Effect of Ratio of Scrap to Iron Source on Slag–Metal Reaction at the Bottom of Blast Furnace and Packed Bed Type Partial Smelting Reduction Furnace

Abstract

With the depletion of high-grade iron ore and increase in amount of steel scrap, a new ironmaking process utilizing both low-grade iron ore and/or steel scrap is required. The blast furnace and packed bed type partial smelting reduction process (PSR) are the most prospective reactors. When steel scrap is used as an iron source, the hot metal composition should be precisely controlled, because tramp elements such as Cu, Sn, Ni, and Cr are dissolved in hot metal. An analysis model was developed to simulate the equilibrium of the slag–metal reaction at the bottom of such reactors. The effect of scrap ratio (iron mass ratio of scrap to scrap and sinter) on hot metal and molten slag composition was thermodynamically analyzed and the optimal composition of hot metal under controlled temperature and P_O2 was investigated. Si and Mn were found to be significantly oxidized relative to the equilibrium state, and the S content was equal to that at equilibrium under a blast furnace condition. As the scrap ratio increased, the Si, Mn, and P contents decreased. The Si content decreased to 0.1 mass% at T = 1773 K and P_O2 > 10⁻¹³ atm or at P_O2 = 3.03×10⁻¹⁵ atm and T < 1690 K, whereas the phosphorus content decreased at 1773 K and P_O2 > 10⁻¹² atm when the scrap ratio was 0.5. PSR is expected to produce hot metal with a low impurity content by controlling the oxygen partial pressure at the bottom of the furnace.

1. Introduction

Since the steel industry accounts for 14% (in 2018) of CO₂ emission in Japan,¹⁾ the reduction of CO₂ emission is considered as one of the most important issues to achieve the long-term goal of the Paris Agreement. Furthermore, the increased demand for steel products in developing countries has resulted in high iron ore demand, which has led to the depletion of high-grade iron ore.^2,3) However, in developed countries, steel products produced from natural resources have accumulated. These products can be considered as potential valuable resources or urban mines when they are recovered as steel scraps at the end of their service life. The accumulated amount of steel stock in Japan was 1.39 billion tonnes;⁴⁾ and 2% of the steel stock, 26 million tonnes of steel scraps, were supplied to produce crude steel in 2018.⁵⁾ The amount of steel scrap is forecasted to increase with increase in steel stock. In the report of the Japan Iron and Steel Federation on their long-term vision for climate change mitigation, they predicted the global steel stock accumulation and steel production over the years.⁶⁾ According to the report, crude steel production from steel scraps will exceed that from iron ore by 2050. Accordingly, the development of a new ironmaking process that can utilize both iron ore and steel scraps is expected. By utilizing steel scraps, which can be considered as iron resources, it is expected that the CO₂ emissions will decrease. Steel scraps are melted in a basic oxygen furnace (BOF) or in an electric arc furnace (EAF) in the current steelmaking process. At present, the latter accounts for 60% of scrap usage in Japan.⁵⁾ There is a limit to the use of steel scraps in BOF owing to the lack of a heat source. In the EAF process, although it is energy efficient, the primary energy may be lost in the power generation process. The concept of sustainable iron and steel making systems based on material recycling technology (SMART) has been proposed with an aim to achieve carbon neutrality by recycling steel and carbon.^7,8,9) In SMART, smelting of steel scraps and reduction of iron ore are performed simultaneously in ironmaking processes, such as blast furnaces process; moreover, the exhaust CO₂ is reduced to CO and reused as a reducing agent in the process. The advantages of SMART compared to the current scrap melting processes are that the amount of heat source can be arbitrarily controlled and the primary energy can be directly used. Packed bed type partial smelting reduction process (PSR) is considered a new ironmaking process in SMART.⁹⁾ Figure 1 shows a schematic illustration of the PSR furnace, where reduction of iron ore and smelting of steel scraps are performed using a BOF-type low-height shaft furnace equipped with tuyeres.^9,10) However, steel scraps contain tramp elements that are difficult to remove once dissolved in molten iron. Therefore, removal methods^11,12) and the effects of tramp elements have been intensely investigated.¹³⁾ Cu, Sn, Ni, and Cr are inevitably dissolved in molten steel when steel scraps are used as an iron source.¹³⁾ To prevent the harmful effects of such tramp elements on steelmaking processes and steel properties, the activities of alloying elements in steel should be controlled by studying these effects.^14,15,16) Therefore, information on the composition of hot metals is critical. The hot metal composition has been investigated by many researchers because it is related to the thermal conditions at the bottom of the blast furnace.^{17,18,19,20,21,22,23,24,25,26)} The transport mechanism of Si to the hot metal is summarized in Fig. 2. SiO₂ in coke is reduced and SiO(g) forms under a reducing atmosphere at a high temperature around the raceway where gasification of coke occurs.^{17,18,19,20,21,22,23)} SiO(g) is reduced by carbon and Si dissolves in hot metal in the dripping zone.^{20,21,22,23,24,26)} Hot metal droplets fall in molten slag and oxidation of Si and reduction of FeO and MnO in the slag occur.^25,27) According to the investigation of the raceway in an operating blast furnace, the partial pressure of oxygen behind the raceway is in the range of 10⁻¹⁴ to 10⁻¹⁰ atm, and the Si reduction or oxidation in the hot metal occurs depending on the slag FeO content at the bottom of the furnace.²⁷⁾ It is suggested that the hot metal composition changes to the direction of the equilibrium of the slag-metal reactions. The hot metal composition in the PSR is expected to change in a similar manner because the main raw materials are the same as those in the blast furnace. As PSR is a batch process and the reducing gas and oxygen gas are injected from primary and secondary tuyeres, respectively,^7,8,9) the operation of the PSR is considered more flexible than that of the blast furnace. Accordingly, the temperature and partial pressure of oxygen at the bottom of the PSR furnace, which determines the hot metal composition, can be controlled over a wide range. Therefore, it is necessary to determine the equilibrium between the slag and hot metal at such wide ranges. In this study, an analysis model was developed to simulate the equilibrium of the slag–metal reaction. The effects of the scrap ratio on the composition of the hot metal and slag were thermodynamically analyzed and the optimal composition of the hot metal under controlled temperature and partial pressure of oxygen at the bottom of the blast furnace or PSR furnace were investigated.

Fig. 1.

Schematic illustration of a PSR furnace (packed bed type partial smelting reduction process). (Online version in color.)

Fig. 2.

Schematic illustration of transport mechanisms of Si, Mn and S into hot metal at the bottom of the blast furnace. (Online version in color.)

