A mixing process consists of a single stirred-tank

Chapter 11, Problem 11.11

(choose chapter or problem)

A mixing process consists of a single stirred-tank instrumented as shown in Fig. E11.11. The concentration of a single species A in the feed stream varies. The controller attempts to compensate for this by varying the flow rate of pure A through the control valve. The transmitter dynamics are negligible. (a) Draw a block diagram for the controlled process. (b) Derive a transfer function for each block in your block diagram. Process (i) The volume is constant (5m3). (ii) The feed flow rate is constant CiiF = 7m3/min). (iii) The flow rate of the A stream varies but is small compared to qp (qA = 0.5 m3/min). (iv) cp =50 kg/m3 and cA = 800 kg/m3. (v) All densities are constant and equal. Transfer Line (i) The transfer line is 20 m long and has 0.5 m inside diameter. (ii) Pump volume can be neglected. Composition Transmitter Data Cm (rnA) 4 20 Transmitter dynamics are negligible. PID Controller (i) Derivative on measurement only ( cf. Eq. 8-17) (ii) Direct or reverse acting, as required (iii) Current (rnA) input and output signals liP Transducer Data p (rnA) 4 20 Pt (psig) 3 15 Control Valve An equal percentage valve is used, which has the following relation: Pv-3 qA = 0.17 + 0.03 (20) 12 For a step change in input pressure, the valve requires approximately 1 min to move to its new position.