a thermodynamic model of phosphorus distribution ratio...

A Thermodynamic Model of Phosphorus Distribution Ratiobetween CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 Slagsand Molten Steel during a Top–Bottom Combined BlownConverter Steelmaking Process Based on the Ionand Molecule Coexistence Theory

XUE-MIN YANG, JIAN-PING DUAN, CHENG-BIN SHI, MENG ZHANG,YONG-LIANG ZHANG, and JIAN-CHANG WANG

A thermodynamic model for calculating the phosphorus distribution ratio between top–bottomcombined blown converter steelmaking slags and molten steel has been developed by couplingwith a developed thermodynamic model for calculating mass action concentrations of structuralunits in the slags, i.e., CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags, based on the ionand molecule coexistence theory (IMCT). Not only the total phosphorus distribution ratio butalso the respective phosphorus distribution ratio among four basic oxides as components, i.e.,CaO, MgO, FeO, and MnO, in the slags and molten steel can be predicted theoretically by thedeveloped IMCT phosphorus distribution ratio prediction model after knowing the oxygenactivity of molten steel at the slag–metal interface or the FetO activity in the slags and therelated mass action concentrations of structural units or ion couples in the slags. The calculatedmass action concentrations of structural units or ion couples in the slags equilibrated or reactedwith molten steel show that the calculated equilibrium mole numbers or mass action concen-trations of structural units or ion couples, rather than the mass percentage of components, canpresent the reaction ability of the components in the slags. The predicted total phosphorusdistribution ratio by the developed IMCT model shows a reliable agreement with the measuredphosphorus distribution ratio by using the calculated mass action concentrations of iron oxidesas presentation of slag oxidation ability. Meanwhile, the developed thermodynamic model forcalculating the phosphorus distribution ratio can determine quantitatively the respectivedephosphorization contribution ratio of FetO, CaO+FetO, MgO+FetO, and MnO+FetO inthe slags. A significant difference of dephosphorization ability among FetO, CaO+FetO,MgO+FetO, and MnO+FetO has been found as approximately 0.0 pct, 99.996 pct, 0.0 pct,and 0.0 pct during a combined blown converter steelmaking process, respectively. There is agreat gradient of oxygen activity of molten steel at the slag–metal interface and in a metal bathwhen carbon content in a metal bath is larger than 0.036 pct. The phosphorus in molten steelbeneath the slag–metal interface can be extracted effectively by the comprehensive effect of CaOand FetO in slags to form 3CaOÆP2O5 and 4CaOÆP2O5 until the carbon content is less than0.036 pct during a top–bottom combined blown steelmaking process.

DOI: 10.1007/s11663-011-9491-8� The Minerals, Metals & Materials Society and ASM International 2011

I. INTRODUCTION

NOT only the blast furnace ironmaking processbut also most common secondary refining processeshave limited dephosphorization ability. Therefore, thedephosphorization operation in both the hot meatpretreatment and the converter steelmaking process isvery important to fulfill the requirement of phosphoruscontent for molten steel in the routine metallurgicalprocess. Compared with the dephosphorization opera-tion in hot metal pretreatment, phosphorus extrac-tion in converter steelmaking process is almost thefinal dephosphorization operation. Hence, improvingdephosphorization ability in the converter steelmakingprocess is very important to control the phosphoruscontent in the aimed specification of molten steel.

XUE-MIN YANG, Research Professor, is with the State KeyLaboratory of Multiphase Complex Systems, Institute of ProcessEngineering, Chinese Academy of Sciences, Beijing 100190, P. R.China. Contact e-mail: [email protected] JIAN-PINGDUAN, Senior Engineer, and YONG-LIANG ZHANG and JIAN-CHANG WANG, Engineers, are with the Technology Center, ShanxiTaigang Stainless Corporation Limited, Taiyuan 030003, P. R. China.CHENG-BIN SHI, Ph.D. Candidate and Joint-Training Student, iswith the School of Metallurgical and Ecological Engineering,University of Science and Technology Beijing, Beijing 100083, P. R.China, and with the Institute of Process Engineering, ChineseAcademy of Sciences. MENG ZHANG, Master Degree Student andJoint-Training Student, is with the School of Metallurgical andEcological Engineering, University of Science and Technology Beijing,and with the Institute of Process Engineering, Chinese Academy ofSciences.

Manuscript submitted October 20, 2010.Article published online April 21, 2011.

738—VOLUME 42B, AUGUST 2011 METALLURGICAL AND MATERIALS TRANSACTIONS B

As an important function of converter steelmakingprocess, the oxidizing dephosphorization of hot metal ormolten steel, has been investigated by many research-ers[1–19] since the 1940s,[1,2,9] and many phosphorousdistribution ratio prediction models[9–16] have beendeveloped based on some empirical regressions of themeasured data, such as Healy’s model,[10] Suito’s threemodels,[11,12] Sommerville’s model,[9,13] and Balajiva’smodel.[14] However, the phosphorous distribution ratiomodels[9–16] are not enough and scarce from the viewpoint of dephosphorization reactions based on metal-lurgical physicochemistry.

Zhang[20] has developed some thermodynamic modelsfor predicting the phosphorous distribution ratio LP ofFeO-Fe2O3-P2O5, MgO-FeO-Fe2O3-P2O5, CaO-MgO-FeO-Fe2O3-P2O5, CaO-SiO2-MgO-FeO-Fe2O3-P2O5,CaO-SiO2-MgO-FeO-Fe2O3-MnO-P2O5, and CaO-SiO2-MgO-Na2O-FeO-Fe2O3-MnO-P2O5 slags equilibrated withhot metal from the view point of dephosphorizationreactions based on the ion and molecule coexistencetheory (IMCT).[20–25] The results of the developedphosphorous distribution ratio prediction models byZhang[20] show that the predicated LP from the devel-oped models[20] based on IMCT[20–25] have good agree-ment with the measured LP for the previously mentionedslags equilibrated with hot metal. However, no LP

prediction model for steelmaking slags has been devel-oped based on IMCT.[20–25]

According to the accumulation of the developmentof a sulfur distribution ratio LS prediction model[24]

and a sulfide capacity CS2� prediction model[25] of CaO-SiO2-MgO-Al2O3 quaternary ironmaking slags, a LS

prediction model[26] of CaO-SiO2-MgO-FeO-Al2O3-MnO hexabasic slags in ladle furnace (LF) refiningprocess by authors, and some LP prediction models forvarious slags by J. Zhang,[20] a thermodynamic model forpredicting LP between a top–bottom combined blownconverter steelmaking slags and molten steel has beendeveloped according to IMCT.[20–25] To develop thethermodynamic model for predicting LP between CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags andmol-ten steel, a thermodynamic model for calculating massaction concentrations of structural units or ion couplesin the slags must be developed first. The developedthermodynamic model for prediction LP can determinenot only the total phosphorous distribution ratio butalso the respective phosphorous distribution ratio ofeach basic component with dephosphorization abilityunder existing of iron oxides in the slags.

To further verify the feasibility of the developed LP

prediction model, the comparison among the predictedLIMCTP;calculated by IMCT LP model and the measured

LP;measured as well as the predicted LiP;calculated by other

LP models, such as Healy’s model,[10] Suito’s threemodels,[11,12] Sommerville’s model,[9,13] and Balajiva’smodel,[14] have been conducted. The slag–metal dep-hosphorization reactions are oxidization reactions byiron oxides, such as FeO and Fe2O3, usually expressed asFetO, combined with other basic components in the slagsduring a top–bottom combined blown converter steel-making process. The defined mass action concentration

of FetO NFetO by Zhang,[20] which is assigned to presentslag oxidization ability based on IMCT[20–25] like theactivity of iron oxides aFetO in the classically metallur-gical physicochemistry, has been compared with thecalculated iron oxides activity aFetO in the slags. Toreveal the contribution of slag components to LP, theeffects both mass percent and mass action concentrationsfor basic components and iron oxides on LP at top–bottom combined blown converter steelmaking temper-atures are also discussed.The oxygen activity gradient of molten steel at slag–

metal interface and in metal bath has been revealed. Theinfluence of high oxygen activity boundary layer beneathslag–metal interface on dephosphorization reactions hasbeen verified during a combined blown steelmakingprocess. The dephosphorization mechanism in a top–bottom combined blown converter steelmaking processhas been proposed according to the obtained results.The ultimate aim of this study is to develop a

universal method for predicting the phosphorousdistribution ratio between slags and metal for vari-ous metallurgical process units from viewpoint of allpossible dephosphorization reactions according to met-allurgical physicochemistry, to provide fundamentalinformation for optimizing slags composition with theaim of improving dephosphorization ability, and fur-thermore to lay a foundation for developing a phos-phate capacity prediction model in the next studyaccording to IMCT.[20–25]

II. INDUSTRIAL TESTS

The industrial tests were carried out in an 80-ton top–bottom combined blown steelmaking converter at theNo. 2 Steelmaking Plant of Shanxi Taigang StainlessSteel Corporation Limited. The basic parameters of thecombined blown converter are summarized in Table I.The nominal capacity of the converter is 80 tons,whereas the practical output of molten steel from theconverter is about 82 tons. The total charged metallicraw material is approximately 89 tons containing83 tons of pretreated hot metal, i.e., by desiliconization,dephosphorization, and desulphurization, and 6-tonscraps. The average mass of slags forming materialseach heat includes about 4900 kg lime, 2800 kg light–burned dolomite, 360 kg laterite, and 500 kg pellets ofconverter red mud. The samples of both slag and metalin the steelmaking of a typical low-carbon steel weresampled at steelmaking end point. The normalizedchemical compositions of both slags and metal for 27heats are listed in Table II.

III. MODEL FOR CALCULATING MASSACTION CONCENTRATIONS OF STRUCTURALUNITS OR ION COUPLES IN CaO-SiO2-MgO-FeO-

Fe2O3-MnO-Al2O3-P2O5 SLAGS

A. Hypotheses

According to the classic hypotheses of IMCT des-cribed in detail elsewhere,[20–25] the main assumptions in

METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 42B, AUGUST 2011—739

the developed thermodynamic model for calculatingmass action concentrations of structural units or ioncouples in CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags equilibrated or reacted with molten steelcan be briefly summarized as follows:

(a) Structural units in the studied slags equilibrated orreacted with molten steel are composed of Ca2+,

Mg2+, Fe2+, Mn2+, and O2� as simple ions; SiO2,Fe2O3, Al2O3 and P2O5 as simple molecules; sili-cates, aluminates, and so on as complex molecules.Each structural unit has its independent position inthe slags. Every cation and anion generated from thesame component will take part in reactions offorming complex molecules in the form of ion cou-ple as (Me2++O2�) with simple molecules.

Table I. Main Parameters of an 80-ton Top–Bottom Combined Blown Steelmaking Converter

Item Parameters

Converter Nominal capacity (ton) 80Bath diameter (mm) 3860Bath depth (mm) 1050Volume ratio of converter (m3/t) 0.774

Top-blowing oxygen lance Type of oxygen lance (–) Four-apertured Laval lanceJet angle of oxygen lance (�) �12Outlet diameter of oxygen lance (mm) 203Oxygen supply intensity (Nm3/(t min)) 3.4 to 3.75

Bottom-blowing system Number of bottom-blowing elements (–) 4Bottom-blowing gas N2, ArBottom gas supply intensity (Nm3/(t min)) 0.03 to 0.12

Table II. Chemical Composition of CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 Slags and Molten Steel at End Point duringan 80-ton Top–Bottom Combined Blown Converter Steelmaking Process and Calculated Total Equilibrium Mole Numbers of all

Structural Units in 100-g Slags Based on the Ion and Molecule Coexistence Theory for 27 Heats

Test No.

Chemical Composition of Slags (mass pct)Chemical Composition of Molten Steel

(mass pct)

T (K)P

ni (mol)CaO SiO2 MgO FeO Fe2O3 MnO Al2O3 P2O5 [C] [Si] [Mn] [P] [S] [O]

1 40.02 12.12 6.20 14.23 23.04 0.73 2.41 1.25 0.061 <0.01 0.025 0.006 0.018 0.045 1949 1.0882 36.20 10.17 6.19 16.47 27.15 0.67 2.14 1.01 0.028 <0.01 0.015 0.007 0.017 0.097 1951 1.1343 42.28 11.53 6.37 13.56 21.93 0.82 2.09 1.42 0.044 <0.01 0.030 0.008 0.014 0.062 1953 1.0934 36.24 9.10 6.57 15.48 27.59 0.97 2.72 1.34 0.021 <0.01 0.029 0.011 0.016 0.130 1986 1.0965 49.17 10.22 9.25 10.11 16.31 0.81 2.79 1.34 0.035 0.015 0.037 0.011 0.015 0.078 1949 1.2366 43.30 12.02 8.03 11.87 19.28 0.96 3.00 1.54 0.030 <0.01 0.040 0.012 0.013 0.091 1943 1.1177 46.86 16.22 7.50 9.76 14.87 0.82 2.31 1.66 0.042 0.014 0.057 0.019 0.010 0.065 1949 1.0368 46.07 15.36 6.50 10.86 16.18 0.96 2.37 1.70 0.032 <0.01 0.044 0.014 0.021 0.085 1948 0.9989 48.96 16.75 7.49 9.06 13.65 0.86 1.70 1.53 0.130 0.017 0.074 0.018 0.014 0.021 1963 1.01910 49.39 15.55 7.71 8.63 14.11 0.89 2.16 1.57 0.096 0.011 0.076 0.024 0.013 0.028 1963 1.03211 47.38 13.69 7.59 10.35 16.05 0.95 2.38 1.62 0.063 0.023 0.065 0.018 0.016 0.043 1953 1.07012 45.88 14.64 7.36 10.60 16.78 1.00 2.26 1.48 0.083 0.020 0.079 0.025 0.015 0.033 1963 1.03113 43.18 15.22 7.39 13.54 16.56 0.86 1.98 1.27 0.088 0.033 0.073 0.022 0.014 0.031 1973 1.10814 45.45 14.51 6.60 10.43 17.00 1.18 3.26 1.57 0.037 0.013 0.049 0.022 0.039 0.074 1929 0.96815 39.14 9.89 7.51 14.49 24.20 0.74 2.60 1.43 0.024 <0.01 0.022 0.011 0.021 0.113 1976 1.17916 42.91 11.90 7.14 12.42 21.16 0.96 2.15 1.35 0.024 <0.01 0.029 0.009 0.022 0.113 1955 1.07717 40.71 14.54 6.72 13.30 20.58 1.10 1.92 1.13 0.026 <0.01 0.046 0.016 0.028 0.105 1974 1.01218 53.02 19.21 9.03 5.56 8.81 1.09 2.12 1.17 0.110 0.043 0.140 0.046 0.014 0.025 1969 0.96019 48.34 17.67 7.51 8.45 12.55 0.99 3.08 1.42 0.140 <0.01 0.070 0.017 0.022 0.019 1943 0.97320 46.43 17.15 7.25 9.37 14.08 1.12 3.14 1.45 0.070 0.020 0.060 0.016 0.025 0.039 1954 0.95821 46.98 18.52 7.10 6.73 14.61 1.21 3.26 1.58 0.090 <0.01 0.060 0.017 0.021 0.030 1943 0.85222 44.89 17.50 6.82 8.83 16.06 1.14 3.24 1.51 0.040 <0.01 0.040 0.012 0.022 0.068 1973 0.90423 41.47 15.03 8.13 10.43 18.05 1.17 4.34 1.38 0.060 <0.01 0.050 0.015 0.019 0.045 1940 1.00524 42.77 15.11 8.20 11.59 16.25 1.01 3.79 1.28 0.120 <0.01 0.100 0.033 0.019 0.023 1953 1.07525 46.26 17.33 8.59 7.32 14.52 1.18 3.34 1.46 0.080 <0.01 0.070 0.018 0.021 0.034 1955 0.94726 47.98 17.16 7.94 7.63 13.88 1.02 2.98 1.40 0.130 0.023 0.090 0.024 0.024 0.021 1951 0.96427 46.79 17.49 7.60 8.02 14.01 1.28 3.51 1.30 0.080 <0.01 0.090 0.016 0.015 0.034 1945 0.916


(b) Reactions of forming complex molecules areunder chemically dynamic equilibrium betweenbonded ion couples from simple ions and simplemolecules.

(c) Structural units in the slags equilibrated or reactedwith molten steel bear continuity in the range of theinvestigated concentration range.

(d) Chemical reactions of forming complex moleculesobey the mass action law.

B. Model for Calculating Mass Action Concentrationsof Structural Units or Ion Couples in CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 Slags

1. Structural units in CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags

There are eight components as CaO, SiO2, MgO,FeO, Fe2O3, MnO, Al2O3, and P2O5 in CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags, whereas the extrac-ted phosphorus from molten steel gradually enters intothe slags as P2O5, 3FeOÆP2O5, 4FeOÆP2O5, 2CaOÆP2O5, 3CaOÆP2O5, 4CaOÆP2O5, 2MgOÆP2O5, 3MgOÆP2O5, and 3MnOÆP2O5 with the proceeding of dep-hosphorization reactions until dephosphorization reac-tions reach equilibrium or quasi-equilibrium in terms ofthe classic metallurgical physicochemistry. However, theIMCT[20–25] suggests that the extracted phosphorusfrom molten steel into the slags can be bonded with ioncouples (Fe2++O2�), (Ca2++O2�), (Mg2++O2�),and (Mn2++O2�) to form structural units as P2O5,3FeOÆP2O5, 4FeOÆP2O5, 2CaOÆP2O5, 3CaOÆP2O5, 4CaOÆP2O5, 2MgOÆP2O5, 3MgOÆP2O5, and 3MnOÆP2O5 inoxidizing slags containing FetO, respectively. Hence, thetop–bottom combined blown converter steelmaking slagswill change from an open system without phosphorus atthe initial stage to a closed system containing phosphorusat the final stage with the proceeding of convertersteelmaking process. The IMCT[20–25] can be appliedonly to a closed system; therefore, the top–bottomcombined blown converter steelmaking slags containingphosphorus equilibrated or reacted with molten steel ischosen as CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5

slags.It can be obtained reasonably from the preceding

assumptions in Section III–A that there are five simpleions as Ca2+ , Mg2+ , Fe2+ , Mn2+ , and O2�, foursimple molecules as SiO2, Fe2O3, Al2O3, and P2O5 inthe slags under dephosphorization equilibrium orquasi–equilibrium at metallurgical temperatures basedon IMCT.[20–25] According to the reported binary andternary phase diagrams[27,28] of CaO-SiO2, CaO-Al2O3,CaO-Al2O3–SiO2, CaO-Al2O3-MgO, CaO-MgO-SiO2,MgO-Al2O3–SiO2, CaO-FeO-SiO2, Al2O3–SiO2-MnO,and Al2O3–SiO2–FeO slags and so on at the combinedblown converter steelmaking temperatures, i.e., in atemperature range from 1929 K to 1986 K (1656 �C to1713 �C), approximately 36 kinds of complex mole-cules, such as 3CaOÆSiO2, 2CaOÆSiO2, CaOÆSiO2 and soon, can be formed in the slags in a temperature rangefrom 1929 K to 1986 K (1656 �C to 1713 �C) as listedin Table II. All simple ions, as well as simple and

complex molecules in the studied slags at metallurgicaltemperature are summarized and assigned with exclu-sive numbers in Table III.

