Segregation of a Phosphorus Rich Phase During Differential Solidification of BOF Slag

Evaluations were first carried out to obtain suitable time step, mesh size, and appropriate residuals for the above governing equations. The residuals were observed to start flattening out after 50 iterations; hence, this number was set as the number of iterations required for each time step. A mass balance was verified for each of the two species using these configurations. The satisfied scaled residual was found to be 10⁻⁷ for continuity and momentum equations, and 10⁻¹⁰ for energy and species transport equations. The simulations were run on a high performance computer: 32 ×5 12 GB nodes powered by 2.7 GHz Intel Xeon Gold (E5-6150) processor. The initial conditions include temperature at 1873 K and a secondary concentration of the solute at 40 pct.

For the small Pt crucible, different cooling stages were applied (to promote the positive segregation of the P-rich and Fe-rich phases) to match the experimental procedure. Figure 2 shows the temperature profile for both heating-holding (ABC) and cooling (CEDF) stages. However, only the cooling stages (CDEF) were implemented in the simulation while heating and holding (homogenising) stages were not required. This is because the homogeneous temperature can be obtained by initializing the simulation at the first step.

The cooling was controlled at a slow cooling rate of 10 K/min in the first 15 minutes, from 1873 K (stage C) to 1723 K (stage D). It was held at this temperature until homogeneous temperature was achieved (stage E). After that the crucible was cooled in air (stage F). Temperature profile was set as the boundary conditions during stage CDE while heat transfer coefficients were required for the “mixed” boundary conditions during stage EF. Detailed discussion of (a) the temperature profile is presented in Section 3, and (b) boundary conditions (BC), mesh information and time step for the crucible, slat pot and slag pit are in Table II.

Heat transfer coefficients were calculated and applied to the boundary conditions. Detail formulations are given below.

The convective heat transfer coefficient for flat surface used at the top interface is given asFor the side wall, the heat transfer coefficient was calculated using the correlation for natural convection for a vertical cylinder, given as:In the above equations, Nu is Nusselt number, \(Ra_{g}\) is Rayleigh number of the gas phase, \(R{a}_{g}=G{r}_{g}.{Pr}_{g}\), where \(G{r}_{g}=g\beta \left(T-{T}_{a}\right){d}_{cr}^{3}/{\nu }_{g}^{2}\) and \(P{r}_{g}={C}_{p,g}{\nu }_{g}/{k}_{g}\) are the Grashof and Prandtl numbers for air, respectively; \({d}_{cr}\) is the internal diameter of the crucible (d_cr = 4.8mm); \({C}_{p,g},{\nu }_{g}\) and \({k}_{g}\) are the heat capacity, kinematic viscosity, and thermal conductivity of the gas phase, respectively. The temperature dependency of these values was evaluated at the gas-film temperature^[18] using the one third rule as given as:where T_w is temperature at the outer wall (reduces during cooling) and T_a is temperature of the air at the far field.

For the bottom wall, the slag pot was assumed to place onto an alumina slab during cooling. A combined thermal conductivity for the two layers used for the bottom wall is given aswhere δ is thickness and k_b is thermal conductivity of the bottom wall, Pt for Platinum wall and Al₂O₃ for alumina slab (5 mm thickness).

In the CFD model all thermophysical properties were computed as a function of temperature. Details of the properties are presented in Table III.

