UNIFAC equation method

The group interaction parameter anm is found from the large sets of VLE and LLE data in the literature, which are tabulated for many subgroups. It is worth noting that a m a. There are some modifications to the original UNIFAC equation in order to make the model robust for some complex systems. In the UNIFAC-DM method, the modification is made on the combinatorial part ... 

The UNIQUAC equation is the basis for the development of the group contribution method, the UNIFAC equation, which predicts liquid activity coefficients from component structures on the basis of interactions between chemical functional groups. 

The method just described is probably the simplest and most accurate extension of the UNIFAC prediction method to high temperatures and pressures. However, it is accjirate only if the UNIFAC predictions (made by the direct activity coefficient or y -4> method) for this system are accurate. If this is not the case, then the combination of the UNIFAC model with an equation of state as described here will also be inaccurate. That is, combining the UNIFAC model with an equation of state (the 4)-(f>, method) does not improve its accuracy, but merely extends its range of applicability. 

This method deserves special mention because, unlike all of the previous methods, it allows the prediction of activity coefficients based entirely on tabulated parameters i.e., no fitting of parameters is necessary. It builds on UNIQUAC and is based on the premise that a solution maybe regarded as a mixture of structural units rather than of chemical species. For example, a mixture of n-pentane and n-heptane is considered as a mixture of CHa and CH3 subgroups and so is a mixture of cyclohexane and ethane. In this approach, interaction parameters are determined between a finite number of subgroups and are tabulated. It is then possible to calculate activity coefficients for any solution, binary or multicomponent, from a relatively small number of tabulated values. This is the main advantage of the method. Its applicability is limited to components that are liquid at 25 C. Parameters for the UNIFAC equation have been... 

An early model describing the pervaporative reaction of acetic acid with ethanol was presented by Krupiczka and Koszorz (1999). It was a simple, three-parameter model describing the concentration profiles in the process (a kinetic approach was considered) in the form of three differential equations. The activity coefficients were calculated using the UNIFAC property method. A hydrophilic membrane PERVAP 1005 GFT was used. Differently, Tanna and Mayadevi (2007) developed a two-step series model to study the performance of the membrane reactor. In this case, the goal was the assessment of the parameters that drive the process. As a conclusion of this work, the authors suggested using a low-flux membrane with a sufficient surface area when designing a PVMR. 

Formic acid, cumene are used to estimate the activity coefficients from the UNIFAC. Equations 1 and 2 are solved for the mole fraction (x) of component i in the two liquid phases. This method of calculation gives a single tie line. 

UNIFAC andASOG Development. Pertinent equations of the UNIQUAC functional-group activity coefficient (UNIFAC) model for prediction of activity coefficients including example calculations are available (162). Much of the background of UNIFAC involves another QSAR technique, the analytical solution of groups (ASOG) method (163). 

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). 

Another estimation method of mixture flashpointe was sugg ed by Gmehling (note p.63). The method uses the forecast technique of activity coefficients of iiquid mixtures called UNIFAC that would therefore enable calculation of the vapour pressure of the mixtures and, thanks to Le Chdtelier equation, calculate the temperature to which the mixture has to be heated so that its equilibrium concentration reaches the lower explosive limit. 

The UNIQUAC equation developed by Abrams and Prausnitz is usually preferred to the NRTL equation in the computer aided design of separation processes. It is suitable for miscible and immiscible systems, and so can be used for vapour-liquid and liquid-liquid systems. As with the Wilson and NRTL equations, the equilibrium compositions for a multicomponent mixture can be predicted from experimental data for the binary pairs that comprise the mixture. Also, in the absence of experimental data for the binary pairs, the coefficients for use in the UNIQUAC equation can be predicted by a group contribution method UNIFAC, described below. 

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

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. 

Values of the activity coefficients are deduced from experimental data of vapor-liquid equilibria and correlated or extended by any one of several available equations. Values also may be calculated approximately from structural group contributions by methods called UNIFAC and ASOG. For more than two components, the correlating equations favored nowadays are the Wilson, the NRTL, and UNIQUAC, and for some applications a solubility parameter method. The fust and last of these are given in Table 13.2. Calculations from measured equilibrium compositions are made with the rearranged equation... 

The UNIFAC (Unified quasi chemical theory of liquid mixtures Functional-group Activity Coefficients) group-contribution method for the prediction of activity coefficients in non-electrolyte liquid mixtures was first introduced by Fredenslund et al. (1975). It is based on the Unified Quasi Chemical theory of liquid mixtures (UNIQUAC) (Abrams and Prausnitz, 1975), which is a statistical mechanical treatment derived from the quasi chemical lattice model (Guggenheim, 1952). UNIFAC has been extended to polymer solutions by Oishi and Prausnitz (1978) who added a free volume contribution term (UNIFAC-FV) taken from the polymer equation-of-state of Flory (1970). 

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

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. 

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 UNIFAC method is based on the UNIQUAC equation, for which the activity coefficients are given by Eq. (D.S). When applied to a solution of groups, Eqs. (D.6) and (D.7) are written ... 

The equations for the UNIFAC method are presented here in a form convenient for computer programming. In the following example we run through a set of hand calculations to demonstrate their application. 

The extension of ideal phase analysis of the Maxwell-Stefan equations to nonideal liquid mixtures requires the sufficiently accurate estimation of composition-dependent mutual diffusion coefficients and the matrix of thermodynamic factors. However, experimental data on mutual diffusion coefficients are rare, and prediction methods are satisfactory only for certain types of liquid mixtures. The thermodynamic factor may be calculated from activity coefficient models such as NRTL or UNIQUAC, which have adjustable parameters estimated from experimental phase equilibrium data. The group contribution method of UNIFAC may also be helpful, as it has a readily available parameter table consisting of mam7 species. If, however, reliable data are not available, then the averaged values of the generalized Maxwell-Stefan diffusion coefficients and the matrix of thermodynamic factors are calculated at some mean composition between x0i and xzi. Hence, the matrix of zero flux mass transfer coefficients [k ] is estimated by... 

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