A Mathematical Model for the Reduction Stage of the AOD Process. Part II: Model Validation and Results

Abstract

A process model was proposed by Järvinen and co-authors for modelling the side-blowing decarburisation stage of the Argon-Oxygen Decarburisation (AOD) process. In Part I, a new mathematical model was derived for the reduction stage and coupled with the decarburisation model developed earlier. This paper, Part II, considers the validation of the model for the reduction stage with full-scale production data from a 150 t AOD converter in operation at Outokumpu Stainless Oy, Tornio Works, Finland. The results indicate that the model can accurately predict the end composition of the steel bath. Moreover, the model can be used to study rate phenomena during the reduction stage. Model predictions suggest that the reduction rate of chromium oxides is controlled initially by mass transfer of silicon onto the reaction surface and later by the diffusive mass transfer of chromium oxides in the slag droplets. Sensitivity of the model predictions to different initial bath temperatures, blowing times, ferrosilicon particle sizes and ferrosilicon feed rates was studied.

1. Introduction

Argon-Oxygen Decarburisation (AOD) is the primary process in modern stainless steel melt shops and its main process stages are decarburisation and subsequent reduction of slag. Despite dilution of the blowing mixture with N₂ or Ar in the side-blown stage, the Cr₂O₃ content of the slag increases usually to a level of 30 to 40 wt-% by the end of decarburisation. Therefore, the degree of success of the reduction of the chromium oxide –rich decarburisation slag is critical for the overall profitability of the process. Furthermore, a high chromium oxide content of the final slag should be avoided for environmental reasons, as the AOD slag can release noticeable amounts of chromium.¹⁾ From a temporal perspective, the length of the reduction stage is relatively short compared to the decarburisation stage and hence has a smaller effect on the tap-to-tap time.

During the reduction stage, argon is blown through tuyéres to promote mixing and emulsification of top slag. Argon blowing rates are typically in the order of 0.7 Nm³/min per 1 ton of molten steel.^2,3) Reductants, such as FeSi and Al, and fluorspar are added in order to reduce chromium oxide in the slag and decrease the viscosity the slag, respectively. Most modern AOD melt shops operating with low-sulphur raw materials utilise a single slag practice, in which the same slag is used during reduction of slag and subsequent desulphurisation.⁴⁾ Upon successful reduction of slag, the AOD slag consists mainly of CaO and SiO₂, while the Cr₂O₃ content is decreased to less than 2 wt-%.⁵⁾ Reduction of slag is also a prerequisite for efficient desulphurisation, which, although excluded in this paper, is critical for the cleanliness of the stainless steel melt.

In Part I,⁶⁾ it was concluded that although numerous reaction models have been developed for the AOD process, there are only a few models that explicitly cover the emulsification of slag and rate phenomena during the reduction stage. Then, using an approach based on the modified law of mass action, a new mathematical model for the reduction stage was proposed and coupled with the mathematical model for side-blowing decarburisation developed by Järvinen et al.^7,8) This paper, Part II, focuses on the validation of the model with full-scale production data from a 150 t AOD converter at Outokumpu Stainless Oy, Tornio Works, Finland.

2. Experimental

2.1. Validation Data

The validation data consists of production data from five heats conducted at Outokumpu Tornio Works with an AOD converter having a nominal capacity of 150 tonnes. The starting point for the simulations was the sampling at the beginning of the reduction stage, while the end point was the sampling at the end of the reduction stage, respectively. Compositions of the steel and slag samples taken before the reduction stage are presented in Tables 1 and 2, respectively. In Table 2, the category “Other” was used to denote the various slag species (such as B₂O₃, TiO₂ and V₂O₃) that were found in the slag samples but were not considered by the model. The steel and slag samples were analysed with an Optical Emissions Spectrometer (OES) and an X-Ray Fluorescence (XRF) Spectrometer.

Table 1. Bath composition and temperature before the reduction stage.

Heat	T [K]*	Bath composition [wt-%]
		Cr	Mn	Si	C	Ni
1	1996	15.47	0.67	0.01	0.00876	8.43
2	2039	15.90	0.65	0.01	0.004	8.3
3	2034	15.90	0.66	0.02	0.00886	8.4
4	2035	15.90	0.74	0.01	0.00528	8.3
5	2039	16.30	0.64	0.01	0.00406	8.4

*  Highest temperature measured by the temperature probe.

Table 2. Slag compositions before the reduction stage.

