Conversion in equal volume CSTR and PFR

Jaller1404 · Dec 4, 2017

Hello
I've been working on a problem that involves finding which reaction order gives a greater conversion for a CSTR over a PFR (Xcstr>Xpfr).
I was able to solve the mass balance for each reactor, finding:

Equation: X_CSTR divided by (1 minus X_CSTR) raised to the power n equals C_A0 raised to the power n minus 1, times tau, times k.

and

Equation: 1/(1-n) times [1 - (1 - X_PFR)^(1-n)] equals C_A0^(n-1) times tau times k, with X_PFR as the PFR conversion, n the reaction order, C_A0 the inlet concentration, tau the residence time and k the rate constant.

Allowing us to equate them. This is where I've been stuck for a while now, how can I find an inequation that would get me which reaction order gives XCSTR>XPFR? It is known that this happen when n<1

Chestermiller · Dec 4, 2017

Set the two left hand sides equal, and then algebraically solve for Xpfr in terms of Xcstr. Then, for various values of n, plot a graph of Xpfr as a function of Xcstr. I suggest n = 0.5, 1, and 2.

Jaller1404 · Dec 4, 2017

Thanks for the tip, but wouldn't n=1 result in a 1/0 indetermination?

Chestermiller · Dec 5, 2017

Jaller1404 said:

Thanks for the tip, but wouldn't n=1 result in a 1/0 indetermination?

For n = 1, you need to go back to the original differential equation. In the limit of n= 1, the solution approaches a natural log solution.

Conversion in equal volume CSTR and PFR

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