Kinetics Analysis of Iron Oxide Reduction by Solid Carbon in HIsmelt Ironmaking Slag

Abstract

The HIsmelt process is a new molten reduction ironmaking technology with lower energy consumption and carbon emissions than the traditional blast furnace ironmaking route. In the HIsmelt smelting process, the reaction process between solid carbon and iron-bearing slag has its own characteristics. To investigate the kinetic mechanism of iron oxide reduction in slag, the degree of conversion was characterized by measuring the change of CO content of the generated gas during the experiments and analyzed by combining the model fitting method. The experimental results showed the highest agreement with the Avrami-Erofeev equation. The rate-controlling mechanism for the reduction of iron oxides in the slag was judged to be the random nucleation and subsequent growth of the products. In the study, the rate-controlling mechanism and the kinetic parameters of the reduction reaction of iron oxide in slag have been obtained.

1. Introduction

The HIsmelt process is a new molten reduction ironmaking technology, which mainly consists of a rotary kiln process for charge heating and pre-reduction and a SRV (smelting reduction vessel) process for ore smelting.^1,2,3,4,5) The process was originally developed in cooperation with Rio Tinto, Australia, and Nucor Steel, USA, and was formally introduced to China in 2012 in Shouguang, Shandong Province, with stable production in 2018.⁶⁾ HIsmelt melting reduction ironmaking process uses iron ore fines and coal fines as raw materials. Compared to the traditional blast furnace ironmaking route, coking of coal and lumping of iron ore fines are avoided. Therefore, it reduces energy consumption and carbon emissions.^7,8,9,10,11)

In the whole process, iron ore and melt are first transported to the rotary kiln for preheating to 800°C and initial reduction and then sprayed into the molten pool of the main reactor SRV furnace through a water-cooled lance with N₂ as the transport carrier gas. The preheated pulverized coal is also fed into the molten pool of the SRV furnace through the carrier gas, which reduces the iron oxides in the slag to metallic iron and complete the carburization.^12,13) The oxygen lances in the upper part of the SRV furnace inject oxygen-rich hot air with 30%–40% oxygen content at about 1200°C into the furnace. Then, it reacts with CO and H₂ produced by the reduction reaction of the molten pool and the decomposition of pulverized coal to release heat and heat the molten pool. This provides the energy required for various reactions.¹⁴⁾ The generation of gas in the melting pool and the overflow of carrier gas from the melting pool cause the melting pool to surge strongly, a phenomenon that accelerates the heat exchange between the melting pool and the upper space.¹⁵⁾

It is crucial to clarify the reaction mechanism between solid carbon and iron-bearing slag due to the unique reaction process of HIsmelt. The reaction between solid carbon and iron-bearing slag has been extensively studied by many scholars. Min¹⁶⁾ et al. systematically investigated the reaction kinetic mechanism of slag with different FeO contents using mass spectrometry techniques and showed that for FeO contents above 30 wt%, the chemical reaction at the gas/carbon interface would be the rate-limiting step. Meanwhile, for slags with FeO content below 5 wt%, the reduction mechanism will change from a chemical reaction at the carbon surface to a mixed control step of the chemical reaction and FeO transfer. In a recent study, Khasraw¹⁵⁾ et al. used a similar technique to investigate the effect of different carbon-containing materials on the reduction kinetics of iron-bearing slags. They found that the first stage of the reaction is controlled by the chemical reaction at the carbon surface and the second stage is controlled by the chemical reaction and three-dimensional diffusion. The second stage is influenced by a mixed control mechanism of chemical reactions and three-dimensional diffusion.

It was shown that the FeO concentration in the slag has a great influence on the reduction kinetics of solid carbon in iron-bearing slag.^16,17,18) Reduction kinetics studies for the HIsmelt process slag composition have not been reported. Therefore, the study characterizes the conversion rate as a function of time by measuring the CO concentration of the reduction-generated gas for the HIsmelt slag composition. A model-fitting approach was used to determine the rate-controlling mechanism and the kinetic parameters of this reduction reaction.

2. Materials and Methods

In this study, the reduction process of iron-bearing slag in the HIsmelt melting reduction ironmaking process was investigated. According to the HIsmelt plant production data, the simplified slag is a Fe_xO–CaO–SiO₂–MgO–Al₂O₃ five-member slag system. The slag composition at the beginning of the smelting cycle is shown in Table 1. According to the calculated slag composition ratio, the slag is configured using analytically pure chemical reagents. A cylindrical high-purity graphite block with a diameter of 8 mm and a height of 8 mm was used as the reducing agent.

Table 1. Slag composition at the beginning of the smelting cycle (%).

