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Paper on modeling of iron ore pelletizing furnace for induration
  Dynamic simulation of pellet induration process in straight-grate system Mansoor Barati ⁎ Department of Materials Science & Engineering, University of Toronto, WB140-184 College Street, Toronto, ON, Canada M5S 3E4 a b s t r a c ta r t i c l e i n f o  Article history: Received 21 October 2007Received in revised form 16 July 2008Accepted 3 September 2008Available online 19 September 2008 Keywords: Mathematical modelingPellet indurationStraight gratePellet shrinkageIron ore pelletizing A mathematical model of pellet induration process in the straight-grate system is presented. The importantphysical and chemical phenomena known to affect the heat and mass transfer in the process have been takeninto account in the formulation of the model. These include heat transfer between gas and pellet, gas  󿬂 ow,evaporation and condensation of moisture, oxidation of magnetite, combustion of coke breeze, calcination of lime and dolomite, and shrinkage of pellet and pellet bed slump. The model is validated by comparing itspredictions against actual measurements in an industrial scale plant as well as a pilot pot grate. The effect of several process parameters on the induration regime are evaluated using the model. It is demonstratedthrough a case study that the model can be employed as a valuable tool for such purposes as processoptimization and design of the induration machine.© 2008 Elsevier B.V. All rights reserved. 1. Introduction Production of pellet as a desirable feedstock for ironmakingfurnaces has exceeded 300 Mt per year in 2005, accounting forabout 24% of the iron ore processed globally (UNCTAD, 2006). Theproduction of iron ore pellets involves two major steps, forming the “ green ”  pellets in rotary disks or drums, followed by heat hardeningthem subsequently at elevated temperatures around 1200 to 1400 °Cto increase the pellet strength.The heat hardening or  “ induration ”  of pellets employs one of thethree conventional furnace types: vertical shaft furnace, grate-kilnsystem, and travelling straight grate. The latter process that wasprimarily developed by Lurgi and is currently owned by OutoKumpuTechnology,accountsfortwothirdsof theworld'sinstalledpelletizingprocesses capacity. This study is focused on simulation of pelletinduration process in the straight-grate system. 1.1. Description of induration process in straight-grate machine Fig. 1 depicts schematic of a typical straight-grate indurationsystem. The grate bars 󿬁 xed on a moving strand are 󿬁 rst covered witha layer of burnt pellet, known as hearth-layer. The green pelletscontaining 7 to 9 wt.% free moisture and 10 to 14 mm in size are thenfed onto this layer and travel together with the sub-layer throughseveralthermalzonesof thefurnace.Theroleof theheartlayerpelletsis to act as a neutral heat absorbing media and protect the grate barsfrom excessive gas temperatures. The induration process in travellinggrate typically consists of four distinct phases: drying, preheating, 󿬁 ring, and cooling. The  󿬁 rst stage of drying is updraft to preventcondensation of water and consequential pellet deformation in thebottom layers of the pellet bed. Drying is continued in a subsequentdowndraft stageby relativelyhot gasescomingfromthe 󿬁 ring zoneof the furnace. The rate of heat transfer and moisture removal has to becontrolled in a certain range, as otherwise spalling may occur. In thepreheating phase, pellets are heated to about 1000 °C by downdraftgas  󿬂 owing through the bed. Hot gas is typically recycled from thecoolingzoneandaugmentedwithauxiliaryheatfromhoodburners,if required.Duringthisphase,pelletsarecompletelydriedandreactionssuch as decomposition of carbonates (e.g. lime, dolomite), magnetiteoxidation and coke combustion take place. The reactions continue inthe  󿬁 ring stage, where the gas temperature is raised to ~1350 °C. Thestrength of the pellets increases at this stage because of recrystalliza-tion, sintering and formation of partially liquid phases. The pelletporosity on the other hand is decreased. Temperature and  󿬂 owrate of gas together with the duration of the  󿬁 ring phase have to becontrolled with care to produce pellets of high strength and