On the use of sectional techniques for the solution of depolymerization population balances: Results on a discrete-continuous mesh

To study the discrete bond-breaking phenomena of depolymerization, the use of a fully continuous Population Balance Equation (PBE) is inadequate to embody all the inherent characteristics of the process, thus resulting in the need for a discrete-continuous mesh. Here, the performance of the fixed pivot technique (FPT) and the cell average technique (CAT) in approximating discrete depolymerization was extensively compared and evaluated. Both methods show different accuracy depending on the breakage mechanisms. For chain-end scission, the FPT and the CAT solutions coincide and satisfactorily predict the population densities and moments. We identified a previously-not-reported issue of a precipitous drop in the number density at the boundary of discrete and continuous region specifically for chain-end scission. We fixed this problem by modifying the particle allocation functions at the boundary points. For random scission, by introducing modifications that mimic the inherently discrete bond-breaking depolymerization process, both techniques predict the population densities and moments accurately at a very coarse mesh, even though the performance of the CAT pales in comparison with the FPT. In all assessed cases, the FPT is more computationally efficient and easily implemented. The assessments in this present work intend to provide a clear-cut direction to efficient and economical modelling of depolymerization processes.