The stirred tank sketched in figure below is used to heat a process stream so that its premixed components achieve a uniform composition. Temperature control is important because a high temperature tends to decompose the product whereas a low temperature results in incomplete mixing. The tank is heated by steam condensing inside a coil. A proportional integral derivative controller is used to control temperature in tank by manipulating the steam valve position. Derive the complete block diagram and the closed loop transfer function from the following design data.
Process. The feed has a density of 68.0 Ib/ft3 and a heat capacity Cpof 0.8 Btu/Ib-0F. The volume V of the liquid in the reactor is maintained constant at 120ft3. The coil consists of 205 ft of 4-in schedule 40 steel pipe that weighs 10.8 Ib/ft and has a heat capacity of 0.12 Btu/Ib-0F and an outside area of the coil has been estimated as 2.1 Btu/min-ft2-0F. The steam available is saturated at a pressure of 30 psia it can be assumed that its latent heat of condensationl is constant at 966 Btu/Ib. It can also be assumed that the inlet temperature Ti is constant.
Design Conditions. The feed flow f at design conditions is 15ft3/min and its temperature Ti is 1000F. The contents of the tank must be maintained at a temperature T of 1500F. Possible disturbances are changes in feed rate and temperature.
Temperature Sensor and Transmitter. The temperature sensor has a calibrated range of 100 to 2000F and a time constant of 0.75 min.
Control valve. The control valve is to be designed for 100% overcapacity and pressure drop variations can be neglected. The valve is an equal percentage valve with a rangeability parameter a of 50. The actuator has a time constant of 0.2 min.
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