Economic modelling of a ferrochrome furnace

Transcription

1 Economic modelling of feochome funce by W. Biemnn*, R.D. Comty, nd N.F. Dwson *Ppe witten on poject wok cied out in ptil fulfilment of B. Eng (Metllugy) J o u n l Synopsis All industil pocesses e economiclly diven, esulting in the eve incesing need fo pocess optimiztion in ode to sty competitive nd pofitble. Numeous models hs been published depicting the optimiztion of the w mteil usge in n c funce, s well s the theml nd electicl efficiency; howeve, to obtin holistic view of the cost-effectiveness of the pocess one needs to expnd the model to include the cost of ll the opetionl vibles. This poject theefoe imed to not only include the w mteil feeds nd powe consumption s input vibles, but lso the lbou, mintennce, nd envionmentl costs to genete n ll-inclusive finncil blnce. In the end, the model ws ble to mthemticlly optimize the feochome (FeC) poduction pocess though evluting the effect of specified combintion of input pmetes. It could theefoe be used s tool to id in mngeil decisionmking; to ppise nd coespondingly djust cetin opetionl vibles in ode to chieve mximum etun on investment. This ppe fully descibes the esoning behind the choice of the essentil model components, the ssumptions mde duing the models development, the clcultion ppoch, s well s the dvntges, limittions, possible pplictions, nd es fo expnsion of the finl model. Though unning simultions with plnt dt, it ws found tht the ccucy of finl model emined fily constnt when pplied to stble funce conditions, but ws met with numbe of limittions when pplied to moe complex situtions. These limittions could, howeve, be ovecome though futhe development nd expnsion of the existing model to include lge numbe of pocess vibles. Keywods cbon footpint, economic optimiztion, enegy efficiency, feochome, mteil blnce, submeged c funce, tiple bottom line ccounting. Intoduction All industil ventues stive to chieve mximum pofit mgin though incesing the poduction of sleble poducts, loweing opetionl costs nd impoving opetion efficiency. Although ll industil pocesses hve these objectives in common, the mens though which it could be chieved would depend on the opetionl vibles of the specific pocess oute. Thoughout the yes the economic optimiztion of industil pocesses hs developed into espected entepise bsed on the cost-effectiveness of the specific pocess oute. A good exmple of pocess optimiztion is the semi-empiicl model developed by Boekmn nd Fod1, which incopoted the oe supply, smelting opetions, s well s the mkets to pedict nd impove the ovell cost-effectiveness of the pocess. Developing simultion models such s these hs llowed poduces to benchmk numeous opetionl pmetes, s well s evlute diffeent opetionl conditions. Futhemoe, following the globl tend towds geen technology, simultions could be expnded to include the cost of both the envionmentl nd socil esponsibility of the poduce. Pevious wok done in this field ws bsed on the pinciples of mteil nd enegy blnces fo smelting opetions. Accoding to Boekmn nd Fod1, the mss nd enegy blnces wee geneted eithe fom the theoeticl ptition tios of the components between the poduct nd slg mss, o though empiicl eltionships deived fom expeimentl nd plnt dt. These blnces wee used to pedict the metl nd slg constituents fo given combintion of w mteil inputs of known composition. Ultimtely, this llowed poduces to ssess the influence of vious w mteil inputs on the powe consumption, slg popeties, nd lloy gde. Figue 1 indictes the theoeticl minimum mount of enegy nd eductnts equied fo feochome (FeC) poduction utilizing eithe AC o DC funces fo vious w mteil inputs. Influence of chge mteil on powe consumption The type nd combintion of chge mteils used would influence funce opetions nd * Deptment of Mteils Science nd Metllugicl Engineeing, Univesity of Petoi. The Southen Aficn Institute of Mining nd Metllugy, SA ISSN X/ Ppe eceived Dec. 2011; evised ppe eceived M P p e The Jounl of The Southen Aficn Institute of Mining nd Metllugy VOLUME 112 APRIL

