A thermodynamic model of the titanium distribution behaviour between slag and molten steel during LF refining process: description and application

Abstract

Titanium distribution ratio is a key parameter which directly reflect the ability to remove titanium in the LF refining process. A thermodynamic model for calculating the titanium distribution ratio (LTi) between ladle furnace (LF) refining slags, i.e., CaO–SiO₂–MgO–FeO–(CaF2)–MnO–Al₂O₃–TiO₂ slags, and molten steel has been developed by coupling with the ion and molecule coexistence theory (IMCT) and slag–metal equilibrium theory. The reliability of the model was verified by comparing it with industrial data. Using this model, the effects of Al, Si content in steel and CaO, MgO and TiO₂ in slag on the L _Ti were investigated. Meanwhile, the optimal equilibrium slag composition of GCr15SiMn bearing steel was predicted. On this basis, five groups of industrial tests were carried out, and the results indicated that the optimized practice had achieved remarkable results in limiting titanium content compared with the routine process.

Introduction

According to the properties and uses of steel, the role of titanium elements in different steels is also different. On the one hand, titanium is one of the most important micro-alloy elements for the production of several grades of steel. As an example, in stainless steel, it is commonly used to enhance the resistance to intergranular corrosion at high temperatures and improve the mechanical properties of steels, such as strength and toughness [1,2]. On the other hand, titanium content in steel also needs to be limited to a very low level like bearing steel and spring steel, 30 ppm or even less than 10 ppm. This is because titanium has a strong affinity with oxygen, nitrogen and carbon in liquid steel, once they can combine to form the angular and hard inclusions such as TiO₂, and Ti(CN) during solidification, which seriously affect the fatigue properties of steels [3,4]. Therefore, controlling and adjusting titanium content is a prerequisite condition in the iron and steelmaking process. Titanium distribution ratio is a key parameter to evaluate the partition of titanium between slag and metal. In order to predict the inclusions formed and the relationship between titanium in the metal and slag, it is necessary to understand the factors affecting the activity of titanium oxide in slag.

Over the last decade, numerous experimental and theoretical studies have been performed to investigate the influence of slag–metal reaction on the titanium distribution ratio ( ). Kishi et al. [5] performed the equilibrium experiments on CaO–Al₂O₃–TiO_x slags with Fe–20Cr steel at 1873 K and analyzed the effect of Al content on the Ti and TiO_x ratio between steel and slag. It was found that there was a negative linear relationship between log [Al] and 3/4log (TiO₂/Ti). Jung et al. [6] measured the activity of TiO₂ in slag through designed experiments and studied the effect of Al content on in Ti-contained stainless steel. A conclusion consistent with Kishi et al. was obtained. Based on the equilibrium reaction between Fe–C–(16 ∼ 18%)Cr–Ti steel and CaO–SiO₂–Al₂O₃–MgO–TiO_x slags, it was also found that the TiO₂ activity showed different deviation with different TiO₂ content, and the effect of Si and Cr content on the titanium activity in steel was proposed. Based on industrial tests, Zhang et al. [7] explored the influence of the chemical composition of liquid steel and ladle slag on during Ruhrstahl-Heraeus (RH) refining process. Iron oxide (FeO_x) and the binary basicity of slag (CaO/SiO₂) played an important role in realising ultra-low-titanium-bearing steel. Park et al. [8] investigated the effect of Si content and ternary basicity of slag on the activity coefficient of TiO₂ in CaO–SiO₂–Al₂O₃–MgO–CaF₂–(TiO_x) slags. The results showed that the activity coefficient of TiO₂ in slag increased with the increase of Si content in steel and slag basicity (CaO + MgO)/SiO₂), which was unfavourable for enhancing titanium distribution ratio. Besides, an activity model based on the ion and molecule coexistence theory (IMCT) was established by Jiang et al. [9] to study the effect of slag composition on titanium and silicon content during electroslag remelting process. Results indicated that the higher CaO content in slag had a better capacity for avoiding the loss of titanium caused by the reaction of titanium with silica in slag. So far, most researchers have qualitatively evaluated the effects of molten steel or slag composition on , while there are few reports on the quantitative study of titanium distribution behaviour, especially for ladle refining slag.

As a matter of fact, Ladle Furnace (LF) refining process has become a conventional secondary refining technique in steelmaking plants because of its advantages of easy alloy composition adjustment and rapid temperature adjustment. But there is little information about the thermodynamic behaviour of titanium oxide in ladle-type slags. Therefore, the objective of the present work is to develop a reliable thermodynamic model to predict the titanium distribution ratio during the LF refining process.

