Activity coefficient-models UNIFAC

As an alternative to experimental measurements, CMC can be predicted using thermodynamic models like the group contribution activity coefficient model UNIFAC (Flores et al, 2(X)1 Chen, 1996 Cheng,... 

The second group of studies tries to explain the solvent effects on enantioselectivity by means of the contribution of substrate solvation to the energetics of the reaction [38], For instance, a theoretical model based on the thermodynamics of substrate solvation was developed [39]. However, this model, based on the determination of the desolvated portion of the substrate transition state by molecular modeling and on the calculation of the activity coefficient by UNIFAC, gave contradictory results. In fact, it was successful in predicting solvent effects on the enantio- and prochiral selectivity of y-chymotrypsin with racemic 3-hydroxy-2-phenylpropionate and 2-substituted 1,3-propanediols [39], whereas it failed in the case of subtilisin and racemic sec-phenetyl alcohol and traws-sobrerol [40]. That substrate solvation by the solvent can contribute to enzyme enantioselectivity was also claimed in the case of subtilisin-catalyzed resolution of secondary alcohols [41]. 

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... 

For the analytical equations, there are two methods to compute the vapour-liquid equilibrium for systems. The equation of state method (also known as the direct or phi-phi method) uses an equation of state to describe both the liquid and vapour phase properties, whereas the activity coefficient method (also known as the gamma-phi approach) describes the liquid phase via an activity coefficient model and the vapour phase via an equation of state. Recently, there have also been modified equation of state methods that have an activity coefficient model built into the mixing mles. These methods can be both correlative and predictive. The predictive methods rely on the use of group contribution methods for the activity coefficient models such as UNIFAC and ASOG. Recently, there have also been attempts to develop group contribution methods for the equation of state method, e.g. PRSK. " For a detailed history on the development of equations of state and their applications, as well as activity coefficient models, refer to Wei and Sadus, Sandler and Walas. ... 

In Figure 5.1.3 the prediction of the VLB behavior of the various models for the methanol and benzene binary system at 453 K is shown. The direct use of the UNIFAC activity coefficient model in the y-4> model qualitatively behaves differently than the other models and performs relatively poorly. The various EOS-G models show similar behavior that is in qualitative agreement with the experimental data however, quantitatively the WS model is the most accurate. 

This choice results in the use of UNIFAC for the activity coefficient model.)... 

AC-VLE FROM ACTIVITY COEFFICIENT MODELS THE UNIFAC MODEL... 

The GC concept has received great attention for the prediction of activity coefficients during the last 30 years. It has been applied to many different types of properties of pure compounds, as shown in Section 16.2, but also for phase equilibrium calculations for mixtures. Especially well known is the UNIEAC equation for the activity coefficient. The UNIFAC model is available in several modified forms, e.g., by Larsen et al. and Gmehling and Weidlich. ° These modified UNIFAC models contain, unlike the original UNIFAC, temperature-dependent interaction parameters. 

Note Average absolute deviations between experimental and predicted solvent activities for ternary polymer-solvent systems. Predictions are shown with the Entropic-FV and UNIFAC-FV activity coefficient models as well as with two GC equations of state GC-Hory and GCLF. Results are reported based on both the activities and the logarithms of the activities. 

FIGURE 16.6 Molecular structure of the paint Araldit 488 and infinite dilution activity coefficients (Qf) with various models for Araldit 488-solvent systems. Results are shown with the Entropic-FV and UNIFAC-FV activity coefficient models and the GC-Flory equation of state. The calculations with the two activity coefficient models are shown for two different values of the density of the polymer, predicted by the GC-VOL and van Krevelen models. (Modified from Lindvig et al., AIChE J., 47(11), 2573-2584, 2001.)... 

Equation 16.75 represents the basic principle (or starting point) in the development of the EoS/G models (mixing rules). The superscript refers to the specific activity coefficient model used, e.g., UNIFAC or NRTL. Eor polymers, a suitable activity coefficient model such as the ones including FV effects should be used. The subscript P denotes that the equality of Equation 16.75 is valid at a certain pressure, which is called the reference pressure. Various choices have been proposed for the reference pressure. The most popular choices are the infinite and the zero reference pressures, but other choices have also been proposed. 

