UNIQUAC-model

Using the concepts which we have introduced, we shall now present one of the most popular models of solution the UNIQUAC model. 

The UNIQUAC (Universal Quasi-Chemical) model was introduced by Abrams and Prausnitz (1975), using Guggenheim s quasi-chemical model and applying the concepts of conformation with Staverman s relation and Wilson s local-composition model. 

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 states will be characterized by the local areic fractions  

as configuration variables, we can choose a value belonging to each of the two pairs dp or, on the one hand, and or 0 on the other. 

---

In this monograph we use for g the UNIQUAC model of Abrams (1975) as slightly modified by Anderson (1978)... 

TEMPERATURE T(K) AND LIQUID COMPOSITION X, USING THE UNIQUAC MODEL. 

The most recendy developed model is called UNIQUAC (21). Comparisons of measured VLE and predicted values from the Van Laar, Wilson, NRTL, and UNIQUAC models, as well as an older model, are available (3,22). Thousands of comparisons have been made, and Reference 3, which covers the Dortmund Data Base, available for purchase and use with standard computers, should be consulted by anyone considering the measurement or prediction of VLE. The predictive VLE models can be accommodated to multicomponent systems through the use of certain combining rules. These rules require the determination of parameters for all possible binary pairs in the multicomponent mixture. It is possible to use more than one model in determining binary pair data for a given mixture (23). 

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. 

Chapter 18 - The determination region of solubility of methanol with gasoline of high aromatic content was investigated experimentally at temperature of 288.2 K. A type 1 liquid-liquid phase diagram was obtained for this ternary system. These results were correlated simultaneously by the UNIQUAC model. By application of this model and the experimental data the values of the interaction parameters between each pair of components in the system were determined. This revealed that the root mean square deviation (RMSD) between the observed and calculated mole percents was 3.57% for methylcyclohexane + methanol + ethylbenzene. The mutual solubility of methylcyclohexane and ethylbenzene was also demostrated by the addition of methanol at 288.2 K. 

Keywords liquid-liquid equilibria phase equilibria plait point ternary system UNIQUAC model. 

Here y,1 and y,2 are the corresponding activity coefficients of component i in phase 1 and 2, Xj1, and x,2 are the mole fraction of components i in the system and in phase 1 and 2 respectively. The interaction parameters between methylcyclohexane, methanol and ethyl benzene are used to estimate the activity coefficients from the UNIQUAC groups. Eqs. (1) and (2) are solved for the mole fraction (x) of component i in the two liquid phase.The UNIQUAC model (universal quasi -chemical model) is given by Abrams and prausnitz [8] as... 

The UNIQUAC model was successfully used to correlate the experimental liquid-liquid equilibria data. As it can be seen from figure 1, the predicted tie lines (dashed lines) are in good agreement with the experimental data (solid lines). In other words, the UNIQUAC equations adequately fit the experimental data for this multi-component system. 

Moreover, the objective function obtained by minimizing the square of the difference between the mole fractions calculated by UNIQUAC model and the experimental data. Furthermore, he UNIQUAC structural parameters r and q were carried out from group contribution data that has been previously reported [14-15], The values of r and q used in the UNIQUAC equation are presented in table 4. The goodness of fit, between the observed and calculated mole fractions, was calculated in terms RMSD [1], The RMSD values were calculated according to the equation of percentage root mean square deviations (RMSD%) ... 

The optimum UNIQUAC interaction parameters between methyl cyclohexane, methanol and ethylbenzene were determined using the experimental liquid-liquid data. The average RMSD value between the observed and calculated mole percents with a reasonable error for these system were methylcyclohexane + methanol + ethylbenzene, in the UNIQUAC model. 

First a database of solute-solvent properties are created in SoluCalc. The database needs the melting point, the enthalpy of fusion and the Hildebrand solubility parameter of the solute (Cimetidine) and the solvents for which solubility data is available. Using the available data, SoluCalc first prepares a list of the most sensitive group interactions and fits sequentially, the solubility data for the minimum set of group interaction parameters that best represent the total data set. For a small set of solvents, the fitted values from SoluCalc are shown in Table 9. It can be noted that while the correlation is very good, the local model is more like a UNIQUAC model than a group contribution model... 

In the second case, where LLE are lacking, VLE data are used to fit the parameters in the UNIQUAC model. These parameters, for the three binaries, were obtained from the literature in which VLE data were given at the following temperatures ... 

