Mathematical Modeling of Polymerization Reactors

I began my professional career with the Rohm and Haas Company, working in the area of polymerization. In that environment, I had the opportunity to interact with a number of world-class chemists, including Dr. Newman Bortnick. I also had the opportunity to work with a contemporary. Dr. James White, in the mathematical modeling of polymerization reactors. My recent work in polymerization at North Carolina State University is an extension of what I learned at Rohm and Haas. 

Temperature and free-radical concentration are important features that vary along the length of the plug-flow tubular reactor model of the polymerization of ethylene/ Stirred-tank reactor models of the anionic polymerization of styrene and of butadiene have been described and tested against experiments. Mathematical modelling of polymerization reactions receives some attention in the book by Froment and Bischoff. ... 

Tosun, G., 1992. A mathematical model of mixing and polymerization in a semibatch stirred tank reactor. American Institution of Chemical Engineers Journal, 38, 425 37. 

Although a dynamic mathematical model of the polymerization system has been developed (17) it is not capable of providing the necessary operating policies for the reactor in order to preselect the time-averaged MWD in the product. Hence the flow policies for the reagents were selected empirically and for experimental convenience. 

Although the papers represent the whole range of kinds of polymers and processes, there are common themes which reveal the dominant concerns of polymerization reactor engineers. Fully half the papers are concerned rather closely with devising and testing mathematical models which enable process variables to be predicted and controlled very precisely. Such models are increasingly demanded for optimization and com-... 

Mathematical Modeling of Bulk and Solution Polymerization in a Tubular Reactor... 

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. 

The detailed course of a polymerization is determined by the nature of the particular reaction as well as by the characteristics of the reactor which is used. The design and control of the operation are greatly aided by mathematical modeling of the process. Such models may be based on empirical relations between the independent and dependent operating variables. This is not as satisfactory, however, as a model that is derived from accurate knowledge of the polymerization process and reactor operation, because only the latter tool permits extrapolation to reaction conditions that have not yet been tried. 

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. 

Dube, M.A. Soares, J.B.P. Penlidis, A. Hamielec, A.E. Mathematical modeling of multicomponent chain-growth polymerizations in batch, semibatch, and continuous reactors a review. Ind. Eng. Chem. Res. 1997, 36, 966-1015. 

The important problems include the control of polymerization reactors containing rheokinetic liquids. These problems have not been solved in many respects even for more simple situations. Both mathematical modelling and physical understanding of the process are the key problems [112]. 

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). 

It is useful to separate the discussion into processes for polyethylene and polypropylene, as the requirements for these two polymers are different and have led to similar, but by no means identical, processes. A short discussion on the various reactor configurations will be presented first, followed by descriptions on how each reactor configuration is used in different polymerization processes throughout the world. Also listed are a few keys references at the end of the chapter for further reading [72-85]. Finally, the chapter will be concluded with a few considerations on the mathematical modeling of industrial olefin polymerization reactors. 

A complete phenomenological mathematical model for olefin polymerization in industrial reactors should, in principle, include a description of phenomena taking place from microscale to macroscale. It may come as a disappointment to learn that most mathematical models for industrial reactors ignore several of these details. In fact, most models assume... 

Kalfas, G.A. (1992) Experimental Studies and Mathematical Modeling of Aqueous Suspension Polymerization Reactors. PhD Thesis. University of Wisconsin-Madison, USA. 

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]. 

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