1 Introduction
Bath smelting is a key preliminary enrichment and extraction technology for copper concentrates and complex materials containing copper. Among them, the oxygen supply method of the bath smelting process using bottom blowing (such as Shuikoushan Smelting, SKS), side blowing (such as Noranda and Teniente smelting), and top blowing (such as Ausmelt and Isa smelting) is an important development direction in this field [1, 2]. Oxygen-enriched bottom-blowing smelting (also known as SKS) has been developed into more than ten production lines due to the unique kinetic conditions and good smelting effect. The key production indicators of this technology have reached the world’s leading level [3-5].
The oxygen-rich air is injected into the molten pool at high speed and serves as the oxygen source for the smelting reaction, which can support the oxidation and slagging removal of impurity elements. At the same time, bottom-blown gas is also a disturbance source for stirring the melt, which can promote the rapid transfer of momentum, mass, and energy in the molten pool, thereby achieving efficient extraction of valuable metals [6]. Production practice has shown that oxygen supply conditions directly affect the temperature of the molten pool and the fluidity of the slag. At the same time, it will also affect indicators such as copper content in the slag [7, 8]. Therefore, controlling the oxygen supply conditions during the production process of oxygen-rich bottom-blown bath smelting is crucial.
A large amount of researches have been carried out on the bottom-blown furnace, and the understanding and optimization of the bottom-blown furnace have been ongoing. GUO et al [9] studied the growth behavior of bubbles in the bottom-blown furnace molten pool through numerical simulation, clarified the changes in bubbles in the molten pool, and improved researchers’ understanding of gas movement in the furnace. YANG et al [10] obtained the size of the “mushroom head” through thermal equilibrium calculations. A bottom-blown furnace model with a “mushroom head” was established to analyze the effect of a mushroom head on the behavior of bottom-blown gas. It was found that the “mushroom head” makes the volume and surface area of the bubbles generated by bottom-blown larger. Its shape is closer to a sphere and it stays in the furnace longer, which promotes the smelting reaction. JIANG et al [11] systematically studied the plume eye generated by bottom-blown gas on the surface of the molten pool through water model simulation experiments. A mathematical model has been established to predict the size of plume eyes in a single oxygen lance bottom-blown furnace, guiding the acquisition of large plume eyes to improve the reaction rate. LI et al [12] modeled the bottom-blown oxygen lance and discussed in detail the gas-liquid mixing characteristics generated by straight tube and multi-channel spray lances. It was found that the multi-channel spray lance has a more prominent effect in the stirring of the molten pool, and has achieved good application results in production practice. WANG et al [13] built a water simulation platform and established an empirical formula for the average diameter of bubbles through experiments using dimensional analysis methods and Buckingham’s theorem. It was found that the nozzle installation angle and nozzle diameter have the greatest impact on the average diameter of bubbles. SONG et al [14] studied the effect of different tuyere diameters and molten pool depths on the melt flow in the bottom-blown furnace, clarified the effects of various factors on the internal melt flow in the molten pool, and proposed optimization suggestions. SHUI et al [15-17] established a bottom-blown furnace water model and conducted a detailed analysis of the generation of waves on the surface of the bottom-blown furnace and the mixing phenomenon in the molten pool. Summarizing the empirical formula for the generation of waves on the surface of the molten pool is of great significance for optimizing the flow field of the bottom-blown furnace. With the continuous deepening of research, there has been a significant improvement in the working principle, equipment improvement, parameter control, and other aspects of bottom-blown furnaces. However, there are still shortcomings in the current research on oxygen supply control for large bottom-blown furnaces. With the continuous deepening of research, there has been a significant improvement in the working principle, equipment improvement, parameter control, and other aspects of bottom-blown furnaces. However, it is still insufficient in the current research on oxygen supply control for large bottom-blown furnaces.
