Prediction model of sulphur distribution ratio between CaO–FeO–Fe 2 O 3 –Al 2 O 3 –P 2 O 5 slags and liquid iron over large variation range of oxygen potential during secondary refining process of molten steel based on ion and molecule coexistence theory

Abstract

A thermodynamic model for predicting sulphur distribution ratio L _S between CaO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags and liquid iron, i.e. the ion and molecule coexistence theory (IMCT)–L _S model, has been developed for slags in a large variation range of slag oxidisation ability based on the IMCT. The developed IMCT–L _S model has been verified with measured data of oxygen, phosphorus and sulphur distribution equilibria between the slags and liquid iron from the literature. The results indicate that the desulphurisation reaction is mainly controlled by reaction (CaO)+[S] = (CaS)+[O] in the reducing zone with the optimised standard molar Gibbs free energy change of ; the desulphurisation reaction is dominated by reaction (FeO)+[S] = (FeS)+[O] in the oxidising zone with the reported standard molar Gibbs free energy change of . The influence of CaO on the desulphurisation ability of the slags can be counteracted by that of Fe_tO because higher CaO content corresponds to lower Fe_tO content in the slags. An asymmetric V type relationship between sulphur distribution ratio L _S and the mass action concentration ratio or or or , or the mass percentage ratio (%FeO)/(%CaO) or (%Fe₂O₃)/(%CaO) or (%Fe_tO)/(%CaO) or the simplified complex basicity or optical basicity can be established for the slags equilibrated with liquid iron in a temperature range from 1811 to 1927 K (1538 to 1654°C). The abovementioned mass action concentration ratios or mass percentage ratios of various iron oxides to basic oxide CaO can be recommended to represent the comprehensive effect of iron oxides Fe_tO and basic oxide CaO on desulphurisation ability of the slags.

Introduction

CaO based, Na₂CO₃ based or a mixture of CaO and Na₂CO₃ fluxes or slags over a large variation range of slag oxidisation ability have widely been applied in simultaneous dephosphorisation and desulphurisation processes of iron based melts since the 1970s.^1–26 The CaO–Fe_tO–Al₂O₃ slag system has been recommended by Ban-ya et al. ²⁰ for simultaneous dephosphorisation and desulphurisation during secondary refining process of molten steel. The distribution equilibria of oxygen, phosphorus and sulphur between CaO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ and liquid iron were experimentally measured by Ban-ya et al. ²⁰ The applied CaO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags by Ban-ya et al. ²⁰ exhibits a large variation range of slag oxidisation ability, which corresponds to mass percentage of Fe_tO from 1.88 to 55.50%. In addition, the designed chemical composition of the slags by Ban-ya et al. ²⁰ follows the CaO saturation line, but is not saturated with CaO, according to CaO–Fe_tO–Al₂O₃ phase diagram at elevated temperatures. The related information on dephosphorisation and desulphurisation reactions of the slags was discussed by Ban-ya et al. ²⁰ based on mole fraction and activity from the regular solution model. To further study the slags applied by Ban-ya et al.,²⁰ the dephosphorisation ability and potential of CaO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags have been predicted in a previous study²⁷ based on the ion and molecule coexistence theory (IMCT)^27–36 for metallurgical slags. Thus, the results on dephosphorisation ability and potential of the slags will not be involved in this paper in order to concentrate much focus of this work only on desulphurisation.

The recognised viewpoints of desulphurisation^{21,28–32,37–69} by fluxes or slags in a large variation range of slag oxidisation ability for simultaneous dephosphorisation and desulphurisation in secondary refining process of molten steel can be concluded as follows: controlling a reasonable slag oxidisation ability is very important to achieve the aim for simultaneous dephosphorisation and desulphurisation of molten steel;^24,25 fluxes or slags with high content of basic oxides as well as middle or high content of iron oxides can effectively remove phosphorous from iron based melts;^8,9,20,68 and fluxes or slags with higher slag oxidisation ability can only exhibit smaller desulphurisation ability as summarised by Wei⁶⁸ from numerous experimental results^20,54,68,69 and tremendous industrial practices. However, the desulphurisation mechanism and the reasons of greater dephosphorisation ability coupled with smaller desulphurisation ability for a fixed fluxes or slags in a large variation range of slag oxidisation ability are not clearly explained and deep probed.^20,54,68,69

The recognised desulphurisation mechanism of iron based melts from numerous studies since the 1940s^{21,28–32,37–69} can be summarised as follows:^21,43,68,70

slags with high content of basic oxide CaO or Na₂O and low content of ferrous oxide FeO without ferric oxide Fe₂O₃, i.e. slags with lower slag oxidisation ability, is beneficial to desulphurisation reactions^{21,28–32,37–69}

there are huge differences of desulphurisation ability among components of CaO, MgO, FeO and MnO in slags with lower slag oxidisation ability or smaller content of ferrous oxide FeO^{28–32,54,69}

slag oxidisation ability described by oxygen potential of slags is controlled by (Fe_tO)–{O₂} equilibrium reaction during various refining processes of iron based melts,^22,28–36 such as oxygen potential of pure Fe_tO corresponding to 5.50 10^–4 Pa at temperature of 1873 K (1600°C)

sulphide as CaS, MgS, MnS and FeS are desulphurisation products for iron based melts by slags^43,44,71 according to the viewpoint by Richardson and Fincham^43,44 that sulphide will be formed at oxygen potential < 0.101–1.013 Pa, while sulphate can be generated at oxygen potential >10.133–101.325 Pa.

Thus, the desulphurisation products in metallurgical slags for iron based melts must only be sulphide

, rather than sulphate

Comparing with the defined phosphate capacity by Wagner⁷¹ and sulphide capacity by Richardson and Fincham^43,44 based on gas–slag equilibrium reaction, or the defined phosphate capacity index and sulphide capacity index by Yang et al. ^{26,29,31,33,70,72} based on slag–metal equilibrium reaction, phosphorous distribution ratio and sulphur distribution ratio L _S as the easily measure parameters have widely been applied to describe dephosphorisation and desulphurisation abilities of slags equilibrated or reacted with iron based melts.

The obtained asymmetric V type relationship of desulphurisation ability of CaO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags against content of iron oxides was not theoretically explained by Ban-ya et al. ²⁰ Thus, the experimental results of the slags equilibrated with liquid iron by Ban-ya et al. ²⁰ are cited to develop sulphur distribution ratio L _S prediction model based on the IMCT,^27–36 i.e. the IMCT–L _S model.

The IMCT^27–36 was originally developed to represent reaction abilities of structure units including components and the formed complex molecules in metallurgical slags by the defined mass action concentrations N _i of structure units or ion couples according to the mass action law. None of empirical coefficients is embodied in the IMCT^27–36 for predicting reaction abilities of structure units or ion couples. The defined N _i of structure units or ion couples in various slags have been verified^27–36 to be consistent with the reported activities of components relative to pure solid or liquid matter i as standard state. The accuracy of N _i of structural units or ion couples in CaO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags has successfully been verified in a previous study²⁷ on predicting dephosphorisation ability and potential of the slags as and . Therefore, the reaction abilities of structure units or ion couples in CaO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags have been represented by the determined²⁷ N _i based on the IMCT^27–36 to predict desulphurisation ability of the slags in this study.

The desulphurisation mechanism of CaO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags in a large variation range of slag oxidisation ability has first been proposed based on the experimental results by Ban-ya et al. ²⁰ According to the proposed desulphurisation mechanism of the slags, a thermodynamic model for predicting L _S between the slags and liquid iron, i.e. the IMCT–L _S model, has been developed and verified through comparing the measured²⁰ by Ban-ya et al. with the calculated by the developed IMCT–L _S model as well as the predicted by other four L _S models^13,25,58,73 and other eight models^{20,21,58,73–79} from the literature. Furthermore, the influence of chemical composition of the slags including slag oxidisation ability, reaction abilities of components, slag basicity and the comprehensive influence of iron oxides Fe_tO and basic oxide CaO on desulphurisation ability have also been discussed.

It should be emphasised that beside the aforementioned eight models,^{20,21,58,73–79} other models^80–86 had also been proposed based on the framework of the modified quasichemical model in the quadruplet approximation,⁸¹ such as Reddy–Blander model^82–84 and Reddy–Blander–Pelton (RBP) model.^80,81,86 In addition, the core of the proposed model by Moretti and Ottonello⁸⁵ is similar to the RBP model^80,81,86 inasmuch as the sulphide activities are calculated from considerations of the configurational entropy of structural units, whereas the oxide activities are taken from the extensive evaluated thermodynamic databases. The RBP model^80,81,86 has been incorporated into the commercial software of FactSage (jointly developed between Thermfact/CRCT, Montreal, Canada, and GTT-Technologies, Aachen, Germany) for equilibrium calculation⁸⁰ in multicomponent multiphase systems. However, no explicit formulae for predicting in the FactSage software or the RBP model^80,81,86 had been provided due to intellectual property protection. The predicted of the studied slags cannot easily be obtained under the condition of no authorised right for accessing FactSage software. Thus, accuracy of the developed IMCT–L _S model cannot be evaluated by comparing the measured²⁰ by Ban-ya et al. with the predicted by the sulphide capacity model incorporated in FactSage software.