2 Economic modelling of feochome funce with n SAF, it is expected tht the distibution of the het losses would vy fo feochome poduction. Howeve, since the esech ws done on SAF, it is esonble to ssume tht, s with the poduction of steel, the lgest potion of het would be lost to the FeC lloy nd slg, while consideble potion would be lost to the off-gs, the cooling wte, nd miscellneous fctos. Finncil modelling Figue 1 Theoeticl consumption of electicity nd educing gents (Dvittil nd Honkniemi, 2004) ultimtely ffect the electicity consumption. The funce feed typiclly consists of chomite (lumpy oe, pellets, nd biquettes), eductnts (nthcite, ch, coke, nd col), nd fluxes (qutzite, dolomite, nd lime). Xio et l.3 epoted tht though ceful contol of the chge mteil s size nge nd composition, idel funce conditions could be sustined. Close contol of the w mteil type nd size nge would ensue good pemebility within the pcked bed, while the composition would influence the slg popeties. Thee e, howeve, numbe of chge pe-tetments tht could be utilized in ode to impove the funce stbility nd poductivity. Feochome smelting is n enegy intensive pocess, with the typicl electicl consumption nging between 2000 nd 4000 kwh/t FeC, depending on pe-eduction nd peheting of the chge mteil3. Figue 1 illusttes the eduction in powe consumption when using gglometed fines nd sinteed pellets. Dvittil lso found tht the mximum poductivity with the lowest powe consumption ws chieved by the use of sinteed pellets within submeged c funce (SAF) setup2. Enegy losses In conventionl funce opetions, the bulk of the het enegy is lost to the lloy nd slg while smlle potion of the enegy is lost s funce off-gses. Futhemoe, Dvittil climed tht decesed plnt vilbility nd poo powe utiliztion in the AF would led to futhe incese in powe consumption2. This coesponds to the wok done by Wilson et l.4 on the poduction of steel with n SAF, which indicted tht ppoximtely 21 pe cent of the het lost within SAF is due to the emission of flue gses, while 10 pe cent is lost to cooling wte nd 2 pe cent could be ttibuted to miscellneous losses. Chittnnon nd Go5 geneted mss nd theml enegy blnce fo the poduction of steel with SAF fom the expected inputs nd outputs illustted in Figue 2. Figue 3 depicts the het losses typiclly expected duing poduction with n c funce (AF), whee miscellneous het losses included the het lost duing the chging of w mteil, het lost due to n open doo, o fom funce cove opening. Given tht the esech done by Wilson et l.4 nd Chittnnon nd Go5 ws bsed on the poduction of steel Cost distibution Moden-dy feochome poduction fces numbe of chllenges; s mket pices continuously fluctute nd shift in the globl mind set hs incesed pessue to minimize wste poduction nd impove woking conditions. In ode to dpt to these hsh economic conditions, the industy now plces n even gete emphsis on minimizing opetionl nd investment costs. The typicl cost distibution of feochome smelte, s pedicted by Dvittil et l.2, is illustted in Figue 3. The cost distibution fo South Aficn smeltes vies slightly; typiclly chomite oe, eductnts, nd electicity ech ccount fo 30 pe cent of the poduction costs, while fctos such s mintennce, lbou nd wste disposl ccounts fo the emining 10 pe cent6. Loss fom cove opening Loss fom electode Scp Alloy Ai Loss duing chging Loss fom cooling wte Electic Ac funce Oxygen Electicity Othe mteil Loss fom open doo Sufce het losses Molten steel Slg Exhust gs Figue 2 An enegy nd mteil blnce of n electic c funce (Chittnnon nd Go, 2004) Figue 3 Typicl cost distibution expected fo feochome smelte 302 APRIL 2012 VOLUME 112 The Jounl of The Southen Aficn Institute of Mining nd Metllugy

