Dynamic Study on Vanadium Extraction Process in Basic Oxygen Furnance: Modeling Based on Gibbs’ Free Energy Minimization

Abstract

Vanadium extraction process demands low residual vanadium and carbon loss, and variations of dissolved elements in hot metal must be determined to achieve it. A three parts dynamic model that applies the concept of Gibbs’ free energy minimization at the slag–metal interface is proposed. Modeling simulation results shows good uniformity with plant experimental data, and the presented model can describe the vanadium extraction process in BOF qualitatively well. The effects of coolant addition and oxygen flow rate have been studied by modeling. The lack of coolant will reduce (FeO) content and elevate the molten bath temperature, which are harmful to deep vanadium removal with less carbon loss in semi-steel. The excessive oxygen flow rate has little effect on residual [V], and there is more carbon loss because of higher (FeO) content and molten bath temperature.

1. Introduction

Vanadium titanium magnetite (VTM) has the largest reserves among v-bearing resource mineral [1]. The most popular method to extract the widely used rare metal, vanadium, is oxygen blow smelting in Basic Oxygen Furnance from v-bearing hot metal [2]. Vanadium is removed from v-bearing hot metal to form vanadium-enriching slag.

However, vanadium extraction process demands low residual vanadium and high carbon content in semi-steel, which means temperature control plays an extremely important role to ensure the thermodynamics of selective oxidation [3,4]. Reasonable temperature strategy must determine the variations of dissolved elements in hot metal because the oxidizing reactions release a large amount of heat, which has a great impact on molten pool temperature and results in changes in the slag component. However, the extremely high temperature makes it very inconvenient for direct measuring and sampling. Thus, dynamic modeling calculation seems to be more effective and economic. In the recent past, there have been several studies on the dynamic modeling of the BOF vanadium extraction process. Huang et al. applied multi-phase coupling based on mass and energy balances to treat the blow progress [5]. Shukla et al. developed a model based on the way available oxygen is distributed based on respective Gibbs’ free energies of oxidation [6]. Pahlevani et al.’s kinetic model made arbitrary assumption that 20% of the available oxygen is utilized for decarburization and 70% is utilized for FeO generation [7]. As mentioned above, these models have completely ignored the thermodynamic aspects of refining reactions, and the equilibrium of systems is reached only when the total Gibbs’ free energy is minimized. In this paper, a model based on Gibbs’ free energy minimization has been presented that fully considers the physicochemical process during oxygen blowing. The variations of hot metal component were determined considering coolant addition and oxygen flow rate.

2. Model Formulation

2.1. Refining Zone Definitions

In the present model, the refining sites in BOF were divided into three parts, as shown in Figure 1.

—Site 1: Impact zone of oxygen flow.

—Site 2: Emulsion refining zone on the upper bath, where metal droplet was splashed into foaming slag.

—Site 3: Entrapment refining zone, where slag was drawn into molten iron in the lower bath.

2.2. Refining Mechanism of BOF Reactions

a.

Gaseous Oxygen O₂ at the impact site reacts with a layer of metal, oxidizing all elements in it directly. The oxidation products are transferred to the slag phase, except for carbon oxides.

b.

Large numbers of metal droplets are generated at the impact zone, and they too splash into the slag zone in upper bath. Refining reactions of dissolved elements take place at the interface dictated by thermodynamics. Eventually, the droplets fall back to iron bath due to gravity. The two-phase reactions such as silicon take place directly with FeO:

2(FeO) + [Si] = (SiO₂) + 2[Fe]

c.

A number of slag droplets are entrapped in the lower bath. The refining reactions also take place at the interface that is similar to emulsion refining zone.

—Phosphorus and sulphur removal will not be considered during smelting because no CaO will be added into molten bath during vanadium extraction process [8].

2.3. Assumptions of the Model

a.

According to the requirements of vanadium extraction process, the typical smelting time continues only about 6 min (360 s). The initial slag layer in bath is from addictive coolant before blowing and residual slag from previous heat. Slag compositions at this time are assumed from typical reported values from plant.

b.

Oxygen is partitioned among the elements based on their molar fraction available at the impact zone.

c.

Rates of refining reactions are assumed to be controlled only by mass transfer of FeO in the slag phase.

d.

Size distribution of metal droplets generated at the impact zone is heterogeneous. Sauter Mean Diameter is often used to describe it. A single size of metal droplets in emulsion is assumed for keeping the model simple. The size refers to Dogan’s [9].

e.

Residence time of the metal droplets is affected by initial conditions such as diameter and velocity. An average time of residence of metal droplets is assumed for keeping the model simple, which refers to Brooks’ and Sarkar’s studies [10,11].

f.