Desulphurisation mechanism of slags in large variation range of slag oxidisation ability after Ban-ya et al.

The original chemical compositions of both CaO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags and liquid iron for 31 test runs of equilibrium experiments for oxygen, phosphorus and sulphur between 10 g liquid iron without carbon and 15 g CaO–Fe_tO–Al₂O₃ slags from Ban-ya et al. ²⁰ have also been reported by Yang et al. elsewhere²⁷ in a decreasing hierarchy of the calculated oxygen potential of the slags through^87–89 (1a) (1b) where denotes the calculated²⁷ comprehensive mass action concentration of iron oxides for representing reaction ability of iron oxides, like the traditionally applied activity of Fe_tO relative to pure Fe_tO as standard state, depicts the standard pressure of gas at sea level and 273 K as 101 325 Pa. The activity of [Fe] as solvent in liquid iron relative to pure liquid Fe (l) as standard state can be thought as 1.0. For the sake of concision, the calculated²⁷ , , , , and by the IMCT–N _i model for the slags are not repeatedly reported in this study again.

Relationship between reaction abilities of components and various slag oxidation abilities

Three parameters as mass percentage of Fe_tO through based on Fe conservation, the calculated²⁷ and oxygen potential of slags by equation (1) can be applied to represent slag oxidation ability. It should be pointed out that oxygen content in liquid iron in test run nos. 30 and 31, which was not measured by Ban-ya et al.,²⁰ can be determined according to the calculated²⁷ through (Fe_tO)–[O] equilibrium by⁸⁸ (2a) (2b) The activity coefficient of [O] incorporated to activity of [O] in liquid iron referred to 1 mass-% of element [O] as standard state can be calculated by Wagner's equation as (3) Values of the first order activity interaction coefficient of element j to [O] in liquid iron at temperature of 1873 K (1600°C) chosen from the literature^87,90 are summarised as , and respectively. Certainly, the applied temperature from 1811 to 1927 K (1538 to 1654°C) has a very small gap with 1873 K (1600°C).

The relationship of three parameters for representing slag oxidisation ability against the calculated²⁷ or or or for the slags is illustrated in Fig. 1 respectively. Obviously, increasing mass percentage of Fe_tO or or oxygen potential of the slags can result in a slightly decreasing tendency of or , but can lead to a small increasing trend of or for the slags under the condition of mass percentage of Fe_tO or or oxygen potential or 0.0637 or 2.27 × 10^− 6 Pa respectively. Further increasing mass percentage of Fe_tO or or oxygen potential of the slags can cause an obviously decreasing tendency of or , but can bring about an overtly increasing trend of or for the slags under the condition of mass percentage of Fe_tO or or oxygen potential or 0.0637 or 2.27 × 10^− 6 Pa respectively. The variation tendency of or is opposite to that of or with the change of the applied three parameters for representing slag oxidation ability, while the magnitude of or is much greater than that of or .

Relationship of a1, a2 mass percentage of Fe_tO or b1, b2 calculated²⁷ of iron oxides or c1, c2 determined oxygen potential of slags against mass action concentration or or or for CaO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags equilibrated with liquid iron in temperature range from 1811 to 1927 K (1538 to 1654°C) respectively

Influence of various slag oxidation abilities on measured desulphurisation ability by Ban-ya et al.

The relationship between mass percentage of Fe_tO or the calculated²⁷ or oxygen potential of the slags and the measured²⁰ by Ban-ya et al. for the slags is illustrated in Fig. 2. Obviously, an asymmetric V type relationship of the measured²⁰ by Ban-ya et al. against mass percentage of Fe_tO or or oxygen potential of the slags can be observed in Fig. 2. The lowest datum of the measured²⁰ by Ban-ya et al. corresponds to mass percentage of Fe_tO as 6.75% or as 0.0637 or oxygen potential of the slags as 2.27 × 10^− 6 Pa. The desulphurisation ability of the slags shows a sharp decreasing tendency with an increase in mass percentage of Fe_tO from 1.88 to 6.75% or from 0.0185 to 0.0637 or oxygen potential of the slags from 8.18 × 10^− 8 to 2.27 × 10^− 6 Pa. However, desulphurisation ability of the slags displays a slightly increasing trend with an increase in mass percentage of Fe_tO from 6.75 to 55.50% or from 0.0637 to 0.504 or oxygen potential of the slags from 2.27 × 10^− 6 to 3.23 × 10^− 4 Pa.

Relationship of a mass percentage of Fe_tO or b calculated comprehensive mass action concentration of iron oxides or c determined oxygen potential of slags against measured²⁰ sulphur distribution ratio by Ban-ya et al. for CaO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags equilibrated with liquid iron in a temperature range from 1811 to 1927 K (1538 to 1654°C) respectively

Similar results have also been reported by many researchers^54,68,69 and briefly discussed by Wei.⁶⁸ The widely accepted conclusions^20,54,68,69 can be summarised as that slags containing Fe_tO content < 5.0–8.0% as reducing slags show greater desulphurisation ability; slags with Fe_tO content >5.0–8.0% as oxidising slags display a smaller desulphurisation ability; pure Fe_tO at temperature of 1873 K (1600°C) exhibits a smaller desulphurisation ability with L _S as 3.60, i.e. as 0.556. Thus, mass percentage of Fe_tO as 6.75% or as 0.0637 or oxygen potential as 2.27 × 10^− 6 Pa can be treated as the criterion for distinguishing reducing and oxidising zones for the slags in a large variation range of slag oxidisation ability. It should be stressed that the asymmetrical relationship of desulphurisation ability in logarithmic form against slag oxidisation ability cannot distinctly be displayed in the subfigures of Fig. 2 based on normal scale of the horizontal coordinates. It is the main reason that the horizontal coordinates in the subfigures of Figs. 1 and 2 have been split into two zones through adding break symbol. Certainly, adding break symbols on the horizontal coordinates cannot destroy the intrinsic relationship of slag oxidisation ability against for the slags as shown in Fig. 2. To improve display resolution, the distinguished line between reducing and oxidising zones has also been added on the horizontal coordinates in Fig. 2 and other following figures if necessary.

Deduction of desulphurisation mechanism of slags in large variation range of slag oxidisation ability

It has widely been accepted^54,68,69 that calcium sulphide CaS will be the main desulphurisation products in CaO based slags with FeO content < 2.0% as reducing slags, which can be applied in blast furnace ironmaking process or ladle furnace (LF) refining process or reduction period in electric arc furnace (EAF) steelmaking process, while ferrous sulphide FeS will be the major desulphurisation products in CaO based oxidising slags with Fe_tO content >12.0% as oxidising slags, which can be used in LD converter steelmaking process or simultaneous dephosphorisation and desulphurisation operation in secondary refining process of molten steel. Thus, it can be deduced through combining Figs. 1 and 2 that desulphurisation reaction of the studied slags should be controlled by CaO with CaS as desulphurisation product under the condition of mass percentage of Fe_tO or or oxygen potential or 0.0637 or 2.27 × 10^− 6 Pa respectively, while desulphurisation reaction of the slags should be dominated by FeO with FeS as desulphurisation product under the condition of mass percentage of Fe_tO or or oxygen potential or 0.0637 or 2.27 × 10^− 6 Pa respectively. Otherwise, the results in Fig. 2 after Ban-ya et al. ²⁰ and the similar experimental conclusions^54,68,69 cannot reasonably be explained from the basic principles of desulphurisation reactions.

Theoretically, a small amount of FeS can be generated in reducing slags. It has been obtained by Yang et al. ^30,31 that the generated FeS in CaO–SiO₂–MgO–FeO–MnO–Al₂O₃ reducing slags can only account for about 0.60–0.81% of desulphurisation products during LF refining process. Therefore, the contribution of FeS as desulphurisation product in reducing slags can be ignored.

Under this circumstance, the distinguishing line between reducing and oxidising zones in Fig. 2 has been represented by CaS and FeS as desulphurisation product.

