Solution of population balances with breakage and agglomeration by high-order moment-conserving method of classes

A general high-order method of classes framework for numerical solution of population balances is developed and tested. It is based on conservation of an arbitrary number of moments in the numerical discretization of the integrodifferential population balance equation. Optimal construction of the product tables for agglomeration and breakage events are discussed separately. It is shown that if more than two moments are set to be conserved in the numerical scheme, accuracy can be improved by several orders of magnitude compared to the state-of-the-art methods. Several test cases related to pure breakage or agglomeration, and also to simultaneous breakage and agglomeration, are shown. The results show that the present method is extremely accurate for all tested cases already with a limited number of size categories.