Jump to ContentJump to Main Navigation
Show Summary Details
More options …

International Journal of Chemical Reactor Engineering

Ed. by de Lasa, Hugo / Xu, Charles Chunbao


IMPACT FACTOR 2017: 0.881
5-year IMPACT FACTOR: 0.908

CiteScore 2017: 0.86

SCImago Journal Rank (SJR) 2017: 0.306
Source Normalized Impact per Paper (SNIP) 2017: 0.503

Online
ISSN
1542-6580
See all formats and pricing
More options …
Volume 13, Issue 3

Issues

Volume 9 (2011)

Volume 8 (2010)

Volume 7 (2009)

Volume 6 (2008)

Volume 5 (2007)

Volume 4 (2006)

Volume 3 (2005)

Volume 2 (2004)

Volume 1 (2002)

Fischer–Tropsch Synthesis in Slurry Bubble Column Reactors: Experimental Investigations and Modeling – A Review

Omar M. BashaORCID iD: http://orcid.org/0000-0002-5406-3328 / Laurent Sehabiague
  • Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh, PA 15261, USA
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Ahmed Abdel-Wahab / Badie I. Morsi
  • Corresponding author
  • Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh, PA 15261, USA
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2015-04-07 | DOI: https://doi.org/10.1515/ijcre-2014-0146

Abstract

This paper presents an extensive review of the kinetics, hydrodynamics, mass transfer, heat transfer and mathematical as well as computational fluid dynamics (CFD) modeling of Low-Temperature Tropsch Synthesis (LTFT) synthesis in Slurry Bubble Column Reactors (SBCRs), with the aim of identifying potential research and development areas in this particular field. The kinetic expressions developed for F-T synthesis over iron and cobalt catalysts along with the water gas shift (WGS) reactions are summarized and compared. The experimental data and empirical correlations to predict the hydrodynamics (gas holdup, Sauter mean bubble diameter, and bubble rise velocity), mass transfer coefficients and heat transfer coefficients are presented. The effects of various operating variables, including pressure, temperature, gas velocity, catalyst concentration, reactor geometry, and reactor internals on the hydrodynamic and transport parameters as well as the performance of SBCRs are discussed. Additionally, modeling efforts of SBCRs, using axial dispersion models (ADM), multiple cell recirculation models (MCCM) and computational fluid dynamics (CFD), are addressed. This review revealed the following:

  • (1)

    Numerous F-T and WGS kinetic rate expressions are available for cobalt and iron catalysts and one must be careful in selecting the appropriate expressions for LTFT. Iron catalyst suffers from severe attrition and subsequent deactivation in SBCRs and accordingly building a costly catalyst manufacturing facility onsite is required to maintain a steady operation of the F-T reactor;

  • (2)

    Experimental data on the hydrodynamic and transport parameters at high pressures and temperatures, typical to those of actual F-T synthesis, remain scanty when compared with the plethora of studies conducted using air–water systems in small reactors at ambient conditions;

  • (3)

    Several empirical correlations for predicting the hydrodynamic and mass as well heat transfer parameters are available and one should select those which consider the reactor diameter, gas mixtures and the potential foamability of the F-T liquids;

  • (4)

    The effect of cooling internals configuration and sparger design on the hydrodynamic and transport parameters, local turbulence, mixing and catalyst attrition are yet to be seriously addressed;

  • (5)

    The impact of operating variables on the hydrodynamic and transport parameters as well as the overall performance of the SBCRs should be investigated using actual F-T fluid–solid systems under typical pressures and temperatures using a large-scale reactor (>0.15 m ID) in the presence of gas spargers and cooling internals;

  • (6)

    Significant efforts are still required in order to advance CFD modeling of SBCRs, particularly those pertaining to the relevant closure models, such as drag, lift and turbulence. Also, cooling internals configuration and the design as well as orientation of gas spargers should be accounted for in the CFD modeling; and

  • (7)

    Proper validations of the CFD formulations using actual systems for F-T SBCR are needed.

Keywords: Fischer–Tropsch; reactors; SBCR; experiments; modeling; review; kinetics; CFD

References

  • 1.

    Schulz H. Short history and present trends of Fischer–Tropsch synthesis. Appl Catal 1999;186:3–12. .CrossrefGoogle Scholar

  • 2.

    Leckel D. Diesel production from Fischer−Tropsch: the past, the present, and new concepts. Energy Fuels 2009;23:2342–58. 2009/05/21. .CrossrefGoogle Scholar

  • 3.

    Dry ME. The Fischer-Tropsch process: 1950-2000. Catal Today 2002;71:227–41. .CrossrefGoogle Scholar

  • 4.

    Steynberg A, Dry M. Fischer-Tropsch technology. Elsevier Science: Amsterdam, 2004.Google Scholar

  • 5.

    Penniall CL. Fischer-Tropsch based biomass to liquid fuel plants in the New Zealand wood processing industry based on microchannel reactor technology. 2013.Google Scholar

  • 6.

    Sabatier P, Senderens JD. Nouvelles syntheses du methane. CR 1902;134:514.Google Scholar

  • 7.

    Ripfel-Nitsche K, Hofbauer H, Rauch R, Goritschnig M, Koch R, Lehner P, et al. BTL–biomass to liquid (Fischer Tropsch process at the biomass gasifier in güssing), in Proceedings of the 15th European Biomass Conference & Exhibition, Berlin, Germany, 2007.Google Scholar

  • 8.

    Longanbach JR, Stiegel GJ, Rutkowski MD, Buchanan TL, Klett MG, Schoff RL. Capital and operating cost of hydrogen production from coal gasification, Final Report, U.S. DOE Contract No. DE-AM26-99FT40465, Subcontract No. 990700362, Pittsburgh April 2003.Google Scholar

  • 9.

    Botes FG, Niemantsverdriet JW, van de Loosdrecht J. A comparison of cobalt and iron based slurry phase Fischer–Tropsch synthesis. Catal Today 2013;215:112–20. .CrossrefGoogle Scholar

  • 10.

    Collot A-G. Matching gasification technologies to coal properties. Int J Coal Geol 2006;65:191–212. .CrossrefGoogle Scholar

  • 11.

    Espinoza RL, Steynberg aP, Jager B, Vosloo aC. Low temperature Fischer–Tropsch synthesis from a sasol perspective. Appl Catal 1999;186:13–26. .CrossrefGoogle Scholar

  • 12.

    Dry M. The Fischer-Tropsch process – commercial aspects. Catal Today 1990;6:183–206. http://dx.doi.org/10.1016/0920-5861(90)85002-6.Crossref

  • 13.

    Xu J, Froment G. Methane steam reforming, methanation and water-gas shift: I. Intrinsic kinetics. AIChE J 1989;35:88–96. .CrossrefGoogle Scholar

  • 14.

    Mitchell W, Thijssen J, Bentley JM. Development of a catalytic partial oxidation/ethanol reformer for fuel cell applications. Soc Automot Eng 1995;Paper No. 9.Google Scholar

  • 15.

    Bradford M, Vannice M. Catalytic reforming of methane with carbon dioxide over nickel catalysts II. Reaction kinetics. Appl Catal 1996;142:97–122.Google Scholar

  • 16.

    Kusakabe K, Sotowa K-I, Eda T, Iwamoto Y. Methane steam reforming over Ce–ZrO2-supported noble metal catalysts at low temperature. Fuel Process Technol 2004;86:319–26. .CrossrefGoogle Scholar

  • 17.

    Berman a, Karn RK, Epstein M. Kinetics of steam reforming of methane on Ru/Al2O3 catalyst promoted with Mn oxides. Appl Catal 2005;282:73–83. .CrossrefGoogle Scholar

  • 18.

    Wu P, Li X, Ji S, Lang B, Habimana F, Li C. Steam reforming of methane to hydrogen over Ni-based metal monolith catalysts. Catal Today 2009;146:82–6. .CrossrefGoogle Scholar

  • 19.

    de Abreu AJ, Lucrédio AF, Assaf EM. Ni catalyst on mixed support of CeO2–ZrO2 and Al2O3: effect of composition of CeO2–ZrO2 solid solution on the methane steam reforming reaction. Fuel Process Technol 2012;102:140–5. .CrossrefGoogle Scholar

  • 20.

    Roh H-S, Eum I-H, Jeong D-W. Low temperature steam reforming of methane over Ni–Ce(1−x)Zr(x)O2 catalysts under severe conditions. Renewable Energy 2012;42:212–16. .CrossrefGoogle Scholar

  • 21.

    Wood DA, Nwaoha C, Towler BF. Gas-to-liquids (GTL): a review of an industry offering several routes for monetizing natural gas. J Nat Gas Sci Eng 2012;9:196–208. .CrossrefGoogle Scholar

  • 22.

    Schulz H, Schaub G, Claeys M, Riedel T. Transient initial kinetic regimes of Fischer–Tropsch synthesis. Appl Catal 1999;186:215–27. .CrossrefGoogle Scholar

  • 23.

    Deverell R, Yu M. Long run commodity prices: where do we stand? Credit Suisse 27 July, 2011.Google Scholar

  • 24.

    Liu Z, Shi S, Li Y. Coal liquefaction technologies – development in china and challenges in chemical reaction engineering. Chem Eng Sci 2010;65:12–17. .CrossrefGoogle Scholar

  • 25.

    de Klerk A. Fischer-Tropsch refining. Weinheim: Wiley-VCH Verlag & Co. KGaA, 2012.Google Scholar

  • 26.

    Kreutz TG, Larson ED, Liu G, Williams RH. Fischer-Tropsch fuels from coal and biomass, in 25th Annual International Pittsburgh Coal Conference, 2008.Google Scholar

  • 27.

    de Klerk A, Furimsky E. Catalysis in the refining of Fischer-Tropsch syncrude: Cambridge, United Kingdom. Royal Society of Chemistry, 2010.Google Scholar

  • 28.

    Bao B, El-Halwagi MM, Elbashir NO. Simulation, integration, and economic analysis of gas-to-liquid processes. Fuel Process Technol 2010;91:703–13. .CrossrefGoogle Scholar

  • 29.

    Sudiro M, Bertucco A. Production of synthetic gasoline and diesel fuel by alternative processes using natural gas and coal: process simulation and optimization. Energy 2009;34:2206–14. .CrossrefGoogle Scholar

  • 30.

    Sehabiague L, Basha O, Morsi BI. Recycling of tail gas in Fischer-Tropsch bubble column slurry reactor and its impact on the coal-to-liquid process, in Proceedings of the 30th Annual International Pittsburgh Coal Conference, Beijing, China, 2013.Google Scholar

  • 31.

    Sehabiague L. Modeling, scaleup and optimization of slurry bubble column reactors for Fischer-Tropsch synthesis, Doctoral Dissertation, Department of Chemical and Petroleum Engineering, University of Pittsburgh, 2012.Google Scholar

  • 32.

    Chedid R, Kobrosly M, Ghajar R. The potential of gas-to-liquid technology in the energy market: the case of Qatar. Energy Policy 2007;35:4799–811. .CrossrefGoogle Scholar

  • 33.

    van de Loosdrecht J, Botes FG, Ciobica IM, Ferreira A, Gibson P, Moodley DJ, et al. 7.20 – Fischer–Tropsch synthesis: catalysts and chemistry. In: Reedijk J and Poeppelmeier K, editors. Comprehensive inorganic chemistry II, 2nd edition. Amsterdam: Elsevier, 2013:525–57. doi:10.1016/B978-0-08-097774-4.00729-4.CrossrefGoogle Scholar

  • 34.

    Brady RC, Pettit R. On the mechanism of the Fischer-Tropsch reaction. The chain propagation step. J Am Chem Soc 1981;103:1287–9.Google Scholar

  • 35.

    Satterfield CN, Huff GA. Product distribution from iron catalyst in Fischer-Tropsch slurry reactors. Ind Eng Chem Process Des Dev 1982;21:465–70.Google Scholar

  • 36.

    van Dijk HAJ. The Fischer-Tropsch synthesis: a mechanistic study using transient isotopic tracing, Ph.D. Dissertation, Technische Universiteit Eindhoven, Eindhoven, the Netherlands, 2001.Google Scholar

  • 37.

    Inderwildi OR, Jenkins SJ, King DA. Fischer-Tropsch mechanism revisited: alternative pathways for the production of higher hydrocarbons from synthesis gas. J Phys Chem C 2008;112:1305–7.Google Scholar

  • 38.

    Chang J, Bai L, Teng B, Zhang R, Yang J, Xu Y, et al. Kinetic modeling of Fischer–Tropsch synthesis over catalyst in slurry phase reactor. Chem Eng Sci 2007;62:4983–91. .CrossrefGoogle Scholar

  • 39.

    Lox ES, Froment GF. Kinetics of the Fischer-Tropsch reaction on a precipitated promoted iron catalyst. 2. Kinetic modeling. Ind Eng Chem Res 1993;32:71–82. 1993/01/01. .CrossrefGoogle Scholar

  • 40.

    Lox ES, Froment GF. Kinetics of the Fischer-Tropsch reaction on a precipitated promoted iron catalyst. 1. Experimental procedure and results. Ind Eng Chem Res 1993;32:61–70. 1993/01/01. .CrossrefGoogle Scholar

  • 41.

    Wang Y-N, Xu Y-Y, Xiang H-W, Li Y-W, Zhang B-J. Modeling of catalyst pellets for Fischer−Tropsch synthesis. Ind Eng Chem Res 2001;40:4324–35. 2001/10/01. .CrossrefGoogle Scholar

  • 42.

    Todic B, Bhatelia T, Froment GF, Ma W, Jacobs G, Davis BH, et al. Kinetic model of Fischer–Tropsch synthesis in a slurry reactor on Co–Re/Al2O3 catalyst. Ind Eng Chem Res 2012;52:669–79. 2013/01/16. .CrossrefGoogle Scholar

  • 43.

    Wang YN, Xu YY, Li YW, Zhao YL, Zhang BJ. Heterogeneous modeling for fixed-bed Fischer-Tropsch synthesis: reactor model and its applications. Chem Eng Sci 2003;58:867–75.Google Scholar

  • 44.

    Yang GQ, Fan LS. Axial liquid mixing in high-pressure bubble columns. AIChE J 2003;49:1995–2008. .CrossrefGoogle Scholar

  • 45.

    Van der Laan GP, Beenackers AACM, Krishna R. Multicomponent reaction engineering model for Fe-catalyzed Fischer-Tropsch synthesis in commercial scale slurry bubble column reactors. Chem Eng Sci 1999;54:5013–19.Google Scholar

  • 46.

    Satterfield C, Hanlon R. Effect of water on the iron-catalyzed Fischer-Tropsch synthesis. Ind Eng Chem Prod Res Dev 1986;25:407–14.Google Scholar

  • 47.

    Anderson RB. Catalysis, vol 4. New York: P. H. Emmet, 1956.Google Scholar

  • 48.

    Huff Jr GA, Satterfield CN. Intrinsic kinetics of the Fischer-Tropsch synthesis on a reduced fused-magnetite catalyst. Ind Eng Chem Process Des Dev 1984;23:696–705.Google Scholar

  • 49.

    Ledakowicz S, Nettelhoff H, Kokuun R, Deckwer WD. Kinetics of the Fischer-Tropsch synthesis in the slurry phase on a potassium promoted iron catalyst. Ind Eng Chem Process Des Dev 1985;24:1043–9. 1985/10/01. .CrossrefGoogle Scholar

  • 50.

    Botes FG, Breman BB. Development and testing of a new macro kinetic expression for the iron-based low-temperature Fischer−Tropsch reaction. Ind Eng Chem Res 2006;45:7415–26. 2006/10/01. .CrossrefGoogle Scholar

  • 51.

