SIMULATING JOINT CHAIN-LENGTH AND COMPOSITION FRACTIONS FROM SEMIBATCH ETHYLENE COPOLYMERIZATION EXPERIMENTS

Linear low density polyethylenes produced using cy-olefin comonomers a nd heterogeneous Ziegler-Natta catalysts have broad chain length (CL) and copolymer composition (CC) distributions. Multiple types of active sites on the catalyst are the cause of these broad and often multimod al distributions that influence both end-use and processing behaviour of the copolymer. Measurement of the joint CL and CC distribution can be accomplished by cross-fractionating polyethylene by Temperature Ris ing Elution Fractionation (TREF) and Size Exclusion Chromatography (SE C). Using these techniques, copolymer can be separated into bins corre sponding to specific CC and CL ranges. In this article, Stockmayer's ( 1945) bivariate distribution is used to develop a methodology for mode lling the quantity of accumulated copolymer that corresponds to each s pecific bin of the joint CL and CC distribution. First, the instantane ous joint CL and CC distribution for polymer produced at each site typ e is integrated over specified finite ranges of composition and chain length. The end points of these ranges correspond to TREF fraction com position limits and selected chain lengths from SEC analyses. The inst antaneous rate of polymer production from all site types in each of th e bins is then calculated. The polymer accumulated in each bin over th e course of a polymerization experiment is determined by numerically s olving a set of ordinary differential-equations. This methodology can be used to predict experimental TREF and SEC cross-fractionation resul ts for copolymer produced dynamically in semi-batch laboratory reactor s. The resulting predictions can then be used with experimental result s to estimate parameters in kinetic models describing ethylene copolym erization with multiple active site catalysts.