Metallurgical and Materials Transactions B

, Volume 47, Issue 6, pp 3544–3556 | Cite as

A Mathematical Model for the Reduction Stage of the CAS-OB Process

  • Petri SulasalmiEmail author
  • Ville-Valtteri Visuri
  • Aki Kärnä
  • Mika Järvinen
  • Seppo Ollila
  • Timo Fabritius


This paper proposes a novel method for modeling the reduction stage of the CAS-OB process (composition adjustment by sealed argon bubbling–oxygen blowing). Our previous study proposed a model for the heating stage of the CAS-OB process; the purpose of the present study is to extend this work toward a more comprehensive model for the process in question. The CAS-OB process is designed for homogenization and control of the composition and temperature of steel. During the reduction stage, the steel phase is stirred intensely by employing the gas nozzles at the bottom of the ladle, which blow argon gas. It is assumed that the reduction rate of the top slag is dictated by the formation of slag droplets at the steel-slag interface. Slag droplets, which are generated due to turning of the steel flow in the spout, contribute mainly by increasing the interfacial area between the steel and slag phases. This phenomenon has been taken into account based on our previous study, in which the droplet size distribution and generation rate at different steel flow velocities. The reactions considered between the slag and steel phases are assumed to be mass transfer controlled and reversible. We validated the results from the model against the measurements from the real CAS-OB process. The results indicate that the model accurately predicts the end compositions of slag and steel. Moreover, it was discovered that the cooling rate of steel during the gas stirring given by the model is consistent with the results reported in the literature.


Mass Transfer Coefficient Sherwood Number Slag Phase Reduction Stage Refractory Lining 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Area (m2)


Activity (–)


Generation rate of droplets (1/s)


Diameter of the open-eye area (m), mass diffusivity (m2/s)


Nozzle diameter (m)


Bubble diameter (m)


Acceleration due to gravity (m/s2)


Mass transfer coefficient (m/s)


Mass flux [kg/(m2 s)]


Thermal conductivity [W/(m K)]


Forward reaction rate coefficient [kg/(m2 s)]


Characteristic length (m)


Streamed length (m)


Mass (kg)


Number of O-atoms (–)


Pressure (Pa)


Reaction rate [kg/(m2 s)]


Reaction source term [kg/(m2 s)]


Temperature [K (°C)]


Time (s)


Rising velocity (m/s)


Interfacial velocity (m/s)

\( \dot{V}_{\text{G}} \)

Volumetric gas flow rate (m3/s)


Cation fraction (–)


Mole fraction (–)


Mass fraction (–)

Greek Letters


Interaction energy (J), heat transfer coefficient [W/(m2 K)]


Binary operator


Raoultian activity coefficient (–)


Molar first-order interaction parameter, refers also to reaction interface


Dynamic viscosity (Pa s)


Stoichiometric coefficient (–)

\( \tilde{v} \)

Mass-based stoichiometric coefficient (–)


Density (kg/m3)


Gibbs free energy (J/mol)


Conversion energy (J)


Reaction enthalpy (J/mol)


Specific heat of reaction (J/kg)


Reaction entropy [J/(mol K)]


Time step (s)


Width of the mantle (m)


Width of the refractory lining (m)



This research has been conducted within the FIMECC SIMP, a research program coordinated by the Finnish Metals and Engineering Competence Cluster (FIMECC). The authors would like to thank Leena Määttä, the specialized sampler group and the helpful operators at the CAS-OB station. The Jenny and Antti Wihuri Foundation is warmly acknowledged for financial support. The Academy of Finland (Projects 258319 and 26495) is acknowledged as well.


