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Skull formation in dynamic modelling of silicon refining
17th IFAC Symposium on Control, Optimization and Automation in 17th IFAC Symposium on Control, Optimization and Automation in Mining, Mineral and Metal Processing 17th IFAC Symposium on Optimization 17th IFAC Symposium on Control, Control, Optimization and and Automation Automation in in Mining, Mineral and Metal Processing Vienna, Austria. Aug 31 Sept 2, 2016 Available online at www.sciencedirect.com Mining, Mineral and Metal Processing Mining, Mineral and Metal Processing Vienna, Austria. Aug 31 Sept 2, 2016 Vienna, Vienna, Austria. Austria. Aug Aug 31 31 -- Sept Sept 2, 2, 2016 2016
ScienceDirect
Skull Skull Skull Skull
IFAC-PapersOnLine 49-20 (2016) 173–177
formation in dynamic formation in formation in dynamic formation in dynamic dynamic silicon refining silicon silicon refining silicon refining refining
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Ellen Nordg˚ ard-Hansen ∗∗ Kjetil Hildal ∗∗ ∗∗ ∗ Kjetil Hildal ∗∗ Ellen Nordg˚ ard-Hansen Ellen Nordg˚ ard-Hansen Ellen Nordg˚ ard-Hansen ∗ Kjetil Kjetil Hildal Hildal ∗∗ ∗ ∗ Teknova as, Gimlemoen 19, N-4630 Kristiansand, Norway (e-mail: ∗ Teknova as, Gimlemoen 19, N-4630 Kristiansand, Norway (e-mail: ∗ Teknova as, [email protected]). 19, Teknova as, [email protected]). 19, N-4630 N-4630 Kristiansand, Kristiansand, Norway Norway (e-mail: (e-mail: ∗∗ [email protected]). Elkem Technology, Fiskaaveien 100, N-4675 Kristiansand, Norway [email protected]). ∗∗ ∗∗ Technology, Fiskaaveien 100, N-4675 N-4675 Kristiansand, Kristiansand, Norway ∗∗ Elkem Elkem Fiskaaveien 100, Norway (e-mail: [email protected]) Elkem Technology, Technology, Fiskaaveien 100, N-4675 Kristiansand, Norway (e-mail: [email protected]) (e-mail: [email protected]) (e-mail: [email protected]) Abstract: An offline simulation tool for silicon refining is extended with an improved model Abstract: An offline for silicon extended improved model Abstract: An simulation tool for silicon refining is extended with an improved model for skull formation. In simulation this model,tool skulls are seen refining as highlyis viscous slagwith withan droplets of refined Abstract: An offline offline simulation tool forare silicon refining isviscous extended with androplets improved model for skull formation. In this model, skulls seen as highly slag with of refined for skull formation. In this model, skulls are seen as highly viscous slag with droplets of refined silicon trapped within. Since slag viscosity depends strongly on its lime content, the degree of for skull formation. In this model, skulls are seen as highly viscous slag with droplets of refined silicon trapped Since slag viscosity depends strongly on the of silicon trapped within. within. Sincehow slagmuch viscosity depends strongly on its its lime content, the degree degree of skull formation varies with calcium is removed from thelime melt.content, The skulls influence silicon trapped within. Since slag viscosity depends strongly on its lime content, the degree of skull formation with much is removed from the melt. The influence skull formation varies with how much calcium is from The skulls influence the geometry of varies the ladle as how well as the calcium heat balance, and accumulate from tap toskulls tap. It is seen skull formation varies with how much calcium is removed removed from the the melt. melt. Theto skulls influence the geometry of the ladle as well as the heat balance, and accumulate from tap tap. It is seen the geometry of the ladle as well as the heat balance, and accumulate from tap to tap. It is seen that the simulation results reflect data from normal operation. the geometry of the ladle as well as the heat balance, and accumulate from tap to tap. It is seen that the simulation results reflect data from normal operation. that the simulation results reflect data from normal operation. that the simulation results reflect data from normal operation. © 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Process simulators, Metals, Training, Slag, Viscosity Keywords: Keywords: Process Process simulators, simulators, Metals, Metals, Training, Training, Slag, Slag, Viscosity Viscosity Keywords: Process simulators, Metals, Training, Slag, Viscosity 1. INTRODUCTION refining process, and will be a valuable tool for the process 1. refining process, and will will be aa will valuable tool for the 1. INTRODUCTION INTRODUCTION refining process, and be valuable for the process process specialists. A similar model also tool be included in an 1. INTRODUCTION refining process, and will be a will valuable tool for the process specialists. A similar model also be included in an 1.1 Background specialists. A similar model will also be included inwith an online version of the model, which will communicate specialists. A similar model will also be included in an 1.1 Background online version of the model, which will communicate with 1.1 Background Background online version of the model, which will communicate with the control system. 1.1 online version of the model, which will communicate with During oxidative refining of silicon, liquid silicon is tapped the the control control system. system. the control system. During oxidative refining of silicon, liquid silicon is tapped During oxidative refining of silicon, silicon, liquid silicon of is air tapped from theoxidative furnace into a ladle, in which a mixture and 1.2 Previous work During refining of liquid silicon is tapped from the into aa ladle, in which which mixture of air air and 1.2 Previous work from theisfurnace furnace into ladle,the in mixture of and oxygen bubbled through melt. aa As a result, silicon from the furnace into a ladle, in which aAs mixture of air and 1.2 1.2 Previous Previous work work oxygen is bubbled through the melt. a result, silicon oxygen is bubbled through the melt. As a result, silicon oxide forms on the bubble-melt interfaces and also on the oxygen is bubbled through the melt. As a result, silicon Skull formation in silicon refining ladles has some traits oxide forms on the bubble-melt interfaces and also on the oxide forms on the theAsbubble-melt bubble-melt interfaces andimpurities also on on the the top melt surface. the refininginterfaces progresses, in Skull formation in silicon refining ladles some traits oxide forms on and also Skull formation in silicon refining ladles has has some traits in common with ladle glazing in steelmaking, as studied top melt surface. As the refining progresses, impurities in Skull formation in silicon refining ladles has some traits top surface. Asthe thesilicon refining progresses, impurities in in common with ladle the melt react with oxide to form metal oxides, glazing in steelmaking, as studied top melt surface. As the refining progresses, impurities in in common with ladle glazing in steelmaking, as studied by e.g. Song et al. (2011). Here also, a layer of slag the melt react with the silicon oxide to form metal oxides, in common with ladle glazing in steelmaking, as studied the melt react with the silicon oxide to form metal oxides, thereby transferring thesilicon impurities from themetal melt oxides, to the by e.g. Song et al. (2011). Here also, aathis layer of slag the melt transferring react with the oxide from to form by e.g. Song et al. (2011). Here also, layer of slag is also formed on the ladle walls, and layer may thereby the impurities the melt to the e.g. Song etonal.the (2011). Here athis layer of may slag thereby transferring theladle impurities from the melt meltmetal to the the slag phase. When the is full, from the refined is by is also walls, also, and layer thereby transferring the impurities the to is also formed formed ontap theto ladle ladle walls, and this layer may accumulate fromon tap, possibly contaminating the slag phase. When the ladle is full, the refined metal is is also formed the ladle walls, and this layer may slag phase. When the ladle is full, the refined metal is poured into molds, and the remaining slag is removed from tap to tap, possibly contaminating the slag phase. When the ladle isremaining full, the slag refined metal is accumulate accumulate from tap to tap, possibly contaminating the metal. However, the layer is formed when slag comes in poured into molds, and the is removed accumulate from tap to tap, possibly contaminating the poured intonext molds, and can the take remaining slag is removed removed before the tapping place. slag In genereal, the metal. However, the layer is formed when slag in poured into molds, and the remaining is metal. However, the layer is during formedladle whenteeming, slag comes comes in contact with the ladle walls which before the next tapping can take place. In genereal, the metal. However, the layer is formed when slag comes in before the next tapping can take place. In genereal, the empty the ladlenext weight increases fromplace. one tap to the next, ladle ladle which before tapping can take In genereal, the contact contact with the ladleinwalls walls during ladle teeming, teeming, which does notwith takethe place the during same manner as for silicon empty ladle weight from one to with the ladle walls during ladle teeming, which empty ladlesolidified weight increases increases from one istap tap to the the next, next, contact since some material, or skulls, deposited. does not take place in the same manner as for silicon empty ladle weight increases from one tap to the next, does not take place in the same manner as for silicon refining. So, a different mechanism is required to