Accounting for Temperature Effects When Predicting Molecular Weight and Composition Distribution for Gas‐Phase Polyethylene Produced using a Multisite Catalyst

Abstract

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.

Modeling and Parameter Estimation for Gas‐Phase Polyethylene Product Properties Using Dynamic and Steady‐State Data

“…These 16 lab‐scale experimental runs were used in our previous study. [ 9 ] Reaction temperatures and average copolymer properties obtained at the end of each run are summarized in Table 3 . Each SB copolymerization run was performed in an autoclave reactor, shown in Figure 1 , at constant temperatures ranging from 60 to 85 °C.…”

“…Details regarding how the discretization was done can be found in our previous work. [ 9 ] It was assumed that the bins are narrow enough so that the average molar mass and average comonomer incorporation within each bin can be used when converting from MWD to CLD. For this catalyst, the chain lengths of interest range from 10 2 to 10 4.6 monomeric units.…”

“…Equations for the corresponding dynamic SB lab‐scale reactor model, which is also used in the current study are provided in the Supporting Information and have been described in detail elsewhere. [ 9 ]…”

“…The influence of temperature on the kinetic rate constants in Table 6 is considered using the following version of the Arrhenius equation $$$$\begin{equation}k = {k}_{{\rm{ref}}}{e}^{ - \frac{{{E}_{\rm{a}}}}{R}\left( {\frac{1}{T} - \frac{1}{{{T}_{{\rm{ref}}}}}} \right)}\end{equation}$$$$where k ref is the value of the kinetic rate constant at the reference temperature T ref =354.15 K and E a is the activation energy. [ 9,53–55 ] The kinetic scheme in Table 6 involves 30 kinetic parameters, resulting in 60 unknown parameters requiring estimation for the three site types: 30 kinetic parameters at the reference temperature of 81 °C and 30 activation energies.…”

“…[ 7 ] Past deconvolution and modeling studies involving this supported hafnocene catalyst reveal that three types of active sites are required to predict the shape and breadth of the MWD. [ 8,9 ]…”