Thermodynamic model for calculating sulphur distribution ratio L _S between CaO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags and liquid iron based on IMCT

Establishment of IMCT–L _S model for slags based on IMCT

According to the deduced desulphurisation mechanism in the section on ‘Deduction of desulphurisation mechanism of slags in large variation range of slag oxidisation ability’, two kinds of desulphurisation products, CaS and FeS, can individually be generated in CaO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags equilibrated with liquid iron based on the aforementioned criterion for mass percentage of Fe_tO or or oxygen potential of the slags as 6.75% or 0.0637 or 2.27 × 10^− 6 Pa respectively. The ion couple (Ca²⁺ + O^2 −) or (Fe²⁺ + O^2 −) in CaO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags can take part in desulphurisation reaction and contribute to desulphurisation ability according to the IMCT^27–36 as (4a) (4b) The standard equilibrium constant and of desulphurisation reactions in equations (4a) and (4b) can be expressed through inserting the definition^27–36 of and , and the calculated²⁷ or by (5a) (5b) where means the relative atomic mass of sulphur element as 32.07. The respective sulphur distribution ratio of CaS and of FeS in the slags equilibrated with liquid iron based on oxygen potential of 2.27 × 10^–6 Pa as criterion can be derived from equation (5) as (6a) (6b) Theoretically, the total sulphur distribution ratio L _S of the slags equilibrated with liquid iron in a large variation range of slag oxidisation ability can be defined as summation of and as (7) Certainly, the equation group of equations (6) and (7) is composted of the developed IMCT–L _S model for the slags equilibrated with liquid iron in a large variation range of slag oxidisation ability. The embodied parameters as , and have been determined by the developed IMCT–N _i model as reported elsewhere.²⁷ The activity coefficient of [S] in liquid iron can be calculated by Wagner's equation in equation (3). Values of for element j to [S] in liquid iron at temperature of 1873 K (1600°C) chosen from the literature^87,90 are summarised as , and . The developed IMCT–L _S model in equations (6) and (7) can be applied to predict desulphurisation ability of the slags after knowing and from the related standard molar Gibbs free energy change and by van't Hoff equation as .

Determination of standard molar Gibbs free energy change of desulphurisation reaction for forming CaS or FeS in slags

Optimising of desulphurisation reaction for forming CaS in slags

The desulphurisation reaction in equation (4a) for forming CaS as desulphurisation product can be rewritten according to the classically chemical metallurgy as (8a) The reported from various references^{69,81,91–96} have been summarised in the upper region of Table 1. The relationship between temperature T from 1811 to 1927 K (1538 to 1654°C) and the reported from various references^{69,81,91–96} is illustrated in Fig. 3a respectively. The reported from various references^{69,81,91–96} show a large fluctuation from 35.00 to 110.00 kJ mol^− 1 in a temperature range from 1811 to 1927 K (1538 to 1654°C), in which the reported from the references^69,92–96 displays smaller values from 35.00 to 55.00 kJ mol^− 1, while the reported by Pelton et al. ⁸¹ and Zhang⁹¹ exhibits greater data from 105.00 to 110.00 kJ mol^− 1.

Table 1

Summary of reported standard molar Gibbs free energy change of desulphurisation reactions for forming CaS or FeS in slags from various references

Reaction		Reference	Notes
[S]+(CaO) = (CaS)+[O]	115 232.63 − 2.28T	91
	105 784.60 − 28.72T	92,93
	87 110.88 − 21.09T	94
	87 084.68 − 23.55T	69	Based on
	37 900.00	95	Based on and at T = 1873 K (1600°C)
	− 50 635.07+47.09T	96	Based on and
	74 475.31+15.75T	81	Based on of gas–slag reaction
	147 023.63 − 27.94T	This study	Optimised based on experimental data after Ban-ya et al. ²⁰
[S]+(FeO) = (FeS)+[O]	115 526 − 33.35T	98–100	Applied in this study
	123 752.3 − 36.41T	43
	68 647.97	54	At T = 1873 K (1600°C)
	123 633.1 − 40.59	69	Based on
	68 229.38T	97	At T = 1873 K (1600°C)

a comparison of optimised standard molar Gibbs free energy change of desulphurisation reaction (CaO)+[S] = (CaS)+[O] and reported expressions of from various references and b comparison of reported standard molar Gibbs free energy change of desulphurisation reaction (FeO)+[S] = (FeS)+[O] from various references in temperature range from 1811 to 1927 K (1538 to 1654°C)

The smaller values of can result in larger values of both and the calculated in equation (6a) for the slags in reducing zone and vice versa. Using the reported smaller values of from the references,^69,92–96 the calculated for the slags in reducing zone is significantly greater than the measured²⁰ by Ban-ya et al. Under this circumstance, values of were determined based on the defined and the calculated²⁷ for the slags in reducing zone as (8b) The determined (J mol^− 1) by equation (8b) based on the calculated and are also illustrated in Fig. 3a as semisolid circles. The reported as 105.00 kJ mol^− 1 by Pelton et al. ⁸¹ and the reported as 110.00 kJ mol^− 1 by Zhang⁹¹ are very close to the obtained one by equation (8b). According to the relationship of the reported from various references^{69,81,91–96} against temperature T, the optimised expression of against temperature T can be obtained by keeping the similar slope with different intercepts based on experimental data from Ban-ya et al. ²⁰ for the slags in reducing zone as shown in Fig. 3a . The optimised expression of can be expressed as (8c) Thus, the optimised expression of (J mol^− 1) in equation (8c) can be recommended as accurate representation of , which is close to that suggested by Pelton et al. ⁸¹ and Zhang⁹¹ shown in Fig. 3a .

Selecting of desulphurisation reaction for forming FeS in slags

The desulphurisation reaction in equation (4b) for forming FeS as desulphurisation product can also be rewritten as (9) The reported from various references^{54,69,97–100} have also been summarised in the lower region of Table 1. The relationship between temperature from 1811 to 1927 K (1538 to 1654°C) and the reported from various references^{54,69,97–100} is illustrated in Fig. 3b respectively. The reported from various references^{54,69,97–100} show a small fluctuation from 45.00 to 60.00 kJ mol^− 1 except for two points as ∼70.00 kJ mol^− 1 by Shim et al. ⁵⁴ and Ward⁹⁷ at 1873 K (1600°C). It has been verified by Yang et al. ³⁰ that the reported^98–100 = 115 526 − 33.35T (J mol^− 1) can be applied to accurately predict sulphur distribution ratio L _S of CaO–SiO₂–MgO–FeO–Al₂O₃–MnO slags in LF refining process.³⁰ Thus, the reported^98–100 expression of is recommended to predict the respective sulphur distribution ratio of FeS for the slags in oxidising zone.

Verification of developed IMCT–L _S model for slags

Two steps have been applied to evaluate and verify accuracy of the developed IMCT − L _S model. The first step is to compare the measured²⁰ by Ban-ya et al. with the calculated by the developed IMCT − L _S model. The second step is to compare the measured²⁰ by Ban-ya et al. with the predicted by the summarised four L _S models^13,25,58,73 as well as the listed^29,31 eight models^{20,21,58,73–79} in Table 2.

Table 2

Summary of four sulphur distribution ratio L _S prediction models and eight sulphide capacity prediction models from related literature

L _S or model		Slags	Reference
L _S model	Suito's model	CaO–FeO–Fe₂O₃–Al₂O₃–P₂O₅	25
	Narita's model	CaO–SiO₂–FeO–Na₂O–CaF₂	13
	Sosinsky's model*	Various	73
	Tsao's model	CaO–SiO₂–MgO–Al₂O₃	58
model^29,31	Suito's model	CaO–FeO–Fe₂O₃–Al₂O₃–P₂O₅	25
	Tsao's no. 1 model	CaO–MgO–Al₂O₃–SiO₂	58
	Tsao's no. 2 model	CaO–MgO–Al₂O₃–SiO₂	58
	Ban-ya's model	CaO–FeO–Fe₂O₃–Al₂O₃–P₂O₅	20, 74
	Sosinsky's model		73
	Young's model	CaO–SiO₂–MgO–FeO–MnO–Al₂O₃	21



	KTH model	CaO–SiO₂–MgO–FeO–MnO–Al₂O₃	75–78
	Taniguchi's model	CaO–SiO₂–MgO–MnO–Al₂O₃	79

Sulphur distribution ratio in Sosinsky's model⁷³ has been transferred to as shown in Fig. 5.

Comparison between measured and calculated by IMCT–L _S model for slags

Comparison between the measured²⁰ by Ban-ya et al. and the calculated for CaO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags equilibrated with liquid iron is illustrated in Fig. 4. Obviously, values of the calculated are in good agreement with values of the measured²⁰ by Ban-ya et al. except for one point with the measured²⁰ by Ban-ya et al. as 1.43 in the new test run no. 1. This suggests that the developed IMCT–L _S model can be applied to accurately predict L _S between the slags and liquid iron based on from the optimised in equation (8c) and from the recommended^98–100 .

Comparison between measured²⁰ sulphur distribution ratio by Ban-ya et al. and calculated sulphur distribution ratio by developed IMCT–L _S model for CaO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags equilibrated with liquid iron in temperature range from 1811 to 1927 K (1538 to 1654°C)

It should specially be emphasised that the calculated for the slags in the reducing zone is significantly smaller than the calculated . It can be deduced that contribution of FeS as desulphurisation products for the slags in reducing zone can be ignored. Thus, the total sulphur distribution ratio L _S for the slags in the reducing zone can accurately be calculated by the developed IMCT–L _S model in equation (6a). This finding is coincident with the reported conclusion by Yang et al. ^30,31 for other reducing slags applied in LF refining process mentioned in the section on ‘Deduction of desulphurisation mechanism of slags in large variation range of slag oxidisation ability’. Moreover, the calculated for the slags in the oxidising zone is much smaller than the calculated . Therefore, contribution of CaS as desulphurisation products can be omitted for the slags in oxidising zones. Thus, the total sulphur distribution ratio L _S for the slags in oxidising zone can precisely be predicted by the developed IMCT–L _S model in equation (6b).

