Xue-min YANG, 1) Jin-sha JIAO, 1) Ru-cai DING, 2) Cheng-bin SHI 2) and Han-jie GUO 2)

Transcription

1 , pp A Thermodynamic Model for Calculating Sulphur Distribution Ratio between CaO SiO 2 MgO Al 2 O 3 Ironmaking Slags and Carbon Saturated Hot Metal Based on the Ion and Molecule Coexistence Theory Xue-min YANG, 1) Jin-sha JIAO, 1) Ru-cai DING, 2) Cheng-bin SHI 2) and Han-jie GUO 2) 1) State Key Lab of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences, Beijing , P. R. China. 2) School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing , P. R. China. (Received on April 14, 2009; accepted on September 7, 2009) A thermodynamic model for calculating sulphur distribution ratio between CaO SiO 2 MgO Al 2 O 3 ironmaking slags and carbon saturated hot metal has been developed by using a thermodynamic model for calculating mass action concentrations of structural units or ion couples of ironmaking slags based on the ion and molecule coexistence theory. The calculated mass action concentrations of structural units or ion couples in CaO SiO 2 MgO Al 2 O 3 ironmaking slags equilibrated with carbon saturated hot metal at K can be applied to represent reaction ability, like classic concept of activity. The calculated total sulphur distribution ratio shows an acceptable agreement with the tested sulphur distribution ratio between CaO SiO 2 MgO Al 2 O 3 ironmaking slags and carbon saturated hot metal from desulphurization experiments at K. Meanwhile, the developed thermodynamic model for calculating sulphur distribution ratio between CaO SiO 2 MgO Al 2 O 3 ironmaking slags and carbon saturated hot metal can quantitatively determine the respective contribution of free CaO and MgO in CaO SiO 2 MgO Al 2 O 3 slags. A very significant difference of desulphurization ability between free CaO and MgO has been found with free CaO accounting for 97% desulphurization potential comparing with free MgO as about 3% in CaO SiO 2 MgO Al 2 O 3 slags equilibrated with carbon saturated hot metal at K. KEY WORDS: sulphur distribution ratio; CaO SiO 2 MgO Al 2 O 3 slags; hot metal desulphurization; thermodynamic model; desulphurization contribution of CaO; desulphurization contribution of MgO; mass action concentrations; ion and molecule coexistence theory; structural units; ion couples. 1. Introduction The sulphur distribution ratio between slags and hot metal is a common parameter to describe desulphurization ability 1 3) during blast furnace (BF) ironmaking process. Although BF ironmaking process has a strong desulphurization ability, and various hot metal pretreatment processes such as desulphurization, dephosphorization and desiliconization of hot metal have been developed 4 6) in the past three decades, all these hot metal pretreatment technologies have waken the urgency of intensifying desulphurization during BF ironmaking process. However, production of super clean steels needs hot metal with ultra low sulphur content. Therefore, improving desulphurization ability in BF hearth is also one of research hot spots for BF ironmaking process. Keeping ideal fluidity of BF slags, especially slags with high Al 2 O 3 content, in BF hearth is very important to maintain high desulphurization ability of BF slags, BF smooth operation as well as good separation between slag and hot metal during BF tapping 7 9) because largely utilizing the imported iron ore fines in the past decade has lead to improving Al 2 O 3 content from 10 13% to 14 18% 10,11) in BF slags compared with that using total Chinese domestic iron ore fines. Therefore, it is necessary to predict desulphurization ability of the optimized BF slags from the viewpoint of maintaining good fluidity for BF slags with high Al 2 O 3 content. Based on the measured desulphurization results between carbon saturated hot metal and CaO SiO 2 MgO Al 2 O 3 quaternary ironmaking slags with high Al 2 O 3 content, a thermodynamic model for calculating sulphur distribution ratio between CaO SiO 2 MgO Al 2 O 3 slags and carbon saturated hot metal has been developed through a newly established thermodynamic model for calculating mass action concentrations of structural units in CaO SiO 2 MgO Al 2 O 3 slags based on the ion and molecule coexistence theory ) The developed thermodynamic model for calculating sulphur distribution ratio between CaO SiO 2 MgO Al 2 O 3 slags and carbon saturated hot metal can not only calculate the total sulphur distribution ratio of CaO SiO 2 MgO Al 2 O 3 slags equilibrated with carbon saturated hot metal, but also determine the respective sulphur distribution ratio of components with desulphurization ability, such as CaO and MgO; meanwhile, the respective contribution of CaO and MgO on the total sulphur distribution ratio between CaO SiO 2 MgO Al 2 O 3 slags and carbon saturated hot metal can also be computed. The measured and calculated sulphur distribution ratio between CaO SiO 2 MgO Al 2 O 3 slags and carbon saturated hot metal have been compared to provide a prediction method of sulfur distribution ratio for ironmaking slags equilibrated with carbon saturated hot metal. The ultimate aim of this study is to de-

2 velop a universal prediction method of sulfur distribution ratio between various metallurgical slags and molten metal for various metallurgical processes. 2. Model for Calculating Mass Action Concentrations of Structural Units or Ion Couples in CaO SiO 2 MgO Al 2 O 3 Slags 2.1. Hypothesis According to the fact that there are ions and molecules in molten metallurgical slags simultaneously, the main assumptions in the developed thermodynamic model for calculating mass action concentrations of structural units or ion couples in CaO SiO 2 MgO Al 2 O 3 slags equilibrated with carbon saturated hot metal can be proposed based on the ion and molecule coexistence theory 12 15) as follows. (1) The structural units in CaO SiO 2 MgO Al 2 O 3 slags equilibrated with carbon saturated hot metal at metallurgical temperature are composed of Ca 2, Mg 2, O 2 and S 2 as simple ions, SiO 2 and Al 2 O 3 as simple molecules, silicates, aluminates and so on as complex molecules. Each structural unit has its independent position in the slags. Every cation and anion generated from the same component will take part in reaction of forming complex molecules in the form of ion couple as (Me 2 O 2 ). Choosing component CaO in the slags as an example, component CaO can be separated into two ions as Ca 2 and O 2 as two structural units, but both ions of Ca 2 and O 2 will take part in reactions of forming complex molecules and desulphurization reaction as one ion couple like (Ca 2 O 2 ). (2) The reactions of forming complex molecules are under chemical dynamic equilibrium by ion couples generated from simple ions and simple molecules as follows 2(Me 2 O 2 )SiO 2 2MeO SiO 2...