Two-dimensional population balance model with breakage of high aspect ratio crystals for batch crystallization

A two-dimensional population balance model was developed for the description of breakage of crystals with high aspect ratios for a potassium dihydrogen phosphate (KDP) batch crystallization process. Two physical assumptions were made for the modelling. Firstly, the rate of breakage is proportional to the product of the frequency and impact energy of the collisions between the crystals and crystallizer equipment. Secondly, crystals become prone to breakage only when their aspect ratio exceeds a certain limit. Parameters for the rate of breakage were determined by fitting the breakage function in agitation experiments of suspended crystals in a crystallizer. These obtained parameters were validated in batch crystallization experiments. Since the growth rate of KDP is affected by low concentrations of multi-valent ions, Fe(3+) ions were used to control the crystal growth rate resulting in crystals with high aspect ratios. To be able to describe the effect of the used concentrations of Fe(3+) ions on the crystallization process, growth rate equations were derived, which account for the inhibitory effect on the growth rates along widths and lengths of crystals. The results obtained by solving the two-dimensional population balance model accompanied by crystal breakage were compared with seeded cooling batch crystallization experiments at various concentrations of FeCl(3). The model described crystal breakage very well at a wide range of process conditions. Some discrepancies were observed during initial period of the crystallization, which are most likely caused by the growth model used. (C) 2008 Elsevier Ltd. All rights reserved.