It can be deduced that CaS can be considered as the sole desulphurisation product in the slags of the reducing zone, while FeS can be treated as the complete desulphurisation product in the slags of the oxidising zone. Separating reducing and oxidising zones for the slags in a large variation range of slag oxidisation ability is very important to accurately predict desulphurisation ability by the developed IMCT–L _S model in equations (6a) and (6b).

Comparison between measured and calculated by other L _S or models

Comparison between measured and calculated by other L _S models

Four sulphur distribution ratio L _S models for various metallurgical slags such as Suito's model,²⁵ Narita's model,¹³ Tsao's model⁵⁸ and Sosinsky's model⁷³ have chronologically been summarised in the upper region of Table 2. Comparison between the measured²⁰ by Ban-ya et al. and the calculated by the summarised four L _S models^13,25,58,73 for CaO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags equilibrated with liquid iron is illustrated in Fig. 5a–d respectively. Basically, none of the summarised four L _S models^13,25,58,73 can be applied to accurately predict L _S of the slags in a large variation range of slag oxidisation ability. However, each L _S model^13,25,58,73 can more or less predict some points of the measured²⁰ by Ban-ya et al.

Comparison between measured²⁰ sulphur distribution ratio by Ban-ya et al. and calculated sulphur distribution ratio a–d by reported four sulphur distribution ratio L _S prediction models or e–l by reported eight sulphide capacity prediction models for CaO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags equilibrated with liquid iron in temperature range from 1811 to 1927 K (1538 to 1654°C) respectively

It can be concluded through comparing Fig. 4 with Fig. 5a–d that the developed IMCT–L _S model is better than the summarised four L _S models for predicting desulphurisation ability of the slags in a large variation range of slag oxidisation ability. The summarised four L _S models correspond to their specially assigned slag type and chemical composition range. In addition, the embodied empirical coefficients in the summarised four L _S models are regressed from the assigned experimental data. The deduced desulphurisation mechanism as described in the section on ‘Deduction of desulphurisation mechanism of slags in large variation range of slag oxidisation ability’ should be applied for the investigated slags in a large variation range of slag oxidisation ability.

Comparison between measured and calculated by other models

Numerous data of sulphide capacity or sulphide capacity index of various slags have been accumulated in the past several decades. Eight sulphide capacity models^{20,21,58,73–79} for various slags have been developed by various researchers as listed^29,31 in the lower region of Table 2. The relationship between L _S and for slags can be expressed as^29,31,101 (10) Thus, the proposed sulphide capacity models^{20,21,58,73–79} can be applied to predict sulphur distribution ratio L _S between CaO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags and liquid iron in this study.

Comparison between the measured²⁰ by Ban-ya et al. and the calculated by the listed eight models for CaO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags equilibrated with liquid iron is shown in Fig. 5e–l respectively. It should specially be pointed out that the applied optical basicity Λ of the slags in Suito's model,²⁵ Tsao's no. 2 model,⁵⁸ Sosinsky's model,⁷³ Young's model,²¹ and Taniguchi's model⁷⁹ was determined by taking and , which are similar as the recommended and by Young et al. ²¹

It can be observed in Fig. 5e–l that Ban-ya's model^20,74 and the KTH model^75–78 can be applied to precisely predict L _S of the slags, while other six models such as Suito's model,²⁵ Tsao's no.1 model,⁵⁸ Tsao's no. 2 model,⁵⁸ Sosinsky's model,⁷³ Young's model,²¹ and Taniguchi's model⁷⁹ cannot be applied to predict L _S of the slags because the investigated SiO₂ free slags is out of the application limitation of the aforementioned six models. It should be emphasised that Ban-ya's model^20,74 was developed based on the same data as in this study. This implies that Ban-ya's model^20,74 cannot be applied or evaluated in this study to avoid self-evidencing. The KTH model^75–78 can be applied to successfully predict L _S of the slags because the related coefficients including interaction coefficient of component i to j as listed in Table 2 are regressed from tremendous experiments in a large range of slag oxidisation ability although the deduced desulphurisation mechanism in the section on ‘Deduction of desulphurisation mechanism of slags in large variation range of slag oxidisation ability’ is not involved in the KTH model.^75–78 This finding indicates that the experimental results by Ban-ya et al. ²⁰ are accurate enough.

Influence of slag chemical composition on desulphurisation ability of slags

Influence of reaction abilities of components on desulphurisation ability of slags

It has been verified²⁷ that the calculated mass action concentrations N _i of CaO, FeO, Fe₂O₃ and Al₂O₃ in the slags are more reasonable than the mass percentage of the corresponding components for representing reaction abilities of the slags. The relationship of the calculated²⁷ N _i of CaO, FeO, Fe₂O₃ and Al₂O₃ against the measured²⁰ by Ban-ya et al. or the calculated for CaO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags is illustrated in Fig. 6a–d respectively. The newly formed structural unit has an eight time contribution to the defined^32–35 slag oxidation ability expressed as the calculated²⁷ of iron oxides as according to the IMCT. Therefore, the relationship between the calculated²⁷ and desulphurisation ability for the slags is also shown in Fig. 6e . It can be observed in Fig. 6 that the criterion for distinguishing reducing and oxidising zones corresponds to as 0.778, as 0.0626, as 1.00 × 10^− 4, as 1.50 × 10^− 3 and as 4.10 × 10^− 5 respectively. It should be pointed out that the criterion for distinguishing reducing and oxidising zones is equivalent to the calculated²⁷ of iron oxides as 0.0637 as shown in Figs. 1b or 2b .

Relationship of calculated²⁷ mass action concentration N _i of (a) CaO, (b) FeO, (c) Fe₂O₃, (d) Al₂O₃ and (e) FeO·Fe₂O₃ as structural units or ion couples against measured²⁰ sulphur distribution ratio by Ban-ya et al. or calculated sulphur distribution ratio by developed IMCT–L _S model for CaO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags equilibrated with liquid iron in temperature range from 1811 to 1927 K (1538 to 1654°C) respectively

The forward tick shaped or the asymmetric V type relationship between and or for the slags can be observed in Fig. 6a and d respectively. However, the backward tick shaped or the asymmetric V type relationship between and or for the slags can be observed in Fig. 6b and e respectively. In addition, a backward tick shaped or an asymmetric V type relationship between and for the slags can be observed in Fig. 6c with lower correlation degree.

Obviously, the effect of or on in Fig. 6a or d can be counteracted by that of or or as illustrated in Fig. 6b or c or e . Increasing or or can result in a decreasing tendency of or for the slags as shown in Fig. 7. The backward tick shaped relationship of against or or must be changed to the forward tick shaped relationship of against or for the slags in a large variation of slags oxidisation ability.

Relationship of calculated²⁷ mass action concentration or or against calculated²⁷ mass action concentration or for CaO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags equilibrated with liquid iron in temperature range from 1811 to 1927 K (1538 to 1654°C) respectively

To the result that the influence of or on can be counteracted by that of or or for the slags in reducing zone as shown in Fig. 6, it can reasonably be explained by the deduced desulphurisation mechanism or the developed IMCT–L _S model for the slags in the reducing zone in equation (6a) as that a slightly decreasing tendency of or from the maximum value to the criterion corresponds to a small increasing trend of or or as shown in the left region of Fig. 7, i.e. a small increasing trend of from 0.0185 to 0.0637 or mass percentage of Fe_tO from 1.88 to 6.75%, or oxygen potential of the slags from 8.18 × 10^− 8 to 2.27 × 10^− 6 Pa and the desulphurisation reaction of the slags in the reducing zone is mainly controlled by basic oxide CaO, rather than by ferrous oxide FeO, with CaS as the sole desulphurisation product. Thus, desulphurisation ability of the slags as shows a rapidly decreasing tendency with the decreasing or as shown in the right region of Fig. 6a or d , or with the increasing or or as illustrated in the left region of Fig. 6b or c or e .

To the finding that the effect of or on desulphurisation ability can be counteracted by that of or or for the slags in oxidising zone as illustrated in Fig. 6, it can also be explained by the deduced desulphurisation mechanism or the developed IMCT–L _S model for the slags in oxidising zone in equation (6b) as that a largely decreasing tendency of or from the criterion to the lowest value corresponds to a sharply increasing trend of or or as illustrated in the right region of Fig. 7, i.e. a largely increasing trend of from 0.0637 to 0.504 or mass percentage of Fe_tO from 6.75 to 55.50% or oxygen potential of the slags from 2.27 × 10^− 6 to 3.23 × 10^− 4 Pa and the desulphurisation reaction for the slags in oxidising zone is predominately decided by ferrous oxide FeO, rather than by basic oxide CaO, with FeS as the single desulphurisation product. Thus, desulphurisation ability of the slags as shows a slightly increasing trend with the increasing or or as illustrated in the right region of Fig. 6b or c or Fig. 6e , or with the decreasing or as shown in the left region of Fig. 6a or d .

