Kinetic model of dephosphorization in the new double slag converter steelmaking process

Abstract

The kinetic investigation of the dephosphorization in the new double slag converter steelmaking process was carried out based on the coupled reactions model combining with a heat balance temperature model for the 220-ton industrial experiment. The calculated results of [%C], [%Si], [%P] in the hot metal, and the slag compositions are in good agreement with the experimental results. When the heat balance temperature model is applied, the P prediction results are better rather than those predicted by using the fixed temperatures. The calculated phosphorus distribution ratio increases with the refining time, while the phosphate capacity shows a downward trend due to the decrease in slag basicity and the increase in temperature. The rate-controlling step of the dephosphorization is determined to be the mixed control of the mass transfer of P in the hot metal and P₂O₅ in the slag. As the initial Si concentration is increased, the interfacial oxygen activity required for starting the dephosphorization is increased, leading to the delay of the dephosphorization start time.

List of symbols

the content in slag

the total mass per cent of iron element

the mass per cent of the content in slag

the content in the metal phase

the mass per cent of the content in hot metal

the temperature coefficients of heat capacities [J K⁻¹ mol⁻¹]

the activity

the reaction area of the interface [m²]

the temperature coefficients of heat capacities [J K⁻² mol⁻¹]

the constant with a value of 0.25

the temperature coefficients of heat capacities [J K mol⁻¹]

the heat capacity of hot metal [kJ kg^-1 K⁻¹]

the heat capacity of scrap [kJ kg^-1 K^-1]

the molarity of slag [mol cm⁻³]

the phosphate capacity of slag

the temperature coefficients of heat capacities [J K⁻³ mol⁻¹]

the diameter of the nozzles of the top oxygen lance [m]

the diameter of bath [m]

the effective equilibrium constants

the activity coefficient of content in hot metal

the effective mass transfer coefficient [mol cm⁻² s⁻¹]

the gravitational constant [m s⁻²]

the phenomenological generation rate constant of carbon monoxide [mol cm⁻² s⁻¹]

the oxygen supplying rate [mol cm⁻² s⁻¹]

the heat transfer coefficient [W m⁻² K⁻¹]

the lance height [m]

the bath depth [m]

the reaction heat released by per kg of solutes in hot metal [kJ kg⁻¹]

the molar enthalpy [J mol⁻¹]

the phase change heat [J mol⁻¹]

the molar flux [mol cm⁻² s⁻¹]

the equilibrium constant

the mass transfer coefficient [m s⁻¹]

the phosphorus distribution ratio

the molecular mass [g mol⁻¹]

the coordination number

the number of oxygen atoms in the molecule

the standard atmosphere pressure [Pa]

the partial pressure of carbon monoxide [atm]

the latent heat of fusion of scrap [kJ kg⁻¹]

the Ar gas flow rate by bottom blowing [Nm³ s⁻¹]

the heat loss [kJ]

the physical heat of hot metal and slag, respectively [kJ]

the oxygen flow rate by top blowing [Nm³ s⁻¹]

the melting heat of scrap [kJ]

the melting heat of sintered ore [kJ]

the heat released by oxidation reaction [kJ]

the radius of scrap or lime [m]

the molar gas constant [J mol⁻¹ K⁻¹]

the time [s]

the temperature of hot metal [K]

the liquidus temperature of scrap [K]

the melting temperature of metal [K]

the room temperature [K]

the temperature of position x in scrap [K]

the volume [m³]

the weight [kg]

the weight of scrap [kg]

the weight of sintered ore [kg]

the weight of oxide in slag [kg]

the total weight change of slag [kg]

the distance to the surface of scrap [m]

the mole per cent of composition in slag

the constant with a value of 1.7

the conversion ratio of oxygen

the activity coefficient of content in slag

the power consumption of mixing by top and bottom blowing, respectively [W m⁻³]

the inclination angle of the nozzles of top oxygen lance [deg.]

the number of nozzles in top oxygen lance

the total optical basicity

the optical basicity of composition

the density [kg m⁻³]

Superscripts

bulk

interface

new value after reaction time

the metal-scrap interface

Subscripts

metal

slag

the content in hot metal

the content in slag

the content in the scrap

Introduction

Since the 1960s, researchers began to conduct fundamental researches on the kinetics of dephosphorization of molten iron at different conditions [1–15], and they came to an agreement that dephosphorization is a first-order reaction. However, it is still disputed on the rate-controlling step. As early as 1967, Kawai et al. [1] suggested that oxygen dissolution from the gas phase to the metal phase is the rate-controlling step in the dephosphorization experiment with a low oxygen potential using H₂O–H₂–Ar gas with CaO crucible. Aratani et al. [2] studied the kinetics of dephosphorization with CaO–FeO–SiO₂ slag at 1550°C and 1600°C and found that the dephosphorization is controlled by the rate of the chemical reaction. In the dephosphorization experiment of molten iron with CaO crucible, Aratani et al. [3] suggested that the dephosphorization reaction should be divided into three periods. In the first period, the rate-controlling step is the chemical reaction. In the second period, the dephosphorization rate depends on the rate of oxygen supply from gas to molten iron. In the third period, the rate-controlling step is the transfer of oxidation product into solid CaO. More researchers showed that the rate-controlling step is the mass transfer of phosphorus in the slag [6–10], or the mixed control of the mass transfer of oxygen in the gas phase and phosphorus in the metal or slag phase [11–15]. The main reason for the different rate-controlling steps is due to the different reaction conditions [16].

Regarding the reaction kinetic model for dephosphorization, Ohguchi et al. [11] developed the coupled reaction model which can meet the demands of different conditions in 1984. The parameters used in this model should also be adjusted according to different reaction conditions. This leads to the problem that in order to obtain good agreement with the experimental results, the appropriate model parameters have to be used [17]. The advantage of this model lies in its ability to simulate multiple reactions at the metal/slag interface simultaneously, which makes the coupled reaction model widely used in dephosphorization kinetic study [10,14,15,17–32]. Recently, Kitamura et al. [21] developed a new reaction kinetic model for hot metal dephosphorization based on the coupled reaction model, which took the effect of the solid phase of dicalcium silicate and the dissolution rate of lime into consideration. In this model, the slag phase was divided into liquid phase and solid phase. The calculated results demonstrated the importance of the solid phase in the slag in dephosphorization. Lytvynyuk et al. [31,32] further modified the coupled reaction model with consideration of the melting and dissolution process of the charged materials, showing the high precisions of temperature and compositions of metal and slag at the blowing end of converters with 170 and 330 ton.

