NRTL model

Whereas the Wilson model has been found to represent a wide variety of nonideal VLE, it caimot handle the case of partial immiscihility of the Hquid phase for this purpose a three-parameter relationship, the nonrandom, two-Hquid (NRTL) model was developed (20). 

There are many simple two-parameter equations for Hquid mixture constituents, including the Wilson (25), Margules (2,3,18), van Laar (3,26), nonrandom two-Hquid (NRTI.v) (27), and universal quasichemical (UNIQUAC) (28) equations. In the case of the NRTL model, one of the three adjustable parameters has been found to be relatively constant within some homologous series, so NRTL is essentially a two-parameter equation. The third parameter is usually treated as a constant which is set according to the type of chemical system (27). A third parameter for Wilson s equation has also been suggested for use with partially miscible systems (29,30,31). These equations all require experimental data to fit the adjustable constants. Simple equations of this type have the additional attraction of being useful for hand calculations. 

The parameter g,j is an energy parameter characteristic of the i-j interaction. The parameter an is related to the non-randomness in the mixture. The NRTL model contains three parameters which are independent of temperature and composition. However, experience has shown that for a large number of binary systems the parameter al2 varies from about 0.20 to 0.47. Typically, the value of 0.3 is set. 

Blanco et al. have also correlated the results with the van Laar, Wilson, NRTL and UNIQUAC activity coefficient models and found all of them able to describe the observed phase behavior. The value of the parameter ai2 in the NRTL model was set equal to 0.3. The estimated parameters were reported in Table 10 of the above reference. Using the data of Table 15.7 estimate the binary parameters in the Wislon, NRTL and UNIQUAC models. The objective function to be minimized is given by Equation 15.11. 

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. 

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. 

In the NRTL model, the local mole fractions Xj-j and xii of species j and i, respectively, in the immediate neighborhood of a central molecule of species i are related by... 

In addition to the experimental results of phase equilibria, the correlation with the widely known GE models was assigned to. It was indicated by many authors that SLE, LLE, and VLE data of ILs can be correlated by Wilson, NRTL, or UNIQUAC models [52,54,64,79,91-101,106,112,131,134]. For the LLE experimental data, the NRTL model is very convenient, especially for the SLE/LLE correlation with the same binary parameters of nonrandom two-liquid equation for mixtures of two components. For the binary systems with alcohols the UNIQUAC equation is more adequate [131]. For simplicity, the IL is treated as a single neutral component in these calculations. The results may be used for prediction in ternary systems or for interpolation purposes. In many systems it is difficult to obtain experimentally the equilibrium curve at very low solubilities of the IL in the solvent. Because this solubility is on the level of mole fraction 10 or 10 , sometimes only... 

The solute activity coefficients, pj, of the saturated solutions were correlated for many mixtures by the NRTL model describing the excess Gibbs energy [140]... 

Experimental studies were carried out to derive correlations for mass transfer coefficients, reaction kinetics, liquid holdup, and pressure drop for the packing MULTIPAK (35). Suitable correlations for ROMBOPAK 6M are taken from Refs. 90 and 196. The nonideal thermodynamic behavior of the investigated multicomponent system was described by the NRTL model for activity coefficients concerning nonidealities caused by the dimerisation (see Ref. 72). 

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. 

Reactive absorption processes occur mostly in aqueous systems, with both molecular and electrolyte species. These systems demonstrate substantially non-ideal behavior. The electrolyte components represent reaction products of absorbed gases or dissociation products of dissolved salts. There are two basic models applied for the description of electrolyte-containing mixtures, namely the Electrolyte NRTL model and the Pitzer model. The Electrolyte NRTL model [37-39] is able to estimate the activity coefficients for both ionic and molecular species in aqueous and mixed solvent electrolyte systems based on the binary pair parameters. The model reduces to the well-known NRTL model when electrolyte concentrations in the liquid phase approach zero [40]. 

The expression for the excess Gibbs energy is built up from the usual NRTL equation normalized by infinite dilution activity coefficients, the Pitzer-Debye-Hiickel expression and the Born equation. The first expression is used to represent the local interactions, whereas the second describes the contribution of the long-range ion-ion interactions. The Bom equation accounts for the Gibbs energy of the transfer of ionic species from the infinite dilution state in a mixed-solvent to a similar state in the aqueous phase [38, 39], In order to become applicable to reactive absorption, the Electrolyte NRTL model must be extended to multicomponent systems. The model parameters include pure component dielectric constants of non-aqueous solvents, Born radii of ionic species and NRTL interaction parameters (molecule-molecule, molecule-electrolyte and electrolyte-electrolyte pairs). 

