Monomer feed policies

Two basic monomer feed policies employed in a semibatch copolymerization can be used to minimize composition drift [163]. Many highly effective commercial processes are based on one or a combination of these policies. Additional promising derivations of these policies have also been presented [167-173]. Henceforth, we refer to the two basic feed policies as Policy I and Policy II, as described in following sections. 

There are two basic monomer feed policies (and several modiflcations of the basic ones) that may be used in semibatch polymerization to minimize compositional drift (or optimize other properties). See Hamielec et al. [22] and Fujisawa and Penlidis [43] for more details. 

There are two basic monomer feed policies which maybe used in semibatch copolymerization to minimize compositional drift. Effective commercial processes are usually based on one or a combination of these feed policies. 

The semibatch approach, where policies are developed for selective reagent feeds to the reactor, has been extensively elaborated, especially for emulsion polymerization, and in the context of controlling composition during copolymerization reactions [68-72,109]. Discussions are provided in Chapters 4, 7, 12, 17-19, and 21. Sun et al. developed model-based semibatch monomer feeding policies for controlled radical polymerization (CRP) [73, 74]. Vicente et al. [75,76] controlled composition and molecular weight distribution in emulsion copolymerization in an open-loop method by maintaining the ratio of comonomers. Yanjarappa et al. [77] synthesized, via a sanibatch method, copolymers with constant composition for biofunctionalization. General semibatch policies are reviewed by Asua [78]. 

Figure 1, Forcing functions for monomer (fu) and initiator (fi) feeds (a) sinusoidal (b) square-wave (c) reception vessel valve operating sequences which are synchronized with the feed policies (see Figure 2 for the location of the valves...

Policy / Using the copolymer composition equation (Eq. 6.11), we first calculate the desired monomer feed composition (Fj) to achieve the desired copolymer composition (Fj). All of the less reactive monomer and sufficient of the more reactive monomer to achieve the desired Fj are added to the reactor initially. Thereafter, the more reactive monomer is fed to the reactor at a time-varying feed rate to maintain the molar ratio of monomer 1 to monomer 2 (N IN2 where A is the number of moles of monomer i) in the reactor constant. Thus, Fj remains constant and, consequently, Fj also remains unchanged. 

The practical implementation of the above policies is not necessarily as straightforward as solving the above equations. As can be deduced from Equations 6.70-6.76, Pjjjj is a function of the propagation rate coefficients, the monomer concentrations, and most importantly, the total radical concentration. Hence, to precalculate the optimal monomer feed rates, the radical concentration must be specified in advance and kept constant via an initiator feed policy and/or a heat production policy. This is especially important considering that a constant radical concentration is not a typical polymer production reality. This raises the notion that one could increase the reactor temperature or the initiator concentration over time to manipulate the radical concentration rather than manipulate the monomer feed flowrates, that is, keep P j constant for simpler pump operation. Furthermore, these semibatch policies provide the open-loop or off-line optimal feed rates required to produce a constant composition product. The online or closed-loop implementation of these policies necessitates a consideration of online sensors for monomer... 

Another practical consideration relates to the use of the semibatch feed policies in emulsion copolymerization. One would need to account for the partitioning of monomers in the different phases as well as the presence of monomer droplets (desired or not) during the particle nucleation and growth stages. 

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]. 

All the methods mentioned above use a mathematical model of the copolymerisation process in one way or another to arrive at a control policy for the production of compositionally homogeneous products. In this work use is made of a dynamic model of the process to control the feed rate of the more reactive monomer to a semi-batch reactor. Feedback from the process comes from an off-line model. The method is a general one and can be readily extended to accomodate feedback loops using on-line measurement devices with an experimental reactor. 

Monomer conversion can be adjusted by manipulating the feed rate of initiator. If on-line MMD is available, initiator flow rate or reactor temperature can be used to adjust MM [59]. A more complex approach involves adjusting initiator feed rate to control monomer conversicm, while by-passing part of the water and monomer around the first reactor in a train to control the PSD [60,61]. Direct control of the surfactant feed rate, based on surface tension measurements also can be used. Optimal policies for changing product grades without shutting down the reactor train are desirable, but what little is done in this area is based on operating experience rather than on optimization approaches. 

Policy 2 A charge of monomers 1 and 2 at the desired monomer concentration levels (to give the desired Fpi) is added to the reactor at time zero. Thereafter, monomers 1 and 2 are fed to the reactor with time-varying feed rates to maintain [Af 1 ], [M2 ] and Fpi constant with time. 

There are two major policies in feeding monomers to the reactor. The strategy is to achieve the constant copolymer composition by maintaining constant monomer composition during polymerization. In policy I, all of the slower reacting... 

Policy I normally requires a separate feeding line for the initiator. However, if the initiator has a very long half-lifetime ti/2 = ln2// d (very small kd), the ratio of I,in /" l,in becomes independent of time. The initiator can then be premixed with the monomer at [I]o and fed to the reactor by a single line. 

From eqns [299] and [303], the feeding rates of initiator and monomers have the same time dependence with constant ratios. Therefore, only a single feeding line is needed in policy II for a premixed initiator and monomer stock. 

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