Overall Effectiveness Factor for Slab Geometry in a Three-Phase Reaction System

Diego E. Boldrini; Gabriela M. Tonetto; Daniel E. Damiani

doi:10.1515/ijcre-2014-0018

Published by De Gruyter June 3, 2014

Overall Effectiveness Factor for Slab Geometry in a Three-Phase Reaction System

Diego E. Boldrini , Gabriela M. Tonetto and Daniel E. Damiani

From the journal International Journal of Chemical Reactor Engineering

https://doi.org/10.1515/ijcre-2014-0018

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Abstract

The overall effectiveness factor for slab geometry applicable to uniform washcoats on a monolith surface for three-phase reaction systems was studied in the present work. Analytical solutions for zero-order reactions and Langmuir–Hinshelwood and power law kinetics were reported. The analysis of the theoretical results showed that not considering the geometry of the monolithic system in a proper way lead to 14% errors in reactions parameters when operating under mixed control (kinetic-internal diffusion) and negligible external mass-transfer resistances.

Keywords: overall effectiveness factor; monolithic catalyst; slab geometry; three-phase reaction; mass transfer; linear and nonlinear kinetics

Acknowledgments

The authors thank the Agencia Nacional de Promoción Científica y Tecnológica (National Agency of Scientific and Technological Promotion, Argentina) and the Consejo Nacional de Investigaciones Científicas y Técnicas (National Council for Scientific and Technological Research, CONICET) for their financial support.

Nomenclature

aL= Gas – liquid interfacial area per unit volume of liquid mGL2/mL3
aS= Liquid – solid interfacial area mcat2/mcat3
Cj= Concentration of j component, j = Di, M, S [mol/m3]
De= Effective diffusivity m2/s
G= Concentration of G in the gas [mol/m3]
G∗= Concentration of G in the liquid in equilibrium with the gas [mol/m3]
GS= Concentration of G at the catalyst surface [mol/m3]
k0= Rate constant mol/kg s
kDM= Rate constant for the kinetic example in eq. (11) mol/kgs
KG= Adsorption equilibrium constant for G m3/mol
kGL= Gas – liquid mass transfer coefficient mL3/mGL2s
km= Rate constant for mth order reaction mol/kgs
kMS= Rate constant for the kinetic examplein eq. (11) mol/kgs
kLS= liquid – solid mass transfer coefficient m/s
kP1= Pseudo first order reaction rate order m3/kgs
KS/KM= Constant adsorption ratio [dimensionless]
m= Order of reaction with respect to species G [dimensionless]
MG= Total mass transfer resistances s−1
RG= Rate of reaction of Gperunit volume of reactor mol/sm3
w= Mass of catalyst per unit volume of reactor kg/m3
L= Thickness of the catalytic slab m
x= Distance in the catalyst measured from the base of the pore m

Greek letters

η= Overall effectiveness factor [dimensionless]
ηc= Catalytic effectiveness factor [dimensionless]
θG= Fraction of surface sites occupied bygas [dimensionless]
λ= Distance from the center of the catalyst at which G concentration becomes zero [m]
ρc= Density of the catalyst [kg/m³]
σG= Parameter defined by eq. (5) [dimensionless]
ϕ= Generalized Thiele modulus [dimensionless]
ϕ0= Thiele modulus [dimensionless]
ΩG= Local rate of chemical reaction perunit weight of catalyst [mol/kg s]

Sub- and superscripts

A= Associative gas adsorption mechanisms
crit= stands for critical
D= Dissociative gas adsorption mechanisms
Di= Diene
M= Monoene.
S= Saturated

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Published Online: 2014-6-3

Published in Print: 2014-1-1

Overall Effectiveness Factor for Slab Geometry in a Three-Phase Reaction System

Abstract

Acknowledgments

Nomenclature

Greek letters

Sub- and superscripts

References

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