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A dynamic model for gas-phase ethylene homopolymerization using a supported metallocene catalyst is developed in this work. A single-site model was first developed, with model parameters estimated from measurements from 11 experimental runs in a semibatch laboratory-scale reactor. Estimability analysis techniques were applied to aid in the parameter estimation. Although the single-site model provided good fits for both the polymerization rate and hydrogen concentration, it failed to accurately predict the molecular weight data and its distribution. Sequentially, a simplified two-site model was built to improve model predictions. The two-site model, which used three additional parameters, showed significant improvements over the single-site model. The two-site model was validated using the data from two 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.

The effects of end-group balance and moisture level on melt-phase polycondensation reactions were investigated using nylon 612. The polycondensation reaction was determined to be firstorder in amine ends and first-order in carboxyl ends at the relatively high temperature (284°C) and low water concentration conditions (0-0.002 mass fraction) studied, which are encountered in the later stages of nylon polymerization processes. Using data from this study and the nonisothermal data of Schaffer et al. (Chemical Pathways and Kinetics of the Later Stages of Nylon Polymerization Processes. Ph.D. Thesis, Queen's University, Kingston, Ontario, Canada, 2003; Experimental Study and Modeling of Nylon Polycondensation in the Melt Phase. Ind. Eng. Chem. Res. 2003, 42, 2946), a mathematical model was developed that can accurately describe changes in both the polyamidation reaction rate and the apparent equilibrium constant, with changing water concentration and temperature.

This paper presents a review of the mathematical modeling of two types of polymer electrolyte membrane fuel cells: hydrogen fuel cells and direct methanol fuel cells. Models of single cells are described as well as models of entire fuel cell stacks. Methods for obtaining model parameters are briefly summarized, as well as the numerical techniques used to solve the model equations. Effective models have been developed to describe the fundamental electrochemical and transport phenomena occurring in the diffusion layers, catalyst layers, and membrane. More research is required to develop models that are validated using experimental data, and models that can account for complex two‐phase flows of liquids and gases.

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Solid-phase polymerization (SPP) reactors are used to increase the degree of polymerization (DP) during nylon 6,6 production. In previous articles, a reactor model with partial differential equations (PDEs) in time and two spatial dimensions was developed to describe dynamic changes in polymer property profiles (DP, temperature, and moisture content) over the height of the reactor and within the polymer particles. In the current article, a simplified model is developed by deriving appropriate expressions for heat-and mass-transfer coefficients and performing a lumped heat-and mass-transfer analysis. Using this approach, the radial dimension is removed from the PDEs, so that the effort required to solve the model equations is substantially reduced. Predictions of the complex and simplified models are compared through simulation of two different start-up processes. Good agreement between simplified and complex models is obtained, indicating that the simplified model can be used in place of the complex model if the polymer properties profiles within individual particles are not of particular concern to the model user.

Gas-phase ethylene and hexene copolymerization using a silica-supported (n-BuCp)2ZrCl2 metallocene catalyst has been investigated in a 2 L laboratory reactor. Replicate experimental runs were conducted to confirm the reproducibility of measured responses, which included polymerization rate, reactant concentrations, and copolymer properties. Comparisons of polymerization rate profiles and catalyst activity were made using a number of designed experimental runs. The experiments revealed that triisobutyl aluminum scavenger was the most important cause of low catalyst activity, and a low initial polymerization rate that was followed by a rate increase. The effects of other influencing factors, including residence time, temperature, pressure, concentration of reactants, catalyst, and cocatalyst, were also investigated. As expected, hydrogen concentration and hexene concentration had significant effects on molecular weight and short-chain branching, respectively. In addition, hexene enhanced the polymerization rate and catalyst activity, while cocatalyst and hydrogen both led to a lower polymerization rate. The results from this study provide important quantitative information that will be used for parameter estimation in fundamental models.

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