The UNIFAC model

Models known as group models have been created, based on the following observation the number of systems - even just the number of binary systems - is extremely high, and new ones are being discovered all 

The UNIFAC model (UNIQUAC Functional Group Activity Coefficient), which was put forward by Fredenslund, Jones and Prausnitz in 1975, is a group model where the idea is to use the existing data on equilibrium states to predict the properties of systems for which no experimental data are available. Thus, it is an entirely predictive model which, unlike the models discussed above, does not require us to determine parameters by calibrating the experimental results found for partial systems 

The group-model method requires us to work back from experimental results to determine parameters which are characteristic of the interactions between pairs of structural groups, and then inject that knowledge back into models to obtain the properties of new systems containing those same structural groups. 

The idea underlying the UNIT AC model is the consideration that a solution of molecules /, j, etc. behaves like a solution of the functional groups k, m, etc. making up those molecules. 

For example, a mixture of linear alkane molecules involves three types of interactions CH3-CH3, CH3-CH2 and CH2-CH2. The properties of any given mixture of alkanes must be able to be deduced from the properties linked to the three types of interactions at play. Of course, this whole construct is founded on a h5qjothesis which stipulates that the interactions between groups do not depend on the environment of these groups in their respective molecules. Yet, indubitably, it is this hypothesis which is the main source of errors that become apparent when the calculation results are contrasted with experimental data. For example, we can see that, in a complex system, the results given by the wholesale use of UNIFAC are much poorer than those given by the use of the UNIQUAC model. For this reason, the UNIFAC model is not used wholesale to model a complex system instead, essentially, it is used to obtain the necessary data on binary systems for which no experimental data are available. These data are then fed back into a UNIQUAC-t5q)e model (see section 3.5). 

The UNIFAC model originally developed by Fredenslund et al. [FRE 75] divides the activity coefficient into two parts  

A particular model, the Dortmund modified UNIFAC model [SKJ 79], is still being revised and its application domain extended. Data from the 

Other studies [OZD 99, NIN 00, GRO 03] show the relevance of UNIFAC models for the prediction of the aw in agri-food industries or in biological systems. However, sugars or polyols are not the only solutes that can reduce the Uw of a medium, in the same manner that the a is not the only property providing stability to food products. Electrolytes and the pH are also involved. 

Appendix 1 gives the equations for calculating the combinational part and the residual part of the activity coefficient for the UNIFAC equation modified by Larsen et al. [LAR 87]. The volume (q) and surface groups (qi) 

Several group-contribution models have been proposed through the years (Pierotti et al, 1959 Derr and Deal, 1969 Fredenslund et al, 1975 etc.). The most recent and promising one, is the UNIFAC model of Fredenslund et al. 

This model is based on the UNIQUAC equation and uses the same expression for the activity coefficient, Eq. 13.12.6. 

The combinatorial part of the activity coefficient is also the same, Eq. 

Only the pure component properties r, and qj enter into this equation and are calculated as the sum of the group volume and area parameters, and (see Section 13.12.4 for the method of evaluating these properties)  

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Chen, F., Holten-Andersen, J., Tyle, P. (1993) New developments of the UNIFAC model for environmental application. Chemosphere 26, 1225-1354. 

In contrast to the NRTL-SAC model, the UNIFAC model developed by Fredenslund et. al. [29] divides each molecule into a set of functional groups that interact with each other on a binaiy basis and whose interactions are combined together to describe the global liquid phase interaction between molecules. Because the segments in UNIFAC are based on functional groups it is possible to model a system provided that all of the molecular structures are known. The problem with pharmaceutical sized molecules is that existing UNIFAC parameter tables do not contain many of the group interaction parameters that are necessary, and even when they do, the interactions are fitted to a database of chemicals that are much smaller and simpler than pharmaceuticals, and typically fail to represent them adequately. 

Kuramochi, H., Noritomi, H., Hoshino, D., and Nagahama, K. Measurements of solubilities of two amino acids in water and prediction by the UNIFAC model, Biotechnol Prog., 12(3) 371-379, 1996. 

Chen, F., J. Holten-Andersen, and H. Tyle, New Developments of the UNIFAC Model for Environmental Application. Chemosphere, 1993 26, 1325-1354. 

The method can be applied for saturated fatty acids, unsaturated fatty acids, fatty esters, fatty alcohols and acyl-glycerols. The regression is based on 1200 data points. The absolute deviation in predicting vapor pressure is 6.82%. Another advantage of Eq. (14.1) is the capability of predicting the VLE of mixtures of fatty acids and esters by using the UNIFAC model for liquid activity. The comparison with experimental data shows good accuracy not achieved by other methods [40]. 

As it was pointed out by Chen et al. [22] the calculation of solubility data requires a proper estimation of sublimation pressures. The data were correlated using the PR EOS with classical mixing rules and the UNIFAC model with previously determined anu, parameters. 

