Advanced Temperature Measurement and Control

Unit 5.2 - Disturbances and Difficulties

5-2. Disturbances and Difficulties

The control of a liquid - liquid exchanger outlet temperature by manipulation of the bypass of hot flow around the exchanger per Fig. 5-6 keeps the total coolant flow fixed, but the flow through the exchanger is still variable. While three-way valves are often used/ the author favors separate valves, as shown, for better throttling flexibility, performance, and diagnostics. The operating point should still be kept below a ratio of three, because the heat transfer, as indicated by the temperature difference Y, becomes nearly constant at higher ratios. If the heat transfer is constant, the temperature of the combined streams at the outlet also remains constant. Thus, the same nonlinearity problem still exists. The optimum ratio lies between a ratio of one half to two to keep the coolant flow high enough to reduce fouling but not so high as to reduce loop sensitivity.

The fraction K of the residence time that becomes dead time typically varies from about 0.2 to 0.8, depending upon the exchanger geometry and flow rate. The remaining portion of the residence time is the time constant. The dead time to time constant ratio increases as the flow decreases or the length-to-diameter (L/D) ratio increases. Exchangers with long narrow tubes or low flow will have a greater portion of the residence time show up as dead time than in designs with shorter larger tubes and high flow.

Fig. 5-6. The manipulation of an exchanger bypass flow provides a fast loop; however, the measurement lag is the largest time constant, and the process gain nonlinearity still exists (Ref. 1).

By the same reasoning, for a given volume, a loop that throttles the fluid on the tube side rather than on the shell side will tend to exhibit more dead time. Fig. 5-7 shows how the dead time to time constant ratio doubles from 0.25 to 0.5 when the flow is cut in half (Ref. 1). The loop period approximately triples. At first glance, it would seem that the loop period should nearly quadruple, because the fraction of residence time that is dead time doubled and the magnitude of the residence time doubled. However, per Eq. (4-17), the loop period moves from four times the dead time towards two times the dead time as the ratio of dead time to time constant increases.

Fig. 5-7. The residence time and the portion of the residence time that is dead time both increase as the flow decreases (Ref. 1).

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Unit 5.2 - Disturbances and Difficulties

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