Dynamic Mathematical Modelling of Polymerization of Olefins Using Heterogeneous and Homogeneous Ziegler-Natta Catalysts

Abstract

<p>An integrated methodology based on Stockmayer's bivariate distribution for the dynamic mathematical modelling of the kinetics of olefin polymerization using heterogeneous and homogeneous Ziegler-Natta catalysts has been developed. This methodology uses polymer characterization via size exclusion chromatography (SEC), temperature rising elution fractionation (TREF), and carbon-13 nuclear magnetic resonance (¹³C NMR) to estimate polymerization kinetics parameters and provide information about the types of active sites of the catalyst.</p> <p>A novel and versatile mathematical model for the dynamic simulation of binary copolymerization of olefins using Ziegler-Natta catalysts has been proposed. This model calculates the complete distributions of chemical composition and molecular weight of polyolefins made with catalysts containing multiple active site types and subject to intraparticle mass and heat transfer resistances. This model has a very attractive mathematical formulation that permits easy adaptation to situations in which intraparticle mass and heat transfer resistances are negligible and can also be conveniently combined with mathematical models for the dynamic macroscopic simulation of polymerization reactors for process simulation, optimization and control studies.</p> <p>The homopolymerization of propylene and ethylene using a titanium-based heterogeneous catalyst was investigated. The presence of hydrogen during the polymerization of propylene was found to increase the rate of propylene polymerization by creating new active site types. This was clearly shown using SEC and TREF analyses of the polypropylenes.</p> <p>A systematic methodology for the deconvolution of the molecular weight distribution (MWD) of linear polyolefins made with multiple site type catalysts has been developed. The MWD of polyolefins measured by SEC is deconvoluted into individual most probable chain length distributions using a mathematical method that takes advantage of the conditional linearity of the optimization problem.</p> <p>A mathematical model for simulation of TREF fractionation of binary copolymers made with multiple site type catalysts using Stoclanayer's bivariate distribution has been developed. This is the first time a mathematical model is proposed to describe the MWD of TREF fractions using a phenomenological approach considering the influence of the bivariate distribution of molecular weights and copolymer composition in the fractionation. The modelling of TREF with this model provides an ideal limiting case for the fractionation of binary linear copolymers with broad molecular weight and composition distributions and is useful in interpreting TREF fractionation results.</p>