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You have been assigned a new fluidized bed reactor that cracks a feed stock into small molecules. The overall stoichiometry of this reaction is: 2

You have been assigned a new fluidized bed reactor that cracks a feed stock into small
molecules. The overall stoichiometry of this reaction is: 2A>B+C. This fluidized bed
reactor can be modeled as a CSTR. This reactor is jacketed and you have available both cooling
and heating fluids. The heat transfer fluid can be cooled or heated within the temperature range
of 200KTa500K. The mass of catalyst in the reactor is 5kg. The feed to this reactor is
gas phase at 300K and consists of the reactant A and an inert I. The pressure inside the reactor
vessel can be assumed to be uniform at a value of P=1.1105Pa. Assume that the reaction is
reversible and elementary. Physical and chemical properties are given in the table below.
a) Give the elementary reaction rate expression for the removal of A.
b) To get you started in this reactor design, your boss asked the chemist intern to make a plot of
the equilibrium conversion as a function of temperature which is given on the following page.
This is plotted as the dashed line. Since your job is on the line you are required to derive an
analytical expression for equilibrium conversion as a function of temperature. Calculate the
equilibrium conversion at 490K and compare it to the value on the dashed line on the plot on
the next page. (e.g.{:xeq=f(T)) Show all of your work including plotting the point.
c) Also as an extra added calculation the chemist intern calculated the conversion as a function
of temperature from the mole balance following company manuals. He never took heat
transfer and didn't know what equations to use for this problem. So he used the mole balance
and assumed a temperature to create the solid curve shown on the next page. Derive the
analytical expression for conversion from the mole balance as a function of temperature andc) Also as an extra added calculation the chemist intern calculated the conversion as a function
of temperature from the mole balance following company manuals. He never took heat
transfer and didn't know what equations to use for this problem. So he used the mole balance
and assumed a temperature to create the solid curve shown on the next page. Derive the
analytical expression for conversion from the mole balance as a function of temperature and
calculate one of the points on the curve. (e.g.xmb=f(T)) Show all of your work.
d) Derive an analytical expression for the conversion in the fluidized bed (CSTR) as a function
of temperature using the energy balance. (e.g.xeb=f(T)) Calculate the conversion from the
mole balance at a temperature of 520K and verify that this is one of the points on the solid
line on the graph on the next page. Show all of your work
e) Using both the energy and mole balance determine the maximum conversion and subsequent
reactor temperature that can be achieved in this reactor with the above operating conditions.
You must choose whether or not you are using the heating/cooling jacket and if using the
jacket then the jacket temperature, Ta Remember that this reactor has the option to run as an
adiabatic reactor or you could use the jacketed section for cooling or heating. The heat
transfer fluid can be cooled or heated within the temperature range of 200K to 500K. Show
all of your work including work on the graph.
g) For your chosen reactor operating conditions in part e) give all of the possible steady-state
operating conditions. State whether or not the maximum steady-state conversion that you
found is a stable or unstable operating condition.
please respond to all qy=uestions with detailed steps
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