describe since some solidified material, or skulls, is deposited. does notSo, take place inmechanism the same is manner as to for silicon since some some solidified solidified material, material, or skulls, is is deposited. deposited. since refining. So, aaaofdifferent different mechanism is required to describe describe Skull formation is a challengeorinskulls, the day-to-day silicon refining. the presence skull material close is to required the walls. refining. So, different mechanism required to describe Skull formation is a challenge in the day-to-day silicon the presence of skull material close to the walls. Skull formation is a challenge in the day-to-day silicon the presence of skull material close to the walls. production, since excessive skull growth causes the ladle Skull formation isexcessive a challenge in the day-to-day silicon of askull the also walls. Thepresence freezing of solidmaterial layer onclose ladletowalls takes place production, since skull causes ladle the production, since excessive skull growth growth causes the the ladle to get smaller while at the same time changing The freezing of a solid layer on ladle walls also takes place production, since excessive skull growth causes the ladle The freezing of a solid layer on ladle walls also takes place in blast furnaces, as described by Zhao et al. (2014), who to get smaller while at the same time changing the ladle The freezing of a solid layer on ladle walls also takes place to get smaller while at the same time changing the ladle thermal balance. On the other hand, some skull formation in blast furnaces, as described by Zhao et al. (2014), who to get smaller while at the same time changing the ladle in blast furnaces, as described by Zhao et al. (2014), who among other things looked at how the skull thickness dethermal balance. On the other hand, some skull formation in blast furnaces, as described by Zhao et al. (2014), who thermal balance. On the other hand, some skull formation may be favourable, since the skulls protect the ladle walls among other things looked looked at howmetal. the skull skull thickness dethermal balance. Onsince the other hand,protect some skull formation among other things at how the thickness depends on the viscosity of the liquid However, typical may be favourable, the skulls the ladle walls other viscosity things looked at howmetal. the skull thickness demay be favourable, since the the skulls skulls protect protect the the ladle ladle walls walls among from be thefavourable, liquid metal. pends the However, typical may since pends on the viscosity oftemperature the liquid liquid metal. metal. However, typical values on forthe theviscosity liquidusof of slags relevant for from the liquid metal. pends on the of the liquid However, typical from the liquid metal. values for the liquidus temperature of slags relevant for from the liquid metal.simulation tool is used for internal values for the the varies liquidus temperature of1520 slags◦◦ C, relevant for indicating Currently, an offline silicon refining between 1370 and values for liquidus temperature of slags relevant for ◦ C, indicating Currently, an offline is internal varies between and ◦ C,inindicating Currently, aneducation offline simulation simulation tool is used used for forand internal silicon refining varies of between 1370 and 1520 1520 either refining solidification all or 1370 no slag, while practice training and of processtool metallurgists oper- silicon C,inindicating Currently, an offline simulation tool is used for internal silicon refining varies between 1370 and 1520 either solidification of all or no slag, while practice training and education of process metallurgists and opereither solidification of all or no slag, while in practice training and education of process metallurgists and opersome skull formation is observed in both cases. Again, the ators. The kinetics and thermodynamics of the silicon reeither solidification of all or noinslag, while in practice training and education of process metallurgists and opersome skull formation is observed both cases. Again, the ators. The kinetics and thermodynamics of the silicon resome skull skull formation formation isskull observed in both both cases.at Again, the ators. The kinetics kinetics and relation thermodynamics of the theparameters silicon rere- some mechanism for makingis material available the ladle fining process and their to operational observed in cases. Again, the ators. The and thermodynamics of silicon mechanism for making skull material available at the ladle fining process and their relation to operational parameters mechanism for making skull material available at the ladle fining process and their relation to operational parameters walls is different in silicon refining ladles. are visualized in atheir simple manner. The operator can use mechanism for making skull material available at the ladle fining process and relation to operational parameters is different in silicon refining ladles. are visualized aa to simple manner. The can walls is different in refining ladles. are visualized in in simple manner. The operator can use use walls the simulation tool investigate how to operator respond properly walls is liquid different in silicon silicon refining ladles. are visualized in a to simple manner. The operator can use Slag in silicon forms an emulsion, since the slag does the simulation tool investigate how to respond properly the simulation tool to investigate how to respond properly to operational challenges. For example, what is the proper Slag in liquid silicon forms an emulsion, since the slag does the simulation tool to investigate how to respond properly Slag in liquid silicon forms an emulsion, since the slag not actually dissolve in the liquid metal. The of to operational challenges. For example, what is the proper Slag in liquid silicon forms an emulsion, since theblowing slag does does to operational challenges. For example, what is is the proper proper response if thechallenges. content of For a specific element exceeds cus- not actually dissolve in the liquid metal. The blowing of to operational example, what the not actually dissolve in the liquid metal. of oxygen and air ensures thorough mixing ofThe thisblowing emulsion, response if the content of a specific element exceeds cusnot actually dissolve in the liquid metal. The blowing of response if the content of a specific element exceeds customer specification? Theofmodel enables the operator tocusdo oxygen and air ensures thorough mixing of this emulsion, response if the content a specific element exceeds oxygen and air ensures thorough mixing of this emulsion, and consequently slag particles frequently come in contact tomer specification? The model enables the operator to do oxygen and air ensures thorough mixing of this emulsion, tomer specification? The model enables the operator to do a risk-free assessment of the system response to imposed and consequently slag particles particles frequently come in contact contact tomer specification? The model enables the operator to do and slag in withconsequently the ladle walls. Due to frequently differencescome in interfacial aachanges risk-free of system consequently slag particles frequently come in contact risk-free assessment of the the system response response to to imposed imposed and in assessment the operational parameters. with the ladle walls. Due to differences in interfacial a risk-free assessment of the system response to imposed with the ladle walls. Due to differences in interfacial tension, slags wet the ladle lining better than the liquid changes with theslags ladlewet walls. Due lining to differences in interfacial changes in in the the operational operational parameters. parameters. the ladle better than the liquid changes in the tension, slags wet the ladle lining better than the liquid silicon does, see e.g. Mills (2011). Over time, this will The purpose ofoperational this study parameters. is to investigate the inclusion tension, tension, slags see wete.g. the Mills ladle (2011). lining better than the liquid silicon does, Over time, this will The purpose of this study is to investigate the inclusion silicon does, see e.g. Mills (2011). Over time, this will The purpose of this study is to investigate the inclusion lead to a layer of liquid slag being formed at the walls. of a simple skull model in this tool, where skulls are silicon does, seeofe.g. Mills (2011). Over time, thiswalls. will The purpose of thismodel studyinis this to investigate theskulls inclusion lead to a layer liquid slag being formed at the of a simple skull tool, where are lead to a layer of liquid slag being formed at the walls. of a simple skull model in this tool, where skulls are Subsequent contact with slag the slag-in-metal emulsion may modelled as highly viscuous slag, with droplets of refinied lead to a layer of liquid being formed at the walls. of a simple skull model in this tool, where skulls are Subsequent contact with the slag-in-metal emulsion may modelled as highly viscuous slag, with droplets of refinied Subsequent contact with the slag-in-metal may modelled as highly highly viscuous slag, with droplets droplets of refinied refinied break free slag droplets, may add slagemulsion to the layer. silicon trapped within. Withslag, this addition, the simulation Subsequent contact with or theit slag-in-metal emulsion may modelled as viscuous with of break free slag droplets, or it may add slag to the layer. silicon trapped within. With this addition, the simulation break free slag droplets, or it may add slag to the layer. silicon trapped within. With this addition, the simulation This is very similar to what is observed in oil spills, where tool offers a complete package for analysing the silicon break free slag droplets, or it may add slag to the layer. silicon trapped within. With this addition, the simulation is very similar to what is observed in oil spills, where tool complete This tool offers offers a complete package package for for analysing analysing the the silicon silicon This This is is very very similar similar to to what what is is observed observed in in oil oil spills, spills, where where tool offers aa complete package for analysing the silicon Copyright © 2016, 2016 IFAC 187 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © IFAC (International Federation of Automatic Control) Copyright © 2016 IFAC 187 Copyright © 2016 IFAC 187 Peer review under responsibility of International Federation of Automatic Copyright © 2016 IFAC 187Control. 10.1016/j.ifacol.2016.10.116
