Reactivity Ratio Estimation in Non‐Linear Polymerization Models using Markov Chain Monte Carlo Techniques and an Error‐In‐Variables Framework

Mathew, Manoj; Duever, Thomas A.

doi:10.1002/mats.201500017

Cited by 8 publications

(25 citation statements)

References 32 publications

(35 reference statements)

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“…Equation ( 59) was defined by Mathew and Duever as the "exact shape" of JCR [42]. In Figures 10-18, the JCRs that do not appear in the graph are so large that they would make the small ones no longer visible.…”

Section: Resultsmentioning

confidence: 99%

Determination of Reactivity Ratios from Binary Copolymerization Using the k-Nearest Neighbor Non-Parametric Regression

Fazakas-Anca¹,

Modrea

Vlase

2021

Polymers

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This paper proposes a new method for calculating the monomer reactivity ratios for binary copolymerization based on the terminal model. The original optimization method involves a numerical integration algorithm and an optimization algorithm based on k-nearest neighbour non-parametric regression. The calculation method has been tested on simulated and experimental data sets, at low (<10%), medium (10–35%) and high conversions (>40%), yielding reactivity ratios in a good agreement with the usual methods such as intersection, Fineman–Ross, reverse Fineman–Ross, Kelen–Tüdös, extended Kelen–Tüdös and the error in variable method. The experimental data sets used in this comparative analysis are copolymerization of 2-(N-phthalimido) ethyl acrylate with 1-vinyl-2-pyrolidone for low conversion, copolymerization of isoprene with glycidyl methacrylate for medium conversion and copolymerization of N-isopropylacrylamide with N,N-dimethylacrylamide for high conversion. Also, the possibility to estimate experimental errors from a single experimental data set formed by n experimental data is shown.

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Section: Resultsmentioning

confidence: 99%

Determination of Reactivity Ratios from Binary Copolymerization Using the k-Nearest Neighbor Non-Parametric Regression

Fazakas-Anca¹,

Modrea

Vlase

2021

Polymers

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“…The apparent dependence of the EVM convergence on the compositional model employed and the necessity of complex optimization algorithms to solve this problem still point to the necessity of further studies. Novel methodologies for estimating the reactivity ratios in copolymerizations are potential alternatives, such as Markov Chain Monte Carlo methods, [ 7 ] generalized polynomial chaos, [ 16 ] and particle swarm optimization methods. [ 17 ]…”

Section: Resultsmentioning

confidence: 99%

“…The reactivity ratio estimation with EVM has been applied to systems with relatively small differences between the reactivity ratios. [ 2,3,7,8 ] The scarce data available for styrene/VeoVa‐10 copolymerization suggest that there is a large difference between their reactivities. For this motive, the first approach was to test EVM and its sensitivity for two artificial cases, one with a significant difference between the reactivity ratios and the other with a small difference.…”

Section: Reactivity Ratio Estimationmentioning

confidence: 99%

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Estimation of Reactivity Ratios in the Copolymerization of Styrene and VeoVa‐10

Santos

Giudici

Barbosa

et al. 2020

Macro Reaction Engineering

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The styrene and vinyl neodecanoate copolymerization system shows a strong tendency to form two separate homopolymers. In order to improve the feeding strategies and hence the copolymer uniformity, it is necessary to know the reactivity ratios between these monomers. The error‐in‐variables‐method (EVM) is the most recommended mathematical procedure for estimating these parameters. Experiments on free‐radical copolymerization in solution in sealed ampoules are carried out to provide data for the conversion (via gravimetry) and fractional monomer compositions (via Fourier transform mid‐infrared (mid‐FT‐IR) spectroscopy). These data allow estimation of the reactivity ratios. EVM appropriately takes into account the experimental errors in the data and allows determination of the reactivity ratio values by the Mayo–Lewis model (r1 = 28.60 and r2 = 1.23). The convergence and robustness of the method decrease considerably with a larger discrepancy between the reactivity values.

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“…However, in situations where the uncertainties in inputs are relatively large, using WLS parameter estimation might result in unrealistic parameter estimates and underprediction of parameter uncertainties. EVM 7–30 has been used in a variety of chemical engineering modeling studies (see Tables 1 and 2).…”

Section: Introductionmentioning

confidence: 99%

Estimation of output measurement variances for error‐in‐variables model parameter estimation

Abdi

McAuley

2022

AIChE Journal

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Error-in-variables model (EVM) methods require information about variances of input and output measured variables when estimating the parameters in mathematical models for chemical processes. In EVM, using replicate experiments for estimating output measurement variances is complicated because true values of inputs may be different when multiple attempts are made to repeat an experiment. To address this issue, we categorize attempted replicate experiments as: (i) true replicates (TRs) when uncertain inputs are the same in replicated runs and (ii) pseudo replicates (PRs) when measured inputs are the same, but unknown true values of inputs are different. We propose methodologies to obtain output measurement variance estimates and associated parameter estimates for both situations. We also propose bootstrap methods for obtaining joint-confidence information for the resulting parameter estimates.A copolymerization case study is used to illustrate the proposed techniques. We show that different assumptions noticeably affect the uncertainties in the resulting reactivity-ratio estimates.copolymerization, error-in-variables model, Mayo-Lewis equation, reactivity-ratio estimation, replicate experiments | INTRODUCTIONFundamental mathematical models are widely used for chemical process development and improvement. These models usually contain unknown parameters that require estimation. 1,2 In conventional parameter-estimation methodologies such as weighted least-squares (WLS) estimation, the model inputs are assumed to be perfectly known (i.e., measured without error), while random measurement errors are considered for the model outputs. 3,4 Nevertheless, there are important situations where model inputs are not perfectly known, but contain significant uncertainties. The error-in-variables model (EVM) technique was developed to account for measurement uncertainties in both inputs and outputs during parameter estimation. 5,6 In

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Reactivity Ratio Estimation in Non‐Linear Polymerization Models using Markov Chain Monte Carlo Techniques and an Error‐In‐Variables Framework

Cited by 8 publications

References 32 publications

Determination of Reactivity Ratios from Binary Copolymerization Using the k-Nearest Neighbor Non-Parametric Regression

Determination of Reactivity Ratios from Binary Copolymerization Using the k-Nearest Neighbor Non-Parametric Regression

Estimation of Reactivity Ratios in the Copolymerization of Styrene and VeoVa‐10

Estimation of output measurement variances for error‐in‐variables model parameter estimation

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