Multi-level solution of population balance models employing a hierarchical two-tier strategy

A computationally-efficient solution technique was presented by C.D. Immanuel and F.J. Doyle III (2003) for population balance models accounting for nucleation, growth and coagulation (aggregation). The technique exploits the hierarchy of the process and formulates a two-tier solution strategy. The technique was employed for the solution of emulsion polymerisation models that are characterised by one-dimensional population balances. In that application, very fine gridding was employed for the internal coordinates for accuracy of discretisation, and very efficient computation times were obtained. Several other systems to which this technique is applicable necessitate a multi-dimensional characterisation of the population (distribution along multiple internal coordinates). In such cases, a fine gridding of the independent variable is usually infeasible. The present study proposes a multi-level gridding strategy to operate within the hierarchical two-tier technique.