This Demonstration plots the temperature and molar flow rate of the reactant as a function of distance down a plug flow reactor for an exothermic, gas-phase reaction. The reactor has heat exchange through the walls. Vary the feed temperature, activation energy for the reaction, and total molar flow rate with the sliders. Conditions that lead to thermal runaway are highly sensitive to feed temperature and the activation energy of the reaction. Parametric sensitivity refers to the analysis of how these parameters affect the runaway behavior.
This is a model of the partial oxidation of o-xylene in a large excess of oxygen in a 1.5 m long plug flow reactor.
The first-order rate expression:
r = k e−Ea/(R2 T) · P/(R T) · Fx/Ftot ,
where r is rate of reaction (mol/[m3 s]), k is the pre-exponential factor in the rate constant (1/s), Ea is activation energy (kJ/mol), R2 is the ideal gas constant (kJ/[mol K]), T is absolute temperature in the reactor (K), P is pressure (atm), R is the ideal gas constant ([atm m3]/[mol K]), Fx is the molar flow rate of the reactant o-xylene (kmol/s), and Ftot is the total molar flow rate of the feed (kmol/s).
Mole balance as a function of reactor length:
dFx/dz = −A r ,
where z is distance down the PFR (m), A = πr2 is the cross section area of the PFR (m2), and r is the PFR radius (m).
Energy balance as a function of length:
dT/dz = −β r + γ (Ta − T) ,
β = ΔH A/(m Cpm) ,
γ = 2πrU/(m Cpm) ,
where β and γ are simplification terms, Ta is the temperature of heat transfer fluid surrounding the reactor (K), ΔH is heat of reaction (kJ/kmol), m is mass flow rate (kg/s), Cpm is the mass heat capacity of gas in reactor (kJ/[kg K]) and U is the overall heat transfer coefficient (kJ/[m2 s K]).
At the PFR inlet (z = 0) T = Tf and Fx = yx,f Ftot, where Tf is the feed temperature (K) and yx,f is the mole fraction of reactant in the feed.
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 Muqbil Alkhalaf, Rachael L. Baumann, Neil Hendren, and John L. Falconer. 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.