Importance of mass transfer fluctuations on reaction outcome in multiphase reactors.  

This notebook has been written in Mathematica by

Mark J. McCready
Professor and Chair of Chemical Engineering
University of Notre Dame
Notre Dame IN 46556

It is copyrighted to the extent allowed by whatever laws pertain to the World Wide Web and the Internet.

I would hope that as a professional courtesy that this notice remain visible to other users.
There is no charge for copying and dissemination.  

Version:  5/30/00
A more recent version of this notebook may be available at


This notebook is intended to show how periodic fluctuations in the mass transfer coefficient can cause not only differences in the total conversion but differences in the selectivity of the products if the fluctuation frequency is of the correct order of magnitude.  The intended application is gas-liquid reactions involving a solid phase catalyst such as trickle bed reactors.   

A CSTR (Continuous flow Stirred Tank Reactor) model is used.  First the model is demonstrated for a single phase reaction.  Next a simple liquid-solid model is used.  When fluctuations in the liquid-solid mass transfer coefficient are included, there is a change in selectivity with frequency.  Finally the complete gas-liquid-solid model of Wu, McCready and Varma (1995) is done.  This shows a maximum in selectivity at an intermediate frequency.     

Mathematica aside


Chemical reaction engineering, reaction selectivity, gas-liquid reaction, multiphase reactor, trickle-bed reactor, reactor dynamics     


R. Wu, M. J. McCready and A. Varma (1995), Chemical Engineering Science, 50, pp3333-3334.   T. W. F. Russell and M. M. Denn (1972), Introduction to Chemical Engineering Analysis, Wiley.  R. W. Felder and R. W. Rousseau (1986) Elementary Principles of Chemical Processes, 2nd Edition. Wiley.   

Development of the model equations and solution of the model

Transient and Steady Single Phase CSTR model

Transient and Steady Two-phase CSTR model

Two-phase CSTR model with mass transfer fluctuations

Three-phase CSTR model, with solid catalyst sites. (from Wu, McCready and Varma, 1995).  


1.  If you are just interested in transient and steady state CSTR calculations that are just a little too complex to solve analytically, we show how to easily do this.  The transient CSTR calculations for a single phase reactor show a simple transient leading to a steady state.  

2.  If the model includes a second phase, there can be a competition between products that are produced in different phases.   

3.  For a two phase system, there can be a change in selectivity with frequency.    

4.  For a gas-liquid reaction with a solid catalyst.  The reaction selectivity can exhibit a maximum at an intermediate frequency.  This effect can have important consequences for reactor scale-up as the dominant frequency for pulses decreases significantly as the column diameter is increased.

Converted by Mathematica      May 30, 2000