2. Analysis Model Description

The slag–metal reactions at the bottom of the blast furnace are redox reactions between molten oxides of the CaO–SiO₂–Al₂O₃–MgO–FeO–MnO–S–P₂O₅ system and the liquid metal of the Fe–C–O–Si–Mn–S–P(–Cu–Sn–Ni–Cr) system. In addition to Cu, Ni, and Sn, which are nobler than Fe, it is considered that Cr is not oxidized in the present analysis because Cr content of hot metal is significantly low as 0.01 to 0.1 mass%. When considering the oxidation of C in molten iron, there are 16 (or 20) chemical species: CaO, SiO₂, Al₂O₃, MgO, MnO, FeO, S, P₂O₅, Fe, C, O, Si, Mn, S, P (, Cu, Sn, Ni, Cr), and CO. When considering the oxidation equilibrium of Fe, C, Si, Mn, S, and P, the number of independent components is 16 – 6 = 10 (or 20 – 6 = 14). Because there are three phases in the system: slag, hot metal, and gas phase, the degree of freedom in the system is calculated to be f = c – p + 2 = 10 – 3 + 2 = 9 (or 14 – 3 + 2 = 13). Therefore, nine (or 13) more relations are needed to determine the equilibrium. In this study, slag and hot metal masses were added to the variables, and the mass conservation of the elements Ca, Si, Al, Mg, Mn, Fe, S, and P (Cu, Sn, Ni, Cr) was considered. The independent variables are reduced to four, and the degree of freedom becomes f = c – p + 2 = 4 – 3 + 2 = 3. Therefore, the equilibrium can be calculated when the temperature and partial pressures of oxygen and CO(g) are fixed. In the present thermodynamic model, the oxidation of Fe, C, Si, Mn, S, and P, and mass conservation of Ca, Si, Al, Mg, Mn, Fe, S, and P (Cu, Sn, Ni, and Cr) was calculated simultaneously by considering the mass and composition of the slag and the hot metal as variables. When C(s) exists under blast furnace and PSR conditions, the equilibrium carbon content is determined from the solubility. In this case, CO is removed from the chemical components, and C(s) is considered as the phase instead of the gas phase. The degree of freedom was calculated to be 2. Therefore, the equilibrium can be determined when the temperature and partial pressure of oxygen are fixed.

2.1. Redox Equilibria of C, Si, Mn, S, P, and Fe between Slag and Hot Metal

The redox reactions of C, Si, Mn, S, P, and Fe are expressed as follows:   

$$\underset{\_}{\mathrm{C}}+\underset{\_}{\mathrm{O}}=\mathrm{C}\mathrm{O}\left(\mathrm{g}\right)$$(1)

  

$$\underset{\_}{\mathrm{S}\mathrm{i}}+2\underset{\_}{\mathrm{O}}=\mathrm{S}\mathrm{i}{\mathrm{O}}_2\left(in\mathrm{\hspace{0.17em} } slag\right)$$(2)

  

$$\underset{\_}{\mathrm{M}\mathrm{n}}+\underset{\_}{\mathrm{O}}=\mathrm{M}\mathrm{n}\mathrm{O}\left(in\mathrm{\hspace{0.17em} } slag\right)$$(3)

  

$$\underset{\_}{\mathrm{S}}+{\mathrm{O}}^{2-}\left(in\mathrm{\hspace{0.17em} }slag\right)=\underset{\_}{\mathrm{O}}+{\mathrm{S}}^{2-}\left(in\mathrm{\hspace{0.17em} } slag\right)$$(4)

  

$$\underset{\_}{\mathrm{P}}+5/2\underset{\_}{\mathrm{O}}+3/2{\mathrm{O}}^{2-}\left(in\mathrm{\hspace{0.17em} } slag\right)=\mathrm{P}{\mathrm{O}}_4^{3-}\left(in\mathrm{\hspace{0.17em} } slag\right)$$(5)

  

$$\mathrm{F}\mathrm{e}\left(l\right)+\underset{\_}{\mathrm{O}}=\mathrm{F}\mathrm{e}\mathrm{O}\left(in\mathrm{\hspace{0.17em} } slag\right)$$(6)

The equilibrium constants of reactions (1)–(3) and (6) are as follows:^28,29)   

$$log{K}_{\mathrm{C}\mathrm{O}}=log\frac{P_{\mathrm{C}\mathrm{O}}}{a_{\mathrm{C}}\cdot a_{\mathrm{O}}}=\frac{1\mathrm{\hspace{0.17em} }168}{T}+2.070$$(7) ²⁸⁾

  

$$log{K}_{\mathrm{S}\mathrm{i}}=log\frac{a_{\mathrm{S}\mathrm{i}{\mathrm{O}}_2}}{a_{\mathrm{S}\mathrm{i}}\cdot a_{\mathrm{O}}{}^2}=\frac{30\mathrm{\hspace{0.17em} }110}{T}-11.40$$(8) ²⁹⁾

  

$$log{K}_{\mathrm{M}\mathrm{n}}=log\frac{a_{\mathrm{M}\mathrm{n}\mathrm{O}}}{a_{\mathrm{M}\mathrm{n}}\cdot a_{\mathrm{O}}}=\frac{12\mathrm{\hspace{0.17em} }760}{T}-5.62$$(9) ²⁹⁾

  

$$log{K}_{\mathrm{F}\mathrm{e}}=log\frac{a_{\mathrm{F}\mathrm{e}\mathrm{O}}}{a_{\mathrm{F}\mathrm{e}}\cdot a_{\mathrm{O}}}=\frac{6\mathrm{\hspace{0.17em} }150}{T}-2.604$$(10) ²⁹⁾

where K_i, a_i, P_CO are the equilibrium constants of the redox reaction of i, activities of i, and partial pressure of CO(g), respectively. The activities of C, Si, Mn, S, and P are relative to a dilute solution, and that of Fe is relative to an ideal solution. The partition ratios of S and P were calculated using sulfide and phosphate capacities, which are expressed as Eqs. (11) and (12), respectively   

$$C_{{\mathrm{s}}^{2-}}={\left(\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\text{\%}\mathrm{S}\right)}_{in\mathrm{\hspace{0.17em} } slag}{\left(\frac{P_{{\mathrm{O}}_2}}{P_{{\mathrm{S}}_2}}\right)}^{1/2}$$(11)

  

$$C_{\mathrm{P}{\mathrm{O}}_4{}^{3-}}=\frac{{\left(\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\text{\%}\mathrm{P}{\mathrm{O}}_4{}^{3-}\right)}_{in\mathrm{\hspace{0.17em} } slag}}{P_{{\mathrm{P}}_2}{}^{1/2}\cdot P_{{\mathrm{O}}_2}{}^{5/4}}$$(12)

where P_j denotes the partial pressures of gas j (j: O₂, S₂, or P₂), which are calculated using the equilibrium constants of reactions (13)–(15). The equilibrium constants for reactions (13)–(15) are given by Eqs. (16), (17), (18).²⁹⁾   

$$\frac{1}{2}{\mathrm{O}}_2\left(\text{g}\right)=\underset{\_}{\mathrm{O}}$$(13)

  

$$\frac{1}{2}{\mathrm{S}}_2\left(\text{g}\right)=\underset{\_}{\mathrm{S}}$$(14)

  

$$\frac{1}{2}{\mathrm{P}}_2\left(\text{g}\right)=\underset{\_}{\mathrm{P}}$$(15)

  

$$log{K}_{{\mathrm{O}}_2}=log\frac{a_{\mathrm{O}}}{P_{{\mathrm{O}}_2}{}^{1/2}}=\frac{6\mathrm{\hspace{0.17em} }116}{T}+0.18$$(16) ²⁹⁾

  

$$log{K}_{{\mathrm{S}}_2}=log\frac{a_{\mathrm{S}}}{P_{{\mathrm{S}}_2}{}^{1/2}}=\frac{6\mathrm{\hspace{0.17em} }535}{T}-0.964$$(17) ²⁹⁾

  

$$log{K}_{{\mathrm{P}}_2}=log\frac{a_{\mathrm{P}}}{P_{{\mathrm{P}}_2}{}^{1/2}}=\frac{8\mathrm{\hspace{0.17em} }236}{T}-0.28$$(18) ²⁹⁾

When the hot metal is saturated with C(s), the dissolution of C in liquid iron is considered as reaction (19).   

$$\mathrm{C}\left(\mathrm{s}\right)=\underset{\_}{\mathrm{C}}$$(19)

The equilibrium constant reported by Rist and Chipman³⁰⁾ was used for the reaction (19).   

$$log{K}_{\mathrm{C}}=log\frac{a_{\text{C}}}{a_{\mathrm{C}\left(\mathrm{s}\right)}}=-\frac{1\mathrm{\hspace{0.17em} }180}{T}+2.20$$(20) ³⁰⁾

