Question about Plug flow reactors

[u/Maurus39]

Basically, I want to calculate the concentration distribution within a plug flow reactor (PFR). I know there’s a simplified formula on Wikipedia, but I tried to develop my own approach and am curious if it would work.

A PFR can essentially be imagined as an extremely long cascade of continuous stirred-tank reactors (CSTRs) with infinitesimally small volumes, right? Each "plug" would have a constant concentration.

For a first-order reaction in a CSTR, the concentration of the reactant is given by: C(t) = C(0) · exp(-k · t), where t is the average residence time in the reactor, defined as the ratio of volume to volumetric flow rate.

My approach would be to calculate the average residence time for a very small length (e.g., 1 millimeter), plug it into the formula, and—since the constant concentration at the outlet of one CSTR becomes the inlet concentration for the next—describe the reactant concentration at any given length as: C(t) = C(0) · exp(-k · n · t) with n being the given length . This assumes a constant volumetric flow rate and isothermal conditions.

Question: If I plot this, would I get a reasonably accurate result?

[u/ProcessNomad]

Sounds like you are ready to compare two methods for a given reaction and reactor design. You know what the answer is. Now you can check your method against it and think about how they relate, think about why PFR models use the math they use.