The NRTL Equation

Renon and Prausnitz (1968 and 1969) modified Wilson s equation for the local mole fractions by introducing the parameter a to account for the non-randomness of liquid solutions  

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The NRTL equation contains three parameters for a binary system and is written ... 

The NRTL equation developed by Renon and Prausnitz overcomes the disadvantage of the Wilson equation in that it is applicable to immiscible systems. If it can be used to predict phase compositions for vapour-liquid and liquid-liquid systems. 

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 vapour-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 the binary pairs, the coefficients for use in the UNIQUAC equation can be predicted by a group contribution method UNIFAC, described below. 

A method was also developed to predict the parameters required for the NRTL equation the ASOG method, Kojima and Tochigi (1979). 

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. 

Table 4.14 Data for water (1) and 1-butanol (2) for the NRTL equation at 1 atm6.

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). 

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... 

Antoine equation for pressure in bar and temperature in Kelvin are given in Table 4.196. Data for the NRTL equation at 1 atm are given in Table 4.206. Assume the gas constant R = 8.3145 kJ-kmoH-K-1. 

Among the various models incorporating the local composition concept for short-range interactions, the NRTL equation is adopted in this study. Electrolyte systems are characterized by extraordinarily large heats of mixing. 

Compared to the heat of mixing, the nonideal entropy of mixing is negligible, which is consistent with the basic assumption behind the NRTL equation. In addition, the NRTL equation is algebraically simple while applicable to mixtures which exhibit phase splitting. No specific volume or area data are required. 

As an example, the system ethyl acetate-acetic acid-water can be used and equilibrium data using the UNIQUAC equation calculated [6]. Using the NRTL equation would have given similar results. 

Solubility of toluene and p-mononitrotoluene in sulfuric acid are available (1 ,20). These data were correlated using the NRTL equation. In the preliminary model presented here, all mononitrotoluenes are assumed to have the same solubility and nitric acid is assumed to have negligible effect on their solubility. 

Jefferson Tester I would like to shift gears and direct a question to John Prausnitz regarding his comments. You didn t talk very much about some of your own contributions and those of your students, for instance, the NRTL equation and UNIQUAC-UNIFAC models for nonideal solutions now in widespread use throughout the chemical industry and certainly employed by many people making practical calculations. There have been extensions of that local composition approach, in particular to electrolyte systems, by C. C. Chen and others. I wonder how you personally feel about that and... 

Renon and Prausnitz (8) recommend values of aa for various classes of mixtures. If these values are valid then Equation 5 has only two adjustable parameters per binary. The NRTL equation was used in this work. 

To test the NRTL equation for predicting VLE data for ternary mixtures, experimental data for the ternary mixtures and for the binary components of the mixtures are necessary. A literature survey showed that data were not readily available for any of the ternaries or for the two binaries ethanol-3-methyl-l-propanol and 3-methyl-l-butanol-water, and it was therefore necessary to obtain these data experimentally. 

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. 

An additional program took the energy parameters of the binary systems making up ternary mixtures and calculated the boiling point of the ternary and the equilibrium composition of the vapor phase. Comparison of the measured boiling point with the predicted boiling point for the same composition and pressure was used as a criterion of successful performance of the NRTL equation. 

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. 

The success of the NRTL equation in undergoing this test would suggest that it will be a powerful tool in the design of processes involving azeotropic or extractive distillation. The effect of the addition of a third... 

Work tire preceding problem for the NRTL equation. 

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