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Experimentation and correlation development of mass transfer in a mimicked Fischer–Tropsch slurry bubble column reactor

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Abstract

Gas–liquid volumetric mass transfer coefficient “\({\mathrm{k}}_{\mathrm{L}}\mathrm{a}\)” for \({\mathrm{CH}}_{4}\), \({\mathrm{CO}}_{2}\), and \(\mathrm{Ar}\) were experimentally measured at different conditions in a mimicked Fischer–Tropsch (FT) slurry bubble column reactor by using a non-invasive gaseous tracer technique and the axial dispersion model. Results validate the square root relation, between \({\mathrm{k}}_{\mathrm{L}}\mathrm{a}\) and diffusivity “\({\mathrm{D}}_{\mathrm{g}}\)”, that can be used to predict \({\mathrm{k}}_{\mathrm{L}}\mathrm{a}\) for different species with \({\mathrm{k}}_{\mathrm{L}}\mathrm{a}\) values available in the literature. Additionally, Higbie’s penetration theory was adopted along with bubble dynamics parameters estimation to develop a correlation for predicting \({\mathrm{k}}_{\mathrm{L}}\mathrm{a}\) at wide range of conditions. Current results were used to tune and modify the developed correlation. Predictions of the modified correlation were found to be in line with the findings of previous studies and hence can used to predict \({\mathrm{k}}_{\mathrm{L}}\mathrm{a}\) for different gases including the syngas (i.e., \({\mathrm{H}}_{2}\) and \(\mathrm{CO}\)) at conditions close to FT conditions.

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Abbreviations

\({\mathrm{k}}_{\mathrm{L}}\mathrm{a}\) :

Volumetric mass transfer coefficient, s−1

\({\mathrm{k}}_{\mathrm{L}}{\mathrm{a}}^{\mathrm{o}}\) :

Reference volumetric mass transfer coefficient, s−1

\({\mathrm{k}}_{\mathrm{L}}{\mathrm{a}}^{\mathrm{estimated}}\) :

Volumetric mass transfer coefficient estimated from correlation, s−1

\({\mathrm{k}}_{\mathrm{L}}{\mathrm{a}}^{\mathrm{exp}}\) :

Experimental volumetric mass transfer coefficient, s−1

\(t\) :

Time, s

\({\mathrm{C}}_{\mathrm{in}}\) :

Normalized tracer concentration, mol/m3

\({\mathrm{C}}_{\mathrm{g},\mathrm{in}}\) :

Inlet gas concentration, mol/m3

\({\mathrm{C}}_{\mathrm{g}}\) :

Tracer gas concentration obtained by the detector at the exit, mol/m3

\({\mathrm{C}}_{\mathrm{inj}}\) :

Tracer gas concentration after injection, mol/m3

\({\mathrm{D}}_{\mathrm{g}}\) :

Gas diffusivity, m2/s

\({{\mathrm{D}}_{\mathrm{g}}}^{\mathrm{o}}\) :

Reference gas diffusivity, m2/s

\({\mathrm{D}}_{\mathrm{L}}\) :

Liquid diffusivity, m2/s

\(\mathrm{H}\) :

Henry’s constant, dimensionless

\({\mathrm{u}}_{\mathrm{g}}\) :

Superficial gas velocity, m/s

\({\mathrm{n}}_{\mathrm{data}}\) :

Number of data points

\({\mathrm{t}}_{\mathrm{e}}\) :

Exposure time, s

\({\mathrm{d}}_{\mathrm{bm}}\) :

Geometric mean bubble diameter, m

\({\mathrm{d}}_{\mathrm{bs}}\) :

Sauter mean diameter, m

\({\mathrm{u}}_{\mathrm{bt}}\) :

Terminal bubble rise velocity, m/s

\(g\) :

Acceleration gravity, m2/s

\(a\) :

Interfacial area, m2

\({\mathrm{d}}_{\mathrm{c}}\) :