Thermodynamic non-idealities are taken into account while calculating necessary physical properties such as densities, viscosities, and diffusion coefficients. In addition, non-ideal phase equilibrium behavior is accounted for. In this respect, the Elec-trolyte-NRTL model (see Section 9.4.1) is used and supplied with the relevant parameters from Ref. [50]. The mass transport properties of the packing are described via the correlations from Refs. [59, 61]. This allows the mass transfer coefficients, specific contact area, hold-up and pressure drop as functions of physical properties and hydrodynamic conditions inside the column to be determined. 

A limitation on the Wilson equation is that it is not applicable to systems having more than one liquid phase. The NRTL model, which is similar to the Wilson equation, may be used for systems forming two liquid phases. 

Table 1.7 Temperature-dependent parameters of the NRTL model...

Here, a, al2. and a21 are the binary parameters estimated from experimental vapor-liquid equilibrium data. The adjustable energy parameters, al2 and a2l, are usually assumed to be independent of composition and temperature. However, when the parameters are temperature dependent, prediction ability of the NRTL model enhances. Table 1.7 tabulates the temperature-dependent parameters of the NRTL model for some binary liquid mixtures. 

Figure 1.7. Gibbs energy of mixing for 1-propanol(1)-water(2) by the Aspen Plus simulator using the NRTL model.

Next, we specify the x, between 0 and 1, and estimate the total pressure P and yx from Eq. (1.193) to prepare the total pressure and equilibrium compositions shown in Table 1.10. In Figure 1.9, we can compare both the Tyx and Pyx diagrams obtained from Raoult s law and the NRTL model using the Aspen Plus simulator. As we see, ideal behavior does not represent the actual behavior of the acetone-water mixture, and hence we should take into account the nonideal behavior of the liquid phase by using an activity coefficient model. 

Figure 1.9. Phase equilibrium diagrams for acetone(1)-water(2) mixture estimated from the Raoult s law and the NRTL model...

Plot the Gibbs energy of mixing versus mole fraction of acetone for acetone(l)-water(2) mixture using the NRTL model at 1 atm and 50°C. 

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. 

According to the NRTL model, the activity coefficients can be expressed as ... 

First, we need a predictive activity coefficient model for electrolyte systems. The electrolyte NRTL model is correlative, and it requires extensive experimental data sets from which NRTL binary interaction parameters can be identified. The OLI electrolyte model, with its extensive parameter database, has been serving as a pseudo-predictive model. However, use of the OLI electrolyte model is limited to dilute aqueous electrolytes, its parameter database is not open to the public, and its electrolyte speciation is not supported by experiments. 

Second, we need an equation-of-state for electrolyte solutions. Equations-of-state are needed for modeling high-pressure applications with electrolyte solutions. Significant advances are being made in this area. Given that the electrolyte NRTL model has been widely applied for low-pressure applications, we are hopeful that, some day, there will be an equation-of-state for electrolytes that is compatible with the electrolyte NRTL activity coefficient model. 

The Electrolyte NRTL model " and the Extended UNIQUAC model" are examples of activity coefficient models derived by combining a Debye-Hiickel term with a local composition model. Equation of state models with electrostatic terms for... 

According to Chen et al. [9], the NRTL-SAC model is based on the derivation of the original NRTL model for polymers. From Equation (32), the activity coefficient is made up of two terms, combinatorial and residual. Like the UNIFAC model, the activity coefficients must be generated in order to obtain solubility. In the NRTL-SAC model, the combinatorial part is calculated by Equation (45) ... 

Interfacial tension MOSCED polarity parameter NRTL model parameter Volume fraction Volume fraction of dispersed phase (holdup)... 

As in Example 4, the EXTRACT block in the Aspen Plus process simulation program (version 12.1) is used to model this problem, but any of a number of process simulation programs such as mentioned earlier may be used for this purpose. The first task is to obtain an accurate fit of the liquid-liquid equilibrium (LLE) data with an appropriate model, realizing that liquid-liquid extraction simulations are very sensitive to the quality of the LLE data fit. The NRTL liquid activity-coefficient model [Eq. (15-27)] is utilized for this purpose since it can represent a wide range of LLE systems accurately. The regression of the NRTL binary interaction parameters is performed with the Aspen Plus Data Regression System (DRS) to ensure that the resulting parameters are consistent with the form of the NRTL model equations used within Aspen Plus. 

DATA The Hessian matrix of the Gibbs free energy [G] may be calculated with the nonrandom two liquid (NRTL) model. The NRTL parameters are... 

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