3 Economic modelling of feochome funce Although the cost distibution would diffe slightly fo vious egions nd diffeent ppoches to plnt opetion, it is cle tht w mteil nd electicl costs ccount fo the bulk of the pocess costs. Tiple bottom line ccounting As peviously mentioned, the globl economic climte hs chnged fom the 1900s to the 21st centuy, with the pivte secto becoming moe we of copote esponsibility. Accoding to Hmson7 this weness hs led to the expnsion of the tditionl fme of efeence fo finncil pefomnce to include both socil nd ecologicl spects, giving ise to the tem tiple bottom line ccounting. Tiple bottom line ccounting hs lso been defined in tems of the thee pills; nmely people, plnet, nd pofit. The fist pill petins to humn cpitl, with the focus on beneficil copote policies towd lbou pctices nd the helth nd sfety of the suounding community. The second pill could lso be efeed to s ntul cpitl. This petins to minimizing the ecologicl footpint of n entepise though ceful mngement of esouce consumption, s well s wste poduction nd disposl. This concept of ccounting is simil to tht of ecocpitlism, whee the pofit is not consideed just s the tunove fte deduction of the input costs, but includes the economic benefit enjoyed by society. Using this integted ppoch, smll expenditues on socil nd ecologicl spects my ultimtely led to incesed pofit7. Wste disposl nd envionmentl considetions Applying the integted ppoch of tiple bottom line ccounting to feochome smelting opetions, it becomes cle tht envionmentl considetions such s the disposl of feochome slg nd off gs emissions need to be ccounted fo. Feochome slg The molten poducts obtined fom the feochome smelte opetion e lloy nd slg. Accoding to Beukes et l.8, South Aficn poduces genete slg- to- metl tios of between t slg pe t FeC. These tios e woying, consideing the cuent poduction volumes nd the SA Minimum Requiements fo Wste Act, which indictes tht the mximum disposl te pemitted fo FeC slg is 585 t/h/month. Futhemoe, wetheed nd cuent ising slg heps hve mostly been clssified s hzdous wste mteil due to the pesence of Mn, Fe nd C(VI). Howeve, tetment of the slg could llow fo its use in building ggegte nd cement bick poduction, s well s od constuction. The use of FeC slg s sleble poduct would not only genete evenue, but could educe the cost of wste disposl nd the use of ntul esouces. Off-gs emission Accoding to Niemelä et l.9, feochome poduction genetes lge mounts of CO gs the composition nd volume of which depend on the combintion of the w mteils used, feed pe-tetment, funce type, nd opeting conditions. These opeting conditions include chnges in tempetue, electicl input, mteil flow, segegtion, nd electode position, s well s the time to tp. Within open nd semi-closed funce setups the gs geneted would be buned off s it leves the funce, while closed funce setup llows the gs to be extcted by fns, scubbed, nd utilized s fuel. Futhemoe, the volume of off-gs geneted within closed funce setup is much lowe thn tht of ny othe funce setup. Off-gs volumes nge between Nm3/t FeC, whees semi-closed nd open funces genete off-gs volumes of up to Nm3/t FeC. The off-gs typiclly consists 8 of pe cent CO, 2 15 pe cent H 2, 2 10 pe cent CO 2, nd 2 7 pe cent N 2 nd depending on the composition of the off-gs, the enegy of combustion would vy between MWh/t FeC o MJ/t FeC9. Possible uses fo off-gs in plnt opetion Off-gs fomed within closed funce setup is souce of enegy tht could be utilized s fuel in viety of diffeent pocesses on the plnt. Accoding to Niemel et l.9, the heting vlue of the gs is close to 60 pe cent of the enegy supplied by the eductnt nd could ccount fo ppoximtely 70 pe cent of the electicl enegy equied fo smelting. Dvittil2 suggested tht insted of losing the ltent het of the CO gs fomed duing smelting, it could be utilized fo pe-heting o pe-eduction pocesses in ode to educe the plnt}s ovell powe consumption. Futhemoe, consideing funce off-gs s sleble poduct would not only educe wste disposl costs, but could lso compenste fo the incese in opetionl costs due enegy losses. Cost of cbon emissions Cbon emission tx my be implemented in the South Aficn industy, t n estimted R150 to R200 pe ton CO 2, ccoding to esech by Deloitte10. Though detemining the cost of the cbon emissions fom n estimted pice of R165 pe ton CO 2, it could be seen tht, ppoximtely R207 would be chged pe ton CO. Model development nd opetion The objective duing modelling ws to incopote ll the specified pocess vibles while mintining ese of opetion nd llowing fo the possibility of expnsion. The optimiztion model consists of finncil blnce of the pocess input nd output costs in ode to chieve mximum pofitbility, while minimizing the socil