Necessary coolant for keeping reasonable thermodynamics [12] was added at 30th s, 90th s, and 150th s. The coolant consisted of FeO and Fe₂O₃, each 50%. Dissolving rate of addictive coolant depended on mass transfer of Fe₂O₃ to slag phase. Coolant meltage continued at 30 s equably.

2.4. Governing Equations

a.

Oxygen distribution at the impact zone

According to Assumption b, oxygen distribution at the impact zone is based on their molar fraction. The rate equations of each elements including Fe are as follows:

$$\frac{d{m}_{[\mathrm{i}]}}{dt}=\frac{x{M}_{(\mathrm{i})}{R}_{\mathrm{O}}}{16y}\ast \frac{x_{[i]}}{x_{[Fe]}+x_{[C]}+x_{[Si]}+x_{[Mn]}+x_{[V]}+x_{[Ti]}}$$

(1)

$$\frac{d{W}_{({\mathrm{i}}_{\mathrm{p}}{\mathrm{O}}_q)}}{dt}=\frac{M_{({\mathrm{i}}_p{\mathrm{O}}_q)}{R}_{\mathrm{O}}}{16y}\ast \frac{x_{[i]}}{x_{[Fe]}+x_{[C]}+x_{[Si]}+x_{[Mn]}+x_{[V]}+x_{[Ti]}}$$

(2)

where m_[i] stands for quantity of components in molten iron, kg. W_[ipOq] stands for quantity of reaction product in slag, kg. x_[i] stands for molar fraction. M_[i] and M_[ixOy] stand for molecular mass. R_O is the mass of oxygen flow during per time-step, kg.

b.

Calculation of droplet generation rate

Metal droplets generation rate is calculated by empirical equation proposed by Subagyo et al. [13].

$$\frac{R_B}{F_G}=\frac{{(N_B)}^{3.2}}{{[2.6\times {10}^6+2.0\times {10}^{-4}{N}_B^{12}]}^{0.2}}$$

(3)

where R_B is droplets generation rate, kg/s. F_G is the top oxygen Flow Rate in Nm³/s. N_B is constant defined as follows:

$$N_B=\frac{{\rho }_g{v}_{\mathrm{g}}^2}{2\sqrt{\sigma g{\rho }_m}}$$

(4)

where ρ_g is gas density of top flow, kg/m³. ρ_m is density of molten iron, kg/m³. v_g (m/s) is gas velocity related to the axial velocity at the point of impact, v_j, as

v_g = 0.44721v_j

(5)

and v_j is expressed as a function of the dynamic lance height, using He et al.’s correlation [14].

c.

Calculation slag–metal interface area

Area of slag–metal interface consists of two parts, as shown in Figure 1: metal droplets splashed to slag at upper bath and slag droplets entrapped into lower bath.

Slag–metal interface area of splashed metal droplets in emulsion refining zone is calculated following Assumption 4 and droplet generation rate R_B.

$$A_{\Delta \mathrm{t}}=\frac{R_B}{{\rho }_m\frac{1}{6}\pi d_m^3}\times \pi \frac{d_m^2}{4}=\frac{R_B}{\frac{2}{3}{\rho }_m{d}_m^{}}$$

(6)

where d_m is average diameter of metal droplets, m.

Area of entrapped slag droplets into lower bath is calculated by empirical relationship proposed by F.Oersted.

$$A_{\mathrm{ES}}=\pi \frac{0.4153D{\rho }_s^{1/2}{\eta }_s^{1/2}{l}_s^{1/2}{v}_s^{5/2}}{\sigma +\frac{1}{6}{d}_s^{2}g({\rho }_m-{\rho }_s)\cos \beta }$$

(7)

where D is diameter of impact ring, m. η_s is viscosity of slag, Pa.s. σ is surface tension of slag, N/m. β is the angle between buoyancy force and interfacial tension.

d.

