Thomas A. Duever

Case studies and literature review on the estimation of copolymerization reactivity ratios

The enhanced features of a computer program ( RREVM ) for the estimation of copolymerization reactivity ratios using statistically sound techniques are illustrated with experimental and simulated case studies. In parallel, a literature review is given on the estimation of reactivity ratios. Both aspects are extensions based on the articles by Dube et al. 1 and Rossignoli and Duever.

Combined metallocene catalysts : an efficient technique to manipulate long-chain branching frequency of polyethylene

The solution polymerization of ethylene in Isopar E in a semi-batch reactor using combined CGC-Ti and Et[Ind]2ZrCl2 catalysts was studied. Methylaluminoxane (MAO) and tris(pentafluorophenyl)borane were used as co-catalysts. Samples were analyzed by 13C NMR and gel permeation chromatography (GPC) for their branching content and molecular weight distribution. It was shown that there was an optimum ratio of CGC-Ti/Et[Ind]2ZrCl2 that maximizes the number of long-chain branches of the formed polyethylene.

Production of polyolefins with controlled long chain branching and molecular weight distributions using mixed metallocene catalysts

Polyethylene with long-chain branches can be produced with certain metallocene catalysts, such as monocyclopentadienyl derivatives, by incorporation of macromonomers formed in-situ into the polymer backbone. This investigation demonstrates how dual metallocene systems can be used to control and enhance the level of long chain branching of polyethylene made with these catalysts. For instance, a catalyst that favors long chain branch formation, such as Dows constrained geometry catalyst, can be combined with another metallocene that produces macromonomers at a faster rate. In this way, the concentration of macromonomers in the reactor increases, thus favoring the formation of long chain branches. This leads, however, to a complex microstructural control problem, since both the molecular weight and long chain branch distribution are affected simultaneously by the presence of the second catalyst. Several mathematical models will be used to describe this challenging microstructural control problem.

Model discrimination via designed experiments: Discrimination between the terminal and penultimate models based on rate data

Abstract Simulations have been used to study the application of model discrimination methods to the problem of discriminating between the terminal and penultimate copolymerization models on the basis of composition and rate data. Both models are reviewed and the three model discrimination methods chosen for study are explained. Composition data have been used in conjunction with rate data due to the high correlation between estimated parameters based solely on rate data. This correlation has been discussed. The simulation programs are then explained including the generation of simulated data. Data are presented to show that the simulation programs can duplicate the experimental observations of other researchers. The results show that both the modified Buzzi-Ferraris method and the exact entropy method are able to correctly discriminate between the models in greater than 95% of the simulations. Differences between the three model discrimination methods are discussed along with differences between the three copolymer measurements that have been studied.

Fault detection and diagnosis with parametric uncertainty using generalized polynomial chaos

Abstract This paper presents a new methodology to identify and diagnose intermittent stochastic faults occurring in a process. A generalized polynomial chaos (gPC) expansion representing the stochastic inputs is employed in combination with the nonlinear mechanistic model of the process to calculate the resulting statistical distribution of measured variables that are used for fault detection and classification. A Galerkin projection based stochastic finite difference analysis is utilized to transform the stochastic mechanistic equation into a coupled deterministic system of equations which is solved numerically to obtain the gPC expansion coefficients. To detect and recognize faults, the probability density functions (PDFs) and joint confidence regions (JCRs) of the measured variables to be used for fault detection are obtained by substituting samples from a random space into the gPC expansions. The method is applied to a two dimensional heat transfer problem with faults consisting of stochastic changes combined with step change variations in the thermal diffusivity and in a boundary condition. The proposed methodology is compared with a Monte Carlo (MC) simulations based approach to illustrate its advantages in terms of computational efficiency as well as accuracy.