The processing capacity of large-scale bottom-blown furnaces has increased several times, and the demand for oxygen supply has also increased. A large amount of oxygen-rich air is sprayed into the molten pool through more than twenty oxygen lances, providing dynamic support for smelting. Currently, a large number of oxygen lances are set in two rows, with the center line of the oxygen lances forming a certain angle with the vertical direction. The upper row is set with a large angle (24°) and 7 pairs of oxygen lances. The lower row is set with a small angle (9°) and 7 pairs of oxygen lances [18]. The oxygen lance is installed in double staggered rows and is located on the same side of the furnace body. Due to the same oxygen supply intensity for each oxygen lance, the stirring zone formed is more concentrated on the side where the oxygen lance is located. Insufficient stirring near the falling point of the material (i.e., the center of the molten pool) results in insufficient heat and mass transfer between materials, leading to a significant problem of high copper content in the slag. The fundamental way to solve the above problems is to strengthen the regulation of oxygen supply, and the effectiveness of this measure has been widely verified in the metallurgical industry practice [19, 20].
To further promote the stirring of melt and raw materials by bottom-blown gas in large bottom-blown furnaces, strengthen the occurrence of smelting reactions, and improve smelting efficiency, this paper changes the traditional oxygen supply method of the oxygen bottom-blown furnace and proposes the idea of a “strong and weak coupling” oxygen supply mode. An equivalent model was established based on a large bottom-blown furnace. The changes of initial bubbles under different flow ratios of two rows of oxygen lances, as well as the disturbance of the molten pool and melt splashing were studied to guide the regulation of oxygen supply in large oxygen bottom-blown furnaces.
2 Models and algorithms
2.1 Physical problems and model assumptions
The large bottom-blown furnace copper smelting process involves a complex process of multiphase and multi-field coupling. It includes not only complex heat and mass transfer processes but also complex interactions between gas-matte-slag. All these processes have a significant impact on the smelting effect. In recent years, numerical simulation has shown significant value in equipment development, optimization, and effect prediction due to its good intuitiveness, flexibility, and economy. Therefore, it is widely used to solve the problem of multiphase flow in non-ferrous smelting equipment [21]. However, replicating the actual production situation of large bottom-blown furnaces will greatly increase the complexity of the model, resulting in a significant decrease in computational efficiency and stability. It is necessary to simplify the model reasonably and make assumptions. Combined with existing studies [22], this paper makes the following simplifications and assumptions: 1) The calculation domain is established based on the internal area of the furnace, without considering furnace lining, water-cooled jackets, etc; 2) Do not consider the internal structure of the oxygen lance and replace it with the cross-section between the oxygen lance and the furnace body; 3) Focus on fluid flow without considering chemical reactions and their effects during the smelting process; 4) The furnace is equipped with three phases of air, copper slag, and copper matte, without considering the feeding, slag discharge, and copper discharge processes.
Based on the above assumptions and combined with actual large-scale bottom-blown furnace equipment [18], a large-scale bottom-blown furnace model is established as shown in Figure 1. This study used ANSYS series software for research, and the geometric model was established using Space Claim software. The oxygen lances are distributed on the same side of the furnace body. It is at an angle to the centerline of the furnace body (9° and 24°, respectively). The two rows of oxygen lances are staggered, totaling 28 oxygen lances. The geometric model and equipment prototype size are 1:1, with a furnace length of 28000 mm, a furnace diameter of 4700 mm, and an oxygen lance diameter of 60 mm. The mesh is divided using Fluent Meshing software, and the bubble motion area is encrypted. The mesh validation adopts the same method as previous research work [23]. Four sets of mesh are generated using the Ploy-Hexcore method, with the number of mesh being 893187, 901813, 1021375 and 2182938, respectively. In the mesh-independence validation, the average melt velocity hardly fluctuates significantly with the increase in the amount of mesh beyond 901813. The error between the solutions of the third and fourth mesh is within 7%, with an average error of less than 0.5%. The impact of the mesh on the results is within an acceptable range. Therefore, the final amount of mesh in the mesh model is 1021375, which can better meet the computational requirements, and the experimental equipment can meet the computational consumption.
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2.2 Mathematical model
Based on the aforementioned simplification and assumptions, as well as existing research reports [24], the VOF multiphase flow model and the realizable k-ε turbulence model were selected to numerically simulate the flow characteristics in a large bottom-blown furnace.
