Numerical solution of mixed continuous–discrete population balance models for depolymerization of branched polymers

• A mixed continuous–discrete population balance equation is formulated.
• Chemical considerations on the random-chain scission mechanism are included.
• A bivariate population balance with three scission mechanisms is solved with DQMOM.
• DQMOM is used for a bivariate mixed continuous–discrete formulation.
• DQMOM is validated for breakage with Monte Carlo simulations.

A simulation technique to describe the depolymerization of branched polymers via bivariate population balance modeling was developed. The polymers were characterized by two internal coordinates: the number of monomer units and branching bonds. Three commonly used mechanisms for depolymerization (random chain, end chain, and random debranching scission) were applied and formulated such that only physically possible polymers were created. The mechanisms and the population balance equation were formulated in a mixed continuous–discrete manner. The population balance equation was solved using the Direct Quadrature Method of Moments (DQMOM). With this algorithm, the time evolution of the distribution with respect to the internal coordinate was computed. In addition, the algorithm was validated through comparison with Monte Carlo simulations. Notably, the accuracy of the mixed continuous–discrete formulation was significantly higher that of the continuous formulation. However, DQMOM was found to be unsuitable for describing the temporal evolution of the distribution for random scission.