Robust optimal temperature swing operations for size control of seeded batch cooling crystallization

Robust optimal temperature swing operations for a seeded batch cooling crystallization process with size-dependent kinetics were derived for minimizing the amount of fines, and their robust performances were evaluated through simulation studies. The nominal optimal temperature swing profile, which does not incorporate any model errors or operating condition perturbations in the optimization calculation, was found to have a robustness problem. Complete dissolution of seed crystals may occur because of the temperature swing operation, although the temperature swing, if appropriately applied, can significantly reduce the amount of fine crystals. The robust optimal trajectory, which was obtained from a robust particle swarm optimization calculation by considering model errors, outperformed the nominal trajectory model, avoiding complete dissolution in all 50 000 cases in a Monte Carlo experiment. Furthermore, k-means clustering analysis was applied to the simulation data to reveal that the performance was still sensitive to initial perturbations in the operating conditions, i.e., the initial super-saturation and seed size.