2 Physico-Chemical Principles of Steelmaking Processes

Transcription

1 2 Physic-Chemical Principles f Steelmaking Prcesses 2.1 INRODUCION Irnmaking and steelmaking invlve a variety f chemical reactins, and ther physicchemical prcesses, such as viscus flw, interfacial phenmena, mass transfer, etc. at high temperatures. Physical chemistry cnstitutes the mst imprtant scientific fundamental fr understanding the metallurgical aspects f irnmaking and steelmaking. f which chemical thermdynamics, cnsisting f reactin free energies and enthalpies, chemical equilibria, has fund the mst widespread applicatin. 2.2 HERMODYNAMICS OF SEELMAKING PROCESS Principal Cncepts f Physical Chemistry Useful in Steelmaking A system is a grup f bdies which interact with ne anther and can be islated, either mentally r physically frm the surrundings metal-slag systems, refractry lining-metal systems In practice, ne mst ften must deal with cmplex systems lining-metal-slag-furnace atmsphere system Real systems are t cmplicated t be analysed easily usually subdivided int several simpler systems, e.g. metal-slag, slag-furnace atmsphere etc. Hetergeneus vs hmgeneus systems metal, slag, furnace atmsphere, etc. In practice, they are far frm hmgeneus metal may cntain nn-metallic inclusins and gas bubbles slag may cntain undisslved slag frmers, metal beads, and gas bubbles furnace atmsphere may carry suspended slag particles (melting dust) and smetimes, metal particles. Unifrm vs nn-unifrm system identical cmpsitin (a chemical unifrm system) r identical prperties (a physically unifrm system) in the real steelmaking prcesses, the cmpsitin and the prperties f varius prtins f a system are mstly nt unifrm

2 Rashid. Ferrus Prductin Metallurgy he state f a system is characterised by the parameters f state (P,, X, etc.) A prcess is characterised by prcess parameters (Q and W) Steelmaking prcesses are essentially isbaric ( H = Q P) hree cmmn parameters t cnsider G, H and Q Fr enthalpy change, abslute value f enthalpy H are still nn-existent, and instead, H, is cnsidered enthalpy f simple substances (elements) at 298 K is zer (H 298 = ) entrpies f all substances at abslute zer are equal t zer, i.e., S = at = K. he relatins between the principal thermdynamic functins: H = U + PV G = H S Free energy change at temperature is determined by the equatin G = H S Fr practical calculatins, changes under standard cnditins (1 atm P and 298 K ) are cnsidered: G 298, H 298, S 298 Steelmaking prcesses take place high temperatures and change f H with is calculated as H = H n c P d n = number f mles, c P = = specific heat capacity c P = a + b + c 2 + d 1 + e 2 c P = c rp sr P c P he cefficients a, b, c, etc. can be fund in tables. When state f a cmpnent changes (an alltrpic transfrmatin, melting, vaprisatin): L tr, = latent heat f the transfrmatin tr H = H n c P d ± L tr + n c P d Similar treatment can be used t determine entrpy change f reactin: tr S = S n c P d 298 ± L tr tr tr + n c P d If there are n transfrmatins in the given temperature range, G can be fund as fllws: G 298 = H 298 S 298 If the specific heat changes nly insignificantly with temperature ( c P = ): G = H 298 S 298 Cnsidering the effect f temperature n H and S, the effect f temperature n G is: G = a + b + c lg In mst cases, the effect f n G can be apprximated, with a gd accuracy, by a straight line: G = H S = A + B where H and S are taken as the average values in a given temperature interval. tr 2

