation of chemical processes. 

Table II compares predictions of Kes for the benzene-hexane-water-ethanol system with the experimental clata of El-Zoobi (13). The Wilson constant for the benzene-hexane pair for these calculations was taken from the compilation of Holmes and Van Winkle (14) derived from vapor liquid equilibrium data. The agreement of the prediction with experiment is satisfactory.

When bienry vapor-liquid equilibrium data are reduced to yield binary parameters in UNlQUAC or in some other expression for g . it is usually not possible to obtain a unique set of bianty parameters that are in some significant sease "bsst for that bianry. Fora given binary mixture, bisary parameters are almost always at least partially correlated so that, when experimental uncertainties are taken into account, there are many sets of binary parameters dial can represent equally well the experimental data, When the gonl of data reduction is limited to representing the binary data, it does not matter which of these many sets of binary parameters is ured in the calculations. But when binary parameters are used lo predict ternary liquid-liquid equilibria (Type I), calculated results depend strongly on which set of binary parameters is used. 

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