Analysis of Reaction Rate between Solid Carbon and Molten Iron by Mathematical Models

Transcription

1 ISIJ Intenational, Vol. 45 (2005), No. 10, pp Analysis of Reaction Rate between Solid abon and Molten Ion by Matheatical Models Haiping SUN R fo oal in Sustainable Developent, School of Mateials Science and Engineeing, Univesity of New South Wales, Sydney NSW 2052 Austalia. E-ail: h.sun@unsw.edu.au (Received on Octobe 18, 2004; accepted on June 20, 2005) The factos affecting the cabon dissolution ate into liquid ion and the intedependency between these ate influencing factos wee discussed with aid of a kinetic odel. These ate influencing factos include tepeatue, cabon stuctue, intefacial active eleents, etal coposition, liquid agitation, wettability between solid and liquid, solid paticle size, ash in cabonaceous ateials and side eactions. Expeients wee caied out on cabon dissolution fo gaphite and coke into liquid Fe alloy using esistance o induction funaces at The kinetic paaetes descibing cabon dissolution ate wee obtained fo the copaison of obseved cabon dissolution ates and odel calculations. The dissolution ates at highe tepeatues o in an induction funace wee found oe apid than those at lowe tepeatues o in a esistance funace. The ass tansfe in liquid was found to be the ajo liiting step fo the cabon dissolution pocess. EY WORDS: ionaking; coke; coal; kinetics; dissolution. 1. Intoduction The ion aking pocess is an ion oxide eduction and heating-elting pocess. High speed eduction and low tepeatue elting ae ost ipotant pocesses fo ipoving the efficiency of the pocess. 1) Since eaction ates stongly depend on tepeatue, to aintain high poductivity of blast funace, the ajo eactions in the pocess ust occu at high speed at lowe tepeatue. abuisation of the ion is one of the ajo eactions in the blast funace pocess. It is clea that the high speed cabuisation can not be expected though gas. And without futhe inceasing tepeatue, high speed cabuisation can not be expected though the solid contact eithe. In a coke packed bed, the elting of educed ion occus at the contacting points between coke and educed ion. At high tepeatues, liquid ion is initially geneated by cabuisation at these points because elting tepeatue of ion is loweed by cabon pickup. And then the ion elts though siultaneous cabon dissolution into liquid ion and cabuisation of solid ion by the liquid ion. Theefoe, high speed elting of educed ion is achieved via cabon dissolution in a blast funace. The dissolution of cabon into liquid ion was taditionally consideed to be liited by the ass tansfe in liquid ion. 2 8) This was ainly evidenced by the stong dependency of the dissolution ate on the liquid agitation and weak dependency of the ate on the tepeatue and sulfu in liquid. In the ecent seies of eseaches, the dissociation eaction at the inteface was suggested to be ipotant fo the cabonaceous ateials with less odeed atoic stuctue. 9 17) This was ainly evidenced by the stong dependency of the dissolution ate on the cystallite size of cabonaceous ateials and sulfu in the liquid. Lack of ageeent on the cabon dissolution echanis aong these investigations equies a kinetic teatent of the dissolution ates with both possible liiting echaniss, i.e., the intefacial dissociation eaction and the ass tansfe. The piay objectives of this study wee to futhe develop the undestanding of the cabon dissolution echanis. Discussion on the factos that influence the cabon dissolution ate was caied out based on the odel that includes the intefacial dissociation eaction and ass tansfe pocesses. The kinetics of cabon dissolution was discussed with expeiental obsevations. 2. Model Developent and Discussions 2.1. Eleentay Steps of abon Dissolution When a solid cabon ateial contacts with liquid ion at high tepeatue, the dissolution of cabon fo the solid into liquid ion occus. The oveall dissolution eaction is (solid) []...(1) whee, (solid) is cabon in solid stuctue, and [] is cabon in liquid, ass%. The equilibiu elation of this eaction is a a solid EQ...(2) whee is the equilibiu constant fo the eaction (1). o a a solid 2005 ISIJ 1482

