Parametric Sensitivity of Plug Flow Reactor With Heat Exchange

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. Thermal runaway occurs at certain conditions and it is a sensitive function (parametric sensitivity) of the feed temperature and the activation energy.

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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:
,
where is rate of reaction (), is the pre-exponential factor in the rate constant (1/s), is activation energy (kJ/mol), is the ideal gas constant (kJ/[mol K]), is absolute temperature in the reactor (K), is pressure (atm), is the ideal gas constant (), is the molar flow rate of the reactant o-xylene (kmol/s), and is the total molar flow rate of the feed (kmol/s).
Mole balance as a function of reactor length:
,
where is distance down the PFR (m), is the cross section area of the PFR (), and is the PFR radius (m).
Energy balance as a function of length:
,
,
,
where and are simplification terms, is the temperature of heat transfer fluid surrounding the reactor (K), is heat of reaction (kJ/kmol), is mass flow rate (kg/s), is the mass heat capacity of gas in reactor (kJ/[kg K]) and is the overall heat transfer coefficient ().
At the PFR inlet () and , where is the feed temperature (K) and is the mole fraction of reactant in the feed.
The screencast video at [2] explains how to use this Demonstration.
References
[1] J. B. Rawlings and J. G. Ekerdt, Chemical Reactor Analysis and Design Fundamentals, Madison, WI: Nob Hill Publishing, 2002 pp. 323–326.
[2] Parametric Sensitivity of Plug Flow Reactor With Heat Exchange. www.colorado.edu/learncheme/kinetics/SensitivityOfPFRHeatExchange.html.
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