Modeling and optimization of a seeded suspension polymerization process

Lin, Weijie; Biegler, Lorenz T.; Jacobson, Annette M.

doi:10.1016/j.ces.2010.03.052

Cited by 39 publications

(33 citation statements)

References 26 publications

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“…An important product of suspension polymerization processes is expandable beads, which find applications in many fields such as packaging industry and metal casting technology [1][2][3][4]. Attempts made to find new polymerization methods for producing high quality and selective products led to emersion of seeded polymerization.…”

Section: Introductionmentioning

confidence: 99%

Synthesis of core-shell PS/PMMA expandable particles via seeded suspension polymerization

et al. 2015

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Expandable core-shell beads were synthesized by dosing methyl methacrylate (and styrene) in a constant rate and polymerizing in the presence of polystyrene seeds and pentane. The morphological studies of beads indicated that there were larger poly(methyl methacrylate)-rich domains near the shell. The sizes of these domains were decreased towards the core of the particles. For better surveying the likely structures of domains and the extent of expansion agent diffusion, the beads having the shells formed with copolymerization of styrene and methyl methacrylate in the presence of polystyrene seeds were studied. From the morphological studies, the parallel regular and the onion-like structures were recognizable. In addition, another shell was formed around the dispersed phase showing a complex core/shell structure both in particle and in domain scales. The pentane content in the beads with copolymerized styrene and methyl methacrylate monomers on the polystyrene seeds was increased compared to the beads having the shells of pure poly(methyl methacrylate). This was because the onset of gel effect was longer with adding the styrene to methyl methacrylate monomer hence there was more time for expansion agent to diffuse into the beads. The different amounts of pentane distributed in polystyrene-and poly(methyl methacrylate)-rich phases were discussed in terms of the changes in glass transition temperature of two phases.

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Section: Introductionmentioning

confidence: 99%

Synthesis of core-shell PS/PMMA expandable particles via seeded suspension polymerization

et al. 2015

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“…Because the direct approach failed to converge, the multistep methodology was used. In the deconvolution step, IPOPT required 155 iterations and 2.3 CPU s to solve problem (32). The value of MWD deviations from the noise-free target profiles is 3.90 3 10 23 , which is much larger than that in the noise-free case.…”

Section: Estimation Using Simulation Resultsmentioning

confidence: 99%

“…However, the direct approach failed to converge; instead, the multistep methodology was used. In the deconvolution step, IPOPT required 104 iterations and 1.5 CPU s to solve problem (32). The value of MWD deviations is 4.20 3 10 216 , equivalent to zero to numerical precision, and the decision variables, s and mf , converged to a unique optimal point, as seen in the fourth column of Table 10.…”

Section: Estimation Using Simulation Resultsmentioning

confidence: 99%

“…Obtaining a subset of estimable parameters and evaluating their reliability is an important task in parameter estimation. 32 Here, an approach for parameter selection and evaluation is proposed to determine which kinetic parameters can be estimated. The flowchart of the parameter selection approach is presented in Figure 2.…”

Section: Selection Of Estimated Parametersmentioning

confidence: 99%

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Kinetic parameter estimation of HDPE slurry process from molecular weight distribution: Estimability analysis and multistep methodology

et al. 2014

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This study addresses kinetic parameter estimation for a high-density polyethylene (HDPE) slurry process based on fitting molecular weight distributions (MWDs). From the process model, we conduct an estimability analysis by assessing the relative sensitivity between output variables and kinetic parameters as well as confidence intervals. This determines which parameters can be estimated. Conversely, a major challenge remains with the solution of an ill-conditioned parameter estimation problem with MWD as the output variable. To overcome the convergence difficulties with the associated problem, we develop a novel multistep methodology where we first obtain MWD parameters by matching to data and then estimate kinetic parameters by matching to the regressed MWD parameters. Computational results and eigenvalue analysis show this multistep methodology separates an ill-conditioned problem into two well-conditioned subproblems. Moreover, we consider simulation-based and industrial HDPE case studies. These results demonstrate the applicability, potential, and efficiency of this solution procedure.The kinetic mechanism 24 of ethylene homopolymerization with Ziegler-Natta catalyst system is summarized in Table Figure 1. Flow sheet of HDPE slurry process in series.

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“…SE can be further refined by extracting the diagonal components with the cross product (SE) T (SE). The information matrix of the parameters can be expressed as, 8,21 …”

Section: Incremental Objective Based Large Scale Drpementioning

confidence: 99%

Programming Strategies of Sequential Incremental-Scale Subproblems for Large Scale Data Reconciliation and Parameter Estimation with Multi-Operational Conditions

Zhang

Shao

Chen

2015

Ind. Eng. Chem. Res.

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Data reconciliation and parameter estimation (DRPE) is a crucial issue in model-based applications, such as realtime optimization and process control. In order to obtain more reliable parameter estimates, a series of measurement data sets from different operational conditions will be used for DRPE problems. However, the dimensionality of DRPE problems increases directly with the number of measurement data sets. The number of degrees of freedom in DRPE problems is usually very large. Therefore, it is very difficult to solve the DRPE problem with multioperational conditions. On the basis of the characteristics of the DRPE problem, two directions, including the direction of incremental objectives of the DRPE problem and the direction of incremental parameters of the DRPE problem, are considered to decompose the original DRPE optimization problem into a series of incremental-scale subproblems. Three programming strategies are proposed to solve a series of incremental-scale subproblems one by one. The solutions to the current subproblem are used as a set of good initial guesses of the next optimum subproblem after including a new subproblem. By solving a series of subproblems, the optimum values of the original large scale DRPE optimization problem can be derived efficiently. The effectiveness of the proposed strategies can be demonstrated through two industrial processes, including free radical polymerization of styrene and the purified terephthalic acid oxidation process system.

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Modeling and optimization of a seeded suspension polymerization process

Cited by 39 publications

References 26 publications

Synthesis of core-shell PS/PMMA expandable particles via seeded suspension polymerization

Synthesis of core-shell PS/PMMA expandable particles via seeded suspension polymerization

Kinetic parameter estimation of HDPE slurry process from molecular weight distribution: Estimability analysis and multistep methodology

Programming Strategies of Sequential Incremental-Scale Subproblems for Large Scale Data Reconciliation and Parameter Estimation with Multi-Operational Conditions

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