In addition to the coupled reaction model, there are several kinetic models for the converter steelmaking process in which the slag is treated as an emulsion zone containing gas bubbles, metal droplets and undissolved flux. Dogan et al. [33] developed a first-principle kinetic model for the decarburization which divided carbon oxidation into emulsion zone and impact zone. The formation and residence of metal droplets in the emulsion zone were considered. In the multi-zone reaction kinetic model established by Rout et al. [34], the reaction zones were divided into jet impact zone, slag-bulk zone and slag-metal-gas emulsion zone. Dering et al. [35] further incorporated a model for slag formation and energy balances into the first-principle kinetic model. The model predictions for the end-point carbon content, slag composition and temperature agree reasonably well with the data for a wide range of operating conditions.

To reduce the production cost, the new double slag converter steelmaking process was developed by Nippon Steel, namely Multi-Refining Converter (MURC) process [36]. In this process, the desiliconization and dephosphorization are conducted in the converter at first. After intermediate deslagging of the dephosphorization slag, the decarburization is performed in the same converter and the decarburization slag is left in the converter for reusing in the next charge. Therefore, the lime consumption can be greatly reduced to decrease the production cost. In recent years, more and more steelmaking plants began to adopt the new double slag converter steelmaking process [37].

Compared with the conventional steelmaking process, the hot metal is dephosphorized with the slag at the relatively low basicity of 1.3–2.2 and at the low temperature of approximately 1350°C in the new double slag converter steelmaking process [36]. Wang et al. [38] indicated that the basicity of the dephosphorization slag should be controlled within the range of 1.3–1.5, and the temperature after dephosphorization was about 1350°C. For the dephosphorization at low basicity and low temperature, few kinetic studies have been carried out. Matsui et al. [27] designed a 200 kg scale experiment at a constant temperature of 1350°C to develop a new kinetic model for the iron oxide formation based on the coupled reaction model. In the experiment, the basicity of slag dropped from 4 to about 2.8 after 10 min of dephosphorization. Sato et al. [19] examined the oxidation rate of phosphorus in high carbon iron melts with the different silicon contents at 1400°C for about 1800 s, with the initial slag basicity of 2.9 and 3.2 using the converter slag. The kinetic studies on the dephosphorization behaviour in the new double slag steelmaking process with the low slag basicity of 1.3–2.2 at the low temperature of about 1350°C are quite limited, which are needed to be done in detail.

In this paper, a dephosphorization kinetic model for the dephosphorization stage of the new double slag converter steelmaking process was developed based on the coupled reaction model with a heat balance temperature model to predict the temperature change during the process. The industrial experiment was conducted to verify the kinetic model. The changes in the compositions of metal and slag with time were calculated. From the calculated results of the phosphorus distribution ratio and the phosphate capacity of slag, the change in dephosphorization capability of slag with the dephosphorization process was studied. The rate-controlling step of dephosphorization was investigated by comparison of the calculated P contents in the hot metal bulk and at the metal/slag interface, and P₂O₅ contents in the slag bulk and at the metal/slag interface. The effect of the initial Si concentration on the dephosphorization rates in the new double slag converter steelmaking process was also made clear.

The dephosphorization kinetic model

The industrial experiment of the new double slag converter steelmaking process was conducted in a steelmaking plant in China. The schematic diagram is shown in Figure 1. The decarburization (De-C) slag was left inside the converter after tapping to be splashed and reused in the next heat. The dolomite was charged during the slag splashing to cool down the leftover hot slag. In order to improve the utilization efficiency of lime and further cool down the leftover hot slag, all the lime was added into the converter before blowing. Only after the slag was fully cooled down and confirmed to be solidified, the hot metal was allowed to be charged into the converter to avoid the violent splash of hot metal. Then the scrap and the hot metal after KR (Kambara Reactor) desulphurization (De-S) were charged into the converter. Then the desiliconization (De-Si) and dephosphorization (De-P) were conducted. During the De-P stage, two batches of sintered ore were added into the converter to promote the formation of the molten slag. No flux other than sintered ore was added during the De-P stage. After 331 s of blowing, the slag was poured out as much as possible by tilting the converter. Then the decarburization was carried out in the same converter. The present paper focuses on the kinetic study on the De-P in the new double slag converter steelmaking process.

Figure 1.

Schematic diagram of the new double slag converter steelmaking process.

The new dephosphorization kinetic model is developed based on the coupled reaction model [11]. In the steelmaking process in Basic Oxygen Furnace (BOF), the reactions proceed under non-equilibrium conditions. In order to simplify, it is assumed that the reactions at the metal/slag interface are always in the equilibrium state.

The reactions considered in this model are shown in Equation (1). (1) Further assumptions are given as follows:

After KR desulphurization as shown in Figure 1, the sulphur concentration in the hot metal is lower than 50 ppm, which is not usually further decreased in the following De-P stage. So the model does not take the desulphurization into consideration. On the other hand, sulphur in the metal phase does not react with oxygen directly, but reacts with the calcium oxide in the slag phase, as shown in Equation (2). The consumption of calcium oxide and the generation of oxygen will unnecessarily complicate the calculation if the desulphurization is considered. (2)

Since the dolomite wasn’t added during the De-P stage, the change in magnesium oxide content in the slag is ignored and the weight of MgO is regarded as a constant.

The mass transfer coefficients of various contents in the metal phase are assumed to be equal, so are those of various contents in the slag phase.

The equilibrium constants of Equation (1) can be represented as Equations (3) and (4). (3) (4) where is the equilibrium constant. and are the activity coefficients of contents in the slag and hot metal, respectively. and are the mass per cent of the contents in the slag and hot metal, respectively. is the activity of oxygen. is the coordination number. For Si-O and P-O reactions, the values of are 2 and 2.5, respectively. is the partial pressure of carbon monoxide. can be Fe, Si, Mn, P here.

In steelmaking, the oxide in the slag phase is commonly expressed in the form of mass per cent. The conversion formula from mole per cent to mass per cent is shown in Equation (5). (5)

where

is the mass per cent of the content in the slag.

is the molecular mass of the oxide [g mol⁻¹].

is the density of slag [kg m⁻³].

indicates the molarity of slag [mol cm⁻³], which is calculated by the industrial experiment slag. The typical compositions and molarities of dephosphorization slag and decarburization slag are presented in Table 1. According to Table 1, although the two kinds of slag are different in composition and basicity, the calculated molarities are similar, which are 0.0881 mol cm⁻³ and 0.0836 mol cm⁻³, respectively. To simplify the calculation, 0.085 mol cm⁻³ is used as the value of

in the present work.

Table 1.

The compositions and molarities of slag.