2. Model for calculating mass action concentrationsof structural units or ion couples in CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slagsThe mole number of previously mentioned eight

components, such as CaO, SiO2, MgO, FeO, Fe2O3,MnO, Al2O3, and P2O5, in 100-g CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags is assigned as b1 ¼n0CaO; b2 ¼ n0SiO2

; b3 ¼ n0MgO; b4 ¼ n0FeO; b5 ¼ n0Fe2O3; b6 ¼

n0MnO; b7 ¼ n0Al2O3and b8 ¼ n0P2O5

to present chemicalcomposition of the slags. The defined[20–25] equilibriummole numbers ni of all previously mentioned structuralunits in 100-g slags equilibrated or reacted with moltensteel at metallurgical temperatures are given Table III.The total equilibrium mole number

Pni of all structural

units in 100-g slags equilibrated or reacted with moltensteel can be expressed as followsX

ni ¼ 2n1 þ n2 þ 2n3 þ 2n4 þ n5 þ 2n6 þ n7 þ n8

þ nc1 þ nc2 þ � � � þ nc36 molð Þ ½1�

According to the definition of mass action concen-trations[20–25] Ni of structural units, which is a ratio ofequilibrium mole number of structural units i to thetotal equilibrium mole numbers of all structural unitsin a closed system with a fixed amount, Ni ofstructural unit i and ion couples (Me2++O2�) inmolten slags can be calculated by

Ni ¼niPni

�ð Þ ½2a�

NMeO ¼ NMe2þ;MeO þNO2�;MeO

¼nMe2þ;MeO þ nO2�;MeOP

ni¼ 2nMeOP

ni�ð Þ [2b]

All definitions of Ni for the formed ion couples fromsimple ions, as well as the simple and complex moleculesin CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slagsare listed in Table III.The chemical reaction formulas of 36 kinds of the

possibly formed complex molecules, their standardmolar Gibbs free energy change DrG

Hm;ci of formation

reactions as a function of absolute temperature T,reaction equilibrium constant KH

ci , and presentation ofmass action concentration of all complex moleculesNci expressed by using KH

ci ; N1 NCaOð Þ; N2 NSiO2ð Þ; N3

NMgO

� �; N4 NFeOð Þ; N5 ðNFe2O3

Þ; N6 ðNMnOÞ;N7 NAl2O3ð Þ

and N8 NP2O5ð Þ based on the mass action law are

summarized in Table IV.The mass conservation equations of eight compo-

nents in 100-g CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags equilibrated or reacted with moltensteel can be established from the definitions[20–25] of niand Ni of all structural units listed in Tables III and IVas follows:


Table III. Expression of Structural Units as Ion Couples, Simple or Complex Molecules, Their Mole Numbers, and Mass Action

Concentrations in 100-g CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 Slags Equilibrated with Molten Steel at Top–Bottom

Combined Blown Converter Steelmaking Temperatures based on the Ion and Molecule Coexistence Theory

Item

Structural Unitsas Ion Couplesor Molecules

Number ofStructural Unitsor Ion Couples

Mole Numberof Structural Units

Mass Action Concentrationof Structural Unitsor Ion Couples

Simple cationand anion (4)

Ca2++O2� 1 n1 ¼ nCa2þ;CaO ¼ nO2� ;CaO ¼ nCaO N1 ¼ 2n1Pni¼ NCaO

Mg2++O2� 3 n3 ¼ nMg2þ;MgO ¼ nO2� ;MgO ¼ nMgO N3 ¼ 2n3Pni¼ NMgO

Fe2++O2� 4 n4 ¼ nFe2þ ;FeO ¼ nO2�;FeO ¼ nFeO N4 ¼ 2n4Pni¼ NFeO

Mn2++O2� 6 n6 ¼ nMn2þ ;MnO ¼ nO2� ;MnO ¼ nMnO N6 ¼ 2n6Pni¼ NMnO

Simplemolecules (4)

SiO2 2 n2 ¼ nSiO2N2 ¼ n2P

ni¼ NSiO2

Fe2O3 5 n5 ¼ nFe2O3N5 ¼ n5P

ni¼ NFe2O3

Al2O3 7 n7 ¼ nAl2O3N7 ¼ n7P

ni¼ NAl2O3

P2O5 8 n8 ¼ nP2O5N8 ¼ n8P

ni¼ NP2O5

Complexmolecules (36)

3CaOÆSiO2 c1 nc1 ¼ n3CaO�SiO2Nc1 ¼ nc1P

ni¼ N3CaO�SiO2

2CaOÆSiO2 c2 nc2 ¼ n2CaO�SiO2Nc2 ¼ nc2P

ni¼ N2CaO�SiO2

CaOÆSiO2 c3 nc3 ¼ nCaO�SiO2Nc3 ¼ nc3P

ni¼ NCaO�SiO2

3CaOÆAl2O3 c4 nc4 ¼ n3CaO�Al2O3Nc4 ¼ nc4P

ni¼ N3CaO�Al2O3

12CaOÆ7Al2O3 c5 nc5 ¼ n12CaO�7Al2O3Nc5 ¼ nc5P

ni¼ N12CaO�7Al2O3

CaOÆAl2O3 c6 nc6 ¼ nCaO�Al2O3Nc6 ¼ nc6P

ni¼ NCaO�Al2O3

CaOÆ2Al2O3 c7 nc7 ¼ nCaO�2Al2O3Nc7 ¼ nc7P

ni¼ NCaO�2Al2O3

CaOÆ6Al2O3 c8 nc8 ¼ nCaO�6Al2O3Nc8 ¼ nc8P

ni¼ NCaO�6Al2O3

2MgOÆSiO2 c9 nc9 ¼ n2MgO�SiO2Nc9 ¼ nc9P

ni¼ N2MgO�SiO2

MgOÆSiO2 c10 nc10 ¼ nMgO�SiO2Nc10 ¼ nc10P

ni¼ NMgO�SiO2

MgOÆAl2O3 c11 nc11 ¼ nMgO�Al2O3Nc11 ¼ nc11P

ni¼ NMgO�Al2O3

2FeOÆSiO2 c12 nc12 ¼ n2FeO�SiO2Nc12 ¼ nc12P

ni¼ N2FeO�SiO2

FeOÆAl2O3 c13 nc13 ¼ nFeO�Al2O3Nc13 ¼ nc13P

ni¼ NFeO�Al2O3

MnOÆSiO2 c14 nc14 ¼ nMnO�SiO2Nc14 ¼ nc14P

ni¼ NMnO�SiO2

2MnOÆSiO2 c15 nc15 ¼ n2MnO�SiO2Nc15 ¼ nc15P

ni¼ N2MnO�SiO2

MnOÆAl2O3 c16 nc16 ¼ nMnO�Al2O3Nc16 ¼ nc16P

ni¼ NMnO�Al2O3

3Al2O3Æ2SiO2 c17 nc17 ¼ n3Al2O3�2SiO2Nc17 ¼ nc17P

ni¼ N3Al2O3 �2SiO2

2CaOÆAl2O3ÆSiO2 c18 nc18 ¼ n2CaO�Al2O3 �SiO2Nc18 ¼ nc18P

ni¼ N2CaO�Al2O3�SiO2

CaOÆAl2O3Æ2SiO2 c19 nc19 ¼ nCaO�Al2O3�2SiO2Nc19 ¼ nc19P

ni¼ NCaO�Al2O3 �2SiO2

CaOÆMgOÆSiO2 c20 nc20 ¼ nCaO�MgO�SiO2Nc20 ¼ nc20P

ni¼ NCaO�MgO�SiO2

CaOÆMgOÆ2SiO2 c21 nc21 ¼ nCaO�MgO�2SiO2Nc21 ¼ nc21P

ni¼ NCaO�MgO�2SiO2

2CaOÆMgOÆ2SiO2 c22 nc22 ¼ n2CaO�MgO�2SiO2Nc22 ¼ nc22P

ni¼ N2CaO�MgO�2SiO2

3CaOÆMgOÆ2SiO2 c23 nc23 ¼ n3CaO�MgO�2SiO2Nc23 ¼ nc23P

ni¼ N3CaO�MgO�2SiO2

2MgOÆ2Al2O3Æ5SiO2 c24 nc24 ¼ n2MgO�2Al2O3�5SiO2Nc24 ¼ nc24P

ni¼ N2MgO�2Al2O3�5SiO2

2CaOÆFe2O3 c25 nc25 ¼ n2CaO�Fe2O3Nc25 ¼ nc25P

ni¼ N2CaO�Fe2O3

FeOÆFe2O3 c26 nc26 ¼ nFeO�Fe2O3Nc26 ¼ nc26P

ni¼ NFeO�Fe2O3

MgOÆFe2O3 c27 nc27 ¼ nMgO�Fe2O3Nc27 ¼ nc27P

ni¼ NMgO�Fe2O3

MnOÆFe2O3 c28 nc28 ¼ nMnO�Fe2O3Nc28 ¼ nc28P

ni¼ NMnO�Fe2O3

2CaOÆP2O5 c29 nc29 ¼ n2CaO�P2O5Nc29 ¼ nc29P

ni¼ N2CaO�P2O5


ni¼ N3CaO�P2O5


b1 ¼ 1

2N1 þ 3Nc1 þ 2Nc2 þNc3 þ 3Nc4 þ 12Nc5

þNc6 þNc7 þNc8 þ 2Nc18 þNc19

þNc20 þNc21 þ 2Nc22 þ 3Nc23 þ 2Nc25

þ2Nc29 þ 3Nc30 þ 4Nc31

!X

ni

¼ 1

2N1 þ 3KH

c1N31N2 þ 2KH

c2N21N2 þ KH

c3N1N2

þ3KHc4N

31N7 þ 12KH

c5N121 N7

7 þ KHc6N1N7

þKHc7N1N

27 þ KH

c8N1N67 þ 2KH

c18N21N2N7

þKHc19N1N7N

22 þ KH

c20N1N2N3 þ KHc21N1N3N

22

þ2KHc22N

21N3N

22 þ 3KH

c23N31N

22N3 þ 2KH

c25N21N5

þ2KHc29N

21N8 þ 3KH

c30N31N8 þ 4KH

c31N41N8

!X

ni

¼ n0CaO molð Þ [3a]

b2 ¼�N2 þNc1 þNc2 þNc3 þNc9 þNc10 þNc12

þNc14 þNc15 þ 2Nc17 þNc18 þ 2Nc19 þNc20

þ2Nc21 þ 2Nc22 þ 2Nc23 þ 5Nc24ÞX

ni

¼�N2 þ KH

c1N31N2 þ KH

c2N21N2 þ KH

c3N1N2

þKHc9N2N

23 þ KH

c10N2N3 þ KHc12N2N

2

4

þKHc14N2N6 þ KH

c15N2N26 þ 2KH

c17N22N

37

þKHc18N

21N2N7 þ 2KH

c19N1N22N7 þ KH

c20N1N2N3

þ2KHc21N1N3N

22 þ 2KH

c22N21N

22N3 þ 2KH

c23N31N

22N3

þ5KHc24N

23N

27N

52ÞX

ni ¼ n0SiO2molð Þ [3b]

b3 ¼ 1

2N3 þ 2Nc9 þNc10 þNc11 þNc20 þNc21 þNc22

þNc23 þ 2Nc24 þNc27 þ 2Nc35 þ 3Nc36

!X

ni

¼ 1

2N3 þ 2KH

c9N2N23 þ KH

c10N2N3 þ KHc11N3N7

þKHc20N1N2N3 þ KH

c21N1N3N22 þ KH

c22N21N

22N3

þKHc23N

31N

22N3 þ 2KH

c24N23N

27N

52 þ KH

c27N3N5

þ2KHc35N

23N8 þ 3KH

c36N33N8

!X

ni ¼ n0MgO molð Þ

½3c�

b4¼1

2N4þ2Nc12þNc13þNc26þ3Nc32þ4Nc33

� �Xni

¼ 1

2N4þ2KH

c12N2N24þKH

c13N4N7þKHc26N4N5

þ3KHc32N

34N8þ4KH

c33N44N8

!X

ni¼ n0FeO molð Þ

½3d�

b5 ¼ N5 þNc25 þNc26 þNc27 þNc28ð ÞX

ni

¼�N5 þ KH

c25N21N5 þ KH


þKHc28N6N5Þ

Xni ¼ n0Fe2O3

molð Þ [3e]

b6 ¼1

2N6þNc14þ 2Nc15þNc16þNc28þ 3Nc34

� �Xni

¼ 1

2N6þKH

c14N2N6þ 2KHc15N2N

26þKH

c16N6N7

þKHc28N6N5þ 3KH

c34N36N8

!X

ni ¼ n0MnO molð Þ

½3f�

Table III. continued

Item

Structural Unitsas Ion Couplesor Molecules

Number ofStructural Unitsor Ion Couples

Mole Numberof Structural Units

Mass Action Concentrationof Structural Unitsor Ion Couples


ni¼ N4CaO�P2O5

3FeOÆP2O5 c32 nc32 ¼ n3FeO�P2O5Nc32 ¼ nc32P

ni¼ N3FeO�P2O5

4FeOÆP2O5 c33 nc33 ¼ n4FeO�P2O5Nc33 ¼ nc33P

ni¼ N4FeO�P2O5

3MnOÆP2O5 c34 nc34 ¼ n3MnO�P2O5Nc34 ¼ nc34P

ni¼ N3MnO�P2O5

2MgOÆP2O5 c35 nc35 ¼ n2MgO�P2O5Nc35 ¼ nc35P

ni¼ N2MgO�P2O5

3MgOÆP2O5 c36 nc36 ¼ n3MgO�P2O5Nc36 ¼ nc36P

ni¼ N3MgO�P2O5


Table

IV.

Chem

icalReactionForm

ulasofPossibly

Form

edComplexMolecules,TheirStandard

MolarGibbsFreeEnergyChange,

Equilibrium

Constants,andMass

Action

Concentrationsin

CaO-SiO

2-M

gO-FeO

-Fe 2O

3-M

nO-A

l 2O

3-P

2O

5SlagsatTop–Bottom

Combined

BlownConverter

SteelmakingTem

peratures

Reactions

DrG

H m;ci(J/m

ol)

Reference

KH ci

Nci

3(C

a2++

O2�)+

(SiO

2)=

(3CaO

ÆSiO

2)

�118,826�

6.694T

29

KH c1¼

Nc1

N3 1N

2N

c1¼

KH c1N

3 1N

2

2(C

a2++

O2�)+

(SiO

2)=

(2CaO

ÆSiO

2)

�102,090�

24.267T

30

KH c2¼

Nc2

N2 1N

2N

c2¼

KH c2N

2 1N

2

(Ca2++

O2�)+

(SiO

2)=

(CaO

ÆSiO

2)

�21,757�

36.819T

30

KH c3¼

Nc3

N1N

2N

c3¼

KH c3N

1N

2

3(C

a2++

O2�)+

(Al 2O

3)=

(3CaO

ÆAl 2O

3)

�21,757�

29.288T

30

KH c4¼

Nc4

N3 1N

7N

c4¼

KH c4N

3 1N

7

12(C

a2++

O2�)+

7(A

l 2O

3)=

(12CaO

Æ7Al 2O

3)

617,977�

612.119T

30

KH c5¼

Nc5

N12

1N

7 7

Nc5¼

KH c5N

12

1N

7 7

(Ca2++

O2�)+

(Al 2O

3)=

(CaO

ÆAl 2O

3)

59,413�

59.413T

30

KH c6¼

Nc6

N1N

7N

c6¼

KH c6N

1N

7

(Ca2++

O2�)+

2(A

l 2O

3)=

(CaO

Æ2Al 2O

3)

�16,736�

25.522T

30

KH c7¼

Nc7

N1N

2 7

Nc7¼

KH c7N

1N

2 7

(Ca2++

O2�)+

6(A

l 2O

3)=

(CaO

Æ6Al 2O

3)

�22,594�

31.798T

31

KH c8¼

Nc8

N1N

6 7

Nc8¼

KH c8N

1N

6 7

2(M

g2+

+O

2�)+

(SiO

2)=

(2MgO

ÆSiO

2)

�56,902�

3.347T

30

KH c9¼

Nc9

N2N

2 3

Nc9¼

KH c9N

2N

2 3

(Mg2+

+O

2�)+

(SiO

2)=

(MgO

ÆSiO

2)

23,849�

29.706T

30

KH c10¼

Nc10

N2N

3N

c10¼

KH c10N

2N

3

(Mg2+

+O

2�)+

(Al 2O

3)=

(MgO

ÆAl 2O

3)

�18,828�

6.276T

30

KH c11¼

Nc11

N3N

7N

c11¼

KH c11N

3N

7

2(Fe2

++

O2�)+

(SiO

2)=

(2FeO

ÆSiO

2)

�9,395�

0.227T

29,32,33

KH c12¼

Nc12

N2N

2 4

Nc12¼

KH c12N

2N

2 4

(Fe2

++

O2�)+

(Al 2O

3)=

(FeO

ÆAl 2O

3)

�59,204+

22.343T

34

KH c13¼

Nc13

N4N

7N

c13¼

KH c13N

4N

7

(Mn2+

+O

2�)+

(SiO

2)=

(MnO

ÆSiO

2)

38,911�

40.041T

29

KH c14¼

Nc14

N2N

6N

c14¼

KH c14N

2N

6

2(M

n2+

+O

2�)+

(SiO

2)=

(2MnO

ÆSiO

2)

36,066�

30.669T

29

KH c15¼

Nc15

N2N

2 6

Nc15¼

KH c15N

2N

2 6

(Mn2+

+O

2�)+

(Al 2O

3)=

(MnO

ÆAl 2O

3)

�45,116+

11.81T

35

KH c16¼

Nc16

N6N

7N

c16¼

KH c16N

6N

7

3(A

l 2O

3)+

2(SiO

2)=

(3Al 2O

3Æ2SiO

2)

