Effect of Slag Compositions on Change Behavior of Nitrogen in Molten Steel

Abstract

The problem of nitrogen pickup in the smelting process of the electric arc furnace (EAF) has not been solved well. Using seven slag–steel equilibrium experiments and theoretical analysis, the relation of the foaming index and optical basicity with the nitrogen capacity of slag was clarified. Meanwhile, the effect of slag composition on the equilibrium distribution ratio of nitrogen and the mass transfer coefficient of nitrogen pickup was also studied. The results show that, with the increase in slag basicity, the nitrogen pickup amount, nitrogen pickup rate, and nitrogen equilibrium distribution ratio L_N increase. Increasing the foaming index of slag and reducing its optical basicity will increase the nitrogen capacity of slag, which is conducive to hindering the nitrogen pickup of molten steel. The relationship between slag optical basicity and nitrogen capacity can be expressed as lgC_N = −5.59lgΛ − 12.41. With the increase in the Al₂O₃ content of slag, the nitrogen pickup amount of molten steel decreases and the nitrogen pickup rate decreases. The test with MgO = 7.5% showed the highest nitrogen pickup rate and the highest nitrogen pickup mass transfer coefficient, which were 0.21 × 10⁻⁴%/min and 1.97 × 10⁻⁴ cm/s, respectively. The test with Al₂O₃ = 7.5% in slag showed the lowest nitrogen pickup rate and the lowest nitrogen pickup mass transfer coefficient, which were 0.08 × 10⁻⁴%/min and 1.35 × 10⁻⁴ cm/s, respectively.

1. Introduction

Electric arc furnace (EAF) is one of the main tools used for steelmaking in the world [1,2]. However, the problem of nitrogen pickup in the smelting process of EAF has not been solved well. There are several factors that affect the nitrogen content of molten steel in EAF, such as the addition of direct reduced iron, bottom blowing, foaming slag, and the mount of scrap [3,4,5,6]. Neuschütz [3] injected methane into the arc of EAF and increased the arc voltage under a constant arc current and arc length, finding that nitrogen removal was considerably accelerated after methane injection. Wei [4] reported on the effect of bottom-blowing gas on the nitrogen content of molten steel through experiments combining theoretical calculations and established kinetic models of nitrogen change in molten steel with bottom-blowing nitrogen, argon, and carbon dioxide. Derda [5] studied the effect of scrap on the nitrogen content of EAF through various experiments, finding that limiting the mass of scrap had a significant effect on reducing the nitrogen content. Brooks [6] found that injecting direct reduced iron (DRI) fines into EAF had the potential to greatly lower the nitrogen level. Fan [7] measured the dissolution of nitrogen into molten iron at 1873 K using ¹⁵N-¹⁴N isotope exchange technology and an online mass spectrometer, reporting that the nitrogen dissolution reaction apparent rate constant in pure liquid iron is k_a = 4.8 × 10⁻⁶ mol∙m⁻²∙s∙Pa. Wang [8] explored the nitrogen absorption behavior of molten steel under different nitrogen partial pressures. The results showed that the higher the nitrogen partial pressure was, the greater the solubility of nitrogen in the molten steel was.

Some researchers have studied the behavior of nitrogen in slag. The functions of slag are to accelerate the submerged arc heating, protect the refractories from thermal radiation, and avoid the exposure of the molten steel surface to nitrogen and hydrogen [9,10]. The effect of the slag depends on the thickness of the slag layer and the foaming index [11]; the former affects the rate of nitrogen infiltration into the slag layer, while the latter affects the length of time taken by slag to isolate molten steel from the atmosphere. Meanwhile, the thickness of the slag layer is positively correlated with the foaming index and affected by the slag composition and the amount of slag. However, Matsuura [12] computed the foam height, which was limited by either the foam stability or the amount of slag. Li [13] reviewed the research progress made on denitrification slag and pointed out that adjusting the composition of slag is the key to achieving denitrification in molten steel.

Wang [14] obtained the correlative formula for nitrogen capacity, temperature, and optical basicity by regression analysis and provided two kinds of reaction mechanism for the absorption of nitrogen by slag. Their results found that slag with a high nitrogen capacity had an excellent denitrification ability. Ling [15] and Xiang [16] both studied the behavior of nitrogen in slag and molten steel through experiments; the former gave the quantitative relationship between the equilibrium distribution ratio of nitrogen and temperature, while the latter determined the mass transfer coefficient of nitrogen between slag and molten steel. Yamanaka [17] conducted a slag denitrification experiment and investigated the reaction rates. The results showed that the slag of the CaO-Al₂O₃-CaF₂-BaF₂-SiO₂-MgO system was effective for use in nitrogen desorption from molten steel and that the rate of nitrogen transfer from steel to a gas phase could be increased.

Although some studies have confirmed the phenomenon of nitrogen absorption by slag, the mechanism by which slag compositions affect the change behavior of nitrogen is still unclear, and there are few related studies on this topic. Thus, the present study focused on investigating the influence of slag compositions on the nitrogen behavior in molten steel. Combining the MoSi₂ furnace experiments and theoretical analysis, the relation of the foaming index and optical basicity with the nitrogen capacity of slag was clarified. Meanwhile, the effect of slag composition on the equilibrium distribution ratio of nitrogen and the mass transfer coefficient of nitrogen pickup were also studied. These results will provide guidance for slag selection and the process control of the electric arc furnace.