In this section, the steps undertaken to obtain a simplified (pseudo) binary diagram for a BOF slag from its representative CaO–FeO–SiO₂ ternary diagram^[21] is presented. The slag composition used in this study came from a set of synthetic slag experiments with basicity CaO/SiO₂ of 2.6, used in the authors earlier work,^[12] i.e. 39.1 pct CaO, 30.8 pct Fe₂O₃, 14.8 pct SiO₂, 5.7 pct P₂O₅, 4.7 pct MgO, and 4.95 pct Al₂O₃. To allow the slag solidification to be simulated using Ansys Fluent, some simplifications had to be made, as Fluent only accepts pseudo binary, eutectic phase diagram in its solidification model. Some compromises had to be made in order to meet this requirement: (i) the composition was chosen that represented steelmaking slag as closely as possible, and (ii) relative proportions of the P-rich and Fe-rich phases were kept aligned with the proportions calculated using MTData. Therefore, the above full composition of the slag was first simplified to a ternary mixture of CaO, Fe₂O₃, and SiO₂; MgO was assumed to partition with the Fe₂O₃ phase, P₂O₅ was assumed to partition with CaO, and Al₂O₃ was assumed to behave similarly to SiO₂. This results in the simplified ternary mixture of ≈ 35 pct Fe₂O₃, 47 pct CaO and 18 pct SiO₂, by which the slag basicity was maintained at 2.6 as the original basicity. Following this, the ternary diagram was then converted into the pseudo binary eutectic diagram (2CaO·SiO₂ and 2FeO·SiO₂). The binary mixture was obtained approximately 60 pct 2CaO·SiO₂ (or P-rich) phase and 40 pct 2FeO·SiO₂ (or Fe-rich) phase, in line with MTData results. As noted, P is known to preferentially partition to the C₂S–C₃P solid solution phase leaving behind iron-rich phase with other minerals such as MgO, MnO, free CaO and wustite.^[3,4] Based on the partitioning characteristics of P and Fe, the present study assumed that the slag is comprised two major phases, viz. phosphorus rich (P-rich) phase and iron-rich (Fe-rich) phase. This simplification is important for the solidification simulations discussed in the next section. Two component phase diagram of 2CaO·SiO₂ and 2FeO·SiO₂ have been proposed in literature including the review of Hidayat et al.^[22] There is sufficient confidence about the liquidus temperatures of these two phases, 2CaO·SiO₂ and 2FeO·SiO₂. However, it is still necessary to redraw a linear binary eutectic diagram presenting a liquidus slope and a single eutectic point, which is required for the solidification model used. This means that a simple linear version of the binary diagram is required.

From the above initial compositions, a mass balance was calculated showing approximately 60 pct of the P-rich phase and 40 pct of the Fe-rich phase. The melting temperatures of the P- and Fe-rich phases were 2403 K and 1478 K (2130 °C and 1205 °C), respectively. The liquidus temperature for a slag with 40 pct Fe-rich phase is 1989 K (i.e. point (2) in Figure 3) obtained from MTData, which is a commercial thermodynamic software package developed at the National Physical Laboratory in the United Kingdom. From these known data points which are presented from points (1) to (5), a linear pseudo binary eutectic phase diagram was drawn as shown in Figure 3. The calculated liquidus temperature from MTData (point “2”) was found consistent with the phase diagram reported elsewhere.^[22] This diagram is necessary for the simulations as described in Section 3.

It is worth noting that the present phase diagram derived in Figure 3 can be only used for the BOF slags with similar composition compared with one used in this study (i.e. wt pct: 40 CaO, 30 Fe₂O₃, 30 SiO₂). Any significant change of the above composition may cause considerable variation in the physical and thermodynamic properties of the slag.

The simulation commenced at an initial temperature of 1873 K, with a concentration of 40 wt pct of the iron-rich phase. The following sections show temperature distributions, velocity, mass fraction and species concentration at different sequences, from stage ‘C’ to ‘F’, as depicted in Figure 2.

The solution for temperature distribution is obtained from the energy equation Eq. (4) coupled with solutions from Eqs. [1] through [24]. The cooling was controlled in the first two cooling stages CD and DE, and then cooled naturally in air for stage EF. Figures 4(a) and (b) shows the temperature distribution at stages D and F, respectively. At stage D, temperature is slightly higher at the centre of the crucible by approximately 0.5 K. This small discrepancy in temperature is due to the slow cooling CD stage at 10 K/min (which takes 900 s (15 minutes) to reduce the temperature from 1873 K at C to 1723 at D). After 50 seconds of holding, the slag at stage E was found to be at a uniform temperature with less than 0.1 K deviation, which is considered as “homogeneous”. The slag was quickly cooled in air from stage E to F.

