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Kinetic Instabilities for Finite Transport Inside the Catalyst

More complex patterns of behavior can be found for finite transport resistances inside the porous catalyst [74]. Here, kinetic instabilities occur on two different length scales. On a first, macroscopic scale, multiplicity is induced by ignition and extinction of every single reactive column tray. On a second, microscopic scale, multiplicity comes from isothermal multiplicity of the single catalyst pellet, which is due to the finite transport resistance inside the catalyst.

In tray columns the first mechanism is dominant. This can lead to a large number of different steady state solutions for a given set of operating conditions. If N is the number of steady states (typically an odd number). Then (N + l)/2 of these steady states are stable. This can lead to complex multi-stable dynamic behavior during column startup and set-point or load changes. These phenomena were observed for vanishing as well as for finite intra-particle mass transfer resistance. An example with a total number of six trays (two reactive and two non-reactive trays plus reboiler and condenser) is shown in Fig. 10.16 for the well-known MTBE process. In contrast to the previous section, the column is now operated in the kinetic

Fig. 10.16 Multiple steady states for MTBE synthesis in a tray column at a pressure of 7 bar: negligible intraparticle diffusion for small particles (left) and finite intraparticle diffusion for large particles (right)

Fig. 10.17 Multiple steady states for MTBE synthesis in a packed column at a pressure of 7 bar: negligible intraparticle diffusion for small particles (left) and finite intraparticle diffusion for large particles (right)

Fig. 10.17 Multiple steady states for MTBE synthesis in a packed column at a pressure of 7 bar: negligible intraparticle diffusion for small particles (left) and finite intraparticle diffusion for large particles (right)

regime with a column pressure of 7 bar and high feed rates: further details are available elsewhere [74],

In case of packed columns, a qualitatively different behavior can be found for finite and infinite intra-particle mass transfer resistance. For vanishing mass transfer resistance inside the catalyst a 'small' number of solutions, typically three, can be observed. Note, that this is consistent with the TAME case discussed above. Instead, for finite transport inside the catalyst a very large number of solutions can be observed. An example is shown in Fig. 10.17, right. It was conjectured by Mohl et al. [74], that this behavior is caused by isothermal multiplicity of the single catalyst pellet and is therefore similar to the well-known fixed-bed reactor [38, 77]. However, further research is required to verify this hypothesis. Further, it was shown by Mohl et al. [74] that in both cases the number of solutions may crucially depend on the discretization of the underlying continuously distributed parameter system. A detailed discussion is given by Mohl et al. [74].

In all cases, kinetic multiplicity can be avoided by an increase of the Damkohler number, that is an increase of the number of active sites on the catalyst, or a decrease of the feed rate. Moreover, multiplicity will vanish if the column pressure is increased. In all cases the column gets closer to chemical equilibrium. This is consistent with previous experimental studies for the MTBE process at 7 bar and low feed rates [103] where no multiplicity was found.

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