RETRACTION. Retraction: A Prediction Model of Phosphorus Distribution between CaO SiO 2 MgO FeO Fe 2 O 3 P 2 O 5 Slags and Liquid Iron

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1 RERACI he ollowg hee acles wee whdaw upo eques o he auhos o cobe,, because hey wee submed whou he cose o all he auhos. Reaco: Repeseao o Dephosphozao Ably o Ca Coag Slags Based o he Io ad Molecule Coexsece heoy eg-cheg LI,) ad Ja-lag ZHAG ) ) Sae ey Laboaoy o Advaced Meallugy, Uvesy o Scece ad echology Bejg, Bejg, 8. R. Cha. ) Sae ey Laboaoy o Mulphase Complex Sysems, Isue o ocess Egeeg, Chese Academy o Sceces, Bejg, 9. R. Cha. hs acle was publshed ISIJ I., (), o., Reaco: A edco Model o hosphous Dsbuo bewee Ca S Mg Slags ad Lqud Io eg-cheg LI,,) ad Ja-lag ZHAG,) ) Sae ey Laboaoy o Advaced Meallugy, Uvesy o Scece ad echology Bejg, Bejg, 8. R. Cha. ) School o Meallugcal ad Ecologcal Egeeg, Uvesy o Scece ad echology Bejg, Bejg, 8. R. Cha. ) Sae ey Laboaoy o Mulphase Complex Sysems, Isue o ocess Egeeg, Chese Academy o Sceces, Bejg, 9. R. Cha. hs acle was publshed ISIJ I., (), o., Reaco: Repeseao o Reaco Ably o Sucual Us Al Bay Mels eg-cheg LI,,) ad Ja-lag ZHAG,) ) Sae ey Laboaoy o Advaced Meallugy, Uvesy o Scece ad echology Bejg, Bejg, 8. R. Cha. ) School o Meallugcal ad Ecologcal Egeeg, Uvesy o Scece ad echology Bejg, Bejg, 8. R. Cha. ) Sae ey Laboaoy o Mulphase Complex Sysems, Isue o ocess Egeeg, Chese Academy o Sceces, Bejg, 9. R. Cha. hs acle was publshed ISIJ I., (), o. 6, ISIJ

2 ISIJ Ieaoal, Vol. (), o., pp A edco Model o hosphous Dsbuo bewee Ca S Mg Slags ad Lqud Io eg-cheg LI,,) * ad Ja-lag ZHAG,) ) Sae ey Laboaoy o Advaced Meallugy, Uvesy o Scece ad echology Bejg, Bejg, 8. R. Cha. ) School o Meallugcal ad Ecologcal Egeeg, Uvesy o Scece ad echology Bejg, Bejg, 8. R. Cha. ) Sae ey Laboaoy o Mulphase Complex Sysems, Isue o ocess Egeeg, Chese Academy o Sceces, Bejg, 9. R. Cha. (Receved o Sepembe 8, ; acceped o Decembe, ) Ca S Mg slags s ypcal he basc oxyge seelmakg(bs) pocess. hosphae dsbuo bewee slags ad lqud o s a dex o he phosphous holdg capacy o he slag, whch deemes he phosphous coe achevable he shed seel. I hs sudy, a hemodyamc model o calculag phosphous dsbuo bewee Ca S Mg slags ad lqud o,.e., L p model, has bee developed coupled wh a developed hemodyamc model o calculag mass aco coceaos o sucual us,.e., model, based o o ad molecule coexsece heoy. Smple bay bascy R have a lage eec o equlbum mole umbe Σ o sucual us Ca S Mg slags, he omula o equlbum mole umbe Σ agas he smple bay bascy R o slags ca be egessed as Σ.6.9*exp( R/.9), ad he g degee s.99. he compaso o he calculaed phosphoous dsbuo by L p model wh he measued phosphoous dsbuo epoed om dee leaues shows ha he ageeme bewee he calculaed phosphoous dsbuo ad measued phosphoous dsbuo s good. Meawhle, some ohe L p pedco models have also bee ake o cosdeao o calculag phosphae dsbuo bewee Ca S Mg slags ad lqud o, ad he esuls shows ha L p model have moe accuacy compaed wh ohe L p pedco models. he developed L p model ca quaavely calculae he especve cobuo o, Ca ad Mg he slags. A sgca deece o dephosphozao ables amog, Ca ad Mg ca be oud as appoxmaely.%, 99.98%,.%. Meawhle, he phosphous lqud o ca be eecvely exaced by Ca slags o om complex molecules Ca whch made he ma cobuo o dephosphozao Ca S Mg slags. EY WRDS: phosphoous dsbuo; mass aco coceao; sucual us; o ad molecule coexsece heoy.. Ioduco hosphous ca make he seel poe o embleme dug hea eame ad cause degadao o eleccal popees. I s heeoe useul o sudy suable meal-slag eacos wh he objecve o emove phosphous om seel mels below up-o-dae lms. May sudes wee caed ou o measue phosphoous dsbuo bewee vaous slags ad lqud o. 6) Colclough,) have made expemes volvg he dephosphozao om he lqud o a basc ope-heah uace, ad he poposed ha he phosphous lqud o was maly exaced he om o ea-calcum phosphae (Ca ). Hey ) caed ou a sees o expemes usg a expemeal uace as well as basc