Importance of heterogeneous energy dissipation in the modeling and optimization of batch cooling crystallization

The influence of the local energy dissipation rate on the kinetics of crystallization has been widely reported in the literature. It is also well-known that, in an agitated vessel, the energy dissipation rate (EDR) usually exhibits a heterogeneous distribution. The objective of this paper is to investigate the validity of a homogeneity assumption associated with the EDR for batch cooling crystallization through numerical simulations and optimization studies. The results of the numerical studies, based on a homogeneous model, are compared with those obtained from a compartmental model that takes into account the distribution of the EDR within a vessel. The crystallization of citric acid in water is the system that forms the basis of the comparative study. The results of the numerical simulation studies for the crystallizer, in the presence of sufficient macro-mixing, confirm that the assumption of homogeneity, with respect to the EDR, is valid only when a linear relationship exists between the secondary nucleation rate and the local EDR. When the relationship is of an order lower (higher) than unity, the average product size predicted by a compartmental model tends to be higher (lower) than that predicted by a model where homogeneity is assumed. Such observations are confirmed through a theoretical analysis. The numerical studies further revealed that the difference between the computational and homogeneous model can be considerable when the order significantly exceeds unity. This becomes more pronounced when the secondary nucleation rate increases. However, in contrast, through the optimization of the temperature profile to maximize the average product size, qualitatively similar cooling profiles are attained. This is not dependent on whether the compartmental or homogeneous model is utilized.