Numerical Simulation of Desulfurization Behavior in Ladle with Bottom Powder Injection

Abstract

A computation fluid dynamics–population balance model–simultaneous reaction model (CFD–PBM–SRM) coupled model was used to predict the reaction kinetic and desulfurization behavior in 80 ton ladle with bottom powder injection. The reaction rate and evolution of multi-components including Al, S, Si, Mn and Fe at the powder droplet–liquid steel interface, bubble–liquid steel interface, top slag–liquid steel interface and air–liquid steel interface were revealed. Then, the effects of different kinetic conditions on the desulfurization efficiency were investigated, and the importance of various mechanisms was discussed and clarified. The results show that at the lower powder injection rate, the desulfurization is mainly attributed to the joint effort of both powder–liquid steel reaction and top slag–liquid steel reaction which is the prevailing mechanism. At the higher powder injection rate, the powder particle–liquid steel and bubble–liquid steel interface reaction become more important and then predominate the desulfurization behavior. With the increase of gas flow rate, the total desulfurization ratio gradually decreases, and with the increasing of powder injection rate, the total desulfurization ratio increases.

1. Introduction

With the increase of demands for high quality and ultra-low sulfur grade steel, high efficiency of ladle desulfurization has become one of main objectives in the steelmaking process because sulfur in most of steel products is detrimental. Ladle bottom powder injection (L–BPI), is a new refining technology that the fine refining powders are injected into liquid steel for desulfurization through bottom slot plugs in ladle,^1,2,3,4,5) as shown in Fig. 1. This technology has great potential to significantly enhance the refining efficiency and effectiveness and to lower the cost due to itself better kinetic conditions and technology features, and it may also overcome some problems existing in the traditional refining processing, such as serious splashing, inflexibility, threat of cleanliness caused by top lance.

Fig. 1.

Schematic diagram of new technology of ladle bottom powder injection. (Online version in color.)

In order to implement industrial application of this new technology, it is a key issue to use L–BPI to achieve higher desulfurization efficiency of liquid steel. Therefore, it is foundational and necessary to reveal clearly the slag-metal-powder particle multiphase reactions and desulfurization efficiency in ladle with bottom powder injection. Currently, the slag-metal two-phase reaction behavior in gas-stirred ladle has been studied by many researchers.^{6,7,8,9,10,11,12,13,14,15)} However, the slag-steel-powder multiphase reaction in ladle with bottom powder injection is still rarely studied. As shown in Fig. 2, in the process of bottom powder injection, the multiphase flow transport and chemical reactions in ladle involve many complex phenomena, which would occur simultaneously and interact with each other, and in turn would directly determine desulfurization efficiency and effectiveness. In our latest literature,¹⁶⁾ a mathematical model had been developed to describe the multiphase flow and reaction kinetic in the bottom powder injection process, and model validation was carried out using hot tests in 2–ton induction furnace with bottom powder injection.

Fig. 2.

Schematic diagram of multiphase flow transport behavior and reaction kinetics in ladle with bottom powder injection. (Online version in color.)

In present work, the objectives of present work were to use the CFD–PBM–SRM coupled model to predict desulfurization efficiency in 80–ton ladle with bottom powder injection. The mechanisms of multi–component simultaneous reactions including Al, S, Si, Mn, Fe and O at multi–interface including top slag–liquid steel interface, air–liquid steel interface, powder droplet–liquid steel interface and bubble–liquid steel interface were presented, and the effect of sulfur solubility in powder droplet on the desulfurization was also taken into account. The reaction rate and evolution of multiple interphase reactions involving dealumination, desilication, demanganization and desulfurization were revealed. The effects of different kinetic conditions on the desulfurization efficiency were investigated, and the importance of various reaction mechanisms was discussed and clarified.

2. Model Description and Numerical Scheme

2.1. Model Structure

The model assumptions have been listed in our previous work,¹⁶⁾ and the basic ideas of the present model are schematically structured in Fig. 3. The entire model consists of three main blocks, i.e., a CFD block, population balance model (PBM) block and simultaneous reaction model (SRM) block. In CFD model, the local flow field, volume fraction and turbulent energy dissipation rate were obtained by solving the mass, momentum and k−ε turbulent equations, as well, the species mass transport model was solved to obtain the local content distribution and overall removal ratio of each species in 80-ton ladle. Then the related parameters were transferred into PBM and SRM. In PBM model, by solving the particle–particle collision rate, particle–bubble adhesion rate and particle removal rate, the particle size and mass concentration distribution could be obtained and then were transferred into CFD and SRM to update the source terms of each equation for the next time step. In SRM model, the chemical reaction rates at the top slag–liquid steel interface $S_i^{l-slag}$, air–liquid steel interface $S_i^{l-air}$, powder droplet–liquid steel interface $S_i^{l-p}$ and bubble–liquid steel interface $S_i^{l-b}$ were calculated and transferred into CFD to update the source terms of species transport equation for next time step. In present model, the convergence needs to be guaranteed in each time step in order to get more accurate predicted results, and the time step of 0.25 was selected. The iteration residual was set to fall below 1 × 10⁻³ at each time step for all the subsequent simulations

Fig. 3.

Overall solution schematic of the CFD–PBM–SRM coupled model. (Online version in color.)