adequateporosity. Someof the off-gasfrom the 󿬁 ringzoneis recuperatedtothedrying zone after mixing with air. The remainder of the gas is ventedoff through the stack.The induration zone of the furnace is generally divided into severalsections and the gas  󿬂 owrate through each section is controlled by aseparatefan.Thisisintendedtoprovidetheoperatorwiththe 󿬂 exibilityof controlling the heating pro 󿬁 le for better pellet quality and grate barprotection.After 󿬁 ring,burntpelletsundergocoolingwhereambientairis drawn upward through the bed. The hearth layer prevents a severethermalshocktothepelletsbypreheatingtheair.Theoff-gasleavingthe Int. J. Miner. Process. 89 (2008) 30 – 39 ⁎  Tel.: +1 416 978 5637; fax: +1 416 978 4155. E-mail address:  mansoor.barati@utoronto.ca.0301-7516/$  –  see front matter © 2008 Elsevier B.V. All rights reserved.doi:10.1016/j.minpro.2008.09.008 Contents lists available at ScienceDirect Int. J. Miner. Process.  journal homepage: www.elsevier.com/locate/ijminpro  early stage of cooling has a temperature around 1000 °C. The gas isdirectedtothe 󿬁 ringandpreheatingzoneswhereisitfurtherheatedbythe burners. The gases from the later stages of cooling have lowertemperature, hence they are used for drying of pellets.It is clear from the description of the process that considerableattention has been paid to enhancing the energy ef  󿬁 ciency of theoverallprocess.Numerousadvancementshavebeenmadethatenablethe operators to alter the process conditions (e.g. gas  󿬂 ow andtemperature,gratespeed,etc.)andachievebothhighpelletqualityandlowenergyconsumption.However,optimizationofthermaltreatmentof pellet is inherently an iterative process and determination of theoptimumoperatingconditionsinaworkingplantisextremelydif  󿬁 cult,time consuming and costly. Besides, the measurement of criticalprocess data such as temperature within the pellet bed is virtuallyimpossible. As a result, induration processes have traditionally reliedon laboratory pot grate test results for determination of optimumdesignandoperatingparameters.However,resultsofasinglepotgrateexperiment are de 󿬁 cient in making distinction between the effects of different variables on the heating pro 󿬁 le and pellet quality. On theother hand, a complete study of the effect of even one variable on theprocess requires numerous experiments, with other variables keptunchanged. Also, pilot tests do not directly provide information onlocal interactions, reactions rates and heat and material balance. As acomplementary, and sometimes alternative, method of processanalysis, mathematical modeling has been put forward (Young,1963)soon after the pelletizing technologies came on stream. 1.2. Previous models of pellet induration in straight-grate machine The srcinal works on calculation of temperature pro 󿬁 le in movingpellet bedsdate backtoover fourdecadesago.Earlystudiesonapurelytheoretical approach to modeling of the process by Hasenack et al.(1975)andVoskampandBrasz(1975)presentedsigni 󿬁 cantinsightsintothe details which have to be considered. Hasenack et al. took intoaccountconvectiveheattransferaswellasconductionresistancewithineach pellet. Intheircalculations, theyomitted to considercalcinationof carbonates as well as oxidation of carbon since they used non- 󿬂 uxedpellet with no addition of carbonaceous materials. They collected veryvaluable information from an operating plant and showed that theirmodel provided satisfactory agreement with the measurements.Voskamp and Braz assumed that the temperature gradient inside eachpelletisnegligible.Theyfurtherapproximatedthermalpropertiesofgas,pellet and grate bar with constant values in each furnace zone.Following these pioneers, a substantial number of models havebeen put forward for iron ore sintering (Cumming and Thurlby,1990;Young, 1977), and pellet induration in shaft furnaces (Norgate et al.,1985)), grate-kiln system (Cross and Young,1976; Davis and Englund,2003; Pape et al., 1976; Thurlby, 1988a,b,c; Young et al., 1979), andtravelling grate machine (Drugge,1975,1981; Breitholtz and Hillberg,1980; Thurlby et al.,1979). Several authors have also simulated pelletinduration in pot grate (Kucukada et al., 1994; Seshadri and da SilvaPereira, 1985). Wynnyckyj and Batterham (1985) have presented a comprehensive review of the