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

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1 A Thermodynamic Model of Phosphorus Distribution Ratio between CaO-SiO -MgO-FeO-Fe -MnO-Al -P O Slags and Molten Steel during a Top Bottom Combined Blown Converter Steelmaking Process Based on the Ion and Molecule Coexistence Theory UE-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 uts in the slags, ie, CaO-SiO -MgO-FeO-Fe -MnO-Al -P O 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, ie, 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 uts or ion couples in the slags The calculated mass action concentrations of structural uts or ion couples in the slags equilibrated or reacted with molten steel show that the calculated equilibrium mole numbers or mass action concentrations of structural uts 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 Oin the slags A sigficant 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 00 pct, 9999 pct, 00 pct, and 00 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 00 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 CaOÆP O and CaOÆP O until the carbon content is less than 00 pct during a top bottom combined blown steelmaking process DOI: 10100/s Ó The Minerals, Metals & Materials Society and ASM International 011 UE-MIN YANG, Research Professor, is with the State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences, Beijing , P R China Contact yangxm1@homeipeaccn JIAN-PING DUAN, Seor Engineer, and YONG-LIANG ZHANG and JIAN- CHANG WANG, Engineers, are with the Technology Center, Shanxi Taigang Stainless Corporation Limited, Taiyuan 0000, P R China CHENG-BIN SHI, PhD Candidate and Joint-Traing Student, is with the School of Metallurgical and Ecological Engineering, Uversity of Science and Technology Beijing, Beijing 1000, P R China, and with the Institute of Process Engineering, Chinese Academy of Sciences MENG ZHANG, Master Degree Student and Joint-Traing Student, is with the School of Metallurgical and Ecological Engineering, Uversity of Science and Technology Beijing, and with the Institute of Process Engineering, Chinese Academy of Sciences Manuscript submitted October 0, 010 Article published online April 1, 011 I INTRODUCTION NOT only the blast furnace ironmaking process but also most common secondary refing 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 operation in hot metal pretreatment, phosphorus extraction 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 VOLUME B, AUGUST 011

2 As an important function of converter steelmaking process, the oxidizing dephosphorization of hot metal or molten steel, has been investigated by many researchers [1 19] since the 190s, [1,,9] and many phosphorous distribution ratio prediction models [9 1] have been developed based on some empirical regressions of the measured data, such as Healy s model, [10] Suito s three models, [11,1] Sommerville s model, [9,1] and Balajiva s model [1] However, the phosphorous distribution ratio models [9 1] are not enough and scarce from the view point of dephosphorization reactions based on metallurgical physicochemistry Zhang [0] has developed some thermodynamic models for predicting the phosphorous distribution ratio L P of FeO-Fe -P O, MgO-FeO-Fe -P O, CaO-MgO- FeO-Fe -P O, CaO-SiO -MgO-FeO-Fe -P O, CaO-SiO -MgO-FeO-Fe -MnO-P O, and CaO-SiO - MgO-Na O-FeO-Fe -MnO-P O slags equilibrated with hot metal from the view point of dephosphorization reactions based on the ion and molecule coexistence theory (IMCT) [0 ] The results of the developed phosphorous distribution ratio prediction models by Zhang [0] show that the predicated L P from the developed models [0] based on IMCT [0 ] have good agreement with the measured L P for the previously mentioned slags equilibrated with hot metal However, no L P prediction model for steelmaking slags has been developed based on IMCT [0 ] According to the accumulation of the development of a sulfur distribution ratio L S prediction model [] and a sulfide capacity C S prediction model [] of CaO- SiO -MgO-Al quaternary ironmaking slags, a L S prediction model [] of CaO-SiO -MgO-FeO-Al - MnO hexabasic slags in ladle furnace (LF) refing process by authors, and some L P prediction models for various slags by J Zhang, [0] a thermodynamic model for predicting L P between a top bottom combined blown converter steelmaking slags and molten steel has been developed according to IMCT [0 ] To develop the thermodynamic model for predicting L P between CaO- SiO -MgO-FeO-Fe -MnO-Al -P O slags and molten steel, a thermodynamic model for calculating mass action concentrations of structural uts or ion couples in the slags must be developed first The developed thermodynamic model for prediction L P can determine not only the total phosphorous distribution ratio but also the respective phosphorous distribution ratio of each basic component with dephosphorization ability under existing of iron oxides in the slags To further verify the feasibility of the developed L P prediction model, the comparison among the predicted L IMCT by IMCT L P model and the measured L P;measured as well as the predicted L i by other L P models, such as Healy s model, [10] Suito s three models, [11,1] Sommerville s model, [9,1] and Balajiva s model, [1] have been conducted The slag metal dephosphorization reactions are oxidization reactions by iron oxides, such as FeO and Fe, usually expressed as Fe t O, combined with other basic components in the slags during a top bottom combined blown converter steelmaking process The defined mass action concentration of Fe t O N Fet O by Zhang, [0] which is assigned to present slag oxidization ability based on IMCT [0 ] like the activity of iron oxides a Fet O in the classically metallurgical physicochemistry, has been compared with the calculated iron oxides activity a Fet O in the slags To reveal the contribution of slag components to L P, the effects both mass percent and mass action concentrations for basic components and iron oxides on L P at top bottom combined blown converter steelmaking temperatures are also discussed The oxygen activity gradient of molten steel at slag metal interface and in metal bath has been revealed The influence of high oxygen activity boundary layer beneath slag metal interface on dephosphorization reactions has been verified during a combined blown steelmaking process The dephosphorization mechasm in a top bottom combined blown converter steelmaking process has been proposed according to the obtained results The ultimate aim of this study is to develop a uversal method for predicting the phosphorous distribution ratio between slags and metal for various metallurgical process uts from viewpoint of all possible dephosphorization reactions according to metallurgical physicochemistry, to provide fundamental information for optimizing slags composition with the aim of improving dephosphorization ability, and furthermore to lay a foundation for developing a phosphate capacity prediction model in the next study according to IMCT [0 ] II INDUSTRIAL TESTS The industrial tests were carried out in an 0-ton top bottom combined blown steelmaking converter at the No Steelmaking Plant of Shanxi Taigang Stainless Steel Corporation Limited The basic parameters of the combined blown converter are summarized in Table I The nominal capacity of the converter is 0 tons, whereas the practical output of molten steel from the converter is about tons The total charged metallic raw material is approximately 9 tons containg tons of pretreated hot metal, ie, by desilicozation, dephosphorization, and desulphurization, and -ton scraps The average mass of slags forming materials each heat includes about 900 kg lime, 00 kg light burned dolomite, 0 kg laterite, and 00 kg pellets of converter red mud The samples of both slag and metal in the steelmaking of a typical low-carbon steel were sampled at steelmaking end point The normalized chemical compositions of both slags and metal for heats are listed in Table II III MODEL FOR CALCULATING MASS ACTION CONCENTRATIONS OF STRUCTURAL UNITS OR ION COUPLES IN CaO-SiO -MgO-FeO- Fe -MnO-Al -P O SLAGS A Hypotheses According to the classic hypotheses of IMCT described in detail elsewhere, [0 ] the main assumptions in VOLUME B, AUGUST 011 9