(1.1) 3(Me 2 O 2 )SiO 2 3MeO SiO 2...(1.2) 2(Me 2 O 2 )SiO 2 Al 2 O 3 2MeO SiO 2 Al 2 O 3...(1.n) (3) The structural units in CaO SiO 2 MgO Al 2 O 3 slags bear continuity in the range of investigated concentration. (4) The chemical reactions of forming complex molecules as shown in Eq. (1) obey the mass action law. (5) Considering the large difference of desulphurization ability between ion couple (Ca 2 O 2 ) and (Mg 2 O 2 ), the extracted sulphur in BF slags from carbon saturated hot metal is assumed only to be bonded as ion couple (Ca 2 S 2 ), while content of extracted sulphur in BF slags bonded as ion couple (Mg 2 S 2 ) is ignored, i.e., treated as zero Model for Calculating Mass Action Concentrations of Structural Units or Ion Couples in CaO SiO 2 MgO Al 2 O 3 Slags Structural Units in CaO SiO 2 MgO Al 2 O 3 Slags Generally speaking from the viewpoint of traditional metallurgical physicochemistry, sulphur free CaO SiO 2 MgO Al 2 O 3 slags is certainly composed of four components as CaO, SiO 2, MgO and Al 2 O 3, while the extracted sulphur from carbon saturated hot metal must gradually enter into the slags as CaS and MgS with the proceeding of desulphurization reactions until desulphurization reactions reach equilibrium. The ion and molecule coexistence theory suggests 12 15) that the extracted sulphur in CaO SiO 2 MgO Al 2 O 3 slags exists as S 2 as a structural unit, which can be bonded with ions of Ca 2 and Mg 2 to form ion couples as (Ca 2 S 2 ) and (Mg 2 S 2 ), respectively. Hence, the open system of sulfur free CaO SiO 2 MgO Al 2 O 3 slags will become to a close system when desulphurization reactions reach equilibrium. Because the ion and molecule coexistence theory 12 15) can be exactly applied to a close system, the CaO SiO 2 MgO Al 2 O 3 slags equilibrated with carbon saturated hot metal, i.e., containing sulphur, is chosen to replace the sulphur free CaO SiO 2 MgO Al 2 O 3 quaternary slags in this study. However, the routine chemical analysis method can not easily analyze content of sulphur bonded as CaS or MgS at metallurgical production in-situ analysis as well as at further laboratory analysis. Only total sulphur content in slags can be analyzed and provided by routine sulphur analysis. Considering the large difference of desulphurization ability between CaO and MgO, total S 2 in the slags is treated to exist as CaS, while no S 2 is bonded as MgS during developing the thermodynamic model for calculating mass action concentrations of structural units or ion couples in CaO SiO 2 MgO Al 2 O 3 slags as an assumption describled in Sec Usually, sulphur content in common BF slags is less than 1.2%, which is much smaller than other four components as CaO, SiO 2, MgO and Al 2 O 3 in BF slags. Hence, assuming total S 2 as CaS in Sec. 2.1 can not bring distinct deviation on amount of other structural units in the close system of CaO SiO 2 MgO Al 2 O 3 slags equilibrated with carbon saturated hot metal. From above mentioned analysis and discussion, it can be obviously deduced that there are four simple ions as Ca 2, Mg 2, O 2 and S 2, two simple molecules as SiO 2 and Al 2 O 3 in CaO SiO 2 MgO Al 2 O 3 slags under desulphurization equilibrium at metallurgical temperature with respect to the ion and molecule coexistence theory ) According to the reported ternary phase diagrams 16) of CaO Al 2 O 3 SiO 2, CaO Al 2 O 3 MgO, CaO MgO SiO 2 and MgO Al 2 O 3 SiO 2 slags at ironmaking temperature, i.e., in a temperature range from to K, about 17 kinds of complex molecules listed in Table 1, such as 3CaO SiO 2 and so on, can be formed in CaO SiO 2 MgO Al 2 O 3 slags in ironmaking temperature range from to K. Surly, the chosen 17 kinds of complex molecules can be considered to exist at K as equilibrium temperature between CaO SiO 2 MgO Al 2 O 3 slags and carbon saturated hot metal which described in Sec All simple ions, simple and complex molecules in CaO SiO 2 MgO Al 2 O 3 slags equilibrated with hot metal at metallurgical temperature are summarized and assigned exclusive numbers in Table 1, for example, No. ci presents complex molecule i as a structural unit, No. 1 means structural unit Ca 2 or O 2 in ion couple (Ca 2 O 2 ) as two structural unit, or ion couple (Ca 2 O 2 ), No. 2 depicts simple molecule SiO 2 as a structural unite, and so on Definition and Presentation of Mass Action Concentrations for Structural Units or Ion Couples in CaO SiO 2 MgO Al 2 O 3 Slags The percentage change of CaO, SiO 2, MgO and Al 2 O 3 in 100 g of sulfur free CaO SiO 2 MgO Al 2 O 3 quaternary slags caused by the extracted sulphur from desulphurization reactions is ignored as sulphur content in the slags is lower than 1.6%. Obviously, there are six components in CaO SiO 2 MgO Al 2 O 3 slags equilibrated with hot metal as CaO, SiO 2, MgO, Al 2 O 3, CaS and MgS. Although content or amount of MgS in the slags is neglected, MgS as a component in the slags can not be omitted during development of the thermodynamic model for calculating mass action concentrations of structural units or ion couple. Otherwise, the logic rationality of the developed thermodynamic model will be challenged. Thus, mole number of six components as CaO, SiO 2, MgO, Al 2 O 3, CaS and MgS in 100 g of CaO SiO 2 MgO Al 2 O 3 slags is assigned as b 1 n 0 CaO,

3 Table 1. Expression of structural units as ion couples, simple or complex molecules, their mole numbers and mass action concentrations in 100 g of CaO SiO 2 MgO Al 2 O 3 slags equilibrated with carbon saturated hot metal at metallurgical temperature based on the ion and molecule coexistence theory. Table 2. Chemical reaction formulas of possibly formed complex molecules, their standard molar Gibbs free energy, equilibrium constants and mass action concentrations in CaO SiO 2 MgO Al 2 O 3 quaternary slags at metallurgical temperature.