�4,351�

10.46T

30

KH c17¼

Nc17

N2 2N

3 7

Nc17¼

KH c17N

2 2N

3 7

2(C

a2+

+O

2�)+

(Al 2O

3)+

(SiO

2)=

(2CaO

ÆAl 2O

3ÆSiO

2)

�116,315�

38.911T

30

KH c18¼

Nc18

N2 1N

2N

7N

c18¼

KH c18N

2 1N

2N

7

(Ca2+

+O

2�)+

(Al 2O

3)+

2(SiO

2)=

(CaO

ÆAl 2O

3Æ2SiO

2)

�4,184�

73.638T

30

KH c19¼

Nc19

N1N

2 2N

7N

c19¼

KH c19N

1N

2 2N

7

(Ca2+

+O

2�)+

(Mg2+

+O

2�)+

(SiO

2)=

(CaO

ÆMgO

ÆSiO

2)

�124,683+

3.766T

29

KH c20¼

Nc20

N1N

2N

3

Nc20¼

KH c20N

1N

2N

3

(Ca2+

+O

2�)+

(Mg2+

+O

2�)+

2(SiO

2)=

(CaO

ÆMgO

Æ2SiO

2)

�80,333�

51.882T

30

KH c21¼

Nc21

N1N

3N

2 2

Nc21¼

KH c21N

1N

3N

2 2

2(C

a2+

+O

2�)+

(Mg2+

+O

2�)+

2(SiO

2)=

(2CaO

ÆMgO

Æ2SiO

2)

�73,638�

63.597T

30

KH c22¼

Nc22

N2 1N

2 2N

3

Nc22¼

KH c22N

2 1N

2 2N

3

3(C

a2+

+O

2�)+

(Mg2+

+O

2�)+

2(SiO

2)=

(3CaO

ÆMgO

Æ2SiO

2)

�205,016�

31.798T

31

KH c23¼

Nc23

N3 1N

2 2N

3

Nc23¼

KH c23N

3 1N

2 2N

3

2(M

g2+

+O

2�)+

2(A

l 2O

3)+

5(SiO

2)=

(2MgO

Æ2Al 2O

3Æ5SiO

2)

�14,422�

14.808T

36,37

KH c24¼

Nc24

N2 3N

2 7N

5 2

Nc24¼

KH c24N

2 3N

2 7N

5 2

2(C

a2+

+O

2�)+

(Fe 2O

3)=

(2CaO

ÆFe 2O

3)

�53,137�

2.510T

29

KH c25¼

Nc25

N2 1N

5

Nc25¼

KH c25N

2 1N

5

(Fe2

++

O2�)+

(Fe 2O

3)=

(FeO

ÆFe 2O

3)

�78,451+

30.813T

29,32,33

KH c26¼

Nc26

N4N

5

Nc26¼

KH c26N

4N

5

(Mg2+

+O

2�)+

(Fe 2O

3)=

(MgO

ÆFe 2O

3)

�19,246�

2.092T

29

KH c27¼

Nc27

N3N

5

Nc27¼

KH c27N

3N

5

(Mn2+

+O

2�)+

(Fe 2O

3)=

(MnO

ÆFe 2O

3)

�35,726+

13.138T

29

KH c28¼

Nc28

N6N

5

Nc28¼

KH c28N

6N

5

2(C

a2+

+O

2�)+

(P2O

5)=

(2CaO

ÆP2O

5)

�484,372�

26.569T

29

KH c29¼

Nc29

N2 1N

8N

c29¼

KH c29N

2 1N

8

3(C

a2+

+O

2�)+

(P2O

5)=

(3CaO

ÆP2O

5)

�709,890+

6.150T

29

KH c30¼

Nc30

N3 1N

8N

c30¼

KH c30N

3 1N

8

4(C

a2+

+O

2�)+

(P2O

5)=

(4CaO

ÆP2O

5)

�661,356�

3.473T

38

KH c31¼

Nc31

N4 1N

8N

c31¼

KH c31N

4 1N

8


b7 ¼�N7þNc4þ 7Nc5þNc6 þ 2Nc7 þ 6Nc8þNc11

þNc13þNc16þ 3Nc17þNc18 þNc19þ 2Nc24ÞX

ni

¼�N7þKH

c4N31N7þ 7KH

c5N121 N7

7þKHc6N1N7

þ2KHc7N1N

27þ 6KH

c8N1N67þKH

c11N3N7þKHc13N4N7

þKHc16N6N7þ 3KH

c17N22N

37þKH

c18N21N2N7

þKHc19N1N

22N7þ 2KH

c24N23N

27N

52

�Xni

¼ n0Al2O3molð Þ [3g]

b8 ¼�N8 þNc29 þNc30 þNc31 þNc32 þNc33 þNc34

þNc35 þNc36ÞX

ni

¼�N8 þ KH

c29N21N8 þ KH

c30N31N8 þ KH

c31N41N8

þKHc32N

34N8 þ KH

c33N44N8

þKHc34N

36N8 þ KH

c35N23N8 þ KH

c36N33N8Þ

Xni

¼ n0P2O5molð Þ [3h]

According to the principle that the sum of molefraction for all structural units in a fixed amount ofCaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slagsunder equilibrium condition is equal to 1.0, the follow-ing equation can be obtained:

N1 þN2 þN3 þN4 þN5 þN6 þN7 þN8 þNc1

þNc2 þ � � � þNc36

¼ N1 þN2 þ � � � þN8 þ KHc1N

31N2 þ KH

c2N21N2 þ � � �

þ KHc36N

33N8 ¼

XNi ¼ 1:0 �ð Þ ½4�

The equation group of Eqs. [3] and [4] is the governingequations of the developed thermodynamic model forcalculating the mass action concentrations Ni of struc-tural units or ion couples in CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags equilibrated or reactedwith molten steel. Obviously, there are nine unknownparameters as N1; N2; N3; N4; N5; N6; N7; N8 and

Pni

with nine independent equations in the developedequation group of Eqs. [3] and [4]. The unique solutionof Ni;

Pni; and ni can be calculated by solving these

algebraic equation group of Eqs. [3] and [4] by combin-ing with the definition of Ni in Eq. [2].It should be pointed out that considering P2O5 as one

component, no convergent solutions can be obtained bysolving the equation group of Eqs. [3] and [4] becausethe solved values of NP2O5

is less than 10�20, like thereported aP2O5

is less than 10�17 in an oxidizationslags.[39,40] Under this circumstance, the P2O5 free CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3 slags was applied tosubstitute CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5

slags. The P2O5 content in the slags is less than 2.0 pct;replacing CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5

slags by CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3 slagscan not generate inconceivable errors on Ni;

Pni; and ni

Therefore, Eqs. [3a] through [3g] and [4] can be rewrittenby deleting N8 and Nc29 �Nc36 as

Table

IV.

continued

Reactions

DrG

H m;ci(J/m

ol)

Reference

KH ci

Nci

3(Fe2

++

O2�)+

(P2O

5)=

(3FeO

ÆP2O

5)

�587,683�

71.706T

20,32,33

KH c32¼

Nc32

N3 4N

8N

c32¼

KH c32N

3 4N

8

4(Fe2

++

O2�)+

(P2O

5)=

(4FeO

ÆP2O

5)

�512,251+

128.083T

20,32,33

KH c33¼

Nc33

N4 4N

8N

c33¼

KH c33N

4 4N

8

3(M

n2+

+O

2�)+

(P2O

5)=

(3MnO

ÆP2O

5)

�543,259+

41.812T

28

KH c34¼

Nc34

N3 6N

8N

c34¼

KH c34N

3 6N

8

2(M

g2+

+O

2�)+

(P2O

5)=

(2MgO

ÆP2O

5)

168,369�

339.357T

20

KH c35¼

Nc35

N2 3N

8N

c35¼

KH c35N

2 3N

8

3(M

g2+

+O

2�)+

(P2O

5)=

(3MgO

ÆP2O

5)

�267,641�

115.186T

29

KH c36¼

Nc36

N3 3N

8N

c36¼

KH c36N

3 3N

8


b1 ¼�1

2N1 þ 3Nc1 þ 2Nc2 þNc3 þ 3Nc4 þ 12Nc5 þNc6

þNc7 þNc8 þ 2Nc18 þNc19 þNc20 þNc21


�Xni

¼ 1

2N1 þ 3KH

c1N31N2 þ 2KH

c2N21N2 þ KH

c3N1N2

þ3KHc4N

31N7 þ 12KH

c5N121 N7

7 þ KHc6N1N7

þKHc7N1N

27 þ KH

c8N1N67 þ 2KH

c18N21N2N7

þKHc19N1N7N

22 þ KH

c20N1N2N3 þ KHc21N1N3N

22

þ2KHc22N

21N3N

22 þ 3KH

c23N31N

22N3 þ 2KH

c25N21N5

!

�X

ni ¼ n0CaO molð Þ [5a]

b2 ¼�N2 þNc1 þNc2 þNc3 þNc9 þNc10 þNc12 þNc14

þNc15 þ 2Nc17 þNc18 þ 2Nc19 þNc20 þ 2Nc21


�Xni

¼�N2 þ KH

c1N31N2 þ KH

c2N21N2 þ KH

c3N1N2

þKHc9N2N

23 þ KH

c10N2N3 þ KHc12N2N

24 þ KH

c14N2N6

þKHc15N2N

26 þ 2KH

c17N22N

37 þ KH

c18N21N2N7

þ2KHc19N1N

22N7 þ KH

c20N1N2N3 þ 2KHc21N1N3N

22

þ2KHc22N

21N

22N3 þ 2KH

c23N31N

22N3

þ5KHc24N

23N

27N

52ÞX

ni ¼ n0SiO2molð Þ [5b]

b3 ¼�1

2N3 þ 2Nc9 þNc10 þNc11 þNc20 þNc21 þNc22

þNc23 þ 2Nc24 þNc27

�Xni

¼�1

2N3 þ 2KH

c9N2N23 þ KH


þKHc20N1N2N3 þ KH

c21N1N3N22 þ KH

c22N21N

22N3

þKHc23N

31N

22N3 þ 2KH

c24N23N

27N

52 þ KH

c27N3N5

�

�X

ni ¼ n0MgO molð Þ [5c]

b4¼1

2N4þ2Nc12þNc13þNc26

� �Xni

¼ 1

2N4þ2KH

c12N2N24þKH

c13N4N7þKHc26N4N5

� �Xni

¼ n0FeO molð Þ [5d]

b5 ¼ ðN5 þNc25 þNc26 þNc27 þNc28ÞX

ni

¼�N5 þ KH

c25N21N5 þ KH


þKHc28N6N5Þ

Xni ¼ n0Fe2O3

molð Þ [5e]

b6 ¼� 1

2N6 þNc14 þ 2Nc15 þNc16 þNc28

�Xni

¼� 1

2N6 þ KH

c14N2N6 þ 2KHc15N2N

26 þ KH

c16N6N7

þ KHc28N6N5

�Xni ¼ n0MnO molð Þ [5f]

b7¼�N7þNc4þ7Nc5þNc6þ2Nc7þ6Nc8þNc11

þNc13þNc16þ3Nc17þNc18þNc19þ2Nc24ÞX

ni

¼�N7þKH

c4N31N7þ7KH

c5N121 N7

7þKHc6N1N7

þ2KHc7N1N

27þ6KH

c8N1N67þKH

c11N3N7þKHc13N4N7

þKHc16N6N7þ3KH

c17N22N

37þKH

c18N21N2N7

þKHc19N1N

22N7þ2KH

c24N23N

27N

52ÞX

ni¼ n0Al2O3molð Þ½5g�

N1 þN2 þN3 þN4 þN5 þN6 þN7 þNc1 þNc2 þ � � �þNc28 ¼ N1 þ � � � þN7 þ KH

c1N31N2 þ KH

c2N21N2 þ � � �

þ KHc28N6N5 ¼

XNi ¼ 1:0 �ð Þ ½6�

This means that equation group of Eqs. [5a] through[5g] and [6] is composed of the applied thermodynamicmodel for calculating the mass action concentrationsNi of structural units or ion couples in CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags equilibratedor reacted with molten steel during calculation. Thecalculated

Pni in 100-g slags during a top–bottom

combined blown converter steelmaking process for27 heats is also summarized in Table I, respectively.

3. Principle of choosing standard molar Gibbs freeenergies of formed complex moleculesThe basic meaning of the defined Ni from IMCT[20–25]

is the equilibrium mole fraction of structural unit i in aclosed system relative to pure solid or liquid matter asstandard state according to the matter existing state atthe elevated temperature. The physicochemistry mean-ing of Ni is almost consistent with the traditionallyapplied activity ai of component i in slags, in which puresolid or liquid matter is chosen as standard state andmole fraction is selected as concentration unit. Tremen-dous studies have proved that Ni of structural units orion couples in various slags has a good agreement withthe reported ai of the related components in MnO-SiO2

slags,[20,41] FeO-Fe2O3–SiO2 slags,[20,42] CaO-SiO2–Al2O3-MgO slags,[20,43] CaO-FeO-SiO2 slags,[20,44]

CaO-Al2O3-SiO2 slags,[20,45] Na2O-SiO2 slags,[20,46] CaO-MgO slags and NiO-MgO slags,[20,47] and CaO-MgO-SiO2-Al2O3-Cr2O3 slags.[48] Therefore, the formulas ofreaction equilibrium constant KH

i and the relatedstandard molar Gibbs free energy change DrG

Hm;i of

reaction for forming structural unit i as complexmolecule can be presented by Ni to replace ai accordingto IMCT[20–25] as listed in Table IV.The standard molar Gibbs free energy change of

dissolving a solid component into slags is always equalto zero relative to the pure solid or liquid matter asstandard state according to the basic principles ofmetallurgical physicochemistry.[39,49] Therefore, thestandard molar Gibbs free energy change of reactionsfor formation liquid complex molecules in Table IV canbe determined from that for formation of solid complexmolecules. Taking the dissolution of solid CaO intoslags as (Ca2++O2�) as an example, the melting


process and the standard molar Gibbs free energychange for melting (Ca2++O2–)(s) can be presented asfollows

Ca2þ þO2�� sð Þ ¼ Ca2þ þO2��

lð ÞDfusG

Hm;CaO ¼ l�CaOðlÞ � l�CaOðsÞ J/molð Þ [7a]

The dissolution process and the standard molar Gibbsfree energy change for dissolving (Ca2++O2–)(l) intothe slags as (Ca2++O2–) relative to pure solid matteras standard state can be presented as

ðCa2þ þO2�Þ lð Þ ¼ ðCa2þ þO2�ÞDsolG

Hm;CaO ¼ lH

CaO � l�CaOðlÞ

¼ l�CaOðsÞ � l�CaOðlÞ 39;49½ � J/molð Þ [7b]

Comparing Eqs. [7a] with [7b], the following equationcan be obtained

DsolGHm;CaO ¼ �DfusG

Hm;CaO J/molð Þ ½7c�

Therefore, the value of standard molar Gibbs free energychange of melting or fusing component i from solid intoliquid DfusG

Hm;i is equal to the opposite value for the

standard molar Gibbs free energy change of dissolvingliquid component i into the slags DsolG

Hm;i relative to

pure solid as standard state. The standard molar Gibbsfree energy change for dissolution reaction of solidCaO(s) into slags as (Ca2++O2–) will be zero by com-bining Eq. [7a] and [7b] with considering Eq. [7c] as follows

ðCa2þ þO2�Þ sð Þ ¼ ðCa2þ þO2�ÞDrG

Hm;CaO ¼ DsolG

Hm;CaO þ DfusG

Hm;CaO ¼ 0 J/molð Þ ½8�

Thismeans the standardmolarGibbs free energy changeof the related reactions for forming complex molecules inTable IV will not change by presenting either solid orliquid as an existing state for reactants and products atcombined blown converter steelmaking temperatures forcalculating Ni becauseNi is defined as pure solid or liquidmatter as standard state according to IMCT.[20–25]

C. Results of Mass Action Concentrations for StructuralUnits or Ion Couples in Top–Bottom Combined BlownConverter Steelmaking Slags

1. Relationship between mass percent of sevencomponents and equilibrium mole numbers of relatedstructural units or ion couples in CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags

The relationship between mass percent of CaO, SiO2,MgO, FeO, Fe2O3, MnO, and Al2O3 as components inTable II and the calculated equilibriummole number ni ofstructural units or ion couples, i.e., (Ca2++O2�), SiO2,(Mg2++O2�), (Fe2++O2�), Fe2O3, (Mn2+ + O2�),and Al2O3, in CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags at top–bottom combined blown convertersteelmaking temperatures is illustrated in Figure 1,respectively. Obviously, the calculated equilibrium molenumbers ni of all seven structural units or ion couples havesome relationship withmass percent of the correspondingcomponents; a good linear relationship can be found for

five components of MgO, FeO, Fe2O3, MnO, and Al2O3,whereas a scattered corresponding relationship for othertwo components of CaO and SiO2 can be observed,respectively. The scattered relationship for CaO and SiO2

can be explained as that some CaO can react with SiO2 toform CaOÆSiO2, 2CaOÆSiO2, and 3CaOÆSiO2 as complexmolecules shown in Table III, Table IV, and Section III–B–2; therefore, the equilibriummole number of bothCaOand SiO2, i.e., free ion couple (Ca2++O2�) and freesimple molecule SiO2 cannot be corresponded with masspercent of both CaO and SiO2 in the slags.The linear relations for other five components can be

explained as that not so many mole numbers of complexmolecules can be formed compared with mass percent ofcorresponding components shown in Tables III, IV, andSection III–C–3. Therefore, the mass percent of bothCaO and SiO2 cannot be applied to the current reactionability of the slags according to IMCT.[20–25]

2. Relationship between mass percent of sevencomponents and mass action concentrations of relatedstructural units or ion couples in CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slagsThe relationshipbetween themasspercent ofCaO,SiO2,

MgO, FeO, Fe2O3, MnO, and Al2O3 as components inTable II and the calculated mass action concentrationsNi

of structural units or ion couples, i.e., (Ca2++O2�), SiO2,(Mg2++O2�), (Fe2++O2�), Fe2O3, (Mn2++O2�)and Al2O3 in CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags at top–bottom combined blown convertersteelmaking temperatures is shown in Figure 2, respec-tively. A linear relationship between mass percent and Ni

canbeobserved forMgO,FeO,Fe2O3,MnO,andAl2O3 ascomponents; however, a scattered linear relationship canbe correlated for CaO and SiO2 although somemass of ioncouple (Ca2++O2�) and simple molecule SiO2 can bondas CaOÆSiO2, 2CaOÆSiO2, and 3CaOÆSiO2 as complexmolecules shown in Table III, Table IV, and Section III–B–2. Therefore, the calculated mass concentration Ni ismuch better than the equilibrium mole number ni topresent the reaction ability of component i in the slags.