ope-heah uace ad came o he cocluso ha omed -calcum phosphae (Ca ), bu o ea-calcum phosphae (Ca ). Cosdeg he ac ha he measueme o phosphoous dsbuo bewee mole slag ad lqud o was cosly ad dcul he opeao, seveal aemps 8) wee made o descbe ad pedc phosphous pao aos as a uco o slag composo. Healy ) coduced a sees o expemes volvg he measueme o phosphous dsbuo bewee slags ad lqud o, ad publshed he amous coelao o equlbum phosphous pao * Coespodg auho: E-mal: lpegcheg@6.com DI: hp://dx.do.og/./sjeaoal..76 a wde age o slag composos ad empeaues as lg (% ) 8. (% Ca). lg(% ) 6. Smlaly, may phosphoous dsbuo pedco models have bee developed based o some empcal egessos o he measued daa, such as Suo s models, 6,7) Sommevlle s model 8) ad Balajva s model. 9) All he above-meoed phosphoous dsbuo pedco models,6 9) have bee evaluaed he ollowg secos. May eseaches,6,, ) have woked owads esmao o γ meallugcal slags wh dee chemcal composos. ukdoga ad easo ) poposed a expesso o acvy coece o as a uco o slag composos.e., lgγ.(x Ca X Mg X M X X S ).8. I 98, o he bass o he measued phosphous dsbuo bewee Mg sauaed Ca Mg S slags, coag % Ca, he empeaue age om 8 o 9, Suo e al. 6) moded ukdoga s coelao ) as ha lgγ. 6 (X Ca 7X Mg 8X ).. he coelao poposed by Suo e al. 6) dcaes sgcaly lowe empeaue depedece o γ, compaed wh ukdoga s expesso. ) Basu e al. ) obseved ha he elaoshp bewee he measued γ ad he calculaed γ by ukdoga s γ pedco model ) o Suo s γ pedc- ISIJ 76

3 ISIJ Ieaoal, Vol. (), o. o model 6) was o good, ad developed wo γ pedco models as lgγ 6.77 Ca Mg.77 S 99. (. 77 ) ad lgγ 8.7X Ca 7.69X.X Mg.77X S.66 (.86). Boh o Basu s models ) wee sasacoly applcable o he daa o ohe pevous wokes.,6) Suo e al. ) ad obayash e al. ) made exesve wok o he dephosphozao ably o seelmakg slags coag M, ad hey obseved ha he addo o M had a egave eec o dephosphozao. I 7, Basu e al. ) coduced expemes o esablsh o equlbum phosphous pao bewee Ca S Mg slags ad mole whch s ee om Al o M, ad poposed he coelao o equlbum phosphous pao ems o oc. Fom he above dscusso, ca be obvously obseved ha much o he pevous wok was caed ou usg acal paamees, ad mos o he egessed paamees wee vald oly wh cea lms o coceao. he pese sudy developed a esh model whou acal egessed paamees o esablsh phosphous pao bewee Ca S Mg slags ad lqud o based o he o ad molecule coexsece heoy. he measued daa o phosphous dsbuo o Ca S Mg slags equlbaed wh lqud o a empeaue age om 8 o 9 epoed by agabayash e al. ) ad he measued daa o phosphous dsbuo o Ca S Mg slags equlbaed wh lqud o a empeaue age om 87 o 9 by Basu e al. ) wee boh seleced o vey he accuacy o he developed L p pedco model. I should be poed ou ha Ca S Mg slags was a specal Ca S Mg slags wh he assumpo ha he coe o equal o zeo. Howeve, he majo am o hs sudy s o epese a vesgao o ue chaacescs o dephosphozao Ca S Mg slags. Hece, oly he epoed daa o Ca S Mg slags by agabayash e al. ) was ake o cosdeao o epeseao o eaco ables o sucue us he ollowg secos.. Model o Calculag Mass Aco Coceaos o Sucual Us Ca S Mg Slags.. Hypoheses I vew o he ac ha hee ae os ad molecules mole meallugcal slags smulaeously, 9,) he ma vewpos o he o ad molecule coexsece heoy o slag sucues he developed hemodyamc model ca be smply summazed as ollows: ) Mole slags o Ca S Mg ae composed o Ca, Mg,, ad as smple os, S ad as smple molecules, slcaes, alumaes as complex molecules. Each sucual u has s depede poso he slags. Evey cao ad ao geeaed om he same compoe wll ake pa eacos o omg complex molecules he om o o couple as (Me ). ) Reacos o omg complex molecules ae ude chemcally dyamc equlbum bewee boded o couples om smple os ad smple molecules. ) Sucual us he seleced slags equlbaed wh lqud o bea couy he age o vesgaed coceao age. ) Chemcal eacos o omg complex molecules obey he mass aco law... Model o Calculag Mass Aco Coceaos o Sucual Us Ca S Mg Slags... Sucual Us Ca S Mg Slags Accodg o adoal meallugcal physcochemsy, Ca S Mg slags s