Optimization of Simple Batch Crystallization Systems Considering Crystal Shape and Nucleation

Abstract

Optimal control theory (OCT) is applied to derive nearly analytical solution to single- and multiobjective dynamic optimization problems for a two-dimensional batch crystallization system. Objective functions based on the product crystal aspect ratio, number of nuclei, and nucleated volume are studied. It is shown that applying a constant growth rate trajectory can minimize the product aspect ratio while early- and late-growth trajectories can minimize the nucleated number and volume, respectively. It is also found that there exists an optimal target aspect ratio between the maximum and minimum feasible values which permits a solution with the best single objective values for case of minimizing nucleated number or nucleated volume. Pareto-optimal fronts (PFs) for nucleated number and volume under different target aspect ratio are also plotted to understand the trade-off between objectives. The result suggests that the trade-off is stronger when the value of the aspect ratio constraint is near the midpoint of the feasible interval.