Desulfurization Behavior of Low-sulfur Plastic Die Steel during ESR Process under Different Atmospheres

Abstract

Experimental investigation and kinetics model ware carried out to study the effect of the atmosphere on the desulfurization of low-sulfur plastic die steel during the electroslag remelting process. 55Cr17Mo1VN plastic die steel was applied as the electrode and remelted with two different kinds of atmospheres using a laboratory-scale ESR furnace. It was found that the sulfur content of 50 ppm in the electrode decreased to 8–12 ppm in the air atmosphere, while reduced to 9–14 ppm in a protective atmosphere. The desulfurization rates were 82% and 78%, respectively. Correspondingly, the sulfur content of 0.12% in initial slag increased to 0.125% and 0.15%. The coupled desulfurization kinetics model was established, the oxygen activity (a_O) and sulfur distribution coefficient (L_s) are taken into consideration, and they change with the remelting time during the calculation. The results show that the calculated values are in good agreement with the experimental values. The desulfurization effect at the electrode tip is significantly better than the positions where the droplet passes through the slag layer and the slag pool/molten pool interface. The L_s and comprehensive mass transfer coefficient of sulfur (k_S^*) decrease with the remelting time, while the a_O at each reaction position increases. Compared with the protective atmosphere, L_s and k_S^* have larger values during the air atmosphere ESR process, but the a_O value is equal. Under the different atmospheres, the most types of inclusions in the steel are MnS, and the refining atmosphere has no significant effect on the types of inclusions.

1. Introduction

With the rapid growth of the production and consumption of plastic products in recent years, the demand for plastic die steel is increasing. Plastic die steel not only has higher requirements for wear resistance, hardness, and welding performance but also has perfect corrosion resistance.¹⁾ Sulfur mainly exists in the form of inclusions in steel, such inclusions are disposed to micro-cracks and pitting pits in plastic die steel, which seriously affects their service life.^2,3,4) Therefore, to control the formation of sulfide inclusions, and improve the cleanliness of steel, the sulfur content in steel must be decreased as much as possible.

At present, electroslag remelting (ESR) process has been widely used for producing high-quality plastic die steel due to its advantages, such as excellent solidification structure and strong ability to remove inclusions, especially remove sulfide inclusions in steel.^{5,6,7,8,9,10,11,12)} A multitude of paper points out that desulfurization in the ESR refining process is affected by many factors, such as slag composition, electrode composition, remelting rate, power supply parameters, remelting atmosphere, and so on. Eissa et al.¹³⁾ studied the influence of the physical properties of slag on desulfurization, and the desulfurization is the result of the combined slag-metal reaction and slag-gas reaction during the ESR process. Liu et al.¹⁴⁾ found that increasing the remelting current increased sulfur content in the ingot. Cao et al.¹⁵⁾ found that the desulfurization ability was improved under single power two-circuits ESR process. Besides, Shi et al.¹⁶⁾ systematically described the relationship between deoxidation and desulfurization during ESR process. Ban-Ya, Bronson, and Pierre et al.^17,18) all pointed out that increasing the content of CaO and CaF₂ in the slag and increasing the temperature is beneficial to desulfurization. In addition, Wang et al.^19,20,21) established a transient three-dimensional coupled mathematical model to study the desulfurization behavior and predicted the sulfur content during the ESR process. Besides, Mattar et al.²²⁾ demonstrated that the nitrogen alloying process delayed the removal of sulfur during the ESR process.

Besides, the atmosphere of the ESR process also has a crucial effect on desulfurization. Dong et al.²³⁾ used electrode with sulfur content of 0.01% and found that the desulfurization rate was reduced due to the weakened gas-phase desulfurization under the protective atmosphere. Hou et al.²⁴⁾ established the desulfurization model of the protective ESR process by using 1Cr21Ni5Ti steel with a sulfur content of 0.035% and explained the desulfurization mechanism. However, Previous studies on the influence of ESR on desulfurization were mostly carried out in the case of high sulfur content in the electrode, few studies have reported the desulfurization behavior of low-sulfur steel in the ESR process under different atmospheres. Moreover, in order to make the calculation more accurate, the L_s (sulfur distribution coefficient) and a_O (oxygen activity) should be regarded as variables in the ESR process. Therefore, it is necessary to further improve the accuracy and rationality of the desulfurization model during the ESR process.

In the current works, experimental and model research on the desulfurization behavior of low-sulfur plastic die steel during the ESR process in different atmospheres were conducted. The experiments were performed in an air atmosphere and a protective atmosphere. Then, the desulfurization kinetics models in two kinds of atmospheres were established, which provide a theoretical basis to further reduce the sulfur content in the steel and improve the purity of steel grades.

2. Experimental

2.1. Experimental Procedure

The experiments were carried out in a 50 kg ESR furnace with the copper mold had an inner diameter of 130 mm. The atmosphere in the furnace can be controlled by the sliding seal ring. When the protective atmosphere is selected, the sliding seal ring is connected with the upper plane of the copper, and the inert gas is supplied through the upper gas pipeline of the mold. Figure 1 shows the equipment image and schematic diagram. The consumable electrode used in experiments was 55Cr17Mo1VN plastic die steel with a diameter of 72 mm and a length of 1000 mm, the chemical composition of the electrode listed in Table 1. The weight of the pre-melted slag employed in the experiments was 3.25 kg. Before ESR experiments, slag was heated in a muffle furnace at 873 K for at least 6 hours to remove moisture. The two experiments were carried out in an air atmosphere (Exp1) and the protective atmosphere with high-purity (99.999%) nitrogen (Exp2), respectively. In two experiments, the experimental voltage and current were controlled at 39 V and 2400 A correspondingly. During the remelting stable stage, the electrode remelting rate was managed at 39 kg/h.

Fig. 1.

(a) Equipment image of ESR (b) Schematic diagram of ESR. (Online version in color.)

Table 1. Chemical composition of electrode, wt%.

C	Si	Mn	S	O	N	Al	Cr	Mo	V	Fe
0.55	0.47	0.41	0.005	0.0014	0.1609	0.007	17.5	1.1	0.1	Bal

2.2. Chemical Analysis

After the experiments, the ingots were divided into six equal parts along the height direction, and samples were taken at each height position. The height of the sample selected could correspond to the remelting time. The contents of Cr, Mo, Mn, Si, Al, and V in steel were determined by direct reading spectrometer. Nitrogen content was measured by inert gas fusion thermal conductivity method while the total oxygen content was determined by inert gas fusion infrared absorption method. High frequency combustion infrared absorption method was used for the determination of carbon, sulfur content in steel and sulfur content in slag.