	Dephosphorization slag	Decarburization slag
Composition [mass%]	CaO: 39.66	CaO: 39.88
	SiO₂: 21.27	SiO₂: 12.63
	P₂O₅: 3.37	P₂O₅: 2.24
	MgO: 8.27	MgO: 8.76
	T.Fe: 12.77	T.Fe: 22.17
	MnO: 6.62	MnO: 4.14
Basicity	1.86	3.16
Weight [g]	5	8
Volume [cm³]	1.2	2.15
Molarity [mol cm⁻³]	0.0881	0.0836

The equilibrium constants in Equations (3) and (4) can be modified to the effective equilibrium constants of , which indicate that the reactions at the interface are under equilibrium conditions. are shown in Equations (6)–(8). (6) (7) (8)

The superscript indicates the metal/slag interface. in Equation (8) can be Si, Mn, and P. According to the two-film theory [39], the molar flux of [mol cm⁻² s⁻¹] can be expressed as Equation (9). (9) The superscript indicates the bulk of hot metal or slag. and indicate the effective mass transfer coefficient in the hot metal and slag, respectively [mol cm⁻² s⁻¹], which are represented as Equations (10) and (11), respectively. (10) (11) where and are the mass transfer coefficients in the hot metal phase and slag phase, respectively [m s⁻¹]. is the density of the hot metal [kg m⁻³]. is the molecular mass of the composition in the hot metal [g mol⁻¹].

The molar fluxes considered in the present model are shown as Equations (12)–(15). (12) (13) (14) (15)

in Equation (13) means the phenomenological generation rate constant of carbon monoxide [mol cm⁻² s⁻¹]. in Equation (14) can be Si, Mn, and P. in Equation (15) indicates the oxygen content in hot metal, which can be calculated according to the thermodynamic data [40].

The mass conservation equation of oxygen can be obtained by combining Equations (12)–(15), as shown in Equation (16). (16) in Equation (16) is the oxygen supplying rate by the top oxygen lance [mol cm⁻² s⁻¹], which can be calculated by Equation (17). (17) where is the conversion ratio of oxygen. is the oxygen flow rate supplied by top blowing [Nm³ s⁻¹]. is the reaction area of the metal/slag interface [m²].

Furthermore, the equilibrium constants of are calculated from thermodynamic data [40]. The activity coefficients of contents in the slag phase of are calculated based on the regular solution model [41]. The activity coefficients of contents in the hot metal phase of can be calculated through the activity interaction coefficients from the Steelmaking Data Sourcebook [40].

The mass transfer coefficient in the slag phase of is calculated by Equations (18)–(20) [27,39,42]. (18) (19) (20) where and are the power consumption of mixing by top and bottom blowing, respectively [W m⁻³]. is the inclination angle of the nozzles of the top oxygen lance [deg.]. is the volume of the hot metal [m³]. is the molecular mass of oxygen [g mol⁻¹]. is the number of nozzles of the top oxygen lance. is the diameter of the nozzles [m]. is the lance height, which indicates the distance from the reaction interface to the lance [m]. is the Ar gas flow rate by bottom blowing [Nm³ s⁻¹]. is the temperature of the hot metal [K]. is the room temperature [K]. is the gravitational constant [m s⁻²]. is the bath depth [m]. is the standard atmosphere pressure [Pa]. is the molar gas constant [J mol⁻¹ K⁻¹]. and in Equation (20) are constants with values of 1.7 and 0.25, respectively, according to Matsui’s research [27].

The mass transfer coefficient in the hot metal phase of is calculated by Equation (21) [5]. (21) is the weight of the hot metal [kg]. is the diameter of the bath [m].

The unknown parameters in the oxygen mass conservation equation of Equation (16) are the mass per cent of the compositions at the metal/slag interface. These unknown parameters can be expressed as equations correlated with the unknown quantity of , which indicates the activity of oxygen at the interface. Fe concentrations at the interface as well as in the bulk of hot metal are assumed to be unit. The FeO concentration at the interface is obtained by transforming Equation (6), as shown in Equation (23). (22) (23)

C concentration at the interface is represented as Equation (24) by combining Equation (7) with Equation (13). (24) where is the partial pressure of carbon monoxide at the interface. In the present work, the value of is assumed to be 1.

Si, Mn, and P have similar expressions, as shown in Equations (25) and (26). (25) (26) O concentration at the interface in Equation (15) is assumed to be equal to , as shown in Equation (27). (27) The mass per cent of the compositions at the reaction interface has been converted to the form of . The value of can be obtained through solving Equation (16). Since is obtained, the other interfacial concentrations can be calculated through Equations (23)–(27).

The influence of scrap dissolution is taken into account. The melted scrap will enter the hot metal and increase the weight of the hot metal, which will also change the compositions of the hot metal. When the bath temperature is lower than the melting point of the scrap, the dissolution of scrap is mainly in the form of diffusion [31]. Assuming that the scrap is cylindrical, then the dissolution rate of scrap can be expressed as Equation (28) [31,43]. (28)

where

is the mass transfer coefficient between the hot metal and the scrap [m s⁻¹]. The superscript

indicates the metal-scrap interface. The value of

is determined by the heat transfer and carbon transfer between the hot metal and the scrap as shown in Equation (29) [44]. (29)

where

is the heat transfer coefficient [W m⁻² K⁻¹].

is the liquidus temperature of scrap [K].

is the density of scrap [kg m⁻³].

is the latent heat of fusion of scrap [kJ kg⁻¹].

is the heat capacity of hot metal [kJ kg⁻¹ K⁻¹].

is the mass transfer coefficient [m s⁻¹]. The parameters used for calculating the dissolution of scrap are listed in Table 2.

is a function of

, which is obtained by using Fe-Fe₃C phase diagram generated by Factsage FeSstel database.

Table 2.

Parameters used for calculating the dissolution of scrap [43–45].

Symbol	Description	Value
	Mass transfer coefficient between hot metal and scrap	1.39 × 10⁻⁴ m s⁻¹
	C concentration in the scrap	0.12 mass%
	Heat transfer coefficient	5280 W m⁻² K⁻¹
	Density of scrap	7800 kg m⁻³
	Latent heat of fusion of scrap	251 kJ kg⁻¹
	Heat capacity of hot metal	0.837 kJ kg⁻¹ K⁻¹

The weight of the melted scrap is determined by the dissolution rate of scrap calculated by Equation (28) and the diameter of the cylindrical scrap. In the present industrial experiment, 28,720 kg scrap was charged. The scraps include four types of heavy scrap, medium scrap, light scrap and slag-metal scrap. The four types of scrap are presented in Table 3. The slag-metal scrap is the mixture of slag and steel, which is extracted from the converter slag to reduce the cost, in which the contents of Fe, CaO and SiO₂ are 85%, 7.5% and 7.5%, respectively. There is an assumption that all the CaO and SiO₂ in the slag-metal scrap enter the slag phase before blowing. The dissolution rate of each type of scrap is calculated to obtain the total weight of the melted scrap of

Table 3.

Charged scrap types in industrial experiment.