physical and chemical phenomenapertaining to sintering and pellet  󿬁 ring and the approaches towardsmodeling of such phenomena.Despitetheconsiderablestudiesonmodelingoftheseprocessesandpellet induration in particular, only a few have developed a model forstraight-grate induration process consisting of complete drying,  󿬁 ringandcoolingcycles.Inaddition,eachmodelhasbeendevelopedbytakingintoaccountafewofthemanyreactionsandphysicalchangesinvolved.One phenomenon that is generally overlooked, yet plays a signi 󿬁 cantrole in the process performance, is variations of pellet porosity andcorresponding bed shrinkage as the pellet bed passes through differentthermalzonesofthefurnace.Thepresentarticledescribesdevelopmentand validation of a complete mathematical model for pellet indurationby the straight-grate method. The major improvements over theprevious studies in this area are  󿬁 rst, including all important reactionsin the model and second, taking into account pellet shrinkage and theresulting pellet bed slump as they undergo the thermal treatment. Themodelisbasedentirelyontheexistingknowledgepertainingtophysicaland chemical changes in the pellet induration process. 2. Mathematical model The mathematical model is developed to predict the detailedprocess information includingtemperature, 󿬂 owrateandcompositionof gases, rate and extent of progress for the reactions, porosity andchemical composition of pellet, and bed slump at any position and indifferent times. In the formulation of the model, the followingphenomena have been taken into account.i. Heattransferbetweenpelletandgaswithtemperatureandcom-position dependent thermophysical properties for both phasesii. Evaporation and condensation of moistureiii. Oxidation of magnetiteiv. Calcinations of limestone (CaCO 3 ) and dolomite ((Ca,Mg)CO 3 )v. Combustion of carbon (e.g. coke breeze)vi. ReductioninpelletporosityandthecorrespondingbedshrinkageCertain assumptions with acceptablysmall impacton the accuracyof calculations were made. These include:i. The induration process is at steady state conditionsii. Gas distribution through the pellet bed is uniform, i.e. nochanneling of the gas occursiii. Thethermalconductivityofindividualpelletsisin 󿬁 nitelyhighsothat temperature gradient within each pellet can be neglectediv. Thepelletbedisrepresentedasaporouspackedbedofuniformlysized spheresv. Vertical gas velocity is much greater than the horizontal gratespeed Fig.1.  Schematic diagram of the straight-grate pellet induration system.31 M. Barati / Int. J. Miner. Process. 89 (2008) 30 –  39  vi. Heatconductionwithinthepelletbedisinsigni 󿬁 cantrelativetothe convective gas – solid heat transfer ratevii. Heat losses are limited only to the initial heat storage in thegrate barsviii. Heat released/absorbed by the chemical reactions is solelyexchanged with the solids, except the heat of moisturecondensation that is split equally between gas and solid.The equations forming the mathematical model are presentedbelow. The de 󿬁 nition of all symbols is provided in nomenclature atthe end of the paper. Some thermokinetic properties and constantsthat have been used in the model development are given in theAppendix.  2.1. Heat transfer  The dominant heat transfer mechanisms are conduction andradiation between gas and pellet. Using an effective heat transfercoef  󿬁 cient( h )that containsthecontributionofradiation,thegoverningequations are given by: − GC   g  A T   g  A  z   ¼ hA T   g  − T   p   þ X  1 − α  i ð Þ R i Δ H  i  ð 1 Þ for the gas phase, and  ρ b C   p A T   p A  z   ¼ hA T   g  − T   p   −  X α  i R i Δ H  i  ð 2 Þ for the pellets.Thegas and pelletheattransferareais calculatedfrom:  A ¼ 6 1 − ε b ð Þ / d  p :  ð 3 Þ InEqs.(1)and(2), α  i isthe fractionofheatfrom i threaction,thatisretained by the solids. As indicated in the assumptions,  α  i  is set to 0.5for water vapor condensation and unity for all other reactions. It wasnoticed that because of a high heat transfer coef  󿬁 cient, the heat of reactions is immediately distributed between the two phases,regardless of the initial share of each phase from the heat.It is evident from Eqs. (1) and (2) that the heat transfer coef  󿬁 cienthas a signi 󿬁 cant contribution tothe rate of heat transfer. Awide rangeof correlations have been put forward by several authors forcalculation of the heat transfer coef  󿬁 cient in packed beds. Seshadriand Pereira (1986) evaluated the validity of different heat transferexpressions in predicting the temperature distribution for pellet bedsand concluded that Eq. (4) known as the Ranz – Marshall correlation(Ranz, 1952) correlation provides the best agreement between theexperimental and the calculated results.  