Control of Emulsion Polymerization Reactors

In the control scheme, x are state variables of the polymerization reactor, y are measurable properties of the polymer latex, ymeas are properties that are monitored on-line, and u are the manipulated variables of the process (basically flow rates of monomers and chain-transfer agents). 

The closed-loop control strategy requires calculation of the set-point, that is, the trajectories or profiles of the state variables as a function of a measured variable (overall conversion). These profiles can be calculated by means of an optimization algorithm. In what follows, a brief description of the calculation of the optimal trajectories for copolymer composition and the MWD control is presented. The goal of the optimization algorithm is to calculate the set-pornt trajectories of the state (controlled) variables that ensure the production of an emulsion polymer of the desired copolymer composition and MWD in the minimum process time. To achieve this goal, the objective function to be minimized is as expressed in Eq. (74), where Rp is the polymerization rate and Xj is the overall conversion. 

Constraint 1 product composition and MWD The polymer produced must have the desired copolymer composition and the final MWD. 

The condition to produce a latex with a given copolymer composition is that the ratio of the monomer concentrations in the polymer particles must be kept at the value that ensures the production of the desired composition. This comonomer ratio can be calculated from the Mayo-Lewis equation, Eq. (75), where ri and t2 are the reactivity ratios and yu is the instantaneous composition referred to monomer 1. 

The calculation of the condition to produce a latex with a given MWD is based on the fact that for linear polymers produced by free-radical polymerization, the polymer chains do not suffer any modification once they are formed. This opens the possibility of decomposing the desired final MWD in a series of instantaneous MWDs to be produced at different stages of the reaction [130]. When chain transfer to a CTA is the main termination event, each of those MWDs can be characterized by the number-average chain length, according to Eq. (76). 

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Dimitratos J, Elicabe G, Georgakis C. Control of emulsion polymerization reactors. AIChE J 1994 40 1993-2021. 

Leiza, J.R. and Asua, J.M. (1997) Feedback control of emulsion polymerization reactors a critical review and future directions. In J.M. Asua (ed.). Polymeric Dispersions Principles and Applications. Kluwer Academic Publishers, Dordrecht. 

Research on the modelling, optimization and control of emulsion polymerization (latex) reactors and processes has been expanding rapidly as the chemistry and physics of these systems become better understood, and as the demand for new and improved latex products increases. The objectives are usually to optimize production rates and/or to control product quality variables such as polymer particle size distribution (PSD), particle morphology, copolymer composition, molecular weights (MW s), long chain branching (LCB), crosslinking frequency and gel content. 

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. 

Because of its importance, continuous on-line monitoring of emulsion polymerization reactors continues to be an area of considerable investment in terms of research and development. It is evident that to better understand the nucleation mechanisms, and to develop better control strategies,... 

Achieving optimal control and operation of emulsion polymerization reactors requires the integration of mechanistic... 

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. 

A Simulation Study on the Use of a Dead-Time Compensation Algorithm for Closed-Loop Conversion Control of Continuous Emulsion Polymerization Reactors... 

Several control techniques have been developed to compensate for large dead-times in processes and have recently been reviewed by Gopalratnam, et al. (4). Among the most effective of these techniques and the one which appears to be most readily applicable to continuous emulsion polymerization is the analytical predictor method of dead-time compensation (DTC) originally proposed by Moore ( 5). The analytical predictor has been demonstrated by Doss and Moore (6) for a stirred tank heating system and by Meyer, et al. (7) for distillation column control in the only experimental applications presently in the literature. Implementation of the analytical predictor method to monomer conversion control in a train of continuous emulsion polymerization reactors is the subject of this paper. 

Emulsion polymerization reactors are made of stainless steel and are normally equipped with top-entry stirrers and ports for addition of reactants. Control of the reaction exotherm and particle size distribution of the polymer latex is achieved most readily by semibatch (also called semicontinuous) processes, in which some or all of the reactants are fed into the reactor during the course of the polymerization. Examples are given in Chapter 8. In vinyl acetate copolymerizations, a convenient monomer addition rate is such that keeps the vinyl acetate/water azeotrope retluxing. at about 70°C. 

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. 

R. F. Dickinson, Dynamic behavior and minimum norm control of continuous emulsion polymerization reactors, PhD thesis, Univ. Waterloo, Ontario, 1976... 

One of the first considerations in establishing a strategy for controlling emulsion polymerization reactors is to categorize all system inputs and outputs into those which are to be controlled, those which may be adjusted to achieve this control, and those which are beyond the control of the engineer. System outputs may be divided into three categories ... 

An optimal predictive controller was developed and implemented to allow for maximization of monomer conversion and minimization of batch times in a styrene emulsion polymerization reactor, using calorimetric measiuements for observation and manipulation of monomer feed rates for attainment of control objectives [31]. Increase of 13% in monomer conversion and reduction of 28% in batch time were reported. On-line reoptimization of the reference temperature trajectories was performed to allow for removal of heater disturbances in batch bulk MMA polymerizations [64]. Temperature trajectories were manipulated to minimize the batch time, while keeping the final conversion and molecular weight averages at desired levels. A reoptimization procediue was implemented to remove disturbances caused by the presence of unknown amounts of inhibitors in the feed charge [196]. In this case, temperatiue trajectories were manipulated to allow for attainment of specified monomer conversion and molecular weight averages in minimum time. 

Monomer conversion can be adjusted by manipulating the feed rate of initiator or catalyst. If on-line M WD is available, initiator flow rate or reactor temperature can be used to adjust MW [38]. In emulsion polymerization, initiator feed rate can be used to control monomer conversion, while bypassing part of the water and monomer around the first reactor in a train can be used to control PSD [39,40]. Direct control of surfactant feed rate, based on surface tension measurements also can be used. Polymer quality and end-use property control are hampered, as in batch polymerization, by infrequent, off-line measurements. In addition, on-line measurements may be severely delayed due to the constraints of the process flowsheet. For example, even if on-line viscometry (via melt index) is available every 1 to 5 minutes, the viscometer may be situated at the outlet of an extruder downstream of the polymerization reactor. The transportation delay between the reactor where the MW develops, and the viscometer where the MW is measured (or inferred) may be several hours. Thus, even with frequent sampling, the data is old. There are two approaches possible in this case. One is to do open-loop, steady-state control. In this approach, the measurement is compared to the desired output when the system is believed to be at steady state. A manual correction to the process is then made, based on the error. The corrected inputs are maintained until the process reaches a new steady state, at which time the process is repeated. This approach is especially valid if the dominant dynamics of the process are substantially faster than the sampling interval. Another approach is to connect the output to the appropriate process input(s) in a closed-loop scheme. In this case, the loop must be substantially detuned to compensate for the large measurement delay. The addition of a dead time compensator can... 

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