Consequently, it can be derived that the effect of or on desulphurisation ability of the slags as can be counteracted by that of or or for the slags in a large variation of slag oxidisation ability. It can further be deduced that not only the reaction ability of iron oxides Fe_tO but also that of basic oxide CaO affects the desulphurisation ability of the slags.

Influence of slag basicity on desulphurisation ability of slags

The commonly applied complex basicity ^87–91 can be simplified as for the slags without SiO₂. Three-group values of optical basicity for FeO and Fe₂O₃ have been recommended as and , which are measured from Pauling electronegativity;⁷³ and , which are derived from average electron density;¹⁰² and and , which are mathematically regressed¹⁰³ from numerous experimental data. Higher mass percentage of Fe_tO in the slags can make different magnitudes of optical basicity with various values of optical basicity for FeO and Fe₂O₃. According to the evaluation results of the aforementioned three-group values of optical basicity for FeO and Fe₂O₃, the obtained and from mathematical regression¹⁰³ should be recommended to represent optical basicity values for FeO and Fe₂O₃, similar as the recommended and by Young et al. ²¹ The relationship between the simplified complex basicity or optical basicity of the slags and the measured²⁰ by Ban-ya et al. or the calculated for CaO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags is illustrated in Fig. 8a and b respectively. The asymmetric V type relationship between the simplified complex basicity or optical basicity and desulphurisation ability of the slag as can be observed with the simplified complex basicity as 1.56 or optical basicity as 0.80 corresponding to the lowest value of . Thus, the effect of the simplified complex basicity or optical basicity on desulphurisation ability of the slags as the backward tick shaped or the asymmetric V type curve is similar with that of slag oxidisation ability as shown in Fig. 2. Increasing the simplified complex basicity over a very small range from 1.31 to 1.56 or optical basicity over a very narrow range from 0.77 to 0.80 can result in a sharply decreasing tendency of desulphurisation ability of the slags with CaS as desulphurisation product. Further increasing the simplified complex basicity over a very large range from 1.56 to 28.26 or optical basicity over a wide range from 0.80 to 0.95 can lead to a slightly increasing trend of desulphurisation ability of the slags with FeS as desulphurisation product.

Relationship between a simplified complex basicity (%CaO)/[(%Al₂O₃)+(%P₂O₅)] or b optical basicity of slags by taking , and measured²⁰ sulphur distribution ratio by Ban-ya et al. or calculated sulphur distribution ratio by developed IMCT–L _S model for CaO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags equilibrated with liquid iron in temperature range from 1811 to 1927 K (1538 to 1654°C) respectively

In addition, the obtained criterion of optical basicity as 0.80 for distinguishing reducing and oxidising zones is the same as the applied one for describing relationship between and optical basicity by Young et al. ²¹ as listed in Table 2. It can further be deduced that the accuracy of experimental results from Ban-ya et al. ²⁰ is highly precise. Additionally, the proposed two-zone desulphurisation mechanism of the slags in the section on ‘Deduction of desulphurisation mechanism of slags in large variation range of slag oxidisation ability’ is reasonable.

Comprehensive effect of Fe_tO and CaO on desulphurisation ability of slags

It has been proposed by Yang et al. ^32,33,35 that the mass percentage ratios and the mass action concentration ratios of various iron oxides to basic oxide CaO expressed by (%FeO)/(%CaO) or (%Fe₂O₃)/(%CaO) or (%Fe_tO)/(%CaO) and or or can be applied to elucidate the comprehensive effect of various iron oxides and basic oxide CaO on dephosphorisation^27,32,33 and desulphurisation reaction³⁵ of slags. Meanwhile, the mass percentage ratio (%FeO)/(%Fe_tO) or (%Fe₂O₃)/(%Fe_tO) and the mass action concentration ratio or or can be applied to represent contribution of various iron oxides to slag oxidisation ability. The relationship between the mass percentage ratio (%FeO)/(%CaO) or (%Fe₂O₃)/(%CaO) or (%Fe_tO)/(%CaO) and the corresponding mass action concentration ratio or or for the slags is shown in Fig. 9a–c respectively. Similarly, the relationship between (%FeO)/(%Fe_tO) or (%Fe₂O₃)/(%Fe_tO) and or for the slags is also illustrated in Fig. 9d and e . Obviously, the mass percentage ratio (%FeO)/(%CaO) or (%Fe₂O₃)/(%CaO) or (%Fe_tO)/(%CaO) can correlate good linear relationship with the mass action concentration ratio or or for the slags as shown in Fig. 9a–c respectively. In addition, the mass percentage ratio (%Fe₂O₃)/(%Fe_tO) can also display a good linear corresponding relationship with the mass action concentration ratio for the slags as shown in Fig. 9e . However, no clear relationship between (%FeO)/(%Fe_tO) and for the slags can be observed in Fig. 9d . Thus, the aforementioned mass action concentration ratios of various iron oxides to basic oxide CaO can reliably be replaced by the corresponding mass percentage ratios.

Relationship between mass percentage ratio a (%FeO)/(%CaO) or b (%Fe₂O₃)/(%CaO) or c (%Fe_tO)/(%CaO) or d (%FeO)/(%Fe_tO) or e (%Fe₂O₃)/(%Fe_tO) and corresponding mass action concentration ratio or or or or for CaO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags equilibrated with liquid iron in temperature range from 1811 to 1927 K (1538 to 1654°C) respectively

The relationship between or or or and the measured²⁰ by Ban-ya et al. or the calculated for the slags is shown in Fig. 10a–d respectively. The relationship between or or and is also illustrated in Fig. 10e–g . The criterion for distinguishing the reducing and oxidising zones corresponds to as 0.08, as 1.59 × 10^− 4, as 5.27 × 10^− 5, as 0.082, as 0.98, as 1.60 × 10^− 3 and as 6.44 × 10^− 4 respectively.

Relationship between mass action concentration ratio a or b or or d or e or f or g and measured²⁰ sulphur distribution ratio by Ban-ya et al. or calculated sulphur distribution ratio by developed IMCT–L _S model for CaO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags equilibrated with liquid iron in temperature range from 1811 to 1927 K (1538 to 1654°C) respectively

The asymmetric V type relationship between or or or or and can be observed in Fig. 10a–d and g respectively. Therefore, the influence of or or or or on of the slags as the backward tick shaped or the asymmetric V type curve is similar with that of slag oxidisation ability as illustrated in Fig. 2.

However, a forward tick shaped or an asymmetric V type relationship of against for the slags can be observed in Fig. 10e with lower fitting degree. This result can be explained as that the magnitude of is controlled by that of as reported by Yang et al. elsewhere.²⁷ In addition, no corresponding relationship between and for the slags can be correlated from Fig. 10f . Thus, the influence of the contribution of various iron oxides to slag oxidisation ability on is less than the comprehensive effect of iron oxides Fe_tO and basic oxide CaO. The comprehensive effect of iron oxides Fe_tO and basic oxide CaO on desulphurisation ability of the slags should be considered. The mass action concentration ratio of various iron oxides to basic oxide CaO as or or or or mass percentage ratio as (%FeO)/(%CaO) or (%Fe₂O₃)/(%CaO) or (%Fe_tO)/(%CaO) can be recommended to describe the comprehensive effect of various iron oxides and basic oxide CaO on desulphurisation ability of the slags in a large variation range of slag oxidisation ability.

Conclusions

A thermodynamic model for predicting sulphur distribution ratio L _S between CaO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags and liquid iron, i.e. the IMCT–L _S model, has been developed by coupling with the deduced desulphurisation mechanism for the slags in a large variation range of slag oxidisation ability, which corresponds to mass percentage of Fe_tO changing from 1.88 to 55.50%, based on the IMCT. The developed IMCT–L _S model has been verified by comparing the measured by Ban-ya et al. with the calculated sulphur distribution ratio by the developed IMCT–L _S model and the predicted sulphur distribution ratio by the other four sulphur distribution ratio L _S models as well as the other eight sulphide capacity models from the literature. The main summary remarks can be obtained as follows:

The desulphurisation reaction is mainly controlled by (CaO)+[S] = (CaS)+[O] for the slags in the reducing zone corresponding to mass percentage of Fe_tO smaller than 6.75%. However, the desulphurisation reaction is completely predominated by (FeO)+[S] = (FeS)+[O] for the oxidising zone corresponding to mass percentage of Fe_tO>6.75%. The standard molar Gibbs free energy change of desulphurisation reaction (CaO)+[S] = (CaS)+[O] can be optimised as ; meanwhile, the reported standard molar Gibbs free energy change of desulphurisation reaction (FeO)+[S] = (FeS)+[O] as is accurate enough.

The measured sulphur distribution ratio between the slags and liquid iron in a large variation range of slag oxidisation ability can accurately be predicted by the developed IMCT–L _S model and the KTH model, rather than by other summarised models.