Oxygen distribution at the slag–metal interface

Refining reaction at the slag–metal interface plays an extremely important role during LD converter smelting. Thus, oxygen distribution at the slag–metal interface directly relates to the reasonability of present model. In a multi-component system, the equilibrium composition tends to be such that the Gibb’s free energy of the entire system is minimized [11]. Refining reactions at the slag–metal interface follow this thermodynamic principle. Let consider the following reactions:

(FeO) + [C] = CO(g) + [Fe]
2(FeO) + [Si] = (SiO₂) + 2[Fe]
2(FeO) + [Ti] = (TiO₂) + 2[Fe]
(FeO) + [Mn] = (MnO) + [Fe]
3(FeO) + 2[V] = (V₂O₃) + 3[Fe]

and if ΔG_C-FeO, ΔG_Si-FeO, ΔG_Mn-FeO, ΔG_Ti-FeO, and ΔG_V-FeO are the Gibbs’ free energy changes per mol atom of oxidized element for the above reactions in the same order as they are mentioned, then the actual Gibbs’ free energy changes ΔG_T associated with these reactions can be calculated as follows:

$$\Delta {\mathrm{G}}_{\mathrm{T}}=R_{\mathrm{C}}.\Delta {\mathrm{G}}_{\mathrm{C}-\mathrm{FeO}}+R_{Si}.\Delta {\mathrm{G}}_{\mathrm{Si}-\mathrm{FeO}}+R_{Mn}.\Delta {\mathrm{G}}_{\mathrm{Mn}-\mathrm{FeO}} +R_V.\Delta {\mathrm{G}}_{\mathrm{V}-\mathrm{FeO}}+R_{Ti}.\Delta {\mathrm{G}}_{\mathrm{Ti}-\mathrm{FeO}}$$

(8)

where R_C, R_Si, R_Mn, R_V, and R_Ti are the molar quantity of oxidized elements during per time step.

The restrictive steps of refining reactions are considered as mass transfer of FeO in slag and dissolved elements in metal; the equations are as follows:

$$J_{\mathrm{FeO}}=A_{sm}{k}_{\mathrm{FeO}}{\rho }_{\mathrm{s}}(C_{[\mathrm{FeO}]}^{*}-C_{[\mathrm{FeO}]}^{\mathrm{b}})\mathrm{mol}/(\mathrm{s}.{\mathrm{m}}^2)$$

(9)

$$J_{\mathrm{i}}=A_{sm}{k}_{\mathrm{i}}{\rho }_{\mathrm{m}}(C_{[\mathrm{i}]}^{\mathrm{b}}-C_{[\mathrm{i}]}^{*})\mathrm{mol}/(\mathrm{s}.{\mathrm{m}}^2)$$

(10)

where A_sm is the area of slag–metal interface, m². k is the mass transfer coefficient of components, m.s⁻¹. C^b and C* are bulk concentration and interface concentration, mol/kg.

An equation set is obtained as follows, and R_C, R_Si, R_Mn, R_V, and R_Ti are computed based on the constraint that ΔG_T is minimized.

$$J_{FeO}=R_C+R_{Si}+R_{Mn}+R_V+R_{Ti}$$

$$R_C\le J_C R_{Si}\le 2J_{Si} R_{\mathrm{Mn}}\le J_{Mn} R_V\le \frac{3}{2}{J}_V R_{Ti}\le 2J_{Ti}$$

(11)

Thus, total quantity of each oxidized element during per time step is calculated based on Equations (1), (2) and (10), as follows:

$$\frac{d{m}_{[\mathrm{i}]}}{dt}=\frac{M_i{R}_{\mathrm{O}}}{16}\ast \frac{x_{[\mathrm{i}]}}{x_{[Fe]}+x_{[C]}+x_{[Si]}+x_{[Mn]}+x_{[V]}+x_{[Ti]}}+R_{\mathrm{i}}*\frac{M_{\mathrm{i}}}{1000}$$

(12)

3. Results and Discussion

Typical smelting time for one heat is about 360 s. As mentioned earlier, simulations were performed for input and process parameters shown in

Table 1. List of input parameters used for calculations.

Quantity	Unit	Value
Initial hot metal condition	−	1573 K (1300 °C), 200,000 kg, and 4.3%C-0.13%Si-0.22%Mn-0.36%V-0.12%Ti
Initial slag condition	−	1573 K (1300 °C), 3000 kg, and 94%FeO-3%SiO2-3%TiO2
Coolant condition	−	50%FeO-50%Fe2O3, 1800 kg (30th s), 1800 kg (90th s), and 1800 kg (150th s)
Density of steel	kg/m3	6900
Density of slag	kg/m3	3200
Density of gas	kg/m3	1.25
Viscosity of slag	Pa.s	1.82
Surface tension of steel	N/m	1.7
Mass transfer coefficient of FeO in slag phase	m/s	3.4 × 10−6
Average diameter of metal droplets [9]	mm	15
Average residual time of metal droplets	s	30

. Further parameters such as interaction coefficients of solute elements in metal and mass transfer coefficients in metal and slag are given in

Table 2. Interaction coefficients of solute elements in metal.

i	j
	C	Si	Mn	V	Ti
C	0.1659	0.0948	−0.0142	−0.0913	−0.045
Si	0.2133	0.1304	0.0024	0.0296	0.0367
Mn	−0.083	0.0024	0.0000	0.0000	0.0051
V	−0.4029	0.0498	0.0000	0.0178	0.0000
Ti	−0.1955	0.0593	0.0051	0.0000	0.0154

and

Table 3. Mass transfer coefficient in metal and slag.