Heat	Slag composition [wt-%]
	FeO	Cr2O3	MnO	SiO2	CaO	MgO	Al2O3	Other
1	1.7	39.6	2.4	8.5	43.0	1.5	1.7	1.5
2	2.3	37.3	3.1	10.7	40.6	2.2	2.1	1.7
3	2.1	38.2	2.8	9.1	42.4	1.9	1.8	1.7
4	2.6	37.6	2.7	8.2	43.4	2.2	1.5	1.7
5	2.6	36.1	2.3	10.2	40.9	4.2	1.8	1.9

75-ferrosilicon, silicon manganese, lime, dolomite and fluorspar were added in all the heats. Additionally, stainless steel scrap was added in heat 5. The measured average compositions and the amounts of the additions are shown in Table 3. Feeding of all the additions was started immediately at the beginning of the reduction stage.

Table 3. Description of the additions.

Material	Composition [wt-%]				Amount of addition [kg]
					per 1 kg of top slag
	Fe	Si	Mn	C	Heat 1	Heat 2	Heat 3	Heat 4	Heat 5
75FeSi	23.8	75	0	0.04	0.16	0.16	0.17	0.18	0.15
SiMn	10.3	29.1	60.2	0.036	0.08	0.10	0.09	0.09	0.12
Stainless	73.1	0.57	0	0.057	0.00	0.00	0.00	0.00	0.10
steel scrap

Material	Composition [wt-%]				Amount of addition [kg]
					per 1 kg of top slag
	CaO	MgO	CaF2	C	Heat 1	Heat 2	Heat 3	Heat 4	Heat 5
Lime	99	1	0	0.8	0.15	0.20	0.18	0.20	0.23
Dolomite	56	39	0	0	0.16	0.19	0.17	0.18	0.17
Fluorspar	0	0	92	0.4	0.09	0.10	0.09	0.10	0.08

In the studied heats, the duration of argon-blowing was six minutes, while the blowing rates roughly corresponded to the typical blowing rates discussed earlier. As stated in the derivation of the model,⁶⁾ the plume diameter and the interfacial velocity at the steel-slag interface are considered independent from the gas flow rate. Therefore, the gas flow rate has no direct influence on the emulsification phenomena.

2.2. Modelling Parameters

The AOD Converter Process Simulator employs numerous physical and chemical parameters as well as parameters related to operating practice of an AOD converter. The blowing mixture, gas flow rates, length of the treatment as well as timing, type, quantity and properties of additions are adjustable via user interface. The modelling parameters used in this paper are presented in Table 4.

Table 4. Simulated converters and model parameters.

Property	Value	Ref
Nominal capacity [t]	150	–
dPlume [m]	1.5	9)
hBath [m]	1.93	–
hNozzle [m]	0.4	–
Time step [s]	1	–
ε	0.2	7)
λL [W/(m·K)]	30	10)
λG [W/(m·K)]	0.1	11)
λS [W/(m·K)]	0.1	12)
ΦSlag [W/m2]	4000	7)
ΦLining [W/m2]	12500	7)
µL [Pa·s]	0.0049	13)
tres [s]	20
dp [mm]	50
Feed rate [kg/min], CaO	2000
Feed rate [kg/min], others	1000
Loss of lining thickness per heat [mm]	10	14)

A uniform particle size d_p = 50 mm was assumed for 75FeSi, SiMn and stainless steel scrap, while the effective heat conductivities were estimated with equations provided in Part I. More precisely, it was assumed that the effective heat conductivity and melting behaviour of stainless steel scrap corresponds to that of carbon steel scrap. It was assumed that fluorspar forms lime with a stoichiometric ratio. In addition, the carbon content of the lime was not taken into account in the simulations. The feeding rate of the additions was assumed to be 2000 kg/min for lime and 1000 kg/min for others.

The converter geometry affects, for example, the height of the steel bath and the thickness of the top slag layer. The effect of refractory wear on the converter geometry was taken into account as a loss of refractory lining thickness, which was set to 10 mm per heat based on laser measurements.¹⁴⁾ The number of previous heats with the same lining was defined individually for each simulated heat. Reactions between the top slag and the refractory lining were taken into account with an average dissolution rate of refractory material into the top slag, which was calculated from the loss of refractory lining thickness per heat. Here, it was assumed that half of the refractory wear is associated with the reduction stage.¹⁵⁾ Composition of the doloma lining was approximately 41 wt-% MgO, 57 wt-% CaO, 0.7 wt-% SiO₂ and 0.7 wt-% Fe₂O₃. The latter was taken as FeO in the simulations.

