An operator-splitting finite element method for the efficient parallel solution of multidimensional population balance systems

A finite element method for solving multidimensional population balance systems is proposed where the balance of fluid velocity, temperature and solute partial density is considered as a two-dimensional system and the balance of particle size distribution as a three-dimensional one. The method is based on a dimensional splitting into physical space and internal property variables. In addition, the operator splitting allows to decouple the equations for temperature, solute partial density and particle size distribution. Further, a nodal point based parallel finite element algorithm for multi-dimensional population balance systems is presented. The method is applied to study a crystallization process assuming, for simplicity, a size independent growth rate and neglecting agglomeration and breakage of particles. Simulations for different wall temperatures are performed to show the effect of cooling on the crystal growth. Although the method is described in detail only for the case of d=2 space and s=1 internal property variables it has the potential to be extendable to d+s variables, d  =2, 3 and s≥1s≥1.

► An efficient and novel numerical scheme is presented for multidimensional population balance systems.
► It alleviates the “curse of dimensionality” associated with the solution of highdimensional population balance equation.
► Fully practical nodal point based operator-splitting parallel finite element algorithm is presented.
► Model are present for 2D–3D population balance system, which models crystallization process in 2D crystallizer.