Optimal periodic control batch reactor

A comparison of the various types of reactor concepts, in a general sense, is actually only possible between the batch, the CSTR and the PFR. The cascade of CSTRs, depending on the number of vessels n in the series, more or less behaves as an ideal mixer for n->l or an ideal plug flow for n- - . The fed-batch reactor is more difficult to situate. Although the concentration of compounds important for the rate of reaction can be controlled optimally during the whole fed period, the reactor volume is only partially utilized, especially in the beginning. Nevertheless, this reactor concept certainly has decisive advantages in many cases, as shown by the fact that it is one of the most widely used. 

The optimal temperature policy in a batch reactor, for a first order irreversible reaction was formulated by Szepe and Levenspiel (1968). The optimal situation was found to be either operating at the maximum allowable temperature, or with a rising temperature policy, Chou el al. (1967) have discussed the problem of simple optimal control policies of isothermal tubular reactors with catalyst decay. They found that the optimal policy is to maintain a constant conversion assuming that the decay is dependent on temperature. Ogunye and Ray (1968) found that, for both reversible and irreversible reactions, the simple optimal policies for the maximization of a total yield of a reactor over a period of catalyst decay were not always optimal. The optimal policy can be mixed containing both constrained and unconstrained parts as well as being purely constrained. 

Very frequently non-optimal setpoint trajectories are used for controlling reactor temperatures in batch reactors [25,39,179,180]. Reactor temperatures maybe allowed to increase from ambient temperatures up to a maximum temperature value, in order to use the heat released by reaction to heat the reaction medium and save energy (reduce energy costs). The temperature increase is almost always performed linearly, because of hardware limitations and simplicity of controller programming. After reaching the maximum allowed temperature value, reactor temperature is kept constant for a certain time interval, for production of polymer material at isothermal conditions. At the end of the batch, the reaction temperature is increased in order to reduce the residual monomer content of the final resin, usually with the help of a second catalyst. Heuristic optimum temperature trajectories were also formulated for batch polymerizations of acrylamide and quaternary ammonium cationic monomers, in order to use the available heat of reaction [181]. The batch time was split into two batch periods an isothermal reaction period and an adiabatic reaction period. 

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