Rate Based Model:
* Model 4: Mass & heat transport S reaction kinetics at these stages. Reaction kinetics are the same as in Model 2, Murphree efficiencies are used to give the desired separation capacity. In the rate-based approach (Model 4) heat and mass transfer are directly taken into account using two-film theory. Multicomponent diffusion is modeled with the Maxwell-Stefan equations. Bulk reaction kinetics are included as in Models 2 and 3.
Obviously, parameterizing these models meaningfully requires a very different amount of experimental data, increasing from Model 1 to Model 4. The minimum requirement is reliable information on vapor-liquid and chemical equilibrium (Model 1). The phase equilibrium model and the chemical equilibrium model should be consistent, as discussed in more detail below. Extending the equilibrium model to Model 2, which accounts for reaction kinetic effects, is not straightforward. In the case of methyl acetate, the reaction kinetic model obtained from stir-red-tank experiments is not in agreement with the results obtained from trickle-bed experiments, so that empirical factors have to be introduced [4, 7]. Furthermore, the macrokinetic model requires information on the liquid flow velocity, so that the thermodynamic design and the fluid dynamic design, which can be done sequentially when using Model 1, are now directly coupled. The reaction kinetic model should be consistent with the chemical equilibrium model.
Going from Model 2 to Model 3, the only additional information needed is the residence time distribution of the packing, which is available for Katapak-S . The residence time distribution of a packing segment of length L is modeled using a cascade of Nrea stirred tank reactors. The same packing segment has a known number of theoretical stages Nsep. As Nrea is always larger than Nsep, the differences in separation and reaction capacity of one stage (stirred tank) can easily be accounted for by introducing a Murphree efficiency.
In the fluid dynamic design with Models 1-3, information on the density and viscosity of the mixtures is needed, which usually has to be estimated as no experimental data is available. This can, however, be done with an accuracy sufficient for most cases using standard methods ,
The amount of additional information needed to be able directly to take into account heat and mass transfer in Model 4 is high. Using the two-film theory, information on the film thickness is needed, which is usually condensed into correlations for the Sherwood number. That information was not available for Katapak-S so that correlations for similar non-reactive packing had to be adopted for that purpose. Furthermore, information on diffusion coefficients is usually a bottleneck. Experimental data is lacking in most cases. Whereas diffusion coefficients can generally be estimated for gas phases with acceptable accuracy, this does unfortunately not hold for liquid multicomponent systems. For a discussion, see Reid et al.  and Taylor and Krishna . These drawbacks, which are commonly encountered in applications of rate-based models to reactive separations, limit our ability to judge their value as deviations between model predictions and experimen tal results may stem either from an inadequate model itself or from bad parameters.
Fig. 4.3 shows a comparison of Models 1-4 with data from an RD experiment, which is typical of the results from the study discussed here; other examples can be found elsewhere . All model results are predictions in the sense that no adjustments to RD data were made. The predictions from the stage models, which take into account reaction kinetics (Models 2 and 3), are good and do not differ largely.
Differences between Model 2 and Model 3 would only have been expected for residence time sensitive reaction systems, such as, for instance, ethylene glycol production from ethylene oxide and water, but not for the esterification studied here. The very simple Model 1 still gives reasonable predictions, which would, for instance, be sufficient for conceptual design studies. The fact that the rate-based Model 4 gives entirely wrong predictions in the present case should not be overemphasized and may be due to the very limited amount of available thermophysical and fluid dynamic input data.
Obviously, the choice of an appropriate modeling level for RD processes strongly depends on the input available to parameterize the different models. Thermodynamics plays a key role in providing that input.
Equilibrium Thermodynamics of Reacting Multiphase Mixtures
In any reactive separation process the mixtures involved undergo changes driving them towards chemical and phase equilibrium. As stated in the previous section, stage models with the simple assumption of chemical equilibrium in the streams leaving the stage and phase equilibrium between these streams often already provide a process model with reasonable predictive power. Any more detailed model will include an equilibrium model as a limiting case and will therefore have to be based on reliable information about the equilibrium. We will give a brief outline of the basic concepts of thermodynamic modeling of simultaneous chemical and phase equilibrium here. The focus is on the options provided by classical thermodynamics. A discussion of different GE models or equations of state is not within the scope of the present chapter. The reader is referred to standard textbooks for that purpose (for instance, Walas  and Prausnitz et al. ).
It is expected that entirely new options for thermodynamic modeling of simultaneous chemical and phase equilibrium will become available from molecular simulations techniques. Such methods are beginning to become available [12, 13], but can not be covered in the scope of the present chapter.
The conditions for simultaneous phase and chemical equilibrium at constant temperature T and pressure p derived from the second law of thermodynamics are well known and are given here for a system of N components i, P phases j, in which R chemical reactions r occur.
where f is the chemical potential of component i in phase j, v^ is the stoichiometric coefficient of component i in reaction r in phase j. v? is positive for products, negative for educts, and zero if the component i does not take part in reaction r in phase j.
For practical purposes, working equations have to be derived from the fundamental relations (4.2) and (4.3) by using appropriate normalizations of the chemical potential. Which working equation is appropriate will depend on the application. Some popular choices for the normalization of the chemical potential are as follows.
For components in vapor, liquid, and supercritical phases
for condensable components in liquid phases (normalization according to Raoult)
for non-condensable components in liquid phases (normalization according to Henry)
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