Figure 4(c) shows transient temperatures of the slag at different locations in the crucible. There is no real temperature difference between points O, M, and N (positions shown in Figure 4(a)) during the stages CD and DE because of the slow cooling and holding, respectively. The cooling rate during stage EF resulted from the natural heat transfer coefficients applied as the boundary conditions. The average heat transfer coefficient h = 25 W/m²K (with deviation of ± 5 W/m²K) was found at the top and bottom wall, whereas h = 27 W/m²K (with deviation of ± 6 W/m²K) at the side wall (h is the average value obtained from temperature between 1673 K and 373 K for the outer wall). Temperature at point Q (Figure 4(a)) drops faster during stage EF due to the radiative heat loss at the top interface. Deviations between point Q and points O, M, N at the same time can go up to about 200 K which confirms the finite magnitude of the slag’s thermal conductivity. Non-linear cooling was found for the stage EF. The cooling time was approximately 2 minutes for reduction of temperature from 1723 K (stage C) to about 750 K (stage F).

Note that a curved gas-slag interface formed due to interfacial tension and wetting effects in the 5 mm crucible experiments was not considered in the simulation. This concave interface can lead to greater radiative heat loss due to larger surface area. However, the concave interface also results in reflection of radiative heat back to the slag medium due to the less-than-unity view factor effect which compensated for the heat loss due to larger surface area. The opposing effects were demonstrated in the authors previous work.^[12]

A simplified version of the above momentum equation can be represented via a characteristic velocity driven by the thermalsolutal convection, which can be written as:where L_c is the characteristic length. This equation indicates that velocity of the fluid is driven by thermal gradients represented by \({\upsigma }_{T}\), concentration gradients by \({\upsigma }_{C}\), and viscous resistance represented by dynamic viscosity \(\mu \), which is a function of the liquid fraction β. For example, for a unit of temperature difference (\(\Delta T=1 K)\), Eq. [25] gives v_c ≈ 10⁻⁴ m/s at L_c = 5 mm, assuming no concentration gradient (\(\Delta Y=0)\), and using the above discussed thermophysical properties at 1873 K.

Sequential snapshots of the velocity, liquid fraction, solute, and solvent concentration on the XY plane (Z = 0) are shown in Figure 5. Equation [25] demonstrates that there are no flows in the solid region because of the considerable viscous resistance, whereas high velocities can be obtained in the regions of low viscosity and high temperature and concentration gradients. Such regions are likely on the liquid side of the mushy zones shown in Figure 5. Higher velocity magnitudes shown near the bottom and top of the crucible at stage C (at t = 0.001 seconds) are due to the difference in the heat transfer boundary conditions at the top and bottom walls (h = 27 W/m²K) compared with the side wall (h = 25 W/m²K). The highest local velocity was shown to be about ~  0.13 × 10^-4 m/s.

Unlike solidification of the pure compounds, the liquid fraction of the binary mixtures is influenced by the convection and diffusion of the two species, as shown between Eqs. [8] and [12]. The mass fraction of the species on the liquidus (Y_i,liq), and the solidus side (Y_i,sol) was computed by Eqs. [15] and [17], respectively. Mass fraction of species i in the mushy region is bounded between Y_i,liq and Y_i,sol. Concentration of each species shown in Figure 5 was obtained in this mushy zone based on the previously obtained liquid fraction.

