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Critical Assessment of P2O5 Activity Coefficients in CaO-based Slags during Dephosphorization Process of Iron-based Melts

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Abstract

According to the experimental results of hot metal dephosphorization by CaO-based slags at a commercial-scale hot metal pretreatment station, activity \( a_{{{\text{P}}_{ 2} {\text{O}}_{ 5} }} \) of P2O5 in the CaO-based slags has been determined using the calculated comprehensive mass action concentration \( N_{{{\text{Fe}}_{t} {\text{O}}}}^{{}} \) of iron oxides by the ion and molecule coexistence theory (IMCT) for representing the reaction ability of Fe t O, i.e., activity of \( a_{{{\text{Fe}}_{t} {\text{O}}}}^{{}} \). The collected ten models from the literature for predicting activity coefficient \( \gamma_{{{\text{P}}_{ 2} {\text{O}}_{ 5} }} \) of P2O5 in CaO-based slags have been evaluated based on the determined activity \( a_{{{\text{P}}_{ 2} {\text{O}}_{ 5} }} \) of P2O5 by the IMCT as the criterion. The collected ten models of activity coefficient \( \gamma_{{{\text{P}}_{ 2} {\text{O}}_{ 5} }} \) of P2O5 in CaO-based slags can be described in the form of a linear function as \( \log \gamma_{{{\text{P}}_{ 2} {\text{O}}_{ 5} }} \equiv y = c_{0} + c_{1} x \), in which independent variable \( x \) represents the chemical composition of slags, intercept \( c_{0} \) including the constant term depicts temperature effect and other unmentioned or acquiescent thermodynamic factors, and slope \( c_{1} \) is regressed by the experimental results. Thus, a general approach for obtaining good prediction results of activity \( a_{{{\text{P}}_{ 2} {\text{O}}_{ 5} }} \) of P2O5 in CaO-based slags is proposed by revising the constant term in intercept \( c_{0} \) for the collected ten models. The better models with an ideal revising possibility or flexibility in the collected ten models have been selected and recommended.

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Abbreviations

a i :

Activity of component i in slags or element i in liquid iron, (–)

\( a_{{{\text{R, }}i}} \) :

Activity of components i in slags or element i in liquid iron relative to pure solid or liquid component i or element i as standard state with mole fraction \( x_{i} \) as concentration unit and following Raoult’s law under the condition of taking ideal solution as reference state, i.e., \( a{_{{\rm R},i}} = x{_{i}} \gamma{_{i}} \), (–)

\( a_{\%,{{i}}} \) :

Activity of element i in liquid iron referred to 1 mass percentage of element i as a standard state with mass percentage [pct i] as a concentration unit and obeying Henry’s law under the condition of taking the infinitely dilute ideal solution as a reference state, i.e., \( a_{\%,{{i}}} = [{\text{pct }}i]f_{\%,{{i}}} \), (–)

\( c_{0} \) :

Coefficient of intercept in linear function of \( y = c_{0} + c_{1} x \), (–)

\( c^{\prime}_{0} \) :

Coefficient of intercept in linear function of \( y_{{}}^{\prime} = c_{0}^{\prime} + c_{1}^{\prime} x \), (–)

\( c_{1} \) :

Coefficient of slope in linear function of \( y = c_{0} + c_{1} x \), (–)

\( c^{\prime}_{1} \) :

Coefficient of slope in linear function of \( y_{{}}^{\prime} = c_{0}^{\prime} + c_{1}^{\prime} x \), (–)

\( d_{0}^{{}} \) :

Coefficient of intercept in linear function of \( \log \gamma_{{{\text{P}}_{ 2} {\text{O}}_{ 5} ,{\text{ predicted}}}}^{{}} = d_{0}^{{}} + d_{1}^{{}} \log \gamma_{{{\text{P}}_{ 2} {\text{O}}_{ 5} ,{\text{determined}}}}^{{}} \), (–)

\( d_{1}^{{}} \) :

Coefficient of slope in linear function of \( \log \gamma_{{{\text{P}}_{ 2} {\text{O}}_{ 5} ,{\text{ predicted}}}}^{{}} = d_{0}^{{}} + d_{1}^{{}} \log \gamma_{{{\text{P}}_{ 2} {\text{O}}_{ 5} ,{\text{determined}}}}^{{}} \), (–)

\( f_{\%,{{i}}} \) :

Activity coefficient of element i in liquid iron related with activity \( a_{\%,{{i}}}\), (–)

\( \Delta_{\text{r}} G_{{{\text{m, }}i}}^{\Theta } \) :

Standard molar Gibbs free energy change of reaction for forming component i or structural unit i, (J/mol)