2 ISIJ Intenational, Vol. 45 (2005), No. 10 a solid, a and a ae the cabon activities of solid cabon, liquid and liquid satuated (o in equilibiu) with the solid cabon, espectively. The dissolution occus though two consecutive steps; the fist step is the dissociation of cabon atos fo solid stuctue into intestitial positions of ion atos at the liquid side of the inteface as expessed by Eq. (3), (solid) []*...(3) whee []* is the cabon content at the liquid side of the inteface, ass%. The dissociation eaction ate is the diffeence between the fowad eaction ate and the evese eaction ate and is given by, a J Ak asolid...(4) whee J is the dissociation eaction ate of cabon, g/s, A is solid liquid contact aea, c 2, k is ate constant of the dissociation eaction (1), g/s c 2, and a* is the cabon activity at liquid side of the inteface. Accoding to the ecent study, 11) the dissociation eaction is futhe divided into dissociation of cabon stuctue, accuulation of libeated cabon at the inteface and adsoption of cabon into intestitial position aong ion atos. Theefoe, k can be consideed as oveall ate constant fo these pocesses at the inteface. The second step is the ass tansfe of cabon atos in the intestitial positions of liquid stuctue at the liquid side of the inteface into liquid bulk as expessed by Eq. (5), []* []...(5) It is assued that a static fil of liquid is pesent at the inteface. Thee is no cabon concentation gadient in the liquid bulk beyond this bounday fil, but tanspot acoss the static laye is contolled by diffusion. It was also assued that steady-state conditions exist in the bounday fil; thus, Fick s Fist Law is used to descibe the linea vaiation of the concentation of cabon acoss the bounday fil: Akρ J...(6) ([]* []) 100 whee J is the ass tansfe ate of cabon fo the inteface into liquid bulk, g/s, k is the ass tansfe coefficient in the liquid, c/s, and is the density of the liquid, g/ c Mixed Liiting by Mass Tansfe and Intefacial Dissociation Thee is no accuulation of cabon at the liquid side of the inteface. Thus, the cabon flux down to the bulk ust equal to the flux of cabon geneated fo eaction (3) o J, J d J J...(7) whee J d is the dissolution ate of cabon, g/s. The intefacial cabon content can be expessed by Eq. (8) fo Eqs. (4), (6) and (7), 100ka solid kρ []* []...(8) f kρ 100k whee f * is the cabon activity coefficient at the liquid side of the inteface. Replacing the intefacial cabon in eithe Eq. (4) o Eq. (6) with that in Eq. (8), the dissolution ate of cabon is given by, f [] J Ak a...(9) d t solid whee k t is oveall ate constant of cabon dissolution, g/s c 2, which is f...(10) kt k kρ Equation (9) is the cabon dissolution ate equation involving intefacial dissociation eaction and ass tansfe pocesses. The total esistance (R t ), the esistance of dissociation eaction (R ), and the esistance of ass tansfe (R ) to the cabon dissolution pocess ae given by Eqs. (11), (12) and (13), espectively....(11)...(12) f R...(13) 100 fρ whee R t, R and R have a unit of c 2 s/g. It is noted that, the esistance of the ass tansfe to the cabon dissolution pocess, R, is a function of intefacial cabon activity coefficient, f *, which is a dependence of intefacial cabon content ([]*). This indicates R and k t vay with tie duing cabon dissolution pocess. The diving foce fo the ixed liiting dissolution pocess is a solid f *[]/ Mass Tansfe Liiting When the cabon dissolution is liited by ass tansfe, i.e., R R, the equilibiu of the eaction (1) is achieved at the inteface because the ate of intefacial dissociation eaction is uch faste than that of the ass tansfe. If the intefacial contents of othe alloying eleents ae equal to thei bulk countepats, intefacial values of cabon ae able to be obtained fo equilibiu elation of eaction (1) as, []* [], f * f, and a* a...(14) whee f is cabon activity coefficient in the liquid when cabon eaches satuation. Replacing the intefacial values in Eq. (9) with those in Eq. (14) and ignoing R, the dissolution ate equation becoes, J d 1 Rt R R k R Akρ 100M t 1 k ([] [])...(15) Equation (15) descibes the dissolution ate that is liited by the liquid phase ass tansfe. The diving foce fo the dissolution pocess is [] []. The ate is dictated by ass tansfe coefficient, k and cabon satuation content, ISIJ

