Exercise: Modeling and simulation of an exothermic reaction
From FBSwiki
(Contributed by Anand Asthagiri, 3 Oct 04)
Consider a chemical reactor in which species A undergoes a first-order, exothermic conversion to species B. To remove the heat of reaction, a jacket surrounds the reactor where a coolant is maintained at 100 deg F. Suppose that such a reactor is performing at steady-state conditions provided in the table below:
Inevitably, under normal process conditions, the reactor will experience disturbances in the inlet temperature (Ti(t)) and concentration of species A (cAi(t)) in the input stream. Thus, we would like to know what impact these fluctuations in inlet conditions might have on the concentration of species A (cA(t)) and the temperature (T(t)) of the effluent stream.
Suggestions: Assume that the reactor contents are well-mixed and that the heat capacity (Cp) and density (ρ) of reactants and products are equal.
Develop a set of equations that could be used to predict temporal changes in effluent temperature and species A concentration (T(t) and cA(t), respectively).
Since we are interested in deviations in process variables, it is useful to reformulate the above equations in terms of deviation variables. A deviation variable (Y') for a process variable (Y) is defined as
where 
is the steady-state value. Reformulate
equations in terms of such deviation variables, and solve for c'A(t) and
T'(t).
</li>Plot c'A(t) and T'(t) versus time for the following cases: (a) T'i(t) = − 5 deg R and (b) T'i(t) = − 10 deg R. Explain the observed behavior of the reactor. Does it always return to the same steady-state value? Is the dynamic response ``smooth or oscillatory? </li>