Finally, we must select appropriate methods of estimating thermodynamic properties. lime (op. cit.) used the SRK equation of state to model this column, whereas Klemola and lime (op. cit.) had earlier used the UNIFAC model for liquid-phase activity coefficients, the Antoine equation for vapor pressures, and the SRK equation for vapor-phase fugacities only. For this exercise we used the Peng-Robinson equation of state. Computed product compositions and flow rates are shown in the table below. 

From the predictive category, we bring some examples of the application of the UNIFAC model. In one study, this model has been used to predict the solubility of naphtalene, anthracene, and phenanthrene in various solvents and their mixtures [8], They showed the applicability of the UNIFAC model in prediction of the phase behavior of solutes in solvents. There have been efforts to make the UNIFAC model more robust and powerful in the prediction of phase behaviors [14], In one study, the solubility of buspirone-hydrochloride in isopropyl alcohol was measured and evaluated by the modified UNIFAC model [15]. It was concluded that for highly soluble pharmaceutics, the modified form of the UNIFAC model was not suitable. In another study, the solubility of some chemical species in water and some organic solvents was predicted by the UNIFAC model [16]. For some unknown functional groups, they used other known groups which had chemical structures that were similar to unknown ones. 

In conclusion, it was stated that the UNIFAC model is not a proper model for use in crystallization and related processes. The UNIFAC model also has been utilized to predict the solubility of some aromatic components as well as long-chain hydrocarbons [17]. The results showed that the predictions for the linear hydrocarbons are not as good as the ones for the aromatics. 

In which yi is the activity coefficient of component i in the solution, yf is the combinatorial part and ytR is the residual part. Up to this point, all of the group contribution and activity coefficient methods (i.e. NRTL-SAC) have been the same, but the methods in which the activities have been calculated are different. In the UNIFAC model, the combinatorial part for component i is found from the following equation [8] ... 

Figure 3. The algorithm of converging to the solubility of a ternary system using the UNIFAC model.

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) ... 

It is worth noting that the main difference in Figures 3 and 4 is the use of parameter estimation method for the calculation of the NRTL-SAC parameters, while for the UNIFAC model, the calculation is straightforward. Once the parameters (here, the segment numbers) are found, then they could be used for validation against other experimental data. 

From Figure 6, the UNIFAC model has the capability of predicting the system of ethanol-water, perfectly. However, this is not the case for the systems using ethylene glycol-water and... 

Two modified versions of the UNIFAC model, based on temperature-dependent parameters, have come into use. Not only do they provide a wide temperature range of applicability, but also they allow correlation of various kinds of property data, including phase equilibria, infinite dilution activity coefficients, and excess properties. The most recent revision and extension of the modified UNIFAC (Dortmund) model is provided by Gmehling et al. [Ind. Eng. Chem. Res. 41 1678-1688 (2002)]. An extended UNIFAC model called KT-UNI-FAC is described in detail by Kang et al. [Ind. Eng. Chem. Res. 41 3260-3273 (2003)]. Both papers contain extensive literature citations. 

The UNIFAC model has also been combined with the predictive Soave-Redlich-Kwong (PSRK) equation of state. The procedure is most completely described (with background literature citations) by Horstmann et al. [Fluid Phase Equilibria 227 157-164 (2005)]. 

Activity models have also been used to compute incipient hydrate conditions in the presence of polymers. Englezos and Hall presented a predictive model for the calculation of the incipient hydrate formation conditions in a hydrocarbon-water-polymer system. The activity of water in the polymer-water solution is computed using the UNIFAC model. 

Hwang SM, Lee JM, and Lin H. New Group-interaction Parameters of the UNIFAC Model Aromatic Methoxyl Binaries. Ind Eng Chem Res 2001 40 1740-1747. 

When using the UNIFAC model one needs to identify the functional subgroups present in each molecule by means of the UNIFAC group table. Next, similar to the UNIQUAC model, the activity coefficient for each species is written as eqn. (2.4.14), except for the the residual term, which is evaluated by a group contribution method in UNIFAC, The residual contribution of the logarithm of the activity coefficient of group k in the mixture. In F., is obtained from... 

Here we consider the prediction of the VLE behavior of mixtures, the constituents of which exist as pure liquids at the temperature and pressure at which the UNIFAC model parameters are evaluated. The reason for this restriction is that the excess free energy in most models is defined with respect to the pure liquid state. However, it is also possible to treat mixtures of noncondensable gases with condensable compounds by means of such predictive models, and this is the subject of Section 5.3. 

In the remainder of this section we examine several EOS-G models using three prototype binary mixtures that form sti ongly nonideal solutions. For comparison, we also include the predictions of the UNIFAC model used directly in the y-(p method wherever applicable. The systems considered are the methanol and benzene (Butcher and Medani 1968), the acetone and water (Gmehling and Onken 1977), and the 2-propanol and water (Barr-David and Dodge 1959) binary mixtures. Note that there are many systems with small to moderate solution nonideality for which all or most of the methods mentioned above work reasonably well. We are not concerned with such systems here because the method selection would not be a problem in such cases. Rather we consider only those systems that are more nonideal and for which the differences between the models discussed here are clearly evident. 

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