The total Ca, Al₂O₃, MnO, SiO₂, and Cr₂O₃ in the slag were measured by X-ray fluorescence spectrometry. FeO content was determined by potassium dichromate titration method, and fluorine content was determined by the EDTA titration method. The content of CaF₂ can be calculated by fluorine content, and the remaining Ca can be considered as the form of CaO in the slag, so the specific content of CaO in slag can be obtained. The phases in the original and the final slag was measured at room temperature by X-ray diffraction using Cu Kα radiation. The types of inclusions in the electrode and ingots were detected by SEM/EDS.

2.3. Experimental Results

Table 2 shows the original and the final slag composition under Exp1 and Exp2, respectively. The sulfur content increases from 0.12% to 0.125% and 0.15% in Exp1 and Exp2, correspondingly, which is mainly due to the effect of the atmosphere. Figure 2 presents the X-ray diffraction analysis of the slags, the results show that all slags contain the CaS phase, but the Exp1 slag also contains the CaSO₄ phase as a result of the reaction (1)²⁵⁾ under Exp1 condition.   

$$(\mathrm{C}\mathrm{a}\mathrm{S})+2\left\{{\mathrm{O}}_2\right\}=(\mathrm{C}\mathrm{a}\mathrm{S}{\mathrm{O}}_4)$$(1)

Where the bracket ( ) represents the components of molten slag, and the brace { } indicates the components in gas phase. The above symbolic representation is also applicable to other reaction equations in this paper.

Table 2. Slag composition at the beginning and end of ESR, wt%.

	CaF2	CaO	Al2O3	SiO2	MnO	Cr2O3	FeO	S
original composition	60.83	15.28	22.26	1.17	<0.01	<0.01	0.31	0.12
Exp1	57.53	17.02	21.28	2.75	0.06	0.23	0.78	0.125
Exp2	58.06	16.41	21.47	2.66	0.05	0.20	0.58	0.15

Fig. 2.

XRD analysis of slags. (Online version in color.)

As shown in Table 3, the sulfur content decreases to 8–12 ppm in Exp1, while reduced to 9–14 ppm in Exp2, and the desulfurization rates were 82% and 78%, respectively. The oxygen content under Exp1 is slightly higher than that under Exp2, which may be related to the fact that the dissolved oxygen generated by desulfurization reaction can be absorbed by molten steel. The results indicate that there is a slight effect of the atmosphere on sulfur content in the ingots, which contradicts the important role of gas-phase desulfurization mentioned in previous research reports.^26,27,28,29) Therefore, the desulfurization mass transfer model is adopted to better understand the effect of remelting atmosphere on the desulfurization of low-sulfur plastic die steel.

Table 3. Chemical composition of ingots, wt./%.

Chemical composition		C	Si	Mn	S	O	N	Al	Cr	Mo	V	Fe
Exp1	Bottom	0.53	0.35	0.41	0.0008	0.00198	0.1422	0.028	16.94	1.02	0.12	Bal
	Top	0.53	0.40	0.41	0.0012	0.00215	0.1526	0.019	18.07	1.07	0.13	Bal
Exp2	Bottom	0.54	0.35	0.41	0.0009	0.00176	0.1523	0.029	17.76	1.05	0.13	Bal
	Top	0.53	0.42	0.41	0.0014	0.00188	0.1711	0.022	18.15	1.07	0.13	Bal

3. Coupled Model of Desulfurization

3.1. Model Assumptions

As displayed in Fig. 1(b), ESR is a refining process with complex chemical reactions, which mainly consists of following fundamental processes: the electrode tip metal film-slag interface, droplets passing through the slag layer, molten pool-slag pool reaction interface, and sometimes including slag-gas reaction interface. To simplify the desulfurization kinetic model, the following assumptions are needed:

(1) For each reaction position of ESR, the slag-metal system can be regarded as composed of two semi-infinite systems.

(2) In the two phases of slag and metal, the initial concentration of each reactant is evenly distributed.

(3) The chemical reaction takes place at the interface of the slag-metal phase at a high speed, and the reaction reaches thermodynamic equilibrium instantaneously, and each reaction is considered to be part of the entire interface equilibrium system.

(4) There are no obvious refining reactions in the solidification process of molten steel.

(5) Under the air atmosphere experimental conditions, the partial pressure of oxygen on the slag pool surface is equal to that in the air.

3.2. Mass Transfer Equations

3.2.1. Slag-metal Interface

According to the characteristics of the film theory and the permeability theory,³⁰⁾ at the slag-metal interface, the slag-metal reaction rate is controlled by mass transport processes in slag and metal phases and can be expressed by   

$$-\frac{d{w}_i^{\mathrm{m}}}{dt}=\frac{A}{V_m}{k}_i^{*}\left(w_i^{\mathrm{m},\mathrm{o}}-\frac{w_{i{\mathrm{O}}_n}^{\mathrm{s},\mathrm{o}}}{L_i}\right)$$(2)

Where $w_i^{\mathrm{m}}$ and $w_i^{\mathrm{m},\mathrm{o}}$ are the mass fraction of species i in metal at any moment and initial time, respectively. A is the area of the slag-metal reaction interface; V_m is the liquid metal volume. $w_{\mathrm{i}{\mathrm{O}}_n}^{\mathrm{s},\mathrm{o}}$ and $w_{\mathrm{i}{\mathrm{O}}_n}^{\mathrm{s}}$ are the original mass fraction of species iO_n in slag at the original time and any moment. L_i is the interfacial distribution coefficient of elements i at the metal-slag interface; t is the contact reaction time, $k_i^{*}$ is the comprehensive mass transfer coefficient of species i.

In Eq. (2), the $k_i^{*}$ can be calculated by   

$$\frac{\text{1}}{k_i^{*}}=\frac{1}{k_i}+\frac{{\rho }_m}{k_{i{O}_n}{L}_i{\rho }_s}$$(3)

Where ρ_m and ρ_s are the density of metal and slag, respectively, k_i and $k_{i{O}_n}$ are the mass transfer coefficient of the elements i in the molten steel and slag, respectively. The L_i in Eqs. (2) and (3) can be defined as   

$$L_i=\frac{w_{i{\mathrm{O}}_n}^{\mathrm{s}}{}^{\text{*}}}{w_i^{\mathrm{m}}{}^{*}}$$(4)

Where symbol * represents a value of reaction equilibrium at the slag-metal interface. It should be noted out that L_i will change with reaction positions and remelting time during the ESR process.

3.2.2. Slag-air Interface

According to Kato’s³¹⁾ work, the desulfurization rate at the slag-air interface can be expressed by   

$$-\frac{d{w}_{{\mathrm{S}}^{2-}}^{\mathrm{s}}}{dt}=\frac{A_g}{V_S}\cdot k_{\mathrm{s} \mathrm{g}}\cdot p_{{\mathrm{O}}_2}^{1/2}\cdot w_{{\mathrm{S}}^{2-}}^{\mathrm{s}}$$(5)

Where k_sg is the mass transfer coefficient between the slag and gas phase. p_O2 is the oxygen partial pressure.

