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FIG 9.6. Bypassing the exchanger will not improDe linearity, but does reduce response time.
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the rate of heat transfer is scarcely affected by the flow of either stream for reasonable rates of flow. If the heat transfer rate is nearly constant, the final temperature of the process stream after reunion with the bypassed flow will also be nearly constant; consequently the linearity of response is not noticeably improved. Bypassing can help the dynamic response, however, in that the flow of coolant is maintained at a high rate, rather than being throttled, as it would be if it were the manipulated variable. Furthermore, the bypass stream shortens the time delay between a change in valve position and the response of final temperature.
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The control situation is much more favorable where a change in phase is encountered. Because the latent heat of vaporization, H,, predominates, a measurement of the mass flow W of the boiling or condensing medium is also a measure of the rate of heat transfer: Q = WH, (9.14) Furthermore, the temperature of the boiling or condensing medium scarcely changes from inlet to outlet of the exchanger. Whenever steam is used as a heating medium, manipulation of its flow t o bring about temperature control of the process fluid is effective. If the process fluid is boiling, steam flow directly infers its rate of vaporization. The pressure of the steam in the exchanger is only an indication of steam temperature and is not a particularly useful measure of heat transfer; it can be used to estimate the heat transfer coefficient, however. Exchangers supplied with steam as a heating medium exhibit a strong tendency toward self-regulation. Since the film transfer coefficient for condensing steam is much greater than a flowing gas or liquid, the rate of heat transfer is principally governed by the film coefficient of the process fluid. Since this coefficient varies almost linearly with fluid velocity, heat transfer will vary almost linearly with flow, if steam temperature is maintained. The latter is achieved simply by regulating the pressure of the steam in the exchanger. Thus without being directly controlled, the exit temperature of the process fluid will nonetheless be well regulated.
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The flow of steam to a process heater or reboiler may also be manipulated by a valve in the condensate line. The rate of heat transfer is actually changed by partially flooding the exchanger wit h condensate. Because :I cshange in condcnsatc level is necessary to a.ffect steam flow, this system may respond more slowly than direct manipulation of steam flow, hut it has the distinct advantage of requiring a much smaller valve. M%ether sufficient heat has been removed to totally condense a vapor can be determined by the temperature of its condensate, if constant pressure prevails, or more accurately, by vapor pressure if the vessel is closed. Control of condensate temperature or vapor pressure is not so straightforward since the flow of the condensing vapor is the load and not the manipulated variable. The relationship between heat transfer and cool-. ant flow WC can be found simply by solving the equat ions developed earlier using constant temperature , for the condensing vapor: T, - TCI = l/UA + 1/2WcCc (9.15)
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Sotice the similarity between Eqs. (9.15) and (9.8). This indicates that the response of heat, transfer to coolant flow will be ident ical to the curve IYIICII/C A = CC of Fig. 9.3. For the manipulation of coolant flow, then, the nonlinearity problem is just as severe as it is when there is no phase change. Under conditions of constant condensate temperature, the heat transfer rate is entirely dependent, upon coolant flow. If coolant flow is maintained constant, bypassing part of the vapor around the condenser will not affect the rate of heat transfer unless t he condensate becomes appreciably subcooled. Under these conditions, t,he condenser begins to act more like the liquid-liquid heat exchanger, which is described in Fig. 9.6. The most effective way to control a condenser is to vary its heat t ransfer area. This is done by manipulating the flow of condensate so as to partially flood the condenser, thereby reducing the surface available for condensation. The level of condensate within the condenser is an indication of the heat load on the process. The system is described in Fig. 9.7. To be sure, a certain amount of subcooling always takes place, in whatever area is not used for condensing. The amount. of subcooling varies
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FIG 9.7. The heat transfer area available for condensation can be changed by manipulating the flow of condensate.
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