Decarburization Kinetics of Fe–C Melt with CO₂–O₂ Mixed Gas by Isotope Tracing Method

Abstract

The partial substitution of O₂ with CO₂ in steelmaking process is an important technology to reduce CO₂ emission and recycle. In order to improve CO₂–O₂ decarburization utilization, the decarburization kinetics of Fe–C melt with CO₂–O₂ mixed gas have been studied using ¹³CO₂–¹⁸O₂ dual isotope tracing method and established the decarburization kinetic model. The results show that less than 40% of the oxygen is partially replaced by CO₂, which improves the O₂ utilization involved in the decarburization reaction and the CO₂ utilization is still more than 80%. For the rate limiting steps, regarding O₂, it is governed by the mixed control mechanism involving gas-phase mass transfer and interfacial chemical reaction; regarding CO₂, with the increase of CO₂ partial pressure, the rate limiting step changes from the mixed control to gas-phase mass transfer control only. As bath temperature increase from 1723 to 1873 K, the overall decarburization rate increases; bath temperature mainly affects O₂ decarburization rates, whereas, the rates of CO₂ are not significantly affected. The apparent activation energy of CO₂–O₂ mixed gas decarburization is 21.5 kJ·mol⁻¹.

1. Introduction

As iron and steel enterprises are large carbon dioxide (CO₂) emitters, it is of great significance to develop CO₂ utilization technology in steelmaking industry. Decarburization is undoubtedly one of the most important heterogeneous reactions occurring in the steelmaking processes.^1,2) Under the pressure of energy saving and emission reduction in the world, the conditions encountered in the development of emerging ironmaking and steelmaking technologies include complex gas environments containing O₂ and CO₂.^{3,4,5,6,7,8,9,10,11,12)} It is necessary to study the decarburization reaction kinetics of Fe–C with CO₂–O₂ mixed gas to improve CO₂–O₂ utilization in steelmaking process.

The possible reaction mechanisms between Fe–C melt and CO₂–O₂ mixed gas involve the following phenomena:

(i) Mass transfer in gas phase;

(ii) Interfacial reactions;

(iii) Mass transfer in liquid phase.

The observed rate may be dominated or influenced by one or more of these steps. There are some studies^{13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31)} on the mechanism and kinetics of decarburization of Fe–C melts with oxidizing gases using levitation and crucible techniques. Regarding CO₂ decarburization, Nomura^13,14,15,16) found that in the high concentration with carbon content higher than 0.02–0.05 mass%, the rate of decarburization was controlled primarily by gaseous mass transfer in Ar–CO–CO₂ atmospheres at 1873 K. Moreover, Sain,^17,18) and Byrne¹⁹⁾ found that the interfacial reaction step controlled the rate in CO₂–CO atmosphere at 1433–1873 K and at carbon dioxide pressures below about 0.5 atm with carbon content higher than 1 mass% and in 30–40 L·min⁻¹. However, Fruehan^20,21) found that the decarburization rate in both CO–CO₂ mixtures at high C contents was controlled primarily by diffusion in the gas film boundary layer near the surface of the liquid at 1800 K. Furthermore, Lee²⁾ developed a theoretical model to represent the decarburization kinetics of iron-carbon melts containing sulfur on the basis of a mixed-control mechanism involving gas-phase mass transfer and dissociative adsorption of CO₂. Regarding O₂ decarburization, Greenberg²²⁾ concluded that the rate controlling mechanism for the dissolution process was oxygen transport in the gas phase surrounding iron droplets levitated at 1873 K containing 0.001% oxygen. Sun²³⁾ believed that transport in the gas phase controlled the rate of decarburization or oxygen absorption before FeO generation. Widlund²⁴⁾ found that the rate depended mainly on the partial pressure of decarburizing gas (O₂) in He–O₂ mixture. Regarding CO₂–O₂ decarburization, Simento^25,26,27) concluded that the rate was mixture controlled by the O₂ and CO₂ transport in the gas phase with additional resistance arising from the interfacial reaction kinetics of CO₂. Zughbi^28,29) concluded that the gas flow rate from 8 to 4 L·min⁻¹ brought the reactions into a mixed control regime (mass transport and chemical kinetics). Yan^30,31) found that in the carbon dioxide partial pressure range of 0–1.0 atm, the decarburization mechanism of the mixed gas has changed; (1) P_CO2 = 0–0.6 atm, transport in the gas phase; (2) P_CO2 = 0.7–1.0 atm, a mixed control regime.

In summary, the decarburization kinetic models were not always quantitatively consistent due to the complex reactions. Therefore, introducing the isotope tracing method in crucible blowing experiments can distinguish the decarburization reactions due to the different mass numbers of gas molecules shown in Fig. 1.

Fig. 1.

CO₂–O₂ mixed gas decarburization mechanism. (Online version in color.)

Thus, reasonable control of injection conditions can reduce the disturbance of post combustion and two oxygen decarburization reactions so as to real-time quantitative analysis of interface reaction. In our previous works,^{32,33,34) 13}CO₂–¹⁸O₂ dual isotope tracing method was established to study the reaction behavior of Fe–C melt with CO₂–O₂ mixed gas. In this paper, the mixed gas composition and flowrates were changed to analyze the CO₂–O₂ decarburization utilization, and the rate-limiting step was determined during the decarburization process.