3 2. Physic-Chemical Principles f Steelmaking Prcesses Based n nature f entrpy change, the fllwing generalisatin f G with can be made: 1. Fr vlume expansin accmpanying a reactin (gas evlutin), S at cnstant P and is psitive, hence, G decreases with an increasing. C + CO 2 = 2CO; G = 166, Jules 2. Fr vlume cntractin, i.e. gas cnsumed in the reactin, S at cnstant P and is negative, hence, G increases with an increasing. H S 2 = H 2S; G = 91, Jules 3. Fr little r n vlume change, S, hence temperature has little effect n G. C + O 2 = CO 2; G = 395,3.5 Jules Mst irnmaking and steelmaking systems are chemically reactive systems he standard free energy change is directly assciated with the equilibrium cnstant, K e f the reactin: G = R ln K e where, fr the chemical reactin bb + dd = mm + nn the equilibrium cnstant can be expressed as K e = [ (a M) m (a N ) n (a B ) b (a D ) d ] e he free energy change f any chemical reactin at any given cnditin: G = G + R ln Q here Q = activity qutient and is defined as Q = [ (a M) m (a N ) n (a B ) b (a D ) d ] ne Replacement f the value f G yields the value f G, the mlar Gibbs free energy change f a reactin in the given temperature and pressure G = R ln K e + R ln Q = R ln ( Q K e ) his relatin is knwn as the van t Hff Istherm, and can be used t determine thermdynamic pssibility f a reactin. If G is psitive, the reactin wuld nt ccur. 21

4 Rashid. Ferrus Prductin Metallurgy Example 2.1 Calculate the rati f partial pressures f CO 2 and CO gas in a CO-CO 2 gas mixture at equilibrium with p O2 = 1 6 atm at 16 C. Calculate the chemical ptential f xygen and predict whether slid FeO can be reduced t metallic irn by this gas mixture at a temperature f 1 C. Slutin: Fr the chemical reactin the free energy f frmatin (CO) + 1/2(O 2 ) = (CO 2 ) G f = R ln K e = R ln [ p CO 2 p CO 1 x (p O2 ) 1/2] e Nw, cmbining the free energy f frmatins f CO and CO 2, we get the free energy f the abve reactin at 1873 K is -119,85 cal/ml. hen = (8.314)(1873) ln [ p CO 2 1 x p CO (1 6 ) 1/2] e p CO2 = p CO Nw the chemical ptential f xygen is μ O2 = R ln p O2 = (8.314)(1873) ln(1 6 ) = kj/ml Nw the reductin reactin f FeO with the CO-CO 2 gas mixture can be written as < FeO > +(CO) =< Fe > +(CO 2 ); G = G f (CO 2 ) G f (FeO) G f (CO) Using data frm able 2.1, G fr the reactin at 1273 K is G = J ml = R ln (p CO 2 p CO )e his gives (p CO2 /p CO ) e =.466, which is lwer than the (p CO2 /p CO ) a f hus, the reactin is nt pssible. Reactins in the steelmaking prcesses can be generalised, using 1 ml f xygen, as 2x y M + O 2 = 2 y M xo y Examples are: <C> + (O 2 ) = (CO 2 ) <Si> + (O 2 ) = <SiO 2 > 4 3 {Al} + (O 2) = 2 3 <Al 2O 3 > Fr determining equilibrium and stability f the resultant xide frmed by these reactins, the standard free energy f frmatin G f f xides per mle f xygen can be calculated. G f = H S = A + B Figure 2.1 (Ellingham diagram) able 2.1 (Data fr standard free energies f reactins encuntered in ferrus metallurgical prcesses. 22

