Modelling the cyclic behaviour in a DTB crystallizer—a two-population balance model approach

• Published in: Journal of crystal growth 2005-02, Vol.275 (1), p.e1373-e1381
• Main Authors: Menon, A.R., Kramer, H.J.M., Grievink, J., Jansens, P.J.
• Format: Article
• Language: English
• Subjects: A1. Dynamic simulation; A1. Oscillatory behaviour; A2. Growth from solutions; A2. Industrial crystallization; A2. Population balance model; A2. Primary nucleation
• ISSN: 0022-0248; 1873-5002
• DOI: 10.1016/j.jcrysgro.2004.11.211

A novel approach is introduced here to improve the description of the dynamic behaviour of industrial crystallizers using a two-population balance model to discriminate between primary and secondary nuclei. A heterogeneous primary nucleation model is implemented in a rigorous crystallizer model framework to explain the sustained oscillatory behaviour observed in industrial draft-tube baffle (DTB) crystallizers. The distinction between primary and secondary nuclei in the modelling framework is realized by using two different growth rates within the dispersed phase. The total crystal population is split up into two distinct and interacting populations, one representing the primary (no strain) population of crystals and the other the secondary (strained) population. Such a two-population balance model exhibits the sustained cyclic response for a 1100L DTB crystallizer, for an ammonium–sulphate water system. Including the degree of heterogeneity ( ψ ) and the two parameters; surface integration rate constant ( k r ) and condition for deformation ( Γ s ) from the growth model, the primary nucleation model framework has three unknown parameters which are fitted using measured transients from experiments performed on the pilot-plant crystallizers. The effect of the heterogeneity factor ( ψ ) on the dynamics of the process, suggests that the parameter ψ is very sensitive and hence, plays a very critical role in predicting the start-up and dynamics of the process. Validation of the model with the experimental data shows that the inclusion of a primary nucleation event definitely increases the descriptive capability of the model, thus justifying it's inclusion as a critical factor. The simulation results give a very good description of the start-up phase of the crystallizer operation, the dynamics of the process as well as the final steady-state values.