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I have been working on a very interesting problem out of Fogler's Chemical Reaction Engineering. I have completed the problem (parts (a) through (c) which is what i'll do because I've been working on this problem for a while and I'm too tired to do part (d) right now), but I want to share my results and ask for some help in the interpretation of the results.

The equations used were the design equations for PFR and CSTR, which are

[tex]V_{CSTR} = \frac {F_{out} - F_{in}}{r_{A}}[/tex]

[tex]\frac {dF_{A}}{dV_{PFR}} = r_{A}[/tex]

where ##V## is the volume of the reactor, ##F## is the molar flow rate of the species, and ##r_{A}## is the reaction rate of the species.

I went beyond the scope of the problem and did some work in Matlab to write some code to plot reactor size vs. input stream flow rate, for fun and to gain a deeper understanding for this as well as keep up with my matlab skills! For the sake of context, I will post the problem as well as share my m-file and plots.

One preliminary detail I want to ask about is the following. Why is it that when you have the reaction rate for species A ##r_{A} = -kC_{A}##, ##C_{A}## is the concentration of A in the exit stream, and not some sort of instantaneous concentration?

So now for the meat of the interpretation.

So to begin with the zeroth order reaction, why is it that they require the same volume for a given input feed? As I worked and refined through this problem, it became very apparent to me that the reaction order makes a great deal of difference.

For the first and second order reactions, why is it that the CSTR requires such a larger volume to have the same conversion than the PFR? The difference between zeroth and first order is extremely obvious, but even for the second order reaction, it appears that the relative difference in size requirement decreases more than for the first order. My prediction for a third order reaction would be that the line for the PFR would become even flatter compared to the CSTR. What is the physical reason for this?

My observation is that as the order of the reaction increases, the relative difference in reactor volume between the PFR and CSTR increases. It seems that the PFR begins to flatten out, and the PFR continues to slope up. I haven't done the test, but I would suppose at some ##n^{th}## order reaction, the line for the PFR would eventually have zero slope.

Why does the relative difference between the two seem to decrease as the order of the reaction increases?

You can see that the actual value of the reactor size increases by orders of magnitude, from ##10^3## to ##10^4## to ##10^5## liters for zeroth, first, and second order reactions, respectively. Why does the order of a reaction affect the actual size of the reactor necessary to convert a input the same amount, so much as an increase of a magnitude of order? I am looking for some sort of physical reasoning.

Lastly, to follow up with this problem I was wondering if there are any other relations I should look at and plot to gain physical insight into sizing of a chemical reactor?

Thank you

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# PFR vs. CSTR reactor size for various order reactions

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