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Keywords:

  • crystallization;
  • process control;
  • process synthesis

Abstract

Determination of the optimal temperature (or supersaturation) trajectory for a seeded batch crystallizer is a well studied problem. The majority of researchers find that the optimal trajectory has a greater supersaturation at the end of the batch. A significant minority of researchers, however, using very similar models and different but equally justifiable objective functions, find that the optimal trajectory has the greatest supersaturation at the beginning of the batch. Still other researchers have suggested that crystallization processes should be operated with constant supersaturation. These apparent conflicts are resolved into different equivalence classes of objectives and corresponding operating policies. It is shown that the equivalence classes arise as a result of an inherent tradeoff for seeded batch crystallizers involving secondary nucleation: Early growth operating policies tend to minimize the number of nuclei formed because supersaturation is greatest when the mass of crystals is least. However, those nuclei which are formed early have an opportunity to grow to a larger size and compete with the growth of the seed crystals. By contrast, late growth operating policies tend to produce more nuclei because supersaturation is greatest when the mass of crystals is greatest. However, nuclei formed late in the batch do not have a chance to grow as large, and the total mass of nucleus-grown crystals is small. Which of these outcomes is preferred depends on the particular application. © 2006 American Institute of Chemical Engineers AIChE J, 2006