  1. 1.
    L. Nilsson, K. Andersson and K. Lindquist: Scan. J. Metall., 1996, vol. 25, pp. 73-79Google Scholar
  2. 2.
    K. Andersson, L. Nilsson, H. Breu and G. Stolte, Stahl Eisen, 1995, vol. 115, pp. 59-64Google Scholar
  3. 3.
    G. Stolte, W. Pulvermacher and T. Thülig, Stahl Eisen, 1989, vol. 109, pp. 67-72Google Scholar
  4. 4.
    H.-M. Wang, G.-R. Li, Q.-X. Dai, X.-J. Zhang and G.-M. Shi, Ironmak. Steelmak., 2007, vol. 34, pp. 350-353CrossRefGoogle Scholar
  5. 5.
    H.-M. Wang, G.-R. Li and Q.-X. Dai, ISIJ Int., 2006, vol. 46, pp. 637-640CrossRefGoogle Scholar
  6. 6.
    X.-C. Ju: Refractories (Chin.), 2001, vol. 35, pp. 6Google Scholar
  7. 7.
    S. Tuomikoski: Master’s thesis, University of Oulu, 2009, pp. 1–102Google Scholar
  8. 8.
    C. Ha and J.-M. Park: Arch. Metall. Mater., 2008, vol. 53, pp. 637Google Scholar
  9. 9.
    L. Jonsson, G.-E. Grip, A. Johansson and P. Jönssön: 80th Steelmaking Conference, Chicago, Illinois, 1997, p. 69Google Scholar
  10. 10.
    T. Kulju, S. Ollila, R. L. Keiski and E. Muurinen: Mater. Sci. Forum, 2013, vol. 762, pp. 248-252CrossRefGoogle Scholar
  11. 11.
    P. Sulasalmi, V. -V. Visuri and T. Fabritius: Mater. Sci. Forum, 2013, vol. 762, pp. 242-247CrossRefGoogle Scholar
  12. 12.
    P. Sulasalmi, V.-V. Visuri, A. Kärnä and T. Fabritius: Steel Res. Int., 2015, vol. 85, pp. 212-222CrossRefGoogle Scholar
  13. 13.
    M. Järvinen, A. Kärnä, V.-V. Visuri, P. Sulasalmi, E.-P. Heikkinen, K. Pääskylä, C. DeBlasio and T. Fabritius: ISIJ Int., 2014, vol. 54, pp. 2263-2272CrossRefGoogle Scholar
  14. 14.
    M. P. Järvinen, A. Kärnä and T. Fabritius: Steel Res. Int., 2009, vol. 80, pp. 429-436Google Scholar
  15. 15.
    M. P. Järvinen, S. Pisilä, A. Kärnä, T. Ikäheimonen, P. Kupari and T. Fabritius: Steel Res. Int., 2011, vol. 82, pp. 638-649CrossRefGoogle Scholar
  16. 16.
    M. Järvinen, V.-V. Visuri, A. Kärnä, P. Sulasalmi, E.-P. Heikkinen, C. De Blasio, and T. Fabritius: ISIJ Int., 2016, vol. 56, DOI: 10.2355/isijinternational.ISIJINT-2016-241
  17. 17.
    V.-V. Visuri, M. Järvinen, A. Kärnä, P. Sulasalmi, E.-P. Heikkinen, P. Kupari and T. Fabritius: A Mathematical Model for Reaction during Top-Blowing in the AOD Process: Derivation of the Model. Unpublished workGoogle Scholar
  18. 18.
    V.-V. Visuri, M. Järvinen, P. Sulasalmi, J. Savolainen, E.-P. Heikkinen and T. Fabritius: ISIJ Int., 2013, vol. 53, pp. 603-612CrossRefGoogle Scholar
  19. 19.
    P. Sulasalmi, A. Kärnä and T. Fabritius, J. Savolainen: ISIJ Int., 2009, vol. 24, pp. 1661-1667CrossRefGoogle Scholar
  20. 20.
    F. Oeters: Metallurgy of Steelmaking, Verlag Stahleisen mbH, Düsseldorf, 1989, pp. 221–38, 284–95, 325–34Google Scholar
  21. 21.
    K. Krishnapisharody and G. Irons: Metall. Mater. Trans. B, 2006, vol. 37B, pp. 763-772CrossRefGoogle Scholar
  22. 22.