2. Experimental Condition and Procedure

2.1. Experimental Condition

The experimental device used was a MoSi₂ furnace, as shown in Figure 1. A MgO crucible with a size of Φ53 × 65 mm was adopted as the smelting vessel, and the temperature measuring instrument used was a double platinum rhodium thermocouple (PtRH30/PtRH6S). A four-hole corundum tube with an inner diameter of 1 mm was adopted as the blow tube, and the inner diameter of the quartz tube used for sampling was 4 mm. Argon with a purity of 99.99% and nitrogen with a purity of 99.9% were used as the injection gases. The gas flow was regulated by a rotameter.

Referring to the composition of the electric arc furnace slag in a steel plant, the compositions of the slags designed for the present experiments are shown in

Table 1. Compositions of designed slag, mass%.

No.	CaO	SiO2	Al2O3	MgO	MnO	FeO	R
1#	42.0%	28.0%	5.0%	5.0%	7.0%	13.0%	1.5
2#	46.5%	23.5%	5.0%	5.0%	7.0%	13.0%	2.0
3#	50.0%	20.0%	5.0%	5.0%	7.0%	13.0%	2.5
4#	45.0%	22.5%	7.5%	5.0%	7.0%	13.0%	2.0
5#	48.5%	24.0%	2.5%	5.0%	7.0%	13.0%	2.0
6#	45.0%	22.5%	5.0%	7.5%	7.0%	13.0%	2.0
7#	48.5%	24.0%	5.0%	2.5%	7.0%	13.0%	2.0

. The raw materials used in the experiments were chemically pure reagents, which were baked in a muffle furnace at 873 K for 240 min before the experiment. The composition of the initial steel refers to the composition of the metal material fed into the EAF, and the mass fractions of the main components were as follows: C, 0.229%; Si, 0.068%; Mn, 0.160%; P, 0.010%; and S, 0.003%.

2.2. Experimental Procedure

In the experiment, 600 g of steel sample and slags with different compositions accounting for 6% of the steel mass were placed in the MgO crucible. Then, the MoSi₂ furnace (Jinzhou Electric Furnace Co., Ltd., Jinzhou, China) was energized, and argon with a flow rate of 0.1 NL/min was injected into the furnace through the top blow tube. When the furnace temperature was stable at 1873 K, nitrogen was injected into the furnace at a flow rate 0.4 NL/min. Steel samples were taken with a Φ4 mm quartz tube at the time points of 0, 2, 5, 10, 15, 20, 30, 40, 50, 60, 80, 100, and 120 min. After the samples were cut and polished, the nitrogen content of the samples was detected by a LECO-TC500 Nitrogen-Oxygen Analyzer (LECO Co., St. Joseph, MI, USA). The ZSX Primus Ⅱ X-ray fluorescence spectrometer (Rigaku Co., Ltd., Akishima-shi, Japan) and Ultima Ⅳ X-ray diffractometer (XRD, Rigaku Co., Ltd., Akishima-shi, Japan) were used to analyze the slag samples collected from the crucible.

3. Experimental Results

3.1. Effect of Slag Composition on Nitrogen Content in Steel

Figure 2 and Figure 3 present the variation in the nitrogen content and nitrogen pickup rate in molten steel over time, respectively. It can be seen that within 0–5 min, the nitrogen content in molten steel increased the fastest, and the amount of nitrogen pickup was higher than 2.5 × 10⁻⁶. The nitrogen pickup rate was relatively high over 0–5 min. Except for the test of Al₂O₃ = 7.5%, the nitrogen pickup rate of the other tests was higher than 1.0 × 10⁻⁴%/min. The amount of nitrogen pickup and the nitrogen pickup rate were maintained at a higher level over 5–10 min. However, after 10 min, the nitrogen pickup rate of each test decreased significantly. The average nitrogen pickup rate of each test was lower than 0.21 × 10⁻⁴%/min, and the No. 4# was reduced to 0.08 × 10⁻⁴%/min. Although the nitrogen content of molten steel still showed an upward trend and the nitrogen pickup reaction in the furnace had not yet reached equilibrium at 120 min, the nitrogen pickup rate became low. Over 0–120 min, the test with the largest amount of nitrogen increased by 25.2 × 10⁻⁶.

The amount of nitrogen pickup and the nitrogen pickup rate increased with the increase in the basicity of the slag. The test of R = 2.5 had the largest pickup amount of nitrogen and the fastest nitrogen pickup rate of 0.18 × 10⁻⁴%/min. With the increase in the Al₂O₃ content in slag, the pickup amount of nitrogen and the nitrogen pickup rate decreased correspondingly at the same time. The test with Al₂O₃ = 7.5% had the lowest nitrogen pickup rate of 0.08 × 10⁻⁴%/min. The pickup amount of nitrogen and the nitrogen pickup rate increased with the increase in the MgO content in slag. The test of MgO = 7.5% had the fastest nitrogen pickup rate of 0.21 × 10⁻⁴%/min.