5 2. Physic-Chemical Principles f Steelmaking Prcesses hermdynamics f Slutin Steelmaking prcess cnsists f ne r mre hmgeneus parts r phases and frequently each phase is nt a pure substance slutin perfectly hmgeneus mixture f tw r mre substances whse cncentratins in the mixture may vary cntinuusly within definite slubility limits. All practical steel-making prcesses invlve the interactin between slutins either chemically r physically with ne anther reactin between liquid metal and liquid slag, slid additins, and gas bubbles Frmatin f a slutin Sme cases, invlve n chemical reactins and ne cmpnent f a slutin is simply diluted by anther In ther cases, the slvent and slute may react chemically with each ther with the evlutin r absrptin f heat. HIS IS IMPORAN. Example: much heat is liberated n disslutin f silicn in irn practically utilised in the manufacture f steel grades high in silicn (dynam, silicn and ther high ally steels). high-silicn ferr-allys charged in the ladle in the slid state withut running the risk f cling r even chilling the tapped metal Ideal and Nn-Ideal Behaviur Ideal slutin frces f interactin between like and unlike atms are equal chemical r physical behaviur f the slute i is prprtinal t its atmic r mlecular cncentratin in the slutin. At steelmaking temperatures, ideal behaviur is fllwed by slutins f gases metallic slutins such as Fe-Ni, Fe-Mn, Fe-C many inic melts cntaining a cmmn in such FeO-MnO, FeS-FeO, Fe 2SiO 4-Mg 2SiO 4. If the slutin were ideal, the vapur pressure wuld be prprtinal t the cncentratin f i, i.e. p i = p i X i If the slutin were nt ideal, p i = p i a i a i = Raultian activity p i = prprtinality cnstant = the vapur pressure f pure i at the same, X i = the atm fractin f i Standard State (where activity is unit) Raultian standard state f i is that f the pure element at the same temperature and in the same physical cnditin slid, liquid r gaseus as in the slutin. Fr ideal slutin, a i = X i ( Rault s Law) Slutins shwing ideal behaviur are ften referred t as Raultian Slutins f nickel, cbalt, manganese and chrmium in irn are almst ideal. 23

6 Rashid. Ferrus Prductin Metallurgy Deviatin frm ideality Psitive deviatin frm ideality (activities greater than thse indicated by Raultian behaviur) the system is bserved t expand ( V > ) and t absrb heat ( H > ) cpper in irn (strng Fe-Fe and Cu-Cu bnding and a weak Fe-Cu attractin) the tendency is s pwerful that a separatin int an irn-rich and a cpper-rich phase ccurs Negative deviatin frm ideality (activities lwer than thse indicated by Raultian behaviur) the evlutin f heat ( H < ) with a decrease f its vlume ( V < ) strng Fe-Si attractins, giving a tendency fr Si atms t have Fe atms fr nearest neighburs ( rdering behaviur) ultimately results in the frmatin f the slid-state cmpund FeSi when the liquid cls. Figure 2.2: Activities in liquid Fe Si and Fe Cu allys at 16 C shwing strng negative and psitive departures frm Rault s law. A measure f the deviatin frm ideality f nn-ideal slutins; γ i = X i γ i = Raultian Activity Cefficient ( = 1 fr ideal slutins, ( < 1 fr negative deviatins, ( > 1 fr psitive deviatins) a i Analytical crrelatins between activity and cmpsitins fr nn-ideal slutins he simplest is the regular slutin mdel. Fr a binary slutin with cmpnents A and B, it predicts R ln γ A = α X B 2 ; R ln γ B = α X A 2 = cnstant at cnstant temperature, X A + X B = 1. Mlten slags are cncentrated slutins minimum cncentratin f any cmpnent xide is mre than a few weight percent activity-cmpsitin relatin in binary slag systems can be represented as shwn in Fig. 2.2 fr binary ally systems Mle fractin is the cmpsitin scale, activity and activity cefficients defined with Rault s law as the reference state (i.e. pure cmpnents) 24