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sea waves tend to break oil slicks apart, see Shaw (2003) or Moldestad et al. (2006). Oil droplets may afterwards remerge with the oil slick, sometimes in the form of waterin-oil emulsions, having water droplets trapped within. This dispersion is reduced over time, as the oil viscosity increases due to increased water content. This approach to studying slag entrainment in liquid metal was used by several authors, see e.g. Iguchi et al. (1994), Savolainen et al. (2009) or Hagemann et al. (2013), all agreeing that increased slag viscosity reduces the tendency of emulusification, and each yielding different quantitative relations between slag viscosity and their chosen metric for this tendency. It is well known that slag viscosity in the system SiO2 Al2 O3 - CaO depends strongly on the content of CaO and on temperature, see Schei et al. (1998). During the years, several slag viscosity models of varying complexity have been used and verified experimentally, see e.g. Kondratiev et al. (2002) for an overview. 2. THEORY 2.1 Viscosity model In order to keep the model as transparent as possible, it was decided to use a simple tabular viscosity model where the slag viscosity at the reference temperature depends only on the CaO content of the slag. The temperature dependence of the viscosity is modelled using an Arrheniustype relation as shown in (1), where η is the viscosity at temperature T, η0 is a reference viscosity, and R is the gas constant. The activation energy Eη is fitted to the experimental knowledge that an increase in temperature from 1500 to 1600◦ C approximately halves the slag viscosity, see Schei et al. (1998). η = η0 exp
Eη RT
(1)
2.2 Skull thickness Liquid slag, solid slag, and the ladle wall all have similar thermal conductivities, see e.g. Mills (2011). Thus, depositing a few millimeters of highly viscous or frozen slag on the ladle walls will not significantly influence the temperature distribution in the ladle. As a result, a heat balance across the ladle walls cannot be used to determine the thickness of this viscous layer. Another consequence is that the main contribution to the model from skulls formed in previous taps, is a change in ladle geometry. If slag with a viscosity higher than a given threshold value ηlim is considered immune to emulsification, this corresponds to a temperature Tlim determined by the viscosity model. If this temperature is far below the melt temperature, little or no skulls will be formed, but if the limiting temperature is close to the melt temperature, more skulls is formed. This is expressed in its most basic form in (2). ∆xs =
k (Tm − Tlim )
(2) 188
The proportionality constant k depends on the slag surface tension and on the slag density, both relative to the corresponding metal properties. The constant also depends on how well the ladle is stirred, expressed by the gas velocity. 3. IMPLEMENTATION 3.1 Overview The offline simulation tool models the refining by following the flow of gas bubbles from the bottom of the ladle, where it is injected through a bottom plug, and up to the bath surface. The gas is a combination of air and oxygen. The model calculates the concentrations of the different elements present on the slag film surrounding the bubble as they rise to the surface. Each time step, the model updates the bulk concentrations with the contributions from both the bubbles and surface reactions. This model formulation results in several state variables, describing the different melt and slag properties as a function of time and position. Two new state variables are added as part of the present work: newly formed skulls, or viscous layer, and frozen skulls from previous tappings. Each of these consists of several segments: one for each vertical step plus one for the bottom skulls. Each skull segment contains local values for the skull thickness, the vertical height at the top of the segment, the temperature at the wall-skull interface, and the amount of each constituent. The initial vertical step size is set to the increase in metal height per time step, but segments with similar thickness, temperature and composition are aggregated to increase the calculation speed. 3.2 Geometry The skulls influence the ladle geometry, for instance when finding the current metal height. The volume of the skulls at the ladle bottom is given by (3), where φ is the ladle cone angle, and the radius r0 is given by (4). It is here assumed that the skull thickness at the bottom is equal to the skull thickness of the lower vertical ladle segment.
Vs,b =
πr02 ∆xs
∆xs 1 ∆x2s 1+ tan(φ) + tan2 (φ) r0 3 r02 r0 = rB −
∆xs cos(φ)
(3) (4)
Since the skulls may have different thickness at different heights, the skull volume is calculated at each segment, and summed up to the current metal height. The skull volume for a vertical ladle segment of height H is given by (5), where r is the radius of the skull-free ladle at the bottom of the segment. Figure 1 shows a sketch of the skulls with the relevant dimensions used in (3) - (5)
Vs,H
∆xs = 2πrH cos(φ)
H ∆xs 1+ tan(φ) − 2r 2r cos(φ)
(5)
The user supplies a parameter indicating the mass fraction of the skulls that consists of silicon trapped in the highly
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175
Fig. 2. Weights routinely logged during operation
Fig. 1. Skull geometry viscous slag. Based on this, and on the available amounts of slag and silicon, (3) and (5) are summed for the current metal height, and solved numerically to find the corresponding maximum possible skull thickness. Espescially when the simulation starts, this may limit the skull growth. In general, the skulls resulting from one tapping form the starting-point of the next tapping. Thus, solidified slag and silicon from several tappings may be released by heating the ladle. The user may also select to set the skull thickness to zero before next tap, emulating ladle maintenance. 3.3 Composition The liquid phase is seen as homogeneous, thus having one composition at any given time, defined by the metal mass with impurities expressed as mass%, combined with the amounts of slag, expressed as mols of each constituent. The composition of the slag in the viscous layer of newly formed skulls depends on the slag composition at the time when material is added to this layer. The fraction of trapped liquid silicon is fixed, but the amount of impurities in the silicon will also depend on the liquid composition at the time material is added to the layer. As a consequence, the composition of the viscous layer will vary with vertical position in the ladle.
Fig. 3. Skull formation as a function of CaO content in slag high viscosity, the model does not include any enthalpy change related to the deposition. The viscous layer is assumed to freeze when the ladle is emptied, and the temperature decreases sufficiently. At the melt top, the melt temperature is modelled as a linear combination of the overall melt temperature and the temperature of the air just above the melt. As can be seen from (2), this reduction of Tm results in an increased ∆xs at the melt top, which is also observed during daily operation. 4. COMPARISON TO MEASUREMENTS 4.1 Interpretation of operational data
3.4 Heat balance The simulator considers heat loss from radiation from the melt top, conduction through the ladle walls and bottom, heating of additions, reaction heat, as well as heat added to the laddle through liquid silicon. Of these, only the heat loss through the ladle walls and bottom are directly related to the skull growth. The heat loss through the ladle walls and bottom is given by (6). Here, Aw and Ab are the interfacial areas between skulls and melt, at the ladle walls and bottom, respectively, hsm is the heat transfer coefficient between melt and viscous skull layer, Tsm is the temperature at the interface viscous skull layer - melt, and Tm is the temperature in the melt.
Operational data shows that the amount of skulls formed per tap depends strongly on the amount of Ca removed from the melt during refining. Intuitively, the amount of Ca removal is linked to the CaO concentration in the slag phase, which is again known to be strongly linked to slag viscosity. This is explored more quantitatively using mass balances for Ca, Si, O, and Al. These are combined with weights and concentrations routinely logged during operation,as visualized in figure 2. The rectangles represent positions where the ladle is weighed, and the text below the arrows represent material added or removed from the ladle between the weighings.
