Utilization Rate of Magnesium in Hot Metal Desulfurization by Magnesium Vapor Injection

Abstract

To solve the technical problems such as serious splashing and low utilization rate of the desulfurizer in the traditional hot metal desulfurization by granular magnesium injection, a new idea of hot metal desulfurization with continuously controllable bottom blowing magnesium vapor is presented in this paper. An estimation model of the utilization rate of magnesium vapor was established based on the double-film theory, which shows that the utilization rate of magnesium vapor decreases with the increase of the flow rate of the carrier gas, and increases significantly with the decrease of the bubble radius of the magnesium vapor. The theoretical calculation results show that when the desulfurization temperature reaches 1573 K and the bubble radius of the magnesium vapor is refined to 0.175 mm, the residence time of magnesium vapor in the molten iron is equal to the reaction time, and the theoretical utilization rate of magnesium vapor can reach 100%. The model was validated by high temperature experiments using bottom blowing method. The experimental results indicate that the utilization rate of magnesium vapor in the desulfurization process is inversely proportional to the desulfurization temperature, the flow rate of the carrier gas and the mass of magnesium injection. Under the condition of 1573 K, the mass of hot metal 4.5 kg, the flow rate of 3 L/min and the injection mass of magnesium 1.55 g, the utilization rate of magnesium vapor can reach 83%. The calculated results of the model are well matched with the experimental data.

1. Introduction

The hot metal desulfurization technologies which are widely used in industry mainly include the KR method and the granular magnesium injection method. The granular magnesium injection method has the advantages of low temperature drop of hot metal, small slag volume and high desulfurization rate. However, due to the high vapor pressure and the low boiling point of magnesium, some defects still exist in the practical desulfurization process of granular magnesium injection, such as serious splashing problems and low utilization rate of magnesium. The utilization rate of magnesium is less than 40% in the industrial applications.^1,2,3) Therefore, improving the utilization rate of magnesium and avoiding the spattering during the desulfurization process are the technical goals of magnesium injection to be achieved urgently.

Guo Hanjie^4,5) optimized the process of hot metal desulfurization by granular magnesium injection, but the utilization rate of magnesium was still difficult to reach 50%. G. A. Irons⁶⁾ proposed a desulfurization method of injecting the magnesium vapor into hot metal from the top of the molten pool by a nozzle. But the actual utilization rate of magnesium vapor was less than 5% because of the large diameter of the bubbles and the uncontrollable process of magnesium vapor injection. Yang Jian and Masamichi Sano^7,8,9,10,11) proposed that MgO-based desulfurizer (MgO + C or MgO + Al) can be used to directly desulfurize the hot metal with the magnesium vapor generated in situ at a high temperature. The results showed that the reduction process of the magnesium oxide restricts the total desulfurization reaction of hot metal. Due to the low reduction efficiency, the actual utilization rate of magnesium was less than 50%. Moreover, the method has some defects such as large consumption of desulfurizer and large temperature drop. In recent years, some studies on desulfurization in refining process has made a good performance on the desulfurization efficiency.^12,13,14,15) But the problem of desulfurization by magnesium injection has not been solved. Therefore, improving the utilization rate of magnesium and developing new desulfurization technology with high efficiency are still the key and difficult points in the research of the desulfurization technology of hot metal with magnesium injection.

In view of the fact that refining the bubbles of the magnesium vapor and prolonging the residence time of the magnesium vapor in hot metal are conductive to increase the utilization rate of magnesium vapor and enhance the desulfurization efficiency, a new idea of hot metal desulfurization with bottom blowing magnesium vapor is put forward. The high temperature magnesium vapor is continuously injected into the molten iron by blowing inert carrier gas through a bottom-blown permeable brick connected with a high temperature pipeline. The refined bubbles of the magnesium vapor react with the dissolved sulfur in the molten iron rapidly.

