Next Article in Journal
Catalytic Behaviour of Flame-Made CuO-CeO2 Nanocatalysts in Efficient CO Oxidation
Previous Article in Journal
Ruthenium Supported on Ionically Cross-linked Chitosan-Carrageenan Hybrid MnFe2O4 Catalysts for 4-Nitrophenol Reduction
Article Menu
Issue 3 (March) cover image

Export Article

Open AccessArticle
Catalysts 2019, 9(3), 255;

Approximating Catalyst Effectiveness Factors with Reaction Rate Profiles

Department of Chemical and Metallurgical Engineering, School of Chemical Engineering, Aalto University, PO Box 11000, FI-00076 AALTO, Finland
Received: 28 January 2019 / Revised: 28 February 2019 / Accepted: 4 March 2019 / Published: 13 March 2019
(This article belongs to the Special Issue Reactors and Models in Catalysis)
Full-Text   |   PDF [5157 KB, uploaded 14 March 2019]   |  


A novel approximate solution for catalyst effectiveness factors is presented. It is based on carefully selected approximate reaction rate profiles, instead of typical assumption of composition profiles inside the catalyst. This formulation allows analytical solution of the approximate model, leading to a very simple iterative solution for effectiveness factor for general nonlinear reaction stoichiometry and arbitrary catalyst particle shape. The same model can be used with all practical Thiele modulus values, including multicomponent systems with inert compounds. Furthermore, the correct formulation of the underlying physical model equation is discussed. It is shown that an incorrect but often-used model formulation where convective mass transfer has been neglected may lead to much higher errors than the present approximation. Even with a correctly formulated physical model, rigorous discretization of the catalyst particle volume may have unexpectedly high numerical errors, even exceeding those with the present approximate solution. The proposed approximate solution was tested with a number of examples. The first was an equimolar reaction with first order kinetics, for which analytical solutions are available for the standard catalyst particle geometries (slab, long cylinder, and sphere). Then, the method was tested with a second order reaction in three cases: (1) with one pure reactant, (2) with inert present, and (3) with two reactants and non-stoichiometric surface concentrations. Finally, the method was tested with an industrially relevant catalytic toluene hydrogenation including Maxwell-Stefan formulation for the diffusion fluxes. In all the tested systems, the results were practically identical when compared to the analytical solutions or rigorous finite volume solution of the same problem. View Full-Text
Keywords: reactive systems; effectiveness factor; diffusion; convection; catalyst; discretization reactive systems; effectiveness factor; diffusion; convection; catalyst; discretization

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

Alopaeus, V. Approximating Catalyst Effectiveness Factors with Reaction Rate Profiles. Catalysts 2019, 9, 255.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Catalysts EISSN 2073-4344 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top