\( K_{i}^{\Theta } \) :

Standard equilibrium constant of chemical reaction for forming component i or structural unit i, (–)

M i :

Relative atomic mass of element i or relative molecular mass of component i, (–)

m :

Number of experimental points, (–)

\( p_{i} \) :

Partial pressure of species i in gaseous phase, (Pa)

\( p^{\Theta } \) :

Standard pressure of gas at sea level and 273 K as 101,325 Pa, (Pa)

R :

Gas constant, (8.314 J/(mol·K))

\( R^{2} \) :

Adjusted parameter of the regressed function, (–)

T :

Absolute temperature, (K)

\( x \) :

Independent variable, (–)

\( x_{i} \) :

Mole fraction of component i, (–)

\( y \) :

Dependent variable, (–)

\( y_{{}}^{\prime} \) :

Dependent variable, (–)

\( \Delta y \) :

Disagreements between determined and predicted results of \( \log \gamma_{{{\text{P}}_{ 2} {\text{O}}_{ 5} }} \), i.e., \( \Delta y = \Delta \log \gamma_{{{\text{P}}_{ 2} {\text{O}}_{ 5} }} = \left| {y - y^{\prime} } \right| = \left| {c_{0} - c_{0}^{\prime} } \right| \), (–)

\( \overline{\Delta y} \) :

Mean disagreements between determined and predicted results of \( \log \gamma_{{{\text{P}}_{ 2} {\text{O}}_{ 5} }} \) for m experimental points, i.e., \( \overline{\Delta y} = \frac{{\Delta \log \gamma_{{{\text{P}}_{ 2} {\text{O}}_{ 5} }} }}{m} = \frac{{\left| {y - y_{{}}^{\prime\prime} } \right|}}{m} = \frac{{\left| {\Delta y} \right|}}{m} \), (–)

(pct i):

Mass percentage of component i in slags, (\( \times \)10−2, –)

[pct i]:

Mass percentage of element i in liquid iron, (\( \times \)10−2, –)

(i):

Species i in slag phase, (–)

[i]:

Species i in liquid iron phase, (–)

\( \varLambda \) :

Optical basicity of slags, (–)

\( \varLambda_{i} \) :

Optical basicity of component i in slags, (–)

\( \delta_{{{\text{slope, }}\gamma_{{{\text{P}}_{ 2} {\text{O}}_{ 5} }} }} \) :

Deviation of slope \( c_{1}^{\prime} \) relative to measured slope \( c_{1}^{{}} \) as a basis, defined as \( \delta_{{{\text{slope, }}\gamma_{{{\text{P}}_{ 2} {\text{O}}_{ 5} }} }} = \frac{{\left| {c_{1}^{{}} - c_{1}^{\prime} } \right|}}{{c_{1}^{{}} }} \times 100 \), (\( \times \)10−2, –)

\( \delta_{\text{slope}}^{{}} \) :

Deviation of slope \( d_{1}^{{}} \) relative to 1.0 as a basis, defined as \( \delta_{\text{slope}}^{{}} = \sum {\left( {\frac{{\left| {1.0 - d_{1}^{{}} } \right|}}{1.0}} \right)} \times 100 \), (\( \times \)10−2, –)

\( \delta_{{\gamma_{{{\text{P}}_{ 2} {\text{O}}_{ 5} }} }} \) :

Mean deviation of \( \log \gamma_{{{\text{P}}_{ 2} {\text{O}}_{ 5} }} \) between determined and predicted ones by model for m points, defined as \( \delta_{{\gamma_{{{\text{P}}_{ 2} {\text{O}}_{ 5} }} }} = \frac{1}{m}\sum {\left( {\frac{{\left| {\log \gamma_{{{\text{P}}_{ 2} {\text{O}}_{ 5} ,{\text{determined}}}}^{{}} - \log \gamma_{{{\text{P}}_{ 2} {\text{O}}_{ 5} ,{\text{ predicted}}}}^{i} } \right|}}{{\left| {\log \gamma_{{{\text{P}}_{ 2} {\text{O}}_{ 5} ,{\text{determined}}}}^{{}} } \right|}}} \right)} \times 100 \), (\( \times \)10−2, –)

References

  1. A. Bergman and A. Gstafsson: Steel Res., 1988, vol. 59, no. 7, pp. 281-8.

    Google Scholar 

  2. R. Selin. Ph.D. Dissertation, Royal Institute of Technology, Stockholm, 1987.

  3. R. Selin: Scand. J. Metall., 1991, vol. 20, no. 5, pp. 279-99.

    Google Scholar 

  4. E. Schürmann and H. Fischer: Steel Res., 1991, vol. 62, pp. 338-45.

    Google Scholar 

  5. X.M. Yang, J.Y. Li, G.M. Chai, D.P. Duan, and J. Zhang: Metall. Mater. Trans. B, 2016, DOI:10.1007/s11663-016-0653-6.

    Google Scholar 

  6. X.M. Yang, J.P. Duan, C.B. Shi, M. Zhang, Y.L Zhang, and J.C. Wang: Metall. Mater. Trans. B, 2011, 42B, no. 4, pp. 738-70.