Scrap types	Weight (kg)	Proportion	Average radius (m)
Heavy	7000	24.4%	0.20
Medium	2740	9.50%	0.15
Light	5380	18.7%	0.10
Slag-metal	13,600	47.4%	0.15
Total	28,720	100%	–

The dissolution rate of the pre-charged lime is shown in Equation (30). (30) where is the mass transfer coefficient of lime dissolution [m s⁻¹]. is the density of the lime [kg m⁻³]. is the value of the saturation concentration minus the actual concentration of CaO in the slag, representing the driving force of lime dissolution (mass%). can be expressed as dimensionless values and then be obtained [21,46]. is 2500 kg m⁻³. is assumed to be 20 mass%. The dissolved lime will enter the slag and increase the CaO content in the slag phase.

After a short time of reaction of , the concentration change of , and the new concentration of are presented as Equations (31) and (32). (31) (32) where is the concentration of X in the scrap.

In Equation (31), the reaction area of is the slag area calculated with the inner diameter of the converter, which is suitable for the metal-slag reaction. For a metal-gas reaction, an oxygen jet is injected through the lance onto the surface of the metal bath at supersonic speed. Tiny bubbles of oxygen may increase the metal-gas reaction area. So the metal-gas reaction area should be increased. In the present work, the metal-gas reaction area is assumed to be to match the industrial experiment results, especially the C concentration result.

Regarding the compositions in the slag, the weight of each oxide changes after , as shown in Equation (33). Moreover, there are two batches of sintered ore added during the De-P stage, which will lead to changes in slag weight and contents. From Equation (33), one can calculate a certain composition weight change in the slag. The weight changes of all contents add up to the total weight change of [kg]. The new concentration of is given by Equation (34). The weight of slag will also increase with the formation of the oxides. (33) (34) where is the weight of the slag [kg]. is the weight of the sintered ore [kg]. There is an assumption that the sintered ore completely melts immediately when it is added into the converter. The value of is 0 except for the moments when the sintered ore is added.

The new contents obtained from Equations (32) to (34) are treated as new initial contents to repeat the calculations. The repetitions depend on the reaction time and the span of time of . In the present work, the reaction time is 360 s, and the span of time is 1 s.

The heat balance temperature model

The bath temperature during the De-P stage of the new double slag converter steelmaking process varies with the reaction time. The heat balance calculation provides a simple way to obtain the temperature change. The heat income includes the physical heat of hot metal and slag at the temperature , and the oxidation heat of the solutes in the hot metal. The heat expense includes the new physical heat of hot metal and slag at the new temperature of , the melting heat of scrap and sintered ore, and the heat loss from the emission gas, heat radiation of hot metal, and furnace wall. The mean heat capacities used are the same as those used in Liu’s research [45].

Calculation of heat income

The physical heat of hot metal before the reaction of [kJ] can be expressed as Equation (35). (35) where is the melting temperature of the metal [K], which can be calculated by the empirical Equation (36) [44]. (36)

The physical heat of slag before the reaction of

[kJ] can be expressed as Equation (37). (37)

The reaction heat effect varies with the temperature, which is calculated by Equations (38)–(40) [47]. (38)

(39)

(40)

where

is the molar enthalpy [J mol⁻¹], which means the heat that can be released by the formation of per molar element. The molar enthalpy of oxide of

[J mol⁻¹] can also be calculated by a similar equation, as shown in Equation (39). a, b, c, d indicate the temperature coefficients of heat capacities.

indicates the phase change heat [J mol⁻¹].

can be Fe, C, Si, Mn, P here. From Equation (40), one can calculate the heat income of

[kJ] released by oxidation, depending on the concentration changes of the solutes. The reaction heat of

[kJ kg⁻¹], which indicates the heat released by per kilogram of the solutes, can be calculated by Equations (38)–(40) at 1623 K, as shown in Table 4. Reaction heats at other temperatures can be obtained in the same way.

Table 4.

Reaction heats at 1623 K.

Reaction	H [kJ kg⁻¹]
[C] + [O] = CO (g)	−8832
[C] + 2[O] = CO₂ (g)	−30,319
[Si] + 2[O] = (SiO₂)	−30,430
[Mn] + [O] = (MnO)	−6931
[P] + 2.5[O] = (PO_2.5)	−10,736
[Fe] + [O] = (FeO)	−4393

In the present work, 90% of carbon is assumed to be oxidized to form carbon monoxide, and the remaining 10% is oxidized to form carbon dioxide [48].

Calculation of heat expense

After , the mass per cent of compositions in hot metal changes. As a result, the melting temperature of hot metal has to be recalculated by Equation (36) to obtain the new melting temperature of . The new physical heat of hot metal and slag should also be recalculated by Equations (35) and (37) by replacing with the new temperature of [K].

The initial temperature of the scrap is 298 K. The scrap absorbs the heat from the hot metal with time, and its temperature keeps rising. The temperature change of the scrap with time can be calculated based on the unsteady heat conduction principle as shown in Equation (41). (41) where x is the distance between a certain point inside the scrap and the surface of the scrap [m]. is the temperature of this point [K]. The liquidus temperature of in the scrap dissolution model mentioned above is regarded as the temperature of the scrap surface. erf () is the Gauss error function. is the heat capacity of scrap, with the value of 0.745 kJ kg⁻¹ K⁻¹. is the thermal conductivity of scrap [W m⁻¹ K⁻¹]. The value of changes with temperature. In the present work, 29 W m⁻¹ K⁻¹ is used as the value of . is the contact time between the scrap and hot metal [s].

Since the four types of scrap have different radii as shown in Table 3, the temperature distributions inside the four types of scrap are calculated respectively according to Equation (41). The effects of weight and radius changes of the scrap through the scrap dissolution model should also be considered. The melting heat of scrap of [kJ] can be expressed as Equation (42). (42) The heat loss of [kJ] is assumed to be constant as shown in Equation (43). The value of is calculated assuming that the total heat loss is 8% of the total heat expense and the value of total heat expense is 2187.66 kJ per kg of hot metal [48]. The time of the BOF process is assumed to be 15 min. (43)

The added sintered ore also absorbs heat. The melting heat of sintered ore of (kJ) is shown in Equation (44). (44)

Calculation of heat balance

Equations (35), (37), (40)–(44) can be modified to a heat balance equation, as shown in Equation (45). (45) The new temperature of is the only unknown parameter, which can be calculated numerically.

To conduct the calculations of the coupled reaction model and the heat balance temperature model, the programming language of Python was used. In the first step, the initial data and conditions were inputted into the model, such as the constants in the equations, the initial mass per cent of compositions, the converter blowing parameters, the weights of hot metal and slag, etc. Then, through the calculation method described above, the new mass per cent of compositions and temperature could be obtained. Finally, the original mass per cent of compositions and temperature were replaced by the new ones. The process was repeated until the time was greater than the preset reaction time.

