Model UNIQUAC equation

An adequate prediction of multicomponent vapor-liquid equilibria requires an accurate description of the phase equilibria for the binary systems. We have reduced a large body of binary data including a variety of systems containing, for example, alcohols, ethers, ketones, organic acids, water, and hydrocarbons with the UNIQUAC equation. Experience has shown it to do as well as any of the other common models. V7hen all types of mixtures are considered, including partially miscible systems, the... 

Unfortunately, good binary data are often not available, and no model, including the modified UNIQUAC equation, is entirely adequate. Therefore, we require a calculation method which allows utilization of some ternary data in the parameter estimation such that the ternary system is well represented. A method toward that end is described in the next section. 

These models are semiempirical and are based on the concept that intermolecular forces will cause nonrandom arrangement of molecules in the mixture. The models account for the arrangement of molecules of different sizes and the preferred orientation of molecules. In each case, the models are fitted to experimental binary vapor-liquid equilibrium data. This gives binary interaction parameters that can be used to predict multicomponent vapor-liquid equilibrium. In the case of the UNIQUAC equation, if experimentally determined vapor-liquid equilibrium data are not available, the Universal Quasi-chemical Functional Group Activity Coefficients (UNIFAC) method can be used to estimate UNIQUAC parameters from the molecular structures of the components in the mixture3. 

A model is needed to calculate liquid-liquid equilibrium for the activity coefficient from Equation 4.67. Both the NRTL and UNIQUAC equations can be used to predict liquid-liquid equilibrium. Note that the Wilson equation is not applicable to liquid-liquid equilibrium and, therefore, also not applicable to vapor-liquid-liquid equilibrium. Parameters from the NRTL and UNIQUAC equations can be correlated from vapor-liquid equilibrium data6 or liquid-liquid equilibrium data9,10. The UNIFAC method can be used to predict liquid-liquid equilibrium from the molecular structures of the components in the mixture3. 

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 methods most generally used for the calculation of activity coefficients at intermediate pressures are the Wilson (1964) and UNIQUAC (Abrams and Prausnitz, 1975) equations. Wilson s equation was used by Sato et al. (1985) to predict the composition of fhe condensate gas stripped from a packed bed fermenter at 30°C, whilst Beck and Bauer (1989) used the UNIQUAC equation, with temperature-dependent parameters given by Kolbe and Gmehling (1985), for their model of an anaerobic gas-solid fluidized bed fermenter at 36°C. In this case it was necessary to go beyond the temperature range of fhe source data down to 16°C in order to predict the composition of the fluidizing gas leaving the condenser. 

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 UNIQUAC equation and the UNIFAC method are models of greater complexity and are treated in App. D. 

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 models which need experimental data at various temperatures, pressures, and compositions of the mixture, such as UNIQUAC equation. 

For most LLE applications, the effect of pressure on the y can be ignored, and Eq. (4-354) then constitutes a set of N equations relating equilibrium compositions to one another and to temperature. For a given temperature, solution of these equations requires a single expression for the composition dependence of suitable for both liquid phases. Not all expressions for G suffice, even in principle, because some cannot represent liquid/liquid phase splitting. The UNIQUAC equation is suitable, and therefore prediction is possible by UNIFAC models. A special table of parameters for LLE calculations is given by Magnussen et al. [Ind. Eng. Chem. Process Des. Dev. 20 331-339 (1981)]. 

The UNIQUAC equation (Abrams and Prausnitz, 1975) is based on the two-liquid model in which the excess Gibbs energy is assumed to result from differences in molecular sizes and structures and from the energy of interaction between the molecules. 

Highly promising models were obtained by using so-called G models for cubic equations of state. Apart from the description or precalculation of the behavior of highly polar systems, these models allow supercritical components to be taken into account. A further advantage of these models is that, in addition to phase equilibria, other important quantities such as densities and caloric data can be calculated. The required G values can be obtained either by fitting the parameters of proven G models (e.g., Wilson, NRTL, or UNIQUAC equation) to experimental phase equilibrium data, or with the aid of group-contribution methods such as UNIFAC. 

Later, further g -models based on the local composition concept were published, such as the NRTL [14] and the UNIQUAC [15] equation, which also allow the prediction of the activity coefficients of multicomponent systems using only binary parameters. In the case of the UNIQUAC equation the activity coefficient is calculated by a combinatorial and a residual part. While the temperature-independent combinatorial part takes into account the size and the shape of the molecule, the interactions between the different compounds are considered by the residual part. In contrast to the Wilson equation the NRTL und UNIQUAC equation can also be used for the calculation of LLE. 

The analytical expressions of the activity coefficients for binary and multi-component systems for the three -models are given in Table 5.6. While for the Wilson and the UNIQUAC model two binary interaction parameters (AXi2,AL2] resp. Aui2, Au2i) are used, in the case of the NRTL equation besides the two binary interaction parameters (Agn, Ag2i) additionally a nonrandomness factor au is required for a binary system, which is often not fitted but set to a defined value. For the Wilson equation additionally molar volumes and for the UNIQUAC equation relative van der Waals volumes and surface areas are required. These values are easily available. 

For a large number of binary systems the required binary -model parameters for the Wilson, NRTL, and UNIQUAC equation and the results of the consistency tests can be found in the VLE Data Collection of the DECHEMA Chemistry Data Series published by Gmehling et al [6]. One example page is shown in Figure 5.30. It shows the VLE data for the system ethanol and water at 70 ""C published by Mertl [8]. On every page of this data compilation the reader will find the system, the reference, the Antoine constants with the range of validity, the experimental... 

VLE data, the results of two thermodynamic consistency tests, and the parameters of different -models, such as the Wilson, NRTL, and UNIQUAC equation. Additionally, the parameters of the Margules [28] and van Laar [29] equation are listed. Furthermore, the calculated results for the different models are given. For the model which shows the lowest mean deviation in vapor phase mole fraction the results are additionally shown in graphical form together with the experimental data and the calculated activity coefficients at infinite dilution. In the appendix of the data compilation the reader will find the additionally required pure component data, such as the molar volumes for the Wilson equation, the relative van der Waals properties for the UNIQUAC equation, and the parameters of the dimerization constants for carboxylic acids. Usually, the Antoine parameter A is adjusted to A to start from the vapor pressure data given by the authors, and to use the -model parameters only to describe the deviation from Raoult s law. Since in this data compilation only VLE data up to 5000 mm Hg are presented, ideal vapor phase behavior is assumed when fitting the parameters. For systems with carboxylic acids the association model is used to describe the deviation from ideal vapor phase behavior. 

Based on the UNIQUAC equation, an electrolyte model has been developed by Li et al [21], called LIQUAC. 

For the SR part in the LIQUAC model, the UNIQUAC equation is used (see Chapter 5), where the relative van der Waals surface areas and volumes of the ions were fixed to one. This means that the activity coefficients are split into a combinatorial (C) and a residual part (R) ... 

Here, a, a 2, and fl2i are the binary adjustable parameters estimated from experimental vapor-liquid equilibrium data. The adjustable energy parameters, a 2 and 21. are independent of composition and temperature. However, when the parameters are temperature-dependent, prediction ability of the NRTL model enhances. The Wilson, NRTL, and UNIQUAC equations are readily generalized to multicomponent mixtures. 

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