The control equation system describing the three-phase flow of gas-matte-slag is as follows:
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where αi is the volume fraction of the i phase (air, copper matte, copper slag); ρi is the density of the i phase (kg/m3); v is the i phase velocity vector (m/s); t is the time (s); p is the pressure (Pa); μ is the viscosity (Pa·s); g is the gravitational acceleration (m/s2); F is the interfacial force source term (N); E is energy (J); T is the temperature (K); keff is the effective thermal conductivity (W/(m·K)); Sh is the source term of the energy equation (W/m3).
In the realizable k-ε turbulence model, the transport equations for k and ε are as follows:
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where k is the turbulent kinetic energy (m2/s2); ε is the turbulent dissipation rate (%); Gk is the turbulent kinetic energy generated by the average velocity gradient (kg/(m·s3)); YM is the turbulent kinetic energy generated by the influence of buoyancy (kg/(m·s3)); Gb is the effect of the compressible turbulent pulsation expansion on the total dissipation rate (kg/(m·s3)); μt is the turbulent viscosity coefficient (Pa·s). The constants in the turbulence model are C1ε=1.44, C2=1.9, σk=1.0, σε=1.2.
2.3 Numerical simulation and condition setting
This study used ANSYS Fluent 2020R2 software to conduct simulation calculations on a Dell PowerEdge R6525 server. Three phases of air, copper matte, and copper slag are set up in the calculation domain, and their physical parameters are shown in Table 1. The initial and boundary condition settings are shown in Table 2.
| Physical phase | Density/ (kg·m-3) | Viscosity/ (Pa·s) | Specific heat capacity/ (J·kg-1·K-1) | Thermal conductivity/ (W·m-1·K-1) | Initial temperature/K | Melt thickness/m |
|---|---|---|---|---|---|---|
| Air | Ideal gas | 1.7×10-5 | 1006.43 | 0.024 | 298.15 | — |
| Copper slag | 3500 | 0.15 | 1260 | 1.2 | 1503.15 | 0.8 |
| Copper matte | 5000 | 0.03 | 600 | 3 | 1473.15 | 1.3 |
| Calculate boundary | Parameter setting |
|---|---|
| Inlet | Mass flow inlet, air |
| Outlet | Pressure outlet, -20 Pa |
| Wall | No slip |
| Fluid | Global initialization adopts standard initialization; Local initialization uses the patch method. |
The focus of this study is on controlling the flow rate of the two rows of oxygen lances. According to the characteristics of large bottom-blown furnaces, the oxygen lances can be divided into two rows. The first row is a small-angle oxygen lance, and the center of the oxygen lance is at 9° with the centerline of the furnace body; The second row is a large-angle oxygen lance, and the center of the oxygen lance is at 24° with the centerline of the furnace body. So, the single oxygen lance flow rate for small-angle oxygen lances is defined as Q1, and the single oxygen lance flow rate for large-angle oxygen lances is defined as Q2. The flow ratio between the two is defined as R, as shown in Eq. (6). To ensure that the ratio of oxygen to mineral parameters does not change during the production process, the total oxygen supply should be fixed. Under the premise of maintaining the total oxygen supply unchanged, four operating conditions were set, as shown in Table 3.
| Working condition | Q1/(kg·s-1) | Q2/(kg·s-1) | R |
|---|---|---|---|
| 1 | 0.662 | 0.662 | 1.0 |
| 2 | 0.723 | 0.601 | 1.2 |
| 3 | 0.772 | 0.552 | 1.4 |
| 4 | 0.814 | 0.510 | 1.6 |
Condition 1 represents the current oxygen supply method, with each oxygen lance having the same oxygen supply intensity; Working conditions 2-4 represent a strong-weak coupling oxygen supply mode, and the strong side gradually strengthens. Meanwhile, to ensure the normal operation of the large-angle oxygen lance, the maximum of R is only set to 1.6.
