Kinetics of CO Gas Dissolution into Stirred Liquid Fe at 1823 K and Its Impact on Nozzle Clogging during Continuous Casting

Abstract

CO gas generated by a carbothermic reaction in Submerged Entry Nozzle (SEN) can reoxidize an Ultra Low C (ULC) steel during continuous casting. When Ti presents in the ULC steel, the CO gas oxidizes the liquid steel and Fe_tO–Al₂O₃–TiO_x liquid oxide mixed with solid alumina forms at the interface between the steel and the nozzle. The reoxidation is partly responsible for the nozzle clogging. In the present study, the kinetics of CO gas dissolution into liquid Fe at 1823 K was investigated in order to understand how fast the reoxidation occurs, which is responsible for the liquid oxide formation and the nozzle clogging. A series of gas-liquid reaction experiments were carried out under various conditions (gas flow rate, stirring speed, the partial pressure of CO). Dissolved C and O contents in the liquid Fe were analyzed in order to find possible rate controlling step. It was found that a gas phase mass transfer is a possible rate controlling step at low rate of CO gas supply if the flow rate (Q) is lower than 0.75 L min⁻¹, which is thought to be higher than the actual CO gas supply rate in a typical SEN (~0.15 L min⁻¹, volume corrected at room temperature). Therefore, the reoxidation is limited by the supply of CO gas to liquid steel. Decreasing CO gas generation from the nozzle is recommended to suppress the nozzle clogging.

1. Introduction

Outer panel of automobiles is one of the main products of a number of steel companies. It should satisfy a number of required properties such as elongation, strain hardening, and anisotropy, which are associated with formability to manufacture the sophisticated outer panel shapes. An Ultra Low Carbon (ULC) steel with Ti shows an enhanced formability by capturing interstitial elements such as C and N.^1,2) However, it is also well known that Ti deteriorates clogging of Submerged Entry Nozzle (SEN) during continuous casting to a significant level. Contrary to the conventional nozzle clog deposits (mostly alumina clusters³⁾), the addition of Ti causes not only the alumina but also substantial amount of frozen steel.^4,5,6,7) This has an adverse effect on the product quality and productivity. Nevertheless, it has not been clearly known why the nozzle clogging becomes severe in the presence of Ti.

According to previous studies conducted by the present authors, the clogging during Ti-added ULC (hereafter Ti-ULC) steel casting is partly initiated from an interfacial reaction between CO gas from the nozzle and Ti-ULC steel.^{8,9,10,11,12)} Since major constituents for normal SENs are Al₂O₃, SiO₂, and C, it could be expected that CO gas is emitted by a carbothermic reaction between SiO₂ and C:^3,13,14)   

$$\begin{array}{l}\mathrm{S}\mathrm{i}{\mathrm{O}}_2\left(\mathrm{r}\mathrm{e}\mathrm{f}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{y}\right)+3\mathrm{C}\left(\mathrm{r}\mathrm{e}\mathrm{f}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{y}\right)=\mathrm{S}\mathrm{i}\mathrm{C}\left(\mathrm{s}\right)+2\mathrm{C}\mathrm{O}\left(\mathrm{g}\right)\\ \mathrm{\Delta }°\mathrm{G}=-11\mathrm{\hspace{0.17em} }206\mathrm{\hspace{0.17em} }\mathrm{J}\mathrm{\hspace{0.17em} }\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1}\end{array}$$(1)

or   

$$\begin{array}{l}\mathrm{S}\mathrm{i}{\mathrm{O}}_2\left(\mathrm{r}\mathrm{e}\mathrm{f}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{y}\right)+\mathrm{C}\left(\mathrm{r}\mathrm{e}\mathrm{f}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{y}\right)=\mathrm{S}\mathrm{i}\mathrm{O}\left(\mathrm{g}\right)+\mathrm{C}\mathrm{O}\left(\mathrm{g}\right)\\ \mathrm{\Delta }°\mathrm{G}=68\mathrm{\hspace{0.17em} }005\mathrm{\hspace{0.17em} }\mathrm{J}\mathrm{\hspace{0.17em} }\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1}\end{array}$$(2)

where Δ°G is the standard Gibbs energy change of the reaction at 1823 K, calculated by FactPS database of FactSage software.¹⁵⁾

It was also reported that Al₂O₃ in the refractory can react with the graphite:¹⁶⁾   

$$\begin{array}{l}\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3\left(\mathrm{r}\mathrm{e}\mathrm{f}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{y}\right)+2\mathrm{C}\left(\mathrm{r}\mathrm{e}\mathrm{f}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{y}\right)=\mathrm{A}{\mathrm{l}}_2\mathrm{O}\left(\mathrm{g}\right)+2\mathrm{C}\mathrm{O}\left(\mathrm{g}\right)\\ \mathrm{\Delta }°\mathrm{G}=280\mathrm{\hspace{0.17em} }851\mathrm{\hspace{0.17em} }\mathrm{J}\mathrm{\hspace{0.17em} }\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1}\end{array}$$(3)

In the above carbothermic reactions, CO(g) is a common reaction product. And the Gibbs energy change of the Reaction (1) is most negative, therefore, it is likely that the CO(g) is a main gas component after the carbothermic reactions.