The hot metal is assumed to be saturated with carbon when the carbon content calculated using Eq. (20) is less than that calculated using Eq. (7). The activities of i (i: C, O, Si, Mn, S, and P) and Fe are expressed by Eqs. (21) and (22), respectively, where f_i and γ_Fe are the Henrian activity coefficients of i relative to the dilute solution (mass%) and activity coefficient of Fe relative to pure liquid, respectively.   

$$a_i=f_i\times {\left[\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\text{\%}i\right]}_{in\mathrm{\hspace{0.17em} } Fe}$$(21)

  

$$a_{\mathrm{F}\mathrm{e}}={\gamma }_{\mathrm{F}\mathrm{e}}\times x_{\mathrm{F}\mathrm{e}}$$(22)

The activity coefficient of i, except for carbon, is expressed by Eq. (23), where e_i^j is the interaction parameter between i and j.   

$$log{f}_i={\sum }_{j\ne \mathrm{F}\mathrm{e}}{e}_i^j{\left[\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\text{\%}j\right]}_{in\mathrm{\hspace{0.17em} } \mathrm{F}\mathrm{e}}$$(23)

Because the carbon content of the hot metal is much higher than that of the dilute solution, the activity coefficient in carbon-saturated iron, f_C, was calculated using Eq. (24).   

$$log{f}_{\mathrm{C}}=log{f}_{\mathrm{C}\mathrm{\hspace{0.17em} } in\mathrm{\hspace{0.17em} } \mathrm{F}\mathrm{e}-\mathrm{C}satd.}+{\sum }_{j\ne \mathrm{F}\mathrm{e}}{e}_{\mathrm{C}}^j{\left[\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\text{\%}j\right]}_{in\mathrm{\hspace{0.17em} } \mathrm{F}\mathrm{e}}$$(24)

From the aforementioned equations, the equilibrium conditions of C, Si, Mn, S, P, and Fe are obtained as equations in terms of concentrations, which are summarized in Table 1.

Table 1. Equations in terms of concentrations for the calculation of redox equilibrium between slag and hot metal.

