Metallurgical and Materials Transactions B

, Volume 48, Issue 6, pp 3281–3300 | Cite as

A Gibbs Energy Minimization Approach for Modeling of Chemical Reactions in a Basic Oxygen Furnace

  • Ari KruskopfEmail author
  • Ville-Valtteri Visuri


In modern steelmaking, the decarburization of hot metal is converted into steel primarily in converter processes, such as the basic oxygen furnace. The objective of this work was to develop a new mathematical model for top blown steel converter, which accounts for the complex reaction equilibria in the impact zone, also known as the hot spot, as well as the associated mass and heat transport. An in-house computer code of the model has been developed in Matlab. The main assumption of the model is that all reactions take place in a specified reaction zone. The mass transfer between the reaction volume, bulk slag, and metal determine the reaction rates for the species. The thermodynamic equilibrium is calculated using the partitioning of Gibbs energy (PGE) method. The activity model for the liquid metal is the unified interaction parameter model and for the liquid slag the modified quasichemical model (MQM). The MQM was validated by calculating iso-activity lines for the liquid slag components. The PGE method together with the MQM was validated by calculating liquidus lines for solid components. The results were compared with measurements from literature. The full chemical reaction model was validated by comparing the metal and slag compositions to measurements from industrial scale converter. The predictions were found to be in good agreement with the measured values. Furthermore, the accuracy of the model was found to compare favorably with the models proposed in the literature. The real-time capability of the proposed model was confirmed in test calculations.


\( \rho \)

Density (kg/m3)


Area (m2)


Volume (m3)

\( m \)

Mass (kg)

\( \dot{m} \)

Mass flux (kg/s)


Time (s)


Gibbs energy (J/mol)


Universal gas constant (J/(mol K))


Temperature (K)


Dimensionless Gibbs energy and gravitational acceleration (m/s2) in Chapter III.B

x, X

Mole fraction

\( \mu \)

Chemical potential of constituent (J/mol)


Molar amount (mol)


Mass constraint

\( a_{ij} \)

Stoichiometric matrix


Number of degrees of freedom

\( C \)

Number of components

\( {{\Phi }} \)

Total number of phases

\( {{\Gamma }} \)

Dimensionless chemical potential of component


Jacobian matrix


Dimensionless driving force

\( \gamma \)

Activity coefficient

\( \varepsilon \)

First-order interaction parameter

\( {{\Delta }}g \)

Gibbs energy of pair formation

\( Z \)

Coordination number


Mass fraction and coordination equivalent fraction in Chapter 3.2

\( {\text{q}} \)

Gibbs energy coefficient of the pair fraction polynomial (J/mol)

\( {{\omega }} \)

Temperature independent part of the Gibbs energy coefficient (J/mol)

\( {{\eta }} \)

Temperature dependent part of the Gibbs energy coefficient [J/(mol K)]

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

Volume flow rate (m 3 /s)

\( H \)

Enthalpy (J)


Entropy [J/(mol K)]

\( \dot{H} \)

Enthalpy flux (J/s)

\( h \)

Specific enthalpy (J/kg)

\( c_{\text{p}} \)

Heat capacity (J/(kg K))

\( \varphi \)

Enthalpy or mass source (J/s), (kg/s)

\( \alpha \)

Volume fraction

\( h_{T} \)

Heat transfer coefficient (W/(m2 K))

\( h_{Y} \)

Mass transfer coefficient (m/s)

\( k \)

Thermal conductivity (W/(m K))

\( I \)

Momentum (kg*m)/s2

\( v \)

Velocity (m/s)

\( R_{\text{p}} \)

Plume momentum ratio (dimensionless)










i, j, l, k

Generic indices

A, B, C

Components A, B, and C


Reaction zone











Excess Gibbs energy


Standrard state


Pure phase


Solution phase


Iteration index


Time level





This work was partly funded by the Finnish Funding Agency for Technology and Innovation (TEKES). The research was carried out within the framework of the DIMECC SIMP research program.