In the electric arc furnace, the smelting period was less than 60 min. Due to the ionization of nitrogen around the arc zone, the nitrogen pickup rate increased. The amount of nitrogen pickup was less than 18 × 10⁻⁶ in all tests within 0–60 min. Thus, if the experimental slag can achieve a submerged arc better and the average nitrogen pickup rate is less than 0.15 × 10⁻⁴%/min, it may meet the control requirements for the nitrogen content of molten steel in the electric arc furnace smelting process.

3.2. Compositions of Experimental Slags and Experimental Steels

Table 2. Slag compositions in different tests after smelting, mass%.

No.	CaO	SiO2	Al2O3	MgO	MnO	FeO	R
1#	41.8%	32.2%	7.1%	11.7%	4.4%	2.8%	1.30
2#	51.6%	31.1%	4.6%	6.1%	3.8%	2.8%	1.66
3#	55.4%	27.6%	7.5%	3.8%	2.9%	2.8%	2.01
4#	48.0%	29.6%	8.7%	7.6%	4.0%	2.1%	1.62
5#	54.9%	31.9%	3.1%	4.5%	3.2%	2.4%	1.72
6#	52.2%	31.8%	4.6%	6.5%	2.9%	2.0%	1.64
7#	53.9%	31.7%	4.6%	5.6%	2.6%	1.6%	1.70

shows the change in the slag composition after the experiment. It was found that after the experiment, the mass fraction of FeO and MnO in slag decreased significantly, while the mass fraction of SiO₂ increased. Similarly, the basicity of slag decreased to a certain extent. The chemical reactions that took place between the silicon in the molten bath and the FeO and MnO in the slag could account for the above phenomena, as shown in Equations (1) and (2). These are consistent with the reaction phenomenon in the electric arc furnace. The mass fractions of the main elements in steel after the experiment were as follows: C, 0.051–0.069%; Si, 0.005–0.009%; Mn, 0.140–0.157%; P, 0.005–0.008%; S, 0.003%.

$$2(\mathrm{FeO})+[\mathrm{Si}]=(\mathrm{Si}{\mathrm{O}}_2)+2[\mathrm{Fe}]$$

(1)

$$2(\mathrm{MnO})+[\mathrm{Si}]=(\mathrm{Si}{\mathrm{O}}_2)+2[\mathrm{Mn}]$$

(2)

3.3. The XRD Results of the Experimental Slags

The XRD results of the slag after the experiment are shown in Figure 4, from which we can see that CaMgSiO₄ (monticellite), Ca₃MgSi₂O₈ (merwinite), Ca₂Al₂SiO₇ (calcium aluminum pyrite), Ca₂SiO₄ (dicalcium silicate), Al₂O₃, and SiO₂ are in the slag.

It can be seen from Figure 4 that the slag with a basicity of 1.5 after smelting mainly contains CaMgSiO₄ (monticellite), Ca₃MgSi₂O₈ (merwinite), and Ca₂Al₂SiO₇ (calcium aluminum pyrite). The SiO₂ content is relatively large, and it cannot be completely combined with CaO; thus, some free SiO₂ with a high activity will react with MgO to form monticellite and merwinite with a low melting point, as shown in Equations (3) and (4) [18]. When the basicity rises to 2.0, the amount of CaO in the slag increases and the saturated solubility of MgO decreases. A small amount of Ca₂SiO₄ (dicalcium silicate) is generated by the reaction between CaO and merwinite, as shown in Equation (5) [18]. Therefore, the main components are merwinite and a small amount of dicalcium silicate, and the melting point of dicalcium silicate can be as high as 2403 K. When the basicity is 2.5, the main component is dicalcium silicate with a high melting point, which is produced by the reaction of CaO and merwinite.

At 1873 K, with the increase in the Al₂O₃ content in the slag, the dicalcium silicate precipitated from the slag is gradually transformed into calcium aluminum pyrite, and the amount of low-melting-point merwinite is also gradually increased, as shown in Equation (6). This indicates that in the smelting process, increasing the amount of Al₂O₃ in slag can reduce the melting temperature of the slag (the calculation result obtained by Factsage is shown in Figure 5).

When the amount of MgO in the slag increases from 2.5% to 7.5%, the low-melting-point Al₂O₃ in the slag begins to transform into calcium aluminum feldspar, gradually precipitating high-melting-point SiO₂ and wollastonite. Therefore, it can be seen that the melting temperature of the slag increases with the increase in MgO, but the increase in the melting point is not conducive to the covering the molten steel with slag, resulting in the greater nitrogen pickup of the molten steel, which is consistent with the research results of Meng et al. [19].

$$\begin{gathered} {({\mathrm{Ca}}^{2+}+{\mathrm{O}}^{2-})}_{(\mathrm{s})}+{({\mathrm{Mg}}^{2+}+{\mathrm{O}}^{2-})}_{(\mathrm{s})}+{\mathrm{SiO}}_2{}_{(\mathrm{s})}={\mathrm{CaMgSiO}}_{4(\mathrm{s})} \\ \Delta G^{\mathsf{\theta }}=-124766.6+3.768T \end{gathered}$$

