commercially using metallocene catalysts in a variety of different reactor technologies including gas-phase and solution reactors. [3] Metallocene catalysts are organometallic compounds with a transition metal such as Zr or Hf, surrounded by cyclic organic ligands. [3] Metallocene aluminoxane catalysts can produce PE with narrow molecular weight distribution (MWD) and comonomer composition distribution (CCD), which can result in excellent mechanical properties, but limited processability. The MWD of PE produced using metallocene catalysts can be broadened using several techniques. Using a combination of two or more metallocene catalysts in the same reactor can produce PE products with a tailored joint MW and composition distribution that leads to favorable processing and end-use properties. [3] Supporting a single type of metallocene catalyst on a solid support can also result in the formation of two or more types of active catalyst sites, which may have a beneficial influence on polymer properties. [2] Interactions with different activators or scavengers in the reactor system can also result in multi-site behavior. [4] When multiple types of active sites are present in a reactor, each site type instantaneously produces PE of a different MW and composition distribution. For example, in a two-site metallocene system, one site may tend to produce PE with higher molecular weight and higher comonomer incorporation than the other site, resulting in broad orthogonal composition distribution (BOCD). [4,5] The joint MW and composition distribution of ethylene/α-olefin copolymers produced using metallocene catalysts depends on the reactor operating conditions (e.g., temperature and the concentrations of ethylene, comonomer, and hydrogen, which is used as a chain-transfer agent to control average molecular weight). As a result, PE with tailored properties can also be produced using multiple reactors in series or a single reactor containing multiple zones with different operating conditions in each. [6] When designing new product grades and deciding how best to make them, PE producers benefit from mathematical models that predict product properties from reactor operating conditions. [6] The main difficulty associated with model development for PE processes is determining suitable values for the many kinetic A dynamic model is developed to predict detailed chain-length and comonomer incorporation behavior during gas-phase ethylene/hexene copolymerization using a supported hafnocene catalyst. The multi-site catalyst results in a copolymer with a broad orthogonal composition distribution (BOCD) where the high molecular-weight tail has high hexene incorporation. The model relies on gel permeation chromatography measurements obtained using multiple detectors (GPC-4D), so that the composition of the copolymer is determined for different chain-length fractions. Chainlength distributions are discretized into bins so that comparisons can be made between GPC-4D data and model predictions. Parameter estimation is aided by an estimabil...

A dynamic model is developed for gas-phase ethylene/1-hexene polymerization with a three-site hafnocene catalyst. The model accurately predicts molecular weight and comonomer composition distributions for 15 lab-scale copolymerization runs performed at different temperatures. The experimental runs used to fit this model are performed at temperatures between 60 and 85 °C. Gas-phase concentrations are measured every 2.7 min throughout each run. Predicted chain-length distributions are discretized to aid model development, keeping the number of ordinary differential equations manageable. Kinetic parameters at the reference temperature of 81 °C and activation energies are estimated. Using parameter subset selection techniques, it is determined that 53 of the 60 model parameters should be estimated using the product characterization and reactor data. An additional data set obtained at 85 °C is used for model validation, confirming the predictive power of the model. The proposed model and its parameter estimates can aid selection of operating conditions to achieve targeted polymer properties.

A three-site metallocene catalyst is used in a gas-phase semi-batch reactor to produce ethylene/hexene copolymers. At the end of each batch, polyethylene (PE) is collected and analyzed to determine the carbon-13 nuclear magnetic resonance ( 13 C-NMR) triad sequence distribution. Joint molecular weight (MW) and composition distribution data are obtained using gel permeation chromatography with an infrared detector (GPC-IR). Data from ten experimental runs are used for kinetic parameter estimation. Using a mean-squared error (MSE) selection methodology, 23 of the 36 model parameters are selected for estimation using the available polymerization rate and PE characterization data. The remaining parameters are held at initial guesses to avoid overfitting. Addition of the triad data to the parameter estimation problem allows for one additional parameter to be estimated and results in improved parameter estimates. Standard deviations of all but one of the estimated parameters decreased due to inclusion of triad data. The updated parameter estimates result in good fits for the triad data and for joint MW and composition data. The model accurately predicts four validation data sets not used for parameter estimation. The new model and its updated parameter estimates will be valuable for scaling up new polymer grades from laboratory-scale to commercial-scale.