    Zhou L-P, Hao X, Gao J-H, Yang Y, Wu B-S, Xu J, et al. Studies and discriminations of the kinetic models for the iron-based Fischer−Tropsch catalytic reaction in a recycle slurry reactor. Energy Fuels 2010;25:52–9. 2011/01/20. .CrossrefGoogle Scholar

  • 52.

    Wojciechowski BW. The kinetics of the Fischer-Tropsch synthesis. Catal Rev 1988;30:629–702. 1988/12/01. .CrossrefGoogle Scholar

  • 53.

    Van Der Laan GP, Beenackers AACM. Kinetics and selectivity of the Fischer–Tropsch synthesis: a literature review. Catal Rev 1999;41:255–318. 1999/01/10. .CrossrefGoogle Scholar

  • 54.

    Zennaro R, Tagliabue M, Bartholomew CH. Kinetics of Fischer–Tropsch synthesis on titania-supported cobalt. Catal Today 2000;58:309–19. .CrossrefGoogle Scholar

  • 55.

    Das T, Conner W, Li J, Jacobs G. Fischer-Tropsch synthesis: kinetics and effect of water for a CO/SiO2 catalyst. Energy Fuels 2005;19:1430–9.Google Scholar

  • 56.

    Outi A, Rautavuoma I, van der Baan HS. Kinetics and mechanism of the Fischer Tropsch hydrocarbon synthesis on a cobalt on alumina catalyst. Appl Catal 1981;1:247–72. .CrossrefGoogle Scholar

  • 57.

    Sarup B, Wojciechowski BW. Studies of the Fischer-Tropsch synthesis on a cobalt catalyst II. Kinetics of carbon monoxide conversion to methane and to higher hydrocarbons. Can J Chem Eng 1989;67:62–74. .CrossrefGoogle Scholar

  • 58.

    Yates IC, Satterfield CN. Intrinsic kinetics of the Fischer-Tropsch synthesis on a cobalt catalyst. Energy Fuels 1991;5:168–73. 1991/01/01. .CrossrefGoogle Scholar

  • 59.

    Botes FG, van Dyk B, McGregor C. The development of a macro kinetic model for a commercial Co/Pt/Al2O3 Fischer−Tropsch catalyst. Ind Eng Chem Res 2009;48:10439–47. 2009/12/02. .CrossrefGoogle Scholar

  • 60.

    Gracia J, Prinsloo F, Niemantsverdriet JW. Mars-van Krevelen-like mechanism of CO hydrogenation on an iron carbide surface. Catal Lett 2009;133:257–61. 2009/12/01. .CrossrefGoogle Scholar

  • 61.

    Deng L-J, Huo C-F, Liu X-W, Zhao X-H, Li Y-W, Wang J, et al. Density functional theory study on surface CxHy formation from CO activation on Fe3c(100). J Phys Chem C 2010;114:21585–92. 2010/12/16. .CrossrefGoogle Scholar

  • 62.

    Brötz W. Zur systematik der Fischer-Tropsch-katalyse. Z Elektro Angew Phys Chem 1949;53:301–6. .CrossrefGoogle Scholar

  • 63.

    Hall CC, Gall D, Smith SL. A comparison of the fixed-bed, liquid phase ('slurry'), and fluidized-bed techniques in the Fischer-Tropsch synthesis. J Inst Pet 1952;38:845–76.Google Scholar

  • 64.

    Anderson JR, Boudart M. Catalysis: science and technology, vol. 4. Springer-Verlag: Berlin, Germany, 1983.Google Scholar

  • 65.

    Anderson RB, Karn FS. A rate equation for the Fischer-Tropsch synthesis on iron catalysts. J Phys Chem 1960;64:805–8. 1960/06/01. .CrossrefGoogle Scholar

  • 66.

    Kölbel H. Kinetics and reaction mechanism of the hydrocarbon synthesis from carbon monoxide and water vapor on iron, cobalt, and nickel catalysts, in the Actes du 2ème Congrès International de Catalyse, Paris, 1960.Google Scholar

  • 67.

    Anderson RB, Karn FS, Shultz JF. Kinetics of the Fischer-Tropsch synthesis on iron catalysts. US Bur Mines Bull 1964;614:1–42.Google Scholar

  • 68.

    Dry ME, Shingles T, Boshoff LJ. Rate of the Fischer-Tropsch reaction over iron catalysts. J Catal 1972;25:99–104.Google Scholar

  • 69.

    Dry ME. Advances in Fischer-Tropsch chemistry. Ind Eng Chem Process Des Dev 1976;15:282–6.Google Scholar

  • 70.

    Atwood HE, Bennett CO. Kinetics of the Fischer-Tropsch reaction over iron. Ind Eng Chem Process Des Dev 1979;18:163–70. 1979/01/01. .CrossrefGoogle Scholar

  • 71.

    Thomson WJ. Applied Fischer-Tropsch kinetics for a flame sprayed iron catalyst. Prepr Pap - Am Chem Soc. Div Fuel Chem 1979;25:101–18.Google Scholar

  • 72.

    Feimer JL, Silveston PL, Hudgins RR. Steady-state study of the Fischer-Tropsch reaction. Ind Eng Chem Prod Res Dev 1981;20:609–15. 1981/12/01. .CrossrefGoogle Scholar

  • 73.

    Leib TM, Kuo JCW. Modeling the Fischer-Tropsch synthesis in slurry bubble-column reactors, in AIChE Annual Meeting, San Francisco, 1984.Google Scholar

  • 74.

    Nettelhoff H. Studies on the kinetics of Fischer-Tropsch synthesis in slurry phase. Ger Chem Eng 1985;8:177–85.Google Scholar

  • 75.

    Deckwer WD, Kokuun R, Sanders E, Ledakowicz S. Kinetic studies of Fischer-Tropsch synthesis on suspended iron/potassium catalyst– rate inhibition by carbon dioxide and water. Ind Eng Chem Process Des Dev 1986;25:643–9. 1986/07/01. .CrossrefGoogle Scholar

  • 76.

    Zimmerman WH, Bukur DB. Reaction kinetics over iron catalysts used for the Fischer Tropsch synthesis. Can J Chem Eng 1990;68:292–300.Google Scholar

  • 77.

    Liu H-S, Chiung W-C, Wang Y-C. Effect of lard oil, olive oil and castor oil on oxygen transfer in an agitated fermentor. Biotechnol Tech 1994;8:17–20. .CrossrefGoogle Scholar

  • 78.

    Liu Z-T, Li Y-W, Zhou J-L, Zhang B-J. Intrinsic kinetics of Fischer-Tropsch synthesis over an Fe-Cu-K catalyst. J Chem Soc Faraday Trans 1995;91:3255–61. .CrossrefGoogle Scholar

  • 79.

    van der Laan GP, Beenackers AACM. Hydrocarbon selectivity model for the gas−solid Fischer−Tropsch synthesis on precipitated iron catalysts. Ind Eng Chem Res 1999;38:1277–90. 1999/04/01. .CrossrefGoogle Scholar

  • 80.

    Van Berge PJ. Fischer-Tropsch studies in the slurry phase favouring wax production. Potchefstroom Campus: North-West University, 1994.Google Scholar

  • 81.

    van der Laan GP, Beenackers AaCM. Intrinsic kinetics of the gas–solid Fischer–Tropsch and water gas shift reactions over a precipitated iron catalyst. Appl Catal 2000;193:39–53. .CrossrefGoogle Scholar

  • 82.

    Jess A, Popp R, Hedden K. Fischer–Tropsch-synthesis with nitrogen-rich syngas: fundamentals and reactor design aspects. Appl Catal 1999;186:321–42. .CrossrefGoogle Scholar

  • 83.

    van Steen E, Schulz H. Polymerisation kinetics of the Fischer–Tropsch CO hydrogenation using iron and cobalt based catalysts. Appl Catal 1999;186:309–20. .CrossrefGoogle Scholar

  • 84.

    Eliason SA, Bartholomew CH. Reaction and deactivation kinetics for Fischer–Tropsch synthesis on unpromoted and potassium-promoted iron catalysts. Appl Catal 1999;186:229–43. .CrossrefGoogle Scholar

  • 85.

    Wang YN. Modelization and simulation of fixed-bed Fischer-Tropsch synthesis: kinetics, pellet and reactor, Ph.D. Dissertation, Institute of Coal Chemistry, Chinese Academy of Sciences, Taiyuan, China, 2001.Google Scholar

  • 86.

    Wang Y-N, Ma W-P, Lu Y-J, Yang J, Xu Y-Y, Xiang H-W, et al. Kinetics modelling of Fischer–Tropsch synthesis over an industrial Fe–Cu–K catalyst. Fuel 2003;82:195–213. .CrossrefGoogle Scholar

  • 87.

    Yang J, Liu Y, Chang J, Wang Y-N, Bai L, Xu Y-Y, et al. Detailed kinetics of Fischer−Tropsch synthesis on an industrial Fe−Mn catalyst. Ind Eng Chem Res 2003;42:5066–90. 2003/10/01. .CrossrefGoogle Scholar

  • 88.

    Teng B-T, Chang J, Zhang C-H, Cao D-B, Yang J, Liu Y, et al. A comprehensive kinetics model of Fischer–Tropsch synthesis over an industrial Fe–Mn catalyst. Appl Catal 2006;301:39–50. .CrossrefGoogle Scholar

  • 89.

    Botes FG, Breman BB. Development of a new kinetic expression for the iron-based Fischer-Tropsch reaction, in AIChE Annual Meeting, Conference Proceedings, 2006.Google Scholar

  • 90.

    Chang J, Bai L, Teng B, Zhang R, Yang J, Xu Y, et al. Kinetic modeling of Fischer-Tropsch synthesis over Fe-Cu-K-SiO2 catalyst in slurry phase reactor. Chem Eng Sci 2007;62:4983–91. .CrossrefGoogle Scholar

  • 91.

    Zhou L-P, Hao X, Gao J-H, Yang Y, Wu B-S, Xu J, et al. Studies and discriminations of the kinetic models for the iron-based Fischer−Tropsch catalytic reaction in a recycle slurry reactor. Energy Fuels 2011;25:52–9. 2011/01/20. .CrossrefGoogle Scholar

  • 92.

    Laan GPvd. Kinetics, selectivity and scale up of the Fischer-Tropsch synthesis. Groningen, The Netherlands: University of Groningen, 1999.Google Scholar

  • 93.

    Shen WJ, Zhou JL, Zhang BJ. Kinetics of Fischer-Tropsch synthesis over precipitated iron catalyst. J Nat Gas Chem 1994;4:385–400.Google Scholar

  • 94.

    Keyser MJ, Everson RC, Espinoza RL. Fischer−Tropsch kinetic studies with cobalt−manganese oxide catalysts. Ind Eng Chem Res 2000;39:48–54. .CrossrefGoogle Scholar

  • 95.

    Botes FG. Water–gas-shift kinetics in the iron-based low-temperature Fischer–Tropsch synthesis. Appl Catal 2007;328:237–42. .CrossrefGoogle Scholar

  • 96.

    van der Laan GP, Beenackers AACM, Krishna R. Multicomponent reaction engineering model for Fe-catalyzed Fischer–Tropsch synthesis in commercial scale slurry bubble column reactors. Chem Eng Sci 1999;54:5013–19.Google Scholar

  • 97.

    Yang C-H, Massoth FE, Oblad AG. Kinetics of CO + H2 reaction over Co-Cu-Al2O3 catalyst. In: Kugler EL and Steffgen FW, editors. Hydrocarbon synthesis from carbon monoxide and hydrogen, vol 178. American Chemical Society, 1979:35–46. doi:10.1021/ba-1979-0178.ch005.ed.CrossrefGoogle Scholar

  • 98.

    Pannell RB, Kibby CL, Kobylinski TP. A steady-state study of Fischer-Tropsch product distributions over cobalt, iron and ruthenium. In: Seivama T and Tanabe K, editors. Studies in surface science and catalysis, vol 7. Elsevier: Amsterdam, The Netherlands, 1981: 447–59. doi:10.1016/S0167-2991(09)60290-1.Part A.CrossrefGoogle Scholar

  • 99.

    Withers HP, Eliezer KF, Mitchell JW. Slurry-phase Fischer-Tropsch synthesis and kinetic studies over supported cobalt carbonyl derived catalysts. Ind Eng Chem Res 1990;29:1807–14. 1990/09/01. .CrossrefGoogle Scholar

  • 100.

    Visconti CG, Tronconi E, Lietti L, Zennaro R, Forzatti P. Development of a complete kinetic model for the Fischer–Tropsch synthesis over Co/Al2O3 catalysts. Chem Eng Sci 2007;62:5338–43. .CrossrefGoogle Scholar

  • 101.

    Anfray J, Bremaud M, Fongarland P, Khodakov A, Jallais S, Schweich D. Kinetic study and modeling of Fischer–Tropsch reaction over a catalyst in a slurry reactor. Chem Eng Sci 2007;62:5353–6. .CrossrefGoogle Scholar

  • 102.

    Kaiser P, Pöhlmann F, Jess A. Intrinsic and effective kinetics of cobalt-catalyzed Fischer-Tropsch synthesis in view of a power-to-liquid process based on renewable energy. Chem Eng Technol 2014;37:964–72. .CrossrefGoogle Scholar

  • 103.

    Inga JR. Scaleup and scaledown of slurry reactors: a new methodology, 1997.Google Scholar

  • 104.

    Deckwer W-D, Louisi Y, Zaidi A, Ralek M. Hydrodynamic properties of the Fischer-Tropsch slurry process. Ind Eng Chem Process Des Dev 1980;19:699–708. 1980/10/01. .CrossrefGoogle Scholar

  • 105.

    Bukur DB, Patel SA, Daly JG. Gas holdup and solids dispersion in a three-phase slurry bubble column. AIChE J 1990;36:1731–5.Google Scholar

  • 106.

    Krishna R, Swart JWAD, Ellenberger J, Martina GB, Maretto C. Gas holdup in slurry bubble columns: effect of column diameter and slurry concentration. AIChE J 1997;43:311–16.Google Scholar

  • 107.

    Vandu CO, Koop K, Krishna R. Volumetric mass transfer coefficient in a slurry bubble column operating in the heterogeneous flow regime. Chem Eng Sci 2004;59:5417–23. .CrossrefGoogle Scholar

  • 108.

    Behkish A, Lemoine R, Sehabiague L, Oukaci R, Morsi BI. Gas holdup and bubble size behavior in a large-scale slurry bubble column reactor operating with an organic liquid under elevated pressures and temperatures. Chem Eng J 2007;128:69–84. .CrossrefGoogle Scholar

  • 109.

    Behkish A, Men Z, Inga JR, Morsi BI. Mass transfer characteristics in a large-scale slurry bubble column reactor with organic liquid mixtures. Chem Eng Sci 2002;57:3307–24. .CrossrefGoogle Scholar

  • 110.

    Woo K-J, Kang S-H, Kim S-M, Bae J-W, Jun K-W. Performance of a slurry bubble column reactor for Fischer-Tropsch synthesis: determination of optimum condition. Fuel Process Technol 2010;91:434–9. .CrossrefGoogle Scholar

  • 111.

    Sehabiague L, Morsi BI. Hydrodynamic and mass transfer characteristics in a large-scale slurry bubble column reactor for gas mixtures in actual Fischer–Tropsch cuts. Int J Chem Reactor Eng 2013;11:1–20. .CrossrefGoogle Scholar

  • 112.