Results and discussion

Experimental and calculated conditions

To verify the accuracy of the calculated results, the 220 ton BOF industrial experiment was conducted. The experimental and calculated conditions are shown in Table 5. In actual production, the gas flow rate fluctuates with time rather than a fixed value, so the total gas supply was divided by the reaction time to obtain the average gas flow rate. The top blowing oxygen gas flow rate of 8.89 Nm³ s⁻¹ was lower than the value in the conventional process, and the average Ar gas flow rate of bottom blowing was 0.089 Nm³ s⁻¹. The lance height was changed from 2 to 1.8 m at 270 s.

Table 5.

Experimental and calculated conditions.

Furnace size	Inner diameter	5.464 m
	Bath depth	1.69 m
	Reaction interface area	23.448 m² for metal-slag reaction
		42.206 m² for metal-gas reaction
Top blowing	Average oxygen gas flow rate	8.89 Nm³ s⁻¹
	Number of nozzles	5
	Nozzle diameter	0.0372 m
	Lance height	2 m during 0–270 s
		1.8m during 270–360 s
	Oxygen outlet angle	15°
Bottom blowing	Average Ar gas flow rate	0.089 Nm³ s⁻¹

Some necessary physical parameter values were needed in the kinetic model. The densities of hot metal and slag were 7000 and 3000 kg m⁻³, respectively. The weight of the hot metal, the recycled slag, and the scrap were 195,150, 7500, and 28,720 kg, respectively. The weights of the hot metal and scrap were the measured values, while the weight of the recycled slag was the average value in the converter blowing process. The value of the slag molarity was taken to be 0.085 mol cm⁻³. The equilibrium constants and activity coefficients used in the calculation were adopted from Steelmaking Data Sourcebook [40]. The activity coefficients of compositions in the slag phase were calculated based on the regular solution model [41]. Lower lance height will strengthen the mixing of the molten pool and promote the mass transfer. When the lance height was 2.0 m, the conversion ratio of oxygen was set to be 0.6 [27]. When the lance height decreased to 1.8 m at 270 s, the value of the conversion ratio of oxygen was 0.7. The value of the phenomenological generation rate constant of CO of

was determined by the fitting of the calculated results to the measured results [18,29]. In the present work,

was expressed as a function of decarburization rate rather than a fixed constant. (46)

The initial conditions of scrap, hot metal, and slag of the industrial experiment are given in Table 6. The same initial conditions were inputted into the present kinetic model to calculate.

Table 6.

Initial concentrations, temperatures, and weights of scrap, hot metal, and slag.

Scrap	[%C]	[%Si]	[%Mn]	[%P]	W _scrap [kg]
Scrap	0.12	0.15	0.5	0.02	28720

Hot metal	[%C]	[%Si]	[%Mn]	[%P]	Temperature [K]	W _m [kg]
Hot metal	4.65	0.31	0.21	0.14	1623	195150
Slag	(%CaO)	(%SiO₂)	(%MnO)	(%P₂O₅)	(%FeO)	(%MgO)	W _s [kg]
Slag	45.5	11.3	2.8	2.5	29.0	8.9	7500

Moreover, two batches of sintered ore were added into the converter during the De-P stage. The contents other than iron oxide in the sintered ore were ignored. The weights of two batches of sintered ore were 1046.64 and 837.48 kg, which were added at 60 and 240 s, respectively.

The added flux, including dolomite, lime and sintered ore, are listed in Table 7. 1000 kg dolomite was added during slag splashing. The weight of the charged lime was 2142 kg. All the lime was charged before charging scrap. Moreover, two batches of sintered ore were added into the converter during the De-P stage. The contents other than iron oxide in the sintered ore were ignored. The weights of two batches of sintered ore were 1047and 837 kg, which were added at 60 and 240 s, respectively.

Table 7.

Added fluxes in industrial experiment.

Flux	Weight [kg]	Time of charging into converter
Dolomite	1000	All during slag splashing
Lime	2142	All before charging scrap
Sintered ore	1047 + 837	At 60 and 240 s in De-P stage, respectively

Experimental and calculated results

Figure 2(a) is the changes in hot metal compositions with time, and Figure 3 displays the changes in slag compositions and basicity with time. The lines represent the calculated results, while the symbols represent the industrial experiment results. The De-P stage of this industrial experiment took 331 s. In the course of the experiment, no intermediate sampling or temperature measurement could be conducted, so that there were only 0-s and 331-s experimental results.

Figure 2.

(a) Changes in hot metal compositions with time, (b) the influence of lance height on the decarburization rate.

Figure 3.

Changes in slag compositions and basicity with time.

As shown in Figure 2(a), all the contents of [%C], [%Si] and [%P] in the hot metal show a downward trend. The desiliconization reaction drastically occurs firstly. After six minutes of blowing, only a trace of [%Si] can be detected. Both the decarburization and dephosphorization begin to proceed about one minute after blowing. This is in agreement with the results obtained by Ohguchi et al. [11] that only when the [%Si] is reduced to a certain extent, the decarburization and dephosphorization can be taken place. It can be seen in Figure 2(a) that the calculated results of [%C], [%Si], and [%P] are very close to the industrial experiment results.

Figure 2(b) represents the change in decarburization rate with time. It can be seen that when the lance height changes from 2.0 to 1.8 m, the decarburization rate increase, which shows a similar trend to Dering et al.’s results [35].

In Figure 3, the changes in slag compositions with time are displayed. The additions of two batches of sintered ore at 60 and 240 s lead to two sudden rises in the curve of (%FeO). As the proportion of FeO increases, the concentrations of other compositions in the slag decrease accordingly. (%SiO₂) and (%MnO) have upward trends due to the oxidation reactions of Si and Mn, respectively. The additions of two batches of sintered ore keep the final content of FeO at about 30 mass% after the De-P stage finished, which is conducive to the formation of foaming slag. The decrease of (%CaO) is due to the increases of SiO₂, MnO, and P₂O₅ contents in the slag. Since MgO does not participate in the reaction, (%MgO) changes little. The content of P₂O₅ first rises and then remains unchanged, which is in correspondence to the calculation result of [%P] in Figure 2. It can be seen that the calculated results are in good agreement with the industrial experiment results, and the present kinetic model has good accuracy in the prediction of slag concentration. Figure 3 also displays the basicity change with time. The basicity of slag is obtained by dividing the concentration of calcium oxide by the concentration of silicon dioxide ( ). The initial basicity of slag is high because the basicity of the recycled decarburization slag is generally greater than 3. The basicity of the slag will gradually decrease with the desiliconization. At 331 s, the calculated slag basicity is 1.67, which is close to the industrial measurement result of 1.71.