${\displaystyle \underset{\_}{\mathrm{C}}+\underset{\_}{\mathrm{O}}=\mathrm{C}\mathrm{O}\left(\mathrm{g}\right)}$	${\displaystyle log{\left[\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%\mathrm{C}\right]}_{in\mathrm{\hspace{0.17em} } \mathrm{F}\mathrm{e}}+log{f}_{\mathrm{C}\mathrm{\hspace{0.17em} } in\mathrm{\hspace{0.17em} } \mathrm{F}\mathrm{e}-\mathrm{C}satd.}+{\displaystyle \sum }_{j\ne \mathrm{F}\mathrm{e}}{e}_{\mathrm{C}}^j{\left[\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%j\right]}_{in\mathrm{\hspace{0.17em} } \mathrm{F}\mathrm{e}}+1/2log{P}_{{\mathrm{O}}_2}+log{K}_{{\mathrm{O}}_2}-log{P}_{\mathrm{C}\mathrm{O}}+log{K}_{\mathrm{C}\mathrm{O}}=0}$
${\displaystyle \mathrm{C}\left(\mathrm{s}\right)=\underset{\_}{\mathrm{C}}}$ (carbon saturation)	${\displaystyle log{\left[\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%\mathrm{C}\right]}_{in\mathrm{\hspace{0.17em} } \mathrm{F}\mathrm{e}}+log{f}_{\mathrm{C}\mathrm{\hspace{0.17em} } in\mathrm{\hspace{0.17em} } \mathrm{F}\mathrm{e}-\mathrm{C}satd.}+{\displaystyle \sum }_{j\ne \mathrm{F}\mathrm{e}}{e}_{\mathrm{C}}^j{\left[\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%j\right]}_{in\mathrm{\hspace{0.17em} } \mathrm{F}\mathrm{e}}-log{K}_{\mathrm{C}}=0}$
${\displaystyle \frac{1}{2}{\mathrm{O}}_2\left(\text{g}\right)=\underset{\_}{\mathrm{O}}}$	${\displaystyle log{\left[\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%\mathrm{O}\right]}_{in\mathrm{\hspace{0.17em} } \mathrm{F}\mathrm{e}}+{\displaystyle \sum }_{j\ne \mathrm{F}\mathrm{e}}{e}_{\mathrm{O}}^j{\left[\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%j\right]}_{in\mathrm{\hspace{0.17em} } \mathrm{F}\mathrm{e}}-1/2log{P}_{{\mathrm{O}}_2}-log{K}_{{\mathrm{O}}_2}=0}$
${\displaystyle \underset{\_}{\mathrm{S}\mathrm{i}}+2\underset{\_}{\mathrm{O}}=\mathrm{S}\mathrm{i}{\mathrm{O}}_2\left(inslag\right)}$	${\displaystyle log{\left[\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%\mathrm{S}\mathrm{i}\right]}_{in\mathrm{\hspace{0.17em} } \mathrm{F}\mathrm{e}}+{\displaystyle \sum }_{j\ne \mathrm{F}\mathrm{e}}{e}_{\mathrm{S}\mathrm{i}}^j{\left[\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%j\right]}_{in\mathrm{\hspace{0.17em} } \mathrm{F}\mathrm{e}}+log{P}_{{\mathrm{O}}_2}+2log{K}_{{\mathrm{O}}_2}-log{a}_{\mathrm{S}\mathrm{i}{\mathrm{O}}_2}+log{K}_{\mathrm{S}\mathrm{i}}=0}$
${\displaystyle \underset{\_}{\mathrm{M}\mathrm{n}}+\underset{\_}{\mathrm{O}}=\mathrm{M}\mathrm{n}\mathrm{O}\left(in\mathrm{\hspace{0.17em} } slag\right)}$	${\displaystyle log{\left[\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%\mathrm{M}\mathrm{n}\right]}_{in\mathrm{\hspace{0.17em} } \mathrm{F}\mathrm{e}}+{\displaystyle \sum }_{j\ne \mathrm{F}\mathrm{e}}{e}_{\mathrm{M}\mathrm{n}}^j{\left[\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%j\right]}_{in\mathrm{\hspace{0.17em} } \mathrm{F}\mathrm{e}}+1/2log{P}_{{\mathrm{O}}_2}+log{K}_{{\mathrm{O}}_2}-log{a}_{\mathrm{M}\mathrm{n}\mathrm{O}}+log{K}_{\mathrm{M}\mathrm{n}}=0}$
${\displaystyle \underset{\_}{\mathrm{S}}+{\mathrm{O}}^{2-}\left(in\mathrm{\hspace{0.17em} }slag\right)=\underset{\_}{\mathrm{O}}+{\mathrm{S}}^{2-}\left(in\mathrm{\hspace{0.17em} } slag\right)}$	${\displaystyle log{\left[\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%\mathrm{S}\right]}_{in\mathrm{\hspace{0.17em} } \mathrm{F}\mathrm{e}}+{\displaystyle \sum }_{j\ne \mathrm{F}\mathrm{e}}{e}_{\mathrm{S}}^j{\left[\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%j\right]}_{in\mathrm{\hspace{0.17em} } \mathrm{F}\mathrm{e}}-1/2log{P}_{{\mathrm{O}}_2}-log{\left(\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\text{\%}{\mathrm{S}}^{2-}\right)}_{in\mathrm{\hspace{0.17em} } slag}+log{C}_{{\mathrm{s}}^{2-}}-log{K}_{{\mathrm{S}}_2}=0}$
${\displaystyle \underset{\_}{\mathrm{P}}+5/2\underset{\_}{\mathrm{O}}+3/2{\mathrm{O}}^{2-}\left(in\mathrm{\hspace{0.17em} } slag\right)=\mathrm{P}{\mathrm{O}}_4^{3-}\left(in\mathrm{\hspace{0.17em} } slag\right)}$	${\displaystyle log{\left[\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%\mathrm{P}\right]}_{in\mathrm{\hspace{0.17em} } \mathrm{F}\mathrm{e}}+{\displaystyle \sum }_{j\ne \mathrm{F}\mathrm{e}}{e}_{\mathrm{P}}^j{\left[\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%j\right]}_{in\mathrm{\hspace{0.17em} } \mathrm{F}\mathrm{e}}+5/4log{P}_{{\mathrm{O}}_2}-log{\left(\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\text{\%}\mathrm{P}{\mathrm{O}}_4{}^{3-}\right)}_{in\mathrm{\hspace{0.17em} } slag}+log{C}_{\mathrm{P}{\mathrm{O}}_4{}^{3-}}-log{K}_{{\mathrm{P}}_2}=0}$
${\displaystyle \mathrm{F}\mathrm{e}\left(l\right)+\underset{\_}{\mathrm{O}}=\mathrm{F}\mathrm{e}\mathrm{O}\left(in\mathrm{\hspace{0.17em} } slag\right)}$	${\displaystyle log{x}_{\mathrm{F}\mathrm{e}}+log{\gamma }_{\mathrm{F}\mathrm{e}}+1/2log{P}_{{\mathrm{O}}_2}+log{K}_{{\mathrm{O}}_2}-log{a}_{\mathrm{F}\mathrm{e}\mathrm{O}}+log{K}_{\mathrm{F}\mathrm{e}}=0}$
Mass conservation of CaO	${\displaystyle {\left(\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\text{\%}\mathrm{C}\mathrm{a}\mathrm{O}\right)}_{in\mathrm{\hspace{0.17em} } slag}\cdot W_{slag}-W_{\mathrm{C}\mathrm{a}\mathrm{O}\mathrm{\hspace{0.17em} } total}=0}$
Mass conservation of SiO2	${\displaystyle {\left(\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%\mathrm{S}\mathrm{i}{\mathrm{O}}_2\right)}_{in\mathrm{\hspace{0.17em} } slag}\cdot W_{slag}+\frac{M_{\mathrm{S}\mathrm{i}{\mathrm{O}}_2}}{M_{\mathrm{S}\mathrm{i}}}{\left[\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%\mathrm{S}\mathrm{i}\right]}_{in\mathrm{\hspace{0.17em} } \mathrm{F}\mathrm{e}}\cdot W_{hot\mathrm{\hspace{0.17em} } metal}-W_{\mathrm{S}\mathrm{i}{\mathrm{O}}_2\mathrm{\hspace{0.17em} } total}=0}$
Mass conservation of Al2O3	${\displaystyle {\left(\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}{\text{\%Al}}_2{\text{O}}_3\right)}_{in\mathrm{\hspace{0.17em} } slag}\cdot W_{slag}-W_{\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3\mathrm{\hspace{0.17em} } total}=0}$
Mass conservation of MgO	${\displaystyle {\left(\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\text{\%}\mathrm{M}\mathrm{g}\mathrm{O}\right)}_{in\mathrm{\hspace{0.17em} } slag}\cdot W_{slag}-W_{\mathrm{M}\mathrm{g}\mathrm{O}\mathrm{\hspace{0.17em} } total}=0}$
Mass conservation of FeO	${\displaystyle {\left(\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%\mathrm{F}\mathrm{e}\mathrm{O}\right)}_{in\mathrm{\hspace{0.17em} } slag}\cdot W_{slag}+\frac{M_{\mathrm{F}\mathrm{e}\mathrm{O}}}{M_{\mathrm{F}\mathrm{e}}}{\left[\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%\mathrm{F}\mathrm{e}\right]}_{in\mathrm{\hspace{0.17em} } \mathrm{F}\mathrm{e}}\cdot W_{hot\mathrm{\hspace{0.17em} } metal}-W_{\mathrm{F}\mathrm{e}\mathrm{O}\mathrm{\hspace{0.17em} } total}=0}$
Mass conservation of MnO	${\displaystyle {\left(\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%\mathrm{M}\mathrm{n}\mathrm{O}\right)}_{in\mathrm{\hspace{0.17em} } slag}\cdot W_{slag}+\frac{M_{\mathrm{M}\mathrm{n}\mathrm{O}}}{M_{\mathrm{M}\mathrm{n}}}{\left[\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%\mathrm{M}\mathrm{n}\right]}_{in\mathrm{\hspace{0.17em} } \mathrm{F}\mathrm{e}}\cdot W_{hot\mathrm{\hspace{0.17em} } metal}-W_{\mathrm{M}\mathrm{n}\mathrm{O}\mathrm{\hspace{0.17em} } total}=0}$
Mass conservation of S	${\displaystyle {\left(\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%\mathrm{S}\right)}_{in\mathrm{\hspace{0.17em} } slag}\cdot W_{slag}+{\left[\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%\mathrm{S}\right]}_{in\mathrm{\hspace{0.17em} } \mathrm{F}\mathrm{e}}\cdot W_{hot\mathrm{\hspace{0.17em} } metal}-W_{\mathrm{S}\mathrm{\hspace{0.17em} } total}=0}$
Mass conservation of P	${\displaystyle {\left(\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%{\mathrm{P}}_2{\mathrm{O}}_5\right)}_{in\mathrm{\hspace{0.17em} } slag}\cdot W_{slag}+\frac{M_{{\mathrm{P}}_2{\mathrm{O}}_5}}{M_{\mathrm{P}}}{\left[\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%\mathrm{P}\right]}_{in\mathrm{\hspace{0.17em} } \mathrm{F}\mathrm{e}}\cdot W_{hot\mathrm{\hspace{0.17em} } metal}-W_{{\mathrm{P}}_2{\mathrm{O}}_5\mathrm{\hspace{0.17em} } total}=0}$
Mass conservation of Cu	${\displaystyle {\left[\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%\mathrm{C}\mathrm{u}\right]}_{in\mathrm{\hspace{0.17em} } \mathrm{F}\mathrm{e}}\cdot W_{hot\mathrm{\hspace{0.17em} } metal}-W_{\mathrm{C}\mathrm{u}\mathrm{\hspace{0.17em} } total}=0}$
Mass conservation of Sn	${\displaystyle {\left[\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%\mathrm{S}\mathrm{n}\right]}_{in\mathrm{\hspace{0.17em} } \mathrm{F}\mathrm{e}}\cdot W_{hot\mathrm{\hspace{0.17em} } metal}-W_{\mathrm{S}\mathrm{n}\mathrm{\hspace{0.17em} } total}=0}$
Mass conservation of Ni	${\displaystyle {\left[\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%\mathrm{N}\mathrm{i}\right]}_{in\mathrm{\hspace{0.17em} } \mathrm{F}\mathrm{e}}\cdot W_{hot\mathrm{\hspace{0.17em} } metal}-W_{\mathrm{N}\mathrm{i}\mathrm{\hspace{0.17em} } total}=0}$
Mass conservation of Cr	${\displaystyle {\left[\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%\mathrm{C}\mathrm{r}\right]}_{in\mathrm{\hspace{0.17em} } \mathrm{F}\mathrm{e}}\cdot W_{hot\mathrm{\hspace{0.17em} } metal}-W_{\mathrm{C}\mathrm{r}\mathrm{\hspace{0.17em} } total}=0}$
Total sum of mass percentage in hot metal	${\displaystyle {\displaystyle \sum }_j{\left[\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%j\right]}_{in\mathrm{\hspace{0.17em} } \mathrm{F}\mathrm{e}}-100=0}$
Total sum of mass percentage in slag	${\displaystyle {\displaystyle \sum }_j{\left(\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%j\right)}_{in\mathrm{\hspace{0.17em} } slag}-100=0}$

The solubility of C in Fe–C(l),³¹⁾ activity coefficients of C,³⁰⁾ and Fe,³²⁾ the activity of oxides in slag,^{21,22,33,34,35)} and sulfide and phosphate capacities^36,37) are shown in Table 2. The interaction parameters^15,16,29) are listed in Table 3.