Composition	CaO	SiO2	MgO	Al2O3	FeO	Fe3O4
Content	19.40	15.73	4.88	8.92	2.38	48.68

The melting reduction experiment was performed in a tube resistance furnace with a CO gas analysis recorder with a resolution of 1 ppm (One in a million). The experimental setup for this experiment is shown in Fig. 1. During the experiment, argon gas is passed through the tube furnace at a flow rate of 5 L/min via a flow meter to ensure an inert atmosphere in the experimental setup. The crucible containing the chemical reagents composing the slag was placed in the tube furnace and heated to the experimental temperatures (1475°C, 1500°C, 1525°C) at a heating rate of 300°C/h and held for 2 hours to allow the slag to fully melt. The cylindrical graphite grains were put into the slag using a quartz tube. The CO gas analysis recorder measured and recorded the CO content in the gas as a function of time.

Fig. 1. Schematic diagram of the melting reduction experimental setup. (Online version in color.)

3. Results and Discussion

3.1. Variation of the Conversion Rate of Melting Reduction Reaction at Different Temperatures

As shown in Eq. (1), the iron oxides in the slag are reduced by the solid carbon to produce CO, which is the total reaction between the iron oxides in the slag and the solid carbon. According to the widely used reaction model,^19,20,21) the gas produced by the reaction forms a gas film between the solid carbon and the slag.

  

$$\mathrm{F}\text{e}{\mathrm{O}}_{\mathrm{x}}+\mathrm{C}=\mathrm{F}\mathrm{e}{\mathrm{O}}_{(\mathrm{x}-1)}+\mathrm{C}\mathrm{O}$$(1)

As shown in Fig. 2. The reduction reaction can be decomposed into the following steps.

Fig. 2. Schematic diagram of the mechanism of iron oxides in solid carbon reduction slag. (Online version in color.)

• CO at the slag-gas interface reduces the iron oxides in the slag to produce metallic iron and CO₂;

• The reaction of CO₂ with solid carbon at the solid carbon-gas interface forms CO.

• Material transport of iron oxides form the slag to the slag-gas interface.

• Diffusion of CO and CO₂ in the gas film.

The oxygen content in the gas generated by the reduction reaction is the oxygen loss from the iron oxide in the slag. According to the oxygen balance, the relationship can be obtained as follows.

  

$$-J_{\text{O}}=J_{\text{CO}}$$(2)

Where J_i is the molar flux of the material phase (mol·m⁻³·s⁻¹). Assuming CO as the ideal gas, only two components, CO and Ar, are present in the reacted gas. Therefore, the value of J_CO can be calculated from the known argon flow rate and the CO content in the gas as shown in Eq. (3).¹¹⁾

  

$$J_{\text{CO}}=\frac{273}{298}\cdot F_{\text{Ar}}\cdot \frac{Pc{t}_{\text{CO}}}{22.4\times Pc{t}_{\text{Ar}}}\cdot \frac{1}{A}$$(3)

Where A is the reaction area (m³). F_Ar is the flow rate of argon (mol/s) and Pct_i is the content of component i in the gas. Therefore, the reduction reaction produces CO as shown in Eq. (4). The conversion rate α at a certain moment can be expressed as the ratio of the amount of CO produced at this moment to the total amount of CO generated by the reaction, as shown in Eq. (5).

  

$$\mathrm{\Delta }\text{CO}=A\cdot {\int }_0^t{J}_{\text{CO}}={\int }_0^t\frac{273}{298}\cdot F_{\text{Ar}}\cdot \frac{Pc{t}_{\text{CO}}}{22.4\times Pc{t}_{\text{Ar}}}\cdot dt$$(4)

  

$$\alpha =\frac{{\int }_0^{t}Pc{t}_{\text{CO}}}{{\int }_0^{t_0}Pc{t}_{\text{CO}}}$$(5)

Where ΔCO denotes the amount of CO produced by the reduction reaction; t₀ denotes the total reaction time; α is the degree of conversion.

Figure 3 shows the curves of CO concentration in the melting reduction gas with time at different temperatures. The CO concentration in the generated gas showed a trend of increasing and then decreasing. When the experimental temperature is higher the peak CO concentration appears earlier. The CO concentration decreases more sharply after the peak, while at a lower temperature (1475°C) the CO concentration changes more slowly. The CO detection value in the gas generated from the melting reduction experiment at higher temperatures disappeared first. However, the difference at different temperatures was not obvious, indicating that changing the temperature did not have a significant effect on shortening the reaction time.

