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Controlling Chemical Reactions
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diminishes to zero as conversion is completed. There is no heat evolution during the cure phase. Equation (10.19) gave the thermal time constant of a continuous reactor. Among other things, it depended on reactant concentration and conversion. Since these are both variable in a batch reactor, it is entirely possible to proceed from an unstable to a stable condition with the passage of time. Control settings necessarily must favor the more difficult situation. In some batch reactions, one of the ingredients is introduced continuously until the other reactants are entirely consumed. The rate at which this ingredient is added is usually limited by the rate of heat removal. In order to carry out the reaction in minimum time, the batch must be heated to reaction temperature as rapidly as possible, where full cooling is applied. The temperature controller then must manipulate the addition of reactant through a linear cascade flow loop. An interlock must be arranged to prevent reactant from being introduced until the batch is approaching reaction temperature. Otherwise a quantity could accumulate accidentally within the batch, and once the reaction began, could generate heat in excess of the capabilities of the cooling system.
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End-point Control
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At the completion of the reaction, heat evolution will subside, causing the temperature controller to increase reactant flow. Since this is obviously incorrect action, some logic must be arranged to override tempera-
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Proportion01 + derivative
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FIG 10.20. The temperature-control loop must be disabled at both the start and finish of the reaction.
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ture control upon the termination of the reaction. If there is no way of measuring the completion of the reaction, reactant flow may be stopped by a flow totalizer, once a predetermined quantity has been introduced. The termination of some react,ions is indicated by a fall in pressure; others are indicated by a rise in pressure. In either case, a pressure switch may be used to shut off flow. End-point control of a batch reaction has one outstanding characteristic-reset must not be used. The bulk of the reaction is conducted away from the set point-reset would try to overcome this offset and ultimately result in overshoot. The controller should be proportional-plusderivative, with zero bias, so that the valve is shut when the set point is reached. If the measurement is pH, reagent should be added through an equal-percentage valve (without a cascade flow loop), to match the process characteristic. A system employing temperature and end-point control is shown in Fig. 10.20.
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1. Corrigan, T. E., and E. F. Young: General Considerations in Reactor Design, Chem. Eng., October, 1955. 2. Harriott, P.: Process Control, p. 311, McGraw-Hill Book Company, New York, 1964. 3. Shinskey, F. G.: Temperature Control for Gas-phase Reactors, C h e m . E n g . , October 5, 1959. 4. -----: Designing Stability into Plant Operations, Petro.-Chem. Eng., October, November, 1962. 5. Daniels, F.: Outlines of Physical Chemistry, p. 460, John Wiley & Sons, Inc, New York, 1948. 6. Shinskey, F. G.: Controls for Nonlinear Processes, Chem. Eng., March 19, 1962. 7. Green, R. M.: A Unique Approach to Process Control Using Nonlinear Electrochemical Analyzers, 6th 1Vatl. Symp. on Instrumental Methods of Analysis, June, 1960. 8. Shinskey, F. G.: Analog Computing Control for On-line Applications, Control Eng., November, 1962. 9. Weinstein, W. I).: The Four-bar Linkage as a Function Generator, Elec. Manufacturing, October, 1959. 10. Shinskey, F. G., and J. L. Weinstein: A Dual-mode Control System for a Batch Exothermic Reactor, 20th Annual ZSA Conf., October, 1965.
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PROBLEMS
1 0 . 1 The reaction whose characteristics appear in Fig. 10.2 is to be conducted Temperature at 50 percent conversion with V/F = 1 hr in a back-mixed re&ctor. is to be controlled at 230 F by manipulation of coolant temperature. Feed is preheated to reaction temperature. What is the lowest coolant temperature that will ensure st,ability in manual control 10.2 For the same reactor, the heat of reaction is 5000 Btu/lb, F is 4,000 lb/hr, and r. is 0.2. Coolant temperature required for control is 190 F. The
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