Currently, the ion and molecule coexistence theory (IMCT) has been successfully used to predict sulfur, phosphorus and manganese distribution behaviour in the steelmaking process [10–13]. Therefore, in the slag–metal equilibrium system, a predicting model for calculating the titanium distribution ratio between the LF refining slag and molten steel has been developed by coupling with a thermodynamic model for calculating the mass action concentrations of slag components, that is, CaO–SiO₂–MgO–FeO–(CaF₂)–MnO–Al₂O₃–TiO₂ slags, based on the IMCT. In order to verify the accuracy of the model, GCr15SiMn steel was used as the research steel (due to the improper addition of deoxidiser or the existence of unstable slag components such as FeO and TiO₂, it is easy to cause fluctuations in the titanium distribution ratio in the LF refining process), and an industrial test was carried out in a special plant in China. And then, the effects of Al and Si contents of steel and slag composition on the titanium distribution ratio were investigated by using the model. Lastly, the optimised tests were carried out using the prediction results of the model. The practice shows that the model has a certain guiding significance for the industrial production of low-titanium GCr15SiMn steel.

Establishment of model

Model mechanism and hypothesis

Figure 1 is the mechanism diagram of the model. According to the classical IMCT and slag–metal equilibrium theory, the basic hypotheses of the model are as follows.

The prominent reactions of interest include oxygen, Al, Si, Mn, Ti elements. It is assumed that a thermodynamic equilibrium at the slag–metal interface does exist between Al + Al₂O₃, Si + SiO₂, Mn + MnO, Fe + FeO and Ti + TiO₂ systems.

The slag system used during LF process is generally composed of eight components: CaO, SiO₂, MgO, FeO, CaF₂, MnO, Al₂O₃ and TiO₂. According to the IMCT [14–16], structural units in the studied slags are composed of simple ions Ca²⁺, Mg²⁺, Fe²⁺, Mn²⁺, F⁻ and O²⁻, simple molecules SiO₂, Al₂O₃ and TiO₂, and complex molecules such as , silicates and aluminates. Each structural unit is independent of each other in the slags.

Reactions between simple ions and simple molecules to form complex molecules by bonding ion couples are in a dynamic equilibrium. The equilibrium reaction mainly occurs in both slag bulk and the surface layer of molten steel.

Chemical reactions of forming complex molecules obey the mass action law and do not participate in the slag–metal interface reactions. Thus, the chemical reaction equilibrium constant can be represented by the defined mass action concentration.

Figure 1.

Schematic diagram of the model.

Equilibrium expressions at slag–metal interface

According to the slag–metal equilibrium theory, the chemical reactions occurring at the interface between slag and molten steel are shown in Equations (1a–1e): (1a) (1b) (1c) (1d) (1e)

The expressions of standard equilibrium constants of Equations (1a–1e) are shown in Equations (2a–2e): (2a) (2b) (2c) (2d) (2e)

where is the activity of the component in slag, the activity coefficient ( ) is calculated by Wagner’s law, as shown in Equation (3). (3)

The first-order interaction coefficients

corresponding to each alloying element (

) are determined from the elemental composition and listed in Table 1.

Table 1.

First-order interaction coefficients of the constituents in molten steel [17].

	C	Si	Mn	Cr	Al	Ti	O
Al	0.091	0.056	—	0.012	63/T+0.011	0.004	−34740/T + 11.95
Si	380/T − 0.023	0.1	0.002	−0.0003	0.058	0.84[18]	−0.23
Mn	−0.07	0.0	0.0	0.0039	—	−0.05	−0.083
Ti	−221/T − 0.072	−0.0256[19]	−0.043[7]	0.028[20]	0.0037	0.048[19]	−1.8
O	−0.436[21]	−0.131	−0.021	−0.0459	−20600/T+7.15	−0.54	−1750/T + 0.734

As can be seen from Equations (2a–2e), based on the given contents of molten steel (such as Al, Si and Mn), there are six unknowns which are [%O], , , , , , respectively, but there are only five equations. Therefore, another equation is needed. With the mass conservation law of IMCT, the six unknowns could be solved.

Calculation of equilibrium slag action concentration

In the period of LF refining, the TiO₂-containing slag system equilibrated or reacted with molten steel is chosen as CaO–SiO₂–MgO–FeO–(CaF₂)–MnO–Al₂O₃–TiO₂. According to the reported phase diagrams [16,22,23] of CaO–TiO₂, TiO₂–MgO, TiO₂–FeO, TiO₂–MnO, TiO₂–Al₂O₃, CaF₂–CaO–SiO₂, CaF₂–CaO–Al₂O₃, CaO–MnO–SiO₂, CaO–SiO₂–Al₂O₃–MgO, it is found that there are 40 complex molecules in slag system as well as eight simple components, such as CaO-SiO₂, CaO-TiO₂, FeO-TiO₂. In Table 2, all simple ions, simple molecules and complex molecules in CaO–SiO₂–MgO–FeO–(CaF₂)–MnO–Al₂O₃–TiO₂ slag at metallurgical temperature (1823 ∼ 1893 K) are summarised and assigned specific numbers.