Fig. 3. The plot of CO concentration detection values versus time for melting reduction reaction experiments at different temperatures. (Online version in color.)

Figure 4 shows the degree of conversion variation at different temperatures. The higher the reaction temperature for the same time, the higher the conversion rate. The degree of conversion increases with time and then decreases, and finally leveled off. From the figure, it can be seen that the phase with the greatest increase in the degree of conversion is located in the period of 0.4–0.5, which corresponds to the peak of the CO concentration curve.

Fig. 4. Relationship between conversion degree and time at different reaction. temperatures. (Online version in color.)

3.2. Model Fitting Solution for the Kinetic Constants

Equation (6) represents the dependence of the conversion rate on the degree of reaction, in which t represents the reaction time and k(T) represents the temperature dependence of the apparent rate constant.²²⁾

  

$$G(\alpha )={\int }_0^{\alpha }\frac{d\alpha }{f(\alpha )}=k(T)\cdot t$$(6)

The form of the G-function is determined by the mechanism of the reaction process. For typical reaction mechanisms, a summary was made by Vyazovkin^23,24,25) et al. The best reaction model matched by the reaction can be judged by comparing the fit match between the experimental data and each model. After the pre-fitting calculations, the models that matched well with the data of this study are shown in Table 2. Figure 5 shows the test of the models in Table 2 for the experimental data at different temperatures.

Table 2. The kinetic reaction models are used in this work.

Number	Reaction model (Code)	f (α)	G (α)
1	Three-dimensional diffusion (D6)	1.5(1+α)2/3[(1+α)1/3−1]−1	[(1+α)1/3−1]2
2	Three-dimensional diffusion (D8)	1.5(1+α)4/3[(1+α)−1/3−1]−1	[(1+α)−1/3−1]2
3	Power law (R1)	1	α
4	Contracting cylinder (R2)	2(1−α)1/2	1−(1−α)1/2
5	Contracting sphere (R3)	3(1−α)2/3	1−(1−α)1/3
6	Mampel Power law (P2/3)	2/3α−1/2	α3/2
7	Avrami-Erofeev equation (A2)	2(1−α) [−ln(1−α)]1/2	[−ln(1−α)]1/2

Fig. 5. The dependence of G (α) on reaction time (t). (Online version in color.)

Table 3 provides the parameters for the linear regression of Fig. 5, including the coefficient of determination R² and k(T). The experimental data fitted to any model had a good linear relationship with time, which indicates that it was not possible to select a response model that best fits this study by simple comparison.

Table 3. The rate constant (k) dependence on temperature for various models and the corresponding correlation coefficient (R²).

Reaction model	Temperature/K (°C)	1748 (1475)	1773 (1500)	1798 (1525)
Model 1	k(T)/s−1	0.00002517	0.00002822	0.00003279
	R2	0.9674	0.9845	0.9671
Model 2	k(T)/s−1	0.00001657	0.00001843	0.00002112
	R2	0.9753	0.9855	0.9605
Model 3	k(T)/s−1	0.0004163	0.0004559	0.0005105
	R2	0.9896	0.9834	0.9496
Model 4	k(T)/s−1	0.0003242	0.0003634	0.0004282
	R2	0.9817	0.9962	0.9860
Model 5	k(T)/s−1	0.0002628	0.0002974	0.0003604
	R2	0.9634	0.9894	0.9945
Model 6	k(T)/s−1	0.0003819	0.0004259	0.0004907
	R2	0.9766	0.9910	0.9651
Model 7	k(T)/s−1	0.0007762	0.0008587	0.0010213
	R2	0.9865	0.9878	0.9834

3.3. Apparent Activation Energy Calculation

The apparent activation energy can be calculated based on the Arrhenius relationship between the rate constant k(T) and temperature, as shown in Eq. (7).

  

$$k(T)=Aexp\left(-\frac{E}{RT}\right)$$(7)

where A is the pre-exponential factor, E is the apparent activation energy, and R is the universal gas constant (8.314 J·mol⁻¹·k⁻¹). Figure 6 shows the Arrhenius plot based on the data in Table 3. Table 4 provides E and A for the different models calculated according to the Arrhenius equation. However, the results are not sufficient to conclude which reaction model may be most consistent with the experimental data.

Fig. 6. Arrhenius plots for determining the apparent activation energy. (Online version in color.)

Table 4. Comparison of melt reduction kinetic parameters based on different reaction models and conversion rates derived from average residual sum of squares (S²) and normalized deviation (F) models with experimental values.

