Non-Random Two-Liquid Model

NRTL (non-random two-liquids) model developed by Renon and Prausnitz (1968) is an extension of the local composition concept that accounts for the non-randomness of interaetions. The following expression for is obtained ... 

ME 2-methoxyethanol M, Molar mass of i-th component N Avogadro number NRTL Non Random Two Liquids model... 

In order to know the activity coefficients of the binary systems of TEA + 2-ethyl-l-hexanol and NEA+2-ethyl-l-hexanol, the VLE data are also needed. These experimental data are determined using a method based on gas chromatographic technique described previously (Ghannadzadeh, 1993a). The experimental activity coefficients and VLE data can be correlated to several eqtrilibritrm methods such as universal qira-si-chemical (UNIQUAC) and NTRL models. Eqtrilibrium models, such as the UNI-QUAC model (Renon and Prausnitz, 1968) and the non-random two-liquid model (NRTL) (Abrams and Prausnitz, 1975) have been successfully applied for the correlation of several liquid-liquid and vapor-liquid systems. These models depend on optimized interaction parameters between each pair of components in the systems, which can be obtained by experiments. 

Gas chromatography Liquid liquid equilibria Multi-component system Non-random two-liquid model Objective function Universal quasi-chemical model Vapor-liquid equilibrium... 

This model, which yields excellent results for polar and non-polar molecular liquids, is especially well suited for the study of liquid/ vapor equilibrium and the equilibrium between two liquids that are not completely miscible. Regardless of the number of components of the solution, the application of this model only requires the knowledge of two adjustment parameters per binary system, which can be deduced from the solution. The model is so widely applicable that it actually contains a number of previously classic models such as the models put forward by Van Laar, Wilson, Renon et al. (the NRTL - Non Random Two Liquids -model), Scatchard and Hildebrand, Flory and Huggins as special cases. In addition, it lends a physical meaning to the first three coefficients P, 5 and , in the Margules expansion (equation [2.1]). 

The non-random two-liquid segment activity coefficient model is a recent development of Chen and Song at Aspen Technology, Inc., [1], It is derived from the polymer NRTL model of Chen [26], which in turn is developed from the original NRTL model of Renon and Prausznitz [27]. The NRTL-SAC model is proposed in support of pharmaceutical and fine chemicals process and product design, for the qualitative tasks of solvent selection and the first approximation of phase equilibrium behavior in vapour liquid and liquid systems, where dissolved or solid phase pharmaceutical solutes are present. The application of NRTL-SAC is demonstrated here with a case study on the active pharmaceutical intermediate Cimetidine, and the design of a suitable crystallization process. 

Chen, C.-C.., Song, Y., 2004, Solubility Modeling with a Non-Random Two-Liquid Segment Activity Coefficient Model, Ind. Eng. Chem. Res., 43, 8354-... 

About the same time Beutier and Renon (11) also proposed a similar model for the representation of the equilibria in aqueous solutions of weak electrolytes. The vapor was assumed to be an ideal gas and < >a was set equal to unity. Pitzer s method was used for the estimation of the activity coefficients, but, in contrast to Edwards et al. (j)), two ternary parameters in the activity coefficient expression were employed. These were obtained from data on the two-solute systems It was found that the equilibria in the systems NH3+ H2S+H20, NH3+C02+H20 and NH3+S02+H20 could be represented very well up to high concentrations of the ionic species. However, the model was unreliable at high concentrations of undissociated ammonia. Edwards et al. (1 2) have recently proposed a new expression for the representation of the activity coefficients in the NH3+H20 system, over the complete concentration range from pure water to pure NH3. it appears that this area will assume increasing importance and that one must be able to represent activity coefficients in the region of high concentrations of molecular species as well as in dilute solutions. Cruz and Renon (13) have proposed an expression which combines the equations for electrolytes with the non-random two-liquid (NRTL) model for non-electrolytes in order to represent the complete composition range. In a later publication, Cruz and Renon (J4J, this model was applied to the acetic acid-water system. 

The LCM is a semi-theoretical model with a minimum number of adjustable parameters and is based on the Non-Random Two Liquid (NRTL) model for nonelectrolytes (20). The LCM does not have the inherent drawbacks of virial-expansion type equations as the modified Pitzer, and it proved to be more accurate than the Bromley method. Some advantages of the LCM are that the binary parameters are well defined, have weak temperature dependence, and can be regressed from various thermodynamic data sources. Additionally, the LCM does not require ion-pair equilibria to correct for activity coefficient prediction at higher ionic strengths. Thus, the LCM avoids defining, and ultimately solving, ion-pair activity coefficients and equilibrium expressions necessary in the Davies technique. Overall, the LCM appears to be the most suitable activity coefficient technique for aqueous solutions used in FGD hence, a data base and methods to use the LCM were developed. 