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The solving algorithm adopts the PISO algorithm, and the second-order upwind discretization scheme is used for density, momentum, and energy-related equations. The first-order upwind discretization scheme is used for equations related to turbulent kinetic energy and turbulent dissipation rate, and the sub-relaxation factor remains at the default value. The time step is 0.001 s, the number of solving time steps is 5000, and the calculation time is 5 s. It is worth mentioning that the simulation results are highly consistent with the fluid flow characteristics (bubble morphology, motion trend, molten pool stirring) of the water model research results in the literature [26], as shown in Figure 2.
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It is very consistent with the fluid flow characteristics in the molten pool of a large bottom-blown furnace, so the established mathematical model can be considered reasonable and reliable.
3 Results and discussion
3.1 Motion of bottom-blown bubbles
In the early stage of research on the principle of pneumatic stirring in large bottom-blown furnaces, it was found that bubbles are the basic unit of pneumatic stirring in large bottom-blown furnaces [27]. Figure 3 shows the movement of bubbles from formation to rupture in a large bottom-blown furnace.
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As can be seen from Figure 3(a), the gas just enters the molten pool at 0.1 s of blowing. It is subjected to great pressure, forming spherical bubbles in the molten pool. When blowing for 0.4 s (Figure 3(b)), the initial bubbles are gradually detached from the root of the oxygen lance by buoyancy and move upward freely. During the upward movement of the bubbles, the bubbles undergo splitting or fusion changes, resulting in a change in both the shape and trajectory of the bubbles. There are two main reasons for this change: firstly, multiple bubbles in a large bottom-blown furnace float at the same time, and there are also interactions between bubbles moving side-by-side, significantly affecting the tendency of bubbles to collide and agglomerate. Secondly, when the bubbles traverse the copper matte layer and the copper slag layer, there are interactions between the copper matte, the copper slag, and the bubbles, and the melts with different physical parameters affect the bubbles. At 1.2 s of blowing (Figure 3(d)), the bubbles had moved to the copper slag-air interface and then ruptured. Thereafter, periodic movements such as growth, detachment, splitting, fusion, and rupture continue to occur in the molten pool. Accompanied by violent phenomena such as collision and crushing of bubbles, the bottom-blowing gas forms a strong agitation of the melt.
3.2 Analysis of initial bubble changes
The violent motion of the fluid in the molten pool depends on the deformation capacity of the bubbles. The initial bubble is the important foundation of the whole movement. The size of the initial bubble determines the strength of the gas’s ability to perturb the melt. At 0.3 s of blowing, the initial bubble is formed at the nozzle of a large bottom-blown furnace. Equivalent surfaces with gas phase volume fraction equal to 0.9 were extracted using CFD-Post software as shown in Figure 4.
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According to the results, it can be seen that changing the oxygen supply mode does not cause significant changes in the morphology of the initial bubbles, and they all appear mushroom-like. The initial bubbles in a row of oxygen lances with a small angle (9°) are relatively full, while the initial bubbles in a row of oxygen lances with a large angle (24°) are relatively slender and deformed to some extent. However, the initial bubble size varies under different operating conditions.
To further analyze the size of the initial bubbles, ImageJ software was used to measure the area of the initial bubbles, and the results are shown in Figure 5.
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By comparing the initial bubble area under various working conditions, it can be found that as the flow rate ratio of the two rows of oxygen lances increases, the small angle (9°) of oxygen lances obtains a greater oxygen supply intensity. The initial bubble area at its nozzle gradually increases, indicating an increasing ability to disturb the melt. The oxygen supply intensity of the oxygen lances decreases with a large angle (24°). The initial bubble area at its nozzle gradually decreases, and the disturbance to the melt will also gradually weaken. Compared to the operating condition with a flow ratio of 1.0, under the operating condition with a flow ratio of 1.6, the initial bubble area of the small angle oxygen lance increased by 28.18%, while the initial bubble area of the large angle oxygen lance decreased by 27.62%.
Therefore, through a strong-weak coupling oxygen supply mode, two stirring sources, “one strong and one weak”, can be formed in the molten pool. The strong stirring source plays a stirring role, stirring the melt evenly through strong pneumatic stirring. The weak stirring source plays a compensating role, increasing the gas-liquid contact area through dispersed bubbles. Two types of stirring sources work together to provide good smelting reaction conditions for the melt in the molten pool.