3.3. Thermodynamic Reactions and Kinetic Model

3.3.1. Slag-metal Reaction Interface

At the slag-metal reaction interface, the desulfurization process in ESR can be expressed by the following reaction:   

$$[\mathrm{S}]+({\mathrm{O}}^{2-})=[\mathrm{O}]+({\mathrm{S}}^{2-})$$(6)

Where square brackets [ ] denotes the components of liquid metal, which are the same in the following article.

The sulfur distribution ratio L_s is usually used to describe the thermodynamics ability of desulfurization, and the expression is as follows.^32,33)   

$$\mathrm{l}\mathrm{g}{L}_{\mathrm{S}}=\mathrm{l}\mathrm{g}\frac{w_{{\text{S}}^{2-}}^{\text{s}}}{w_{\mathrm{S}}^{\mathrm{m}}}=\frac{-935}{T}+1.375+\mathrm{l}\mathrm{g}{C}_{\mathrm{S}}+\mathrm{l}\mathrm{g}{f}_{\mathrm{S}}-\mathrm{l}\mathrm{g}{a}_{\mathrm{O}}$$(7)

Where a_O is oxygen activity. f_S is the sulfur activity coefficient in the metal. T is the temperature at the slag-metal interface at each reaction position. C_s is the sulfur capacity of slag. In the model established in this paper, the sulfur capacity is calculated by Young’s³⁴⁾ model, the specific expression is   

$$\begin{array}{l}\mathrm{l}\mathrm{g}{C}_{\mathrm{S}}=-13.913+42.84\mathrm{\Lambda }-23.82{\mathrm{\Lambda }}^2-{\displaystyle \frac{11\mathrm{\hspace{0.17em} }710}{T}}-0.02223w_{\mathrm{S}\mathrm{i}{\mathrm{O}}_2}^{\mathrm{s}}\\ \mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }- 0.02275w_{\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3}^{\mathrm{s}}\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\Lambda }<0.8\\ \mathrm{l}\mathrm{g}{C}_{\mathrm{S}}=-0.6261+0.4804\mathrm{\Lambda }+0.7197{\mathrm{\Lambda }}^2+{\displaystyle \frac{1\mathrm{\hspace{0.17em} }697}{T}}-{\displaystyle \frac{2\mathrm{\hspace{0.17em} }587\mathrm{\Lambda }}{T}}\\ \mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }+5.144\times 10^{-4}{w}_{\mathrm{F}\mathrm{e}\mathrm{O}}^{\mathrm{s}}\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\Lambda }\ge 0.8\end{array}$$(8)

Where Λ is the optical basicity calculated based on the assumptions of Duffy and Ingram,³⁵⁾ and given by Eqs. (9) and (10):   

$$\mathrm{\Lambda }=\frac{\sum (N_{i{\mathrm{O}}_n}{n}_i{\mathrm{\Lambda }}_i)}{\sum (N_{i{\mathrm{O}}_n}{n}_i)}$$(9)

  

$$N_i={\displaystyle \frac{w_{i{\mathrm{O}}_n}^{\mathrm{s}}}{M_i\sum {\displaystyle \frac{w_{i{\mathrm{O}}_n}^{\mathrm{s}}}{M_i}}}}$$(10)

Where i are the components of CaO, CaF₂, Al₂O₃, MnO, FeO, and SiO₂. N_iOn is the mole fraction of components i in the slag phase. M_i is the molar mass of species i. n_i is the number of oxygen atoms of components i in the slag. Λ_i is the optical basicity of each pure oxides in slag, it is summarized in Table 4 calculated from Pauling’s³⁶⁾ electronegativity.

Table 4. Optical basicities of pure oxides.

	CaO	CaF2	Al2O3	MnO	FeO	SiO2
Λi	1.0	0.67	0.61	0.59	0.51	0.48

Based on the 55Cr17Mo1VN chemical composition, the related reactions at the slag-metal interface can be classified to the systems of [S] − (S²⁻), [Mn] − (MnO), [Si] − (SiO₂), [Al] − (Al₂O₃), [Cr] − (Cr₂O₃) and [Fe] − (FeO). Figure 3 shows the schematic diagram of components transmission at metal-slag-air interface. The [S] − (S²⁻) reaction has been expressed in Eq. (6), the rest of the reactions and equilibrium constant expressions are listed by Eqs. (11), (12), (13), (14), (15), (16), (17), (18), (19), (20).^37,38,39,40)   

$$[\mathrm{M}\mathrm{n}]+[\mathrm{O}]=(\mathrm{M}\mathrm{n}\mathrm{O})$$(11)

  

$$\mathrm{l}\mathrm{g}{K}_{\mathrm{M}\mathrm{n}}=\mathrm{l}\mathrm{g}\frac{a_{\mathrm{M}\mathrm{n}\mathrm{O}}}{a_{\mathrm{M}\mathrm{n}}{a}_{\mathrm{O}}^{*}}=\frac{16\mathrm{\hspace{0.17em} }751}{T}-8.12$$(12)

  

$$[\mathrm{S}\mathrm{i}]+2[\mathrm{O}]=(\mathrm{S}\mathrm{i}{\mathrm{O}}_2)$$(13)

  

$$\mathrm{l}\mathrm{g}{K}_{\mathrm{S}\mathrm{i}}=\mathrm{l}\mathrm{g}\frac{a_{\mathrm{S}\mathrm{i}{\mathrm{O}}_2}}{a_{\mathrm{S}\mathrm{i}}{a}_{\mathrm{O}}^{*}{}^2}=\frac{30\mathrm{\hspace{0.17em} }110}{T}-11.4$$(14)

  

$$[\mathrm{A}\mathrm{l}]+1.5[\mathrm{O}]=(\mathrm{A}\mathrm{l}{\mathrm{O}}_{1.5})$$(15)

  

$$\mathrm{l}\mathrm{g}{K}_{\mathrm{A}\mathrm{l}}=\mathrm{l}\mathrm{g}\frac{a_{\mathrm{A}\mathrm{l}{\mathrm{O}}_{1.5}}}{a_{\mathrm{A}\mathrm{l}}{a}_{\mathrm{O}}^{*}{}^{1.5}}=\frac{32\mathrm{\hspace{0.17em} }000}{T}-10.285$$(16)

  

$$[\mathrm{C}\mathrm{r}]+1.5[\mathrm{O}]=(\mathrm{C}\mathrm{r}{\mathrm{O}}_{1.5})$$(17)

