Skip to main content
SpringerLink
Log in

A Decarburization Model for a Fe–C Droplet Reacting in Oxidizing Slag

  • Original Research Article
  • Published:
Metallurgical and Materials Transactions B Aims and scope Submit manuscript

Abstract

A decarburization model has been developed for a Fe–C–S liquid droplet reacting in an oxidizing slag at high temperature (1580 °C to 1640 °C). The model incorporates the partitioning of oxygen at the slag/metal interface between decarburization at the slag/metal interface and transport into the droplet. The kinetics of nucleation and growth of CO bubbles within the liquid metal droplet have also been introduced to describe internal decarburization. The model parameters were determined using one set of experimental conditions and then used to predict behavior over a wide range of conditions. The prediction was validated for variation of, sulfur concentration, droplet mass, temperature, and droplet carbon concentration. Decarburization was found to proceed in three stages. The model was found to show good agreement for the initial two stages of decarburization: the incubation period and peak decarburization period. This observation suggested that the oxygen partitioning and nucleation kinetics had been incorporated properly. The model failed to predict the sudden shutdown of decarburization at the end stage of decarburization.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

Abbreviations

[pct C]:

Concentration of dissolved carbon in liquid metal (wt pct)

[pct O]:

Concentration of dissolved oxygen in liquid metal (wt pct)

[pct Al2O3]:

Slag Al2O3 concentration (wt pct)

[pct CaO]:

Slag CaO concentration (wt pct)

[pct FeO]:

Slag FeO concentration (wt pct)

[pct SiO2]:

Slag SiO2 concentration (wt pct)

A :

Interfacial area (m2)

\({A}_{\mathrm{g}/\mathrm{m}}^{\mathrm{gr}}\left(t\right)\) :

Total gas/metal surface area generated from the growth at time t (m2)

\({A}_{\mathrm{g}/\mathrm{m}}^{\mathrm{nuc}}\left(t\right)\) :

Total gas/metal interfacial area generated due to nucleation at time step t (m2)

J C :

Flux of C in the metal (mol/s)

J FeO :

Flux of FeO in the slag (mol/s)

J O :

Flux of O in the metal (mol/s)

K CO :

Equilibrium constant of CO formation reaction (–)

\({K}_{{\mathrm{FeO}}_{\mathrm{eq}}}\) :

Equilibrium constant of FeO dissociation reaction (–)

K j :

Adsorption coefficient of species j, where j are [S] and [O] (–)

\({M}_{\mathrm{C}}\), \({M}_{\mathrm{O}}\) :

Molecular weight of C and O (kg/mol)

\({M}_{\mathrm{FeO}}\), \({M}_{\mathrm{CaO}}\), \({M}_{{\mathrm{SiO}}_{2}}\), \({M}_{{\mathrm{Al}}_{2}{\mathrm{O}}_{3}}\) :

Molecular weight of FeO, CaO, SiO2 and Al2O3, respectively (kg/mol)

N 0 :

No of nucleation sites per unit volume (/m3)

P L :

Liquid pressure (Pa)

P ve :

Pressure of CO bubble at equilibrium (Pa)

P CO :

Pressure of CO at the interface (Pa)

R CO :

Rate of CO formation at the slag/metal interface (mol/s)

R FeO :

Rate of FeO dissociation reaction at the slag/metal interface (mol/s)

\({V}_{\mathrm{CO}}{\left(t\right)}^{\mathrm{nuc}}\), \({V}_{\mathrm{CO}}{\left(t\right)}^{\mathrm{gr}}\) :

Volume of CO bubbles which are generated from nucleation and growth, respectively, at time t (m3)

\({V}_{\mathrm{CO}}\left(t\right)\) :

Volume of the CO bubbles remaining in the droplet at time t (m3)

\({V}^{\mathrm{esc}}(t)\) :

Volume of bubbles which are escaping from the bloated droplet at time t (m3)

\({V}_{\mathrm{m}}\) :

Volume of liquid metal (m3)

\({W}_{\mathrm{slag}}^{\mathrm{dense}}\) :

Mass of dense slag (kg)

\({W}_{\mathrm{slag}}^{\mathrm{foamy}}\) :

Mass of foamy slag (kg)

\({W}_{\mathrm{slag}}^{\mathrm{tot}}\) :

Total slag mass (kg)

X FeO, \({X}_{Si{O}_{2}}\), X CaO :