    Article  Google Scholar 

  7. X.M. Yang, C.B. Shi, M. Zhang, J.P. Duan, and J. Zhang: Metall. Mater. Trans. B, 2011, 42B, no. 5, pp. 951-76.

    Article  Google Scholar 

  8. X.M. Yang, M. Zhang, G.M. Chai, J.Y. Li, and J. Zhang: Ironmaking Steelmaking, 2015, 10.1179/1743281215Y.0000000032

    Google Scholar 

  9. E.T. Turkdogan and J. Pearson: J. Iron Steel Inst., 1953, vol. 175, no. 12, pp. 398-401.

    Google Scholar 

  10. E.T. Turkdogan and J. Pearson: J. Iron Steel Inst., 1954, vol. 176, no. 1, pp. 59-63.

    Google Scholar 

  11. H. Suito, R. Inoue, and M. Takada: Trans. ISIJ, 1981, vol. 21, no. 4, pp. 250-9.

    Article  Google Scholar 

  12. H. Suito, R. Inoue, and M. Takada: Tetsu-to-Hagané, 1981, vol. 67, no. 16, pp. 2645-54.

    Google Scholar 

  13. H. Suito and R. Inoue: Trans. ISIJ, 1982, vol. 22, no. 11, pp. 869-77.

    Article  Google Scholar 

  14. T. Mori: Bull. Jap. Inst. Metals, 1984, vol. 23, no. 4, pp. 354-61.

    Article  Google Scholar 

  15. T. Mori: Trans. Jpn. Inst. of Met., 1984, vol. 25, no. 11, pp. 761-71.

    Article  Google Scholar 

  16. T. Ting, H.G. Katayama, and A. Tanaka: Tetsu-to-Hagané, 1986, vol. 77, no. 2, pp. 225-32.

    Google Scholar 

  17. D.R. Gaskell: Metall. Trans. B, 1989, vol. 20B, no. 1, pp. 113-8.

    Article  Google Scholar 

  18. T. Usui, K. Yamada, Y. Kawal, S. Inoue, H. Hiroaki, and Y. Nimura: Tetsu-to-Hagané, 1991,vol. 77, no. 10, pp. 1641-8.

    Google Scholar 

  19. H. Suito and R. Inoue: ISIJ Int., 1995, vol. 35, no. 3, pp. 258-65.

    Article  Google Scholar 

  20. E.T. Turkdogan: ISIJ Int., 2000, vol. 40, no. 10, pp. 964-70.

    Article  Google Scholar 

  21. S. Basu, A.K. Lahiri, and S. Seetharaman: ISIJ Int., 2007, vol. 47, no. 8, pp. 1236-8.

    Article  Google Scholar 

  22. X.M. Yang, J.Y. Li, G.M. Chai, D.P. Duan, and J. Zhang: Metall. Mater. Trans. B, 2016, DOI:10.1007/s11663-016-0652-7.

