Question

A stirred tank flow reactor is operating in continuous mode (shown below), and an exothermic (heat generating) chemical reaction is taking place inside the reactor. The control objective is to maintain the concentration of product at a desired value (set point). The conversion of chemical reaction is highly dependent on the reaction temperature. To maintain the reaction temperature at the desired value, a cooling water jacket is used for the reactor. The major input disturbance is fluctuation in the temperature of the Reactant in stream. The temperature of the reactor is controlled by adjusting the flow rate of cooling water.

Q1. (a) A stirred tank flow reactor is operating in continuous mode (shown below), and an exothermic (heat generating) chemical reaction is taking place inside the reactor. The control objective is to maintain the concentration of product at a desired value (set point). The conversion of chemical reaction is highly dependent on the reaction temperature. To maintain the reaction temperature at the desired value, a cooling water jacket is used for the reactor. The major input disturbance is fluctuation in the temperature of the Reactant in stream. The temperature of the reactor is controlled by adjusting the flow rate of cooling water. Reactant in Inlet cooling water ob - Outlet cooling water Product Jacketed stirred tank reactor (1) Draw a simple diagram to show the physical representation of how a Feedback control loop

Answer 1

(i) Feedback Control Loop

Composition Controller Asp xck XT Compositin Sensor Reactant in Flow Control Valve Inlet cooling water Outlet cooling water Product Jacketed stirred tank reactor

(ii)

Distrubance (Inlet Temperature) Xsp +> Error Error GC Control Output Control Output Gf Gр | Set point Feedback Controller Process (Composition) Final Control Element (Flow control valve) Xm (Measured Composition) Gm Measuring device BLOCK DIAGRAM
INPUT and OUTPUT variables:

Block	INPUT	OUTPUT
Process	Inlet Temperature, Water flow Rate	Composition
Measuring Device	Composition	Measured Composition
Controller	Error signal (Xsp- Xm )	Pressure Signal
Final Control Valve	Pressure Signal	Cooling water Flow rate

Transfer Functions:

# Process: The process transfer function converts the inlet temperature and cooling water flow rate to the composition inside the vessel. Since the reaction is exothermic, as the inlet temperature would increase the composition will decrease. Also, with a decrease in the cooling water flow rate, the composition will decrease.

# Measuring Device: The measuring device transfer function depends on the device being used. In general cases, G_m can be considered 1 for ideal devices.

# Controller: The controller transfer function converts the error signal into a pressure output signal for the flow control valve. If the error signal is positive (Xsp> X_m ) the controller outputs to close the flow control valve to reduce the cooling water flow rate and hence the composition too. If the error signal is negative (Xsp< X_m ) the controller outputs to open the flow control valve more to increase the cooling water flow rate and hence the composition too.

# Final Control Element: The final control element transfer function given the cooling water flow rate provided the pressure signal. The transfer function depends on the type of control valve being used ( air-to-open or air-to-close) .