The change in bath temperature with time is shown in Figure 4. The temperature is calculated with the heat balance temperature model. As the reaction progresses, the bath temperature first decreases because of the dissolution of scrap. Then the temperature keeps rising due to the exothermic reaction. In the present work, in order to improve the utilization efficiency of lime, all the lime was added into the converter before charging scrap and hot metal. This method can increase the contact time between the lime and the hot metal to promote the melting of the lime. For this reason, the lime has already been heated for a few minutes before the oxygen gas blowing begins. The cooling effect of scrap is calculated based on the unsteady heat conduction principle. As shown in Figure 4, the curve of temperature has two inflection points at 60 and 240 s, respectively, due to the additions of two batches of sintered ore at these times. The sintered ore with a room temperature of 298 K absorbs a lot of heat after being added into the converter, resulting in the drops of the bath temperature. Under the present experimental conditions, the bath temperature rises from 1623 to 1708 K in 360 s.

Figure 4.

Change in bath temperature with time.

The changes in [%P] with time under different temperature models are shown in Figure 5. The three temperature models are the constant temperature of 1623 K, the constant temperature of 1698 K, and the temperature calculated by the heat balance temperature model in the present work as shown in Figure 4, respectively. 1623 and 1698 K are the initial temperature and the final temperature of the De-P stage in the new double slag converter steelmaking process, respectively. When the temperature during the De-P stage is kept at the constant value of 1623 K, the [%P] value in hot metal decreases at the fastest rate. It shows that the low temperature is conducive to dephosphorization. After 331 s of blowing, the calculated [%P] at constant temperatures of 1623 and 1698 K are 0.0671% and 0.0927%, respectively. When the heat balance temperature model is applied, the P prediction results are better rather than those predicted by using the fixed temperatures. The calculated [%P] value in this case is 0.0852%, which is closest to the experimental results of 0.0769%. It can be seen that there is a small increase in [%P] in the early period of the De-P stage. This is the rephosphorization phenomenon caused by the high concentration of P₂O₅ in the recycled decarburization slag and the low interfacial oxygen potential due to the high initial [%Si]. The rephosphorization phenomenon is more obvious at high-temperature condition of 1698 K.

Figure 5.

Changes in [%P] with time under different temperature models.

The changes in basicity and FeO content under three temperature conditions are shown in Figure 6. It can be seen that the results of constant temperature at 1623 K and temperature model in the present work are similar in both basicity and FeO predictions. However, the results of constant temperature at 1698 K are a little different. It seems that the FeO prediction with a constant temperature at 1698 K is the closest to the experimental result, but in fact, the errors of these three temperature conditions are all small.

Figure 6.

Changes in basicity and FeO content with time under different temperature models.

Since the predictions of the composition changes and the temperature change are reliable, the phosphorus distribution ratio and the phosphate capacity are calculated to study the dephosphorization effect of the recycled decarburization slag.

The phosphorus distribution ratio of represents the dephosphorization effect. is defined as the mass per cent of P in the slag divided by the mass per cent of P in the hot metal, as shown in Equation (47). (47) where (%P) is the mass per cent of P in the slag, which is converted from the concentration of (P₂O₅).

The phosphate capacity of

represents the potential dephosphorization capacity of the slag. In the present work, the Yang empirical formula [49] is selected. One can calculate the phosphate capacity by Equations (48) and (49). (48)

(49)

where n_i is the number of oxygen atoms in the molecule.

is the optical basicity of oxide, and

is the total optical basicity. The optical basicity of each oxide is shown in Table 8.

Table 8.

Optical basicity of various oxides.

Oxide	CaO	SiO₂	MnO	P₂O₅	FeO	MgO
Λ_i	1.00	0.48	0.59	0.40	0.51	0.78

Through Equations (47)–(49), the calculated results of changes in and with time can be obtained, as shown in Figure 7. P in the hot metal phase transfers to the slag phase, resulting in an increase of , while decreases with time. Two major reasons are contributed to the decrease of . The first reason is the initial slag with high basicity, which is beneficial to combine phosphorus from the hot metal phase to form 3CaO-P₂O₅ in the slag phase. Besides, higher basicity will reduce the activity of P₂O₅, which is beneficial to the dephosphorization. Second, at the beginning of the reaction, the bath temperature is lower. Since the dephosphorization is a strong exothermic reaction, increasing temperature will reduce the equilibrium constant of the reaction. As a result, the higher is the bath temperature, the more difficult is it for dephosphorization. It can be concluded that the recycled decarburization slag has a good dephosphorizing potential in the De-P stage of the new double slag converter steelmaking process, especially in the early period of blowing due to the high basicity of the slag and the low bath temperature, which are beneficial to dephosphorization in thermodynamics. The two drops in curves in Figure 7 are due to the additions of two batches of sintered ore, which cause reductions in the proportion of CaO in the slag.

Figure 7.

Changes in and with time.

Rate-controlling step of the dephosphorization

The concentrations of P in the hot metal of and at the interface of can be obtained through the kinetic model, and their changes with time are compared in Figure 8(a). The value of minus is the driving force of the mass transfer of P in the hot metal phase, which is presented in Equation (31). When is larger than , phosphorus in the hot metal will transfer from the bulk of hot metal to the metal/slag interface to dephosphorize the hot metal. Otherwise, when is smaller than , the rephosphorization occurs.

Figure 8.

Relationships between P contents in the hot metal bulk and at the metal/slag interface, and P₂O₅ contents in the slag bulk and at the metal/slag interface.

Regarding the mass transfer of P₂O₅ in the slag phase, the changes in and with time are displayed in Figure 8(b). When is larger than , P₂O₅ at the metal/slag interface will transfer from the metal/slag interface to the bulk of the slag phase to promote the dephosphorization reaction. In contrast, the rephosphorization takes place when is lower than .

The addition of sintered ore will cause a reduction in the value of and the increase in the value of as displayed in Figure 8. This is because that the addition of the sintered ore will improve the slag oxidability, which can promote dephosphorization.

Regarding the Rate-Controlling Step (RCS) of the dephosphorization, there are three cases as shown in Figure 9. In the case in Figure 9(a), when the P concentration at the metal/slag interface is much lower than that in the bulk of the hot metal, while the P₂O₅ concentration in the bulk of the slag and at the interface are almost the same, the RCS is the mass transfer of P in the hot metal. In the case in Figure 9(b), the P concentration in the bulk of the hot metal and at the interface is almost the same, while the P₂O₅ concentration at the interface is much higher than that in the bulk of the slag. The RCS is the mass transfer of P₂O₅ in the slag. Figure 9(c) indicates that the RCS are mixed control of the mass transfer of P in the hot metal and P₂O₅ in the slag when the P concentration at the metal/slag interface is much lower than that in the bulk of the hot metal, and the P₂O₅ concentration at the interface is much higher than that in the bulk of the slag.

Figure 9.

Schematic diagram of P and P₂O₅ concentration near the hot metal/slag interface.

In Figure 8, during the dephosphorization step, there are both large P content gradients and P₂O₅ content gradients near the metal/slag interface, which is consistent with the case in Figure 9(c). Therefore, both the mass transfer of P from the bulk of hot metal to the interface and P₂O₅ from the interface to the bulk of slag are the rate-controlling steps.