(3)

$$\begin{gathered} 3{({\mathrm{Ca}}^{2+}+{\mathrm{O}}^{2-})}_{(\mathrm{s})}+{({\mathrm{Mg}}^{2+}+{\mathrm{O}}^{2-})}_{(\mathrm{s})}+2{\mathrm{SiO}}_2{}_{(\mathrm{s})}={\mathrm{Ca}}_3{\mathrm{MgSi}}_2{\mathrm{O}}_{8(\mathrm{s})} \\ \Delta G^{\mathsf{\theta }}=-315469+24.786T \end{gathered}$$

(4)

$$\begin{gathered} 2({\mathrm{Ca}}^{2+}+{\mathrm{O}}^{2-})+\left({\mathrm{SiO}}_2\right)=\left({\mathrm{Ca}}_2{\mathrm{SiO}}_4\right) \\ \Delta G^{\mathsf{\theta }}=-160431+4.106T \end{gathered}$$

(5)

$$2({\mathrm{Ca}}^{2+}+{\mathrm{O}}^{2-})+\left({\mathrm{Al}}_2{\mathrm{O}}_3\right)+\left({\mathrm{SiO}}_2\right)=\left({\mathrm{Ca}}_2{\mathrm{Al}}_2{\mathrm{SiO}}_7\right), \Delta G^{\mathsf{\theta }}=-61964.64-60.29T$$

(6)

4. Discussion

4.1. Relation of Foaming Index of Slag with Nitrogen Capacity

The research shows that there are two ways for nitrogen in the gas phase to enter the slag [20,21]:

(1) When the slag does not contain network oxides such as SiO₂ and Al₂O₃, nitrogen enters the slag in the form of free nitrogen. The corresponding nitrogen dissolution reaction is shown in Equation (7), and the calculation formula for the nitrogen capacity of slag is shown in Equation (8).

$$\frac{3}{2}{\mathrm{O}}^{2-}+\frac{1}{2}{\mathrm{N}}_2={\mathrm{N}}^{3-}+\frac{3}{4}{\mathrm{O}}_2$$

(7)

$$C_{\mathrm{N}}=({\mathrm{N}}^{3-})\frac{P_{{\mathrm{O}}_2}^{\frac{3}{4}}}{P_{{\mathrm{N}}_2}^{\frac{1}{2}}}=k\frac{a_{{\mathrm{O}}^{2-}}^{\frac{3}{2}}}{f_{{\mathrm{N}}^{3-}}}$$

(8)

(2) When the slag contains SiO₂, Al₂O₃, and other network oxides, nitrogen reacts with SiO₂ and Al₂O₃ network oxides in the slag and enters the slag in the form of combined nitrogen. The corresponding nitrogen dissolution reaction is shown in Equation (9), and the calculation formula for the nitrogen capacity of slag is shown in Equation (10).

$$\frac{3}{2}{\mathrm{O}}^0+\frac{1}{2}{\mathrm{N}}_2={\mathrm{N}}^0+\frac{3}{4}{\mathrm{O}}_2$$

(9)

$$C_{\mathrm{N}}=({\mathrm{N}}^0)\frac{P_{{\mathrm{O}}_2}^{\frac{3}{4}}}{P_{{\mathrm{N}}_2}^{\frac{1}{2}}}=k\frac{a_{{\mathrm{O}}^0}^{\frac{3}{2}}}{f_{{\mathrm{N}}^0}}$$

(10)

where C_N is the nitrogen capacity of slag; (N⁰) is the nitrogen content in slag, %; $P_{{\mathrm{N}}_2}$ is the partial pressure of nitrogen in the gas phase, kPa; $P_{{\mathrm{O}}_2}$ is the partial pressure of oxygen in the gas phase, kPa; k is the equilibrium constant of nitrogen dissolution reaction; $a_{{\mathrm{O}}^0}$ is the activity of O⁰ in slag; $f_{{\mathrm{N}}^0}$ is the activity coefficient of N atom in slag.

Equation (9) can be changed into Equations (11) and (13) [15] in the present slag:

$$\frac{3}{4}{\mathrm{SiO}}_2+\frac{1}{2}{\mathrm{N}}_2={\mathrm{Si}}_{0.75}\mathrm{N}+\frac{3}{4}{\mathrm{O}}_2$$

(11)

$$\lg k_{11}=-21926/T+0.737$$

(12)

$${\mathrm{AlO}}_{1.5}+\frac{1}{2}{\mathrm{N}}_2=\mathrm{AlN}+\frac{3}{4}{\mathrm{O}}_2$$

(13)

$$\lg k_{13}=-27014/T+2.505$$

(14)

The seven slags contain network oxides such as SiO₂ and Al₂O₃. Therefore, the thermodynamic mechanism of nitrogen reaction between gas and slag was analyzed in the second way. Since there was about five times the amount of SiO₂ in the seven slags as Al₂O₃, k₁₁ was selected as the equilibrium constant of nitrogen in Equation (9) at the gas–slag interface and k₁₁ was 1.07 × 10⁻¹¹ at 1873 K. The activity coefficients $f_{{\mathrm{N}}^0}$ and $f_{{\mathrm{O}}^0}$ were both 1 in the present study. The oxygen content was obtained from the slag compositions after the experiment. Thus, the nitrogen capacity of the seven slags can be calculated, as shown in

Table 3. Nitrogen capacity of slags.

No.	1#	2#	3#	4#	5#	6#	7#
CN, 10−12	1.85	1.59	1.39	1.66	1.49	1.53	1.62

.

