Modelling and control considerations for particle populations in particulate processes within a multi-scale framework

Abstract

This article deals with a class of distributed parameter systems, the socalled particulate processes that are modelled by population balances. Population balances have been employed in modelling chemical, physical and biological processes for over 40 years. The population balance equation is a hyperbolic partial differential equation that presents challenges in numerical solution. Recent advances in the understanding of the underlying mechanisms of the particulate processes enables formulation of more comprehensive population balance models for these complex processes by the incorporation of multi-scale representations for the kernels of the constituent rate processes. These multi-scale modelling ventures lead to additional numerical challenges for model solution. Further, the purposes of these comprehensive models is towards use for control of distributions in these processes. This control becomes challenging in view of the different scales represented by the manipulated and controlled variables and in view of the underlying process complexity. This article first presents an efficient numerical solution technique to handle multi-scale population balance models, and then discusses a potential model-based strategy for control of distributions in particulate processes. © 2006 Springer-Verlag Berlin Heidelberg.