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 SiO
2 and Al
2O
3, 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).
(2) When the slag contains SiO
2, Al
2O
3, and other network oxides, nitrogen reacts with SiO
2 and Al
2O
3 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).
where
CN is the nitrogen capacity of slag; (N
0) is the nitrogen content in slag, %;
is the partial pressure of nitrogen in the gas phase, kPa;
is the partial pressure of oxygen in the gas phase, kPa;
k is the equilibrium constant of nitrogen dissolution reaction;
is the activity of O
0 in slag;
is the activity coefficient of N atom in slag.
Equation (9) can be changed into Equations (11) and (13) [
15] in the present slag:
The seven slags contain network oxides such as SiO
2 and Al
2O
3. 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 SiO
2 in the seven slags as Al
2O
3,
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
and
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.
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-SiO
2-MgO-A1
2O
3-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):
where
Σ is the slag foaming index, s;
μ is the viscosity, Pa·s;
ρ is the density, kg/m
3; 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.
According to reference [
23], the slag density at 1673 K can be calculated by empirical Equation (16).
where
ρ: slag density, 10
3 kg/m
3; (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).
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-SiO
2-Al
2O
3-MgO-MnO-FeO slag system in the present study, Equation (18) can be expressed as Equation (21). Moreover,
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.
and
are known values from references [
26,
27]. Combining Equations (20) and (21),
and
σ can be calculated. The surface tensions of different slags are shown in
Table 4.
where
i is the composition of slag;
σ is the surface tension of slag, 10
−3 N·m
−1;
is the surface tension of pure
i, 10
−3 N·m
−1;
Ai is the molar surface area of molten pure
i, 10
−4 m
2/mol; N
0 is the Avogadro constant, mol
−1;
Vi is the molar volume of pure molten
i, L/mol;
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 Ca
2SiO
4 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).
4.4. 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).
The calculation of the nitrogen pickup mass flow in molten steel is shown in Equation (32).
where
βs and
βm are the mass transfer coefficients of nitrogen in slag and steel, cm/s;
Cs and
Cm are the nitrogen concentrations in slag and steel, respectively, g/cm
3; and
and
are the nitrogen concentrations on the slag side and the steel side at the slag–steel interface, g/cm
3, respectively.
In the steady state, the two mass flows should be equal, as shown in Equation (33).
Meanwhile, there is an equilibrium distribution of nitrogen concentration at the interface between the slag and molten steel, as shown in Equation (34).
where
h is the distribution ratio of nitrogen expressed in mass concentration (g/cm
3). Then, Equation (35) can be obtained.
When expressed by the nitrogen content in molten steel, Equation (35) can be transformed into Equation (36) [
17].
where
kN is the total mass transfer coefficient,
, cm/s;
Wm is the mass of molten steel, g;
Ws is the mass of slag, g;
A is the slag–steel interface area, cm
2; and
V is the volume of molten steel, cm
3.
Equation (37) can be obtained by integrating it with Equation (36).
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.