3 ISIJ Intenational, Vol. 45 (2005), No. 10 the foe vaies with tepeatue, liquid coposition, liquid phase agitation and the latte with tepeatue, liquid coposition and solid stuctue. Eq. (15) o its integated fo as given in Eq. (16) is fequently used to descibe the dissolution ate if liquid phase ass tansfe liits the dissolution ate. ln ([] []) Ak t...(16) ([] [] ) V 0 whee t is the tie peiod ove which the dissolution occus, s, V is volue of liquid ion, c 3, and [] 0 is the initial cabon content in the liquid, ass% Liiting by Intefacial Dissociation When the dissolution is liited by the dissociation eaction at the inteface, i.e., R R, the equilibiu of the ass tansfe shown in Eq. (5) is achieved because intefacial dissociation is uch slowe than the ass tansfe pocess. Intefacial values ae equal to thei bulk values as, []* [], f * f and a* a...(17) whee f is the cabon activity coefficient in the bulk of the liquid. Replacing the intefacial values in Eq. (9) with bulk values in Eq. (17) and ignoing R, the dissolution ate becoes, a J...(18) d Ak asolid Equation (18) descibes the dissolution ate liited by the intefacial dissociation eaction. The diving foce fo the pocess is a solid a /. Since activity of pue solid is usually unity, a solid 1, the ate is dictated by dissociation eaction ate constant, cabon activity, and equilibiu constant fo the eaction (1). The dissociation ate constant vaies with tepeatue, stuctue of solid and intefacial active eleents. The cabon activity vaies with tepeatue and liquid coposition, and the equilibiu constant vaies with tepeatue and solid stuctue. abon with diffeent stuctues has diffeent fee enegy changes fo eaction (1) at standad state and thus has diffeent values of at a given tepeatue. Using equilibiu elation in Eq. (2), a hypothetic solid activity (a solid(eq) ) in equilibiu with cabon in the liquid bulk can be obtained as a solid(eq) a /...(19) This hypothetic solid activity can be thought as solid cabon potential of the liquid. With this elation, the Eq. (18) becoes J d Ak (a solid a solid(eq) )...(20) The diving foce is a solid a solid(eq), which is the diffeence between solid activity and a solid activity in equilibiu with cabon in the liquid bulk. Altenatively, a hypothetic cabon content in equilibiu with solid and an instantaneous f can be defined fo equilibiu elation fo eaction (1) as, [] EQ a solid /f...(21) [] EQ can be thought as liquid cabon potential of the solid with an instantaneous f. With this elation, the Eq. (18) becoes, J d Ak ([] EQ [])...(22) whee k is appaent eaction ate constant, expessed by, f k...(23) k The diving foce is then [] EQ [], which is the diffeence between bulk cabon content and the cabon content in equilibiu with solid and the instantaneous f. It is noted that (22) has a siila fo as Eq. (15) fo ass tansfe liiting pocess. Howeve, k and [] EQ in Eq. (22) ae not constant since they vay with instantaneous f. This will fobid Eq. (22) to be integated into siila fo as Eq. (16) because f vaies with cabon content, and the cabon content vaies with dissolution tie Rate Influencing Factos inetic and Theodynaic Paaetes vs. Thei Influencing Factos Table 1 suaized the dissolution ate equations fo the cabon dissolution pocess fo thee cases. ase (A), ase (B) and ase () epesent the ate is liited by the ass tansfe, intefacial dissociation eaction, and by the Table 1. Liiting step(s), ate equation, and kinetic and theodynaic paaetes fo cabon dissolution ISIJ 1484

4 ISIJ Intenational, Vol. 45 (2005), No. 10 Table 2. Rate influencing factos fo cabon dissolution. both of the, espectively. The paaetes involved in the cabon dissolution ate of each case wee also suaised in the Table. Fo all cases, the dissolution ate is stongly influenced by the contact aea A. The dissolution ates fo ase (A) and ase () vay with k, those fo ase (B) and ase () vay with k and, and that fo ase (A) vaies with cabon satuation content, [] sat. The intedependency between [] and can be obtained fo Eq. (2) as, solid [] a...