4 b 2 n 0 SiO 2, b 3 n 0 MgO, b 4 n0 Al 2 O 3, b 5 n CaS and b 6 n 0 MgS0 to represent chemical composition of the slags. The defined 12 15) equilibrium mole numbers n i of all above mentioned structural units in CaO SiO 2 MgO Al 2 O 3 slags equilibrated with hot metal at metallurgical temperature have also been given out one by one in Table 1. According to the ion and molecule coexistence theory, 12 15) each ion couple is electroneutral and can be electrolyzed into cation and anion based on electrovalence balance principle. Hence, the equilibrium mole number of each ion couple is defined 12 15) as the sum of equilibrium mole number of the separated cation and anion. Choosing ion couple (Ca 2 O 2 ) as an example, (Ca 2 O 2 ) can be separated into Ca 2 and O 2, the equilibrium mole number of Ca 2 and O 2 can be expressed as n 1 n Ca 2,CaO n O 2,CaO n CaO. Therefore, ion couple (Ca 2 O 2 ) with a fixed amount under equilibrium condition can produce two times amount of structural units, 12 15) i.e., n Ca 2,CaO n O 2,CaO 2n CaO 2n 1. The total equilibrium mole number of all structural units in 100 g of CaO SiO 2 MgO Al 2 O 3 slags equilibrated with hot metal n i can be expressed as follows ni 2 n1n2 2 n3n4 2 n5 2 n6nc1nc2lnc17 (mol)...(2) With respect to the definition of mass action concentrations 12 15) for structural units, which is a ratio of equilibrium mole number of structural units i to the total equilibrium mole number of all structural units in a close system with a fixed amount, the mass action concentration of structural units i in molten slags N i can be calculated as follows ni Ni ( )...(3) ni Hence, the physical meaning of N i is equilibrium mole fraction of structural unit i. It should be emphasized that mass action concentrations of all structural units in the form of ions, simple and complex molecules can be directly calculated from Eq. (3); however, mass action concentrations of ion couples, such as (Me 2 O 2 ), should be calculated as follows 12 15) n 2 Me MeO n 2, O, MeO NMeON 2 Me MeON 2, O, MeO n i 2nMeO ( )...(4) n i Each simple and complex molecule can provide only one structural unit under equilibrium condition, hence, the definitions 12 15) of mass action concentration for simple and complex molecules in CaO SiO 2 MgO Al 2 O 3 slags equilibrated with hot metal sulphur from Eq. (3) are listed in Table 1; meanwhile, the mass action concentrations of ion couples, such as (Ca 2 O 2 ) and (Mg 2 O 2 ) defined by Eq. (4), 12 15) are also represented in Table 1. The chemical reaction formulas of 17 kinds of possibly formed complex molecules, their standard molar Gibbs free energy D r Gm,ci Q as a function of absolute temperature T, reaction equilibrium constant Kci Q and representation of mass action concentration of all complex molecules expressed by using Kci Q, N CaO (N 1 ), N SiO 2 (N 2 ), N MgO (N 3 ) and N Al2 O 3 (N 4 ) based on the mass action law are summarized in Table Model for Calculating Mass Action Concentrations of Structural Units or Ion Couples in CaO SiO 2 MgO Al 2 O 3 Slags The mass conservation equations for six components in 100 g of CaO SiO 2 MgO Al 2 O 3 slags equilibrated with hot metal can be established from definitions 12 15) of equilibrium mole numbers n i and mass action concentrations N i of all structural units listed in Table 1 and Table 2 as follows 1 b1 N13N 2N N 3N 12N N N 2 Nc82Nc13Nc14Nc152Nc163Nc17 ni 1 N1 3K N1 3 N2 2K N1 2 c1 c2 N2Kc3N1N2 2 3K N1 3 N412K N1 12 c4 c5 N Kc6N N Kc7N N K N1N4 6 K N1 2 c8 2 c13 N2N4Kc14N1N2 2 N4 K N N N 2K N N N b2( N2N N N N N 2N N 2N 2Nc152Nc162Nc17) ni N2 K N1 3 N2 K N1 2 ( c1 c2 N2Kc3N1N2Kc9N2N3 2 K N2N32K N2 2 N4 3 c10 c12 Kc13N1 2 N2N4 2K N N N 2K N N N 2K N N N c Kc17N N N3 ni ncao (mol)...(5a) c1 c2 c3 c9 c10 c12 c13 c c14 c15 c c K N N N ) n n (mol)...(5b) 1 b3 N32Nc9Nc10Nc11Nc15Nc16Nc17 ni 2 1 N3 2K N2N3 2 c9 Kc10N2N3Kc11N3N4 2 K N N N K N N N c15 c1 c2 c3 c4 c5 c6 c c c Kc17N1 3 N2 2 N3 ni nmgo (mol)...(5c) b4( N4Nc47Nc5Nc62Nc76Nc8Nc113Nc12 Nc13Nc14) ni N4 K N1 3 N4 7K N1 12 N4 7 ( K N1N42K N1N4 2 c4 c5 c6 c7 6K N N K N N 3K N N K N N N c8 c11 c12 c13 Kc14N1N2 2 N4 ) ni n i 0 SiO 0 Al O (mol)...(5d) 1 b5 N5 ni n...(5e) 2 0 CaS (mol) 1 b6 N6 ni n...(5f) 2 0 MgS 0 (mol) According to the principle that the sum of mole fraction for all structural units in CaO SiO 2 MgO Al 2 O 3 slags with a fixed amount under equilibrium condition is equal to 1.0, the following expression can be obtained N1N2N3N4N5N6Nc1Nc2LNc17 N N N N N N K N N K N N L c c K c17 N1 3 N2 2 N3 N i 1 ( )...(6)

