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?