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

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

A first-order, irreversible, gas-phase reaction takes place in two isothermal, packed-bed catalytic reactors; they have the same diameter but different lengths (14 and 21 m). Only is fed to the reactors. The inlet pressure is the same for each reactor; the outlet pressure changes when particle diameter is changed with the slider, but each reactor has the same outlet pressure. As a result, the inlet molar flow rate of is lower for the longer reactor. Show plots of conversion, pressure, reactant molar flow rate, and volumetric flow rate as a function of distance down the reactor for both reactors with buttons. The Ergun equation is used to model the pressure drop.

Contributed by: Rachael L. Baumann (June 2013)
Additional contributions by: John L. Falconer and Nick Bongiardina
(University of Colorado Boulder, Department of Chemical and Biological Engineering)
Open content licensed under CC BY-NC-SA



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.

The Ergun equation for pressure drop in a packed bed reactor (PBR) is:




where is pressure, is PBR length, is void fraction, is volumetric flow rate, is viscosity, is the diameter of catalyst particles, is cross sectional area of the PBR, is mass flow rate, is a laminar flow term, and is the turbulent flow term.

Material balance on reactant for a first-order reaction:


where is the molar concentration of reactant , is the molar flow rate of , is a rate constant, and is the inlet molar flow rate of .

Since the reaction is , and only is fed to the reactor, the total molar flow rate .

Volumetric flow rate in reactor (from the ideal gas law):

where is the ideal gas constant, and is absolute temperature.

Conversion of reactant:


Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.