This paper deals with the development of a mathematical model for emulsion copolymerization of styrene and butyl acrylate carried out in the presence of n-dodecyl mercaptan as chain transfer agent (CTA). The model consisted of a system of differential algebraic equations in which the population balances is based on a new approach that reduces significantly the number of equations involved and the corresponding computational time. Most of the unknown kinetic and thermodynamic parameters of the model were estimated from experimental measurements using a stochastic optimization method based on a genetic algorithm. The results showed a fairly good agreement between model predictions and experiments. The model was then successfully validated through additional experiments carried out in batch and fedbatch reactors and clearly showed that the model was able to predict the time-evolution of overall conversion, amounts of each residual monomer, number and weight average molecular weights of the resulting copolymers and average diameters of the corresponding latex particles for different operating conditions, mainly CTA concentration and reaction temperature. The model was finally used to investigate and confirm the effects of CTA concentration, previously observed by several authors, on the kinetics of this polymerization process and on the main properties of the resulting macromolecules and latex particles.
Accurate estimation of the model parameters is required to obtain reliable predictions of the products end-use properties. However, due to the mathematical model structure and/or to a possible lack of measurements, the estimation of some parameters may be impossible. This paper will focus on the case where the main limitations to the parameters estimability are their weak effect on the measured outputs or the correlation between the effects of two or more parameters. The objective of the method developed in this paper is to determine the subset of the most influencing parameters that can be estimated from the available experimental data, when the complete set of model parameters cannot be estimated. This approach has been applied to the mathematical model of the emulsion copolymerization of styrene and butyl acrylate, in the presence of n-dodecyl mercaptan as a chain transfer agent. In addition, a new approach is used to better assess the true confidence regions and evaluate the accuracy of the parameters estimates in more reliable way.
Acrylonitrile and styrene radical copolymerization in a dispersed medium has been investigated. Experiments were carried out in a continuous stirred-tank reactor in the presence of a stabilizing agent elaborated in situ during polymerization. The continuous phase was a polyol. The numerous elementary chemical mechanisms concerning the copolymerization as well as synthesis and grafting of the stabilizing agent together with several physical phenomena clearly show the complexity of the process. Using justified assumptions and a simplified kinetic scheme, a tendency model of the process was developed, using mass balances and thermodynamics. Its unknown parameters were identified by use of an evolutionary algorithm and experimental data resulting from an adapted experimental strategy. This model was then validated and allowed to forecast, with an acceptable order of magnitude, the number and weight average molecular weights, monomers and transfer agent conversions, amounts of solids, copolymer composition, amounts of grafted copolymer, and average particle diameters versus the operating conditions.
This article deals with the development of a multicriteria analysis, and its application to the optimization of batch emulsion polymerization processes. This new approach in the domain of polymer reaction engineering illustrates how a multiobjective optimization aided by a genetic algorithm and using the Pareto concept of domination is useful. In this process (emulsion homopolymerization of styrene), several objectives were simultaneously required, e.g., a high quality of the resulting products together with a high productivity. The aim of this study was to find the optimal experimental conditions to obtain simultaneously the minimum reaction time and designed values for both average molecular weights and particles size. To do that, an adapted mathematical model, able to describe all the process physicochemical phenomena, was been first elaborated. The multicriteria analysis then gave a set of nondominated points with conflicting criteria. A decision support system was then developed and applied to rank the Pareto solutions set and to propose some good solutions by taking into account the decision maker's preferences.
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