Kinetic study of olefin polymerization with a supported metallocene catalyst. IV. Comparison of bridged and unbridged catalyst in gas phase

Chakravarti, S.; Ray, W. Harmon; Zhang, Simon X.

doi:10.1002/app.1571

Cited by 24 publications

(38 citation statements)

References 10 publications

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“…The comonomer is able to activate some catalyst sites that cannot be activated by ethylene. Site transformation 9. The higher α ‐olefin is able to transform active catalyst sites, which are activated by ethylene, into a new more‐active type of site. More rapid catalyst site activation 9,10. Higher α ‐olefins can activate catalyst sites much faster than ethylene. Slow deactivation 9,10.…”

Section: Accounting For the Comonomer Effectmentioning

confidence: 99%

“…The higher α ‐olefin is able to transform active catalyst sites, which are activated by ethylene, into a new more‐active type of site. More rapid catalyst site activation 9,10. Higher α ‐olefins can activate catalyst sites much faster than ethylene. Slow deactivation 9,10. Higher α ‐olefins can stabilize catalyst sites activated by ethylene, which slows deactivation and enhances polymerization rate.…”

Section: Accounting For the Comonomer Effectmentioning

confidence: 99%

“…More rapid catalyst site activation 9,10. Higher α ‐olefins can activate catalyst sites much faster than ethylene.…”

Section: Accounting For the Comonomer Effectmentioning

confidence: 99%

“…These models can give qualitative explanations of important phenomena during ethylene polymerization and qualitative predictions of the relationships between operating conditions and polymer properties, but no experiments have been used to verify these explanations and predictions. Although a few researchers have estimated the unknown parameters in their models using experimental data, they have resorted to adjusting kinetic parameters manually8 or they have dealt with a simplified mechanism resulting in fewer model parameters 9–11. In this article, mathematical models are developed to simulate gas‐phase ethylene/hexene copolymerization using a supported metallocene catalyst.…”

Section: Introductionmentioning

confidence: 99%

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Mathematical Model and Parameter Estimation for Gas‐Phase Ethylene/Hexene Copolymerization With Metallocene Catalyst

Kou

McAuley

Hsu

et al. 2005

Macro Materials & Eng

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Summary: Models were developed to simulate gas‐phase ethylene/hexene copolymerization using a silica‐supported (BuCp)2ZrCl2 catalyst in a semi‐batch laboratory reactor. The models are able to predict ethylene consumption rate, gas composition drift during the experimental runs, as well as number‐and weight‐average molecular weight, and short‐chain branching levels, and triad sequence distributions of copolymer removed from the reactor at the end of each run. A single‐site model was first developed, but it failed to accurately predict the molecular weight data and its distribution. Sequentially, a two‐site model was built to improve model predictions. Parameter estimability analysis was performed to guide model simplification and to ensure that the parameter estimation problem would be well conditioned. After model simplification, which reduced the number of unknown parameters from 55 to 37, the parameters were estimated and good fitting of most experimental data was obtained. The simplified two‐site model was validated using the data from four extra experimental runs, which were not employed in the parameter estimation process. Most of the model predictions fall within the 95% confidence intervals of the experimental data.Model validation of hexene concentration. (The lines are model predictions and the solid diamonds with error bars are experimental data.)magnified imageModel validation of hexene concentration. (The lines are model predictions and the solid diamonds with error bars are experimental data.)

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Section: Accounting For the Comonomer Effectmentioning

confidence: 99%

Section: Accounting For the Comonomer Effectmentioning

confidence: 99%

“…More rapid catalyst site activation 9,10. Higher α ‐olefins can activate catalyst sites much faster than ethylene.…”

Section: Accounting For the Comonomer Effectmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Mathematical Model and Parameter Estimation for Gas‐Phase Ethylene/Hexene Copolymerization With Metallocene Catalyst

Kou

McAuley

Hsu

et al. 2005

Macro Materials & Eng

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“…For example, the parameters believed a priori to have an insignificant effect on model predictions can be fixed at a nominal value. 11 Alternatively, correlation information can be used to sequentially fix parameters at nominal values. 12 Other methods for parameter reduction include the following.…”

Section: àE=rtmentioning

confidence: 99%

Reparameterization of inestimable systems with applications to chemical and biochemical reactor systems