  1. 1.
    H. Jalkanen and L. Holappa: Treatise on Process Metallurgy, vol. 3, S. Seetharaman, A. McLean, R. Guthrie and S. Sridhar, eds., Elsevier, Oxford, 2014, pp. 223–70.Google Scholar
  2. 2.
    N. Molloy: J. Iron Steel Inst., 1970, vol. 208, pp. 943–950.Google Scholar
  3. 3.
    F.-R. Block, A. Masui and G. Stolzenberg: Arch. Eisenhüttenwes., 1973, vol. 44, pp. 357–361.CrossRefGoogle Scholar
  4. 4.
    W. Kleppe and F. Oeters: Arch. Eisenhüttenwes., 1976, vol. 47, pp. 271–275.CrossRefGoogle Scholar
  5. 5.
    F. R. Cheslak, J. A. Nicholls and M. Sichel: J. Fluid Mech., 1969, vol. 36, pp. 55–63.CrossRefGoogle Scholar
  6. 6.
    Subagyo, G. A. Brooks, K. S. Coley and G. A. Irons: ISIJ Int., 2003, vol. 43, pp. 983–989.CrossRefGoogle Scholar
  7. 7.
    B.K. Rout, G. Brooks, M. Subagyo, A. Rhamdhani and Z. Li: Metall. Mater. Trans. B, 2016, vol. 47, pp. 3350–3361.CrossRefGoogle Scholar
  8. 8.
    S. C. Koria and K. W. Lange: Metall. Trans. B, 1984, vol. 15, pp. 109–116.CrossRefGoogle Scholar
  9. 9.
    S. C. Koria and K. W. Lange: Ironmaking Steelmaking, 1986, vol. 13, pp. 236–240.Google Scholar
  10. 10.
    R. C. Urquhart and W. G. Davenport: Can. Metall. Q., 1973, vol. 12, pp. 507–516.CrossRefGoogle Scholar
  11. 11.
    E. Schürmann, G. Mahn, J. Schoop and W. Resch: Arch. Eisenhüttenwes., 1977, vol. 48, pp. 515-519.CrossRefGoogle Scholar
  12. 12.
    T. Kootz, K. Behrens, H. Maas and P. Baumgarten: Stahl Eisen, 1965, vol. 85, pp. 857–865.Google Scholar
  13. 13.
    F. Oeters: Arch. Eisenhüttenwes., 1966, vol. 37, pp. 209–219.CrossRefGoogle Scholar
  14. 14.
    K. W. Lange: Arch. Eisenhüttenwes., 1971, vol. 42, pp. 233–241.CrossRefGoogle Scholar
  15. 15.
    K. Koch, W. Fix and P. Valentin: Arch. Eisenhüttenwes., 1976, vol. 47, pp. 659–663.CrossRefGoogle Scholar
  16. 16.
    K. Koch, W. Fix and P. Valentin: Arch. Eisenhüttenwes., 1978, vol. 49, pp. 109-114.CrossRefGoogle Scholar
  17. 17.
    S. Asai and I. Muchi: Trans. Iron Steel Inst. Jpn, 1970, vol. 10, pp. 250–263.Google Scholar
  18. 18.
    K.-C. Chou, U. B. Pal and R. G. Reddy: ISIJ Int., 1993, vol. 33, pp. 862–868.CrossRefGoogle Scholar
  19. 19.
    S.-Y. Kitamura, H. Shibata and N. Maruoka, Steel Res. Int., 2008, vol. 79, pp. 586–590.CrossRefGoogle Scholar
  20. 20.
    F. Pahlevani, S. Kitamura, H. Shibata and N. Maruoka: Steel Res. Int., 2010, vol. 81, pp. 617–622.CrossRefGoogle Scholar
  21. 21.
    N. Dogan, G. A. Brooks and M. A. Rhamdhani: ISIJ Int., 2011, vol. 51, pp. 1086–1092.CrossRefGoogle Scholar
  22. 22.
    N. Dogan, G. A. Brooks and M. A. Rhamdhani: ISIJ Int., 2011, vol. 51, pp. 1093–1101.CrossRefGoogle Scholar
  23. 23.
    N. Dogan, G. A. Brooks and M. A. Rhamdhani: ISIJ Int., 2011, vol. 51, pp. 1102–1109.CrossRefGoogle Scholar