2.2. CFD Model

In the present study, based on Euler-Euler approach, the mass and momentum balance equations are solved for each phase separately. The mass balance equation of each phase which can be expressed as   

$$\frac{\partial }{\partial t}\left({\alpha }_k{\rho }_k{\overrightarrow{u}}_k\right)+\nabla \cdot \left({\alpha }_k{\rho }_k{\overrightarrow{u}}_k\right)=S_k$$(1)

where ρ_k, α_k, ${\overrightarrow{u}}_k$ and S_k are the density, volume fraction, averaged velocity vector and mass source term of liquid phase (k = l), gas phase (k = g) and powder particle phase (k = p) respectively. Both S_l and S_g are zero, and S_p is calculated by PBM of particles and discussed later. For the momentum equations, the drag and turbulent dispersion force among three phases are considered as momentum exchange source terms, and the detailed expression for the gas-liquid-particle three phase hydrodynamic equations together with the k−ε turbulence model had been described in our recent publication¹⁷⁾ and would not be reproduced here.

2.3. Population Balance Model (PBM)

In the bottom powder injection process, the powders particle growth and removal behavior have a significant impact on the multiphase flow transport and desulfurization kinetic, and they would be described by Population Balance Model (PBM):   

$$\begin{array}{l}\frac{\partial \left({\rho }_p{\alpha }_i\right)}{\partial t}+\nabla \cdot \left({\rho }_p{\overline{u}}_p{\alpha }_i\right)\\ ={\rho }_p{V}_i\left(\sum _{k=1}^N\sum _{j=1}^N\left(1-\frac{1}{2}{\delta }_{kj}\right){\beta }_{kj}\left(V_k,V_j\right)n_k{n}_j{\xi }_{kj}-\sum _{j=i}^N{\beta }_{ij}\left(V_i,V_j\right)n_i{n}_j\right)\\ +{\rho }_p{V}_i{S}_i^{tot}\\ \left(i,j=0,1,\cdot \cdot \cdot ,N-1\right)\end{array}$$(2)

  

$${\xi }_{kj}=\{\begin{array}{l}\frac{V-V_{i-1}}{V_i-V_{i-1}}\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }for\mathrm{\hspace{0.17em} }{V}_{i-1}<V_{ag}<V_i\\ \frac{V_{i+1}-V_{ag}}{V_{i+1}-V_i}\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }for\mathrm{\hspace{0.17em} }{V}_i<V_{ag}<V_{i+1}\\ \\ 0\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }otherwise\mathrm{\hspace{0.17em} }\end{array}$$(3)

where ρ_p and u_p are the density and velocity of the particle phase respectively, δ_kj is assigned to 0 (k ≠ j) or 1 (k = j), V_ag is the volume resulting from the aggregation of two particle, and α_i is the volume fraction of particle size i, β(V_i, V_j) represents the total coalescence rate between particles due to a variety of collision mechanism, $S_i^{tot}$ represents the total removal rate from liquid steel due to a variety of removal mechanism. These parameters can be written as   

$${\beta }_{ij}={\beta }_{ij}^{TR}+{\beta }_{ij}^{TS}+{\beta }_{ij}^S$$(4)

  

$$S_i^{tot}=S_i^{Wall}+S_i^{IF}+S_i^{BIB}+S_i^{BIR}+S_i^{BIR}+S_i^{Wake}$$(5)

where ${\beta }_{ij}^{TR}$, ${\beta }_{ij}^{TS}$ and ${\beta }_{ij}^S$ represent particle coalescence rate due to turbulent random collision, shear collision in turbulent eddies and Stokes buoyancy collision respectively, and $S_i^{Wall}$, $S_i^{IF}$, $S_i^{BIB}$, $S_i^{BIR}$, $S_i^{BIS}$ and $S_i^{Wake}$ represent the mass source terms of particle removal due to wall adhesion, particle own floating near slag–metal interface, bubble–particle buoyancy collision, bubble–particle turbulence random collision, bubble–particle turbulent shear collision and bubble wake capture respectively. The detailed expressions for particle coalescence and removal rate due to these mechanisms have been studied and described in our latest publication¹⁷⁾ and will not be reproduced here.

2.4. Multi–interface and Multi–component Simultaneous Reaction Model (SRM)

In the bottom powder injection process, as shown in Fig. 2. there are four main chemical reaction places in ladle, namely top slag–liquid steel interface, air–liquid steel interface in slag eyes, dispersion powder droplet–liquid steel interface and bubble–liquid steel interface, respectively, and the multi–component reactions including Al, S, Si, Mn, Fe and O are simultaneously involved in each interface.