(6)
The result is shown in figure 3, where data from several weeks of operation is grouped into average values, each representing one specific ladle.
Since skull formation is not considered as freezing or reaction of any kind, just slag and melt with sufficiently
The low average skull growth for the groups in the lower right part of figure 3 results from a combination of mod-
Qloss cond
= (Aw + Ab )hsm (Tm − Tsm )
189
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erate negative and moderate positive values. On the other hand, the upper left group growth mostly results from large positive values, but also contains rare negative values, related to major clean-up operations. This indicates that the skulls formed from slags with high lime content not only form to a lesser degree, but are also easier to remove. 4.2 Skull thickness for single taps Within each of the groups used to aggregate data in 3, there are large variations. These variations may be related to the state of the equipment used, the operators’ degree of experience, etc. As a consequence, the simulator cannot predict these within-group variations in skull growth. On the other hand, in order to be useful, the simulator should show a large change in skull growth when the slag composition changes significantly. This is exemplified in tables 1 - 2, where two taps are compared. First, the relevant simulator parameters were fitted to the low Cameasurements. When transferring to the high Ca tap, the only simulator changes were the input parameters composition, feed rate and additions.
Fig. 4. Time variations in ladle weight
Table 1. Comparison at low Ca Variable Tap rate (tons/hr) Metal produced (kg) Slag produced (kg) CaO content in slag (%) Casting temperature (C) Skulls (kg)
Measured 3.04 6108 642 5 1474 220
Simulated
Fig. 5. Final temperatures and cooling effort
6166 614 5 1474 214
4.4 Heat balance If skulls influence the ladle heat balance, it would be expected that the temperature at the end of tappings with high skull growth would be significantly different from the end temperature of tappings with low skull growth. Or, one could expect that the effort to reach a suitable casting temperature would be different between the two groups. Both parameters are shown as a function of slag lime content in figure 5 for the same operational data as used earlier.
Table 2. Comparison at high Ca Variable Tap rate (tons/hr) Metal produced (kg) Slag produced (kg) CaO content in slag (%) Casting temperature (C) Skulls (kg)
Measured 3.43 7788 492 15 1478 140
Simulated 7802 557 13 1474 120
4.3 Skull growth over several taps Figure 4 shows the weight development over time for the material tapped from the furnace to one particular ladle. The data is for a product which gives a slag with low lime content, and thus significant skull growth. The sawtooth pattern reflects the operators filling the ladles to approximately the same height each tap, with increased deposition followed by maintenance, where skulls are removed. The blue asterisks on one of the sawtooths in figure 4 show the resulting tap weights from the simulator, where the parameters found in section 4.2 are used, only changing the input parameters composition and additions. For each tap, the total metal height from the bottom of the skull-free ladle was the same, fitted to the first tap in the series. The skulls were allowed to grow from tap to tap. This shows that a large portion of the periodic variations in observed amount tapped from the furnace can be described by the geometric change of the ladle as the skulls accumulate. It is also seen that the amount of skulls predicted by the simulator is similar to the amounts observed during normal operation. 190
It is seen that the temperature measured when the ladle is full does not correlate strongly with the average lime content in the slag. The cooling effort is somewhat higher for the tappings with high lime content in the slag, but this is related to the slightly lower casting temperature for this group, as can be seen in figure 5. In the simulator, this is explained by the largest sources of temperature change being the radiation loss from the top of the ladle and the heat of reaction from the refining reaction. A slight change in the temperature at the melt skull interface will thus not change the melt temperature significantly. 5. DISCUSSION The main assumptions made are listed and discussed below. Skulls can be seen as slag with silicon droplets trapped within This assumption is motivated from manual observations and analyses made when silicon ladles are maintained or
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refurbished. It is also similar to what is seen when oil spills are attacked by sea wavers. Skull formation is mainly determined by slag viscosity The operational data discussed in the present work, see figure 3, suggests the lime content of the slag as a factor that correlates well with the main trends in skull formation. Furthermore, the comparisons between measured and modelled skull growth in sections 4.2 and 4.3, suggest that the major variations in skull growth can be described by this model. A more rigorous parameter estimation will make the comparisons more accurate, and thus improve the understanding. The freeezing point of slag also correlates with the slag’s lime content. During normal operation, the temperatures at the ladle walls may not be low enough to allow actual freezing, but slag near its freezing point will be highly viscous and immobile. Slag with low lime content will also have a higher tendency to freeze once the ladle is emptied, thus causing more skull formation. Further investigations are required to determine if the composition-related variations in melting temperature of slag play an important role in the skull freezing that takes place when the ladle is empty. The simulator allows the user to choose between finding Tlim from a viscosity model or using the liquidus temperature for the current slag composition. Slag viscosity is mainly governed by slag temperature and lime content in the slag In future work, it may be useful to look into the effect of inclusions, as discussed by Schei et al. (1998), as well as the more advanced models reviewed by Kondratiev et al. (2002). The skull thickness can be estimated from a viscosity model and a single proportionality constant This is clearly a simplification, where such factors as how well the layer wets the wall, how well the layer molecules bond to each other, and also how easily the slag is transported through the melt are lumped together. For one particular process, where the slag and melt compositions do not vary much, and the ladle wall material is the same in all cases, this can be a useful approximation. For operator training at a specific plant, the simplification can be justified. On the other hand, for the model to improve the general understanding of skull formation, the different phenomena mentioned above should each be quantified. This improvement is also required if the model or simulator shall be used for slightly different processes, thus replacing processspecific lumped parameters with parameters that have a clear chemical interpretation. 6. CONCLUSION It is seen that modelling skulls as highly viscous slag, having low lime content, is useful in order to determine 191
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skull growth. The simple model presented here is able to predict the major variations in skull growth observed during operation. It is also able to predict the main effects of skull growth on ladle geometry and heat balance. Thus, the offline simulator’s use for training purposes is extended, now allowing the users to see the skull-related effects of their actions. In order to further improve the model, the lumped parameter currently describing the tendency of skull growth as a function of temperature, should be replaced with more fundamental slag and melt properties. In addition, more rigorous parameter estimation is required. Finally, the simulator should contain a more sofisticated viscosity model, regarding both inclusions, composition and temperature. ACKNOWLEDGEMENTS E. Nordg˚ ard-Hansen acknowledges the financial support provided by the Norwegian Research Council project CORRESI (contract no. 235159/O30). K. Hildal acknowledges the financial support provided by EC Spire project RECOBA (H2020-636820). REFERENCES Hagemann, R., Schwarze, R., Heller, H., and Scheller, P. (2013). Model investigations on the stability of the steel-slag interface in continuous-casting process. Metallurgical and Materials Transactions B: Process Metallurgy and Materials Processing Science, 44(1), 80– 90. Iguchi, M., Sumida, Y., Okada, R., and Morita, Z.i. (1994). Evaluation of critical gas flow rate for the entrapment of slag using a water model. ISIJ International, 34(2), 164–170. Kondratiev, A., Jak, E., and Hayes, P. (2002). Predicting slag viscosities in metallurgical systems. JOM, 54(11), 41–45. Mills, K. (2011). The estimation of slag properties. Short course presented as part of Southern African Pyrometallurgy 2011. Moldestad, M.Ø., Leirvik, F., Johansen, i., Daling, P.S., and Lewis, A. (2006). Environmental Emulsions: A Practical Approach, 365. CRC Press, 2 edition. Savolainen, J., Fabritius, T., and Mattila, O. (2009). Effect of fluid physical properties on the emulsification. ISIJ International, 49(1), 29–36. Schei, A., Tuset, J., and Tveit, H. (1998). Production of high silicon alloys. Tapir, Trondheim, Norway. Shaw, J. (2003). A microscopic view of oil slick break-up and emulsion formation in breaking waves. Spill Science and Technology Bulletin, 8(5-6), 491–501. Song, M., Ragnarsson, L., Nzotta, M., and Sichen, D. (2011). Mechanism study on formation and chemical changes of calcium aluminate inclusions containing SiO2 in ladle treatment of tool steel. Ironmaking and Steelmaking, 38(4), 263–272. Zhao, Y., Fu, D., Lherbier, L., Chen, Y., Zhou, C., and Grindey, J. (2014). Investigation of skull formation in a blast furnace hearth. Steel Research International, 85(5), 891–901.
