Crystallization Dynamics

As indicated in the introduction, problems in the operation of continuous crystallization processes can lead to large disturbances in the dynamics of an industrial crystallizer. In addition, slow oscillations in the CSD may occur, which do not seem to be caused by process disturbances, but are an intrinsic property for certain process configurations and are related to the internal feedback mechanisms which are present in the crystallization process. This so-called slow cyclic behaviour is only seen in DTB and fluidized bed types of crystallizer configurations in the presence of fines dissolution and/or classified product removal. Figure 3 shows an example of this behaviour for a 1000 L evaporative DTB crystallizer. For higher values of the fines removal flow rate a limit cycle was reached in the median crystal size, during which the median crystal size varied between 240 and 1040 |im in cycles of about 5-6 h. Oscillatory behaviour has also been reported after selective product removal.

The stability of an open loop continuous crystal-lizer has been the subject of many studies. The techniques used involve the Laplace transformation of the linearized version of the population balance or conversion to a set of ordinary differential equations using the moment transformation. These solution methods, however, pose severe limitations on the models.

Based on a stability analysis, two types of unstable behaviour, have been identified, namely low order and high order cycling. High order cycling can be caused by very high orders in the power law equation for the nucleation kinetics, which seems unlikely for most crystallization systems. Low order cycling on the other hand can be caused by nonrepresentative product removal.

In more recent work it has been established that simple power law kinetics are unable to explain the

Figure 3 Experimental time response in a DTB crystallizer at start-up of the median crystal size for different fines removal flows (f and thus different residence times for the fines (rf). Eeketal., 1995b.

dynamic behaviour in industrial DTB crystallizers. Nucleation models that only take into account crystals beyond a certain minimum crystal size have been shown to give a much better description of the crystallization kinetics.

Some of these limitations in the stability analysis have been removed by using modern analytical techniques, which are based on the reduction of the system of balance and kinetic equations into one single integro-differential implicit equation. The steady state solution of this equation and that of the linearized equation around that point enables an analysis of more complex crystallization models.

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