Jurnal f Minerals & Materials Characterizatin & Engineering, Vl. 10, N.9, pp.865-874, 011 jmmce.rg Printed in the US. ll rights reserved Mdel fr FeSiMg lly Prductin by Reductin Technique Saeed Nabil Saeed Ghali Steel Technlgy Department, Central Metallurgical Reseach & Develpment Institute (CMRDI, P.O x 87 Helwan, 117, Egypt. STRCT Ferrsilicn magnesium is basic fundry allys used fr the prductin f ductile cast irn. Magnesium cntent plays an imprtant rle in the prduced ally grades frm dlmite re. The fcus f the present wrk is t simulate mathematical mdel t predict magnesium cntent in the ferrsilicn magnesium, which prduced by silicthermic reductin f calcined dlmite. The basic assumptins f this mdel are: cnstant lw viscsity f mlten charge, the reactin is irreversible f secnd rder and the reactin is isthermal. The reactin is based n the fllwing equatin: + Si Mg Si + SiO The results f previus wrk was fund t be in a gd cincidence with the predicted values by the mdel [ [ Si ( [ Si ][ e 1] [ Si ( [ e ] [ where [ is the cncentratin f magnesium metal in ferrsilicn magnesium ally in ml/l. [Si ] and ( are the initial cncentratin f silicn and magnesium xide in charge in ml/l, while t is time in secnd, is the reactin rate cnstant ( 3.6588x10-7 L Sec -1 ml -1. The predicted values are greater than the experimental values; this may be attributed t the use f cncentratin instead f the activity. The predicted values f magnesium cntent in ferrsilicn magnesium ally are in a gd agreement with the experimental results btained in previus wrk at lw viscsity. eywrds: activity, mdel, ferrsilicn, magnesium, reductin, viscsity 1. INTRODUCTION Ferrsilicn magnesium is the ne ally f magnesium that is used t prduce all types f ductile irn casting under all types f fundry cnditins. Dlmite represents a surce f bth magnesium and calcium as it cnsists mainly f duble carbnate f Ca and Mg. Calcinated dlmite seems t be a suitable cheap raw material fr the prductin f 865
866 Saeed Nabil Saeed Ghali Vl.10, N.9 ferrsilicn magnesium ally in EF r in inductin furnace [1-7]. The prductin f ferrsilicn magnesium frm dlmite culd be carried ut either by metallthermic prcess using silicn and / r l r by carbthermic prcess [8-13]. Magnesium cntent plays an imprtant rle in the prduced ally grades frm dlmite re. The silicthermic prcess f magnesium xide is cntrlled by factrs. The mst imprtant factrs are physical prperties f slag, the cncentratins f reactants, reactin rate cnstant, reactin time and reactin temperature. t cnstant temperature, time and lw viscsity the reactin rate mainly depends n the cncentratins f reactants. In this paper, a mathematical mdel will be designed t predict magnesium cntent in ferrsilicn magnesium ally which is prduced by silicthermic reactin f calcinated dlmite at lw viscsity f slag.. MTHEMTICL MODEL The fcus f the present wrk is t create a mathematical mdel t predict magnesium cntent in ferrsilicn magnesium ally, which is prduced by silicthermic reductin f calcinated dlmite. The basic assumptin f this mdel is the lw and almst unchangeable viscsity f slag during the reactin. Ferrsilicn magnesium ally is prduced by reductin f calcinated dlmite re with ferrsilicn cntaining silicn 75 mass cntent in %. The reactin is based n the equatin: ( + [ Si] [ Mg Si] + ( SiO (1 This system is cntrlled by chemical and kinetic rles. The limitatins f this mdel are the fllwing: The reactin takes place at lw slag viscsity and nearly unchanged The abve reactin is isthermal and irreversible The reactin is secnd rder Cncentratin f reducing agent (in mlar is greater than the magnesium xide ( [Si] > ( There is a mass balance in the abve reactin The rate f change f magnesium cntent in ferrsilicn magnesium ally is directly prprtinal t the cncentratin f magnesium xide and silicn metal. There is a mass balance in this system. 1 1 + [ Si] [ Mg Si] + ( SiO ( ( [Mg Si] g t mlten metal and (SiO g t slag. Every ne mle frm [Mg Si] has tw mles frm Mg, i.e. the rate f change f Mg with time depends n the initial cncentratins f the reactants.