2. Experimental Details

2.1. Experimental Procedure

The experimental apparatus was followed by the previous work.³²⁾ An alumina tube containing 25.00±0.01 g of a metal sample heated in a high-temperature vertical tube furnace with argon (Ar, Purity ≥ 99.999%). The experimental temperature was monitored by a type-B thermocouple within the error of ±1 K. After the sample melting more than half an hour, the switchover was made from Ar to CO₂–O₂ mixed gas (CO₂, O₂ Purity ≥ 99.99%; ¹³CO₂ Purity >99%, ¹⁸O₂ Purity >98.5%). During CO₂–O₂ mixed gas blowing onto the surface of the molten alloy, a quadrupole-type mass spectrometer (Pfeiffer Vacuum, PrismaPlus QMG 220) and a mass flowmeter (error<0.1%) was used to monitor the gas composition and flowrates, respectively. After reactions, mixed gas was converted to Ar and then the samples were removed from the furnace to measure the carbon content and oxygen content in chemical analysis (HORIBA Scientific, EMIA-920V2; HORIBA Scientific, EMGA-830). The injection height was 20 mm, the inner diameter of the blowing tube was 4 mm, and the inner diameter of the outlet tube was 2 mm. The inlet flow rates of CO₂ and O₂ were also controlled by two mass flowmeters, respectively.

In our previous work,³³⁾ it was found that the liquid phase mass transfer can be ignored when the initial carbon content was larger than 1 mass%. Moreover, Wang³⁵⁾ conducted that the critical value of carbon content affected by liquid phase mass transfer was 0.6–0.1 mass%; similarly, in the study of Nomura,¹⁶⁾ the critical value was 0.02–0.05 mass%. Hence, in the present work, the metal samples with 2 mass% [C] were made up of a mixture of electrolytically pure iron and master alloy to neglect the effect of liquid phase mass transfer; the raw material components are shown in Table 1.

Table 1. The compositions of raw metal.

Chemical composition/mass%	C	S	O	N	P
pure iron	0.003	0.008	0.015	–	0.0011
master alloy	3.972	0.001	0.002	0.0016	–

Since there was no competition when P_CO2 = 0 or 1.0 atm, the decarburization rate can be calculated based on the conservation of matter using CO₂ or O₂ ordinary gases. The experimental program is shown in Table 2. Since the oxygen supply intensity of the converter was in the range of 0.8–4.5 Nm³·t⁻¹·min⁻¹, in the present condition, the total flowrate of 50 and 80 mL(STP)·min⁻¹, corresponding to the gas supply intensity of 2.0 and 3.2 Nm³·t⁻¹·min⁻¹, which can effectively reflect the decarburization process of the converter.

Table 2. The experimental program.

T (K)	Carbon content/mass%	Inner diameter of the alumina tube (mm)	Gas composition/(mL(STP)·min−1)
			18O2	13CO2
1773	2	16.2	40	10
1773	2	16.3	30	20
1773	2	16.0	20	30
1773	2	16.1	10	40
1773	2	16.7	32	48
1773	2	17.1	16	64
1723	2	17.1	40	10
1823	2	17.0	40	10
1873	2	16.2	40	10
			O2	CO2
1773	2	15.8	50	0
1773	2	17.2	0	50
1773	2	16.4	0	80

2.2. The Principle of Isotope Tracing Method

According to the mass balance, the flowrate of CO₂ at outlet had three sources: a part of uninvolved reaction, a part of generation by O₂ reacting with [C] directly and a part of CO₂ from post combustion, assumed as Q_x1, Q_x2 and Q_x3 (mL(STP)·min⁻¹), respectively. There are four destinations for O₂: the consumption reacting with [C] to generate CO₂, the consumption reacting with [C] to generate CO, the consumption of post combustion and uninvolved reaction, which flowrates were assumed as Q_y1, Q_y2, Q_y3 and Q_y4 (mL(STP)·min⁻¹) respectively. As for CO, there were two sources and one destination: generation by O₂ and [C], generation by CO₂ and [C], and the consumption of post combustion, which flowrates were assumed as Q_z1, Q_z2 and Q_z3 (mL(STP)·min⁻¹) respectively. Moreover, the flow monitoring converts different gases based on gas viscosity,^32,33,34) when CO₂-based gas, 1 mL(STP)·min⁻¹ O₂, CO and Ar (SCCM) can be converted into 1.38 mL(STP)·min⁻¹,1.20 mL(STP)·min⁻¹ and 1.50 mL·min⁻¹ CO₂ (SCCM), respectively. Therefore, the relationship based on the chemical reaction can be established simultaneously:   

$$Q_{x_1}+\frac{1}{2}{Q}_{z_2}=Q_{\alpha }\mathrm{\hspace{0.17em} };\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }{Q}_{y_1}+Q_{y_2}+Q_{y_3}+Q_{y_4}=Q_{\beta }$$(1)

  

$$(Q_{x_1}+Q_{x_2}+Q_{x_3})+1.38Q_{y_4}+1.2(Q_{z_1}+Q_{z_2}-Q_{z_3})=Q_{total}$$(2)

  

$$Q_{x_2}=Q_{y_1}\mathrm{\hspace{0.17em} };\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }{Q}_{x_3}=2Q_{y_3}=Q_{z_3}\mathrm{\hspace{0.17em} };\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }2Q_{y_2}=Q_{z_1}$$(3)

where Q_total, Q_α, Q_β are the total outlet flowrate, inlet CO₂ and O₂ flowrates, respectively.

Additionally, the quadrupole-type mass spectrometer monitored the ion currents of molecules of different mass numbers. Hence, the proportional relationship can be expressed by Eqs. (4), (5):   

$$\frac{Q_{z_2}}{Q_{z_1}}=\frac{I_{28}+I_{29}}{I_{30}};\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\frac{Q_{x_1}}{Q_{x_2}+Q_{x_3}}=\frac{I_{45}}{I_{46}+I_{47}+I_{48}}$$(4)

  

$$\frac{Q_{y_4}}{Q_{y_1}+Q_{y_2}+Q_{y_3}+Q_{y_4}}=\frac{Q_{y_4}}{Q_{\beta }}=\frac{I_{{36}_{OUT}}}{I_{{36}_{IN}}}$$(5)

where I₂₈, I₂₉, I₃₀, I₄₅, I₄₆, I₄₇, I₄₈ are the ion currents of ¹²C¹⁶O, ¹³C¹⁶O, ¹²C¹⁸O, ¹³C¹⁶O¹⁶O, ¹²C¹⁶O¹⁸O, ¹³C¹⁶O¹⁸O and ¹²C¹⁶O¹⁸O, respectively. I_36OUT and I_36IN are the ion currents of ¹⁸O¹⁸O at outlet and inlet, respectively.