2.4.1. Top Slag–Liquid Steel Interface Reactions

In the bottom powder injection process in ladle, the top slag–liquid steel reaction is one of main chemical reaction place, and has an important contribution on the desulfurization efficiency. At top slag–liquid steel interface, the multiple reactions involving [Al], [Si], [Mn], [Fe], [O] and [S] are considered to occur simultaneously, and the reaction rate of species i can be written as   

$$S_i^{l-slag}=-{\alpha }_l{\rho }_l{k}_{eff,i}\frac{A_{cell}}{100V_{cell}}\left\{\left[\% Y_i\right]-\frac{\left(\%Y_i\right)}{L_i}\right\}$$(6)

where, i is the species element in liquid steel, namely, S, Al, Si, Mn and Fe. k_eff,i characterizes the overall mass transfer coefficient of species i from steel to slag. A_cell and V_cell are the local interface area and volume of cell on the liquid steel surface, respectively. L_i is interfacial distribution ratio of element i at equilibrium, which represents thermodynamics capacity of slag–metal reaction and is a function of oxygen activity $a_{\mathrm{O}}^{*}$. In order to close the equation, oxygen kinetic balance equation of slag–metal reactions must be solved with a numerical iteration technique.   

$$1.5\frac{S_{\text{Al}}^{l-slag}}{M_{\text{Al}}}+2\frac{S_{\text{Si}}^{l-slag}}{M_{\text{Si}}}+\frac{S_{\text{Mn}}^{l-slag}}{M_{\text{Mn}}}=\frac{S_{\text{FeO}}^{l-slag}}{M_{\text{FeO}}}+\frac{S_{\text{S}}^{l-slag}}{M_{\text{S}}}+\frac{S_{\text{O}}^{l-slag}}{M_{\text{O}}}$$(7)

where, M_i is the molecular weight of species i in liquid steel and slag. The detailed description of thermodynamic and kinetic parameters mentioned above in Eqs. (6) and (7) have been clarified in our previous work.¹⁴⁾

2.4.2. Air–Liquid Steel Interface Reactions

When liquid steel contacted with air at higher temperature, the oxygen would be absorbed from atmosphere into steel, and some elements in liquid steel would be oxidized by dissolved oxygen. These oxidation reactions rate of species i in slag eyes could be written as   

$$S_i^{l-air}=-k_{m,i}{\alpha }_l{\rho }_l\frac{A_{cell}}{100V_{cell}}\left\{\left[\%Y_i\right]-{\left[\%Y_i\right]}^{*}\right\}$$(8)

where, i is Al, Si, Mn, Fe and C in liquid steel. k_m,i is the mass transfer coefficient of species i in liquid steel, and [%Y_i]^* is the equilibrium concentration of species i at air–liquid steel interface. In order to close the equation, the oxygen mass balance and carbon mass balance equations must be solved with a numerical iteration technique. The detailed description of these parameters have been clarified in our previous work.¹⁴⁾

2.4.3. Powder Droplet–Liquid Steel Interface Reaction

Compared with the top slag–liquid steel reaction, the reaction rates of these fine powder droplets are more rapid due to the superior dynamic conditions, and the sulfur concentration in these droplets would quickly increase to the saturation state. Then the solid phase of CaS would be produced, and the related thermodynamics and kinetics of desulphurization would vary, which in turn affect the desulphurization rate of powder. Based on the literature measured date,^18,19) the solubility of CaS in the liquid slag can be approximated as   

$$N_{\text{CaS, sat}}=3.33\%\frac{\left(N_{\text{CaO}}\right)}{\left(N_{{\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}}\right)}-0.216\%$$(9)

where, N_CaS,sat is the molar saturation concentration of CaS in droplet. N_CaO and N_Al2O3 represent the molar concentration of CaO and Al₂O₃ in powder droplet, respectively.

Depending on whether the molar concentration of CaS in powder droplet reaches saturation, the powder droplet–liquid steel interface reactions can be divided into the following two categories:

(1) Unsaturated state, i.e. N_CaS ≤ N_CaS,sat

Before the molar concentration of CaO reaches saturation state, the reaction rate of species i at the powder droplet–liquid steel interface can be written as   

$$S_i^{l-p}=-{\alpha }_l{\rho }_l{k}_{eff,i}^{l-p}\frac{6{\alpha }_p}{100d_p}\left\{\left[\% Y_i\right]-\frac{{\left(\%Y_{\text{i}}\right)}_p}{L_i^{l-p}}\right\}$$(10)

where, i is the species element involved reactions, namely, Al, Si, Mn, S and Fe. [%Y_i] and (%Y_i)_p are the local mass fraction of species i in liquid steel and powder droplet, respectively. d_p is the diameter of powder droplet, and k_eff,i characterizes the overall mass transfer coefficient of species i from steel to powder droplet.

In Eq. (10), $L_i^{l-p}$ is the interfacial distribution ratio of each element i between droplet and liquid steel, which represents thermodynamics capacity of powder droplet–liquid steel reaction and can be expressed as a function of the interfacial oxygen activity $a_{\text{O,} l-p}^{*}$ at the powder droplet–liquid steel interface. Similar to the previous parameter, $a_{\text{O,} l-p}^{*}$ must also be obtained by solving the oxygen kinetic balance Eq. (11) of powder droplet–liquid steel reactions with a numerical iteration technique.   

$$1.5\frac{S_{\text{Al}}^{l-p}}{M_{\text{Al}}}+2\frac{S_{\text{Si}}^{l-p}}{M_{\text{Si}}}+\frac{S_{\text{Mn}}^{l-p}}{M_{\text{Mn}}}=\frac{S_{\text{FeO}}^{l-p}}{M_{\text{FeO}}}+\frac{S_{\text{S}}^{l-p}}{M_{\text{S}}}+\frac{S_{\text{O}}^{l-p}}{M_{\text{O}}}$$(11)