The utilization rate of magnesium is one of the important parameters for evaluating the hot metal desulfurization technology by magnesium vapor. Irons,⁶⁾ Jian Yang^7,8,9,10,11) and Haiping Sun¹⁾ have elaborated the basic principle of desulfurization reaction with magnesium vapor, but the effect on the utilization rate of magnesium caused by different injection conditions has not been analyzed in detail. Based on the double-film theory, an estimation model of the utilization rate of magnesium vapor for the desulfurization process of hot metal by bottom blowing magnesium vapor is established. The influence of different factors on the utilization rate of magnesium vapor is discussed and verified by high temperature experiments.

2. Establishment of the Model of the Utilization Rate of Magnesium Vapor

The process of hot metal desulfurization by bottom blowing magnesium vapor can be described as follows: the magnesium vapor is carried by the inert carrier gas and uniformly injected into the molten iron, dissolved and gasified rapidly to form a gas-liquid interface. The desulfurization reaction occurs when the magnesium and sulfur diffuse to the gas-liquid interface in the molten iron. The generated magnesium sulfide floats up and separates from the melt to finish the desulfurization reaction. In order to simplify the desulfurization reaction process, the following assumptions are put forward according to the double-film theory:¹⁶⁾

Hypothesis: (1) the desulfurization reaction of hot metal with magnesium vapor is controlled by the mass transfer process; (2) the concentration of the sulfur and the temperature of the melt are uniform, and the shape of the bubbles of magnesium vapor are spherical; (3) Under ideal conditions, it is considered that the carrier gas and the magnesium vapor carried by it are continuously and uniformly blown into the molten pool.¹³⁾ Then the partial pressure of magnesium vapor can be calculated by the molar number of magnesium; (4) the desulfurization reaction of magnesium and sulfur occurs on the surface of the bubbles, and the mass transfer rate of the magnesium in bubbles and the sulfur in hot metal is a constant at a certain temperature; (5) the effect of the dissolved magnesium in the reaction process is not considered.

Based on the above assumptions, the residence time t_m of magnesium vapor and the reaction time tr of magnesium vapor in the molten pool are calculated. Then the utilization rate of magnesium vapor η_Mg can be expressed as follows:   

$${\eta }_{Mg}=t_m/t_r$$(1)

2.1. Residence Time of Magnesium Vapor t_m

The residence time of magnesium vapor depends on the floating rate of the bubbles of the magnesium vapor in the molten pool, and the bubble diameter is the main factor affecting the floating rate of the bubbles. The bubble diameter in the nozzle can be expressed as follows:^17,18)   

$$\text{D}=1.88{\left(\frac{{\text{w}}_0}{\sqrt{{\text{gd}}_0}}\right)}^{1/3}\cdot {\text{d}}_0$$(2)

Here, D is the detachment diameter of the bubbles in the nozzle, m; w₀ is the flow rate of the carrier gas, m³/s; d₀ is the pore diameter of the permeable brick, φ0.4 mm × 4; and g is the gravity acceleration m/s². The flow rate of the carrier gas does not change with the number of pores.

Then, the bubble volume at the nozzle can be expressed as follows:   

$${\text{V}}_0=\frac{1}{6}\pi {\text{D}}^3=0.984\frac{{\text{w}}_0}{\sqrt{\text{g}}}{\text{d}}_0^{5/2}$$(3)

The pressure in the bubbles at the nozzle is P₀ and the pressure in the bubbles at the height of x above the nozzle is P_x, then P_x can be expressed as follows:   

$${\text{P}}_{\text{x}}={\text{P}}_0-{\rho }_{\text{l}}\text{gx}$$(4)

Here, ρ_l is the density of the molten iron, kg/m³. According to the ideal gas equation P_xV_x = P₀V₀, so the bubble volume at the height of x can be expressed as follows:   

$${\text{V}}_{\text{x}}={\text{P}}_0{\text{V}}_0/{\text{P}}_{\text{x}}={\text{P}}_0{\text{V}}_0/({\text{P}}_0-{\rho }_{\text{l}}\text{gx})$$(5)

The floating rate of the bubbles can be expressed as:^15,16)   

$$u_g=\frac{\text{dx}}{\text{dt}}=0.79{\text{g}}^{1/2}{\text{V}}_{\text{x}}^{1/6}=0.79{\text{g}}^{1/2}{\left[\frac{{\text{P}}_0{\text{V}}_0}{{\text{P}}_0-{\rho }_{\text{l}}\text{gx}}\right]}^{1/6}$$(6)

Here, V_x is the bubble volume at the height of x above the nozzle, m³; u_g is the floating rate of the bubbles at the volume of V_x, m/s.

