ASOG model

The goal of predictive phase equilibrium models is to provide reliable and accurate predictions of the phase behavior of mixtures in the absence of experimental data. For low and moderate pressures, this has been accomplished to a considerable extent by using the group contribution activity coefficient methods, such as the UNIFAC or ASOG models, for the activity coefficient term in eqn. (2.3.8). The combination of such group contribution methods with equations of state is very attractive because it makes the EOS approach completely predictive and the group contribution method... 

Koj ima, K., and Tochigi, K. Prediction of Vapor Liquid Equilibria by the ASOG Model, 1979. Elsevier, Amsterdam. 

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). 

Linking this molecular model to observed bulk fluid PVT-composition behavior requires a calculation of the number of possible configurations (microstmctures) of a mixture. There is no exact method available to solve this combinatorial problem (28). ASOG assumes the athermal (no heat of mixing) FIory-Huggins equation for this purpose (118,170,171). UNIQUAC claims to have a formula that avoids this assumption, although some aspects of athermal mixing are still present in the model. 

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. ... 

A modest data base for aqueous systems has beSen obtained by the use of these techniques. The data are reasonably reliable for systems with y values less then a couple thousand and not measured by the liquid-liquid chromatography technique. A reliable data base is required in the development of predictive techniques for y. Several predictive techniques are currently available the MOSCED (45) model has not yet been extended to aqueous systems. UNIFAC (46-48), which is really an outgrowth of ASOG (21,49) does include water, but with mixed results at best. Linear solvation energy relationships (LSER s) have been used to correlate ratios of y values for aqueous systems (50) and may be capable of some prediction. Nonetheless, a more extensive and accurate data base is what is really needed for correlation development... 

The UNIFAC-FV and Entropic-FV models are not the only extensions of UNIFAC to polymers. Similar models have been presented by Iwai and Arai ° ° and by Choi etal. ° Choi s model is not based on UNIFAC but on ASOG. ASOG (Analytical Solution of Groups) is a predictive GC method for calculating activities, similar to UNIFAC, but which has not experienced the widespread use of UNIFAC. It is mostly employed in Japan. Besides this difference, the models of Aral and Choi contain an FV, which is different from that of Equation 16.49. These two models have been applied with success for some polymer-solvent systems but not for LEE. 

All models perform clearly less satisfactorily for the activities of heavy alkanes in short-chain ones, especially as the size asymmetry increases. Models without FV corrections such as UNIFAC, ASOG, and FH are particularly poor in these cases. Unfortunately, such activity coefficient measurements, which are used for testing the performance of the models for the activities of polymers, are scarce. Direct measurements for polymer... 

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. 

The phase separations predicted by the ASOG calculations appear to be inconsistent with the experimental observations on these binarys. The solutions have the appearance of being homogeneous. On the other hand, molecular aggregation without precipitation is anticipated by the model presented here and strongly suggested by the observations of... 

Other approaches to the computation of solid-liquid equilibria are shown in Table 11.2-3. The Soave-Redlich-Kwong equation of state evaluates fugacities to calculate solid-liquid equilibria,7 while Wenzel and Schmidt developed a modified van der Waals equation of state forthe representation ofphase equilibria. The Wenzel-Scbmidt approach generates fugacities, from which the authors developed a trial-and-error approach to compute solid-liquid equilibrium. Unno et a .9 recently presented a simplification of the solution of groups model (ASOG) that allows prediction of solution equilibrium from limited vapor-liquid equilibrium data. 

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. 

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). 

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. 

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