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... 

Binary interaction parameters for NRTL and UNIQUAC models... 

Nitric acid is a strong electrolyte. Therefore, the solubilities of nitrogen oxides in water given in Ref. 191 and based on Henry s law are utilized and further corrected by using the method of van Krevelen and Hofhjzer (77) for electrolyte solutions. The chemical equilibrium is calculated in terms of liquid-phase activities. The local composition model of Engels (192), based on the UNIQUAC model, is used for the calculation of vapor pressures and activity coefficients of water and nitric acid. Multicomponent diffusion coefficients in the liquid phase are corrected for the nonideality, as suggested in Ref. 57. 

Basically, DESIGNER can use different physical property packages that are easy to interchange with commercial flowsheet simulators. For the case considered, the vapor-liquid equilibrium description is based on the UNIQUAC model. The liquid-phase binary diffusivities are determined using the method of Tyn and Calus (see Ref. 72) for the diluted mixtures, corrected by the Vignes equation (57), to account for finite concentrations. The vapor-phase diffusion coefficients are assumed constant. The reaction kinetics parameters taken from Ref. 202 are implemented directly in the DESIGNER code. 

For Tasks 1 and 3 two time intervals are used. For Task 2 only one time interval is used. Within each interval the reflux ratio, the solvent feed rate and the length of the interval are optimised. Vapour liquid equilibrium is calculated using UNIQUAC model. A number of cases were studied for different amount of initial feed charge (Bo) to the reboiler. For each case, the optimal reflux and solvent feed profiles for each Task, percentage of Acetone and solvent recovered and the overall profit of the operation are shown in Table 10.10. 

Inside the reactive zone, chemical and phase equilibrium occur simultaneously. The composition of phases can be found by Gibbs free-energy minimization. The UNIQUAC model is adopted for phase equilibrium, for which interaction parameters are available, except the binary fatty-ester/water handled by UNIFAC-Dortmund. 

Table 8.6 Surface (q) and volume (r) parameters for the UNIQUAC model. ...

The pressure range of about 60-360 bar and temperature range from 35-70 °C are involved. Table 3 reports the results of the solubility calculations with 18 selected models. An important point must be emphasized, the Wong-Sandler mixing rule coupled with the UNIQUAC model generated a serious instability such that it was impossible to converge. Table 4 illustrates the variation of solid solubility and mixture density for a typical binary mixture. 

We can estimate the activity coefficients by using the excess Gibbs energy models. Based on the local composition concept, the Wilson, NRTL, and UNIQUAC models for excess Gibbs energy provide relations for activity coefficient... 

The Oishi-Prausnitz model cannot be defined strictly as a lattice model. The combinatorial and residual terms in the original UNIFAC and UNIQUAC models can be derived from lattice statistics arguments similar to those used in deriving the other models discussed in this section. On the other hand, the free volume contribution to the Oishi-Prausnitz model is derived from the Flory equation of state discussed in the next section. Thus, the Oishi-Prausnitz model is a hybrid of the lattice-fluid and free volume approaches. 

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... 

The phase diagrams shown in Figures 1 were calculated with the Extended UNIQUAC model,and the experimental data marked with circles in the diagrams come from various sources. 

It is difficult to fit data with the local composition models due to their complex logarithmic forms. However, they are readily generalizable to multicomponent systems. Smith, van Ness, and Abbott and Prausnitz, Lichtenthaler, and Gomes de Azevedo present the Wilson and UNIQUAC models extended for multi-component solutions. They both employ the constants from binary data. However, the constants are not unique in the sense that valid, but different constants may be obtained from different sets of data. Wilson s equations cannot be employed for immiscible solutions, but the UNIQUAC model may be used to describe such solutions. However, Wilson s equations are good for polar or associating compounds. A compilation of Wilson parameters can be found by Hirata, Ohe, and Nagahama. ... 

Huron and Vidal showed that equating the infinite pressure Gibbs energy of mixing to that of an activity model like the NRTL or UNIQUAC models provided a mixing rule that was sufficiently flexible to describe very complex phase behavior. With this modification, simple cubic equations like Soave s could be applied to nearly any kind of mixture at any conditions, including supercritical conditions. The Huron-Vidal mixing rule combined with NRTL activity model is illustrated below. 

---