  24. 24.
    A. K. Shukla, B. Deo, S. Millman, B. Snoeijer, A. Overbosch and A. Kapilashrami: Steel Res. Int., 2010, vol. 81, pp. 940–948.CrossRefGoogle Scholar
  25. 25.
    Y. Lytvynyuk, J. Schenk, M. Hiebler and A. Sormann: Steel Res. Int., 2014, vol. 85, pp. 537–543.CrossRefGoogle Scholar
  26. 26.
    Y. Lytvynyuk, J. Schenk, M. Hiebler and A. Sormann: Steel Res. Int., 2014, vol. 85, pp. 544–563.CrossRefGoogle Scholar
  27. 27.
    S. Sarkar, P. Gupta, S. Basu and N. B. Ballal: Metall. Mater. Trans. B, 2015, vol. 46, pp. 961–976.CrossRefGoogle Scholar
  28. 28.
    M. Han, Y. Li and Z. Cao, Neurocomputing, 2014, vol. 123, 415–423.CrossRefGoogle Scholar
  29. 29.
    M. Han and C. Liu, Appl. Soft Comput., 2014, vol. 19, pp. 430–437.CrossRefGoogle Scholar
  30. 30.
    H.-J. Odenthal, N. Uebber, J. Schlüter, M. Löpke, K. Morik and H. Blom: Stahl Eisen, 2014, vol. 134, pp. 62–67.Google Scholar
  31. 31.
    D. Laha, Y. Ren and P. N. Suganthan: Expert Syst. Appl., 2015, vol. 42, pp. 4687–4696.CrossRefGoogle Scholar
  32. 32.
    A. Sorsa, J. Ruuska, J. Lilja and K. Leiviskä: IFAC-PapersOnLine, 2015, vol. 48, pp. 177–182.CrossRefGoogle Scholar
  33. 33.
    T.W. Miller, J. Jimenez, A. Sharan, and D.A. Goldstein: The Making, Shaping and Treatment of Steels: Steelmaking and Refining, vol. 2, R.J. Fruehan, ed., The AISE Steel Foundation, Pittsburgh, 1998, pp. 475–524.Google Scholar
  34. 34.
    C. Cicutti, M. Valdez, T. Pérez, J. Petroni, A Gómez, R. Donayo, and L. Ferro: Proceedings of the Sixth International Conference on Molten Slags, Fluxes and Salts, Stockholm-Helsinki, 2000.Google Scholar
  35. 35.
    C. Cicutti, M. Valzed, T. Pérez, R. Donayo and J. Petroni: Latin Am. Appl. Res., 2002, vol. 32, pp. 237–240.Google Scholar
  36. 36.
    H. Jalkanen: Advanced Processing of Metals and Materials (Sohn International Symposium), Thermo and Physicochemical Principles: Iron and Steel Making, vol. 2, F. Kongoli and R. G. Reddy, eds., 2006, pp. 541–54.Google Scholar
  37. 37.
    M. Järvinen, V.-V. Visuri, E.-P. Heikkinen, A. Kärnä, P. Sulasalmi, C. De Blasio and T. Fabritius: ISIJ Int., 2016, vol. 56, pp. 1543–1552.CrossRefGoogle Scholar
  38. 38.
    M. Ersson, L. Höglund, A. Tilliander, L. Jonsson and P. Jönsson: ISIJ Int., 2008, vol. 48, pp. 147–153.CrossRefGoogle Scholar
  39. 39.
    M. Ek, Q. F. Shu, J. van Boggelen and D. Sichen: Ironmaking Steelmaking, 2012, vol. 39, pp. 77–84.CrossRefGoogle Scholar
  40. 40.
    A. Kruskopf: Metall. Mater. Trans. B, 2015, vol. 46, pp. 1195-1206.CrossRefGoogle Scholar
  41. 41.
    A. Kruskopf and S. Louhenkilpi: Proceedings of the METEC & 2nd ESTAD, Düsseldorf, Germany, 2015, p. 165.Google Scholar
  42. 42.