The CO gas propagates through inner pores in the nozzle refractory and arrives at the interface between the nozzle and the liquid steel inside the SEN (inner wall). In a usual Al-killed steel, the CO(g) then oxidizes Al dissolved in the molten steel, and forms Al₂O₃(s) that adheres on the inner wall. This is already well-known mechanism for network alumina formation.¹⁷⁾ On the other hand, in case of Ti-ULC steel, different phenomena occur. It reacts not only with Al but also with Ti and Fe in the steel.^10,11) As a result, a liquid oxide composed of Fe_tO–Al₂O₃–TiO_x with solid alumina form at the interface. This was thermodynamically predicted^8,9) and experimentally validated by the present authors.^10,11) A schematic explanation can be seen in Fig. 1. Because the liquid oxide is likely to wet both to liquid steel and to the nozzle,¹⁵⁾ this may act as a precursor of clog deposit which is mainly composed of frozen steel and solid alumina. A possible mechanism was discussed in the previous articles by the present authors.^10,11,12) Actual reaction between SEN and Ti-ULC steel was also experimentally investigated by the present authors using a rotating finger method. This was recently published by the present authors.¹²⁾ In this research, it was found that clog deposit found in a number of used nozzles contained Ti oxide. This was also found in a series of independent laboratory scale experiments. Source of the Ti must be the dissolve Ti in liquid steel, and source of the oxidation should be CO gas generated from the refractory. Therefore, suppressing the interfacial reaction seems to be beneficial to prevent the nozzle clogging. In order to suppress the reaction, the oxidation by CO gas should be controlled.

Fig. 1.

Proposed mechanism for nozzle clogging during continuous casting of Ti-ULC steels relevant to a CaO-free nozzle.¹⁰⁾ (Online version in color.)

Oxidation of Ti-ULC steel by O₂ gas was investigated by Sasai and Matsusawa¹⁹⁾ by blowing a gas mixture of Ar and O₂ onto Fe–Al–Ti melt. This was aimed at observing oxidation phenomena during a tundish operation where air can easily entrap to the liquid steel. They found that a Fe_tO–Al₂O₃–TiO_x was generated on the surface due to oxidation by O₂ included in the gas. Possible rate controlling steps were proposed to be mass transport of O in the oxide film or mass transport of O₂ gas in the gas phase, depending on grade and stirring condition of the steel. While this investigation provides an important insight to enhance cleanliness of the steel during a tundish operation, the oxygen partial pressure employed in this study (5–23 kPa corresponding to 5 – 23 × 10⁻² atm) was higher than that may be found in the SEN (below 10⁻¹¹ atm¹⁰⁾), unless there is an air leak into the SEN. It is necessary to have information how CO oxidizes Ti-ULC steel. Oxidation of the Ti-ULC steel by CO gas was already reported by the present authors.^10,11) After 30 minutes reaction with CO gas at 1833 K, the formation of Fe_tO–Al₂O₃–TiO_x with alumina was confirmed. However, the oxidation rate of Ti-ULC steels by CO gas was not fully investigated yet. Moreover, how fast the CO gas can dissolve into liquid steel is not known so far:   

$$\mathrm{C}\mathrm{O}\left(\mathrm{g}\right)=\underset{\_}{\mathrm{C}}+\underset{\_}{\mathrm{O}}$$(4)

The dissolution behavior of CO gas into liquid steel has been rarely studied. In most previous studies, the reverse direction (C + O = CO(g)) was considered, because this is essential to understand decarburization of liquid steel in various vacuum degassers including RH process.²⁰⁾ Only limited information has been known for the kinetics of the Reaction (1).^{21,22,23,24,25)} Previous investigations on the kinetics of the Reaction (1) are summarized in Table 1. Earlier investigations employed Sievert’s method^21,22,23) in which mass transport of gas species did not limit the reaction rate due to the guaranteed supply of the CO gas to the surface of the liquid phase. Therefore, these investigations provided either diffusion coefficients²³⁾ or mass transfer coefficients of C and O^21,22) in liquid iron. Investigations by Kajiwara et al.²⁴⁾ and Tsuchiya et al.²⁵⁾ employed generally higher C content in liquid iron which limits the Reaction (4). Therefore, the Reaction (4) was partly involved to be the rate controlling step. A more recent investigation by Ito et al.^26,27) employed an electromagnetic levitation melting technique and a crucible melting technique. They found that one or both of the mass transfer at gas and melt determined the reaction rate.

Table 1. Previous investigations of the dissolution kinetics of CO(g) = C + O.

Author	Year	Method	T (K)	Initial [%C]	Gas flow controlled	Metal stirring	Rate controlling step
Parlee et al.21)	1958	Sievert method in induction melting furnace	1813 to 1903	0.15 to 4.4	No	No	Liquid phase mass transfer
King et al.22)	1970	Sievert method in resistance heating furnace	1853	? – 0.3	No	No	Liquid phase mass transfer
Kajiwara et al.24)	1972	Resistance heating furnace, %C analysis	1823 to 1933	0.04 to 0.13	a few ml min−1	No	Mixed control by gasification, liquid phase mass transfer and gas phase mass transfer
Tsuchiya et al.25)	1972	Resistance heating furnace, %C analysis	1843 to 1993	0, 0.5, 2.8	0.6 L min−1	No	Chemical reaction
Solar and Guthrie23)	1972	Sievert method (pressure drop) in resistance heating furnace	1853 to 1973	?	No	No	Liquid phase mass transfer
Ito et al.26,27)	1983	Electromagnetic levitation melting	2013 to 2373	0	0.3 to 0.6 L min−1	Yes	Mixed control by liquid phase mass transfer and gas phase mass transfer
		Induction melting	1873		1.5 L min−1	No