  

$$\mathrm{l}\mathrm{g}{K}_{\mathrm{C}\mathrm{r}}=\mathrm{l}\mathrm{g}\frac{a_{\mathrm{C}\mathrm{r}{\mathrm{O}}_{1.5}}}{a_{\mathrm{C}\mathrm{r}}{a}_{\mathrm{O}}^{*}{}^{1.5}}=\frac{\text{22}\mathrm{\hspace{0.17em} }\text{020}}{T}-\text{9}\text{.71}$$(18)

  

$$[\mathrm{F}\mathrm{e}]+[\mathrm{O}]=(\mathrm{F}\mathrm{e}\mathrm{O})$$(19)

  

$$\mathrm{l}\mathrm{g}{K}_{\mathrm{F}\mathrm{e}\mathrm{O}}=\mathrm{l}\mathrm{g}\frac{a_{\mathrm{F}\mathrm{e}\mathrm{O}}}{a_{\mathrm{F}\mathrm{e}}{a}_{\mathrm{O}}^{*}}=\frac{6\mathrm{\hspace{0.17em} }150}{T}-2.604$$(20)

Where the K_Mn, K_Si, K_Al, K_Cr, and K_FeO are the equilibrium constants of each reaction. a_Mn, a_Si, a_Al, a_Cr, and a_Fe are the activities of components in the metal, a_Fe can be considered equal to 1, and the activities of other species can be calculated by   

$$a_i=f_i{w}_i^{\mathrm{m}}$$(21)

Where f_i is the activity coefficient of component i, which is mainly related to the metal composition and temperature. The f_i can be calculated as follows:   

$$\mathrm{l}\mathrm{g}{f}_i={\sum }_j(e_i^j{w}_j^{\mathrm{m}}+r_i^j{w}_j^{\mathrm{m}2})$$(22)

  

$$e_{i(T)}^j=\frac{1\mathrm{\hspace{0.17em} }873}{T}{e}_{i(1\mathrm{\hspace{0.17em} }873)}^j$$(23) ⁴¹⁾

Where $e_i^j$ and $r_i^j$ are the first-order and the second-order activity interaction coefficients, respectively, and the values at 1873 K are listed in Tables 5⁴¹⁾ and 6,⁴²⁾ respectively.

Fig. 3.

The diagram of mass transfer among slag-metal-gas interface.

Table 5. The first-order interaction coefficients $e_i^j$ used in this study.

$e_i^j$	C	Si	Mn	P	S	Al	O
S	0.111	0.075	−0.026	0.035	0.018	0.041	–
Mn	−0.0538	−0.0327	–	−0.0035	−0.048	–	−0.083
Si	0.24	0.37	0.002	0.11	0.056	0.07	−0.23
Al	0.091	0.06	–	–	0.049	0.048	−6.60

Table 6. The second-order interaction coefficients $r_i^j$ used in this study.

$r_i^j$	C	Si	P	S	Al	Mn
S	0.0058	0.0017	0.0006	−0.0009	0.0009	–

In Eqs. (12), (14), (16), (18), and (20), a_MnO, a_SiO2, a_AlO1.5, a_CrO1.5, and a_FeO are the activities of the oxides in the slag, and these activities can be calculated by   

$$a_{i{\mathrm{O}}_n}={\gamma }_{i{\mathrm{O}}_n}{N}_{i{\mathrm{O}}_n}$$(24)

Where N_iOn is the mole fraction of component i in the slag. γ_iOn is the Raoult activity coefficient of component i in the slag which is given by Eqs. (25), (26), (27), (28), (29):⁴³⁾   

$$\begin{array}{l}\mathrm{l}\mathrm{g}{\gamma }_{\mathrm{F}\mathrm{e}\mathrm{O}}=\frac{11\mathrm{\hspace{0.17em} }800}{\mathrm{T}}{N}_{\mathrm{C}\mathrm{a}\mathrm{O}}(N_{\mathrm{S}\mathrm{i}{\mathrm{O}}_2}+0.25N_{\mathrm{A}\mathrm{l}{\mathrm{O}}_{1.5}}+\text{0}\text{.45}{N}_{\mathrm{C}\mathrm{r}{\mathrm{O}}_{1.5}})\\ \mathrm{\hspace{1em}\hspace{1em}\hspace{1em}}+\frac{3\mathrm{\hspace{0.17em} }562}{T}{N}_{\mathrm{S}\mathrm{i}{\mathrm{O}}_2}{N}_{\mathrm{A}\mathrm{l}{\mathrm{O}}_{1.5}}+\frac{4\mathrm{\hspace{0.17em} }916}{T}{N}_{\mathrm{M}\mathrm{n}\mathrm{O}}(N_{\mathrm{S}\mathrm{i}{\mathrm{O}}_2}+\text{0}\text{.45}{N}_{\mathrm{C}\mathrm{r}{\mathrm{O}}_{1.5}})\\ \mathrm{\hspace{1em}\hspace{1em}\hspace{1em}}+\frac{123}{T}{N}_{\mathrm{M}\mathrm{n}\mathrm{O}}{N}_{\mathrm{A}\mathrm{l}{\mathrm{O}}_{1.5}}\text{+}\frac{1\mathrm{\hspace{0.17em} }\text{978}}{T}{N}_{\mathrm{S}\mathrm{i}{\mathrm{O}}_2}{N}_{\mathrm{A}\mathrm{l}{\mathrm{O}}_{1.5}}\end{array}$$(25)

  

$$\text{ lg}{\gamma }_{\text{MnO}}=\mathrm{l}\mathrm{g}{\gamma }_{\mathrm{F}\mathrm{e}\mathrm{O}}-\frac{4\mathrm{\hspace{0.17em} }916}{T}(N_{\mathrm{S}\mathrm{i}{\mathrm{O}}_2}+\text{0}\text{.45}{N}_{\mathrm{C}\mathrm{r}{\mathrm{O}}_{1.5}})-\frac{123}{T}{N}_{\mathrm{A}\mathrm{l}{\mathrm{O}}_{1.5}}$$(26)

  

$$\begin{array}{l}\text{lg}{\gamma }_{{\text{SiO}}_{\text{2}}}=\text{lg}{\gamma }_{\mathrm{F}\mathrm{e}\mathrm{O}}-\frac{11\mathrm{\hspace{0.17em} }800}{T}{N}_{\mathrm{C}\mathrm{a}\mathrm{O}}-\frac{4\mathrm{\hspace{0.17em} }916}{T}{N}_{\mathrm{M}\mathrm{n}\mathrm{O}}\\ \mathrm{\hspace{1em}\hspace{1em}\hspace{1em}}-\frac{3\mathrm{\hspace{0.17em} }562}{T}{N}_{\mathrm{A}\mathrm{l}{\mathrm{O}}_{1.5}}-\frac{1\mathrm{\hspace{0.17em} }978}{T}\text{0}\text{.45}{N}_{\mathrm{C}\mathrm{r}{\mathrm{O}}_{1.5}}\end{array}$$(27)

