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A Thermodynamic Model of Phosphate Capacity for CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 Slags Equilibrated with Molten Steel during a Top–Bottom Combined Blown Converter Steelmaking Process Based on the Ion and Molecule Coexistence Theory

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Abstract

A thermodynamic model for predicting the phosphate capacity of CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags at the steelmaking endpoint during an 80-ton top–bottom combined blown converter steelmaking process has been developed based on the ion and molecule coexistence theory (IMCT). The phosphate capacity has a close relationship with the phosphate capacity index, whereas the logarithm of phosphate capacity is 12.724 greater than that of phosphate capacity index at 1873 K (1600 °C). The developed phosphate capacity prediction model can be also used to predict the phosphate capacity index with reliable accuracy compared with the measured and the predicted phosphate capacity index of the slags by other models in literatures. The results from the IMCT phosphate capacity prediction model show that the comprehensive effects of iron oxides and basic components control the dephosphorization reaction with an optimal ratio of (pct FeO)/(pct Fe2O3) as 0.62. The determined contribution ratio of Fe t O, CaO + Fe t O, MgO + Fe t O, and MnO + Fe t O to the phosphate capacity or phosphate capacity index of the slags is approximately 0.0 pct, 99.996 pct, 0.0 pct, and 0.0 pct, respectively. The generated 2CaO·P2O5, 3CaO·P2O5, and 4CaO·P2O5 as products of dephosphorization reactions accounts for 0.016 pct, 96.01 pct, and 3.97 pct of the phosphate capacity or phosphate capacity index of the slags, respectively.

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Abbreviations

a i :

activity of component i in slags or molten steel (−)

\( a_{{{\text{O, (Fe}}_{t} {\text{O)}} - [ {\text{O]}}}}^{\text{interface}} \) :

activity of dissolved oxygen in molten steel at slag–metal interface based on (Fe t O)–[O] equilibrium (−)

B :

binary slag basicity of slags, i.e., the ratio of (pct CaO) to (pct SiO2) (−)

\( B^{'} \) :

ratio of mole fraction between CaO and SiO2 in slags, i.e., \( {{x_{\text{CaO}} } \mathord{\left/ {\vphantom {{x_{\text{CaO}} } {x_{{{\text{SiO}}_{ 2} }} }}} \right. \kern-\nulldelimiterspace} {x_{{{\text{SiO}}_{ 2} }} }} (-) \)

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

phosphate capacity of slags (−)

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

phosphate capacity index of slags (−)

\( C_{{{\text{P}}^{ 3- } }} \) :

phosphide capacity of slags (−)

\( C_{{{\text{P}}^{ 3- } , {\text{ index}}}} \) :

phosphide capacity index of slags defined as \( {{ ( {\text{pct P)}}} \mathord{\left/ {\vphantom {{ ( {\text{pct P)}}} { [ {\text{pct P]}} \cdot [ {\text{pct O]}}^{{{ 5\mathord{\left/ {\vphantom { 52}} \right. \kern-\nulldelimiterspace} 2}}} }}} \right. \kern-\nulldelimiterspace} { [ {\text{pct P]}} \cdot [ {\text{pct O]}}^{{{ 5\mathord{\left/ {\vphantom { 52}} \right. \kern-\nulldelimiterspace} 2}}} }} \) in Suito’s and Young’s model (−)

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

sulfide capacity of slags (−)

\( C_{{{\text{PO}}_{ 4}^{ 3- } }}^{{N_{{{\text{Fe}}_{t} {\text{O}}}} , {\text{ IMCT }}}} \) :

calculated phosphate capacity of slags by IMCT model using \( N_{{{\text{Fe}}_{t} {\text{O}}}} \) to present slag oxidation ability (−)

\( C_{{{\text{PO}}_{ 4}^{ 3- } }}^{{a_{\text{O}} , {\text{ IMCT}}}} \) :

calculated phosphate capacity of slags by IMCT model using \( a_{\text{O}} \) to present molten steel oxidation ability (−)

\( C_{{{\text{PO}}_{ 4}^{ 3- } , {\text{ index}}}}^{{N_{{{\text{Fe}}_{t} {\text{O}}}} , {\text{ IMCT}}}} \) :

calculated phosphate capacity index of slags by IMCT model using \( N_{{{\text{Fe}}_{t} {\text{O}}}} \) to present slag oxidation ability (−)