nd envionmentl costs. The vibles focussed on duing the investigtion e illustted in Figue 4. Fo the puposes of this poject, the model geneted ws bsed on the poduction of feochome with submeged c funce. Howeve, the im ws to develop the model in such wy tht by chnging the input vibles it could be pplicble to viety of electic c funce types nd feochome lloys of diffeent gdes nd cbon contents. The model ws developed in Micosoft Excel s vious woksheets fo the diffeent sections of inteest. Initilly, the opetionl vibles hd to be specified ccoding to the plnt conditions being simulted. The opetionl vibles petined to the poduct equiements, the funce type nd J o u n l P p e The Jounl of The Southen Aficn Institute of Mining nd Metllugy VOLUME 112 APRIL

4 Economic modelling of feochome funce Electicity Electode pste Cooling wte Mintennce Oe Feochome Poduction Reductnts Lbou Flux Figue 4 Input nd output vibles used fo economic modelling Alloy Slg Off gs Dust opeting conditions, the outine mintennce done on the funce, s well s the type nd composition of the chge mteil. Once the opetionl vibles hd been specified, the model itetes within the stipulted nges nd empiicl eltionships developed fo the mss nd enegy blnces, to pedict the quntity nd composition of the poducts geneted, s well s the enegy lost duing poduction. The cost of the inputs nd outputs fom the vious woksheets is ccounted fo s the diect opeting cost o OPEX, in the woksheet lbeled Finncil blnce. Poduct equiements In ode to nlyse the influence of numeous w mteil combintions on the cost of poduction, minimum nd mximum vlue hd to specified fo ech element of specific lloy gde, the desied C nd Fe ecovey to the metl, s well s the minimum nd mximum llowble vlues fo the slg bsicity. As cn be seen fom Tble I, the model llowes the use to tck the vlues pedicted fo the cuent combintion of w mteil inputs nd poduct equiements. The vlues clculted by the model wee colou-coded in vying shdes of geen, yellow- nd ed; whee geen indictes tht the pedicted vlues e sfely within the lowe egion of the specified nge, nd shdes of onge though ed indicte tht the pedicted vlues e moving towds the mximum specified limit. This inceses the ese with which the use cn keep tck of chnges within the model nd tke coective ction if equied. Funce setup nd opeting conditions The funce setup nd opeting conditions wee specified though numeous dop-down lists, which llows the use to choose the funce type (AC o DC), the ooftop configution (open, semi-closed, o closed), the funce shpe (cicul o ectngul), the numbe nd configution of tpholes, s well s the electode configution. Futhemoe, by llowing the use to specify the minimum nd mximum funce cpcity, the model cn simulte the cost of opeting t loweed funce cpcities, s well s funce shut-down nd stt-up pocedues. Routine mintennce Due to the difficulties in pedicting the effect of plnt opetion on the equipment nd efctoy life, the outine mintennce cost of plnt opetion ws divided into subctegoies of shot-tem, long-tem- nd tue long-tem costs. The bse infstuctue ws tken s 30 pe cent of the totl cpitl cost (CAPEX), while the mjo nd mino infstuctue costs wee tken s 60 pe cent nd 10 pe cent of the bse infstuctue costs espectively. The outine mintennce costs in the fist 12 months wee specified s 5 pe cent of the mino infstuctue cost. Mino infstuctue genelly efes to smll pumps, fns, hoses, cetin instuments, lights etc. In months the mintennce costs wee clculted s 3 pe cent of the mjo infstuctue cost, which efes to the funce shell, efctoies, s well s sections of the coppe wte cooling system. Once exceeding the 120 month peiod, the mintennce costs wee clculted s 1 pe cent of the bse infstuctue cost6. Rw mteil feed Once the bove specifictions hve been enteed by the use, vious oe combintions cn be exmined in the woksheet lbelled Rw mteil inputs. In this woksheet, the use hd the bility to vy the w mteil inputs in ode to detemine the most cost-effective combintion, while Tble I Illusttion of the Poduct equiements input sheet 304 APRIL 2012 VOLUME 112 The Jounl of The Southen Aficn Institute of Mining nd Metllugy

