Reachability of particle size distribution in semibatch emulsion polymerization



Reachability analysis is critical in the determination of achievable end-point products for complex process systems. In emulsion polymerization, an economically important method of producing various products, particle size distribution (PSD) is an important property of the latex produced. However, the population balance modeling framework does not yield direct solutions to reachability analysis for the resulting nonlinear distributed systems. In this article, a programming-based approach is introduced for the reachability analysis of the final PSD for general particulate systems described by population balance models. In the application to a semibatch styrene homopolymerization system, the reachable region is defined for both the nominal and perturbed cases, with final PSDs characterized as multi-Gaussian distributions. Sensitivity studies reveal the limiting factors in determining the achievable final products, and quantitative criteria are developed. The evolution of the reachable region in the case of midcourse correction reveals the difficulties encountered during in-batch control, and shows the best control performance achievable given the limited on-line measurements. © 2004 American Institute of Chemical Engineers AIChE J, 50: 3049–3059, 2004