Non Random Two Liquids

Renon used the concept of local composition to develop a non-random, two-liquid (NRTL) three parameter (al2, tp, ti() equations given below (Prausnitz et al., 1986). 

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. 

The development of equations that successfully predict multicomponent phase equilibrium data from binary data with remarkable accuracy for engineering purposes not only improves the accuracy of tray-to-tray calculations but also lessens the amount of experimentation required to establish the phase equilibrium data. Such equations are the Wilson equation (13), the non-random two-liquid (NRTL) equation (14), and the local effective mole fractions (LEMF) equation (15, 16), a two-parameter version of the basically three-parameter NRTL equation. Larson and Tassios (17) showed that the Wilson and NRTL equations predict accurately ternary activity coefficients from binary data Hankin-son et al. (18) demonstrated that the Wilson equation predicts accurately... 

The Non-Random, Two Liquid Equation was used in an attempt to develop a method for predicting isobaric vapor-liquid equilibrium data for multicomponent systems of water and simple alcohols—i.e., ethanol, 1-propanol, 2-methyl-l-propanol (2-butanol), and 3-methyl-l-butanol (isoamyl alcohol). Methods were developed to obtain binary equilibrium data indirectly from boiling point measurements. The binary data were used in the Non-Random, Two Liquid Equation to predict vapor-liquid equilibrium data for the ternary mixtures, water-ethanol-l-propanol, water-ethanol-2-methyl-1-propanol, and water-ethanol-3-methyl-l-butanol. Equilibrium data for these systems are reported. 

The Wilson Equation and the Non-Random Two-Liquid (NRTL) Equation... 

The non-random, two-liquid (NRTL) equation proposed by Renon and Prausnitz (8) seems to predict successfully multicomponent (ternary) mixtures of alcohols and water. The alcohols studied in this work ethanol, 1-propanol, 2-methyl-l-propanol, and 3-methyl-l-butanol, which occur from the fermentation of sugar solutions, show highly non-ideal behavior in aqueous solutions and present a severe test of the effectiveness of any prediction method. 

Another attempt to relate the results from the use of a solvatochromic probe (Phenol Blue (66)) to the inherent properties of solvent mixtures was made by Phillips and Brennecke122. They obtained the interaction energies (required for the application of the non-random two-liquid (NRTL) approach) of 66 with each of the solvent components from its solubility in the neat solvent. The mixtures studied contained cyclohexane as one component and acetone, triethylamine, ethyl butyrate, cyclohexanone, toluene and acetophenone as the other. Then the local compositions deduced from the solvatochromism of 66 were compared with those calculated by the NRTL equation and reasonable agreement was found. 

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... 

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 ... 

PR=Peng-Robinson PRSV=Peng-Robinson Stryjek-Vera GS=Grayson-Streed ZJ=Zudkevitch Jolfee CS=Chao-Seader NRTL=Non-Random-Two-Liquid... 

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