The followings could be identified from the above investigations:

1) Dissolution of CO gas into liquid iron was very fast: saturated to the CO gas within a few seconds (levitation melting) or within a few minutes (crucible melting in the case of almost pure iron.²⁶⁾ On the other hand, dissolution rate decreased as initial C content increased.²⁵⁾

2) Once the liquid iron was saturated by CO gas, O content in the liquid iron decreased while C content kept increased, provided that CO₂ partial pressure in the incoming gas was lower than approximately 1 volume pct.²⁶⁾

3) Most of the investigations considered the diffusion of C and O in a boundary layer in the liquid iron side.^21,22,23) Therefore, the possibility of the rate limited by the gas delivery was not taken into account.

4) When the initial content of C was high, it slowed down the dissolution rate of CO gas.^24,25) These investigations were designed to reveal reactions inside the blast furnace operation.

5) At the high temperature employed in these investigations, the surface reaction must proceed extremely rapid, and it cannot be a rate controlling step.^21,28)

6) Many experiments in the previous investigations were carried out at high temperature (over 1873 K) with stagnant liquid iron, except for the levitation melting study by Ito et al.²⁶⁾

On the other hand, conditions inside the SEN during the casting of ULC steel is lower temperature, fast-moving liquid steel, very low C content, natural movement of the CO gas from the SEN. These conditions are considered to be different from those employed in the previous investigations. Therefore, the dissolution rate of CO gas into pure Fe should be investigated under the condition of the SEN refractory/liquid steel interface.

In the present study, the kinetics of CO gas dissolution into liquid iron was investigated using an induction melting furnace. In order to evaluate the role of mass transfer in gas/liquid iron to the dissolution rate, the flow rate of the gas supplied and stirring in the liquid iron was controlled. Only almost pure liquid iron was used in order to measure the dissolution rate not altered by the formation of any oxide phase on the surface of the iron. With the obtained data, the possible rate controlling step was discussed. Also, it is shown how the dissolution kinetics of CO gas influences to the nozzle clogging during continuous casting of ULC steel.

2. Experimental

A schematic figure of the experimental apparatus is shown in Fig. 2. An induction heating furnace equipped with a quartz chamber was used in the present study. 0.5 kg of an electrolytic iron (Toho Zinc Co. Ltd, Japan, compositions in Table 2) was charged in an alumina crucible (OD 60 × ID 54 × H 100 mm). The crucible was put in the quartz chamber which was then sealed by brass end caps. The temperature of the crucible was raised by the induction heating and was measured by a B-type thermocouple located at the bottom of the crucible. Ar gas was purified by passing through a Drierite (CaSO₄) column and the cylinder filled with Mg chips at 773 K. A flow rate at 1.0 L min⁻¹ of the Ar was maintained during the heating and subsequent thermal homogenization in the liquid iron. Once a target temperature was achieved at 1823 K, a cylindrical alumina rod (purity: ~99.7%, D 10 × H 160 (mm)) was dipped into the liquid iron to initiate a stirring. The rod was connected to a motor via a brass jig, and was rotated at a speed (ω) of 100 to 300 rpm. The stirring in the Ar atmosphere was maintained for 5 min in order to secure homogenization of liquid Fe, and a small portion of the liquid iron was sampled using a quartz tube. Then, the Ar gas supply was stopped and a CO gas or a mixture of Ar and CO gas was injected using an alumina lance onto the surface of the liquid Fe, and the reaction time was set to be zero. The CO gas was purified by passing through both Drierite and Ascarite (NaOH) in order to remove trace gas (moisture and CO₂). A flow rate of the CO gas or the mixture of Ar and CO gas (Q) was set in the range of 0.3–1.5 L min⁻¹. While the liquid iron was stirred, it was periodically sampled at intervals of a minute. After the stirring, the alumina rod was withdrawn from the crucible, and then the CO gas (or the mixture) was replaced with an Ar gas, followed by a termination of the experiment. The surface of the samples was ground to remove any oxide film. Concentrations of C and O of the samples were obtained by using oxygen gas fusion infrared absorption method (LECO CS844) and inert gas fusion infrared absorption method (LECO ON836), respectively. In some samples, pores were observed by an optical microscope. Detailed experimental information for the experiment was summarized in Table 3. It was assumed that the dissolution reaction took place through a reaction area (A) of 2.290 × 10⁻³ m², which was the cross-sectional area of the crucible used.

Fig. 2.

Experimental apparatus used in the present study.

Table 2. Electrolytic Fe used in the present study (concentration in mass ppm).

Element	Fe	C	O	N	H	P	S	Si	Mn	Cu	As	Sn	B	Pb	Co	Ni	Zn	Cr
ppm	Bal.	5	70	5	3	7	5	<5	1	1	1	1	2	1	4	1	1	3

Table 3. Experimental conditions employed in the present study.

