recycle ratio 13
fresh feed temperature Tf (K) 300
guess T0 until the correct value of Tf is calculated below
PFR feed temperature T0 (K) 411

A first-order reaction is carried out in an adiabatic plug flow reactor (PFR) with recycle. The fresh feed concentration is known. Select the fresh feed temperature Tf and the recycle ratio with sliders. The correct exit temperature Te is obtained iteratively. The PFR feed temperature T0 is guessed with the slider (and the feed concentration to the PFR calculated using the adiabatic relation between temperature and concentration), the PFR mass and energy balances are solved to determine Tf and CA,f, and an energy balance around the mixing point before the PFR is then solved to determine the calculated Tf. Next, change the T0 guess until the calculated Tf (black arrow on the left) equals the Tf value that was set with the fresh feed temperature slider (the center of the green circle). The graph shows the temperature in the PFR as a function of distance down the reactor using the guessed value for T0. Multiple solutions are obtained under some conditions, and the solution observed depends on how the reactor starts up. High recycle ratios approach continuous stirred-tank reactor (CSTR) behavior.

Mass and energy balance:

dT/dz = −k CA ΔH / (u0 CA,0 Cp) ,
dCA/dz = −k CA / u0 ,
k = ko e−Ea/(R T) ,
Tf = (1 + ξ) T0 − ξ Te ,
u0 = uf (1 + ξ) ,

where

T = temperature (K)
z = length down the reactor (m)
u0 = velocity of the stream exiting the reactor (m/s)
CA,0 = concentration of A entering the reactor (mol/m3)
Cp = heat capacity (J/[m3 K])
ΔH = heat of reaction (J/mol)
k = rate constant (1/s)
CA = concentration of reactant A (mol/m3)
ko = pre-exponential factor (1/s)
T0 and Te = temperatures of the stream entering and exiting the reactor (K)
Tf = fresh feed temperature (K)
Ea = activation energy (J/mol)
R = ideal gas constant (J/[mol K])
ξ = recycle ratio
uf = velocity of the fresh feed (m/s)

This simulation was created in the Department of Chemical and Biological Engineering at University of Colorado Boulder for LearnChemE.com by John L. Falconer using Claude AI. It is a JavaScript/HTML5 implementation of a Mathematica simulation by Rachael L. Baumann. It was prepared with financial support from the National Science Foundation (DUE 2336987 and 2336988) in collaboration with Washington State University. Address any questions or comments to LearnChemE@gmail.com.