In the last sections three different types of chemical systems that can favorably be processed by means of RD have been presented. Most of the known results on multiplicities and oscillations have been obtained from an analysis of these systems. These results indicate that multiplicities and oscillations may occur quite frequently in RD. Depending on the characteristics of the reaction system and operating conditions these multiplicities and oscillations can have different sources. In principal, each of the individual unit operations 'distillation' and 'reaction' combined in an RD process has it's own sources, which can also be relevant for RD. Further, the combination of both unit operations can give rise to new phenomena.

For a classification of different patterns of behavior let us first focus on systems with a single reversible reaction. Today, these constitute the most important class of applications of RD technology in industries. Typical examples are esterification and etherification processes as treated above. For large Damkohler numbers (fast reaction and/or high residence time) the reaction is close to chemical equilibrium. In first approximation, such a process can be can be analyzed and explained by means of reactive residue curve maps using »/»-analysis [34, 35]. This procedure is completely analogous to the non-reactive case. Consequently, similar phenomena can be observed as in non-reactive azeotropic distillation including multiple steady states and self-sustained oscillations. However, the regions in the space of the adjustable operating parameters with multiple steady state or oscillatory behavior are small and are typically further reduced if finite inter- or intraphase transport is taken into account. Hence, practical relevance seems to be low. Typical examples are the autocatalytic methyl formate system and the heterogeneously catalyzed MTBE system at high pressures as treated above. Other examples from the literature are the homogeneously catalyzed ethanol and butanol esterifications.

By decreasing the rate of reaction or decreasing the residence time we enter the kinetic regime of the chemical reaction. In an RD column, the rate of reaction is decreased by decreasing the column pressure or by decreasing the amount of catalyst.

In the kinetic regime, the nonlinear temperature and concentration dependence of the reaction rate becomes dominant. If the boiling temperatures of the different components lie in the same range, the temperature is almost fixed by the pressure and only the nonlinear concentration dependence of the reaction rate is important. Typical examples are the TAME and the MTBE system at sufficiently low pressures as treated above. If, in addition, the intraparticle diffusion inside the catalyst is fast compared to the rate of reaction, similar patterns of behavior can be observed as in an isothermal CSTR [73]. The latter has been studied intensively in chemical reaction engineering and two different sources have been identified for isothermal steady state multiplicity (e.g., [18, 68]). The first is self-inhibition by the reactants. The second is autocatalysis by the products. In the open literature only little is known about the application of RD technology to autocatalytic systems. Although there seems to be some potential in such applications [84]. In contrast to this, self-inhibition of the reactants is frequently observed in heterogeneously catalyzed RD. Typical examples are the etherification processes that were treated above. Other examples are hydration processes for the production of tert-alcohols [31, 32, 84]. The multiplicity regions can be fairly large like for the TAME process. Therefore, practical relevance can be high and particular attention has to be given to these phenomena when designing and operating these type of processes. The number of steady states can further increase if the diffusional transport inside the porous catalyst is not negligible compared to the rate of reaction. This can be avoided by reducing the size of the catalyst particles to overcome intraparticle diffusional transport resistances or by increasing the pressure or total amount of catalyst to overcome kinetic limitations of the chemical reaction.

According to the investigations in Mohl et al. [73] oscillations are unlikely to occur in the kinetic regime of the chemical reaction for systems with close boiling points.

A different pattern of behavior occurs in the kinetic regime of an equilibrium limited reaction or more complex multi reaction systems, if the boiling points of the individual components differ significantly. This can introduce a positive feedback between reaction and separation via nonlinear temperature dependence of the reaction rate also giving rise to multiplicities and instabilities. It should be noted, that this situation is different from a single phase non-isothermal CSTR. In the single phase CSTR temperature represents a dynamic degree of freedom. Instead, in the two phase region temperature is fixed by the boiling point condition and therefore depends algebraically on the composition. A prototypical example for this class ofprocesses is the ethylene glycol system, which has a more complex reaction mechanism involving consecutive reaction steps. Because this type of reaction mechanism is in particular sensitive to backmixing, additional complexity in the nonlinear behavior is introduced by non-ideal flow patterns on the column trays of an RD column.

Finally, it should be noted that this classification is not complete but represents the authors present point of view based on the experience with the RD systems from above. Certainly, new patterns of behavior will be identified, when applying RD technology to more complex reaction systems or within more complex plant configurations involving mass and energy recycles.

264 | A. Kienle and W. Marquardt 10.7

Nonlinear Wave Propagation

Another nonlinear type of dynamic behavior found in many chemical processes is spatiotemporal pattern formation of the concentration and temperature profiles [66]. This phenomenon is also termed as nonlinear wave propagation. Nonlinear waves are particularly useful to understand and predict the qualitative dynamic behavior without any tedious calculations.

In this section some basic features of nonlinear wave propagation in non-reactive and RD processes will be illustrated and compared with each other. The simulation results presented are based on simple equilibrium or non-equilibrium models [51, 65] for non-reactive separations. In the reactive case, similar models are used, assuming either kinetically controlled chemical reactions or chemical equilibrium. We focus on concentration (and temperature) dynamics and neglect fluid dynamics. Consequently, for equimolar reactions constant flows along the column height are assumed. However, qualitatively similar patterns of behavior are also displayed by more complex models [28, 57, 65] and have been confirmed in experiments [41, 59, 89, 107] for non-reactive multi-component separations. First experimental results on nonlinear wave propagation in reactive columns are presented subsequently.

For an introduction into the subject, we first focus on non-reactive columns. For the case of binary distillation, Marquardt [64] as well as Hwang and Helfferich [42] independently showed by means of the theory of quasi-linear hyperbolic systems that there is a single wave front connecting two pinch regions in a distillation column section without side streams. Hence, a single concentration (and temperature) front may occur in a column section indicating the region of intense mass transfer between the phases. For ideal mixtures, the concentration front is of the constant pattern type. After a disturbance, the front will travel through the column with initially constant shape and velocity. The propagation velocity w of the front can be computed approximately from

where V, L, Ax, and Ay represent the molar flow rates and the pinch concentration differences in both phases. The boundaries of the column section act as repellors. Hence, the propagation velocity is gradually reduced to zero when the front approaches the section boundary to settle down to a new steady state. Fig. 10.18 shows such a situation. A concentration wave propagates to the top of a rectifying section separating methanol and 1-propanol after a step change of the reflux rate L.

The analysis can be extended to the multi-component case [43, 44, 51, 65, 66]. The number of the fronts is directly related to the number of components nc in the mixture. For ideal and moderately non-ideal mixtures the concentration and temperature profiles consist of nc - 1 fronts connecting two pinch points. Again, constant pattern waves occur for ideal and moderately non-ideal mixtures. Addi-

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