Polymerization reactors, modeling

Kiparissides, C. Polymerization reactor modeling a review of recent developments and future directions. Chem. Eng. Sci. 1996, 51 (10), 1637-1659. 

Kiparissides C (2006) Challenges in particulate polymerization reactor modeling and optimization A population balance perspective. J Process Control 16 205-224... 

Based on the previous discussion, the design of the optimum operation policy (computation of u) requires the minimization of an objective function that is subject to equality and inequality constraints. It is important to emphasize that x, y, u, ce, x and may (or may not) depend on time, depending on the particular analyzed problem. It is also important to observe that initial conditions required to solve dynamic problems (as during the analysis of batch reactions) can be included in the set u of manipulated variables. Simulation platforms have been proposed and used to solve these complex optimization problems and they are robust enough to cope with imstable dynamic trajectories and large polymerization reactor models [38, 162-164]. 

G. Maschio, T. Bello, C. Scali, Optimization of batch polymerization reactors Modelling and experimental results for suspension polymerization of methyl methacrylate , Chem. Eng. Sci., 1992, 47, 2609. 

A theoretical polymerization tubular reactor model was used to study the effects of reactor operating parameters on conversion... 

The literature on the modeling and design of precipitation polymerization reactors is limited primarily to reactor for the bulk polymerization of vinyl chloride (31-38), although other systems have been discussed, particularly in the patent literature (39,40,41). 

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-... 

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. 

In this paper we present a meaningful analysis of the operation of a batch polymerization reactor in its final stages (i.e. high conversion levels) where MWD broadening is relatively unimportant. The ultimate objective is to minimize the residual monomer concentration as fast as possible, using the time-optimal problem formulation. Isothermal as well as nonisothermal policies are derived based on a mathematical model that also takes depropagation into account. The effect of initiator concentration, initiator half-life and activation energy on optimum temperature and time is studied. 

On the other hand, very few ncdels for nulticonponent systans have been reported in the literature. Apart from models for binary systems, usually restricted to "zero-one" systans (5) (6), the most detailed model of this type has been proposed by Hamielec et al. (7), with reference to batch, semibatch and continuous emilsion polymerization reactors. Notably, besides the usual kinetic informations (nonomer, conversion, PSD), the model allows for the evaluation of IWD, long and short chain brandling frequencies and gel content. Comparisons between model predictions and experimental data are limited to tulK and solution binary pwlymerization systems. 

In this work, a comprehensive kinetic model, suitable for simulation of inilticomponent aiulsion polymerization reactors, is presented A well-mixed, isothermal, batch reactor is considered with illustrative purposes. Typical model outputs are PSD, monomer conversion, multivariate distritution of the i lymer particles in terms of numtoer and type of contained active Chains, and pwlymer ccmposition. Model predictions are compared with experimental data for the ternary system acrylonitrile-styrene-methyl methacrylate. 

In this work, therefore we aim to combine the stochastic observer to input/output prediction model so that it can be robust against the influence of noise. We employ the modified I/O data-based prediction model [3] as a linear part of Wimra" model to design the WMPC and these controllers are applied to a continuous mefihyl methacrylate (MMA) solution polymerization reactor to examine the performance of controller. 

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. 

Models for emulsion polymerization reactors vary greatly in their complexity. The level of sophistication needed depends upon the intended use of the model. One could distinguish between two levels of complexity. The first type of model simply involves reactor material and energy balances, and is used to predict the temperature, pressure and monomer concentrations in the reactor. Second level models cannot only predict the above quantities but also polymer properties such as particle size, molecular weight distribution (MWD) and branching frequency. In latex reactor systems, the level one balances are strongly coupled with the particle population balances, thereby making approximate level one models of limited value (1). 

TABLE I. Recent Work on the Modelling of Emulsion Polymerization Reactors... 

A valid mechanistic model can be very useful, not only in that it can appreciably add to our process understanding, but also in that it can be successfully employed in many aspects of emulsion polymerization reactor technology, ranging from latex reactor simulation to on-line state estimation and control. A general model framework has been presented and then it was shown how it can be applied in a few of these areas. The model, being very flexible and readily expandable, was further extended to cover several monomer and comonomer systems, in an effort to illustrate some of its capabilities. 

An advantage of this approach to model large-scale fluidized bed reactors is that the behavior of bubbles in fluidized beds can be readily incorporated in the force balance of the bubbles. In this respect, one can think of the rise velocity, and the tendency of rising bubbles to be drawn towards the center of the bed, from the mutual interaction of bubbles and from wall effects (Kobayashi et al., 2000). In Fig. 34, two preliminary calculations are shown for an industrial-scale gas-phase polymerization reactor, using the discrete bubble model. The geometry of the fluidized bed was 1.0 x 3.0 x 1.0 m (w x h x d). The emulsion phase has a density of 400kg/m3, and the apparent viscosity was set to 1.0 Pa s. The density of the bubble phase was 25 g/m3. The bubbles were injected via 49 nozzles positioned equally distributed in a square in the middle of the column. 

For the discrete bubble model described in Section V.C, future work will be focused on implementation of closure equations in the force balance, like empirical relations for bubble-rise velocities and the interaction between bubbles. Clearly, a more refined model for the bubble-bubble interaction, including coalescence and breakup, is required along with a more realistic description of the rheology of fluidized suspensions. Finally, the adapted model should be augmented with a thermal energy balance, and associated closures for the thermophysical properties, to study heat transport in large-scale fluidized beds, such as FCC-regenerators and PE and PP gas-phase polymerization reactors. 

Bokkers, G. A., Multi-level modelling of the hydrodynamics of gas phase polymerization reactors, PhD thesis, University of Twente (2005). 

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