The only actual fitting parameter used in the model is the residence time of the slag droplets in the steel bath. As pointed out by Mietz et al.,¹⁶⁾ in reality there is a distribution of different droplet sizes with residence times that vary correspondingly. The model presented this paper considers only one average droplet size and therefore, only a single value is needed for the residence time. Model experiments have shown that residence times increase with increasing interfacial velocity and decrease with increasing droplet size.¹⁶⁾ Moreover, the degree of emulsification is characteristically lower for eccentric blowing than for centric blowing,¹⁷⁾ which indicates that residence times should be shorter with eccentric blowing.

While the information on the residence times of slag droplets in the AOD process is scarce, some useful comparison can be extracted from experiments in ladle metallurgy. Mietz et al.¹⁶⁾ approximated the residence time as 60 s for a mean slag droplet size of 0.4 mm. In their desulphurisation model, Lachmund et al.¹⁸⁾ approximated an average residence time of five seconds for a mean droplet size of 0.8 mm. Despite some similarities, it should be taken into account that in the AOD process, the blowing rates are substantially higher than in ladle metallurgy. Furthermore, the density difference between steel bath and slag is higher.

As the residence time only affects the surface area of the slag droplets, it defines how long it takes for the system to reach its equilibrium. At first, all the heats were modelled with different residence times and it was observed that with large values, the system reached a state finitely close to its equilibrium. Figure 1 illustrates the effect of different residence times on the predicted changes in Cr and Si contents in heat 3.

Fig. 1.

Predicted Cr and Si contents in heat 3 with different residence times for the slag droplets.

The end compositions of the steel samples were generally close to the equilibrium composition predicted by the model. Therefore, a residence time could be chosen so that it would the shortest discrete length of time sufficient for the system to reach a state finitely close to its equilibrium within the duration of the heats. Using this approach, the residence time was set to t_res = 20 s for all the simulated heats.

3. Results

3.1. Predicted end Compositions

Comparison of steel samples and model predictions are provided in Table 5. It is apparent that the predicted Mn and Si contents were slightly higher than in the samples, while the predicted C contents were generally lower than in the samples. For the five heats studied, the mean squared errors in the predicted end contents of Cr, Mn, Si and C were 0.05, 0.03, 0.03 and 0.0052 weight percent units, respectively, while the mean squared error in predicted end temperature was 19 K.

Table 5. Comparison of steel samples and model predictions after the reduction stage.

Heat	Type	T [K]	Bath composition [wt-%]
			Cr	Mn	Si	C	Ni
1	Sample	1991*	18.02	1.49	0.38	0.0163	7.97
	Predicted	1938	18.16	1.52	0.34	0.0143	7.97
2	Sample	1947*	18.01	1.53	0.31	0.0152	7.95
	Predicted	1949	18.12	1.61	0.34	0.0100	7.88
3	Sample	1976*	18.16	1.52	0.40	0.0166	8.00
	Predicted	1965	18.18	1.55	0.40	0.0141	7.97
4	Sample	1947*	18.13	1.54	0.40	0.0198	7.97
	Predicted	1958	18.06	1.55	0.47	0.0108	7.89
5	Sample	1959*	18.12	1.57	0.37	0.0162	7.99
	Predicted	1939	18.14	1.57	0.38	0.0092	8.01

*  Highest temperature measured by the temperature probe.

Taking into account the limited representativeness of the slag samples before the reduction stage, the predicted slag compositions also agree reasonably well with the slag samples (see Table 6). The FeO, Cr₂O₃, MnO contents are reasonably well predicted, but the predicted SiO₂ contents are systematically lower than in the samples. The mean squared errors in the predicted end contents of FeO, Cr₂O₃, MnO and SiO2 were 0.81, 0.93, 0.24 and 2.25 weight percent units, respectively. It is apparent that the predicted CaO contents are too high and the predicted MgO contents too low compared to the slag samples. Again, the category “Other” was used to denote the various slag species that were found in the slag samples but were not considered by the model.

Table 6. Comparison of slag samples and model predictions after the reduction stage.

