A method is presented for preparing critical seed loading diagrams for nonaggregating systems knowing only the nucleation kinetics. This is advantageous because it is much less time-consuming than developing and solving a complete batch process model including solubility expressions and growth rate kinetics. Furthermore, there are many more reports available in the literature of nucleation kinetics alone than there are of complete batch crystallization process models, because expressions for the nucleation rate as a function of crystal growth rate can be rapidly determined from mixed-suspension, mixed-product-removal (MSMPR) data without measuring the supersaturation. The results for 43 systems show that there is a great deal of variability in the critical seed loading, and a single correlation is inadequate to describe the relationship between critical seed loading and seed size. For a seed size of 10 m, seed loading can effectively suppress nucleation in 92% of cases, while for seeds of size 50, 100, and 200 m, seed loading can suppress nucleation in 74, 61, and 39% of cases, respectively.
Pontryagin’s
minimum principle is applied to determine Pareto-optimal
fronts for multiobjective optimization of seeded batch crystallization
processes. For cases with two objectives, when both objectives are
based on properties of the higher moments or lower moments of the
crystal size distribution (for example, weight mean size and weight
mean coefficient of variation), there is relatively little difference
among the trajectories along the optimal front. By contrast, when
one objective is based on the lower moments (e.g., minimizing the
number of nuclei) and another objective is based on the higher moments
(e.g., minimizing the nucleated mass), the difference in the shape
of the trajectories along the front is more pronounced. In this case,
a constant growth rate trajectory may represent a reasonable compromise
between the competing objectives.
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