Mole fraction of FeO, SiO2 and CaO (–)

\({a}_{\mathrm{j}}\) :

Activity of species j, where j can be [O], [C], [S] in metal or (FeO) in slag (–)

f C :

Henrian activity coefficient of carbon (–)

f O :

Henrian activity coefficient of oxygen (–)

\(\overrightarrow{k}\) :

Forward reaction rate constant of FeO dissociation (mol/m2 s)

K O :

Overall growth rate constant (mol/m2 s)

\({k}_{\mathrm{eff}}\) :

Effective slag mass transfer coefficient (m/s)

\({k}_{\mathrm{m}}\) :

Mass transfer coefficient of species in metal (m/s)

\({k}_{\mathrm{r}}\) :

Forward reaction rate constant of CO formation (kg/m2 s)

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

Slag Mass transfer coefficient (m/s)

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

No of moles of CO in a bubble of radius r (mol)

\({r}^{\mathrm{crit}}\) :

Critical radius of CO bubble in liquid metal (m)

\({r}_{t}\) :

Radius of a bubble at t times step (m)

\({y}_{t}^{\mathrm{Model}}\) :

Model predicted data point at time t (mol)

\({y}_{t}^{\mathrm{exp}}\) :

Experimentally found data point at time t (mol)

γFeO :

Activity coefficient of FeO of the bulk slag concentration (–)

\({\theta }_{\mathrm{j}}\) :

Fraction of surface area blocked due to poisoning (–)

\({\rho }_{\mathrm{d}}\left(t\right)\) :

Density of droplet at time t (kg/m3)

\({\rho }_{\mathrm{m}}\) :

Density of metal (kg/m3)

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

Density of slag (kg/m3)

\({\sigma }_{0}\) :

Surface tension of the metal (N/m)

\(\Delta t\) :

Time step

R :

Universal gas constant (J/mol K)

\(J\) :

Rate of nucleation (number of nuclei/m3 s)

\(N\) :

No of bubble at any time t (–)

\(N^{\prime}\) :

No of data points (–)

\(T\) :

Temperature (K)

\(k\) :

Boltzmann constant (m2 kg s−2 K−1)

\(m\) :

Mass of one CO molecule (kg)

\(n\) :

Coefficient of mass transfer model

\(\eta \) :

Slag viscosity (Pa s)

\(\psi \) :

Surface tension modifying parameter (–)

\(\mathrm{i}\) :

At the slag/metal interface

\(\mathrm{b}\) :

Within the bulk

\(\mathrm{s}/\mathrm{m}\) :

Slag/metal interface

\(\mathrm{g}/\mathrm{m}\) :

