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A Thermodynamic Model of Sulfur Distribution Ratio between CaO–SiO2–MgO–FeO–MnO–Al2O3 Slags and Molten Steel during LF Refining Process Based on the Ion and Molecule Coexistence Theory

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Abstract

A thermodynamic model for calculating the sulfur distribution ratio between ladle furnace (LF) refining slags and molten steel has been developed by coupling with a developed thermodynamic model for calculating the mass action concentrations of structural units in LF refining slags, i.e., CaO–SiO2–MgO–FeO–MnO–Al2O3 hexabasic slags, based on the ion and molecule coexistence theory (IMCT). The calculated mass action concentrations of structural units in CaO–SiO2–MgO–FeO–Al2O3–MnO slags equilibrated or reacted with molten steel show that the calculated equilibrium mole numbers or mass action concentrations of structural units or ion couples, rather than mass percentage of components, in the slags can represent their reaction abilities. The calculated total sulfur distribution ratio shows a reliable agreement with the measured or the calculated sulfur distribution ratio between the slags and molten steel by other models under the condition of choosing oxygen activity based on (FeO)–[O] equilibrium. Meanwhile, the developed thermodynamic model for calculating sulfur distribution ratio can quantitatively determine the respective contribution of free CaO, MgO, FeO, and MnO in the LF refining slags. A significant difference of desulfurization ability among free component as CaO, MgO, FeO, and MnO has been found with approximately 87–93 pct, 11.43–5.85 pct, 0.81–0.60 pct and 0.30–0.27 pct at both middle and final stages during LF refining process, respectively. A large difference of oxygen activity is found in molten steel at the slag–metal interface and in bulk molten steel. The oxygen activity in molten steel at the slag–metal interface is controlled by (FeO)–[O] equilibrium, whereas the oxygen activity in bulk molten steel is controlled by [Al]–[O] equilibrium. Decreasing the high-oxygen-activity boundary layer beneath the slag–metal interface can promote the desulfurization reaction rate effectively or shorten the refining period during the LF refining process.

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Abbreviations

A :

constant, (–)

a i :

activity of component i in molten steel or slags, (–)

a O,interface :

oxygen activity of molten steel at slag–metal interface, (–)

a O,bath :

oxygen activity of bulk molten steel, (–)

a O,sensor :

measured oxygen activity in molten steel by oxygen sensor, (–)

a O,[Al]–[O] :

calculated oxygen activity of bulk molten steel based on [Al]–[O] equilibrium, (–)

\( a_{{{\text{O,}}\left( {{\text{Al}}_{2} {\text{O}}_{3} } \right) - [{\text{O}}]}} \) :

calculated oxygen activity of molten steel at slag–metal interface based on (Al2O3)–[O] equilibrium, (–)

a O,(FeO)–[O] :

calculated oxygen activity of molten steel at slag–metal interface based on (FeO)–[O] equilibrium, (–)

\( a_{{{\text{O}}^{2 - } }} \) :

oxygen ion activity in slags, (–)

b i :

mole number of component i in 100-g slags, (mol)

B :

constant, (–)

\( C_{{{\text{S}}^{2 - } }} \) :

sulfide capacity of the slags, (–)

\( e_{i}^{j} \) :

activity interaction coefficient of component j on component i in molten steel based on mass percentage as concentration unit and one mass percent (1 pct) as standard state, (–)

f i :

activity coefficient of component i in molten steel, (–)

\( \Updelta_{\text{r}} G_{{{\text{m,}}i}}^{\Uptheta } \) :

standard molar Gibbs free energy change of forming component i or structural unit i in slags, (J/mol)

\( \Updelta_{\text{r}} G_{{{\text{m,}}i({\text{s}})}}^{\Uptheta } \) :

standard molar Gibbs free energy change of forming component i as solid, (J/mol)

\( \Updelta_{\text{fus}} G_{{{\text{m,}}i}}^{\Uptheta } \) :

standard molar Gibbs free energy change of melting component i or structural unit i from solid to liquid, (J/mol)

\( \Updelta_{\text{sol}} G_{{{\text{m,}}i}}^{\Uptheta } \) :

standard molar Gibbs free energy change of dissolving component i or structural unit i into slags, (J/mol)

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

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

L S :

sulfur distribution ratio between slags and molten steel, (–)

L S,i :

calculated respective sulfur distribution ratio of free component i or ion couple i in slags, (–)

L S,measured :

measured sulfur distribution ratio, (–)

L S,calculated :

calculated total sulfur distribution ratio between slags and molten steel, (–)

L S,i, measured :

calculated respective sulfur distribution ratio of component i or ion couple i in slags from measured data, (–)

\( L_{\text{S,calculated}}^{\text{IMCT}} \) :

calculated total sulfur distribution ratio between slags and molten steel by the IMCT model, (–)

\( L_{\text{S,calculated}}^{{[{\text{Al}}] - [{\text{O}}]}} \) :

calculated total sulfur distribution ratio between slags and molten steel based on [Al]–[O] equilibrium for determining activity of oxygen at slag–metal interface a O,interface, (–)

\( L_{\text{S,calculated}}^{{\left( {{\text{Al}}_{2} {\text{O}}_{3} } \right) - [{\text{O}}]}} \) :

calculated total sulfur distribution ratio between slags and molten steel based on (Al2O3)–[O] equilibrium for determining activity of oxygen at slag–metal interface a O,interface, (–)

