Group contribution models modified

The Achard model combines the UNIFAC group contribution model modified by Larsen et al. [LAR 87], the Pitzer-Debye-Hiickel equation [PIT 73a, PIT 73b] and solvation equations (Figure 2.1). The latter are based on the definition of the number of hydration for each ion, which corresponds to the assumed number of water molecules chemically related to the charged species. It divides the activity coefficient into two terms ... 

Larsen, B.L., Rasmussen, P, and Eredenslund, A. A modified UNIFAC group-contribution model for prediction of phase equilibria and heats of mixing, Ind. Eng. Chem. Res., 26, 2274, 1987. 

As shown before the group contribution method modified UNIFAC is a powerful and reliable predictive -model. 11 was continuously further developed in the last 20 years so that the method provides reliable results and a large range of applicability. 

The calculation of the liquid-fluid equilibria with the group contribution method has been presented elsewhere [4], The matrix of the parameters of group interaction (Table 1) contains values readjusted relative to the matrix obtained considering only liquid-fluid equilibria [4], These parameters are Ai5, A35, A45 and A59. The introduction of supplementary increments for the form of the molecules (a3 and P3.5) enables good results to be obtained for the calculation of solid-fluid equilibria and does not essentially modify the representation of liquid-fluid equilibria. The average relative deviation 5r(x) for the experimental data as a whole is 16 7% for the group contribution method and 13.3% for the model with E12 adjusted. The experimental data concern 40 isotherms (P,x) for 11 binary mixtures of solid aromatic hydrocarbon with supercritical C02. 

High and Danner (1989, 1990) modified the Panayiotou-Vera equation of state by developing a group contribution approach for the determination of the molecular parameters. The basic equation of state from the Panayiotou-Vera model remains the same ... 

Holten-Andersen et al. (1987) modified the Flory equation of state in order to develop an equation that is applicable to the vapor phase, to make it more applicable to associating fluids, and to introduce a group contribution approach. Chen et al. (1990) revised and improved the equation of state. The final model takes the following form. 

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. ... 

Various thermodynamic methods based on -models (Wilson, NRTL, UNIQUAC) or group contribution methods (UNIFAC, modified UNIFAC, ASOG, PSRK) can be used for either calculating or predicting the required activity coefficients for the components under given conditions of temperature and composition (Reference 2). 

Like the continuous physico-chemical descriptor Z variables, indicators of the presence or absence of certain substructures have also been treated by multiple regression analysis. As modified by Fujita and Ban (Seydel and Schaper, 1979), this group contribution method can be a useful alternative to the LFER approach, if only limited knowledge is available about the relevant molecular properties or no uniform physico-chemical descriptors for the various compounds in the data set are accessible. For activities and properties of compounds that may be attributed to the occurrence of certain substructures in the molecules (e.g. biodegradation section 4.8), Free-Wilson-type substructure models have their major application in environmental sciences. 

In the case of nonideal systems, the real behavior has to be taken into account using activity coefficients obtained from g -models, e.g. group contribution methods like modified UNIFAC. The required activity coefficients can of course also be calculated using an equation of state or group contribution equation of state. 

The results of Examples 11.2 and 11.3 show that today even predictive models can be applied successfully to find the binary and higher azeotropes of a multicomponent system. With the development of the group contribution equations of state like PSRK and VTPR, the range of applicability was extended to compounds which are not covered by group contributions methods such as UNI FAC or modified UNIFAC... 

Instead of a -model or a group contribution method like modified UN I FAC also an equation of state or a group contribution equation of state can be used for the calculation of residue curves and distillation boundaries. In Figure 11.15, the results are shown for the ternary system carbon dioxide-hydrogen sulfide-ethane at 266.5 K using VTPR. As can be seen, two binary azeotropes and one distillation boundary is observed. 

Lai, C.H., Paul, D.R., and Barlow, (.W. (1988) Group contribution methods for predicting polymer-polymer miscibility from heats of mixing of liquids. 1. Comparison of the modified Guggenheim quasiUNIQUAC models. Macromolecules, 21, 2492-2502. 

Kieffer has estimated the heat capacity of a large number of minerals from readily available data [8], The model, which may be used for many kinds of materials, consists of three parts. There are three acoustic branches whose maximum cut-off frequencies are determined from speed of sound data or from elastic constants. The corresponding heat capacity contributions are calculated using a modified Debye model where dispersion is taken into account. High-frequency optic modes are determined from specific localized internal vibrations (Si-O, C-0 and O-H stretches in different groups of atoms) as observed by IR and Raman spectroscopy. The heat capacity contributions are here calculated using the Einstein model. The remaining modes are ascribed to an optic continuum, where the density of states is constant in an interval from vl to vp and where the frequency limits Vy and Vp are estimated from Raman and IR spectra. 

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