Isothermal Plug Flow Reactor with Recycle
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A first-order reaction is carried out in an isothermal plug flow reactor (PFR) with recycle. The fresh feed concentration (
 ) and volumetric flow rate  are known. Use sliders to change the recycle ratio and the PFR volume. The correct reactant exit concentration  is obtained iteratively: the reactor feed concentration  is guessed with the slider, the PFR mass balance is then solved to determine  , and a mass balance around the mixing point before the PFR yields the calculated  value. Next, change the " guess" using the slider until the calculated  (the black arrow on the left) equals 0.2 mol/L (the center of the green circle). The graph on the right plots the reactant concentration down the PFR using the guessed  value. For larger values of the recycle ratio, the PFR with recycle behaves like a continuous stirred-tank reactor (CSTR).
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Details:
Mole balance:
,
,
,
where 
is the rate of reaction (mol/[L s]), 
is the rate constant (1/s), 
is the concentration of the reactant (mol/L), 
is molar flow rate of reactant (mol/s), 
is the volumetric flow rate entering the PFR (L/s), and 
is reactor volume (L).
Initial conditions:
,
,
,
where 
is the concentration of the fresh feed (mol/L), 
is pressure (bar), 
is the ideal gas constant ([L bar]/[mol K]), 
is temperature (K), 
is the calculated fresh feed concentration from 
(mol/L), is the concentration of PFR inlet, guessed using the slider (mol/L), 
is recycle ratio, 
is the concentration at the exit of the PFR (mol/L), and 
is the volumetric flow rate of fresh feed (L/s).