Estimation of copolymerization kinetic parameters by maximum likelihood method (original) (raw)
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Advanced manufacturing, 2015
The interest for models on a polymerization plant of acrylonitrile is (a) to predict the maximum capacity of an industrial reactor, (b) to increase the robustness of the process by defining stable operational conditions, and (c) to help the development of new copolymers. Using design of experiments (DOE), the copolymerization and terpolymerization of acrylonitrile with vinyl acetate and methyl-2 propene-1 sodium sulfonate were studied in aqueous suspension initiated by the redox system KClO 3 /NaHSO 3 /Fe 2þ. The molar fraction of the copolymers and terpolymers produced ranged from 93.0 to 98.2% for acrylonitrile, from 1.7 to 7.0% for vinyl acetate, and from 0.0 to 0.5% for sodium sulfonate. The mass molecular weight ranged from 76 000 to 419 000 g/gmol. Experiments were done in a pilot plant, consisting of 227 L of continuously stirred tank reactor, stripping and recycle systems, drum filter, and band dryer. The experiments were conducted according to a fractioned factorial 2 823 matrix with five central points. A statistic kinetic model was built, which explains well the copolymerization and terpolymerization of acrylonitrile. This model was applied with success on an industrial polymerization reactor, showing the potential of production increase, confirming the robustness of the process, and supporting the development of new copolymers of acrylonitrile. The focus of this paper is the development of a kinetic statistical polymerization model, the criteria to interrupt the regression analysis, and its application in the understanding of the polymerization phenomena.
A Kinetic Investigation on High Conversion Copolymerization of Lauryl Methacrylate
2002
Copolymers of isobutylmethacrylate (i-BMA), and laurylmethacrylate (LMA), wereprepared by solution free radical copolymerizations at 70°C using 2,2’-azobi-sisobutyronitrile, as initiator. The synthesis of these copolymers were investigated over a wide composition and conversion range. Copolymer compositions were deter-mined as a function of conversion from the %C, %H, and %O contents of copolymer by elemental analysis. In order to avoid the complications of copolymerization kinetics, the “pseduokinetic rate constant method ” (PKRC) was applied to constant and variable vol-ume polymerization system. Theoretical values of coupled parameter kp / k 0.5 t calculated from the “implicit penultimate unit effect ” model (IPUE) based on instantaneous monomer feed composition, were determined from Meyer-Lowery integrated copolymer composi-tion equation. The results have been compared with experimentally determined kinetic parameters.
Kinetic study of methacrylate copolymerization systems by thermoanalysis methods
Journal of Applied Polymer Science, 2008
The free-radical solution copolymerization of isobutyl methacrylate with lauryl methacrylate in the presence of an inhibitor was studied with thermoanalysis methods. A set of inhibited polymerization experiments was designed. Four different levels of initial inhibitor/initiator molar ratios were considered. In situ polymerization experiments were carried out with differential scanning calorimetry. Furthermore, to determine the impact of the polymerization media on the rate of initiation, the kinetics of the initiator decomposition were followed with nonisothermal thermoanalysis methods, and the results were compared with in situ polymerization counterparts. The robust M-estimation method was used to retrieve the kinetic parameters of the copolymerization system. This estimation method led to a reasonable prediction error for the dataset with strong multicollinearity. The model-free isoconversional method was employed to find the variation of the Arrhenius activation energy with the conversion. It was found that robust M-estimation outperformed existing methods of estimation in terms of statistical precision and computational speed, while maintaining good robustness.
Polymer, 2011
A population balance approach is described to follow the time evolution of molecular properties in freeradical copolymerization. The model formulation is based on the two dimensional orthogonal collocation on finite difference (2-OCFD) and method of generating functions (GF) which was properly adopted to calculate time-conversion behavior of styrene-methyl methacrylate copolymerization. A comprehensive model which uses the free volume theory to account for diffusion controlled termination and propagation reactions as well as the variation of the initiator efficiency with respect to the monomer conversion was developed. The model is capable of predicting the conversion, composition and molecular weight development up to limiting conversions. The plasticizing effect of a blowing agent on the rate of copolymerization has been investigated. The phenomenological aspect of rate data is analyzed for the copolymerization of styrene with methyl methacrylate over a full range of conversion and the gel effect index is used to systematize the observations.
Chemical Engineering Science, 2008
In the present study, a two-dimensional fixed pivot technique (2-D FPT) and an efficient Monte Carlo (MC) algorithm are described for the calculation of the bivariate molecular weight-copolymer composition (MW-CC) distribution in batch free-radical copolymerization reactors. A comprehensive free-volume model is employed to describe the variation of termination and propagation rate constants as well as the variation of the initiator efficiency with respect to the monomer conversion. Simulations are carried out, under different reactor conditions, to calculate the individual monomer conversions, the leading moments of the`live' and`dead' polymer chain length distributions as well as the dynamic evolution of the distributed molecular properties (i.e., molecular weight distribution (MWD), copolymer composition distribution (CCD) and joint MW-CC distribution). The validity of the numerical calculations is examined via a direct comparison of the simulation results, obtained by the two numerical methods, with experimental data on the styrene-methyl methacrylate batch free-radical copolymerization. Additional comparisons between the 2-D FPT and the MC methods are carried out for different polymerization conditions. It is clearly shown that both numerical methods are capable of predicting the distributed molecular and copolymer properties, with high accuracy, up to very high monomer conversions. It is also shown that the proposed dynamic MC algorithm is less computationally demanding than the 2-D FPT.
Batch solution polymerization of methyl methacrylate: Parameter estimation
The Chemical Engineering Journal, 1988
generally attributed to variations in the values of the kinetic rate constants and other model parameters. If one has a mathematical model of the process, it sometimes becomes necessary to re-estimate at least some of the parameters of the model so that results measured in the field and model predictions are in agreement. Once the model parameters are established under or close to actual production conditions, a certain model could subsequently be used wtih a higher degree of confidence in developing optimization or control strategies, or in predicting polymer properties under different reactor operating conditions. G. Odian, Principles of Polymerization, Wiley, New York, 1981. A. K. Agarwal and M. L. Brisk, Znd. Eng. Chem., Proc. Des. Dev., 24 (1985) 203.