    Vandu CO, Krishna R. Volumetric mass transfer coefficients in slurry bubble columns operating in the churn-turbulent flow regime. Chem Eng Process Process Intensif 2004;43:987–95. .CrossrefGoogle Scholar

  • 113.

    Hikita H, Asai S, Tanigawa K. Gas hold-up in bubble columns. Chem Eng J 1980;20:59–67.Google Scholar

  • 114.

    Akita K, Yoshida F. Gas holdup and volumetric mass transfer coefficient in bubble columns. Effects of liquid properties. Ind Eng Chem Process Des Dev 1973;12:76–80. .CrossrefGoogle Scholar

  • 115.

    Deckwer WD, Field RW. Bubble column reactors. Wiley: New York, USA, 1992.Google Scholar

  • 116.

    Shah YT, Kelkar BG, Godbole SP, Deckwer W-D. Design parameters estimations for bubble column reactors. AIChE J 1982;28:353–79. .CrossrefGoogle Scholar

  • 117.

    Deckwer WD, Burckhart R, Zoll G. Mixing and mass transfer in tall bubble columns. Chem Eng Sci 1974;29:2177–88. .CrossrefGoogle Scholar

  • 118.

    Krishna R, Ellenberger J. Gas holdup in bubble column reactors operating in the churn-turbulent flow regime. AIChE J 1996;42:2627–34.Google Scholar

  • 119.

    Clark KN. The effect of high pressure and temperature on phase distributions in a bubble column. Chem Eng Sci 1990;45:2301–7.Google Scholar

  • 120.

    Behkish A. Hydrodynamic and mass transfer parameters in large-scale slurry bubble column reactors, 2004.Google Scholar

  • 121.

    Wilkinson PM, Dlerendonck Lv. Pressure and gas density effects on bubble break-up and gas hold-up in bubble columns. Chem Eng Sci 1990;45:2309–15.Google Scholar

  • 122.

    Jiang P, Lin T-J, Luo X, Fan L-S. Flow visualization of high pressure (21 MPa) bubble column: bubble characteristics. Chem Eng Res Des 1995;73:269–74.Google Scholar

  • 123.

    Therning P, Rasmuson A. Liquid dispersion, gas holdup and frictional pressure drop in a packed bubble column at elevated pressures. Chem Eng J 2001;81:331–5.Google Scholar

  • 124.

    Oyevaar M, De La Rie T, Van der Sluijs C, Westerterp K. Interfacial areas and gas hold-ups in bubble columns and packed bubble columns at elevated pressures. Chem Eng Process Process Intensif 1989;26:1–14.Google Scholar

  • 125.

    Smith G, Gamblin B, Newton D. X-ray imaging of slurry bubble column reactors: the effects of system pressure and scale. Int J Multiphase Flow 1996;22:102.Google Scholar

  • 126.

    Soong Y, Harke FW, Gamwo IK, Schehl RR, Zarochak MF. Hydrodynamic study in a slurry-bubble-column reactor. Catal Today 1997;35:427–34. .CrossrefGoogle Scholar

  • 127.

    öztürk SS, Schumpe A, Deckwer WD. Organic liquids in a bubble column: holdups and mass transfer coefficients. AIChE J 1987;33:1473–80. .CrossrefGoogle Scholar

  • 128.

    Bhaga D, Pruden BB, Weber ME. Gas holdup in a bubble column containing organic liquid mixtures. Can J Chem Eng 1971;49:417–20. .CrossrefGoogle Scholar

  • 129.

    Stegeman D, Knop PA, Wijnands AJG, Westerterp KR. Interfacial area and gas holdup in a bubble column reactor at elevated pressures. Ind Eng Chem Res 1996;35:3842–7. .CrossrefGoogle Scholar

  • 130.

    Godbole SP, Schumpe A, Shah YT, Carr NL. Hydrodynamics and mass transfer in non-Newtonian solutions in a bubble column. AIChE J 1984;30:213–20.Google Scholar

  • 131.

    Yasunishi A, Fukuma M, Muroyama K. Measurement of behavior of gas bubbles and gas holdup in a slurry bubble column by a dual electroresistivity probe method. J Chem Eng Jpn 1986;19:444–9. .CrossrefGoogle Scholar

  • 132.

    Neme F, Coppola L, Böhm U. Gas holdup and mass transfer in solid suspended bubble columns in presence of structured packings. Chem Eng Technol 1997;20:297–303.Google Scholar

  • 133.

    Wilkinson PM, Spek AP, van Dierendonck LL. Design parameters estimation for scale-up of high-pressure bubble columns. AIChE J 1992;38:544–54. .CrossrefGoogle Scholar

  • 134.

    Kluytmans JHJ, Kuster BFM, Schouten JC. Gas holdup in a slurry bubble column: influence of electrolyte and carbon particles. Ind Eng Chem Res 2001;40:5326–33. .CrossrefGoogle Scholar

  • 135.

    Crabtree JR, Bridgwater J. Bubble coalescence in viscous liquids. Chem Eng Sci 1971;26:839–51. .CrossrefGoogle Scholar

  • 136.

    Fan L, Yang G, Lee D, Tsuchiya K, Luo X. Some aspects of high-pressure phenomena of bubbles in liquids and liquid–solid suspensions. Chem Eng Sci 1999;54:4681–709.Google Scholar

  • 137.

    Kara S, Kelkar BG, Shah YT, Carr NL. Hydrodynamics and axial mixing in a three-phase bubble column. Ind Eng Chem Process Des Dev 1982;21:584–94. .CrossrefGoogle Scholar

  • 138.

    Koide K, Takazawa A, Komura M, Matsunaga H. Gas holdup and volumetric liquid-phase mass transfer coefficient in solid-suspended bubble columns. J Chem Eng Jpn 1984;17:459–66.Google Scholar

  • 139.

    Kojima H, Anjyo H, Mochizuki Y. Axial mixing in bubble column with suspended solid particles. J Chem Eng Jpn 1986;19:232–4.Google Scholar

  • 140.

    De Swart J, Krishna R. Influence of particles concentration on the hydrodynamics of bubble column slurry reactors. Chem Eng Res Des 1995;73:308–13.Google Scholar

  • 141.

    Krishna R, van Baten JM, Urseanu MI, Ellenberger J. Design and scale up of a bubble column slurry reactor for Fischer-Tropsch synthesis. Chem Eng Sci 2001;56:537–45.Google Scholar

  • 142.

    Lee DJ, Luo X, Fan L-S. Gas disengagement technique in a slurry bubble column operated in the coalesced bubble regime. Chem Eng Sci 1999;54:2227–36. .CrossrefGoogle Scholar

  • 143.

    Gandhi B, Prakash A, Bergougnou Ma. Hydrodynamic behavior of slurry bubble column at high solids concentrations. Powder Technol 1999;103:80–94. .CrossrefGoogle Scholar

  • 144.

    Saxena SC, Rao NS, Thimmapuram PR. Gas phase holdup in slurry bubble columns for two- and three-phase systems. Chem Eng J 1992;49:151–9. .CrossrefGoogle Scholar

  • 145.

    Colmenares A, Sevilla M, Goncalves JJ, González-Mendizabal D. Fluid-dynamic experimental study in a bubble column with internals. Int Commun Heat Mass Transfer 2001;28:389–98. .CrossrefGoogle Scholar

  • 146.

    Thorat BN, Kataria K, Kulkarni AV, Joshi JB. Pressure drop studies in bubble columns. Ind Eng Chem Res 2001;40:3675–88. 2001/08/01. .CrossrefGoogle Scholar

  • 147.

    Yamashita F. Effect of clear liquid height and gas inlet height on gas holdup in a bubble column. J Chem Eng Jpn 1998;31:285–8. .CrossrefGoogle Scholar

  • 148.

    Kastanek F, Zahradnik J, Kratochvil J, Cermak J. Modeling of large-scale bubble column reactors for non-ideal gas–liquid systems. In: Doraiswamy LK and Mashelkar RA, editors. Frontiers in Chemical Reaction Engineering, vol 1. Wiley: Bombay, India, 1984:330.Google Scholar

  • 149.

    Fair JR, Lambright AJ, Andersen JW. Heat transfer and gas holdup in a sparged contactor. Ind Eng Chem Res Process Des Dev 1962;1:33–6. 1962/01/01. .CrossrefGoogle Scholar

  • 150.

    Yoshida F, Akita K. Performance of gas bubble columns: volumetric liquid-phase mass transfer coefficient and gas holdup. AIChE J 1965;11:9–13. .CrossrefGoogle Scholar

  • 151.

    Pino LZ, Solari RB, Siquier S, Estevez LA, Yepez MM, Saez AE. Effect of operating conditions on gas holdup in slurry bubble columns with a foaming liquid. Chem Eng Commun 1992;117:367–82.Google Scholar

  • 152.

    Reilly IG, Scott DS, Debruijn TJW, Macintyre D. The role of gas phase momentum in determining gas holdup and hydrodynamic flow regimes in bubble column operations. Can J Chem Eng 1994;72:3–12.Google Scholar

  • 153.

    Smith JS, Burns LF, Valsaraj KT, Thibodeaux LJ. Bubble column reactors for wastewater treatment. 2. The effect of sparger design on sublation column hydrodynamics in the homogeneous flow regime. Ind Eng Chem Res 1996;35:1700–10. 1996/01/01. .CrossrefGoogle Scholar

  • 154.

    Tsuchiya K, Haryono MH, Tomida T, Hatano H, Oaki H. Performance of a hollow-fiber spiral disk for effective gas dispersion toward high mass transfer rate. Ind Eng Chem Res 1996;35:613–20. 1996/01/01. .CrossrefGoogle Scholar

  • 155.

    Elgozali A, Linek V, Fialová M, Wein O, Zahradnı́k J. Influence of viscosity and surface tension on performance of gas–liquid contactors with ejector type gas distributor. Chem Eng Sci 2002;57:2987–94. .CrossrefGoogle Scholar

  • 156.

    Mersmann A. Design and scale-up of bubble and spray columns. Ger Chem Eng 1978;1:1–11.Google Scholar

  • 157.

    Behkish A, Lemoine R, Oukaci R, Morsi BI. Novel correlations for gas holdup in large-scale slurry bubble column reactors operating under elevated pressures and temperatures. Chem Eng J 2006;115:157–71. .CrossrefGoogle Scholar

  • 158.

    Kim SD, Baker CGI, Bergougnou MA. Phase holdup characteristics of three phase fluidized beds. Can J Chem Eng 1975;53:134–9. .CrossrefGoogle Scholar

  • 159.

    Kito M, Tabei K, Murata K. Gas and liquid holdups in mobile beds under the countercurrent flow of air and liquid. Ind Eng Chem Process Des Dev 1978;17:568–71. 1978/10/01. .CrossrefGoogle Scholar

  • 160.

    Oh JS, Kim SD. Phase holdup characteristics of three phase fluidized beds of mixed particles. Hwahak Konghak (J Korean Inst Chem Eng) 1980;18:375–84.Google Scholar

  • 161.

    Begovich JM, Watson J. Hydrodynamic characteristics of three-phase fluidized beds. Cambridge: Cambridge University Press, 1978.Google Scholar

  • 162.

    Khang S, Schwartz J, Buttke R. A practical wake model for estimating bed expansion and holdup in three phase fluidized systems, in AIChE Symposium Series, 1983: 47–54.Google Scholar

  • 163.

    Sivakumar V, Senthilkumar K, Kannadasan T. Prediction of gas holdup in the three-phase fluidized bed: air/Newtonian and non-Newtonian liquid systems. Pol J Chem Technol 2010;12:64. .CrossrefGoogle Scholar

  • 164.

    Smith DN, Fuchs W, Lynn RJ, Smith DH, Hess M. Bubble behavior in a slurry bubble column reactor model. In: Dudukovic MP and Mills PL, editors. Chemical and catalytic reactor modeling, vol 237. American Chemical Society: Washington, DC, USA, 1984:125–47. doi:10.1021/bk-1984-0237.ch008.ed.CrossrefGoogle Scholar

  • 165.

    Reilly IG, Scott DS, De Bruijn T, Jain A, Piskorz J. A correlation for gas holdup in turbulent coalescing bubble columns. Can J Chem Eng 1986;64:705–17. .CrossrefGoogle Scholar

  • 166.

    Schumpe A, Saxena AK, Fang LK. Gas/liquid mass transfer in a slurry bubble column. Chem Eng Sci 1987;42:1787–96.Google Scholar

  • 167.

    Sauer T, Hempel D. Fluid dynamics and mass transfer in a bubble column with suspended particles. Chem Eng Technol 1987;10:180–9.Google Scholar

  • 168.

    Lee SLP, de Lasa HI. Phase holdups in three-phase fluidized beds. AIChE J 1987;33:1359–70. .CrossrefGoogle Scholar

  • 169.

    Bukur DB, Daly JG. Gas hold-up in bubble columns for Fischer-Tropsch synthesis. Chem Eng Sci 1987;42:2967–9. .CrossrefGoogle Scholar

  • 170.

    Krishna R, Sie ST. Design and scale-up of the Fischer-Tropsch bubble column slurry reactor. Fuel Process Technol 2000;64:73–105. .CrossrefGoogle Scholar

  • 171.

    Chen C-M, Leu L-P. Hydrodynamics and mass transfer in three-phase magnetic fluidized beds. Powder Technol 2001;117:198–206.Google Scholar

  • 172.

    Ramesh K, Murugesan T. Minimum fluidization velocity and gas holdup in gas–liquid–solid fluidized bed reactors. J Chem Technol Biotechnol 2002;77:129–36. .CrossrefGoogle Scholar

  • 173.

    Jena HM, Roy GK, Meikap BC. Prediction of gas holdup in a three-phase fluidized bed from bed pressure drop measurement. Chem Eng Res Des 2008;86:1301–8. .CrossrefGoogle Scholar

  • 174.

    Sehabiague L, Morsi BI. Modeling and simulation of a Fischer–Tropsch slurry bubble column reactor using different kinetic rate expressions for iron and cobalt catalysts. Int J Chem Reactor Eng 2013;11:1–22. .CrossrefGoogle Scholar

  • 175.

    Zehner P. Mehrphasenströmungen in gas-flüssigkeits-reaktoren. DECHEMA Monogr 1989;114:215–33.Google Scholar

  • 176.

    Eissa SH, El-Halwagi MM, Saleh MA. Axial and radial mixing in a cocurrent bubble column. Ind Eng Chem Process Des Dev 1971;10:31–6. 1971/01/01. .CrossrefGoogle Scholar

  • 177.

    Reith T, Renken S, Israël BA. Gas hold-up and axial mixing in the fluid phase of bubble columns. Chem Eng Sci 1968;23:619–29. .CrossrefGoogle Scholar

  • 178.

    Kantak MV, Shetty SA, Kelkar BG. Liquid phase backmixing in bubble column reactors – a new correlation. Chem Eng Commun 1994;127:23–34. 1994/01/01. .CrossrefGoogle Scholar

  • 179.

    Camacho Rubio F, Sánchez Mirón A, Cerón García MC, García Camacho F, Molina Grima E, Chisti Y. Mixing in bubble columns: a new approach for characterizing dispersion coefficients. Chem Eng Sci 2004;59:4369–76. .CrossrefGoogle Scholar

  • 180.

    Pozin LS, Aérov ME, Bystrova TA. Study of turbulent diffusion coefficients in bubble-bed liquid phases. Theor Found Chem Eng 1969;3:714.Google Scholar

  • 181.

