Process modeling of semibatch reaction crystallization
Sammanfattning: This thesis aims at increasing the fundamental understanding of reaction crystallization by modeling, simulations and parameter estimation. Benzoic acid is used as the model compound. A population balance model of single-feed semi-batch reaction crystallization is developed, accounting for chemical reaction, mixing, nucleation, growth, and growth rate dispersion. The model is evaluated by comparing the results with data from previously published semi-batch experiments. Two different mechanistic mixing models are used to describe mixing: the engulfment model with mesomixing and the segregated feed model. When the engulfment mixing model is used, the semi-batch model correctly captures the variation in weight mean size with varying agitation rate, feed point location, reactant concentration, feed pipe diameter, and total feed time. However, at scaling-up, a decrease in weight mean size with increasing crystallizer volume is predicted, which is not found experimentally. When the segregated feed model is used to describe mixing, the results are unsatisfactory. The crystallization kinetics have a great impact on the performance of the model, influencing both the final mean size, and the predicted influence of changes in the processing conditions. The kinetics of nucleation and growth are determined from T-mixer experiments. Three population balance models of increasing complexity are developed and used in parameter estimations by non-linear optimization. The T-mixer model accounts for nucleation, growth and growth rate dispersion. Five or six kinetic parameters are estimated using data from 14 experiments at 8 different initial supersaturation levels. Depending on the assumptions in the model, different kinetics are estimated. The main differences are found in the nucleation and growth rate constants. The T-mixer kinetics yields unsatisfactory results in the semi-batch simulations, with a predicted mean size that is significantly smaller than the experimental and a less pronounced influence of processing conditions that are related to mesomixing. An attempt is made to model aging of benzoic acid precipitates formed at high supersaturation. A model of Ostwald ripening gives a reasonably good description of the changes in the size distribution, provided that the observed shape change during aging is accounted for. However, significant deviations remain, in particular, the broadening of the aged size distribution is more pronounced in the experiments than in the simulations. There are indications that the observed aging might be caused by kinetic ripening, driven by a transformation to a more regular shape or a less strained crystal, rather than by Ostwald ripening.
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