3. Relationship between equilibrium mole numbersand mass action concentrations of structural unitsor ion couples in CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slagsThe relationship between the calculated equilibrium

mole numbers ni and mass action concentrationsNi of allion couples, as well as simple and complex molecules inCaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags attop–bottom combined blown converter steelmaking tem-peratures is illustrated in Figure 3, respectively. Thecalculated ni and Ni for all 35 (7+28) ion couples orsimple molecules or complex molecules in the slags have agood linear relationship. The meaning of slope for linearrelationship between ni and Ni in terms of IMCT[20–25] isthe total equilibrium mole number

Pni in 100-g slags;

however,P

ni does not show wide variation in theinvestigated 27 heats as listed in Table II with 1.0 as theaverage value. As reported in previous investiga-tions,[24,26]

Pni in 100-g CaO-SiO2-MgO-Al2O3 slags

with simple binary basicity (pct CaO)/(pct SiO2) as 1.0


applied in blast furnace ironmaking is approximately0.85[24]; however,

Pni in 100-g CaO-SiO2-MgO-FeO-

Al2O3-MnO slags with simple binary basicity as 7.0applied in LF refining slags is approximately 1.3.[26]

Changing the simple binary basicity of slags has a largeeffect on the values of

Pni. The top–bottom combined

blown converter steelmaking slags has a smaller value ofPni than that of LF refining slags, but the value of

Pni is

larger than that of blast furnace ironmaking slags.

IV. MODEL FOR CALCULATINGPHOSPHORUS DISTRIBUTION RATIO

BETWEEN CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 SLAGS AND MOLTEN STEEL

A. Establishment of LP Prediction Model Based on SlagOxidization Ability

The dephosphorization reactions between CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags and molten

steel can be presented by all basic ion couples (Fe2++O2�), (Ca2++O2�), (Mg2++O2�), and (Mn2++O2�) in oxidizing slags, which can be described byFetO, to form nine dephosphorization products ormolecules including P2O5, 3FeOÆP2O5, 4FeOÆP2O5,2CaOÆP2O5, 3CaOÆP2O5, 4CaOÆP2O5, 2MgOÆP2O5,3MgOÆP2O5, and 3MnOÆP2O5 according to IMCT[20–25]

as follows

2 P½ � þ 5 FetOð Þ ¼ P2O5ð Þ þ 5t Fe½ �

DrGHm;P2O5

¼ �122; 412þ 312:522T J/molð Þ ½9a�

2 P½ �þ5 FetOð Þþ3 Fe2þþO2�� ¼ 3FeO �P2O5ð Þþ5t Fe½ �

DrGHm; 3FeO�P2O5

¼ �552; 816þ 405:23T J/molð Þ ½9b�

2 P½ �þ5 FetOð Þþ4 Fe2þþO2�� ¼ 4FeO �P2O5ð Þþ5t Fe½ �

0 5 10 15 200.0

0.1

0.2

0.3

0.4

0.5

2nF

eO (

mol

)

Mass percent of FeO (%)

FeO

0 10 20 300.00

0.01

0.02

0.03

0.04

n Fe 2O

3 (m

ol)

Mass percent of Fe2O

3 (%)

Fe2O

3

0.4 0.6 0.8 1.0 1.2 1.40.01

0.02

0.03

0.04

2 nM

nO (

mol

)

Mass percent of MnO (%)

MnO

0 2 4 60.000

0.001

0.002

0.003

0.004

n Al 2O

3 (m

ol)

Mass percent of Al2O

3 (%)

Al2O

3

0 10 20 300.0000

0.0001

0.0002

0.0003

0.0004

n SiO

2 (m

ol)

Mass percent of SiO2 (%)

SiO2

30 40 50 600.2

0.3

0.4

0.5

0.6

2nC

aO (

mol

)

Mass percent of CaO (%)

CaO

5 6 7 8 9 100.2

0.3

0.4

0.5

2nM

gO (

mol

)

Mass percent of MgO (%)

MgO

(a) (b) (c)

(d) (e) (f)

(g)

Fig. 1—Relationship between mass percent of CaO, SiO2, MgO, FeO, Fe2O3, MnO, and Al2O3 as components and calculated equilibrium molenumber of (Ca2++O2�), SiO2, (Mg2++O2�), (Fe2++O2�), Fe2O3, (Mn2++O2�), and Al2O3 as structural units or ion couples in 100-gCaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags equilibrated with molten steel at top–bottom combined blown converter steelmaking temper-atures for 27 heats, respectively.


DrGHm;4FeO�P2O5

¼ �504; 243þ 359:889T J/molð Þ ½9c�

2 P½ �þ5 FetOð Þþ2 Ca2þþO2�� ¼ 2CaO �P2O5ð Þþ5t Fe½ �

DrGHm; 2CaO�P2O5

¼ �707; 619þ 347:96T J/molð Þ ½9d�


DrGHm;3CaO�P2O5

¼ �832; 302þ 318:672T J/molð Þ ½9e�


DrGHm; 4CaO�P2O5

¼ �783; 768þ 309:049T J/molð Þ ½9f�

2 P½ �þ5 FetOð Þþ2 Mg2þþO2�� ¼ 2MgO�P2O5ð Þþ5t Fe½ �

DrGHm; 2MgO�P2O5

¼ 45; 957� 26:835T J/molð Þ ½9g�

2 P½ �þ5 FetOð Þþ3 Mg2þþO2�� ¼ 3MgO�P2O5ð Þþ5t Fe½ �

DrGHm; 3MgO�P2O5

¼ �511; 389þ 272:230T J/molð Þ ½9h�

2 P½ �þ5 FetOð Þþ3 Mn2þþO2�� ¼ 3MnO�P2O5ð Þþ5t Fe½ �

DrGHm; 3MnO�P2O5

¼ �665; 671þ 354:344T J/molð Þ ½9i�

30 40 50 600.2

0.3

0.4

0.5

NC

aO (

−)


CaO

0 10 20 300.0000

0.0001

0.0002

0.0003

0.0004

NS

iO2 (

−)


SiO2

5 6 7 8 9 100.15

0.20

0.25

0.30

NM

gO (

−)


MgO

0 5 10 15 200.0

0.1

0.2

0.3

0.4

NF

eO (

−)


FeO

0 10 20 300.00

0.01

0.02

0.03

NF

e 2O3 (

−)


3 (%)

Fe2O

3

0.4 0.6 0.8 1.0 1.2 1.40.01

0.02

0.03

NM

nO (

−)


MnO

0 2 4 60.000

0.001

0.002

0.003

NA

l 2O3 (

−)


3 (%)

Al2O

3

(a) (b) (c)

(d) (e) (f)

(g)

Fig. 2—Relationship between mass percent of CaO, SiO2, MgO, FeO, Fe2O3, MnO, and Al2O3 as components and calculated mass actionconcentration of (Ca2++O2�), SiO2, (Mg2++O2�), (Fe2++O2�), Fe2O3, (Mn2++O2�), and Al2O3 as structural units or ion couples inCaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags equilibrated with molten steel at top–bottom combined blown converter steelmaking temper-atures for 27 heats, respectively.


0.2 0.4 0.6 0.80.2

0.3

0.4

0.5

NC

aO (

−)

2nCaO

(mol)

CaO

0.0000 0.0002 0.00040.0000

0.0002

0.0004

NS

iO2 (

−)

nSiO

2

(mol)

SiO2

0.2 0.3 0.4 0.50.15

0.20

0.25

0.30

NM

gO (

−)

2nMgO

(mol)

MgO

0.00 0.02 0.040.00

0.01

0.02

0.03

NF

e 2O3 (

−)

nFe

2O

3

(mol)

2O

3

0.0 0.1 0.2 0.3 0.4 0.50.0

0.2

0.4

NF

eO (

−)

2nFeO

(mol)0.01 0.02 0.03 0.04

0.01

0.02

0.03

NM

nO (

−)

2nMnO

(mol)

0.000 0.002 0.0040.000

0.001

0.002

0.003

NA

l 2O3 (

−)

nAl

2O

3

(mol)

2O

3

0.00 0.01 0.02 0.030.00

0.01

0.02

0.03

N

3CaO

·SiO

2 (−)

n3CaO·SiO

2

(mol)

·SiO2

0.0 0.1 0.2 0.30.0

0.1

0.2

0.3

N

2CaO

·SiO

2 (−)

n2CaO·SiO

2

(mol)

·SiO2

0.000 0.004 0.008 0.0120.000

0.002

0.004

0.006

N

3CaO

·Al 2O

3 (−)

n3CaO·Al

2O

3

(mol)

·Al2O

3

0.00E+000 2.00E-011 4.00E-0110.00E+000

1.00E-011

2.00E-011

3.00E-011

N

12C

aO·7

Al 2O

3 (−)

n12CaO·7Al

2O

3

(mol)

·7Al2O

3

0.00 0.01 0.02 0.030.00

0.01

0.02

0.03

N

CaO

·SiO

2 (−)

nCaO·SiO

2

(mol)

·SiO2

0.00 0.01 0.02 0.030.00

0.01

0.02

N

CaO

·Al 2O

3 (− )

nCaO·Al

2O

3

(mol)

·Al2O

3

0.00000 0.00006 0.000120.00000

0.00003

0.00006

0.00009

N

CaO

· 2A

l 2O3 (

− )

nCaO·2Al

2O

3

(mol)

·2Al2O

3

0.00E+000 6.00E-015 1.20E-0140.00E+000

3.00E-015

6.00E-015

9.00E-015

N

CaO

·6A

l 2O3 (

− )

nCaO·6Al

2O

3

(mol)

Fe FeO MnO

Al 3CaO 2CaO

3CaO 12CaO CaO

CaO CaO CaO·6Al2O

3

(a) (b) (c)

(d) (e) (f)

(g) (h1) (h2)

(h3) (h4) (h5)

(h6) (h7) (h8)

Fig. 3—Relationship between calculated equilibrium mole number and mass action concentrations of ion couples, simple and complex moleculesin 100-g CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags equilibrated with molten steel at top–bottom combined blown converter steelmakingtemperatures for 27 heats, respectively.


0.00000 0.00003 0.00006 0.000090.00000

0.00002

0.00004

0.00006

0.00008

N2F

eO·S

iO2 (

−)

n2FeO·SiO

2

(mol)

2FeO·SiO2

0.0000 0.0007 0.0014 0.00210.0000

0.0004

0.0008

0.0012

0.0016

N

FeO

·Al 2O

3 (−)

nFeO·Al

2O

3

(mol)

FeO·Al2O

3

0.00000 0.00006 0.000120.00000

0.00004

0.00008

0.00012

N

MnO

·SiO

2 (−)

nMnO·SiO

2

(mol)

MnO·SiO2

0.0000000 0.0000006 0.00000120.0000000

0.0000004

0.0000008

0.0000012

N

2MnO

·SiO

2 (−)

n2MnO·SiO

2

(mol)

2MnO·SiO2

0.0000 0.0001 0.0002 0.00030.00000

0.00015

0.00030

N

MnO

· Al 2O

3 (− )

nMnO·Al

2O

3

(mol)

MnO·Al2O

3

0.00E+000 3.00E-015 6.00E-0150.00E+000

2.00E-015

4.00E-015

N

3Al 2O

3·2S

iO2 (

−)

n3Al

2O

3·2SiO

2

(mol)

3Al2O

3·2SiO

2

0.000 0.002 0.004 0.0060.000

0.002

0.004

0.006

N

2CaO

· Al 2O

3·SiO

2 (−)

n2CaO·Al

2O

3·SiO

2

(mol)

2CaO·Al2O

3·SiO

2

0.00000000 0.00000025 0.000000500.0000000

0.0000001

0.0000002

0.0000003

0.0000004

N

CaO

· Al 2O

3·2S

iO2 (

−)

nCaO·Al

2O

3·2SiO

2

(mol)

CaO·Al2O

3·2SiO

2

0.00 0.01 0.02 0.030.000

0.006

0.012

0.018

0.024

N

CaO

·MgO

·SiO

2 (−)

nCaO·MgO·SiO

2

(mol)

CaO·MgO·SiO2

0.0000 0.0003 0.00060.0000

0.0002

0.0004

N

CaO

·MgO

· 2S

iO2 (

− )

nCaO·MgO·2SiO

2

(mol)

CaO·MgO·2SiO2

0.0000 0.0001 0.0002 0.00030.0000

0.0001

0.0002

0.0003

N

2CaO

·MgO

· 2S

iO2 (

−)

n2CaO·MgO·2SiO

2

(mol)

2CaO·MgO·2SiO2

0.000 0.002 0.004 0.0060.000

0.002

0.004

0.006

N

3CaO

·MgO

·2S

iO2 (

−)

n3CaO·MgO·2SiO

2

(mol)

3CaO·MgO·2SiO2

0.0000 0.0003 0.0006 0.00090.0000

0.0002

0.0004

0.0006

NM

gO·S

iO2 (

−)

nMgO·SiO

2

(mol)

MgO·SiO2

0.000 0.002 0.004 0.0060.000

0.002

0.004

0.006

N

MgO

·Al 2O

3 (−)

nMgO·Al

2O

3

(mol)

MgO·Al2O

3

0.0000 0.0004 0.0008 0.00120.0000

0.0002

0.0004

0.0006

0.0008

N

2MgO

·SiO

2 (−)

n2MgO·SiO

2

(mol)

2MgO·SiO2

(h9) (h10) (h11)

(h12) (h13) (h14)

(h15) (h16) (h17)

(h18) (h19) (h20)

(h21) (h22) (h23)

Fig. 3—continued.


The corresponding equilibrium constants of Eq. [9]can be expressed according to IMCT[20–25] as

KHP2O5¼ aP2O5

a5tFea5FetOa

2P

¼ NP2O5� 1

N5FetO½pct P�2f2P

¼ðpct P2O5ÞP2O5

=MP2O5

.P

ni

� �

N5FetO½pct P�2f2P

�ð Þ [10a]

KH3FeO�P2O5

¼ a3FeO�P2O5a5tFe

a5FetOa3FeOa

2P

¼ N3FeO�P2O5� 1

N5FetO

N3FeO½pct P�

2f2P

¼ðpct P2O5Þ3FeO�P2O5

=MP2O5

.P

ni

� �

N5FetO

N3FeO½pct P�

2f2P�ð Þ

½10b�

KH4FeO�P2O5

¼ a4FeO�P2O5a5tFe

a5FetOa4FeOa

2P

¼ N4FeO�P2O5� 1

N5FetO

N4FeO½pct P�

2f2P


=MP2O5

.P

ni

� �

N5FetO

N4FeO½pct P�

2f2P�ð Þ

½10c�

KH2CaO�P2O5

¼ a2CaO�P2O5a5tFe

a5FetOa2CaOa

2P

¼ N2CaO�P2O5� 1

N5FetO

N2CaO½pct P�

2f2P

¼ðpct P2O5Þ2CaO�P2O5

=MP2O5

.P

ni

� �

N5FetO

N2CaO½pct P�

2f2P�ð Þ

½10d�

KH3CaO�P2O5


a5FetOa3CaOa

2P


N5FetO

N3CaO½pct P�

2f2P


=MP2O5

.P

ni

� �

N5FetO

N3CaO½pct P�

2f2P�ð Þ

½10e�

KH4CaO�P2O5


a5FetOa4CaOa

2P


N5FetO

N4CaO½pct P�

2f2P


=MP2O5

.P

ni

� �

N5FetO

N4CaO½pct P�

2f2P�ð Þ

½10f�

KH2MgO�P2O5

¼ a2MgO�P2O5a5tFe

a5FetOa2MgOa

2P

¼ N2MgO�P2O5� 1

N5FetO

N2MgO½pct P�

2f2P

¼ðpct P2O5Þ2MgO�P2O5

=MP2O5

.P

ni

� �

N5FetO

N2MgO½pct P�

2f2P�ð Þ

½10g�

KH3MgO�P2O5

¼ a3MgO�P2O5a5tFe

a5FetOa3MgOa

2P

¼ N3MgO�P2O5� 1

N5FetO

N3MgO½pct P�

2f2P


=MP2O5

.P

ni

� �

N5FetO

N3MgO½pct P�

2f2P�ð Þ

½10h�

0.02 0.04 0.06 0.08 0.100.00

0.02

0.04

0.06

0.08

N

2CaO

·Fe 2O

3 (−)

n2CaO·Fe

2O

3

(mol)

2CaO·Fe2O

3

0.00E+000 3.00E-024 6.00E-024

0.00E+000

2.00E-024

4.00E-024

6.00E-024

N

2MgO

·2A

l 2O3·5

SiO

2 (−)

n2MgO·2Al

2O

3·5SiO

2

(mol)

2MgO·2Al2O

3·5SiO

2

0.00 0.02 0.04 0.060.00

0.01

0.02

0.03

0.04

N

FeO

·Fe 2O

3 (−)

nFeO·Fe

2O

3

(mol)

FeO·Fe2O

3

0.00 0.01 0.02 0.030.00

0.01

0.02

0.03

N

MgO

·Fe 2O

3 (−)

nMgO·Fe

2O

3

(mol)

MgO·Fe2O

3

0.0000 0.0004 0.0008 0.00120.0000

0.0003

0.0006

0.0009

NM

nO·F

e 2O3 (

−)

nMnO·Fe

2O

3

(mol)

MnO·Fe2O

3

(h24) (h25)

(h27) (h28)

(h26)

Fig. 3—continued.


KH3MnO�P2O5

¼ a3MnO�P2O5a5tFe

a5FetOa3MnOa

2P

¼ N3MnO�P2O5� 1

N5FetO

N3MnO½pct P�

2f2P

¼ðpct P2O5Þ3MnO�P2O5

=MP2O5

.P

ni

� �

N5FetO

N3MnO½pct P�

2f2P�ð Þ

½10i�

where MP2O5is molecular mass of P2O5 as 141.94 (–).