The calculated mass action concentrations N _i of structural units or ion couples, like activity of components in the slags relative to pure liquid matters as standard state, are recommended to represent reaction abilities of components involved in desulphurisation reaction. The influence of CaO on sulphur distribution ratio L _S of the slags can be counteracted by that of iron oxides Fe_tO.

The backward tick shaped or the asymmetric V type relationship between sulphur distribution ratio L _S and the simplified complex basicity or optical basicity can be established for the slags.

The asymmetric V type relationship between sulphur distribution ratio L _S and the mass action concentration ratio or or or , or mass percentage ratio (%FeO)/(%CaO) or (%Fe₂O₃)/(%CaO) or (%Fe_tO)/(%CaO) can be established for the slags. The aforementioned mass action concentration ratios or mass percentage ratios of various iron oxides to basic oxide CaO can be recommended to represent the comprehensive effect of various iron oxides and basic oxide CaO on desulphurisation ability of the slags.

Footnotes

Acknowledgement

This work is supported by the National Natural Science Foundation of China (NSFC) under grant no. 51174186.

References

Takenouchi

Suzuki

: ‘Effect of slag composition on the desulphurization and dephosphorization of molten steel’, Tetsu-to-Hagané, 1978, 64, (8), 1133–1142.

Suito

Ishizaka

Inoue

Takahashi

: ‘On the simultaneous dephosphorization and desulphurization of carbon-saturated iron by sodium carbonate and sodium sulphate flux’, Tetsu-to-Hagané, 1979, 65, (13), 1848–1857.

Moriya

Fujii

: ‘Dephosphorization and desulphurization of molten pig iron by Na₂CO₃’, Trans. ISIJ, 1981, 21, (10), 732–741.

Marukawa

Shirota

Anezaki

Hirahara

: ‘Refining process of molten iron by sodium carbonate’, Tetsu-to-Hagané, 1981, 67, (2), 323–332.

Yang

S. S.

Dong

Y. C.

Shen

: ‘Optimum oxygen potential and electrode potential of simultaneous dephosphorization and desulphurization in hot metal pretreatment’, J. Univ. Sci. Technol. Beijing, 1990, 12, (5), 421–430.

Yamamoto

Fujikake

Sakaguchi

: ‘Distribution ratios of phosphorous, sulphur and manganese between hot metal and sodium carbonate slag’, Tetsu-to-Hagané, 1982, 68, (14), 1896–1904.

Takeuchi

S. J.

Ozawa

Nozaki

Emi

Ohtani

: ‘Effect of oxygen potential on simultaneous dephosphorization and desulphurizaiton of hot metal by injecting CaO base flux’, Tetsu-to-Hagané, 1983, 69, (15), 1771–1778.

Nakajima

Mukai

Moriya

: ‘Comparison of refining characteristics in hot metal treatment by bottom injection with top blowing using soda ash’, Tetsu-to-Hagané, 1983, 69, (15), 1863–1870.

Yamamoto

Ishikawa

Fujikake

Sarro

Kajioka

: ‘Continuous refining of hot metal with soda ash in the trough-type refining furnace’, Tetsu-to-Hagané, 1983, 69, (15), 1871–1877.

10.

Inoue

Shigeno

Tokuda

Ohtani

: ‘On simultaneous dephosphorization and desulphurisation of pig iron with CaO–CaCl₂ fluxes’, Tetsu-to-Hagané, 1983, 69, (2), 210–219.

11.

Umezawa

Matsunaga

Arima

Tonomura

Furugaki

: ‘The influence of operating condition on dephosphorization and desulphurisation reactions of hot metal with lime-based flux’, Tetsu-to-Hagané, 1983, 69, (15), 1810–1817.

12.

Hara

Kurata

Ogino

: ‘Dephosphorization and desulphurisation of molten pig iron by injection of CaO-based fluxes’, Tetsu-to-Hagané, 1983, 69, (15), 1832–1836.

13.

Narita

Makino

Matsumoto

Hikosaka

Oonishi

Takagi

: ‘Dephosphorization and desulphurization of hot metal by lime based flux injection–oxygen top blowing method’, Tetsu-to-Hagané, 1983, 69, (15), 1825–1831.

14.

Shinme

Matsuo

Aoki

: ‘Dephosphorization and desulphurisation of hot metal by CaO-based flux containing MnO₂’, Tetsu-to-Hagané, 1983, 69, (15), 1787–1794.

15.

Zhong

L. C.

Xing

Y. L.

Liu

B. H.

: ‘Investigation on simultaneous dephosphorization and desulphurization of molten iron by injecting CaO-based fluxes’, Steelmaking, 1988, (1), 58–63.

16.

Mori

Wada

Pehlke

R. D.

: ‘Simultaneous desulphurization and dephosphorization reactions of molten iron by soda ash treatment’, Metall. Trans. B, 1985, 16B, (2), 303–312.

17.

Inoue

Suito

: ‘Dephosphorization and desulphurization equilibria between liquid iron containing Cr and BaO–Cr₂O₃–Fe_tO slags’, Tetsu-to-Hagané, 1988, 74, (10), 1939–1945.

18.

Nagabayashi

Hino

Ban-ya

: ‘Solubilities of CaO, MgO, SiO₂ and 2CaO·SiO₂, and ferric–ferrous equilibrium in Fe_tO–(CaO+MgO)–(SiO₂+P₂O₅) phosphate slags’, Tetsu-to-Hagané, 1988, 74, (8), 1577–1584.

19.

Iwai

Kunisada

: ‘Desulphurizaiton and simultaneous desulphurizaiton and dephosphorizaiton of molten iron by Na₂O–SiO₂ and Na₂O–CaO–SiO₂ fluxes’, ISIJ Int., 1989, 29, (2), 135–139.

20.

Ban-ya

Hino

Sato

Terayama

: ‘O, P and S distribution equilibria between liquid iron and CaO–Al₂O₃–Fe_tO slag saturated with CaO’, Tetsu-to-Hagané, 1991, 77, (3), 361–368.

21.

Young

R. W.

Duffy

J. A.

Hassall

G. J.

: ‘Use of optical basicity concept for determining phosphorus and sulphur slag-metal partitions’, Ironmaking Steelmaking, 1992, 19, (3), 201–219.

22.

Hino

Yamamoto

Ban-ya

: ‘Estimation of phosphorus and sulphur distribution equilibria in bath smelting process’, Tetsu-to-Hagané, 1993, 79, (9), 1039–1045.

23.

Hernandez

Romero

Chavez

Angeles

Morales

R. D.

: ‘Dephosphorization and desulphurization pretreatment of molten iron with CaO–SiO₂–CaF₂–FeO–Na₂O slags’, ISIJ Int., 1998, 38, (2), 126–131.

24.

Inoue

Suito

Ohtani

: ‘Hot metal pretreatment (III) laboratory scale experiment on dephosphorization and desulphurization’, Bull. Res. Inst. Miner. Dress. Metall., 1985, 40, (2), 199–220.

25.

Suito

Inoue

: ‘Flux characteristics and its refining limit during simultaneous dephosphorisation and desulphurisation of molten steel’, Tetsu-to-Hagané, 1983, 69, (2), A25–A28.

26.

Yang

X. M.

Guo

Z. C.

Wang

D. G.

Xie

Y. S.

: ‘Investigation on the correlation between sulfide capacity and phosphate capacity of metallurgical slags’, Iron Steel, 1996, 31, 25–31.

27.

Yang

X. M.

Zhang

Chai

G. M.

J. Y.

Zhang

: ‘Thermodynamic models for predicting dephosphorization ability and potential of CaO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags during secondary refining process of molten steel based on the ion and molecule coexistence theory’, Ironmaking Steelmaking 2015, DOI 10.1179/1743281215Y.0000000032.

28.

Yang

X. M.

Jiao

J. S.

Ding

R. C.

Shi

C. B.

Guo

H. J.

: ‘A thermodynamic model for calculating sulphur distribution ratio between CaO–SiO₂–MgO–Al₂O₃ ironmaking slags and carbon saturated hot metal based on the ion and molecule coexistence theory’, ISIJ Int., 2009, 49, (12), 1828–1837.

29.

Shi

C. B.

Yang

X. M.

Jiao

J. S.

Guo

H. J.

: ‘A sulphide capacity prediction model of CaO–SiO₂–MgO–Al₂O₃ ironmaking slags based on the ion and molecule coexistence theory’, ISIJ Int., 2010, 50, (10), 1362–1372.

30.

Yang

X. M.

Shi

C. B.

Zhang

Chai

G. M.

Wang

: ‘A thermodynamic model of sulphur distribution ratio between CaO–SiO₂–MgO–FeO–MnO–Al₂O₃ slags and molten steel during LF refining process based on the ion and molecule coexistence theory’, Metall. Mater. Trans. B, 2011, 42B, (6), 1150–1180.

31.

Yang

X. M.

Shi

C. B.

Zhang

Chai

G. M.

Zhang

: ‘A sulfide capacity prediction model of CaO–SiO₂–MgO–FeO–MnO–Al₂O₃ slags during LF refining process based on the ion and molecule coexistence theory’, Metall. Mater. Trans. B, 2012, 43B, (2), 241–266.