5 Economic modelling of feochome funce monitoing funce stbility nd poduct qulity. The funce cpcity fo the instnce illustted in Tble II ws expessed s the mximum mount of w mteil tht could be fed into the funce pe dy. Mss blnce inputs The w mteil inputs wee linked to mss nd enegy blnce tht involved complete elementl nlysis of ll the inputs nd outputs. This ws done though using the econstituted vlues of the given w mteil compositions, in ode to ccount fo the pesence of tce elements s well s plnt spillge. The influence of w mteil petetments ws tken into ccount by llowing the use to specify the tempetue ( C) t which the w mteil ws teted. Mss blnce outputs The elementl nlysis fo the desied combintion of w mteil inputs ws elted to the equied poduct specifi ctions, s stted by the use. This ws done fo single btch, which ws esticted to the mximum specified funce cpcity. All the clcultions wee iteted within the specified poduct compositionl nges. The slg composition ws clculted fom the excess constituents tht did not epot to the lloy. The C nd Fe distibution tio ws chosen by the use in the woksheet lbelled Poduct equiements, s the pecentge ecovey to the lloy. This ws done ccoding to wht would genelly be expected fo the specific plnt s opetion. The totl mount of CO, MgO, nd Al 2 O 3 pesent in the feed ws ssumed to epot to the slg nd the bsicity ws clculted ccodingly. Futhemoe, the slg- to- metl tios wee llowed to itete within specified nge. The excess cbon nd sulphu tht did not epot to the metl would epot to the off-gs s CO x nd SO 2 espectively. Futhemoe, ny moistue pesent in the w mteils would lso epot to the off-gs, long with ll the nitogen pesent in the system. Accoding to litetue, the off-gs typiclly consists of pe cent CO nd only 2 5 pe cent CO 2. It ws theefoe decided tht the excess cbon in the system would be combusted s CO, while the CO 2 pesent in the off-gs would oiginte fom the CO 2 intoduced into the system though the dolomite nd lime. Enegy blnce Fo the theml blnce, the enthlpy vlues of the diffeent w mteil inputs nd poducts wee clculted t the specified tempetues, fo the specific mol mss of ech of the constituents. The totl enegy equied fo the smelting opetion ws then clculted s the diffeence between the chemicl enegy of the poducts nd the totl chemicl enegy of the w mteil inputs. J o u n l P p e Tble II Illusttion of section of the Rw mteil input sheet The Jounl of The Southen Aficn Institute of Mining nd Metllugy VOLUME 112 APRIL

6 Economic modelling of feochome funce The chemicl enegy ws conveted to MWh/t FeC nd incopoted into the ovell enegy blnce. Fo the ovell enegy blnce, the totl equied electicl input cn be clculted fom the enegy equied fo smelting, s well s the typicl het losses expected fo funce of the specified size. On the othe hnd, the typicl het losses cn be detemined by deducting the enegy equied fo smelting fom the totl electicl input s specified by the use. The cost of the electicl inputs ws clculted ccoding to Eskom s Meg flex pek, off-pek, nd stndd tiffs fo Within this woksheet, the use hs to specify the month fom the dop-down list illustted in Tble III, in ode to ccount fo the pice incese fom the low to high demnd seson. The electicity cost in Tble III ws clculted on monthly bsis ssuming tht the funce ws opeted continuously without inteuption. Fo the finncil blnce, the monthly cost ws conveted to the cost pe ton FeC. Cbon footpint The woksheet Cbon footpint ws developed with the im of nlysing the effect of the CO off-gs on the poductivity nd pofitbility of the pocess. This ws done by exmining the effect of cbon txes on the pofit mgin, s well s investigting the possibility of educing the enegy equiements by ecycling the off-gs geneted duing the smelting opetion. The woksheet ws linked to the Mteil nd Enegy blnce sheet, in ode to obtin the mount of off-gs geneted fo the given set of w mteil inputs. Fom this the mount of off-gs geneted ws conveted fom ton to Nm3, ssuming density of kg/nm3. The woksheet ws developed in such wy tht the ecycling of the off gs could be simulted only fo closed funces setup. If this ws the cse, the use hd to specify the pecentge of off-gs tht could