The boundary conditions are: t = 0, x = 0; t = t_m, x = h. The integral of Eq. (6) obtained by introducing Eq. (3) can be expressed as follows:   

$$\begin{array}{l}{\text{t}}_{\text{m}}={\displaystyle \frac{1.08}{{({\text{P}}_0{\text{V}}_0)}^{{\displaystyle \frac{1}{6}}}\cdot {\rho }_{\text{l}}{\text{g}}^{{\displaystyle \frac{3}{2}}}}}\left[{\text{P}}_0^{{\displaystyle \frac{7}{6}}}-{({\text{P}}_0-{\rho }_{\text{l}}\text{gh})}^{{\displaystyle \frac{7}{6}}}\right]\\ \hspace{1em}={\displaystyle \frac{1.08}{{\text{P}}_0{}^{{\displaystyle \frac{1}{6}}}{\text{w}}_0^{1/6}{\text{d}}_0^{5/12}{\rho }_{\text{l}}{\text{g}}^{{\displaystyle \frac{17}{12}}}}}\left[{\text{P}}_0^{{\displaystyle \frac{7}{6}}}-{({\text{P}}_0-{\rho }_{\text{l}}\text{gh})}^{{\displaystyle \frac{7}{6}}}\right]\end{array}$$(7)

Here, h is the depth of the molten pool, 0.1 m.   

$${\text{t}}_{\text{m}}=\frac{0.022}{{\text{w}}_0^{1/6}{\text{d}}_0^{5/12}}$$(8)

2.2. Reaction Time of Magnesium Vapor t_r

The mass transfer process of magnesium and sulfur during the desulfurization process of hot metal by magnesium vapor injection can be expressed as:^19,20)   

$$\frac{{\text{dn}}_{\text{Mg}}}{\text{dt}}=\frac{V}{RT}\cdot \frac{{\text{dP}}_{\text{Mg}}}{\text{dt}}+\frac{P_{\text{Mg}}}{RT}\cdot \frac{dV}{\text{dt}}$$(9)

  

$$\frac{{\text{dn}}_{\text{s}}}{\text{dt}}=-4\pi {\text{r}}_{\text{g}}^2{\text{k}}_{\text{d}}({\text{C}}_{\text{s}}-{\text{C}}_{\text{i}})$$(10)

Where, P_Mg is the partial pressure of magnesium in the bubbles, Pa; r_g is the bubble radius, m; k_d is the mass transfer coefficient of sulfur, m/s; C_S is the concentration of sulfur in the molten iron, mol/m³; and C_i is the concentration of sulfur at the reaction interface, mol/m³.

The mass transfer coefficients k_d can be expressed as:⁸⁾   

$$k_d=2{({\text{D}}_S/\pi \tau )}^{1/2}$$(11)

  

$$\tau =\text{D}/u_g$$(12)

Where D_S is the diffusion coefficient of sulfur, 1.1*10⁻⁹ m²/s at 1573 K; 1.5*10⁻⁹ m²/s at 1623 K; 2.2*10⁻⁹ m²/s at 1673 K; 3.2*10⁻⁹ m²/s at 1723 K.²⁰⁾ τ is the contact time, s.

In the desulfurization process, the bubble diameter is mainly affected by the hydrostatic pressure of hot metal. Equation (5) shows when the bubbles float to the surface of the melt, x = h, and h is small enough to negligible in the calculation. Thus, the hydrostatic pressure of the molten iron has little effect on the bubble diameter in the process of bubbles floating. It can be considered that the bubble volume does not change with the location of the bubble during the floating process, then dV/dt = 0, V = V₀.