composed o Ca, S, Mg,, ad, whle he exaced phosphous gadually ee o he slags wh he poceedg o dephosphozao eacos ul dephosphozao eacos each equlbum. Howeve, he,) suggess ha he exaced phosphous om lqud o o he slags exss as ca be boded wh o couples ( ), (Ca ) ad (Mg ) o om molecules as,,, Ca, Ca, Ca, Mg, ad Mg oxdzg slags coag o oxdes, especvely. I vew o he epoed bay ad eay phase dagams,) o Ca S slags, Ca slags, slags, Mg slags, Ca Mg slags, Ca Mg S slags, Mg S slags, ad Ca S slags a empeaue age om 67 o 986, abou kds o complex molecules ca be omed he slags as lsed able.... Model o Calculag Mass Aco Coceaos o Sucual Us Ca S Mg Slags he mole umbe o above meoed sx compoes, such as Ca, S, Mg,, ad g o Ca S Mg slags s assged as b Ca, b, b,, ad o b 6 S Mg b b pese chemcal composo o he slags. he deed,) equlbum mole umbes o all abovemeoed sucual us g slags equlbaed wh lqud o a meallugcal empeaues have bee also gve ou able. Accodg o he o ad molecule coexsece heoy,,) each o couple s elecoeual ad ca be elecolyzed o cao ad ao based o elecovalece balace pcple. Hece, o couple (Me ) wh a xed amou ude equlbum codo ca poduce wo mes amou o sucual us,.e., - Me,Me,Me Me. he oal equlbum mole umbe Σ o all sucual us g slags equlbaed wh lqud o ca be expessed as ollows Ca S Mg... () c c c ( mol) Wh espec o he deo o mass aco coceaos,) o sucual us, whch s a ao o equlbum mole umbe o sucual us o he oal equlbum mole umbes o all sucual us a close sysem wh a xed amou, o sucual us ad o couples (Me ) mole slags ca be calculaed by...(a) Me - Me,Me,Me -... (b) Me,Me,Me Me 77 ISIJ

4 ISIJ Ieaoal, Vol. (), o. able. Chemcal eaco omulas o possbly omed complex molecules, he sadad mola Gbbs ee eegy chages, mole umbes, mass aco coceaos ad equlbum cosas Ca S Mg slags. Mole umbes o Mass aco coceaos Reacos c (J/mol) sucual us (mol) o sucual us ( ) c (Ca )(S )(Ca S ) ) c c Ca S c Ca S c c (Ca )(S )(Ca S ) 9.67 ) c c Ca S c Ca S c c (Ca )(S )(Ca S ) ) c c Ca S c Ca S c c (Mg )(S )(Mg S ) ) c c Mg S c Mg S c c (Mg )(S )(Mg S ) ) c c Mg S c Mg S c c ( )(S )( S ) 9 9.7,7,8) c6 c6 S c6 S c6 c6 (Ca )(Mg )(S ) (Ca Mg S ) c7 c7 Ca Mg S c7 Ca Mg S c7 c7 (Ca )(Mg )(S ) 8.88 (Ca Mg S c8 ) c8 Ca Mg S c8 Ca Mg S c8 c8 (Ca )(Mg )(S ) (Ca Mg S c9 ) c9 Ca Mg S c9 Ca Mg S c9 c9 (Ca )(Mg )(S ) (Ca Mg S ) c ) c Ca Mg S c Ca Mg S c c (Ca )( )(Ca ) 7. ) c c Ca c c Ca c ( )( )( ) ,7) c c c c c (Mg )( )(Mg ) ) c c Mg c Mg c c (Ca )( )(Ca ) ) c c Ca c Ca c c 6 (Ca )( )(Ca ) ) c c Ca c Ca c c 6 (Ca )( )(Ca ) ) c6 c6 Ca c6 Ca c6 c6 6 ( )( )( ) ,8) c7 c7 c7 c7 c7 6 ( )( )( ) 8.8 7,8) c8 c8 c8 c8 c8 6 (Mg )( )(Mg ) ) c9 c9 Mg c9 Mg c9 c9 6 (Mg )( )(Mg ) ) c c Mg c Mg c c 6 All deos o o omed o couples om smple os, smple ad complex molecules Ca S Mg slags wee lsed able. Meawhle, should be poed ou ha he physcochemsy meag o s almos cosse wh he adoally appled acvy a o compoe slags, whch pue mae s chose as sadad sae ad mole aco s seleced as coceao u.,) he chemcal eaco omulas o kds o possbly omed complex molecules, he sadad mola Gbbs ee eegy G o omao eacos as a uco o absolue empeaue, eaco equlbum cosa m,c c ad peseao o mass aco coceao o all complex molecules c expessed by usg c, ( Ca ), ( S ), ( Mg), ( ), ( ) ad 6 ( ) based o he mass aco law wee summazed able. he mass cosevao equaos o sx compoes g o Ca S Mg slags equlbaed wh lqud o ca be esablshed accodg o he deo,) o ad mass aco coceaos o all sucual us lsed able as ollows b ( c c c c7 c8 c9 c c c c6) ( c c c c7 c8 c9 c c 6 ) ( ) c 6 c6 6 Ca mol b ( c9 c ) ( c c c c c c6 c7 c8 c9 c ) S ( mol) c c c c c c6 c7 c8...(a)... (b) ISIJ 78