Heat	Type	Slag composition [wt-%]
		FeO	Cr2O3	MnO	SiO2	CaO	MgO	Al2O3	Other
1	Sample	1.1	1.6	0.3	29.7	56.4	8.5	1.6	0.6
	Predicted	0.1	1.0	0.1	27.7	58.8	6.7	1.4	4.3
2	Sample	0.4	0.6	0.3	29.2	58.1	8.8	1.9	0.6
	Predicted	0.1	1.1	0.1	26.8	58.3	7.6	1.6	4.5
3	Sample	0.8	1.0	0.4	29.9	56.7	8.9	1.7	0.6
	Predicted	0.1	0.9	0.1	27.1	59.1	6.9	1.4	4.3
4	Sample	0.8	0.9	0.3	28.4	58.0	9.4	1.5	0.7
	Predicted	0.1	0.6	0.1	25.7	60.5	7.4	1.1	4.4
5	Sample	1.4	4.4	0.4	27.2	55.5	8.8	1.6	0.7
	Predicted	0.1	1.1	0.1	25.9	58.8	8.4	1.3	4.2

3.2. Predicted Changes in Bath Composition and Temperature

Figures 2, 3, 4, 5, 6 illustrate the predicted Cr, Si and Mn content of the steel bath with respect to processing time in the reduction stage in heats 1–5. At first, Si and Mn contents increase sharply due to addition of FeSi and SiMn. Shortly thereafter, Cr content starts to increase rapidly, until the driving force starts to diminish after 4 minutes of processing. During 75FeSi feed, the silicon content of the bath is defined by the difference between the melting rate of 75FeSi and the oxidation rate of Si, while the accumulation of manganese is defined by the melting rate of SiMn and the reduction rate of MnO.

Fig. 2.

Predicted Cr, Mn and Si contents in heat 1.

Fig. 3.

Predicted Cr, Mn and Si contents in heat 2.

Fig. 4.

Predicted Cr, Mn and Si contents in heat 3.

Fig. 5.

Predicted Cr, Mn and Si contents in heat 4.

Fig. 6.

Predicted Cr, Mn and Si contents in heat 5.

Figure 7 illustrates the predicted changes in bath temperature in heat 2. It should be noted that initial temperatures used in the simulations were the maximum temperatures that could be measured by the temperature probe before its breakdown, and thus it is obvious that the predicted end temperatures of the steel bath must be lower than the measured ones. However, previous modelling results⁸⁾ suggest that the actual initial bath temperature should be less than 2100 K.

Fig. 7.

Predicted bath temperature in heat 2.

The sensitivity of the reduction rate of Cr₂O₃ to temperature was studied using three different initial bath temperatures of 1984 K, 2034 K and 2084 K for heat 3, with the temperature probe measurement being represented with the value of 2034 K. The predicted end Cr contents for the initial bath temperatures of 1984 K, 2034 K and 2084 K were 18.19 wt-%, 18.18 wt-% and 18.16 wt-%, respectively, and thus the difference in the predicted Cr content varied only 0.03 weight percent units between the lowest and the highest simulated temperature. With this in mind, the accuracy of the initial temperature measurement should have only a minor effect on the predicted end content of the steel bath.

3.3. Rate Phenomena during the Reduction Stage

Because the chemical reactions are expressed as simple oxidation/reduction reactions, which are reaction steps for more complex reactions, it is possible to observe the behaviour of various intermediate oxides. The reduction rates of species in the surface element are used here to illustrate the rate phenomena during the reduction stage. Using average rates for the whole surface element, the reduction rate of species to the bulk phases can be expressed mathematically as:   

$$\text{Reduction} \text{rate}=-{\displaystyle \sum }_{\text{k}=1 }^{{\text{N}}_{\text{R}}}{\text{R}}_{\text{k}}^{\prime \prime }{\overline{\nu }}_{\text{i}, \text{k}}{\text{A}}_{\text{SE}}$$(1)

where ${\overline{\nu }}_{\text{i}, \text{k}}$ is the mass-based stoichiometric coefficient of species i in reaction k, ${\text{R}}_{\text{k}}^{\prime \prime }$ is the reaction rate of reaction k and A_SE is the total reaction area in the surface element.

Figure 8 depicts the simulated reduction rate of Fe, Cr, Mn and Si in heat 3. The results suggest that FeO and MnO are the first species to start reducing during the reduction of slag, although they are quickly followed by Cr₂O₃, which comprises a far larger proportion of the top slag. The reduction rate of Cr₂O₃ and oxidation rate of Si starts to diminish towards the end of the treatment, suggesting that the system is close to its equilibrium composition. Oxidation of C was negligible in the simulated heats.