Equation (9) can be expressed as follows:   

$$\frac{{\text{dn}}_{\text{Mg}}}{\text{dt}}=\frac{V_0}{RT}\cdot \frac{{\text{dP}}_{\text{Mg}}}{\text{dt}}$$(13)

From Eqs. (10) and (11), it can be obtained as follows:   

$$\int {\text{dP}}_{\text{Mg}}=\int -4\pi {\text{r}}_{\text{g}}^2{\text{k}}_{\text{d}}\frac{RT}{V_0}\cdot ({\text{C}}_{\text{s}}-{\text{C}}_{\text{i}})\text{dt}$$(14)

The boundary conditions are: t = 0, ${\text{P}}_{\text{Mg}}={\text{P}}_{\text{Mg}}^0$; t = t, P_Mg = P_Mg. the integral can be obtained as follows:   

$$\mathrm{t}=-\frac{V_0({\mathrm{P}}_{\mathrm{M}\mathrm{g}}-{\mathrm{P}}_{\mathrm{M}\mathrm{g}}^0)}{4\pi {\mathrm{r}}_{\mathrm{g}}^2\mathrm{R}\mathrm{T}{\mathrm{k}}_{\mathrm{d}}({\mathrm{C}}_{\mathrm{s}}-{\mathrm{C}}_{\mathrm{i}})}$$(15)

  

$${\text{C}}_{\text{s}}=\frac{\left[\%S\right]{\rho }_l}{100M_s}$$(16)

Here M_s is the molar mass of sulfur, kg/mol.

It is assumed that when the bubble of magnesium has been fully reacted with the sulfur in hot metal, the partial pressure of magnesium in the bubbles P_Mg tends to be zero. At that time t is named t_r. Therefore, when t_r ≤ t_m, it indicates that the magnesium vapor can be completely reacted with the sulfur in desulfurization reaction. The absorption time of magnesium vapor can be expressed as follows:   

$${\text{t}}_{\text{r}}=\frac{100{\text{r}}_{\text{g}}{M}_s{\text{P}}_{Mg}^0}{3\text{RT}{\rho }_m{\text{k}}_{\text{d}}([\%S]-{[\text{\%S}]}_i)}$$(17)

Thus, the model of the utilization rate of magnesium vapor can be expressed as follows:   

$${\eta }_{Mg}=\frac{0.022}{{\text{w}}_0^{1/6}{\text{d}}_0^{5/12}}/\frac{100{\text{r}}_{\text{g}}{M}_s{\text{P}}_{Mg}^0}{3\text{RT}{\rho }_m{\text{k}}_{\text{d}}([\%S]-{[\text{\%S}]}_i)}$$(18)

The Eq. (14) can be simplified as follows:   

$${\eta }_{Mg}=\epsilon \cdot \frac{1.7\times {10}^{-4}}{{\text{w}}_0^{1/6}{\text{d}}_0^{5/12}{\text{r}}_{\text{g}}}$$(19)

Here, $\epsilon =[{\text{Tk}}_{\text{d}}{\rho }_m([\%S]-{[\text{\%S}]}_i)]/{\text{P}}_{Mg}^0$. Because the desulfurization process of a single magnesium bubble exert little effect on the sulfur content in molten iron, the mass concentration of sulfur in molten iron [%S] tends to be the initial concentration of 0.046. The reaction proceeds very quickly at high temperature, so the chemical equilibrium can be achieved at the reaction interface. [%S]_i and ${\text{P}}_{Mg}^0$ can be obtained by equations as follows:²¹⁾   

$${[\%S]}_i=\frac{1}{{\text{P}}_{Mg}^0{K}^{\theta }}=\text{exp}\left(\frac{-404\mathrm{\hspace{0.17em} }070+169.21\mathrm{\hspace{0.17em} }T}{8.314\mathrm{\hspace{0.17em} }T}\right)/{\text{P}}_{Mg}^0$$(20)

  

$${\text{lgP}}_{Mg}^0=-\frac{6\mathrm{\hspace{0.17em} }802}{T}+4.993$$(21)

3. Experiment

The cast iron of HT250 was used in this experiment. The mass of cast iron in each group is about 4.5 kg. The composition of the cast iron is shown in Table 1.

Table 1. Initial composition of cast iron.