According to Eq. [10], the respective phosphorusdistribution ratio of structural units or ion couples asbasic components under existing iron oxides in theslags LP;i can be expressed by

LP;P2O5¼ðpct P2O5ÞP2O5

½pct P�2¼MP2O5

KHP2O5

N5FetO

f2P

Xni �ð Þ

½11a�

LP;3FeO�P2O5¼ðpct P2O5Þ3FeO�P2O5

½pct P�2

¼ MP2O5KH

3FeO�P2O5N5

FetON3

FeOf2P

Xni �ð Þ½11b�

LP;4FeO�P2O5¼ðpct P2O5Þ4FeO�P2O5

½pct P�2

¼ MP2O5KH

4FeO�P2O5N5

FetON4

FeOf2P

Xni �ð Þ½11c�

LP;2CaO�P2O5¼ðpct P2O5Þ2CaO�P2O5

½pct P�2

¼ MP2O5KH

2CaO�P2O5N5

FetON2

CaOf2P

Xni �ð Þ½11d�


½pct P�2

¼ MP2O5KH

3CaO�P2O5N5

FetON3

CaOf2P

Xni �ð Þ½11e�


½pct P�2

¼ MP2O5KH

4CaO�P2O5N5

FetON4

CaOf2P

Xni �ð Þ½11f�

LP;2MgO�P2O5¼ðpct P2O5Þ2MgO�P2O5

½pct P�2

¼ MP2O5KH

2MgO�P2O5N5

FetON2

MgOf2P

Xni �ð Þ½11g�

LP;3MgO�P2O5¼ðpct P2O5Þ3MgO�P2O5

½pct P�2

¼MP2O5KH

3MgO�P2O5N5

FetON3

MgOf2P

Xni �ð Þ½11h�

LP;3MnO�P2O5¼ðpct P2O5Þ3MnO�P2O5

½pct P�2

¼ MP2O5KH

3MnO�P2O5N5

FetON3

MnOf2P

Xni �ð Þ½11i�

where fP is activity coefficient of the dissolved phos-phorus in molten steel (–) and can be calculated byconsidering chemical composition of molten steel andtemperature as

lg fP ¼X

ejP½pct j� �ð Þ ½12a�

ejP ¼A

TþB �ð Þ ½12b�

where A and B are two parameters related to tempera-ture (–). Therefore, the total phosphorus distributionratio between CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags and molten steel can be obtainedfrom Eq. [11] as follows

LP ¼ LP;P2O5þ LP;3FeO�P2O5

þ LP;4FeO�P2O5þ LP;2CaO�P2O5

þ LP;3CaO�P2O5þ LP;4CaO�P2O5

þ LP;2MgO�P2O5

þ LP;3MgO�P2O5þ LP;3MnO�P2O5

¼pct P2O5ð ÞP2O5

½pct P�2þ

pct P2O5ð Þ3FeO�P2O5

½pct P�2

þpct P2O5ð Þ4FeO�P2O5

½pct P�2þ

pct P2O5ð Þ2CaO�P2O5

½pct P�2

þpct P2O5ð Þ3CaO�P2O5

½pct P�2þ


½pct P�2

þpct P2O5ð Þ2MgO�P2O5

½pct P�2þ

pct P2O5ð Þ3MgO�P2O5

½pct P�2

þpct P2O5ð Þ3MnO�P2O5

½pct P�2

¼ MP2O5N5

FetOf2P

�KH

P2O5þ KH

3FeO�P2O5N3

FeO

þKH4FeO�P2O5

N4FeO þ KH

2CaO�P2O5N2

CaO

þKH3CaO�P2O5

N3CaO þ KH

4CaO�P2O5N4

CaO

þKH2MgO�P2O5

N2MgO þ KH

3MgO�P2O5N3

MgO

þKH3MnO�P2O5

N3MnOÞ

Xni �ð Þ ½13�

Therefore, the developed LP prediction model byNFetO to the current slag oxidization ability is composedof Eqs. [11] and [13] based on IMCT.[20–25] According tothe calculated Ni and

Pni in Section III, KH

i by Eq. [10]and fP by Eq. [12], the total phosphorus distributionratio LP of the slags and the respective phosphorusdistribution ratio LP;i of structural units or ion couples


as basic components under existing iron oxides in theslags can be calculated. The standard molar Gibbs freeenergy change DrG

Hm;i of dephosphorization reactions in

Eq. [9] for forming dephosphorization products i isdetermined from the reported data and summarized inTable V.

B. Establishment of LP Prediction Model Basedon Molten Steel Oxidization Ability

The slag oxidization ability presented by FetO has aclose relationship with the oxidization ability of moltensteel by connecting the oxygen content of molten steel atslag–metal interface with FetO in the slags as follows:

t Fe½ � þ O½ � ¼ FetOð Þ

KHFetO¼ aFetO

atFeaO¼ NFetO

aO � 1

DrGHm;FetO

¼ �116; 100þ 48:79T½51� J=molð Þ [14a]

The dephosphorization reactions in Eq. [9] can berewritten by replacing NFetO by aO as follows:

2 P½ � þ 5 O½ � ¼ P2O5ð Þ

K0HP2O5¼ aP2O5

a5Oa2P

¼pct P2O5ð ÞP2O5

=MP2O5

.P

ni

� �

a5O½pct P�2f2P

�ð Þ

½15a�

2 P½ � þ 5 O½ � þ 3 Fe2þ þO2�� ¼ 3FeO � P2O5ð Þ

K0H3FeO�P2O5

¼ a3FeO�P2O5

a5Oa3FeOa

2P


=MP2O5

.P

ni

� �

a5ON3FeO½pct P�

2f2P�ð Þ

½15b�

2 P½ � þ 5 O½ � þ 4 Fe2þ þO2�� ¼ 4FeO � P2O5ð Þ

K0H4FeO�P2O5

¼ a4FeO�P2O5

a5Oa4FeOa

2P


=MP2O5

.P

ni

� �

a5ON4FeO½pct P�

2f2P�ð Þ

½15c�

2 P½ � þ 5 O½ � þ 2 Ca2þ þO2�� ¼ 2CaO � P2O5ð Þ

K0H2CaO�P2O5

¼ a2CaO�P2O5

a5Oa2CaOa

2P


=MP2O5

.P

ni

� �

a5ON2CaO½pct P�

2f2P�ð Þ

½15d�


K0H3CaO�P2O5

¼ a3CaO�P2O5

a5Oa3CaOa

2P


=MP2O5

.P

ni

� �

a5ON3CaO½pct P�

2f2P�ð Þ

½15e�


K0H4CaO�P2O5

¼ a4CaO�P2O5

a5Oa4CaOa

2P


=MP2O5

.P

ni

� �

a5ON4CaO½pct P�

2f2P�ð Þ

½15f�

2 P½ � þ 5 O½ � þ 2 Mg2þ þO2�� ¼ 2MgO � P2O5ð Þ

K0H2MgO�P2O5

¼ a2MgO�P2O5

a5Oa2MgOa

2P


=MP2O5

.P

ni

� �

a5ON2MgO½pct P�

2f2P�ð Þ

½15g�

2 P½ � þ 5 O½ � þ 3 Mg2þ þO2�� ¼ 3MgO � P2O5ð Þ

K0H3MgO�P2O5

¼ a3MgO�P2O5

a5Oa3MgOa

2P


=MP2O5

.P

ni

� �

a5ON3MgO½pct P�

2f2P�ð Þ

½15h�

2 P½ � þ 5 O½ � þ 3 Mn2þ þO2�� ¼ 3MnO � P2O5ð Þ

K0H3MnO�P2O5

¼ a3MnO�P2O5

a5Oa3MnOa

2P

¼ðpct P2O5Þ3MnO�P2O5

=MP2O5

.P

ni

� �

a5ON3MnO½pct P�

2f2P�ð Þ

½15i�

Therefore, the developed respective phosphorus distri-bution ratio LP;i prediction model in Eq. [11] byNFetO can be also rewritten as L

0P;i by aO, i.e.,

aO;ðFetOÞ�½O�, of molten steel at the slag–metal interfaceas follows:


Table

V.

CalculationofStandard

MolarGibbsFreeEnergiesforNineDephosphorizationReactionsfrom

theReported

Data

ofStandard

MolarGibbsFreeEnergies

ReactionNumber

Chem

icalReaction

DrG

H m;i(J/m

ol)

Reference

Notes

Reaction[1]

1 =2P2

=[P]

�157,700+

5.4T

33

Reaction[2]

1 =2O

2=

[O]

�117,110�

3.39T

33

Reaction[3]

2[P]+

5[O

]=

(P2O

5)(l)

�702,912+

556.472T

50

Reaction[4]

P2+

5 =2O

2=

(P2O

5)(l)

�1,603,862+

550.322T

33,50

From

Reactions[1]through[3]

Reaction[5]

t[Fe]+

[O]=

(Fe tO)

�116,100+

48.79T

51

Eq.[9a]

2[P]+

5(Fe tO)

=(P

2O

5)+

5t[Fe]

�122,412+

312.522T

Thisstudy

From

Reactions[3]and[5]

Reaction[6]

3(FeO

)+

(P2O

5)=

(3FeO

ÆP2O

5)

�430,404+

92.708T

20

Eq.[9b]

2[P]+

5(Fe tO)+

3(Fe2

++

O2�)=

(3FeO

ÆP2O

5)+

5t[Fe]

�552,816+

405.23T

Thisstudy

From

Eq.[9a]andReaction[6]

Reaction[7]

4(FeO

)+

(P2O

5)=

(4FeO

ÆP2O

5)

�381,831+

47.367T

20

Eq.[9c]

2[P]+

5(Fe tO)+

4(Fe2

++

O2�)=

(4FeO

ÆP2O

5)+

5t[Fe]

�504,243+

359.889T

Thisstudy

From


Reaction[8]

2(C

aO)+

P2+

5 =2O

2=

(2CaO

ÆP2O

5)(s)

�2,189,069+

585.76T

29

Reaction[9]

2(C

aO)+

(P2O

5)(l)

=(2CaO

ÆP2O

5)(s)

�585,207+

35.438T

29

From

Reactions[4]and[8]

Eq.[9d]

2[P]+

5(Fe tO)+

2(C

a2+

+O

2�)=

(2CaO

ÆP2O

5)+

5t[Fe]

�707,619+

347.96T

Thisstudy

From


Reaction[10]

3(C

aO)+

P2+

5 =2O

2=

(3CaO

ÆP2O

5)(s)

�2,313,752+

556.472T

29

Reaction[11]

3(C

aO)+

(P2O

5)(l)

=(3CaO

ÆP2O

5)(s)

�709,890+

6.15T

29

From

Reactions[4]and[10]

Eq.[9e]

2[P]+

5(Fe tO)+

3(C

a2+

+O

2�)=

(3CaO

ÆP2O

5)(s)+

5t[Fe]

�832,302+

318.672T

Thisstudy

From


Reaction[12]

4(C

aO)+

(P2O

5)(l)

=(4CaO

ÆP2O

5)(l)

�661,356�

3.473T

38

Eq.[9f]

2[P]+

5(Fe tO)+

4(C

a2+

+O

2�)=

(4CaO

ÆP2O

5)+

5t[Fe]

�783,768+

309.049T

Thisstudy

From


Reaction[13]

2(M

gO)+

(P2O

5)=

(2MgO

ÆP2O

5)

168,369�

339.357T

20

Eq.[9g]

2[P]+

5(Fe tO)+

2(M

g2+

+O

2�)=

(2MgO

ÆP2O

5)+

5t[Fe]

45,957�

26.835T

Thisstudy

From


Reaction[14]

3(M

gO)+

P2+

5 =2O

2=

(3MgO

ÆP2O

5)(s)

�1,992,839+

510.0296T

29

Reaction[15]

3(M

gO)+

(P2O

5)=

(3MgO

ÆP2O

5)(s)

�388,977�

40.283T

29

From

Reactions[4]and[14]

Eq.[9h]

2[P]+

5(Fe tO)+

3(M

g2+

+O

2�)=

(3MgO

ÆP2O

5)+

5t[Fe]

�511,389+

272.230T

Thisstudy

From


Reaction[16]

2[P]+

5[O

]+3(M

nO)=

(3MnO

ÆP2O

5)

�1,248,715+

598.312T

28

Reaction[17]

3(M

nO)+

(P2O

5)=

(3MnO

ÆP2O

5)

�543,259+

41.812T

28

From

Reactions[3]and[16]

Eq.[9i]

2[P]+

5(Fe tO)+

3(M

n2+

+O

2�)=

(3MnO

ÆP2O

5)+

5t[Fe]

�665,671+

354.344T

Thisstudy

From



L0

P;P2O5¼

pct P2O5ð ÞP2O5

pct P½ �2

¼ MP2O5K0HP2O5

a5O;ðFetOÞ�½O�f2P

Xni �ð Þ

½16a�

L0

P;3FeO�P2O5

¼pct P2O5ð Þ3FeO�P2O5

pct P½ �2

¼MP2O5K0H3FeO�P2O5

a5O;ðFetOÞ�½O�N3FeOf

2P

Xni �ð Þ

½16b�

L0

P;4FeO�P2O5

¼pct P2O5ð Þ4FeO�P2O5

pct P½ �2

¼MP2O5K0H4FeO�P2O5

a5O;ðFetOÞ�½O�N4FeOf

2P

Xni �ð Þ

½16c�

L0

P;2CaO�P2O5


½pct P�2

¼MP2O5K0H2CaO�P2O5

a5O;ðFetOÞ�½O�N2CaOf

2P

Xni [16d]

L0

P;3CaO�P2O5

¼pct P2O5ð Þ3CaO�P2O5

pct P½ �2



2P

Xni �ð Þ

½16e�

L0

P;4CaO�P2O5

¼pct P2O5ð Þ4CaO�P2O5

pct P½ �2



2P

Xni �ð Þ

½16f�

L0

P;2MgO�P2O5

¼pct P2O5ð Þ2MgO�P2O5

pct P½ �2

¼MP2O5K0H2MgO�P2O5

a5O;ðFetOÞ�½O�N2MgOf

2P

Xni �ð Þ½16g�

L0

P;3MgO�P2O5

¼pct P2O5ð Þ3MgO�P2O5

pct P½ �2

¼MP2O5K0H3MgO�P2O5

a5O;ðFetOÞ�½O�N3MgOf

2P

Xni �ð Þ½16h�

L0

P;3MnO�P2O5

¼pct P2O5ð Þ3MnO�P2O5

pct P½ �2

¼MP2O5K0H3MnO�P2O5

a5O;ðFetOÞ�½O�N3MnOf

2P

Xni �ð Þ

½16i�

The total LP prediction model in Eq. [13] by NFetO canalso be rewritten as L

0P by aO;ðFetOÞ�½O� of molten steel

at the slag–metal interface as follows:

L0

P ¼ L0

P;P2O5þ L

0

P;3FeO�P2O5þ L

0

P;4FeO�P2O5þ L

0

P;2CaO�P2O5

þ L0

P;3CaO�P2O5þ L

0

P;4CaO�P2O5þ L

0

P;2MgO�P2O5

þ L0

P;3MgO�P2O5þ L

0

P;3MnO�P2O5

¼pct P2O5ð ÞP2O5

pct P½ �2þ

pct P2O5ð Þ3FeO�P2O5

pct P½ �2

þpct P2O5ð Þ4FeO�P2O5

pct P½ �2þ


pct P½ �2

þpct P2O5ð Þ3CaO�P2O5

pct P½ �2þ


pct P½ �2

þpct P2O5ð Þ2MgO�P2O5

pct P½ �2þ

pct P2O5ð Þ3MgO�P2O5

pct P½ �2

þpct P2O5ð Þ3MnO�P2O5

pct P½ �2

¼ MP2O5a5O;ðFetOÞ�½O�f

2P

�K0HP2O5þ K

0H3FeO�P2O5

N3FeO

þK0H4FeO�P2O5N4

FeO þ K0H2CaO�P2O5

N2CaO

þK0H3CaO�P2O5N3

CaO þ K0H4CaO�P2O5

N4CaO

þK0H2MgO�P2O5N2

MgO þ K0H3MgO�P2O5

N3MgO

þK0H3MnO�P2O5N3

MnOÞX

ni �ð Þ ½17�

The relationship between KHi in Eqs. [10], [11], and

[13], and K0Hi in Eqs. [15] through [17] can be deduced by

considering KHFetO

in Eq. [14a] as

KHi ¼

K0Hi

KHFetO

� �5 �ð Þ ½18�

It is well known that the equilibrium constant KHi

of formation reaction for molecule i can be deter-mined from its standard molar formation Gibbs freeenergy change DrG

Hm;i as

KHi ¼ exp �DrG

Hm;i=RT

� ��ð Þ ½19�

The standard molar Gibbs free energy change of thepreviously mentioned nine dephosphorization reac-tions in Eq. [15] can be calculated by combining therelated values of standard molar Gibbs free energychange for the nine dephosphorization reactions inEq. [9] listed in Table V.


C. Definition of Mass Action Concentration for FetOin CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 SlagsBased on IMCT

According to the developed LP prediction modelbased on IMCT,[20–25] the mass action concentration ofFetO, i.e., NFetO, is recommended by Zhang to presentthe slag oxidization ability rather than NFeO; NFe2O3

;or NFeO�Fe2O3

. The IMCT[20–25] proposed that all ironoxides in metallurgical slags are composed of ion couple(Fe2++O2�), simple molecule Fe2O3, and complexmolecule FeOÆFe2O3; therefore, the related structuralunits of iron oxides can equilibrate among thosestructural units dynamically as follows:

Fe2O3ð Þ þ Fe½ � ¼ 3 Fe2þ þO2�� ½20a�

FeO � Fe2O3ð Þ þ Fe½ � ¼ 4 Fe2þ þ O2�� ½20b�

Obviously, the contribution of simple molecule Fe2O3

to oxygen potential of slags or slag oxidization abilityis equivalent to three times that of the ion couple(Fe2++O2–) from Eq. [20a]. Similarly, the contribu-tion of complex molecule FeOÆFe2O3 to slags oxidiza-tion ability is four times as that of ion couple(Fe2++O2–) from Eq. [20b]. Therefore, the slags oxi-dization ability or NFetO can be defined as

NFetO ¼ NFeO þNFeO;Fe2O3!FeO þNFeO;Fe3O4!FeO

¼ NFeO þ3ðnFe2þ;Fe2O3!FeO þ nO2�;Fe2O3!FeOÞP

ni

þ4ðnFe2þ;Fe3O4!FeO þ nO2�;Fe3O4!FeOÞP

ni

¼ NFeO þ3� 2nFe2O3P

niþ 4� 2nFe3O4P

ni

¼ NFeO þ 6NFe2O3þ 8NFe3O4

�ð Þ ½21�

It should be emphasized that the defined NFetO fromIMCT[20–25] has the similar meaning with aFetO from theviewpoint of traditionally metallurgical physicochemist-ry, which can be calculated according to (FetO)–[O]equilibrium via Eq. [14a] as

aFetO ¼ KHFetO

aO ¼ KHFetO½pct O�fO ½14b�

where fO is oxygen activity coefficient (–) and can bedetermined by

lg fO ¼ eOO½pct O� þ eCO½pct C� þ eSO½pct S� ½22�

The related values of interaction coefficients are chosenas eOO = �0.2, eCO = �0.45, and eSO = �0.133.[52]

It is well known that product of [pct C] 9 [pct O]is a constant around 0.0024 at top–bottom combinedblown converter steelmaking temperatures, i.e., 1873 K(1600 �C). The measured product of [pct C] 9 [pct O] inthe 80-ton top–bottom combined blown converter is0.0027. Therefore, the oxygen content in molten steel inthis study can be calculated by ½pct O]¼ 0:0027=½pct C].Hence, the iron oxides activity aFetO in slags can becalculated from Eq. [14b] as

aFetO ¼ KHFetO

aO ¼ KHFetO

fO0:0027.½pct C� �ð Þ ½14c�

D. Comparison of Measured LP;measured

and Calculated LIMCTP;calculated

The calculated LP by Eq. [13] has the same values withthat by Eq. [17] based on the developed IMCT LP

prediction model. The logarithm of the calculatedLIMCTP;calculated by IMCT LP model for all 27 investigated

heats has been compared with the logarithm of themeasured LP;measured, which is equal to (pct P2O5)/[pct P]2, as shown in Figure 4(a). Although the calcu-lated LIMCT

P;calculated for most heats is to some degree larger

than the measured LP;measured, a relative agreement

between LIMCTP;calculated and LP;measured can be obtained for

27 heats. This finding implies that the developed IMCTLP prediction model can be applied basically to predictLP during a top–bottom combined blown convertersteelmaking process.When NFetO in Eq. [13] is replaced by aFetO, which is

calculated from Eq. [14c], or when aO, i.e., aO;ðFetOÞ�½O�,in Eq. [17] is substituted by aO;½C��½O� ¼ ½pct O�fO ¼0:0027fO=½pct C], the calculated L

aFetO;IMCT

P;calculated or

L0aO;½C��½O�;IMCT

P;calculated has no corresponding relationship with

LP;measured as illustrated in Figure 4(b). The reason ofdifference between NFetO and aFetO, or aO;ðFetOÞ�½O� andaO;½C��½O�, will be discussed in Section VI–C. Therefore,aFetO from the [C]–[O] equilibrium in a metal bathcannot be applied to the oxygen potential of the slags;however, aO;½C��½O� cannot be also applied to the oxygenpotential of molten steel at slag–metal interface during atop–bottom combined blown converter steelmakingprocess. Under these circumstances, the calculated

LNFetO;IMCT

P;calculated or L0aO;ðFetOÞ�½O�;IMCT

P;calculated from the developed IMCT

model is presented by LIMCTP;calculated or L

0IMCTP;calculated in the

next sections, respectively.