Fig. 8.

Reduction rate of slag species in heat 3.

The temperature dependence of the Cr reduction rate in heat 3 is depicted in Fig. 9 using three different initial bath temperatures for the reduction stage: 1984 K, 2034 K and 2084 K. Again, the actual temperature probe measurement is represented here with the value of 2034 K. The results suggest that the differences in the reduction rates of Cr with the studied initial bath temperatures are marginal.

Fig. 9.

Temperature dependency of Cr reduction rate in heat 3.

The oxygen supply of slag species can be derived from their reduction rate. Figure 10 illustrates the simulated changes in oxygen supply of FeO, Cr₂O₃, MnO and SiO₂ in heat 3. It is apparent that the oxygen supply by MnO and FeO is significant only during the first minute of processing. Thereafter, the reduction reaction of Cr₂O₃ supplies most of the oxygen consumed in the oxidation reactions.

Fig. 10.

Oxygen supply of FeO, Cr₂O₃, MnO and SiO₂ in heat 3.

In the following, the concept of a control factor is used for assessing the rate controlling effect of the mass transfer of different species by comparing the composition at the slag droplet surface and in the corresponding bulk phase. The control factor may be defined as follows:   

$$\text{Control} \text{factor}=1-{\mathrm{\Gamma }}_{\text{i}, \text{L}}\frac{{\text{y}}_{\text{i}}^{\text{SE}}}{{\text{y}}_{\text{i}}^{\text{Bath}}}-{\mathrm{\Gamma }}_{\text{i}, \text{G}}\frac{{\text{y}}_{\text{i}}^{\text{SE}}}{{\text{y}}_{\text{i}}^{\text{Plume}}}-{\mathrm{\Gamma }}_{\text{i}, \text{S}}\frac{{\text{y}}_{\text{i}}^{\text{SE}}}{{\text{y}}_{\text{i}}^{\text{Slag}}}$$(2)

where Γ are binary variables predefined 1 for species present in the phase and 0 for others. The values for y are obtained from the compositions solved at each time step. Figures 11 and 12 show the calculated control factors for Si and Cr₂O₃ in heats 3 and 5, respectively. It is observable that the reduction rate of Cr₂O₃ is controlled initially by the mass transfer of Si to the reaction surface. Subsequently, as the Si content of the bath increases and Cr₂O₃ content of the top slag decreases simultaneously, diffusive mass transfer of Cr₂O₃ in the slag droplets begins to control the reduction rate.

Fig. 11.

Control factors of Si and Cr₂O₃ in heat 3.

Fig. 12.

Control factors of Si and Cr₂O₃ in heat 5.

3.4. Emulsification of Slag

Figure 13 illustrates the average slag droplet size, interfacial velocity and critical velocity as a function of time in heat 3. It is apparent that the interfacial velocity fulfilled the emulsification criterion, i.e. exceeded the critical interfacial velocity, throughout the process stage. In this heat, the average interfacial velocity and average critical interfacial velocity were 1.53 m/s and 0.54 m/s, respectively.

Fig. 13.

Droplet size, interfacial velocity and critical interfacial velocity in heat 3.

Due to the same equation for slag droplet size employed in the models, the results compare well with the droplet sizes suggested by Mietz et al.¹⁶⁾ and Lachmund et al.¹⁸⁾ Sulasalmi et al.¹³⁾ studied the emulsification of slag in the AOD process using a Computational Fluid Dynamics model based on the Volume of Fluid (VOF) method and reported that the dominant droplet size varied between 1–2 mm and 2–3 mm, while the weighted average droplet diameters varied between 3.12 to 3.63 mm. However, due to the relatively coarse grid employed in the study, the smallest droplets might not be identified by the CFD-model. Simulated slag droplet diameters for tundish are typically smaller than 1 mm.¹⁹⁾ Many physical water-experiments have also been reported in the literature.^{16,17,20,21,22)} Frohberg et al.²⁰⁾ reported mean diameters ranging from 2.3 to 2.8 mm, while Savolainen et al.²²⁾ observed average droplet sizes in the range of 2.0 to 8.5 mm.

In addition to the equation proposed by Oeters,²³⁾ two other equations were tested alongside for comparison. The equation proposed by Asai²⁴⁾ predicted relatively large droplets sizes in excess of 10 mm, thus being substantially large compared to results in the literature. The equation presented by Sulasalmi et al.¹³⁾ produced negative values using the critical interfacial velocities employed in the model.