Therefore, combing the Eqs. (1), (2), (3), (4), (5), the flowrates of CO₂ and O₂ participation in different reactions can be expressed by Eqs. (6), (7), (8), (9).   

$$\begin{array}{l}{Q}_{z_2}=\\ {\displaystyle \frac{10I_{45}{Q}_{total}+14Q_{\alpha }(I_{46}+I_{47}+I_{48})-10I_{45}{Q}_{\alpha }-24I_{45}{Q}_{\beta }+10.2{\displaystyle \frac{I_{{36}_{OUT}}}{I_{{36}_{IN}}}}{I}_{45}{Q}_{\beta }}{7\left(I_{45}+I_{46}+I_{47}+I_{48}\right)}}\end{array}$$(6)

  

$$Q_{x_1}=Q_{\alpha }-\frac{Q_{z_2}}{2}$$(7)

  

$$\begin{array}{l}{Q}_{y_1}=\\ {\displaystyle \frac{5Q_{total}-8.9{\displaystyle \frac{I_{{36}_{OUT}}}{I_{{36}_{IN}}}}{Q}_{\beta }+2Q_{\beta }-5Q_{\alpha }-\left(7{\displaystyle \frac{I_{30}}{I_{28}+I_{29}}}+3.5\right)Q_{z_2}}{7}}\end{array}$$(8)

  

$$Q_{y_2}=\frac{I_{30}}{2(I_{28}+I_{29})}{Q}_{z_2};Q_{y_3}=\left(1-\frac{I_{{36}_{OUT}}}{I_{{36}_{IN}}}\right)Q_{\beta }-Q_{y_1}-Q_{y_2}$$(9)

Hence, the rates of oxygen and carbon dioxide can be expressed by Eqs. (10), (11).   

$$-{\frac{dC}{dt}}_{(O_2)}=\frac{100m_C}{{\rho }_{m}V}\cdot \frac{Q_{y_1}+2Q_{y_2}}{22.4\times {10}^3}\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%\mathrm{C}\cdot \mathrm{m}\mathrm{i}{\mathrm{n}}^{-1}$$(10)

  

$$-{\frac{dC}{dt}}_{(C{O}_2)}=\frac{100m_C}{{\rho }_{m}V}\cdot \frac{\frac{1}{2}{Q}_{z_2}}{22.4\times {10}^3}\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%\mathrm{C}\cdot \mathrm{m}\mathrm{i}{\mathrm{n}}^{-1}$$(11)

where m_C, ρ_m and V are the molar mass of carbon, the melt density and volume, respectively. 22.4 × 10³ are milliliters per mole of gas at normal conditions used to convert the gas flow to moles rather than mL.

Regarding experiments with pure oxygen or pure carbon dioxide injection, since there was no competitive oxidation, the flowrates of participation can be calculated using the correction factors^36,37) and expressed by Eqs. (12), (13), (14):   

$$Q_{C{O}_{2out}}=\frac{Q_{total}}{1+1.38k_{O_2-C{O}_2}\cdot \frac{I_{32}}{I_{44}}+1.20k_{CO-C{O}_2}\cdot \frac{I_{28}}{I_{44}}}$$(12)

  

$$Q_{O_{2out}}=\frac{k_{O_2-C{O}_2}\cdot \frac{I_{32}}{I_{44}}{Q}_{total}}{1+1.38k_{O_2-C{O}_2}\cdot \frac{I_{32}}{I_{44}}+1.20k_{CO-C{O}_2}\cdot \frac{I_{28}}{I_{44}}}$$(13)

  

$$Q_{C{O}_{out}}=\frac{k_{CO-C{O}_2}\cdot \frac{I_{28}}{I_{44}}{Q}_{total}}{1+1.38k_{O_2-C{O}_2}\cdot \frac{I_{32}}{I_{44}}+1.20k_{CO-C{O}_2}\cdot \frac{I_{28}}{I_{44}}}$$(14)

where Q_CO2out, Q_COout and Q_O2out are the outlet flowrate of CO₂, CO and O₂, respectively. I₂₈, I₃₂, I₄₄ represent the ion currents of CO, O₂ and CO₂, respectively. The correction factors³⁷⁾ are as follows: k_O2–CO2 is 1.23 and k_CO–CO2 is 0.75. Therefore, the decarburization rates can be calculated using Eq. (15).   

$$-{\frac{dC}{dt}}_{(O_2\mathrm{\hspace{0.17em} }\text{or}\mathrm{\hspace{0.17em} }C{O}_2)}=\frac{100m_C}{{\rho }_{m}V}\cdot \frac{Q_{C{O}_{out}}+Q_{C{O}_{2out}}-Q_{\alpha }}{22.4\times {10}^3}\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%\mathrm{C}\cdot \mathrm{m}\mathrm{i}{\mathrm{n}}^{-1}$$(15)

In summary, the decarburization process can be analyzed in real time using the corresponding ion currents and flowrate at any time.