2 4 62

4

6

(a)

NFe

tO or a

O,(FetO) −[O]

lgLP, measured

(−)

lgLN

Fe tO

, IM

CT

P, c

alcu

late

d or

lgL'a

O, (

Fe tO

)−[

O], I

MC

T

P, c

alcu

late

d (

− )

0 2 4 60

2

4

6

lgLP, measured

(−)

lgLa F

e tO, I

MC

T

P, c

alcu

late

d or

lgL'a

O, [

C]−

[O], I

MC

T

P, c

alcu

late

d (

− )

(b)

aFe

tO or a

O, [C]−[O]

Fig. 4—Comparison between calculated and measured phosphorusdistribution ratio of CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5

slags equilibrated with molten steel at top–bottom combined blownconverter steelmaking temperatures with NFetO or aO;ðFetOÞ�½O� (a)and aFetO or aO;½C��½O� (b) presenting slag or molten steel oxidizationability for 27 heats, respectively.


V. COMPARISON OF CALCULATED LP

BY SOME LP PREDICTION MODELS

Comparing the predicted results both by the IMCTLP model and by the other LP models is important toverify the feasibility of the developed IMCT LP modelbesides a comparison of the measured LP;measured and thepredicted LIMCT

P;calculated by IMCT LP model.

A. Evaluation of LP Prediction Models

The widely recognized LP prediction models forvarious oxidizing slags by different researchers[9–14] havebeen summarized briefly in Table VI, in which thecomprehensive effects of temperature and slag compo-sition, such as CaO, MgO, MnO, SiO2, FetO, or TÆFe orFeO, on LP have been considered; however, most ofthem are empirically thermodynamic models frommathematical regression of experimental data. The mainresults of the LP prediction models in Table VI can besummarized as follows:

(a) Increasing basic components content, such as CaO,MgO, and MnO, can improve dephosphorizationability, such as Healy’s model,[10] Suito’s three mod-els,[11,12] Sommerville’s model,[9,13] and Balajiva’smodel.[14] Most models in Table VI, such as Suito’sthree models,[11,12] Sommerville’s model,[9,13] andBalajiva’s model,[14] suggest that the contribution ofCaO on dephosphorization ability is larger than thatof MgO and MnO.

(b) Iron oxides expressed as FetO in Suito’s No. 1model,[11,12] Suito’s No. 2 model,[11,12] and Balajiva’smodel[14]; as TÆFe in Healy’s model[10] and Suito’sNo. 3 model[11,12]; or as FeO in Sommerville’smodel[9,13] has a positive effect on LP. The contri-bution of iron oxides expressed as FetO, TÆFe, orFeO is less than that of each basic component asCaO, MgO, and MnO with the same mass percent.

(c) High temperature can directly decrease dephosph-orization ability as shown in Healy’s model,[10]

Suito’s three models,[11,12] Sommerville’s model,[9,13]

and Balajiva’s model[14]; meanwhile, high tempera-ture can decrease dephosphorization ability of basiccomponents as CaO, MgO, and MnO as shown inSommerville’s model.[9,13]

(d) SiO2 has a very small contribution to decreasedephosphorization ability of the slags.

(e) Most models suggest that P2O5 can reduce thedephosphorization ability of slags, except Suito’sNo. 3 model.[11,12]

B. Comparison of Calculated LP by Different Models

The comparison between the measured LP;measured andthe calculated Li

P;calculated in logarithmic form by the

various models listed in Table VI for 27 heats atcombined blown converter steelmaking temperatures isshown in Figure 5. Obviously, lgLIMCT

P;calculated by the

IMCT LP model, lgLHealyP;calculated by Healy’s LP model,[10]

lgLSuito0sNo:1P;calculated by Suito’s No. 1 LP model,[11,12]

Table

VI.

Form

ulasofPhosphorusDistributionRatioPredictionModelsReported

inRelatedLiteratures

LPModel

Slags

Form

ulasofLPmodels

Reference

Healy’smodel

CaO-SiO

2-M

gO-Fe tO-M

nO-A

l 2O

3slags

lgðpctPÞ

½ pctP�¼

22;350

Tþ0:08ðpctCaOÞþ

2:5lgðpctT�F

eÞ�16

10

Suito’sNo.1model

CaO-SiO

2-M

gO-Fe tO-P

2O

5slags

lgðpctP

2O

5Þ

½pctP�2 ðpctFe tOÞ5¼

0:145½ðp

ctCaOÞþ

0:3ðpctMgOÞ

�0:5ðpctP2O

5Þþ

0:6pctðM

nO)]þ

22;810

T�20:506

11,12

Suito’sNo.2model

CaO-SiO

2-M

gO-Fe tO-P

2O

5slags

lgðpctP

2O

5Þ

½ pctP�2 ðpctFe tOÞ5¼

7:87lg½ðp

ctCaOÞþ

0:3ðpctMgOÞ

�0:05ðpctFe tOÞ�

0:5ðpctP2O

5Þþ

0:6pctðM

nO)]þ

22;240

T�27:124

11,12

Suito’sNo.3model

CaO-SiO

2-M

gO-Fe tO-P

2O

5slags

lgðpctPÞ

½ pctP�ðp

ctT�FeÞ

5=2¼

0:0720½ðp

ctCaOÞþ

0:3ðpctMgOÞþ

0:6pctðP

2O

5Þ

þ0:6pctðM

nOÞ�þ

11;570

T�10:520

11,12

Sommerville’smodel

CaO-SiO

2-M

gO-FeO

-MnO

slags

lgðpctP

2O

5Þ

½pctP�¼

11;000

Tþ2:5lgðpctFeOÞþ

½162ðpctCaOÞþ

127:5ðpctMgOÞþ

28:5ðpctMnOÞ�

T

�0:0006287:04lgðpct

SiO

2Þ2�10:40

9,13

Balajiva’smodel

CaO-SiO

2-M

gO-Fe tO-M

nO-P

2O

5slags

lgðpctP2O

5Þ

½pctP�2¼

5lgðpctFe tOÞþ

0:145½ðp

ctCaOÞ

þ0:3ðpctMgOÞ�

0:5ðpctP2O

5Þþ

0:6ðpctMnOÞ�þ

22;810

T�20:506

14


lgLSuito0sNo:2P;calculated by Suito’s No. 2 LP model,[11,12]

lgLSommervilleP;calculated by Sommerville’s LP model,[9,13] and

lgLBalajivaP;calculated by Balajiva’s LP model[14] are in basic

agreement with the measured lgLP;measured except

lgLSuito0sNo:3P;calculated by Suito’s No. 3 LP model.[11,12] Among

lgLIMCTP;calculated; lgL

HealyP;calculated; lgLSuito0sNo:1

P;calculated; lgLSuito0sNo:2P;calculated;

lgLSommervilleP;calculated ; and; lgL

BalajivaP;calculated; lgLSuito0sNo:1

P;calculated; and,

lgLBalajivaP;calculated are larger than lgLP;measured, only lg

LIMCTP;calculated; lgL

HealyP;calculated; lgL

Suito0sNo:2P;calculated; and lgLSommerville

P;calculated

have a relatively good agreement with lgLP;measured.It should be emphasized that the calculated Li

P;calculatedby various models listed in Table VI has been trans-ferred into ðpct P2O5Þ

�½pct P]2, rather than the defined

phosphorus distribution ratio as ðpct PÞ=½pct P] inHealy’s model,[10] as ðpct P2O5Þ

�½pct P]2ðpct FetOÞ5 in

Suito’s No. 1 and No. 2 models,[11,12] asðpct P2O5Þ

�½pct P]2ðpct T � FeÞ5 in Suito’s No. 3

model,[11,12] or as ðpct P2O5Þ=½pct P] in Sommerville’smodel[9,13] as listed in Table VI.

VI. RESULTS AND DISCUSSIONON OXIDIZATION ABILITY OF CaO-SiO2-MgO-

FeO-Fe2O3-MnO-Al2O3-P2O5 SLAGS

The comprehensive effects of slags oxidation abilityexpressed as NFetO and mass action concentrations ofbasic components, i.e., FeO, CaO, MgO, and MnO,have been considered in the developed IMCT LP

prediction model. The slag oxidization ability, i.e.,NFetO in CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5,and slags at combined blown converter steelmakingtemperatures should be discussed in detail.

A. Relationship between Mass Percent of Iron Oxidesand NFetO or aFetO

The relationship between mass percent of various ironoxides, i.e., FeO, Fe2O3, and FetO, and the calculatedtotal mass action concentrations of structural unitscontaining iron oxides NFetO or calculated iron oxide

activity aFetO ¼ KHFetO

aO ¼ KHFetO

fO0:0027.½pctC� from

Eq. [14c] based on (FetO)–[O] equilibrium is illustratedin Figures 6(a) and 6(b). The comparison between aFetOand mass action concentrations of various structuralunits or ion couples containing iron oxides such asNFeO; NFe2O3

; NFeO�Fe2O3; and NFetO for the slags at

combined blown converter steelmaking temperaturesis shown in Figure 6(c). It can be observed fromFigure 6(a) that not only the mass percent of FeO andFe2O3 but also the sum of mass percent for FeO andFe2O3 corresponds well with NFetO in the slags; however,no obvious corresponding relationship between (pctFeO), (pct Fe2O3), or (pct FetO) and aFetO can beobserved from Figure 6(b) for the slags. Meanwhile, noclear corresponding relationship between aFetOand NFeO; NFe2O3

, NFeO�Fe2O3, or NFetO can be observed

from Figure 6(c). The value of NFe2O3or NFeO�Fe2O3

isvery small compared with that of NFeO, although NFe2O3

or NFeO�Fe2O3has a large contribution to NFetO according

to IMCT[20–25] in Eq. [21].Therefore, the oxidization ability of the slags, i.e.,

NFetO, according to IMCT[20–25] in Eq. [21] is larger thanthe calculated aFetO based on (FetO)–[O] equilibrium.

0 10 20 30 40 50

0.0

0.2

0.4

0.6

0.8

1.0

NF

e O

Mass percent of iron oxides (%)

FeOFe

2O

3

FetO

(a)

0 10 20 30 40 500.0

0.2

0.4

0.6

(b)

FeOFe

2O

3

FetO

a Fe tO

(− )

Mass percent of iron oxides (%)0.0 0.1 0.2 0.3 0.4 0.5

0.0

0.2

0.4

0.6

0.8

1.0

(c)

aFe

tO (−)

NFeO

NFe

2O

3

NFeO·Fe

2O

3

NFe

tO

N

i (−)

(− )

t

Fig. 6—Relationship between mass percent of iron oxides, i.e., FeO, Fe2O3 and FetO, and the calculated mass action concentration of FetONFetO (a) or FetO activity aFetO based on (FetO)–[O] equilibrium (b), and comparison between aFetO and Ni for various iron oxides, i.e., NFeO,NFe2O3

, NFeO�Fe2O3, and NFetO (c), in CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags equilibrated with molten steel at top–bottom combined

blown converter steelmaking temperatures for 27 heats, respectively.

2 3 4 52

4

6

8

10

IMCT model Healy's modelSuito's No. 1 model Suito's No. 2 modelSuito's No. 3 model Sommerville's modelBalajiva's model

lgLP, measured

(−)

lgLi P

, cal

cula

ted (

−)

Fig. 5—Comparison between lgLP;measured and lgLiP;calculated of

CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags equilibratedwith molten steel at top–bottom combined blown converter steel-making temperatures by seven LP prediction models containingIMCT LP model for 27 heats.


B. Relationship between Mass Percent of FeO and Fe2O3

or NFeO and NFe2O3

The relationship between the mass percent of FeOor NFeO and the mass percent of Fe2O3 or NFe2O3

inCaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags atcombined blown converter steelmaking temperatures isillustrated in Figure 7, respectively. The mass percent ofFeO has a very good linear relationship with masspercent of Fe2O3 in the slags from Figure 7(a). Thisindicates that (pct Fe2O3) increases with a increasing of(pct FeO) in the slags. Meanwhile, the linear relation-ship between NFeO and NFe2O3

or NFeO�Fe2O3implies that

higher NFeO can result in the increase of NFe2O3or

NFeO�Fe2O3in the slags as shown in Figure 7(b).

C. Comparison of Calculated ½pct O�½C��½O� withCalculated ½pctO�ðFetOÞ�½O�

It has shown from Figure 6(c) that there is no goodrelationship between aFetO ¼ KH

FetOaO ¼ KH

FetOfO0:0027=

½pctC� from Eq. [14c] based on (FetO)–[O] equilibrium

and NFetO. This finding indicates that aO;½C��½O� ¼fO½pct O] ¼ fO0:0027=½pctC� in the formula of aFetOshown in Eq. [14c] cannot be applied to the oxygenactivity of molten steel at the slag–metal interface.Replacing aFetO by NFetO in (FetO)–[O] equilibrium asshown in Eqs. [14a] through [14c], the oxygen activityand oxygen content of molten steel at the slag–metalinterface can be determined by

aslag�metal interfaceO;ðFetOÞ�½O�

¼ NFetO

.KH

FetO½23a�

½pctO�slag�metal interfaceðFetOÞ�½O� ¼ NFetO

.KH

FetOfO ½23b�

Figure 8(a) illustrates the relationship between the

calculated ½pctO�bath½C��½O� of metal in a metal bath accord-

ing to the constant product of [pct C] and [pct O] as0.0027, i.e., [pct C] 9 [pct O] = 0.0027, and

½pctO�slag�metal interfaceðFetOÞ�½O� in molten steel at slag–metal

interface according to (FetO)–[O] equilibrium withreplacing aFetO by NFetO for all 27 heats at combined

blown converter steelmaking temperatures. The rela-tionship between the ratio of oxygen activity of moltensteel at the slag–metal interface based on (FetO)–[O]

equilibrium aslag�metal interfaceO;ðFetOÞ�½O�

to the oxygen activity of

metal in metal bath based on [C]–[O] equilibriumabathO;½C��½O� ¼ fO½pct O] or the measured carbon content

[pct C] and ½pct O�bath½C��½O� is also shown in Figure 8(b).

Obviously, ½pct O�slag�metal interfaceðFetOÞ�½O� is larger than

½pct O�bath½C��½O� as shown in Figure 8(a), whereas the ratio

of aslag�metal interfaceO;ðFetOÞ�½O�

.abathO;½C��½O� decreases from 6 to 1 with

increasing ½pct O�bath½C��½O� from 0.025 to 0.075 as shown in

Figure 8(b). It is well known that an increasing of

½pct O�bath½C��½O� from 0.025 to 0.1 corresponds to a decrease

of [pct C] from 0.15 to 0.03. This finding indicates thatthere is a high oxygen activity layer beneath the slag–

metal interface when ½pct O�bath½C��½O� is less than 0.075, in

which [pct C] is larger than 0.03. This result is in goodagreement with the converter steelmaking experiencethat the molten steel containing low [pct C] and high O[pct O] corresponds with the slag characteristics duringthe converter steelmaking process.

VII. RESULTS AND DISCUSSION ON LP

A. Influences of Components on LP

1. Relationship between mass action concentrationsof components and lg LP;measured or lg LIMCT

P;calculatedThe effect of the calculated mass action concen-

trations of components NFeO�Fe2O3and NFetO, on

lgLP;measured or lgLIMCTP;calculated for the slags equilibrated

with molten steel during the combined blown convertersteelmaking process is shown in Figure 9, respectively. Itcan be observed from Figures 9(a), (c), and (f) thatincreasing NCaO, NMgO, and NMnO can lead to a decreasein LP; however, improving NFeO, NFe2O3

, NFeO�Fe2O3, and

NFetO will result in increasing LP from Figures 9(d), (e),(h), and (i). No corresponding relationship betweenlgLP;measured or lgLIMCT

P;calculated and NSiO2or NAl2O3

can be

0.00 0.05 0.10 0.150

2

4

6

8

(b)

aslag−metal interface

O, (FetO)−[O]

/abath

O, [C]−[O]

[%C

] (− )

[%O]bath

[C]−[O] (−)

Rat

io o

f asl

ag− m

etal

inte

rfac

e

O, (

Fe tO

)−[O

] to

aba

th

O, [

C]−

[O] ( −

)

0.00

0.05

0.10

0.15

0.20

[%C]

0.0 0.1 0.2 0.30.0

0.1

0.2

0.3

(a)

[%O]bath

[C]−[O] (−)

[%O

]slag

−met

al in

terf

ace

(Fe tO

)−[O

] (

−)

Fig. 8—Relationship between calculated oxygen content of metal inmetal bath ½pct O�bath½C��½O� based on [C]–[O] equilibrium and oxygencontent of metal at slag–metal interface ½pctO�slag�metal interface

ðFetOÞ�½O� basedon (FetO)–[O] equilibrium with replacing aFetO by NFetO (a), and plotof ratio for aslag�metal interface

O;ðFetOÞ�½O�to abathO;½C��½O� ¼ fO½pct O], or carbon con-

tent of metal in metal bath against ½pct O�bath½C��½O� (b) for 27 heats,respectively.