Figure 14 displays the simulated surface area of the emulsified slag droplets and the degree of emulsification in heat 3. It is apparent that the surface area of the emulsified droplets, being in the order of hundreds or thousands of square meters, is far larger than the oval steel-slag interface around the plume eye.

Fig. 14.

Surface area of the slag droplets and degree of emulsification in heat 3.

4. Discussion

4.1. Model Predictions

The predictions for the end composition of the steel bath were found to be well in line with the measurements conducted at Outokumpu Stainless Oy, Tornio Works, Finland. The compositions of the steel bath and the top slag were described using average compositions and due to efficient mixing in the AOD converter, the assumption of one average steel bath composition does not seem to cause significant error. The results indicated that in most of the studied heats, the predicted Cr and Si contents were slightly higher than in the samples. The predicted carbon contents were also lower than the carbon contents found in the samples, which is partly due to the fact that the dissolution of carbon from the added lime was not taken into account in the simulations.

However, some notable inaccuracies still prevail with respect to slag composition. It is apparent that the too high predicted Si contents of the steel bath are reflected in the too low predicted SiO₂ contents of the top slag. Moreover, the predicted CaO contents were higher and the predicted MgO contents lower than in the samples. This inaccuracy is caused largely by the assumption that all CaF₂ forms CaO with a stoichiometric ratio. The fluorine from the fluorspar additions was assumed to end up to the category denoted as “Other” and, consequently, the predicted mass fractions of these species in the end content of the top slag were several weight percent units higher than measured.

With respect to predicted of top slag composition, the limit in accuracy is defined to a great extent by the accuracy and representativeness of the slag samples taken before the reduction stage. It is essential to note that the AOD slag is relatively heterogeneous after the decarburisation period; the difficulty of representative sampling is accentuated by the fact that the top slag is partly solid at this point. Therefore, the initial slag composition of the reduction stage should be held approximate and should not be used as a basis for rigorous optimisation of modelling parameters.

The measurement scale of the temperature probes was proven insufficient for measuring the initial temperature of the steel bath. However, it was deduced that the measured temperatures are less than 50 K below the actual values and with this in mind, the predicted end temperatures, which were systemically lower than the measured end temperatures, appeared reasonable. Subsequently, the sensitivity of the reduction rate of Cr₂O₃ to temperature was studied and it was concluded that decreasing or increasing the initial temperature of the reduction stage by 50 K had only a minor effect on the reduction rates and the predicted end contents.

Using a desktop computer, the typical calculation times of the reduction stages of the studied heats were less than 5 minutes, being only a fraction of the typical calculation times reported for CFD-based approaches, such as the decarburisation model proposed by Andersson et al.²⁵⁾

4.2. Rate Phenomena

The results of this study indicate that reduction of FeO and MnO occurs during the first minute of argon blowing during the reduction stage. The bulk of the FeO and MnO is reduced by Si according to the following reactions:

  

$$\left(\text{FeO}\right)+\frac{1}{2}\underset{\_}{\mathrm{S}\mathrm{i}}\rightleftharpoons \underset{\_}{\mathrm{F}\mathrm{e}}+\frac{1}{2}\left({\text{SiO}}_2\right)$$(3)

  

$$\left(\text{MnO}\right)+\frac{1}{2}\underset{\_}{\mathrm{S}\mathrm{i}}\rightleftharpoons \underset{\_}{\mathrm{M}\mathrm{n}}+\frac{1}{2}\left({\text{SiO}}_2\right)$$(4)

Subsequently, as Si starts to dissolve and mix into the steel bath, the reduction rate of Cr₂O₃ is closely linked to the oxidation rate of Si, suggesting that the main reduction mechanism of Cr₂O₃ can be expressed by:

  

$$\left({\text{Cr}}_2{\text{O}}_3\right)+\frac{3}{2}\underset{\_}{\mathrm{S}\mathrm{i}}\rightleftharpoons 2\underset{\_}{\mathrm{C}\mathrm{r}}+\frac{3}{2}\left({\text{SiO}}_2\right)$$(5)

Nakasuga et al.^26,27) have studied the recovery rate of chromium from stainless steel slag using a kinetic reduction reaction model proposed by Shibata et al.²⁸⁾ In these studies, it was suggested that the reduction rate of Cr₂O₃ increases with increasing temperature. Görnerup & Lahiri²⁹⁾ reported that increased temperature both decreased the incubation time and increased the reduction rate of Cr₂O₃. In this paper, the temperature dependency of the chromium reduction rate was simulating heat 3 using three different initial bath temperatures for the reduction stage. The differences in the chromium recovery rate were found negligible.