3 Table I Main Parameters of an 0-ton Top Bottom Combined Blown Steelmaking Converter Item Parameters Converter Nominal capacity (ton) 0 Bath diameter (mm) 0 Bath depth (mm) 100 Volume ratio of converter (m /t) 0 Top-blowing oxygen lance Type of oxygen lance ( ) Four-apertured Laval lance Jet angle of oxygen lance ( ) 1 Outlet diameter of oxygen lance (mm) 0 Oxygen supply intensity (Nm /(t min)) to Bottom-blowing system Number of bottom-blowing elements ( ) Bottom-blowing gas N,Ar Bottom gas supply intensity (Nm /(t min)) 00 to 01 Table II Chemical Composition of CaO-SiO -MgO-FeO-Fe -MnO-Al -P O Slags and Molten Steel at End Point during an 0-ton Top Bottom Combined Blown Converter Steelmaking Process and Calculated Total Equilibrium Mole Numbers of all Structural Uts in 100-g Slags Based on the Ion and Molecule Coexistence Theory for Heats Chemical Composition of Slags (mass pct) Chemical Composition of Molten Steel (mass pct) Test No CaO SiO MgO FeO Fe MnO Al P O [C] [Si] [Mn] [P] [S] [O] T (K) P < < < < < < < < < < < < < < < < the developed thermodynamic model for calculating mass action concentrations of structural uts or ion couples in CaO-SiO -MgO-FeO-Fe -MnO-Al - P O slags equilibrated or reacted with molten steel can be briefly summarized as follows: (a) Structural uts in the studied slags equilibrated or reacted with molten steel are composed of Ca +, Mg +,Fe +,Mn +, and O as simple ions; SiO, Fe, Al and P O as simple molecules; silicates, aluminates, and so on as complex molecules Each structural ut has its independent position in the slags Every cation and aon generated from the same component will take part in reactions of forming complex molecules in the form of ion couple as (Me + +O ) with simple molecules 0 VOLUME B, AUGUST 011

4 (b) Reactions of forming complex molecules are under chemically dynamic equilibrium between bonded ion couples from simple ions and simple molecules (c) Structural uts in the slags equilibrated or reacted with molten steel bear continuity in the range of the investigated concentration range (d) Chemical reactions of forming complex molecules obey the mass action law B Model for Calculating Mass Action Concentrations of Structural Uts or Ion Couples in CaO-SiO -MgO- FeO-Fe -MnO-Al -P O Slags 1 Structural uts in CaO-SiO -MgO-FeO-Fe - MnO-Al -P O slags There are eight components as CaO, SiO, MgO, FeO, Fe, MnO, Al, and P O in CaO-SiO -MgO- FeO-Fe -MnO-Al -P O slags, whereas the extracted phosphorus from molten steel gradually enters into the slags as P O, FeOÆP O, FeOÆP O, CaOÆ P O, CaOÆP O, CaOÆP O, MgOÆP O, MgOÆ P O, and MnOÆP O with the proceeding of dephosphorization reactions until dephosphorization reactions reach equilibrium or quasi-equilibrium in terms of the classic metallurgical physicochemistry However, the IMCT [0 ] suggests that the extracted phosphorus from molten steel into the slags can be bonded with ion couples (Fe + +O ), (Ca + +O ), (Mg + +O ), and (Mn + +O ) to form structural uts as P O, FeOÆP O,FeOÆP O,CaOÆP O,CaOÆP O,CaOÆ P O, MgOÆP O, MgOÆP O, and MnOÆP O in oxidizing slags containg Fe t O, respectively Hence, the top bottom combined blown converter steelmaking slags will change from an open system without phosphorus at the itial stage to a closed system containg phosphorus at the final stage with the proceeding of converter steelmaking process The IMCT [0 ] can be applied only to a closed system; therefore, the top bottom combined blown converter steelmaking slags containg phosphorus equilibrated or reacted with molten steel is chosen as CaO-SiO -MgO-FeO-Fe -MnO-Al -P O slags It can be obtained reasonably from the preceding assumptions in Section III A that there are five simple ions as Ca +,Mg +,Fe +,Mn +, and O, four simple molecules as SiO,Fe,Al, and P O in the slags under dephosphorization equilibrium or quasi equilibrium at metallurgical temperatures based on IMCT [0 ] According to the reported binary and ternary phase diagrams [,] of CaO-SiO, CaO-Al, CaO-Al SiO, CaO-Al -MgO, CaO-MgO-SiO, MgO-Al SiO, CaO-FeO-SiO, Al SiO -MnO, and Al SiO FeO slags and so on at the combined blown converter steelmaking temperatures, ie, in a temperature range from 199 K to 19 K (1 C to 11 C), approximately kinds of complex molecules, such as CaOÆSiO, CaOÆSiO, CaOÆSiO and so on, can be formed in the slags in a temperature range from 199 K to 19 K (1 C to 11 C) as listed in Table II All simple ions, as well as simple and complex molecules in the studied slags at metallurgical temperature are summarized and assigned with exclusive numbers in Table III Model for calculating mass action concentrations of structural uts or ion couples in CaO-SiO -MgO- FeO-Fe -MnO-Al -P O slags The mole number of previously mentioned eight components, such as CaO, SiO, MgO, FeO, Fe, MnO, Al, and P O, in 100-g CaO-SiO -MgO-FeO- Fe -MnO-Al -P O slags is assigned as b 1 n 0 CaO ; b n 0 SiO ; b n 0 MgO ; b n 0 FeO ; b n 0 Fe ; b n 0 MnO ; b n 0 Al and b n 0 P O to present chemical composition of the slags The defined [0 ] equilibrium mole numbers n i of all previously mentioned structural uts in 100-g slags equilibrated or reacted with molten steel at metallurgical temperatures are given Table III The total equilibrium mole number P n i of all structural uts in 100-g slags equilibrated or reacted with molten steel can be expressed as follows n 1 þ n þ n þ n þ n þ n þ n þ n þ n c1 þ n c þþn c molþ ½1Š According to the defition of mass action concentrations [0 ] N i of structural uts, which is a ratio of equilibrium mole number of structural uts i to the total equilibrium mole numbers of all structural uts in a closed system with a fixed amount, N i of structural ut i and ion couples (Me + +O ) in molten slags can be calculated by N i n i P Þ ½aŠ N MeO N Me þ ;MeO þ N O ;MeO n Me þ ;MeO þ n O ;MeO P n MeO P Þ [b] All defitions of N i for the formed ion couples from simple ions, as well as the simple and complex molecules in CaO-SiO -MgO-FeO-Fe -MnO-Al -P O slags are listed in Table III The chemical reaction formulas of kinds of the possibly formed complex molecules, their standard molar Gibbs free energy change D r G H m;ci of formation reactions as a function of absolute temperature T, reaction equilibrium constant K H ci, and presentation of mass action concentration of all complex molecules N ci expressed by using K H ci ; N 1 N CaO Þ; N N SiO Þ; N N MgO ; N N FeO Þ; N N Fe Þ; N N MnO Þ; N N Al Þ and N N P O Þ based on the mass action law are summarized in Table IV The mass conservation equations of eight components in 100-g CaO-SiO -MgO-FeO-Fe -MnO- Al -P O slags equilibrated or reacted with molten steel can be established from the defitions [0 ] of n i and N i of all structural uts listed in Tables III and IV as follows: VOLUME B, AUGUST 011 1