Variables	Values
Temperature, T (K)	1823
Steel mass, W (kg)	0.5
Flowrate of CO gas (+ Ar gas), Q (L min−1) at 298 K	0.30, 0.50, 0.75, 1.00, 1.50
Stirring speed, ω (rpm)	100, 200, 300
Partial pressure of CO, PCO (atm)	0.3, 0.5, 1.0
Reaction time, t (min)	0, 1, 2, 3, 4, 5

3. Results

Figure 3 shows one of the typical results obtained in the present study. [pct C] and [pct O] at each reaction time (from the initial sample to 5 minutes) are shown by open circles. Numbers on each circle are the reaction time in minute. The initial [pct C] and [pct O] were 0.00447 and 0.00912, respectively, and those were measured just before the CO gas was introduced. A full curve represents the equilibrium contents of C and O in the liquid iron at 1823 K, 1 atm in equilibrium with a gas phase calculated by using FactSage 7.1 with FTmisc/FactPS databases.¹⁵⁾ The gas is almost 95% CO and 5% CO₂ at the equilibrium.

Fig. 3.

[pct C] and [pct O] changes during the reaction CO(g) = C + O at 1823 K, P_CO = 1, Q = 1 L min⁻¹, and ω = 200 rpm. A full line represents the equilibrium [pct C] vs [pct O] in liquid Fe–C–O in equilibrium with CO gas, and dashed lines are composition paths of pure liquid Fe in equilibrium with various P_CO/P_CO2 ratios, all calculated using FactSage.¹⁵⁾ (Online version in color.)

In general, contents of C and O (in mass percent) increased during the reaction between the gas and the liquid iron. This is mostly due to the Reaction (4). When there was only CO(g), [pct C] and [pct O] are expected to increase linearly by the stoichiometry of the Reaction (1) (Δ[pct O]/Δ[pct C] = 1.33 as Δn_O = Δn_C, where n_i is the number of moles of i in the liquid iron). This stoichiometric relationship is shown by a dotted line (P_CO/P_CO2 = ∞) which was also calculated by FactSage. The analyzed contents show that [pct O] deviated from the stoichiometric relationship as the reaction time passed. At the surface of the liquid iron, the following reactions could be thought, apart from the Reaction (4):   

$$\mathrm{C}\mathrm{O}\left(\mathrm{g}\right)+\underset{\_}{\mathrm{O}}=\mathrm{C}{\mathrm{O}}_2\left(\mathrm{g}\right)$$(5)

  

$$2\mathrm{C}\mathrm{O}\left(\mathrm{g}\right)=\underset{\_}{\mathrm{C}}+\mathrm{C}{\mathrm{O}}_2\left(\mathrm{g}\right)$$(6)

According to the Reactions (5) and (6), either decreasing [pct O] or increasing [pct C] from the stoichiometric relationship (the dotted line) should be observed. Therefore, the above two reactions were not likely to happen. This was also in agreement with a report by Ito et al.²⁶⁾ Two additional thermodynamic calculations were carried out where some portion of CO₂ was assumed in the incoming gas (P_CO/P_CO2 = 9, 19). These were shown in the Fig. 3 by two other dashed lines, respectively. If the CO₂ was involved (backward reactions of (5) and (6)) due to dissociation of the CO before its contact to the surface of the liquid iron, or slight oxidation of the CO while the reaction chamber was shortly open due to the sampling), the CO₂ can increase [pct O] as can be seen in the figure. In addition to this, a number of pores were observed in the quenched sample as shown in Fig. 4. The estimated volume of the pores increased as the reaction time increased. The surface of the pores could not be removed completely since the pore shape was irregular. It may be concluded that the analyzed [pct O] might be overestimated. On the other hand, the analyzed [pct C] is thought to be less influenced by the above facts. Therefore, in the present study, the dissolution kinetics of CO in liquid Fe was interpreted using analyzed [pct C], instead of [pct O], assuming the equimolar dissolution of C and O by the Reaction (4).

Fig. 4.

Optical microscope image of the cross-section of Fe samples after reaction at (a) 2 min and (b) 4 min. (Online version in color.)

Experimental data obtained in the present study ([pct C] in liquid iron) under various conditions are shown in Fig. 5: (a) varying the rotating speed of the alumina rod, (b) varying the flow rate of CO gas, and (c) varying partial pressure of the CO gas in the Ar + CO gas mixture.

Fig. 5.

Increase of [pct C] in liquid Fe during the reaction CO(g) = C + O at 1823 K: (a) under various ω at P_CO = 1 atm, Q = 1 L min⁻¹, (b) under various Q at P_CO = 1 atm, ω = 300 rpm, and (c) under various P_CO at Q = 1 L min⁻¹, ω = 300 rpm. (Online version in color.)

It is seen that [pct C] increased in all cases. Rate of C absorption (the increasing [pct C] due to the dissolution of CO) was almost constant irrespective of the stirring condition (rotating speed) as can be seen in Fig. 5(a). It means that the effect of the stirring condition in liquid iron on the CO dissolution was negligible in the present experimental condition. This is different from the reported rate controlling step in some of the earlier studies^21,22,23) where the Sievert’s method was employed. As liquid steel passing through SEN is in highly stirred condition, the experimental condition employed in the present study should be suitable to interpret the dissolution kinetics of CO.

Increasing the flow rate of CO at ω = 300 rpm showed that the rate of C absorption generally increases up to 0.75 L min⁻¹ (Fig. 5(b)). Higher flow rate did not noticeably increase the rate of C absorption. This implies that there was a resistance in the gas phase when the flow rate was lower than 0.75 L min⁻¹, but the resistance in the gas phase became less significant at a higher flow rate.

