A Continuous Model for Ziegler-Natta Polymerization

Abstract

Our purpose here is the construction of a mathematical model for the phenomenon of polymerization in a Ziegler-Natta reactor. In this device a gaseous monomer diffuses through an agglomerate of catalytic particles. The process of polymerization takes place on the surface of each particle, so that a polymeric layer grows around it. The growth of such layers is affected, among other factors, by the local concentration of monomer, so that equations describing the expansion of the polymeric layer must be coupled with a diffusion equation for the monomer. Moreover that polymerization releases heat, so that an energy equation, determining temperature, is to be included in the model too. In fact, this is one of the most interesting features of the phenomenon, because the polymerization rate is affected by temperature; moreover, if the polymer becomes too hot, it may partially melt, thereby preventing the monomeric gas from reaching the catalyst surface (see [4]). Of course one tries to avoid the last occurrence.