5 Table III Expression of Structural Uts as Ion Couples, Simple or Complex Molecules, Their Mole Numbers, and Mass Action Concentrations in 100-g CaO-SiO -MgO-FeO-Fe -MnO-Al -P O Slags Equilibrated with Molten Steel at Top Bottom Combined Blown Converter Steelmaking Temperatures based on the Ion and Molecule Coexistence Theory Item Simple cation and aon () Structural Uts as Ion Couples or Molecules Number of Structural Uts or Ion Couples Mole Number of Structural Uts Mass Action Concentration of Structural Uts or Ion Couples Ca + +O 1 n 1 n Ca þ ;CaO n O ;CaO n CaO N 1 P n1 N CaO Mg + +O n n Mg þ ;MgO n O ;MgO n MgO N P n N MgO Fe + +O n n Fe þ ;FeO n O ;FeO n FeO N P n N FeO Simple molecules () Complex molecules () Mn + +O n n Mn þ ;MnO n O ;MnO n MnO N P n N MnO SiO n n SiO N P n N SiO Fe n n Fe N P n N Fe Al n n Al N P n N Al P O n n PO N P n N PO CaOÆSiO c1 n c1 n CaOSiO N c1 P nc1 N CaOSiO CaOÆSiO c n c n CaOSiO N c P nc N CaOSiO CaOÆSiO c n c n CaOSiO N c P nc N CaOSiO CaOÆAl c n c n CaOAl N c P nc N CaOAl 1CaOÆAl c n c n 1CaOAl N c P nc N 1CaOAl CaOÆAl c n c n CaOAl N c P nc N CaOAl CaOÆAl c n c n CaOAl N c P nc N CaOAl CaOÆAl c n c n CaOAl N c P nc N CaOAl MgOÆSiO c9 n c9 n MgOSiO N c9 P nc9 N MgOSiO MgOÆSiO c10 n c10 n MgOSiO N c10 P nc10 N MgOSiO MgOÆAl c11 n c11 n MgOAl N c11 P nc11 N MgOAl FeOÆSiO c1 n c1 n FeOSiO N c1 P nc1 N FeOSiO FeOÆAl c1 n c1 n FeOAl N c1 P nc1 N FeOAl MnOÆSiO c1 n c1 n MnOSiO N c1 P nc1 N MnOSiO MnOÆSiO c1 n c1 n MnOSiO N c1 P nc1 N MnOSiO MnOÆAl c1 n c1 n MnOAl N c1 P nc1 N MnOAl Al ÆSiO c1 n c1 n AlSiO N c1 P nc1 N AlSiO CaOÆAl ÆSiO c1 n c1 n CaOAlSiO N c1 P nc1 N CaOAlSiO CaOÆAl ÆSiO c19 n c19 n CaOAlSiO N c19 P nc19 N CaOAlSiO CaOÆMgOÆSiO c0 n c0 n CaOMgOSiO N c0 P nc0 N CaOMgOSiO CaOÆMgOÆSiO c1 n c1 n CaOMgOSiO N c1 P nc1 N CaOMgOSiO CaOÆMgOÆSiO c n c n CaOMgOSiO N c P nc N CaOMgOSiO CaOÆMgOÆSiO c n c n CaOMgOSiO N c P nc N CaOMgOSiO MgOÆAl ÆSiO c n c n MgOAlSiO N c P nc N MgOAlSiO CaOÆFe c n c n CaOFe N c P nc N CaOFe FeOÆFe c n c n FeOFe N c P nc N FeOFe MgOÆFe c n c n MgOFe N c P nc N MgOFe MnOÆFe c n c n MnOFe N c P nc N MnOFe CaOÆP O c9 n c9 n CaOPO N c9 P nc9 N CaOPO CaOÆP O c0 n c0 n CaOPO N c0 P nc0 N CaOPO VOLUME B, AUGUST 011

6 Table III continued Item Structural Uts as Ion Couples or Molecules Number of Structural Uts or Ion Couples Mole Number of Structural Uts Mass Action Concentration of Structural Uts or Ion Couples CaOÆP O c1 n c1 n CaOPO N c1 P nc1 N CaOPO FeOÆP O c n c n FeOPO N c P nc N FeOPO FeOÆP O c n c n FeOPO N c P nc N FeOPO MnOÆP O c n c n MnOPO N c P nc N MnOPO MgOÆP O c n c n MgOPO N c P nc N MgOPO MgOÆP O c n c n MgOPO N c P nc N MgOPO b 1 1 N 1 þ N c1 þ N c þ N c þ N c þ 1N c b 1 N þ N c9 þ N c10 þ N c11 þ N c0 þ N c1 þ N c þn c þ N c þ N c þ N c1 þ N c19 þn c þ N c þ N c þ N c þ N c! þn c0 þ N c1 þ N c þ N c þ N c þn c9 þ N c0 þ N c1! 1 N þ K H c9 N N þ KH c10 N N þ K H c11 N N þk H c0 N 1N N þ K H c1 N 1N N þ KH c N 1 N N 1 N 1 þ K H c1 N 1 N þ K H c N 1 N þ K H c N 1N þk H c N 1 N þ 1K H c N1 1 N þ KH c N 1N þk H c N 1N þ KH c N 1N þ KH c1 N 1 N N þk H c19 N 1N N þ KH c0 N 1N N þ K H c1 N 1N N þk H c N 1 N N þ KH c N 1 N N þ K H c N 1 N þk H c9 N 1 N þ K H c0 N 1 N þ K H c1 N 1 N! b þk H c N 1 N N þ K H c N N N þ KH c N N! n 0 þk H c N N þ K H c N N MgO molþ ½cŠ 1 N þ N c1 þ N c1 þ N c þ N c þ N c 1 N þ K H c1 N N þ KH c1 N N þ K H c N N n 0 CaO molþ [a] þk H c N N þ K H c N N! n 0 FeO molþ b N þ N c1 þ N c þ N c þ N c9 þ N c10 þ N c1 ½dŠ þn c1 þ N c1 þ N c1 þ N c1 þ N c19 þ N c0 þn c1 þ N c þ N c þ N c Þ n i N þ K H c1 N 1 N þ K H c N 1 N þ K H c N 1N þk H c9 N N þ KH c10 N N þ K H c1 N N b b N þ N c þ N c þ N c þ N c Þ n i N þ K H c N 1 N þ K H c N N þ K H c N N þk H c N N Þ n i n 0 Fe molþ [e] 1 N þ N c1 þ N c1 þ N c1 þ N c þ N c þk H c1 N N þ K H c1 N N þ KH c1 N N þk H c1 N 1 N N þ K H c19 N 1N N þ K H c0 N 1N N þk H c1 N 1N N þ KH c N 1 N N þ K H c N 1 N N 1 N þ K H c1 N N þ K H c1 N N þ KH c1 N N þk H c N N þ K H c N N! n 0 MnO molþ þk H c N N N Þ n i n 0 SiO molþ [b] ½fŠ VOLUME B, AUGUST 011