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

calculated phosphate capacity index of slags by IMCT model using a O to present molten steel oxidation ability (−)

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

measured phosphate capacity of slags (−)

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

measured phosphate capacity index of slags (−)

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

calculated phosphate capacity of slags by model i (−)

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

calculated phosphate capacity index of slags by model i (−)

\( C_{{{\text{PO}}_{ 4}^{ 3- } , { }i , {\text{ calculated}}}}^{\text{IMCT}} \) :

calculated respective phosphate capacity of structural unit i containing P2O5 in slags by IMCT model (−)

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

calculated respective phosphate capacity index of structural unit i containing P2O5 in slags by IMCT model (−)

\( C_{{{\text{PO}}_{ 4}^{ 3- } , { }i , {\text{ measured}}}}^{\text{IMCT}} \) :

calculated respective phosphate capacity of structural unit i containing P2O5 in slags by IMCT model based on measured phosphate capacity \( C_{{{\text{PO}}_{ 4}^{ 3- } , {\text{ measured}}}} \) of slags (−)

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

calculated respective phosphate capacity index of structural unit i containing P2O5 in slags by IMCT model based on measured phosphate capacity index \( C_{{{\text{PO}}_{ 4}^{ 3- } , {\text{ index, measured}}}} \) of slags (−)

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

activity interaction coefficient of component j to component i in molten steel (−)

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 (J/mol)

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

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

L P :

calculated phosphorus distribution ratio between slags and metal phase using \( N_{{{\text{Fe}}_{t} {\text{O}}}} \) to present the slag oxidation ability based on IMCT with the same meaning of \( L_{\text{P, calculated}}^{\text{IMCT}} \) or defined phosphorus distribution ratio between slags and metal phase as \( L_{\text{P}} = {{({\text{pct}} \, {\text{P}}_{ 2} {\text{O}}_{ 5} )} \mathord{/ {\vphantom {{({\text{pct}} \, {\text{P}}_{ 2} {\text{O}}_{ 5} )} {[{\text{pct}} {\text{P]}}^{2} }}} \kern-\nulldelimiterspace} {[{\text{pct}} \,{\text{P]}}^{2} }} \) (–)

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

calculated phosphorus distribution ratio between the slags and metal phase using a O to present the molten steel oxidation ability based on IMCT with the same meaning of \( L_{{{\text{P}},{\text{ calculated}}}}^{{\prime {\text{IMCT}}}} \) or defined phosphorus distribution ratio between the slags and metal phase as \( L_{\text{P}}^{\prime } = {{({\text{pct}}\,{\text{P}}_{ 2} {\text{O}}_{ 5} )} \mathord{\left/ {\vphantom {{({\text{pct}}\,{\text{P}}_{ 2} {\text{O}}_{ 5} )} {[{\text{pct}}\,{\text{P]}}^{2} }}} \right. \kern-\nulldelimiterspace} {[{\text{pct}}\,{\text{P]}}^{2} }} \equiv L_{\text{P}} \) (–)

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

phosphorus distribution ratio between the slags and molten steel defined as \( L_{\text{P}}^{\prime \prime } = {{({\text{pct}}\,{\text{PO}}_{ 4}^{ 3- } )} \mathord{\left/ {\vphantom {{({\text{pct}}\,{\text{PO}}_{ 4}^{ 3- } )} {[{\text{pct}}\,{\text{P]}}}}} \right. \kern-\nulldelimiterspace} {[{\text{pct}}\,{\text{P]}}}} \) (–)

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

phosphorus distribution ratio between the slags and molten steel defined as \( L_{\text{P}}^{\prime \prime \prime } = {{({\text{pct}}\,{\text{P}}_{ 2} {\text{O}}_{ 5} )} \mathord{\left/ {\vphantom {{({\text{pct}}\,{\text{P}}_{ 2} {\text{O}}_{ 5} )} {[{\text{pct}}\,{\text{P]}}}}} \right. \kern-\nulldelimiterspace} {[{\text{pct}}\,{\text{P]}}}} \) (–)

