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To solve this problem we need to find out how to relate
the two reactors. In both cases we are not given a catalyst weight or a
reaction rate constant. We can try to solve for each individually.
If that is not possible then we can lump them together and solve for both.
From the Type 1 Home Problem solution:
which can be rearranged to form:
Solving for Wk1 :
Now we can solve for catalyst weight and the rate constant for the PFR, but we still need some way to relate the two reactors. Looking at the information given, we see that the two reactors are at different temperatures. The way to realate two equations at different temperatures is through the Arrhenius equation :
In the problem we are given that W1 = W2. We can replace both with W and multiply both sides of the previous equation by it:
Solving for Wk2 :
Now we have the realation we need between the two reactors. Next, we need to develop an equation to find the conversion in the CSTR. We start with the CSTR design equation:
Unfortunately, the design equation deals with volume where we have been given catalyst weight. To solve this problem we can multiply the design equation by the catalyst density to get the catalyst weight:
When the reaction rate is divided by the catalyst density it becomes the reaction rate with respect to catalyst weight and is designated with a prime:
Simplifying, we get a CSTR design equation with respect to catalyst weight instead of volume:
The reaction rate is :
From stoichiometry :
Substituting in for the reaction rate of the CSTR equation :
Rearranging and substituting in the numbers from the problem gives :
Solving for conversion :
Conversion can never be greater than 1 and it can never be negative so the first answer can not be correct. Therefore:
Back to Heterogeneous Example 2