Fast High-Resolution Method for Solving Multidimensional Population Balances in Crystallization

Abstract

High-resolution (HR) finite-volume methods can provide an accurate numerical solution of population balance equations describing crystallization processes. To satisfy the stability requirements, the time step (Δt) for the available HR methods needs to be selected conservatively, rendering them computationally expensive for processes with size-dependent growth rates. In this paper, we propose a coordinate transformation scheme to improve the solution time of HR methods applied to batch crystallization processes with nucleation and size-dependent growth. The coordinate transform takes advantage of the functional form that is used to describe the size dependency of the growth rate. Using benchmark examples, we demonstrate that the proposed method provides a more significant reduction in the solution time than existing HR methods, while retaining the same level of accuracy.