90 80 70 0 60 T (deg. C) 50 40 40 30 0 20 20 40 40 60 80 100 120 140 160 180 200 Time (min)
The feed flow rate to an adiabatic continuous stirred tank reactor (CSTR) in which an exothermic
reaction is occurring is increased from 1000 to 1400. kg/h, causing the outlet temperature to change as shown:
a) Briefly explain on a physical basis why the temperature in this system oscillates after a step increase
in the inlet flow rate. Be clear, complete, and concise.
c) You know that this oscillating response cannot be that of two first order processes with real time
constant acting in series. Assuming the reaction is first order and the CSTR operates with constant holdup,
derive the block diagram with all transfer functions indicating how the temperature would respond to the feed
flow rate step change (W’(s) as input and T’(s) as output). An intermediate variable in this block diagram will
be the concentration of A in the reactor, represented by CA’(s).
d) A correct result for part c) will include a feedback loop in the block diagram, indicating the response
in T to a change in w is not simply two first order responses acting in series. Without attempting to simplify the
block diagram, use what you understand about the loop law together with the oscillating response to draw a
conclusion about the sign of some gain or combination of gains in the system. Explain your conclusion clearly,
completely, and concisely.
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