    Google Scholar 

  23. X.M. Yang, J.S. Jiao, R.C. Ding, C.B. Shi, and H.J. Guo: ISIJ Int., 2009, 49, no. 12, pp. 1828-37.

    Article  Google Scholar 

  24. C.B. Shi, X.M. Yang, J.S. Jiao, C. Li, and H.J. Guo: ISIJ Int., 2010, 50, no. 10, pp. 1362-72.

    Article  Google Scholar 

  25. X.M. Yang, C.B. Shi, M. Zhang, G.M. Chai, and F. Wang: Metall. Mater. Trans. B, 2011, 42B, no. 6, pp. 1150-80.

    Article  Google Scholar 

  26. X.M. Yang, C.B. Shi, M. Zhang, G.M. Chai, and J. Zhang: Metall. Mater. Trans. B, 2012, 43B, no. 2, pp. 241-66.

    Article  Google Scholar 

  27. X.M. Yang, C.B. Shi, M. Zhang, and J. Zhang: Steel Res. Int., 2012, 83, no. 3, pp. 244-58.

    Article  Google Scholar 

  28. X.M. Yang, M. Zhang, J.L. Zhang, P.C. Li, J.Y. Li, and J. Zhang: Steel Res. Int., 2014, 85, no. 3, pp. 347-75.

    Article  Google Scholar 

  29. X.M. Yang, J.Y. Li, G.M. Chai, M. Zhang, and J. Zhang: Metall. Mater. Trans. B, 2014, 45B, no. 6, pp. 2118-37.

    Article  Google Scholar 

  30. J.Y. Li, M. Zhang, M. Guo, and X.M. Yang: Metall. Mater. Trans. B, 2014, 45B, no. 5, pp. 1666-82.

    Article  Google Scholar 

  31. X.M. Yang, J.Y. Li, M. Zhang, and J. Zhang: Ironmaking Steelmaking, 2016, vol. 43, no. 1, pp. 39-55.

    Article  Google Scholar 

  32. J. Zhang: Computational Thermodynamics of Metallurgical Melts and Solutions, Metallurgical Industry Press, Beijing, China, 2007.

    Google Scholar 

  33. J.X. Chen: Handbook of Common Figures, Tables and Data for Steelmaking, 2nd ed., Metallurgical Industry Press, Beijing, China, 2010.

    Google Scholar 

  34. H. Suito and R. Inoue: Trans. ISIJ, 1984, 24, no. 4, pp. 301-7.

    Article  Google Scholar 

  35. S. Ban-ya and S. Matoba: Tetsu-to-Hagané, 1962, vol. 48, no. 8, pp. 925-32.

    Google Scholar 

  36. X.H. Huang: Principles of Ironmaking and Steelmaking, 3rd ed., Metallurgical Industry Press, Beijing, China, 2005.

    Google Scholar 

  37. A.S. Venkatadri, C.R. Srinivasan, and S.K. Gupta: Sand. J. Metall., 1989, vol. 18, no. 2, pp. 89-94.

    Google Scholar 

  38. D.J. Sosinsky and I.D. Sommerville: Metall. Trans. B, 1986, vol. 17B, no. 2, pp. 331-7.

    Article  Google Scholar 

  39. T. Nakamura, Y. Ueda, and J.M. Toguri: Proc. Third Int. Conf. Metall. Slags and Fluxes, University of Strathclyde, The Institute of Metals, London, UK. 1988. pp. 146–49.

  40. K.C. Mills and S. Sridhar: Ironmaking Steelmaking, 1999, vol. 26, no. 4, pp. 262-8.

    Article  Google Scholar 

  41. J.A. Duffy and M.D. Ingram: J. Am. Chem. Soc., 1971, vol. 93, no. 24, pp 6448-54.

    Article  Google Scholar 

  42. J.A. Duffy and M.D. Ingram: J. Inorg. Nucl. Chem., 1975, vol. 37, no. 5, pp. 1203-6.

    Article  Google Scholar 

  43. J.A. Duffy, M.D Ingram, and I.D. Sommerville: J. Chem. Soc., Faraday Trans., I, 1978, vol. 74, pp. 1410-9.

    Article  Google Scholar 

  44. J.A. Duffy: Geochimica et Cosmochimica Acta, 1993, vol. 57, no. 16, pp. 3961-70.

    Article  Google Scholar 

  45. K.C. Mills: in Basicity and Optical basicities of Slags (Chapter 2), in Slag Atlas, 2nd ed., Ed. V. D. Eisenhüttenleute, Woodhead Publishing Limited, Abington Hall, Abington, Cambridge, CB21 6AH, UK. 1995. pp. 9–19.

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (NSFC) under Grant No. 51174186.

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Authors and Affiliations

  1. Key Laboratory of Green Process and Engineering, Institute of Process Engineering, Chinese Academy of Sciences, Beijing, 100190, P.R. China

    Xue-min Yang (Research Professor), Jin-yan Li (Ph.D. Candidate and Joint-Training Student), Guo-Ming Chai (Engineer, Ph. D. Candidate) & Dong-ping Duan (Research Professor)

  2. School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing, 100083, P.R. China

    Jin-yan Li (Ph.D. Candidate and Joint-Training Student) & Jian Zhang (Professor Emeritus)

  3. No. 2 Steelmaking Plant, Shanxi Taigang Stainless Steel Corporation Limited, Taiyuan, 030003, P.R. China

    Guo-Ming Chai (Engineer, Ph. D. Candidate)

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  1. Xue-min Yang
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Correspondence to Xue-min Yang.

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Manuscript submitted October 2, 2015.

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Yang, Xm., Li, Jy., Chai, GM. et al. Critical Assessment of P2O5 Activity Coefficients in CaO-based Slags during Dephosphorization Process of Iron-based Melts. Metall Mater Trans B 47, 2330–2346 (2016). https://doi.org/10.1007/s11663-016-0654-5

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