Throughout the reduction of slag, there is a thermodynamic potential for reduction of chromium oxides by carbon. In spite of a suitable temperature window,³⁰⁾ in the simulated heats the reduction of slag droplets by carbon was found to be inconsequential vis-à-vis the total reduction rate of Cr₂O₃. In the literature, it has been was suggested that reduction of Cr₂O₃ by C continues at a slow rate throughout the reduction period.^31,32)

The simulation results indicated that during initial moments of the reduction stage, MnO had the highest oxygen supply, followed by FeO. Görnerup & Lahiri²⁹⁾ studied the reduction of EAF slag and postulated likewise that there is a pronounced incubation period for reduction of Cr₂O₃ in the slag, but no observable incubation time for FeO. In contrast to the results of this paper, Wei et al.³²⁾ proposed that FeO, followed by MnO, has the highest initial oxygen supply rate, but also suggested that Cr₂O₃ supplies the bulk of the oxygen towards the end of the treatment. Regarding the oxygen supply by FeO and MnO, it is necessary to note that the heats studied by Wei et al.³²⁾ have markedly lower Cr, Mn and Si contents than the heats studied in this paper.

The rate-controlling mass transfer of species was studied and it was suggested that the reduction of rate of Cr₂O₃ is controlled initially by mass transfer of Si in the steel phase and subsequently by mass transfer of Cr₂O₃ in the slag phase. Similar observations have been made with stainless steel slags by Görnerup & Lahiri³³⁾ and Nakasuga et al.^26,27)

4.3. Emulsification of Slag

The droplet size equation²³⁾ used in the model was compared to other equations for slag droplet size presented in the literature.^13,24) It was found that the equation proposed by Asai²⁴⁾ yields too large droplet sizes, which was suggested also by Sulasalmi et al.¹³⁾ Using this equation, the predicted surface area of the emulsified slag droplets would be smaller. Moreover, according to surface renewal theory, the mass transfer of slag species would be considerably slower than with the relatively small droplet sizes observed in this paper. The equation presented by Sulasalmi et al.,¹³⁾ which is a best linear fit to their modelling results, produced negative values with the given initial values and hence no comparison could be provided.

As stated earlier, a fully liquid slag has been assumed in the model. In the AOD process, fluorspar is added in order to lower the viscosity of slag and empirical observations confirm that the top-slag is fully liquid during the treatment. However, without the addition of fluorspar, the dissolution rate of lime and dolomite would be very slow³⁴⁾ and consequently the added lime and limestone would remain at least partially solid. Therefore, the assumption of a liquid top slag would not hold under such circumstances.

In the studied melts, the mass transfer coefficients for species in the steel bath and slag species varied between 7.34–7.81×10^–4 m/s and 0.46–1.09×10^–4 m/s, respectively. For a 120 t AOD converter, Wei & Zuo³⁵⁾ reported mass transfer coefficients in the range of 0.73–3.84×10^–4 m/s for the solute. This difference is largely due to the relatively small size of the emulsified slag droplets compared to oxygen bubbles.

4.4. Practical Considerations

The purpose of the reduction of slag is to reduce the loss of chromium to slag. Moreover, efficient process practices aims to minimise lead time and use of argon. The rate-limiting steps identified in this paper are discussed briefly below.

It has been suggested that higher gas flow rates increase the amount of droplets formed, but decrease their size, thus contributing to higher specific surface area of emulsified slag droplets¹⁷⁾ and more efficient mass transfer.²⁰⁾ Higher gas flow rates also promote nitrogen removal,²⁾ which is one of the objectives of the treatment. A practical limit for increasing the flow rate is set by for example the relatively high price of argon gas and more intensive vibration of the vessel,^36,37) which results in higher equipment wear.