Varying P_CO of the incoming gas mixture also affected the rate of C absorption (Fig. 5(c)). Increasing P_CO increased the rate. From the observations in Figs. 5(b) and 5(c), it is thought that conditions in the gas phase have a significant impact on the dissolution rate of CO gas into liquid iron.

4. Discussions

4.1. Rate Controlling Step of CO Gas Dissolution into Pure Liquid Fe

The dissolution of CO gas into liquid iron may be controlled by one or more than one of the followings steps:

a) Diffusion of C and/or O in liquid iron (Liquid Phase Mass Transfer, LPMT)

b) Diffusion of CO gas in the gas phase (Gas Phase Mass Transfer, GPMT)

c) Gas adsorption at a gas-steel interface (Chemical Reaction)

Among the above steps, the slowest step would determine the dissolution rate, and conform with the experimental data reported in the present study. Previous reports on the dissolution kinetics of CO gas agreed that the surface reaction must proceed extremely fast and thus cannot be a rate controlling step.^21,23,26,28) Therefore, the following relationship is assumed to hold:   

$${\left[\mathrm{p}\mathrm{c}\mathrm{t}\mathrm{C}\right]}^{\mathrm{i}}\times {\left[\mathrm{p}\mathrm{c}\mathrm{t}\mathrm{O}\right]}^{\mathrm{i}}={\mathrm{K}}_{(4)}\times P_{\mathrm{C}\mathrm{O}}{}^{\mathrm{i}}$$(7)

where ⁱ and K₍₄₎ refer to interface and the equilibrium constant of the Reaction (4), respectively. And the possibility of the step c) was not considered in the present study.

4.1.1. Possible Rate Controlling Step: LPMT

Assuming that LPMT is the rate controlling step for the CO dissolution, the following equation holds:   

$$J_{\text{C}}=k_m\left(C_{\text{C}}^i-C_{\text{C}}^b\right)$$(8)

where J_C represents the molar flux of the diffusing C in a boundary layer of the liquid iron (mol m² sec⁻¹); k_m the mass transfer coefficient of the C in the liquid (m sec⁻¹), $C_{\text{C}}^i$ the molar concentration of C at the interface (mol m⁻³), $C_{\text{C}}^b$ the molar concentration of C in the bulk (mol m⁻³), respectively. The Eq. (8) is then reformulated into:   

$$\frac{d\left[\text{pct}\mathrm{\hspace{0.17em} }\text{C}\right]}{dt}=k_m\frac{\mathrm{A}}{\mathrm{V}}({[\mathrm{p}\mathrm{c}\mathrm{t}\mathrm{\hspace{0.17em} }\mathrm{C}]}^i-[\mathrm{p}\mathrm{c}\mathrm{t}\mathrm{\hspace{0.17em} }\mathrm{C}])$$(9)

where t, A, and V stand for reaction time (sec), the surface area of the liquid iron (m²), and volume of the liquid iron (m³). ^b was omitted for convenience. In this regime, a thermodynamic equilibrium at the surface of the liquid iron is assumed by the Eq. (7). With the stoichiometric relationship (Δ[pct O]/Δ[pct C] = 1.33) and the equilibrium constant K₍₄₎, [pct C]ⁱ can be calculated, in principle. The actual calculation was carried out using the FactSage 7.1, assuming P_CO = 1 in the incoming gas (“a” in the Fig. 3). By integrating the Eq. (9) (t= 0 to t) yields, the following equation is obtained.   

$$ln\frac{{\left[\text{pct}\mathrm{\hspace{0.17em} }\text{C}\right]}_e-\left[\text{pct}\mathrm{\hspace{0.17em} }\text{C}\right]}{{\left[\text{pct}\mathrm{\hspace{0.17em} }\text{C}\right]}_e-{\left[\text{pct}\mathrm{\hspace{0.17em} }\text{C}\right]}_0}=-k_m\frac{\text{A}}{\text{V}}t$$(10)

where [pct C]_e is the same as the [pct C]ⁱ due to the local surface equilibrium, and [pct C]₀ is the initial C content. Figure 6(a) shows a corresponding plot of the data in Fig. 5(a) where the stirring condition in the liquid iron was varied. In order to conform the data into the Eq. (9), a linear change with the reaction time was assumed. From the experimental condition (V = 7.169 × 10⁻⁵ m³ (using a density of liquid iron at 1823 K (7000 kg m⁻³),²⁹⁾ A = 2.290 × 10⁻³ m²), the k_m was extracted. The k_m at each ω is shown in Fig. 6(b). There is no clear dependence of k_m on the ω. In general, a rate constant of a reaction limited by the LPMT is dependent on the intensity of the stirring.^30,31,32) For example, a correlation between mass transfer coefficient and fluid velocity may be found as:³¹⁾   

$$\mathrm{S}\mathrm{h}=0.429\mathrm{S}{\mathrm{c}}^{0.33}\mathrm{R}{\mathrm{e}}^{0.42}$$(11)

where Sh, Sc, and Re are the Sherwood number, the Schmidt number, and the Reynolds number, respectively. Increasing the fluid velocity (Re) should increase the mass transfer coefficient (Sh), in the regime of the LPMT. From the analysis shown in this section with the Fig. 5, it can be concluded that the dissolution rate of CO gas was not limited by the mass transfer in the liquid iron under the present experimental condition. Since liquid steel passes the SEN quickly, it is also reasonable that there is not a noticeable resistance in the liquid steel for the mass transfer of C and O after the CO dissolution from the nozzle refractory.