Column diameter, m

\({\upvarepsilon }_{\mathrm{L}}\) :

Liquid holdup, m3/m3

\({\upvarepsilon }_{\mathrm{g}}\) :

Gas holdup, m3/m3

\(\uptau\) :

Residence time, s

\({\uprho }_{\mathrm{s}}\) :

Solid (catalyst) density, kg/m3

\({\uprho }_{\mathrm{g}}\) :

Gas density, kg/m3

\({\uprho }_{\mathrm{L}}\) :

Liquid density, kg/m3

\({\upmu }_{\mathrm{L}}\) :

Liquid viscosity, Pa

\(\sigma\) :

Surface tension, N/m

\(\Phi\) :

Proportionality constant or arbitrary correction

FT:

Fischer-Tropsch

SBCRs:

Slurry bubble column reactors

BCRs:

Bubble column reactors

PPH:

Perforated plate with huge holes

SCFM:

Standard cubic feet meter

ADM:

Axial dispersion model

TCD:

Thermal conductivity detector

AARE:

Average absolute relative error

References

  1. Mahmoudi H et al (2017) A review of Fischer Tropsch synthesis process, mechanism, surface chemistry and catalyst formulation. Biofuels Engineering 2(1):11–31

    Article  Google Scholar 

  2. De Klerk A (2012) Fischer-tropsch refining. John Wiley & Sons

  3. Doustdar O et al (2016) Enhancing the properties of Fischer-Tropsch fuel produced from syngas over Co/SiO2 catalyst: lubricity and calorific value. In: IOP Conference Series: Materials Science and Engineering. IOP Publishing

  4. Gill SS et al (2011) Combustion characteristics and emissions of Fischer–Tropsch diesel fuels in IC engines. Prog Energy Combust Sci 37(4):503–523

  5. Yang J et al (2014) Fischer-Tropsch synthesis: A review of the effect of CO conversion on methane selectivity. Appl Catal A 470:250–260

    Article  Google Scholar 

  6. Vik CB et al (2018) Interfacial mass transfer limitations of the Fischer-Tropsch synthesis operated in a slurry bubble column reactor at industrial conditions. Chem Eng Sci 192:1138–1156

    Article  Google Scholar 

  7. Strasser W, Wonders A (2008) Commercial scale slurry bubble column reactor optimization. WIT Trans Eng Sci 59:275–287

    Article  MATH  Google Scholar 

  8. Basha OM, Morsi BI (2018) CFD for the design and optimization of slurry bubble column reactors. Computational Fluid Dynamics-Basic Instruments and Applications in Science

  9. Basha OM et al (2015) Fischer-Tropsch synthesis in slurry bubble column reactors: experimental investigations and modeling–a review. Int J Chem Reactor Eng 13(3):201–288

    Article  Google Scholar 

  10. Maretto C, Krishna R (2001) Design and optimisation of a multi-stage bubble column slurry reactor for Fischer-Tropsch synthesis. Catal Today 66(2–4):241–248

    Article  Google Scholar 

  11. Steynberg AP (2004) Fischer-Tropsch technology. Netherland, Elsevier, Amsterdam

    Book  Google Scholar 

  12. Krishna R, Sie ST (2000) Design and scale-up of the Fischer-Tropsch bubble column slurry reactor. Fuel Process Technol 64(1–3):73–105

    Article  Google Scholar 

  13. Dudukovic MP, Larachi F, Mills PL (1999) Multiphase reactors - revisited. Chem Eng Sci 54(13–14):1975–1995

    Article  Google Scholar 

  14. Parkinson G (1997) Fischer-Tropsch comes back. Chem Eng Technol 104(4):39–41

    Google Scholar 

  15. Krishna R, De Swart JWA, Ellenberger J, Martina GB, Maretto C (1997) Gas holdup in slurry bubble columns: effect of column diameter and slurry concentrations. AIChE J 43(2):311–316