    A. Kruskopf: Metall. Mater. Trans. B, 2017, vol. 48, pp. 619–631.CrossRefGoogle Scholar
  43. 43.
    M.H.A. Piro, Doctoral thesis, Royal Military College of Canada, 2011.Google Scholar
  44. 44.
    M. H. A Piro, S. Simunovic, T. M. Besmann, B.J. Lewis and W.T. Thompson, Comput. Mater. Sci., 2013, vol. 67, pp. 266–272.CrossRefGoogle Scholar
  45. 45.
    M. H. A. Piro and S. Simunovic, CALPHAD, 2012, vol. 39, pp. 104–110.CrossRefGoogle Scholar
  46. 46.
    A.D. Pelton and C. W. Bale, Metall. Mater. Trans. A, 1985, vol. 17, pp. 1211–1215.Google Scholar
  47. 47.
    G.K. Sigworth and J.F. Elliot, Metal Sci., 1973, vol. 8, pp. 298–310.CrossRefGoogle Scholar
  48. 48.
    J. Miettinen, IAD—Thermodynamic Database for Iron-based alloys, Casim Consulting Oy, Espoo, 2017.Google Scholar
  49. 49.
    A. D. Pelton and M. Blander, Metall. Trans. B., 1986, vol. 17, pp. 805–815.CrossRefGoogle Scholar
  50. 50.
    C. R. Swaminathan and V. R. Voller: Int. J. Num. Meth. Heat Fluid Flow, 1993, vol. 3, pp. 233–244.Google Scholar
  51. 51.
    J. R. Taylor and A. T. Dinsdale, CAPHAD, 1990, vol. 14, pp. 71–88Google Scholar
  52. 52.
    HSC Chemistry 8, version 8.1.0, Outotec Technologies, 1974–2015.Google Scholar
  53. 53.
    M. Timucin and A.E. Morris, Metall. Trans., 1970, vol. 1, pp. 3193–3201.Google Scholar
  54. 54.
    Slag Atlas, 1981, Verlag Stahleisen M.B.H., Düsseldorf, Germany, p. 68.Google Scholar
  55. 55.
    P. V. Riboud and M. Olette: Proceedings of the 7th International Conference on Vacuum Metallurgy, 1982, pp. 879–889, Iron and Steel Institute of Japan, Tokyo, Japan.Google Scholar
  56. 56.
    S. Paul and D.N. Ghosh, Metall. Mater. Trans. B, 2007, vol. 17B, pp. 461-469.Google Scholar
  57. 57.
    M. Hirasawa, K. Mori, M. Sano, A. Hatanaka, Y. Shimatani and Y. Okazaki, Trans. Iron Steel Inst. Jpn, 1987, vol. 27, pp. 277–282.CrossRefGoogle Scholar
  58. 58.
    A. Chatterjee, N.-O. Lindfors and J.Å. Wester, Ironmaking Steelmaking, 1976, vol. 3, pp. 21–32.Google Scholar
  59. 59.
    K. Krishnapisharody and G.A Irons, Metall. Mater. Trans. B, 2013, vol. 44, pp. 1486–1498.CrossRefGoogle Scholar
  60. 60.
    A. Kärnä, M. P. Järvinen and F. Fabritius, Steel Res. Int., 2013, vol. 86, pp. 1370–1378.CrossRefGoogle Scholar
  61. 61.
    S. Ban-Ya, ISIJ Int., 1993, vol. 33, pp. 2–11.CrossRefGoogle Scholar

Copyright information

© The Minerals, Metals & Materials Society and ASM International 2017

Authors and Affiliations

  1. 1.Research Group for Materials Processing and Powder Metallurgy, Department of Chemical and Metallurgical EngineeringAalto UniversityAaltoFinland
  2. 2.Process Metallurgy Research UnitUniversity of OuluUniversity of OuluFinland

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