    Walter JF, Blanch HW. Liquid circulation patterns and their effect on gas holdup and axial mixing in bubble columns. Chem Eng Commun 1983;19:243–62. 1983/01/01. .CrossrefGoogle Scholar

  • 182.

    Miyauchi T, Furusaki S, Morooka S, Ikeda Y. Transport phenomena and reaction in fluidized catalyst beds. Adv Chem Eng 1981;11:275–448.Google Scholar

  • 183.

    Chaouki J, Larachi F, Dudukovic P. Non-invasive monitoring of multiphase flows. Elsevier Science: Amsterdam, The Netherlands, 1997.Google Scholar

  • 184.

    Fan LS, Tsuchiya K. Bubble wake dynamics in liquids and liquid-solid suspensions. Butterworth-Heinemann: Massachusetts, USA, 1990.Google Scholar

  • 185.

    Rigby GR, Capes CE. Bed expansion and bubble wakes in three-phase fluidization. Can J Chem Eng 1970;48:343–8. .CrossrefGoogle Scholar

  • 186.

    Morooka S, Uchida K, Kato Y. Recirculating turbulent flow of liquid in gas-liquid-solid fluidized bed. J Chem Eng Jpn 1982;15:29–34. .CrossrefGoogle Scholar

  • 187.

    Yu YH, Kim SD. Bubble characteristics in the radial direction of three-phase fluidized beds. AIChE J 1988;34:2069–72. .CrossrefGoogle Scholar

  • 188.

    Wu C, Suddard K, Al-dahhan MH. Bubble dynamics investigation in a slurry bubble column. AIChE J 2008;54:1203–12. .CrossrefGoogle Scholar

  • 189.

    De Swart JWA, Van Vilet RE, Krishna R. Size, structure and dynamics of large bubbles in a two-dimensional slurry bubble column. Chem Eng Sci 1996;51:4619–29.Google Scholar

  • 190.

    Ellenberger J, Krishna R. A unified approach to the scale-up of gas–solid fluidized bed and gas–liquid bubble column reactors. Chem Eng Sci 1994;49:5391–411.Google Scholar

  • 191.

    Krishna R, Ellenberger J. A unified approach to the scale-up of fluidized multiphase reactors. Trans IChemE 1995;73:217–21.Google Scholar

  • 192.

    Rados N, Al-Dahhan MH, Dudukovic MP. Modeling of the Fischer-Tropsch synthesis in slurry bubble column reactors. Catal Today 2003;79–80:211–18.Google Scholar

  • 193.

    Bukur D. Some comments on models for Fischer-Tropsch reaction in slurry bubble column reactors. Chem Eng Sci 1983;38:441–6.Google Scholar

  • 194.

    Bukur D, Kumar VR. Effect of catalyst dispersion on performance of slurry bubble column reactors. Chem Eng Sci 1986;41:1435–44. .CrossrefGoogle Scholar

  • 195.

    Sehabiague L, Lemoine R, Behkish A, Heintz YJ, Sanoja M, Oukaci R, et al. Modeling and optimization of a large-scale slurry bubble column reactor for producing 10,000bbl/day of Fischer–Tropsch liquid hydrocarbons. J Chin Inst Chem Eng 2008;39:169–79. .CrossrefGoogle Scholar

  • 196.

    Maretto C, Krishna R. Modelling of a bubble column slurry reactor for Fischer-Tropsch synthesis. Catal Today 1999;52:279–89.Google Scholar

  • 197.

    de Swart JWa,Krishna R. Simulation of the transient and steady state behaviour of a bubble column slurry reactor for Fischer–Tropsch synthesis. Chem Eng Process Process Intensif 2002;41:35–47. .CrossrefGoogle Scholar

  • 198.

    Zheng Y, Gu T. Analytical solution to a model for the startup period of fixed-bed reactors. Chem Eng Sci 1996;51:3773–9.Google Scholar

  • 199.

    Fan LS. Gas-liquid-solid fluidization engineering. Butterworths: Massachusetts, USA, 1989.Google Scholar

  • 200.

    Iliuta I, Larachi F, Desvigne D. Multicompartment hydrodynamic model for slurry bubble columns. Chem Eng Sci 2008;63:3379–99.Google Scholar

  • 201.

    Iliuta I, Larachi F, Anfray J, Dromard N, Schweich D. Multicomponent multicompartment model for Fischer-Tropsch SCBR. AIChE J 2007;53:2062–83.Google Scholar

  • 202.

    Eversole WG, Wagner GH, Stackhouse E. Rapid formation of gas bubbles in liquids. Ind Eng Chem 1941;33:1459–62. 1941/11/01. .CrossrefGoogle Scholar

  • 203.

    VanKrevelen D, Hoftijzer P. Studies of gas-bubble formation-calculation of interfacial area in bubble contactors. Chem Eng Prog 1950;46:29–35.Google Scholar

  • 204.

    Benzing RJ, Myers JE. Low frequency bubble formation at horizontal circular orifices. Ind Eng Chem 1955;47:2087–90. 1955/10/01. .CrossrefGoogle Scholar

  • 205.

    Leibson I, Holcomb EG, Cacoso AG, Jacmic JJ. Rate of flow and mechanics of bubble formation from single submerged orifices. I. Rate of flow studies. AIChE J 1956;2:296–300. .CrossrefGoogle Scholar

  • 206.

    Leibson I, Holcomb EG, Cacoso AG, Jacmic JJ. Rate of flow and mechanics of bubble formation from single submerged orifices. II. Mechanics of bubble formation. AIChE J 1956;2:300–6. .CrossrefGoogle Scholar

  • 207.

    Nedeltchev S, Schumpe A. New approaches for theoretical estimation of mass transfer parameters in both gas-liquid and slurry bubble columns. In: M. El-Amin, editor. InTech, 2011:780.Google Scholar

  • 208.

    Davidson JF, Schüler BOG. Bubble formation at an orifice in a viscous liquid. Chem Eng Res Des 1997;75: S105–S115. .CrossrefGoogle Scholar

  • 209.

    Khurana AK, Kumar R. Studies in bubble formation – III. Chem Eng Sci 1969;24:1711–23. .CrossrefGoogle Scholar

  • 210.

    Kumar R, Kuloor N. The formation of bubbles and drops. Adv Chem Eng 1970;8:255–368.Google Scholar

  • 211.

    Ramakrishnan S, Kumar R, Kuloor NR. Studies in bubble formation – I: bubble formation under constant flow conditions. Chem Eng Sci 1969;24:731–47. .CrossrefGoogle Scholar

  • 212.

    Satyanarayan A, Kumar R, Kuloor NR. Studies in bubble formation—II bubble formation under constant pressure conditions. Chem Eng Sci 1969;24:749–61. .CrossrefGoogle Scholar

  • 213.

    Wraith AE. Two stage bubble growth at a submerged plate orifice. Chem Eng Sci 1971;26:1659–71. .CrossrefGoogle Scholar

  • 214.

    Park Y, Lamont Tyler A, de Nevers N. The chamber orifice interaction in the formation of bubbles. Chem Eng Sci 1977;32:907–16. .CrossrefGoogle Scholar

  • 215.

    Acharya A, Ulbrecht JJ. Note on the influence of viscoelasticity on the coalescence rate of bubbles and drops. AIChE J 1978;24:348–51. .CrossrefGoogle Scholar

  • 216.

    Rabiger N, Vogelpohl A. Bubble formation and its movement in Newtonian and non-Newtonian liquids. In: Cheremisinoff NP, editor. Encyclopaedia of fluid mechanics. Houston: Gulf Publishing, 1986:59.Google Scholar

  • 217.

    Rice RG, Lakhani NB. Bubble formation at a puncture in a submerged rubber membrane. Chem Eng Commun 1983;24:215–34. .CrossrefGoogle Scholar

  • 218.

    Gaddis ES, Vogelpohl A. Bubble formation in quiescent liquids under constant flow conditions. Chem Eng Sci 1986;41:97–105. .CrossrefGoogle Scholar

  • 219.

    Tsuge H, Hibino S-I. Bubble formation from an orifice submerged in liquids. Chem Eng Commun 1983;22:63–79. 1983/07/01. .CrossrefGoogle Scholar

  • 220.

    Tsuge H, Nakajima Y, Terasaka K. Behavior of bubbles formed from a submerged orifice under high system pressure. Chem Eng Sci 1992;47:3273–80. .CrossrefGoogle Scholar

  • 221.

    Tsuge H, Tanaka Y, Terasaka K, Matsue H. Bubble formation in flowing liquid under reduced gravity. Chem Eng Sci 1997;52:3671–6. .CrossrefGoogle Scholar

  • 222.

    Tsuge H, Din U,P, Kammel R. Bubble formation from a vertically downward facing nozzle in liquids and molten metals. J Chem Eng Jpn 1986;19:326–30. .CrossrefGoogle Scholar

  • 223.

    Sada E, Katoh S, Yoshii H, Tanaka T. Bubble formation in molten sodium nitrate. Ind Eng Chem Process Des Dev 1986;25:838–9. 1986/07/01. .CrossrefGoogle Scholar

  • 224.

    Wilkinson PM, Van Dierendonck LL. A theoretical model for the influence of gas properties and pressure on single-bubble formation at an orifice. Chem Eng Sci 1994;49:1429–38. .CrossrefGoogle Scholar

  • 225.

    Pamperin O, Rath H-J. Influence of buoyancy on bubble formation at submerged orifices. Chem Eng Sci 1995;50:3009–24. .CrossrefGoogle Scholar

  • 226.

    Jamialahmadi M, Zehtaban MR, Müller-Steinhagen H, Sarrafi A, Smith JM. Study of bubble formation under constant flow conditions. Chem Eng Res Des 2001;79:523–32. .CrossrefGoogle Scholar

  • 227.

    Akita K, Yoshida F. Bubble size, interfacial area, and liquid-phase mass transfer coefficient in bubble columns. Ind Eng Chem Process Des Dev 1974;13:84–91.Google Scholar

  • 228.

    Hinze JO. Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes. AIChE J 1955;1:289–95. .CrossrefGoogle Scholar

  • 229.

    Lin TJ, Tsuchiya K, Fan LS. Bubble flow characteristics in bubble columns at elevated pressure and temperature. AIChE J 1998;44:545–60.Google Scholar

  • 230.

    Levich VG. Physicochemical hydrodynamics: (by) veniamin G. Levich.Transl. by Scripta Technical, Inc. Prentice-Hall: New Jersey, USA, 1962.Google Scholar

  • 231.

    Luo X, Lee DJ, Lau R, Yang G, Fan L-S. Maximum stable bubble size and gas holdup in high-pressure slurry bubble columns. AIChE J 1999;45:665–80. .CrossrefGoogle Scholar

  • 232.

    Krishna R, De Swart JWA, Hennephof DE, Ellenberger J, Hoefsloot HCJ. Influence of increased gas density on hydrodynamics of bubble-column reactors. AIChE J 1994;40:112–19. .CrossrefGoogle Scholar

  • 233.

    Lin TJ, Tsuchiya K, Fan L-S. On the measurements of regime transition in high-pressure bubble columns. Can J Chem Eng 1999;77:370–4. .CrossrefGoogle Scholar

  • 234.

    Lozano-Blanco G, Thybaut JW, Surla K, Galtier P, Marin GB. Simulation of a slurry-bubble column reactor for Fischer-Tropsch synthesis using single-event microkinetics. AIChE J 2009;55:2159–70. .CrossrefGoogle Scholar

  • 235.

    Ahón VR, Costa EF, Monteagudo JEP, Fontes CE, Biscaia EC, Lage PLC. A comprehensive mathematical model for the Fischer–Tropsch synthesis in well-mixed slurry reactors. Chem Eng Sci 2005;60:677–94. .CrossrefGoogle Scholar

  • 236.

    Wang Y, Fan W, Liu Y, Zeng Z, Hao X, Chang M, et al. Modeling of the Fischer–Tropsch synthesis in slurry bubble column reactors. Chem Eng Process Process Intensif 2008;47:222–8. .CrossrefGoogle Scholar

  • 237.

    de Swart JWA, Krishna R. Simulation of the transient and steady state behavior of a bubble column slurry reactor for Fischer-Tropsch synthesis. Chem Eng Process 2002;41:35–47.Google Scholar

  • 238.

    Stokes GG. On the effect of the internal friction of fluids on the motion of pendulums, Transactions of the Cambridge Philosophical Society. 1851;9:8.Google Scholar

  • 239.

    Dumitrescu DT. Strömung an einer luftblase im senkrechten rohr. ZAMM J Appl Math Mech/Z Angew Math Mech 1943;23:139–49. .CrossrefGoogle Scholar

  • 240.

    Peebles FN, Garber HJ. Studies on the motion of gas bubbles in liquids. Chem Eng Prog 1953;49:88.Google Scholar

  • 241.

    Haberman WL, Morton RK. An experimental study of bubbles moving in liquids. Trans Am Soc Civil Eng 1956;121:227–50.Google Scholar

  • 242.

    Harmathy TZ. Velocity of large drops and bubbles in media of infinite or restricted extent. AIChE J 1960;6:281–8. .CrossrefGoogle Scholar

  • 243.

    Angelino H. Hydrodynamique des grosses bulles dans les liquides visqueux. Chem Eng Sci 1966;21:541–50.Google Scholar

  • 244.

    Mendelson HD. The prediction of bubble terminal velocities from wave theory. AIChE J 1967;13:250–3. .CrossrefGoogle Scholar

  • 245.

    Grace JR, Wairegi T, Nguyen TH. Shapes and velocities of single drops and bubbles moving freely through immiscible liquids. Trans Inst Chem Eng 1976;54:167–73.Google Scholar

  • 246.

    Lehrer IH. A rational terminal velocity equation for bubbles and drops at intermediate and high Reynolds numbers. J Chem Eng Jpn 1976;9:237–40. .CrossrefGoogle Scholar

  • 247.

    Clift R, Grace JR, Weber ME. Bubbles, drops, and particles. Academic Press: New York, USA, 1978.Google Scholar

  • 248.

    Fukuma M, Muroyama K, Yasunishi A. Properties of bubble swarm in a slurry bubble column. J Chem Eng Jpn 1987;20:28–33.Google Scholar

  • 249.

    Nickens HV, Yannitell DW. The effects of surface tension and viscosity on the rise velocity of a large gas bubble in a closed, vertical liquid-filled tube. Int J Multiphase Flow 1987;13:57–69. .CrossrefGoogle Scholar

  • 250.

    Jamialahmadi M, Müller-Steinhagen H. Effect of solid particles on gas hold-up in bubble columns. Can J Chem Eng 1991;69:390–3.Google Scholar

  • 251.

    Karamanev DG. Rise of gas bubbles in quiescent liquids. AIChE J 1994;40:1418–21. .CrossrefGoogle Scholar

  • 252.

    Maneri CC. New look at wave analogy for prediction of bubble terminal velocities. AIChE J 1995;41:481–7. .CrossrefGoogle Scholar

  • 253.

    Nguyen AV. Prediction of bubble terminal velocities in contaminated water. AIChE J 1998;44:226–30. .CrossrefGoogle Scholar

  • 254.

    Krishna R, Urseanu MI, van Baten JM, Ellenberger J. Rise velocity of a swarm of large gas bubbles in liquids. Chem Eng Sci 1999;54:171–83.Google Scholar

  • 255.

    Yang G, Luo X, Lau R, Fan L. Heat-transfer characteristics in slurry bubble columns at elevated pressures and temperatures. Ind Eng Chem Res 2000;39:2568–77. .CrossrefGoogle Scholar

  • 256.