Nu ¼ 2 : 0 þ 0 : 6  Re  p ε b   1 = 2 Pr  ð Þ 1 = 3 :  ð 4 Þ Thecoef  󿬁 cientforheattransfertothegratebar iscalculatedbytheequation presented by Voskamp and Bransz (1975)  Nu ¼ 5  Re ð Þ 1 = 2 :  ð 5 Þ It is important to note that the heat transfer coef  󿬁 cient calculatedfrom these equations has essentially the effect of radiation embeddedin, as it has been validated at high temperatures where radiation hasan appreciable contribution to the heat exchange.  2.2. Evaporation and condensation of moisture Thedryingofpelletcanbebestrepresentedbyathree stage model(Cumming and Thurlby,1990; Seshadri and da Silva Pereira,1985). Inthis model, before the pellet water content reaches a criticalconcentration, the rate of drying is controlled by mass transfer fromthe pellet surface to the gas bulk. The rate expression for this stage ispresented as: R w  ¼ k w  A w e g   − w  g     ð 6 Þ where the mass transfer coef  󿬁 cient,  k w , can be derived from acorrelation similar to that of the heat transfer coef  󿬁 cient (Keey,1972;Perry and Chilton, 1973) as: k w  ¼ D H  2 O d  p 2 : 0 þ 0 : 6  Re  p ε b   1 = 2 Sc ð Þ 1 = 3 # :  ð 7 Þ The saturation water vapor pressure of the gas,  w  g e ,  is calculatedfromtheequilibriumconditionsatthepelletsurfacetemperature.Thediffusivity of water vapor through the gas phase can be obtained fromthe correlation provided by Fuller et al. (1966). D H 2 O  ¼ 1 : 2  10 − 9 T  1 : 75  g  P   V  :  ð 8 Þ The value of criticalmoisture content was assumed to be120 kg/m 3 (Hasenack et al.,1975; Voskamp and Brasz,1975).Inthesecondstepofdrying,whenthepellethumiditydropsbelowthe critical concentration, an evaporation front penetrates toward thepellet centre and pore diffusionwithin the dryshell begins to play therole as the rate limiting step. A mixed control model consisting of tworesistances, diffusion through the dry shell and mass transfer in thegas phase, may be used to express the drying rate as: R w  ¼  A w e g   − w  g    1 k w þ r   p  r   p − r  w ð Þ 2 r  w D e H2O ð 9 Þ where D H 2 O e istheeffectivediffusioncoef  󿬁 cientofwatervaporthroughthepellet pores and is calculated from the following correlation (Perry andChilton,1973): D e H 2 O  ¼ D H 2 O ε  p τ   ð 10 Þ withtortuosity( τ  )relatedtothepelletporosity( ε   p )via(PerryandChilton,1973): τ  ¼ ε − 0 : 41  p  :  ð 11 Þ Towards the end of drying, the evaporation rate is controlled byheat transfer from the gas to the pellet and is represented by: R w  ¼ hA T   g   − T  w   Δ H  v r  w r   p :  ð 12 Þ The point of transition between the two latter mechanisms of drying is when the rate of drying in the heat transferred controlledregime becomes smaller than that of the mixed control regime.  T  w  inEq. (12) is wet bulb temperature and can be calculated throughiterative methods (Parsons, 2005) or expressions obtained byregression through the experimental data (Seshadri and da SilvaPereira, 1985), as presented in the Appendix.Condensation of water vapor occurs in the layers of pellet withtemperature lower than the saturation temperature of the gas. Eq. (6)presents the rate of condensation as a negative value and the heat of condensation is portioned equally between the gas and the pellets.  2.3. Chemical reactions The rates of all chemical reactions including decomposition of carbonates,combustionofcokeandoxidationofmagnetiteareexpressedusing a topochemical or unreacted shrinking core model (Levenspiel,1972). In this model, as schematically illustrated in Fig. 2, reaction commences at the pellet surface and progresses toward the centre,leaving behind a shell of reaction products (voidage in case of carbon). 32  M. Barati / Int. J. Miner. Process. 