    Article  Google Scholar 

  16. Beenackers A, Van Swaaij WPM (1993) Mass transfer in gas-liquid slurry reactors. Chem Eng Sci 48(18):3109–3139

    Article  Google Scholar 

  17. Nedeltchev S, Schumpe A (2007) Theoretical prediction of mass transfer coefficients in a slurry bubble column operated in the homogeneous regime. Chem Biochem Eng Q 21(4):327–334

    Google Scholar 

  18. Lefebvre J, Bajohr S, Kolb T (2020) Modeling of the transient behavior of a slurry bubble column reactor for CO2 methanation, and comparison with a tube bundle reactor. Renewable Energy 151:118–136

    Article  Google Scholar 

  19. Nedeltchev S (2017) Theoretical prediction of mass transfer coefficients in both gas–liquid and slurry bubble columns. Chem Eng Sci 157:169–181

    Article  Google Scholar 

  20. Vandu C, Krishna R (2004) Volumetric mass transfer coefficients in slurry bubble columns operating in the churn-turbulent flow regime. Chem Eng Process 43(8):987–995

    Article  Google Scholar 

  21. Abdulkareem HA, Gheni SA, Rafi’J Y (2016) Study of the hydrodynamics and mass transfer coefficient in a 2D mimicked FT slurry bubble columns for alternative clean energy and chemical production. Int J Chem React Eng 14(5):975–990

  22. Zaidi A et al (1979) Mass transfer in the liquid phase Fischer-Tropsch synthesis. German Chemical Engineering 2(2):94–102

    Google Scholar 

  23. Deckwer W-D et al (1980) Hydrodynamic properties of the Fischer-Tropsch slurry process. Ind Eng Chem Process Des Dev 19(4):699–708

    Article  Google Scholar 

  24. Yang W, Wang J, Jin Y (2001) Mass transfer characteristics of syngas components in slurry system at industrial conditions. Chemical Engineering and Technology: Industrial Chemistry-Plant Equipment-Process Engineering-Biotechnology 24(6):651–657

    Article  Google Scholar 

  25. Jin H et al (2014) Gas–liquid mass transfer characteristics in a gas–liquid–solid bubble column under elevated pressure and temperature. Chin J Chem Eng 22(9):955–961

    Article  Google Scholar 

  26. Behkish A et al (2002) Mass transfer characteristics in a large-scale slurry bubble column reactor with organic liquid mixtures. Chem Eng Sci 57(16):3307–3324

    Article  Google Scholar 

  27. Sehabiague L, Morsi BI (2013) 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 11(1):83–102

    Article  Google Scholar 

  28. Gourich B et al (2008) Influence of hydrodynamics and probe response on oxygen mass transfer measurements in a high aspect ratio bubble column reactor: Effect of the coalescence behaviour of the liquid phase. Biochem Eng J 39(1):1–14

    Article  Google Scholar 

  29. Han L, Al-Dahhan MH (2007) Gas–liquid mass transfer in a high pressure bubble column reactor with different sparger designs. Chem Eng Sci 62(1–2):131–139

    Article  Google Scholar 

  30. Han L, Said IA, Al-Dahhan M (2018) Gas phase back-mixing in a mimicked Fischer-Tropsch slurry bubble column using an advanced gaseous tracer technique. Int J Chem React Eng 17(2)

  31. Calderbank P, Moo-Young M (1961) The continuous phase heat and mass-transfer properties of dispersions. Chem Eng Sci 16(1–2):39–54

  32. Akita K, Yoshida F (1973) Gas holdup and volumetric mass transfer coefficient in bubble columns. Effects of liquid properties. Industrial and Engineering Chemistry Process Design and Development 12(1):76–80

  33. Yang W, Wang J, Jin Y (2001) Mass transfer characteristics of syngas components in slurry system at industrial conditions. Chem Eng Technol 24(6):651–657

