Numerical simulation of the dolomite in-situ desulfurization in molten iron

With the growing need for high-quality steel, the requirement for efficient deep desulfurization technologies is growing, and lots of research have be conducted. The desulfurization in hot iron with Mg produced in situ by the aluminothermic reduction of decomposed dolomite was simulated. The magnesium generated at the molten matte-slag interface is dissolved in the molten iron and desulfurizing while spread downwards The process has been studied by experiment and computational fluid dynamics simulation. Some analysis and assumptions were made for the simulation conditions and the simulated data are in good agreement with the experimental results. The rate of desulfurization depended mainly on the reaction rate and is almost independent of the rate of diffusion of Al, S and Mg according to the results. Under the present experimental conditions, the desulfurization rate increased with the increase in temperature and the amount of reactants. However, the effect is not obvious when the temperature is higher than 1623K. The adjustment in diffusion coefficient has minimal influence on the desulfurization efficiency. The desulfurization reaction is mainly in the homogeneous phase, and the proportion of magnesium bubble desulfurization could be ignored when the temperature is between 1523 K–1723 K.


Introduction
High-quality, ultra-low sulfur steel is in high demand, notably for the fabrication of external steel plates for highend automobiles, petroleum pipelines, and liquefied natural gas ship plates [1,2]. The type and content of the elements in the steel have a great influence on its quality. Sulfur in steel causes thermal brittleness, and a high sulfur concentration reduces steel's corrosion resistance. As a result, extensive desulfurization of iron has become a critical concern in high-quality steel manufacturing [3].
One of the primary unit processes for eliminating sulfur from fuels and raw materials used in the production of iron is the pretreatment of molten iron [4,5]. At present, typical desulfurization reagents used in the industry are lime, magnesium, and mixtures of them [6][7][8][9][10][11]. Kinetic and thermodynamic study [12][13][14], and experimental and physical research has been carried out by many researchers, e.g. flux additions, reagent injection, resulfurization, and reagent dispersion [15][16][17][18][19]. To forecast the desulfurization behavior in the ladle, several researchers [20][21][22] also suggested mathematical models including the thermodynamic processes and the computational fluid dynamics (CFD) model. To simulate the desulfurization process in the kambara reactor (KR), Wang et al [23] developed a three-dimensional transient coupling mathematical model utilizing the volume of fluid (VOF) and discrete phase model. They compared the desulfurization efficiency of different impellers quantitatively by the model. Compared to regular blades, the new blade increases the desulfurization rate from 95.7% to 97.1%. For modeling hot metal desulfurization using mono-injection (CaC2) and coinjection (CaC2 and CaO) techniques, Barron et al [24] created a CFD-based reaction model. In both situations, it was expected that mass transfer in the liquid phase would control the pace of desulfurization. According to their CFD simulations, hot metal desulfurization in a ladle is a good fit for the assumption of a well-stirred tank. Based on the Euler-Euler method, Jonsson et al [25][26][27] used a two-dimensional model to represent the bubbly plume flow and species transport in a gas-stirred ladle, and the source was modified using the species mass transfer equation to include the removal rate of dissolved element caused by interactions at the slag-metal contact.
These studies are for conventional desulfurization agents and a new method of in situ desulfurization has emerged in recent years. A pellet form of mixed MgO and Al, Si, etc was proposed [28][29][30] as a cheaper desulfurization flux by using gaseous Mg generated by the reduction of MgO by Al, Si, C, etc. Yang et al [28,29] modeled the desulfurization process and conducted desulfurization tests utilizing Mg vapor generated in situ from the carbothermic or aluminothermic reduction of MgO pellets. In this technique, the pellet is immersed in the hot metal using a special lance with carrier gas. The pressure of the magnesium vapor is much less than 100kpa, which is very favorable for the reaction and easier to control.
The MgO in this MgO-based desulfurizer is usually made from dolomite outside the furnace which requires a lot of energy, and this process can be further simplified to streamline processes and reduce consumption. This research simulated the process of desulfurization of molten iron with magnesium produced in situ by the aluminothermic reduction of dolomite. The dolomite and Al power are mixed and pressed into flakes then put into the hot metal where together they undergo a decomposition reaction. The experimental results were analyzed to get the condition and parameters for numerical simulation. Figure 1 is a schematic diagram of the experimental apparatus. A high-frequency induction furnace was used to melt raw iron of 200 ± 3 g in a corundum crucible of 70 mm in height and 35 mm in diameter. The temperature was measured with an infrared thermometer.

