Optimization of batch crystallization with constraints

Three published crystallization kinetics from batch crystallizer is compiled, and the simulation and optimization of crystallization process are also provided. The results suggest that a late growth policy would be appropriate to minimize the final nucleated crystal mass. However determining the optimal curve of temperature or solvent mass is difficult and requires a kinetic model. Adding constraints on operating curve is a common method in industries. The simulation results of optimal procedure with constraints illustrate a trade-off between mass of nucleated crystals and equipment costs. Another problem often encountered in practical operation is hard to collecting useful data to find crystal kinetics. When dimensionless temperature or solvent mass is plotted versus dimensionless time, the optimal trajectory for many systems is similar for a given constraint. Therefore, for each constraint the results of many systems are fitted to a single curve which can be applied without knowledge of the kinetic parameters. Knowing the total batch time, initial and final value of manipulated variable, we can find a nearly optimal operating curve in a specific constraint. The average deviation between each optimal trajectory and regressed curve is 5.03%. Mullin-nyvlt, cubic trajectory and regressed curve may applicable in different system. Linear trajectory is no applicable in any system.