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A Critical Review of Limitations of Slag Capacity Concepts in Metallurgical Applications by Taking Sulfide and Phosphate Capacities as Examples

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Abstract

The desulfurization and dephosphorization performances have been considered to be the most challenging operations for refining ultra-clean steel. The distribution ratios of sulfur and phosphorus in the form of \( L_{i} = {{\left( {\% \, i} \right)} \mathord{\left/ {\vphantom {{\left( {\% \, i} \right)} {\left[ {\% \, i} \right]}}} \right. \kern-0pt} {\left[ {\% \, i} \right]}} \) as well as slag capacity concepts of sulfide and phosphate capacities in the form of \( C_{{i^{m - } }} \propto (\% \, i^{m - } ) \) have been extensively studied and widely applied for the description of desulfurization and dephosphorization abilities and potentials, respectively. However, the intrinsic limitations of two slag capacity concepts as sulfide and phosphate capacities regardless of slag oxygen potential \( p_{{{\text{O}}_{2} }} \) have seriously limited their direct applications into guiding the practical refining operations compared with the partitions or distribution ratios \( L_{i} \). The theoretical limitations of sulfide and phosphate capacities have been extensively reviewed and critically assessed by comparison with the distribution ratios \( L_{i} \) in this contribution by taking two preferred thermodynamic conditions of both basic oxides concentration or slag basicity and slag oxygen potential as criteria. Meanwhile, the merits of two slag capacity concepts as measures for describing slag basicity like optical basicity have also been reviewed to be disruptive because the ratios of activity of free oxygen ion \( a_{{{\text{O}}^{2 - } }} \) in slags to activity coefficients \( f_{{{\text{H}},i}} \) of sulfide and monomer phosphate \( {\text{PO}}_{4}^{3 - } \) in slags as implicit parameters in the defined two slag capacity concepts cannot hold constants in most complex slags. Furthermore, the limitations of phosphate capacity in two ways have been restated. Moreover, the oxygen potential \( p_{{{\text{O}_{2}} }} \) shows a great effect on plots of the desulfurization and dephosphorization abilities against two slag capacity concepts of slags at a given temperature. The abnormally higher oxygen potential \( p_{{{\text{O}_{2}} }} \) can result in a suppression of the desulfurization ability of slags with a greater desulfurization potential, while the unreasonably smaller oxygen potential \( p_{{{\text{O}_{2}} }} \) can lead to a diminishing of the dephosphorization ability of slags with a larger dephosphorization potential. It has been verified by five case-studies covering desulfurization and dephosphorization operations that the partitions or distribution ratios \( L_{i} \) related to equilibrium quotients \( k_{i} \) of desulfurization and dephosphorization reactions of Fe-based melts by slags can be in good accordance with two preferred thermodynamic conditions. The reasonable application of two slag capacity concepts is recommended to estimate or determine the distribution ratios between slags and Fe-based melts with the aid of activity \( a_{{\% ,{\text{O}}}} \) of oxygen and activity coefficient \( f_{\% ,i} \) of sulfur and phosphorus in Fe-base melts.

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Abbreviations

\( a_{i} \) :

Activity of element i or compound i, (–)

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

Activity of element i or compound i relative to pure matter i (l or s or g) as the 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., \( a_{{{\text{R, }}i}} = \gamma_{i} x_{i} \), (–)

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

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

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

Activity of element i relative to hypothetical pure matter i (l or s or g) as the standard state with mole fraction \( x_{i} \) as concentration unit and conforming to Henry’s law under the condition of taking infinitely dilute ideal solution as reference state, i.e., \( a_{{{\text{H, }}i}} = f_{{{\text{H, }}i}} x_{i} \), (–)

B :

Binary slag basicity expressed as \( B = {{(\% {\text{ CaO}})} \mathord{\left/ {\vphantom {{(\% {\text{ CaO}})} {(\% {\text{ SiO}}_{2} )}}} \right. \kern-0pt} {(\% {\text{ SiO}}_{2} )}} \), (–)

\( B^{\prime} \) :

Modified binary slag basicity expressed as \( B^{\prime} = {{x_{\text{CaO}} } \mathord{\left/ {\vphantom {{x_{\text{CaO}} } {x_{{{\text{SiO}}_{2} }} }}} \right. \kern-0pt} {x_{{{\text{SiO}}_{2} }} }} \), (–)

\( B_{\text{carb}} \) :