Table 2.

Expression of structural units as ion couples or complex molecules, their mole numbers and mass action concentrations in CaO–SiO₂–MgO–FeO–(CaF₂)–MnO–Al₂O₃–TiO₂ slags.

Structural units	Number of structural unit	Mole number of structural unit (mol)	Mass action concentration of structural unit
Ca²⁺ +O^2–	1
Mg²⁺ +O^2–	3
Fe²⁺ + O^2-	4
Ca²⁺ + 2F^–	5
Mn²⁺ + O^2–	6
SiO₂	2
	7
	8
CaO · SiO₂	9
	10
	11
	12
	13
	14
	15
	16
	17
	18
	19
	20
	21
	22
	23
	24
	25
	26
	27
	28
	29
	30
	31
	32
	33
	34
	35
	36
	37
	38
	39
	40
	41
	42
	43
	44
	45
	46
	47

In 100-g LF refining slags of CaO–SiO₂–MgO–FeO–(CaF₂)–MnO–Al₂O₃–TiO₂, the initial mole fraction numbers of eight components are expressed as , , , , , , , , respectively. The total equilibrium mole number of all structural units can be obtained as Equation (4). (4)

The mass action concentration ( ) of each structural unit is defined as a ratio of the equilibrium mole number of structural unit to the total equilibrium mole numbers of all structural units in a closed system according to IMCT, which can be calculated by Equation (5). (5)

It should be emphasised that the free Me²⁺ and O²⁻ keep independent form, each other cannot form MeO on liquid or solid-state. Therefore, the mass action concentration of MeO should be calculated by Equation (6). (6)

The chemical reaction formulas of 48 kinds of possibly formed the complex molecules, their standard Gibbs energy as a function of temperature (

), reaction equilibrium constant (

) and expressions of mass action concentrations of all complex molecules expressed by

based on the mass action law are listed in Table 3.

Table 3.

Chemical reaction formulas of possibly formed complex molecules in CaO–SiO₂–MgO–FeO–(CaF₂)–MnO–Al₂O₃–TiO₂ slags.

Reactions		Ref.
(Ca²⁺ +O^2–) +SiO₂ = CaO · SiO₂	–22476–38.52T	[16]
	–100986–24.03T	[16]
	–93366–23.03T	[16]
	–18120–18.62T	[24]
	–16400–26.80T	[24]
	–17430–37.20T	[24]
	–17000–32.0T	[24]
	–86100–205.1T	[24]
	–79900–3.35T	[23]
	–207108–11.51T	[23]
	–292880–17.573T	[23]
	43400–40.0T	[25]
	–77403 + 11.0T	[25]
	–35530–2.09T	[16]
	–26355 + 3.14T	[23]
	–27614 + 0.6276T	[23]
	–25522 + 1.255T	[23]
	–28596 + 3.349T	[26]
	–33272.8 + 6.1028T	[27]
	27293.75–26.25T	[16]
	–16188.703	[16]
	–33913.08 + 5.86T	[16]
	–30013–5.02T	[28]
	–86670 + 16.81T	[28]
	–45116 + 11.81T	[29]
	–24662 + 1.254T	[23]
	–37620–1.672T	[23]
	−4354.27-10.467T	[30]
	–25271 + 3.933T	[23]
	–124766.6 + 3.768T	[31]
	–80387–51.916T	[30]
	–73688–63.639T	[30]
	–315469 + 24.786T	[16]
	–13816.44–55.27T	[30]
	–61964.64–60.29T	[30]
	–114683 + 7.32T	[23]
	−255180 −8.20T	[32]
	−44492−73.15T	[32]
	−228 760 −155.8T	[32]

On the basis of IMCT, the sum of mass action concentrations of all structural units in a fixed amount of CaO–SiO₂–MgO–FeO–(CaF₂)–MnO–Al₂O₃–TiO₂ slag under equilibrium condition is equal to 1.0, which can be expressed as Equation (7): (7)

The mass conservation equations for eight components in LF refining slags equilibrated with molten steel can be established as follows: (8a) (8b) (8c) (8d) (8e) (8f)

(8g) (8h)

The sum of the mass of all the components in the LF refining slag is equal to 100, which can be expressed as: (9)

Programme and computation process

As mentioned above, the calculation equations for slag and molten steel at the slag–metal interface are established, respectively. The contents of CaF₂, CaO, MgO and TiO₂ in the slag are defined as known values when calculating the equilibrium slag activities. Based on the fact that the action concentrations of slag components (

) calculated by IMCT are the activities of slag components (

), thus the slag-steel equilibrium reaction can be established.