ScienceDirect
Skull Skull Skull Skull
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formation in dynamic formation in formation in dynamic formation in dynamic dynamic silicon refining silicon silicon refining silicon refining refining
modelling modelling modelling modelling
of of of of
Ellen Nordg˚ ard-Hansen ∗∗ Kjetil Hildal ∗∗ ∗∗ ∗ Kjetil Hildal ∗∗ Ellen Nordg˚ ard-Hansen Ellen Nordg˚ ard-Hansen Ellen Nordg˚ ard-Hansen ∗ Kjetil Kjetil Hildal Hildal ∗∗ ∗ ∗ Teknova as, Gimlemoen 19, N-4630 Kristiansand, Norway (e-mail: ∗ Teknova as, Gimlemoen 19, N-4630 Kristiansand, Norway (e-mail: ∗ Teknova as, [email protected]). 19, Teknova as, [email protected]). 19, N-4630 N-4630 Kristiansand, Kristiansand, Norway Norway (e-mail: (e-mail: ∗∗ [email protected]). Elkem Technology, Fiskaaveien 100, N-4675 Kristiansand, Norway [email protected]). ∗∗ ∗∗ Technology, Fiskaaveien 100, N-4675 N-4675 Kristiansand, Kristiansand, Norway ∗∗ Elkem Elkem Fiskaaveien 100, Norway (e-mail: [email protected]) Elkem Technology, Technology, Fiskaaveien 100, N-4675 Kristiansand, Norway (e-mail: [email protected]) (e-mail: [email protected]) (e-mail: [email protected]) Abstract: An offline simulation tool for silicon refining is extended with an improved model Abstract: An offline for silicon extended improved model Abstract: An simulation tool for silicon refining is extended with an improved model for skull formation. In simulation this model,tool skulls are seen refining as highlyis viscous slagwith withan droplets of refined Abstract: An offline offline simulation tool forare silicon refining isviscous extended with androplets improved model for skull formation. In this model, skulls seen as highly slag with of refined for skull formation. In this model, skulls are seen as highly viscous slag with droplets of refined silicon trapped within. Since slag viscosity depends strongly on its lime content, the degree of for skull formation. In this model, skulls are seen as highly viscous slag with droplets of refined silicon trapped Since slag viscosity depends strongly on the of silicon trapped within. within. Sincehow slagmuch viscosity depends strongly on its its lime content, the degree degree of skull formation varies with calcium is removed from thelime melt.content, The skulls influence silicon trapped within. Since slag viscosity depends strongly on its lime content, the degree of skull formation with much is removed from the melt. The influence skull formation varies with how much calcium is from The skulls influence the geometry of varies the ladle as how well as the calcium heat balance, and accumulate from tap toskulls tap. It is seen skull formation varies with how much calcium is removed removed from the the melt. melt. Theto skulls influence the geometry of the ladle as well as the heat balance, and accumulate from tap tap. It is seen the geometry of the ladle as well as the heat balance, and accumulate from tap to tap. It is seen that the simulation results reflect data from normal operation. the geometry of the ladle as well as the heat balance, and accumulate from tap to tap. It is seen that the simulation results reflect data from normal operation. that the simulation results reflect data from normal operation. that the simulation results reflect data from normal operation. © 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Process simulators, Metals, Training, Slag, Viscosity Keywords: Keywords: Process Process simulators, simulators, Metals, Metals, Training, Training, Slag, Slag, Viscosity Viscosity Keywords: Process simulators, Metals, Training, Slag, Viscosity 1. INTRODUCTION refining process, and will be a valuable tool for the process 1. refining process, and will will be aa will valuable tool for the 1. INTRODUCTION INTRODUCTION refining process, and be valuable for the process process specialists. A similar model also tool be included in an 1. INTRODUCTION refining process, and will be a will valuable tool for the process specialists. A similar model also be included in an 1.1 Background specialists. A similar model will also be included inwith an online version of the model, which will communicate specialists. A similar model will also be included in an 1.1 Background online version of the model, which will communicate with 1.1 Background Background online version of the model, which will communicate with the control system. 1.1 online version of the model, which will communicate with During oxidative refining of silicon, liquid silicon is tapped the the control control system. system. the control system. During oxidative refining of silicon, liquid silicon is tapped During oxidative refining of silicon, silicon, liquid silicon of is air tapped from theoxidative furnace into a ladle, in which a mixture and 1.2 Previous work During refining of liquid silicon is tapped from the into aa ladle, in which which mixture of air air and 1.2 Previous work from theisfurnace furnace into ladle,the in mixture of and oxygen bubbled through melt. aa As a result, silicon from the furnace into a ladle, in which aAs mixture of air and 1.2 1.2 Previous Previous work work oxygen is bubbled through the melt. a result, silicon oxygen is bubbled through the melt. As a result, silicon oxide forms on the bubble-melt interfaces and also on the oxygen is bubbled through the melt. As a result, silicon Skull formation in silicon refining ladles has some traits oxide forms on the bubble-melt interfaces and also on the oxide forms on the theAsbubble-melt bubble-melt interfaces andimpurities also on on the the top melt surface. the refininginterfaces progresses, in Skull formation in silicon refining ladles some traits oxide forms on and also Skull formation in silicon refining ladles has has some traits in common with ladle glazing in steelmaking, as studied top melt surface. As the refining progresses, impurities in Skull formation in silicon refining ladles has some traits top surface. Asthe thesilicon refining progresses, impurities in in common with ladle the melt react with oxide to form metal oxides, glazing in steelmaking, as studied top melt surface. As the refining progresses, impurities in in common with ladle glazing in steelmaking, as studied by e.g. Song et al. (2011). Here also, a layer of slag the melt react with the silicon oxide to form metal oxides, in common with ladle glazing in steelmaking, as studied the melt react with the silicon oxide to form metal oxides, thereby transferring thesilicon impurities from themetal melt oxides, to the by e.g. Song et al. (2011). Here also, aathis layer of slag the melt transferring react with the oxide from to form by e.g. Song et al. (2011). Here also, layer of slag is also formed on the ladle walls, and layer may thereby the impurities the melt to the e.g. Song etonal.the (2011). Here athis layer of may slag thereby transferring theladle impurities from the melt meltmetal to the the slag phase. When the is full, from the refined is by is also walls, also, and layer thereby transferring the impurities the to is also formed formed ontap theto ladle ladle walls, and this layer may accumulate fromon tap, possibly contaminating the slag phase. When the ladle is full, the refined metal is is also formed the ladle walls, and this layer may slag phase. When the ladle is full, the refined metal is poured into molds, and the remaining slag is removed from tap to tap, possibly contaminating the slag phase. When the ladle isremaining full, the slag refined metal is accumulate accumulate from tap to tap, possibly contaminating the metal. However, the layer is formed when slag comes in poured into molds, and the is removed accumulate from tap to tap, possibly contaminating the poured intonext molds, and can the take remaining slag is removed removed before the tapping place. slag In genereal, the metal. However, the layer is formed when slag in poured into molds, and the remaining is metal. However, the layer is during formedladle whenteeming, slag comes comes in contact with the ladle walls which before the next tapping can take place. In genereal, the metal. However, the layer is formed when slag comes in before the next tapping can take place. In genereal, the empty the ladlenext weight increases fromplace. one tap to the next, ladle ladle which before tapping can take In genereal, the contact contact with the ladleinwalls walls during ladle teeming, teeming, which does notwith takethe place the during same manner as for silicon empty ladle weight from one to with the ladle walls during ladle teeming, which empty ladlesolidified weight increases increases from one istap tap to the the next, next, contact since some material, or skulls, deposited. does not take place in the same manner as for silicon empty ladle weight increases from one tap to the next, does not take place in the same manner as for silicon refining. So, a different mechanism is required to describe since some solidified material, or skulls, is deposited. does notSo, take place inmechanism the same is manner as to for silicon since some some solidified solidified material, material, or skulls, is is deposited. deposited. since refining. So, aaaofdifferent different mechanism is required to describe describe Skull formation is a challengeorinskulls, the day-to-day silicon refining. the presence skull material close is to required the walls. refining. So, different mechanism required to describe