Population balance discretization for growth, attrition, aggregation, breakage and nucleation

Abstract

This paper presents a new discretization method to solve one-dimensional population balance equations (PBE) for batch and unsteady/steady-state continuous perfectly mixed systems. The numerical technique is valid for any size change mechanism (i.e., growth, aggregation, attrition, breakage and nucleation occurring alone or in combination) and different discretization grids.The developed strategy is based on the moving pivot technique of Kumar and Ramkrishna and the cell-average method of Kumar et al. A novel contribution is proposed to numerically handle the growth and attrition terms, for which a new representation of the number density function within each size class is developed. This method allows describing the number particle fluxes through the class interfaces accurately by preserving two sectional population moments.By comparing the numerical particle size distributions with analytical solutions of one-dimensional PBEs (including different size change mechanisms and particle-size dependent kinetics), the accuracy of the proposed numerical method was proved.