Experimental procedures
Dolomite powder with an average diameter of 0.15 mm and a purity of more than 99.9%, as well as aluminum powder with an average diameter of 0.15 mm and a purity of more than 99.9%, were the components used to make the pellet. These powders are weighed according to the theoretical value and then kept under 20kPa pressure for 3 min and pressed into an 8 mm diameter pellet.
The initial sulfur content was adjusted by adding ferrous sulfide powder. Then, the pellet was submerged into the molten iron using an iron wire. The experiment time is set to 30 min as the desulfurization rate is stable after that. The desulfurization process was tested by taking a sample from the hot metal at 2, 7, 12, 20, 30 min for testing. To validate and correct the model, experiments were carried out with initial sulfur content of 200 ∼400 ppm at 1523 K ∼1723 K.  The magnesium desulfurization reaction is an apparent secondary reaction. The desulfurization kinetics is determined using reference equation (2) required for the calculation of the desulfurization rate [31].
Where K 1 is the apparent rate constant of reaction which was obtained from experiment data. Appropriate adjustments could be made of K 1 in the actual setup based on the fit and the references [31]. The desulfurization process is assumed to be controlled by liquid-phase mass transfer as the chemical reaction is sufficiently fast. In equation (2) = The process can be considered as a series reaction and the aluminothermic kinetics is determined using reference equation (6) needed for the calculation of the net production rate of Mg.
Where K 2 is the apparent rate constant of reaction(4) which was obtained from experiment data and could be adjusted according to the fitting.

Assumption and grid of the model
The coupling model of desulfurization-flow-heat transfer-solute transport was established to reveal the complex metallurgical behavior in the crucible. To reasonably reveal the chemical phenomenon, a few assumptions have been made in the present computations, which are as follows: (1)The decomposition of dolomite and the agitation of CO 2 on the molten iron are so short (a few seconds) that can be ignored. There are only two kinds of basic reactions during the process: aluminothermic reduction of magnesium oxide and desulfurization.
(2)Mass transfer in the ladle heavily stirred by CO 2 is fast enough so that Al in the molten iron is homogeneous at the start of the calculation.
(3)The generated Mg can be completely dissolved in hot metal and there is no Mg bubble escaping.
(4)No oxygen enters the melt from the liquid surface due to the ability of aluminum to deoxidize and the low concentration of oxygen in the hot metal.
(5)The reactor is assumed to be isothermal.
The computational domain of the crucible considered for modeling is shown in figure 2. The vertically cylindrical smelting region in the crucible was chosen as the computational domain. Hexahedral meshes were utilized for the model. Different meshes have been employed with a total element count ranging from 55,000 to 1,550,000 to get grid-independent results. The slag-metal interfacial region of the mesh is fine-tuned to capture the gradients seamlessly. By contrasting the simulation outcomes of different grid sizes, the optimal grid size at the slag-metal contact is determined. The largest grid size deemed acceptable for the current investigation is the lowest at which mesh refinement close to the interface has no impact on simulation outcomes. It is determined that the 1,133,430 element mesh with a grid size of 0.001 m near the slag-metal region is appropriate for the computational domain. All simulation experiments utilize this mesh as their foundation.