Skull formation is a challenge in the day-to-day silicon the presence of skull material close to the walls. Skull formation is a challenge in the day-to-day silicon the presence of skull material close to the walls. production, since excessive skull growth causes the ladle Skull formation isexcessive a challenge in the day-to-day silicon of askull the also walls. Thepresence freezing of solidmaterial layer onclose ladletowalls takes place production, since skull causes ladle the production, since excessive skull growth growth causes the the ladle to get smaller while at the same time changing The freezing of a solid layer on ladle walls also takes place production, since excessive skull growth causes the ladle The freezing of a solid layer on ladle walls also takes place in blast furnaces, as described by Zhao et al. (2014), who to get smaller while at the same time changing the ladle The freezing of a solid layer on ladle walls also takes place to get smaller while at the same time changing the ladle thermal balance. On the other hand, some skull formation in blast furnaces, as described by Zhao et al. (2014), who to get smaller while at the same time changing the ladle in blast furnaces, as described by Zhao et al. (2014), who among other things looked at how the skull thickness dethermal balance. On the other hand, some skull formation in blast furnaces, as described by Zhao et al. (2014), who thermal balance. On the other hand, some skull formation may be favourable, since the skulls protect the ladle walls among other things looked looked at howmetal. the skull skull thickness dethermal balance. Onsince the other hand,protect some skull formation among other things at how the thickness depends on the viscosity of the liquid However, typical may be favourable, the skulls the ladle walls other viscosity things looked at howmetal. the skull thickness demay be favourable, since the the skulls skulls protect protect the the ladle ladle walls walls among from be thefavourable, liquid metal. pends the However, typical may since pends on the viscosity oftemperature the liquid liquid metal. metal. However, typical values on forthe theviscosity liquidusof of slags relevant for from the liquid metal. pends on the of the liquid However, typical from the liquid metal. values for the liquidus temperature of slags relevant for from the liquid metal.simulation tool is used for internal values for the the varies liquidus temperature of1520 slags◦◦ C, relevant for indicating Currently, an offline silicon refining between 1370 and values for liquidus temperature of slags relevant for ◦ C, indicating Currently, an offline is internal varies between and ◦ C,inindicating Currently, aneducation offline simulation simulation tool is used used for forand internal silicon refining varies of between 1370 and 1520 1520 either refining solidification all or 1370 no slag, while practice training and of processtool metallurgists oper- silicon C,inindicating Currently, an offline simulation tool is used for internal silicon refining varies between 1370 and 1520 either solidification of all or no slag, while practice training and education of process metallurgists and opereither solidification of all or no slag, while in practice training and education of process metallurgists and opersome skull formation is observed in both cases. Again, the ators. The kinetics and thermodynamics of the silicon reeither solidification of all or noinslag, while in practice training and education of process metallurgists and opersome skull formation is observed both cases. Again, the ators. The kinetics and thermodynamics of the silicon resome skull skull formation formation isskull observed in both both cases.at Again, the ators. The kinetics kinetics and relation thermodynamics of the theparameters silicon rere- some mechanism for makingis material available the ladle fining process and their to operational observed in cases. Again, the ators. The and thermodynamics of silicon mechanism for making skull material available at the ladle fining process and their relation to operational parameters mechanism for making skull material available at the ladle fining process and their relation to operational parameters walls is different in silicon refining ladles. are visualized in atheir simple manner. The operator can use mechanism for making skull material available at the ladle fining process and relation to operational parameters is different in silicon refining ladles. are visualized aa to simple manner. The can walls is different in refining ladles. are visualized in in simple manner. The operator can use use walls the simulation tool investigate how to operator respond properly walls is liquid different in silicon silicon refining ladles. are visualized in a to simple manner. The operator can use Slag in silicon forms an emulsion, since the slag does the simulation tool investigate how to respond properly the simulation tool to investigate how to respond properly to operational challenges. For example, what is the proper Slag in liquid silicon forms an emulsion, since the slag does the simulation tool to investigate how to respond properly Slag in liquid silicon forms an emulsion, since the slag not actually dissolve in the liquid metal. The of to operational challenges. For example, what is the proper Slag in liquid silicon forms an emulsion, since theblowing slag does does to operational challenges. For example, what is is the proper proper response if thechallenges. content of For a specific element exceeds cus- not actually dissolve in the liquid metal. The blowing of to operational example, what the not actually dissolve in the liquid metal. of oxygen and air ensures thorough mixing ofThe thisblowing emulsion, response if the content of a specific element exceeds cusnot actually dissolve in the liquid metal. The blowing of response if the content of a specific element exceeds customer specification? Theofmodel enables the operator tocusdo oxygen and air ensures thorough mixing of this emulsion, response if the content a specific element exceeds oxygen and air ensures thorough mixing of this emulsion, and consequently slag particles frequently come in contact tomer specification? The model enables the operator to do oxygen and air ensures thorough mixing of this emulsion, tomer specification? The model enables the operator to do a risk-free assessment of the system response to imposed and consequently slag particles particles frequently come in contact contact tomer specification? The model enables the operator to do and slag in withconsequently the ladle walls. Due to frequently differencescome in interfacial aachanges risk-free of system consequently slag particles frequently come in contact risk-free assessment of the the system response response to to imposed imposed and in assessment the operational parameters. with the ladle walls. Due to differences in interfacial a risk-free assessment of the system response to imposed with the ladle walls. Due to differences in interfacial tension, slags wet the ladle lining better than the liquid changes with theslags ladlewet walls. Due lining to differences in interfacial changes in in the the operational operational parameters. parameters. the ladle better than the liquid changes in the tension, slags wet the ladle lining better than the liquid silicon does, see e.g. Mills (2011). Over time, this will The purpose ofoperational this study parameters. is to investigate the inclusion tension, tension, slags see wete.g. the Mills ladle (2011). lining better than the liquid silicon does, Over time, this will The purpose of this study is to investigate the inclusion silicon does, see e.g. Mills (2011). Over time, this will The purpose of this study is to investigate the inclusion lead to a layer of liquid slag being formed at the walls. of a simple skull model in this tool, where skulls are silicon does, seeofe.g. Mills (2011). Over time, thiswalls. will The purpose of thismodel studyinis this to investigate theskulls inclusion lead to a layer liquid slag being formed at the of a simple skull tool, where are lead to a layer of liquid slag being formed at the walls. of a simple skull model in this tool, where skulls are Subsequent contact with slag the slag-in-metal emulsion may modelled as highly viscuous slag, with droplets of refinied lead to a layer of liquid being formed at the walls. of a simple skull model in this tool, where skulls are Subsequent contact with the slag-in-metal emulsion may modelled as highly viscuous slag, with droplets of refinied Subsequent contact with the slag-in-metal may modelled as highly highly viscuous slag, with droplets droplets of refinied refinied break free slag droplets, may add slagemulsion to the layer. silicon trapped within. Withslag, this addition, the simulation Subsequent contact with or theit slag-in-metal emulsion may modelled as viscuous with of break free slag droplets, or it may add slag to the layer. silicon trapped within. With this addition, the simulation break free slag droplets, or it may add slag to the layer. silicon trapped within. With this addition, the simulation This is very similar to what is observed in oil spills, where tool offers a complete package for analysing the silicon break free slag droplets, or it may add slag to the layer. silicon trapped within. With this addition, the simulation is very similar to what is observed in oil spills, where tool complete This tool offers offers a complete package package for for analysing analysing the the silicon silicon This This is is very very similar similar to to what what is is observed observed in in oil oil spills, spills, where where tool offers aa complete package for analysing the silicon Copyright © 2016, 2016 IFAC 187 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © IFAC (International Federation of Automatic Control) Copyright © 2016 IFAC 187 Copyright © 2016 IFAC 187 Peer review under responsibility of International Federation of Automatic Copyright © 2016 IFAC 187Control. 10.1016/j.ifacol.2016.10.116