  

$$\text{lg}{\mathrm{\gamma }}_{\mathrm{A}{\mathrm{l}}_2{O}_3}=\text{lg}{\gamma }_{\mathrm{F}\mathrm{e}\mathrm{O}}-\frac{2\mathrm{\hspace{0.17em} }950}{T}{N}_{\mathrm{C}\mathrm{a}\mathrm{O}}-\frac{3\mathrm{\hspace{0.17em} }562}{T}{N}_{\mathrm{S}\mathrm{i}{\mathrm{O}}_2}-\frac{123}{T}{N}_{\mathrm{M}\mathrm{n}\mathrm{O}}$$(28)

  

$$\text{lg}{\gamma }_{\mathrm{C}\mathrm{r}{\mathrm{O}}_{1.5}}=\mathrm{l}\mathrm{g}{\gamma }_{\mathrm{F}\mathrm{e}\mathrm{O}}-\frac{\text{5}\mathrm{\hspace{0.17em} }\text{310}}{T}{N}_{\mathrm{C}\mathrm{a}\mathrm{O}}-\frac{\text{2}\mathrm{\hspace{0.17em} }\text{212}}{T}{N}_{\mathrm{M}\mathrm{n}\mathrm{O}}-\frac{1\mathrm{\hspace{0.17em} }978}{T}{N}_{\mathrm{S}\mathrm{i}{\mathrm{O}}_2}$$(29)

Based on the relationship between the molar fraction and the mass fraction, the expressions of the equilibrium constants of the slag-metal reaction are converted to obtain the expressions of the equilibrium L_i of the species i at the slag-metal interface. Finally, L_i is expressed as Eqs. (30), (31), (32), (33), (34):   

$$L_{\mathrm{M}\mathrm{n}}=\frac{w_{\mathrm{M}\mathrm{n}\mathrm{O}}^{\mathrm{s}}{}^{*}}{w_{\mathrm{M}\mathrm{n}}^{\mathrm{m}}{}^{*}}=\frac{K_{\mathrm{M}\mathrm{n}}{M}_{\mathrm{M}\mathrm{n}\mathrm{O}}{f}_{\mathrm{M}\mathrm{n}}{\sum }_i\frac{w_{i{\mathrm{O}}_n}^{\mathrm{s}}}{M_i}}{{\gamma }_{\mathrm{M}\mathrm{n}\mathrm{O}}}{a}_{\mathrm{O}}^{*}$$(30)

  

$$L_{\mathrm{S}\mathrm{i}}=\frac{w_{\mathrm{S}\mathrm{i}{\mathrm{O}}_2}^{\mathrm{s}}{}^{*}}{w_{\mathrm{S}\mathrm{i}}^{\mathrm{m}}{}^{*}}=\frac{K_{\mathrm{S}\mathrm{i}}{M}_{\mathrm{S}\mathrm{i}{\mathrm{O}}_2}{f}_{\mathrm{S}\mathrm{i}}{\sum }_i\frac{w_{i{\mathrm{O}}_n}^{\mathrm{s}}}{M_i}}{{\gamma }_{\mathrm{S}\mathrm{i}{\mathrm{O}}_2}}{a}_{\mathrm{O}}^{*2}$$(31)

  

$$L_{\mathrm{A}\mathrm{l}}=\frac{w_{\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3}^{\mathrm{s}}{}^{*}}{w_{\mathrm{A}\mathrm{l}}^{\mathrm{m}}{}^{*}}=\frac{K_{\mathrm{A}\mathrm{l}}{M}_{\mathrm{A}\mathrm{l}{\mathrm{O}}_{1.5}}{f}_{\mathrm{A}\mathrm{l}}{\sum }_i\frac{w_{i{\mathrm{O}}_n}^{\mathrm{s}}}{M_i}}{{\gamma }_{\mathrm{A}\mathrm{l}{\mathrm{O}}_{1.5}}}{a}_{\mathrm{O}}^{*1.5}$$(32)

  

$$L_{\mathrm{C}\mathrm{r}}=\frac{w_{\mathrm{C}{\mathrm{r}}_2{\mathrm{O}}_3}^{\mathrm{s}}{}^{*}}{w_{\mathrm{C}\mathrm{r}}^{\mathrm{m}}{}^{*}}=\frac{K_{\mathrm{C}\mathrm{r}}{M}_{\mathrm{C}\mathrm{r}{\mathrm{O}}_{1.5}}{f}_{\mathrm{C}\mathrm{r}}{\sum }_i\frac{w_{i{\mathrm{O}}_n}^{\mathrm{s}}}{M_i}}{{\gamma }_{\mathrm{C}\mathrm{r}{\mathrm{O}}_{1.5}}}{a}_{\mathrm{O}}^{*1.5}$$(33)

  

$$L_{\mathrm{F}\mathrm{e}\mathrm{O}}=w_{\mathrm{F}\mathrm{e}\mathrm{O}}^{\mathrm{s}}{}^{*}=\frac{K_{\mathrm{F}\mathrm{e}\mathrm{O}}{M}_{\mathrm{F}\mathrm{e}\mathrm{O}}{\sum }_i\frac{w_{i{\mathrm{O}}_n}^{\mathrm{s}}}{M_i}}{{\gamma }_{\mathrm{F}\mathrm{e}\mathrm{O}}}{a}_{\mathrm{O}}^{*}$$(34)

We can obtain the relationship of the content of species i with time by substituting each L_i into Eq. (2). When L_s is substituted and the integral transformation is performed, the expression for $w_{\mathrm{S}}^{\mathrm{m}}$ is shown in Eq. (35), and expressions for other components are similar to $w_{\mathrm{S}}^{\mathrm{m}}$.   

$$w_{\mathrm{S}}^{\mathrm{m}}=\mathrm{e}\mathrm{x}\mathrm{p}\left(-\frac{A}{V_{\mathrm{m}}}{k}_{\mathrm{S}}^{*}t\right)\times \left(w_{\mathrm{S}}^{\mathrm{m},\mathrm{o}}-\frac{w_{{\mathrm{S}}^{2-}}^{\mathrm{w},\mathrm{o}}}{L_{\mathrm{S}}}\right)+\frac{w_{{\mathrm{S}}^{2-}}^{\mathrm{w},\mathrm{o}}}{L_{\mathrm{S}}}$$(35)

Correspondingly, the mass transfer rate equations of the relevant components in the slag can be acquired. Finally, in the desulfurization kinetic Eq. (35), only the $a_{\mathrm{O}}^{*}$ is unknown parameters at each reaction position. Therefore, the desulfurization kinetic Eq. (35) can be regarded as a function of $a_{\mathrm{O}}^{*}$. According to the mass balance of oxygen between slag and metal, Eq. (36) can be obtained.   

$$\begin{array}{l}{\displaystyle \frac{1}{{\mathrm{M}}_{\mathrm{M}\mathrm{n}}}}{\displaystyle \frac{\mathrm{d}{w}_{\mathrm{M}\mathrm{n}}^{\mathrm{m}}}{\mathrm{d}t}}+{\displaystyle \frac{2}{{\mathrm{M}}_{\mathrm{S}\mathrm{i}}}}{\displaystyle \frac{\mathrm{d}{w}_{\mathrm{S}\mathrm{i}}^{\mathrm{m}}}{\mathrm{d}t}}+{\displaystyle \frac{1.5}{{\mathrm{M}}_{\mathrm{A}\mathrm{l}}}}{\displaystyle \frac{\mathrm{d}{w}_{\mathrm{A}\mathrm{l}}^{\mathrm{m}}}{\mathrm{d}t}}+{\displaystyle \frac{1.5}{{\mathrm{M}}_{\mathrm{C}\mathrm{r}}}}{\displaystyle \frac{\mathrm{d}{w}_{\mathrm{C}\mathrm{r}}^{\mathrm{m}}}{\mathrm{d}t}}\\ ={\displaystyle \frac{1}{{\mathrm{M}}_{\mathrm{S}}}}{\displaystyle \frac{\mathrm{d}{w}_{\mathrm{S}}^{\mathrm{m}}}{\mathrm{d}t}}+{\displaystyle \frac{1}{{\mathrm{M}}_{\mathrm{F}\mathrm{e}\mathrm{O}}}}{\displaystyle \frac{\mathrm{d}{w}_{\mathrm{F}\mathrm{e}\mathrm{O}}^{\mathrm{s}}}{\mathrm{d}t}}\end{array}$$(36)

The left-hand side of Eq. (36) is the consumption rate of oxygen to the slag-metal interface, and the right-hand side is the supply rate of oxygen to the slag-metal interface.

3.3.2. Slag-air Reaction Interface

In the Exp1 experimental condition, due to gas-phase desulfurization, ESR generally has a higher desulfurization rate in theory. Reactions (37) and (38) occur at the slag-gas interface, which decreases the sulfur content and promote the desulfurization process in the slag.   

$$({\mathrm{S}}^{2-})+\frac{1}{2}\left\{{\mathrm{O}}_2\right\}=\left\{{\mathrm{S}}_2\right\}+({\mathrm{O}}^{2-})$$(37)

  

$$\frac{1}{2}\left\{{\mathrm{S}}_2\right\}+\left\{{\mathrm{O}}_2\right\}=\left\{\mathrm{S}{\mathrm{O}}_2\right\}$$(38)

The desulfurization reaction rate at the slag-gas interface has been given by the Eq. (5). Substituting Eq. (5) integrals into Eq. (35), the change rule of sulfur content in steel under air atmosphere can be calculated by follows:   

$$w_{\mathrm{S}}^{\mathrm{m}}=\mathrm{e}\mathrm{x}\mathrm{p}\left(-\frac{A}{V_{\mathrm{m}}}{k}_{\mathrm{S}}^{*}t\right)\times \left(w_{\mathrm{S}}^{\mathrm{m},\mathrm{o}}-\frac{w_{{\mathrm{S}}^{2-}}^{\mathrm{s},\mathrm{o}}-w_{{\mathrm{S}}^{2-}}^{\mathrm{s}}}{L_{\mathrm{S}}}\right)+\frac{w_{{\mathrm{S}}^{2-}}^{\mathrm{s},\mathrm{o}}-w_{{\mathrm{S}}^{2-}}^{\mathrm{s}}}{L_{\mathrm{S}}}$$(39)

To calculate the sulfur content changes during the ESR process under different atmospheres, the following types of data are required: thermodynamic data, kinetic data, geometric data, etc.

3.4. Model Parameters

3.4.1. Reaction Temperature

The liquidus temperature of 55Cr17Mo1VN plastic die steel can be calculated by Thermo-calc: T_liquidus = 1720 K. According to related reference,⁴⁴⁾ the temperature of the electrode tip/slag interface is generally higher than the liquidus temperature by 20–30 K, assumed that the reaction temperature at this position is 1750 K. Furthermore, when the droplet formed from at the electrode tip to pass through the slag layer, it is continuously heated by the slag and the temperature of the droplet reaches 1960 K. The temperature at the slag-metal pool is taken as 1895 K.

3.4.2. Mass Transfer Coefficients

According to the permeation theory, the expressions mass transfer coefficients of the metal side and slag at each reaction stage can be obtained from Eqs. (40) and (41), respectively. Where the $D_i^{\mathrm{m}}$ and $D_{i{\mathrm{O}}_n}^{\mathrm{s}}$ are diffusion coefficients of i and iO_n in metal and slag side, the $D_{\mathrm{S}}^{\mathrm{m}}$ and $D_{\mathrm{S}}^{\mathrm{s}}$ can be taken as (0.0068T − 10.46) × 10⁻⁴ cm²/s and 3.8 × 10⁻⁴ cm²/s according to the reference;²⁴⁾ t_e is contact reaction time. The t_e at the electrode tip can be calculated by Eq. (42).⁴⁵⁾   

$$k_i=2\sqrt{\frac{D_i^{\mathrm{m}}}{\pi t_e}}$$(40)

  

$$k_{i{\mathrm{O}}_n}=2\sqrt{\frac{D_{i{\mathrm{O}}_n}^{\mathrm{s}}}{\pi t_e}}$$(41)

  

$$t_e=3.35{\left(\frac{2\pi \mathrm{c}\mathrm{o}\mathrm{s}\theta }{3Q_m}\right)}^{2/3}{\left(\frac{{\mu }_m}{\mathrm{g}{\rho }_m\mathrm{s}\mathrm{i}\mathrm{n}\theta }\right)}^{1/3}{\left(\frac{r_{\mathrm{E}}}{\mathrm{c}\mathrm{o}\mathrm{s}\theta }\right)}^{5/3}$$(42)

Where, θ is the taper angle of the electrode tip, as shown in Fig. 4, Q_m is the volume remelting rate. μ_m is the viscosity of the metal. r_E is the radius of the consumable electrode. To make the calculation more accurate, the electrode was immediately lifted after the experiments, as shown in Fig. 4(b), and the simplified diagram is shown in Fig. 4(a). After calculation, t_e = 1.02 s at electrode tip. According to the reference,²⁴⁾ the average velocity of metal droplets passing through the slag layer is 31 cm/s, and the velocity of the molten slag at the droplet is taken as 10 cm/s. Combining the height of the molten slag and the electrode immersed depth, the t_e for the droplet to pass through the slag layer can be calculated, 0.19 s. Further, the mass transfer coefficient at each position can be obtained by Eqs. (40) and (41). At the slag-air interface, according to the reference,³¹⁾ k_sg = 0.01 cm/s.