5 The following five formulas can be obtained by combining Eqs. (5a) Eq. (5f) to eliminate n i, as 1 bn 1 2 bn 2 1 b1 b2 K N1 3 ( 3 ) c1 N2( b12b2) Kc2N1 2 N2 2 b1 b2 K N1N2 b2k N1 3 ( ) c3 3 c4 N412b2Kc5N1 12 N4 7 bk 2 c6nn 1 4bK 2 c7nn bk 2 c8nn bkc9n N bkc10n N 2bKc12N N ( b2b ) Kc13N N N ( 2bb ) K N N N ( 2bb ) K N N N 0 b1 b2 K N1 2 N2 2 ( 2 2 ) c16 N3( 2b1 3b2) Kc17N1 2 N2 2 N3 0 (mol)...(7a) 1 1 bn bn3bkc1n N2bKc2N NbKc3NN 2 2 3bKc4N N12bKc5N N bkc6nn bkc7nn bk 3 NN c8 2bK 1 c9n2n3 2 bk 1 c10n2n3bk 1 c11n3n4 2b Kc13N N N b Kc14N N N ( bb ) Kc15N N N ( b2b ) K N N N ( b3b ) K N N N c c (mol)...(7b) 1 bn 1 4 bn 4 1 bk 4 N1 3 N2 bk 4 N1 2 3 c1 2 c2 N2bK 4 c3nn b1 b4 K N1 3 ( 3 ) c4 N4( 7b112b4) Kc5N1 12 N4 7 ( b1b4) Kc6N1N4( 2b1b4) Kc7N1N4 2 ( 6b b ) Kc8NN bk 1 c11n3n43bk 1 c12n2 2 N ( 2bb ) Kc13N N2N4( b1b4) Kc14N1N2 2 N bk NN N32bK 4 N1 2 N2 2 c15 c16 N33bK 4 c17n1 3 N2 2 N3 0 (mol)...(7c) bn bn bkc1n N22bK 5 c2n1 2 N bkc3nn bkc4n N412bK 5 c5n1 12 N4 7 bk 5 NN 1 4bK 5 NN c6 c7 bk 5 c8nn bK N N N b K N N N b K N N N 5 c c c c c bkc16n N N33bK 5 c17n1 3 N2 2 N30 (mol)...(7d) N (7e) Hence, equation group of Eq. (5) and Eq. (6) or Eq. (6) and Eq. (7) is the governing equations of the developed thermodynamic model for calculating mass action concentrations of structural units or ion couples in CaO SiO 2 MgO Al 2 O 3 slags equilibrated with hot metal. There are seven unknown parameters as N 1, N 2, N 3, N 4, N 5, N 6 0 and n i with seven independent equations in equation group of Eq. (5) and Eq. (6), or six unknown parameters as N 1, N 2, N 3, N 4, N 5 and N 6 0 with six independent equations in equation group of Eq. (6) and Eq. (7). The sole real solutions for unknown parameters, such as N i, n i and n i, can be obtained by solving these algebraic equation group of Eq. (5) and Eq. (6) or Eq. (6) and Eq. (7) by combining with the definition of N i in Eq. (3) and Eq. (4). It should be specially pointed out that mass action concentrations of all ion couples, simple and complex molecules in CaO SiO 2 MgO Al 2 O 3 slags equilibrated with hot metal can be calculated from the developed thermodynamic model based on the ion and molecule coexistence theory ) However, only activity data of six components in CaO SiO 2 MgO Al 2 O 3 slags containing sulphur as CaO, SiO 2, MgO, Al 2 O 3, CaS and MgS can be determined from viewpoints of traditional experimental tests and classic thermodynamics. Choosing CaO as an example, the real meaning of mass action concentration for CaO N CaO is the sum of mass action concentration for two structural units as Ca 2 and O 2 in ion couple (Ca 2 O 2 ). From absolute viewpoint of the ion and molecule coexistence theory, 12 15) there is no mass action concentration of CaO as an independent structural unit because no independent CaO molecule can exist in CaO SiO 2 MgO Al 2 O 3 slags at metallurgical temperature. Applying the expression of mass action concentration for ion couple (Ca 2 O 2 ), i.e., free CaO, as N CaO in this paper is just for convenience to represent the reaction ability of free CaO in the slags, like measured CaO activity Results of Desulphurization Tests and Calculated Mass Action Concentrations for Structural Units or Ion Couples in CaO SiO 2 MgO Al 2 O 3 Slags Experiments on Desulphurization of Carbon Saturated Hot Metal by CaO SiO 2 MgO Al 2 O 3 Slags The desulphurization experiments of carbon saturated hot metal by CaO SiO 2 MgO Al 2 O 3 quaternary slags have been carried out at K using hot metal dropping into slags method as shown in Fig. 1. The sample of carbon saturated hot metal was obtained from a BF ironmaking works with [%C] as 4.853% and [%S] as 0.51%. Because mass ratio of slag to hot metal in BF hearth is usually maintained as 0.3, hence g of hot metal sample was applied to equilibrate with 30.0 g slags. Considering BF binary slag basicity (%CaO)/(%SiO 2 ) changing in a range of , content of (%MgO) and (%Al 2 O 3 ) varying in a range of % and %, respectively, 13 runs of desulphurization tests were designed as listed in Table 3. The chemical pure reagents of CaO, SiO 2, MgO and Al 2 O 3 were applied to prepare the synthetic sulphur free CaO SiO 2 MgO Al 2 O 3 quaternary slags. All applied chemical pure reagent were heated in an oven at K to dry at least 3 h. The dropping desulphurization experiments were carried out using double-layer graphite crucibles as shown in Fig. 1 at K. The upper graphite crucible with three small holes at bottom was designed to load carbon saturated hot metal ingot, the lower graphite crucible was assigned to put the synthetic slags. The desulphurization reaction time was set as 90 min because dropping process of hot metal at dropping zone in BF was about 90 min. During the desulphurization test, a three-hole graphite crucible with 30.0 g of mixed reagents in each separate crucible was firstly put into an elevated heating furnace at K under protection of high purity Ar gas to melt slags at least 30 min; then, a upper graphite crucible containing