(24) f [] depends on tepeatue and alloying eleents in the liquid, while solely depends on tepeatue fo a given solid. Table 2 shows the influencing factos on paaetes that diectly dictate the dissolution ate. The intedependencies between these factos ae suaised in Table 3. As can be seen in Tables 1 though 3, a thoough thought ust be given when investigating the dissolution pocess of ipue cabon ateials such as coke, coal o natual gaphite. Effots should be ade to isolate the ate influencing facto of inteest; othewise its influence could be asked by the uncontollable vaiation of othe ate influencing facto(s). The ate influencing factos in Table 3 and the intedependencies between the ae discussed in the following sections Tepeatue Tepeatue will not diectly affect the contact aea, but tepeatue ay indiectly, though affect wettability between solid cabon and liquid, viscosity and fusion of the ash to affect the contact aea. Tepeatue has a stonge ipact on the k than on k because cheical eaction usually has lage activation enegy. and [] ae functions of tepeatue. Tepeatue also affects k though affecting intefacial adsoption blockage and solid cabon stuctue. As will be discussed late, soe side eactions ae sensitive to the tepeatue, which will in tun affect the cabon dissolution ate Solid Stuctue Stuctue of solid ay affect k, and []. This is because k descibes the dissociation eaction ate of cabon atos fo solid lattice into the intestitial positions suounded by ion atos in the liquid. The dissociation pocess includes the uptues of atoic bonds between cabon atos in solid, and atoic bonding type and the bonding stength ae deteined by the solid stuctue. is elated to the fee enegy change of eaction (1) which depends on the solid stuctue. Gaphite, natual gaphite, vaious cokes and coal, and diaond ae cabon of diffeent stuctue, and they have diffeent at a given tepeatue. [] is the equilibiu cabon content with the solid and vaies with and thus with solid stuctue. The intefacial tension between solid and liquid vaies with the solid stuctue, this indicates the adsoption blockage by intefacial active eleents and the wettability between liquid and solid ay be affected by the solid stuctue. Table 3. Intedependency between influencing factos Adsoption Blockage Intefacial active eleents in the liquid, such as sulfu, will occupy the eaction sites to educe k. The investigation on the sulfu effect 18) suggested that the dissolution ate was contolled by both ass tanspot and phase bounday eactions when sulfu was pesent in the liquid. The faction of intefacial eaction sites occupied by the intefacial active eleents is the tepeatue dependency which is quantitatively descibed by Gibbs Lunngi adsoption isothe. The liquid coposition will affect the faction of the occupied sites by affecting activity of the intefacial active eleents in the liquid. The bette wetting can be expected between liquid and solid with inceasing intefacial active eleents in the liquid because the intefacial tension between liquid and solid deceases. The ate of side eactions that ae liited by the eaction at inteface, fo exaple eductions of silica 20) o titania 21) in ash by dissolved cabon in the liquid, ae vey sensitive to the intefacial adsoption blockage Alloying Eleents Eleents pesent in the liquid, such as Si, Mn and S, affect the activity coefficient of cabon in liquid and theefoe the cabon satuation content. Alloying eleent will also affect k though affecting diffusivity of cabon in liquid and viscosity of the liquid. Fo exaple, the addition of 0.2 ass% sulfu can decease the ass tanspot coeffi ISIJ

5 ISIJ Intenational, Vol. 45 (2005), No. 10 cient fo the dissolution of gaphite by appoxiately 20%, 22) and diffusivity of cabon in liquid is deceased by addition of silicon in the elt. 3) Wettability between liquid and solid would vay with etal coposition because the intefacial tension between the two phases is influenced lagely by the liquid copositions. 19) As will be discussed late, the side eactions ae influenced by the liquid copositions Liquid Agitation Liquid agitation inceases k though educing the bounday laye thickness in liquid, and thus diffusion distance. The ate of side eactions that ae liited by ass tansfe pocess, fo exaple, eaction of sulfu, phosphous and anganese between ash and liquid, 23) ae sensitive to the liquid agitation Liquid Solid Wettability Wettability between solid cabon and liquid affects the contact aea when poous o sall paticles of solid ae in contact with the liquid. This is because good wetting will allow liquid to penetate into poes of the solid o intestitial space between paticles to incease the contact aea. Good wetting eans highe wok of adheence (stength of bonds between two edia) that ay help to tea off cabon