Fig. 4.

Schematic diagram and topography of electrode tip. (Online version in color.)

3.4.3. Area/Volume Ratio

At the electrode tip, according to Fig. 4(a), the area and volume of the metal film can be estimated by the following Eqs. (43) and (44):   

$$A_f={\displaystyle \frac{\pi {\left(r_{\mathrm{E}}+{\displaystyle \frac{\delta }{2\mathrm{c}\mathrm{o}\mathrm{s}\theta }}\right)}^2}{\mathrm{c}\mathrm{o}\mathrm{s}\theta }}=54.39\mathrm{\hspace{0.17em} }\mathrm{c}{\mathrm{m}}^2$$(43)

  

$$V_f={\displaystyle \frac{\pi r_{\mathrm{E}}^2{\displaystyle \frac{\delta }{\mathrm{s}\mathrm{i}\mathrm{n}\theta }}}{3}}=0.54\mathrm{\hspace{0.17em} }\mathrm{c}{\mathrm{m}}^3$$(44)

Where δ is the average liquid film thickness, based on the reference⁴⁴⁾ estimation of 76 mm diameter consumable electrode, δ is taken as 0.03 cm. During the droplet pass through the slag pool, it assumed that the Area/Volume is 24 cm⁻¹.⁴⁴⁾ Numerical simulation Fluent software was used to calculate the shape of the molten pool under the experimental conditions, as shown in Fig. 5. The molten pool is considered to be composed of a cylinder and an approximate ellipsoid.

Fig. 5.

Morphology of the molten pool. (Online version in color.)

According to the numerical simulation results, the cylindrical volume (V_cylinder) and approximate spherical void volume (V_{Spherical void}) can be calculated by Eqs. (45) and (46) respectively.   

$$V_{\mathrm{M}\mathrm{e}\mathrm{t}\mathrm{a}\mathrm{l} \mathrm{P}\mathrm{o}\mathrm{o}\mathrm{l}}=V_{\mathrm{C}\mathrm{y}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{r}}+V_{\mathrm{S}\mathrm{p}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{ }\mathrm{v}\mathrm{o}\mathrm{i}\mathrm{d}}=\pi R_{\mathrm{E}}^2{h}_{\mathrm{I}1}+\frac{\pi h_{\mathrm{I}2}^2(3R_{\mathrm{E}}^2+h_{\mathrm{I}2}^2)}{6}$$(45)

  

$$A_{\mathrm{M}\mathrm{e}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{\hspace{0.17em} }\mathrm{P}\mathrm{o}\mathrm{o}\mathrm{l}}=\pi R_{\mathrm{E}}^2$$(46)

Where h_I1 is the height of the cylindrical section. h_I2 is the height of the spherical void section. R_E is the internal radius of the ESR mold. During the ESR process, since the electrode is immersed in the slag pool, the slag-air contact interface can be regarded as a ring, which can be calculated on the basis of the following equation.   

$$A_{\mathrm{g}}=\pi (R_{\mathrm{E}}^2-r_{\mathrm{E}}^2)$$(47)

The volume of slag can be calculated according to the quality and density of the slag. When the ρ_s = 2.6 g/cm³, the calculated slag volume is 1320 cm³.

So far, the relevant parameters in the desulfurization kinetic model have been solved and summarized in Table 7. Only the mass transfer coefficients of sulfur in slag and steel are listed in the table, and the solution method of mass transfer coefficients of other components is similar.

Table 7. Related parameters in the desulfurization kinetic model.

Parameters	Reaction positions
	electrode tip/slag	droplet/slag	metal pool/slag	slag/air
ks, cm/s	0.0167	0.037	0.0069	–
kS2−, cm/s	0.027	0.06	0.008	0.01
Reaction area, cm2	54.39	–	273	89
Liquid volume, cm3	0.54	–	910	1250
Area/volume, cm−1	100	24	0.3	0.07
Reaction time, s	1.02	0.19	–	tmelt

Figure 6 shows the flow chart of the overall solution in the framework of the desulfurization kinetics model under different atmospheres, which is calculated by Matlab software.

Fig. 6.

Overall solution schematic of the desulfurization kinetics model.

4. Calculated Results and Discussion

Figure 7 shows the variation of sulfur content in steel and slag with remelting time. The results display that the predicted values of the model are in good agreement with the experimentally measured values. As shown in Fig. 7(a), the sulfur content in Exp1 is reduced from 50 ppm of the original consumable electrode to 6–10 ppm, and it is reduced to 7–12 ppm in Exp2. The sulfur content in the slag increased from 0.12% to 0.125% under Exp1 experimental conditions and increased to 0.15% under Exp2 experimental conditions as displayed in Fig. 7(b). Judging from the simulated values under the two experimental conditions in detail, the initial sulfur content is close, which is due to the strong desulfurization ability of slag in the early stage of the ESR process. In the beginning, although the remelting atmosphere was different, the sulfur content in the slag was equivalent, and the effect of the atmosphere was not obvious at the beginning of the remelting. Therefore, the desulfurization capacity of the slag was roughly equal in both experiments. With the extension of ESR time, under the condition of Exp1, the sulfur in the slag is continuously discharged into the atmosphere in the form of SO₂ based on the reactions (37) and (38). As shown in Fig. 7(b), from the beginning to the ending of the ESR process, the calculated results show that the sulfur content in the slag is roughly unchanged. However, due to the lack of gas-phase desulfurization conditions in Exp2, the sulfur content in the slag continues to accumulate, and the desulfurization effect is weakened.

Fig. 7.

Variation of sulfur content in steel and slag with remelting time. (Online version in color.)

To compare the effect of the atmosphere on the changes in a_O and L_s, the model was used to calculate the variation and the results are shown in Fig. 8. The results reveal that the desulfurization effect of the three stages from the end of the electrode, the droplet passing through the slag layer, and the molten pool-slag pool reaction interfaces are different. The oxygen activity at the electrode tip is the lowest, and its value is less than 10⁻⁵, but the oxygen activity under the two experimental conditions is roughly equal at the same reaction position as shown in Fig. 8(a). This result indicates that the influence of the atmosphere on the internal metal-slag reaction is not obvious. Furthermore, the calculation result of L_s is given in Fig. 8(b), the highest L_s value reached 800 under Exp1 conditions and 700 under Exp2 experimental conditions at the beginning. Although the value of L_s decreases continuously with the increase of remelting time, it always has the maximum value at the tip of the electrode melt film. The above results indicate that the desulfurization capacity is the strongest at the electrode tip under two experimental conditions, and the desulfurization capacity under the air atmosphere is slightly greater than that under the protective atmosphere.

