Time optimal production of a specified particle size distribution in emulsion polymerization

The particle size distribution (PSD) is a key feature of a latex that strongly influences the viscosity and other attributes of the product which are critical in applications. The objective of this contribution is to establish a rigorous model for the simulation of the PSD and to use this model to perform optimal control of the PSD. The established model consists of two major parts: a lumped and a distributed submodel. The lumped part is a kinetic submodel that describes the reaction kinetics, mass balances, computation of the average number of radicals per particle. The essence of this submodel is the growth rate kernel which connects the two submodels. The distributed part makes use of a population balance equation (PBE) to compute the evolution of the PSD. In the optimization section, the computation of the monomer feed rate is performed because the solution of a constrained optimization problem where the batch time is the performance index which is minimized and the difference between the specified and obtained PSDs (error) and the heat removal capacity of the reactor jacket enter as constrains. The different aspects of the optimization problem solution are reported and discussed.