g prepared hot metal ingot in each separate crucible with a small hole at bottom was put into the furnace on the lower graphite crucible; after that, the melted hot metal will drop into lower separate crucibles, mix and start desulphurization reaction with melted slags. After 90 min desulphurization reation, the upper and lower graphite crucibles were taken out of the heating furnace immediately and put the lower graphite crucible into a water cooled copper box with cover to quench. The samples of hot metal and slags in each separate crucible were taken to analyze sulfur content. The analyzed sulfur content in hot metal and slags are also summarized in Table Results of Mass Action Concentrations for Structural Units or Ion Couples in CaO SiO 2 MgO Al 2 O 3 Slags The relationship between mass percent of CaO, SiO 2, MgO and Al 2 O 3 as components and calculated equilibrium

6 Table 3. Chemical composition of CaO SiO 2 MgO Al 2 O 3 quaternary slags and desulphurization results between CaO SiO 2 MgO Al 2 O 3 slags and carbon saturated hot metal with carbon content as 4.853% and initial sulphur content as 0.51% at K. Fig. 1. Schematic illustration of dropping desulphurization test between carbon saturated hot metal and CaO SiO 2 MgO Al 2 O 3 slags with three-hole double-layer crucibles. mole number of CaO, SiO 2, MgO and Al 2 O 3 as structural units or ion couples in CaO SiO 2 MgO Al 2 O 3 slags equilibrated with carbon saturated hot metal at K from the developed thermodynamic model is shown in Fig. 2, respectively. It should be specially emphasized that the calculated equilibrium mole number of each structural unit has explicit meaning to represent amount of corresponding structural unit, while two times of the calculated equilibrium mole number of ion couple has the meaning to represent amount of cation and anion in the ion couple, i.e., mole number of ion couple (Ca 2 O 2 ) and (Mg 2 O 2 ) can be represented as 2n CaO and 2n MgO, respectively. The calculated n SiO2 and 2n MgO has obvious relation with (%SiO 2 ) and (%MgO) as shown in Fig. 2(b) and Fig. 2(c), respectively; however, a very scattered relation between 2n CaO and (%CaO), n Al2 O 3 and (%Al 2 O 3 ) can be observed in Fig. 2(a) and Fig. 2(d), respectively. It is because beside free ion couple (Ca 2 O 2 ), which can react with sulphur in hot metal to proceed desulphurization reaction, a large amount of ion couple (Ca 2 O 2 ), generated from component CaO, can be bonded as complex molecules, such as CaO SiO 2, 2CaO SiO 2, CaO Al 2 O 3 and so on; meanwhile, beside free simple molecules Al 2 O 3, an obvious amount of structural units Al 2 O 3 from component Al 2 O 3 can be bonded as CaO Al 2 O 3, CaO 2Al 2 O 3, MgO Al 2 O 3, 2CaO Al 2 O 3 SiO 2 and so on, as shown in Table 1 and Table 2. The relationship between calculated equilibrium mole number n i and mass action concentration N i for 22 structural units or ion couples exception ion couple (Mg 2 S 2 ), such as 3 ion couples, 2 simple molecules and 17 complex molecules in CaO SiO 2 MgO Al 2 O 3 slags equilibrated with carbon saturated hot metal at K is illustrated in Fig. 3, respectively. Obviously, linear relation between n i and N i for 22 structural units or ion couples in CaO SiO 2 MgO Al 2 O 3 slags equilibrated with carbon saturated hot metal at K can be obtained. This implies that the calculated equilibrium mole number of structural units, but not mass percent of components, can be applied to represent real concentration in CaO SiO 2 MgO Al 2 O 3 slags equilibrated with carbon saturated hot metal at K. Although a small amount of SiO 2 or MgO is also bonded as complex molecules as listed in Table 1 and Table 2, the bonded amount of SiO 2 or MgO is less than that of CaO or Al 2 O 3 as shown in Fig. 3. Fig. 2. Relationship between mass percent of CaO, SiO 2, MgO and Al 2 O 3 as components and calculated equilibrium mole number of CaO, SiO 2, MgO and Al 2 O 3 as structural units or ion couples in CaO SiO 2 MgO Al 2 O 3 slags equilibrated with carbon saturated hot metal at K, respectively. These results can be further confirmed from Fig. 4, in which relationship between mass percent of CaO, SiO 2, MgO and Al 2 O 3 as components and calculated mass action concentration of (Ca 2 O 2 ), (SiO 2 ), (Mg 2 O 2 ) and (Al 2 O 3 ) as structural units or ion couples in CaO SiO 2 MgO Al 2 O 3 slags equilibrated with carbon saturated hot metal is presented respectively, that only (%MgO) and (%SiO 2 ) have linear relation with N MgO and N SiO, no clear corresponding relation between (%CaO) and N CaO, (%Al 2 O 3 ) and N Al2 O 3 can be observed. 3. Model for Sulphur Distribution Ratio between CaO SiO 2 MgO Al 2 O 3 Slags and Hot Metal 3.1. Establishment of Model for Sulphur Distribution Ratio between CaO SiO 2 MgO Al 2 O 3 Slags and Hot Metal According to the ion and molecule coexistence theory 12 15) that only free ion couples (Ca 2 O 2 ) and

