A new framework and a simpler method for the development of batch crystallization recipes

Abstract

We use a new generalized dimensionless model of a seeded batch crystallization process to compare results from four crystal growth rate/concentration trajectories: a numerically-computed optimal trajectory, a constant growth rate trajectory, a trajectory proposed by Mullin and Nyvlt that can be calculated without a kinetic model, and a linear concentration-time trajectory. Because the model is generalized and dimensionless it is not specific to any particular solute-solvent system. We show that if seed properties are good, all trajectories achieve a good result, whereas if seed properties are poor all trajectories achieve a poor result. If seed properties are intermediate, the linear concentration trajectory performs much worse than the other trajectories. On the basis of this, we conclude: (1) Linear trajectories and natural cooling trajectories are poor and should be avoided. When evaluating the benefit derived from an optimization of a temperature/saturation concentration trajectory, the appropriate benchmark should be the Mullin-Nyvlt trajectory, which typically performs much better than the linear trajectory and can be calculated knowing only the mass of seeds at the beginning of the batch. (2) Changing seed properties is more likely to improve batch crystallizer performance than optimizing the growth/saturation concentration trajectory. (3) For rapid process development, the most reasonable approach is to use the Mullin-Nyvlt trajectory and seek to improve process performance by adjusting seed properties.

The best objective function for seeded batch crystallization

“…It does not depend on any kinetic parameters such as k g , k b , etc. Ward, et al showed that in almost all cases, this trajectory performs almost as well as the optimal trajectory at minimizing the nucleated mass.…”

“…The initial seed crystal size distribution is parabolic (as discussed by Ward et al) with dimensionless width w ′ = 1, seed mean size x ′ 0 = 1.5, and dimensionless seed mass m ′ s = 0.1. The growth rate trajectory that minimized each objective function was determined using the simulated annealing toolbox in Matlab.…”

“…The crystallization process model used in this work is the dimensionless model originally presented by Ward et al This model has the advantage that it is not particular to any solute–solvent system. The key equations are presented here, and the reader is referred to Ward et al for the details.…”

“…With a suitable choice of dimensionless variables (see Table and Ward et al for further details), the following dimensionless model can be obtained …”

“…Table provides an incomplete list of journal articles in which an optimal saturation concentration trajectory is determined based on an objective that is formulated in terms of the final moments of the CSD (either seed crystals, nucleated crystals, or a combination of these). There are more than 10 different objectives reported in 22 different articles . Many of these objective functions can be classified into one of three broad groups: those that aim to maximize a product average size (either the number‐average size or weight‐average size), those that aim to maximize a moment of the seed crystals or minimize a moment of the nucleated crystals, and those that attempt to minimize a coefficient of variation (either the number coefficient of variation or the mass coefficient of variation).…”