Ben-Zvi

2008

AIChE Journal

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in Wiley InterScience (www.interscience.wiley.com).Mathematical models of physical systems often have parameters that must be estimated from measured data. Inestimable models have more parameters than can be estimated from available data. In this work, a method for identifying inestimable parameters or parameter combinations is proposed. The method is based on partitioning the parameter space into estimable and inestimable subspaces. Parameter combinations in the inestimable subspace have little effect on measured values and can therefore be fixed at a nominal value. The number of effective parameters is thereby reduced to the dimension of the estimable subspace. The proposed method is applicable over a range of experimental conditions. Detailed examples, including a batch bioreactor and a three-phase reactor system, are included for illustration. Keywords: process control, control, parameter estimation IntroductionMathematical models of physical systems are used in almost every branch of science and engineering. Such models are, generally, functions of unknown parameters that must be estimated from available data. Often, models contain more parameters than can be estimated from a given data set. In this case the model parameters are said to be inestimable. Inestimability implies that there are several possible parameter values that yield statistically indistinguishable predictions.Estimability in models is a very useful property. If a model is estimable (from a given data set) then the value of each parameter in the model can be accurately determined. As a result, the model, or parameters, can be used for design, analysis, and scale-up. Furthermore, accurate parameter estimates allow system behavior to be extrapolated beyond the region where data is collected. This is especially useful for systems whose behavior cannot be studied under all conditions. For example, accurate parameter estimation may allow a clinician to choose an appropriate drug dosage for a human patient.The problem of inestimability has been well documented in the literature. [1][2][3][4] For every model that is inestimable there exists a simpler, estimable, model (i.e., one with fewer parameters) that provides near identical predictions over the region for which data is available. Usually, a sensitivitybased approach 1,3,4 is used to identify model parameters that have little or no effect on model predictions and can therefore be either lumped, discarded, or held at a fixed value for the purpose of estimation.The sensitivity-based framework for model simplification holds that a simpler identifiable model can be obtained by effectively removing some of the model parameters. However, the sensitivities of the model predictions to parameter values are functions of estimated parameter values and the experimental conditions. As a result, sensitivity analysis can suggest reparameterizations that only hold locally (i.e., near a nominal parameter value).In this work, a method is proposed for reparameterizing inestimable models. The proposed approach al...

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Dual‐site supported metallocene catalyst design for bimodal polyolefin synthesis

2007

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in Wiley InterScience (www.interscience.wiley.com).The processability of various polyolefins may be enhanced by producing one having a bimodal molecular weight distribution. Such polymers can be produced by loading the reactor with a catalyst on which two different catalytic sites are impregnated. The catalysts must be loaded with a proper ratio between the two catalytic sites to produce the desired polymer. The total loading should enable a maximum polymer production in the specified residence time while keeping the maximum transient temperature below a specified maximum, in order to avoid local melting and sheet formation. A model is presented that enables this catalyst design based on kinetic information about the initiation, propagation, and deactivation reaction rates of the two individual catalytic sites. The model simulations provide insight about the factors affecting the maximum safe loading of the two catalytic sites. We show here how to utilize kinetic information about each of the two catalytic sites to predict the optimum loading of dual-site metallocene catalysts. As the maximum temporal temperature occurs during the initial stages of the reaction, the site that leads to a faster generation of a temperature peak, exerts a stronger bound on the total polymer production than the second site. The larger the propagation and/or the initiation rate constants or their activation energies are, the lower should be the catalyst loading. The deactivation rate constants affect both the relative site loading of the two sites as well as the total production. The total polymer production can be increased by decreasing the deactivation rate of the more active site.

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Kinetic study of olefin polymerization with a supported metallocene catalyst. IV. Comparison of bridged and unbridged catalyst in gas phase

Cited by 24 publications

References 10 publications

Mathematical Model and Parameter Estimation for Gas‐Phase Ethylene/Hexene Copolymerization With Metallocene Catalyst

Mathematical Model and Parameter Estimation for Gas‐Phase Ethylene/Hexene Copolymerization With Metallocene Catalyst

Reparameterization of inestimable systems with applications to chemical and biochemical reactor systems

Dual‐site supported metallocene catalyst design for bimodal polyolefin synthesis

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