Table 4.

Chemical compositions of slags and molten steel, measured , and temperature at middle stage during LF refining process of GCr15SiMn steel.

Heat No	Metal composition, mass%					Slag composition, mass%								Temp. (K)
Heat No	C	Si	Mn	Al	Ti	CaO	SiO₂	MgO	FeO	Al₂O₃	MnO	TiO₂		Temp. (K)
1	1.00	0.56	1.00	0.035	0.0034	61.21	10.70	2.78	0.88	21.73	0.080	0.129	37.94	1845
2	0.95	0.56	1.05	0.025	0.0021	63.72	11.82	3.15	0.63	16.60	0.057	0.104	49.52	1838
3	0.93	0.54	1.07	0.038	0.0028	56.50	11.50	3.66	0.49	24.70	0.079	0.148	52.93	1847
4	0.92	0.55	1.11	0.048	0.0023	63.53	9.35	4.20	0.19	17.62	0.078	0.143	62.17	1842
5	0.99	0.56	1.06	0.028	0.0028	59.27	16.07	4.07	0.37	16.54	0.064	0.121	43.11	1856
6	0.95	0.52	1.04	0.025	0.0025	57.32	10.82	4.12	0.43	20.23	0.127	0.132	52.80	1823
7	0.96	0.44	1.03	0.035	0.0028	60.26	14.18	5.28	0.37	16.71	0.062	0.145	51.79	1838
8	0.94	0.52	1.11	0.031	0.0024	56.34	13.81	4.70	0.24	18.98	0.098	0.165	68.75	1849
9	0.94	0.58	0.98	0.023	0.0028	57.63	9.07	4.29	0.26	25.43	0.033	0.158	56.43	1862
10	0.93	0.49	0.98	0.023	0.0025	60.77	8.79	3.32	0.75	21.68	0.067	0.132	52.80	1853
11	0.92	0.54	1.03	0.040	0.0026	61.04	6.84	3.09	0.35	22.44	0.110	0.155	59.62	1824
12	0.92	0.55	0.93	0.020	0.0021	54.56	11.95	5.97	0.44	21.68	0.085	0.145	69.05	1843
13	0.96	0.48	0.98	0.028	0.0025	58.70	8.78	4.32	0.21	23.49	0.063	0.128	51.20	1831
14	0.88	0.53	1.09	0.050	0.0024	60.55	11.42	1.81	0.32	20.16	0.098	0.163	67.92	1835
15	0.97	0.55	1.08	0.038	0.0021	57.70	16.93	5.99	0.10	17.46	0.053	0.127	60.48	1837
16	0.99	0.60	1.00	0.022	0.0020	57.18	14.71	3.52	0.12	17.34	0.128	0.173	86.50	1851
17	0.95	0.59	1.03	0.026	0.0027	54.80	15.49	6.49	0.21	19.88	0.083	0.132	48.89	1832
18	0.97	0.55	1.01	0.031	0.0025	61.13	10.99	4.14	0.28	18.07	0.085	0.149	59.88	1838
19	0.97	0.55	1.07	0.030	0.0030	55.32	12.04	5.69	0.86	21.58	0.063	0.128	42.57	1838
20	0.96	0.54	0.98	0.033	0.0022	58.76	12.69	3.74	0.37	21.25	0.098	0.147	66.82	1835

Figure 2 shows the flow chart of the calculated model. First, the initial contents of Al, Si and Mn in steel, the components of CaF₂, CaO, MgO and TiO₂ in slag, and temperature ( ) are given, respectively. Second, the expressions of slag–metal reactions and their standard equilibrium constants are determined. Next, the mass action concentration expressions of all structural units are determined, and the standard equilibrium constant of all reactions forming the complex molecule are collected. Then, the slag–metal equilibrium Equations (2a, 2b, 2c, 2d, 2e) and the mass conservation Equations (7, 8a, 8b, 8h, 9) related to IMCT are listed. Next, the mass action concentration ( ) of all structural units in slag and equilibrium contents of dissolved O and Ti can be calculated by the Fsolve Function. Last, the composition of unknown slag (SiO₂, Al₂O₃, etc.) can be derived, and the titanium distribution ratio ( ) can be expressed by Equation (10). (10)

Figure 2.

Calculation flow of the model.

All the above simulations are implemented using the software Matlab 2017b on a personal computer platform.