Table 2. Thermodynamic data of activities and capacities used in this work.

Thermodynamic data	Reference
${\displaystyle log{x}_{\text{C}\mathrm{\hspace{0.17em} } \text{satd}.\left(\text{binary}\right)}=-12.728/T+0.727logT-3.049}$	31)
${\displaystyle log{f}_{\mathrm{C}}=\left(\frac{4\mathrm{\hspace{0.17em} }530}{T}\right)\left[T+4\cdot {10}^{-4}\left(T-1\mathrm{\hspace{0.17em} }770\right)\right]\left(2-x_{\mathrm{C}}\right)\cdot x_{\mathrm{C}}+log\left\{\left(M_{\mathrm{F}\mathrm{e}}\left(1-x_{\mathrm{C}}\right)+M_{\mathrm{C}}{x}_{\mathrm{C}}\right)/M_{\mathrm{F}\mathrm{e}}\right\}}$	30)
${\displaystyle log{\gamma }_{\text{Fe}}=\left(-1\mathrm{\hspace{0.17em} }700/T-0.36\right)\cdot {\left\{x_{\text{C}}\left(1-x_{\text{C}}\right)\right\}}^2}$	32)
${\displaystyle a_{{\text{SiO}}_2}=4.634x_{{\text{SiO}}_2}{}^3-0.7552x_{{\text{SiO}}_2}{}^2}$	21, 33)
${\displaystyle a_{\text{MnO}}=\left(\text{\%MnO}\right)\times \left\{5.9\left(\left(\text{\%CaO}\right)+1.4\left(\text{\%MgO}\right)\right)/\left({\text{\%SiO}}_2\right)+1.6\right\}\times {10}^{-3}}$	22, 34)
${\displaystyle log{a}_{{\text{Fe}}_t\text{O}}=log{x}_{{\text{Fe}}_t\text{O}}+0.366\left(x_{\text{CaO}}+0.6x_{\text{MgO}}\right)/\left(x_{{\text{SiO}}_2}+1.8x_{{\text{Al}}_2{\text{O}}_3}\right)+1\mathrm{\hspace{0.17em} }748.5/T+0.921}$	35)
${\displaystyle log{C}_{{\text{S}}^{2-}}=1.39\left(x_{\text{CaO}}+x_{\text{MgO}}/2\right)/\left(x_{{\text{SiO}}_2}+x_{{\text{Al}}_2{\text{O}}_3}/3\right)-6\mathrm{\hspace{0.17em} }911/T-1.649}$	36)
${\displaystyle log{C}_{{\text{PO}}_4^{3-}}=2.60\left\{\left(\text{\%CaO}\right)+0.33\left(\text{\%MnO}\right)+0.55\left(\text{\%MgO}\right)-0.90\left({\text{\%Fe}}_t\text{O}\right)-0.77\left({\text{\%PO}}_{2.5}\right)\right\}/\left({\text{\%SiO}}_2\right)+40\mathrm{\hspace{0.17em} }400/T-6.48}$	37)

Table 3. Interaction parameters of elements in iron $e_i^j$ at 1773 K used in this work.^15,16,29)

j i	C	O	Si	Mn	S	P	Cu	Sn	Ni	Cr
C	0.000	0.000	0.029	−0.003	0.036	0.030	0.006	0.029	0.004	−0.005
O	−0.001	−1750/T +0.76	−0.070	−0.022	−0.141	0.074	−0.014	−0.012	0.006	−0.058
Si	0.061	−0.126	0.109	−0.015	0.070	0.095	0.0152	0.017	0.005	−0.0003
Mn	−0.030	−0.088	−1838/T +0.964	0.000	−0.049	−0.057	–	–	−0.008	0.0041
S	0.089	−0.285	0.077	−0.027	−120/T +0.018	0.036	−0.009	−0.005	0.000	−94.2/T +0.04
P	0.069	0.137	0.105	−0.030	0.035	0.057	−0.033	0.013	0.003	−0.019
Cu	0.015	−0.069	0.029	–	−0.022	−0.070	−0.021	−86.9/T +0.0336	−0.001415)	0.019
Sn	0.243	−0.116	0.059	–	−0.029	0.037	−162.4/T +0.0627	0.0018	−0.03016)	0.016
Ni	0.003	0.011	0.006	−0.008	−0.004	0.002	−0.000915)	−0.01216)	0.001	−0.0003
Cr	−0.037	−0.1997	−0.004	0.004	−0.020	−0.035	0.017	0.009	0.0002	−0.0003

_____: values in carbon saturated Fe(l) ($e_{\mathrm{C}}^i$ were estimated from the influence of element i on the solubility of carbon in molten iron, $e_i^{\mathrm{C}}$ were calculated from $e_{\mathrm{C}}^i$ as $e_i^{\mathrm{C}}=\frac{M_i}{M_{\mathrm{C}}}{e}_{\mathrm{C}}^i+\frac{1}{100ln10}\frac{M_{\mathrm{C}}-M_i}{M_{\mathrm{C}}}$)

2.2. Mass Conservation Equations

The mass conservation of the elements Ca, Si, Al, Mg, Mn, Fe, S, and P (Cu, Sn, Ni, and Cr) was considered. These elements can be classified into three groups: 1. exists only in the slag phase (Ca, Al, and Mg); 2. exists in both the slag and metal phases (Si, Mn, S, P, and Fe), and 3. exists only in the metal phases (Cu, Sn, Ni, and Cr). The mass conservation equations for Ca, Si, and Cu are expressed in Eqs. (25), (26), (27), respectively.   

$${\left(\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\text{\%}\mathrm{C}\mathrm{a}\mathrm{O}\right)}_{in\mathrm{\hspace{0.17em} } slag}\cdot W_{slag}-W_{\mathrm{C}\mathrm{a}\mathrm{O}\mathrm{\hspace{0.17em} } total}=0$$(25)

  

$$\begin{array}{l}{\left(\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\text{\%}\mathrm{S}\mathrm{i}{\mathrm{O}}_2\right)}_{in\mathrm{\hspace{0.17em} } slag}\cdot W_{slag}+\frac{M_{\mathrm{S}\mathrm{i}{\mathrm{O}}_2}}{M_{\mathrm{S}\mathrm{i}}}{\left[\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\text{\%}\mathrm{S}\mathrm{i}\right]}_{in\mathrm{\hspace{0.17em} } \mathrm{F}\mathrm{e}}\cdot W_{hot\mathrm{\hspace{0.17em} } metal}\\ -W_{\mathrm{S}\mathrm{i}{\mathrm{O}}_2\mathrm{\hspace{0.17em} } total}=0\end{array}$$(26)

  

$${\left[\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\text{\%}\mathrm{C}\mathrm{u}\right]}_{in\mathrm{\hspace{0.17em} } \mathrm{F}\mathrm{e}}\cdot W_{hot\mathrm{\hspace{0.17em} } metal}-W_{\mathrm{C}\mathrm{u}\mathrm{\hspace{0.17em} } total}=0$$(27)

where W_slag, W_metal, W_{j total}, and M_j denote the masses of the slag and hot metal, and the total mass and molar mass of chemical component j, respectively. First, the total mass of each element was calculated from the input amount and composition of the raw materials. Because Si exists both in the slag and in the metal phases, the Si mass in the hot metal was converted to SiO₂ in Eq. (26). The mass conservation equations are summarized in Table 1. Furthermore, the total mass% concentration in each phase must be 100. This relationship was also considered, as shown in Table 1. As can be seen in Table 1, 17 (or 21) equations were obtained for 17 (or 21) variables. The variables are the concentrations of CaO, SiO₂, Al₂O₃, MgO, FeO, MnO, S, and P₂O₅ in the slag, and Fe, C, O, Si, Mn, S, and P (Cu, Sn, Ni, and Cr) in the hot metal, in addition to W_slag and W_metal. These nonlinear equations were simultaneously solved by a numerical method in this study.

