Skip to content
Licensed Unlicensed Requires Authentication 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 EMAIL logo and Daniel E. Damiani


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.


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.


  • 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/kgs

  • 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 s1

  • 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


1. CybulskiA, MoulijnJA. Monoliths in heterogeneous catalysis. Catal Rev Sci Eng1994;36:179270.10.1080/01614949408013925Search in Google Scholar

2. IrandoustS, AnderssonB. Monolithic catalyst for non-automobile applications. Catal Rev Sci Eng1988;30:31492.Search in Google Scholar

3. KapteijnF, NijhuisTA, HeiszwolfJJ, MoulijnJA. New non-traditional multiphase catalytic reactor based on monolithic structures. Catal Today2001;66:13344.10.1016/S0920-5861(00)00614-3Search in Google Scholar

4. BogerT, ZieverinkMM, KreutzerMT, KapteijnF, MoulijnJA, AddiegoWP. Monolithic catalyst as an alternative to slurry systems: hydrogenation of edible oil. Ind Eng Chem Res2004;43:233744.10.1021/ie030809vSearch in Google Scholar

5. BogerT, RoyS, HeibelAK, BorchersOA. Monolith loop reactor as an alternative to slurry reactors. Catal Today2003;79–80:44151.10.1016/S0920-5861(03)00058-0Search in Google Scholar

6. BroekhuisRR, MachadoRM, NordquistAF. The ejector-driven monolith loop reactor: experiments and modeling. Catal Today2001;69:8793.10.1016/S0920-5861(01)00358-3Search in Google Scholar

7. BussardAG, WaghmareYG, DooleyKM, KnopfFC. Hydrogenation of alpha-methyl styrene in a piston oscillating monolith reactor. Ind Eng Chem Res2008;47:462331.10.1021/ie701708wSearch in Google Scholar

8. Edvinsson-AlbersRK, HoutermanMJ, VergunstT, GrolmanE, MoulijnJA. Novel monolithic stirrer reactor. AIChE J1998;44:245964.10.1002/aic.690441113Search in Google Scholar

9. HeiszwolfJJ, EngelvaartLB, van den EijndenMG, KreutzerMT, KapteijnF, MoulijnJA. Hydrodynamic aspects of the monolith loop reactor. Catal Today2001;56:80512.10.1016/S0009-2509(00)00292-XSearch in Google Scholar

10. IrandoustS, AndersenB. Mass transfer and liquid-phase reactions in a segmented two-phase flow monolithic catalyst reactor. Chem Eng Sci1988;43:19838.10.1016/0009-2509(88)87072-6Search in Google Scholar

11. NijhuisT, KreutzerM, RomijnA, KapteijnF, MoulijnJ. Monolithic catalysts as efficient three-phase reactors. Chem Eng Sci2001;56:8239.10.1016/S0009-2509(00)00294-3Search in Google Scholar

12. MarwanH, WinterbottomJM. The selective hydrogenation of butyne-1,4-diol supported palladiums: a comparative study on slurry, fixed bed, and monolith downflow bubble column reactors. Catal Today2004;97:32530.10.1016/j.cattod.2004.07.003Search in Google Scholar

13. BoldriniDE, SánchezJF, TonettoGM, DamianiDE. Monolithic stirrer reactor: performance in the partial hydrogenation of sunflower oil. Ind Eng Chem Res2012;51:1222232.10.1021/ie3013727Search in Google Scholar

14. Pérez-CadenasA, KapteijnF, ZieverinkM, MoulijnJ. Selective hydrogenation of fatty acid methyl esters over palladium on carbon-based monoliths: structural control of activity and selectivity. Catal Today2007;128:1317.10.1016/j.cattod.2007.05.006Search in Google Scholar

15. SánchezJF, González BelloOJ, MontesM, TonettoGM, DamianiDE. Pd/Al2O3-cordierite and Pd/Al2O3-fecralloy monolithic catalysts for the hydrogenation of sunflower oil. Catal Commun2009;10:14469.10.1016/j.catcom.2009.03.016Search in Google Scholar

