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.

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 because A reacts to B), which decreases the rate of reaction.

Following is the Ergun equation for the pressure drop in a packed bed:

= laminar flow term

= turbulent flow term

= pressure

= void fraction

= volumetric flow rate

= viscosity

= diameter of catalyst particles

= mass flow rate

= cross section area of PBR

= length of PBR

Material balance on reactant A for a first-order reaction: