Mass-Transfer Model for Steel, Slag, and Inclusions during Ladle-Furnace Refining

Slag–steel kinetic model

A coupled-reaction model, frequently applied to describe the dephosphorization and desulfurization reactions in molten iron and the reoxidation reactions in molten steel by slag, was adopted [8, 9, 10]. The coupled-reaction kinetic model was based on the CaO–Al₂O₃–MgO–SiO₂–FeO–P₂O₅ slag and the Ca–Al–Mg–Si–Fe–P–O steel systems. Equation (1) describes the reactions between slag and steel:

The oxidation of elements including Mg, Al, Ca, Mn, Si, P, Fe in the molten steel can be expressed by eq. (1). Equation (2) describes the equilibrium constant K_M:

The desulphurization reaction was described by eq. (3), and the equilibrium constant was defined by eq. (4):

The effective equilibrium constants E_m for elements including M=Mg, Al, Ca, Mn, Si, P in the molten steel were expressed by eq. (5):

Equations (6) and (7) describe the effective equilibrium constants for the oxidation of Fe and the desulphurization reaction:

During the transfer of component M from molten steel to slag, the flux density should be constant; this was expressed by eq. (8):

where J_M is the molar flux density (mol·mm⁻²·s⁻¹), k_m is the conventional mass-transfer coefficient defined by mole/volume concentrations (mm·s⁻¹), and ρ is the density of the metal or slag phase (kg·m⁻³).

The flux densities of Fe, S, and dissolved oxygen were given by eqs (9), (10), and (11), respectively:

The concentrations of the species at the interface of molten steel and slag were calculated using eqs (12)–(17).

Equation (18) expressed the electrical neutrality and suggested that the total molar flux densities of cations and anions were equal. The oxygen activity at the interface of molten steel and slag was calculated using eq. (18):

The mass transfer of each component in the slag and molten steel was then calculated at a time step (Δt) using eqs (19) and (20), respectively. The cross-sectional area of the bath was used as the interfacial area between the metal and slag phases.

where Δ[%M] is the concentration change of a component in the metal phase (mass %) and ΔW_x is the mass change of each component (g).

Kinetic model for inclusions and steel

The inclusion and steel model was based on two-film theory. The diffusions of Mg and Ca in molten steel were assumed to be rate-controlled steps, and the shapes of the inclusions were considered to be spherical with an outer diameter (Ro) that remained constant with time.

Based on eq. (21) and the balance of Mg and Ca in the metal and inclusions, the compositions of the inclusions were given by eqs (22) and (23):

Refractory erosion

Refractory erosion affects the chemical composition of molten steel. A model was therefore developed for evaluating erosion of the refractory lining, including at the slag line and ladle wall. The reaction between slag and the slag line was modeled by the dissolution of MgO in the ladle wall into the slag. The reaction between the ladle wall and molten steel was modeled using eqs (24) and (25):

A flow chart for the computations is shown in Figure 2.

Figure 2:

Flow chart of the kinetic model.

Equilibrium constant

The equilibrium constants of the reactions [11, 12] in the model are shown in Table 1.

Activities of molten steel component

The activities of the molten steel components were calculated using the interaction parameter model proposed by Wagner [13], as given by eqs (26) and (27). The interaction coefficients [14] of the molten steel components are shown in Table 2.

Activities of slag component

The activities of the slag components were conveniently calculated using the regular solution model proposed by Landsmen [15]. The Lumsden model is given by eqs (28) and (29). The interaction energies [16] between cations of components in the slag αij are given in Table 3; the activity conversion factors [16] are given in Table 4. The activity of CaS, which could not be deduced from the model, was set as 5 [11].

Mass-transfer coefficient

The argon blowing rate was also considered in the model. The mass-transfer coefficient of the metal phase was calculated using the empirical eqs (30), (31), and (32), given by Kitamura et al. [4]

where k_m and k_s are the mass-transfer coefficients (m/s) in the film layer of liquid metal and slag phase, respectively, ε(w/t) is the stirring energy, Q_g is the Ar gas flow rate (Nm³/min), T_L and T_n are the temperatures (K) of molten steel and the gas, respectively, W is the mass of molten steel (kg), h₀ (m) and h_v (m) are the injection and bath depths, respectively, P_a is the atmospheric pressure (Pa), and d_v (m) is the diameter of the bath. The values of the parameters are given in Table 5.

Initial conditions

The initial chemical compositions of the molten steel (0.027%C–0.25%Mn–0.013%S–0.012%P–0.007%Si–0.0474%Al–0.0005%O) and slag (1.44%FeO–4.35%SiO₂–54.16%CaO–8.03%MgO–30.92%Al₂O₃–0.05%P₂O₅–0.235%MnO–0.837%CaS) were based on actual production data at the beginning of LF treatment.

Erosion rate of refractory lining

The erosion rate of the refractory lining was calculated using data from 120 heats. The erosion rate of the slag line was 0.025 mm/min for a refractory composition of 80% MgO and 20% C. The erosion rate of the ladle wall was 0.0125 mm/min for a 80%Al₂O₃–10%MgO–10%C composition.

Process parameters

The process to produce MR-T2.5 steel comprises the sequence: basic oxygen furnace (BOF) → LF → 1015×200 mm² continuous casting (CC) → hot rolling → cold rolling. The steel-making process is performed in a 100 t BOF. After tapping the ladle, slag-skimming is performed and new premelted slag then added as a deoxidizer. Samples were taken during LF refining. The operating conditions and sampling scheme are shown in Figure 3. Aluminum was added as a deoxidizer. When the temperature and composition of molten steel satisfied the target requirements, the ladle was moved to the LF station. High-basicity refining slag was used for desulphurization; Fe–Mn alloy and Ca–Al wire were added to satisfy the compositional and performance requirements. After 35 min of LF refining, Ar gas was allowed to flow at 0.05 Nm³/min for 4 min.

Figure 3:

Operating conditions in the Tangsteel plant.

Composition of molten steel and slag

Figures 4, 5, and 6 show the compositional variations in the molten steel for the various elements. The calculated results are in agreement with the industrial data. The increase in the concentration of Mg is attributed to the reaction between slag and steel (Figure 4(a)). The increase in the concentration of Ca is attributed to the reaction between slag and steel at the start of ladle refining, and sharply increased on addition of Ca; the decrease is attributed to the reaction between inclusions and steel after Ca addition (Figure 4(a)). The decrease in the concentration of Al in the molten steel is attributed to its reaction with slag; however, this sharply increased on the addition of Al, as shown in Figure 4(b). Si and Mn concentrations increased because of deoxidation of slag, as shown in Figure 4(b). The calculated results for Ca, Mg, Al, Si, and Mn were in good agreement with the industrial results. The concentration of P in the molten steel increased slightly, while that in the slag decreased due to its deoxidation, as shown in Figure 5. The high basicity and low oxidizability suppressed the rephosphorization reaction. The predicted sulfur distribution between molten steel and slag increased with refining time (Figure 6). The concentrations of SiO₂ and MnO decreased, whereas Si and Mn concentrations in the molten steel increased (Figures 4 and 7, respectively).

Figure 4:

Comparison of calculated results with industrial data as a function of time for (a) Mg and Ca and (b) Al, Si, and Mn.

Figure 5:

Comparison of calculated results and industrial data as a function of time for [P] and (P₂O₅).

Figure 6:

Comparison of calculated results and industrial data as a function of time for [S] and (S).

Figure 7:

Comparison of calculated results and industrial data as a function of time for (a) FeO and MnO and (b) Al₂O₃, SiO₂, MgO, and CaO.

With respect to the slag (Figure 7), the decrease in the concentration of FeO is attributed to deoxidation of the slag, and the calculated results agreed well with industrial results, as shown in Figure 7(a). The concentrations of CaO and MgO in slag hardly changed, as shown in Figure 7(b). The increase in the Al₂O₃ concentration of the slag is attributed to oxidation of Al in the molten steel.

Oxygen activity at the slag–molten steel interface

Figure 8 shows the predicted oxygen activity at the slag–molten steel interface and that calculated, ao, from the equilibrium of the reaction [Fe] + [O]=(FeO). ao* immediately dropped following the addition of Al. ao was larger than ao* at the beginning of the process, but their difference decreased during LF treatment. The reaction [Fe] + [O]=(FeO) at the interface was therefore not at equilibrium. The industrial result gave an activity of dissolved oxygen in molten steel of less than 5 ppm, while ao* at the slag–molten steel interface was 30–45 ppm. The oxygen activity at the slag–molten steel interface was higher than that in the molten steel; therefore, oxygen is expected to move from slag to molten steel during LF refining, even though the concentration of FeO in slag was approximately 1%.

Figure 8:

Oxygen activity as a function of time: (a) ao* at the slag–steel interface and (b) ao in molten steel from the equilibrium of the reaction Fe + O=FeO.

It should be noted that ao* depends on the slag and steel compositions and affects the coupled reactions. The amount of the slag is an important factor: first, the amount of the slag fluctuates according to different amounts of top slag and final sulfur contents in the hot metal; second, the amount of the slag differs according to the steel grade. Figure 9(a) shows the effect of Si in molten steel on ao*. Obviously, ao* decreased with increasing Si in molten steel because such Si consumes interfacial oxygen. Figure 9(b) shows the effect of slag basicity on ao*, which decreased with increasing basicity because of the corresponding decreased activity of SiO₂ in the slag. The effect of FeO in slag on ao* is shown in Figure 9(c). ao* increased with increasing concentration of FeO in the slag, presumably because of the reaction [Fe] + [O]=(FeO). Finally, the effect of slag mass on ao* is inferred from Figure 9(d): ao* increased as the slag mass increased because the FeO and SiO₂ concentrations in the slag increased.

Figure 9:

Oxygen activity at the slag–molten steel interface as a function of time: (a) Si in molten steel, (b) slag basicity, (c) slag FeO, and (d) slag mass.

Composition of inclusions

The changes in the average concentrations of MgO, CaO, and Al₂O₃ in an inclusion over time were also calculated by the model. Inclusion size is critical because it affects the metal–inclusion interfacial area. The size of the inclusions in the industrial samples was in the range of 2–5 μm, so, in the calculations, the inclusion size was set as 5 μm. Figure 10 shows the average change in the mass percent of the inclusions over time. The concentration of Al₂O₃ decreased, whereas the MgO and CaO concentrations increased because of reactions between the inclusions and steel. Particularly, the concentration of CaO in the inclusions increased rapidly after addition of Ca. The calculated changes in the Al₂O₃, MgO, and CaO concentrations were in agreement with the operational results.

Figure 10:

Inclusion mass percent as a function of time and calculated concentrations of CaO, Al₂O₃, and MgO in the inclusions.

Figure 11 shows the calculated results and observed average compositions of the inclusions in the MgO–Al₂O₃–CaO ternary system. Operation in Region A, with w_CaO of 40–60%, w_Al2O3 of 35–65%, and w_MgO of 0–20%, is most suitable for avoiding clogging of the nozzles with liquid inclusions at 1873 K. The calculated results and observed average compositions suggested that the average composition of the inclusions does not fall in the low-melting region at the end of LF treatment, as shown in Figure 11. Figure 12 shows that some of the inclusions move to the low-melting region, but most are not in the low-melting region by the end of LF treatment. Moving all inclusions into the low-melting region would require longer Ar blowing times; this is a topic for future study.

Figure 11:

Comparison of calculated results and industrial data for the average CaO, Al₂O₃, and MgO concentrations in the inclusions in the CaO–MgO–Al₂O₃ ternary system.

Figure 12:

Industrial data for the distribution of inclusions in the CaO–MgO–Al₂O₃ ternary system.

The average compositions of molten steel, slag, and inclusions can be predicted by using the proposed model.