Vapor-liquid equilibrium NRTL Equation

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. 

Example 4.6 Mixtures of water and 1-butanol (n-butanol) form two-liquid phases. Vapor-liquid equilibrium and liquid-liquid equilibrium for the water-1-butanol system can be predicted by the NRTL equation. Vapor pressure coefficients in bar with temperature in Kelvin for the Antoine equation are given in Table 4.136. Data for the NRTL equation are given in Table 4.14, for a pressure of 1 atm6. Assume the gas constant R = 8.3145 kJ-kmoL -K-1. 

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... 

In order to correlate the results obtained, a modified SRK equation of state with Huron-Vidal mixing rules was used. Details about the model are reported in the paper by Soave et al. [16]. This approach is particularly adequated when experimental values of the critical temperature and pressure are not available as it was the case for limonene and linalool. Note that the flexibility of the thermodynamic model to reproduce high-pressure vapor-liquid equilibrium data is ensured by the use of the Huron-Vidal mixing rules and a NRTL activity coefficient model at infinite pressures. Calculation results are reported as continuous curves in figure 2 for the C02-linalool system and in figure 3 for C02-limonene. Note that the same parameters values were used to correlated the data of C02-limonene at 45, 50 e 60 °C. 

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. 

Vapor/liquid equilibrium (VLE) block diagrams for, 382-386, 396,490 conditions for stability in, 452-454 correlation through excess Gibbs energy, 351-357, 377-381 by Margules equation, 351-357 by NRTL equation, 380 by Redlich/Kister expansion, 377 by the UNIFAC method, 379, 457, 678-683... 

NRTL equation was used to express jCy in terms of the overall composition. The parameters of the NRTL equation were taken from the Gmehlings vapor—liquid equilibrium (VLE) data compilation. The results of the calculations are compared with experimental data in Figures 1 and 2. 

A modified local composition (LC) expression is suggested, which accounts for the recent finding that the LC in an ideal binary mixture should be equal to the bulk composition only when the molar volumes of the two pure components are equal. However, the expressions available in the literature for the LCs in binary mixtures do not satisfy this requirement. Some LCs are examined including the popular LC-based NRTL model, to show how the above inconsistency can be eliminated. Further, the emphasis is on the modified NRTL model. The newly derived activity coefficient expressions have three adjustable parameters as the NRTL equations do, but contain, in addition, the ratio of the molar volumes of the pure components, a quantity that is usually available. The correlation capability of the modified activity coefficients was compared to the traditional NRTL equations for 42 vapor—liquid equilibrium data sets from two different kinds of binary mixtures (i) highly nonideal alcohol/water mixtures (33 sets), and (ii) mixtures formed of weakly interacting components, such as benzene, hexafiuorobenzene, toluene, and cyclohexane (9 sets). The new equations provided better performances in correlating the vapor pressure than the NRTL for 36 data sets, less well for 4 data sets, and equal performances for 2 data sets. Similar modifications can be applied to any phase equilibrium model based on the LC concept. 

Compilations of infinite-dilution activity coefficients, when available for the solute of interest, may be used to rank candidate solvents. Partition ratios at finite concentrations can be estimated from these data by extrapolation from infinite dilution using a suitable correlation equation such as NRTL [Eq. (15-25)]. Examples of these lands of calculations are given by Walas [Phase EquU ria in Chemical Engineering (Butterworth-Heinemann, 1985)]. Most activity coefficients available in the literature are for small organic molecules and are derived from vapor-liquid equilibrium measurements or azeotropic composition data. 

Figure 4.3. (a) Thermodynamic factor for the system ethanol-water at 40°C obtained from different activity coefficient models. Parameters from Gmehling and Onken (1977ff Vol. I/la p. 133). (h) Thermodynamic factor for the system ethanol-water at 50°C obtained using the NRTL equation using parameters fitted to isothermal vapor-liquid equilibrium data. Parameters from Gmehling and Onken... 

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. 

Binary and ternary forms of the NRTL equation were evaluated and compared to other equations for vapor-liquid equilibrium applications by Renon and Prausnitz, Larson and Tassios, Mertl, Marina and Tassios, and Tsu-boka and Katayama. In general, the accuracy of the NRTL equation is comparable to that of the Wilson equation. Although is an adjustable constant, there is little loss in accuracy over setting its value according to the rules described above. Methods for determining best values of NRTL binary parameters are considered in detail in the above references. Mertl tabulated NRTL parameters obtained from 144 sets of data covering 102 different binary systems. Other listings of NRTL parameters are also available. 

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). 

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. 

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. 

To ensure that the predicted two-phase region corresponds with that for the saturated vapor-liquid-liquid equilibrium, the temperature must be specified to be bubble-point predicted by the NRTL equation at either x = 0.59 or x = 0.98 (366.4 K in this case). 

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... 

---