7 Table IV Chemical Reaction Formulas of Possibly Formed Complex Molecules, Their Standard Molar Gibbs Free Energy Change, Equilibrium Constants, and Mass Action Concentrations in CaO-SiO-MgO-FeO-FeO-MnO-AlO-PO Slags at Top Bottom Combined Blown Converter Steelmaking Temperatures Reactions DrG H m;ci (J/mol) Reference K H ci Nci (Ca + +O ) + (SiO ) = (CaOÆSiO ) 11, 9T 9 K H Nc1 c1 Nc1 N N Nc1 K H c1 N 1 N Nc K H N N 1 N (Ca + +O ) + (SiO) = (CaOÆSiO) 10,090 T 0 K H Nc c Nc N N c N 1 N 1 N (Ca + +O ) + (SiO ) = (CaOÆSiO ) 1, 19T 0 K H c Nc Nc K H c N 1 N N 1 N (Ca + +O ) + (Al ) = (CaOÆAl ) 1, 9T 0 K H Nc c Nc N N Nc K H c N 1 N 1 N 1(Ca + +O ) + (AlO) = (1CaOÆAlO) 1,9 1119T 0 K H c Nc (Ca + +O ) + (AlO) = (CaOÆAlO) 9,1 91T 0 K H c Nc N 1 N (Ca + +O ) + (Al ) = (CaOÆAl ) 1, T 0 K H c Nc (Ca + +O ) + (AlO) = (CaOÆAlO),9 19T 1 K H c Nc (Mg + +O ) + (SiO) = (MgOÆSiO),90 T 0 K H c9 Nc9 (Mg + +O ) + (SiO ) = (MgOÆSiO ),9 90T 0 K H c10 Nc10 NN (Mg + +O ) + (AlO) = (MgOÆAlO) 1, T 0 K H c11 Nc11 (Fe + +O ) + (SiO) = (FeOÆSiO) 9,9 0T 9,, K H c1 Nc1 (Fe + +O ) + (Al ) = (FeOÆAl ) 9,0 + T K H c1 Nc1 (Mn + +O ) + (SiO ) = (MnOÆSiO ), T 9 K H c1 Nc1 (Mn + +O ) + (SiO ) = (MnOÆSiO ),0 09T 9 K H c1 Nc1 (Mn + +O ) + (AlO) = (MnOÆAlO), T K H c1 Nc1 (AlO) + (SiO) = (AlOÆSiO),1 10T 0 K H c1 Nc1 N 1 1 N N 1 N N1N N N NN NN NN NN NN N N N N Nc K H c N1 1 N Nc K H c N 1N Nc K H c N 1N Nc K H c N 1N Nc9 K H c9 N N Nc10 K H c10 N N Nc11 K H c11 N N Nc1 K H c1 N N Nc1 K H c1 N N Nc1 K H c1 N N Nc1 K H c1 N N Nc1 K H c1 N N Nc1 K H c1 N N (Ca + +O ) + (AlO) + (SiO) = (CaOÆAlOÆSiO) 11,1 911T 0 K H c1 Nc1 NN Nc1 K H c1 N 1 N N 1 NN Nc19 K H c19 N 1N N H (Ca + +O ) + (Al ) + (SiO ) = (CaOÆAl ÆSiO ),1 T 0 K H c19 Nc19 N1N N N Nc0 K H c0 N 1NN (Ca + +O ) + (Mg + +O ) + (SiO) = (CaOÆMgOÆSiO) 1, + T 9 K H Nc0 c0 Nc0 N1NN N N N Nc1 K H c1 N 1 N N (Ca + +O ) + (Mg + +O ) + (SiO) = (CaOÆMgOÆSiO) 0, 1T 0 K H c1 Nc1 1 (Ca + +O ) + (Mg + +O ) + (SiO ) = (CaOÆMgOÆSiO ), 9T 0 K H c Nc (Ca + +O ) + (Mg + +O ) + (SiO) = (CaOÆMgOÆSiO) 0,01 19T 1 K H c Nc (Mg + +O ) + (AlO) + (SiO) = (MgOÆAlOÆSiO) 1, 10T, K H c Nc (Ca + +O ) + (FeO) = (CaOÆFeO),1 10T 9 K H c Nc N 1 N N N 1 N N N N N N 1 N Nc K H c N 1 N N Nc K H c N 1 N N Nc K H c N N N Nc K H c N 1 N (Fe + +O ) + (FeO) = (FeOÆFeO),1 + 01T 9,, K H c Nc NN Nc K H c N N Nc K H N N (Mg + +O ) + (FeO) = (MgOÆFeO) 19, 09T 9 K H c Nc NN c N Nc K H N N (Mn + +O ) + (FeO) = (MnOÆFeO), + 11T 9 K H c Nc NN c N Nc9 K H N N (Ca + +O )+(PO) = (CaOÆPO), 9T 9 K H c9 Nc9 N N c9 N 1 N 1 N (Ca + +O )+(P O ) = (CaOÆP O ) 09, T 9 K H Nc0 c0 Nc0 N N Nc0 K H c0 N 1 N Nc1 K H N N 1 N (Ca + +O )+(PO) = (CaOÆPO) 1, T K H c1 Nc1 N 1 N c1 N 1 N VOLUME B, AUGUST 011

8 Table IV continued Reactions DrG H m;ci (J/mol) Reference K H ci Nci (Fe + +O )+(PO) = (FeOÆPO), 10T 0,, K H Nc c Nc N N Nc K H c N N Nc K H N N N (Fe + +O )+(PO) = (FeOÆPO) 1,1 + 10T 0,, K H c Nc N N c N N N (Mn + +O )+(P O ) = (MnOÆP O ),9 + 11T K H Nc c Nc N N Nc K H c N N Nc K H N N N (Mg + +O )+(PO) = (MgOÆPO) 1,9 9T 0 K H Nc c Nc N N c N N Nc K H N N N (Mg + +O )+(PO) = (MgOÆPO),1 111T 9 K H Nc c Nc N N c N N b N þ N c þ N c þ N c þ N c þ N c þ N c11 þn c1 þ N c1 þ N c1 þ N c1 þ N c19 þ N c Þ n i N þ K H c N 1 N þ K H c N1 1 N þ KH c N 1N þk H c N 1N þ KH c N 1N þ KH c11 N N þ K H c1 N N þk H c1 N N þ K H c1 N N þ KH c1 N 1 N N þk H c19 N 1N N þ K H c N N N n 0 Al molþ [g] b N þ N c9 þ N c0 þ N c1 þ N c þ N c þ N c þn c þ N c Þ n i N þ K H c9 N 1 N þ K H c0 N 1 N þ K H c1 N 1 N þk H c N N þ K H c N N þk H c N N þ K H c N N þ K H c N N Þ n i n 0 P O molþ [h] According to the principle that the sum of mole fraction for all structural uts in a fixed amount of CaO-SiO -MgO-FeO-Fe -MnO-Al -P O slags under equilibrium condition is equal to 10, the following equation can be obtained: N 1 þ N þ N þ N þ N þ N þ N þ N þ N c1 þ N c þþn c N 1 þ N þþn þ K H c1 N 1 N þ K H c N 1 N þ þ K H c N N N i 1:0 Þ ½Š The equation group of Eqs [] and [] is the governg equations of the developed thermodynamic model for calculating the mass action concentrations N i of structural uts or ion couples in CaO-SiO -MgO-FeO- Fe -MnO-Al -P O slags equilibrated or reacted with molten steel Obviously, there are ne unknown parameters as N 1 ; N ; N ; N ; N ; N ; N ; N and P n i with ne independent equations in the developed equation group of Eqs [] and [] The uque solution of N i ; P n i ; and n i can be calculated by solving these algebraic equation group of Eqs [] and [] by combing with the defition of N i in Eq [] It should be pointed out that considering P O as one component, no convergent solutions can be obtained by solving the equation group of Eqs [] and [] because the solved values of N P O is less than 10 0, like the reported a P O is less than 10 1 in an oxidization slags [9,0] Under this circumstance, the P O free CaO- SiO -MgO-FeO-Fe -MnO-Al slags was applied to substitute CaO-SiO -MgO-FeO-Fe -MnO-Al -P O slags The P O contentintheslagsislessthan0pct; replacing CaO-SiO -MgO-FeO-Fe -MnO-Al -P O slags by CaO-SiO -MgO-FeO-Fe -MnO-Al slags can not generate inconceivable errors on N i ; P n i ; and n i Therefore, Eqs [a] through [g]and[] can be rewritten by deleting N and N c9 N c as VOLUME B, AUGUST 011