At the initially homogeneous stage (stage C, t = 0 seconds), at a temperature of 1873 K, liquid mass fraction was 0.65 comprising Fe-rich phase mass fraction of 0.40 and P-rich phase of 0.60. At stage D, liquid mass fraction varied within a range between 0.32 and 0.67 while the mass fraction (concentration) of the Fe-rich and P-rich phase varied between 0.29 and 0.44, and 0.56 and 0.71, respectively. Only slight variations were found during the isothermal stage DE due to thermalsolutal effects and redistribution of the solute. During the fast-cooling stage EF, large heat loss at the top interface leads to the first solidified layer, which grows quickly towards the bottom of the crucible at which the heat loss is lowest, because crystals tend to grow in the direction opposite to the heat flow (hotter at the bottom). The P-rich phase, according to the phase diagram, solidifies first so the Fe-rich phase is rejected into the inside area. This diffusion effect quantified by the partition coefficient of solute K_i in Eq. [17] makes the liquid fraction higher in the inside region. The mushy zone with higher liquid content in turn enables the macro-segregation by thermalsolutal convection, which continues until the slag completely solidifies. At the fully solidified state, the liquid fraction or “porosity” becomes zero and therefore velocity becomes zero according to the ‘porous media’ approach. Segregation occurs most during the stage EF giving the highest concentration of Fe-rich phase of ~ 0.55 near the bottom wall, and the highest concentration of P-rich phase of ~ 0.7 near the top interface. This increase of ~ 17 pct of the P-rich concentration (from 0.6 at stage C to 0.7 at stage F) at the top portion is discussed further in the next section.

It is worth noting that the mass fraction snapshot shows a mushy zone ‘pocket’ at stage F in Figure 5, which is entrapped inside the solid bulk (blue colour). As no diffusion in the solid phase is predicted by the Scheil model, the Y_liq value of the solute (Fe-rich) shown in Eq. [15] is supposed to reach its eutectic stage in this pocket according to the phase diagram in Figure 3. However, this never happens even when the temperature drops below the eutectic temperature. This is because of the high effective viscosity of the suspension, which goes up steeply once solid fraction becomes significant (i.e. from ~ 25 pct for the current slag composition). Therefore, there is no real change in the concentration of the P-rich and Fe-rich phases once the system is close to complete solidification (stage F), which can be seen in stage F in Figure 5.

In the crucible experiments—which was carried out for model validation prior to performing the large-scale simulations—a number of approaches to characterizing the segregation and recovery of the phosphorus have been evaluated. These are based on scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDS), in combination with image analysis and the TESCAN Integrated Mineral Analyser (TIMA-X) techniques. All approaches used to assess the phosphorus segregation showed similar and consistent results.

It can be seen in Figure 6 that coarse dendrites identified as C₂S–C₃P (P-rich phase) are present at the top of the crucible while fine grains identified as Fe-rich matrix are present in the bottom portion of the crucible. Chemical compositions of these phases are based on EDS analysis and shown in Table IV. From this analysis it can be seen that most P in the slag is in the C₂S–C₃P, P-rich phase; along with most of the CaO and SiO₂. Most Fe₂O₃, Al₂O₃ and MgO were found in the Fe-rich matrix phase. Quantitatively, higher concentrations of the P-rich phase was shown in the upper portion and higher concentrations of the Fe-rich phase in the lower portion of the crucible. This is consistent with the model prediction.

Distributions of P₂O₅ and Fe₂O₃ matrices along the crucible’s height were quantified and shown in Figure 7. From the area percentage analysis using TIMA-X (Figure 7(b)) the percentage of P-rich phase in the upper half portion is approximately 3 times higher than in the lower half, whereas the Fe content in the lower half portion is approximately 1.5 times the Fe content in the upper half. These partition deviation figures imply the possible segregation of the two main phases. From the mass percentage analysis using EDS (Figure 7(d)), the P₂O₅ concertation was about 3.8 pct in the slag in the lower portion (approximately 40 wt pct). The slag in the top portion of the crucible (approximately 60 wt pct) has P₂O₅ concentration of ~ 6.5 pct compared with the initial concentration of 5.5 pct. This means an increase of about 18 pct in the P-rich phase found in the top portion. This agrees reasonably well with the model prediction of ~ 17 pct.

Model runs were carried out to simulate solidification and separation of phosphorus in an industrial slag pot. Variations of local temperature at different positions within the slag domain are presented in Figure 8(a), and local wall heat flux are presented in Figure 8(b).