Fig. 6.

(a) Integrated rate plot in the regime of LPMT rate controlling at various ω, (b) k_m at each ω. (Online version in color.)

4.1.2. Possible Rate Controlling Step: GPMT

By a similar approach, the dissolution rate of CO gas in the regime of GPMT rate control may be expressed as:   

$$\frac{d\left[\text{pct C}\right]}{dt}=\frac{100{\text{M}}_{\text{C}}\text{A}{k}_{\text{g}}\left(P_{\text{CO}}^b-P_{\text{CO}}^i\right)}{\text{WR}T}$$(12)

where P_CO, W, R, k_g, T, and M_C represent partial pressure of CO in the gas phase (atm), mass of liquid Fe (kg), the universal gas constant (atm m³ mol⁻¹ K⁻¹), mass transfer coefficient (m sec⁻¹), absolute temperature (K), and the atomic mass of C (kg mol⁻¹), respectively. $P_{\text{CO}}^b$ was taken from volume fraction of CO gas relative to the total gas volume at 1 atm. For $P_{\text{CO}}^i$, it can be obtained by the Eq. (7) assuming [pct C]ⁱ = [pct C] and [pct O]ⁱ = [pct O] in principle. The [pct O] was not obtained by the direct analysis using inert gas fusion infrared absorption method (LECO ON836) as described in the Sec. 2, but was derived from the relationship (Δ[pct O]/Δ[pct C] = 1.33) due to the already mentioned fact in the Sec. 3. Therefore,   

$$\left[\mathrm{p}\mathrm{c}\mathrm{t}\mathrm{O}\right]=1.33\left(\left[\mathrm{p}\mathrm{c}\mathrm{t}\mathrm{C}\right]-{\left[\mathrm{p}\mathrm{c}\mathrm{t}\mathrm{C}\right]}_0\right)+{\left[\mathrm{p}\mathrm{c}\mathrm{t}\mathrm{O}\right]}_0$$(13)

The actual calculation of the $P_{\text{CO}}^i$ was carried out by FactSage 7.1 as described in the Sec. 3.¹⁵⁾

By changing the Eq. (12) in a finite time frame:   

$$\mathrm{\Delta }\left[\text{pct}\mathrm{\hspace{0.17em} }\text{C}\right]\frac{\mathrm{W}\mathrm{R}T}{100{\mathrm{M}}_{\mathrm{C}}\mathrm{A}\left(P_{\mathrm{C}\mathrm{O}}^b-P_{\mathrm{C}\mathrm{O}}^i\right)}=k_{\mathrm{g}}\mathrm{\Delta }t$$(14)

k_g can be obtained by plotting Δ[pct C] at each Δt, along with the calculated $P_{\text{CO}}^i$. The calculated [pct O] and $P_{\text{CO}}^i$ for the experimental data shown in Fig. 5(b) are listed in Table 4. And the corresponding plot of the Eq. (14) is shown in Fig. 7(a). When Δt = 300 sec, there are significant scatters from the above linear relationship (Eq. (14)). Except for these scatters, the mass transfer coefficient k_g was obtained from the slope at each Q, and it was shown in Fig. 7(b). Up to Q = 0.75 L min⁻¹, the slope became steeper as the Q increased. Above this flow rate, the slope was almost similar. Therefore, the dissolution rate of CO gas is likely determined by GPMT in the low flow rate region (Q < 0.75 L min⁻¹). However, the flow rate of CO gas was sufficiently high (Q > 0.75 L min⁻¹), the dissolution rate was not solely determined by GPMT.

Table 4. $P_{\text{CO}}^i$ calculated using analyzed [pct C] and FactSage.¹⁵⁾

Q (L min−1)	t (sec)	[pct C]	[pct O]a)	$P_{\text{CO}}^i$ (atm)b)
0.30	60	0.00340	0.01158	0.02119
	120	0.00427	0.01274	0.02928
	180	0.00688	0.01621	0.06013
	240	0.01070	0.02129	0.12311
	300	0.01130	0.02209	0.13493
0.50	60	0.00358	0.01690	0.03258
	120	0.00489	0.01864	0.04912
	180	0.00925	0.02444	0.12213
	240	0.01240	0.02863	0.19213
	300	0.01570	0.03302	0.28108
0.75	60	0.00503	0.01414	0.03832
	120	0.00879	0.01914	0.09085
	180	0.01300	0.02474	0.17407
	240	0.01980	0.03379	0.36346
	300	0.02430	0.03977	0.52644
1.00	60	0.00591	0.01067	0.03959
	120	0.01150	0.01810	0.11251
	180	0.01600	0.02408	0.20883
	240	0.02070	0.03034	0.34122
	300	0.02620	0.03765	0.53772
1.50	60	0.00726	0.01283	0.05225
	120	0.01210	0.01927	0.12606
	180	0.01730	0.02618	0.24566
	240	0.01910	0.02858	0.29633
	300	0.02570	0.03735	0.52318

a)  Using the Eq. (13).

b)  Using FactSage with FactPS, FTmisc databases.

Fig. 7.

(a) Integrated rate plot in the regime of GPMT rate controlling at various Q, (b) k_g at each Q. (Online version in color.)