32.

Yang

X. M.

Duan

J. P.

Shi

C. B.

Zhang

Y. L

Wang

J. C.

: ‘A thermodynamic model of phosphorus distribution ratio between CaO–SiO₂–MgO–FeO–Fe₂O₃–MnO–Al₂O₃–P₂O₅ slags and molten steel during top–bottom combined blown converter steelmaking process based on the ion and molecule coexistence theory’, Metall. Mater. Trans. B, 2011, 42B, (4), 738–770.

33.

Yang

X. M.

Shi

C. B.

Zhang

Duan

J. P.

Zhang

: ‘A thermodynamic model of phosphate capacity for CaO–SiO₂–MgO–FeO–Fe₂O₃–MnO–Al₂O₃–P₂O₅ slags equilibrated with molten steel during a top–bottom combined blown converter steelmaking process based on the ion and molecule coexistence theory’, Metall. Mater. Trans. B, 2011, 42B, (5), 951–976.

34.

Yang

X. M.

Shi

C. B.

Zhang

: ‘A thermodynamic model for prediction of iron oxide activity in some FeO-containing slag systems’, Steel Res. Int., 2012, 83, (3), 244–258.

35.

Yang

X. M.

Zhang

J. L.

P. C.

J. Y.

Zhang

: ‘Representation of oxidation ability for metallurgical slags based on the ion and molecule coexistence theory’, Steel Res. Int., 2014, 85, (3), 347–375.

36.

Zhang

: ‘Computational thermodynamics of metallurgical melts and solutions’, 2007, Beijing, Metallurgical Industry Press.

37.

Fetters

K. L.

Chipman

: ‘Equilibria of liquid iron slags of the system CaO–MgO–FeO–SiO₂’, Trans. AIME, 1941, 145, 95–112.

38.

Darken

L. S.

Larsen

B. M.

: ‘Distribution of manganese and of sulphur between slag and metal in the open-hearth furnace’, Trans. AIME, 1942, 150, 87–112.

39.

Grant

N. J.

Chipman

: ‘Sulphur equilibria between liquid iron and slags’, Trans. AIME, 1946, 167, (1), 134–154.

40.

Hatch

G. G.

Chipman

: ‘Sulphur equilibria between iron blast furnace slags and metal’, Trans. AIME, 1949, 185, 274–284.

41.

Rocca

Grant

N. J.

Chipman

: ‘Distribution of sulphur between liquid iron and slags of low iron–oxide concentrations’, Trans. AIME, 1951, 191, 319–326.

42.

Grant

N. J.

Kalling

Chipman

: ‘Effects of manganese and its oxide on desulphurisation by blast–furnace type slags’, Trans. AIME, 1951, 191, 666–671.

43.

Richardson

F. D.

Fincham

C. J. B.

: ‘Sulphur in silicate and aluminate slags’, J. Iron Steel Inst., 1954, 178, (1), 4–15.

44.

Fincham

C. J. B.

Richardson

F. D.

: ‘The behaviour of sulphur in silicate and aluminate melts’, Proc. R. Soc. Lond. A, 1954, 223A, 40–62.

45.

Taylor

Stobo

J. J.

: ‘The sulphur distribution reaction between blast–furnace slag metal’, J. Iron Steel Inst., 1954, 180, (4), 360–367.

46.

Turkdogan

E. T.

Pearson

: ‘Further considerations of reaction equilibria in basic open hearth steelmaking with particular reference to sulphur’, ‘Report SM/C/41/55’, 1–6; 1955, London, UK, British Iron and Steel Research Association.

47.

St. Pierre

G. R.

Chipman

: ‘Sulphur equilibria between gases and slags containing FeO’, J. Met., 1956, 8, (10), 1474–1483.

48.

Carter

P. T.

Macfarlance

T. G.

: ‘Thermodynamics of slag systems’, J. Iron Steel Inst., 1957, 185, (1), 54–66.

49.

Kalyanram

M. R.

Macfarlane

T. G.

Bell

H. B.

: ‘The activity of calcium oxide in slags in the systems CaO–MgO–SiO₂, CaO–Al₂O₃–SiO₂, and CaO–MgO–Al₂O₃–SiO₂ at 1500°C’, J. Iron Steel Inst., 1960, 195, (1), 58–64.

50.

Abraham

K. P.

Davies

M. W.

Richardson

F. D.

: ‘Sulphide capacities of silicate melts’, J. Iron Steel Inst., 1960, 196, (3), 309–317.

51.

Cameron

Gibbons

T. B.

Taylor

: ‘Calcium sulphide solubilities and lime activities in the lime–alumina–silica system’, J. Iron Steel Inst., 1966, 204, (12), 1223–1228.

52.

Venkatradi

A. S.

Bell

H. B.

: ‘Sulphur partition between slag and metal in the iron blast furnace’, J. Iron Steel Inst., 1969, 207, (8), 1110–1113.

53.

Kor

G. J. W.

: ‘Effect of fluorspar and other fluxes on slag-metal equilibria involving phosphorus and sulphur’, Metall. Trans. B, 1977, 8B, (1), 107–113.

54.

Shim

Ban-ya

: ‘Equilibria of sulphur between liquid iron and FetO–SiO₂–CaO–MgO slags saturated with MgO’, Tetsu-to-Hagané, 1982, 68, (2), 251–260.

55.

Kärsrud

: ‘Sulphide capacities in TiO₂ containing slags’, Scan. J. Metall., 1984, 13B, (3), 173–175.

56.

Ozturk

Turkdogan

E. T.

: ‘Equilibrium S distribution between molten calcium aluminate and steel. Part 1: CaS–CaO–Al₂O₃ melts equilibrated with liquid Fe containing Al and S’, Met. Sci., 1984, 18, (6), 299–305.

57.

Kärsrud

: ‘Sulphide capacities of synthetic blast furnace slags at 1500°C’, Scan. J. Metall. B, 1984, 13B, (3), 144–150.

58.

Tsao

Katayama

H. G.

: ‘Sulphur distribution between liquid iron and CaO–MgO–Al₂O₃–SiO₂ slags used for ladle refining’, Trans. ISIJ, 1986, 26, (8), 717–723.

59.

Chan

A. H.

Fruehan

R. J.

: ‘The sulphur partition ratio and the sulfide capacity of Na₂O–SiO₂ slags at 1200°C’, Metall. Trans. B, 1986, 17B, (3), 491–496.

60.

Berryman

Sommerville

I. D.

Ishii

: ‘The influence of oxygen potential on the sulphide capacity of slags’, Iron Steelmaker (Trans. ISS), 1987, 14, (7), 49–54.

61.

Tsukihashi

Nakamura

Orimoto

Sano

: ‘Thermodynamics of phosphorus for the CaO–BaO–CaF₂–SiO₂ and CaO–Al₂O₃ Systems’, Tetsu-to-Hagané, 1990, 76, (10), 1664–1671.

62.

Nzotta

M. M.

Sichen

Seetharaman

: ‘A study of the sulfide capacities of iron–oxide containing slags’, Metall. Mater. Trans. B, 1999, 30B, (5), 909–920.

63.

Susaki

Maeda

Sano

: ‘Sulfide capacity of CaO–CaF₂–SiO₂ slags’, Metall. Trans. B, 1990, 21B, (1), 121–129.

64.

Rachev

I. P.

Tsukihashi

Sano

: ‘The thermodynamic behavior of sulphur in BaO–BaF₂ slags’, Metall. Trans. B, 1991, 22B, (3), 333–338.

65.

Simeonov

S. R.

Sridhar

Toguri

J. M.

: ‘Sulfide capacities of fayalite-base slags’, Metall. Mater. Trans. B, 1995, 26B, (2), 325–334.

66.

Kobayashi

Morita

Sano

: ‘Thermodynamics of sulphur in the BaO–MnO–SiO₂ flux system’, Metall. Mater. Trans. B, 1996, 27B, (4), 652–657.

67.

Taniguchi

Wang

L. J.

Sano

Seetharaman

: ‘Sulfide capacities of CaO–Al₂O₃–SiO₂ slags in the temperature range 1673 K to 1773 K (1400°C to 1500°C)’, Metall. Mater. Trans. B, 2012, 43B, (3), 477–484.

68.

Wei

S. K.

: ‘The effect of iron oxide content in molten slags upon desulphurisation’, Acta Metall. Sin., 1964, 7, (2), 157–164.

69.

Zhang

X. F.

Toguri

J. M.

: ‘The equilibrium distribution of sulphur between basic slags and steel’, Can. Metall. Q., 1987, 26, (2), 117–122.

70.

Yang

X. M.

Liu

T. Z.

Guo

Z. C.

X. P.

Wang

D. G.

: ‘Correlation between sulphide capacity index and slag basicity’, J. Iron Steel Res., 1995, 7, (6), 1–8.

71.

Wagner

: ‘The concept of the basicity of slags’, Metall. Trans. B, 1975, 6B, (3), 405–409.