9 1 b 1 N 1 þ N c1 þ N c þ N c þ N c þ 1N c þ N c þn c þ N c þ N c1 þ N c19 þ N c0 þ N c1 þn c þ N c þ N c 1 N 1 þ K H c1 N 1 N þ K H c N 1 N þ K H c N 1N þk H c N 1 N þ 1K H c N1 1 N þ KH c N 1N þk H c N 1N þ KH c N 1N þ KH c1 N 1 N N þk H c19 N 1N N þ KH c0 N 1N N þ K H c1 N 1N N þk H c N 1 N N þ KH c N 1 N N þ K H c N 1 N n i n 0 CaO! molþ [a] b N þ N c1 þ N c þ N c þ N c9 þ N c10 þ N c1 þ N c1 þn c1 þ N c1 þ N c1 þ N c19 þ N c0 þ N c1 þn c þ N c þ N c N þ K H c1 N 1 N þ K H c N 1 N þ K H c N 1N þk H c9 N N þ KH c10 N N þ K H c1 N N þ KH c1 N N þk H c1 N N þ KH c1 N N þ KH c1 N 1 N N þk H c19 N 1N N þ K H c0 N 1N N þ K H c1 N 1N N þk H c N 1 N N þ K H c N 1 N N þk H c N N N Þ n i n 0 SiO molþ [b] b 1 N þ N c9 þ N c10 þ N c11 þ N c0 þ N c1 þ N c þn c þ N c þ N c 1 N þ K H c9 N N þ KH c10 N N þ K H c11 N N þk H c0 N 1N N þ K H c1 N 1N N þ KH c N 1 N N þk H c N 1 N N þ K H c N N N þ KH c N N n i n 0 MgO molþ [c] b 1 N þ N c1 þ N c1 þ N c 1 N þ K H c1 N N þ KH c1 N N þ K H c N N n 0 FeO molþ [d] b N þ N c þ N c þ N c þ N c Þ n i N þ K H c N 1 N þ K H c N N þ K H c N N þk H c N N Þ n i n 0 Fe molþ [e] 1 b N þ N c1 þ N c1 þ N c1 þ N c 1 N þ K H c1 N N þ K H c1 N N þ KH c1 N N þ K H c N N n 0 MnO molþ [f] b N þ N c þ N c þ N c þ N c þ N c þ N c11 þn c1 þ N c1 þ N c1 þ N c1 þ N c19 þ N c Þ n i N þ K H c N 1 N þ K H c N1 1 N þ KH c N 1N þk H c N 1N þ KH c N 1N þ KH c11 N N þ K H c1 N N þk H c1 N N þ K H c1 N N þ KH c1 N 1 N N þk H c19 N 1N N þ K H c N N N Þ n i n 0 Al molþ ½gŠ N 1 þ N þ N þ N þ N þ N þ N þ N c1 þ N c þ þ N c N 1 þþn þ K H c1 N 1 N þ K H c N 1 N þ þ K H c N N N i 1:0 Þ ½Š This means that equation group of Eqs [a] through [g] and [] is composed of the applied thermodynamic model for calculating the mass action concentrations N i of structural uts or ion couples in CaO-SiO - MgO-FeO-Fe -MnO-Al -P O slags equilibrated or reacted with molten steel during calculation The calculated P n i in 100-g slags during a top bottom combined blown converter steelmaking process for heats is also summarized in Table I, respectively Principle of choosing standard molar Gibbs free energies of formed complex molecules The basic meang of the defined N i from IMCT [0 ] is the equilibrium mole fraction of structural ut i in a closed system relative to pure solid or liquid matter as standard state according to the matter existing state at the elevated temperature The physicochemistry meang of N i is almost consistent with the traditionally applied activity a i of component i in slags, in which pure solid or liquid matter is chosen as standard state and mole fraction is selected as concentration ut Tremendous studies have proved that N i of structural uts or ion couples in various slags has a good agreement with the reported a i of the related components in MnO-SiO slags, [0,1] FeO-Fe SiO slags, [0,] CaO-SiO Al -MgO slags, [0,] CaO-FeO-SiO slags, [0,] CaO-Al -SiO slags, [0,] Na O-SiO slags, [0,] CaO- MgO slags and NiO-MgO slags, [0,] and CaO-MgO- SiO -Al -Cr slags [] Therefore, the formulas of reaction equilibrium constant K H i and the related standard molar Gibbs free energy change D r G H m;i of reaction for forming structural ut i as complex molecule can be presented by N i to replace a i according to IMCT [0 ] as listed in Table IV The standard molar Gibbs free energy change of dissolving a solid component into slags is always equal to zero relative to the pure solid or liquid matter as standard state according to the basic principles of metallurgical physicochemistry [9,9] Therefore, the standard molar Gibbs free energy change of reactions for formation liquid complex molecules in Table IV can be determined from that for formation of solid complex molecules Taking the dissolution of solid CaO into slags as (Ca + +O ) as an example, the melting VOLUME B, AUGUST 011