3. Results and Discussion

3.1. Analysis of Slag and Hot Metal Compositions in Practical Blast Furnace

The data of raw materials is needed for the present analysis model; however, there is little available data in the literature. First, the slag–metal equilibria were analyzed based on the composition data of the slag and the hot metal,²¹⁾ as shown in Table 4. Subsequently, the raw material data was estimated based on the results of the equilibrium analysis in the next section. The partial pressure of CO(g) was estimated from the blast pressure using the method reported by Tsuchiya et al.²¹⁾ The partial pressure of oxygen in the operation data was estimated assuming the equilibrium between CO(g) and C(s) as follows:   

$$\mathrm{C}\left(\mathrm{s}\right)+1/2{\mathrm{O}}_2\left(\mathrm{g}\right)=\mathrm{C}\mathrm{O}\left(\mathrm{g}\right)$$(28)

  

$$log{K}_{\left(28\right)}=\frac{P_{\mathrm{C}\mathrm{O}}}{a_{\mathrm{C}\left(\mathrm{s}\right)}\cdot P_{{\mathrm{O}}_2}{}^{1/2}}=log{K}_{\mathrm{C}\mathrm{O}}+log{K}_{\mathrm{C}}+log{K}_{{\mathrm{O}}_2}$$(29)

Table 4. Operation data of the blast furnace.²¹⁾

Hot metal temperature (K)	Hot metal composition (mass%)				Slag composition (mass%)						Partition ratio (–)			Blast pressure (kg/cm2)	Partial pressure of CO (atm)	Partial pressure of O2 (atm)
	C	Si	Mn	S	CaO	SiO2	Al2O3	MgO	MnO	S	LSi	LMn	LS
1780	4.66	0.58	0.87	0.040	39.8	34.0	14.8	6.4	1.15	1.21	0.017	0.757	0.033	2.64	4.4	3.33×10−15
1784	4.63	0.57	0.73	0.036	40.2	34.3	14.8	6.4	0.93	1.19	0.017	0.785	0.030	2.69	4.4	3.53×10−15
1785	4.65	0.54	0.73	0.034	40.3	33.9	14.7	6.2	1.02	1.14	0.016	0.716	0.030	2.54	4.3	3.33×10−15
1782	4.53	0.45	0.80	0.038	39.7	33.6	15.1	6.4	1.18	1.07	0.013	0.678	0.036	2.5	4.2	3.18×10−15
1781	4.60	0.46	0.83	0.034	40.2	33.2	14.7	6.9	1.17	1.16	0.014	0.709	0.029	2.56	4.3	3.24×10−15
1783	4.62	0.47	0.82	0.035	40.4	33.4	14.8	6.6	1.09	1.19	0.014	0.752	0.029	2.59	4.3	3.34×10−15
1773	4.60	0.60	0.83	0.042	40.1	33.9	15	6.1	1.13	1.21	0.018	0.735	0.035	2.39	4.1	2.79×10−15
1768	4.63	0.52	0.84	0.045	40.0	34.3	14.9	6.2	1.22	1.11	0.015	0.689	0.041	2.24	4.0	2.48×10−15
1778	4.59	0.50	0.74	0.038	40.6	33.7	15.0	6.0	1.02	1.13	0.015	0.725	0.034	2.27	4.0	2.76×10−15
1784	4.53	0.50	0.56	0.037	40.5	33.2	15.7	6.1	0.94	1.10	0.015	0.596	0.034	2.34	4.1	3.01×10−15
1782	4.61	0.49	0.47	0.034	40.8	33.1	15.1	6.2	0.77	1.20	0.015	0.610	0.028	2.38	4.1	3.01×10−15
1778	4.43	0.47	0.59	0.034	40.8	33.3	15.1	6.3	0.84	1.18	0.014	0.702	0.029	2.38	4.1	2.90×10−15
1781	4.82	0.60	0.92	0.041	40.3	33.4	15.3	6.1	1.32	1.17	0.018	0.697	0.035	2.75	4.5	3.52×10−15
1856	4.76	0.57	0.89	0.040	40.1	33.8	15.2	6.3	1.26	1.13	0.017	0.706	0.035	2.64	4.4	6.36×10−15
1778	4.58	0.48	0.87	0.045	40.2	33.4	15.3	6.0	1.4	1.06	0.014	0.621	0.042	2.6	4.3	3.21×10−15
1779	4.43	0.45	0.81	0.043	39.8	33.0	15.7	6.3	1.38	1.01	0.014	0.587	0.043	2.67	4.4	3.34×10−15
1781	4.56	0.42	0.81	0.041	40.3	33.1	15.0	6.4	1.34	1.06	0.013	0.604	0.039	2.77	4.5	3.55×10−15
1781	4.48	0.45	0.79	0.041	40.1	33.5	15.0	6.5	1.26	1.06	0.013	0.627	0.039	2.84	4.6	3.66×10−15
Calculation condition
1773	4.60	0.51	0.77	0.039	40.2	33.6	15.1	6.3	1.1	1.1	0.015	0.683	0.034	2.54	4.3	3.03×10−15

The equilibrium compositions of the slag and hot metal were analyzed using the average values in Table 4. The temperature was fixed at 1773 K, and the slag amount was assumed to be 300 kg/THM. The equilibrium contents of C, Si, Mn, and S are shown in Fig. 3 at P_O2 ranging from 10⁻¹⁶ to 10⁻¹⁰ atm. As can be seen in Fig. 3, the hot metal was saturated with carbon when P_O2 was less than 3.03×10⁻¹⁵ atm. The solubility of carbon increased with P_O2 because the concentration of Si, which has a repulsive interaction with C, decreased. When P_O2 was higher than 3.03×10⁻¹⁵ atm, the C content of the hot metal was decreased by oxidation. Similarly, the SiO₂ and MnO contents of the slag increased because Si and Mn in the hot metal were oxidized at higher P_O2. By contrast, the hot metal S content increased owing to the oxidation of S²⁻ in the slag. The local maximum of SiO₂ content of the slag was found at around P_O2 = 1.2×10⁻¹³ atm, as can be seen in Fig. 3(b). This is caused by both the increase in the amount of SiO₂ due to the oxidation of Si and the dilution by FeO due to the oxidation of Fe. Similarly, the local maximum of MnO content of the slag was found at around P_O2 = 1.3×10⁻¹³ atm, as can be seen in Fig. 3(c). The comparison of the operation data with the results of the present analysis revealed that the Si and Mn were significantly oxidized relative to the equilibrium, and the S content was equal to the equilibrium composition at the bottom of the blast furnace. This result is consistent with the report indicating the rate of the slag–metal reaction of S was fast and equilibrium was attained at the bottom of the blast furnace.²²⁾ The Si and SiO₂ contents correspond to the equilibrium values at 1.5×10⁻¹⁴ atm-P_O2. According to Nagata et al., the partial pressure of oxygen in the slag was 10 times higher than that of the hot metal after tapping of the blast furnace.³⁸⁾ Moreover, the reduction rate of SiO₂ in the slag was significantly low.¹⁷⁾ These results suggest that Si and Mn in the hot metal were oxidized when the metal droplets fell in the slag layer at higher P_O2. The SiO₂ in the slag was not reduced when P_O2 decreased in the presence of C(s) at the bottom of the blast furnace. The present model is considered to be used to discuss the slag and hot metal compositions of blast furnace and PSR.