    Rodrigue D. Generalized correlation for bubble motion. AIChE J 2001;47:39–44. .CrossrefGoogle Scholar

  • 257.

    Vermeer D, Krishna R. Hydrodynamics and mass transfer in bubble columns in operating in the churn-turbulent regime. Ind Eng Chem Res 1981:475–82.Google Scholar

  • 258.

    Stern D, Bell AT, Heinemann H. Effects of mass transfer on the performance of slurry reactors used for Fischer-Tropsch synthesis. Chem Eng Sci 1983;38:597–605.Google Scholar

  • 259.

    Inga JR, Morsi BI. Effect of catalyst loading on gas-liquid mass transfer in a slurry reactor: a statistical experimental approach. Can J Chem Eng 1997;75:872–81. .CrossrefGoogle Scholar

  • 260.

    Lemoine R, Behkish A, Morsi BI. Hydrodynamic and mass transfer characteristics in organic liquid mixtures in a large-scale bubble column reactor for the toluene oxidation process. Ind Eng Chem Process Des Dev 2004;43:6195–212.Google Scholar

  • 261.

    Lemoine R, Morsi BI. Hydrodynamic and mass transfer parameters in agitated reactors part II: gas-holdup, sauter mean bubble diameters, volumetric mass transfer coefficients, gas-liquid interfacial areas, and liquid-side mass transfer coefficients. Int J Chem Reactor Eng 2005;3:1166.Google Scholar

  • 262.

    Huff GA, Satterfield CN. Intrinsic kinetics of the Fischer-Tropsch synthesis on a reduced fused-magnetite catalyst. Ind Eng Chem Process Des Dev 1984;23:696–705.Google Scholar

  • 263.

    Sauer T, Hempel D-C. Fluid dynamics and mass transfer in a bubble column with suspended particles. Chem Eng Technol 1987;10:180–9.Google Scholar

  • 264.

    Guo YX, Rathor MN, Ti HC. Hydrodynamics and mass transfer studies in a novel external-loop airlift reactor. Chem Eng J 1997;67:205–14. .CrossrefGoogle Scholar

  • 265.

    Gestrich W, Esenwein H, Krauss W. Der flüssigkeitsseitige stoffübergangskoeffizient in blasenschichten. Chem Ing Tech 1976;48:399–407. .CrossrefGoogle Scholar

  • 266.

    Fukuma M, Muroyama K, Yasunishi A. Specific gas-liquid interfacial area and liquid-phase mass transfer coefficient in a slurry bubble column. J Chem Eng Jpn 1987;20:321–4.Google Scholar

  • 267.

    Salvacion J, Murayama M. Effects of alcohols on gas holdup and volumetric liquid-phase mass transfer coefficient in gel-particle-suspended bubble column. J Chem Eng Jpn 1995;28:434–42.Google Scholar

  • 268.

    Calderbank PH, Moo-Young MB. The continuous phase heat and mass transfer properties of dispersions. Chem Eng Sci 1995;50:3921–34. .CrossrefGoogle Scholar

  • 269.

    Vázquez G, Alvarez E, Navaza JM, Rendo R, Romero E. Surface tension of binary mixtures of water + monoethanolamine and water + 2-amino-2-methyl-1-propanol and tertiary mixtures of these amines with water from 25 °C to 50 °C. J Chem Eng Data 1997;42:57–9. 1997/01/01. .CrossrefGoogle Scholar

  • 270.

    Dewes I, Schumpe A. Gas density effect on mass transfer in the slurry bubble column. Chem Eng Sci 1997;52:4105–9. .CrossrefGoogle Scholar

  • 271.

    Yang W, Wang J, Jin Y. Mass transfer characteristics of syngas components in slurry system at industrial conditions. Chem Eng Technol 2001;24:651–7. doi:10.1002/1521-4125(200106)24:6651::aid-ceat651.3.0.co;2-x.CrossrefGoogle Scholar

  • 272.

    Kölbel H, Siemes W, Maas R, Müller K. Wärmeübergang an blasensäulen. Chem Ing Tech 1958;30:400–4. .CrossrefGoogle Scholar

  • 273.

    Kölbel H, Borchers E, Martins J. Wärmeübergang in blasensäulen III. Messungen an gasdurchströmten suspensionen. Chem Ing Tech 1960;32:84–8.Google Scholar

  • 274.

    Kast W. Untersuchungen zum wärmeübergang in blasensäulen. Chem Ing Tech 1963;35:785–8. .CrossrefGoogle Scholar

  • 275.

    Burkel W. Auslegung von gasverteilern und gasgehalt in blasensäulen. Chem Ing Tech 1974;46:205–205.Google Scholar

  • 276.

    Shaykhutdinov A, Bakirov N, Usmanov A. Determination and mathematical correlation of heat transfer coefficient under conditions of bubble flow, cellular and turbulent foam. Int Chem Eng J 1975;11:641–5.Google Scholar

  • 277.

    Nishikawa M, Kato H, Hashimoto K. Heat transfer in aerated tower filled with non-Newtonian liquid. Ind Eng Chem Process Des Dev 1977;16:133–7. 1977/01/01. .CrossrefGoogle Scholar

  • 278.

    Baker CGJ, Armstrong ER, Bergougnou MA. Heat transfer in three-phase fluidized beds. Powder Technol 1978;21:195–204. .CrossrefGoogle Scholar

  • 279.

    Louisi Y. Ermittlung von fluiddynamischen kenngröβen fur die Fischer-Tropsch-synthese in blasensäulenreaktoren. Technical University of Berlin: Berlin, Germany, 1979.Google Scholar

  • 280.

    Deckwer WD. On the mechanism of heat transfer in bubble column reactors. Chem Eng Sci 1980;35:1341–6. .CrossrefGoogle Scholar

  • 281.

    Deckwer W-D, Louisi Y, Ralek M, Zaidi A. Hydrodynamic properties of the Fischer-Tropsch slurry process. Ind Eng Chem Process Des Dev 1980;19:699–708.Google Scholar

  • 282.

    Joshi JB, Sharma MM, Shah YT, Singh CPP, Ally M, Klinzing GE. Heat transfer in multiphase contactors. Chem Eng Commun 1980;6:257–71. 1980/01/01. .CrossrefGoogle Scholar

  • 283.

    Kato Y, Uchida K, Kago T, Morooka S. Liquid holdup and heat transfer coefficient between bed and wall in liquid solid and gas-liquid-solid fluidized beds. Powder Technol 1981;28:173–9. .CrossrefGoogle Scholar

  • 284.

    Zehner P. Momentum, mass and heat transfer in bubble columns– 1. Flow model of the bubble column and flow velocities. Verfahrenstechnik 1982;16:347–51.Google Scholar

  • 285.

    Zehner P. Impuls-, stoff- und wärmetransport in blasensäulen. Chem Ing Tech 1982;54:248–51. .CrossrefGoogle Scholar

  • 286.

    Wendt R. Untersuchungen zum wärmeübergang an einzelrohren und querangeströmten rohrbündelwärmeaustauschern in blasensäulenreaktoren. Technical University of Dortmund: Dortmund, Germany, 1983.Google Scholar

  • 287.

    Michael R, Reichert KH. Polymerisation von ethylen in blasensäulenreaktoren–untersuchungen zum stoffübergang und gasgehalt. Chem Ing Tech 1983;55:564–5.Google Scholar

  • 288.

    Chiu T-M, Ziegler EN. Heat transfer in three-phase fluidized beds. AIChE J 1983;29:677–85. .CrossrefGoogle Scholar

  • 289.

    Kang Y, Suh IS, Kim SD. Heat transfer characteristics of three-phase fluidized beds, in Proc. PAChE III, Seoul, Korea, 1983: 1.Google Scholar

  • 290.

    Muroyama K, Fukuma M, Yasunishi A. Wall-to-bed heat transfer coefficient in gas–liquid–solid fluidized beds. Can J Chem Eng 1984;62:199–208. .CrossrefGoogle Scholar

  • 291.

    Chiu T-M, Ziegler EN. Liquid holdup and heat transfer coefficient in liquid-solid and three-phase fluidized beds. AIChE J 1985;31:1504–9. .CrossrefGoogle Scholar

  • 292.

    Kang Y, Suh I, Kim S. Heat transfer characteristics of three phase fluidized beds. Chem Eng Commun 1985;34:1–13.Google Scholar

  • 293.

    Saberian-Broudjenni M, Wild G, Midoux N, Charpentier JC. Contribution à l‘étude du transfert de chaleur à la paroi dans les récteurs à lit fluidisé gaz-liquide-solide à faible vitesse de liquide. Can J Chem Eng 1985;63:553–64. .CrossrefGoogle Scholar

  • 294.

    Suh IS, Jin GT, Kim SD. Heat transfer coefficients in three phase fluidized beds. Int J Multiphase Flow 1985;11:255–9. .CrossrefGoogle Scholar

  • 295.

    Kim SD, Kang Y, Kwon HK. Heat transfer characteristics in two‐and three‐phase slurry‐fluidized beds. AIChE J 1986;32:1397–400.Google Scholar

  • 296.

    Muroyama K, Fukuma M, Yasunishi A. Wall-to-bed heat transfer in liquid–solid and gas–liquid–solid fluidized beds part II: gas–liquid–solid fluidized beds. Can J Chem Eng 1986;64:409–18. .CrossrefGoogle Scholar

  • 297.

    Muroyama K, Fukuma M, Yasunishi A. Wall-to-bed heat transfer in liquid–solid and gas–liquid–solid fluidized beds part I: liquid–solid fluidized beds. Can J Chem Eng 1986;64:399–408. .CrossrefGoogle Scholar

  • 298.

    Hatate Y, Tajiri S, Fujita T, Fukumoto T, Ikari A, Hano T. Heat transfer coefficient in three-phase vertical upflows of gas-liquid-fine solid particle systems. J Chem Eng Jpn 1987;20:568–74.Google Scholar

  • 299.

    Korte H. Heat transfer in bubble columns with and without internals, PhD Thesis, University of Dortmund, 1987.Google Scholar

  • 300.

    Korte HJ. Wärmeübergang in blasensäulen mit und ohne einbauten. Technical University of Dortmund: Dortmund, Germany, 1987.Google Scholar

  • 301.

    Magiliotou M, Chen Y-M, Fan L-S. Bed-immersed object heat transfer in a three-phase fluidized bed. AIChE J 1988;34:1043–7. .CrossrefGoogle Scholar

  • 302.

    Kim JO, Park DH, Kim SD. Heat transfer and wake characteristics in three-phase fluidized beds with floating bubble breakers. Chem Eng Process Process Intensif 1990;28:113–19. .CrossrefGoogle Scholar

  • 303.

    Zaidi A, Deckwer WD, Mrani A, Benchekchou B. Hydrodynamics and heat transfer in three-phase fluidized beds with highly viscous pseudoplastic solutions. Chem Eng Sci 1990;45:2235–8. .CrossrefGoogle Scholar

  • 304.

    Saxena S, Rao N, Saxena A. Estimation of heat transfer coefficient for immersed surfaces in bubble columns involving fine powders. Powder Technol 1990;63:197–202.Google Scholar

  • 305.

    Kumar S, Fan L-S. Heat-transfer characteristics in viscous gas-liquid and gas-liquid-solid systems. AIChE J 1994;40:745–55. .CrossrefGoogle Scholar

  • 306.

    Kantarci N, Ulgen KO, Borak F. A study on hydrodynamics and heat transfer in a bubble column reactor with yeast and bacterial cell suspensions. Can J Chem Eng 2005;83:764–73. .CrossrefGoogle Scholar

  • 307.

    Patnail KSKR. Heat transfer coefficients in three-phase sparged reactors: a unified correlation, in Proceedings of the World Congress on Engineering and Computer Science, San Francisco, USA, 2007.Google Scholar

  • 308.

    Jhawar AK, Prakash A. Influence of bubble column diameter on local heat transfer and related hydrodynamics. Chem Eng Res Des 2011;89:1996–2002. .CrossrefGoogle Scholar

  • 309.

    Hulet C, Clement P, Tochon P, Schweich D, Dromard N, Anfray J. Literature review on heat transfer in two-and three-phase bubble columns. Int J Chem Reactor Eng 2009;7:1–94.Google Scholar

  • 310.

    Kölbel H, Ralek M. The Fischer-Tropsch synthesis in the liquid phase. Catal Rev Sci Eng 1980;21:225–74.Google Scholar

  • 311.

    Bernemann K. On the hydrodynamics and mixing of the liquid phase in bubble columns with longitudinal tube bundles, PhD Thesis, University of Dortmund, 1989.Google Scholar

  • 312.

    Saxena S, Rao N, Thimmapuram P. Gas phase holdup in slurry bubble columns for two-and three-phase systems. Chem Eng J 1992;49:151–9.Google Scholar

  • 313.

    Pradhan AK, Parichha RK, De P. Gas hold-up in non-Newtonian solutions in a bubble column with internals. Can J Chem Eng 1993;71:468–71. .CrossrefGoogle Scholar

  • 314.

    Chen J, Li F, Degaleesan S, Gupta P, Al-Dahhan MH, Dudukovic MP, et al. Fluid dynamic parameters in bubble columns with internals. Chem Eng Sci 1999;54:2187–97. .CrossrefGoogle Scholar

  • 315.

    Forret A, Schweitzer J-M, Gauthier T, Krishna R, Schweich D. Liquid dispersion in large diameter bubble columns, with and without internals. Can J Chem Eng 2003;81:360–6. .CrossrefGoogle Scholar

  • 316.

    Larachi Fç, Desvigne D, Donnat L, Schweich D. Simulating the effects of liquid circulation in bubble columns with internals. Chem Eng Sci 2006;61:4195–206. .CrossrefGoogle Scholar

  • 317.

    Youssef AA, Al-Dahhan MH. Impact of internals on the gas holdup and bubble properties of a bubble column. Ind Eng Chem Res 2009;48:8007–13. 2009/09/02. .CrossrefGoogle Scholar

  • 318.

    Youssef A. Fluid dynamics and scale-up of bubble columns with internals, 2010.Google Scholar

  • 319.

    Blass E, Cornelius W. The residence time distribution of solid and liquid in multistage bubble columns in the cocurrent flow of gas, liquid and suspended solid. Int J Multiphase Flow 1977;3:459–69. .CrossrefGoogle Scholar

  • 320.

    Kemoun A, Rados N, Li F, Al-Dahhan MH, Dudukovic MP, Mills PL, et al. Gas holdup in a trayed cold-flow bubble column. Chem Eng Sci 2001;56:1197–205. .CrossrefGoogle Scholar

  • 321.

    Westerterp KR, van Swaaij WPM, Beenackers AACM, Kramers H. Chemical reactor design and operation. Wiley: New York, USA, 1984.Google Scholar

  • 322.

    Mashelkar R, Sharma M. Mass transfer in bubble and packed bubble columns. Trans Inst Chem Eng 1970;48:T162.Google Scholar

  • 323.

    Palaskar SN, De JK, Pandit AB. Liquid phase RTD studies in sectionalized bubble column. Chem Eng Technol 2000;23:61–9. doi:10.1002/(sici)1521-4125(200001)23:161::aid-ceat61.3.0.co;2-k.CrossrefGoogle Scholar

  • 324.

    Nosier SA. Solid-liquid mass transfer at gas sparged tube bundles. Chem Eng Technol 2003;26:1151–4. .CrossrefGoogle Scholar

  • 325.

    Alvaré J, Al-Dahhan MH. Liquid phase mixing in trayed bubble column reactors. Chem Eng Sci 2006;61:1819–35. .CrossrefGoogle Scholar

  • 326.