It was identified that the reduction rate of Cr₂O₃ is controlled initially by melting and dissolving of Si into the steel bath. In the AOD process, violent stirring promotes short mixing times^38,39) and effective dispersion of reductant additions.⁴⁰⁾ Therefore, it can be assumed that melting is the ratecontrolling step. Smaller particle sizes increase the specific surface area of the melting particles and thus shorten the melting time, although not linearly, as discussed in Part I. Moreover, it has been suggested that smaller particles are more evenly distributed in the AOD converter.⁴¹⁾ In conclusion, when the overall reduction rate of Cr₂O₃ is constrained by mass transfer of Si, faster feeding rate of 75FeSi and smaller particle size should enable a more efficient reduction of slag.

The deduction presented above was then tested by simulating heat 3 using different 75FeSi feed rates and average particle sizes. At first, heat 3 was simulated using three different 75FeSi feed rates: 1000 kg/min, 1500 kg/min and 2000 kg/min, with the first representing the actual feed rate employed in the process. The results shown in Fig. 15 suggest that higher feed rates of 75FeSi should enable a considerably faster reduction of slag. Secondly, the same heat was simulated with three different 75FeSi average particle sizes: 40 mm, 50 mm and 60 mm, with 50 mm representing the actual average particle size. Figure 16 illustrates the calculated amount of solid 75FeSi as a function of time in the reduction stage. Although the smaller particle sizes markedly decreased the amount of solid 75FeSi present in the steel bath at the beginning of the reduction stage, the effect on the reduction rate was found negligible.

Fig. 15.

Effect of 75FeSi feed rate on the predicted changes in Cr and Si contents in heat 3.

Fig. 16.

Effect of average particle size on the amount of solid 75FeSi in heat 3.

Finally, the effect of blowing time on the predicted end content of the steel bath in heat 3 was studied. Figure 17 shows that prolonging the length of the reduction stage from 6 to 7 minutes had only a marginal impact on the chromium yield. Actually, the results suggest that nearly the same degree of reduction could be achieved with a shorter blowing time of 5 minutes.

Fig. 17.

Effect of blowing time on the predicted changes in Cr, Mn and Si contents in heat 3.

4.5. Future Work

At this point, reduction by aluminium was not included in the model, but can be added for comparison in future work. Moreover, descriptions for desulphurisation and nitrogen removal can be incorporated into the model. The modelling approach taken in this paper can be used to assess the effect of top slag composition on the decarburisation rate during the decarburisation stage.

The applicability of the parameters employed in the UIP model for concentrated stainless steel melts remains equivocal, as most interaction parameters are determined for pure liquid iron as the solvent. In addition, a more generalised model should be found for calculating the activities of the slag species.

5. Conclusions

Based on the validation, the following conclusions are postulated:

(1) The approach based on the modified law of mass action, which is used for simultaneous solution of thermodynamic equilibrium at the reaction surface and constraining mass transfer onto the reaction surface, is computationally efficient and well-suited for modelling mass-transfer controlled reversible reactions at high temperatures during the reduction stage.

(2) The bulk of the reduction reactions should occur between steel bath and the emulsified slag droplets due to both the large surface area of the droplets and efficient mass transfer resulting from their small size.

(3) Before any 75FeSi is dissolved in the bath, FeO and MnO in the top slag are reduced by Cr in the bath. Reduction of Cr₂O₃ does not commence before addition and dissolving of reductants. Moreover, reduction of top slag by carbon is insignificant in relation to the total reduction rate of the top slag during the reduction stage.

(4) The reduction rate of Cr₂O₃ is limited initially by melting and dissolution of FeSi and subsequently by diffusive mass transfer of Cr₂O₃ in the slag droplets. In order to expedite the melting and dissolution of ferrosilicon into the steel bath, high ferrosilicon feed rates should be used. In the studied cases, the particle size of 75FeSi had only a minor effect on the reduction rate of Cr₂O₃.

Acknowledgements

This research is a part of the Energy Efficiency & Lifecycle Efficient Metal Processes (ELEMET), a research program coordinated by the Finnish Metals and Engineering Competence Cluster (FIMECC). Outokumpu Stainless Oy, Finnish Funding Agency for Technology and Innovation (TEKES), Graduate School in Chemical Engineering (GSCE) and Academy of Finland (projects 258319 and 26495) are gratefully acknowledged for funding this work.

The authors would like to thank Dr Paavo Hooli, Mr Pentti Kupari and Mr Veikko Juntunen from Outokumpu Stainless Oy for their support and productive discussions regarding the paper. In addition, Mr Tuomas Alatarvas is acknowledged for support. Mr Aaron Bergdahl is acknowledged for revising the language of this paper.

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