Industrial polymerization reactors, modeling

Modeling and Control of Continuous Industrial Polymerization Reactors... 

Control of industrial polymerization reactors is a challenging task because, in general, control engineers lack rigorous polymerization process knowledge, process model, and rapid online or inline sensors to measure polymer properties. Exothermic polymerization processes often exhibit strongly nonlinear dynamic behaviors (e.g., multiple steady states, autonomous oscillations, limit cycles, parametric sensitivity, and thermal runaway), particularly when continuous stirred tank... 

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. 

H. Seki, M. Ogawa, S. Ooyama, K. Akamatsu, M. Ohshima, and W. Yang. Industrial application of a nonlinear model predictive control to polymerization reactors. Control Engineering... 

Solution Polymerization in a CSTR. Although many polymerization reactors in use by industry have the residence time distribution of a CSTR, they may not, at first glance, have the appearance of a CSTR (cf. Figure 1). Nevertheless, CSTR models, perhaps with some allowance for imperfect micromixing, are successfully employed to describe these reactors. Thus the behavior of the CSTR is of great practical interest. 

These models require information about mean velocity and the turbulence field within the stirred vessels. Computational flow models can be developed to provide such fluid dynamic information required by the reactor models. Although in principle, it is possible to solve the population balance model equations within the CFM framework, a simplified compartment-mixing model may be adequate to simulate an industrial reactor. In this approach, a CFD model is developed to establish the relationship between reactor hardware and the resulting fluid dynamics. This information is used by a relatively simple, compartment-mixing model coupled with a population balance model (Vivaldo-Lima et al., 1998). The approach is shown schematically in Fig. 9.2. Detailed polymerization kinetics can be included. Vivaldo-Lima et a/. (1998) have successfully used such an approach to predict particle size distribution (PSD) of the product polymer. Their two-compartment model was able to capture the bi-modal behavior observed in the experimental PSD data. After adequate validation, such a computational model can be used to optimize reactor configuration and operation to enhance reactor performance. 

An important application of this approach is the radical polymerization of ethylene at high pressure. In101 an attempt is made to model a process which takes place in an industrial mixing reactor. It appears that by solving an inverse kinetic problem, the researchers have verified the pre-exponential factors and the E values for a series of elementary stages, although what these stages are is not mentioned in the paper. 

A complete phenomenological mathematical model for olefin polymerization in industrial reactors should, in principle, consider phenomena taking place from microscale to macroscale, but this is seldom the case. Most models assume that the conditions in the polymerization reactor are uniform and neglect any mesoscale phenomena, which may be a good approximation for solution polymerization reactors, but may not apply to polymerizations using heterogeneous catalysts. 

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. 

Since many industrial finishing polymerization reactors are equipped with devices of complex geometry to provide maximum interfacial area for mass transfer areas, it is practically quite difficult to develop a model that accurately includes the detailed geometric structure of the reactor. 

Extensions of Kalman filters and Luenberger observers [131 Solution polymerizations (conversion and molecular weight estimation) with and without on-line measurements for A4w [102, 113, 133, 134] Emulsion polymerization (monomer concentration in the particles with parameter estimation or not (n)) [45, 139[ Heat of reaction and heat transfer coefficient in polymerization reactors [135, 141, 142] Computationally fast, reiterative and constrained algorithms are more robust, multi-rate (having fast/ frequent and slow measurements can be handled)/Trial and error required for tuning the process and observation model covariance errors, model linearization required The number of industrial applications is scarce A critical article by Wilson eta/. [143] reviews the industrial implementation and shows their experiences at Ciba. Their main conclusion is that the superior performance of state estimation techniques over open-loop observers cannot be guaranteed. 

V. Touloupides et al.. Modeling and simulation of an industrial slurry-phase catal dic olefin polymerization reactor series, Chem. Eng. Sci., 65, 3208-3222 (2010)... 

Summary. Recently, in a paper of Chylla and Haase [2], a model of a multiproduct semibatch polymerization reactor has been developed which is representative of those foimd in the speciality chemical processing industry. One of the aims in these processes is to keep a certain reaction temperature setpoint, in order to fit the quality requirements for the polymer. 

The same type of oscillations seen in laboratory-scale reactors have been reported for industrial copolymerization reactors (Keane, 1972). In a model of vinyl acetate polymerization in an industrial-scale reactor, Teymour and Ray (1992b) discovered a wide range of dynamical behavior, including a perioddoubling route to chaotic oscillations. Oscillations in temperature ranged in amplitude from 70 to 140 °C. The extent of conversion oscillated from about 0.5 to almost 1. Obviously, behavior of this type would be detrimental to the operation of a plant. 

These three theoretical distributions describe only a very small portion of the diversity of polymer microstructures that are produced every day in academia and industry. Even for the polymerization systems they describe, they are only strictly valid as instantaneous distributions. If conditions in the polymerization reactor fluctuate as a function of time or spatial location, the distributions for the polymer product may be considerably more complex. In this case, it is very difficult to And a mathematical model precise enough to describe the complete polymer microstructure, and we must rely solely on experimental fractionation for its determination. In fact, the comparison of experimentally-measured mi-crostructural distributions with the ones predicted by theory is a powerful tool to investigate pol5mierization mechanisms and imderstand polymer reactor nonidealities. Nonetheless, these distributions are essential to realize the complexity of polymer microstructure and the interdependency of the distributions of molecular weight, chemical composition (or tacticity), and long-chain branching. This interdependency should always be kept in mind when interpreting the firactionation data from any experimental technique. 

Lewin, D.R., 1996. Modelling and Control of an Industrial PVC Suspension Polymerization Reactor. Computers Chem Engng 20 S865-S870. 

In this section, the proposed process-control design approach is illustrated with a representative starved emulsion semibatch polymerization and numerical simulations, with a model that emulates and industrial size reactor [11], Moreover, the simulation example corresponds to a scaled-up version of the theoretical-experimental calorimetrie estimation study presented before with a laboratory scale reactor [15]. 

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