3. Results and Discussion

3.1. Effect of CO₂–O₂ Gas Composition on Decarburization Rate

The decarburization process in real-time were conducted in environments containing CO₂ in range of 0 to 1.0 atm with O₂ at 1773 K to investigate the effect of CO₂–O₂ gas composition. Figure 2 shows the gas flowrates involved in different reactions during the decarburization process maintaining the total flowrate at 50 mL(STP)·min⁻¹. In the case of ignoring the effect of the gas fluctuation during the gas transfer, the results indicated that at 50 mL(STP)·min⁻¹, O₂ decarburization only produced CO on the surface; as the partial pressure of CO₂ increased, the O₂ flowrate involved in post combustion was gradually larger than that involved in the decarburization reaction. Regarding CO₂, increasing CO₂ partial pressure larger than 0.6 atm, the O₂ decarburization rate was lower than that of CO₂.

Fig. 2.

The flowrates of gases involved in different reactions during the decarburization process (a) 50 mL(STP)·min⁻¹, 0% CO₂-100% O₂; (b) 50 mL(STP)·min⁻¹, 20% CO₂-80% O₂; (c) 50 mL(STP)·min⁻¹, 40% CO₂-60% O₂; (d) 50 mL(STP)·min⁻¹, 60% CO₂-40% O₂; (e) 50 mL(STP)·min⁻¹, 80% CO₂-20% O₂; (f) 50 mL(STP)·min⁻¹, 100% CO₂-0% O₂. (Online version in color.)

It was seen from Fig. 2 that there was in a stable process of decarburization, thus, the average ratio of gas participation in decarburization is shown in Fig. 3. It clearly indicated that as the increase of CO₂ partial pressure, CO₂ utilization decreased; differently, regarding O₂, the proportion of O₂ participation in decarburization first rose then fell. Furthermore, less than 40% O₂ was replaced by CO₂, which improved the utilization of O₂ involved in decarburization and the CO₂ utilization is still more than 80%. At 50 mL(STP)·min⁻¹, P_CO2 = 0.4 atm and P_O2 = 0.6 atm, the CO₂ utilization reached 87.7%, and the O₂ decarburization ratio reached 60.2%. Further, the average decarburization rates changing with mixture gas composition are shown in Fig. 4. In the range of P_CO2 = 0–0.4 atm, the overall rate increased, however, when P_CO2 increased to above 0.4 atm, it decreased. It may be because that an appropriate amount of CO₂ to substitute O₂ could inhibit the positive reaction of post combustion and improve the decarburization rate, but when the replacement ratio was larger than 40%, the effect of the competition of the carbon active sites on the interface was greater. One O₂ molecule needs two active sites to react, but one CO₂ molecule only needs one active site to react, thus, the competition active sites became the dominant factor in the decarburization rate.

Fig. 3.

The ratio of gas participation in decarburization. (Online version in color.)

Fig. 4.

The average decarburization rates changing with the partial pressure. (Online version in color.)

3.2. Development of Reaction Model

In the present work, the liquid phase mass transfer during the decarburization process was ignored. To analysis the effect of gas-phase mass transfer, the average reaction rates changing with flowrates are shown in Fig. 5. It indicated that the rate increased with the increase of the flowrate, therefore, it was reasonable to study the kinetic model based on the gas-phase mass transfer resistance combined with the effect of the interfacial reactions.

Fig. 5.

The average reaction rates changing with flowrates. (Online version in color.)

In CO₂–O₂ mixed gas atmosphere at 50–80 mL(STP)·min⁻¹, the kinetic model development was based on the mass transfer in gas phase, taking into account that there may be a controlling step on the interface reaction. More derivation process was described in the appendix. Table 3 shows the mixed rate controlling models.

Table 3. The reaction controlling models.

No.	Reaction rate controlling model	dC/dt/(mass%·s−1)
1	O2–CO2 mass transfer in gas phase	$\left(\frac{1\mathrm{\hspace{0.17em} }200A}{\rho V}\right)\left[2k_g^{\prime }ln\left(1+P_{O_2}^b\right)+k_g^{\prime }ln\left(1+P_{C{O}_2}^b\right)\right]$
2	O2–CO2 mixed control	$\left(\frac{1\mathrm{\hspace{0.17em} }200A}{\rho V}\right)\left[2\frac{k_g^{\prime }\cdot k_{c,O_2}}{k_g^{\prime }+k_{c,O_2}}ln\left(1+P_{O_2}^b\right)+\frac{k_g^{\prime }\cdot k_{c,C{O}_2}}{k_g^{\prime }+k_{c,C{O}_2}}ln\left(1+P_{C{O}_2}^b\right)\right]$
3	O2 mixed control and CO2 mass transfer in gas phase	$\left(\frac{1\mathrm{\hspace{0.17em} }200A}{\rho V}\right)\left[2\frac{k_g^{\prime }\cdot k_{c,O_2}}{k_g^{\prime }+k_{c,O_2}}ln\left(1+P_{O_2}^b\right)+k_g^{\prime }ln\left(1+P_{C{O}_2}^b\right)\right]$
4	O2 mass transfer in gas phase and CO2 mixed control	$\left(\frac{1\mathrm{\hspace{0.17em} }200A}{\rho V}\right)\left[2k_g^{\prime }ln\left(1+P_{O_2}^b\right)+\frac{k_g^{\prime }\cdot k_{c,C{O}_2}}{k_g^{\prime }+k_{c,C{O}_2}}ln\left(1+P_{C{O}_2}^b\right)\right]$

k_g is a function of experimental conditions and the geometry of the system. The gas-phase mass transfer coefficient can be calculated using Eq. (16)^38,39)   

$$k_g=\frac{D}{d}(0.32\pm 0.06){\left(\frac{r_s}{d}\right)}^{-1.5}{Re}^{0.66}{\text{Sc}}^{0.5}$$(16)

where Re (duρ/μ) and Sc (μ/ρD) are the Reynolds and Schmidt numbers, respectively; d and r_s are the diameter of the gas-blowing tube and the radius of the alumina tube, respectively; u is the gas velocity in the gas-blowing tube; and D, ρ, and μ is the diffusion coefficient, density, and viscosity of gas, respectively. The diffusion coefficient and viscosity of gas were calculated by the Chapman-Enskog equation.⁴⁰⁾ The gas mass transfer coefficient varied little with the gas composition; the k_g values are also listed in appendix. Accordingly, it was reasonable to ignore the effect of the k_g change.