    Sekizawa T, Kubota H. Liquid mixing in multistage bubble columns. J Chem Eng Jpn 1975;7:441–6. .CrossrefGoogle Scholar

  • 327.

    Doshi YK, Pandit AB. Effect of internals and sparger design on mixing behavior in sectionalized bubble column. Chem Eng J 2005;112:117–29. .CrossrefGoogle Scholar

  • 328.

    Kawasaki H, Hirano H, Tanaka H. Effects of multiple draft tubes with perforated plates on gas holdup and volumetric mass transfer coefficient in a bubble column. J Chem Eng Jpn 1994;27:669–70. .CrossrefGoogle Scholar

  • 329.

    O’Dowd W, Smith DN, Ruether JA, Saxena SC. Gas and solids behavior in a baffled and unbaffled slurry bubble column. AIChE J 1987;33:1959–70. .CrossrefGoogle Scholar

  • 330.

    Yamashita F. Effects of vertical pipe and rod internals on gas holdup in bubble columns. J Chem Eng Jpn 1987;20:204–6. .CrossrefGoogle Scholar

  • 331.

    Balamurugan V, Subbarao D, Roy S. Enhancement in gas holdup in bubble columns through use of vibrating internals. Can J Chem Eng 2010;88:1010–20. .CrossrefGoogle Scholar

  • 332.

    Aksel’rod L, Vorotnikova NI, Kozlov AA. Heat transfer and several aspects of hydrodynamics of bubble beds on sieve trays equipped with tube bundles. Heat Transfer Soviet Res 1976;8:25–33.Google Scholar

  • 333.

    Shah Y, Ratway C, McIlvried H. Back-mixing characteristics of a bubble column with vertically suspended tubes. Trans Inst Chem Eng 1978;56:107–12.Google Scholar

  • 334.

    Gray D, Elsawy A, Tomlinson G, Stiegel GJ, Srivastava RD. Proceedings of the DOE Liquefaction Contractors’ Review Meeting, 1991:344.Google Scholar

  • 335.

    Maretto C, Krishna R. Modelling of a bubble column slurry reactor for Fischer–Tropsch synthesis. Catal Today 1999;52:279–89.Google Scholar

  • 336.

    Gidaspow D. Multiphase flow and fluidization: continuum and kinetic theory descriptions. Access Online via Elsevier, 1994.Google Scholar

  • 337.

    Grevskott S, Sannæs BH, Duduković MP, Hjarbo KW, Svendsen HF. Liquid circulation, bubble size distributions, and solids movement in two- and three-phase bubble columns. Chem Eng Sci 1996;51:1703–13. .CrossrefGoogle Scholar

  • 338.

    Mitra-Majumdar D, Farouk B, Shah YT. Hydrodynamic modeling of three-phase flows through a vertical column. Chem Eng Sci 1997;52:4485–97. .CrossrefGoogle Scholar

  • 339.

    Rice RG, Tupperainen JMI, Hedge RM. Dispersion and hold-up in bubble columns – comparison of rigid and flexible spargers. Can J Chem Eng 1981;59:677–87. .CrossrefGoogle Scholar

  • 340.

    Wen CY, Fan LT. Models for flow systems and chemical reactors. Dekker: New York, USA, 1975.Google Scholar

  • 341.

    Levenspiel O, Fitzgerald TJ. A warning on the misuse of the dispersion model. Chem Eng Sci 1983;38:489–91. .CrossrefGoogle Scholar

  • 342.

    Hatton TA, Lightfoot EN. Dispersion, mass transfer and chemical reaction in multiphase contactors: part I: theoretical developments. AIChE J 1984;30:235–43. .CrossrefGoogle Scholar

  • 343.

    Myers KJ, Duduković MP, Ramachandran PA. Modelling churn-turbulent bubble columns – I. Liquid-phase mixing. Chem Eng Sci 1987;42:2301–11. .CrossrefGoogle Scholar

  • 344.

    Rice RG, Littlefield MA. Dispersion coefficients for ideal bubbly flow in truly vertical bubble columns. Chem Eng Sci 1987;42:2045–53. .CrossrefGoogle Scholar

  • 345.

    Shah YT, Stiegel GJ, Sharma MM. Backmixing in gas-liquid reactors. AIChE J 1978;24:369–400. .CrossrefGoogle Scholar

  • 346.

    Kaštánek F, Sharp DH. Chemical reactors for gas-liquid systems. Ellis Horwood: Chichester, England, 1993.Google Scholar

  • 347.

    Baird MH, Rice RG. Axial dispersion in large unbaffled columns. Chem Eng J 1975;9:171–4.Google Scholar

  • 348.

    Kolmogorov AN. The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Proc Math Phys Sci 1991;434:9–13. .CrossrefGoogle Scholar

  • 349.

    Joshi J, Sharma M. A circulation cell model for bubble columns. Chem Eng Res Des 1979;57:244–51.Google Scholar

  • 350.

    McHenry KW, Wilhelm RH. Axial mixing of binary gas mixtures flowing in a random bed of spheres. AIChE J 1957;3:83–91. .CrossrefGoogle Scholar

  • 351.

    Ohki Y, Inoue H. Longitudinal mixing of the liquid phase in bubble columns. Chem Eng Sci 1970;25:1–16. .CrossrefGoogle Scholar

  • 352.

    Kato Y, Nishiwaki A. Longitudinal dispersion coefficient of a liquid in a bubble column. Int Chem Eng 1972;12:182–7.Google Scholar

  • 353.

    Towell GD, Ackerman GH. Axial mixing of liquid and gas in large bubble column reactor, in Proceedings of 2nd International Symposium Chem. React. Engng. Amsterdam, The Netherlands, 1972, pp. B3.1–B3.13.Google Scholar

  • 354.

    Badura R, Deckwer W-D, Warnecke H-J, Langemann H. Durchmischung in blasensäulen. Chem Ing Tech 1974;46:399–399. .CrossrefGoogle Scholar

  • 355.

    Hikita H, Kikukawa H. Liquid-phase mixing in bubble columns: effect of liquid properties. Chem Eng J 1974;8:191–7. .CrossrefGoogle Scholar

  • 356.

    Field RW, Davidson JF. Axial dispersion in bubble columns. Trans Inst Chem Eng 1980;58:228–36.Google Scholar

  • 357.

    Joshi JB, Shah YT. Kinetics of organic sulphur removal from coal by oxydesulphurization. Fuel 1981;60:612–14. .CrossrefGoogle Scholar

  • 358.

    Riquarts H-P. Strömungsprofile, impulsaustausch und durchmischung der flüssigen phase in blasensäulen. Chem Ing Tech 1981;53:60–1. .CrossrefGoogle Scholar

  • 359.

    Mangartz KH, Pilhofer T. Interpretation of mass transfer measurements in bubble columns considering dispersion of both phases. Chem Eng Sci 1981;36:1069–77. .CrossrefGoogle Scholar

  • 360.

    Kawase Y, Moo-Young M. Liquid phase mixing in bubble columns with Newtonian and non-Newtonian fluids. Chem Eng Sci 1986;41:1969–77. .CrossrefGoogle Scholar

  • 361.

    Bernemann K. Zur fluiddynamik und zum vermischungsverhalten der flüssigen phase in blasensaulen mit langsangeströmten rohrbu Ph.D. Thesis, University of Dortmund, 1989.Google Scholar

  • 362.

    Smith DN, Ruether JA. Dispersed solid dynamics in a slurry bubble column. Chem Eng Sci 1985;40:741–53. .CrossrefGoogle Scholar

  • 363.

    Fernandes FAN. Modeling and product grade optimization of Fischer−Tropsch synthesis in a slurry reactor. Ind Eng Chem Res 2006;45:1047–57. .CrossrefGoogle Scholar

  • 364.

    Wang T, Wang J, Jin Y. Slurry reactors for gas-to-liquid processes: a review. Ind Eng Chem Res 2007;46:5824–47.Google Scholar

  • 365.

    de Toledo ECV, de Santana PL, Maciel MRW, Maciel Filho R. Dynamic modelling of a three-phase catalytic slurry reactor. Chem Eng Sci 2001;56:6055–61. .CrossrefGoogle Scholar

  • 366.

    Mills PL, Turner JR, Ramachandran PA, Dudukovic MP. The Fischer-Tropsch synthesis in slurry bubble column reactors: analysis of reactor performance using the axial dispersion model. In: Nigam KDP and Schumpe A, editors. Three phase sparged reactors. Amsterdam: Gordon and Breach, 1996:339–86.Google Scholar

  • 367.

    Iliuta I, Larachi F, Anfray J, Dromard N, Schweich D. Comparative simulations of cobalt- and iron-based Fischer-Tropsch synthesis slurry bubble column reactors. Ind Eng Chem Res 2008;47:3861–9. 2008/06/01. .CrossrefGoogle Scholar

  • 368.

    Prakash A. On the effects of syngas composition and water gas shift reaction rate on FT synthesis over iron based catalyst in a slurry reactor. Chem Eng Commun 1994;128:143–58. 1994/01/01. .CrossrefGoogle Scholar

  • 369.

    Rados N, Al-Dahhan MH, Duduković MP. Dynamic modeling of slurry bubble column reactors. Ind Eng Chem Res 2005;44:6086–94. 2005/08/01. .CrossrefGoogle Scholar

  • 370.

    Song H-S, Ramkrishna D, Trinh S, Espinoza RL, Wright H. Multiplicity and sensitivity analysis of Fischer–Tropsch bubble column slurry reactors: plug-flow gas and well-mixed slurry model. Chem Eng Sci 2003;58:2759–66.Google Scholar

  • 371.

    Stern D, Bell AT, Heinemann H. A theoretical model for the performance of bubble-column reactors used for Fischer-Tropsch synthesis. Chem Eng Sci 1985;40:1665–77. .CrossrefGoogle Scholar

  • 372.

    Turner JR, Mills PL. Comparison of axial dispersion and mixing cell models for design and simulation of Fischer-Tropsch slurry bubble column reactors. Chem Eng Sci 1990;45:2317–24.Google Scholar

  • 373.

    Grund G, Schumpe A, Deckwer WD. Gas-liquid mass transfer in a bubble column with organic liquids. Chem Eng Sci 1992;47:3509–16.Google Scholar

  • 374.

    Krishna R, Urseanu MI, van Baten JM, Ellenberger J. Liquid phase dispersion in bubble columns operating in the churn-turbulent flow regime. Chem Eng J 2000;78:43–51. .CrossrefGoogle Scholar

  • 375.

    Calderbank P, Evans F, Farley R, Jepson G, Poll A. Catalysis in practice, in Symposium of the Institution of Chemical Engineers, London, 1963.Google Scholar

  • 376.

    Satterfield C, Huff G. 25 effects of mass transfer on Fischer-Tropsch synthesis in slurry reactors. Chem Eng Sci 1980;35:195–202.Google Scholar

  • 377.

    Deckwer WD, Serpemen Y, Ralek M, Schmidt B. On the relevance of mass transfer limitations in the Fischer-Tropsch slurry process. Chem Eng Sci 1981;36:773–4. .CrossrefGoogle Scholar

  • 378.

    Deckwer WD, Serpemen Y, Ralek M, Schmidt B. Modeling the Fischer-Tropsch synthesis in the slurry phase. Ind Eng Chem Process Des Dev 1982;21:231–41. 1982/04/01. .CrossrefGoogle Scholar

  • 379.

    Kuo J, Sanzo F, Garwood W, Gupte K, Lang C, Leib T, et al. Slurry Fischer-Tropsch/mobil two-stage process of converting syngas to high octane gasoline, DOE Contract No. DE-AC22-80PC30022, Final Report, June 1983.Google Scholar

  • 380.

    Leib T, Mills P, Lerou J, Turner J. Evaluation of neural networks for simulation of 3-phase bubble-column reactors. Chem Eng Res Des 1995;73:690–6.Google Scholar

  • 381.

    Inga JR, Morsi BI. A novel approach for the assessment of the rate-limiting step in Fischer–Tropsch slurry process. Energy Fuels 1996;10:566–72. 1996/01/01. .CrossrefGoogle Scholar

  • 382.

    Song H-S, Ramkrishna D, Trinh S, Wright H. Operating strategies for Fischer-Tropsch reactors: A model-directed study. Korean J Chem Eng 2004;21:308–17. 2004/03/01. .CrossrefGoogle Scholar

  • 383.

    Iliuta I, Larachi F, Desvigne D. Multicompartment hydrodynamic model for slurry bubble columns. Chem Eng Sci 2008, 63, 3379–99.Google Scholar

  • 384.

    Guettel R, Turek T. Comparison of different reactor types for low temperature Fischer-Tropsch synthesis: a simulation study. Chem Eng Sci 2009;64:955–64.Google Scholar

  • 385.

    Ueyama K, Miyauchi T. Properties of recirculating turbulent two phase flow in gas bubble columns. AIChE J 1979;25:258–66. .CrossrefGoogle Scholar

  • 386.

    Ishii M, Mishima K. Two-fluid model and hydrodynamic constitutive relations. Nucl Eng Des 1984;82:107–26. .CrossrefGoogle Scholar

  • 387.

    Lahey Jr RT, Drew DA. The three-dimensional time and volume averaged conservation equations of two-phase flow. In: Lewins J and Becker M, editors. Advances in nuclear science and technology, vol 20. Plenum Press: New York, USA, 1988: 1–69. doi:10.1007/978-1-4613-9925-4_1.CrossrefGoogle Scholar

  • 388.

    Drew DA. Mathematical modeling of two-phase flow. Ann Rev Fluid Mech 1983;15:261–91. .CrossrefGoogle Scholar

  • 389.

    Ranade VV. Computational flow modeling for chemical reactor engineering. Academic Press: California, USA, 2002.Google Scholar

  • 390.

    Jakobsen HA. Chemical reactor modeling: multiphase reactive flows. Springer: Cham, Switzerland, 2008.Google Scholar

  • 391.

    Devanathan N, Moslemian D, Dudukovic MP. Flow mapping in bubble columns using CARPT. Chem Eng Sci 1990;45:2285–91. .CrossrefGoogle Scholar

  • 392.

    De Nevers N. Bubble driven fluid circulations. AIChE J 1968;14:222–6. .CrossrefGoogle Scholar

  • 393.

    Zehner P. Momentum, mass and heat transfer in bubble columns. Part 2. Axial blending and heat transfer. Int Chem Eng 1986;26:29–35.Google Scholar

  • 394.

    Zehner P. Momentum, mass and heat transfer in bubble columns. Part 1. Flow model of the bubble column and liquid velocities. Int Chem Eng 1986;26:22.Google Scholar

  • 395.

    Shah YT. Gas-liquid-solid reactor design. McGraw-Hill: New York, USA, 1979.Google Scholar

  • 396.

    Chen J, Jamialahmadi M, Li S. Effect of liquid depth on circulation in bubble columns: a visual study. Chem Eng Res Des 1989;67:203–7.Google Scholar

  • 397.

    Delnoij E, Kuipers JAM, van Swaaij WPM. Dynamic simulation of gas-liquid two-phase flow: effect of column aspect ratio on the flow structure. Chem Eng Sci 1997;52:3759–72. .CrossrefGoogle Scholar

  • 398.

    Delnoij E, Lammers FA, Kuipers JAM, van Swaaij WPM. Dynamic simulation of dispersed gas-liquid two-phase flow using a discrete bubble model. Chem Eng Sci 1997;52:1429–58. .CrossrefGoogle Scholar

  • 399.

