(23f) The Morphological-Population Balance Model (M-PBM) Generator. Application to Additives Controlled Crystallization of KAP

This talk will present a comprehensive framework to develop M-PBM for crystal morphology distributions evolving in a supersaturated solution. The model considers faces on seed crystals and energetically favorable F-faces to assess the polyhedral symmetry and identify internal coordinates. A set of all possible morphologies is generated using a combinatorial approach. These morphologies are further decomposed to yield polyhedral cones representing morphology domains in crystal state space. A bidirected graph is constructed where the nodes and edges correspond to morphology domains and their transitions, respectively. The population balance equations are identified for each node accounting for morphology transformations in dynamic environments. The solution of M-PBM can be readily obtained by the method of characteristics which takes considerably less computation time as compared to other numerical methods. The application of M-PBM to additives controlled crystallization of Potassium Acid Phthalate (KAP) is considered. The optimal profiles of additives concentration are computed for maximizing purity, productivity and sphericity of KAP crystals.