Considering the interfacial reaction rate constant, k_c,O2 and k_c,CO2, can be calculated by the mixed rate control model in Table 3. When P_CO2 = 0 and 1 atm, a single gas component participated decarburization reaction and there was no interference. Since the decarburization process can be real-time monitored using online mass spectrometry,³⁴⁾ the carbon content in real time was compared with the four models, as shown in Fig. 6. Since there was a reaction between O₂ and [C] to generate CO₂ at the beginning process, the time that there was only reaction between O₂ and [C] to generate CO was as the start point. The fitted model changed as the CO₂ partial pressure increased. In the range of P_CO2 = 0–0.4 atm, the experimental data was in good agreement with model 3; differently, in the range of P_CO2 = 0.6–1.0 atm, the experimental data was in good agreement with model 2. It meant that as the CO₂ proportion increased, the rate controlling mechanism of CO₂ decarburization has changed, while O₂ remained unchanged. The average decarburization rate is also compared with the four reaction controlling models as shown in Fig. 7. It was clearer that with the CO₂ partial pressure increase, the decarburization reaction mechanism changed. The results indicated that regarding O₂, it was governed by the mixed control mechanism involving gas-phase mass transfer and interfacial chemical reaction; whereas, regarding CO₂, with the increase of CO₂ partial pressure, the rate limited step changed from the mixed control to gas-phase mass transfer control only. It was probably because under the condition of the same decarburization amount, increasing the CO₂ partial pressure led to an increase in the amount of CO generated, which inhibited the forward progress of the CO₂ decarburization reaction on the reaction interface.

Fig. 6.

Comparison of carbon content change curve and model curve (a) 50 mL(STP)·min⁻¹, 0% CO₂-100% O₂; (b) 50 mL(STP)·min⁻¹, 20% CO₂-80% O₂; (c) 50 mL(STP)·min⁻¹, 40% CO₂-60% O₂; (d) 50 mL(STP)·min⁻¹, 60% CO₂-40% O₂; (e) 50 mL(STP)·min⁻¹, 80% CO₂-20% O₂; (f) 50 mL(STP)·min⁻¹, 100% CO₂-0% O₂. (Online version in color.)

Fig. 7.

The comparison of rate controlling model and average decarburization rate. (Online version in color.)

Through the comparison of final carbon content and the analysis of the model application, the validity of the model was verified. The predicted final carbon content was also compared with chemical analysis. Since the models ignored the dissolution of oxygen in the melt and the reaction process at the beginning fluctuation, the corrections including the two factors were considered to improve the accuracy of the model. Therefore, the results of the final carbon content are listed in Table 4 and the comparison is shown in Fig. 8. It indicated that predicted final carbon content was basically consistent with the chemical analysis. The relative error of the model calculation result was approximately 1.49%. It is clear that the mixed rate controlling model adequately represents the decarburization by mixed oxidants of O₂ and CO₂ at the various ratios.

Table 4. The comparison of final carbon content.

Gas composition/(mL(STP)·min−1)		Chemical analysis		Predicted final [C]/mass%
O2	CO2	[C]/mass%	[O]/mass%	Before correction	After correction
50	0	1.59	0.012	1.52	1.53
40	10	1.65	0.026	1.61	1.63
30	20	1.66	0.017	1.58	1.59
20	30	1.70	0.047	1.63	1.66
10	40	1.64	0.012	1.70	1.70
0	50	1.80	0.008	1.77	1.78

Fig. 8.

The comparison of final carbon content. (Online version in color.)

The mixed control model in the part of P_CO2 = 0.6–1.0 atm was applied to the experimental conditions at 80 mL(STP)·min⁻¹. Figure 9 shows the variation trend of carbon content predicted by model and detected by mass spectrometry. The results showed that the experimental data was in good agreement with the kinetic model, and indicated that the model in the part of P_CO2 = 0.6–1.0 atm predicted the decarburization rate well. However, in our previous work,³³⁾ it was found the reaction of O₂ and [C] to form CO₂ at 80 mL(STP)·min⁻¹, P_CO2 = 0.2 atm, P_O2 = 0.8 atm. Therefore, regarding the part of P_CO2 = 0–0.4 atm, it was considered that the decarburization rate of oxygen was affected by the interface reaction, while CO₂ had almost no effect from the model. Figure 10 shows the decarburization rate change with bath temperature at 50 mL(STP)·min⁻¹, P_13CO2 = 0.2 atm and P_18O2 = 0.8 atm. In four experiments from 1723 to 1873 K, bath temperature mainly effected on O₂ decarburization rates, whereas, the CO₂ decarburization rates were not significantly affected by temperature. Therefore, it was also reasonable to believe that in the part of P_CO2 = 0–0.4 atm, O₂ was governed by the mixed control involving gas-phase mass transfer and interfacial reaction, and CO₂ was controlled by gas-phase mass transfer only. Additionally, the apparent activation energies of CO₂–O₂ decarburization found from the present study was 21.5 kJ·mol⁻¹. The activation energies of 30.38 kJ·mol⁻¹ and 23.2 kJ·mol⁻¹ were obtained from the works of Yan³⁰⁾ and Sain,¹⁷⁾ respectively. These values were in reasonable agreement with each other.