5 ISIJ Ieaoal, Vol. (), o. b ( c c c7 c8 c9 c ) ( c c c7 c8 c9 ) ( mol) c Mg...(c) b ( c6 c7 c8 ) (... (d) c6 c7 6 ) ( mol) c8 6 ( ) b c c c ( c c...(e) c ) ( ) mol b ( ) 6 6 c c c6 c7 c8 c9 c ( 6 c6 c6 c66 c7 6 c8 6 c9 ) c ( 6 mol )...() Accodg o he pcple ha he sum o mole aco o all sucual us a xed amou o Ca S Mg slags ude equlbum codo s equal o., he ollowg equao ca be obaed 6 c... () c 6. he equao goup o Eqs. () ad () s he goveg equaos o he developed hemodyamc model o calculag mass aco coceaos o sucual us Ca S Mg slags equlbaed wh lqud o. bvously, hee ae seve ukow paamees as,,,,, 6 ad Σ wh 7 depede equaos he developed equao goup o Eqs. () ad (). he uque soluo o, Σ ad ca be calculaed by solvg hese algebac equao goup o Eqs. () ad () by combg wh he deo o Eq. ()... Deo o Mass Aco Coceao o Io xdes he Ca S Mg Slags I s well-kow ha hgh oxyge poeal ad bascy o he slags ae eeded o emove phosphous om seel mels. I hs sudy, he mass aco coceao o o oxdes,.e.,, s ecommeded o pese slag oxdzao ably. Meawhle, should be poed ou ha he deed compehesve mass aco coceao o o oxdes slags ca be appled o accuaely eplace acvy o a elave pue lqud mae as sadad sae pevous publcao. ) he,) poposed ha all o oxdes meallugcal slags ae composed o o couple ( ), smple molecule ad complex molecule, heeoe, he elaed sucual us o o oxdes ca dyamcally equlbae amog hose sucual us as ollows ( ) [ ] ( )...(a) ( ) [ ] ( )... (b) bvously, whe he eacos o Eqs. (a) ad (b) each equlbum, cease o sgle molcule o wll lead o he chagg o balace wh cease o oe hd o cou- 6 c c c c ple sce he equlbum cosa s kep cosa. heeoe, he mass aco coceao o ee o couple ( ) ca decly epese pese slag oxdzao ably. Meawhle, should be poed ou ha he symbol o s appled hs sudy o keep cosse wh adoal symbol o o oxdes he elaed ee- ece. heeoe, he slags oxdzao ably o ca be deed as a... (6) Accodg o, he deed om ) has he smla meag wh a om vewpo o adoally meallugcal physcochemsy, whch ca be calcula- ed accodg o ( ) equlbum as [ ] [ ] )...(7a) G m,. ( J/mol) a a a... (7b) [% ] a a whee s oxyge acvy coece ( ), ad ca be deemed by lg e[% ] e... (8) he elaed values o eaco coeces ae chose as e.,.7. e. Resuls o Mass Aco Coceaos o Sucual Us Ca S Mg Slags.. Relao bewee Mass ece o Sx Compoes ad Mass Aco Coceaos o Relaed Sucual Us Ca S Mg Slags he elaoshp bewee mass peceage o Ca, S, Mg,, ad as compoes ad he calculaed mass aco coceaos o sucual us,.e., (Ca ), S, (Mg ), ( ), ad, Ca S Mg slags a empeaue age om 8 o 9 was show Fg., especvely. he good scae lea elaoshp ca be obseved o (Ca ), S, (Mg ), ( ) ad as compoes Fgs. (a), (b), (c), (d) ad (e). he scae coespodg elaoshp ca be oud o Fg. (). he good scae lea elaoshp o (Ca ), S, (Mg ), ( ) ad ca be explaed as ollows ) some basc oxdes such as (Ca ) ad (Mg ) ca eac wh S o om complex molecules Ca S, Ca S, Ca S, Mg S, Mg S, Ca Mg S, Ca Mg S ad Ca Mg S as show able ; ) ( ) ad ca also be cosumed as o oxdes he pocess o dephosphozao... Relao bewee Mass ece o Sx Compoes ad Equlbum Mole umbes o Relaed Sucual Us Ca S Mg Slags he elaoshp bewee mass peceage o Ca, S, Mg,, ad as compoes ad he calculaed equlbum mole umbes o sucual us,.e., (Ca ), S, (Mg ), ( ), ad, Ca S Mg slags a empeaue age om 8 o 9 was llusaed Fg., especvely. bvously, he calculaed equlbum mole umbes o all 6 sucual us have some elao wh mass peceage o he coespodg compoes. he good lea elaoshp ca be oud o S ad 79 ISIJ

6 ISIJ Ieaoal, Vol. (), o. Fgs. (b) ad (d), hs pheomeo ca be explaed as ha o so may molecules o S o ca be bouded o om complex molecules. he scae elaoshp ca be obseved o (Ca ), (Mg ), ad as compoes Fgs. (a), (c), (e) ad (). Howeve, a lea elaoshp ca be coelaed o (Ca ), (Mg ), ad Fgs. (a), (c), (e) ad () alhough some mass o above meoed compoes ca be oud as vaous complex molecules. heeoe, he calculaed equlbum mole umbe o sucual us Ca S Mg slags ca be appled o epese chemcal composo o he slags.,) Fg.. Relaoshp bewee mass pece o Ca, S, Mg,, ad as compoes ad calculaed mass aco coceaos o (Ca ), S, (Mg ), ( ), ad as sucual us g Ca S Mg slags equlbaed wh lqud o a elevaed empeaues, especvely... Relao bewee Equlbum Mole umbes ad Bascy Ca S Mg Slags he elaoshp bewee he calculaed equlbum mole umbes ad smple bay bascy R o slags,.e., ((%Ca)/(%S )) was llusaed Fg.. oal equlbum mole umbe Σ has a vey good lea elaoshp wh smple bay bascy R o slags,.e., ((%Ca)/ (%S )). he omula o equlbum mole umbe Σ agas he smple bay bascy R o slags ca be egessed as Σ.6.9*exp( R/.9), ad he g degee s.99. hs elable g degee esuls sugges ha chagg he smple bay bascy R o slags have a lage eec o Σ.. Model o Calculag hosphous Dsbuo bewee Ca S Mg Slags ad Lqud Io Accodg o he o ad molecule coexsece heoy ha oly ee o couples (Ca ), ad (Mg ), whch ca be combed wh o oxdes Ca S Mg slags, ca ake oles dephosphozao eacos ems o omg 8 dephosphozao molecules as,,, Ca, Ca, Ca, Mg ad Mg accodg o,) as ollows [ ] ( ) ( ) [ ] G. J/mol m, ( ) [ ] ( ) ( ) [ ] G m, 86. ( J/mol) [ ] ( ) ( ) ( ) [ ] G ( J/mol) ( ) m,...(9a)... (9b)...(9c) oal Fg.. Relaoshp bewee mass pece o Ca, S, Mg,, ad as compoes ad calculaed equlbum mole umbes o (Ca ), S, (Mg ), ( ), ad as sucual us g Ca S Mg slags equlbaed wh lqud o a elevaed empeaues, especvely. Fg.. Relaoshp bewee bay bascy R ad calculaed oal equlbum mole umbe o sucual us Σ g Ca S Mg slags equlbaed wh lqud o a elevaed empeaues. ISIJ 76

7 ISIJ Ieaoal, Vol. (), o. [ ] ( ) ( ) [ ] ( J/mol) ( Ca ) Ca G m, Ca [ ] ( ) ( ) [ ] G ( J/mol) ( Ca ) Ca m, Ca [ ] ( ) ( ) [ ] G m, Ca ( J/mol) [ ] ( ) ( Mg ) ( Mg ) [ ] ( J/mol) ( Ca ) Ca G m, Mg [ ] ( ) ( ) [ ] G ( J/mol) ( Mg ) Mg m, Mg... (9d)...(9e)...(9)... (9g)... (9h) he coespodg equlbum cosas o Eq. (9) ca be expessed accodg o,) as a a a a Ca Ca Ca Mg ) / M a a a a a ) / M a a a a a ) / M aca a a a a Ca Ca Ca ) / M Ca Ca aca a a a a Ca Ca Ca ) / M Ca Ca aca a a a a Ca Ca Ca ) / M Ca Ca amg a a a a Mg Mg Mg ) / M Mg Mg...(a)... (b)...(c)... (d)...(e)...()... (g) amg a Mg Mg a a a Mg Mg... (h) ) Mg / M ( ) Mg whee M s molecula mass o as.9 ( ). Accodg o Eq. (), he especve phosphous dsbuo o sucual us as basc compoes he slags L, ca be expessed by ) L, M...(a) ) L,...(b) M ) L,...(c) M ) Ca L, Ca...(d) M Ca Ca ) Ca L, Ca...(e) M Ca Ca ) Ca L, Ca... () M Ca Ca ) Mg L, Mg...(g) M Mg Mg ) Mg L, Mg...(h) M Mg Mg whee s acvy coece o he dssolved phosphous lqud o ( ), ad ca be calculaed as ollows j lg e [% j]...(a) j e cos... (b) he elaed values o eaco coeces o [] [] ae chose as e.6, e. a 87. heeoe, he oal phosphous dsbuo bewee Ca S Mg slags ad lqud o ca be obaed om Eq. () as ollows L L, L L L,,, Ca L, Ca L, Ca L, Mg L, Mg ) ) ) ) Ca ) ) Ca Ca.. () ) Mg ) Mg M ( Ca Ca Ca Ca Ca Ca Mg Mg Mg Mg ) 76 ISIJ

8 ISIJ Ieaoal, Vol. (), o. able. Calculao o sadad mola Gbbs ee eegy o 8 dephosphozao eacos om he epoed daa o sadad mola Gbbs ee eegy. Dephosphozao eacos Resouce eacos (J/mol) [] 7 7. ) []( )( )[] [] 7.9 ) [][]( )(l) ). ( )(l) 6 86.,) [][]( ) ) []( )( )( )[] ()( )( ) ) 86. []( )( )[]. []( )( )( )[] ( )( )( ) ) []( )( )[]. (Ca) (Ca )(s) ) []( )(Ca )(Ca )[] (Ca )(s) (Ca )(l) ) ( )(l) 6 86.,) []( )( )[]. (Ca) (Ca )(s) 76.7 ) []( )(Ca )(Ca )[] ( )(l) 6 86.,) G m, []( )( )[]. []( )(Ca )(Ca )[] (Ca)( )(l)(ca )(l) ) []( )( )[]. []( )(Mg )(Mg )[] (Mg - )( )(Mg ) ) []( )( )[]. (Mg) (Mg )(s) ) []( )(Mg )(Mg )[] (Mg )(s) (Mg )(l) ) ( )(l) 6 86.,) []( )( )[]. heeoe, he developed L pedco model by o pese slag oxdzg ably s composed o Eqs. () ad (). Accodg o he calculaed ad Σ Seco, by Eq. () ad by Eq. (), he oal phosphous dsbuo L o he slags whch equals o he sum o especve phosphous dsbuo L, o basc o couples he slags ca be calculaed. he sadad mola Gbbs ee eegy o dephosphozao eacos Eq. (9) o omg dephosphozao poducs s deemed om he epoed daa ad summazed able.. Resuls ad Dscusso.. Compaso o Measued hosphoous Dsbuo L, measued ad Calculaed hosphoous Dsbuo L, calculaed I ode o exame he applcably o he L model developed he pese sudy based o he o ad molecule coexsece heoy, boh mehods have bee adoped o evaluae he accuacy o he calculaed L, calculaed. e s decly compag he measued L, measued om pevous eeeces,) ad he calculaed L, calculaed based o he o ad molecule coexsece heoy; he ohe s compag he L model wh some ohe epoed phosphoous dsbuo pedco models,,6 9) such as Healy s model, ) Suo s models, 6,7) Sommevlle s model, 8) ad Balajva s model. 