Suggested slag basicity from carbonate capacity ratio as \( B_{\text{carb}} = {{C_{{{\text{CO}}_{3}^{2 - } }} } \mathord / {\vphantom {{C_{{{\text{CO}}_{3}^{2 - } }} } {C_{{{\text{CO}}_{3}^{2 - } }}^{ * } }}} \kern-0pt {C_{{{\text{CO}}_{3}^{2 - } }}^{ * } }} \) by Wagner, (–)

\( B_{\text{sulf}} \) :

Suggested slag basicity from sulfide capacity ratio as \( B_{\text{sulf}} = {{C_{{{\text{S}}^{2 - } }} } \mathord / {\vphantom {{C_{{{\text{S}}^{2 - } }} } {C_{{{\text{S}}^{2 - } }}^{ * } }}} \kern-0pt {C_{{{\text{S}}^{2 - } }}^{ * } }} \) by Wagner, (–)

\( {\text{CB}}i \) :

Complex slag basicity in the ith expression, (–)

\( {\text{BO}}i \) :

Equivalent basic oxides of components in the ith expression or named as “excess base” by Chipman, (–)

\( B^{\text{xs}} \) :

Excess base related to the ion-oxygen attractions for oxides expressed as \( B^{\text{xs}} = \Sigma \left( {x_{i} b_{i} } \right) \), (–)

\( b_{i} \) :

Coefficient of oxide i related to defined excess base as \( B^{\text{xs}} \), (–)

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

Sulfide capacity of slags based on gas–slag equilibrium, or expressed as \( C_{{{\text{S}}^{2 - } }}^{\text{I}} \), (–)

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

Sulfide capacity index of slags based on slag–metal equilibrium, or expressed as \( C_{{{\text{S}}^{2 - } }}^{\text{II}} \), (–)

\( C_{{{\text{PO}}_{4}^{3 - } }} \) :

Phosphate capacity of slags based on gas–slag equilibrium, or expressed as \( C_{{{\text{PO}}_{4}^{3 - } }}^{\text{I}} \), (–)

\( C_{{{\text{PO}}_{4}^{3 - } ,{\text{ index}}}} \) :

Phosphate capacity index of slags based on slag–metal equilibrium, or expressed as \( C_{{{\text{PO}}_{4}^{3 - } }}^{\text{II}} \), (–)

\( C_{{i^{m - } }} \) :

Capacity of anionic ion \( i^{m - } \) with m– valence absorbed impurity in slags from gas–slag reaction, which is described as \( C_{{i^{m - } }} \propto (\% \, i^{m - } ) \), (–)

\( C_{{i^{m - } , {\text{ index}}}} \) :

Capacity index of anionic ion \( i^{m - } \) with m– valence absorbed impurity in slags from slag–metal reaction, which is described as \( C_{{i^{m - } }} \propto (\% \, i^{m - } ) \), (–)

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

First-order activity interaction coefficient of element j to element i related to activity coefficient \( f_{\%,i} \), (–)

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

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

\( f_{{{\text{H, }}i}} \) :

Activity coefficient of element i in liquid iron related to activity \( a_{{{\text{H, }}i}} \), (–)

\( f\left( {i,j} \right) \) :

Function with i and j as independent variables, (–)

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

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

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

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

\( k_{i} \) :

Equilibrium quotient of chemical reaction for forming component i or structural unit i, (–)

\( L_{\text{S}} \) :

Sulfur partition or distribution ratio between slags and liquid iron, defined as \( L_{\text{S}} = {{(\% {\text{ S}})} \mathord{\left/ {\vphantom {{(\% {\text{ S}})} {[\% {\text{ S]}}}}} \right. \kern-0pt} {[\% {\text{ S]}}}} \), (–)

\( L_{\text{P}} \) :

Phosphorus partition or distribution ratio between slags and liquid iron, defined as \( L_{\text{P}} = {{(\% {\text{ P}}_{2} {\text{O}}_{5} )} \mathord / {\vphantom {{(\% {\text{ P}}_{2} {\text{O}}_{5} )} {[\% {\text{ P}}]^{2} }}} \kern-0pt {[\% {\text{ P}}]^{2} }} \), (–)

\( L_{\text{P}}^{\text{II}} \) :

