mathematical modeling the effect of catalyst initial shape and the crack pattern in olefin copolymerization

a two-dimensional (2d) single particle model for the copolymerization of propylene-ethylene with heterogeneous ziegler-natta catalyst is developed. the model accounts for the effects of the initial shape of the catalyst and carck/ pore patterns on the copolymer composition, polymerization rate and the average molecular weight properties. the spherical and oblate ellipsoidal shapes of catalyst particle and four different pattern distributions of cracks and pores in a growing particle are studied in this simulation. it is assumed that the diffusion coefficient of monomers in the cracks/pores is 10 times higher than the compact zone of the particle.in other word, the cracks are distinguished from parts with higher monomer diffusion coefficient.the dynamic 2d monomer diffusion-reaction equation is solved together with a two-site catalyst kinetic mechanism using the finite element method. simulation results indicate that the initial shape of catalyst changes the average copolymer composition only in the early stage of polymerization, but the crack/pore patterns in the growing particle have a strong impact on the copolymer composition in the polymer particles due to the change ofmass transfer limitations.