Loulli and Tassius used the cubic equation of state of Peng-Robinson; where the parameters a energy and b co-volume for the polymers were obtained by experiments. The EOS was applied to the low-pressure vapor-liquid equilibrium for various polymeric solutions through the use of an interaction parameter with three mixing rules: van der Walls, Zhong and Masuoka ZM , and Huron-Vidal of first order MHV1.
These rules were used together with the cubic equation of state and the model of Flory-Huggins. They applied the VLE model in a large variety of solvent-polymer systems, and the best result was obtained with the ZM mixing rule.
In the present work, kinetic and thermodynamic models of styrene polymerization in solution, using data from an industrial plant, were developed. Based on these models, a dynamic mathematical model for a series of two auto-refrigerated reactors was built to predict the quality of the polymer product for different process operating conditions. The reactors were modeled as reactive separation systems with two equilibrium stages.
The reacting system considered is constituted, mainly, by the monomer styrene , the solvent ethyl-benzene and the polymer polystyrene. The heat of the exothermic reaction is removed, in the form of heat of vaporization, by the vapor phase stream leaving the reactor.
For the phase equilibrium calculation, the Peng-Robinson EOS and the ZM mixture rule with the extension of Louli and Tassios for the energy and co-volume parameters for the polymer were used. The kinetic and binary interaction parameters were estimated with the use of available and limited data in the industry. In the next three sections, the kinetic, the thermodynamic, and the process models are presented, respectively. The polymerization of styrene can be initiated thermally and by bi-functional peroxide, following the conventional kinetics of free-radical initiation, propagation, termination, and chain transfer.
The thermal initiation mechanism proposed by Hui and Hamielec is represented by a third-order kinetics with respect to the styrene monomer. The decomposition of the bi-functional initiator takes place by the bond scission of one peroxide group and not by the simultaneous bond scission of the two peroxide groups Villalobos et al.
It is also considered that the chain termination occurs exclusively by combination. Termination by disproportion is negligible in the polymerization of styrene Chen, The gel effect must be taken into account for free-radical polymerization reactions with high conversions, where the termination reaction becomes controlled by diffusion, and the effective constant for termination decreases considerably with the increase of the monomer conversion.
The correlation suggested by Hui and Hamielec , as function of the conversion X and the reaction temperature T , was used in the gel effect for the polymerization reaction of styrene, represented in Equation 1. The chain transfer to sub-products of the thermally initiated reaction must be considered in order to have an effective constant of transfer to monomer. The importance of the chain transfer to. In order to explain this kind of anomalous behavior, it was suggested that the transfer to monomer controls the chain termination in low-conversion processes.
However, when the concentration of AH increases, the transfer to AH becomes more important for chain termination. On this basis, a large parcel of the chain transfer constant to styrene is, in reality, the result of the chain transfer to AH:. However, because the kinetic constants of the intermediary reactions of thermal initiation are unknown, the empirical form of Hui and Hamielec is an alternative to the use of Equation 5.
During an experimental study, the authors considered that all the constants are independent of the size of the polymer chain but can vary with the conversion and they suggest Equations 6 to In this experimental study, Hui and Hamielec also considered that the propagation reactions are influenced by the conversion and that Equation 6 could be used to obtain the variation of the kinetic constant k p with the conversion. However, according to Chen , it is not necessary to take into account the effect of the conversion on the propagation reaction for solution polymerization.
Undertaking a mass balance of the species, without considering their inflow and outflow at this stage, and by applying the method of moments while using the assumption of QSSA quasi-steady-state approximation for the radicals, the final kinetic model is obtained:. Different sets of kinetic parameters were found in the literature, showing a high variability in their values as illustrated in Table 2 for the propagation rate constants.
In order to select an appropriate set of kinetic parameters, a sensitivity analysis was carried out among several combinations of parameters. The more suitable set of published kinetic constants employed to fit the available plant data is given in Table 3. The Peng-Robinson equation of state Equation 31 , with the values of the parameters a energy and b co-volume determined experimentally by Loulli and Tassius for the polymer, was used to predict the low-pressure vapor-liquid thermodynamic equilibrium.
The equations that express the mixing rule ZM Loulli and Tassios, are as follow:. The mathematical model proposed for two auto-refrigerated reactors in series of an industrial plant is illustrated in Figure 1. Auto-refrigerated chemical reactors are also known as chemical reactors with evaporative cooling. The vapor boiled from the liquid is condensed in a heat exchanger and, generally, the condensate is returned to the reactor.
The condenser operates at lower pressure than the reactor since there must be a pressure gradient to drive the vapor from the reactor to the condenser. Several polymerization reactions are carried out in industry in auto-refrigerated reactors Beckman, ; Henderson III and Cornejo, ; Toledo et al. In the studied process, the condensate is returned to the feed stream, before a heat exchanger that controls the feed temperature of the first reactor, see Figure 1.
Each reactor was modeled as a reactive distillation system with two equilibrium stages, as illustrated in Figure 2. The liquid phase in the bottom stage, where the polymerization reactions occur, was considered at its bubble point. No liquid holdup was considered in the top stage, acting as an instantaneous flash drum of the feed stream. Find more information on the Altmetric Attention Score and how the score is calculated.
Unlike many other products from the chemical industries, polymer molecules cannot easily be separated from each other. Therefore, the material has to be produced with the required specification at the reactor stage. The correct choice of reaction model is crucial for the prediction of reactor behavior. Allowance must be made for the effects of high viscosities on both heat transfer and reaction kinetics. In suspension polymerization, drop sizes, drop mixing, and sedimentation all require particular attention.
With emulsion polymerization, a change in the reactor start-up procedure can lead to changes in dynamic behavior, monomer conversion, and product quality. If we can learn from nature, polymerization reactors may take new forms in the future. View Author Information. Cite this: Ind. Article Views Altmetric -. Citations Abstract Unlike many other products from the chemical industries, polymer molecules cannot easily be separated from each other.
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