As to the effect of partial pressure shown in the Fig. 5(c), since the present experiment was carried out at Q = 1 L min⁻¹ which turned out to be out of the GPMT rate controlling regime, it is not adequate to discuss the rate controlling step clearly. Because the C absorption rate increased as P_CO increased, the dissolution reaction rate might be limited by chemical reaction for the Reaction (4) where the P_CO is a driving force for the forward reaction of (4). However, at present, it is not evident whether the GPMT also partly contributed to the rate controlling step in this case or not.

4.2. Assessment of Nozzle Clogging by Dissolution of CO Gas into Liquid Steel

Generally, SEN contains fused silica and graphite in order to secure its thermal shock resistivity and chemical erosion during continuous casting. When the silica and the graphite react each other at their contact point, CO gas generates:¹⁰⁾   

$$\mathrm{S}\mathrm{i}{\mathrm{O}}_2\left(\mathrm{s},\mathrm{\hspace{0.17em} }\mathrm{r}\mathrm{e}\mathrm{f}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{y}\right)+3\mathrm{C}\left(\mathrm{s},\mathrm{\hspace{0.17em} }\mathrm{r}\mathrm{e}\mathrm{f}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{y}\right)=\mathrm{S}\mathrm{i}\mathrm{C}\left(\mathrm{s}\right)+2\mathrm{C}\mathrm{O}\left(\mathrm{g}\right)$$(1)

By the above carbothermic reaction, the mass of the SEN decreases by the amount of the CO gas emitted, provided that only the CO gas is produced. From the present study, it is understood that CO gas dissolution into liquid steel is influenced by the supplying rate of the gas. Therefore, it is necessary to assess whether the emitted CO gas is critical to oxidize the liquid steel. In order to know how much the CO gas can be generated in the nozzle by the Reaction (1), relevant information on the contents of SiO₂ and C in the SEN and their reaction rate should be known. As an example case, dimension and composition of a typical SEN were obtained from the literature.^33,34) The composition and bulk density are listed in Table 5,³³⁾ and a dimension of an SEN is shown in Fig. 8.³⁴⁾ For the sake of simplicity, the followings were assumed:

Table 5. Composition and bulk density of a SEN refractory.³³⁾

Constituent	Al2O3	ZrO2	SiO2	C	SiC
Content (mass pct)	40	7	18	25	8
Bulk density of nozzle (kg m−3)	2.2 × 103

Fig. 8.

A simplified geometry of SEN³⁴⁾ showing a volume generating CO(g) by the carbothermic reaction (Reaction (1)) for an example assessment in Sec. 4.2.

(a) Dissolution of CO gas into liquid steel is not limited by LPMT, but is limited by GPMT when the supply rate of CO (Q) is not higher than 0.75 L min⁻¹. Above this rate, increasing P_CO can additionally increase the dissolution rate. Reaction area (A) was 2.290 × 10⁻³ m².

(b) SiO₂ and C are homogeneously dispersed in the SEN in order to ensure enough reaction area between them. Different constitution inside the nozzle refractory is ignored.

(c) Reaction (1) takes place inside the refractory regardless of location. CO gas generated in the half-inner side of the refractory propagates into the inner wall SEN, thereby dissolving into the liquid steel. Other constituents in the refractory do not produce CO gas.

In order to get information about CO gas generation rate in the SEN, an additional experiment was carried out in the present study. Details of the experiment are described in Appendix A. As a result, it was obtained that the Reaction (1) held at 1823 K produces CO gas as much as 2.33 L min⁻¹ per mole of SiO₂ (with an excess C).

From the geometry of the SEN shown in Fig. 8, the height of the part of the nozzle that yields inner interfacial area as much as 2.290 × 10⁻³ m² is 9.1 × 10⁻³ m. Volume and corresponding mass of the nozzle providing CO gas into the liquid steel are calculated to be 5.73 × 10⁻⁵ m³ and 0.13 kg, respectively. Mass of SiO₂ in the volume is 2.36 × 10⁻² kg (0.39 mole) which can be calculated from the composition of the refractory given in Table 5. Since there is an excessive amount of graphite, assuming this amount of SiO₂ produces CO gas by the Reaction (1), it can be obtained that the CO gas is generated as much as 0.92 L min⁻¹ at 1823 K, which is then supplied to the inner surface of the SEN (A = 2.290 × 10⁻³ m²). The volume of CO gas may be corrected to 0.15 L min⁻¹ at 298 K. This shows that once the produced CO gas in the SEN dissolves into the liquid steel, the reaction is limited by the GPMT: propagation of the CO gas from inside the nozzle to the inner surface of the nozzle. The CO gas can oxidize Ti-ULC steel at the interface between the SEN and the steel, and the liquid oxide mixed with solid alumina form.^10,11) Its consequences on nozzle clogging were discussed in the previous report by the present authors utilizing thermodynamic analysis and experimental trials.^8,9,10,11) A probable cause of nozzle clogging often observed during continuous casting of Ti-ULC steel was proposed also by inspecting a series of plant-used nozzles.¹²⁾ From the results obtained in the present study, it is likely that the generation of CO gas needs to be suppressed since the CO gas dissolution can be controlled by its supplying rate from the SEN. Optimizing the nozzle refractory constitution is required to suppress CO gas generation, consequently to suppress reoxidation of the liquid steel and nozzle clogging. Countermeasure to suppressing the CO gas generation in SEN has been investigated by the present authors, and it will be reported elsewhere.