Result and discussion

Experiment verification of the model

In order to verify the rationality of the model, an industrial test with CaO–SiO₂–MgO–FeO–(CaF₂)–MnO–Al₂O₃–TiO₂ slags system was carried out in Xining Special Steel Group, Co., Ltd, Xining, Qinghai. In this section, the titanium distribution ratio between GCr15SiMn steel and the slag in a 70-ton LF was calculated. GCr15SiMn is one of the typical full-hardenability bearing steel with high hardenability and wear resistance, widely used in bearings of wind power equipment and heavy machinery. The steelmaking route of GCr15SiMn was 110 t EAF→70 t LF refining→70 t VD refining→ingot casting. According to the refining requirements and characteristics of LF refining, its basic operation procedure is illustrated in Figure 3 and summarised as follows. (1) Before the ladle enters LF refining, a certain amount of ferroalloys and complex slag formers are added into a 70-ton ladle for alloying pre-treatment and slagging. (2) Arriving at LF station, Ar gas is introduced from the bottom ladle to stir the molten steel, and the electricity is also switched on through graphite electrodes to improve the temperature. After 25 minutes, the temperature of molten steel is measured by means of a thermocouple sensor. The samples of slag and molten steel are taken to analyze their chemical compositions, regarded as the middle stage samples. (3) Subsequently, a fixed amount of Al-deoxidiser and ferroalloys with known composition are specially introduced into the ladle according to the feedback results of the sample. (4) And keep the refining operation for more than 40 minutes. Meanwhile, heating by electricity and stirring by Ar gas continues. The taken samples are assigned as the final stage samples when the chemical composition and temperature meet the requirement of aimed steel.

Figure 3.

Smelting flow chart and sampling positions of GCr15SiMn steel in a 70-ton LF.

The normalised chemical compositions of both slag and metal with the definite temperature for 20 heats in the middle stage and final stage of 70-ton LF were measured, as listed in Tables 4 and 5, respectively. The chemical compositions of Al, C, Si, Mn and Ti in steel are measured by the inductively coupled plasma optical emission spectrometry (ICP–OES) with ±5% relative standard deviation. The compositions of slag samples are carefully determined by using an X-ray fluorescence spectrometer (XRF). It should be emphasised that since CaF₂ is not added in these industrial experiments, the initial CaF₂ in the refining slag is set as 0 in the simulation process. Besides, the total mass percentages of iron oxide and titanium oxide in slags are less than 1.0 wt%, so all iron oxide and titanium oxide in the slags are treated in the form of FeO and TiO₂, respectively.

Table 5.

Chemical compositions of slags and molten steel, measured , and temperature at finial stage during LF refining process of GCr15SiMn steel.

Heat No	Metal composition, mass%					Slag composition, mass%								Temp. (K)
Heat No	C	Si	Mn	Al	Ti	CaO	SiO₂	MgO	FeO	Al₂O₃	MnO	TiO₂		Temp. (K)
1	1.03	0.59	1.03	0.028	0.0040	60.32	10.60	2.97	0.48	22.60	0.074	0.121	30.25	1856
2	0.96	0.57	1.07	0.023	0.0023	62.50	12.31	3.66	0.29	16.93	0.038	0.097	42.17	1848
3	0.98	0.54	1.06	0.031	0.0031	56.43	11.40	3.67	0.48	25.22	0.073	0.108	34.84	1850
4	0.97	0.56	1.11	0.038	0.0025	60.41	9.08	4.06	0.12	21.25	0.071	0.077	30.80	1842
5	0.98	0.545	1.08	0.026	0.0031	58.26	15.21	4.56	0.15	17.43	0.053	0.166	53.55	1859
6	0.97	0.54	1.06	0.024	0.0033	57.32	10.82	4.12	0.43	20.23	0.103	0.116	35.15	1851
7	0.98	0.53	1.07	0.026	0.0028	57.93	14.67	5.46	0.12	17.93	0.056	0.148	52.86	1845
8	0.94	0.52	1.11	0.029	0.0031	56.64	14.27	4.26	0.32	19.06	0.079	0.146	47.10	1856
9	0.95	0.572	1.05	0.020	0.0028	57.64	9.07	4.29	0.26	25.43	0.036	0.128	45.71	1849
10	0.97	0.57	1.13	0.023	0.0025	57.63	9.99	4.43	0.17	23.94	0.056	0.067	26.80	1858
11	1.01	0.59	1.05	0.026	0.0031	59.80	7.03	3.11	0.18	21.79	0.102	0.098	32.67	1854
12	0.95	0.56	1.03	0.018	0.0022	54.02	12.07	6.03	0.48	21.97	0.079	0.129	58.63	1854
13	0.96	0.48	0.98	0.028	0.0028	57.81	12.74	4.32	0.3	20.43	0.053	0.121	43.21	1851
14	1.02	0.54	1.09	0.025	0.0029	57.30	11.52	3.40	0.13	20.99	0.104	0.112	38.62	1847
15	0.97	0.55	1.08	0.030	0.0026	52.68	13.38	7.08	0.21	19.84	0.068	0.128	49.23	1848
16	0.99	0.60	1.01	0.023	0.0021	56.25	13.21	4.14	0.4	19.58	0.093	0.099	47.14	1851
17	0.95	0.59	1.03	0.025	0.0032	55.98	13.53	5.49	0.29	21.96	0.072	0.149	49.67	1853
18	0.97	0.55	1.01	0.030	0.0025	61.13	10.99	4.15	0.28	18.07	0.078	0.084	33.60	1848
19	0.96	0.55	1.07	0.028	0.0033	54.16	12.57	5.40	0.62	22.76	0.056	0.154	46.67	1853
20	0.96	0.54	0.98	0.028	0.0025	58.63	12.69	3.65	0.24	21.19	0.053	0.105	42.00	1845