(2) Saturated State, i.e. N_CaS > N_CaS,sat

In the process of bottom powder injection, once the CaS concentration in powder droplet reaches the saturation, the solid phase of CaS would be produced, and the related desulfurization rate after sulfur saturated in droplet could be written as   

$$S_{\text{S}}^{l-p}=-{\alpha }_l{\rho }_l{k}_m^{l-p}\frac{6{\alpha }_s}{100d_s}\left\{\left[\% Y_{\text{S}}\right]-{\left[\%Y_{\text{S}}\right]}_{l-p}^{*}\right\}$$(12)

where ${\left[\%Y_{\text{S}}\right]}_{l-p}^{*}$ is the interface equilibrium concentration of element i at the liquid surface, which can be expressed as a function of $a_{\text{O,} l-p}^{*}$. The related expressions are as follows   

$${\left[\%Y_{\text{S}}\right]}_{l-p}^{*}=\frac{a_{\text{O,}l-p}^{*}}{K_{\text{S}}{f}_{\text{S}}{a}_{\text{CaO}}}$$(13)

Therefore, using Eqs. (11), (12), (13), the oxygen activity at the droplet–liquid steel interface can be obtained for the saturated state of CaS in droplet, which in turn can give the reaction rate of each element $S_i^{l-p}$.

2.4.4. Bubble–Liquid Steel Interface Reaction

In bubbly plume flow zone, a large amount of powder particles will be adhered to bubble surface, and become an integral part of the bubble, as shown in Fig. 2. With the bubbles floating, these powder droplets would also contact and react with the liquid steel at the bubble–liquid steel interface. Similar to the powder droplet–liquid steel interface reaction, the bubble–liquid steel interface reaction can also be divided into the two categories depending on whether the molar concentration of CaO reach saturation in powder droplet adhered on bubble.

(1) Unsaturated state, i.e. (N_CaS)_g ≤ (N_CaS,sat)_g

Before the molar concentration of CaO reaches saturation state, the reaction rate of species i at the bubble–liquid steel interface can be written as   

$$S_i^{l-b}=-{\alpha }_l{\rho }_l{k}_{eff,i}^{l-b}\frac{6f{\alpha }_g{\rho }_g\left(1-\frac{{\left(\%Y_{Ar}\right)}_g}{100}\right)}{100{\rho }_p{d}_p}\left\{\left[\% Y_{\text{i}}\right]-\frac{{\left(\%Y_{\text{i}}\right)}_{g,real}}{L_i^{l-b}}\right\}$$(14)

where, f represents the ratio of the effective contact area between adhered droplet and liquid steel. In this paper, f was uniformly set to 0.5. ρ_g is the density of bubble after adhering powder particles and could be calculated using the following expression.   

$${\rho }_g=\left(1-{\left(\%Y_{\text{Ar}}\right)}_g\right){\rho }_p+{\left(\%Y_{\text{Ar}}\right)}_g{\rho }_{\text{Ar}}$$(15)

In Eq. (14), $L_i^{l-b}$ is the interfacial distribution ratio of each element i between bubble and liquid steel, and can be expressed as a function of the interfacial oxygen activity $a_{\text{O},l-b}^{*}$, which must be obtained by solving the following oxygen kinetic balance of bubble–metal reactions with a numerical iteration technique.   

$$1.5\frac{S_{\text{Al}}^{l-b}}{M_{\text{Al}}}+2\frac{S_{\text{Si}}^{l-b}}{M_{\text{Si}}}+\frac{S_{\text{Mn}}^{l-b}}{M_{\text{Mn}}}=\frac{S_{\text{FeO}}^{l-b}}{M_{\text{FeO}}}+\frac{S_{\text{S}}^{l-b}}{M_{\text{S}}}+\frac{S_{\text{O}}^{l-b}}{M_{\text{O}}}$$(16)

(2) Saturated state i.e. (N_CaS)_g > (N_CaS,sat)_g

In the bubble–liquid steel reaction process, once the product CaS concentration in powder droplet which was adhered on bubble reaches the saturation, the solid phase of CaS would be produced, and the desulfurization rate can be expressed by the following expression.   

$$S_{\text{S}}^{l-b}={\alpha }_l{\rho }_l{k}_{m,i}\frac{6f{\alpha }_g{\rho }_g\left(1-\frac{{\left(\%Y_{Ar}\right)}_g}{100}\right)}{100{\rho }_p{d}_p}\left\{\left[\% Y_{\text{S}}\right]-{\left[\%Y_{\text{S}}\right]}_{l-b}^{*}\right\}$$(17)

where, ${\left[\%Y_{\text{S}}\right]}_{l-b}^{*}$ is the equilibrium concentration of sulfur at the bubble–liquid interface, which can be expressed as a function of $a_{\text{O},l-b}^{*}$   

$${\left[\%Y_{\text{S}}\right]}_{l-b}^{*}=\frac{a_{\text{O}}^{*}}{K_{\text{S}}{f}_{\text{S}}{a}_{\text{CaO,g}}}$$(18)

Therefore, using Eqs. (16), (17), (18), the oxygen activity at the bubble–liquid steel interface can be obtained for the saturated state of CaS, which in turn can give the reaction rate of each element $S_i^{l-b}$.