16. SánchezMJ, BoldriniDE, TonettoGM, DamianiDE. Palladium catalyst on anodized aluminum monoliths for the partial hydrogenation of vegetable oil. Chem Eng J2011;187:35561.10.1016/j.cej.2010.12.085Search in Google Scholar

17. MachadoR, BroekhuisR, NordquistA, RoyB, CarneyS. Applying monolith reactors for hydrogenations in the production of specialty chemicals-process and economic. Catal Today2005;105:30517.10.1016/j.cattod.2005.06.036Search in Google Scholar

18. CordovaWA, HarriotP. Mass transfer resistances in the palladium-catalyzed hydrogenation of methyl linoleate. Chem Eng Sci1975;30:12016.10.1016/0009-2509(75)85040-8Search in Google Scholar

19. FernándezMB, TonettoGM, CrapisteG, DamianiDE. Kinetics of the hydrogenation of sunflower oil over alumina supported palladium catalyst. Int J Chem Reactor Eng2007;5:A10.10.2202/1542-6580.1380Search in Google Scholar

20. SantacesariaE, ParellaP, Di SerioM, BorelliG. Role of mass transfer and kinetics in the hydrogenation of rapeseed oil on a supported palladium catalyst. Appl Catal A Gen1994;116:26994.10.1016/0926-860X(94)80294-7Search in Google Scholar

21. TsutoK, HarriotP, BischoffKB. Intraparticle mass transfer effects and selectivity in the palladium-catalyzed hydrogenation of methyl linoleate. Ind Eng Chem1978;17:199205.10.1021/i160067a010Search in Google Scholar

22. RamachandranPA, ChaudhariRV. Overall effectiveness factor of a slurry reactor for non-linear kinetics. Can J Chem Eng1980;58:41215.10.1002/cjce.5450580322Search in Google Scholar

23. RamachandranPA, ChaudhariRV. Three phase catalytic reactors. New York: Gordon and Breach Science Publishers, 1983.Search in Google Scholar

24. SylvesterD, KulkarniAA, CarberryJJ. Slurry and trickle-bed reactor effectiveness. Can J Chem Eng1975;53:31316.10.1002/cjce.5450530312Search in Google Scholar

25. RamachandranPA, ChaudhariRV. Theoretical analysis of reaction of two gases in a catalytic slurry reactor. Ind Eng Chem Proc Des Dev1979;18:7038.10.1021/i260072a022Search in Google Scholar

26. FromentGF, BischoffKB. Chemical reactor analysis and design. New York: Wiley, 1990.Search in Google Scholar

27. HashimotoK, MuroyamaK, NagataSJ. Kinetics of the hydrogenation of fatty oils. JAOCS1971;48:2915.10.1007/BF02638464Search in Google Scholar

28. ChaudhariRV, RamachandranPA. Influence of mass transfer on zero-order reaction in a catalytic slurry reactor. Ind Eng Chem Fundam1980;19:2016.10.1021/i160074a013Search in Google Scholar

29. ChaudhariRV, RamachandranPA. Three phase slurry reactors. AIChE J1980;26:177201.10.1002/aic.690260202Search in Google Scholar

30. PetersonEE. Chemical reactor analysis. New Jersey: Prentice Hall, 1965.Search in Google Scholar

31. WheelerA. Reaction rates and selectivity in catalysts pores. Adv Catal1951;3:249327.10.1016/S0360-0564(08)60109-1Search in Google Scholar

32. ArisR. The mathematical theory of diffusion and reaction in permeable catalysts. London: Oxford University Press, 1975.Search in Google Scholar

Published Online: 2014-6-3
Published in Print: 2014-1-1

©2014 by De Gruyter

Downloaded on 21.9.2023 from
Scroll to top button