Vl.10, N.9 Mdel fr FeSiMg lly Prductin 867 The reactin in equatin ( means that ne mle frm magnesium xide reduced by ne mle f silicn metal t give ne mle f magnesium. This can be writing as: ( + [ Si] [ (3 The abve reactin can be rewrite as: + X (4 ( X + ( X X (5 Where at zer time: ( initial cncentratin f magnesium xide ( (6 [Si] initial cncentratin f silicn metal [Si ] (7 [ initial cncentratin f magnesium metal X Zer (8 t any time: ( X (9 [Si] X (10 [ X (11 Frm equatin (3, the rate f change in magnesium cntent is directly prprtinal with the cncentratins f reactants. d[ ( [ Si] (1 dt Frm equatins 9, 10, 11 & 1, we btain dx ( X ( X (13 dt Rearrange and integratin f tw sides f equatin (13 dx dt ( X ( X dx t + cns tan t ( X ( X (14 (15 The left side f equatin (15 1 C1 C + ( X( X ( X ( X ( X( C1 ( X + C ( X X ( X( X 1 (16 (17
868 Saeed Nabil Saeed Ghali Vl.10, N.9 Frm the parameters f X 0 C1 C (18 Frm the parameters f X 0 1 + 0 C1 C (19 Frm equatins (18 and (19 1 C1 (0 1 C (1 Frm equatins (15, (16, (0 and (1, the left side f equatin (15 dx 1 dx 1 dx + ( X( X ( X ( X ( Take y 0 x (3 and hence dy -dx (4 z 0 x (5 and hence dz -dx (6 Frm equatins (-6 dx 1 dy dz [ + ] ( X( X y z (7 dx 1 dy dz [ ] (8 ( X( X y z dx 1 [lny lnz] (9 ( X( X dx 1 y [ln ] (30 ( X( X z Frm equatins (3, (5 and (30 dx 1 ( X [ln ] (31 ( X( X ( X Frm equatins (15 and (31 1 ( [ln ( X ] t X + cnst. Frm bundary cnditins, at zer time, frm equatin (8, X 0 1 [ln ] cnst. Frm equatins (3 and (33 1 ( [ln ( X ] t+ X 1 [ln 1 ( X 1 [ln ] [ln ] t ( X ] (3 (33 (34 (35
Vl.10, N.9 Mdel fr FeSiMg lly Prductin 869 1 ( X [ln ] t ( X [ln ( ( ( ( ( X ] t( X ( X t ( e X t( X ( X e (39 t( X ( X e (40 ( t( t( X * e X e (41 t( t( X [ e 1] [ e 1] (4 t( [ e 1] X (43 t( [ e 1] [ e X t( [ e t( 1] [ [ Si ( [ Si ][ e 1] [ Si ( [ e ] [ t initial time, t 0 ] 0 ( [ Si ][ e 1] Mg ] 1 (46 ( [ e ] [ [ 0 This means that the mdel verifies the bundary cnditins In case f is very large, and [Si] > (, Frm equatin (45 * t[( [ [ Si ( [ Si ][ e 1] * t[( [ Si ( [ e ] [ [ ( [ Si ( [ e ][ e ] [ Si 1] ] ( [ Si ] Mg ] ( (49 [ [ This means that all magnesium xide will be reduced by silicn In case f at infinity time and [Si]> ( * *[( [ [ Si ( [ Si ][ e 1] ( * *[( [ Si ( [ e ] [ (36 (37 (38 (44 (45 (47 (48 (50
870 Saeed Nabil Saeed Ghali Vl.10, N.9 It is clear that the mdel verify bth the bundary cnditins and lgical limits. Frm equatin (1, it can be calculate the rate f reactin using Gibbs free energies f cnstituents ( + [ Si] [ Mg Si] + ( SiO (1 G G P G R (51 G G + G (5 P R MgSi SiO G G + G (53 Si 3 G 6.4 10 /. 6796 Mg x Cal ml.8j / ml. Si [14] (54 G H T S [15] (55 G SiO 17570 (1873( 48.79 16186.33 Cal/ ml 5834.16 J / ml [ 53754 (1873( 41.9 G 17575.3 Cal/ ml 733848.37 J / ml. Frm equatins (51 & (54-57 G [ 6796.8 + ( 5834.16] [ 733848.37 + 0] 3303.01J / ml. G.3RT 6.486 10 7 1 3.6588x10 L * ml * 10 Sec 1 (56 (57 (58 The mdel is applied fr the experimental results f Hda et al [16]. Tables (1- shw the cnstituents and chemical cmpsitins f charges respectively. Table 1: The charge f experimental N Input Output. Dlmite FeSi Flurspar Limestne l Quartzite auxite CaSO 4 Metal mass Mg mass cntent in % 1 150 750 100 50 5 75.5 4.38 150 750 100 70 5 590.86 5.30 3 150 750 100 100 5 550 4.1 5.54 4 150 750 100 130 5 430.0 6.90 5 150 750 100 150 5 441.5 1.3 6.61 6 150 600 160 50 50 5 480 1.7 5.48 7 150 600 160 50 75 5 558 1.8 4.60 8 150 600 160 50 100 5 6 3. 4.04 9 150 600 160 50 150 5 813 1.6.96 10 150 600 40 50 5 750 1.76 4.11 11 150 600 80 50 5 489 3.5 6.06 1 150 600 10 50 5 550 3.5 5.19 13 150 600 160 50 5 575 4.4 4.78 14 150 600 00 50 5 595 3.5 4.45 15 150 600 400 50 5 550 3.5 4.05 16 150 950 160 50 5 983.45 3.19 17 150 950 160 100 5 88.84 3.67 18 150 950 160 150 5 731 3.05 3.99 19 150 950 160 00 5 805.5 3.50 0 150 950 160 50 5 750.63 3.6 Mg mass cntent in % Predicted
