UNIFAC methods

The first group contribution method for the prediction of VLE (activity coefficients) was the so-called analytical solution of groups (ASOG) method [50, 51], developed within Shell. The ASOG method uses the Wilson model to describe the concentration dependence of the group activity coefficients required in the solution of groups concept. 

In 1975, the UNIFAC group contribution method was published by Fredenslund etal. [27, 52, 53]. Like the ASOG method, the UNIFAC method is based on the 

The combinatorial part In can be calculated using the following equation, which is identical to the UNIQUAC model  

For the UN I FAC group contribution method the relative van der Waals properties r, and q[ can be obtained using the relative van der Waals group volumes Rk and relative van der Waals group surface areas Qc, which can be derived from x-ray data. Tabulated values for Rk and Qjc can be found by Hansen et al. [53]. They can also be derived from the tabulated van der Waals properties published by Bondi [54. For selected groups the Rk and Qjt values are given in the Appendix H  

The temperature-dependent residual part Iny- takes into account the interactions between the different compounds. In group contribution methods, this part is calculated via the solution of groups concept using group activity coefficients Vk and rf  

---

Detailed and extensive information on the UNIFAC method for estimating activity coefficients with application to vapor-liquid equilibria at moderate pressures. 

When no experimental data at all are available, activity coefficients can sometimes be estimated using the UNIFAC method (Fredenslund et al., 1977a, b). However, for many real engineering problems it is often necessary to obtain new experimental data. 

For most LLE applications, the effect of pressure on the Yi < an be ignored, and thus Eq. (4-327) constitutes a set of N equations relating equilibrium compositions to each other 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 suffice, even in principle, because some cannot represent liquid/liquid phase splitting. The UNIQUAC equation is suitable, and therefore prediction is possible by the UNIFAC method. A special table of parameters for LLE calculations is given by Magnussen, et al. (Jnd E/ig Chem Process Des Dev, 20, pp. 331-339 [1981]). 

For the monomers in the polymerization under consideration the fugacity coefficients were estimated by Redlich-Kwong equation of state and were found to be close to unity. The activity coefficients (8) for the monomers were estimated by Scatchard-Hildebrand s method (5) for the most volatile monomer there was a temperature dependence but none for the other monomer. These were later confirmed by applying the UNIFAC method (6). The saturation vapor pressures were calculated by Antoine coefficients (5). 

More extensive work has been done to develop the UNIFAC method, to include a wider range of functional groups see Gmeling et al. (1982) and Magnussen et al. (1981). 

Care must be exercised in applying the UNIFAC method. The specific limitations of the method are ... 

The UNIQUAC equation can be used to estimate activity coefficients and liquid compositions for multicomponent liquid-liquid systems. The UNIFAC method can be... 

The linearisation method of Naphtali and Sandholm has been used by Fredenslund et al. (1977) for the multicomponent distillation program given in their book. Included in then-book, and coupled to the distillation program, are methods for estimation of the liquid-vapour relationships (activity coefficients) using the UNIFAC method (see Chapter 8, Section 16.3). This makes the program particularly useful for the design of columns for... 

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. 

Dallos, A., Wienke, G., Ilchmann, A., Gmehling, J. (1993) Vorausberechnung von octanoFwasser-verteilungskoeffizienten mit hilfe der UNIFAC-methode. Chem.-Ing.-Tech. 65, 291-303. 

The vapour pressure of BHET is approximately three orders of magnitude lower than that of EG. Nevertheless, evaporation of BHET still occurs in significant amounts under vacuum. In Figure 2.26, the experimentally determined vapour pressure of BHET is compared to the vapour pressure predicted by the Unifac group contribution method [95], The agreement between the measured and calculated values is quite good. In the open literature, no data are available for the vapour pressure of dimer or trimer and so a prediction by the Unifac method is shown in Figure 2.26. The correspondence between measured and predicted data for BHET indicates that the calculated data for dimer and trimer... 

Three other methods are applicable in certain circumstances, particularly if there is prior experience in their use. These are the connectivity, solvatochromic, and UNIFAC methods. 

Because of the lack of quantitativeness of the Regular Solution Theory and large amount of effort and computing power required for the UNIFAC method, yet another way will be taken here. This way leads to values using simple means which can adequately estimate values for the most important practical cases. The method described in this section is based on the potential already recognised in gas chromatography that the partition of a substance between a gas and a polymer liquid can be estimated based on its structural increments and these can be used as characteristic quantities for identification. 

In the case of polar liquids and polymers an estimation of the activity coefficients for z and z + 1 in L or P can be tried using another method, e.g. the UNIFAC method. If this is not possible then both the partition coefficient for z and z + 1 in the gas/liquid or gas/polymer system must be experimentally determined. For the relatively volatile alkanes this is possible without a great amount of work. 

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

Finally, the input information includes parameters for the UNIFAC method (App. D). The calculated values of T and the vapor-phase mole fractions yk compare favorably with experimental values. Also listed in Table 12.1 are final computed values of P , [Pg.205]

Values of parameters for the Margules, van Laar, Wilson, NRTL, and UNIQUAC equations are given for many binary pairs by Gmehling et al.t in a summary collection of the world s published VLE data for low to moderate pressures. These values are based on reduction of data through application of Eq. (11.74). On the other hand, data reduction for determination of parameters in the UNIFAC method (App. D) is carried out with Eq. (12.1). 

The compositions of the vapor and liquid phases in equilibrium for partially miscible systems are calculated in the same way as for miscible systems. In the regions where a single liquid is in equilibrium with its vapor, the general nature of Fig. 13.17 is not different in any essential way from that of Fig. I2.9< Since limited miscibility implies highly nonideal behavior, any general assumption of liquid-phase ideality is excluded. Even a combination of Henry s law, valid for a species at infinite dilution, and Raoult s law, valid for a species as it approaches purity, is not very useful, because each approximates real behavior only for a very small composition range. Thus GE is large, and its composition dependence is often not adequately represented by simple equations. However, the UNIFAC method (App. D) is suitable for estimation of activity coefficients. 

The UNIFAC method for evaluation of activity coefficients depends on the concept that a liquid mixture may be considered a solution of the structural units from which the molecules are formed rather than a solution of the molecules themselves. These structural units are called subgroups, and a few of them are listed in the second column of Table D.l. An identifying number, represented by k, is associated with each subgroup. The relative volume Rk and relative surface area Qk are properties of the subgroups, and values are listed in columns 4 and 5 of Table D.l. Also shown (column 6) are examples of the subgroup compositions of molecular species. When it is possible to construct a molecule... 

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. 

---