Control of Batch Reactors

In real systems, the increase of temperature is accompanied by a corresponding increase of pressure, which may lead to an explosion (i.e., to an uncontrolled increase of pressure). Nevertheless, the analysis of temperature patterns with simple kinetics is enough to study the problem for adiabatic reactors and for constant wall temperature (isoperibolic) reactors, whereas the more complex case of controlled wall temperature requires the adoption of more advanced methods. 

the equations describing the thermal stability of batch reactors are written, and the relevant dimensionless groups are singled out. These equations have been used in different forms to discuss different stability criteria proposed in the literature for adiabatic and isoperibolic reactors. The Semenov criterion is valid for zero-order kinetics, i.e., under the simplifying assumption that the explosion occurs with a negligible consumption of reactants. Other classical approaches remove this simplifying assumption and are based on some geometric features of the temperature-time or temperature-concentration curves, such as the existence of points of inflection and/or of maximum, or on the parametric sensitivity of these curves. 

Finally, the application of some of those criteria to the phenol-formaldehyde reaction gives some interesting insights on the thermal behavior of the system and also highlights the operation limits arising from an imposed maximum allowable temperature in the reactor. 

Chapter 5 is focused on the temperature control of chemical batch reactors, with special emphasis on model-based control approaches. 

Therefore, the chapter is mainly focused on the design of model-based control approaches. Namely, a controller-observer control strategy is considered, where an observer is designed to estimate the heat released by the reaction, together with a cascade temperature control scheme. The performance of this control strategy are further improved by introducing an adaptive estimation of the heat transfer coefficient. Finally, the application of the proposed methods to the phenol-formaldehyde reaction studied in the previous chapters is presented. 

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N. Aziz, M.A. Hussain, I.M. Mujtaba, Optimal control of batch reactor comparison of neural network based GMC and inverse model control approach, in Proceedings of the Sixth World Congress of Chemical Engineering, Melbourne, Australia, 23-27 September 2001. 

R. Berber, Control of batch reactors a review, Trans. IChemE 74 (Part A) (1996) 3-20. 

In the following, an overview of the above discussed linear and nonlinear approaches to temperature control of batch reactors is provided. 

R. Luus and O.N. Okongwu. Towards practical optimal control of batch reactors. Chemical Engineering Journal, 75 1-9, 1999. 

Aziz, N., Dynamic Optimization and Control of Batch Reactors. PhD Thesis, (University of Bradford, 2001). 

R. L. Luus and O. N. Okongwu [Chem. Eng. J., IS, 1-9 (1999)] studied several issues relevant to the practical optimal control of batch reactors. In particnlar, they considered the sequence of consecutive first-order reactions... 

Huzmezan, M., B. Gough, and S. Kovac, Advanced Control of Batch Reactor Temperature, Proc. Amer. Control Conf, 1156 (2002). 

This temperature dependency is exploited in optimal control problems of batch reactor where optimal temperature profile is obtained by either maximizing conversion, yield, profit, or minimizing batch time for the reaction. One of the earliest works on optimal control of batch reactor was presented by Denbigh[25] where he maximized the yield. The review paper by Srinivasan et al.[26] describes various optimization and optimal control problems in batch processing and provides examples of semi-batch and fed-batch reactor optimal control. 

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