Quantity	Value/mm.s−1	Quantity	Value/mm.s−1
kC	0.003	kFeO	0.0034
kV	0.035	kMnO	0.000034
kSi	0.019	kSiO2	0.00005
kMn	0.0265	kV2O3	0.000032
kTi	0.024	kTiO2	0.00007
kO	0.005

.

3.1. Description of Vanadium Extraction Process

Reasonable convergence of modeling result is obtained with a time-step of 0.1 s. Variations of elements content in hot metal and components in slag based on modeling calculation are shown in Figure 2. The results show good uniformity with plant experimental data mentioned in previous study [12].

Titanium and silicon oxidation are the front part of the reaction sequence of vanadium extraction refining. These are in accord with thermodynamics prediction due to the higher affinity to oxygen. Contents of [Ti] and [Si] show a relatively low level at about 120 s, which determines that the oxidizing removals of [Ti] and [Si] have been done. Meanwhile, rapid oxidizing rates of [Ti] and [Si] appear till 20th second because not enough slag layers have been formed, and refining reaction remains low. Vanadium oxidation and manganese oxidation increase after about 120 s and decrease after 300 s, due to studied thermodynamics condition. Vanadium and manganese oxidation are prior to carbon when content is high and molten temperature remains low [15,16]. Carbon oxidation increases rapidly beginning at 120 s, which is similar to [V] and [Mn]. Thus, carbon oxidation plays an important role in vanadium removal; reasonable temperature strategy has been devised to guarantee the preferential oxidation of vanadium to carbon [15].

3.2. Effect of Coolant Addition

Coolant addition has great influence on molten temperature and (FeO) content in slag, which directly affect the thermodynamics condition. Two schemes on coolant addition have been carried out, as shown in

Table 4. Schemes of coolant addition.

Scheme	60 s Before Blowing	30th s	90th s	150th s
A	3000 kg	1800 kg	1800 kg	1800 kg
B	3000 kg	1000 kg	1000 kg	1000 kg

. Coolant component is shown in Table 1 (50%FeO-50%Fe₂O₃). Modeling calculation results are shown in Figure 3.

Compared with Scheme A, not enough coolant has been added in Scheme B. This leads to lower (FeO) content in slag, which is unfavorable for refining reactions, and also leads to higher molten pool temperature that prevents the achievement of good thermodynamics to ensure [V] removal prior to [C] oxidation [15,16]. Thus, deep removal of [Ti] and [Si] have been delayed till about 180 s. Residual vanadium [V] have increased from 0.06 to 0.10%, and carbon content in semi-steel decreased from 3.5 to 3.3%.

3.3. Effect of Oxygen Flow Rate

Oxygen flow rate has effect on generation of metal-droplets in bath and (FeO) generation at impact zone. Vanadium extraction blowing with oxygen flow rate 24,000 Nm³/h and 26,000 Nm³/h has been modeled, and variations on element in hot metal are shown in Figure 4.

With the increase of oxygen flow rate, (FeO) content in slag increased with more oxygen supply, which is beneficial to refining reactions. Thus, deep removal of [Ti] and [Si] increased slightly. However, higher oxygen flow rate means more oxidizing reactions with more heat release in bath, which results in higher molten pool temperature. Therefore, residual vanadium [V] content changes very little, for the following reasons: advantage of higher (FeO) in refining reactions, and disadvantage of higher molten bath temperature in preferential oxidation of [V]. Carbon content in semi-steel decreased from 3.5 to 3.2%.

4. Conclusions

(1)

The three-part model, including the impact zone, emulsion zone, and entrapment zone, has been developed to model the vanadium extraction process in BOF. The concept of Gibbs’ free energy minimization at the slag–metal interface has been adopted to model the refining reactions.

(2)

Simulation results predicting variations of dissolved elements have shown good uniformity with plant experimental data. The present model describes the vanadium extraction process in BOF qualitatively well.

(3)

The effects of coolant addition and oxygen flow rate have been studied. The lack of coolant will reduce (FeO) content and elevate the molten bath temperature, harming deep vanadium removal, resulting in less carbon loss in semi-steel. Excessive oxygen flow rate has little affect on residual [V] but results in more carbon loss because of higher (FeO) content and molten bath temperature.