Vl.10, N.9 Mdel fr FeSiMg lly Prductin 871 Table : Chemical cmpsitin f charge Cnstituents Chemical cmpsitin, mass cntent in % Calcinated dlmite Flurspar Rare earth metals Limestne Quartzite auxite FeSi l SiO 1.4 1.6 3.88 95 6.43 Fe O 3 1.45 0.35 0.5 0. CaO 6.4 1 51.78 33.6 1 0.6 0.3 L.O.I. at 1000 C 0.43 41.3 l O 3 1.4 0.8.5 85 Na O 1 1.64 O 0.35 CaF 8 CaCO 3. P O 3 0.01 CeO /ReO 45 Fe 0.005 0.34 0.14 3.3 Pb 0.001 P O 5 0.001 SO 3 0.03 FeO 1.8 C 0.09 S 0.003 P 0.031 l 1.41 99. Ca 0.31 Si 74.8 Figs (1-4 shw the actual and predicted magnesium cntent at different cntents f bauxite, limestne, flurspar and quartzite respectively, the time f reactin is tw hurs. Fig. 1 shws that the effect f bauxite (alumina cntent as given in Tables (1- n the magnesium cntent and the difference between predicted and actual magnesium cntent. It is clear that the difference between the magnesium mass cntent in % pred. and magnesium mass cntent in % actual increase as the alumina increase. This behaviur can be attributed t the negative effect f l O 3 n the activity f magnesium xide due t the frmatin f calcium aluminates [8; 17-18]. Fig. shws the difference between the predicted magnesium cntent and the actual magnesium cnt at different limestne. It is nted that as clear frm Fig. - the difference between the predicted and the actual magnesium cntent decreases as the limestne increases (frm heats 1 t 3 then the difference, by further limestne increase (heats 4 & 5, the difference sharply increase. This can be explained by tw significant ppsite effect. The first ne is the psitive effect f increasing CaO cntent due t increase limestne- in SiO rich slag leading t the frmatin f CaO.SiO, 3CaO.SiO and CaO.SiO [19-5]. these cmpunds are frmed first and are very stable leading t free fr reductin, this mean that the activity f magnesium xide increase by increasing limestne t sme extent. The secnd factr, is the negative effect f increasing the cntent f these high mlten cmpunds CaO.SiO, CaO.SiO and 3CaO.SiO with melting temperatures f 1564 C, 130 C and 070 C, respectively, resulting in higher viscus slag and hence the activity f magnesium xide decrease. Furthermre, the presence f CO gas, resulting frm the decmpsitin f limestne leads t mre xidatin f magnesium. Fig. 3 shws the variatin between the
87 Saeed Nabil Saeed Ghali Vl.10, N.9 predicted and actual magnesium cntent with difference flurspar cntent. The actual magnesium cntent near t the predicted magnesium cntent by increasing flurspar cntent in the charge thrugh heat numbers 10 up t 13, but by further additin f flurspar, the actual values f magnesium cntent began t far frm predicted values. These results can be illustrated as fllw, the lw deviatin f actual magnesium cntent frm predicted ne; this is as a result f increasing activity f magnesium xide [6]. On the ther hand, additin f mre flurides t silicate slag results in silicn tetra fluride (SiF 4 vapur [7], and hence cncentratin f silicn decreases. Fig.1: The difference between calculated and actual Mg cntent in presence f auxite Fig. : The difference between calculated and actual Mg cntent in