Calculation of the Optimal Distribution of the Active Metal Site Concentration in a Ziegler-Natta Catalyst to Maximize Polymer Yield in Olefin Polymerizations

Abstract

Abstract It is well-known that depending on the catalyst preparation conditions the concentration of active metal sites in Ziegler-Natta catalysts can vary considerably with particle radius. This non-uniform concentration of active metal sites can result in non-uniform polymerization conditions in the catalyst particle that can affect the particle morphology and polymerization rate. In the present study, a comprehensive single particle growth model is developed to investigate the effect of the active metal site concentration distribution on particle growth, particle overheating and polymer yield in heterogeneous Ziegler-Natta catalytic olefin polymerizations. Following the original work of Kanellopoulos et al. (2004) a random pore polymeric flow model for a single particle was developed to describe the spatial-temporal monomer concentration and temperature profiles in a growing catalyst/particle. To assess the effect of the active metal site concentration distribution in a Ziegler-Natta catalyst/particle on particle growth and particle overheating, a number of numerical simulations were carried out, using the developed random pore polymeric flow model, by varying the initial catalyst diameter, monomer partial pressure, particle morphology (e.g., porosity) and catalyst active metal site distribution. It was shown that depending on the initial active metal site distribution, the predicted polymerization rate, particle overheating and polymer yield can vary considerably. Finally, a non-linear optimization problem was formulated to calculate the optimal active metal sites spatial distribution in a Ziegler-Natta catalyst in to maximize the polymer productivity or/and minimize the total active metal concentration. In particular, via the combined solution of the single particle’s PDEs and a non-linear optimizer, the optimal spatial distribution of active metal sites in the catalyst was calculated that minimized the total active metal concentration for a given value of polymer yield and productivity.