2.5. Numerical Scheme

In the present work, the CFD–PBM–SRM coupled model was solved using the commercial computational fluid dynamics software fluent 12.0 combined with User–Defined Function (UDF), to describe the multiphase transport behavior and reaction kinetics in 80-ton ladle with bottom powder injection, and the dual slot plugs were placed symmetrically at 0.5R from the bottom center (R is the bottom radius of the ladle). Figure 4 shows the mesh of 80-ton ladle used in the present model, and the dimensions of ladle and other parameters are listed in Table 1. Due to the symmetry of the flow, only half of the geometric model was built as computational domain, and the mesh consisting 160743 control volumes was used. The bottom and side walls were set as no–slip solid walls, and the standard wall function was used to model the turbulence characteristic in the near–wall region. The velocity–inlet was used for gas blowing and powder injection at the bottom tuyeres, and a flat surface was assumed at the top surface. In present work, the initial velocity of powder particle was assumed to the same as the gas velocity at bottom slot, and the rising velocity of powder is obtained by solving the momentum conservation equation, which considered the drag force and turbulent dispersion force among three phases as momentum exchange source terms. The typical working conditions of actual ladle desulfurization, was as an initial condition for bottom powder injection process in 80-ton ladle, and the chemical compositions of liquid steel, top slags and powders were given in Tables 2 and 3.

Fig. 4.

The mesh of 80-ton ladle used in present model. (Online version in color.)

Table 1. The dimensions of 80-ton ladle and other parameters employed in model.

Diameter of ladle (up)	2633 mm
Diameter of ladle (down)	2388 mm
Height of ladle	2340 mm
Argon gas flow rate	200 to 800 NL/min
Powder injection rate	3 to12 kg/min
Thickness of slag	95 mm
Density of liquid steel	7100 kg/m3
Density of slag	3000 kg/m3
Density of gas	0.865 kg/m3
Molecular viscosity of molten steel	0.0055 Pa s

Table 2. Initial chemical composition of slag and liquid steel in 80-ton ladle.

Composition in steel (%)					Composition in slag (%)							Temperature (K)
[Al]	[Si]	[Mn]	[C]	[S]	(Al2O3)	(SiO2)	(CaO)	(MnO)	(S)	(FeO)	(MgO)
0.060	0.230	0.620	0.350	0.025	20.82	7.52	53.52	0.15	0.13	1.25	10.31	1842

Table 3. Chemical composition of powder injected in 80-ton ladle.

(Al2O3)	(SiO2)	(CaO)	(S)	(CaF)	(FeO)	(MnO)
21.32%	6.12%	57.62%	0.08%	13.07%	1.23%	0.12%

3. Results and Discussion

In the bottom powder injection process, the multiphase flow transport and chemical reactions behavior affect significantly desulfurization efficiency and effectiveness, and need to be accurately described and predicted. In our previous work,^14,15,16,17) by the CFD model, the predicted bubbly plume flow including gas volume fraction, liquid velocity and turbulent kinetic energy had been validated against experimental data,¹⁶⁾ and by the CFD–SRM coupled model, the predicted multicomponent simultaneous reaction at top slag–liquid steel interfacial in ladle agrees well with the measured data.^14,15) In our latest literature,¹⁷⁾ a CFD–PBM–SRM couple model had been developed to describe the multiphase flow and reaction kinetic in the bottom powder injection process. Model validation was carried out using hot tests in 2–ton induction furnace with bottom powder injection, and the predicted sulfur content in 2–ton furnace agreed well with the measured data.

In present work, the CFD–PBM–SRM coupled model was used to predict desulfurization efficiency in 80–ton ladle with bottom powder injection. The reaction rate and evolution of multiple interphase reactions involving dealumination, desilication, demanganization and desulfurization were revealed. The effects of different kinetic conditions on the desulfurization efficiency were investigated, and the importance of various reaction mechanisms was discussed and clarified.

3.1. Multiple Interface Reactions Kinetics

In the bottom powder injection process, as shown in Fig. 2, there are four main chemical reaction sites in ladle, namely top slag–liquid steel interface, air–liquid steel interface in slag eye, dispersion powder particle–liquid steel interface and bubble–liquid steel interface, respectively, and in these interfaces, the multi–component reactions including Al, S, Si, Mn, Fe and O would occur simultaneously and impact with each other.

3.1.1. Powder Particle–liquid Steel Interface Reaction

Figure 5 shows the predicted mole reaction rates of different species at the powder particle–liquid steel interface in 10 min after the start of bottom powder injection. The initial component concentration of liquid steel, top slag and powder were given in Tables 2 and 3. The gas flow rate is 600 NL/min, and the powder injection rate is 6 kg/min. $n_i^{l-p}$ represents the reaction mole rate of species i at the powder particle–liquid steel interface, which can be expressed as   

$$n_i=-\frac{S_i^{l-p}}{M_i}$$(19)

where, $S_i^{l-p}$ is the mass source of species i due to powder particle–liquid steel interface reaction, M_i is the molecular weight of species i.

Fig. 5.

Predicted the reaction mole rates of different species at the powder–metal interface: (a) $n_{\text{Al}}^{l-p}$, (b) $n_{\text{Si}}^{l-p}$, (c) $n_{\text{Fe}}^{l-p}$, (d) $n_{\text{Mn}}^{l-p}$, (e) $n_{\text{S},melt}^{l-p}$, (f) $n_{\text{S},solid}^{l-p}$. (Online version in color.)

