Emulsion polymerization reactors mathematical modeling

Using copolymerization theory and well known phase equilibrium laws a mathematical model is reported for predicting conversions in an emulsion polymerization reactor. The model is demonstrated to accurately predict conversions from the head space vapor compositions during copolymerization reactions for two commercial products. However, it appears that for products with compositions lower than the azeotropic compositions the model becomes semi-empirical. 

The derivation and development of a mathematical model which is as general as possible and incorporates detailed knowledge from phenomena operative in emulsion polymerization reactors, its testing phase and its application to latex reactor design, simulation, optimization and control are the objectives of this paper and will be described in what follows. 

Penlidis, A. Macgregor, J.F. Hamielec, A.E. Mathematical-modeling of emulsion polymerization reactors—a population balance approach and its applications. ACS Symp. Ser. 1986, 313, 219-240. 

A considerable amount of work has been published during the past 20 years on a wide variety of emulsion polymerization and latex problems. A list of 11, mostly recent, general reference books is included at the end of this chapter. Areas in which significant advances have been reported include reaction mechanisms and kinetics, latex characterization and analysis, copolymerization and particle morphology control, reactor mathematical modeling, control of adsorbed and bound surface groups, particle size control reactor parameters. Readers who are interested in a more in-depth study of emulsion polymerization will find extensive literature sources. 

The commercially used emulsion polymerization reactors (stirred-tank and continuous-loop) are designed to achieve perfect mixing. As will be discussed in Section 6.4.5, perfect mixing is not always achieved. Nevertheless, this flow model allows a good prediction of the emulsion polymerization reactor performance with a moderate mathematical effort, and it will be used here. Macroscopic balances (i.e., considering the reactor as a whole) are used. For the sake of generality, inlet and outlet streams are included in the balances. Both terms should be removed for batch operation, the outlet term should be eliminated in semibatch and both maintained in continuous processes. 

Min, K.W., W.H. Ray, The computer simulation of batch emulsion polymerization reactors through a detailed mathematical model. J. Appl. Polym. Sci. 22, (1978), 89-112. 

Our final goal in the present paper is to devise an optimal type of the first stage reactor and its operation method which will maximize the number of polymer particles produced in continuous emulsion polymerization. For this purpose, we need a mathematical reaction model which explains particle formation and other kinetic behavior of continuous emulsion polymerization of styrene. 

The analytical predictor, as well as the other dead-time compensation techniques, requires a mathematical model of the process for implementation. The block diagram of the analytical predictor control strategy, applied to the problem of conversion control in an emulsion polymerization, is illustrated in Figure 2(a). In this application, the current measured values of monomer conversion and initiator feed rate are input into the mathematical model which then calculates the value of conversion T units of time in the future assuming no changes in initiator flow or reactor conditions occur during this time. 

Single Phase Polymerization Mathematical Modelling Ziegler-Natta Polymerization Polymerization Processes (Monograph) Emulsion Polymerization Polymerization Reactions and Reactors Continuous Reactors (ed. volume)... 

The objective was to develop a model for continuous emulsion polymerization of styrene in tubular reactors which predicts the radial and axial profiles of temperature and concentration, and to verify the model using a 240 ft. long, 1/2 in. OD Stainless Steel Tubular reactor. The mathematical model (solved by numerical techniques on a digital computer and based on Smith-Ewart kinetics) accurately predicts the experimental conversion, except at low conversions. Hiqh soap level (1.0%) and low temperature (less than 70°C) permitted the reactor to perform without plugging, giving a uniform latex of 30% solids and up to 90% conversion, with a particle size of about 1000 K and a molecular weight of about 2 X 10 . 

Mathematical modeling is a powerful tool not only for the development of process understanding but also for that of the advanced reactor controls in polymerization processes. The modeling techniques for polymerization processes are reasonably well developed and several commercial simulation packages are available. The modeling of heterogeneous polymerizations such as precipitation polymerization and emulsion polymerization remains a challenge. In the past decade, excellent... 

Polymerization reactors are a specific kind of chemical reactors in which polymerization reactions take place therefore, in principle, they can be analyzed following the same general rules applicable to any other chemical reactor. The basic components of a mathematical model for a chemical reactor are a reactor model and rate expressions for the chemical species that participate in the reactions. If the system is homogeneous (only one phase), these two basic components are pretty much what is needed on the other hand, for heterogeneous systems formed by several phases (emulsion or suspension polymerizations, systems with gaseous monomers, slurry reactors or fluidized bed reactors with solid catalysts, etc.), additional transport and/or thermodynamic models may be necessary to build a realistic mathematical representation of the system. In this section, to illustrate the basic principles and components needed, we restrict ourselves to the simplest case, that of homogeneous reactors in other sections, additional components and more complex cases are discussed. 

In a simulation study, Leffew and Deshpande [62] have evaluated the use of a dead-time compensation algorithm in the control of a train of CSTRs for flie emulsion polymerization of vinyl acetate. In this study, monomer conv ion was controlled by manipulating the initiator flow rate. Experiments indicate that there is a period of no response (dead-time) between the time of increase in the flow of initiator and the response of monomer conversion. Dead-time compensation attempts to correct for this dead-time by using a mathematical model of the polymerization system. Reported results indicate that if the reactor is operated at low surfoctant concentration (where oscillations are observed), the control algorithm is incapable of controlling monomer conversion by the manipulation of either initiator flow rate or reactor temperature. The inability of the controller to eliminate oscillations is most probably due to the choice of manipulated variable (initiator flow rate) rather than to the perfotmance of the control algorithm (deadtime conq)ensation). 

In copolymerization, the more reactive monomer may be added to the reactor over time to produce a more uniform copolymer composition distribution. This may be done by feeding comonomer at fixed rates, by adding various comonomers at predetermined times, or by following a complex monomer addition policy determined by off-line optimization of a mathematical model of the polymerization process. If copolymer composition is measured or estimated on-line, the reactive monomer can be added in a closed-loop fashion [35]. In emulsion polymerization, surfactant may be added over time to control the formation of new particles, and hence the particle size distribution (PSD) [36]. 

The purpose of this work is to extend the quantitative analysis of Harkins mechanism of emulsion polymerization to include the consideration of the distribution of polymer particle sizes and the accompanying molecular weight distribution. In the development of the mathematical model we have assumed the isothermal operation of a well mixed batch reactor, that micelles are the only source of polymer particles, that particles (and micelles) receive radicals at a rate proportional to their surface area, that polymer termination takes place by chain transfer to monomer or instantaneous recombination with the entry of a second radical into the particle, and that all radicals produced in the aqueous phase are absorbed into the micelles and polymer particles. 

One unique but normally undesirable feature of continuous emulsion polymerization carried out in a stirred tank reactor is reactor dynamics. For example, sustained oscillations (limit cycles) in the number of latex particles per unit volume of water, monomer conversion, and concentration of free surfactant have been observed in continuous emulsion polymerization systems operated at isothermal conditions [52-55], as illustrated in Figure 7.4a. Particle nucleation phenomena and gel effect are primarily responsible for the observed reactor instabilities. Several mathematical models that quantitatively predict the reaction kinetics (including the reactor dynamics) involved in continuous emulsion polymerization can be found in references 56-58. Tauer and Muller [59] developed a kinetic model for the emulsion polymerization of vinyl chloride in a continuous stirred tank reactor. The results show that the sustained oscillations depend on the rates of particle growth and coalescence. Furthermore, multiple steady states have been experienced in continuous emulsion polymerization carried out in a stirred tank reactor, and this phenomenon is attributed to the gel effect [60,61]. All these factors inevitably result in severe problems of process control and product quality. 

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