10854

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

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
  • Additional contributions by: John L. Falconer and Nick Bongiardina
  • (University of Colorado Boulder, Department of Chemical and Biological Engineering)

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

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.
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:
.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2016 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+