(400a) Numerical Approximation of a Population Balance Equation Involving Aggregation, Growth and Nucleation

This work is concerned with the derivation of the numerical solution of a population balance equation (PBE) for simultaneous aggregation, growth and nucleation processes which usually occurs in many granulation units like sprayed fluidized bed granulator, twin screw granulator etc. In order to find the numerical solution of combined aggregation and growth PBE, an approach namely finite volume scheme for the aggregation and a Lagrangian method for growth is proposed. However, for a simultaneous aggregation and nucleation processes, nucleation is handled by considering another source located near particle size 0. Additionally, the numerical approximation of accompanying aggregation, growth and nucleation is also derived using the notion of finite volume scheme. In contrast to Qamar et al. (2009), it is shown that no reformulation of the original PBE in mass balance form is required to derive the stable numerical solutions for simultaneous processes. The finite volume scheme authenticates the applicability, generality, robustness and efficiency to handle complex simultaneous processes. The proposed finite volume approximation is compared with an existing finite volume scheme (Qamar et al., 2009) as well as with newly derived analytical solutions of zeroth and first order moments. It is demonstrated that the proposed finite volume scheme is highly accurate, efficient and has the tendency to overcome numerical diffusion and dispersion as compared to the existing finite volume scheme.