successfully be ecycled bck into the system. Since CO nd H 2 e the only flmmble components in the off-gs, the enegy of the off-gs ws ssumed to be between 10.1 nd 11.5 MJ/Nm3. The eduction in the enegy equiements (MWh) due to the ecycled off-g ws then clculted fom the het geneted (MJ/Nm3) multiplied by the mount of off-gs ecycled (Nm3). Once the mount of ecycled off-gs hs been clculted, the tx levied on the mount of CO nd CO 2 emitted is clculted ccoding to the cbon emissions cost estimtes of Deloitte. Finncil nlysis The vlues obtined fom the woksheets mentioned bove, wee elted bck to Finncil Sheet ; whee the costs wee expessed pe ton feochome poduced. This ws done fo the lbou, mintennce, ovehed, w mteil, utility, pollution, nd lbotoy costs; ccoding to the diect opetion cost (OPEX) clcultions suggested by Vtvuk11. The utility costs wee clculted fo the mount of electicity, wte, nd electode pste consumed. It ws ssumed tht the mount of wte consumed by the cooling system, would vy between 2 3 t pe ton feochome, t cost of R3 R5 pe ton wte. Futhemoe, it ws ssumed tht ppoximtely 10 kg electode pste would be equied pe ton feochome, t cost of R pe ton pste6. The pollution cost clcultions wee bsed solely on the cost of cbon emissions nd did not include the cost of slg disposl. The litetue indicted tht numeous wys exist to educe the cost of slg disposl nd possibly genete nothe venue fo evenue; theefoe it would be dvisble to expnd futue vesions to include these costs. Results nd discussion Once the model hd been completed, the vlidity nd level of ccucy of the esults geneted hd to be detemined. This ws done by unning numeous simultions with plnt dt obtined fo the w mteil nd electicl inputs, the chemicl composition of the lloy nd slg, s well s the cost distibution expected fo genel plnt opetion. When feeding the plnt dt into the model, it ws found tht the weight pe cent clculted fo the vious lloy constituents emined within the specified nge s illustted fo the dt simulted in Tble I. The clculted vlues, howeve, hd popensity to devite towds the uppe limit of the nge. Futhemoe, the clculted slg compositions nd bsicities coelted well with those indicted by the litetue, s well s with ctul plnt dt. In ode to vlidte the esults obtined fo the poduct nd slg compositions, the ctul weight pe cent chomite in the slg ws comped to the clculted vlues. The decision to compe the weight pe cent of chome oxide in the slg, the thn the weight pe cent chomium in the lloy, ws Tble III Illusttion of the woksheet petining to the clcultion of the electicl costs 306 APRIL 2012 VOLUME 112 The Jounl of The Southen Aficn Institute of Mining nd Metllugy

7 Economic modelling of feochome funce bsed on the fct tht the lloy composition ws limited to specified nge; whees the slg composition could vy ccoding to the empiicl eltionships developed duing modelling. The pecentge eo due to the vitions in the clculted nd ctul slg mss ws detemined to be ± 0.2 pe cent. Fom Figue 5 line coeltion cn be seen between the clculted nd ctul weight pe cent chome oxide, obtined fom plnt dt. This indicted tht chnges in the pedicted vlues emined fily close to the chnges in the ctul vlues, unde noml opeting conditions. Howeve, the model fed pooly in pedicting the lloy nd slg composition fo dt obtined duing peiods of instbility, whee instbility efes to ny devition fom noml opetion. Fom the theml enegy blnce it ws found tht, the enegy equied fo smelting would vy between 2.3 nd 2.8 MWh/t FeC. Deducting the enegy equied fo the smelting opetion fom the ctul electicl inputs obtined fom plnt dt, the theoeticl het losses wee detemined to be between 1.1.nd 1.17 MWh/t FeC. This coesponds to the plnt dt, whee the het losses wee indicted to be between kwh/m2. Sensitivity nlysis As cn be seen fom the cost distibution clculted bove, the electicl costs ccount fo ppoximtely 40 pe cent of the ovell poduction cost, which is 10 pe cent moe thn wht ws expected fom dt in the litetue. It ws theefoe decided to nlyse the sensitivity of the poduction cost to chnges in the electicl inputs to the funce. Fom the sensitivity nlysis in Figue 6 it cn be seen tht 5 pe