Element	Fe	C	Si	Mn	P	S
Content wt.%	surplus	4.74	0.787	0.441	0.125	0.046

The device for desulfurization with bottom blowing magnesium vapor is shown in Fig. 1. The experiment was carried out in a 5 kg medium frequency induction furnace. A crucible made of magnesia-alumina spinel with an internal dimension of φ90 mm × 140 mm is set in the furnace. A pipeline for transporting magnesium vapor is connected with a permeable brick at the bottom of the crucible with an inner diameter of 14 mm. The permeable brick is made of magnesia-alumina spinel with a slit size of φ0.4 mm × 4. The slits of permeable bricks are arranged along the radial direction. Magnesium powder is set in a gasification chamber in advance. Magnesium vapor is obtained under a temperature of 1100°C in the gasification chamber. Then the magnesium vapor is carried by the inert gas (argon), and transported to the molten pool through the pipeline which keep magnesium being gaseous. According to the hypothesis in Section 2, it can be considered that the partial pressure of magnesium vapor remains unchanged during the injection process. When the temperature of the molten iron is risen to a preset value, the magnesium vapor is injected. Samples were taken every 2 min and 12 times in each group. The flow rate is measured by a GFM900 high temperature gas flowmeter with a temperature measurement range of −193–1400°C. The sulfur content of the samples was detected by a carbon and sulfur analyzer of G4 ICARUS Series 2 produced by the Bruker Company of Germany. The actual utilization rate of magnesium vapor η_Mg can be calculated as follows:   

$${\eta }_{Mg}^{*}=({[\text{\%S}]}_0^{*}-{[\%\text{S}]}^{*})m_{Fe}\times 24\times 100\%/32m_{Mg}$$(22)

Fig. 1.

Device for desulfurization with magnesium vapor. (Online version in color.)

Here, ${\eta }_{Mg}^{*}$ is the utilization rate of magnesium vapor calculated by the actual experimental data, ${[\text{\%S}]}_0^{*}$ is the initial sulfur content in the cast iron, [%S]^* is the final sulfur content in the molten iron, m_Fe is the mass of the cast iron, kg, and m_Mg is the mass of magnesium powder weighed before gasification, kg.

4. Result and Discussion

4.1. Effect of the Reaction Temperature on Desulfurization

The effect of the reaction temperature on desulfurization was studied at the gas flow rate of 3 L/min and the molar ratio of magnesium injection to sulfur in molten iron is 1:1. Figure 2 shows the variation of the sulfur content and the utilization rate of magnesium vapor with the desulfurization temperature in the molten iron. As shown in Fig. 2, the desulfurization reaction with bottom blowing magnesium vapor proceeds rapidly, and the equilibrium of the desulfurization process can be reached within about 8 min under the same injection conditions. With the increase of the desulfurization temperature, the final sulfur content of the hot metal increases gradually and the reaction rate becomes higher. It indicates that the desulfurization reaction with magnesium vapor is an exothermic reaction, the increase of the temperature may restrict the desulfurization reaction. The increase of temperature may lead to the decrease of the viscosity of the molten iron and promote the thermal movement of particles in the molten pool, which results in a higher reaction rate.

Fig. 2.

Effect of the reaction temperature on desulfurization. (Online version in color.)

In addition, the actual utilization rate of magnesium vapor decreases significantly with the increase of the desulfurization temperature. Since the magnesium vapor is obtained by gasification of magnesium powder and magnesium powder is quantitatively added each time, the magnesium vapor is quantitatively injected into the molten iron. Under the same injection conditions, the utilization rate of magnesium vapor can reach 83.15% at the desulfurization temperature of 1573 K, which is consistent with the theoretical utilization rate of 85% calculated by the model. But when the desulfurization temperature rises to 1723 K, the utilization rate of magnesium vapor is only 63.40%. The Eqs. (17) and (18) can be used to explain the decline of the utilization rate of magnesium vapor. The increase of temperature leads to the increase of equilibrium sulfur content, and result in the decreases of the reaction time. Thus the actual utilization rate of magnesium vapor is significantly reduced.

