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Volumetric Flow Rates in a Plug Flow Reactor

This Demonstration shows how the reaction stoichiometry affects the volumetric flow rate in an isothermal, constant-pressure, plug flow reactor by following a control volume (initially 10 mL of ) through the reactor. In the gas phase reaction , the reactant is blue and the product is green. Use the buttons to change the reaction stoichiometry and reaction order. Use the slider to change the reactor pressure. The rate constants are chosen so that the initial rates are the same for all orders at 10-bar pressure. The inlet velocity is fixed at 1.4 cm/s, independent of pressure, so the feed molar flow rates change when pressure changes. Click the "Play" button to run the reaction and click the "Reset" button to start over. The volumetric flow rate is shown below the reactor, and the change in the 10-mL inlet volume is shown above the reactor.

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DETAILS

The molar flow rate for species through the reactor is related to the volumetric flow rate using the ideal gas law:
,
,
where is the total molar flow rate, is conversion, is reactor pressure, and is the volumetric flow rate.
Mass balances are used to calculate the molar flow rates of and down the reactor:
,
,
where is the reaction order, is the moles of formed for each mole of reacted, is distance down the reactor, is the cross-sectional area of the reactor, and is concentration. The rate constants are chosen so the rate at the reactor inlet is the same for each reaction order at a pressure of 10 bar.
The concentration of is related to molar flow rates using the ideal gas law:
.
The conversion of is:
,
where is the inlet molar flow rate of .
The change in the control volume is the control volume at any location minus the initial control volume ():
.
For more information on solving plug flow reactor problems, view the screencast videos at [2] and [3].
References
[1] H. S. Fogler, Essentials of Chemical Reaction Engineering, Upper Saddle River, NJ: Prentice Hall, 2011.
[2] Mole Balance on a Plug Flow Reactor [Video]. (Jun 7, 2017) www.youtube.com/watch?v=MqHvapTy21I.
[3] Effect of Ignoring Density Change in PFR [Video]. (Jun 7, 2017) www.youtube.com/watch?v=_MsM8 _jq6Yo.
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