3.3 Disturbance of molten pool
In a large oxygen bottom-blown furnace, raw materials fall from the feeding port to the surface of the molten pool, and heat and mass transfer are carried out under pneumatic stirring in the furnace. Therefore, the disturbance of the bottom-blown gas on the surface of the molten pool is particularly important. The initial bubbles generated at the nozzle are subjected to upward forces such as buoyancy and rise to the surface of the molten pool to rupture (t=1.2 s), forming a stirring zone within a certain range of the molten pool surface. Figure 6 shows the velocity distribution on the surface of the molten pool (Y=-0.25 m) under different working conditions.
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From Figure 6, it can be seen that in the middle area of the molten pool, 14 approximately circular stirring zones are formed on the surface of the molten pool, which are staggered and arranged in the corresponding area above the oxygen lance. At both ends of the molten pool, the surface of the molten pool is not affected by the bottom-blowing gas and is in a relatively calm state. For the two rows of oxygen lances in a large bottom-blown furnace, oxygen lances with the same angle (both 9° or 24°) form a similar size of stirring zone on the surface of the molten pool.
When the flow rate ratio of the two rows of oxygen lances is 1.0, the size of each circular stirring zone formed on the surface of the molten pool is the same, providing the same strength of stirring energy. As the flow rate ratio of the two rows of oxygen lances increases, the stirring zone formed on the surface of the molten pool by the row of oxygen lances with a small angle (9°) gradually increases, while the stirring zone formed on the surface of the molten pool by the row of oxygen lances with a large angle (24°) gradually decreases. At this time, the molten pool center region of the disturbance is more intense, the melt can sufficiently scour the material, for the smelting reaction provides a good kinetic condition.
According to a recent study [28], there are two reaction pathways for copper concentrates entering the furnace. In the first way, the copper concentrate falls into the slag layer and then completes the melting and reaction, but the generated copper matte needs to cross the slag layer to enter the copper matte layer, which is easy to cause the loss of copper mechanical entrainment. In the second way, the copper concentrate falls into the copper matte layer and then completes the melting and reaction, but the generated copper matte is integrated into the copper matte layer.
Through the above analysis, in the strong-weak coupling oxygen supply mode, if the center area of the molten pool gets strongly disturbed, then the copper slag in the upper layer of the molten pool is pushed away. The formation of a plume eye on the surface of the molten pool, where the material is in direct contact with the copper matte, can form the second reaction pathway described above. Under these conditions, the reaction rate of the smelting process will increase dramatically. At the same time, since the smelting reaction generates copper matte in the copper matte layer without the need to settle in the copper slag layer, the copper content in the copper slag can be reduced. The above regulation measures are very obvious for the optimization of the smelting process.
In the actual production process of the large bottom-blown furnace, the bottom-blowing gas continuously stirs the melt, and the melt movement in the molten pool enters into a dynamic equilibrium, i.e. “quasi-steady state”. In this state, a stable functional zone is formed inside the molten pool, and the reaction zone (i.e., strongly stirred zone) and settling zone (i.e., weakly stirred zone) have obvious boundaries. In the previous simulation [29], it was found that the static molten pool was disturbed for some time, and the molten pool entered into the “quasi-steady state”, and this paper analyzes the data at 4 s as the “quasi-steady state”.
Figure 7 shows the surface velocity distribution of the molten pool during stable stirring. As can be seen from the figure, with the increase of the flow rate ratio of the two rows of oxygen lances, the strong stirring zone is produced by the small angle oxygen lance, its range is expanding, and the distance from the center of the oxygen lance to the edge of the stirring zone continues to increase (d4>d3>d2>d1). In the meantime, the falling point of the incoming material on the surface of the molten pool produces more intersection with the stirring zone on the surface of the molten pool. It makes the material falling into the center of the molten pool get more agitation, which is conducive to accelerating the mass and heat transfer process, thus improving the efficiency of the smelting reaction.