atos fo solid lattice and this ay give a highe k. The factos that affect the intefacial tension between solid and liquid will affect the wettability, since wettability between two phases is the esult of the balance of intefacial tension foces at the inteface; these factos include tepeatue, solid stuctue, intefacial active eleents and etal coposition. The wettability ay deceases when sall solid paticles ae in contact with the liquid because lotus phenoenon (A phenoenon of non wetting of liquid on a ough solid suface) ay occu. The wettability ay daatically incease by dynaic low intefacial tension due to the side eactions. Side eactions will change etal coposition including intefacial active eleent contents to change the wetting chaacte Solid Paticle Size abon paticle size will affect the contact aea paticulaly duing powde injection pocess such pulveized coal injection (PI). The wetting chaacte could be affected by the paticle size as entioned befoe Ash Ash in cabonaceous ateials would accuulate at the inteface and becoe physical baies at the inteface, which will educe contact aea available fo futhe cabon dissolution. The stength of the baie depends on the intefacial and physical popeties of ash, such as viscosity, fusion tepeatue, and intefacial tension between ash and ion o solid cabon. These popeties depend on tepeatue and the ash coposition and the latte is stongly affected by the side eactions. oke ash accuulation at the inteface will change wetting chaacte since a potion of liquid/solid inteface aea will be eplaced by ash Side Reactions Ash coponents povide eactant fo ost of side eactions occuing at the inteface. The side eactions will not diectly affect the cabon dissolution ate, but they will indiectly affect cabon dissolution ate by the eaction with dissolved cabon o by changing copositions of the liquid and the ash. The ajo coponent in ash is silica, and the silica eduction will occu when fused ash contacts the liquid though the eaction: SiO 2 2[] [Si] 2O...(25) This eaction will take a potion of cabon away fo liquid, incease silicon in the liquid, and educe silica in the ash. The foe will cause confusion when obseving the cabon dissolution ate, the second will cause the cabon satuation content to change with tie duing the dissolution pocess, and Eq. (15), fo exaple, will not be able to be integated, and the last will decease the viscosity of the ash. Sulfu usually pesents in cabonaceous ateials, eithe in cabon stuctue o in ash phase. The sulfu pickup fo coke o coal occus duing cabon dissolution. The ate of sulfu pickup due to cabon dissolution is consideed to be in popotion to the cabon dissolution ate and sulfu/cabon atio in coke. The sulfu pickup will change cabon satuation content and k by sulfu adsoption blockage duing cabon dissolution pocess. When fluxing ateials such as ao pesent in the syste, following eaction will occu to consue dissolved cabon and the poduct of this eaction, as, ay eain at the inteface to educe contact aea. [S] [] ao as O...(26) O geneated fo side eactions, as seen in eaction (25) and eaction (26) ay contibute to the liquid phase agitation to incease k. 8) On the othe hand, the gas bubbles could be jaed at the inteface to educe the aea available fo cabon dissolution. 3. Expeiental Seveal expeients wee caied out on cabon dissolution using stationay iesion ethod to copae the odel calculations. About 100 g of ion-cabon alloy was fist elted in an aluina cucible (ID 30, height 50 ) in esistance o induction funaces unde an agon atosphee. Afte the expeiental tepeatue was attained, the gaphite o coke cylinde (diaete 13, height 20 ) was iesed into the liquid Fe alloy to stat the cabon dissolution pocess. Befoe being iesed, the solid cabon was heated to the expeiental tepeatue nea the elt suface fo seveal inutes to ensue the constant of tepeatue duing the cabon dissolution. The solid saple was iesed fo a pedeteined tie peiod and was withdawn fo the elt. Soe etal saples (1 3 g) fo cabon analyses wee withdawn befoe and afte the iesion. The contact aea fo each iesed saple was calculated fo the aveage diensions of the solid cylinde befoe and afte its iesion, and the contact aea of each un was deteined fo the aveage aeas of all saples iesed in the un. To keep the solid saple size o contact aea constant, the above pocedue was epeated using a new solid saple to ceate a cabon content vesus tie elationship. Table 4 suaises the 2005 ISIJ 1486