4.2. Effect of the Injection Mass of Magnesium Vapor on Desulfurization

The effect of the injection mass of magnesium vapor on desulfurization was studied at the temperature of 1573 K and the gas flow rate of 3 L/min. Since the increase of reactant concentration will make the reaction equilibrium move towards direction of promoting the reaction according to the basic principle of chemical reaction, the study on the injection mass of magnesium vapor is important for the utilization rate of magnesium. Magnesium vapor is injected into the hot metal by different the molar ratios of magnesium to sulfur (1:1, 1.5:1, 2:1, 3:1). According to the hypothesis (3), the partial pressure of magnesium vapor is affected by the injection mass of magnesium, which will also affect the utilization rate of magnesium in the reaction according to the utilization rate model. Figure 3 shows the variation of the sulfur content and the utilization rate of magnesium vapor with the injection mass of magnesium vapor in the molten iron. As shown in Fig. 3, the final sulfur content of the hot metal decreases with the increase of the injection mass of magnesium vapor. It indicates that increasing the injection mass of magnesium vapor can promote the desulfurization equilibrium to move in a positive direction to a certain extent and contribute to the desulfurization reaction. However, with the increase of the injection mass of magnesium vapor, the actual utilization rate of magnesium vapor decreases gradually. The actual utilization rate of magnesium vapor is only 56.29%, when the theoretical equivalence of magnesium vapor injection is increased to 1.5 times.

Fig. 3.

Effect of the injection mass of magnesium vapor on desulfurization. (Online version in color.)

4.3. Effect of the Gas Flow Rate on Desulfurization

The effect of the flow rate of the carrier gas on desulfurization was studied under the temperature of 1573 K and the molar ratio of magnesium injection to sulfur in the molten iron is 1:1. Figure 4 shows the variation of the sulfur content and the utilization rate of magnesium vapor with the flow rate of the carrier gas in the molten iron. As shown in Fig. 4, with the increase of the flow rate of the carrier gas, the final sulfur content in the molten iron increases gradually. It indicates that the increase of the flow rate of the carrier gas decreases the partial pressure of magnesium vapor in the molten iron, which decreases the probability of effective contact and the contact area between the bubbles of the magnesium vapor and the sulfur of the molten iron, and deteriorates the kinetic and thermodynamic equilibrium conditions of desulfurization reaction. Therefore, the final sulfur content of the molten iron increases. Moreover, with the increase of the flow rate of the carrier gas, the residence time of the bubbles in the molten iron is shortened, which restricts the desulfurization reaction and leads to a decrease of the utilization rate of magnesium vapor. When the flow rate of the carrier gas is 3 L/min, the utilization rate of magnesium vapor is 83.15%. When the flow rate of the carrier gas is increased to 12 L/min, the utilization rate of magnesium vapor drops rapidly to 68.5%. Therefore, the high flow rate of the carrier gas is not conducive to the desulfurization of the hot metal, and also causes a decrease in the utilization rate of magnesium vapor.

Fig. 4.

Effect of the gas flow rate on desulfurization. (Online version in color.)

4.4. Experimental Verification of the Model of the Utilization Rate of Magnesium Vapor

Figure 5 is the comparison between the model calculation results and the experimental results of the utilization rate of magnesium vapor. Equation (19) is a prediction model of the utilization rate of magnesium obtained by theoretical calculation. And the experimental results of the utilization rate of magnesium vapor are obtained by Eq. (22). In Eq. (19), the sulfur content in the molten iron is obtained by the hypothesis and the equilibrium sulfur content is obtained by thermodynamic calculation. The sulfur content in Eq. (22) is measured by the carbon and sulfur analyzer.

Fig. 5.

Comparison between the results of calculation and experiment. (a) under different temperatures; (b) under different mass of magnesium injection; (c) under different flow rates.

As shown in Fig. 5, the calculated results of the model are well matched with the experimental results, and the deviation between the calculated results and the experimental results is about ±2.5%. The deviation comes from the inconsistency of the conditions between the hypothesis of the model and the actual desulfurization process of the experiment. Firstly, the model assumes that the bubbles of the magnesium vapor are ideal homogeneous spheres, while the bubbles of the magnesium vapor should be ellipsoidal with different bubble diameters in the actual desulfurization process; secondly, the bubbles of the magnesium vapor will continue to expand and grow when it is injected into the molten iron pool; thirdly, the effect of the dissolution of magnesium in the molten iron is not taken into account in this model, and it assumes that the mass transfer rate of the magnesium in the bubbles and the sulfur in the molten iron is a constant. That makes the calculated value of the model deviates from the experimental desulfurization data. When the shapes of bubbles are identical and the sizes of bubbles are uniform under the experimental conditions, the theoretical model and the actual results can be consistent.