7 Fig. 3. Relationship between calculated equilibrium mole number and mass action concentration of ion couples, simple and complex molecules in CaO SiO 2 MgO Al 2 O 3 slags equilibrated with carbon saturated hot metal at K, respectively. Fig. 4. Relationship between mass percent of CaO, SiO 2, MgO and Al 2 O 3 as components and mass action concentration of (Ca 2 O 2 ), (SiO 2 ), (Mg 2 O 2 ) and (Al 2 O 3 ) as structural units or ion couples in CaO SiO 2 MgO Al 2 O 3 slags equilibrated with carbon saturated hot metal at K, respectively. (Mg 2 O 2 ) can take roles in desulphurization reactions and provide desulphurization potential in CaO SiO 2 MgO Al 2 O 3 slags. The desulphurization reactions of free ion couples (Ca 2 O 2 ) and (Mg 2 O 2 ) as ion couples in CaO SiO 2 MgO Al 2 O 3 slags from carbon saturated hot metal and their standard molar Gibbs free energy are presented as follows (Ca 2 O 2 )[S](Ca 2 S 2 )[O] D r Gm,CaS Q 25,26) T (J/mol)...(8a) Fig. 3. (Mg 2 O 2 )[S](Mg 2 S 2 )[O] D r Gm,MgS Q 26,27) T (J/mol)...(8b)

8 The equilibrium constant of desulphurization reactions shown in Eq. (8a) and Eq. (8b) can be expressed respectively based on calculated N CaO and N MgO, and definition of N CaS, N MgS, a O and a S as follows 2( %S) CaS / M S [%O] f a a N a n CaS O CaS O i K CaS acaoas NCaOaS NCaO[%S] fs 2( %S) CaS / 32 [%O] n i fo N [%S] f (%S) CaS[%O] fo ( )...(9a) 16 N [%S] n f 2( %S) MgS / M S [%O] f a a N a n MgS O MgS O i K MgS amgoas NMgOaS NMgO[%S] fs 2( %S) MgS / 32 [%O] n i fo N [%S] f (%S) MgS[%O] fo ( )...(9b) 16 NMgO[%S] ni fs Therefore, the sulphur distribution ratio of (Ca 2 O 2 ) and (Mg 2 O 2 ) as ion couples in CaO SiO 2 MgO Al 2 O 3 slags equilibrated with hot metal can be easily deduced from Eq. (9a) and Eq. (9b) as follows L L S,CaO S,MgO CaO CaO MgO (%S) CaS KCaSNCaO ni fs [%S] 16 [%O] ( f )...(10a) (%S) MgS KMgSNMgO ni fs [%S] 16 [%O] ( f )...(10b) The activity coefficient of [S] and [O] in hot metal, f S and f O, at K can be calculated by lg f O eo O[%O]eC O [%C]eS O [%S] lg f S e S S [%S]e C S [%C]e O S [%O] ()...(11a) ()...(11b) where e O O 0.140, ec O 0.00, es O ) ; e S S 0.028, e S C 0.083, e S O ) The calculated f S and f O in carbon saturated hot metal with various [S] contents at each test runs is summarized in Table 3, respectively. The total sulphur distribution ratio of (Ca 2 O 2 ) and (Mg 2 O 2 ) as ion couples in CaO SiO 2 MgO Al 2 O 3 slags equilibrated with carbon saturated hot metal is the sum of them, as follows (%S) LS LS,CaOLS,MgO [%S] (%S) CaS MgS CaS (%S) MgS 16( K N K N ) ni f [%O] f i CaS CaO MgS MgO S ( )...(12) Therefore, not only the total sulphur distribution ratio L S, but also the respective sulphur distribution ratio of S S S O O O [%S] O O (Ca 2 O 2 ) and (Mg 2 O 2 ) as ion couples, L S,CaO and L S,MgO, in CaO SiO 2 MgO Al 2 O 3 slags equilibrated with carbon saturated hot metal can be calculated after knowing KCaS Q, KQ MgS, N CaO, N MgO, n i, f S, f O and oxygen content [%O] in hot metal. In addition, ignoring sulfur boned with ion couple (Mg 2 O 2 ) as (Mg 2 S 2 ) described in Sec. 2.1, i.e., b 6 n 0 MgS0, can only cause very limited deviation on L S,CaO, L S,MgO and L S through affecting N CaO, N MgO and n i in Eq. (10) and Eq. (12), but can not affect rationality of defined L S,MgO as Eq. (10b). This means assuming sulfur bonded as (Mg 2 S 2 ) in equilibrium slags as zero can not destroy logic rationality of defined L S,MgO and L S in this study. The equilibrium constant of KCaS Q and KQ MgS can be determined from D r Gm,CaS Q and D r GQ m,mgs shown in Eq. (8a) and Eq. (8b) by K Q i exp(d r Gm,i Q /RT) ()...(13) where R is gas constant (8.314 J/(mol K)), T is absolute temperature (K). The oxygen content [%O] in hot metal shown in Eq. (11) can be calculated via [C] [O] reaction in hot metal as [C][O]CO(g) D r Gm,CO Q 16) T (J/mol)...(14) therefore, the equilibrium constant of [C] [O] reaction can be expressed as K CO p CO / a a [%C] f [%O] f C O C O ( )...(15) where p CO is partial pressure of CO (Mpa), and assumed as MPa. Hence, [%O] in hot metal can be easily determined by Eq. (15) after knowing [%C], f C, f O, T and KCO Q. The activity coefficient of [C] in hot metal f C at K can be calculated by lg f C e C C [%C]e O C [%O]eC S[%S] ()...