Figure 8(a) shows a higher cooling rate at the early stage due to the larger temperature difference between the slag and the surrounding air. Within the slag, temperature difference may be up to 1000 °C due to the finite thermal conductivity of the slag (k = 2 W/mK). No linear cooling rate was found during the 16-hour cooling period. However, an approximate cooling rate ~ 1 K/min obtained from the volume average temperature curve (solid curve in Figure 8(a)) was found in the first 4 hours of cooling, which is frequently quoted as the industrial linear cooling rate in open slag pit or yard (Nguyen et al. 2021). Temperature is lowest at the location adjacent to the wall, and highest at the centre of the pot. Temperature at point M is higher than that at point N because the heat transfer coefficient at top (h = 6 W/m²K) is lower than that at the side wall (h = 7 W/m²K). Temperature at point O is higher than that of point M and N because of the thicker slab placed at the bottom of the slag pot. Figure 8(b) presents the local wall heat flux at different local points M, N, and O. The heat flux, which was computed from the conductive thermal resistance and temperatures at the two sides of the wall, was found to be lower at point O compared with point M and N because the bottom wall is thicker (higher thermal resistance) than the other sides.

Figure 9(a) shows the temperature distribution after 16 hours of cooling from its initial stage at 1873 K. The black solid line indicates the mass fraction at 0.5. After 16 hours of cooling, a solidified layer (liquid fraction of less than 0.1) was found near the side and the top wall. The thickness was shown to be approximately 18 cm.

Distributions of the P-rich and Fe-rich phases resulted from convection and diffusion using Scheil model, as discussed in the crucible simulations section. For the slag pot, the solidification commenced from the top and side walls which undergo the highest heat loss. Therefore, the earlier solidified layer containing higher phosphorus occurs near the side and top wall. Figure 10 shows the sequential change in velocity, liquid fraction, P-rich, and Fe-rich concentrations at the XY plane (at the centre, Z = 0) during the cooling. Similar to the solidification in the small Pt crucible, higher thermal-solutal convections were found in the liquid region adjacent to the mushy zones where significant gradients of density and concentration exist. After 16 hours of cooling, a thick layer of solid was formed at the wall while a considerable amount of liquid was still found inside the slag pot. The P-rich phase concentration reached its largest value at 0.74 near the walls compared with its initial 0.6. The Fe-rich phase reached 0.69 at the inside region compared with its initial 0.4. This means that the possibility of segregation of the two phases after cooling is significant. Once the slag solidifies, there is no more variation in the species because the Scheil model was used in this study i.e. no back diffusion. Comparable results with the published experimental data are given in the next section.

Figure 11 shows the result reported originally in the work by Pietruck et al.^[8,23] for the 16-tonne slag pot. After 16 hours of cooling, the solid layer was found at the outside of the slag pot and the thickness was reported to be above 20 cm. The liquid amount was reported at 27 wt pct.

From the present simulation, the ‘solidified layer’ is considered to be the layer with liquid fraction of less than 0.1 (or solid fraction greater than 0.9). The thickness of this layer was found to be approximately 18 cm. The total liquid amount with liquid fraction of greater than 0.5 was found to be approximately 32 wt pct. This liquid quantity was assumed to be similar to the liquid that was poured out onto the ground in the work by Pietruck et al.^[8,23] i.e. as noted, 27 wt pct. Both the experimental and simulation results found higher P-rich phase near the top lid and side wall. Liquid with higher Fe-rich phase was found in the centre of the slag pot. For the experiment results, the P₂O₅ content at the bottom region of the slag pot was reported lower than other regions which may be due to the thick skull amount that decreased heat loss in that region. As summarised in Table V, a comparison between simulations and experimental data show reasonable agreement.