89 (2008) 30 –  39  For magnetite oxidation, the reaction consists of three steps:transfer of oxygen from the gas bulk to the pellet surface, porediffusion through the hematite layer, and interfacial surface reactionwith the magnetite particles, i.e.2Fe 3 O 4 þ 12O 2  Y  3Fe 2 O 3 :  ð 13 Þ Akineticmodelbasedonmixedcontrolmechanismandapplicableto the entire oxidation duration has beenproposed by Papanastassiouand Bitsianes (1973a) in the following form: dr  m dt   ¼ −  C   g  O 2 − C  e O 2    ρ m 4 r  2 m r  2 m k O2 þ  r  2 m D e O2 1 r  m −  1 r   p   þ  1 k  V m    ð 14 Þ where  k O 2  is the rate of oxygen gas phase mass transfer and ispresented by an equation similar to Eq. (7), with  D O 2  replacing  D H 2 O .Diffusivityof oxygen can becalculated from the correlationdevelopedby Fuller et al. (1966) D O 2  ¼ 9 : 2  10 − 10 T  1 : 75  g  P   V  :  ð 15 Þ k ′ m  in Eq. (14) is the  󿬁 rst order rate constant for magnetite oxidationwhichcanbecalculatedfromthecorrelationsgatheredfromliteratureand provided in the Appendix.An expression similar to Eq. (14) is valid for the rate of carboncombustion, with the difference being that the equilibrium oxygenconcentration is approximately zero in this case.Calcination of carbonates is controlled only by temperature andcan take place within the entire pellet when it reaches an appropriatetemperature. The rate of calcinations of dolomite or limestone is thusexpressed as: R l = d  ¼ k  V l = d m l = d  ð 16 Þ where  m l / d  is the concentration of the species of interest. Dolomite isconsideredtodecomposeastwoseparatecarbonatesCaCO 3 andMgCO 3 .It must be emphasized that in the reactions' sub-model, it isassumed that all of the considered reactions can take placesimultaneously with distinct boundaries.  2.4. Mass balance on gas and pellet  Thegas 󿬂 owrateinanysectionof themachineischie 󿬂 ydecidedbythe pressure drop across the bed, which is controlled by the fan draft.The equation proposed by Ergun (1952) relates the pressure gradientand gas  󿬂 ux as: A P  A  z   ¼ 150  μ   g   1 − ε b ð Þ 2 Φ d  p   2 ε 3 b  ρ  g  G þ 1 : 75 1 − ε b ð Þ Φ d  p ε 3 b  ρ  g  G 2 :  ð 17 Þ However, as the gas exchanges mass with solids through evapora-tion/condensation or other reactions, the quantity and compositionsof both phases change with time and position. The changes in the gas 󿬂 owrate and concentration of individual gas species are related to therate of reactions via Eqs. (18) and (19). A G A  z   ¼ X  − R i  ð 18 Þ A w i A  z   ¼ −  R i v  g  B i :  ð 19 Þ B i  in Eq. (19) is a stoichiometric coef  󿬁 cient relating the changes inthe mass of the reacting gas species to that of the solid through thecorresponding reaction  i . (1 for water, 32/928 for magnetite oxidationand so on).  v  g   is the super 󿬁 cial gas velocity and is calculated from: v  g   ¼  G  ρ  g  :  ð 20 Þ Concentration of pellet constituents also changes according to: A w  j A t   ¼ − R i 11 − ε b ð Þ :  ð 21 Þ  2.5. Pellet and bed shrinkage Gas  󿬂 owrate and temperature pro 󿬁 le of the pellet bed is stronglyin 󿬂 uenced by the compactness and the height of the pellet bed. Theprevious models of pellet induration in straight-grate have beendeveloped on the assumption that the pellet bed height remainsconstant during the process. However, it is well known that the pelletporosity decreases signi 󿬁 cantly after  󿬁 ring due to formation of semi-liquid slag phase and more importantly, due to solid state sintering(Wynnayckyj and Fahidy, 1974). It is important to consider in themodel formulation the changes in the pellet physical properties andtheir impact on the heat and mass transport phenomena.Wynnayckyj and Fahidy (1972) have indicated that the shrinkageof pellet is a thermally activated process and can be related to the 󿬁 ring time and temperature as  β  1 −  β  ¼ V  0 − V  t  V   p − V  t  ¼ k s t  n :  ð 22 Þ This equation can be rearranged and differentiated to provide therate of change in the pellet volume as: dV   p dt   ¼  nk s t  n − 1 1 þ k s t  n  V  t  − V  0 þ V  t  k s t  n 1 þ k s t  n   :  ð 23 Þ For a commercial iron ore concentrate, regression analysis of theirexperimental data yields the following expressions for  k s  and  n . k s  ¼ 3 : 3  10 21 exp − 77000 T     ð 24 Þ n ¼ 13 : 1850 − 1 : 58622  10 − 2 T   þ 4 : 88318  10 − 6 T  2 :  ð 25 Þ Fig. 2.  Schematic of the topochemical reaction progress model.33 M. Barati / Int. J. Miner. Process. 89 (2008) 30 –  39
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