cent incese in the electicl inputs coesponds to 1 pe cent incese in the ovell poduction cost. The poduction cost theefoe shows 2 pe cent sensitivity to vitions in the electicl inputs, which could ccount fo the discepncy in the pedicted cost distibution. Conclusion Though the use of mteil nd enegy blnces, obust model ws developed to pedict the influence of numeous pocess vibles on the pofitbility of feochome smelting opetion. It ws found tht the model emined fily ccute when pplied to stble funce conditions, but ws met with numeous limittions when pplied to moe complex situtions. These limittions could, howeve, be J o u n l P p e Cbon footpint Recycling of the off-gs By unning simultions with plnt dt it ws clculted tht, the mount of off-gs poduced vied fom Nm3/t FeC, ssuming tht the density of the off-gs nged fom kg/nm3. This is slightly highe thn the Nm3/t FeC epoted by Niemelä et l.9. Assuming tht CO nd H 2 e the only buning components of the off-gs, the het geneted by the off-gs ws clculted to be 2.72 kwh/nm-3 off-gs o 2.05 MWh/t-1 FeC, fo the simultion. This vied only slightly fo the est of the dt sets nd coesponds well to the kwh/nm-3 off-gs o MWh/t FeC pedicted by Niemelä et l. Futhemoe, it ws found tht ecycling the off-gs could led to pe cent eduction in the enegy equiements, ssuming tht pe cent of the off gs could be ecycled effectively. Cbon txes Assuming tht the tx levied on the CO nd CO 2 ws R nd R espectively, it ws clculted tht the cost of cbon tx on vege would be R pe ton FeC. Howeve, though ecycling ppoximtely 85 pe cent of the off gs to pe-tetment pocesses, the cost could be educed dmticlly, to n estimted R45.00 pe ton FeC. Finncil nlysis The cost distibution emined fily constnt, with the w mteils ccounting on vege fo 50 pe cent of the cost, the electicity fo 40 pe cent, nd lbou, mintennce nd cbon txes fo the emining 10 pe cent. Should the off-gs be ecycled, decese of up to 25 pe cent in the poduction costs could be obtined; with the w mteils now ccounting fo ppoximtely 70 pe cent of the costs, electicity fo 20 pe cent, nd lbou, mintennce, nd pollution costs fo the emining 10 pe cent. Actul weight pe cent C2O Clculted weight pe cent C 2O 3 R2 = Figue 5 Compison of the clculted weight pe cent chome oxide to the ctul weight pe cent chome oxide in the slg Pe cent incese in poduction cost Pe cent chnge in electicl equiements y = 0.238x - 5E-15 R2 = Figue 6 Sensitivity nlysis to chnges in the electicl input equiements of Submeged c funce The Jounl of The Southen Aficn Institute of Mining nd Metllugy VOLUME 112 APRIL

8 Economic modelling of feochome funce ovecome though futhe development of the existing model with moe plnt-specific dt nd expnsion to include lge numbe of pocess vibles. Advntges The model setup ws chosen due to its simplicity nd the fct tht it llows the use to specify the poduct composition nge while monitoing the slg composition nd popeties in ode to optimize the w mteil inputs. The dvntge to this type of setup is tht it gives the use the feedom to evlute the funce pefomnce nd pofitbility using pticul oes, eductnts nd electicl inputs t specified costs. Futhemoe, the utiliztion of woksheet-bsed pogms mkes models such s these esily expndble, nd the model could with time be developed to include lmost ny pocess vible tht cn be pedicted o quntified. Limittions Although the model hs been developed to tke numeous opetionl pmetes into ccount, it cnnot ccutely ccount fo cetin pocess phenomen, such s the electode penettion opetion, the ectivity of the vious types of w mteil inputs, o mteil etention. Futhemoe, to coectly quntify the tnsient funce conditions such s those expeienced duing plnt stt-up nd shut-down pocedues, one would hve to ccount fo the sensitivity of the electodes to cyclicl loding, the possibility of the efctoies expeiencing theml shock due to the goss tempetue fluctutions, nd finlly the cost of mteil losses. Theefoe in ode to mintin high degee of ccucy, the cuent model cn ultimtely be pplied only to stble funce conditions. Applictions The model could lso be extended to pplictions such s detemining the futue selection nd pofitbility of