5. Conclusion

Nozzle clogging of Ti-ULC steel during continuous casting may occur due to reoxidation of the steel by CO gas generated in SEN. In order to assess the possibility of the nozzle clogging, dissolution of CO gas into liquid iron was investigated at 1823 K using an induction heating furnace with a stirring device. Various experimental conditions were tested in order to find the rate controlling step. It was found that stirring in the liquid iron was not influencing the rate, while flow rate (Q) and partial pressure of CO (P_CO) gas affect the rate significantly. Under the present experimental condition, the rate was controlled by the gas phase mass transfer when the Q was lower than 0.75 L min⁻¹. Above Q = 0.75 L min⁻¹, the rate was not dependent on Q, but it was still dependent on P_CO.

In the context of a reoxidation of Ti-ULC steel by CO gas being responsible for the nozzle clogging,^10,11) a typical condition of SEN^33,34) was considered in order to assess whether a CO gas generated in the SEN has a decisive role in the nozzle clogging. It was revealed that supplying rate of CO gas from the SEN falls in the regime of the gas phase mass transfer control on the dissolution of CO into liquid steel. Since the CO gas can reoxidize the Ti-ULC steel and initiate the nozzle clogging, its suppression during the casting operation is thought to be important in order to suppress the nozzle clogging.

Acknowledgment

The authors would like to express the generous support from POSCO to the present authors’ research laboratory.

Appendix A. Rate of Carbothermic Reaction in SiO₂ + C Mixture at 1823 K

Silica powder (35 μm, No. 37974-00, Kanto chemical, Japan) and graphite powder (~1–2 μm, No. 28286-3, Aldrich chemical, USA) were pre-heated respectively for 1 hour in an Ar atmosphere at 1273 K in order to remove volatile impurities and moisture, before the carbothermic reaction was allowed. One mole of the silica (6.0 × 10⁻² kg) and one more of the graphite (1.2 × 10⁻² kg) were then thoroughly mixed for 1 hour for homogeneous distribution. 2 × 10⁻⁴ kg out of the mixture was taken, weighed, and placed in a Mo crucible (OD 12 × ID 8 × H 12 mm). Then, it was put in a quartz tube equipped with an RF generator (40 kW, 260 kHz). The tube was sealed by end caps in order to control the atmospheric condition. Ar gas purified by passing through CaSO₄ column, and MgO chips at 773 K was fed into the tube at 0.5 L min⁻¹ through an inner quartz tube. Power of the RF generator was adjusted in order to set a temperature at 1823 K. Once target temperature was achieved, the Mo crucible with a mixture of silica and graphite was kept for predetermined time (5, 10, 20, 30, and 60 minutes). After then, the power was turned off in order to quench the specimen, and was weighed in the same manner before the reaction. The mass change was calculated through the mass difference before and after the reaction. The samples of both before reaction and after reaction for 60 minutes were analyzed through X-Ray Diffraction (XRD) analysis in order to identify phase transition during the reaction.

According to a thermodynamic analysis for SiO₂–C reaction at 1823 K using FactSage with FactPS database,¹⁵⁾ it was found that the equilibrium phases were gas (mostly CO(g)), SiC(s) and SiO₂(s). Since SiO₂(s) and SiC(s) are a solid phase at 1823 K, these remained the sample without mass change after the reaction. In contrast, CO(g) leaves out of the sample, resulting in the mass decrease: net mass loss is −5.6 × 10⁻² kg per mole of reacted SiO₂(s). The XRD analysis showed that SiC(s) was formed after 1 hr reaction, as shown in Fig. A1. Therefore, in the present study, the Reaction (1) was the main carbothermic reaction.

Fig. A1.

Stable phases observed by XRD analysis in a mixture of SiO₂(s) and C(s): (a) before the reaction (b) after the reaction at 1823 K for 1 hr. (Online version in color.)

Mass change of all the samples is shown in Fig. A2. With respect to the initial mass (2 × 10⁻⁴ kg), it is seen that the samples lost their mass linearly with the reaction time, except for the sample reacted for 60 minutes. Also, from the linear trend (a dashed line), it is postulated that the samples had lost their mass during heating to 1823 K, although it was not significant. By neglecting the loss during the heating and the sample heated for 60 minutes, it can be concluded that the mixture of SiO₂ and C at 1823 K lost their mass as much as 3.64 × 10⁻⁵ kg for 30 minutes (or 1.21 × 10⁻⁶ kg min⁻¹). From stoichiometry of the Reaction (1), the number of moles of CO gas emitted at 1823 K was 4.33 × 10⁻⁵ mole min⁻¹ from the mixture. This corresponds to 6.47 × 10⁻³ L min⁻¹ at 1823 K assuming the ideal gas law. Since the Reaction (1) was not completed during the first 30 minutes, and number of moles of the SiO₂ in the reacted sample was 2.77 × 10⁻³ mole, the calculated volume of CO may be considered as a volume of CO gas generated by the Reaction (1) at 1823 K per 2.77 × 10⁻³ mole of the SiO₂, with enough C to react (or 2.33 L min⁻¹ per mole SiO₂ at 1823 K).

Fig. A2.

Mass changes of the mixture of SiO₂(s) and C(s) during the reaction at 1823 K.

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