    Millies M, Mewes D. Calculation of circulating flows in bubble columns. Chem Eng Sci 1995;50:2093–106. .CrossrefGoogle Scholar

  • 400.

    Kumar SB, Devanathan N, Moslemian D, Dudukovic MP. Effect of scale on liquid recirculation in bubble columns. Chem Eng Sci 1994;49:5637–52. .CrossrefGoogle Scholar

  • 401.

    Clark NN, Atkinson CM, Flemmer RLC. Turbulent circulation in bubble columns. AIChE J 1987;33:515–18. .CrossrefGoogle Scholar

  • 402.

    Rice RG, Geary NW. Prediction of liquid circulation in viscous bubble columns. AIChE J 1990;36:1339–48. .CrossrefGoogle Scholar

  • 403.

    Anderson KG, Rice RG. Local turbulence model for predicting circulation rates in bubble columns. AIChE J 1989;35:514–18. .CrossrefGoogle Scholar

  • 404.

    Luo H, Svendsen HF. Turbulent circulation in bubble columns from eddy viscosity distributions of single-phase pipe flow. Can J Chem Eng 1991;69:1389–94. .CrossrefGoogle Scholar

  • 405.

    Kumar MM, Natarajan E. CFD simulation for two-phase mixing in 2d fluidized bed. Int J Adv Manuf Technol 2009;40:1–4. .CrossrefGoogle Scholar

  • 406.

    Groen JS, Oldeman RGC, Mudde RF, van den Akker HEA. Coherent structures and axial dispersion in bubble column reactors. Chem Eng Sci 1996;51:2511–20. .CrossrefGoogle Scholar

  • 407.

    Adkins D, Shollenberger K, O‘Hern T, Torczynski J. Pressure effects on bubble column flow characteristics, in ANS Proceedings of the 1996 National Heat Transfer Conference, 1996:318–25.Google Scholar

  • 408.

    Geary NW, Rice RG. Circulation and scale-up in bubble columns. AIChE J 1992;38:76–82. .CrossrefGoogle Scholar

  • 409.

    Freedman W. Hold-up and liquid circulation in bubble columns. Trans Inst Chem Eng 1969;47:251–62.Google Scholar

  • 410.

    Rietema K, Otengraf SPP. Laminar liquid circulation and bubble street formation in a gas-liquid system. Trans Inst Chem Eng 1970;48:54–62.Google Scholar

  • 411.

    Rietema K. Science and technology of dispersed two-phase systems – I and II. Chem Eng Sci 1982;37:1125–50.Google Scholar

  • 412.

    Whalley P, Davidson JF. Liquid circulation in bubble columns, in Symposium on Multi-phase Flow Systems, Institute of Chemical Engineering Symposium Series, 1974.Google Scholar

  • 413.

    Joshi J. Axial mixing in multiphase contactors– a unified correlation. Trans Inst Chem Eng 1980;58:155–64.Google Scholar

  • 414.

    Clark NN, Van Egmond JW, Nebiolo EP. The drift-flux model applied to bubble columns and low velocity flows. Int J Multiphase Flow 1990;16:261–79. .CrossrefGoogle Scholar

  • 415.

    Gasche HE, Edinger C, Kömpel H, Hofmann H. Hydrodynamics in bubble columns. Chem Eng Process Process Intensif 1989;26:101–9. .CrossrefGoogle Scholar

  • 416.

    Geary NW, Rice RG. Circulation in bubble columns: corrections for distorted bubble shape. AIChE J 1991;37:1593–4. .CrossrefGoogle Scholar

  • 417.

    Grienberger J, Hofmann H. Investigations and modelling of bubble columns. Chem Eng Sci 1992;47:2215–20. .CrossrefGoogle Scholar

  • 418.

    Svendsen HF, Jakobsen HA, Torvik R. Local flow structures in internal loop and bubble column reactors. Chem Eng Sci 1992;47:3297–304. .CrossrefGoogle Scholar

  • 419.

    Ranade VV. Flow in bubble columns: some numerical experiments. Chem Eng Sci 1992;47:1857–69. .CrossrefGoogle Scholar

  • 420.

    Sokolichin A, Eigenberger G. Gas–liquid flow in bubble columns and loop reactors: part I. Detailed modelling and numerical simulation. Chem Eng Sci 1994;49:5735–46. .CrossrefGoogle Scholar

  • 421.

    Millies M. Fluiddynamik, vermischung und stoffübertragung in zirkulationszellen in blasensäulen Ph.D. Thesis, University of Hannover, 1992.Google Scholar

  • 422.

    Hamidipour M, Chen J, Larachi F. CFD study on hydrodynamics in three-phase fluidized beds – application of turbulence models and experimental validation. Chem Eng Sci 2012;78:167–80. .CrossrefGoogle Scholar

  • 423.

    Panneerselvam R, Savithri S, Surender GD. CFD simulation of hydrodynamics of gas–liquid–solid fluidised bed reactor. Chem Eng Sci 2009;64:1119–35. .CrossrefGoogle Scholar

  • 424.

    Li Y, Zhang J, Fan L-S. Numerical simulation of gas–liquid–solid fluidization systems using a combined CFD-VOF-DPM method: bubble wake behavior. Chem Eng Sci 1999;54:5101–7. .CrossrefGoogle Scholar

  • 425.

    Gamwo IK, Halow JS, Gidaspow D, Mostofi R. CFD models for methanol synthesis three-phase reactors: reactor optimization. Chem Eng J 2003;93:103–12. .CrossrefGoogle Scholar

  • 426.

    Silva Jr JL, Mori ED, Soccol Jr R, d’Ávila MA, Mori M. Interphase momentum study in a slurry bubble column. Chem Eng Trans 2013;32:1507–12. .CrossrefGoogle Scholar

  • 427.

    Matos EM, Guirardello R, Mori M, Nunhez JR. Modeling and simulation of a pseudo-three-phase slurry bubble column reactor applied to the process of petroleum hydrodesulfurization. Comput Chem Eng 2009;33:1115–22. .CrossrefGoogle Scholar

  • 428.

    Pan Y, Banerjee S. Numerical simulation of particle interactions with wall turbulence. Phys Fluids (1994–present) 1996;8:2733–55. .CrossrefGoogle Scholar

  • 429.

    Jianping W, Shonglin X. Local hydrodynamics in a gas-liquid-solid three-phase bubble column reactor. Chem Eng J 1998;70:81–4. .CrossrefGoogle Scholar

  • 430.

    Feng W, Wen J, Fan J, Yuan Q, Jia X, Sun Y. Local hydrodynamics of gas–liquid-nanoparticles three-phase fluidization. Chem Eng Sci 2005;60:6887–98. .CrossrefGoogle Scholar

  • 431.

    Matonis D, Gidaspow D, Bahary M. CFD simulation of flow and turbulence in a slurry bubble column. AIChE J 2002;48:1413–29. .CrossrefGoogle Scholar

  • 432.

    Zhang X, Ahmadi G. Eulerian–Lagrangian simulations of liquid–gas–solid flows in three-phase slurry reactors. Chem Eng Sci 2005;60:5089–104. .CrossrefGoogle Scholar

  • 433.

    Schallenberg J, Enß JH, Hempel DC. The important role of local dispersed phase hold-ups for the calculation of three-phase bubble columns. Chem Eng Sci 2005;60:6027–33. .CrossrefGoogle Scholar

  • 434.

    Sivaguru K, Begum KMMS, Anantharaman N. Hydrodynamic studies on three-phase fluidized bed using CFD analysis. Chem Eng J 2009;155:207–14. .CrossrefGoogle Scholar

  • 435.

    Joshi J. Computational flow modelling and design of bubble column reactors. Chem Eng Sci 2001;56:5893–933.Google Scholar

  • 436.

    Marchisio DL, Fox RO. Multiphase reacting flows: modelling and simulation: modelling and simulation. Springer-Verlag GmbH: Vienna, Austria, 2007.Google Scholar

  • 437.

    Yeoh GH, Tu J. Computational techniques for multiphase flows. Elsevier Science: Amsterdam, The Netherlands, 2009.Google Scholar

  • 438.

    Yeoh GH, Cheung CP, Tu J. Multiphase flow analysis using population balance modeling: bubbles, drops and particles. Elsevier Science: Amsterdam, The Netherlands, 2013.Google Scholar

  • 439.

    Gidaspow D, Jiradilok V. Computational techniques: the multiphase CFD approach to fluidization and green energy technologies. Nova Science Publishers: New York, USA, 2009.Google Scholar

  • 440.

    Cheng L, Mewes D. Advances in multiphase flow and heat transfer. Bentham Science Publishers: Sharjah, United Arab Emirates, 2012.Google Scholar

  • 441.

    Becker S, Sokolichin A, Eigenberger G. Gas–liquid flow in bubble columns and loop reactors: part II. Comparison of detailed experiments and flow simulations. Chem Eng Sci 1994;49:5747–62. .CrossrefGoogle Scholar

  • 442.

    Oey RS, Mudde RF, van den Akker HEA. Sensitivity study on interfacial closure laws in two-fluid bubbly flow simulations. AIChE J 2003;49:1621–36. .CrossrefGoogle Scholar

  • 443.

    Hooshyar N, van Ommen JR, Hamersma PJ, Sundaresan S, Mudde RF. Dynamics of single rising bubbles in neutrally buoyant liquid-solid suspensions. Phys Rev Lett 2013;110:244501. .CrossrefGoogle Scholar

  • 444.

    Hooshyar N. Hydrodynamics of structured slurry bubble columns, Ph.D. Dissertation, Delft University of Technology, 2013.Google Scholar

  • 445.

    Zhang J, Li Y, Fan L-S. Numerical studies of bubble and particle dynamics in a three-phase fluidized bed at elevated pressures. Powder Technol 2000;112:46–56. .CrossrefGoogle Scholar

  • 446.

    Torvik R, Svendsen HF. Modelling of slurry reactors. A fundamental approach. Chem Eng Sci 1990;45:2325–32. .CrossrefGoogle Scholar

  • 447.

    Troshko AA, Zdravistch F. CFD modeling of slurry bubble column reactors for Fisher–Tropsch synthesis. Chem Eng Sci 2009;64:892–903. .CrossrefGoogle Scholar

  • 448.

    Yates I, Satterfield C. Intrinsic kinetics of the Fischer-Tropsch synthesis on a cobalt catalyst. Energy Fuels 1991:168–73.Google Scholar

  • 449.

    Kulkarni AA, Joshi JB, Ramkrishna D. Determination of bubble size distributions in bubble columns using LDA. AIChE J 2004;50:3068–84. .CrossrefGoogle Scholar

  • 450.

    Bahary M. Experimental and computational studies of hydrodynamics in three-phase and two-phase fluidized beds, Ph.D. Dissertation, Chemical Engineering, Illinois Institute of Technology, 1994.Google Scholar

  • 451.

    Kashiwa BA, Gore RA. A four equation model for multiphase turbulent flow, in the First Joint ASME/JSME Fluids Engineering Conference, 1991.Google Scholar

  • 452.

    Pironti FF, Medina VR, Calvo R, Sáez AE. Effect of draft tube position on the hydrodynamics of a draft tube slurry bubble column. Chem Eng J BioChem Eng J 1995;60:155–60. .CrossrefGoogle Scholar

  • 453.

    Padial NT, VanderHeyden WB, Rauenzahn RM, Yarbro SL. Three-dimensional simulation of a three-phase draft-tube bubble column. Chem Eng Sci 2000;55:3261–73. .CrossrefGoogle Scholar

  • 454.

    Lin TJ, Reese J, Hong T, Fan LS. Quantitative analysis and computation of two-dimensional bubble columns. AIChE J 1996;42:301–18. .CrossrefGoogle Scholar

  • 455.

    Zhang J, Li Y, Fan L-S. Discrete phase simulation of gas–liquid–solid fluidization systems: single bubble rising behavior. Powder Technol 2000;113:310–26. .CrossrefGoogle Scholar

  • 456.

    Dziallas H, Michele V, Hempel DC. Measurement of local phase holdups in a two- and three-phase bubble column. Chem Eng Technol 2000;23:877–84. doi:10.1002/1521-4125(200010)23:10877::aid-ceat877.3.0.co;2-f.CrossrefGoogle Scholar

  • 457.

    Michele V, Hempel DC. Liquid flow and phase holdup – measurement and CFD modeling for two-and three-phase bubble columns. Chem Eng Sci 2002;57:1899–908. .CrossrefGoogle Scholar

  • 458.

    Rampure MR, Buwa VV, Ranade VV. Modelling of gas-liquid/gas-liquid-solid flows in bubble columns: experiments and CFD simulations. Can J Chem Eng 2003;81:692–709. .CrossrefGoogle Scholar

  • 459.

    Chen C, Fan L-S. Discrete simulation of gas-liquid bubble columns and gas-liquid-solid fluidized beds. AIChE J 2004;50:288–301. .CrossrefGoogle Scholar

  • 460.

    Cartland Glover GM, Generalis SC. Gas–liquid–solid flow modelling in a bubble column. Chem Eng Process Process Intensif 2004;43:117–26. .CrossrefGoogle Scholar

  • 461.

    Wiemann D, Mewes D. Calculation of flow fields in two and three-phase bubble columns considering mass transfer. Chem Eng Sci 2005;60:6085–93. .CrossrefGoogle Scholar

  • 462.

    van Sint Annaland M, Deen NG, Kuipers JAM. Numerical simulation of gas–liquid–solid flows using a combined front tracking and discrete particle method. Chem Eng Sci 2005;60:6188–98. .CrossrefGoogle Scholar

  • 463.

    Nguyen K-T, Huang S-C. Simulation of hydrodynamic characteristics of glass beads in gas-liquid-solid three phase fluidized beds by computational fluid dynamics. J Eng Technol Educ 2007;8:248–61.Google Scholar

  • 464.

    Wang F, Mao Z-S, Wang Y, Yang C. Measurement of phase holdups in liquid–liquid–solid three-phase stirred tanks and CFD simulation. Chem Eng Sci 2006;61:7535–50. .CrossrefGoogle Scholar

  • 465.

    Kiared K, Larachi F, Chaouki J, Guy C. Mean and turbulent particle velocity in the fully developed region of a three-phase fluidized bed. Chem Eng Technol 1999;22:683–9. doi:10.1002/(sici)1521-4125(199908)22:8683::aid-ceat683.3.0.co;2-m.CrossrefGoogle Scholar

  • 466.

    Yu YH, Kim SD. Bubble-wake model for radial velocity profiles of liquid and solid phases in three-phase fluidized beds. Ind Eng Chem Res 2001;40:4463–9. 2001/10/01. .CrossrefGoogle Scholar

  • 467.

    Cao C, Liu M, Wen J, Guo Q. Experimental measurement and numerical simulation for liquid flow velocity and local phase hold-ups in the riser of a GLSCFB. Chem Eng Process Process Intensif 2009;48:288–95. .CrossrefGoogle Scholar

  • 468.

    Muthiah P, Ponnusamy K, Radhakrishnan TK. CFD modeling of flow pattern and phase holdup of three phase fluidized bed contactor. Chem Prod Process Model 2009;4:Art. 36. .CrossrefGoogle Scholar

  • 469.

    O’Rourke PJ, Zhao P, Snider D. A model for collisional exchange in gas/liquid/solid fluidized beds. Chem Eng Sci 2009;64:1784–97. .CrossrefGoogle Scholar

  • 470.

    Jia X, Wen J, Feng W, Yuan Q. Local hydrodynamics modeling of a gas−liquid−solid three-phase airlift loop reactor. Ind Eng Chem Res 2007;46:5210–20. 2007/07/01. .CrossrefGoogle Scholar

  • 471.