From Fig. 5, it can be seen that $n_{\text{Al}}^{l-p}$ is positive in bubbly plume zone, which indicate [Al] would be removed from liquid steel into powder droplets due to the reaction at the powder–liquid steel interface. Simultaneously, $n_{\text{Si}}^{l-p}$ and $n_{\text{Fe}}^{l-p}$ are negative, which indicate that the (SiO₂) and (FeO) would be reduced by [Al] from powder droplets into liquid steel. Furthermore, it can be also found that as the powder droplets floating up, the reaction mole rates decrease because each component is gradually close to the equilibrium state. However, in the vicinity of the liquid surface, the reaction rate suddenly increases, this is because that the powder particles adhered on bubble would return to the liquid steel with the rupture of the bubbles in the slag eye zone, and the components in these particles are still not reached an equilibrium state and in turn react intensely with the liquid steel.

In Figs. 5(e) and 5(f), $n_{\text{S},melt}^{l-p}$ and $n_{\text{S},solid}^{l-p}$ represent the desulfurization mole rates when the desulfurization products CaS are liquid phase and solid phase, respectively. It should be noted that in the vicinity of bottom slot plugs, the desulfurization products CaS is liquid phase, while in the upper region of the ladle, the desulfurization products CaS is solid phase. This is mainly because as the refining powder is injected into liquid steel, the chemical reactions would strongly take place between fine powder droplet and liquid steel, and the liquid product CaS and Al₂O₃ concentration would rapidly increase, while the CaO concentration would decrease, as seen in Fig. 6. According to the Eq. (9) summarized from the literature measure,^17,18) the solubility of CaS in powder droplet would decrease rapidly with these droplets floating, as seen in Fig. 6(c). Once the sulphur reaches saturation, i.e. N_CaS > N_CaS,sat, the solid phase of CaS would be produced, and the related thermodynamics and kinetics of desulphurization would varied, which in turn reduce the desulphurization rate of powder.

Fig. 6.

Predicted the contour map of (a) CaO molar concentration, (b) Al₂O₃ molar concentration, and (c) CaS saturation molar concentration in powder droplet. (Online version in color.)

Figure 7 gives the predicted the change of species reaction molar rate at the powder particle–liquid steel interface with time in 80-ton ladle with bottom powder injection. The powder injection rate is 6 kg/min and the gas flow rate is 600 NL/min. From this figure, it can be found that the dealumination rate $n_{\text{Al}}^{l-p}$ and desulfurization rate $n_{\text{S},solid}^{l-p}$ are obviously larger than other reaction rates. This is because that initial components [Al] was mainly consumed to produce lower interfacial oxygen potential and promotes the desulfurization reaction. Simultaneously, the redundant [Al] in liquid steel would be consumed to promote the reduction rate of (SiO₂)_p and (FeO)_p. These reactions can be mainly expressed as   

$$\text{[Al]}+\text{[S]}+{\left(\text{CaO}\right)}_p={\left(\text{CaS}\right)}_{p,solid}+{\left({\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}\right)}_p$$(20)

  

$$\text{[Al]}+\text{[S]}+{\left(\text{CaO}\right)}_p={\left(\text{CaS}\right)}_{p,melt}+{\left({\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}\right)}_p$$(21)

  

$$\text{[Al]}+{\left({\text{SiO}}_2\right)}_p=\left[\text{Si}\right]+{\left({\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}\right)}_p$$(22)

  

$$\text{[Al]}+{\left(\text{FeO}\right)}_p=\left[\text{Fe}\right]+{\left({\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}\right)}_p$$(23)

Fig. 7.

Predicted the change of species reaction molar rate at the powder–metal interface with time in 80-ton ladle. (Online version in color.)

Furthermore, it can also be observed that with the powder injection time, these reaction rates gradually decreased, and $n_{\text{Mn}}^{l-p}$ is positive but very small, because its initial concentration in the powder droplet is very low and close to the interfacial equilibrium concentration.

3.1.2. Bubble–liquid Steel Interface Reaction

In bubbly plume flow zone, a large amount of powder particles will be adhered to bubble surface. With the bubbles floating, these adhered particles would also contact and react with the molten steel, and their dynamics condition are quite different from that of dispersion powders in liquid steel. Therefore, the reaction behavior between particles adsorbed on bubble and liquid steel need to be considered separately.

Figure 8 shows the predicted different species reaction molar rates at the bubble–liquid steel interface in 10 min after the start of bottom powder injection in 80-ton ladle, and Fig. 9 gives the curve change of different species reaction molar rate at the bubble–liquid interface with time. In these figures, the gas flow rate is 600 NL/min, the powder injection rate is 6 kg/min. $n_i^{l-b}$ represents the reaction mole rate of species i at the bubble– liquid steel interface, which can be expressed as   

$$n_i^{l-b}=-\frac{S_i^{l-b}}{M_i}$$(24)

where $S_i^{l-b}$ is the mass source of species i due to powder particle–liquid steel interface reaction.

Fig. 8.

Predicted the species reaction molar rate at the bubble–metal interface: (a) $n_{\text{Al}}^{l-b}$, (b) $n_{\text{Si}}^{l-b}$, (c) $n_{\text{Fe}}^{l-b}$, (d) $n_{\text{Mn}}^{l-b}$, (e) $n_{\text{S},melt}^{l-b}$, (f) $n_{\text{S},solid}^{l-b}$. (Online version in color.)