The slag foaming index refers to the average moving time of gas in the slag foam. When the crucible diameter is greater than 30 mm, the foaming index has nothing to do with the size of the crucible and is only related to the physical properties of the slag. The larger the foaming index is, the better the foaming property of the slag is and the greater the thickness of slag. According to the study of CaO-SiO₂-MgO-A1₂O₃-FeO slag conducted by Fruehan R J et al. [22], the relationship between the foaming index and slag viscosity, surface tension, and density is shown in Equation (15):

$$\Sigma =359\frac{\mu }{\sqrt{\rho g\sigma }}$$

(15)

where Σ is the slag foaming index, s; μ is the viscosity, Pa·s; ρ is the density, kg/m³; and σ is the surface tension, N/m.

The viscosity of molten slag after the experiment was calculated using the Factsage software; the calculation results are shown in

Table 4. Physical parameters of the slags.

No.	1#	2#	3#	4#	5#	6#	7#
μ, Pa∙s (1873 K)	0.050	0.042	0.037	0.044	0.039	0.041	0.042
ρ, 103 kg∙m−3	2.912	2.982	3.039	2.970	3.002	2.978	2.994
σ, 10−3 N∙m−1	528.386	528.393	528.406	527.944	528.804	529.081	527.666

.

According to reference [23], the slag density at 1673 K can be calculated by empirical Equation (16).

$$\begin{array}{cc}\hfill 1/\rho & =0.45\left({\mathrm{SiO}}_2\right)+0.286\left(\mathrm{CaO}\right)+0.204\left(\mathrm{FeO}\right)+0.35\left({\mathrm{Fe}}_2{\mathrm{O}}_3\right)+\hfill \\ & 0.237\left(\mathrm{MnO}\right)+0.367\left(\mathrm{MgO}\right)+0.48\left({\mathrm{P}}_2{\mathrm{O}}_5\right)+0.402\left({\mathrm{Al}}_2{\mathrm{O}}_3\right)\hfill \end{array}$$

(16)

where ρ: slag density, 10³ kg/m³; (M_xO_y): content of oxide M_xO_y, %.

When the temperature T > 1673 K, the slag density at any temperature can be calculated using Equation (17).

$${\rho }_T={\rho }_{1673 \mathrm{K}}+0.07\left(\frac{1673-T}{100}\right)$$

(17)

From the slag composition after the experiment, using Equations (16) and (17), the slag density under the experimental conditions can be obtained. The calculation results are shown in Table 4.

According to the chemical potential and surface energy, based on ion and molecule coexistence theory, the surface tension of slag can be calculated using Equation (18) [24,25]. For the CaO-SiO₂-Al₂O₃-MgO-MnO-FeO slag system in the present study, Equation (18) can be expressed as Equation (21). Moreover, ${\mathrm{N}}_i^{\mathrm{Bulk}}$ can be calculated from the mole fraction of the slag composition and the chemical equilibrium of the composite molecules based on the coexistence theory of slag structure. ${\sigma }_i^{\mathrm{Pure}}$ and $A_i$ are known values from references [26,27]. Combining Equations (20) and (21), ${\mathrm{N}}_i^{\mathrm{Surf}}$ and σ can be calculated. The surface tensions of different slags are shown in Table 4.

$$\sigma ={\sigma }_i^{\mathrm{Pure}}+\frac{\mathrm{R}T}{A_i}\ln \frac{{\mathrm{N}}_i^{\mathrm{Surf}}}{{\mathrm{N}}_i^{\mathrm{Bulk}}}$$

(18)

$$A_i={\mathrm{N}}_0^{1/3}\cdot V_i^{2/3}$$

(19)

$${\mathrm{N}}_{\mathrm{CaO}}^{\mathrm{Surf}}+{\mathrm{N}}_{{\mathrm{SiO}}_2}^{\mathrm{Surf}}+{\mathrm{N}}_{{\mathrm{Al}}_2{\mathrm{O}}_3}^{\mathrm{Surf}}+{\mathrm{N}}_{\mathrm{MgO}}^{\mathrm{Surf}}+{\mathrm{N}}_{\mathrm{MnO}}^{\mathrm{Surf}}+{\mathrm{N}}_{\mathrm{FeO}}^{\mathrm{Surf}}=1$$

(20)