Effect of the initial Si concentration

Using the model, one can calculate the behaviour in the De-P stage under different conditions. In steelmaking plants, the initial Si concentration in the hot metal of usually fluctuates greatly. To study the effect of the , the changes in hot metal compositions with time were calculated under different values of . The values of were set to be 0.2, 0.3, 0.4, and 0.5 mass%, respectively, and the other parameters including the additional amount of lime are unchanged. The bath temperature was calculated by the present heat balance temperature model.

Figure 10(a) shows the changes in [%Si] with time with different values of initial Si concentrations in hot metal. It can be seen that the Si concentrations decrease rapidly and reach a very low concentration in less than 3 min in all cases. Changes in [%C] with time with different values of are shown in Figure 10(b). After the start of the reactions, decarburization is delayed due to the strong oxidability of silicon. The oxygen supplied by the top lance will preferentially react with the silicon in the hot metal, and the higher value of will consume more oxygen. When the value of [%Si] is low enough, the decarburization starts to take place. The decarburization remains the same rate in the later stage of blowing in all cases.

Figure 10.

Changes in [%Si] and [%C] with time with different values of

Figure 11 shows the changes in [%P] with time with different values of . When the value of is equal or larger than 0.3 mass%, the curves of [%P] show rising trends at first, then fall. The round symbols in Figure 11 represent the inflection points in the curves, which divide the De-P stage into two steps: the rephosphorization step and the dephosphorization step. The rephosphorization step is elongated with the increase of . As the values of increase to 0.3, 0.4, and 0.5 mass%, the beginning time of dephosphorization is 14, 40, and 64 s, respectively. When the value of is 0.2 mass%, there is no rephosphorization step, and the value of [%P] decreases continuously. In the dephosphorization step, [%P] decreases continuously. Since the slag basicity increases with the dissolution of lime, the dephosphorization rate speeds up in the later period of the De-P stage. In the subsequent De-C stage of the new double slag converter steelmaking process, the additional lime will be added to promote further dephosphorization. Regarding the overall dephosphorization effect, the lower value of leads to a higher dephosphorization ratio at 6 min of blowing in the De-P stage of the new double slag converter steelmaking process.

Figure 11.

Changes in [%P] with time with different values of

It can be concluded that when the value of is greater than a certain value between 0.2 and 0.3 mass%, the change in P concentration with time can be divided into two steps:

Transient rephosphorization step with different duration time is caused by the high (P₂O₅) content in the recycled decarburization slag and the duration time deeply depends on the value of .

Fast dephosphorization step begins when the Si concentration in the hot metal decreases to a certain extent.

The changes in interfacial oxygen activity of with time with different values of are shown in Figure 12. The sudden rises in the curves at 60 s are caused by the additions of sintered ore. There are also rises in the curves at 240 s, but the changes are very small. At the beginning of the De-P stage, approaches to be zero, except when the value of is 0.2 mass%. With the progress of desiliconization, the value of increases. In the middle period of the De-P stage, the rate of dephosphorization slows down, which leads to a decrease of . Finally, the rapid decarburization begins to take place, causing to increase again.

Figure 12.

Changes in with time with different values of

The interfacial oxygen activity plays an important role in the progress of dephosphorization. Sato et al. [19] suggested that the high interfacial oxygen activity enables rapid dephosphorization rate, and the dephosphorization occurs when is greater than 10^−3.2. In the present work, the beginning time of the dephosphorization step obtained from Figure 11 is marked in Figure 12 as the round symbols. When the value of is 0.2 mass%, the initial value of is 10^−2.37, which is high enough so that the dephosphorization starts at 0 s. When the values of are 0.3, 0.4, and 0.5 mass%, required for starting the dephosphorization are 10^−2.73, 10^−2.66, and 10^−2.59, respectively, which indicates that the higher is the value of , the higher value of is required for starting dephosphorization. A higher value of will also lead to the prolongation of the rephosphorization step as shown in Figure 11. Therefore, it is important to keep a high interfacial oxygen activity in the dephosphorization stage.

Conclusion

The dephosphorization kinetic model combining the coupled reaction model with a heat balance temperature model is developed for the dephosphorization (De-P) in the new double slag converter steelmaking process. The calculated results were verified with the 220-ton industrial experiment results. The following conclusions can be drawn:

The calculated [%C], [%Si], and [%P] in the hot metal and the compositions in the slag are in good agreement with the industrial experiment results.

The temperature change during the De-P stage can be obtained through the heat balance temperature model in the present work. When the heat balance temperature model is applied, the P prediction results are better rather than those predicted by using the fixed temperatures.

The calculated phosphorus distribution ratio increases with the refining time. The phosphate capacity shows a downward trend with time due to the decrease in basicity and the increase in temperature.

The rate-controlling step of the dephosphorization is determined to be the mixed control of the mass transfer of P in the hot metal and P₂O₅ in the slag since there are large gradients of both P and P₂O₅ contents near the metal/slag interface.

In the cases of the different initial silicon concentrations, the De-P stage can be divided into two steps: the rephosphorization step and the dephosphorization step. As the initial Si concentration is increased, the interfacial oxygen activity required for starting the dephosphorization is increased, leading to the delay of the dephosphorization start time.

Footnotes

Acknowledgements

The authors gratefully acknowledge the financial support from the Natural Science Foundation of China (No. U1960202), and the Science and Technology Commission of Shanghai Municipality (No. 19DZ2270200).

Disclosure statement

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

References

Kawai

Nakashima

On the rate of dephosphorization of liquid iron by solid lime. Tetsu-to-Hagané. 1967;53(11):1188–1191.

Aratani

Sanbongi

Kinetic study of dephosphorization of liquid iron with oxidizing slag. Tetsu-to-Hagané. 1972;58(9):1225–1231.

Aratani

Sanbongi

Kinetic study of dephosphorization of liquid iron with solid CaO. Tetsu-to-Hagané. 1972;58(9):1217–1224.

Kawai

Nakamura

Kawakami

et al. Thermodynamics and kinetics of hot metal dephosphorization by CaO based slag containing CaF₂ . Tetsu-to-Hagané. 1983;69(15):1755–1762.

Kitamura

Shibata

et al. Effect of stirring energy, temperature and flux composition on hot metal dephosphorization kinetics. ISIJ Int 1991;31(11):1322–1328.

Kawai

Doi

Mori

Rate of dephosphorization of liquid iron by CaO-FeO-SiO₂ slag. Tetsu-to-Hagané. 1977;63(3):391–399.

Kunisada

Iwai

Rate of dephosphorization of liquid iron by the slag of CaO-SiO₂-FeO system. Tetsu-to-Hagané. 1984;70(14):1681–1688.

Kawara

Hayashi

Katase

et al. Tetsu-to-Hagané. 1976;62(11):S524.

