M

I T Methanol/ ^Methanol f ] XPiCf)anol ^ ^ 1 1-Propanol

Fig. 10.18 Concentration wave front propagating after a step change in reflux rate to the top of the rectifying section of a binary, non-reactive separation tional fronts may be possible for highly non-ideal, azeotropic mixtures [50], Further, for this class of mixtures, so-called combined waves are possible where only a part of the wave front represents a constant pattern wave, whereas the other part has a variable shape, Constant pattern waves travel at the same velocity given by

Under steady state conditions, at most one of these wave fronts can be located in the middle of a column section, whereas the others are located at either one of the boundaries, where they can overlap and interact. A multicomponent example [51] is shown in Fig. 10.19. Initially, two distinct constant pattern waves can be identified in the concentration profiles of both components traveling at the same velocity to the top of the rectifying section. Close to the upper boundary, the waves start to interact and form some combined steady state pattern.

where

Fig. 10.19 Concentration wave fronts propagating after a step change in reflux rate to the top of the rectifying section of a ternary, non-reactive separation

Similar behavior can also be observed for RD processes. First investigations in this direction have been made by Marquardt and coworkers [25]. They considered the reversible reaction A + B o C for different Damkohler numbers Da. Fig. 10.20 shows the variation of the wave front pattern. A single front is obtained in the limit for large Da. A similar trend can be observed for the propagation velocity, which

Fig. 10.20 Nonlinear waves in reactive separation. Propagating constant pattern concentrations waves. Sensitivity of wave pattern with respect to Damkohler number

approaches the one for the non-reactive case if the reaction is close to chemical equilibrium. In fact, the equation for w obtained for the non-reactive case is perturbed by an additive term indicating the deviation from reaction equilibrium in the reactive case.

For high Da the column is close to chemical equilibrium and behaves very similar to a non-RD column with nc - nr- 1 components. This is due to the fact that the chemical equilibrium conditions reduce the dynamic degrees of freedom by nr the number of reversible reactions in chemical equilibrium. In fact, a rigorous analysis [52] for a column model assuming an ideal mixture, chemical equilibrium and kinetically controlled mass transfer with a diagonal matrix of transport coefficients shows that there are nc - nr - 1 constant pattern fronts connecting two pinches in the space of transformed coordinates [108]. The propagation velocity is computed as in the case of non-reactive systems if the physical concentrations are replaced by the transformed concentrations. In contrast to non-RD, the wave type will depend on the properties of the vapor-liquid and the reaction equilibrium as well as of the mass transfer law.

Despite the analogy between reactive and non-RD, the type of wave pattern may not necessarily comply for similar types of mixtures. In particular, combined waves as described above for non-ideal non-reactive mixtures might occur for ideal, reactive mixtures. Conversely, constant pattern waves may arise for highly non-ideal reactive mixtures.

Fig. 10.21 Concentration wave fronts in a reactive ternary separation after a step change in reflux rate. Ideal vapor-liquid equilibrium, kinetically controlled mass transfer, reversible chemical reaction close to chemical equilibrium
Fig. 10.22 Concentration wave fronts in a reactive ternary separation after a step change in reflux rate. Case as in Fig. 10.21, but reaction in kinetically controlled regime

An example of wave propagation in an RD column is shown in Figs. 10.21 and 10.22. Constant pattern waves can be observed in case of ideal phase equilibrium, kinetically controlled mass transfer and a single reversible reaction close to chemical equilibrium (compare Figs. 10.21). In contrast, at low Da in the kinetically controlled regime of the chemical reaction a different, more complex type of dynamic behavior can be observed (compare Fig. 10.22). The behavior in the kinetic regime is not sufficiently understood today and needs further research.

Nonlinear waves in RD have been studied by Balasubramhanya and Doyle III [4] who treat an idealized esterification system, and by GrĂ¼ner et al. [33] who study a fairly complex, industrial multireaction process. An experimental study of methyl formate synthesis has been carried out by Reder [25, 87] using the lab-scale column introduced above (Fig. 10.2). In all cases the columns are close to chemical equilibrium and therefore behave similar to non-reactive separations.

Fig. 10.23 shows simulated temperature waves in the lab-scale column. A comparison with experimental data is shown for a steady state in Fig. 10.24 showing a satisfactory fit. Clearly, the experiments confirm the pattern of the waves in the rectifying as well as in the stripping section. The flows in the column have been chosen such that the waves are sitting at the lower boundary of the column sections (i.e., close to the feed tray and close to the reboiler).

The extreme sensitivity of the lab-scale column to small variations in the heat duty of the reboiler is shown in Fig. 10.25. The upper left diagram shows the steady state concentrations of the key components in the distillate and in the bottoms

Fig. 10.23 Simulated temperature waves in lab-scale methyl formate column

Fig. 10.23 Simulated temperature waves in lab-scale methyl formate column

Fig. 10.24 Steady state concentration (top) and concentration waves (bottom) in lab-scale methyl formate column. Simulation (lines) and experiment (symbols)

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