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

measured phosphorus distribution ratio between the slags and metal phase defined as \( L_{\text{P, measured}} = {{({\text{pct}}\,{\text{P}}_{ 2} {\text{O}}_{ 5} )} \mathord{\left/ {\vphantom {{({\text{pct}}\,{\text{P}}_{ 2} {\text{O}}_{ 5} )} {[{\text{pct}}\,{\text{P]}}^{2} }}} \right. \kern-\nulldelimiterspace} {[{\text{pct}}\,{\text{P]}}^{2} }} \) (−)

L S :

sulfur distribution ratio between the slags and metal phase defined as \( L_{\text{S}} = {{({\text{pct}}\,{\text{S}})} \mathord{\left/ {\vphantom {{({\text{pct}}\,{\text{S}})} {[{\text{pct}}\,{\text{S]}}}}} \right. \kern-\nulldelimiterspace} {[{\text{pct}}\,{\text{S]}}}} \) (−)

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

calculated phosphorus distribution ratio between the slags and metal phase by IMCT phosphorus distribution ratio model (−)

M i :

relative elemental mass of element i or component i (−)

n i :

equilibrium mole number of structural unit i or ion couple i in slags (mol)

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

total mole number of all components in 100-g slags before reaction equilibrium according to IMCT (mol)

\( \sum n_{i} \) :

total equilibrium mole number of all structural units in 100-g slags according to IMCT (mol)

N i :

mass action concentration of structural unit i or ion couple i in slags (−)

\( [{\text{pct}}\,{\text{O}}]_{{ ( {\text{Fe}}_{t} {\text{O)}} - [ {\text{O]}}}}^{\text{interface}} \) :

calculated mass percent of dissolved oxygen in molten steel at the slag–metal interface based on (Fe t O)–[O] equilibrium with \( N_{{{\text{Fe}}_{t} {\text{O}}}} \) to express the slag oxidization ability or Fe t O activity (−)

\( [{\text{pct}}\,{\text{O}}]_{{ [ {\text{C]}} - [ {\text{O]}}}}^{\text{bath}} \) :

mass percent of dissolved oxygen in metal bath based on [C]–[O] equilibrium with product of [pct C] and [pct O] as a constant at converter steelmaking temperatures (−)

p i :

partial pressure of component i in gas phase (Pa)

\( p^{\Uptheta } \) :

standard pressure of gas at sea level and 273 K (0 °C) as 101325 Pa (Pa)

\([{\text{pct}}\,{\text{P}}]_{\text{interface}}^{\text{equilibrium}} \) :

mass percent of phosphorus in molten steel at slag–metal interface based on dephosphorization reaction equilibrium (−)

\( ({\text{pct}}\,{\text{P}}_{ 2} {\text{O}}_{ 5} )_{i} \) :

mass percent of P2O5 in generated structural unit i or complex molecule i containing P2O5, such as complex molecule 3CaO·SiO2 and so on, in slags (−)

R :

gas constant, (8.314 J/(mol·K))

T :

absolute temperature (K)

x i :

mole fraction of components i in slags (−)

(pct i):

mass percent of component i in slag phase (−)

[pct i]:

mass percent of component i in metal phase (−)

[pct i]interface :

mass percent of component i in molten steel at slag–metal interface (−)

[pct i]bath :

mass percent of component i in metal phase with the same meaning as [pct i] (−)

\( \Uplambda \) :

optical basicity of slags (−)

\( \Uplambda_{i} \) :

optical basicity of component i in slags (−)

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

  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) & Jian Zhang (Professor)

  3. Technology Center, Shanxi Taigang Stainless Corporation Limited, Taiyuan, 030003, P. R. China

    Jian-Ping Duan (Senior Engineer)

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  1. Xue-Min Yang
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Manuscript submitted March 5, 2011.

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Yang, XM., Shi, CB., Zhang, M. et al. A Thermodynamic Model of Phosphate Capacity for CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 Slags Equilibrated with Molten Steel during a Top–Bottom Combined Blown Converter Steelmaking Process Based on the Ion and Molecule Coexistence Theory. Metall Mater Trans B 42, 951–977 (2011). https://doi.org/10.1007/s11663-011-9527-0

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