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# Pressure Drop in a Packed Bed Reactor (PBR) Using the Ergun Equation

A first-order, irreversible reaction takes place in two isothermal packed bed catalytic reactors; their lengths are 14 m and 21 m. This Demonstration compares the conversion, pressure, molar flow rate, and volumetric flow rate for the two reactors as a function of distance down the reactor. The inlet pressure is the same for each reactor and, for a given particle diameter, the outlet pressure is also the same. As a result, the flow rate into the longer reactor is lower. The Ergun equation is used to model the pressure drop; you can vary the diameter of the catalyst particles in the packed bed.

### DETAILS

The pressure decreases down the length of the reactor, and thus the volumetric flow rate increases. As a result, the concentration of the reactant decreases (in addition to the decrease due to conversion), which lowers the rate of reaction.
Following is the Ergun equation for the pressure drop in a packed bed reactor (PBR):
= laminar flow term
= turbulent flow term
= pressure
= void fraction
= volumetric flow rate
= viscosity
= diameter of catalyst particles
= mass flow rate
= cross sectional area of PBR
= length of PBR
Material balance on reactant for a first-order reaction:
= molar flow rate of reactant
= rate constant
= total molar flow rate
= ideal gas constant
= absolute temperature
Volumetric flow rate in reactor (ideal gas law):
Conversion of reactant:
where
= initial molar flow rate through PBR.

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