Fig. 9.

Predicted the change of species reaction molar rate at the bubble–metal interface with time in 80-ton ladle with bottom powder injection. (Online version in color.)

It can be found from these figures that similar to the powder droplet–liquid steel interface reactions, the $n_{\text{Al}}^{l-b}$ and $n_{\text{S,}solid}^{l-b}$ are greater than the other reaction rates, and in the lower region of bubbly plume zone, the desulfurization products CaS was liquid phase, while in the upper region of bubbly plume zone, the desulfurization products CaS was solid phase. Furthermore, compared with the powder particle–liquid steel interface reactions, the bubble–liquid steel interface reaction rate is obviously smaller because the contact specific surface and time between bubble and liquid steel are far lower than that between the dispersion particles and liquid steel.

3.1.3. Top Slag–Liquid Steel and Air–Liquid Steel Interface Reactions

In ladle, the top slag is pushed to the periphery of a ladle by the action of inert gas bubbling to form slag eyes, where the liquid steel is directly exposed to the ambient environment. Therefore, on the liquid steel top surface, there are two main reaction sites, namely the top slag–liquid steel interface and air–liquid steel interface.

Figure 10 shows the predicted reaction molar rates of different species at the top slag–liquid steel interface and air–liquid steel interface in 10 min after the start of bottom powder injection in 80-ton ladle. Figure 11 gives the curves changes of reaction molar rates of different species with time. In these figures, the gas flow rate is 600 NL/min and the powder injection rate is 6 kg/min. $n_i^{l-top}$ represents the reaction mole rate of species i on the liquid steel top surface, which can be expressed as   

$$n_i^{l-top}=-\frac{S_i^{l-top}}{M_i}=\frac{\left(S_i^{l-slag}+S_i^{l-air}\right)}{M_i}$$(25)

where, $S_i^{l-slag}$ and $S_i^{l-air}$ represents the mass source of species i due to top slag–liquid steel interface and air–liquid steel interface reactions, respectively.

Fig. 10.

Predicted the contour map of different species reaction molar rate at the slag–metal interface and air–metal interface: (a) $n_{\text{Al}}^{l-top}$, (b) $n_{\text{Si}}^{l-top}$, (c) $n_{\text{Mn}}^{l-top}$, (d) $n_{\text{Fe}}^{l-top}$, (e) $n_{\text{S}}^{l-top}$. (Online version in color.)

Fig. 11.

Predicted the change of reaction molar rate of different species at the top slag–metal interface and air–metal interface with time in 80-ton ladle. (Online version in color.)

As shown in Fig. 10, in slag eyes, the $S_{\text{Al}}^{l-top}$ and $S_{\text{Si}}^{l-top}$ are negative, while $S_{\text{Mn}}^{l-top}$, $S_{\text{Fe}}^{l-top}$ and $S_{\text{S}}^{l-top}$ are almost zero. This is because the oxygen would be absorbed from atmosphere into liquid steel, and the aluminum and silicon would be preferentially oxidized by dissolved oxygen due to their strong reducibility in liquid steel. At the top slag–liquid steel interface, the S_Si and S_Fe become positive, because dealumination reaction occurs at the slag–liquid steel interface and lowers the oxygen potential, which in turn promote the desulfurization reaction and the reduction reaction of (SiO₂) and (FeO) in top slag. Furthermore, it can be also observed that these kinetic reaction absolute rates are large near the slag eye zone and decrease along the radial.

Figure 11 illustrates the change of species reaction molar rate at the top slag–metal interface and air–metal interface with time in 80-ton ladle with bottom powder injection. From this figure, it can be seen that at the initial moment, the intense dealumination and demanganization reactions promote the desulfurization reaction and the reduction reaction of (SiO₂) and (FeO). With the powder injection time increasing, these reaction rates gradually decreased because each component is gradually close to the equilibrium state. Furthermore, it needs to be noticed that the net reaction rate of [Si] in liquid steel is very small, this is because the consumption rate of silicon due to being oxidized from liquid steel in slag eyes zones, is almost equal to the generation rate due to the reduction reaction of (SiO₂) from top slag into liquid steel at the top slag–liquid steel interface, as shown in Fig. 11(b).

3.2. Sulfur Local Distribution and Desulfurization Efficiency

3.2.1. Sulfur Local Mass Distribution in Ladle

In ladle bottom powder injection process, the species in liquid steel can be transferred by molecular diffusion and liquid turbulent flow, and they can be also produced into or removal from liquid steel due to the chemical reaction at powder–liquid steel interface, bubble–liquid steel interface, top slag–liquid steel interface and air–liquid steel interface.

Figure 12 shows the typical local distribution of sulfur content in ladle in 1 min, 10 min and 20 minutes after the start of bottom powder injection. The gas flow rate is 600 NL/min, the powder injection rate is 6 kg/min, and the initial component concentration of liquid steel, top slag and powder particle were given in Tables 2 and 3. From this figure, it can be found that the sulfur content has the lowest value in the vicinity of bottom slot plugs, and then gradually increases with the upping liquid steel flow due to continuous mixing with surrounding liquid steel flow with high sulfur concentration. When the upping liquid steel flow reaches the top liquid surface, the sulfur content would gradually decrease along the direction of liquid steel flow due to the top slag–liquid steel reaction, and finally the liquid steel surface stream would be re–mixed into the ladle interior along the side wall and the two bubbling flows. Thus, such a process is formed in the whole ladle to transfer and removal sulfur with time, as shown in Figs. 12(b) and 12(c).