From the experimental results of Fig. 5, it can be seen that the model of the utilization rate of magnesium vapor established in this paper can accurately predict the utilization rate of magnesium vapor in the desulfurization process. In addition to changing the thermodynamic equilibrium conditions, prolonging the residence time is an effective way to improve the utilization rate of magnesium vapor. Therefore, controlling the flow rate of the carrier gas and refining the bubble diameter of the magnesium vapor are the keys to improve the utilization rate of magnesium vapor. Figure 6 shows the effect of different bubble radii of magnesium vapor on the utilization rate of magnesium vapor calculated by the model. As shown in Fig. 6, the utilization rate of magnesium vapor decreases significantly with the increase of the bubble radius. At the temperature of 1573 K and the gas flow rate of 3 L/min, if the bubble radius of the magnesium vapor is reduced from 0.4 mm to 0.2 mm, the utilization rate of magnesium vapor can be increased from 50% to 85%. When the bubble radius is reduced to 0.175 mm, the residence time of the magnesium vapor in the molten iron is equal to the time of gas-liquid mass transfer in the desulfurization process, the theoretical utilization rate of magnesium vapor can reach 100%.

Fig. 6.

Effect of the bubble radius on the utilization rate of magnesium.

In order to verify the distribution of bubble diameter in the reactor, the distribution of bubble diameter under the same flow condition was studied by physical simulation. The experiment of physical simulation is carried out on the scale of φ180 mm × 280 mm. By ensuring the consistency of the modified Fr number, it can be deduced that the flow rate of physical simulation experiment should be 1.72 times of the actual flow rate. The physical simulation results shown in Fig. 7 are obtained by the high speed camera of Olympus ispeed-3. And the bubble numbers and diameters in Fig. 8 are obtained by analyzing Fig. 7 with the data statistical module of the software of Image Pro Plus. As can be seen from Fig. 8, the bubble diameter in the molten pool is basically kept in the range of 0–0.4 mm. According to the calculation results of Fig. 6, the utilization rate of magnesium is 70%–80%, which is in agreement with the experimental results.

Fig. 7.

Physical simulation of bubble diameter. (a. 5 L/min; b. 9 L/min; c. 14 L/min; d. 20 L/min).

Fig. 8.

Distribution of bubble diameter. (Online version in color.)

5. Conclusion

(1) The model of the utilization rate of magnesium vapor was established: ${\eta }_{Mg}=\epsilon \cdot {\displaystyle \frac{1.7\times {10}^{-4}}{{\text{w}}_0^{1/6}{\text{d}}_0^{5/12}{\text{r}}_{\text{g}}}}$, in which $\epsilon =[{\text{Tk}}_{\text{d}}{\rho }_m([\%S]-{[\text{\%S}]}_i)]/{\text{P}}_{Mg}^0$. At the temperature of 1573 K and the gas flow rate of 3 L/min, if the bubble radius of the magnesium vapor can be reduced from 0.4 mm to 0.2 mm, the utilization rate of magnesium vapor can be increased from 50% to 85%. When the bubble radius of the magnesium vapor is reduced to 0.175 mm, the theoretical utilization rate of magnesium vapor can reach 100%. The calculated results of the model are well matched with the experimental results.

(2) The desulfurization reaction of hot metal and magnesium vapor is an exothermic reaction, thus the thermodynamic conditions of desulfurization reaction will be deteriorated with the increase of the desulfurization temperature. Moreover, with the increase of the desulfurization temperature, the bubbles of magnesium vapor in the molten pool expand more rapidly, which makes the bubbles float faster in the molten iron and shorten the residence time, resulting in a decrease of the utilization rate of magnesium vapor.

Acknowledgments

This research was supported by the National Natural Science Foundation of China (U1508217, U1702253, 51774078) and the Fundamental Research Funds for the Central Universities (N172506009, N170908001).

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