presence f limestne It is clear that, the difference between the actual and predicted magnesium cntent thrugh heats 6 t9 (in which quartzite cntent increase decreases up t heat number 8 then fllwed by increasing as given in Fig.4. This behaviur can be investigated as fllw. There are tw ppsite factrs. The first ne, there is a cnstant distributin f silicn between metal and slag at a given temperature. Therefre, as the slag is saturated with SiO, the silicn cntent in the ally increases, als leading t high recvery f magnesium cntent which cause lw deviatin in magnesium between actual and predicted cntents. The secnd factr, by further additin f quartzite, the activity f magnesium xide decreases [8-9], this is due t the frmatin f.sio [30]. On the ther side, the excess SiO tends t frm a less stable cmpund such as Ca 3 Mg(SiO [31-3], which is dissciated t Ca SiO 4 with a high melting pint leading t high viscus slag. Fig. 3: The difference between calculated and actual Mg cntent in presence f flurspar Fig. 4: The difference between calculated and actual Mg cntent in presence f quartzite.
Vl.10, N.9 Mdel fr FeSiMg lly Prductin 873 3. CONCLUSIONS The predicted magnesium cntents are greater than the experimental values. The mst imprtant reasn is attributed t the use f cncentratins instead f activities. ased n the assumptins, lw viscsity, and the reductin f magnesium xide by silicn metal, the reactin is cntrlled by rate f reactin and cncentratin f reactants ( and [Si]. The equatin have been derived is functin in initial cncentratin f reactants, time, reactin rate cnstant as shwn, [ [ Si ( [ Si ][ e 1] [ Si ( [ e ] [ The reactin rate cnstant f the reactin : 7 1 1 ( + [ Si] [ Mg Si] + ( SiO is 3.6588x10 L * ml * Sec Vlatilizatin f magnesium metal during the reductin f magnesium xide prcess has a great negative significant effect n the gab between the predicted and actual values f magnesium cntent. Finally the difference between the actual and predicted mainly depends n effect f additins n the activities f magnesium xide and reducing agent, and viscsity f the reactin medium. REFERENCES 1. 461964 (U.S.S.R., 8(1975, M.. ekelidze et al., uth. Cert., ynll. Izbr.,. M.. Ryss et al.: Stal, pril, (1973, p. 303. 3. D. I. Saginadze et al.: Stal, (1977, p.140. 4. D. I. Saginadze et al.: Steel in the USSR, 16 (1986, p. 533 5. F. N. Tavadze et al.: Nauka Prizvdstva, C51, (1983, p. 43. 6. 77704 (U.S.S.R., 14(1980, F. N. Tavadze et al., uth. Cert., ynll. Izbr. 7. V. Varbanv et al.: Wrks f the Irn and Steel Inst., VIII (1977. 8. D. J. G. Ives: Principles f the extractin f metals, Lndn, (1969. 9. H. J. T. Ellingham: I. Sc. Chem. Ind., Lnd., 1944 & C.W. Dannatt and H.J.T. Ellingham: Disc Faraday Sc., 4 (1948, p. 16 10. N. P. Lyakiskev et al.: lyumintermiya "luminthermy", Mscw, (1978, p. 44 11. M.. Merritt and E. V. Marcssi: Electric Furnace Cnf. Prc., New Yrk, 9 (197, p. 184. 1. V. Ryachikv, V. G.. Mizin., and. S. Dubrvin: Steel In U.S.S.R., 1 (198, p. 64. 13. P. Sklv and N. L. Pnmarv: Intrductin t Metallthermic, Mscw, (1990, p. 134. 14. W. lemm and H. Wwstlinning: Z.anrg. Chem., 45, (1941, p. 365. 15. R.G. Ward, M.., Ph. D: n intrductin t the physical chemistry f irn & steel making, Edward rnld (Publishers LTD, (196, p. 1/13. 16. H. El-Faramawy et al.: Ferrsilicn Magnesium Prductin, Scandinavian Jurnal f Metallurgy, 3 (003 p. 37/46. 17. M. lper, et al: J. m. Ceram. Sc., 45 (196 N. 6, p. 63/8
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