Question 4
A continuous stirred tank reactor (CSTR) is shown in Figure 4.
Reactant inflow
Product overflow
Cooling water outlet
[CME3008]
a) Using the differential equation given above, develop a
linear dynamic model that describes how $c_A$ is influenced by
$c_{A,in}$ and $Q$.
[50 marks]
Cooling water inlet
Figure 4: A continuous stirred tank reactor (CSTR)
With a single first order reaction, A \rightarrow B, we have the following
material balance relationship,
$\frac{dc_A}{dt} = Q(c_{A,in} - c_A) - Vk c_A$
In this equation, $c_A$ (kmol m$^{-3}$) is the concentration of component
A in the CSTR, $c_{A,in}$ (kmol m$^{-3}$) is the inlet concentration, $Q$ (m$^3$ s$^{-1}$)
, is the volumetric flowrate, $V$ (m$^3$) is the volume of the
reacting fluid and $k$ (s$^{-1}$) the reaction rate constant.
We will assume that the temperature control scheme keeps the
temperature constant.
b) Using the linear differential equation developed in part (a),
design a feedforward control law that will manipulate the
volumetric flowrate to keep the outlet concentration of the
reactor constant despite disturbances in the inlet
concentration.
[END]
[50 marks]
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