$$\begin{array}{cc}\hfill \sigma & ={\sigma }_{\mathrm{CaO}}^{\mathrm{Pure}}+\frac{RT}{A_{\mathrm{CaO}}}\ln \frac{{\mathrm{N}}_{\mathrm{CaO}}^{\mathrm{Surf}}}{{\mathrm{N}}_{\mathrm{CaO}}^{\mathrm{Bulk}}}={\sigma }_{{\mathrm{SiO}}_2}^{\mathrm{Pure}}+\frac{RT}{A_{{\mathrm{SiO}}_2}}\ln \frac{{\mathrm{N}}_{{\mathrm{SiO}}_2}^{\mathrm{Surf}}}{{\mathrm{N}}_{{\mathrm{SiO}}_2}^{\mathrm{Bulk}}}={\sigma }_{{\mathrm{Al}}_2{\mathrm{O}}_3}^{\mathrm{Pure}}+\frac{RT}{A_{{\mathrm{Al}}_2{\mathrm{O}}_3}}\ln \frac{{\mathrm{N}}_{{\mathrm{Al}}_2{\mathrm{O}}_3}^{\mathrm{Surf}}}{{\mathrm{N}}_{{\mathrm{Al}}_2{\mathrm{O}}_3}^{\mathrm{Bulk}}}\hfill \\ & ={\sigma }_{\mathrm{MgO}}^{\mathrm{Pure}}+\frac{RT}{A_{\mathrm{MgO}}}\ln \frac{{\mathrm{N}}_{\mathrm{MgO}}^{\mathrm{Surf}}}{{\mathrm{N}}_{\mathrm{MgO}}^{\mathrm{Bulk}}}={\sigma }_{\mathrm{MnO}}^{\mathrm{Pure}}+\frac{RT}{A_{\mathrm{MnO}}}\ln \frac{{\mathrm{N}}_{\mathrm{MnO}}^{\mathrm{Surf}}}{{\mathrm{N}}_{\mathrm{MnO}}^{\mathrm{Bulk}}}={\sigma }_{\mathrm{FeO}}^{\mathrm{Pure}}+\frac{RT}{A_{\mathrm{FeO}}}\ln \frac{{\mathrm{N}}_{\mathrm{FeO}}^{\mathrm{Surf}}}{{\mathrm{N}}_{\mathrm{FeO}}^{\mathrm{Bulk}}}\hfill \end{array}$$

(21)

where i is the composition of slag; σ is the surface tension of slag, 10⁻³ N·m⁻¹; ${\sigma }_i^{\mathrm{Pure}}$ is the surface tension of pure i, 10⁻³ N·m⁻¹; A_i is the molar surface area of molten pure i, 10⁻⁴ m²/mol; N₀ is the Avogadro constant, mol⁻¹; V_i is the molar volume of pure molten i, L/mol; ${\mathrm{N}}_i^P$ is the mole fraction of i in P phase (P = surf is the surface phase, P = bulk is the bulk phase), %.

The foaming index can be obtained by substituting the viscosity, surface tension, and density of slag in Table 4 into Equation (15). Furthermore, the relationship between the nitrogen capacity of the slags and the foaming index can be obtained, as shown in Figure 6. It can be seen that the increase in the slag foaming index and the increase in the nitrogen capacity of slag hinder the nitrogen absorption of molten steel, which is consistent with the production practice results of the electric arc furnace [28]. When the slag in the electric arc furnace is foaming well, a good submerged arc can be realized, which can significantly reduce the nitrogen absorption in the smelting process.

It can be seen from Figure 6 that the foaming index of 1# slag is the largest. Slag with a good foamability is more conducive to hindering the nitrogen pickup of molten steel. This confirms the experimental results obtained for the minimum nitrogen pickup in molten steel with a slag basicity of 1.5—i.e., 1# slag—over 0–40 min, as shown in Figure 2. The foaming index of 2# slag is smaller than that of 1# slag. Since the 2# slag produced Ca₂SiO₄ with a high melting point (as shown in Figure 4b), it is likely to exist as solid particles at 1873 K in the slag. According to the previous research [29], a small particle size could induce the formation of foam slag, which is beneficial to hindering the nitrogen pickup of molten steel; thus, the final nitrogen mass fraction of 2# slag is the smallest (as shown in Figure 2).

4.2. Relation of Optical Basicity of Slag with Nitrogen Capacity

In 1978, Duffy J A et al. [30] proposed the concept of optical basicity (Λ). Its calculation equation is shown in Equation (22).

$$\Lambda ={\displaystyle \sum _{i=1}^{\mathrm{n}}{x}_i}{\Lambda }_i$$

(22)

According to the compositions of the experimental slags, Equation (22) can be simplified to Equation (23).

$$\Lambda =\frac{1}{B}({\mathrm{N}}_{Ca\mathrm{O}}\cdot {\Lambda }_{\mathrm{CaO}}+{\mathrm{N}}_{\mathrm{MgO}}\cdot {\Lambda }_{\mathrm{MgO}}+2{\mathrm{N}}_{{\mathrm{SiO}}_2}\cdot {\Lambda }_{{\mathrm{SiO}}_2}+3{\mathrm{N}}_{{\mathrm{Al}}_2{\mathrm{O}}_3}\cdot {\Lambda }_{{\mathrm{Al}}_2{\mathrm{O}}_3}+{\mathrm{N}}_{\mathrm{FeO}}\cdot {\Lambda }_{\mathrm{FeO}}+{\mathrm{N}}_{\mathrm{MnO}}\cdot {\Lambda }_{\mathrm{MnO}})$$

(23)

$$B={\mathrm{N}}_{\mathrm{CaO}}+{\mathrm{N}}_{\mathrm{MgO}}+2{\mathrm{N}}_{{\mathrm{SiO}}_2}+3{\mathrm{N}}_{{\mathrm{Al}}_2{\mathrm{O}}_3}+{\mathrm{N}}_{\mathrm{FeO}}+{\mathrm{N}}_{\mathrm{MnO}}$$

(24)

where Λ is the optical basicity of slag and Λ_i is the optical basicity of oxide. We set the optical basicity of pure CaO as 1; the optical basicity of other oxides is shown in

Table 5. Optical basicity of oxides.