    Kurose R, Komori S. Drag and lift forces on a rotating sphere in a linear shear flow. J Fluid Mech 1999;384:183–206. .CrossrefGoogle Scholar

  • 472.

    Laı́n S, Bröder D, Sommerfeld M, Göz MF. Modelling hydrodynamics and turbulence in a bubble column using the Euler–Lagrange procedure. Int J Multiphase Flow 2002;28:1381–407. .CrossrefGoogle Scholar

  • 473.

    Tomiyama A, Kataoka I, Sakaguchi T. Drag coefficients of bubbles : 1st report, drag coefficients of a single bubble in a stagnant liquid. Trans Jpn Soc Mech Eng B 1995;61:2357–64.Google Scholar

  • 474.

    Mei R, Klausner JF. Shear lift force on spherical bubbles. Int J Heat Fluid Flow 1994;15:62–5. .CrossrefGoogle Scholar

  • 475.

    Snyder MR, Knio OM, Katz J, Le Maître OP. Statistical analysis of small bubble dynamics in isotropic turbulence. Phys Fluids (1994–present) 2007;19:065108-1-24. .CrossrefGoogle Scholar

  • 476.

    Tsuchiya K, Furumoto A, Fan L-S, Zhang J. Suspension viscosity and bubble rise velocity in liquid-solid fluidized beds. Chem Eng Sci 1997;52:3053–66. .CrossrefGoogle Scholar

  • 477.

    Ahmadi G, Ma D. A thermodynamical formulation for dispersed multiphase turbulent flows – 1: basic theory. Int J Multiphase Flow 1990;16:323–40. .CrossrefGoogle Scholar

  • 478.

    Zhang DZ, VanderHeyden WB. The effects of mesoscale structures on the macroscopic momentum equations for two-phase flows. Int J Multiphase Flow 2002;28:805–22. .CrossrefGoogle Scholar

  • 479.

    Schiller L, Naumann Z. A drag coefficient correlation. Ztg Ver Dtsch Ing 1935;77:318–20.Google Scholar

  • 480.

    Ville JMD. Micromeritics. Pitman Publishing Co: New York, USA, 1948.Google Scholar

  • 481.

    Morsi S, Alexander A. An investigation of particle trajectories in two-phase flow systems. J Fluid Mech 1972;55:193–208. .CrossrefGoogle Scholar

  • 482.

    Garside J, Al-Dibouni MR. Velocity-voidage relationships for fluidization and sedimentation in solid-liquid systems. Ind Eng Chem Process Des Dev 1977;16:206–14. .CrossrefGoogle Scholar

  • 483.

    Achenbach E. Experiments on the flow past spheres at very high Reynolds numbers. J Fluid Mech 1972;54:565–75. .CrossrefGoogle Scholar

  • 484.

    Arnold HD. LXXIV. Limitations imposed by slip and inertia terms upon Stoke’s law for the motion of spheres through liquids. Philos Mag Ser 6 1911;22:755–75. 1911/11/01. .CrossrefGoogle Scholar

  • 485.

    Bailey AB, Hiatt J. Sphere drag coefficients for a broad range of Mach and Reynolds numbers. AIAA J 1972;10:1436–40. 1972/11/01. .CrossrefGoogle Scholar

  • 486.

    Beard KV, Pruppacher HR. A determination of the terminal velocity and drag of small water drops by means of a wind tunnel. J Atmos Sci 1969;26:1066–72. 1969/09/01.doi:10.1175/1520-0469(1969)0261066:adottv.2.0.co;2.CrossrefGoogle Scholar

  • 487.

    Davies CN. Definitive equations for the fluid resistance of spheres. Proc Phys Soc 1945;57:259.Google Scholar

  • 488.

    Dennis SCR, Walker JDA. Calculation of the steady flow past a sphere at low and moderate reynolds numbers. J Fluid Mech 1971;48:771–89. .CrossrefGoogle Scholar

  • 489.

    Goin KL, Lawrence WR. Subsonic drag of spheres at Reynolds numbers from 200 to 10,000. AIAA J 1968;6:961–2. .CrossrefGoogle Scholar

  • 490.

    Goldburg A, Florsheim BH. Transition and Strouhal number for the incompressible wake of various bodies. Phys Fluids (1958–1988) 1966;9:45–50. .CrossrefGoogle Scholar

  • 491.

    Gunn R, Kinzer GD. The terminal velocity of fall for water droplets in stagnant air. J Meteorol 1949;6:243–8. 1949/08/01.doi:10.1175/1520-0469(1949)0060243:ttvoff.2.0.co;2.CrossrefGoogle Scholar

  • 492.

    Hoerner S. Tests of spheres with reference to Reynolds number, turbulence, and surface roughness. Luftfahrtforschung 1935;12:42–54.Google Scholar

  • 493.

    Ihme F, Schmidt-Traub H, Brauer H. Theoretische untersuchung über die umströmung und den stoffübergang an kugeln. Chem Ing Tech 1972;44:306–13. .CrossrefGoogle Scholar

  • 494.

    LeClair BP. Viscous flow in multiparticle systems at intermediate Reynolds numbers. McMaster University: ON, Canada, 1970.Google Scholar

  • 495.

    Liebster H. üBer den widerstand von kugeln. Ann Phys 1927;387:541–62. .CrossrefGoogle Scholar

  • 496.

    Masliyah JH. Symmetric flow past orthotropic bodies: single and clusters. University of British Columbia: Vancouver, Canada, 1970.Google Scholar

  • 497.

    Maxworthy T. Accurate measurements of sphere drag at low reynolds numbers. J Fluid Mech 1965;23:369–72. .CrossrefGoogle Scholar

  • 498.

    Maxworthy T. Experiments on the flow around a sphere at high Reynolds numbers. J Appl Mech 1969;36:598–607. .CrossrefGoogle Scholar

  • 499.

    Millikan CB, Klein AL. The effect of turbulence. Aircr Eng Aerosp Technol 1933;5:169–74. .CrossrefGoogle Scholar

  • 500.

    Möller W. Experimentelle untersuchungen zur hydrodynamik der kugel. Hirzel: Stuttgart, Germany, 1937.Google Scholar

  • 501.

    Pettyjohn E, Christiansen E. Effect of particle shape on free-settling rates of isometric particles. Chem Eng Prog 1948;44:157–72.Google Scholar

  • 502.

    Pruppacher HR, Steinberger EH. An experimental determination of the drag on a sphere at low Reynolds numbers. J Appl Phys 1968;39:4129–32. .CrossrefGoogle Scholar

  • 503.

    Rimon Y, Cheng SI. Numerical solution of a uniform flow over a sphere at intermediate Reynolds numbers. Phys Fluids (1958-1988) 1969;12:949–59. .CrossrefGoogle Scholar

  • 504.

    Roos FW, Willmarth WW. Some experimental results on sphere and disk drag. AIAA J 1971;9:285–91. .CrossrefGoogle Scholar

  • 505.

    Woo S-W. Simultaneous free and forced convection around submerged cylinders and spheres, 1971.Google Scholar

  • 506.

    Wieselsberger C. Weitere feststellungen über die gesetze des flüssigkeits- und luftwiderstandes. Phys Z 1922;23:219–24.Google Scholar

  • 507.

    Molerus O. A coherent representation of pressure drop in fixed beds and of bed expansion for particulate fluidized beds. Chem Eng Sci 1980;35:1331–40. .CrossrefGoogle Scholar

  • 508.

    Heywood H. Calculation of particle terminal velocities. J Imperial Coll Chem Eng Soc 1948;4: 140–257.Google Scholar

  • 509.

    Heywood H. Uniform and non-uniform motion of particles in fluids, in the Interaction between Fluids and Particles, London, UK, 1962.Google Scholar

  • 510.

    Lapple CE, Shepherd CB. Calculation of particle trajectories. Ind Eng Chem 1940;32:605–17. 1940/05/01. .CrossrefGoogle Scholar

  • 511.

    Flemmer RLC, Banks CL. On the drag coefficient of a sphere. Powder Technol 1986;48:217–21. .CrossrefGoogle Scholar

  • 512.

    Turton R, Levenspiel O. A short note on the drag correlation for spheres. Powder Technol 1986;47:83–6. .CrossrefGoogle Scholar

  • 513.

    Vlajinac M, Covert EE. Sting-free measurements of sphere drag in laminar flow. J Fluid Mech 1972;54:385–92. .CrossrefGoogle Scholar

  • 514.

    Rosenbrock HH. An automatic method for finding the greatest or least value of a function. Comput J 1960;3:175–84. .CrossrefGoogle Scholar

  • 515.

    Khan AR, Richardson JF. The resistance to motion of a solid sphere in a fluid. Chem Eng Commun 1987;62:135–50. 1987/12/01. .CrossrefGoogle Scholar

  • 516.

    Haider A, Levenspiel O. Drag coefficient and terminal velocity of spherical and nonspherical particles. Powder Technol 1989;58:63–70. 5//. .CrossrefGoogle Scholar

  • 517.

    Wen CY, Yu YH. Mechanics of fluidization. Chem Eng Prog Symp Ser 1966;62:100–11.Google Scholar

  • 518.

    Ergun S. Fluid flow through packed columns. Chem Eng Prog 1952;48:1179–84. .CrossrefGoogle Scholar

  • 519.

    Richardson JF, Zaki WN. Sedimentation and fluidisation: part I. Chem Eng Res Des 1997;75:S82–S100. .CrossrefGoogle Scholar

  • 520.

    Letzel M, Schouten J. Effect of gas density on large bubble holdup in bubble column reactors. AIChE J 1998;44:2333–6.Google Scholar

  • 521.

    Jordan U, Terasaka K, Kundu G, Schumpe a. Mass transfer in high-pressure bubble columns with organic liquids. Chem Eng Technol 2002;25:262–5. doi:10.1002/1521-4125(200203)25:3262::AID-CEAT262.3.0.CO;2-C.CrossrefGoogle Scholar

  • 522.

    Jordan U, Schumpe A. The gas density effect on mass transfer in bubble columns with organic liquids. Chem Eng Sci 2001;56:6267–72.Google Scholar

  • 523.

    Hughmark G. Holdup and mass transfer in bubble columns. Ind Eng Chem Process Des Dev 1967;6:218–20.Google Scholar

  • 524.

    Zou R, Jiang X, Li B, Zu Y, Zhang L. Studies on gas holdup in a bubble column operated at elevated temperatures. Ind Eng Chem Res 1988;27:1910–16. .CrossrefGoogle Scholar

  • 525.

    Godbole SP. Study of hydrodynamic and mass transfer characteristics of multiphase bubble column reactor, 1983.Google Scholar

  • 526.

    Hikita H, Asai S, Tanigawa K, Segawa K, Kitao M. The volumetric liquid-phase mass transfer coefficient in bubble columns. Chem Eng J 1981;22:61–9.Google Scholar

  • 527.

    Kluytmans JHJ, Markusse AP, Kuster BFM, Marin GB, Schouten JC. Engineering aspects of the aqueous noble metal catalysed alcohol oxidation. Catal Today 2000;57:143–55. .CrossrefGoogle Scholar

  • 528.

    Pohorecki R, Moniuk W, Zdrójkowski A. Hydrodynamics of a bubble column under elevated pressure. Chem Eng Sci 1999;54:5187–93.Google Scholar

  • 529.

    Kelkar BG, Shah YT. Hydrodynamics and axial mixing in a three-phase bubble column. Effects of slurry properties. Ind Eng Chem Process Des Dev 1984;23:308–13.Google Scholar

  • 530.

    Pohorecki R, Moniuk W. Hydrodynamics of a pilot plant bubble column under elevated temperature and pressure. Chem Eng Sci 2001;56:1167–74.Google Scholar

  • 531.

    Chabot J, de Lasa HI. Gas holdups and bubble characteristics in a bubble column operated at high temperature. Ind Eng Chem Res 1993;32:2595–601. .CrossrefGoogle Scholar

  • 532.

    Dewes I, Kuksal A, Schumpe A. Gas density effect on mass transfer in three phase sparged reactors. Chem Eng Res Des 1995;73:697–700.Google Scholar

  • 533.

    Kojima H, Sawai J, Suzuki H. Effect of pressure on volumetric mass transfer coefficient and gas holdup in bubble column. Chem Eng Sci 1997;52:4111–16.Google Scholar

  • 534.

    Jin H, Yang S, Wang M, Williams RA. Measurement of gas holdup profiles in a gas liquid cocurrent bubble column using electrical resistance tomography. Flow Meas Instrum 2007;18:191–6.Google Scholar

  • 535.

    Eickenbusch H, Brunn P-O, Schumpe a. Mass transfer into viscous pseudoplastic liquid in large-diameter bubble columns. Chem Eng Process Process Intensif 1995;34:479–85. .CrossrefGoogle Scholar

  • 536.

    Moustiri S, Hebrard G, Thakre S, Roustan M. A unified correlation for predicting liquid axial dispersion coefficient in bubble columns. Chem Eng Sci 2001;56:1041–7.Google Scholar

  • 537.

    Guy C, Carreau PJ, Paris J, Guy PJCC, Paris J. Mixing characteristics and gas hold-up of a bubble column. Can J Chem Eng 1986;64:23–35.Google Scholar

  • 538.

    Saxena SC, Chen ZD. Hydrodynamics and heat transfer of baffled and unbaffled slurry bubble column. Rev Chem Eng 1994;10:195–400.Google Scholar

  • 539.

    Saxena SC, Rao NS, Thimmapuram PR. Gas phase holdup in slurry bubble column for two- and three-phase systems. Chem Eng J 1992;49:151–9.Google Scholar

  • 540.

    De S, Ghosh S, Parichha R, De P. Gas hold-up in two-phase system with internals. Indian Chem Eng 1999;41:112–16.Google Scholar

  • 541.

    Joseph S. Hydrodynamic and mass transfer characteristics of a bubble column. University of Pittsburgh: Pittsburgh, USA, 1985.Google Scholar

About the article

Published Online: 2015-04-07

Published in Print: 2015-09-01


Citation Information: International Journal of Chemical Reactor Engineering, Volume 13, Issue 3, Pages 201–288, ISSN (Online) 1542-6580, ISSN (Print) 2194-5748, DOI: https://doi.org/10.1515/ijcre-2014-0146.

Export Citation

©2015 by De Gruyter.Get Permission

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Camilla Berge Vik, Jannike Solsvik, Magne Hillestad, and Hugo A. Jakobsen
Chemical Engineering Science, 2018, Volume 192, Page 1138
[3]
Branislav Todic, Milos Mandic, Nikola Nikacevic, and Dragomir B. Bukur
Korean Journal of Chemical Engineering, 2018
[7]
Omar M. Basha, Li Weng, Zhuo-wu Men, Wayne Xu, and Badie I. Morsi
Frontiers of Engineering Management, 2016, Volume 3, Number 4, Page 362
[8]
Manuel Götz, Jonathan Lefebvre, Friedemann Mörs, Felix Ortloff, Rainer Reimert, Siegfried Bajohr, and Thomas Kolb
Chemical Engineering Journal, 2017, Volume 308, Page 1209
[9]
Ramazan Orhan and Gülbeyi Dursun
Chemical Engineering Research and Design, 2016, Volume 109, Page 477
[10]
Manuel Götz, Jonathan Lefebvre, Friedemann Mörs, Rainer Reimert, Frank Graf, and Thomas Kolb
Chemical Engineering Journal, 2016, Volume 286, Page 348

Comments (0)

Please log in or register to comment.
Log in