A population balance approach for the description of particle size distribution in suspension polymerization reactors

There exist modelling and experimental methodologies to meet productivity (conversion and batch time) and product molecular weight distribution (MWD) quality specifications in suspension polymerization reactors. However, no counterpart exists to address the issue of particle size distribution (PSD), which is of fundamental importance in determining suspension stability and product quality attributes. In industrial practice, PSD considerations are guided by mean-size correlations from the Weber number theory. The setting up of an industrial reactor usually demands considerable scaling and testing efforts. In this work, we obtain a model to describe the evolution of the PSD in a suspension polymerization reactor. First, relevant phenomena are identified and modelled individually: suspension MWD, suspension viscoelasticity, interfacial tension, injection—dissipation of mechanical energy and drop breakage—coalescence mechanism. A central point is the derivation of analytic expressions for breakage and coalescence rate distributions. A drop population balance leads to an integrodifferential equation whose numerical solution yields the evolution of the PSD. Breakage—coalescence parameters are estimated from the reported experimental data. Modelling identifies the role of individual phenomena and their interplay.