Fig. 9.

The comparison of carbon content change at 80 mL(STP)·min⁻¹. (Online version in color.)

Fig. 10.

The decarburization rates with temperature. (Online version in color.)

Furthermore, the reaction rate controlling models of previous workers’ investigations on the relevant CO₂-mixed gas are summarized in Table 5. The comparison indicated that in the atmosphere such as CO₂–CO, there was only one decarburization reaction; with the changes of the flowrate, there was a transition from the interfacial reaction control to the gas-phase mass transfer control or mixed control. But in this work, in order to avoid the instability of the reaction area, the influence of gas-phase mass transfer must be considered when the total flowrates were small. Additionally, regarding CO₂–O₂ mixed gas, the model of this work in the part of P_CO2 = 0.6–1.0 atm was similar with the results of Simento²⁷⁾ whose experiment range was P_CO2 = 0.5–0.8 atm. Meanwhile, the result that the decarburization rate control mechanism changed with the gas partial pressure in CO₂–O₂ mixed gas was also consistent with Yan’s³⁰⁾ results.

Table 5. Comparison with previous workers’ studies on the reaction rate controlling model.

Authors	Gas composition	Reaction rate controlling model	−dC/dt/(mass%·s−1)
Byrne19)	Gas Flowrate: 40 L·min−1 CO–CO2 mixtures PCO2<0.1 atm	CO2 interfacial reaction control	$kA{P}_{C{O}_2}$
Sain17)	Gas Flowrate: 30–40 L·min−1 CO–CO2 or CO2–Ar mixtures PCO2 = 0.1–0.5 atm	CO2 interfacial reaction control	$k_f{P}_{C{O}_2}$
Fruehan20)	Gas Flowrate: 26.7 L·min−1 CO–CO2 mixtures PCO2 = 0.022–0.090 atm	CO2 mass transfer in gas phase	$\frac{m}{RT}ln\left(\frac{1+P_{C{O}_2}}{1+P_{C{O}_2}^{*}}\right);\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }{m}_0=\frac{D_{CO-C{O}_2}}{{\delta }_0}=k_g^0$
Simento27)	Gas Flowrate: 10 L·min−1 PO2 = 0.04–0.1 atm PCO2 = 0.1–0.16 atm PN2 = 0.3 atm PHe = 0.5 atm	O2 mass transfer in gas phase and CO2 mixed control involving gas-phase mass transfer and interfacial reaction	$\left(\frac{1\mathrm{\hspace{0.17em} }200A}{\rho V}\right)\left[\begin{array}{l}2k_g^{0}ln\left(1+P_{O_2}^b\right)\\ +\frac{k_g^0{k}_c{C}_v}{k_g^0+k_c{C}_v}ln\left(1+P_{C{O}_2}^b\right)\end{array}\right]$
Lee2)	Gas Flowrate: 1.0–1.5 L·min−1 CO2–Ar mixtures PCO2 = 0.1–0.2 atm	CO2 mixed control involving gas-phase mass transfer and interfacial reaction	$\begin{array}{l}\left(\frac{1\mathrm{\hspace{0.17em} }200A}{\rho V}\right)\frac{k_G^0{k}_R(1+Kf{\theta }_u{C}_S)}{(k_G^0+k_R)+(k_G^0+k_R{\theta }_u)Kf{C}_S}\\ ln\left(1+P_{C{O}_2}^b\right)\end{array}$
Yan30)	Gas Flowrate: 0.15 L·min−1 CO2–O2 mixtures PCO2 = 0–1 atm	PCO2 = 0–0.6 atm mass transfer in gas phase PCO2 = 0.7–1 atm mixed control involving gas-phase mass transfer and interfacial reaction	PCO2 = 0–0.6 atm $\left(\frac{1\mathrm{\hspace{0.17em} }200A}{\rho VR{T}_f}\right)\left[\begin{array}{l}{k}_{g,C{O}_2}ln\left(1+P_{C{O}_2}^b\right)+\\ 2k_{g,O_2}ln\left(1+P_{O_2}^b\right)\end{array}\right]$ PCO2 = 0.7–1.0 atm $\left(\frac{1\mathrm{\hspace{0.17em} }200A}{\rho V}\right)k_1{P}_{C{O}_2}+\left(\frac{2\mathrm{\hspace{0.17em} }400A}{\rho VR{T}_f}\right)k_{g,O_2}ln\left(1+P_{O_2}^b\right)$
Present work	Gas Flowrate: 0.05–0.08 L·min−1 CO2–O2 mixtures PCO2 = 0–1 atm	PCO2 = 0–0.4 atm O2 mixed control and CO2 mass transfer in gas phase PCO2 = 0.6–1 atm mixed control involving gas-phase mass transfer and interfacial reaction	PCO2 = 0–0.4 atm $\left(\frac{1\mathrm{\hspace{0.17em} }200A}{\rho V}\right)\left[\begin{array}{l}2\frac{k_g^{\prime }\cdot k_{c,O_2}}{k_g^{\prime }+k_{c,O_2}}ln\left(1+P_{O_2}^b\right)\\ +k_g^{\prime }ln\left(1+P_{C{O}_2}^b\right)\end{array}\right]$ PCO2=0.6–1.0 atm $\left(\frac{1\mathrm{\hspace{0.17em} }200A}{\rho V}\right)\left[\begin{array}{l}2\frac{k_g^{\prime }\cdot k_{c,O_2}}{k_g^{\prime }+k_{c,O_2}}ln\left(1+P_{O_2}^b\right)\\ +\frac{k_g^{\prime }\cdot k_{c,C{O}_2}}{k_g^{\prime }+k_{c,C{O}_2}}ln\left(1+P_{C{O}_2}^b\right)\end{array}\right]$

In summary, the reaction rate controlling model was established and its rationality was verified. It was truly that the gas jet velocity was lower than the oxygen lance blowing velocity in the actual converter, therefore, this work was focused on controlling at a lower gas velocity but the gas supply per unit mass was maintained close to the actual steelmaking. It provided a theoretical basis for future experiments with high flow velocity.