(11c) where e C C 0.049, e O C 0.000, ec S ) The calculated f C of [C] in carbon saturated hot metal with various [S] contents at each test runs is also summarized in Table 3, and the average oxygen content [%O] in carbon saturated hot metal with [%C] as 4.853% can be calculated as % at K. Therefore, equation group of Eq. (10) and Eq. (12) consists of the governing equations of the developed thermodynamic model for calculating sulphur distribution ratio between CaO SiO 2 MgO Al 2 O 3 BF slags and hot metal. Generally speaking, the calculated total sulphur distribution ratio is the theoretical maximum L S of CaO SiO 2 MgO Al 2 O 3 BF slags equilibrated with hot metal Results of Calculated Sulphur Distribution Ratio between CaO SiO 2 MgO Al 2 O 3 Slags and Hot Metal The desulphurization ability of ion couple (Ca 2 O 2 ) is much greater than that of ion couple (Mg 2 O 2 ) from the macro-viewpoint of the equilibrium constants for desulphurization reactions as shown in Eq. (8a) and Eq. (8b) with KCaS Q as and KMgS Q as at K. Hence, the assumption of ignoring contribution of S 2 bonded as ion couple (Mg 2 S 2 ) in Sec. 2.1, which is also discussed in detail in Sec , is reasonable, and can not bring distinct deviation on the calculated mass action concentrations for structural units or ion couples, especially on N CaO, N MgO and n i in Eq. (10) and Eq. (12) as the developed thermodynamic model for calculating sulphur distribution ratio between CaO SiO 2 MgO Al 2 O 3 slags and hot metal.

9 The calculated sulphur distribution ratio L S,calculated is compared with the tested sulphur distribution ratio L S,tested for CaO SiO 2 MgO Al 2 O 3 slags equilibrated with carbon saturated hot metal at K in Fig. 5. Surely, L S,calculated has a relative reliability with L S,tested. When L S,tested is larger than 60, the experimental errors, especially analysis errors of sulphur content in slags and hot metal, can make L S,tested greater than L S,calculated although L S,calculated is considered as the theoretical maximum sulphur distribution ratio. The influence of mole number for CaO and MgO as components and calculated mass action concentration for (Ca 2 O 2 ) and (Mg 2 O 2 ) as ion couples on L S,calculated, L S,CaO,calculated and L S,MgO,calculated in CaO SiO 2 MgO Al 2 O 3 slags equilibrated with carbon saturated hot metal at K is illustrated in Fig. 6, respectively. It can be observed from Fig. 6(a) that there is no obviously corresponding relation between mole number of CaO as component and L S,calculated or L S,CaO,calculated, and no distinct difference between L S,calculated and L S,CaO,calculated can be found at the same mole number of CaO as component. This means that free ion couple (Ca 2 O 2 ) accounts for most of desulphurization contribution in CaO SiO 2 MgO Al 2 O 3 slags. Comparing Fig. 6(a) and Fig. 6(c), a much smaller desulphurization contribution of free ion couple (Mg 2 O 2 ) than that of free ion couple (Ca 2 O 2 ) can be deduced. A very clear corresponding relations between N CaO and L S,calculated or L S,CaO,calculated, and between N MgO Fig. 5. Comparison between tested and calculated sulphur distribution ratio of CaO SiO 2 MgO Al 2 O 3 slags equilibrated with carbon saturated carbon at K. and L S,calculated or L S,MgO,calculated can be observed from Fig. 6(b) and Fig. 6(d) without considering the large different contribution between free ion couple (Ca 2 O 2 ) and (Mg 2 O 2 ). Therefore, not mole number and mass percent of CaO and MgO as components, but calculated mass action concentration or equilibrium mole number of free ion couple (Ca 2 O 2 ) and (Mg 2 O 2 ) can be applied to represent the desulphurization ability of CaO SiO 2 MgO Al 2 O 3 slags equilibrated with carbon saturated hot metal. This result is in good agreement with that shown in Figs Comparison of Desulphurization Ability of CaO and MgO in CaO SiO 2 MgO Al 2 O 3 slags Equilibrated with Hot Metal It is very important to quantitatively find the respective contribution of free (Ca 2 O 2 ) and (Mg 2 O 2 ) as ion couples on total desulphurization potential of CaO SiO 2 MgO Al 2 O 3 slags for optimizing chemical composition of BF slags to further improve desulphurization potential during BF ironmaking process. The calculated sulphur distribution ratio of free (Ca 2 O 2 ) and (Mg 2 O 2 ) as ion couples, L S,CaO,calculated and L S,MgO,calculated, from Eq. (10) for CaO SiO 2 MgO Al 2 O 3 slags equilibrated with carbon saturated hot metal at K is illustrated in Fig. 7, the quantitatively respective contribution of free (Ca 2 O 2 ) and (Mg 2 O 2 ) as ion couples on calculated L S,calculated of CaO SiO 2 MgO Al 2 O 3 slags equilibrated with carbon saturated hot metal at K is also given in Table 3 at each test runs. It can be seen from Fig. 7 and Table 3 that free (Ca 2 O 2 ) as ion couples accounts for about 97% contribution, while free (Mg 2 O 2 ) as ion couples only has about 3% contribution on L S,calculated of CaO SiO 2 MgO Al 2 O 3 slags equilibrated with hot metal at K. Hence, contribution of free (Mg 2 O 2 ) on of CaO SiO 2 MgO Al 2 O 3 slags equilibrated with hot metal can