Morphological population balance model in principal component space

Abstract

AbstractMultidimensional and morphological population balance (PB) models for crystallization processes have been proposed in literature, which can be used to simulate the dynamic evolution of particle shape as well as particle size distribution. These models, however, can become computationally expensive when the crystal has a large number of independent faces, and are not applicable to noncrystalline, irregularly shaped particles such as those encountered in granulation and milling. This article addresses these challenges by introducing principal component analysis (PCA) into morphological PB modeling. PCA transforms the shape description of a particle from a high‐dimensional domain to a lower dimensional, principal component (PC) space. Morphological PB models can then be built in this latent variable space, greatly reducing the computational complexity. It also makes it possible to model noncrystalline irregularly shaped particles. The original particle shape at any time can be reconstructed from the PCs. © 2009 American Institute of Chemical Engineers AIChE J, 2009