Fig. 12.

Predicted local distribution of the sulfur content in (a) 60 s, (b) 600 s and (d) 1200 s after the start of bottom powder injection in 80-ton ladle. (Online version in color.)

Figure 13 shows the change of predicted sulfur mass average content and desulfurization ratio with time in 80-ton ladle. In the current work, the φ_S is proposed to represent the total desulfurization ratio, ${\phi }_{\text{S}}^{l-p}$, ${\phi }_{\text{S}}^{l-b}$ and ${\phi }_{\text{S}}^{l-top}$ are desulfurization sub–ratio attributed by powder particle–liquid steel interface reaction, bubble–liquid steel interface reaction and top slag–liquid steel interface, respectively. From this figure, it can be found that with the increase of powder injection time, the average sulfur concentration [S] in the liquid steel decreases from 250 × 10⁻⁶ to 69.2 × 10⁻⁶, and the final total desulfurization ratio φ_S is 72.3%. For the three main desulfurization mechanisms, the contribution of the powder–liquid steel interface reaction is the largest, which is 45.01%, and then followed by the top slag–liquid steel interface desulfurization with 19.42%, while the contribution of bubble–liquid steel interface desulfurization is the smallest.

Fig. 13.

Predicted (a) the sulfur mass content, and (b) desulfurization ratio due to various reaction mechanisms with time in 80-ton ladle with bottom powder injection. (Online version in color.)

3.2.2. Effect of Gas Flow Rate

Figure 14 gives the effect of gas flow rate on the predicted desulfurization ratio due to various reaction mechanisms in 80-ton ladle with bottom powder injection. The powder injection rate is 6 kg/min, and the initial component concentration of liquid steel, top slag and powder particle are given in Tables 2 and 3. From this figure, it should be stated that with the gas flow rate increasing from 200 NL/min to 800 NL/min, the final average sulfur concentration in liquid steel increases from 69.2 × 10⁻⁶ to 82.4 × 10⁻⁶, i.e. the desulfurization ratio φ_S will decrease from 72.3% to 63.9%. This is because, as the gas flow rate increases, the rate of powder–bubble collision and adhesion increase. The dispersion particle–liquid steel interface desulfurization ratio ${\phi }_{\text{S}}^{l-p}$ would quickly decrease, while the growth rate of bubble–liquid steel interface desulfurization ratio ${\phi }_{\text{S}}^{l-b}$ is relatively slow due to the lower contact specific surface and time between bubble and liquid steel.

Fig. 14.

Effect of gas flow rate on the predicted (a) sulfur mass content, and (b) desulfurization ratio due to various reaction mechanisms in 80-ton ladle. (Online version in color.)

3.2.3. Effect of Powder Injection Rate

Figure 15 shows the effect of powder injection rate on the predicted desulfurization ratio due to various reaction mechanisms in 80-ton ladle with bottom powder injection. The gas flow rate is 600 NL/min, and the initial composition of liquid molten steel, top slag and powders is shown in Tables 2 and 3. From this figure, it can be found that when the bottom powder injection amount is 0.75 kg/t, i.e. the powder injection rate and time is 3 kg/min and 20 min, the desulfurization ratio φ_S is only 51.9% , and the top slag–liquid steel interface reaction is the dominant desulfurization mechanism. With the increases of powder injection rate from 0.75 kg/ton to 3 kg/ton, the desulfurization ratio φ_S quickly increases from 51.9% to 82.5%, and the contribution of powder–liquid steel interface reaction and bubble–liquid steel interface reaction increase and become the dominant desulfurization mechanisms, while the role of the top slag–liquid steel reaction is gradually weakened.

Fig. 15.

Effect of powder injection rate on the predicted (a) sulfur mass content, and (b) desulfurization ratio due to various reaction mechanisms in 80-ton ladle. (Online version in color.)

4. Conclusions

The CFD–PBM–SRM coupled model was used to predict the multiphase flow behavior and reaction kinetic in 80 ton ladle with bottom powder injection. The reaction rate and evolution of multi-components including Al, S, Si, Mn and Fe at the powder droplet–liquid steel interface, bubble–liquid steel interface, top slag–liquid steel interface and air–liquid steel interface were revealed, and the importance of various mechanisms was discussed and clarified.

At the lower powder injection rate, the desulfurization is mainly attributed to the joint effort of both powder–liquid steel reaction and top slag–liquid steel reaction which is the prevailing mechanism. At the higher powder injection rate, the powder–liquid steel and bubble–liquid steel interface reaction becomes more important and then predominates the desulfurization behavior.

With the increasing of gas flow rate, the total desulfurization ratio φ_S gradually decreases, and with the increase of powder injection rate, the total desulfurization ratio φ_S increase. As the gas flow rate is 600 NL/min, with the powder injection rate increasing from 0.75 kg/t to 3 kg/t, the φ_S increases from 51.9% to 82.5%.

Acknowledgment

The authors wish to express thanks to the National Natural Science Foundation of China (51604071) and National Key R&D Program of China (2017YFC0805105) for supporting this work.

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