Process Dynamics and Contr Control ol Problem Set #1 Prepared by : Engr. Joseph R. Ortenero Mapua Institute of Technology at Laguna Malayan Colleges Laguna
Problem #1 1. Consider a system of two continuous tank reactors in series, where the following endothemic reaction takes place A + catalyst B (a) Identify the control objectives for the operation of the two CSTRs. (b) Classify the variables of the system into inputs and outputs and subsequently classify the inputs intodisturbances and manipulated variables and the outputs into measured and unmeasured outputs. Is this a SISO (single-input singleoutput) or a MIMO (multiple-input multiple-output? System?
Problem #1 c) Develop a feedback control configuration that satisfies your objectives using a composition analyzer at the exit stream of the second CSTR. (d) Develop a feedforward control configuration that can also use composition analyzers if they are needed. (e) In your opinion, which system is easier to control, the two-CSTR system or an equivalent one-CSTR system that achieves the same conversion? Explain why?
Problem #2 2. A steam turbine drives a compressor shown whose load can change with time. Small variations in the shaft speed of the turbine are controlled through the use of a flyball speed governor. For this system : (a)
Identify all the external disturbances
(b)
Identify all the available manipulated variables.
(c) Also determine the basic control objective and suggest a feedback control system that can be used to satisfy the control objective.
Problem #3 3. The distillation configuration for the separation of benzene from toluene is given below. The feed to the distillation comes from the reactor, where toluene has been hydrodealkylated to produce benzene: toluene + H2 benzene + CH4 after the excess H2 and the product CH4 have been removed in a flash unit. For the distillation system:
(a)
Identify all the control objectives.
(b)
Identify all the external disturbances.
(c)
All the available measurements and controlled variables.
Problem #4 4. Mathematical model of CSTR Consider a CSTR system. A simple exothermic reaction A B takes place in the reactor, which is in turn cooled by a coolant that flows through a jacket around the reactor. The fundamental dependent quantity for the reactor are: (a) Total mass of the reacting mixture in tank. (b) Mass of chemical A in the reacting mixture. (c) Total energy of the reacting mixture in the tank. Develop a model (differential equation) for the total amount of material, concentration of component A and temperature of the reacting mixture.
Problem #5 5. Consider the graphs shown. These graphs were produced by measuring the concentration of B in the reaction A B, over time, and at various temperatures. Do these graphs represent a mathematical model
Question #6 6. Why do you need to develop the mathematical model of a process you want to control?
Question #7 7. Irreversible consecutive reactions A B C occur in a jacketed, stirred-tank reactor shown in the figure. Derive a dynamic model based on the following assumptions: (i) The contents of the tank and jacket are well-mixed. The volumes of material in the jacket and in the tank do not vary with time. (ii) The reaction rates are given by r1= k1exp[-E1/RT] Ca, mol A/h-L; r2 = k2exp[-E2/RT]Ca mol A/h-L (iii) The thermal capacitances of the tank contents and the jacket contents are significant relative to the thermal capacitances of the jacket and tank walls, which can be neglected. (iv) Constant physical properties and heat transfer coefficients can be assumed.
Question #8 8. Two liquids streams with flow rates F1 and F2 and temperatures T1 and T2 flow through two separate pipes which converge at a mixing junction. We want to maintain constant the flow rate F3 and the temperature T3 of the liquid stream resulting from the mixing of the first two streams. (a)Identify the control objectives, disturbances, available measurements, and manipulated variables. Is this SISO or a MIMO system? (b)Develop a control system that uses only feedback controllers. (c)Develop a control system that uses only feedforward controllers.
Question #9 9. A jacketed vessel shown in the figure is used to heat a liquid by means of condensing steam. The following information is available: (i) The volume of liquid within the tank may vary. (ii) Heat losses are negligible. (iii) The tank contents are well-mixed. Steam condensate is removed from the jacket by a steam trap as soon as it has formed. (iv) Thermal capacitances of the tank and jacket walls are negligible. (v) The steam condensation pressure P1 is set by a control valve and is not necessarily constant. (vi) The overall heat transfer coefficient U for this system is constant. (vii)Flow rates qf and q are independently set by external valves and may vary. Derive a dynamic model for this process. The model should be simplified as much as possible. State any additional assumptions that you make.
Question #10 10. Consider a blending tank that is 2.5 m tall and 2 m in diameter. The liquid has a density of 800 kg/m3. Normal operating procedure is to fill the tank until the liquid level reaches a nominal value of 1.75 m using constant flow rates: m1=120 kg/min, m2=100 kg/min. The tank incorporates a valve on the outflow line that is used to establish the flow rate m3. In addition the nominal inlet stream mass fractions of components A are x1=x2=0.5. The process has been operating for a long time with constant flow rates and inlet concentrations. Under these conditions, it has come to steady state with exit mass fraction x=0.5 ad level h=1.75m.
Question #10 #10 continuation... Using the information below, answer the following questions: (a)What is the value of w3? The constant, Cv? (b)If x1 is suddenly changed from 0.5 to 0.6 without changing the inlet flow rates, what is the final value of x3?How long does it take to come within 1% of this final value? (c)If m3 is changed from 120 kg/min to 100 kg/min wihout changing the inlet concentrations, what will be the final value of the tank level? How long will it take to come within 1% of this final value? (d)Would it have made any difference in part (c) if the concentrations had changed at the same time the flow rate was changed? Useful information: The tank is perfectly mixed. m3 = Cv sqrt(h)
Question #11 11. Bioreactions are often carried out in batch reactors. The fed-batch bioreactor model below is also applicable to batch reactors if the feed flow rate F is set equal to zero. Using the available information below, determine how much time is required to achieve a 90% conversion of the substrate. Assume that the volume V of the reactor contents is constant. Available information: (i) Initial conditions: X(0) = 0.05 g/L, S(0) = 10 g/L, P(0)= 0 g g/L (ii) Parameter values: V = 1L, um = 0.20 hr-1, Ks = 1.0 g /L Y x/s = 0.5 g/g, Yp/s = 0.1 g/g, Yp/x = 0.2 g/g
Question #12 12. Suppose that the fedbatch bioreactor below is converted to a contiuous, stirred-tank bioreactor (also called a chemostat) by adding an exit stream. Assume that the inlet and exit streams have the same mass flow rate F and thus the volume of liquid V in the chemostat is constant.
Question #12 (a)Derive a dynamic model for this chemostat by modifying the fed-batch reactor model. (b)Derive the steady-state relationship between growth rate u and dilution rate D where by definition, D = F/V. Suggest a simple control strategy for controlling the growth rate based on this result. (c)An undesirable situation called wash-out occurs shen all of the cells are washed out of the biorector and thus cell mass X becomes zero. Determine the values of D that result in washout. (Hint: washout occurs if dX/dt is negative for an extended period of time, until X = 0). (d)For the numerical values given below, plot the steady-state cell production rate DX as a function of dilution rate D. Discuss the relationship between the values of D that result in washout and the value that provides the maximum production rate. The parameter values are: um= 0.20 h-1; Ks = 1.0 g/L, and Yx/s = 0.5 g/g. The steady-state condition is D = 0.1 h-1, X = 2.25 g/L, S= 1.0 g/L, and Sf = 10 g/L.