It can be seen that the model prediction of the P-rich phase amount at the top interface is lower compared with the experiments, which can be due to the following facts. It was found that change in the liquidus slope (which is the slope of the line between point (1) and (4) shown in Figure 3) due to either the melting temperature of the P-rich phase or the eutectic temperature, or both, leads to significant change in the liquid mass fraction of the mixture. Attempts were made to evaluate the simulations with an increase in 4 pct in the liquidus slope which results in 5.6 pct (from ~ 0.65 to 0.7) increase in the liquid mass fraction at the initial stage. This leads to an increase in the P-rich mass fraction from 0.74 to 0.78. Therefore, as noted in Section 2.4.3, the phase diagram developed in this study may be an over simplification and not properly represent the slag composition used in the experiments.^[8,23] This may be an explanation for the model predicting a lower P-rich phase amount at the top interface, compared with the experiments. Alternatively, it may be due to the kinetics of nucleation and growth.

It is noted that industrial slag pots do not have any lid. The lid used in the above slag pot case was aimed to match the slag pot used in the experiments.^[8,23] However, for a slag pot without a lid, the top solidified layer acts as insulation for the inner slag similar to a physical lid. Simulations performed for this slag pot system (i.e. without a lid) showed similar heat transfer, solidification, and segregation behaviours to those with a lid. Figure 12 shows the local temperature at the centre point of the top layer, the volume average temperature, and the volume average liquid fraction during 10 hours of cooling for the slag pot with and without a lid. Although temperature at the top point is about 100 K lower (at the same time) for the pot without a lid due to direct radiation to air, there is no real difference in volume average temperature between the two cases. The difference in the predicted liquid fraction is therefore negligible.

Positive segregation between the P- and Fe-rich phases was shown achievable in a slag pot by controlled solidification. However, the practicality for separating each phase is difficult for this geometry, and the number of slag pots required for continuous operation would be prohibitive. Simulation was therefore carried out in a 30-tonne slag pit (~ 10 m³) as shown in Figure 1(c) to investigate the potential phase segregation and separation performance. The slag pit was assumed to be in-ground to utilise insulation of the crust ‘walls’. The top is open so that the solidified layer from the top enables the separation of this P-rich solids using a slag skimmer or similar system.

Local temperatures at different points during this 30-hour cooling are shown in Figure 13. At the last stage temperature of the slag adjacent to top walls reaches 500 K whilst it is still greater than 1800 K in the inside due to great insulation of the crust walls and the top solidified layer. Cooling rate obtained from the volume average temperature curve was found to be approximately 1 K/min in the first four hours of cooling which was comparable with the 16-tonne slag pot case.

Figure 14 shows sequential changes in (i) velocity, (ii) liquid mass fraction, (iii) concentration of Fe-rich phase, and (iv) concentration of P-rich phase at different solidification stages during cooling at the XY plane (at Z = 0) at different stages during cooling. Similar to the above discussed solidification and segregation behaviour, stronger convective flows were present in the regions with low viscosity, and high density or high concentration gradients. A top solid layer was formed due to significant radiative heat loss over the top surface this location. This solidified layer reached a thickness of ~ 12 cm within the first 10 hours of cooling. However, the layer thickness increased slowly from ~ 12 to ~ 23 cm in the next 20 hours of cooling (i.e. thickness ≈ 23 mm at time t = 30 hours). This indicates a slower cooling stage once the first solidified layer is formed, which contributed to insulating the slag underneath. In this top solid layer, concentration of the Fe-rich phase reduced from 0.4 (Figure 14(a), iii) to 0.25 (Figure 14(b) and (c) iii) whilst concentration of the P-rich phase increased from 0.6 (Figure 14(a) a, iv) to 0.75 (Figures 14(b) and (c), iv), which indicate a 25 pct positive segregation for the P-rich phase.

For the purpose of separating the P-rich phase from the Fe-rich phase (which is not the main scope of this study), and if a slag skimmer or similar is to be used, then this has to be carried out while the lower portion of the slag (containing Fe-rich phase) is still in its liquid state. Therefore, it is important to link the solidification stage with an appropriate separation practice to ensure separation of the two phases. For the above slag pit, at t = 30 hours, the volume of the P-rich phase with concentration of 0.75 was found at ~ 2.3 m³ (equivalent to the above 23 cm solidified layer). Modelling suggested that ~ 23 wt pct of the P-rich phase can be separated with 25 pct increase in its concentration.