6 ISIJ Intenational, Vol. 45 (2005), No. 10 Table 4. Expeiental conditions. expeiental conditions. The expeiental conditions diffeed ainly in the tepeatue and elting funace. 4. Results and Discussions The vaiations of cabon in the liquid with tie of all uns ae shown in Fig. 1. It was found that the cabon dissolution ate at highe tepeatues and with induction funace wee faste than those at lowe tepeatues and with esistance funace. Equation (9) fo cabon dissolution whee dissociation eaction and ass tansfe ae involved was used to analyse the obseved ates. Equilibiu constant fo eaction (1),, fo gaphite, and activity inteaction paaete of cabon, e c c, as a function of tepeatue 24) wee used in the odel calculation. A nueical ethod is used fo obtaining the theoetical cabon contents that best fits obseved cabon contents by adjusting the kinetic paaetes, which ae then deteined. Since both k and k ay dictate the dissolution ate, these kinetic paaetes will not be able to be identified if both of the ae unknown. Fo exaple, the esults of un 1 573R can be fitted well by ase (A) using k c/s and k 0.50 g/s c 2, o by ase (B) using k g/s c 2 and k c/s, o by ase () using k c/s and k g/s c 2. The vaiations of cabon content calculated fo the odel using these thee sets of kinetic paaetes fo un 1 573R wee essentially sae and they ae epesented by the solid line in Fig. 1. All cases showed good ageeent. The faction of esistances of each liiting step to the cabon dissolution pocess was calculated fo following equations, FR R 100 R R R FR 100 R R...(27)...(28) whee, FR and FR ae faction of esistances of ass tansfe and intefacial eaction pocesses, espectively, to the dissolution pocess, %. In ase (A), the dissolution pocess is liited by ass tansfe since FR 99% and the dissolution ate is independent of k when k 0.50 g/s c 2 ; in ase (B), the pocess is liited by intefacial dissociation eaction since FR 99% and the dissolution ate is independent of k when k c/s; in ase (), the pocess is evenly liited by the both since FR FR 50% and the dissolution ate vaies with both k and k. The vaiation of [] Fig. 1. Vaiations of cabon in the liquid with tie. calculated fo thee cases ae essentially sae and fits the obseved esults well. The esults of uns 1 673R and 1 773R wee teated in the sae anne fo ase (A) and ase (B). A set of k was obtained when ass tansfe liiting is assued fo dissolution at diffeent tepeatues. They ae k (c/s) Siilaly, a set of k was obtained when intefacial eaction liiting is assued fo the dissolution at diffeent tepeatues. Thee ae k (g/s c 2 ) The solid, dashed and dash-dot lines in Fig. 1 show the esults of the odel using these paaetes fo un 1 573R, 1 673R and 1 773R, espectively. The calculated esults based on the diffeent assuptions wee essentially sae and wee epesented by the sae line fo each un in the figue. All uns showed good ageeent with both assuptions. The activation enegy calculated fo k is E(k ) 50.3 kj/ ol and fo k is E(k ) 71.7 kj/ol. The E(k ) has a low value that is within a easonable ange of the activation enegy fo a ass tansfe pocess, but E(k ) is obviously too low fo a eaction pocess. k is elated to cabon diffusivity by, k D /d...(29) whee D is self diffusivity of cabon, c 2 /s, and d is bounday laye thickness in liquid, c. The activation enegy obtained fo cabon diffusivity was found to be 62.9 kj/ol 25) in Fe elt (S %) which is close to the activation enegy found fo k in this wok. Theefoe, ase (A), i.e., the ass tansfe in the liquid is consideed to be the ajo liiting step fo the cabon dissolution while intefacial dissociation only plays a ino ole. This stateent is suppoted by a faste cabon dissolution ate in un 1 873I whee induction agitation was applied; this is because agitation inceases k by educing the bounday laye thickness, while k was essentially unaffected by the agitation. The tepeatue dependence of k can be estiated using E(k ) 50.3 kj/ol. k ISIJ