The EoS/G method combines the best features of cubic equations of state and classical activity coefficient models. This is because, via this technique, at low pressures the behavior of the activity coefficient model is recovered. However, the model is also applicable at high pressures in a predictive way. It is important to note that existing parameter tables from, e.g., UNIFAC, UNIQUAC, etc. can be used. From the above it is understood that it is essential that the activity coefficient employed in the mixing rule should be as accurate as possible (at the low pressure Umit). 

Various EoS/G models have been proposed over the last several years for polymers. These models combine the SRK, the PR equation of state, or the Sako et al. cubic equation of state with FV activity coefficient models such as UNIFAC-FV, Entropic-FV, EH and the ASOG. 

For binary pairs where no data exist to which to fit parameters in activity-coefficient models, group-contribution methods have been developed to estimate these parameters based on molecular structure. The leading method, UNIFAC [46], usually provides reasonable estimates for mixtures of organic compounds. 

The two most developed group contribution methods are the ASOG (Analytical Solution Of Groups) and UNIFAC (UNIquac Functional-group Activity Coefficient) " models, both of which are the subjects of books. We will consider only the UNIFAC model here. UNIFAC is based on the UNIQUAC model of Sec. 9.5. This model, you will remember, has a combinatorial term that depends on the volume and surface area of each molecule, and a residual term that is a result of the energies of interaction between the molecules. In UNIQUAC the combinatorial term was evaluated using group contributions to compute the size parameters, whereas the residual term had two adjustable parameters for each binary system that were to be fit to experimental data. 

Figure 10.3-12 Vapor-liquid equilibria of the acetone-water binary mixture predicted using the combination of the Peng-Robinson equation of state, the Wong-Sandler mixing rule, and the UNIQUAC activity coefficient model with parameters obtained from the predictive UNIFAC model at 25°C. ...

Alternatively, the van Laar, NRTL. and UNIQUAC activity coefficient models could be used, yielding more accurate results. (The UNIFAC method can also be used to predict liquid-liquid equilibrium, but only with different main group interaction parameters than are used to predict vapor-liquid equilibrium.)... 

For this reaction system, the liquid-phase non-ideality can be described by the UNIFAC activity coefficient model [20]. Panneman and Beenackers [21] studied the reaction kinetics of (5.42) catalyzed by macroporous strongly acidic ion-ex-change resins. Based on their results, Qi et al. [19] proposed an activity-based reaction rate expression for this reaction... 

All other liquid components are present in dilute solutions in water, which require an appropriate activity coefficient model for the dilute component. Here the UNIFAC/UNIQUAC model [197] is selected, where the activity coefficient is calculated as the sum of a combinatorial part and a residual part. The residual part uses fitted binary parameters valid for the components present in the liquid mixture. If no binary parameters are available - which is often the case in syngas preparation - the UNIFAC method may be used to calculate the residual part. 

When there is no built-in binary parameter in Aspen, and also when we cannot find any experimental data in the open literature, another option is to use the group contribution model in Aspen to predict liquid activity coefficient for this binary pair or the entire component system. UNIFAC is an activity coefficient model, like NRTL or UNIQUAC, but it... 

The BIPs for various activity-coefficient models can be estimated by UNIFAC. However, caution... 

The liquid reference fugacity and the liquid activity coefficient models are listed in Figures 12 and 13. At the present time, Henry s Law for supercritical components can be used only with the UNIQUAC equation the unsymmetric convention is not Included in the other liquid activity coefficient models. Vapor pressure with a Poyntlng correction is usually used for the liquid reference fugacity. The Wilson equation and the NTRL equations are the most commonly utilized liquid activity coefficient models. UNIQUAC and UNIFAC have just been added to the system, and if they fulfill our expectations, they will become the most commonly used models. 

A step forward in modelling is provided by the use of activity coefficient models and group contribution methods. One of the most valuable features of these methods is their applicabihty to multi-component systems imder the assumption that local compositions can be described in this case by a relationship similar to that obtained for binary systems. However, one of the main disadvantages of these methods is that they depend on an extremely large amount of experimental data. Furthermore, the absence of the volume and surface p>arameters p>oses a hindrance in the calculation of the binary interaction parameters for UNIQUAC and UNIFAC models. These limitations can be overcome by the use of quantum-based models, such as COSMO-RS (see, for instead, the works of Shah et al., (2002) and of Guo et al. (2007)). In this method no experimental data is needed as an input to model the ionic hquids, being the main constraint the extensive computational time and also that, in some cases, the comparison with experimental data is only qualitative. 

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