Process Dynamics and Control Assignment -

Question 1 - The following reaction occurs in a continuously stirred tank reactor:

A → B

Two streams of volumetric flow rate Q₁ and Q₂ and concentration of A C_A1 and C_A2 are fed to the CSTR. There is a negligible amount of energy generation by the reaction as well as a negligible amount of heat loss. As both streams enter at the same temperature, the CSTR operates isothermally. The volume in tank is relatively constant as well as the fluid density. The radius of the tank is 1 m and C_A1 = 45 mol/L and C_A2 = 30 mol/L.

a) Obtain a dynamic model (only the ODE) that describes the change in the concentration of A in the tank.

b) Obtain the time constant for this process if the residence time is 40 seconds and the reaction rate constant 0.5 sec^-1. Approximately how long will it take to reach a new steady state if one of the inlet concentrations were to change instantaneously (step change)?

c) How could the process respond quicker if the residence time is fixed? (be specific)

d) If Q₁ = 100 L/s and Q₂ = 75 L/s, what is the height (h) of liquid in the tank at steady state?

e) If Q₁ were to drop by 10 % (τv = 2 seconds), obtain the dynamic response of the system (Q₁, h and CA) for the first twenty seconds if the outlet volumetric flow rate does not change.

Question 2 - As part of your duties as newly hired process engineer, you want to evaluate the possibility of preheating water (ρ = 1000 kg/m³, c_p = 4.18 kJ/kg K) using the tubing at your disposal (A = 10 m²). The heat exchange will occur according to the following equation Q = UA(T_H-T); where the overall heat transfer coefficient, U, has been estimated at 1 kW/m² K and the temperature of the hot medium TH is at 70^oC (this value will stay constant due to a high flow rate). The tank at your disposal holds 2000 kg of water. The inlet flow rate of water to the tank is 100 L/s at T₁ = 30^oC.

a) What is the steady state temperature?

b) What is the time constant of the process?

c) What is the process gain if T₁ is the input?

d) What is the process gain if T_H is the input?

e) Using part c) and d), predict (by hand) the new steady state temperature if:

1) The inlet temperature drops from 30 to 10^oC

2) The temperature of the hot fluid drops from 70 to 60^oC

f) Confirm your findings in e) by solving the ODE for these step changes using the software package of your choice (MATLAB, Polymath, etc).