Modern theoretical developments in the molecular thermodynamics of liquid-solution behavior are based on the concept of local composition. Within a liquid solution, local compositions, different from the overall mixture composition, are presumed to account for the short-range order and nonrandom molecular orientations that result from differences in molecular size and intermolecular forces. The concept was introduced by G. M. Wilson in 1964 with the publication of a model of solution behavior since known as the Wilson equation. The success of this equation in the correlation of VLE data prompted the development of alternative local-composition models, most notably the NRTL (Non-Random-Two Liquid) equation of Renon and Prausnitz and the UNIQUAC (UNIversal QUAsi-Chemical) equation of Abrams and Prausnitz. A further significant development, based on the UNIQUAC equation, is the UNIFAC method,tt in which activity coefficients are calculated from contributions of the various groups making up the molecules of a solution. 

In the Non-Random-Two-Liquid (NRTL) model of Renon and Prausnitz (1968), the molar excess Gibbs free energy for a binary mixture is given as... 

Figure 6.10 shows activity coefficient derivatives over the whole composition range for experiment from three correlations and the Verlet method. A procedure for experimental data analysis was described by Wooley and O Connell (1991), in which one extracts the isothermal compressibility, partial molar volumes, and activity coefficient derivatives from experimental data. The activity coefficient derivatives are obtained by fitting mixture vapor-liquid equilibrium data to obtain parameters for at least two different models. Wooley and O Connell employed the Wilson, non-random, two liquid (NRTL) and modified Margules (mM) models. Partial molar volumes are obtained from correlations of mixture densities (Handa and Benson 1979). Isothermal compressibilities are either taken from measurements or estimated with... 

Ammonia is removed by a IM H2SO4 water solution scrubber the liquid solution entering from the top of the tower (a SCDS column settled as packed column mass transfer simulation model) is continuously fed by a make-up quantity corresponding to the amount needed for the ammonia removal. At the bottom of the column gaseous ammonia enters at T = 95°C, it dissolves into the acid solution, diffuses and rapidly reacts with the H+ ions via ammonia protonation following thermodynamics of electrolyte non-random two liquid (Electrolyte NRTL) approach. 

Nonelectrolyte G mcxlels only account for the short-range interaction among non-charged molecules (—One widely used G model is the Non-Random-Two-Liquid (NRTL) theory developed in 1968. To extend this to electrolyte solutions, it was combined with either the DH or the MSA theory to explicitly account for the Coulomb forces among the ions. Examples for electrolyte models are the electrolyte NRTL (eNRTL) [4] or the Pitzer model [5] which both include the Debye-Hiickel theory. Nasirzadeh et al. [6] used a MSA-NRTL model [7] (combination of NRTL with MSA) as well as an extended Pitzer model of Archer [8] which are excellent models for the description of activity coefficients in electrolyte solutions. Examples for electrolyte G models which were applied to solutions with more than one solvent or more than one solute are a modified Pitzer approach by Ye et al. [9] or the MSA-NRTL by Papaiconomou et al. [7]. However, both groups applied ternary mixture parameters to correlate activity coefficients. Salimi et al. [10] defined concentration-dependent and salt-dependent ion parameters which allows for correlations only but not for predictions or extrapolations. 

In eq 5.71, i) is a constant that depends on the particular equation of state used and Gm is an excess Gibbs function of mixing obtained from an activity coefficient model. Activity coefficients are usually obtained from measurements of (vapour-f liquid) equilibria at a pressure relatively low compared with the requirement of eq 5.67 for which p- ao the activity coefficients are tabulated, for example, those in the DECHEMA Chemistry Data Series. This distinction in pressure is particularly important because the excess molar Gibbs function of mixing, obtained from experiment and estimated from an equation of state, depends on pressure d(G /7 r)/d/)<0.002MPa for (methanol-f benzene) at a temperature of 373 K. Equation 5.71 does not satisfy the quadratic composition dependence required by the boundary condition of eq 5.3. However, equations 5.70 and 5.71 form the mixing rules that have been used to describe the (vapour + liquid) equilibria of non-ideal systems, such as (propanone + water), successfully in this particular case the three-parameter Non-Random Two Liquid (known by the acronym NRTL) activity-coefficient model was used for G and the value depends significantly on temperature to the extent that the model, while useful for correlation of data, cannot be used to extrapolate reliably to other temperatures. 

J A Note on Application of Non-random Two-liquid (NRTL) Model... 

There are various liquid activity models available including Margules, van Laar, Wilson, non-random two-liquid (NRTL), and universal quasi-chemical (UNIQUAC) models. Mixing rules are used for mixtures to combine pure component parameters. 

Select a new case in Hysys. For Components, select ethanol and water for Fluid Package, select Non-Random Two Liquid (activity coefficient model), NRTL, and then enter the simulation environment. From the object palette, select Mixer and place it in the PFD area. Create two in let streams and connect one exit stream. Click on stream 1 and enter 25°C for temperature, 5 atm for pressure, and 100 kmol/h for molar flow rate. In the composition page enter the value 0.2 for ethanol and 0.8 for water. Click on stream S2 and enter 25°C for temperature and 5 atm for pressure to ensure that both the ethanol and water are in the liquid phase, and 100 kmol/h for molar flow rate. In the composition page, enter 0.4 for ethanol and 0.6 mole fraction for water. To display the result below the process flow sheet, right click on each stream and select the show table, double click on each table and click on Add Variable, select the component mole fraction and click on Add Variable for both ethanol and water. Remove units and label for stream 2 and remove labels for stream 3. Results should appear like that shown in Figure 3.2. 

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