Governing equations and solution methodology
To simulate the fluid flow and mass transfer, the incompressible, stationary Navier-Stokes equations are calculated. For that purpose, the laminar model was chosen, as the fluid is in laminar flow for there is neither a stirring paddle nor injected gas in the experiment stirring the hot iron. The mass, momentum, and energy balance equations are solved separately and can be expressed as equations (7)-(10) [35,36]. The species in molten iron, such as aluminum, sulfur, manganese, etc, can be conveyed simultaneously by molecular diffusion, liquid flow, and turbulent velocity fluctuations in a desulfurization ladle, and they can be taken out of or added into molten iron through chemical reactions. These processes can be represented in the existing model as equation (11) [37].
where R i is the net rate of production of species i by chemical reaction D i m , is the diffusion coefficient of the chemical component i in the mixture, and D T j , is the thermal diffusion coefficient. With no-slip boundary conditions, the bottom and sides of the crucible are treated as walls, and the conventional wall function is employed to represent the turbulence near-wall region. To accurately represent the behavior of the hot metal surface, a free surface model is used. At the top surface, an opening boundary condition is used. In the computational domain, initial pressure and velocity are both set to 0. The initial volume fraction of sulfur is set as 200 ppm-400 ppm for the hot iron. The amount of Mg required to remove S in the hot metal is calculated according to equation (1), and the Mg are patched to the flow field in the form of MgO. The initial content of Al required to reduce MgO is calculated according to equation (4). So the mass fraction of iron is determined as 1 minus the sum of the mass fractions mentioned above. Similarly, for the slag layer, the initial volume fraction of slag is set to 1. The physical properties of Al, Mg and other materials involved in the calculation at experimental temperature are available in table 1 [38][39][40][41][42].
At the time t = 0, the temperature is set at a certain value beween1523K and 1723K And at all boundaries, the mass fractions of sulfur, aluminum, and magnesium in molten iron have a normal gradient of 0. The implicit density-velocity coupling methodology was used to solve the Navier-Stokes equations based on the finite volume approach. Using second-order upwind formulations, the governing equations for continuity, momentum, and energy were discretized. To get a converged solution for each time step, the convergence criteria are set to 10 −6 for all of the simulation's variables. It could be known from the experiments that the

Validation and verification of the numerical result
The CFD model is validated by comparing the simulation results with experimental data. To make the parameters of the desulfurization model more compatible with the final desulfurization outcomes, they were changed and optimized by comparison with the findings of literature data [43][44][45][46][47]. The ladle processing conditions such as slag thickness of 0.1 mm and molten steel height of 28.9mm have been considered for validation. The weighted average of the mass of S on the midline of the crucible from the experiment and simulation is shown in figure 3. It can be seen that the desulfurization rate is fast in the initial 12 min after the dolomite was added and the reactions were almost completed during this period. Then the desulfurization rate gradually slows down after that and the maximum error is 14.9%. The predicted value of the in situ desulfurization process of dolomite is in good agreement with the experimental data.
The change of sulfur concentration in steel during desulfurization is shown in figure 4. The top portion of the ladle has a lower concentration of sulfur than the bottom portion. This is expected since sulfur is removed from steel using the Mg and because the Mg diffuses and reacts with sulfur from the liquid surface downward. Steel with a reduced sulfur content is transported into the bulk of the steel via fluid flow and diffusion along the steel/slag contact. The distribution of sulfur in the ladle is likewise almost uniform after two minutes, as can be observed. The corresponding change in aluminum content is illustrated in figure 5. Similar to the results in    figure 4, it shows that the decrease in aluminum is highest in the upper part of the ladle. After 5 min of desulfurization, the concentration of dissolved aluminum is also almost homogeneous. It is because the diffusion coefficient is big enough under the set conditions. There is a difference in the spatial distribution of substances such as S, but it can be treated as almost uniform.

Mass fraction of Mg
Hypothesis (3) assumed that the generated Mg can be completely dissolved in hot metal and there is no magnesium bubble escaping. However, steel has a certain solubility limit for magnesium so the possibility of Mg escaping needs to be checked which is done by comparing the actual magnesium mass fraction with the solubility limit in figure 6 which was obtained from experimental data. As can be seen from figure 6, the solubility of magnesium increases with temperature increase in the range of 1523 K-1723 K which is consistent with the properties of the vapor pressure of magnesium in the literature [48,49]. Figure 7 shows the mass fraction of Mg in hot metal at different temperatures. It can be seen that the mass fraction of Mg in molten iron increases rapidly in the early stage, reaching a maximum value of about 21 ppm at about 2 ∼3 min, and then decreases gradually. The effect of temperature on the magnesium content in hot iron is not significant. The maximum content of magnesium at 1523 K is about 1 ppm lower than that at  1623 K and 1723 K. The magnesium content at 1723 K decreases faster at the later stage for high temperatures accelerate the reaction rate.
Comparing the mass fraction of Mg in hot metal shown in figure 7 and the solubility of Mg in hot iron shown in figure 6. At temperatures of 1523K, the maximum value of the mass fraction of magnesium in hot iron is slightly less than its solubility. When the temperature is higher than that, the maximum value of the mass fraction of magnesium in hot iron is much less than its solubility too. As a result, the generated Mg can be treated as completely dissolve in hot metal when the temperature is higher than 1523K under the experimental conditions. This means no Mg is escaping and Mg bubbles desulfurization does not exist. The model is consistent with the assumption (3) when the temperature is between 1523 K-1723 K.