\( L_{\text{S,calculated}}^{{\left( {\text{FeO}} \right) - [{\text{O}}]}} \) :

calculated total sulfur distribution ratio between slags and molten steel based on (FeO)–[O] equilibrium for determining activity of oxygen at slag–metal interface a O,interface, (–)

\( L_{\text{S,calculated}}^{{\left( {\text{FeO}} \right) - [{\text{O}}],{\text{IMCT}}}} \) :

calculated total sulfur distribution ratio between slags and molten steel by the IMCT model based on (FeO)–[O] equilibrium for determining activity of oxygen at slag–metal interface a O,interface, (–)

\( L_{\text{S,calculated}}^{{\left( {\text{FeO}} \right) - [{\text{O}}],{\text{Young}}}} \) :

calculated total sulfur distribution ratio between slags and molten steel by Young’s model based on (FeO)–[O] equilibrium for determining activity of oxygen at slag–metal interface a O,interface, (–)

\( L_{\text{S,calculated}}^{{\left( {\text{FeO}} \right) - [{\text{O}}],{\text{KTH}}}} \) :

calculated total sulfur distribution ratio between slags and molten steel by the KTH model based on (FeO)–[O] equilibrium for determining activity of oxygen at slag–metal interface a O,interface, (–)

\( L_{{\text{S}},i, {\text{calculated}}}^{{\left( {\text{FeO}}\right) - [{\text{O}}],{\text{IMCT}}}} \) :

calculated respective sulfur distribution ratio of component i or ion couple i in slags by the IMCT model based on (FeO)–[O] equilibrium for determining activity of oxygen at slag–metal interface a O,interface, (–)

Me:

metal, (–)

M i :

molecular weight of element i or component i, (g/mol)

\( n_{i}^{0} \) :

mole number of components i in 100-g slags, (mol)

n i :

equilibrium mole number of structural unit i or ion couple i in 100-g slags based on IMCT, (mol)

N i :

mass action concentrations of structural unit i or ion couple i in the slags based on IMCT, (–)

Σn i :

total equilibrium mole number of all structural units in 100-g slags based on IMCT, (mol)

R :

gas constant, (8.314 J/(mol·K))

T :

absolute temperature, (K)

X i :

mole fraction of component i in the slags, (–)

(pct i):

mass percentage of component i in slags, (–)

[pct i]:

mass percentage of component i in molten steel, (–)

(pct S)CaS :

sulfur content in slags boned as CaS, (–)

(pct S)MgS :

sulfur content in slags boned as MgS, (–)

(pct S)FeS :

sulfur content in slags boned as FeS, (–)

(pct S)MnS :

sulfur content in slags boned as MnS, (–)

\( \Uplambda \) :

optical basicity of slags (–)

\( \xi_{\text{interaction}}^{i - j} \) :

interaction coefficient of component i to component j in slags defined in the KTH model, (–)

\( \mu_{i(\rm s)}^{ * } \) :

chemical potential of component i as solid, (J/mol)

\( \mu_{i(1)}^{ * } \) :

chemical potential of component i as liquid, (J/mol)

\( \mu_{i}^{\Uptheta } \) :

standard chemical potential of dissolved component i in slags, (J/mol)

ci :

complex molecule i, (–)

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Acknowledgments

The authors sincerely appreciate Prof. Jian Zhang, who is a founder of the ion and molecule theory, for providing helpful discussions and encouragement. The sincere thanks are also extended to Prof. Chang–xiang Xiang, on metallurgical physicochemistry at the School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, for valuable discussion and helps for preparing Section III–B–4 on deciding the standard molar Gibbs free energy change of related reactions. Meanwhile, heartfelt thanks are also extended to Shougang Qian’an Iron and Steel Company Limited for carrying out the industrial experiments and permitting the authors to publish the related results.

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Authors and Affiliations

  1. State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences, Beijing, 100190, P. R. China

    Xue-Min Yang (Research Professor)

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

    Cheng-Bin Shi (Ph.D. Candidate and Joint-Training Student), Meng Zhang (Master Degree Student and Joint-Training Student), Guo-Ming Chai (Ph.D. Candidate and Joint-Training Student) & Fei Wang (Ph.D. Candidate and Joint-Training Student)

  3. Institute of Process Engineering, Chinese Academy of Sciences, Beijing, 100190, P. R. China

    Cheng-Bin Shi (Ph.D. Candidate and Joint-Training Student), Meng Zhang (Master Degree Student and Joint-Training Student), Guo-Ming Chai (Ph.D. Candidate and Joint-Training Student) & Fei Wang (Ph.D. Candidate and Joint-Training Student)

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  1. Xue-Min Yang
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Manuscript submitted January 15, 2011.

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Yang, XM., Shi, CB., Zhang, M. et al. A Thermodynamic Model of Sulfur Distribution Ratio between CaO–SiO2–MgO–FeO–MnO–Al2O3 Slags and Molten Steel during LF Refining Process Based on the Ion and Molecule Coexistence Theory. Metall Mater Trans B 42, 1150–1180 (2011). https://doi.org/10.1007/s11663-011-9547-9

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