Reaction model	Ea/kJ·mol−1	A/s−1	S2 (×1000)	F
Model 1	138.12	0.34	13.892	4.995
Model 2	126.72	0.10	12.350	4.441
Model 3	106.60	0.64	14.659	5.271
Model 4	145.39	7.12	5.825	2.095
Model 5	164.90	21.98	9.810	3.528
Model 6	130.83	3.08	10.566	3.799
Model 7	143.24	14.63	2.781	1

The degree of fit between the experimental data and the various models was measured quantitatively by calculating the average residual sum of squares (S_j²) and normalized deviation (F) for each model, as shown in Eqs. (8) and (9). This approach was also used by Vyazovkin²⁵⁾ et al. In the equations, α|t_i j and α|t_i denotes the degree of conversion obtained from model j and experiment at reaction time t_i, and n is the number of data points. the smaller the S_j² the better the fit. Comparison between different models can be more easily achieved using F_j, which is calculated by dividing the S_j² of each model by the smallest S_j² of all models (S_min²). This will give F=1 for the model with the smallest deviation over the entire range.

  

$$S_j^2=\frac{1}{n}\sum _{i=1}^n(\alpha {|}_j^{t_i}-\alpha {|}_{experiment}^{t_i}{)}^2$$(8)

  

$$F_j=\frac{S_j^2}{S_{min}^2}$$(9)

The calculations S² and F provided in Table 4 show that the Avrami-Erofeev equation model (model 7) can best describe the melting reduction process throughout the experimental period. In fact, model 7 is a sigmoidal reaction model. Sigmoidal models represent processes whose initial and final stages demonstrate respectively the accelerating and decelerating behavior so that the process rate reaches its maximum at some intermediate values of the extent of conversion. As shown in Fig. 4, the degree of conversion shows three distinct regions:incubation, acceleration and decay. It can be observed that as the process temperature increases, the converted solids exhibit a shorter latency. It is clear from Fig. 4 that the degree of conversion increases rapidly and decreases at a faster rate as the temperature increases.

The Avrami-Erofeev equation model assumes that “germnuclei” of the new phase are distributed randomly within the solid.^26,27,28) Following a nucleation event, the grains grow throughout the old phase until the transformation is completed. It can be seen in Fig. 4, the sigmoid shape of kinetic plots may be analyzed by dividing each curve into three regions corresponding theoretically to: induction period (0 < conversion degree < 0.15), acceleratory region (0.15 < conversion degree < 0.50) and a deceleratory region (0.50 < conversion degree < 1). The induction period is dominated mainly by nucleation while the acceleratory one tends to be dominated by growth phenomena. The deceleratory region corresponds to the termination of growth upon impingement of different growth regions or at the grain boundaries.

The reduction of iron oxides to iron is an important industrial reaction in the conversion of C to CO, which is a complex solid-solid oxidoreduction reaction with kinetics. Reaction kinetics and reaction processes are closely related to chemical reaction processes. In addition, in this process, the progress of the reduction process is strongly controlled by gas diffusion and substance transport in the gas film. The reaction was successfully applied to the Avrami-Erofeev model and the coupled nucleation and growth process equations were used to describe the process. This stage can be theoretically interpreted as nucleation and one-dimensional growth of crystals at the gas/slag interface with a gradual shift to diffusion control.

Therefore, it can be judged that the solid carbon reduction of iron oxides in the HIsmelt slag is controlled by the random nucleation and subsequent growth of the products. The kinetic parameters were calculated as E=143.24 kJ·mol⁻¹ and A=14.63 s⁻¹.

4. Conclusion

The focus of this study is the reduction of FeO in synthetic HIsmelt slag (CaO–SiO₂–Al₂O₃–MgO–Fe_xO) using solid carbon. The reduction rate of FeO in the slag was measured using a gas composition analyzer and kinetic parameters were evaluated based on these results. The following conclusions can be drawn from this study.

• It was found that temperature has a strong effect on the rate of solid carbon reduction of iron Oxide in the slag, with the reduction rate increasing with increasing temperature. This is also evidenced by the significant effect of temperature on the variation of the gaseous product CO.

• The reduction of iron Oxide in slag tends to increase sharply with time in the beginning and then the rate of increase slows down. The entire reaction process conforms to the Avrami-Erofeev equation, with the rate-controlling mechanism being the random nucleation and subsequent growth of the products, which leads to the calculation of an apparent activation energy of 143.24 kJ·mol⁻¹ and a pre-exponential 14.63 s⁻¹ for this reaction process.

Conflicts of Interest

The authors declare no conflicts of interest.

Acknowledgments

This work was supported by the Science and Technology Innovation 2030-Major Project [No.: 2022ZD0119202] and the National Natural Science Foundation of China [No.: 51904026].

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