9) he compasos bewee he measued phosphoous dsbuo L, measued o Ca S Mg slags equlbaed wh lqud o a 87 ad 9 epoed by Basu e al. ) o he measued phosphoous dsbuo L, measued o he Ca S Mg slags a 8, 87 ad 9 epoed by agabayash e al. ) ad he calculaed phosphoous dsbuo based o o ad molecule coexsece heoy L, calculaed Fg.. Compaso bewee calculaed ad measued phosphous dsbuo o Ca S Mg slags equlbaed wh lqud o a empeaue age om 8 o 9.,) was llusaed Fg., especvely. As show Fg., a excelle : ageeme bewee phosphoous dsbuo lg L, measued epoed by Basu e al. ) ad lg L, calculaed based o he o ad molecule coexsece heoy ca be obaed, meawhle, a good : lea elaoshp bewee phosphoous dsbuo lg L, measued epoed by agabayash e al. ) ad lg L, calculaed based o he o ad molecule coexsece heoy ca also be oud. I should be poed ou Ca S Mg slags was eaed as a specal Ca S Mg slags hs pape wh he assumpo ha he coe o equal o zeo. hs esul dcaes ha he developed L pedco model ca be appled o elably pedc he phosphoous dsbuo L o Ca S Mg slags equlbaed wh lqud o... Compaso o Calculaed hosphoous Dsbuo L by Dee Models, calculaed he compasos bewee he measued L, measued ad ISIJ 76

9 ISIJ Ieaoal, Vol. (), o. able. Fomulas o phosphous dsbuo pedco models epoed elaed leaues. L model Slags Fomulas o L models Healy s model ) Ca S Mg M Al slags lg (% ) 8. (% Ca). lg(% ) 6 ) lg. [(% Ca). (% Mg). ). 6%( M)] Suo s o. (% ) model 6,7) Ca S Mg slags 8. 6 ) lg 787. lg[(% Ca). (% Mg). (% ). ) 6.%( M)] Suo s o. (% ) model 6,7) Ca S Mg slags 7. Sommevlle s model 8) Balajva s model 9) Ca S Mg M slags Ca S Mg M slags lg ) [ 6(% Ca) 7. (% Mg) 8. (% M)]. lg(% ) lg(% S ). lg ) lg( % ). [(% Ca). (% Mg). (% 8 6.(% M )]. 6 ) calculaed L logahmc om by vaous models, calculaed lsed able wee show Fg.. bvously, all pedco models have good ageeme wh he measued L, measued o Ca S Mg slags a 87 ad 9 epoed by Ba ya e al. ) excep Suo s o. L model.,6) Howeve, oly lg L, calculaed by L model have : elable lea elaoshp wh he measued L, measued o Ca S Mg slags a 8, 87 ad 9 epoed by agabayash e al., ) compaed wh ohe pedco models such as by Healy s L model, ) Suo's o. Healy lg L, calculaed lg L, calculaed by Suo s o. L model, 6,7) Suo's o. lg L by Suo s o. L model, 6,7) Sommevlle, calculaed lg L by Sommevlle s L model 8), calculaed ad Balajva lg L by Balajva s L model. 9), calculaed I should be specally emphaszed ha he calculaed L by vaous models lsed able has bee, calculaed aseed o (% )/[%], ahe ha he deed phosphous dsbuo as (%)/[%] Healy s model, ) o (% )/[%] (% ) Suo s o. ad o. models, 6,7) o (% )/[%] Sommevlle s model 8) as lsed able... Relao bewee Mass Aco Coceaos o Compoes ad lg L, measued o lg L, calculaed he luece o he calculaed mass aco coceaos o compoes upo lg L, measued o lg L, calculaed o he Ca S Mg slags equlbaed wh lqud o a 8, 87 ad 9 was show Fg. 6, especvely. I was see Fgs. 6(a) ad 6(c) ha ceasg Ca ad Mg ca lead o a cease o phosphous dsbuo lg L, measued o lg L, calculaed ; mpovg S wll esul deceasg o phosphous dsbuo lg L, measued o lg L, om Fg. 6(b). Meawhle, calculaed clealy coespodg elaoshp bewee lg L, measued o lg L, calculaed ad o ca be obseved om Fgs. 6(d) ad 6(e). hs pheomeo ca be explaed as ha dephosphozao pocess s coolled by he compehesve eec o basc oxdes ad o oxdes. heeoe, ude ccumsace o adequae bascy oxdes, ceasg o oxdes ca eecvely cease dephosphozao ably o slags. Howeve, ceasg o oxdes whou eough bascy oxdes ca oly lead o a slghly ceasg o phosphous dsbuo. Fg.. Compaso bewee he measued phosphous dsbuo lg L, measued by pevous leaues,) ad he calculaed phosphous dsbuo lg L, calculaed by vaous phosphous dsbuo pedco models,6 9) o Ca S Mg slags equlbaed wh lqud o a elevaed empeaues. hee ae some exeme poos o suppo hs esuls as ollows: ) A slags wh hgh o oxdes bu vey low Ca, whch s appled deslcozao peeame o lqud o, ca oly exac slco bu o phosphous; ) A slags wh hgh Ca bu vey low, whch s appled a educ- 76 ISIJ