10 process and the standard molar Gibbs free energy change for melting (Ca + +O )(s) can be presented as follows Ca þ þ O Þ s Ca þ þ O Þ l D fus G H m;cao l CaOlÞ l CaOsÞ J/molÞ [a] The dissolution process and the standard molar Gibbs free energy change for dissolving (Ca + +O )(l) into the slags as (Ca + +O ) relative to pure solid matter as standard state can be presented as Ca þ þ O ÞÞ l Ca þ þ O Þ D sol G H m;cao lh CaO l CaOlÞ l CaOsÞ l CaOlÞ ½9;9Š J/molÞ [b] Comparing Eqs [a] with [b], the following equation can be obtained D sol G H m;cao D fusg H m;cao J/molÞ ½cŠ Therefore, the value of standard molar Gibbs free energy change of melting or fusing component i from solid into liquid D fus G H m;i is equal to the opposite value for the standard molar Gibbs free energy change of dissolving liquid component i into the slags D sol G H m;i relative to pure solid as standard state The standard molar Gibbs free energy change for dissolution reaction of solid CaO(s) into slags as (Ca + +O ) will be zero by combing Eq [a] and [b] with considering Eq [c] as follows Ca þ þ O ÞÞCa s þ þ O Þ D r G H m;cao D solg H m;cao þ D fusg H m;cao 0 J/molÞ ½Š This means the standard molar Gibbs free energy change of the related reactions for forming complex molecules in Table IV will not change by presenting either solid or liquid as an existing state for reactants and products at combined blown converter steelmaking temperatures for calculating N i because N i is defined as pure solid or liquid matter as standard state according to IMCT [0 ] C Results of Mass Action Concentrations for Structural Uts or Ion Couples in Top Bottom Combined Blown Converter Steelmaking Slags 1 Relationship between mass percent of seven components and equilibrium mole numbers of related structural uts or ion couples in CaO-SiO -MgO- FeO-Fe -MnO-Al -P O slags The relationship between mass percent of CaO, SiO, MgO, FeO, Fe, MnO, and Al as components in Table II and the calculated equilibrium mole number n i of structural uts or ion couples, ie, (Ca + +O ), SiO, (Mg + +O ), (Fe + +O ), Fe,(Mn + +O ), and Al,inCaO-SiO -MgO-FeO-Fe -MnO-Al - P O slags at top bottom combined blown converter steelmaking temperatures is illustrated in Figure 1, respectively Obviously, the calculated equilibrium mole numbers n i of all seven structural uts or ion couples have some relationship with mass percent of the corresponding components; a good linear relationship can be found for five components of MgO, FeO, Fe, MnO, and Al, whereas a scattered corresponding relationship for other two components of CaO and SiO can be observed, respectively The scattered relationship for CaO and SiO can be explained as that some CaO can react with SiO to form CaOÆSiO, CaOÆSiO, and CaOÆSiO as complex molecules shown in Table III, Table IV, and Section III B ; therefore, the equilibrium mole number of both CaO and SiO, ie, free ion couple (Ca + +O ) and free simple molecule SiO cannot be corresponded with mass percent of both CaO and SiO in the slags The linear relations for other five components can be explained as that not so many mole numbers of complex molecules can be formed compared with mass percent of corresponding components shown in Tables III, IV, and Section III C Therefore, the mass percent of both CaO and SiO cannot be applied to the current reaction ability of the slags according to IMCT [0 ] Relationship between mass percent of seven components and mass action concentrations of related structural uts or ion couples in CaO-SiO -MgO- FeO-Fe -MnO-Al -P O slags The relationship between the mass percent of CaO, SiO, MgO, FeO, Fe,MnO,andAl as components in Table II and the calculated mass action concentrations N i of structural uts or ion couples, ie,(ca + +O ), SiO, (Mg + +O ), (Fe + +O ), Fe, (Mn + +O ) and Al in CaO-SiO -MgO-FeO-Fe -MnO-Al - P O slags at top bottom combined blown converter steelmaking temperatures is shown in Figure, respectively A linear relationship between mass percent and N i can be observed for MgO, FeO, Fe,MnO,andAl as components; however, a scattered linear relationship can be correlated for CaO and SiO although some mass of ion couple (Ca + +O ) and simple molecule SiO can bond as CaOÆSiO, CaOÆSiO, and CaOÆSiO as complex molecules shown in Table III, TableIV, andsectioniii B Therefore, the calculated mass concentration N i is much better than the equilibrium mole number n i to present the reaction ability of component i in the slags Relationship between equilibrium mole numbers and mass action concentrations of structural uts or ion couples in CaO-SiO -MgO-FeO-Fe - MnO-Al -P O slags The relationship between the calculated equilibrium mole numbers n i and mass action concentrations N i of all ion couples, as well as simple and complex molecules in CaO-SiO -MgO-FeO-Fe -MnO-Al -P O slags at top bottom combined blown converter steelmaking temperatures is illustrated in Figure, respectively The calculated n i and N i for all ( + ) ion couples or simple molecules or complex molecules in the slags have a good linear relationship The meang of slope for linear relationship between n i and N i in terms of IMCT [0 ] is the total equilibrium mole number P P n i in 100-g slags; however, does not show wide variation in the investigated heats as listed in Table II with 10 as the average value As reported in previous investigations, [,] P in 100-g CaO-SiO -MgO-Al slags with simple binary basicity (pct CaO)/(pct SiO ) as 10 VOLUME B, AUGUST 011

11 0 CaO 0000 SiO 0 MgO n CaO n SiO n MgO 0 0 n Al n FeO Mass percent of CaO (%) FeO Mass percent of FeO (%) Al Mass percent of SiO (%) n Fe Fe Mass percent of Fe (%) n MnO Mass percent of MgO (%) (a) (b) (c) MnO Mass percent of MnO (%) (d) (e) (f) Mass percent of Al (%) (g) Fig 1 Relationship between mass percent of CaO, SiO, MgO, FeO, Fe, MnO, and Al as components and calculated equilibrium mole number of (Ca + +O ), SiO, (Mg + +O ), (Fe + +O ), Fe, (Mn + +O ), and Al as structural uts or ion couples in 100-g CaO-SiO -MgO-FeO-Fe -MnO-Al -P O slags equilibrated with molten steel at top bottom combined blown converter steelmaking temperatures for heats, respectively applied in blast furnace ironmaking is approximately 0 [] ; however, P n i in 100-g CaO-SiO -MgO-FeO- Al -MnO slags with simple binary basicity as 0 applied in LF refing slags is approximately 1 [] Changing the simple binary basicity of slags has a large effect on the values of P n i The top bottom combined blown converter steelmaking slags has a smaller value of P than that of LF refing slags, but the value of P n i is larger than that of blast furnace ironmaking slags IV MODEL FOR CALCULATING PHOSPHORUS DISTRIBUTION RATIO BETWEEN CaO-SiO -MgO-FeO-Fe -MnO-Al - P O SLAGS AND MOLTEN STEEL A Establishment of L P Prediction Model Based on Slag Oxidization Ability The dephosphorization reactions between CaO-SiO - MgO-FeO-Fe -MnO-Al -P O slags and molten steel can be presented by all basic ion couples (Fe + + O ), (Ca + +O ), (Mg + +O ), and (Mn + + O ) in oxidizing slags, which can be described by Fe t O, to form ne dephosphorization products or molecules including P O, FeOÆP O, FeOÆP O, CaOÆP O, CaOÆP O, CaOÆP O, MgOÆP O, MgOÆP O, and MnOÆP O according to IMCT [0 ] as follows P ½ ŠþFe t OÞ P O Þþt½FeŠ D r G H m;p O 1; 1 þ 1:T J/molÞ ½9aŠ P ½ ŠþFe t OÞþFe þ þo FeO P O Þþt½FeŠ D r G H m; FeOP O ; 1 þ 0:T J/molÞ ½9bŠ P ½ ŠþFe t OÞþFe þ þo FeO P O Þþt½FeŠ VOLUME B, AUGUST 011

12 0 CaO 0000 SiO 00 MgO N CaO 0 0 N SiO N MgO Mass percent of CaO (%) Mass percent of SiO (%) Mass percent of MgO (%) (a) (b) (c) 0 FeO 00 Fe 00 MnO N FeO N Fe N MnO Mass percent of FeO (%) Mass percent of Fe (%) Mass percent of MnO (%) (d) (e) (f) 000 Al N Al Mass percent of Al (%) (g) Fig Relationship between mass percent of CaO, SiO, MgO, FeO, Fe, MnO, and Al as components and calculated mass action concentration of (Ca + +O ), SiO, (Mg + +O ), (Fe + +O ), Fe, (Mn + +O ), and Al as structural uts or ion couples in CaO-SiO -MgO-FeO-Fe -MnO-Al -P O slags equilibrated with molten steel at top bottom combined blown converter steelmaking temperatures for heats, respectively D r G H m;feop O 0; þ 9:9T J/molÞ ½9cŠ P ½ ŠþFe t OÞþMg þ þo MgOP O Þþt½FeŠ P ½ ŠþFe t OÞþCa þ þo CaOP O Þþt½FeŠ D r G H m; CaOP O 0; 19 þ :9T J/molÞ ½9dŠ P ½ ŠþFe t OÞþCa þ þo CaOP O Þþt½FeŠ D r G H m;caop O ; 0 þ 1:T J/molÞ ½9eŠ P ½ ŠþFe t OÞþCa þ þo CaOP O Þþt½FeŠ D r G H m; CaOP O ; þ 09:09T J/molÞ ½9fŠ D r G H m; MgOP O ; 9 :T J/molÞ ½9gŠ P ½ ŠþFe t OÞþMg þ þo MgOP O Þþt½FeŠ D r G H m; MgOP O 11; 9 þ :0T J/molÞ ½9hŠ P ½ ŠþFe t OÞþMn þ þo MnOP O Þþt½FeŠ D r G H m; MnOP O ; 1 þ : T J/molÞ ½9iŠ VOLUME B, AUGUST 011 9

