SIMULATION AND CONTROL OF MULTIDIMENSIONAL CRYSTALLIZATION PROCESSES

Abstract

In this article, solving the population balance equation (PBE) and controlling the final particle size for crystallization problems have been addressed. For solving the general form of multidimensional PBE, a numerical method called conservation element and solution element (CE/SE) has been used. By applying this method to one- and two-dimensional crystallization problems, it has been shown that this technique can handle all types of source terms in the PBE. Model accuracy has been checked with experimental data reported in the literature and also with the analytical solution of PB-type equations. Control of final particle size was formulated in an optimization framework. To obtain a desired final size distribution for one-dimensional crystallization, the optimal temperature trajectory was achieved for size-dependent growth rate case with the agglomeration effect. For the two-dimensional case, the aspect ratio was controlled and the crystallization batch time minimized. To track the optimal temperature trajectories, PI controllers were used. Simulation results indicate that the desired final size distribution for the one-dimensional case and the aspect ratio for the two-dimensional case were approached very closely.