NRTL equation

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. 

Another way to obtain HENRY S constant H of undissociated acid is from high concentration vapor-liquid equilibria where dissociation is negligible. Using NRTL equation for the representation of the data of BROWN and EWALD (6) at high concentration in acetic acid (10 2 < x < 1), he finds the limiting activity coefficient of undissociated acid at 100°C... 

CRUZ (7) equation for gE of binary electrolyte solution which incorporates a DEBYE - HUCKEL term, a BORN - DEBYE - MAC. AULAY contribution for electric work, and NRTL equation, can be used to represent the vapor-liquid equilibria of volatile electrolyte in the whole range of concentration. 

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. 

Nagata, 1. et al.. Ternary liquid-liquid equilibria and their representation by modified NRTL equations, /. Thermochim. Acta, 45, 153,1981. 

Belveze, L.S., Brennecke, J.F., and Stadtherr, M.A., Modeling of activity coefficients of aqueous solutions of quaternary ammonium salts with the electrolyte-NRTL equation, Ind. Eng. Chem. Res., 43, 815, 2004. 

Experimental data on only 26 quaternary systems were found by Sorensen and Arlt (1979), and none of more complex systems, although a few scattered measurements do appear in the literature. Graphical representation of quaternary systems is possible but awkward, so that their behavior usually is analyzed with equations. To a limited degree of accuracy, the phase behavior of complex mixtures can be predicted from measurements on binary mixtures, and considerably better when some ternary measurements also are available. The data are correlated as activity coefficients by means of the UNIQUAC or NRTL equations. The basic principle of application is that at equilibrium the activity of each component is the same in both phases. In terms of activity coefficients this... 

NRTL equation There is a pair of parameters gjk and gkj for each pair of substances in the mixture for three substances, there are three pairs. The other terms of the equations are related to the basic ones by... 

As a typical example from industrial practice we consider the simulation of a process with the reaction of methylphosphinic acid and butanol to methylphosphinic acid butyl ester and water, which was modeled by Gordana Hofmann-Jovic at InfraServ Knapsack [C28]. Because of the lack of experimental data for the binary systems with phosphorous compounds, COSMO-RS was used for the prediction of the binary activity coefficients. Then the results were fitted by an NRTL equation and the entire process was modeled by a commercial process simulator. The resulting phase diagrams were in close agreement with experimental measurements obtained later (Fig. 8.2). 

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