4. Conclusion

Using ¹³CO₂–¹⁸O₂ dual isotope tracing method, mixture gas utilization in decarburization process was investigated. In addition, a decarburization kinetic model with CO₂–O₂ has been developed. Findings from this study are summarized in the following:

(1) Less than 40% O₂ partially replaced by CO₂ improves the O₂ utilization involved in the decarburization reaction and the CO₂ utilization is still more than 80%. At 50 mL(STP)·min⁻¹, P_CO2 = 0.4 atm and P_O2 = 0.6 atm, the CO₂ utilization reach 87.7%, and the O₂ decarburization ratio reach 60.2%.

(2) For the reaction controlling steps, regarding O₂, it is governed by the mixed control mechanism involving gas-phase mass transfer and interfacial chemical reaction; whereas, regarding CO₂, with the increase of CO₂ partial pressure, the rate-limiting step changes from the mixed control to gas-phase mass transfer control only. Therefore, the mixed controlling model is expressed:

P_CO2 = 0–0.4 atm   

$$-\frac{dC}{dt}=\left(\frac{1\mathrm{\hspace{0.17em} }200A}{\rho V}\right)\left[2\frac{k_g^{\prime }\cdot k_{c,O_2}}{k_g^{\prime }+k_{c,O_2}}ln\left(1+P_{O_2}^b\right)+k_g^{\prime }ln\left(1+P_{C{O}_2}^b\right)\right]$$

P_CO2 = 0.6–1.0 atm   

$$\begin{array}{l}-\frac{dC}{dt}=\left(\frac{1\mathrm{\hspace{0.17em} }200A}{\rho V}\right)\\ \left[2\frac{k_g^{\prime }\cdot k_{c,O_2}}{k_g^{\prime }+k_{c,O_2}}ln\left(1+P_{O_2}^b\right)+\frac{k_g^{\prime }\cdot k_{c,C{O}_2}}{k_g^{\prime }+k_{c,C{O}_2}}ln\left(1+P_{C{O}_2}^b\right)\right]\end{array}$$

(3) As temperature increases from 1723 to 1873 K, the overall decarburization rate increases. Bath temperature mainly effects on O₂ decarburization rates, whereas, the rates of CO₂ are not significantly affected by temperature. The apparent activation energies of CO₂–O₂ decarburization is 21.5 kJ·mol⁻¹.

Acknowledgments

This work was supported by the Independent Research and Development Project of the State Key Laboratory of Advanced Metallurgy (No. 41618011). The author (Yuewen Fan) would also like to acknowledge the financial support from the China Scholarship Council (CSC202106460042).

Nomenclature

I₂₈, I₂₉, I₃₀, I₄₅, I₄₆, I₄₇, I₄₈, I_36OUT, I_36IN: ion currents of ¹²C¹⁶O, ¹³C¹⁶O, ¹²C¹⁸O, ¹³C¹⁶O¹⁶O, ¹²C¹⁶O¹⁸O, ¹³C¹⁶O¹⁸O and ¹²C¹⁶O¹⁸O, ¹⁸O¹⁸O at outlet and inlet, respectively (A)

Q_x1, Q_x2, Q_x3: outlet CO₂ flow of uninvolved reaction, produced by oxygen and carbon and post combustion, respectively (mL(STP)·min⁻¹)

Q_y1, Q_y2, Q_y3, Q_y4: the flowrate of O₂ consumed to form carbon dioxide, O₂ consumed to form carbon monoxide, O₂ consumed by post combustion and O₂ uninvolved reaction, respectively (mL(STP)·min⁻¹)

Q_z1, Q_z2, Q_z3: outlet CO flow produced by oxygen and carbon, by carbon dioxide and carbon and the amount of CO consumed by post combustion, respectively (mL(STP)·min⁻¹)

Q_α, Q_β: the inlet gas of CO₂ and O₂, respectively (mL(STP)·min⁻¹)

Q_CO2out, Q_COout, Q_O2out: the outlet flowrate of CO₂, CO and O₂, respectively (mL(STP)·min⁻¹)

Q_total: total outlet flowrate (mL(STP)·min⁻¹)

m_C: the molar mass of carbon

ρ_m, ρ: the density of melts and gas, respectively (g·cm⁻³)

V: the melt volume (cm³)

Re, Sc: Reynolds and Schmidt numbers, respectively

d: the diameter of the gas-blowing tube (cm)

r_s: the radius of the alumina tube (cm)

u: the blowing rate of gas (cm·s⁻¹)

D: the diffusion coefficient (cm²·s⁻¹)

μ: viscosity of gas (g·cm⁻¹·s⁻¹)

k_g: the gas-phase mass transfer coefficient (cm·s⁻¹)

k_g’: k_g/RT (mol·cm⁻²·s⁻¹·atm⁻¹)

k_c,O2, k_c,CO2: the rate constants of O₂ and CO₂, respectively (mol·cm⁻²·s⁻¹·atm⁻¹)

R: the gas constant, 8.314 (J·mol⁻¹·K⁻¹)

T: the temperature (K)

A: the melt surface area (cm²)