7 2. Physic-Chemical Principles f Steelmaking Prcesses Industrial slags are, hwever, multi-cmpnent slutins cannt be represented in the same manner as in Fig. 2.2 ternary CaO-SiO 2-Al 2O 3 cnstitutes the basis fr blast furnace slags, and sme slags encuntered in steelmaking prcesses Figure 2.3 (activity f SiO 2 in the ternary CaO-SiO 2-Al 2O 3 system at 155 C) is-activity lines fr SiO 2, CaO and Al 2O 3 (fr ther, separate diagrams are required) liquid field (i.e., the mlten slag field) is bunded by the liquidus lines Al 2O 3 is written as AlO 1.5, because the mlecular masses f CaO, SiO 2, and AlO 1.5 are clse, being equal t 56, 6 and 51, respectively. herefre, the mle fractin scale becmes apprximately the same as the weight fractin scale. Example 2.2 Determine the activity f SiO 2 in the CaO-SiO 2-AlO 1.5 system at 1823 K at X CaO =.5 and X SiO 2 =.4. Cnsider the equilibrium f this slag with an Fe-Si liquid ally and a gas mixture f CO-CO 2 at this temperature, Calculate (p CO2 /p CO ) rati in the gas mixture at equilibrium. Given data: In the ally, X Si =.2, Si = 1.6*1 3. Slutin: < Si > + 2(CO 2 ) = {SiO 2 } + 2(CO); G = G f {SiO 2 } + 2 G f (CO) 2 G f (CO 2 ) Frm data f able 2.1, at 1823 K, G = -337,179 J/ml. Hence K = = [( p CO p CO2 ) 2 x a SiO 2 a Si ] Frm Fig. 2.3, at X CaO =.5 and X SiO 2 =.4, a SiO2 in slag =.1. Nw, the activity f silicn in the ally a Si = X Si γ Si =.2 ( ) = Substituting the values, p CO2 /p CO = 8.24*1-4. e 25

8 Rashid. Ferrus Prductin Metallurgy Dilute Slutins Liquid steels fall in the categry f dilute slutins cncentratins f slutes (C, O, Si, Mn, S, P, etc.) are mstly belw 1 wt% r s except fr high-ally steels Slvent (Fe) atms X Fe 1 shw apprximately ideal behaviur a i = X i Slute atms mle fractin appraches zer (X k ) activity varies linearly with mle fractin (Henry s Law) a i = γ i X i γ i = cnstant f prprtinality (Henry s Law cefficient), independent f cmpsitin fr lw cncentratin f slute. Deviatin frm Henry s law ccurs when the slute cncentratin increases (Fig. 2.4) Figure 2.4: Activity f carbn in austenite (relative t graphite) at l C, demnstrating deviatin frm Henry's law. Activities in liquid steel are expressed with reference t Henry s law, and nt Rault s law the cmpsitin scale is weight percent, nt mle fractin. With this mdificatin, if the slute i, in slutin with Fe as slvent in the binary Fe-i slutin, 1. beys Henry s law, then h i = wt. %i 2. des nt bey Henry s law, then h i = f i x (wt. %i) h i = Henrian activity, f i = Henrian Activity Cefficient f slute i (in ne weight percent standard state) Fr 1wt% i, h i = 1 (Henry s law is beyed) 26

9 2. Physic-Chemical Principles f Steelmaking Prcesses Cnversin f Raultian activities t the Henrian frm (Fig. 2.5) Figure 2.5: Diagrammatic illustratin f the relatinship between Henrian and Raultian activities in a binary system with mderate negative deviatins frm ideal Raultian behaviur. Rearrangement f this equatin gives: But f i = h i wt%i = a i γ i X i a i = h i γ i X i wt%i wt%i M X i = i wt%i + wt%fe M i M Fe which fr wt%i (and hence wt%fe 1) simplifies t: X i = wt%i M Fe 1 M i hen, by inserting the mlecular weight f irn, M Fe = 56, the Henrian activity simplifies t: a i =.56 h i γ i M i By using this relatin, any thermdynamic expressin initially derived in terms f Raultian activities, can easily be cnverted fr use with the mre cnvenient Henrian activities Fr example, the free energy change f a pure substance n slutin at an activity a i is: G = R ln a i = lg (.56 f i wt%i γ i M i ) e.g. G fr the frmatin f the Henrian reference slutin (1 wt% slutin, f i = 1, is:) is: G = lg(.56 γ i /M i ) = γ i γ i 27