Table 6.

Calculated activities value of simple compounds and containing-TiO₂ molecules in heat No.2.

Molecule	Activity	Molecule	Activity

SiO₂

Using the model developed in the previous section, the titanium distribution ratios ( ) for 20-heat GCr15SiMn steel are predicted and compared with the measured values, as shown in Figure 4. The known initial parameters of the model are taken from Tables 4 and 5. It can be clearly found that the calculated value of in the middle stage is slightly lower than the measured value to some extent, while the model predicted values at the final stage lies close to the measured results, with data points falling within ±20% of the 1:1 line (at which the calculated and measured values are exactly equal). This indicates that compared with the middle stage, the predicted results of the final stage of LF are in good agreement with the actual production data. The difference could be due to the fact that the chemical reaction at the slag–metal interface does not reach equilibrium at the middle stage. As the reaction proceeds, the steel–metal reaction moves towards the direction of the equilibrium state.

Figure 4.

Comparison of calculated and measured titanium distribution ratio during 20 heats of a 70-ton LF refining process (a) at middle stage, (b) at final stage.

In order to further verify the applicability of the model, the equilibrium experiments of Kishi et al. [5], Jung et al. [6] and Park et al. [8] in different slag systems are also calculated. The results of this calculation are plotted in Figure 5, which are basically consistent with the experimental results with permitted error. Hence, the model can be used to predict the equilibrium titanium distribution behaviour between slag and steel under TiO₂-containing slag systems.

Figure 5.

Comparison between and in different slag systems at 1873 K.

Model application during LF refining process

Through the above analysis, the rationality of the model is verified. Then, taking GCr15SiMn as an example, the effects of Al and Si in steel and CaO, MgO and TiO₂ in slag on the equilibrium titanium distribution ratio between slag and steel are discussed in detail.

Effect of Al, Si content on the equilibrium

Figure 6 depicts the effect of dissolved Al content in steel on the titanium distribution ratio (L _Ti) in equilibrium CaO–SiO_2–MgO–FeO–MnO–Al₂O₃–TiO₂ system at 1848 K with Si of 0, 0.02, 0.055 wt%, CaO of 55 wt%, MgO of 4 wt% and TiO2 of 0.1 wt%. Among them, the dotted line represents the result of Bannenber et al. [33] (Si = 0), the dash-dotted line (Si =0.2 wt%) and the solid line (Si = 0.55 wt%) represent the results calculated by the model, and the red dots represent the measured results at LF final stage of 20 heats. It can be seen that with the increase of Al content, the L _Ti decrease significantly. That is, there is an obvious negative relationship between L _Ti and dissolved Al content by the present work, which is in accord with Bannenber's conclusion. In Figure 6, it is also found that the higher the Si content in steel, the lower the required Al content to reach the same value of L _Ti. For example, under the same condition of L _Ti =50, the lower Al content in molten steel with Si=0.55 wt% is 0.023 wt%, while the Al content with Si=0.2 wt% is 0.031 wt%. Furthermore, the variation trend of titanium distribution ratio with Al content under the condition of 0.55 wt% silicon content has also been verified by industrial data. Briefly, the effect of Al content on the equilibrium L _Ti is also closely linked to the content of silicon in steel. Thus, for Si-containing alloy steel, it is imperative to limit the Ti content in steel by adjusting the amount of Al added.

Figure 6.

Effect of Al content on the predicted equilibrium under different Si content.

It is of great significance to reasonably design Al content in molten steel for realising low-titanium and oxygen of bearing steel. Figure 7 depicts the functional relationship between the equilibrium contents of O, Ti and the content of Al at 1848 K. It can be seen that in the process of increasing the Al content from 0.0025 to 0.06 wt%, the equilibrium Ti content keeps increasing; on the contrary, the equilibrium O keeps decreasing during this process. Obviously, the effect of Al content on the equilibrium O and Ti in steel is opposite. Specifically, when the Al content is below 0.015 wt%, the equilibrium O increases rapidly; while the Al content is more than 0.025 wt%, the equilibrium O content decreases and the reduction is negligible. In fact, once the Al content exceeds 0.015 wt%, the O content calculated by the model is less than 3 ppm, which has little effect on the contribution ratio of total oxygen in the final stage of LF. It can be inferred that excessive Al content is unnecessary, and 0.015–0.025 wt% Al is permissible.