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In addition, to further analyze the stirring situation inside the molten pool, 21 monitoring surfaces (XY section) were set up inside the molten pool in the furnace diameter direction. They range from Z=-2 m to Z=2 m, as shown in Figure 8(a). The average velocity of each monitoring surface was extracted to analyze the velocity distribution in the molten pool, as shown in Figure 8(b).
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From Figure 8(b), it can be seen that there are two sharp velocity peaks inside the molten pool in the direction of the furnace diameter, which are generated by the oxygen lance blowing corresponding to the large and small angles, respectively. As the flow ratio of the two rows of oxygen lances increases, the velocity peak generated by the row of oxygen lances with a small angle (9°) is gradually enhanced, while the velocity peak generated by the row of oxygen lances with a large angle (24°) is gradually weakened, thus realizing directional enhancement of stirring in the center region of the molten pool. Compared with the condition with a flow ratio of 1.0, the peak velocity generated by the small-angle oxygen lance increases by 18.92% for the condition with a flow ratio of 1.6, which results in more intense agitation of the melt in the center region of the molten pool. It can be seen that the effect of directional intensification is very obvious.
3.4 Melt splashing in furnace
To analyze the flow of copper matte and copper slag in the furnace during stable stirring, equivalent surfaces with a volume fraction of 0.1 were extracted using CFD-Post software, as shown in Figure 9.
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It can be seen that the continuous stirring of the bottom-blown gas causes intense movement. Some of the copper matte in the lower layer is drawn to the copper slag layer, and even more is sputtered into the furnace chamber. The upper layer of copper slag is subjected to air–matte–slag interaction. A part of the copper slag enters the copper matte layer and a part of the copper slag is splashed into the furnace chamber. At the same time, it can be seen that the height of copper slag spattering is low, and copper matte spattering can reach the upper wall of the furnace. Under the action of bottom-blowing gas, copper matte spattering is more serious than copper slag spattering, and the spatter is dominated by copper matte.
With the increase of the flow ratio of the two rows of oxygen lances, the melt spattering is gradually enhanced. When the flow ratio is greater than 1.4, melt spattering to the furnace wall occurs, and a small portion of the melt has been adhered to the furnace wall. Generally speaking, under the strong and weak coupling oxygen supply mode, the amount of melt splashing is still in the acceptable range and has not reached the degree of affecting production (such as blocking the charging port).
To further analyze the effect of changing the oxygen supply mode on melt sputtering, the melt volume fraction in the upper hearth region of the molten pool at different moments was extracted and plotted in Figure 10.
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From Figure 10, it can be seen that the melt spattering has the same trend in different working conditions. The copper matte in the furnace experiences severe splashing during initial stirring, and reaches a stable state after 2.5 s; The splashing of copper slag in the furnace is similar to that of copper matte, reaching a stable state after 2.8 s. Overall, as the flow rate ratio of the two rows of oxygen lances increases, there is a certain increase in the splashing of copper matte and copper slag in the initial stage of stirring. During stable mixing, the copper matte sputtering volume fluctuates only slightly and does not show a large increase; the copper matte sputtering volume has a small increase. It can be seen that the flow rate of the two rows of oxygen lances has less influence on the melt spattering, and no vicious spattering is formed to hinder the stable operation of the production.
4 Conclusions
1) The bottom-blowing gas is in the form of bubbles that undergo periodic changes such as growth, detachment, and rupture in the molten pool. The bubble deformation ability is significantly affected by the oxygen supply mode, which in turn affects the stirring ability of the bottom-blowing gas to the molten pool.
2) Adjusting the flow ratio of the two rows of oxygen lances creates “one strong and one weak” source of disturbance in the furnace. The strong stirring source plays a stirring role, while the weak stirring source plays a compensating role. This method can selectively enhance the kinetic conditions of the molten pool reaction.
3) When the flow rate of the two rows of oxygen lances is 1.6, the initial bubble area generated by the small angle oxygen lance increases by 28.18%, and the peak velocity generated in the molten pool increases by 18.92%. This measure causes the melt in the central area of the molten pool to be stirred more strongly, and the melt splashing is within an acceptable range, which can be used as a directional control measure to optimize production.
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