Kunisada

Iwai

Rate of dephosphorization of liquid iron by the flux of Na₂O-SiO₂ system. Tetsu-to-Hagané. 1985;71(1):63–69.

10.

Doi

Mori

Kawai

et al. The rate of oxidation of phosphorus and silicon in liquid iron by molten slags. Tetsu-to-Hagané. 1986;72(10):1560–1566.

11.

Ohguchi

Robertson

DGC

Deo

et al. Ironmak Steelmak. 1984;11(4):202–213.

12.

Kawai

Nakao

Mori

Dephosphorization of liquid iron by CaF2-base fluxes. Trans. Iron Steel Inst. Jpn. 1984;24(7):509–514.

13.

Mori

Fukami

Kawai

Rate of dephosphorization of liquid iron-carbon alloys by molten slags. Trans Iron Steel Inst Jpn. 1988;28(4):315–318.

14.

Pan

Sano

Hirasawa

et al. Kinetics of phosphorus transfer between iron oxide containing slag and molten iron of high carbon concentration under Ar-O2 atmosphere. ISIJ Int 1993;33(4):479–487.

15.

Pan

Ohya

Hirasawa

et al. Estimation of slag-metal interfacial oxygen potential in phosphorus reaction between FetO containing slag and molten iron of high carbon concentration. ISIJ Int 1993;33(8):847–854.

16.

Kawai

Fundamentals of the kinetics of metal-slag reactions. Tetsu-to-Hagané. 1984;70(14):1640–1647.

17.

Dong

Jiang

Chai

J East China Inst Metall. 1993;10(2):7–12.

18.

Mukawa

Mizukami

Effect of stirring energy and rate of oxygen supply on the rate of hot metal dephosphorization. ISIJ Int 1995;35(11):1374–1380.

19.

Sato

Nakashima

Mori

Dephosphorization rate of high carbon iron melts by CaO-based slags. Tetsu-to-Hagané. 2001;87(10):643–649.

20.

Ishikawa

Matsuo

Kawaguchi

Hot metal dephosphorization behavior by sintered dephosphorization agent contain Al₂O₃ . Tetsu-to-Hagané. 2005;91(6):528–536.

21.

Kitamura

Shibata

Maruoka

Kinetic model of hot metal dephosphorization by liquid and solid coexisting slags. Steel Res Int 2008;79(8):586–590.

22.

Pahlevani

Shibata

Maruoka

et al. Behavior of vanadium and niobium during hot metal dephosphorization by CaO–SiO₂–FeO slag. ISIJ Int 2011;51(10):1624–1630.

23.

Kitamura

Aida

et al. Development of analysis and control method for hot metal dephosphorization process by computer simulation. ISIJ Int 1991;31(11):1329–1335.

24.

Kitamura

Aoki

Okohira

Dephosphorization reaction of chromium containing molten iron by CaO-based flux. ISIJ Int 1994;34(5):401–407.

25.

Kitamura

Miyamoto

Shibata

et al. Analysis of dephosphorization reaction using a simulation model of hot metal dephosphorization by multiphase slag. ISIJ Int 2009;49(9):1333–1339.

26.

Kitamura

Ito

Pahlevani

et al. Development of simulation model for hot metal dephosphorization process. Tetsu-to-Hagané. 2014;100(4):491–499.

27.

Matsui

Nabeshima

Matsuno

et al. Kinetics behavior of iron oxide formation under the condition of oxygen top blowing for dephosphorization of hot metal in the basic oxygen furnace. Tetsu-to-Hagané. 2009;95(3):207–216.

28.

Pahlevani

Kitamura

Shibata

et al. Simulation of steel refining process in converter. Steel Res Int 2010;81(8):617–622.

29.

Ogasawara

Miki

Uchida

et al. Development of high efficiency dephosphorization System in decarburization converter utilizing FetO dynamic control. ISIJ Int 2013;53(10):1786–1793.

30.

Meng

Liu

China Metall. 2014;24:256–260.

31.

Lytvynyuk

Schenk

Hiebler

et al. Thermodynamic and kinetic model of the converter steelmaking process. Part 1: the Description of the BOF model. Steel Res Int 2014;85(4):537–543.

32.

Lytvynyuk

Schenk

Hiebler

et al. Thermodynamic and kinetic model of the converter steelmaking process. Part 2: the model validation. Steel Res Int 2014;85(4):544–563.

33.

Dogan

Brooks

Rhamdhani

MA.

Comprehensive model of oxygen steelmaking part 1: model development and validation. ISIJ Int 2011;51(7):1086–1092.

34.

Rout

Brooks

Rhamdhani

et al. Dynamic model of basic oxygen steelmaking process based on multi-zone reaction kinetics: model derivation and validation. Metall Mater Trans B. 2018;49(2):537–557.

35.

Dering

Swartz

Dogan

Dynamic modeling and simulation of basic oxygen furnace (BOF) operation. Processes. 2020;8(4):483.

36.

Ogawa

Yano

Kitamura

et al. Development of the continuous dephosphorization and decarburization process using BOF. Steel Res Int 2003;74(2):70–76.

37.

Iwasaki

Matsuo

Shin Nittetsu Giho. 2011;391:88–93.

38.

Wang

Zhu

et al. China Metall. 2013;23(4):40–46.

39.

Sundberg

Scand J Metall 1978;7(2):81–87.

40.

Anon: ‘Steelmaking data sourcebook revised edition’; 1984, Tokyo, The Japan Society for the Promotion of Science(JSPS).

41.

Ban-Ya

Mathematical expression of slag-metal reactions in steelmaking process by quadratic formalism based on the regular solution model. ISIJ Int 1993;33(1):2–11.

42.

Kai

Okohira

Hirai

et al. Influence of bath agitation intensity on metallurgical characteristics in top and bottom blown converter. Tetsu-to-Hagané. 1982;68(14):1946–1954.

43.

Isobe

Maede

Ozawa

et al. Analysis of the scrap melting rate in high carbon molten iron. Tetsu-to-Hagané. 1990;76(11):269–276.

44.

Huang

Principles of Iron and steel metallurgy. Vol 4. Beijing: Publishing house of Metallurgical Industry; 2013.

45.

Liu

Jiang

Wang

Heat balance calculation of chromium ore smelting reduction process in a converter. Adv Mater Res. 2012;460:338–341.

46.

Matsushima

Yadoomaru

Mori

et al. Fundamental study on the dissolution rate of CaO into liquid slag. Tetsu to Hagane. 1976;62(2):182–190.

47.

Liang

Che

Handbook of thermodynamics data of inorganic matter. Shenyang: Northeastern University; 1993.

48.

Jiang

Fundamentals of metallurgical plant design. Beijing: Publishing house of Metallurgical Industry; 2013.

49.

Yang

Shi

et al. Precipitation behaviour of phosphorus in high strength IF steel during laminar cooling. Ironmak Steelmak. 2020: 1–9.