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Appendix

The Reaction Controlling Models

Based on the previous study,^{1,2,25,26,27)} it has been reported that if the decarburization with oxygen is limited by the mass transport in gas phase, the process is expressed as Eq. (17):   

$$O_2^b(g)\to O_2^i(g)$$(17)

where the superscripts “b” and “i” stand for the property in the bulk and at the interface, respectively. The rate of decarburization can be expressed by Eq. (18)   

$$-{\frac{dC}{dt}}_{(O_2)}=\left(\frac{2\mathrm{\hspace{0.17em} }400AP}{{\rho }_{m}V}\right)\left(\frac{k_g}{RT}\right)ln\left(\frac{P+P_{O_2}^b}{P+P_{O_2}^i}\right)$$(18)

where A is the melt surface area (cm²), ρ is the density of the melt (g·cm⁻³), V is the volume of the melt (cm³), k_g is the gas-phase mass transfer coefficient (cm·s⁻¹), R is the gas constant 8.314 J·mol⁻¹·K⁻¹, T is the temperature (K), P is the total pressure as 1 atm, P^b_O2 and Pⁱ_O2 are the oxygen partial pressure in the bulk gas and at the interface gas, respectively. Since the interfacial partial pressure Pⁱ_O2 of O₂ is generally small, one can approximate that ln (1 + Pⁱ_O2) = Pⁱ_O2. Hence,   

$$-{\frac{dC}{dt}}_{(O_2)}=\left(\frac{2\mathrm{\hspace{0.17em} }400A}{{\rho }_{m}V}\right)\left(\frac{k_g}{RT}\right)[ln(1+P_{O_2}^b)-P_{O_2}^i]$$(19)

When the rate of decarburization is controlled by gas-phase mass transfer, it is reasonable to assume that the partial pressure of O₂ at the interface, Pⁱ_O2 = 0. Therefore, Eq. (19) becomes reduced to:   

$$-{\frac{dC}{dt}}_{(O_2)}=\left(\frac{2\mathrm{\hspace{0.17em} }400A}{{\rho }_{m}V}\right)\left(\frac{k_g}{RT}\right)ln(1+P_{O_2}^b)$$(20)

Similarly, for the decarburization with CO₂ gas, the rate of decarburization can be expressed by Eq. (21).   

$$-{\frac{dC}{dt}}_{(C{O}_2)}=\left(\frac{1\mathrm{\hspace{0.17em} }200A}{{\rho }_{m}V}\right)\left(\frac{k_g}{RT}\right)ln(1+P_{C{O}_2}^b)$$(21)

When the rate of decarburization is controlled by interfacial reaction, ignoring the contribution of reverse reaction, the rates of CO₂ and O₂ can be expressed as follows:   

$$-{\frac{dC}{dt}}_{(O_2)}=\left(\frac{2\mathrm{\hspace{0.17em} }400A}{{\rho }_{m}V}\right)k_{c,O_2}{P}_{O_2}^i;\mathrm{\hspace{0.17em} }-{\frac{dC}{dt}}_{(C{O}_2)}=\left(\frac{1\mathrm{\hspace{0.17em} }200A}{{\rho }_{m}V}\right)k_{c,C{O}_2}{P}_{C{O}_2}^i$$(22)

where k_c,O2 and k_c,CO2 are the rate constants (mol·cm⁻²·s⁻¹·atm⁻¹) of O₂ and CO₂, respectively.

Thus, when the decarburization rate is governed by a mixed control mechanism involving gas-phase mass transfer and interfacial chemical reaction, combing Eqs. (20), (21), (22) and k_g’ replacing k_g/RT, the equations for the rate of CO₂ and O₂ decarburization can be obtained:   

$$\begin{array}{l}-{\frac{dC}{dt}}_{(O_2)}=\left(\frac{2\mathrm{\hspace{0.17em} }400A}{{\rho }_{m}V}\right)\left(\frac{\frac{k_g}{RT}\cdot k_{c,O_2}}{\frac{k_g}{RT}+k_{c,O_2}}\right)ln(1+P_{O_2}^b)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.5em}=\left(\frac{2\mathrm{\hspace{0.17em} }400A}{{\rho }_{m}V}\right)\left(\frac{k_g^{\prime }\cdot k_{c,O_2}}{k_g^{\prime }+k_{c,O_2}}\right)ln(1+P_{O_2}^b)\end{array}$$(23)

  

$$\begin{array}{l}-{\frac{dC}{dt}}_{(C{O}_2)}=\left(\frac{1\mathrm{\hspace{0.17em} }200A}{{\rho }_{m}V}\right)\left(\frac{\frac{k_g}{RT}\cdot k_{c,C{O}_2}}{\frac{k_g}{RT}+k_{c,C{O}_2}}\right)ln(1+P_{C{O}_2}^b)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=\left(\frac{1\mathrm{\hspace{0.17em} }200A}{{\rho }_{m}V}\right)\left(\frac{k_g^{\prime }\cdot k_{c,C{O}_2}}{k_g^{\prime }+k_{c,C{O}_2}}\right)ln(1+P_{C{O}_2}^b)\end{array}$$(24)

The results of k_g/RT calculated by Eq. (16) are shown in Table 6. Under the same flowrate, the change of k_g’ was less than 3.2 × 10⁻⁶ (mol·cm⁻²·s⁻¹·atm⁻¹) and its influence can be ignored.

Table 6. The gas phase mass transfer coefficient in different conditions.

T (K)	O2/(mL(STP)·min−1)	CO2/(mL(STP)·min−1)	kg/RT × 10−5/(mol·cm−2·s−1·atm−1)
1773	50	0	2.64
1773	40	10	2.69
1773	30	20	2.73
1773	20	30	2.78
1773	10	40	2.83
1773	0	50	2.88
1773	80	0	3.60
1773	64	16	3.66
1773	48	32	3.73
1773	32	48	3.79
1773	16	64	3.86
1773	0	80	3.92
1723	40	10	2.66
1823	40	10	2.72
1873	40	10	2.74