Heaters, limiting output

Heater power output t from a proportional controller as a function of sensor temperature. The steeply sloping linear ramp extends over a temperature range called the proportional band (PB). The controller gain is inversely proportional to the width of this band IW dWldT= PB b Note that an on-off controller is a limiting case of proportional control with a proportional band of zero width. 

Electrically-heated carbide elements, JO mm in diameter and 0.5 m long, radiating essentially as black bodies, are to be used in the construction of a heater in which thermal radiation from the surroundings is negligible. If the surface temperature of the carbide is limited to 1750 K, how many elements are required to provide a radiated thermal output of 500 kW7... 

Heat is dissipated in the middle resistor (H). The resulting temperature distribution is sensed with two temperature sensitive resistors Tu, Td located symmetrically up- and downstream with respect to the heater. The temperature difference AT as function of the flow shows a maximum which limits the usable flow range of the sensor. A typical output signal of the flow sensor is given in Fig. 20. 

Consider the furnace-fired heater shown in Figure 15.63. Under normal operating conditions, the fuel flow rate is adjusted to control the exit temperature of the process fluid. As the feed rate of the process fluid is increased, the furnace tube temperature increases. At some point, the upper limit on furnace tube temperature (an operational constraint) is encountered. The fuel flow rate to the furnace must be adjusted to keep the furnace tube temperature from exceeding its upper limit, at which point damage to the furnace tubes results. Figure 15.63 shows that the output of both control loops (the temperature controller on the process fluid and the temperature controller on the furnace tube temperature) are combined, and the lower fuel feed rate is actually applied. The LS symbol in Figure 15.63 is called a low select and indicates that the lower fuel feed rate is chosen. When the feed rate is sufficiently low that the temperature of the process fluid can be controlled... 

Signal selectors are used in the most basic form of multivariable control, i.e. multi-input single-output (MISO) applications. The fired heater described also has a maximum limit on burner pressure. This is also approached by increasing feed rate. In order to operate at maximum feed rate the controller must be able to continuously identify which is the more limiting constraint. Figure 8.3 illustrates one possible configuration. 

During the early stages of catalyst reduction, the maximum rate of gas flow is limited by the thermal capacity of the start-up heater to maintain the temperature of the bed. As more catalyst becomes reduced, the exothermic synthesis reaction begins. The heat from this exotherm supplements the output from the start-up heater, and the gas rate can be increased. The rate of increase of a bed inlet temperature should be limited to about 5°C per hour until a maximum outlet temperature of 500°C is reached. During this procedure, the temperature of the remaining unreduced catalyst beds should be just below the reduction temperature that is about 350°C for typical catalysts. As more beds are reduced, gas rates can be increased and the reduction rate is faster despite the larger catalyst volumes in the lower beds. 

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