Figure 7.

Estimated equilibrium Ti and O contents as a function of Al content at 1848 K.

Effect of CaO, MgO content on the equilibrium

Comparing Tables 4 and 5, it can be seen that with the decrease of CaO content, the titanium distribution ratio shows a downward tendency from the LF middle stage to final stage. Therefore, in order to further accurately describe its influence, the 2nd heat is selected as a representative, the activities of the relevant compounds in CaO-SiO₂-MgO-FeO-MnO-Al₂O₃-TiO₂ slag system at 1848 K is calculated using the predicting model, as shown in Table 6.

It can be seen from Table 6 that the CaO, MgO and TiO₂ in the slag have a strong binding ability, and they will react to form the complex molecules CaO·TiO₂, 3CaO·2TiO₂, MgO·TiO₂ and 2MgO·TiO₂, their values more than 10-6 (NTiO₂≈10^-6), which exerts a great effect on the TiO2 activity in slag. Thus, the effects of CaO, MgO on the L _Ti are quantitatively described to better design the equilibrium refining slag composition for GCr15SiMn steel.

Figure 8 depicts the effect of CaO content on the titanium distribution ratio in equilibrium with CaO–SiO₂–MgO–FeO–MnO–Al₂O₃–TiO₂ system at 1848 K with Al of 0.02, 0.03, 0.04 wt%, MgO of 4 wt% and TiO₂ of 0.1 wt%. The measured values of of 8 heats with Al content of (0.03 ± 0.002) wt% are marked in the figure, which are the 1st, 3rd, 8th, 13th, 15th, 18th, 19th and 20th industrial test heats, respectively (see Table 5). It can be clearly found that the measured are basically near the predicted curve, and both of them show a significant downward trend with the increase of CaO content. The reason is obvious that the reduction of the activities of and will lead to the decrease of free TiO₂ activity, then resulting in the decrease of . Also, it is not hard to notice that the L _Ti value changes slowly when the CaO content is less than 55 wt%, which means the change of CaO content has little effect on the titanium content in steel when the L _Ti is nearly constant. Moreover, it has been proved that the lower the slag basicity, the higher the oxygen content in molten steel during LF refining process [10,34]. Thus, it is recommended to limit the CaO content to 50∼55 wt% to achieve a low level of titanium and oxygen content in molten steel.

Figure 8.

Effect of CaO content on the predicted equilibrium .

Similar to CaO, MgO also has an effect on the equilibrium titanium distribution ratio, but it is not significant, as shown in Figure 9. When the Al content is determined as 0.03 wt%, the decreases from 40.9 to 37.4 with the increase of MgO content from 2 to 6 wt%. However, due to the low content of MgO in the actual process, this influence is disturbed by other components in the slag system.

Figure 9.

Effect of MgO content on the predicted equilibrium .

Effect of TiO₂ content on the equilibrium

Figure 10 displays the effect of TiO₂ content on the titanium distribution ratio in equilibrium with CaO–SiO₂–MgO–FeO–MnO–Al₂O₃–TiO₂ system at 1848 K with Al of 0.02, 0.03, 0.04 wt%, CaO of 55 wt% and MgO of 4.0 wt%. The measured values of of 8 heats with Al content of (0.03 ± 0.002) wt% are also marked. The results indicate that the calculated content has no significant change when the TiO₂ increases from 0 to 0.5 wt%, and the variation trend of with 0.03 wt% Al content can be well proven by industrial data. However, in this process, the equilibrium titanium content would have a noticeable increase with the increase of TiO₂ content, as shown in Figure 11. This would imply that the equilibrium titanium content in the steel completely depends on the content of slag TiO₂ when the slag and molten steel are in equilibrium. For instance, when the Al content is determined as 0.02 wt%, it can ensure that the titanium content is less than 0.0020 wt% as long as the content of TiO₂ in slag is controlled below 0.12 wt%. Thus, it can be seen that decreasing the TiO₂ content in LF refining slag is also crucial for limiting titanium content in GCr15SiMn steel.

Figure 10.

Effect of TiO₂ content on the predicted equilibrium .

Figure 11.

Estimated equilibrium Ti content in Al-added steel as a function of TiO₂ content at 1848 K.

