Size Dependence on Solubility for Controlled Continuous Crystallizations (CSTR)
Ingo H. Leubner, submitted for publication
For crystallizations in continuous CSTR (MSMPR) crystallizers, a quantitative model is presented which correlates the average crystal size with reaction conditions. This model is based on the balanced nucleation and growth (BNG) theory. In the present paper, the size dependence on crystal solubility is derived and experimentally supported. For silver chloride as a model system, the solubility was varied from 0.81 to 8.3E-06 mole/l (60C, 3.0 min residence time). The correlation coefficient between model and crystal sizes (0.34 – 0.52 µm) was 0.9996. The model calculated the average maximum crystal growth rate (8.5 A/s) and the ratio of critical to average crystal size (0.39). It further calculated the sizes of nascent (= newly formed) crystals (0.13 – 0.30 um), critical crystal sizes (0.13 – 0.20 um), and supersaturation ratios (1.0049– 1.0075) for the experimental conditions. The model showed a reactant split ratio Rn/Ri (0.06 – 0.26) of incoming reactant addition rate, R0, into growth (Ri) and nucleation streams (Rn). The average crystal size is predicted to be independent of reactant addition rate, suspension density, and reaction volume. This is experimentally confirmed for variation of suspension density from 0.05 to 0.4 mole/l (average crystal size 0.337 +/- 0.009 um). The crystal number increased linearly with suspension density. The BNG based continuous crystallization model thus correctly predicted and quantitatively correlated the crystal size-dependence on solubility and suspension density in the CSTR crystallizer without the need for arbitrary adjustable parameters. It allowed determining important reaction parameters that were previously not accessible. This model does not rely on arbitrary adjustable parameters.