7 ISIJ Intenational, Vol. 45 (2005), No. 10 Table 5. inetic analysis of obseved cabon dissolution ates c/s was estiated at in a esistance funace. But this k value is not lage enough to descibe the fast dissolution ate obseved in un 1 873I in the induction funace. A highe ass tansfe coefficient, k c/ s, was found to povide the best fitting fo the esults of un 1 873I as shown by dotted line in Figue. The incease of k fo c/s estiated fo esistance funace to c/s obtained fo induction funace at is eadily explained by induction foced convection in the liquid phase. This stongly indicates the ipotance of ass tansfe to the oveall dissolution pocess. Anothe fact that suppots this aguent is the ass tansfe coefficient, k, obtained fo this study wee of sae ode with those found by Shibata et al. 23) and Moi et al. 26) fo slag-etal eaction. Howeve, thee was no evidence to show the dissociation eaction ate fo coke is unipotant. Unfotunately, thee is no k epoted fo cabon dissociation eaction ate constant fo vaious cokes, coals o even fo gaphite. Thee is a lack of fo vaious cabonaceous ateials. Futhe aguent on the extent of the elative esistances, fo each of dissociation eaction o ass tansfe, to the cabon dissolution pocess will equie a pofound knowledge of the intefacial dissociation pocess. As can be seen in Table 5, ass tansfe liiting is suppoted by a nube of evidences but thee is no evidence to ule out the possibility of the ixed liiting echanis. 5. onclusions A kinetic odel was developed fo cabon dissolution. The diving foce, kinetic and theodynaic paaetes fo cabon dissolution when the ate is liited by ass tansfe ae diffeent with that liited by the dissociation eaction. The ate influencing factos suggested by the odel discussion wee tepeatue, solid stuctue, intefacial active eleents, etal coposition, liquid agitation, wettability between solid and liquid, solid paticle size, ash and side eactions. Expeients wee caied out fo the investigation of the liiting step. Resistance o induction funaces wee used to investigate the dissolution ate of gaphite and coke at It was found that the dissolution ate at highe tepeatues and with induction funace wee faste than those at lowe tepeatues and with esistance funace, and the ass tansfe in the liquid was the ajo liiting step fo the cabon dissolution. Acknowledgeents The autho wishes to thank Ms. S. T. han and D. R. hana of UNSW fo thei discussions on this wok and the patial suppot fo SD. REFERENES 1). Ishii and J. Yagi: Tetsu-to-Hagané, 87 (2001), ) H. Sun,. Moi, V. Sahajwalla and R. D. Pehlke: J. High Tep. Mate. Pocess, 17 (1998), ) Y. awai and. Moi: Technology Repot of yushu Univesity, (1968), ) R. G. Olsson, V. oup and T. F. Pezak: Tans. Metall. Soc. AIME, 236 (1966), ) L. alvelage, J. Maket and J. Potschke: Ach. Eisenhüttenwes., 50 (1979), ) O. Angeles, G. H. Geige and. R. Lope: AFS Tans., 76 (1968), 3. 7) H. W. Gudenau, J. P. Mulanza and D. G. R. Shaa: Steel Res., 61 (1990), 97. 8) S. Osten and F. Oetes: W. O. Philbook Meoial Syp. onf. Poc., ISS, Waendale, PA, (1988), 27. 9). Wu and V. Sahajwalla: Metall. Tans. B, 31B (2000), ). Wu and V. Sahajwalla: Metall. Tans. B, 31B (2000), ) V. Sahajwalla and R. hanna: Metall. Tans. B, 31B (2000), ) V. Sahajwalla,. Wu and R. Wiblen: Poc. of The Biacobe Meoial Syp., ed. by G. A. Ions and A. W. ab, TMS, ISS, The Metallugical Society of IM, Vancouve, anada, (2000), ) V. Sahajwalla and R. hanna: Scand. J. Metall., 32 (2003), ) V. Sahajwalla and R. hanna: Poc. of Yazawa Int. Syp., ed. by Floian ongoli et al., TMS, Waendale, PA, (2003), ) V. Sahajwalla, B. Waugh, J. M. Langley,. Faell,. Wu and. Gao: AUSIMM Poc., 301 (1996), ) V. Sahajwalla, F. Mcathy, S. T. ha, J. Hat, R. Sakuovs and N. Saha-chaudhuy: Poc. of the Int. Blast Funace Lowe Zone Syp., Pape No. 12, AUSIMM, Illawaa, (2002), 1. 17) R. Wiblen and V. Sahajwalla: Poc. of the 60th Ionaking onf., ISS, Waendale, PA, (2001), ) M. B. Macelo, G. G.. Muthy and J. F. Elloitt: Metall. Tans. B, 24B (1993), ) H. Sun, N. Yoneda,. Nakashia and. Moi: Tetsu-to-Hagané, 83 (1997), 1. 20) H. Sun,. Moi and R. D. Pehlke: Metall. Tans. B, 24B (1993), ) H. Sun, N. Shinozaki and. Moi: ISIJ Int., 30 (1990), ) F. Heistekap and. Lohbeg: Ach. Eisenhüttenwes., 37 (1966), ) E. Shibata, H. Sun and. Moi: Metall. Mate. Tans. B, 30B (1999), ) Y. Ueda,. Fujiua and T. Moi: Tetsu-to-Hagané, 61 (1975), ) M. Inoue and. Moi: Handbook of Physical Popeties of Molten Ion and Molten Slag, ISIJ, Tokyo, (1971), ). Moi, S. Hiwasa and Y. awai: J. Jpn. Inst. Met., 44 (1980), ISIJ 1488