13 0 CaO 0000 SiO 00 MgO N CaO 0 0 N SiO 0000 N MgO n CaO 0 FeO n SiO n MgO (a) (b) (c) Fe 00 MnO N FeO 0 N Fe N MnO n FeO n Fe n MnO (d) (e) (f) Al CaO SiO CaO SiO N Al N CaO SiO N CaO SiO n Al 00 CaO SiO n CaO SiO CaO Al E-011 n CaO SiO (g) (h1) (h) 1CaO Al N CaO SiO N CaO Al N 1CaO Al 00E E n CaO SiO n CaO Al 000E E E E-011 n 1CaO Al (h) (h) (h) E-01 CaO Al CaO Al CaO Al N CaO Al 001 N CaO Al N CaO Al 00E-01 00E n CaO Al n CaO Al 000E E E-01 10E-01 n CaO Al (h) (h) (h) Fig Relationship between calculated equilibrium mole number and mass action concentrations of ion couples, simple and complex molecules in 100-g CaO-SiO -MgO-FeO-Fe -MnO-Al -P O slags equilibrated with molten steel at top bottom combined blown converter steelmaking temperatures for heats, respectively 0 VOLUME B, AUGUST 011

14 0000 MgO SiO 0000 MgO SiO 000 MgO Al N MgO SiO N MgO SiO N MgO Al n MgO SiO n MgO SiO n MgO Al (h9) (h10) (h11) FeO SiO 0001 FeO Al MnO SiO N FeO SiO N FeO Al N MnO SiO n FeO SiO n FeO Al n MnO SiO (h1) (h1) (h1) MnO SiO MnO Al 00E-01 Al SiO N MnO SiO N MnO Al N Al SiO 00E n MnO SiO CaO Al SiO n MnO Al CaO Al SiO 000E E E-01 00E-01 n Al SiO (h1) (h1) (h1) 00 CaO MgO SiO N CaO Al SiO N CaO Al SiO N CaO MgO SiO n CaO Al SiO CaO MgO SiO n CaO Al SiO CaO MgO SiO n CaO MgO SiO (h1) (h19) (h0) CaO MgO SiO N CaO MgO SiO 0000 N CaO MgO SiO N CaO MgO SiO Fig continued n CaO MgO SiO n CaO MgO SiO n CaO MgO SiO (h1) (h) (h) VOLUME B, AUGUST 011 1

15 00E MgO Al SiO CaO Fe FeO Fe N MgO Al SiO 00E-0 00E-0 N CaO Fe N FeO Fe E E E-0 00E-0 00 n MgO Al SiO (h) MgO Fe n CaO Fe (h) MnO Fe n FeO Fe (h) N MgO Fe N MnO Fe n MgO Fe (h) n MnO Fe (h) Fig continued The corresponding equilibrium constants of Eq [9] can be expressed according to IMCT [0 ] as K H P O K H FeOP O a P O a t Fe a Fe t O a P N P O 1 N Fe t O ½pct PŠ f P pct P O Þ P O =M P O P N Fe t O ½pct PŠ f P Þ [10a] a FeOP O a t Fe N FeOP O a 1 Fe t O a FeO a P N Fe t O N FeO ½pct PŠ f P pct P O Þ FeOP O =M P O P N Fe t O N FeO ½pct Þ PŠ f P ½10bŠ K H CaOP O K H CaOP O a CaOP O a t Fe N CaOP O a 1 Fe t O a CaO a P N Fe t O N CaO ½pct PŠ f P pct P O Þ CaOP O =M P O P N Fe t O N CaO ½pct PŠ f P a CaOP O a t Fe N CaOP O a 1 Fe t O a CaO a P N Fe t O N CaO ½pct PŠ f P pct P O Þ CaOP O =M P O P N Fe t O N CaO ½pct PŠ f P Þ ½10eŠ Þ ½10fŠ K H FeOP O K H CaOP O a FeOP O a t Fe N FeOP O a 1 Fe t O a FeO a P N Fe t O N FeO ½pct PŠ f P pct P O Þ FeOP O =M P O P N Fe t O N FeO ½pct PŠ f P a CaOP O a t Fe N CaOP O a 1 Fe t O a CaO a P N Fe t O N CaO ½pct PŠ f P pct P O Þ CaOP O =M P O P N Fe t O N CaO ½pct PŠ f P Þ ½10cŠ Þ ½10dŠ K H MgOP O K H MgOP O a MgOP O a t Fe N MgOP O a 1 Fe t O a MgO a P N Fe t O N MgO ½pct PŠ f P pct P O Þ MgOP O =M P O P N Fe t O N MgO ½pct Þ PŠ f P ½10gŠ a MgOP O a t Fe N MgOP O a 1 Fe t O a MgO a P N Fe t O N MgO ½pct PŠ f P pct P O Þ MgOP O =M P O P N Fe t O N MgO ½pct Þ PŠ f P ½10hŠ VOLUME B, AUGUST 011

16 K H MnOP O a MnOP O a t Fe N MnOP O a 1 Fe t O a MnO a P N Fe t O N MnO ½pct PŠ f P pct P O Þ MnOP O =M P O P N Fe t O N MnO ½pct Þ PŠ f P ½10iŠ where M P O is molecular mass of P O as 119 ( ) According to Eq [10], the respective phosphorus distribution ratio of structural uts or ion couples as basic components under existing iron oxides in the slags L P;i can be expressed by L P;P O pct P O Þ P O ½pct PŠ M P O K H P O N Fe t O f P Þ ½11aŠ L P;MgOP O pct P O Þ MgOP O ½pct PŠ M P O K H MgOP O N Fe t O N MgO f P Þ ½11hŠ L P;MnOP O pct P O Þ MnOP O ½pct PŠ M P O K H MnOP O N Fe t O N MnO f P Þ ½11iŠ where f P is activity coefficient of the dissolved phosphorus in molten steel ( ) and can be calculated by considering chemical composition of molten steel and temperature as lg f P e j P½pct jš Þ ½1aŠ L P;FeOP O pct P O Þ FeOP O ½pct PŠ M P O K H FeOP O N Fe t O N FeO f P Þ ½11bŠ L P;FeOP O pct P O Þ FeOP O ½pct PŠ M P O K H FeOP O N Fe t O N FeO f P Þ ½11cŠ L P;CaOP O pct P O Þ CaOP O ½pct PŠ M P O K H CaOP O N Fe t O N CaO f P Þ ½11dŠ L P;CaOP O pct P O Þ CaOP O ½pct PŠ M P O K H CaOP O N Fe t O N CaO f P Þ ½11eŠ L P;CaOP O pct P O Þ CaOP O ½pct PŠ M P O K H CaOP O N Fe t O N CaO f P Þ ½11fŠ L P;MgOP O pct P O Þ MgOP O ½pct PŠ M P O K H MgOP O N Fe t O N MgO f P Þ ½11gŠ e j P A T þb Þ ½1bŠ where A and B are two parameters related to temperature ( ) Therefore, the total phosphorus distribution ratio between CaO-SiO -MgO-FeO-Fe -MnO- Al -P O slags and molten steel can be obtained from Eq [11] as follows L P L P;P O þ L P;FeOP O þ L P;FeOP O þ L P;CaOP O þ L P;CaOP O þ L P;CaOP O þ L P;MgOP O þ L P;MgOP O þ L P;MnOP O pct P O Þ P O ½pct PŠ þ pct P O Þ FeOP O ½pct PŠ þ pct P O Þ FeOP O ½pct PŠ þ pct P O Þ CaOP O ½pct PŠ þ pct P O Þ CaOP O ½pct PŠ þ pct P O Þ CaOP O ½pct PŠ þ pct P O Þ MgOP O ½pct PŠ þ pct P O Þ MgOP O ½pct PŠ þ pct P O Þ MnOP O ½pct PŠ M P O N Fe t O f P K H P O þ K H FeOP O N FeO þk H FeOP O N FeO þ KH CaOP O N CaO þk H CaOP O N CaO þ KH CaOP O N CaO þk H MgOP O N MgO þ KH MgOP O N MgO þk H MnOP O N MnO Þ n i Þ ½1Š Therefore, the developed L P prediction model by N Fet O to the current slag oxidization ability is composed of Eqs [11] and [1] based on IMCT [0 ] According to the calculated N i and P n i in Section III, K H i by Eq [10] and f P by Eq [1], the total phosphorus distribution ratio L P of the slags and the respective phosphorus distribution ratio L P;i of structural uts or ion couples VOLUME B, AUGUST 011