Fig. 3.

Equilibrium composition of slag and hot metal at P_O2 ranging from 10⁻¹⁶ to 10⁻¹⁰ atm at 1773 K ((a) C, (b) Si and SiO₂, (c) Mn and MnO and (d) S contents). (Online version in color.)

3.2. Estimation of Composition of the Raw Materials

The composition and input amount of raw materials were estimated so that the composition of the slag and the hot metal agree with the analyzed values based on the operation data shown in Section 3.1. The composition of the sinter used in the operation in 1975²¹⁾ was estimated from a report in 2013,³⁹⁾ which is shown in Table 5. According to the transition of the composition of iron ore sinter,⁴⁰⁾ (%Al₂O₃) slightly increased and (%MgO) was almost constant from 1970 to 1990. From this fact, (%SiO₂), (%Al₂O₃), and (%MgO) were estimated to be 5.22, 1.95, and 1.5,⁴⁰⁾ respectively. Furthermore, the basicity index, (%CaO)/(%SiO₂), was 1.34; therefore, (%CaO) was derived to be 6.99. The estimated composition of the sinter in 1975 is presented in Table 5. Note that the total Fe content (T. Fe) was assumed to be the same as that in 2013. The composition of coke was estimated as follows: S content and amount of ash were assumed to be the same as those used by Yamamoto et al.;¹⁰⁾ the ash composition was estimated from the composition data of coke,⁴¹⁾ which has the same S content and amount of ash. The estimated coke composition is shown in Table 5. The input amounts of raw materials to produce 1 tonne of hot metal were estimated and are listed in Table 6. The coke amount was estimated to be 420 kg/THM from the transition of ironmaking technology.⁴⁰⁾ The equilibrium compositions of the slag and hot metal based on the estimated input amounts are shown in Fig. 3 as dotted lines. As shown in Fig. 3(a), the Si and SiO₂ contents were in good agreement with those calculated from the operation data.²¹⁾ Although there was a small difference between the equilibrium Mn and S contents calculated from the input amounts and those from the operation data, it was confirmed that the dependence of Si, Mn, and S contents of the hot metal on P_O2 can be reasonably obtained based on the input amounts of the raw materials.

Table 5. Estimated composition of (a) sinter, (b) coke and (c) steel scrap.

(a) Sinter (mass%)
Material	T. Fe	FeO	CaO	SiO2	Al2O3	MgO	MnO	S	PO2.5	CaO/SiO2
Sinter (2013)39)	58.3	7.75	8.61	4.37	1.72	1.45	1.24	0.058	0.058	1.97
Sinter39,40) (1975 estimated)	58.3	7.75	6.99	5.52	1.95	1.5	1.00	0.058	0.116	1.34

(b) Coke
Material	Ash (mass%)	Ash composition (mass%)
		SiO2	Al2O3	Fe2O3	CaO	MgO	PO2.5	S	Others
Coke10,41)	10.5	50.7	36	4.4	2.7	0.5	2.0	0.54	1.6

(c) steel scrap (mass%)
Material	Fe	C	Si	Mn	S	P	Cu	Sn	Ni	Cr
Steel scrap10,42,43)	99	0.043	0.012	0.19	0.007	0.015	0.278	0.017	0.072	0.175

Table 6. Input amount of raw materials to analyze the effect of scrap ratios.

Scrap ratio	Sinter (kg)	Coke (kg)	Scrap (kg)
0.0	1638	420	0
0.1	1474	420	96
0.2	1310	420	193
0.3	1146	420	289
0.4	982	420	385
0.5	819	420	482

3.3. Effects of Scrap Addition on the Slag and Hot Metal Composition

The composition of steel scrap was estimated in advance for the analysis of the effects of the scrap ratio on the composition of hot metal and slag. C, Si, S, and P contents of the scraps were estimated from the composition of the carbon steel.⁴²⁾ Because it is difficult to estimate the amount of tramp elements (Cu, Sn, Ni, and Cr) contained in steel scraps, their average concentrations in steel bars reported by Daigo et al.⁴³⁾ were used. The iron content was assumed to be 99 mass%, and the Mn content was estimated by subtracting the content of other components from 100 mass%. The estimated composition of the steel scrap is listed in Table 5. Based on the composition of the raw materials, the input amount was calculated and is listed in Table 6, where the coke rate was fixed and the scrap ratio was varied from 0 to 0.5. Scrap ratio (SR) is defined by Eq. (30)   

$$SR=\frac{{\left(\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\mathrm{\hspace{0.17em} } \mathrm{o}\mathrm{f}\mathrm{\hspace{0.17em} } \mathrm{F}\mathrm{e}\right)}_{in\mathrm{\hspace{0.17em} } scrap}}{{\left(\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\mathrm{\hspace{0.17em} } \mathrm{o}\mathrm{f}\mathrm{\hspace{0.17em} } \mathrm{F}\mathrm{e}\right)}_{in\mathrm{\hspace{0.17em} } sinter}+{\left(\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\mathrm{\hspace{0.17em} } \mathrm{o}\mathrm{f}\mathrm{\hspace{0.17em} } \mathrm{F}\mathrm{e}\right)}_{in\mathrm{\hspace{0.17em} } scrap}}$$(30)

