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Although the progress of the chemical industry has been t oward continuous processes, some reactions will inevitably be conductred batchwise. The bulk of commercial batch reactions are polymerizations involved in the production of rubber and many types of plastics. Distribution of molecular weight is an important parameter in polymer manufacture, and it seems to be the most easily controlled batchwise. Another consideration is the great change in viscosity frequently encountered bet meen the reactants and products. The process consists of the several steps listed below, although considerable variation exists from one product to another: 1. Charge the reactor with reactants and catalyst. 2. Heat to operating temperature. 3. Allow the reaction to proceed to completion, normally several hours. 4. Heat or cool to cure temperatures. 5. Cool and empty the reactor. Production reactors are stirred, jacketed vessels of several thousand gallons capacity. If the reaction is first-order, conversion varies with time according to Eq. (10.6) : y = 1 - e--kt The rate of conversion is the derivative of Eq. (10.6) :
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The rate is greatest when the conversion is least, i.e., at time zero. Polymerization reactions are second-order or higher, because they depend on the simultaneous combinat,ion of two or more monomer molecules to form a polymer. In a second-order reaction, the rate depends 011 the square of reactant concentration:
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--= kX2 dxt d
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Dividing both sides by -x2 and integrating, j-l$=lb -kdt ---= let l l X x0
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Controlling Chemical Reactions
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Conversion and its rate can be found by substituting for x: 1 lctxo =y = 1 + 1/%txo 1 + lCtx O (1 (10.35) (10.36)
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dy -=
The rate of conversion is also the rate of production in a batch reactor and is proportional to heat evolution, if the reaction is exothermic. The rate of conversion of first- and second-order reactions is plotted against time in Fig. 10.18.
Temperature Control
In the early stages of a batch reaction, temperature control is most import ant because the rate of conversion is at its highest. Exothermic reactions pose a real control problem because heat must be applied to raise the batch to reaction temperature and then be removed. The cooling system most frequently used is that shown in Fig. 10.11. A proportional controller is used for coolant exit temperature because the proportional band is ordinarily only about 10 percent and offset is not harmful. But the primary controller is three-mode, with special features to permit: 1. Maintenance of optimum settings for operation at reaction temperature 2. Delivery of the batch to reaction temperature without overshoot 3. Conduction of the reaction in a minimum of time If t he reactor is stable, based on its heat transfer characteristics, as discussed earlier with regard to continuous reactors, control of temperature will be simplified. The reactor will respond rapidly, with a period of perhaps 20 min, and 10 percent proportional band may be sufficient for effective damping. All three control modes should be adjusted while at the operating temperature. In order to avoid overshoot, the primary controller must be equipped with an antiwindup switch with preload applied to the reset circuit. I t
FIG 10.18. The rate of conversion of higher-order reactions varies less with time, particularly at low concentration levels.
2 kt
204 1 A p p l i c a t i o n s
r - - 1 prlmory
FIG 10.19. The dual-mode system requires different values of preload for reaction and cure.
is the preload which determines the magnit,ude of overshoot (see Fig. 4.6). The correct value for preload is not difficult to estimate for a known reaction. The initial rate of conversion will release a predictable flow of heat, all of which must be removed t hrough the heat transfer surface. Both the batch and the cooling fluid are circulated at, very high rates to ensure good heat transfer; thus each has little temperature gradient and constant flow. The rate of heat transfer is t herefore directly proportional to the temperature difference between primary and secondary measurements. The output of the primary controller, which is the set point of t he secondary, is predictable, and its predicted value can be introduced as preload. As pointed out in Chap. 4, however, it is necessary to set the preload a few percent below the predicted value t,o allow for t he reset action of the controller from the time the antiwindup switch is released until the set point is reached. A batch reactor can be unstable, in which case its natural period will be perhaps twice as long and its proportional band requirement t wice as great as a physically similar stable one. The control system described above Ioses its effectiveness when a wide proportional band is required. In order to avoid overshoot, the heat input must be thrott led early, which can add considerable time to t he length of the operation. For a problem such as this, the dual-mode control system described in Fig. 5.17 is extremely effective. The prcload is estimated as before, but no correction is required for integration, because reset action is not initiated until the error is nearly zero. Full heating can be applied to within 1 or 2 percent of the set point,, far beyond the capabilities of a 25 percent proportional band. Yet fuII cooling need only be applied for a time delay of perhaps a minute to dissipate the energy stored in the jacket. AS pointed out in Fig. 5.18, the switching parameters are easy to adjust and tolerant of maladjustment. Figure 10.19 shows the relat ionships between primary and jacket temperatures and t he dual-mode output for a typical reactor. If t he settings are correct , jacket tcmperaturc mill fall to meet it,s set point at the preload value when the time delay is over. Notice how the rate of heat transfer
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