0 5 10 15 200

10

20

30

(a)

(%F

e 2O3)

(−)

(%FeO) (−)

0.0 0.1 0.2 0.3 0.40.00

0.01

0.02

0.03

0.04

(b)

NFe

2O

3

NFeO·Fe

2O

3

NF

e 2O3 o

r N

FeO

·Fe 2O

3 (−)

NFeO

(−)

Fig. 7—Relationship between mass percent of FeO and mass percentof Fe2O3 (a) or NFeO and NFe2O3

or NFeO�Fe2O3(b) in CaO-SiO2-

MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags equilibrated with moltensteel at top–bottom combined blown converter steelmaking tempera-tures for 27 heats, respectively.


observed from Figures 9(b) and (g). It should be notedthat NFetO is the sum of NFeO, 6NFe2O3

, and 8NFeO�Fe2O3

as defined by Zhang[20] in Eq. [21]. The comprehensiveeffect of all iron oxides, i.e., NFetO ¼ NFeO þ 6NFe2O3

þ8NFeO�Fe2O3

, on LP also show an obvious promotioneffect on LP as shown in Figure 9(i).

2. Relationship between mass percent of componentsand lg LP;measured or lg LIMCT

P;calculatedThe effect of mass percent for CaO, SiO2, MgO, FeO,

Fe2O3, MnO, and Al2O3 as components in CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3 slags on lgLP;measured or

lgLIMCTP;calculated at top–bottom combined blown converter

steelmaking temperatures is given in Figure 10, respec-tively. It can be observed from Figure 10(a) through (c)

and (f) that increasing the mass percent of CaO, SiO2,MgO, and MnO can result in decreasing lgLP;measured or

lgLIMCTP;calculated; however, improving the mass percent of

FeO and Fe2O3 can lead to increasing lgLP;measured or

lgLIMCTP;calculated from Figure 10(d) and (e). No obvious

relationship between the mass percent of Al2O3 andlgLP;measured or lgLIMCT

P;calculated can be observed from

Figure 10(g).It can be also obtained by comparing Figures 9

and 10 that the mass percent for six components exceptAl2O3 has similar effects on lgLP;measured or lgLIMCT

P;calculatedas mass action concentrations Ni of the correspondingcomponents except Al2O3. Therefore, the components ofCaO, MgO, and MnO have a comprehensive contribu-tion on LP with FetO. Increasing the mass percent of

0.20 0.25 0.30 0.35 0.402

3

4

5

6

7

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (−)

NCaO

(−)

CaOlgL

P, measured

lgLIMCT

P, calculated

0.0000 0.0002 0.00042

3

4

5

6

7

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (−) SiO

2

lgLP, measured

lgLIMCT

P, calculated

NSiO

2

(−)

0.10 0.15 0.20 0.25 0.302

3

4

5

6

7

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (−) MgO

lgLP, measured

lgLIMCT

P, calculated

NMgO

(−)

0.0 0.1 0.2 0.3 0.42

3

4

5

6

7

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (− )

NFeO

(−)

FeOlgL

P, measured

lgLIMCT

P, calculated

0.00 0.01 0.02 0.032

3

4

5

6

7

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (−)

NFe

2O

3

(−)

Fe2O

3

lgLP, measured

lgLIMCT

P, calculated

0.01 0.02 0.032

3

4

5

6

7

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (−)

NMnO

(−)

MnOlgL

P, measured

lgLIMCT

P, calculated

0.000 0.001 0.002 0.0032

3

4

5

6

7

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (−

)

Al2O

3

lgLP, measured

lgLIMCT

P, calculated

NAl

2O

3

(−)

0.00 0.01 0.02 0.03 0.042

3

4

5

6

7

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (−)

NFeO·Fe

2O

3

(−)

FeO·Fe2O

3

lgLP, measured

lgLIMCT

P, calculated

0.0 0.2 0.4 0.6 0.82

3

4

5

6

7

NFe

tO (−)

FetO

lgLP, measured

lgLIMCT

P, calculated

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (−)

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

Fig. 9—Effect of calculated mass action concentration of ion couples or simple or complex molecules of (Ca2++O2�), SiO2, (Mg2++O2�),(Fe2++O2�), Fe2O3, (Mn2++O2�), Al2O3, FeOÆFe2O3, and defined NFetO in CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags on

lgLP;measured and lgLIMCTP;calculated at top–bottom combined blown converter steelmaking temperatures for 27 heats, respectively.


basic oxides, i.e., CaO, MgO, and MnO, or the massaction concentration of ion couples (Ca2++O2�),(Mg2++O2�), and (Mn2++O2�) cannot effectivelyincrease LP when the mass percent of iron oxides orNFetO is small enough in the slags.

There are some extreme proofs to support this resultas follows: (1) slags with high FetO but very low CaO,which is applied in desiliconization pretreatment of hotmetal, can extract only silicon but not phosphorus fromhot metal; (2) slags with high CaO but very low FetO,which is applied at reduction period during electric arcfurnace steelmaking process, can extract only sulfur butnot phosphorus from molten steel. Therefore, thecomprehensive effect of basic components, especiallyCaO and FetO, can make the controlling contribution toLP in the slags during the combined blown convertersteelmaking process.

3. Relationship between slag basicity and lg LP;measured

or lg LIMCTP;calculated

The relationship between lgLP;measured or lgLIMCTP;calculated

and binary basicity (pct CaO)/(pct SiO2), complexbasicity ðpct CaO) + 1:4ðpct MgO)ð Þ= ðpct SiO2Þ þð(pct P2O5Þ + (pct Al2O3ÞÞ, and optical basicity withthree-group optical basicity for FeO and Fe2O3 as (1)KFeO = 0.51 and KFe2O3

= 0.48, which are measuredfrom Pauling electronegativity[53]; (2) KFeO = 0.93 andKFe2O3

= 0.69, which are derived from average electrondensity[54]; and (3) KFeO = 1.0 and KFe2O3

= 0.75,which are mathematically regressed,[55] is illustratedin Figure 11, respectively. It can be observed fromFigures 11(a) and (b) that increasing binary or complexbasicity from 2.5 to 4.0 can improve LP effectively;however, increasing binary or complex basicity from 4.0to 5.0 can bring an obviously decreasing tendency of LP.

0 5 10 15 202

3

4

5

6

7

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (−)


FeOlgL

P, measured

lgLIMCT

P, calculated

0 10 20 302

3

4

5

6

7

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (−)


3 (%)

Fe2O

3

lgLP, measured

lgLIMCT

P, calculated

0.4 0.8 1.2 1.62

3

4

5

6

7

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (− )


MnOlgL

P, measured

lgLIMCT

P, calculated

0 1 2 3 4 52

3

4

5

6

7

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (− ) Al

2O

3

lgLP, measured

lgLIMCT

P, calculated


3 (%)

30 40 50 602

3

4

5

6

7

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (−

)


CaOlgL

P, measured

lgLIMCT

P, calculated

5 10 15 20 252

3

4

5

6

7

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (−) SiO2

lgLP, measured

lgLIMCT

P, calculated


4 6 8 10 122

3

4

5

6

7

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (−) MgO

lgLP, measured

lgLIMCT

P, calculated


(a) (b) (c)

(d) (e)

(g)

(f)

Fig. 10—Effect of mass percent of CaO, SiO2, MgO, FeO, Fe2O3, MnO, and Al2O3 as components in CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-

P2O5 slags on lgLP;measured and lgLIMCTP;calculated at top–bottom combined blown converter steelmaking temperatures for 27 heats, respectively.


Increasing the optical basicity of the slags with KFeO as0.51 and KFe2O3

as 0.48[53] can result in a decrease of LP

like that of the complex basicity; increasing opticalbasicity of the slags with KFeO as 1.0 and KFe2O3

as0.75[55] can lead to an increase of LP like that of simplebasicity from 2.5 to 4.0. No obvious relationshipbetween LP and optical basicity of the slags with KFeO

as 0.93 and KFe2O3as 0.69[54] can be observed. Therefore,

no uniform relationship between LP and optical basicityof the slags with various values for KFeO and KFe2O3

canbe obtained.

4. Relationship between ratio of mass percent of ironoxides to basic oxides and lg LP;measured or lg LIMCT

P;calculatedThe relationship between the mass percent ratio of

iron oxides, i.e., FeO, Fe2O3, FetO, to all basic oxides,such as CaO, MgO, MnO, and lgLP;measured or

lgLIMCTP;calculated for the slags equilibrated with molten steel

at top–bottom combined blown converter steelmakingtemperatures is shown in Figures 12(a) through (i),respectively. The relationship between the mass percentratio of FeO or Fe2O3 to FetO and lgLP;measured or

lgLIMCTP;calculated is illustrated in Figures 12(j) and (k) for a

comparison. The mass percent of FetO is calculated by(pct FetO) = (pct FetO)+0.9(pct Fe2O3). It can beobserved from Figures 12(a) through (i) that increasingthe mass percent ratio of FeO, Fe2O3, or FetO to CaO,MgO, or MnO shows an obviously positive effect onlgLP;measured or lgL

IMCTP;calculated, respectively. Therefore, it is

not the independent effects of iron oxides or basicoxides, but the comprehensive effects of iron oxides andbasic oxides that control the dephosphorization reac-tions during a combined blown converter steelmakingprocess. The optimal dephosphorization condition canbe found at a reasonable mass percent ratio of FeO toFe2O3 as 0.62 (=0.40/0.65) from Figures 12(j) and (k).

5. Relationship between ratio of mass actionconcentrations for iron oxides to basic oxides andlg LP;measured or lg LIMCT

P;calculatedThe relationship between the mass action concentra-

tion ratio of iron oxides, i.e., NFeO, NFe2O3, NFeO�Fe2O3

, toall basic oxides, i.e., NCaO, NMgO, NMnO, and

lgLP;measured or lgLIMCTP;calculated for the slags equilibrated

with molten steel at combined blown steelmakingtemperatures is shown in Figures 13(a) through (i),respectively. The relationship between NFeO=NFetO,NFe2O3

=NFetO, or NFeO�Fe2O3=NFetO, and lgLP;measured or

lgLIMCTP;calculated is also illustrated in Figures 13(j) through

(l) for a comparison. It can be observed fromFigures 13(a) through (i) that increasing the mass actionconcentration ratio of iron oxides to all basic oxidesshows an obvious promotion effect on increasing thedephosphorization ability of the slags. However, smallNFeO=NFetO and large NFeO�Fe2O3

=NFetO as well asreasonable NFe2O3

=NFetO, such as 0.035, can promotethe dephosphorization ability of the slags, as shown inFigures 13(j) through (l).

B. Contribution of Basic Oxides to DephosphorizationAbility of CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags

As described in Eqs. [9a] or [15a], the structural unitP2O5 is generated from phosphorus in molten steeloxidized by FetO in the slags or by [O] in molten steel.Other dephosphorization products presented in Eqs. [9b]through [9i] or Eqs. [15b] through [15i] are complexmolecules, i.e., 3FeOÆP2O5, 4FeOÆP2O5, 2CaOÆP2O5,3CaOÆP2O5, 4CaOÆP2O5, 2MgOÆP2O5, 3MgOÆP2O5, and3MnOÆP2O5.This finding indicates that basic oxides in theslags can make different contributions to the totaldephosphorization under the condition of necessaryoxidation ability presented as NFetO in the slags during atop–bottom combined blown converter steelmakingprocess.It is well known that four basic oxides, such as FeO,

CaO, MgO, and MnO, in the slags can react withphosphorous in molten steel to produce nine stableindependent structural units, including P2O5, 3FeOÆP2O5, 4FeOÆP2O5, 2CaOÆP2O5, 3CaOÆP2O5, 4CaOÆP2O5,2MgOÆP2O5, 3MgOÆP2O5, and 3MnOÆP2O5 as complexmolecules. The respective phosphorus distribution ratioLIMCTP;i;calculated of the previously mentioned nine complex

molecules containing P2O5 in the slags can be deter-mined by the developed IMCT LP model.

0.6 0.7 0.8 0.92

4

6

8

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (−)

Optical basicity (−)

FeO=0.51,

Fe2O

3

=0.48

lgLP, measured

lgLIMCT

P, calculated

FeO=0.93,

Fe2O

3

=0.69

lgLP, measured

lgLIMCT

P, calculated

FeO=1.0,

Fe2O

3

=0.75

lgLP, measured

lgLIMCT

P, calculated

(c)

2 3 4 5 62

3

4

5

6

7

(a)

lgLP, measured

lgLIMCT

P, calculated

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (−

)

Binary basicity (−)1.0 1.5 2.0 2.5 3.02

3

4

5

6

7

(b)

lgLP, measured

lgLIMCT

P, calculated

Complex basicity (−)

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (− )

Fig. 11—Effects of binary basicity (pct CaO)/(pct SiO2) (a), complex basicity ðpct CaO) + 1:4ðpct MgO)ð Þ= ðpct SiO2Þ + (pct P2O5Þþð(pct Al2O3ÞÞ (b), and optical basicity (c) of CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags by taking (1) KFeO = 0.51, KFe2O3

= 0.48; (2)KFeO = 0.93, KFe2O3

= 0.69; or (3) KFeO = 1.0, KFe2O3= 0.75 on lgLP;measured and lgLIMCT

P;calculated at top–bottom combined blown converter steel-making temperatures for 27 heats, respectively.


The relationship between the calculated lgLIMCTP;i;calculated

of nine structural units containing P2O5 and thecalculated lgLIMCT

P;calculated of the slags by the developed

IMCT LP model at combined blown converter steel-making temperatures is illustrated in Figure 14(a),respectively. The slope of the linear relationship between

0.0 0.2 0.4 0.62

4

6

8

(a)

lgLP, measured

lgLIMCT

P, calculated

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (− )

(%FeO)/(%CaO) (−)0.0 0.5 1.0 1.52

4

6

8

(c)

lgLP, measured

lgLIMCT

P, calculated

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (−)

(%FetO)/(%CaO) (−)

0.0 0.2 0.4 0.6 0.8 1.02

4

6

8

(b)

lgLP, measured

lgLIMCT

P, calculated

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (−

)

(%Fe2O

3)/(%CaO) (−)

0 2 4 62

4

6

8

(e)

lgLP, measured

lgLIMCT

P, calculated

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (−)

(%Fe2O

3)/(%MgO) (−)

0 1 2 3 42

4

6

8

(d)

lgLP, measured

lgLIMCT

P, calculated

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d ( −

)

(%FeO)/(%MgO) (−)0 2 4 6 8 10

2

4

6

8

(f)

lgLP, measured

lgLIMCT

P, calculated

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (−

)

(%FetO)/(%MgO) (−)

0 10 20 302

4

6

8

(g)

lgLP, measured

lgLIMCT

P, calculated

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (−)

(%FeO)/(%MnO) (−)0 20 40 60

2

4

6

8

(h)

lgLP, measured

lgLIMCT

P, calculated

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (−

)

(%Fe2O

3)/(%MnO) (−)

0 20 40 60 802

4

6

8

(i)

lgLP, measured

lgLIMCT

P, calculated

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (−

)

(%FetO)/(%MnO) (−)

0.30 0.35 0.40 0.45 0.502

4

6

8

(j)

lgLP, measured

lgLIMCT

P, calculated

(%FeO)/(%FetO) (−)

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (−)

0.55 0.60 0.65 0.70 0.752

4

6

8

(%Fe2O

3)/(%Fe

tO) (−)

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (−)

(k)

lgLP, measured

lgLIMCT

P, calculated

Fig. 12—Relationship between mass percent ratio of iron oxides, i.e., FeO, Fe2O3, FetO, to basic oxides, i.e., CaO, MgO, MnO, and lgLP;measured

or lgLIMCTP;calculated (a) through (i) and plot of the mass percent ratio of FeO or Fe2O3 to FetO against lgLP;measured or lgLIMCT

P;calculated (j) through (k) at

top–bottom combined blown converter steelmaking temperatures for 27 heats, respectively.


LIMCTP;i;calculated and LIMCT

P;calculated can be defined as a contri-

bution ratio of complex molecule i containing P2O5 inthe slags when the intercept of linear relationship is

much smaller than LIMCTP;calculated. The average contribution

ratio of nine complex molecules containing P2O5,such as P2O5, 3FeOÆP2O5, 4FeOÆP2O5, 2CaOÆP2O5,

0.0 0.5 1.0 1.5 2.02

4

6

8

(a)

lgLP, measured

lgLIMCT

P, calculated

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (−

)

NFeO

/NCaO

(−)0.00 0.05 0.10 0.152

4

6

8

(b)

lgLP, measured

lgLIMCT

P, calculated

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (− )

NFe

2O

3

/NCaO

(−)0.00 0.05 0.10 0.152

4

6

8

(c)

lgLP, measured

lgLIMCT

P, calculated

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (−

)

NFeO·Fe

2O

3

/NCaO

(−)

0.0 0.5 1.0 1.5 2.02

4

6

8

(d)

lgLP, measured

lgLIMCT

P, calculated

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (−

)

NFeO

/NMgO

(−)0.00 0.05 0.10 0.15 0.202

4

6

8

(e)

lgLP, measured

lgLIMCT

P, calculated

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (−)

NFe

2O

3

/NMgO

(−)0.00 0.05 0.10 0.15 0.202

4

6

8

(f)

lgLP, measured

lgLIMCT

P, calculated

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (−)

NFeO·Fe

2O

3

/NMgO

(−)

0 5 10 15 20 252

4

6

8

(g)

lgLP, measured

lgLIMCT

P, calculated

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (−)

NFeO

/NMnO

(−)0.0 0.5 1.0 1.5 2.02

4

6

8

(h)

lgLP, measured

lgLIMCT

P, calculated

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (−)

NFe

2O

3

/NMnO

(−)0 1 2 3

2

4

6

8

(i)

lgLP, measured

lgLIMCT

P, calculated

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (−)

NFeO·Fe

2O

3

/NMnO

(−)

0.00 0.02 0.04 0.062

4

6

8

(l)

lgLP, measured

lgLIMCT

P, calculated

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (−)

NFeO·Fe

2O

3

/NFe

tO (−)

0.3 0.4 0.5 0.6 0.7 0.82

4

6

8

(j)

lgLP, measured

lgLIMCT

P, calculated

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d ( −

)

NFeO

/NFe

tO (−)

0.02 0.03 0.04 0.05 0.062

4

6

8

(k)

lgLP, measured

lgLIMCT

P, calculated

lgL P

, mea

sure

d or

lgLIM

CT

P, c

alcu

late

d (−)

NFe

2O

3

/NFe

tO (−)

Fig. 13—Relationship between mass action concentration ratio of iron oxides, i.e., NFeO, NFe2O3, NFeO�Fe2O3

, to basic oxides, i.e., NCaO, NMgO,

NMnO, and lgLP;measured or lgLIMCTP;calculated (a) through (i) and plot of NFeO=NFetO or NFe2O3

=NFetO or NFeO�Fe2O3=NFetO against lgLP;measured or

lgLIMCTP;calculated (j) and (k) at top–bottom combined blown converter steelmaking temperatures for 27 heats, respectively.