The effects of scrap ratio on the composition of hot metal and slag were investigated based on the data in Tables 5 and 6. To evaluate the effects of the scrap ratio under the different conditions of temperature and P_O2, P_O2 was varied from 10⁻¹⁶ to 10⁻¹⁰ atm at 1773 K, and the temperature was varied from 1673 to 1873 K at a constant P_O2 of 3.03×10⁻¹⁵ atm from the operation data of the blast furnace explained in Section 3.1. The effects of scrap ratios on the C, Si, Mn, S, P, and Fe contents of the hot metal are shown in Figs. 4 and 5. As P_O2 increased, the Si and Mn contents decreased due to the oxidation. The P content was also decreased at P_O2 higher than 10⁻¹³ atm, where the FeO content of the slag was more than 0.3 mass%. The local maximum of PO_2.5 content of the slag was found at around P_O2 = 1.6 to 5.4×10⁻¹³ atm, as can be seen in Fig. 4(e), due to the same cause as SiO₂ and MnO. By contrast, the S content increased. Oxidation increased at lower temperatures under a fixed P_O2. The hot metal was saturated with C(s) at temperatures higher than 1773 K. C content of the hot metal was decreased due to the oxidation at temperatures lower than 1773 K. Similarly, Si, Mn, and Fe were also oxidized at lower temperature. P was slightly oxidized at temperatures higher than 1800 K, which was caused by the increase in the basicity of the slag due to the reduction of SiO₂. The effect of scrap ratio on the C content was found to be minimal because the carbon content was determined by the solubility or equilibrium with CO(g). As the scrap ratio increased, the concentration of such elements originating from sinter as Si, Mn, and P decreased, whereas that of S originating from coke increased. The S content is also expected to decrease in practice because the coke rate can be decreased with increasing scrap ratio, which was not considered in this analysis. Furthermore, it was found that the change in slag composition tends to increase with increasing P_O2 and temperature. As can be seen from Fig. 4(b), the SiO₂ content of the slag increased with increasing scrap ratio at higher P_O2 than 3×10⁻¹⁵ atm, which led to a decrease in the basicity of the slag. The decrease in the P content of hot metal at higher P_O2 than 10⁻¹³ atm became modest as the scrap ratio was increased because of the decrease in basicity, as shown in Fig. 4(e). In the PSR furnace, CaO can be added to the bottom of the furnace. Therefore, the P content of the hot metal can be decreased further when the basicity of slag is maintained because the input amount of P decreases as the scrap ratio is increased. Figure 6 shows the effects of the scrap ratio on the slag amount. As shown in Fig. 6(a), the slag amount increased when P_O2 increased. Because the oxidized amounts of Si, Mn, P, and Fe differ and vary depending on P_O2, the curve of the slag amount became wavy line. On the other hand, because Mn, P, and Fe are little oxidized at P_O2= 3.03×10⁻¹⁵ atm, the slag amount was increased due to only the oxidation of Si, thus the curvature of Fig. 6(b) is similar to that of SiO₂ content of the slag, as shown in Fig. 5(b). As the scrap ratio increased, the slag amount decreased because the input amount of mineral compounds originating in the sinter decreased. When the scrap ratio was increased by 0.1, the slag amount decreased by 9%. The decrease in the slag amount is considered to be the cause of the larger change in the slag composition. Figure 7 shows the concentrations of tramp elements at the P_O2 ranging from 10⁻¹⁶ to 10⁻¹⁰ atm. Because tramp elements in molten iron cannot be oxidized, their contents were almost constant and slightly increased due to the oxidation loss of Fe. The effect of the scrap ratio on the concentrations of the tramp elements is shown in Fig. 8. The concentrations of tramp elements increased proportionally with scrap ratio.

Fig. 4.

Effect of scrap ratios on the equilibrium composition of slag and hot metal at P_O2 ranging from 10⁻¹⁶ to 10⁻¹⁰ atm at 1773 K ((a) C, (b) Si and SiO₂, (c) Mn and MnO, (d) S, (e) P and PO_2.5 and (f) Fe and FeO contents). (Online version in color.)

Fig. 5.

Effect of scrap ratios on the equilibrium composition of slag and hot metal at temperatures ranging from 1673 to 1873 K when P_O2 = 3.03×10⁻¹⁵ atm. ((a) C, (b) Si and SiO₂, (c) Mn and MnO, (d) S, (e) P and PO_2.5 and (f) Fe and FeO contents). (Online version in color.)

Fig. 6.

Effect of scrap ratios on the slag amount (a) at P_O2 ranging from 10⁻¹⁶ to 10⁻¹⁰ atm at 1773 K and (b) at the temperature ranging from 1673 to 1873 K at 3.03×10⁻¹⁵ atm P_O2. (Online version in color.)

Fig. 7.

Concentrations of tramp elements at the P_O2 ranging from 10⁻¹⁶ to 10⁻¹⁰ atm ((a) Cu, (b) Sn, (c) Ni, and (d) Cr content). (Online version in color.)

Fig. 8.

Effect of scrap ratio on the concentrations of tramp elements when P_O2 = 3.03×10⁻¹⁵ atm at 1773 K.

Based on the aforementioned discussion, the effects of scrap ratio are summarized as follows.

① The concentrations of these elements originating from sinter as Si, Mn, and P decreased.

② The amount of slag decreased. Therefore, the S content of the hot metal increased when the coke rate was fixed.

③ The P content of the hot metal can be decreased when the basicity of slag is maintained by CaO addition because the input amount of P is decreased.

④ The Cu, Sn, Ni, and Cr contents of the hot metal increased proportionally with the scrap ratio.

Accordingly, the use of steel scrap as an iron source has the following advantages: a decrease in the content of impurity elements originating in iron ore, a decrease in the slag amount and coke rate. Therefore, the utilization of steel scraps is expected to increase low-grade iron ore use, which contains SiO₂ and P at higher concentrations. In the blast furnace, it is considered that FeO does not affect the slag–metal reactions at the bottom of the furnace because FeO in the slag is almost reduced at the cohesive zone.³⁸⁾ In PSR, the partial pressure of oxygen can be controlled by the injection of oxygen from the secondary tuyeres. Therefore, FeO in the slag can be used as an oxidizing agent by controlling the FeO content of the slag at the bottom of the PSR. The Si content decreased to 0.1 mass% at 1773 K and P_O2 higher than 10⁻¹³ atm or at temperatures lower than 1690 K and P_O2= 3.03×10⁻¹⁵ atm. The P content of the hot metal can be decreased by oxidation at P_O2 higher than 10⁻¹³ and 10⁻¹² atm when the scrap ratios are 0 and 0.5, respectively. The FeO contents of the slag corresponded to be 0.3 and 1.4 mass% respectively. In the lower part of blast furnace and PSR furnace, the redox reaction between the slag containing FeO and hot metal occurs. Therefore, the P_O2 described above can be achieved by increasing the initial FeO content of the slag, which would be realized by the injection of fine iron ore from primary tuyere and by blowing oxygen from secondary tuyeres in PSR. Yamamoto et al.¹⁰⁾ conducted scrap melting tests with packed bed type scrap melting process and reported that the fuel efficiency was increased by the post combustion with the air or oxygen-containing gas injection from the secondary tuyeres, and 100% scrap could be melted. Therefore, blowing oxygen from secondary tuyeres can contribute to maintain temperature in the furnace when scarp ratio is increased Therefore, the use of steel scraps in PSR is expected to produce hot metal with a low impurity content by controlling the oxygen partial pressure at the bottom of the furnace.

4. Conclusions

An analysis model was developed to simulate the equilibrium of slag–metal reactions. The effects of the scrap ratio on the composition of the hot metal and slag were thermodynamically analyzed, and the optimal conditions of temperature and partial pressure of oxygen at the bottom of the furnace were investigated. The conclusions are summarized as follows:

(1) Operation data of the composition of the slag and hot metal were compared with the results of the present analysis. Si and Mn were found to be significantly oxidized relative to the equilibrium and the S content was equal to the equilibrium when the hot metal temperature was assumed to be 1773 K, and the partial pressure of oxygen was estimated to be 3.03×10⁻¹⁵ atm from the blast pressure. The Si and SiO₂ contents were equal to the equilibrium values at 1.5×10⁻¹⁴ atm-P_O2, which suggests that Si in the hot metal is oxidized when the metal droplets fall in the slag layer.

(2) The advantages of using steel scraps as an iron source include a decrease in the content of impurity elements originating in the iron ore, and a decrease in the slag amount and the coke rate. The Si content decreased to 0.1 mass% at P_O2 higher than 10⁻¹³ atm at 1773 K or at temperatures lower than 1690 K when P_O2= 3.03×10^-15 atm. The P content of the hot metal can be decreased by oxidation at P_O2 higher than 10⁻¹³ and 10⁻¹² atm when the scrap ratios are 0 and 0.5, respectively. The FeO contents of the slag corresponded to be 0.3 and 1.4 mass%, respectively.

(3) In PSR, the partial pressure of oxygen can be controlled by the injection of oxygen from the secondary tuyeres. FeO in the slag can be used as an oxidizing agent by controlling the FeO content of the slag at the bottom of the PSR. Therefore, PSR is expected to produce hot metal with lower impurity content by controlling the oxygen partial pressure of the slag–metal reaction at the bottom of the furnace when steel scraps are used as an iron source.

Acknowledgments

This study was supported by JSPS KAKENHI (Grant Number JP 20JI0432).

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