Gas/metal interface

References

  1. Subagyo, G.A. Brooks, and K.S. Coley: Can. Metall. Q., 2005, vol. 44, pp. 119–30.

  2. L.A. Baker and R.G. Ward: J. Iron Steel Inst., 1967, vol. 205, pp. 714–17.

    CAS  Google Scholar 

  3. G.G.K. Murthy, Y. Sawada, and J.F. Elliot: Ironmak. Steelmak., 1993, vol. 20, pp. 179–200.

    CAS  Google Scholar 

  4. T. Gare and G.S.F. Hazeldean: Ironmak. Steelmak., 1981, vol. 8, pp. 169–81.

    CAS  Google Scholar 

  5. K. Gao, V. Sahajwalla, H. Sun, C. Wheatley, and R. Dry: ISIJ Int., 2000, vol. 40, pp. 301–8.

    Article  CAS  Google Scholar 

  6. J.H. Zong and J.K. Yoon: Metall. Trans. B., 1990, vol. 21B, pp. 49–57.

    Article  CAS  Google Scholar 

  7. D. Widlund, D.S. Sarma, and P.G. Jönsson: ISIJ Int., 2006, vol. 46, pp. 1149–57.

    Article  CAS  Google Scholar 

  8. N. Simento, H. LEE, and P. Hayes: ISIJ Int., 1999, vol. 39, pp. 1217–23.

  9. E. Chen and K.S. Coley: Ironmak. Steelmak., 2010, vol. 37, pp. 541–5.

    Article  CAS  Google Scholar 

  10. E.W. Mulholland, G.S.F. Hazeldean, and M. Davies: J. Iron Steel Inst., 1973, vol. 211, pp. 632–9.

    CAS  Google Scholar 

  11. L.A. Baker, N.A. Warner, and A.E. Jenkins: Trans. Metall. Soc., 1967, vol. 239, pp. 857–64.

    CAS  Google Scholar 

  12. R.S. Kaplan and W.O. Philbrook: Metall. Trans., 1972, vol. 3, pp. 487–91.

    Article  Google Scholar 

  13. D.J. Min and R.J. Fruehan: Metall. Trans. B., 1992, vol. 23B, pp. 29–37.

    Article  CAS  Google Scholar 

  14. N.H. El Kaddah and D.G.C. Robertson: Metall. Mater. Trans. B., 1988, vol. 19B, pp. 831–7.

    Article  Google Scholar 

  15. N.H. El Kaddah and D.G.C. Robertson: J. Colloid Interface Sci., 1977, vol. 60, pp. 349–60.

    Article  Google Scholar 

  16. K. Gu, N. Dogan, and K.S. Coley: Metall. Mater. Trans. B Process Metall. Mater. Process. Sci., 2017, vol. 48B, pp. 2343–53.

    Article  Google Scholar 

  17. E. Chen and K.S. Coley: McMaster University, 2010.

  18. G.G.K. Murthy, A. Hasham, and U.B. Pal: Ironmak. Steelmak., 1993, vol. 20, pp. 191–200.

    CAS  Google Scholar 

  19. C.L. Molloseau and R.J. Fruehan: Metall. Mater. Trans. B Process Metall. Mater. Process. Sci., 2002, vol. 33B, pp. 335–44.

    Article  CAS  Google Scholar 

  20. G. Brooks, Y. Pan, and K.S. Coley: Metall. Mater. Trans. B., 2005, vol. 36B, pp. 525–35.

    Article  CAS  Google Scholar 

  21. N. Dogan, G.A. Brooks, and M.A. Rhamdhani: ISIJ Int., 2011, vol. 51, pp. 1093–101.

    Article  CAS  Google Scholar 

  22. A. Kadrolkar and N. Dogan: Metall. Mater. Trans. B Process Metall. Mater. Process. Sci., 2019, vol. 50B, pp. 2912–29.

    Article  Google Scholar 

  23. B.K. Rout, G. Brooks, M.A. Rhamdhani, Z. Li, F.N.H. Schrama, and A. Overbosch: Metall. Mater. Trans. B., 2018, vol. 49B, pp. 1022–33.

    Article  Google Scholar 

  24. H.S. Levine: Met. Trans., 1973, vol. 4, pp. 777–82.

    Article  CAS  Google Scholar 

  25. H. Sun: ISIJ Int., 2006, vol. 46, pp. 1560–9.

    Article  CAS  Google Scholar 

  26. C. Kattenbelt and B. Roffel: Metall. Mater. Trans. B., 2008, vol. 39B, pp. 764–9.

    Article  CAS  Google Scholar 

  27. M.D. Pomeroy: McMaster University, 2011.

  28. R. Sarkar, P. Gupta, S. Basu, and N.B. Ballal: Metall. Mater. Trans. B., 2015, vol. 46B, pp. 961–76.

    Article  Google Scholar 

  29. W. van der Knoop, B. Deo, A.B. Snoeijer, G. van Unen, and R. Boom: Proc. 4th Int. Conf. Molten Slags Fluxes, 1992, pp. 302–307.

  30. K. Gu, N. Dogan, and K.S. Coley: Metall. Mater. Trans. B Process Metall. Mater. Process. Sci., 2017, vol. 48B, pp. 2984–3001.

    Article  Google Scholar 

  31. I. Langmuir: J. Am. Chem. Soc., 1918, vol. 40, pp. 1361–403.

    Article  CAS  Google Scholar 

  32. S. Basu, A.K. Lahiri, and S. Seetharaman: Metall. Mater. Trans. B Process Metall. Mater. Process. Sci., 2010, vol. 41B, pp. 414–9.