Comparison of titanium content before and after LF process optimisation

Based on the above analysis, the model can provide some practical guidelines for industrial LF refining operation. The design principle of liquid steel composition and slag system is of great importance to improve the distribution ratio of titanium between slag and steel. For GCr15SiMn steel, the equilibrium slag composition in CaO–SiO₂–MgO–FeO–CaF₂–MnO–Al₂O₃–TiO₂ refining slag is calculated, and the results are shown in Figure 12. In the calculation process, 5 wt% CaF₂ is added into the slag system to improve the overall fluidity of the slag, as well as the content of Si and Mn is set as 0.55 and 1.05 wt% while the initial content of CaO and MgO in the slag is set as 55 and 4 wt%, respectively.

Figure 12.

Predicted equilibrium composition of Al₂O₃, SiO₂, FeO and MnO as a function of Al content at 1848 K.

As shown in Figure 12, it can be seen that when the Al content is 0.015 ∼ 0.025 wt%, the calculated equilibrium Al₂O₃ in slag is 18 ∼ 24 wt%, the SiO₂ content is 12 ∼ 18 wt% and other components are MnO and FeO. According to the calculation results and previous theoretical analysis, relevant experiments were carried out by using the optimised Al content and slag composition. The purpose is to improve the distribution ratio of titanium in LF refining stage and make the steel–metal reaction reach the equilibrium state as soon as possible in the middle stage of LF, which is conducive to avoiding the transfer of TiO₂ in slag to molten steel and reducing the titanium content of steel.

The titanium content and of 5 heats after optimisation in the middle and final stages of LF are shown in Table 7. The results show that the measured results of in the middle and final stage are basically similar to the calculated results, indicating that the liquid steel and slag have reached the equilibrium state after the middle stage of LF. In order to more intuitively describe the beneficial effect of optimised GCr15SiMn, Figure 13 shows the variation of Ti content in steel during LF and compares it with 20 heats mentioned previously. It can be found that the average titanium content at the final stage of LF after optimisation decreases significantly from 28 ppm to 20 ppm, and the fluctuation of molten steel from the middle stage to the final of LF is small (within 4 ppm). As conclusion, the model has certain reliability for the design of GCr15SiMn equilibrium slag composition and the equilibrium , which has important theoretical guiding significance for shortening the time of LF refining and improving production efficiency in the future.

Figure 13.

Comparison of Ti content between routine practice and optimised practice in the middle- and final stage of LF.

Table 7.

Titanium content and in middle- and final stages of five groups of industrial tests after optimisation.

Test No.	Ti content, ppm
Test No.	Middle stage	Final stage	Middle stage	Final stage
1	14	18	33.57	38.82
2	16	19	49.38	45.00
3	17	20	44.12	42.78
4	20	22	46.39	42.59
5	18	22	51.94	47.09

Conclusions

In this work, a thermodynamic model for CaO–SiO₂–MgO–FeO–(CaF₂)–MnO–Al₂O₃–TiO₂ refining slag was developed to investigate the titanium distribution behaviour in the LF refining process based on slag–metal equilibrium theory and IMCT. The following conclusions are obtained.

Given the contents, C, Si, Mn, Al in molten steel, CaO, MgO, CaF₂, TiO₂ in slag and temperature, the titanium distribution ratio and dissolved O, Ti contents are obtained quantitatively by the mathematical model. The calculation results of the proposed model are compared with the 20-heat industrial tests and laboratory data respectively, which verify the correctness of this model.

Based on the industrial experiments and thermodynamic analysis, for GCr15SiMn steel, it is recommended that the Al content should be within 0.015 ∼ 0.025 wt%, the optimum composition range of refining slag could be of 50 ∼ 55 wt% CaO, 12 ∼ 18 wt% SiO₂, 18 ∼ 24 wt% Al₂O₃, ≤5 wt% MgO, about 5 wt% CaF₂, ≤0.12 wt% TiO₂, the rest being MnO and FeO.

Five groups of industrial tests have been carried out on GCr15SiMn steel with optimised Al content and slag composition. Results indicate that the steel/slag reaction reaches an earlier balance in the LF refining process, and the average titanium content at the final of LF is reduced by 8 ppm after optimisation. This model could provide some guidance for controlling titanium practice during the industrial LF refining process.

Footnotes

Disclosure statement

No potential conflict of interest was reported by the author(s).

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A thermodynamic model of the titanium distribution behaviour between slag and molten steel during LF refining process: description and application

Abstract

Introduction

Establishment of model

Model mechanism and hypothesis

Equilibrium expressions at slag–metal interface

Calculation of equilibrium slag action concentration

Programme and computation process

Result and discussion

Experiment verification of the model

Model application during LF refining process

Effect of Al, Si content on the equilibrium

Effect of CaO, MgO content on the equilibrium

Effect of TiO2 content on the equilibrium

Comparison of titanium content before and after LF process optimisation

Conclusions

Footnotes

Disclosure statement

References

Effect of TiO₂ content on the equilibrium