be ignored. Assuming the theoretical contribution of free (Ca 2 O 2 ) and (Mg 2 O 2 ) as ion couples on L S,calculated of CaO SiO 2 MgO Al 2 O 3 slags equilibrated with carbon saturated hot metal, as listed in Table 3, does not change for each test runs, the contribution of free (Ca 2 O 2 ) and (Mg 2 O 2 ) as ion couples on L S,tested of CaO SiO 2 MgO Al 2 O 3 slags equilibrated with hot metal at K can be also predicted as shown in Fig. 8. It can be observed that the average L S,MgO,tested only has a 3% contribution to L S,tested, while L S,CaO,tested has a 97% contribution to L S,tested for CaO SiO 2 MgO Al 2 O 3 slags equilibrated with carbon saturated hot metal at K. 4. Conclusions A thermodynamic model for calculating sulphur distribution ratio between CaO SiO 2 MgO Al 2 O 3 slags and car- Fig. 6. Influence of mole number of CaO and MgO as components or mass action concentration of ion couple (Ca 2 O 2 ) and (Mg 2 O 2 ) on calculated sulphur distribution ratio or calculated sulphur distribution ratio of ion couple (Ca 2 O 2 ) and (Mg 2 O 2 ) in CaO SiO 2 MgO Al 2 O 3 slags equilibrated with carbon saturated hot metal at K, respectively. Fig. 7. Contribution of free ion couple (Ca 2 O 2 ) and (Mg 2 O 2 ) on calculated sulphur distribution ratio between CaO SiO 2 MgO Al 2 O 3 slags and carbon saturated hot metal at K, respectively.

10 Fig. 8. Contribution of free ion couple (Ca 2 O 2 ) and (Mg 2 O 2 ) on tested sulphur distribution ratio between CaO SiO 2 MgO Al 2 O 3 slags and carbon saturated hot metal at K, respectively. bon saturated hot metal has been developed based on calculated mass action concentrations of structural units or ion couples from the ion and molecule coexistence theory. The main summary remarks can be obtained as follows (1) The calculated mass action concentrations of structural units or ion couples in CaO SiO 2 MgO Al 2 O 3 slags equilibrated with carbon saturated hot metal at K show that calculated equilibrium mole number or mass action concentration of structural units or ion couples can represent their reaction ability, rather than mass percent or mole number of components. (2) The total sulphur distribution ratio between CaO SiO 2 MgO Al 2 O 3 slags and carbon saturated hot metal at K can be calculated by the developed thermodynamic model for calculating sulphur distribution ratio with relative reliability. (3) The developed thermodynamic model for calculating sulphur distribution ratio between CaO SiO 2 MgO Al 2 O 3 slags and carbon saturated hot metal can quantitatively calculate the respective contribution of free CaO and MgO, respectively. (4) There is a huge difference of desulphurization ability between free CaO and MgO in CaO SiO 2 MgO Al 2 O 3 slags. Free CaO can account for 97% desulphurization potential comparing with free MgO as about 3% in CaO SiO 2 MgO Al 2 O 3 slags equilibrated with carbon saturated hot metal at K. Acknowledgments The valuable discussions, suggestions and encouragements from the founder of the ion and molecule coexistence theory, Prof. J. Zhang, to one of authors, Dr. Xue-min Yang, are kindly appreciated. Nomenclature a i : Activity of components i () b i : Mole number of components i in 100 g of slags (mol) f i : Activity coefficient of component i in hot metal () Q : K i Chemical equilibrium constant of forming component i or structural unit i () L S : Sulphur distribution ratio between slags and hot metal () L S,calculated : Calculated total sulphur distribution ratio between slags and hot metal () L S,tested : Tested total sulphur distribution ratio between slags and hot metal () L S,CaO,calculated : Calculated sulphur distribution ratio of CaO in slags () L S,MgO,calculated : Calculated sulphur distribution ratio of MgO in slags () L S,CaO,tested : Calculated sulphur distribution ratio of CaO in slags from tested data () L S,MgO,tested : Calculated sulphur distribution ratio of MgO in slags from tested data () Me : Metal () M i : Molecular weight of element i or component i (g/mol) n 0 i : Mole number of components i in 100 g of slags (mol) n i : Equilibrium mole number of structural unit i or ion couple i (mol) N i : Mass action concentrations of structural unit i or ion couple i () p i : Partial pressure of gas i (MPa) R : Gas constant ( kj/(mol K)) T : Absolute temperature (K) D r Gm,i Q : Standard molar Gibbs free energy of complex molecule i (J/mol) n i : Total equilibrium mole number of all structural units (mol) (%i) : Mass percent of component i in slags (%) [%i] : Mass percent of component i in hot metal (%) (%S) CaS : Sulphur content in slags boned as CaS (%) (%S) MgS : Sulphur content in slags boned as MgS (%) Subscripts ci : Complex molecule i () REFERENCES 1) A. 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