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sea waves tend to break oil slicks apart, see Shaw (2003) or Moldestad et al. (2006). Oil droplets may afterwards remerge with the oil slick, sometimes in the form of waterin-oil emulsions, having water droplets trapped within. This dispersion is reduced over time, as the oil viscosity increases due to increased water content. This approach to studying slag entrainment in liquid metal was used by several authors, see e.g. Iguchi et al. (1994), Savolainen et al. (2009) or Hagemann et al. (2013), all agreeing that increased slag viscosity reduces the tendency of emulusification, and each yielding different quantitative relations between slag viscosity and their chosen metric for this tendency. It is well known that slag viscosity in the system SiO2 Al2 O3 - CaO depends strongly on the content of CaO and on temperature, see Schei et al. (1998). During the years, several slag viscosity models of varying complexity have been used and verified experimentally, see e.g. Kondratiev et al. (2002) for an overview. 2. THEORY 2.1 Viscosity model In order to keep the model as transparent as possible, it was decided to use a simple tabular viscosity model where the slag viscosity at the reference temperature depends only on the CaO content of the slag. The temperature dependence of the viscosity is modelled using an Arrheniustype relation as shown in (1), where η is the viscosity at temperature T, η0 is a reference viscosity, and R is the gas constant. The activation energy Eη is fitted to the experimental knowledge that an increase in temperature from 1500 to 1600◦ C approximately halves the slag viscosity, see Schei et al. (1998). η = η0 exp
Eη RT
(1)
2.2 Skull thickness Liquid slag, solid slag, and the ladle wall all have similar thermal conductivities, see e.g. Mills (2011). Thus, depositing a few millimeters of highly viscous or frozen slag on the ladle walls will not significantly influence the temperature distribution in the ladle. As a result, a heat balance across the ladle walls cannot be used to determine the thickness of this viscous layer. Another consequence is that the main contribution to the model from skulls formed in previous taps, is a change in ladle geometry. If slag with a viscosity higher than a given threshold value ηlim is considered immune to emulsification, this corresponds to a temperature Tlim determined by the viscosity model. If this temperature is far below the melt temperature, little or no skulls will be formed, but if the limiting temperature is close to the melt temperature, more skulls is formed. This is expressed in its most basic form in (2). ∆xs =
k (Tm − Tlim )
(2) 188
The proportionality constant k depends on the slag surface tension and on the slag density, both relative to the corresponding metal properties. The constant also depends on how well the ladle is stirred, expressed by the gas velocity. 3. IMPLEMENTATION 3.1 Overview The offline simulation tool models the refining by following the flow of gas bubbles from the bottom of the ladle, where it is injected through a bottom plug, and up to the bath surface. The gas is a combination of air and oxygen. The model calculates the concentrations of the different elements present on the slag film surrounding the bubble as they rise to the surface. Each time step, the model updates the bulk concentrations with the contributions from both the bubbles and surface reactions. This model formulation results in several state variables, describing the different melt and slag properties as a function of time and position. Two new state variables are added as part of the present work: newly formed skulls, or viscous layer, and frozen skulls from previous tappings. Each of these consists of several segments: one for each vertical step plus one for the bottom skulls. Each skull segment contains local values for the skull thickness, the vertical height at the top of the segment, the temperature at the wall-skull interface, and the amount of each constituent. The initial vertical step size is set to the increase in metal height per time step, but segments with similar thickness, temperature and composition are aggregated to increase the calculation speed. 3.2 Geometry The skulls influence the ladle geometry, for instance when finding the current metal height. The volume of the skulls at the ladle bottom is given by (3), where φ is the ladle cone angle, and the radius r0 is given by (4). It is here assumed that the skull thickness at the bottom is equal to the skull thickness of the lower vertical ladle segment.
Vs,b =
πr02 ∆xs
∆xs 1 ∆x2s 1+ tan(φ) + tan2 (φ) r0 3 r02 r0 = rB −
∆xs cos(φ)
(3) (4)
Since the skulls may have different thickness at different heights, the skull volume is calculated at each segment, and summed up to the current metal height. The skull volume for a vertical ladle segment of height H is given by (5), where r is the radius of the skull-free ladle at the bottom of the segment. Figure 1 shows a sketch of the skulls with the relevant dimensions used in (3) - (5)
Vs,H
∆xs = 2πrH cos(φ)
H ∆xs 1+ tan(φ) − 2r 2r cos(φ)
(5)
The user supplies a parameter indicating the mass fraction of the skulls that consists of silicon trapped in the highly
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175
Fig. 2. Weights routinely logged during operation
Fig. 1. Skull geometry viscous slag. Based on this, and on the available amounts of slag and silicon, (3) and (5) are summed for the current metal height, and solved numerically to find the corresponding maximum possible skull thickness. Espescially when the simulation starts, this may limit the skull growth. In general, the skulls resulting from one tapping form the starting-point of the next tapping. Thus, solidified slag and silicon from several tappings may be released by heating the ladle. The user may also select to set the skull thickness to zero before next tap, emulating ladle maintenance. 3.3 Composition The liquid phase is seen as homogeneous, thus having one composition at any given time, defined by the metal mass with impurities expressed as mass%, combined with the amounts of slag, expressed as mols of each constituent. The composition of the slag in the viscous layer of newly formed skulls depends on the slag composition at the time when material is added to this layer. The fraction of trapped liquid silicon is fixed, but the amount of impurities in the silicon will also depend on the liquid composition at the time material is added to the layer. As a consequence, the composition of the viscous layer will vary with vertical position in the ladle.
Fig. 3. Skull formation as a function of CaO content in slag high viscosity, the model does not include any enthalpy change related to the deposition. The viscous layer is assumed to freeze when the ladle is emptied, and the temperature decreases sufficiently. At the melt top, the melt temperature is modelled as a linear combination of the overall melt temperature and the temperature of the air just above the melt. As can be seen from (2), this reduction of Tm results in an increased ∆xs at the melt top, which is also observed during daily operation. 4. COMPARISON TO MEASUREMENTS 4.1 Interpretation of operational data
3.4 Heat balance The simulator considers heat loss from radiation from the melt top, conduction through the ladle walls and bottom, heating of additions, reaction heat, as well as heat added to the laddle through liquid silicon. Of these, only the heat loss through the ladle walls and bottom are directly related to the skull growth. The heat loss through the ladle walls and bottom is given by (6). Here, Aw and Ab are the interfacial areas between skulls and melt, at the ladle walls and bottom, respectively, hsm is the heat transfer coefficient between melt and viscous skull layer, Tsm is the temperature at the interface viscous skull layer - melt, and Tm is the temperature in the melt.
Operational data shows that the amount of skulls formed per tap depends strongly on the amount of Ca removed from the melt during refining. Intuitively, the amount of Ca removal is linked to the CaO concentration in the slag phase, which is again known to be strongly linked to slag viscosity. This is explored more quantitatively using mass balances for Ca, Si, O, and Al. These are combined with weights and concentrations routinely logged during operation,as visualized in figure 2. The rectangles represent positions where the ladle is weighed, and the text below the arrows represent material added or removed from the ladle between the weighings.
(6)
The result is shown in figure 3, where data from several weeks of operation is grouped into average values, each representing one specific ladle.