3CaOÆP2O5, 4CaOÆP2O5, 2MgOÆP2O5, 3MgOÆP2O5, and3MnOÆP2O5, to the calculated total dephosphorization

ability, i.e., LIMCTP;i;calculated

.LIMCTP;calculated, has been summa-

rized in Table VII, respectively. Obviously, the contri-bution of P2O5, 3FeOÆP2O5, 4FeOÆP2O5, 2MgOÆP2O5,3MgOÆP2O5, and 3MnOÆP2O5 to the total dephosphor-ization ability is very small; therefore, they can beignored compared with the contribution ratio of3CaOÆP2O5 as 96.01 pct, 4CaOÆP2O5 as 3.97 pct, and2CaOÆP2O5 as 0.016 pct.

It is assumed that the contribution ratio of nine dephos-phorization reactions to the total dephosphorizationability of the slags is unchangeable, and the calculated

LIMCTP;i;measured of the previously mentioned nine dephosph-

orization reaction products containing P2O5 for themeasured LP;measured can also be obtained. The relation-

ship between lgLIMCTP;i;measured and lgLP;measured is shown in

Figure 14(b) for the slags equilibrated with molten steelat combined blown steelmaking temperatures. Theregressed linear relations between LIMCT

P;i;measured and

LP;measured for nine complex molecules containing phos-phorous as structural units in the slags, such asP2O5, 3FeOÆP2O5, 4FeOÆP2O5, 2CaOÆP2O5, 3CaOÆP2O5,4CaOÆP2O5, 2MgOÆP2O5, 3MgOÆP2O5, and 3MnOÆP2O5,are also summarized in Table VII. The slopes of linearrelationship between LIMCT

P;i;measured and LP;measured as aver-

age contribution ratios of nine simple or complexmolecules containing P2O5 to the total dephosphoriza-tion ability are also listed in Table VII.Therefore, the comprehensive contribution of FetO,

CaO+FetO, MgO+FetO, and MnO+FetO to thecalculated LIMCT

P;calculated by the IMCT LP model or themeasured LP;measured between CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags and molten steel isapproximately 0.0 pct, 99.996 pct, 0.0 pct, and 0.0 pct,respectively.

C. Dephosphorization Mechanism during Top–BottomCombined Blown Converter Steelmaking Process

According to the previously mentioned main resultsand discussion, the dephosphorization mechanism

2 3 4 5 6-18

-12

-6

0

6

12

18

(a)

P2O

5 3FeO·P

2O

5 4FeO·P

2O

5

2CaO·P2O

5 3CaO·P

2O

5 4CaO·P

2O

5

2MgO·P2O

53MgO·P

2O

53MnO·P

2O

5

lgLIMCT

P, calculated (−)

lgLIM

CT

P, i

, ca

lcul

ated

(−)

2 3 4 5 6-18

-12

-6

0

6

12

18

(b)

P2O

5 3FeO·P

2O

5 4FeO·P

2O

5

2CaO·P2O

5 3CaO·P

2O

5 4CaO·P

2O

5

2MgO·P2O

53MgO·P

2O

53MnO·P

2O

5

lgLP, measured

(−)

lgLIM

CT

P, i

, m

easu

red (

− )

Fig. 14—Contribution of nine structural units or complex moleculescontaining P2O5 in slags on lgLIMCT

P;calculated (a) or lgLP;measured (b) attop–bottom combined blown converter steelmaking temperatures for27 heats, respectively.

Table VII. Regressed Expressions of LIMCTP;i;calculated against LIMCT

P;calculated and LIMCTP;i;measured against LP;measured for Nine Simple

or Complex Molecules Containing P2O5, and the Average Contribution Ratio of Nine Simple or Complex Molecules Containing

P2O5 to LIMCTP;calculated or LP;measured for the Slags at Top–Bottom Combined Blown Converter Steelmaking Temperatures Based

on the Ion and Molecule Coexistence Theory

ItemComplexMolecule

Formulas of LIMCTP;i;calculated against LIMCT

P;calculated or LIMCTP;i;measured

against LP;measured for Nine Simple or Complex Molecules

Average ContributionRatio of Nine Simple orComplex Molecules to

LIMCTP;calculated or LP;measured (pct)

Basedon LIMCT

P;calculated

P2O5 LIMCTP;P2O5 ;calculated

¼ �2:4� 10�14 þ 1:3� 10�17LIMCTP;calculated

1.01�10�15

3FeOÆP2O5 LP;3FeO�P2O5 ;calculated ¼ �1:4� 10�8 þ 1:3� 10�12LIMCTP;calculated

4.05�10�11

4FeOÆP2O5 LIMCTP;4FeO�P2O5 ;calculated

¼ �5:0� 10�8 þ 4:2� 10�12LIMCTP;calculated

1.10�10�10

2CaOÆP2O5 LIMCTP;2CaO�P2O5;calculated

¼ �0:223þ 1:79� 10�4LIMCTP;calculated

0.016


¼ 81:01þ 0:965LIMCTP;calculated

96.01


¼ 81:20þ 0:0348LIMCTP;calculated

3.97

2MgOÆP2O5 LIMCTP;2MgO�P2O5;calculated

¼ 0:027þ 6:7� 10�6LIMCTP;calculated

7.83�10�4

3MgOÆP2O5 LIMCTP;3MgO�P2O5;calculated

¼ 0:006þ 6:3� 10�7LIMCTP;calculated

9.19�10�5

3MnOÆP2O5 LIMCTP;3Mn�P2O5 ;calculated

¼ 1:803� 10�6 þ 6:672� 10�11LIMCTP;calculated

1.87�10�10

Basedon LP;measured

P2O5 LIMCTP;P2O5 ;measured ¼ 4:31� 10�15 þ 9:85� 10�18LP;measured 1.01�10�15

3FeOÆP2O5 LIMCTP;3FeO�P2O5 ;measured ¼ �2:73� 10�9 þ 8:51� 10�13LP;measured 4.05�10�11

4FeOÆP2O5 LIMCTP;4FeO�P2O5 ;measured ¼ �9:25� 10�9 þ 2:61� 10�12LP;measured 1.10�10�10

2CaOÆP2O5 LIMCTP;2CaO�P2O5;measured ¼ �0:009þ 1:65� 10�4LP;measured 0.016

3CaOÆP2O5 LIMCTP;3CaO�P2O5;measured ¼ �16:208þ 0:97LP;measured 96.01

4CaOÆP2O5 LIMCTP;4CaO�P2O5;measured ¼ 16:197þ 0:038LP;measured 3.97

2MgOÆP2O5 LIMCTP;2MgO�P2O5;measured ¼ 0:018þ 5:26� 10�6LP;measured 7.83�10�4

3MgOÆP2O5 LIMCTP;3MgO�P2O5;measured ¼ 0:003þ 4:80� 10�7LP;measured 9.19�10�5

3MnOÆP2O5 LIMCTP;3MnO�P2O5;measured ¼ 8:9209� 10�7 þ 5:247� 10�11LP;measured 1.87�10�10


during a top–bottom combined blown converter steel-making process has been illustrated schematically inFigure 15 and is summarized as follows:

(a) Molten steel in a high oxygen content layer beneaththe slag–metal interface can be first dephosphorizedthrough slag-metal dephosphorization reactions,especially by Eqs. [9e] and [9f] or Eqs. [15e] and[15f], to form 3CaOÆP2O5 and 4CaOÆP2O5 during acombined blown steelmaking process in high carboncontent period.

(b) The dephosphorized molten steel in a high oxygencontent layer beneath slag–metal interface willmove to metal bath by top–blowing oxygen orbottom–blowing N2 or Ar gas, or formed CO fromdecarbonization reaction; meanwhile, the moltensteel with high phosphorous content in metal bathwill flow to the slag–metal interface, flow intoslags, or splash into free space of a steelmakingconverter. The dephosphorization reactions willoccur again with CaO+FetO in slags or highoxygen in molten steel beneath slag–metal interfaceto form 3CaOÆP2O5 and 4CaOÆP2O5.

(c) The cyclic process of molten steel from metal bath toslag–metal interface will promote a dephosphoriza-tion reaction with rapid decarbonization of moltensteel until carbon content is less than approximately0.036 pct.

(d) The dephosphorization reactions will weaken grad-ually until the high oxygen layer beneath the slag–metal interface disappears.

VIII. CONCLUSIONS

A thermodynamic model for calculating the phospho-rus distribution ratio between top–bottom combined

blown converter steelmaking slags and molten steel hasbeen developed by coupling with a developed thermo-dynamic model for calculating the mass actionconcentrations of structural units or ion couples inCaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 convertersteelmaking slags based on IMCT. The calculatedphosphorus distribution ratio between the combinedblown converter steelmaking slags and molten steel bythe developed IMCT phosphorus distribution ratioprediction model has been verified with the measuredand the calculated LP by some reported LP models.The main summary remarks can be summarized asfollows:

1. The calculated results from the developed thermody-namic model for calculating mass action concentra-tions of structural units or ion couples in the slagsshow that calculated equilibrium mole numbers ormass action concentrations of structural units or ioncouples, rather than the mass percentage of compo-nent, are recommended to determine the reactionability of components in CaO-SiO2-MgO-FeO-Fe2O3-MnO-Al2O3-P2O5 slags equilibrated or reactedwith molten steel during a combined blown convertersteelmaking process. However, the mass percentage ofMgO, FeO, Fe2O3, MnO, and Al2O3 has a betterlinear relationship with the calculated equilibriummole numbers or mass action concentrations thanthat of other two components, i.e., CaO and SiO2.

2. The phosphorus distribution ratio prediction modelhas been developed based on the oxidization abilityof slags as well as molten steel at slag–metal interfacefrom the viewpoint of dephosphorization reactions.

3. Not only the total phosphorus distribution ratio of acombined blown converter steelmaking slags but alsothe respective phosphorus distribution ratio of fourbasic oxides (FeO, CaO, MgO, and MnO) in the slagscan be predicted reliably by the developed IMCTphosphorus distribution ratio prediction model.

4. The developed IMCT LP model can be applied reli-ably to calculate the phosphorus distribution ratiobetween top–bottom combined blown convertersteelmaking slags and molten steel using the definedmass action concentration of iron oxides as a pre-sentation of slag oxidization ability.

5. The measured phosphorus distribution ratio betweenthe combined blown converter steelmaking slags andmolten steel can be predicted reliably by the devel-oped IMCT LP model as well as by other models,such as Healy’s model, Sommerville’s model, andSuito’s No. 2 model, rather than by Balajiva’s model,Suito’s No. 1 model, and Suito’s No. 3 model.

6. Not the independent effect of iron oxides or basiccomponents but the comprehensive effect of ironoxides and basic oxides controls the dephosphoriza-tion reactions during a combined blown convertersteelmaking process. The contribution ratio of FetO,CaO+FetO, MgO+FetO, and MnO+FetO to thetotal dephosphorization ability is approximately0.0 pct, 99.996 pct, 0.0 pct, and 0.0 pct; 3CaOÆP2O5

and 4CaOÆP2O5 account for 96 pct and 4 pct in thedephosphorization products during a top–bottom

N2 or Ar

Oxygen lance

Slags

Slag-metal Interface

Metal bath

High aO boundary layer

aO of bulk metal is controlled by [C]+[O] =CO

aO of metal at slag-metal interface is controlled by [Fe]+[O] =(FetO)

[P]

3CaO·P2O5

4CaO·P2O5

FetO

[O]+[Fe][P]

O2

Fig. 15—Schematic illustration of proposed dephosphorizationmechanism during the top–bottom combined blown converter steel-making process based on the oxygen potential difference in moltensteel at slag–metal interface and in bulk molten steel.


combined blown converter steelmaking process,respectively. Therefore, the comprehensive effect ofCaO+FetO in the slags controls the dephosphor-ization reactions to form 3CaOÆP2O5 and 4CaOÆP2O5

during a top–bottom combined blown steelmakingprocess.

7. There is a large gradient of oxygen potential or oxygenactivity in molten steel beneath the slag–metal inter-face and in a metal bath when the carbon content isgreater than 0.036 pct. Molten steel with high oxygencontent in the high oxygen content layer beneath theslag–metal interface controls the slag oxidizationability, and the high oxygen content layer beneath theslag–metal interface will disappear rapidly until thecarbon content is less than 0.036 pct during a top–bottom combined blown steelmaking process.

NOMENCLATURE

A constant (–)ai activity of components i in

molten steel or in slags (–)aO;ðFetOÞ�½O� calculated oxygen activity of

molten steel at slag–metalinterface based on (FetO)–[O]equilibrium (–)

aO;½C��½O� calculated oxygen activity ofmolten steel based on[C]–[O] equilibrium (–)

aslag�metal interfaceO;ðFetOÞ�½O�

calculated oxygen activity ofmolten steel at slag–metalinterface based on (FetO)–[O]equilibrium with replacing aFetO

by NFetO (–)abathO;½C��½O� calculated oxygen activity of

bulk molten steel based on [C]–[O] equilibrium (–)

B constant (–)bi mole number of component i in

100-g slags (mol)CS2� sulfide capacity of the slags (–)e

ji interaction coefficient of

component j on component i inmolten steel (–)

fi activity coefficient ofcomponent i in molten steel (–)

DrGHm;i standard molar Gibbs free

energy change of formingcomplex molecule i in slags(J/mol)

DfusGHm;i standard molar Gibbs free

energy change of meltingcomponent i or structural unit ifrom solid to liquid (J/mol)

DsolGHm;i standard molar Gibbs free

energy change of dissolvingcomponent i or structural unit iinto slags (J/mol)

(pct i) mass percentage of component iin the slags (mass pct)

[pct i] mass percentage of component iin molten steel (mass pct)

KHi equilibrium constant of

chemical reaction for formingcomponent i or structural unit i(–)

K0Hi equilibrium constant of

chemical reaction for formingcomponent i or structural unit i(–)

LP phosphorus distribution ratiobetween slags and molten steel(–)

L0P calculated phosphorus

distribution ratio between slagsand molten steel based onmolten steel oxidization abilitywith aO;ðFetOÞ�½O� by IMCTmodel (–)

LS sulfur distribution ratiobetween slags and molten steel(–)

LP;i calculated respectivephosphorus distribution ratioof generated structural unit icontaining P2O5 in slags basedon slag oxidization ability byIMCT model (–)

L0P;i calculated respective

phosphorus distribution ratioof generated structural unit icontaining P2O5 in slags basedon molten steel oxidizationability (–)

LIMCTP;calculated calculated total phosphorus

distribution ratio between slagsand molten steel based on slagoxidization ability by IMCTmodel (–)

L0IMCTP;calculated calculated total phosphorus

distribution ratio between slagsand molten steel based onmolten steel oxidization abilityby IMCT model (–)

LP;measured measured phosphorusdistribution ratio (–)

LaFetO;IMCT

P;calculated calculated total phosphorusdistribution ratio between slagsand molten steel based on slagoxidization ability with aFetO

from aO;½C��½O� via [C]–[O]equilibrium by IMCT model (–)

LNFetO;IMCT

P;calculated calculated total phosphorusdistribution ratio between slagsand molten steel based on slagoxidization ability with NFetO

from (FetO)–[O] equilibrium byIMCT model (–)


L0a

O;ðFetOÞ�½O�;IMCT

P;calculated calculated total phosphorusdistribution ratio between slagsand molten steel based onmolten steel oxidization abilitywith aO;ðFetOÞ�½O� from (FetO)–[O] equilibrium by IMCTmodel (–)

L0aO;½C��½O�;IMCT

P;calculated calculated total phosphorusdistribution ratio between slagsand molten steel based onmolten steel oxidization abilitywith aO;½C��½O� from [C]–[O]equilibrium by IMCT model (–)

LIMCTP;i;calculated calculated respective

phosphorus distribution ratiobetween generated structuralunit i containing P2O5 in slagsand molten steel based on slagoxidization ability by IMCTmodel from calculated data (–)

LIMCTP;i;measured calculated respective

phosphorus distribution ratioof generated structural unit icontaining P2O5 in slags basedon slag oxidization ability byIMCT model from measureddata (–)

LiP;calculated calculated phosphorus

distribution ratio between slagsand molten steel by model i (–)

Me metal (–)MeO metal oxide in slags (–)Mi molecular mass of element i or

component i (g/mol)n0

i mole number of component i in100-g slags (mol)

ni equilibrium mole number ofstructural unit i or ion couple iin 100-g slags (mol)

Ni mass action concentrations ofstructural unit i or ion couple iin the slags (–)P

ni total equilibrium mole numberof all structural units in 100-gslags (mol)

R gas constant (8.314 J/(mol K))T absolute temperature (K)½pct O�½C��½O� mass percentage of oxygen in

molten steel based on [C]–[O]equilibrium (mass pct)

½pct O�ðFetOÞ�½O� mass percentage of oxygen inmolten steel based on (FetO)–[O] equilibrium (mass pct)

½pct O�slag�metal interfaceðFetOÞ�½O� calculated oxygen content of

molten steel at slag–metalinterface based on (FetO)–[O]equilibrium with replacing aFetO

by NFetO (–)½pct O�bath½C��½O� calculated oxygen content of

molten steel in metal bath basedon [C]–[O] equilibrium (–)

GREEK SYMBOLS

K optical basicity of the slags (–)Ki optical basicity of component i in the slags (–)l�iðsÞ chemical potential of component i as solid (J/mol)l�iðlÞ chemical potential of component i as liquid

(J/mol)lH

i standard chemical potential of dissolvedcomponent i in slags (J/mol)

SUBSCRIPTS

ci complex molecule i (–)

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a thermodynamic model of phosphorus distribution ratio...

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