    A. Kondratiev and E. Jak: Metall. Mater. Trans. B, 2001, vol. 32B, pp. 1015-1025CrossRefGoogle Scholar
  23. 23.
    M. Kekkonen, H. Oghbasilasie and S. Louhenkilpi: Viscosity Models for Molten Slags, Aalto University, 2012, pp. 1–30Google Scholar
  24. 24.
    B.J. Keene and K.C Mills: in Slag Atlas, 2nd ed., Verlag Stahleisen GmbH, Düsseldorf, 1995, pp. 313–48Google Scholar
  25. 25.
    E.A. Brandes and G.A. Brook: Smithells Metals Reference Book, 7th ed., Butterworth-Heinemann, Oxford, 1992, pp. 14:1–27Google Scholar
  26. 26.
    A. D. Pelton and C. W. Bale: Metall. Trans. A, 1986, vol. 17A, pp. 1211-1215CrossRefGoogle Scholar
  27. 27.
    G. K. Sigworth and J. F. Elliot: Met. Sci., 1974, vol. 8, pp. 298-310CrossRefGoogle Scholar
  28. 28.
    Z. T. Ma and D. Janke: Acta Metall. Sin., 1999, vol. 12, pp. 127-136Google Scholar
  29. 29.
    S. Ban-Ya: ISIJ Int., 1993, vol. 33, pp. 2-11CrossRefGoogle Scholar
  30. 30.
    D. Sosinsky and I. Sommerville: Metall. Trans. B, 1986, vol. 17B, pp. 331-337CrossRefGoogle Scholar
  31. 31.
    Y. Iguchi: in Elliot Symposium Proceedings, 1990, pp. 129–46Google Scholar
  32. 32.
    S. Ban-Ya and J.-D. Shim: Can. Metall. Quart., 1982, vol. 21, pp. 319-328CrossRefGoogle Scholar
  33. 33.
    F. Ihme, H. Schmidt-Traub and H. Brauer: Chem.-Ing.-Tech., 1972, vol. 44, pp. 306-313CrossRefGoogle Scholar
  34. 34.
    R. Higbie: T. Am. Inst. Chem. Eng., 1935, vol. 31, pp. 365-389Google Scholar
  35. 35.
    K. Nagata, Y. Ono, T. Ejima and T. Yamamura: Handbook of Physico-Chemical Properties at High Temperatures, Chapter 7, Iron and Steel Institute of Japan, Tokyo, 1988, pp. 181–204Google Scholar
  36. 36.
    C. R. Wilke and C. Y. Lee, Ind. Eng. Chem., 1955, vol. 47, pp. 1253-1257CrossRefGoogle Scholar
  37. 37.
    J. Mietz, S. Schneider and F. Oeters: Steel Res., 1991, vol. 62, pp. 1-9Google Scholar
  38. 38.
    J. Mietz, S. Schneider and F. Oeters: Steel Res., 1991, vol. 62, pp. 10-15Google Scholar
  39. 39.
    H. Lachmund, Y. Xie, T. Buhles and W. Pluschkell: Steel Res. Int., 2003, vol. 74, pp. 77-85Google Scholar
  40. 40.
    A. Ghosh: Secondary Steelmaking Principles and Applications, CRC Press, New York, 2000, p. 231Google Scholar
  41. 41.
    J. Szekely, G. Carlson and L. Helle: Ladle Metallurgy, Materials Research and Engineering, Springer-Verlag Inc., New York, 1989, p. 69Google Scholar

Copyright information

© The Minerals, Metals & Materials Society and ASM International 2016

Authors and Affiliations

  • Petri Sulasalmi
    • 1
    Email author
  • Ville-Valtteri Visuri
    • 1
  • Aki Kärnä
    • 1
  • Mika Järvinen
    • 2
  • Seppo Ollila
    • 3
  • Timo Fabritius
    • 1
  1. 1.Research Unit of Process MetallurgyUniversity of OuluOuluFinland
  2. 2.Department of Mechanical EngineeringAalto UniversityAaltoFinland
  3. 3.SSAB Europe OyRaaheFinland

Personalised recommendations