Since skull formation is not considered as freezing or reaction of any kind, just slag and melt with sufficiently
The low average skull growth for the groups in the lower right part of figure 3 results from a combination of mod-
Qloss cond
= (Aw + Ab )hsm (Tm − Tsm )
189
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erate negative and moderate positive values. On the other hand, the upper left group growth mostly results from large positive values, but also contains rare negative values, related to major clean-up operations. This indicates that the skulls formed from slags with high lime content not only form to a lesser degree, but are also easier to remove. 4.2 Skull thickness for single taps Within each of the groups used to aggregate data in 3, there are large variations. These variations may be related to the state of the equipment used, the operators’ degree of experience, etc. As a consequence, the simulator cannot predict these within-group variations in skull growth. On the other hand, in order to be useful, the simulator should show a large change in skull growth when the slag composition changes significantly. This is exemplified in tables 1 - 2, where two taps are compared. First, the relevant simulator parameters were fitted to the low Cameasurements. When transferring to the high Ca tap, the only simulator changes were the input parameters composition, feed rate and additions.
Fig. 4. Time variations in ladle weight
Table 1. Comparison at low Ca Variable Tap rate (tons/hr) Metal produced (kg) Slag produced (kg) CaO content in slag (%) Casting temperature (C) Skulls (kg)
Measured 3.04 6108 642 5 1474 220
Simulated
Fig. 5. Final temperatures and cooling effort
6166 614 5 1474 214
4.4 Heat balance If skulls influence the ladle heat balance, it would be expected that the temperature at the end of tappings with high skull growth would be significantly different from the end temperature of tappings with low skull growth. Or, one could expect that the effort to reach a suitable casting temperature would be different between the two groups. Both parameters are shown as a function of slag lime content in figure 5 for the same operational data as used earlier.
Table 2. Comparison at high Ca Variable Tap rate (tons/hr) Metal produced (kg) Slag produced (kg) CaO content in slag (%) Casting temperature (C) Skulls (kg)
Measured 3.43 7788 492 15 1478 140
Simulated 7802 557 13 1474 120
4.3 Skull growth over several taps Figure 4 shows the weight development over time for the material tapped from the furnace to one particular ladle. The data is for a product which gives a slag with low lime content, and thus significant skull growth. The sawtooth pattern reflects the operators filling the ladles to approximately the same height each tap, with increased deposition followed by maintenance, where skulls are removed. The blue asterisks on one of the sawtooths in figure 4 show the resulting tap weights from the simulator, where the parameters found in section 4.2 are used, only changing the input parameters composition and additions. For each tap, the total metal height from the bottom of the skull-free ladle was the same, fitted to the first tap in the series. The skulls were allowed to grow from tap to tap. This shows that a large portion of the periodic variations in observed amount tapped from the furnace can be described by the geometric change of the ladle as the skulls accumulate. It is also seen that the amount of skulls predicted by the simulator is similar to the amounts observed during normal operation. 190
It is seen that the temperature measured when the ladle is full does not correlate strongly with the average lime content in the slag. The cooling effort is somewhat higher for the tappings with high lime content in the slag, but this is related to the slightly lower casting temperature for this group, as can be seen in figure 5. In the simulator, this is explained by the largest sources of temperature change being the radiation loss from the top of the ladle and the heat of reaction from the refining reaction. A slight change in the temperature at the melt skull interface will thus not change the melt temperature significantly. 5. DISCUSSION The main assumptions made are listed and discussed below. Skulls can be seen as slag with silicon droplets trapped within This assumption is motivated from manual observations and analyses made when silicon ladles are maintained or
IFAC MMM 2016 Vienna, Austria. Aug 31 - Sept 2, 2016 Ellen Nordgård-Hansen et al. / IFAC-PapersOnLine 49-20 (2016) 173–177
refurbished. It is also similar to what is seen when oil spills are attacked by sea wavers. Skull formation is mainly determined by slag viscosity The operational data discussed in the present work, see figure 3, suggests the lime content of the slag as a factor that correlates well with the main trends in skull formation. Furthermore, the comparisons between measured and modelled skull growth in sections 4.2 and 4.3, suggest that the major variations in skull growth can be described by this model. A more rigorous parameter estimation will make the comparisons more accurate, and thus improve the understanding. The freeezing point of slag also correlates with the slag’s lime content. During normal operation, the temperatures at the ladle walls may not be low enough to allow actual freezing, but slag near its freezing point will be highly viscous and immobile. Slag with low lime content will also have a higher tendency to freeze once the ladle is emptied, thus causing more skull formation. Further investigations are required to determine if the composition-related variations in melting temperature of slag play an important role in the skull freezing that takes place when the ladle is empty. The simulator allows the user to choose between finding Tlim from a viscosity model or using the liquidus temperature for the current slag composition. Slag viscosity is mainly governed by slag temperature and lime content in the slag In future work, it may be useful to look into the effect of inclusions, as discussed by Schei et al. (1998), as well as the more advanced models reviewed by Kondratiev et al. (2002). The skull thickness can be estimated from a viscosity model and a single proportionality constant This is clearly a simplification, where such factors as how well the layer wets the wall, how well the layer molecules bond to each other, and also how easily the slag is transported through the melt are lumped together. For one particular process, where the slag and melt compositions do not vary much, and the ladle wall material is the same in all cases, this can be a useful approximation. For operator training at a specific plant, the simplification can be justified. On the other hand, for the model to improve the general understanding of skull formation, the different phenomena mentioned above should each be quantified. This improvement is also required if the model or simulator shall be used for slightly different processes, thus replacing processspecific lumped parameters with parameters that have a clear chemical interpretation. 6. CONCLUSION It is seen that modelling skulls as highly viscous slag, having low lime content, is useful in order to determine 191
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skull growth. The simple model presented here is able to predict the major variations in skull growth observed during operation. It is also able to predict the main effects of skull growth on ladle geometry and heat balance. Thus, the offline simulator’s use for training purposes is extended, now allowing the users to see the skull-related effects of their actions. In order to further improve the model, the lumped parameter currently describing the tendency of skull growth as a function of temperature, should be replaced with more fundamental slag and melt properties. In addition, more rigorous parameter estimation is required. Finally, the simulator should contain a more sofisticated viscosity model, regarding both inclusions, composition and temperature. ACKNOWLEDGEMENTS E. Nordg˚ ard-Hansen acknowledges the financial support provided by the Norwegian Research Council project CORRESI (contract no. 235159/O30). K. Hildal acknowledges the financial support provided by EC Spire project RECOBA (H2020-636820). REFERENCES Hagemann, R., Schwarze, R., Heller, H., and Scheller, P. (2013). Model investigations on the stability of the steel-slag interface in continuous-casting process. Metallurgical and Materials Transactions B: Process Metallurgy and Materials Processing Science, 44(1), 80– 90. Iguchi, M., Sumida, Y., Okada, R., and Morita, Z.i. (1994). Evaluation of critical gas flow rate for the entrapment of slag using a water model. ISIJ International, 34(2), 164–170. Kondratiev, A., Jak, E., and Hayes, P. (2002). Predicting slag viscosities in metallurgical systems. JOM, 54(11), 41–45. Mills, K. (2011). The estimation of slag properties. Short course presented as part of Southern African Pyrometallurgy 2011. Moldestad, M.Ø., Leirvik, F., Johansen, i., Daling, P.S., and Lewis, A. (2006). Environmental Emulsions: A Practical Approach, 365. CRC Press, 2 edition. Savolainen, J., Fabritius, T., and Mattila, O. (2009). Effect of fluid physical properties on the emulsification. ISIJ International, 49(1), 29–36. Schei, A., Tuset, J., and Tveit, H. (1998). Production of high silicon alloys. Tapir, Trondheim, Norway. Shaw, J. (2003). A microscopic view of oil slick break-up and emulsion formation in breaking waves. Spill Science and Technology Bulletin, 8(5-6), 491–501. Song, M., Ragnarsson, L., Nzotta, M., and Sichen, D. (2011). Mechanism study on formation and chemical changes of calcium aluminate inclusions containing SiO2 in ladle treatment of tool steel. Ironmaking and Steelmaking, 38(4), 263–272. Zhao, Y., Fu, D., Lherbier, L., Chen, Y., Zhou, C., and Grindey, J. (2014). Investigation of skull formation in a blast furnace hearth. Steel Research International, 85(5), 891–901.