10 Rashid. Ferrus Prductin Metallurgy Interactin Between Slutes in Dilute Slutins Mlten steel and irn have several disslved slutes in dilute state (e.g., C, Mn, Si, S, P, etc) slute in a multi-cmpnent slutin interact with ne anther and thus influence activities f ther slutes. activity cefficient f a slute B in slutin is altered by the additin f ther slutes, even in dilute slutins he Henrian activity cefficient f slute B, f B, in slutin cntaining ther slutes C, D,..., i, etc. is give apprximately as B C D i f B = f B f B f B. f B B f B = the activity cefficient expressing the effect f the cncentratin f B n the activity f B in the simple binary A-B slutin and defined as f B B = h B A B wt%b f B i = the activity cefficient expressing the effect f i n the activity f B in the A-B-i ternary slutins and defined as f B i = h B A B i wt%b equatin is an apprximate ne as it des nt cnsider the interactins amngst C, D,..., i in slutin Activity f B in an A-B-C-D-...-i multi-cmpnent dilute slutin can be expressed as h B = f B wt%b = (f B B f B C f B D f B i ) wt%b In ternary slutins, the effect f a secnd slute element C n the first slute B usually fllws a lgarithmic law fr lw cncentratins f C, and the behaviur can be summarised by equatins f the type lg f B C = e B C wt%c e B C = cnstant and knwn as the interactin cefficient. It expresses the influence f slute C n the activity cefficient f slute B in the ternary slutin. Lgarithmic frm f the activity equatin lg h B = lg f B B + (e B C wt%c) + (e B D wt%d) + + (e B i wt%i) + lg(wt%b) If ne interactin cefficient is knwn, the ther can be btained by the fllwing relatin: e C B = e B C ( M B M ) (1 M B C M ) C where M is the mlecular weight. his equatin is strictly crrect fr infinitely dilute slutins. able 2.2 (interactin cefficients f slute in liquid irn at 16 C) 28

11 2. Physic-Chemical Principles f Steelmaking Prcesses Example 2.3 An Fe-Mn slid slutin having.1 mle fractin f Mn, is in equilibrium with an FeO-MnO slid slutin in an xygen cntaining atmsphere at 1 K. Calculate the cmpsitin f the xide slutin. Bth metallic and xide slutins are ideal. Given data: <Mn> + 1/2(O 2) = <MnO> ; G f = J/ml Slutin: <Fe> + <MnO> = <Mn> + <FeO>; G = G f (FeO) G f (MnO) Using the given data and able 2.1, at 1 K K = a Mna FeO a Fe a MnO = X MnX FeO X Fe X MnO G = J/ml = (.1)X FeO (1.)X MnO = exp ( x 1 ) (.1)X FeO (1.)X MnO = 1 6 X FeO = 1 3 X MnO Nting that a FeO = X FeO, a MnO = X MnO, and X FeO + X MnO = 1, calculatin yields X FeO =.1 and X MnO =.999 Example 2.4 Calculate the chemical ptential f nitrgen gas at equilibrium with liquid steel at 16 C. he steel cntains.1% N,.5% C,.5%Mn. Given data: [N] ppm std state in irn = K N x p 1/2 N2 where lg K N = (Nte: 1 wt% = 1 4 ppm). Slutin At equilibrium, μ N2 (gas) = μ N2 (steel) = R ln p N2 Frm the given data lg p N2 = 2 [lg h N lg K N ], Nw at 1873 K, lg K N = Again, h N = f N (wt. %Mn) where h N is in ppm lg h N = lg[n] ppm + e N N (wt. % N) + e N C (wt. % C) + e N Mn (wt. %Mn) Substituting values f interactin cefficients frm able 2.2, hus, lg h N = lg(.1 x 1 4 ) + ()(.1) + (.13)(.5) + (.2)(.5) lg h N = 2.55 lg p N2 = μ N2 = 2.33 (8.314)(1873)( )(1 3 ) = kj/ml N 2 29