new oe mteils, fesibility studies on poduction t vious funce cpcities, nd the competiveness of the plnt comped to othe poduces. Possible es fo expnsion As hs been mentioned, the limittions of the model could be ovecome though the development o expnsion of cetin sections. One of the limittions is tht the model does not ccount fo the ectivity of the diffeent w mteil types. When consideing the lge influence the pe-tetment of w mteils hs on the funce s poductivity, it would be dvisble to look into this mtte. Anothe limittion is tht the model does not ccount fo the cost of efctoy we fo vious opeting conditions nd w mteil inputs. Since unfoeseen efctoy filues could esult in extended peiods of downtime, duing which poduction ceses nd mintennce costs skyocket, it could be wothwhile to include the influence of diffeent w mteils nd opeting tempetues on the efctoy we nd mintennce of the funce. Futhemoe, fo the puposes of this model, the sufce het losses wee clculted s the electicl input enegy tht ws not utilized duing the smelting pocess. Howeve, to obtin moe ccute ccount of the mount of enegy lost duing poduction, the miscellneous het losses, s well s the sufce het losses, need to be tken into ccount. Duing the development of the model povisions wee mde to clculte the sufce het losses s function of the funce size. If the electicl input is known, nd the sufce het losses wee clculted ccoding to the funce size, the miscellneous het losses could be exmined. This would llow the use to benchmk the het lost duing opeting pocedues such s chging of w mteils. Fo the puposes of this model, the focus ws mostly on the optimiztion of the funce inputs, the thn the funce outputs. It ws peviously indicted tht the enegy equiements nd poduction cost could be educed significntly by ecycling the off-gs; howeve, one needs to exmine the cost of eecting nd mintining the off-gs ecycling plnt s well. Futhemoe, it ws suggested by Beukes et l.8 tht pocessed slg could be sold s secondy poduct to civil engineeing nd constuction compnies, poviding tht the slg meets the equied specifictions. Theefoe it cn be concluded tht, in ode to effectively optimize n opetion, ny mens of minimizing wste nd geneting evenue lso needs to be evluted. Refeences 1. BROEKMAN, B. nd FORD, K. The development nd ppliction of HCFeMn funce simultion model fo Assmng Ltd. INFACON X. Poceedings of the 10th Intentionl Feolloys Congess, Cpe Town, 1 4 Febuy/Octobe, InfconX/004.pdf [Accessed 15 Dec., 2011]. 2. DAAVITTILA, J. nd HONKANIEMI, M. The tnsfomtion of feochomium smelting technologies duing the lst decdes. INFACON X. Poceedings of the 10th Intentionl Feolloys Congess. Cpe Town, 1 4 Febuy Jounl of the South Aficn institute of Mining nd Metllugy, vol. 104, no.9, pp v104n09p541.pdf [Accsessed 15 Dec., 2011]. 3. XIAO, Y., YANG, Y., nd HOLAPPA, L. Tcking chomium behviou in submeged c. Pocessing, vol. 1, pp WILSON, E., KAN, M., nd MIRLE, A. Intelligent technologies fo electic c funce optimiztion. Poceedings of the 58th Electic Funce Confeence. Ion nd Steel Society of AIME, vol. 56, pp [Accessed15 Dec., 2011]. 5. CHIRATTANANON, S. AND GAO, Z. E.T. Pogm, Enegy Convesion nd Mngement, vol. 37, no. 2, pp DAWSON, N. Xstt, Rustenbug Pesonl communictions, 31 Mch Novembe HAMSON, N Tiple Bottom Line: Beyond Finncil Repoting. BSI Goup. [Accessed 13 Feb. 13, 2011] 8. BEUKES, J., DAWSON, N., nd VAN ZYL, P. Theoeticl nd pcticl spects of C (VI) in the South Aficn feochome industy. Jounl of the Southen Aficn Institute of Mining nd Metllugy, vol. 110, no. 12, pp [Accesse 15 Dec., 2011]. 9. NIEMELÄ, P., KROGERUS, H., nd OIKARINEN, P. Fomtion, chcteistics nd utilistion of CO-gs fomed in feochomium smelting. INDACON X. Poceedings of the 10th Intentionl FeoAlloys Congess. Cpe Town, 1 4 Febuy pp InfconX/014.pdf [Accessed 10 Dec., 2011]. 10. VAN DER MERWE, C. Cbon tx could en Govt. R 82.5bn ye. Engineeing News Online. Webb, M. (ed). 4 Jnuy [Accessed 1 Nov. 1, 2011]. 11. VATAVUK, W.M. Repot, F. How to estimte opeting costs. Chemicl Engineeing, July [Accessed 20 Aug., 2011]. 308 APRIL 2012 VOLUME 112 The Jounl of The Southen Aficn Institute of Mining nd Metllugy