Phosphorus partition or distribution ratio between slags and liquid iron, defined as \( {{L_{\text{P}}^{\text{II}} = (\% {\text{ PO}}_{4}^{3 - } )} \mathord{\left/ {\vphantom {{L_{\text{P}}^{\text{II}} = (\% {\text{ PO}}_{4}^{3 - } )} {[\% {\text{ P]}}}}} \right. \kern-0pt} {[\% {\text{ P]}}}} \equiv L_{\text{P}}^{\text{III}} \), (–)

\( L_{\text{P}}^{\text{IV}} \) :

Phosphorus partition or distribution ratio between slags and liquid iron, defined as \( L_{\text{P}}^{\text{IV}} = {{(\% {\text{ P}}_{2} {\text{O}}_{5} )} \mathord{\left/ {\vphantom {{(\% {\text{ P}}_{2} {\text{O}}_{5} )} {[\% {\text{ P]}}}}} \right. \kern-0pt} {[\% {\text{ P]}}}} \), (–)

\( L_{\text{P}}^{\text{V}} \) :

Phosphorus partition or distribution ratio between slags and liquid iron, defined as \( L_{\text{P}}^{\text{V}} = {{(\% {\text{ P}})} \mathord{\left/ {\vphantom {{(\% {\text{ P}})} {[\% {\text{ P]}}}}} \right. \kern-0pt} {[\% {\text{ P]}}}} \), (–)

\( M_{i} \) :

Relative atomic mass of element or molecule i, (–)

MeO:

Metal oxide as component in slags, (–)

\( n_{{{\text{O}},i}} \) :

Number of oxygen atoms in oxide i related to equivalent mole fraction of cation i \( X_{i} \) (–)

\( N_{i} \) :

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

\( N_{{{\text{Fe}}_{t} {\text{O}}}} \) :

Defined comprehensive mass action concentration of iron oxides in slags based on the IMCT, (–)

\( p_{i} \) :

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

\( p^{\Theta } \) :

Standard pressure of gas at sea level and 273 K (0 °C) as 101,325 Pa, (Pa)

R :

Gas constant, (8.314 J/(mol·K))

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

Second-order activity interaction coefficient of element j to element i, (–)

\( r_{i}^{j,k} \) :

Cross-product second-order activity interaction coefficient of element j and k to element i, (–)

T :

Absolute temperature, (K)

\( x_{i} \) :

Mole fraction of component i in slags, (–)

\( X_{i} \) :

Equivalent mole fraction of cation i expressed by \( X_{i} = {{\left( {n_{{{\text{O, }}i}} x_{i} } \right)} \mathord{\left/ {\vphantom {{\left( {n_{{{\text{O, }}i}} x_{i} } \right)} {\varSigma (n_{{{\text{O, }}i}} x_{i} )}}} \right. \kern-0pt} {\varSigma (n_{{{\text{O, }}i}} x_{i} )}} \), (–)

(% i):

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

[% 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, (–)

\( \gamma_{i} \) :

Activity coefficient of component or element i related to activity \( a_{{{\text{R}},i}} \), (–)

\( \varepsilon_{i}^{i} \) :

First-order activity interaction coefficient of component or element i in metallic melts related to activity coefficient \( \gamma_{i} \), (–)

\( \varLambda \) :

Optical basicity of slags, (–)

\( \varLambda_{\text{corr}} \) :

Corrected optical basicity of slags, (–)

\( \varLambda_{i} \) :

Optical basicity of component i in slags, (–)

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

Interaction coefficient of component i to component j in slags embodied in the KTH model, (–)

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Acknowledgments

This work is supported by the Beijing Natural Science Foundation (Grant No. 2182069). The authors wish to express their sincere gratitude to the anonymous peer reviewers for valuable and insightful suggestions, which were adopted in the revised version.

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

    Xue-Min Yang, Jin-Yan Li, Meng Zhang & Jin-Sha Jiao

  2. China Metallurgical Industry Planning and Research Institute, Beijing, 100711, P.R. China

    Jin-Yan Li & Meng Zhang

  3. Hot Rolling Operation Department, Beijing Shougang Company Limited, Qian’an City, 064400, Hebei Province, P.R. China

    Jin-Sha Jiao

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Yang, XM., Li, JY., Zhang, M. et al. A Critical Review of Limitations of Slag Capacity Concepts in Metallurgical Applications by Taking Sulfide and Phosphate Capacities as Examples. Metall Mater Trans B 52, 714–742 (2021). https://doi.org/10.1007/s11663-020-02045-x

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