Vapor-liquid equilibria prediction

It is very satisfying and useful that the COSMO-RS model—in contrast to empirical group contribution models—is able to access the gas phase in addition to the liquid state. This allows for the prediction of vapor pressures and solvation free energies. Also, the large amount of accurate, temperature-dependent vapor pressure data can be used for the parameterization of COSMO-RS. On the other hand, the fundamental difference between the liquid state and gas phase limits the accuracy of vapor pressure prediction, while accurate, pure compound vapor pressure data are available for most chemical compounds. Therefore, it is preferable to use experimental vapor pressures in combination with calculated activity coefficients for vapor-liquid equilibria predictions in most practical applications. 

The second major, more important success of the theory is that, using the fits to single component data, the theory allows predictions of mixture conditions for any combination of pure components. Due to the ideal solution, solid nature (assumptions 4 and 5) fits of pure component data provide acceptable predictions of all mixture conditions. Since laboratory data are costly both in terms of time and funds (c.g., US 2,000 per data point), it is very efficient to predict rather than to measure each hydrate condition. It is important to emphasize that, in contrast to vapor-liquid equilibria predictions, no interaction parameters are needed for mixture prediction. 

Using UNIQUAC, Table 2 summarizes vapor-liquid equilibrium predictions for several representative ternary mixtures and one quaternary mixture. Agreement is good between calculated and experimental pressures (or temperatures) and vapor-phase compositions. ... 

When applying an equation of state to both vapor and liquid phases, the vapor-liquid equilibrium predictions depend on the accuracy of the equation of state used and, for multicomponent systems, on the mixing rules. Attention will be given to binary mixtures of hydrocarbons and the technically important nonhydrocarbons such as hydrogen sulfide and carbon dioxide -Figures 6-7. 

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... 

What should be stressed is not the poor accuracy of the equation-of-state predictions for the COi-n-decane system, but rather the fact that the same, simple equation of state can lead to good vapor-liquid equilibrium predictions over a wide range of temperatures and pressures, as well as a qualitative description of liquid-liquid equilibrium at lower temperatures. 

Sharma, R., Singhal, D., Ghosh, R. and Dwivedi, A. 1999, Potentional applications of artificial neural networks to thermodynamics vapor-liquid equilibrium predictions. Comp. Chem. Engng., 23, 385. 

In the previous section the use of equations of state for vapor-liquid equilibrium predictions was emphasized. This portion of the paper expands on this topic with some specific vapor-liquid equilibrium example calculations, and also deals with a number of... 

For systems of type II, if the mutual binary solubility (LLE) data are known for the two partially miscible pairs, and if reasonable vapor-liquid equilibrium (VLE) data are known for the miscible pair, it is relatively simple to predict the ternary equilibria. For systems of type I, which has a plait point, reliable calculations are much more difficult. However, sometimes useful quantitative predictions can be obtained for type I systems with binary data alone provided that... 

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. 

This equation may be applied separately to the liquid phase and to the vapor phase to yield the pure-species values ( ) and ( ) For vapor/ liquid equilibrium (Eq. [4-280]), these two quantities are equal. Given parameters Oj and bj, the pressure P in Eq. (4-230) that makes these two values equal is the equihbrium vapor pressure of pure species i as predicted by the equation of state. 

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. 

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. 

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. 

Example 4.5 2-Propanol (isopropanol) and water form an azeotropic mixture at a particular liquid composition that results in the vapor and liquid compositions being equal. Vapor-liquid equilibrium for 2-propanol-water mixtures can be predicted by the Wilson equation. Vapor pressure coefficients in bar with temperature in Kelvin for the Antoine equation are given in Table 4.113. Data for the Wilson equation are given in Table 4.126. Assume the gas constant R = 8.3145 kJ-kmol 1-K 1. Determine the azeotropic composition at 1 atm. 

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. 

The vapor-liquid x-y diagram in Figures 4.6c and d can be calculated by setting a liquid composition and calculating the corresponding vapor composition in a bubble point calculation. Alternatively, vapor composition can be set and the liquid composition determined by a dew point calculation. If the mixture forms two-liquid phases, the vapor-liquid equilibrium calculation predicts a maximum in the x-y diagram, as shown in Figures 4.6c and d. Note that such a maximum cannot appear with the Wilson equation. 

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. 

Prediction of liquid-liquid equilibrium also requires an activity coefficient model. The choice of models of liquid-liquid equilibrium is more restricted than that for vapor-liquid equilibrium, and predictions are particularly sensitive to the model parameters used. 

For the following mixtures, suggest suitable models for both the liquid and vapor phases to predict vapor-liquid equilibrium, a. H2S and water at 20° C and 1.013 bar. 

Air needs to be dissolved in water under pressure at 20°C for use in a dissolved-air flotation process (see Chapter 8). The vapor-liquid equilibrium between air and water can be predicted by Henry s Law with a constant of 6.7 x 104 bar. Estimate the mole fraction of air that can be dissolved at 20°C, at a pressure of 10 bar. 

Mixtures of 2-butanol (.sec-butanol) and water form two-liquid phases. Vapor-liquid equilibrium and liquid-liquid equilibrium for the 2-butanol-water system can be predicted by the NRTL equation. Vapor pressure coefficients for the... 

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. 

Correlation and Prediction of Salt Effect in Vapor-Liquid Equilibrium... 

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. 

Pure-component properties from which prediction of salt effect in vapor-liquid equilibrium might be sought, include vapor pressure lowering, salt solubility, degree of dissociation and ionic properties (charges and radii) of the salt, polarity, structural geometry, and perhaps others. 

Over the years, various other theories and models have been proposed for predicting salt effect in vapor-liquid equilibrium, including ones based on hydration, internal pressure, electrostatic interaction, and van der Waals forces. These have been reviewed in detail by Long and McDevit (25), Prausnitz and Targovnik (31), Furter (7), Johnson and Furter (8), and Furter and Cook (I). Although the electrostatic theory as modified for mixed solvents has had limited success, no single theory has yet been able to account for or to predict salt effect on equilibrium vapor composition from pure-component properties alone. 

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