10 ISIJ Ieaoal, Vol. (), o. Fg. 8. Cobuo o 8 sucual us coag Ca S Mg slags o he oal dephosphozao ably (a), ad he elaoshp bewee lg L, calculaed ad lg L, Ca a elevaed empeaues (b). 9 cao bg a obvous ceasg edecy o lg L, measued o lg L, calculaed due o sauao wh sold phase; as show Fg. 7(b), ceasg complex bascy om. o. ca lead o a obvous ceasg edecy o L, uhe ceasg complex bascy om. o. have lle luece o lg L, measued o lg L, calculaed owg o sauao wh sold phase;. Fg. 6. Fg. 7. Eec o calculaed mass aco coceaos o o couples o smple molecules o (Ca ), S, (Mg ), ( ), ad o lg L, measued ad lg L, calculaed a elevaed empeaues. Eecs o bay bascy (%Ca)/(%S ) (a) ad complex bascy ((%Ca).(%Mg)/(%S )(% )) (b) o lg L, measued ad lg L, calculaed a elevaed empeaues. o peod dug elecc ac uace seelmakg pocess, ca oly exac sulu bu o phosphous. heeoe, he compehesve eec o basc compoes, especally Ca ad, ca make he ma coollg cobuo o dephosphozao he slags... Relaoshp bewee Slag Bascy ad lg L, measued o lg L, calculaed o Al exss he seleced slags, he commoly appled complex bascy ((%Ca).(%Mg)/(%S ) (% )/(%Al )) ) ca be smpled as ((%Ca).(%Mg)/(%S )(% )). he elaoshp bewee lg L, measued o lg L, calculaed ad bay bascy ((%Ca)/ (%S )) o complex bascy ((%Ca).(%Mg)/ (%S )(% )) wee llusaed Fgs. 7(a) ad 7(b). I ca be obseved om Fg. 7(a) ha ceasg bay bascy om. o.7 ca eecvely mpove lg L, measued o lg L, calculaed, uhe ceasg bay bascy om.7 o.. Cobuo o Basc xdes o Dephosphozao Ably o Ca S Mg Slags Accodg o,,) he sucual u s geeaed om he slags o [] lqud o, meawhle, hee compoes as Ca, Mg, ad he slags ca eac wh o geeae,, Ca, Ca, Ca, Mg, ad Mg as complex molecules. As show Eq. (), he especve phosphous dsbuo L, o above-meoed egh molecules ca be calculaed om he developed L model. he elaoshp bewee he calculaed especve phosphous dsbuo lg L,, calculaed o 8 sucual us co- ag phosphous ad he measued lg L, calculaed o he slags was llusaed Fg. 8(a), especvely. bvously, he cobuo o,,, Mg, ad Mg o he oal dephosphozao ably s vey small, heeoe, he cobuo o above meoed complex molecules ca be goed compaed wh he cobuo o Ca as 97.88%, Ca as.% ad Ca as.%. Sce Ca made he ma cobuo o dephosphozao Ca S Mg slags, ad he : coespodg elaoshp bewee lg L, calculaed ad lg L, Ca ca be oud Fg. 8(b), meawhle, he omula o lg L, calculaed agas lg L, Ca was egessed as lg L, calculaed lg L, Ca. Hece, ca be cocluded ha omed -calcum phosphae (Ca ), bu o ea-calcum phosphae, (Ca ) Ca S Mg slags. 6. Coclusos A hemodyamc model o calculag phosphae dsbuo bewee Ca S Mg slags ad lqud o,.e., L model, has bee developed coupled wh a developed hemodyamc model o calculag mass aco coceaos o sucual us,.e., model, based o o ad molecule coexsece heoy. he ma omao ca be summazed as ollows: ISIJ 76

11 ISIJ Ieaoal, Vol. (), o. () he calculaed esuls om model shows ha he calculaed mass aco coceaos o sucual us, ahe ha mass peceage o compoes, ae ecommeded o epese eaco ably o compoes Ca S Mg slags. Smple bay bascy R o slags have a lage eec o oal equlbum mole umbe Σ o sucual us Ca S Mg slags, he omula o oal equlbum mole umbe Σ agas he smple bay bascy R o slags ca be egessed as Σ.6.9*exp( R/.9), ad he g degee s.99. () he developed L pedco model ca be appled o elably pedc he phosphoous dsbuo L o Ca S Mg slags equlbaed wh lqud o. Meawhle, some ohe phosphoous dsbuo pedco models have also bee ake o cosdeao o calculag phosphae dsbuo bewee Ca S Mg slags ad lqud o, ad he esuls shows ha L model have moe accuacy compaed wh ohe phosphoous dsbuo pedco models. () he developed L model ca quaavely calculae he especve cobuo o, Ca ad Mg he slags. A sgca deece o dephosphozao ables amog, Ca ad Mg ca be oud as appoxmaely.%, 99.98%,.