17 as basic components under existing iron oxides in the slags can be calculated The standard molar Gibbs free energy change D r G H m;i of dephosphorization reactions in Eq [9] for forming dephosphorization products i is determined from the reported data and summarized in Table V B Establishment of L P Prediction Model Based on Molten Steel Oxidization Ability The slag oxidization ability presented by Fe t Ohasa close relationship with the oxidization ability of molten steel by connecting the oxygen content of molten steel at slag metal interface with Fe t O in the slags as follows: t½fešþ½oš Fe t OÞ K H Fe t O a Fe t O a t Fe a N Fe t O O a O 1 D r G H m;fe t O 11; 100 þ :9T½1Š Þ [1a] The dephosphorization reactions in Eq [9] can be rewritten by replacing N Fet O by a O as follows: P ½ ŠþO ½ Š P O Þ P O a pct P O Þ P O =M P O P P O a O a P a O ½pct Þ PŠ f P ½1aŠ P ½ ŠþO ½ ŠþFe þ þ O FeO P O Þ FeOP O a FeOP O a O a FeO a P pct P O Þ FeOP O =M P O P a O N FeO ½pct PŠ f P P ½ ŠþO ½ ŠþFe þ þ O FeO P O Þ FeOP O a FeOP O a O a FeO a P pct P O Þ FeOP O =M P O P a O N FeO ½pct PŠ f P P ½ ŠþO ½ ŠþCa þ þ O CaO P O Þ CaOP O a CaOP O a O a CaO a P pct P O Þ CaOP O =M P O P a O N CaO ½pct PŠ f P Þ ½1bŠ Þ ½1cŠ Þ ½1dŠ P ½ ŠþO ½ ŠþCa þ þ O CaO P O Þ CaOP O a CaOP O a O a CaO a P pct P O Þ CaOP O =M P O P a O N CaO ½pct PŠ f P P ½ ŠþO ½ ŠþCa þ þ O CaO P O Þ CaOP O a CaOP O a O a CaO a P pct P O Þ CaOP O =M P O P a O N CaO ½pct PŠ f P P ½ ŠþO ½ ŠþMg þ þ O MgO P O Þ MgOP O a MgOP O a O a MgO a P pct P O Þ MgOP O =M P O P a O N MgO ½pct PŠ f P P ½ Šþ O ½ Šþ Mg þ þ O MgO P O Þ MgOP O a MgOP O a O a MgO a P pct P O Þ MgOP O =M P O P a O N MgO ½pct PŠ f P P ½ ŠþO ½ ŠþMn þ þ O MnO P O Þ MnOP O a MnOP O a O a MnO a P pct P O Þ MnOP O =M P O P a O N MnO ½pct PŠ f P Þ ½1eŠ Þ ½1fŠ Þ ½1gŠ Þ ½1hŠ Þ ½1iŠ Therefore, the developed respective phosphorus distribution ratio L P;i prediction model in Eq [11] by N Fet O can be also rewritten as L 0 P;i by a O, ie, a O;Fet OÞ½OŠ, of molten steel at the slag metal interface as follows: VOLUME B, AUGUST 011

18 Table V Calculation of Standard Molar Gibbs Free Energies for Nine Dephosphorization Reactions from the Reported Data of Standard Molar Gibbs Free Energies Reaction Number Chemical Reaction DrG H m;i (J/mol) Reference Notes Reaction [1] 1 = P = [P] 1,00 + T Reaction [] 1 = O = [O] 11,110 9T Reaction [] [P] + [O] = (PO)(l) 0,91 + T 0 Reaction [] P + = O = (PO)(l) 1,0, + 0T,0 From Reactions [1] through [] Reaction [] t[fe] + [O] = (FetO) 11, T 1 Eq [9a] [P] + (Fe t O) = (P O )+t[fe] 1,1 + 1T This study From Reactions [] and [] Reaction [] (FeO) + (PO) = (FeOÆPO) 0,0 + 90T 0 Eq [9b] [P] + (FetO) + (Fe + +O ) = (FeOÆPO)+t[Fe],1 + 0T This study From Eq [9a] and Reaction [] Reaction [] (FeO) + (PO) = (FeOÆPO) 1,1 + T 0 Eq [9c] [P] + (Fe t O) + (Fe + +O ) = (FeOÆP O )+t[fe] 0, + 99T This study From Eq [9a] and Reaction [] Reaction [] (CaO) + P + = O = (CaOÆPO)(s),19,09 + T 9 Reaction [9] (CaO) + (PO)(l) = (CaOÆPO)(s),0 + T 9 From Reactions [] and [] Eq [9d] [P] + (FetO) + (Ca + +O ) = (CaOÆPO)+t[Fe] 0,19 + 9T This study From Eq [9a] and Reaction [9] Reaction [10] (CaO) + P + = O = (CaOÆP O )(s),1, + T 9 Reaction [11] (CaO) + (P O )(l) = (CaOÆP O )(s) 09,90 + 1T 9 From Reactions [] and [10] Eq [9e] [P] + (FetO) + (Ca + +O ) = (CaOÆPO)(s),0 + 1T This From Eq [9a] and Reaction + t[fe] study [11] Reaction [1] (CaO) + (PO)(l) = (CaOÆPO)(l) 1, T Eq [9f] [P] + (Fe t O) + (Ca + +O ) = (CaOÆP O )+t[fe], T This study From Eq [9a] and Reaction [1] Reaction [1] (MgO) + (PO) = (MgOÆPO) 1,9 9T 0 Eq [9g] [P] + (FetO) + (Mg + +O ) = (MgOÆPO)+t[Fe],9 T This study From Eq [9a] and Reaction [1] Reaction [1] (MgO) + P + = O = (MgOÆPO)(s) 1,99, T 9 Reaction [1] (MgO) + (P O ) = (MgOÆP O )(s),9 0 T 9 From Reactions [] and [1] Eq [9h] [P] + (Fe t O) + (Mg + +O ) = 11,9 + 0T This From Eq [9a] and Reaction (MgOÆP O )+t[fe] study [1] Reaction [1] [P] + [O] + (MnO) = (MnOÆPO) 1,,1 + 91T Reaction [1] (MnO) + (PO) = (MnOÆPO),9 + 11T From Reactions [] and [1] Eq [9i] [P] + (Fe t O) + (Mn + +O ) = (MnOÆP O )+t[fe],1 + T This study From Eq [9a] and Reaction [1] VOLUME B, AUGUST 011