Oxide	CaO	MgO	SiO2	Al2O3	MnO	FeO
Λ	1	0.92	0.48	0.68	0.95	0.93

[31]; x_i is the mole fraction of oxygen ions in the oxide and N is the mole fraction of each component in the slag.

Substituting the compositions of the experimental slags into Equation (23), their optical basicity can be calculated as shown in

Table 6. Optical basicity of the experimental slag.

No.	1#	2#	3#	4#	5#	6#	7#
Λ	0.759	0.777	0.800	0.776	0.782	0.783	0.775

. Then, Figure 7 can be obtained. It can be seen that the nitrogen capacity decreased with the increase in the optical basicity of the slag. This phenomenon is consistent with previous studies [14,21] and can be explained by assuming that the nitride ions are combined with a network of SiO₂ or Al₂O₃. The relationship between lgΛ and lgC_N was obtained by regression, as shown in Equation (25), where the correlation coefficient R² = 0.929.

$$\lg C_{\mathrm{N}}=-5.59\lg \Lambda -12.41$$

(25)

4.3. Effect of Slag Compositions on Equilibrium Distribution Ratio of Nitrogen

In the process of electric arc furnace smelting, the nitrogen in the gas phase will react with liquid steel, as shown in Equation (26). The equilibrium distribution ratio of nitrogen between slag and steel L_N is generally used as a parameter for the measurement of the denitrification ability of molten slag. The greater L_N is, the stronger the denitrification ability of the slag is. The calculation of L_N is shown in Equation (28).

$$\frac{1}{2}{\mathrm{N}}_2=[\mathrm{N}] \Delta G^{\mathsf{\theta }}=3600+23.9T$$

(26)

$$k_{26}=\frac{[\%\mathrm{N}]f_{\mathrm{N}}}{P_{{\mathrm{N}}_2}^{1/2}}$$

(27)

$$L_{\mathrm{N}}=\frac{(\%\mathrm{N})}{[\%\mathrm{N}]}=\frac{f_{\mathrm{N}}}{k_{26}}\cdot C_{\mathrm{N}}\cdot P_{{\mathrm{O}}_2}^{-3/4}$$

(28)

In accordance with the Gibbs free energy, as shown in Equation (26), the equilibrium constant k₂₆ = 0.0448 can be obtained at 1873 K. The oxygen partial pressure at the steel–slag interface $P_{{\mathrm{O}}_2}$ can be calculated by Equation (30), where $a_{[\mathrm{s}i]}$ and $a_{(\mathrm{s}i{\mathrm{O}}_2)}$ can be calculated by Factsage, and the reaction equilibrium constant k₂₉ can be calculated using the Gibbs free energy. The values of C_N in different slags are shown in Table 3. In summary, the calculation results were substituted into Equation (28) to obtain L_N. The influences of the slag compositions on L_N are shown in Figure 8. It was found that L_N decreases with the increase in basicity and the content of MgO in slag—that is, the denitrification ability decreases. L_N increases with the increase in Al₂O₃—that is, the denitrification ability increases.

$${\left[\mathrm{Si}\right]+\mathrm{O}}_2{=(\mathrm{SiO}}_2), \Delta G^{\mathsf{\theta }}=-947700+198.7T$$

(29)

$$k_{29}=\frac{a_{({\mathrm{SiO}}_2)}}{a_{[\mathrm{Si}]}{P}_{{\mathrm{O}}_2}}$$

(30)

4.4. Effect of Slag Compositions on the Mass Transfer Coefficient of Nitrogen Pickup

The reaction speed of slag and molten steel at high temperature is fast, so it is generally considered that the mass transfer of the slag layer and the liquid phase of steel are the rate-determining steps in the nitrogen absorption reaction [32]. The nitrogen pickup reaction speed between slag and molten steel is controlled by two factors [16]: one is the mass transfer of nitrogen in slag and the other is the mass transfer of nitrogen in molten steel. The mass transfer process is expressed by mass flow J. The calculation of the nitrogen pickup mass flow of slag is shown in Equation (31).

$$J_{\mathrm{N}}^{\mathrm{s}}={\beta }_{\mathrm{s}}(C_{\mathrm{s}}-C_{\mathrm{s}}^i)$$

(31)

The calculation of the nitrogen pickup mass flow in molten steel is shown in Equation (32).

$$J_{\mathrm{N}}^{\mathrm{m}}={\beta }_{\mathrm{m}}(C_{\mathrm{m}}-C_{\mathrm{m}}^i)$$

(32)

where β_s and β_m are the mass transfer coefficients of nitrogen in slag and steel, cm/s; C_s and C_m are the nitrogen concentrations in slag and steel, respectively, g/cm³; and $C_{\mathrm{s}}^i$ and $C_{\mathrm{m}}^i$ are the nitrogen concentrations on the slag side and the steel side at the slag–steel interface, g/cm³, respectively.