%. Meawhle, he phosphous lqud o ca be eecvely exaced by Ca slags o om complex molecules Ca whch made he ma cobuo o dephosphozao Ca S Mg slags. omeclaue A: Cosa, ( ); a : Acvy o compoes lqud o o slags, ( ); B: Cosa, ( ); b : Mole umbe o compoe g slags, (mol); j e : Ieaco coece o compoe j o compoe lqud o, ( ); : Acvy coece o compoe lqud o, ( ); : Sadad mola Gbbs ee eegy o omg complex molecule slags, (J/mol); (%): Mass peceage o compoe he slags, (mass%); [%]: Mass peceage o compoe lqud o, (mass%); : Equlbum cosa o chemcal eaco o omg compoe o sucual u, ( ); L : hosphous dsbuo bewee slags ad lqud o, ( ); L, : Calculaed especve phosphous dsbuo o geeaed sucual u coag slags based o slag oxdzao ably by model, ( ); : Calculaed oal phosphous dsbuo bewee slags ad lqud o based o slag oxdzao ably by model, ( ); L, measued: Measued phosphous dsbuo, ( ); L, calculaed L,, calculaed L, calculaed : Calculaed especve phosphous dsbuo bewee geeaed sucual u coag slags ad lqud o based o slag oxdzao ably by model om calculaed daa, ( ); : Calculaed phosphous dsbuo bewee slags ad lqud o by model, ( ); Me: Meal, ( ); Me: xde compoe slags, ( ); M : Molecula mass o eleme o compoe, (g/ mol); : Mole umbe o compoe g slags, (mol); : Equlbum mole umbe o sucual u g slags, (mol); : Mass aco coceaos o sucual u he slags, ( ); Σ : oal equlbum mole umbe o all sucual us g slags, (mol); R: smple bay bascy, ( ); R: Gas cosa, (8. J/(mol )); : Absolue empeaue, (); Subscps c: Complex molecule, ( ); REFERECES ).. Colclough: J. Io Seel Is., 7 (9), o., 67. ).. Colclough: as. Faaday Soc., (9-96),. ) C. H. Hey: as. AIME, 7 (96), 7. ) G. W. Healy: J. Io Seel Is., 8 (97), o. 7, 66. ) E.. ukdoga ad J. easo: J. Io Seel Is., 7 (9), o., 9. 6) H. Suo ad R. Ioue: ISIJ I., (98), o.,. 7) H. Suo, R. Ioue ad M. akada: ISIJ I., (98), o.,. 8) I. D. Sommevlle, X. F. Zhag ad J. M. ogu: as. Io Seel Soc., 6 (98), 9. 9). Balajva, A. G. Quaell ad. Vajagupa: J. Io Seel Is., (96), o.,. ) S. Basu, A.. Lah ad S. Seehaama: Meall. Mae. as. B, 8 (7), o., 7. ) H. Suo ad R. Ioue: ISIJ I., (99), o., 8. ) Y. obayash,. Yoshda ad. aga: ISIJ I., (), o.,. ) R. agabayash, M. Ho ad S. Ba ya: esu-o-hagaé, 7 (988), o. 8, 77. ) X. M. Yag, J. S. Jao, R. C. Dg, C. B. Sh ad H. J. Guo: ISIJ I., 9 (9), o., 88. ) C. B. Sh, X. M. Yag, J. S. Jao, C. L ad H. J. Guo: ISIJ I., (), o., 8. 6) J. Zhag: Compuaoal hemodyamcs o Meallugcal Mels ad Soluos, Meallugcal Idusy ess, Bejg, (7),. 7) J. Zhag: J. Bejg Uv. Io Seel echol., 8 (986), o.,. 8) J. Zhag: J. Bejg Uv. Io Seel echol., (988), o.,. 9) J. Zhag: Aca Meall S., (998), o. 7, 7. ) J. Zhag: Calphad, (), o.,. ) Vee Deusche Esehueleue: Slag Alas, d ed., Woodhead ublshg Lmed, Abgo Hall, Abgo, Cambdge, U, (99). ) J. X. Che: Hadbook o Commo Fgues, ables ad Daa o Seelmakg, d ed., Meallugcal Idusy ess, Bejg, Cha, (). ) X. M. Yag, M. Zhag, J. L. Zhag,. C. L, J. Y. L ad J. Zhag: Seel Res. I., pess, DI:./s.8. ) E.. ukdoga: hyscal Chemsy o Hgh empeaue echology, Academc ess, ew Yok, (98), 8. ) R. H. Re ad J. Chpma: as. Me. Soc. AIME, (96),. 6) H. Gaye ad J. Welge: oc. o he d I. Symp. o Meallugcal Slags ad Fluxes, ed. by H. A. ad D. R. Gaskell, MS AIME, Waedale, A, (98), 7. 7) V. Espejo ad M. Iwase: Meall. Mae. as. B, 6 (99), o., 7. 8) he Japa Socey o he omoo o Scece, he 9h Commee o Seelmakg: Seelmakg Daa Soucebook, Godo ad Beach Scece ublshes, ew Yok, Y, (988), 79. 9) J. B. Bookey: J Io Seel Is., 7 (9), o., 6. ) V. D. Esehüeleue, Slag Alas, d ed., Woodhead ublshg Lmed, Abgo Hall, Abgo, Cambdge, U, (99),. ) J. Zhag ad C. Wag: J. Uv. Sc. echol. Bejg., (99), o.,. ) J. Zhag ad W. X. Yua: J. Uv. Sc. echol. Bejg., 7 (99), o., 8. ) J. Zhag: Rae Meals, (), o., 9. ). aa ad. Shj: obe Seel Eg. Rep., (969),. ) H. Suo, A. Ishzaka, R. Ioue ad Y. akahash: esu-o-hagaé, 6 (979), o., 88. 6). Maukawa, Y. Shoa, S. Aezak ad H. Hahaa: esu-o- Hagaé, 67 (98), o.,. 7). Mo, H. Wada ad R. D. ehlke: Meall. as. B, 6 (98), o.,. 8) E.. ukdoga: ISIJ I., (), o., 96. 9) C. Boga ad. Gaa: Meall. as. B, 8 (977), o., 7. ) R. agabayash, M. Ho ad S. Ba ya: esu-o-hagaé, 7 (988), o. 9, ISIJ