A Thermodynamic Model of Phosphorus Distribution Ratio between CaO-SiO 2 -MgO-FeO-Fe 2 O 3 -MnO-Al 2 O 3 -P 2 O 5 Slags and Molten Steel during a Top–Bottom Combined Blown Converter Steelmaking Process Based on the Ion and 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–bottom combined blown converter steelmaking slags and molten steel has been developed by coupling with a developed thermodynamic model for calculating mass action concentrations of structural units in the slags, i.e., CaO-SiO 2 -MgO-FeO-Fe 2 O 3 -MnO-Al 2 O 3 -P 2 O 5 slags, based on the ion and molecule coexistence theory (IMCT). Not only the total phosphorus distribution ratio but also 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 the developed IMCT phosphorus distribution ratio prediction model after knowing the oxygen activity of molten steel at the slag–metal interface or the Fe t O activity in the slags and the related mass action concentrations of structural units or ion couples in the slags. The calculated mass action concentrations of structural units or ion couples in the slags equilibrated or reacted with 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, can present the reaction ability of the components in the slags. The predicted total phosphorus distribution ratio by the developed IMCT model shows a reliable agreement with the measured phosphorus distribution ratio by using the calculated mass action concentrations of iron oxides as presentation of slag oxidation ability. Meanwhile, the developed thermodynamic model for calculating the phosphorus distribution ratio can determine quantitatively the respective dephosphorization contribution ratio of Fe t O, CaO + Fe t O, MgO + Fe t O, and MnO + Fe t O in the slags. A significant difference of dephosphorization ability among Fe t O, CaO + Fe t O, MgO + Fe t O, and MnO + Fe t O 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 a great gradient of oxygen activity of molten steel at the slag–metal interface and in a metal bath when carbon content in a metal bath is larger than 0.036 pct. The phosphorus in molten steel beneath the slag–metal interface can be extracted effectively by the comprehensive effect of CaO and Fe t O in slags to form 3CaO P 2 O 5 and 4CaO P 2 O 5 until the carbon content is less than 0.036 pct during a top–bottom combined blown steelmaking process. DOI: 10.1007/s11663-011-9491-8 Ó The Minerals, Metals & Materials Society and ASM International 2011 I. INTRODUCTION NOT only the blast furnace ironmaking process but also most common secondary refining processes have limited dephosphorization ability. Therefore, the dephosphorization operation in both the hot meat pretreatment and the converter steelmaking process is very important to fulfill the requirement of phosphorus content for molten steel in the routine metallurgical process. Compared with the dephosphorization opera- tion in hot metal pretreatment, phosphorus extrac- tion in converter steelmaking process is almost the final dephosphorization operation. Hence, improving dephosphorization ability in the converter steelmaking process is very important to control the phosphorus content in the aimed specification of molten steel. XUE-MIN YANG, Research Professor, is with the State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, P. R. China. Contact e-mail: [email protected]JIAN-PING DUAN, Senior Engineer, and YONG-LIANG ZHANG and JIAN- CHANG WANG, Engineers, are with the Technology Center, Shanxi Taigang Stainless Corporation Limited, Taiyuan 030003, P. R. China. CHENG-BIN SHI, Ph.D. Candidate and Joint-Training Student, is with 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, Chinese Academy of Sciences. MENG ZHANG, Master Degree Student and Joint-Training Student, is with the School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, and with the Institute of Process Engineering, Chinese Academy of Sciences. Manuscript submitted October 20, 2010. Article published online April 21, 2011. 738—VOLUME 42B, AUGUST 2011 METALLURGICAL AND MATERIALS TRANSACTIONS B
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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
740—VOLUME 42B, AUGUST 2011 METALLURGICAL AND MATERIALS TRANSACTIONS B
(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:
METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 42B, AUGUST 2011—741
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
742—VOLUME 42B, AUGUST 2011 METALLURGICAL AND MATERIALS TRANSACTIONS B
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
c26N4N5 þ KHc27N3N5
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
4CaOÆP2O5 c31 nc31 ¼ n4CaO�P2O5Nc31 ¼ nc31P
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
METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 42B, AUGUST 2011—743
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
744—VOLUME 42B, AUGUST 2011 METALLURGICAL AND MATERIALS TRANSACTIONS B
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
METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 42B, AUGUST 2011—745
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
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
746—VOLUME 42B, AUGUST 2011 METALLURGICAL AND MATERIALS TRANSACTIONS B
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
METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 42B, AUGUST 2011—747
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]
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.
748—VOLUME 42B, AUGUST 2011 METALLURGICAL AND MATERIALS TRANSACTIONS B
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.
METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 42B, AUGUST 2011—749
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.
750—VOLUME 42B, AUGUST 2011 METALLURGICAL AND MATERIALS TRANSACTIONS B
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.
METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 42B, AUGUST 2011—751
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
¼ðpct P2O5Þ4FeO�P2O5
=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
¼ a3CaO�P2O5a5tFe
a5FetOa3CaOa
2P
¼ N3CaO�P2O5� 1
N5FetO
N3CaO½pct P�
2f2P
¼ðpct P2O5Þ3CaO�P2O5
=MP2O5
.P
ni
� �
N5FetO
N3CaO½pct P�
2f2P�ð Þ
½10e�
KH4CaO�P2O5
¼ a4CaO�P2O5a5tFe
a5FetOa4CaOa
2P
¼ N4CaO�P2O5� 1
N5FetO
N4CaO½pct P�
2f2P
¼ðpct P2O5Þ4CaO�P2O5
=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
¼ðpct P2O5Þ3MgO�P2O5
=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.
752—VOLUME 42B, AUGUST 2011 METALLURGICAL AND MATERIALS TRANSACTIONS B
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�
LP;3CaO�P2O5¼ðpct P2O5Þ3CaO�P2O5
½pct P�2
¼ MP2O5KH
3CaO�P2O5N5
FetON3
CaOf2P
Xni �ð Þ½11e�
LP;4CaO�P2O5¼ðpct P2O5Þ4CaO�P2O5
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
pct P2O5ð Þ4CaO�P2O5
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
METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 42B, AUGUST 2011—753
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
¼ðpct P2O5Þ3FeO�P2O5
=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
¼ðpct P2O5Þ4FeO�P2O5
=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
¼ðpct P2O5Þ2CaO�P2O5
=MP2O5
.P
ni
� �
a5ON2CaO½pct P�
2f2P�ð Þ
½15d�
2 P½ � þ 5 O½ � þ 3 Ca2þ þO2�� �¼ 3CaO � P2O5ð Þ
K0H3CaO�P2O5
¼ a3CaO�P2O5
a5Oa3CaOa
2P
¼ðpct P2O5Þ3CaO�P2O5
=MP2O5
.P
ni
� �
a5ON3CaO½pct P�
2f2P�ð Þ
½15e�
2 P½ � þ 5 O½ � þ 4 Ca2þ þO2�� �¼ 4CaO � P2O5ð Þ
K0H4CaO�P2O5
¼ a4CaO�P2O5
a5Oa4CaOa
2P
¼ðpct P2O5Þ4CaO�P2O5
=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
¼ðpct P2O5Þ2MgO�P2O5
=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
¼ðpct P2O5Þ3MgO�P2O5
=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:
754—VOLUME 42B, AUGUST 2011 METALLURGICAL AND MATERIALS TRANSACTIONS B
METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 42B, AUGUST 2011—755
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
¼ðpct P2O5Þ2CaO�P2O5
½pct P�2
¼MP2O5K0H2CaO�P2O5
a5O;ðFetOÞ�½O�N2CaOf
2P
Xni [16d]
L0
P;3CaO�P2O5
¼pct P2O5ð Þ3CaO�P2O5
pct P½ �2
¼MP2O5K0H3CaO�P2O5
a5O;ðFetOÞ�½O�N3CaOf
2P
Xni �ð Þ
½16e�
L0
P;4CaO�P2O5
¼pct P2O5ð Þ4CaO�P2O5
pct P½ �2
¼MP2O5K0H4CaO�P2O5
a5O;ðFetOÞ�½O�N4CaOf
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 P2O5ð Þ2CaO�P2O5
pct P½ �2
þpct P2O5ð Þ3CaO�P2O5
pct P½ �2þ
pct P2O5ð Þ4CaO�P2O5
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.
756—VOLUME 42B, AUGUST 2011 METALLURGICAL AND MATERIALS TRANSACTIONS B
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.
METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 42B, AUGUST 2011—757
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]
758—VOLUME 42B, AUGUST 2011 METALLURGICAL AND MATERIALS TRANSACTIONS B
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.
METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 42B, AUGUST 2011—759
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.
760—VOLUME 42B, AUGUST 2011 METALLURGICAL AND MATERIALS TRANSACTIONS B
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.
METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 42B, AUGUST 2011—761
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 (−)
Mass percent of FeO (%)
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 (−)
Mass percent of Fe2O
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 (− )
Mass percent of MnO (%)
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
Mass percent of Al2O
3 (%)
30 40 50 602
3
4
5
6
7
lgL P
, mea
sure
d or
lgLIM
CT
P, c
alcu
late
d (−
)
Mass percent of CaO (%)
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
Mass percent of SiO2 (%)
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
Mass percent of MgO (%)
(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.
762—VOLUME 42B, AUGUST 2011 METALLURGICAL AND MATERIALS TRANSACTIONS B
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.
METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 42B, AUGUST 2011—763
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.
764—VOLUME 42B, AUGUST 2011 METALLURGICAL AND MATERIALS TRANSACTIONS B
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.
METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 42B, AUGUST 2011—765
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
766—VOLUME 42B, AUGUST 2011 METALLURGICAL AND MATERIALS TRANSACTIONS B
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.
METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 42B, AUGUST 2011—767
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 (–)
768—VOLUME 42B, AUGUST 2011 METALLURGICAL AND MATERIALS TRANSACTIONS B
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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