Effect of diffusion coefficient on simulation
The whole process was affected by diffusion and reaction, the trend of Mg and S decrease is somewhat similar which are downward curves. Since there is no mechanical or gas stirring in the main time of desulfurization, the flow of the substance is driven by diffusion and the flow field is shown in figure 8. The main form of iron movement is a circulation between the bottom and liquid surface, and the speed is pretty small. So diffusion is the only factor that drives hot iron in the process, and the diffusion coefficient is very important and must be set precisely. However, it is impossible to determine the exact value of diffusion coefficient due to the influence of other substances in molten iron and the temperature. In order to understand the influence of diffusion on desulfurization and improve the accuracy of simulation, it is necessary to investigate the influence of diffusion coefficient on the simulation process.
According to the literature [40][41][42], the diffusion coefficients of the main substances under experimental temperature and elemental conditions are: The effect of the diffusion coefficient is analyzed as shown in figure 9. It can be seen that the diffusion coefficients of Al and Mg near the scope of investigation do not affect the simulation. The diffusion coefficient of S will slightly reduce the desulfurization rate when its value is too small, and the rest of the cases do not affect the simulation. From previous research and literature, it appears that both diffusion and reaction rate should be the controlling steps of the process. However, the result above shows that even in the absence of mechanical or gaseous stirring, the diffusion coefficient of the elements does not have a significant effect on this desulfurization reaction. This means chemical reactions are controlled steps rather than chemical reactions being controlled in conjunction with diffusion. Of course, this conclusion is limited to small reactors, and the situation may be different in medium or large reactors.

Effect of temperature and initial S content on simulation
The effect of temperature on the desulfurization rate is simulated in figure 10. The sulfur content in molten iron decreases with desulfurizing time, and it decreases rapidly in the early stage and slows down in the later stage. And the higher the reaction temperature is, the faster the sulfur content decreases in the early stage. There is an intersection between the different temperature lines of 1623 K and 1723 K. Before the intersection, 1723 K has a lower sulfur content, but after this point, the situation is reversed. And that's because the reactant at 1723 K is consumed faster than at 1623 K, so its reactant concentration goes down faster, and so does the reaction rate. When the reaction rate drops to a certain level, the sulfur content curve becomes flat. The reaction is fast at 1723 K, so the curve flattens first and then intersects with the curve at 1623 K. The final sulfur content decreased with increasing temperature and decreasing initial sulfur content if time is long enough. And the final sulfur content at 30 min is about the same at 1623 K and 1723 K, which is consistent with the experimental results. So increasing the temperature can improve the speed of desulfurization and desulfurization rate. However, the impact of temperature on the desulfurization rate becomes low when it is higher than 1623 K.

The role of CaO
Reaction of MgS generated in equation (1) with O 2 from the air can leads to resulfurization as shown in equation (12). CaO could stabilize the sulfur by react with MgS to form CaS and MgO according to equation (13). At the temperature of molten iron, Δ G is always negative, indicating that as long as there is enough CaO, MgS will be completely transformed [50]. However, the amount of CaO has little influence on the desulfurization rate, as shown in figure 11. When CaO/MgO increases from 0.2 to 1.3, the desulfurization rate only increases by 6%. Because reactions (12) and (13) mainly occur on the surface of molten iron where O 2 is easily absorted from the air . CaO served mainly as a reagent to transform the desulfurization product of MgS into the stable compound of CaS. Mg was largely responsible for the desulfurization in the hot iron [11].