Fig. 8.

Time-dependent relationship between a_O and L_s at different reaction positions. (Online version in color.)

Since the L_s value under both experimental conditions is very huge, the Eqs. (35) and (39) can be approximately written as the Eq. (48). At this point, it can be considered that the sulfur content in the molten steel depends on the initial sulfur content, which further explains under the two experimental conditions, the initial sulfur content is the same. Besides, under this condition, the initial sulfur content is the minimum sulfur content. However, with the increase of the remelting time, the oxygen activities at each reaction sites all tend to increase. Correspondingly, the distribution coefficient of sulfur between the slag and metal decreases, and the desulfurization capacity is relatively weakened. But even at the end of the ESR process, the L_s values at the metal film of the electrode tip are 400 and 350, respectively, so the desulfurization ability is still obvious.   

$$w_{\mathrm{S}}^{\mathrm{m}}\approx \mathrm{e}\mathrm{x}\mathrm{p}\left(-\frac{A}{V_{\mathrm{m}}}{k}_{\mathrm{S}}^{*}t\right)\times w_{\mathrm{S}}^{\mathrm{m},\mathrm{o}}$$(48)

Figure 9 shows the changing trend of the sulfur content during one-unit reaction step from the metal film of the electrode tip to the metal pool. The model result shows good agreement with the measured values. At the initial reaction state, according to the previous analysis, there is no significant difference in the desulfurization effect under the two experimental conditions. At the beginning of the ESR process, the model predicts that the sulfur content decrease from 0.005% to 0.0009% at the metal film, and a slight change occurs when the droplet passes through the slag layer. The same trend was observed at the end of the ESR process under two experiments. The above results show that the desulfurization reaction is mainly concentrated at the metal film at the end of the electrode, and the role of the droplet and the molten pool is not significant. Further analysis, according to the calculation results in Table 7, the area/volume ratio has a larger value at the metal film than other reaction sites, which possesses better kinetic reaction conditions, so the electrode tip desulfurization ability is the strongest. This phenomenon is similar to the reference⁴⁶⁾ research on the changes in oxygen and aluminum elements during the ESR process.

Fig. 9.

Variation trend of sulfur content during one-unit step. (Online version in color.)

Since the desulfurization resistance has an important effect on the ESR desulfurization process, the desulfurization resistance on the molten steel side and the slag side can be calculated from 1/k_s and ρ_m/(k_s²⁻L_sρ_s) respectively based on the Eq. (3). Figure 10 shows the results of 1/k_s and ρ_m/(k_s²⁻L_sρ_s) values variation at each reaction position under different atmospheres. Since the electrode composition, slag height, and electrode immersion depth used in the two experiments are samely, according to Eq. (40), the corresponding mass transfer coefficient of sulfur is equal. As shown in Fig. 10(a), the mass transfer resistance of sulfur on the metal side is alike, and the mass transfer resistance of sulfur at the interface of the metal pool-slag pool is the largest. As shown in Fig. 10(b), since the L_s is larger in Exp (1), the ρ_m/(k_s²⁻L_sρ_s) value is smaller. Also, the mass transfer resistance at the position where the slag contacts the electrode tip is the smallest. Through comparison, it can be observed that the mass transfer resistance of sulfur in the metal side is much greater than that in the slag side during the process of the metal film, droplet, and metal pool. The limit of desulfurization steps in both experiments is on the metal side. By further reducing the sulfur content in the initial electrode will facilitate the desulfurization process during the ESR process.

Fig. 10.

Mass transfer resistance of sulfur on metal side and slag side. (Online version in color.)

The mass transfer resistance of sulfur on metal and slag sides determines the comprehensive mass transfer coefficient of sulfur $(k_{\mathrm{s}}^{*})$, and the calculated results are given in Fig. 11. At different reaction positions, the $k_{\mathrm{s}}^{*}$ tends to decrease as the remelting time increases. The $k_{\mathrm{s}}^{*}$ in the air atmosphere is larger than in the protective atmosphere. Due to the desulfurization of the gas phase, the difference will develop larger and larger as shown in results. Therefore, once the sulfur content and slag composition in the ESR experiment are fixed, the gas phase desulfurization method will benefit to continue to decrease the sulfur content in the steel.

Fig. 11.

Comprehensive mass transfer coefficient of sulfur. (Online version in color.)

Figure 12 shows the inclusions in the electrode and the two experimental ingots. The sulfur-containing inclusions in the electrode are mainly MnS, Al₂O₃, Al₂O₃–MnS inclusions, while the inclusions in the two ingots are mainly small-sized Al₂O₃ inclusions, and no pure MnS inclusions are detected. The results show that the removal of sulfide inclusions in steel is obvious under the two kinds of ESR experimental atmospheres, but the type of inclusions is not changed clearly.

Fig. 12.

The SEM mappings of inclusions in electrode and ingots. (Online version in color.)

5. Conclusions

In this paper, the model and experimental study of coupled desulfurization in the ESR process of low-sulfur plastic die steel under different experimental atmospheres were established, the conclusions are as follows:

(1) Through conducting ESR experiments in different atmospheres, the sulfur content of steel reduced from 50 ppm to an average of 9 ppm (Exp1) and 11 ppm (Exp2), the desulfurization rate is 82% and 78% respectively. The sulfur content of slag increased from 0.12% to 0.125% (Exp1) and 0.15% (Exp2) respectively. The effect of the gas phase desulfurization process makes the sulfur content in the slag in a stable state, which is beneficial to the desulfurization reaction.

(2) The predicted value obtained from the established coupled desulfurization kinetic model is in good agreement with the experimental values. The values of a_O and L_s are obtained through calculation, and the L_s has the largest value at electrode tip metal film in both Exp1 and Exp2. Besides, the L_s value of each reaction stage under Exp1 is greater than that of Exp2. Under the condition that the L_s value in both experiments is large, the remelting atmosphere has little effect on the desulfurization during the ESR process.

(3) By analyzing the change of sulfur content of steel under one-unit reaction step, the desulfurization reaction is mainly concentrated at the electrode tip metal film, the droplet and the molten pool-slag interface have little influence. Under two experimental conditions, the mass transfer resistance of desulfurization is mainly on the metal side.

(4) Under the experimental conditions of Exp1 and Exp2, the main inclusions in the steel were Al₂O₃, and no pure MnS inclusions were detected. The effect of ESR on the removal of MnS in low-sulfur steel is obvious, and the influence of the remelting atmosphere on the inclusions in the steel is not clear.

Acknowledgements

This project was supported by the National Key R&D Program of China (Grant No. 2017YFB0305201), the National Natural Science Foundation of China (Grant 51434004, U1435205 and 51674070), and the Fundamental Research Funds for the Central Universities (N180725021).

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