New Discrete Formulation for Reduced Population Balance Equation: An Illustration to Crystallization
Mehakpreet Singh, Gavin Walker
Abstract
In this paper, we focus on providing a discrete formulation for a reduced aggregation population balance equation. The new formulation is simpler, easier to code, and adaptable to any type of grid. The presented method is extended to address a mixed-suspension mixed-product removal (MSMPR) system where aggregation and nucleation are the primary mechanisms that affect particle characteristics (or distributions). The performance of the proposed formulation is checked and verified against the cell average technique using both gelling and non gelling kernels. The testing is carried out on two benchmarking applications, namely batch and MSMPR systems. The new technique is shown to be computationally less expensive (approximately 40%) and predict numerical results with higher precision even on a coarser grid. Even with a revised grid, the new approach tends to outperform the cell average technique while requiring less computational effort. Thus the new approach can be easily adapted to model the crystallization process arising in pharmaceutical sciences and chemical engineering.