    Article  Google Scholar 

  34. Jordan U et al (2002) Mass transfer in high-pressure bubble columns with organic liquids. Chem Eng Technol 25(3):262–265

    Article  Google Scholar 

  35. Kawase Y, Halard B, Moo-Young M (1987) Theoretical prediction of volumetric mass transfer coefficients in bubble columns for Newtonian and non-Newtonian fluids. Chem Eng Sci 42(7):1609–1617

    Article  Google Scholar 

  36. Nakao K et al (1983) Mass transfer characteristics of bubble columns in recirculation flow regime. Ind Eng Chem Process Des Dev 22(4):577–582

    Article  Google Scholar 

  37. Zhao B et al (2003) Gas–liquid mass transfer in slurry bubble systems: I. Mathematical modeling based on a single bubble mechanism. Chem Eng Sci 96(1–3):23–27

  38. Nedeltchev S, Jordan U, Schumpe A (2007) Correction of the penetration theory based on mass-transfer data from bubble columns operated in the homogeneous regime under high pressure. Chem Eng Sci 62(22):6263–6273

    Article  Google Scholar 

  39. Nedeltchev S (2003) Correction of the penetration theory applied for prediction of mass transfer coefficients in a high-pressure bubble column operated with gasoline and toluene. J Chem Eng Jpn 36(5):630–633

    Article  Google Scholar 

  40. Han L (2007) Hydrodynamics, back-mixing, and mass transfer in a slurry bubble column reactor for Fischer-Tropsch alternative fuels. Washington University: Saint Louis, Missouri

  41. Han L, Kamalanathan P, Al-Dahhan MH (2021) Gas–liquid mass transfer using advanced optical probe in a mimicked FT slurry bubble column. Int J Chem Reactor Eng 19(1):31–42

    Article  Google Scholar 

  42. Rados N, Al-Dahhan MH, Dudukovic MP (2003) Modeling of the Fischer-Tropsch synthesis in slurry bubble column reactors. Catal Today 79:211–218

    Article  Google Scholar 

  43. Ong B (2003) Experimental investigation of bubble column hydrodynamics - effect of elevated pressure and superficial gas velocity. In: Department of Chemical Engineering. Washington University, St. Louis, MO, USA

  44. Shaikh A, Taha MM, Al Dahhan M (2021) Phase distribution in Fischer-Tropsch mimicked slurry bubble column via computed tomography. Chem Eng Sci 231

  45. Abdulmohsin RS, Al-Dahhan MH (2016) Axial dispersion and mixing phenomena of the gas phase in a packed pebble-bed reactor. Ann Nucl Energy 88:100–111

    Article  Google Scholar 

  46. Alexander V, Albazzaz H, Al-Dahhan M (2019) Gas phase dispersion/mixing investigation in a representative geometry of gas-liquid upflow Moving Bed Hydrotreater Reactor (MBR) using developed gas tracer technique and method based on convolution/regression. Chem Eng Sci 195:671–682

    Article  Google Scholar 

  47. Said IA et al (2018) Axial dispersion and mixing of coolant gas within a separate-effect prismatic modular reactor. Nuclear Energy and Technology 4:167

    Article  Google Scholar 

  48. Levenspiel O (1972) Chemical reaction engineering. Wiley Eastern Press, New York

    Google Scholar 

  49. Danckwerts PV (1953) Continuous flow systems: distribution of residence times. Chem Eng Sci 2(1):1–13

    Article  Google Scholar 

  50. Breman BB et al (1996) The gas-liquid mass transfer coefficient (kLa) in the gas-liquid multi-stage agitated contactor (MAC). Chem Eng Res Des 74(8):872–881

    Article  Google Scholar 

  51. Wilcock RJ et al (1978) Solubilities of gases in liquids II. The solubilities of He, Ne, Ar, Kr, O2, N2, CO, CO2, CH4, CF4, and SF6 in n-octane 1-octanol, n-decane, and 1-decanol. J Chem Thermodyn 10(9):817–822