A powerful estimation scheme with the error-in-variables-model for nonlinear cases: Reactivity ratio estimation examples

Abstract This paper gives an overview of the error-in-variables-model (EVM) procedure for parameter estimation with nonlinear models. It is shown that the nested-iterative EVM algorithm, used in this work, is efficient and powerful, since it provides both true values of the variables and the best estimates of the parameters. The step by step illustration along with evaluation techniques for results, are followed by further discussion about the importance and advantages of combining EVM with design of experiments strategies. With the focus on the performance of the EVM algorithm, an illustrative example of reactivity ratio estimation in copolymerization is included, with single-response (composition data) and multi-response (triad fraction data) scenarios.

Mixing analysis of reactive polymer flow in conveying elements of a co-rotating twin screw extruder

In this study, the finite element method was used to investigate the effects of screw speed, entering peroxide distribution, and pressure-to-drag flow ratio on the mixing characteristics of steady non-isothermal reactive flows in a forward conveying element of a self-wiping twin screw extruder. The reaction considered was the peroxide-initiated degradation of a commodity polypropylene resin. The predicted average degree-of-freedom profiles from the simulations largely conformed to expectations. The average flow efficiencies for all runs were found to remain at values close to that for two-dimensional flow, with fluctuations being observed in the channel intermeshing regions. No significant effect of either screw speed or peroxide distribution was found on the flow efficiencies; however, the pressure-to-drag flow ratio was found to have a significant influence.

An experimental verification of statistical discrimination between the terminal and penultimate copolymerization models

In this article, the modified Buzzi-Ferraris model discrimination method was used to design experiments to discriminate between the terminal and penultimate models for styrene methyl methacrylate (STY/MMA) copolymerization. The measured variables were 13 C-NMR peak areas. The peak area assignments of Aerdts 8 were used. After nine experiments, the terminal model was picked over the penultimate model at 99.99% confidence. More importantly, the experimental data showed that computer simulated data used in previous studies were realistic, and the conclusions drawn from the simulation studies were valid. This experimental verification continues to show that the use of statistical model discrimination techniques can improve our ability to discriminate hetween competing copolymerization models.

Comparison of fault detection techniques

Abstract Haar Wave-Net (HWN) and Projection Pursuit Regression (PPR) are two useful modeling tools for pattern classification. In this study, the two methodologies are compared with respect to the problem of misclassification close to class boundaries with sparse training data. A variety of examples were specifically tailored to elucidate their respective properties. It is observed that PPR locates the class boundaries at the midline of two classes of training data, which is a logical choice for the class boundary location, in the absence of sufficient information. For HWN, both the initial positioning of receptive fields and the density of training data near the class boundary may have great impact on the definition of the class boundary. Additionally, PPR and HWN are also compared to the Backpropagation Network (BPN), a standard technique for fault detection, with respect to their sensitivity to noise. The orthonormal and localized properties of the Haar basis functions enable a HWN to limit the noise effect within its local receptive fields. BPN propagates the noise effect throughout the input space. PPR provides a good tradeoff between reasonable generalization and noise localization. The fault diagnosis problem is investigated in a CSTR process, at both steady state and dynamic conditions. It is found that, for the dynamic case, the misclassification close to the class boundary is often due to lack of system observability.

Mathematical Modeling of Acrylonitrile-Butadiene Emulsion Copolymerization: Model Development and Validation

This paper presents a mechanistic model for the production of nitrile-butadiene rubber (NBR). The mathematical dynamic model was developed in order to simulate the industrial production of NBR via emulsion copolymerization of acrylonitrile (AN) and butadiene (Bd) in batch, continuous and trains of continuous reactors. For this reason, the model was constructed in a parsimonious manner to avoid complex and time-consuming computations that typically result when modeling details of specific aspects of micro/macro scale emulsion polymerization phenomena (i.e., full molecular weight and particle size distributions, detailed species phase-partitioning, etc.). Thus, the model provides average properties for typical emulsion characteristics, such as monomer conversion, copolymer composition, number- and weight-average molecular weights, tri- and tetra-functional branching frequencies, and the number and average size of polymer latex particles. The proposed model is an extension of a previous model developed by our group, and allows for the dynamic modeling of different reactor types and configurations. Model comparisons are made between limited literature data for batch operation, while representative simulation profiles are shown for a reactor train.