    Article  CAS  Google Scholar 

  33. M. Hino and K. Ito: Thermodynamic Data for Steelmaking. 2010th ed. KONNO Printing Co. Ltd, Sendai, 2010.

    Google Scholar 

  34. M. Blander and J.L. Katz: AIChE J., 1975, vol. 21, pp. 833–48.

    Article  CAS  Google Scholar 

  35. A. Attar: AIChE J., 1978, vol. 24, pp. 106–15.

    Article  CAS  Google Scholar 

  36. S.D. Lubetkin: Langmuir Am. Chem. Soc., 2003, vol. 19, pp. 2575–87.

    CAS  Google Scholar 

  37. E.N. Harvey, A. Whiteley, W. McElroy, D. Pease, and D. Barnes: J. Cell. Comp. Physiol., 1944, vol. 24, pp. 23–34.

    Article  CAS  Google Scholar 

  38. P.G. Bowers, K. Bar-Eli, and R.M. Noyes: J. Chem. Soc. Faraday Trans., 1996, vol. 92, pp. 2843–9. .

    Article  CAS  Google Scholar 

  39. R.C. Tolman: J. Chem. Phys., 1949, vol. 17, pp. 333–7. .

    Article  CAS  Google Scholar 

  40. Y. Chung and A.W. Cramb: Metall. Mater. Trans. B., 2000, vol. 31B, pp. 957–71. .

    Article  CAS  Google Scholar 

  41. B. von Szyszkowski: Z. Phys. Chem., 1908, vol. 64, pp. 385–414. .

    Article  Google Scholar 

  42. G.R. Belton: Metall. Trans. B., 1976, vol. 7B, pp. 35–42. .

    Article  CAS  Google Scholar 

  43. T.X. Zhu: Bubble Escape Model, Private Communication, Hamilton, 2018.

  44. K. Gu, N. Dogan, and K.S. Coley: Metall. Mater. Trans. B Process Metall. Mater. Process. Sci., 2017, vol. 48B, pp. 2595–606. .

    Article  Google Scholar 

  45. J. Biswas, K. Gu, and K.S. Coley: Decarburization of Bloated Droplets: An Experimental Study to Understand the Kinetics of Decarburization of Metallic Iron Droplets in FeO Containing CaO-SiO2 Slags. McMaster University, Unpublished Research, 2020.

  46. P.A.A. Distin, G.D.D. Hallett, and F.. D. Richardson: J. Iron Steel Inst., 1968, vol. August, pp. 821–33.

  47. J.B. See and N.A. Warner: J. Iron Steel Inst., 1973, vol. 211, pp. 44–52. .

    CAS  Google Scholar 

  48. H. Sun, K. Gao, V. Sahajwalla, K. Mori, and R.D. Pehlke: ISIJ Int., 1999, vol. 39, pp. 1125–33. .

    Article  CAS  Google Scholar 

  49. K. Ito and K. Sano: Tetsu-to-Hagane., 1965, vol. 51, pp. 1252–9. .

    Article  CAS  Google Scholar 

  50. H. Gaye and P.V. Riboud: Metall. Trans. B., 1977, vol. 8B, pp. 409–15. .

    Article  CAS  Google Scholar 

  51. U.B. Pal, S.A. Macdonald, D.W. Woolley, and A.C. Powell: Metall. Mater. Trans. B., 2005, vol. 36B, pp. 209–18. .

    Article  CAS  Google Scholar 

  52. D.E. Woolley and U.B. Pal: Ironmak. Steelmak., 2002, vol. 29, pp. 125–32. .

    Article  CAS  Google Scholar 

  53. K. Gu, N. Dogan, and K.S. Coley: Metall. Mater. Trans. B., 2018, vol. 49B, pp. 1119–35. .

    Article  Google Scholar 

Download references

Acknowledgments

The authors wish to thank McMaster Steel Research Center and Natural Science and Engineering Research Council of Canada for funding this project.

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Author information

Authors and Affiliations

  1. Department of Materials Science and Engineering, McMaster Steel Research Centre, McMaster University, Hamilton, Ontario, L8S 4L8, Canada

    Jayasree Biswas, Kezhuan Gu & Kenneth S. Coley

  2. Department of Mechanical and Materials Engineering, Western University, London, Ontario, N6A5B9, Canada

    Kenneth S. Coley

Authors
  1. Jayasree Biswas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kezhuan Gu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kenneth S. Coley
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jayasree Biswas.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Manuscript submitted April 4, 2021; accepted August 13, 2021.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Biswas, J., Gu, K. & Coley, K.S. A Decarburization Model for a Fe–C Droplet Reacting in Oxidizing Slag. Metall Mater Trans B 52, 3888–3906 (2021). https://doi.org/10.1007/s11663-021-02303-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11663-021-02303-6

Search

Navigation