72.

Yang

X. M.

Liu

T. Z.

Guo

Z. C.

X. P.

Wang

D. G.

: ‘Study on the correlation between phosphate capacity index and slag basicity’, Eng. Chem. Metall., 1995, 16, (3), 194–204.

73.

Sosinsky

D. J.

Sommerville

I. D.

: ‘The composition and temperature dependence of the sulfide capacity of metallurgical slags’, Metall. Trans. B, 1986, 17B, (2), 331–337.

74.

Nagabayashi

Hino

Ban-ya

: ‘Distribution of sulphur between liquid iron and Fe_tO–(CaO+MgO)–(SiO₂+P₂O₅) phosphate slags’, Tetsu-to-Hagané, 1990, 76, (2), 183–190.

75.

Sichen

Nilsson

Seetharaman

: ‘A mathematical model for estimation of sulphide capacities of multi-component slags’, Steel Res., 1995, 66, (11), 458–462.

76.

Nzotta

M. M.

Sichen

Seetharaman

: ‘Sulphide capacities in some multi component slag systems’, ISIJ Int., 1998, 38, (11), 1170–1179.

77.

Nzotta

M. M.

Sichen

Seetharaman

: ‘Sulphide capacities of FeO–SiO₂, CaO–FeO, and FeO–MnO slags’, ISIJ Int., 1999, 39, (7), 657–663.

78.

Nzotta

M. M.

Sichen

Seetharaman

: ‘A study of the sulfide capacities of iron-oxide containing slags’, Metall. Mater. Trans. B, 1999, 30B, (5), 909–920.

79.

Taniguchi

Sano

Seetharaman

: ‘Sulphide capacities of CaO–Al₂O₃–SiO₂–MgO–MnO Slags in the temperature range 1673–1773K’, ISIJ Int., 2009, 49, (2), 156–163.

80.

Kang

Y. B.

Pelton

A. D.

: ‘Thermodynamic model and database for sulfides dissolved in molten oxide slags’, Metall. Mater. Trans. B, 2009, 40B, (6), 979–994.

81.

Pelton

A. D.

Eriksson

Serrano

A. R.

: ‘Calculation of sulfide capacities of multicomponent slags’, Metall. Trans. B, 1993, 24B, (5), 817–825.

82.

Reddy

R. G.

Blander

: ‘Modeling of sulfide capacities of silicate melts’, Metall. Trans. B, 1987, 18B, (3), 591–596.

83.

Reddy

R. G.

Blander

: ‘Sulfide capacities of MnO–SiO₂ slags’, Metall. Trans. B, 1989, 20B, (2), 137–140.

84.

Reddy

R. G.

Zhao

: ‘Sulfide capacities of Na₂O–SiO₂ melts’, Metall. Mater. Trans. B, 1995, 26B, (5), 925–928.

85.

Moretti

Ottonello

: ‘A polymeric approach to the sulfide capacity of silicate slags and melts’, Metall. Mater. Trans. B, 2003, 34B, (4), 399–410.

86.

Kim

Y. J.

Woo

D. H.

Gaye

Lee

H. G.

Kang

Y. B.

: ‘Thermodynamics of MnO–SiO₂–Al₂O₃–MnS liquid oxysulfide, experimental and thermodynamic modeling’, Metall. Mater. Trans. B, 2011, 42B, (3), 535–545.

87.

Chen

J. X.

: ‘Handbook of common figures, tables and data for steelmaking’, 2nd edn; 2010, Beijing, Metallurgical Industry Press.

88.

Suito

Inoue

: ‘Thermodynamic considerations on manganese equilibria between liquid iron and Fe_tO–MnO–MO_x (MO_x = PO_2.5, SiO₂, AlO_1.5, MgO, CaO) slags’, Trans. ISIJ, 1984, 24, (4), 301–307.

89.

The Japan Society for the Promotion of Science : ‘The 19th Committee on Steelmaking. Steelmaking data sourcebook’, 1988, New York, Gordon and Breach Science Publishers.

90.

Sigworth

G. K.

Elliott

J. F.

: ‘The thermodynamics of liquid dilute iron alloys’, Met. Sci., 1974, 8, (9), 298–310.

91.

Zhang

J. Y.

: ‘Metallurgical physicochemistry’, 2004, Beijing, Metallurgical Industry Press.

92.

Tsujino

Nakashima

Hirai

Yamada

: ‘Behavior of desulphurization in ladle steel refining with powder injection at reduced pressures’, ISIJ Int., 1989, 29, (1), 92–95.

93.

Ohya

: ‘Ferrous metallurgy and thermodynamics’, 1971, Tokyo, Nikkan Kogyo Shimbun-sha.

94.

Inoue

Suito

: ‘Sulphur distribution between carbon-saturated iron melt and Na₂O–SiO₂ slags’, Tetsu-to-Hagané, 1982, 68, (3), 417–425.

95.

Han

Q. Y.

Zhang

X. D.

Chen

Wang

P. F.

: ‘The calcium–phosphorus and the simultaneous calcium–oxygen and calcium–sulphur equilibria in liquid iron’, Metall. Trans. B, 1987, 19B, (8), 617–622.

96.

Prešern

Koroušić

Hastie

J. W.

: ‘Thermodynamic conditions for inclusions modification in calcium treated steel’, Steel Res. Int., 1991, 62, (7), 289–295.

97.

Ward

R. G.

: ‘The physical chemistry of iron and steelmaking’, 1962, London, Edward Arnold Ltd.

98.

Turkdogan

E. T.

: ‘Assessment of P₂O₅ activity coefficients in molten slags’, ISIJ Int., 2000, 40, (10), 964–970.

99.

Lee

Morita

: ‘Dynamic interfacial phenomena between gas, liquid iron and solid CaO during desulphurization’, ISIJ Int., 2004, 44, (2), 235–242.

100.

Shankar

Gornerup

Lahiri

A. K.

Seetharaman

: ‘Sulfide capacity of high alumina blast furnace slags’, Metall. Mater. Trans. B, 2006, 37B, (6), 941–947.

101.

Andersson

M. A. T.

Jönsson

P. G.

Nzotta

M. M.

: ‘Application of the sulphide capacity concept on high-basicity ladle slags used in bearing–steel production’, ISIJ Int., 1999, 39, (11), 1140–1149.

102.

Nakamura

Ueda

Toguri

J. M.

: ‘A critical review of optical basicity on metallurgical application’, Proc. 3rd Int. Conf. on ‘Metallurgical slags and fluxes, London, UK, 146–149; 1988, The Institute of Metals.

103.

Mills

K. C.

Sridhar

: ‘Viscosities of ironmaking and steelmaking slags’, Ironmaking Steelmaking, 1999, 26, (4), 262–268.

Prediction model of sulphur distribution ratio between CaO–FeO–Fe 2 O 3 –Al 2 O 3 –P 2 O 5 slags and liquid iron over large variation range of oxygen potential during secondary refining process of molten steel based on ion and molecule coexistence theory

Abstract

Introduction

Desulphurisation mechanism of slags in large variation range of slag oxidisation ability after Ban-ya et al.

Relationship between reaction abilities of components and various slag oxidation abilities

Influence of various slag oxidation abilities on measured desulphurisation ability by Ban-ya et al.

Deduction of desulphurisation mechanism of slags in large variation range of slag oxidisation ability

Thermodynamic model for calculating sulphur distribution ratio L S between CaO–FeO–Fe2O3–Al2O3–P2O5 slags and liquid iron based on IMCT

Establishment of IMCT–L S model for slags based on IMCT

Determination of standard molar Gibbs free energy change of desulphurisation reaction for forming CaS or FeS in slags

Optimising of desulphurisation reaction for forming CaS in slags

Summary of reported standard molar Gibbs free energy change of desulphurisation reactions for forming CaS or FeS in slags from various references

Selecting of desulphurisation reaction for forming FeS in slags

Verification of developed IMCT–L S model for slags

Summary of four sulphur distribution ratio L S prediction models and eight sulphide capacity prediction models from related literature

Comparison between measured and calculated by IMCT–L S model for slags

Comparison between measured and calculated by other L S or models

Comparison between measured and calculated by other L S models

Comparison between measured and calculated by other models

Influence of slag chemical composition on desulphurisation ability of slags

Influence of reaction abilities of components on desulphurisation ability of slags

Influence of slag basicity on desulphurisation ability of slags

Comprehensive effect of Fe t O and CaO on desulphurisation ability of slags

Conclusions

Footnotes

Acknowledgement

References

Thermodynamic model for calculating sulphur distribution ratio L _S between CaO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags and liquid iron based on IMCT

Establishment of IMCT–L _S model for slags based on IMCT

Verification of developed IMCT–L _S model for slags

Summary of four sulphur distribution ratio L _S prediction models and eight sulphide capacity prediction models from related literature

Comparison between measured and calculated by IMCT–L _S model for slags

Comparison between measured and calculated by other L _S or models

Comparison between measured and calculated by other L _S models

Comprehensive effect of Fe_tO and CaO on desulphurisation ability of slags