  52. Lide DR (2004) CRC handbook of chemistry and physics, vol. 85. CRC press

  53. Brunner E (1985) Solubility of hydrogen in 10 organic solvents at 298.15, 323.15, and 373.15 K. J Chem Eng Data 30(3):269–273

  54. Diaz M, Vega A, Coca J (1987) Correlation for the estimation of gas-liquid diffusivity. Chem Eng Commun 52(4–6):271–281

    Article  Google Scholar 

  55. Wu C, Suddard K, Al-dahhan MH (2008) Bubble dynamics investigation in a slurry bubble column. AIChE J 54(5):1203–1212

    Article  Google Scholar 

  56. Luo X et al (1999) Maximum stable bubble size and gas holdup in high-pressure slurry bubble columns. AIChE J 45(4):665–680

    Article  Google Scholar 

  57. Rabha S, Schubert M, Hampel U (2013) Intrinsic flow behavior in a slurry bubble column: a study on the effect of particle size. Chem Eng Sci 93:401–411

    Article  Google Scholar 

  58. Higbie R (1935) The rate of absorption of a pure gas into a still liquid during short periods of exposure. Trans AIChE 31:365–389

    Google Scholar 

  59. Luo X et al (1997) On the rise velocity of bubbles in liquid-solid suspensions at elevated pressure and temperature. Chem Eng Sci 52(21–22):3693–3699

    Article  Google Scholar 

  60. Mendelson HD (1967) The prediction of bubble terminal velocities from wave theory. AIChE J 13(2):250–253

    Article  Google Scholar 

  61. Xue J et al (2008) Bubble velocity, size, and interfacial area measurements in a bubble column by four-point optical probe. AIChE J 54(2):350–363

    Article  Google Scholar 

  62. Kantarci N, Borak F, Ulgen KO (2005) Bubble column reactors. Process Biochem 40(7):2263–2283

    Article  Google Scholar 

Download references

Acknowledgements

The authors are grateful for financial support of the High-Pressure Slurry Bubble Column (HPSBC) Consortium by ConocoPhillips (USA), EniTecnologie (Italy), Sasol (South Africa), and Statoil (Norway).

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Authors and Affiliations

  1. ExxonMobil Research and Engineering, Annandale, NJ, USA

    Lu Han

  2. Chemical Engineering Department, Faculty of Engineering, Alexandria University, Alexandria, 21544, Egypt

    Mahmoud M. Taha

  3. Environmental Engineering Program, Zewail City of Science, Technology, and Innovation, University of Science and Technology, October Gardens, 6th of October, 12578, Giza, Egypt

    Mahmoud M. Taha

  4. Chemical and Biochemical Engineering Department, Missouri University of Science and Technology, Rolla, MO, 65409, USA

    Premkumar Kamalanathan & Muthanna H. Al-Dahhan

  5. Chemical Engineering Department, Higher Technological Institute, 10th of Ramadan City, Ash-Sharqia, Egypt

    Nora Y. Selem

  6. Mining and Nuclear Engineering Department, Missouri University of Science and Technology, Rolla, MO, 65409, USA

    Muthanna H. Al-Dahhan

  7. Mohamed VI Polytechnic Univetsity (UM6P), Ben Guerir, Morocco

    Muthanna H. Al-Dahhan

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  1. Lu Han
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Correspondence to Mahmoud M. Taha or Muthanna H. Al-Dahhan.

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This work was conducted in the Chemical Reaction Engineering Laboratory (CREL), Department of Chemical Engineering, Washington University St. Louis, MO, USA.

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Han, L., Taha, M.M., Kamalanathan, P. et al. Experimentation and correlation development of mass transfer in a mimicked Fischer–Tropsch slurry bubble column reactor. Heat Mass Transfer 58, 1133–1143 (2022). https://doi.org/10.1007/s00231-021-03169-9

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