A model-based methodology is proposed to describe fragmentation of polymer particles during the very early stages of heterogeneous olefin polymerization reactions. The method is based on the analysis of the particle capacity to release the amount of energy that is accumulated in its interior during the polymerization, due to the fast polymer production. The balance between the rates of energy accumulation and dissipation inside the polymer particle is calculated with the help of a dynamic mathematical model of the prepolymerization reaction. The combination of the presented fragmentation criteria and of the dynamic model may allow one to design the prepolymerization step more precisely and to predict the morphology of the final polymer particles as a function of the initial catalyst particle diameter, reactor temperature, reactor pressure and concentration of active sites. Numerical examples are presented for gas and slurry propylene polymerizations.
Summary: A two phase dynamic model is proposed here for the first time to describe the first stages of heterogeneous olefin polymerization and to improve predictions of particle morphology. Taking into account the solid and fluid phases, the two phase model allows for the calculation of the convective flux inside the growing polymer particle. Numerical simulations performed for both gas and slurry polymerizations show that the performances of the traditional diffusion model and of the proposed heterogeneous model are similar when mild polymerization conditions are considered, but may be very different when vigorous polymerization conditions are analyzed. It is shown that the development of convective flow inside the particle can exert a large influence on the course of the polymerization and on the final morphological characteristics of the polymer particle. When the initial catalyst particle contains inert material, it is also shown here that the inert material can contribute to a reduction of local reaction rates during particle breakup and, therefore, to a more uniform particle fragmentation.Schematic representation of a nascent polymer particle.magnified imageSchematic representation of a nascent polymer particle.
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