In the steady state, the two mass flows should be equal, as shown in Equation (33).

$$J_{\mathrm{N}}^{\mathrm{s}}=-J_{\mathrm{N}}^{\mathrm{m}}$$

(33)

Meanwhile, there is an equilibrium distribution of nitrogen concentration at the interface between the slag and molten steel, as shown in Equation (34).

$$h=\frac{C_{\mathrm{s}}^i}{C_{\mathrm{m}}^i}$$

(34)

where h is the distribution ratio of nitrogen expressed in mass concentration (g/cm³). Then, Equation (35) can be obtained.

$$J_{\mathrm{N}}=\frac{1}{\frac{1}{{\beta }_{\mathrm{s}}\cdot h}+\frac{1}{{\beta }_{\mathrm{m}}}}(C_{\mathrm{m}}-\frac{C_{\mathrm{s}}}{h})=\frac{1}{\beta }(C_{\mathrm{m}}-\frac{C_{\mathrm{s}}}{h})$$

(35)

When expressed by the nitrogen content in molten steel, Equation (35) can be transformed into Equation (36) [17].

$$-\frac{\mathrm{d}[\%\mathrm{N}]}{\mathrm{d}t}=k_{\mathrm{N}}\frac{A}{V}([\%\mathrm{N}]-\frac{(\%\mathrm{N})}{L_{\mathrm{N}}})=k_{\mathrm{N}}\frac{A}{V}((1+\frac{W_{\mathrm{m}}}{L_{\mathrm{N}}{W}_{\mathrm{s}}})[\%\mathrm{N}]-\frac{W_{\mathrm{m}}}{L_{\mathrm{N}}{W}_{\mathrm{s}}}{[\%\mathrm{N}]}_0)$$

(36)

where k_N is the total mass transfer coefficient, $k_{\mathrm{N}}=\frac{1}{{\beta }_{\mathrm{s}}\cdot h}+\frac{1}{{\beta }_{\mathrm{m}}}$, cm/s; W_m is the mass of molten steel, g; W_s is the mass of slag, g; A is the slag–steel interface area, cm²; and V is the volume of molten steel, cm³.

Equation (37) can be obtained by integrating it with Equation (36).

$$-\frac{1}{1+\frac{W_{\mathrm{m}}}{L_{\mathrm{N}}{W}_{\mathrm{s}}}}\ln \frac{{[\%\mathrm{N}]}_0}{(1+\frac{W_{\mathrm{m}}}{L_{\mathrm{N}}{W}_{\mathrm{s}}})[\%\mathrm{N}]-\frac{W_{\mathrm{m}}}{L_{\mathrm{N}}{W}_{\mathrm{s}}}{[\%\mathrm{N}]}_0}=k_{\mathrm{N}}\frac{A}{V}\mathrm{t}$$

(37)

The interface area between slag and molten steel A under this experimental condition is only the surface area A₁ of the molten steel in the crucible. The diameter of the crucible is 53 mm and the A/V value is 0.2321 cm⁻¹. The mass of molten steel in the crucible is about 600 g and the mass of slag liquid is 36 g. Referring to the kinetic model shown in Equation (37), we substituted the experimental data into the model for calculation. The fit between the kinetic model and the experimental results is shown in Figure 9. It can be seen that the model calculation results fit well with the experimental data results.

The nitrogen pickup mass transfer coefficient of 2# slag with a basicity of 2.0 is 1.48 × 10⁻⁴ cm/s, meaning that the slag has a stronger ability to hinder the nitrogen pickup of molten steel. With the increase in the Al₂O₃ content in the slag, the viscosity of the slag increases, while the density and surface tension decrease, leading to an increase in the foaming index of the slag. Slag 4# with Al₂O₃ = 7.5% has the lowest nitrogen pickup mass transfer coefficient of 1.35 × 10⁻⁴ cm/s. However, with the increase in the MgO content in the slag, high-melting-point SiO₂ and wollastonite are precipitated, which is not conductive to the slag covering the molten steel. Slag 6# with MgO = 7.5% has the highest nitrogen pickup mass transfer coefficient of 1.97 × 10⁻⁴ cm/s.

5. Conclusions

In the present work, the effect of EAF slag compositions on the nitrogen content of steel was evaluated. The results obtained showed that:

(1)

With the increase in the slag basicity and the MgO content in slag, the nitrogen pickup amount and the nitrogen pickup rate of molten steel increase. The test with MgO = 7.5% had the highest nitrogen pickup rate and the highest nitrogen pickup mass transfer coefficient, which were 0.21 × 10⁻⁴%/min and 1.97 × 10⁻⁴ cm/s, respectively. With the increase in the Al₂O₃ content in slag, the nitrogen pickup amount of molten steel decreased and the nitrogen pickup rate decreased. The test with Al₂O₃ = 7.5% in slag has the lowest nitrogen pickup rate and the lowest nitrogen pickup mass transfer coefficient of 0.08 × 10⁻⁴%/min and 1.35 × 10⁻⁴ cm/s, respectively.

(2)

Increasing the foaming index of slag and reducing the optical basicity of slag will increase the nitrogen capacity of slag, which is conducive to hindering the nitrogen pickup of molten steel. The relationship between the slag optical basicity and nitrogen capacity can be expressed as: lgC_N = −5.59lgΛ − 12.41.

(3)

The nitrogen equilibrium distribution ratio L_N between slag and molten steel decreases with the increase in the basicity, increases with the increase in Al₂O₃, and decreases with the increase in MgO.