Rate of Mass Transfer between Molten Slag and Metal under Gas Injection Stirring*
By Masahiro HIRASA WA, * * Kazumi MORI, * * Masamichi SANG,** Asao HATANAKA,*** Yuhji SHIMATANI**** and Yoshimitsu OKAZAKI*****
Synopsis from producing results describing quantitatively the Model studieshave been made on the rate of mass transfer between effects of gas injection stirring on the rate of the moltenslag and metal withgas injectionstirring. A Li20-Si02A1203 slag-metal reaction. slag-moltenCu reactionsystem for Si oxidationhas beenselected as the In the present study, model experiments were modelreaction system. The exploredreaction is oxidationof Si by FeO, made to investigate the role of gas injection stirring takingplace underthe conditionof rate-controllingby Si transportin the in slag-metal reactions at high temperature with metal phase. Kinetic experimentswere done at .1250°C. The slag- using a molten slag-Cu system where physical prop- metalbath was stirred by Ar gas injectedthrough a nozzlelocated at the cruciblebottom. The apparentmetal-side mass transfercoefficients of Si, erties are similar to those of slag-molten iron system. ksi, are calculatedfrom the rate data. Relationsbetween ks1 and experi- The slag-Cu reaction system has already been estab- mentalconditions (gas flowrate, Vg; metaldepth, hM; cruciblediameter, lished by the authors' investigation to be a suitable d~) have beeninvestigated. model reaction system for studying the role of stirring It isfound that the dependenceof k1 on the gas flow rate variesat certain on the mass transfer between slag and metal.6~ On gas flow rates denotedby Vg and V*. In the low Vg range (Vg < V), the basis of this previous study, the present model ks1 is proportionalto (VgJd~). In the mediumVg range (Vg
I. Introduction II. Experimental In recent years, the kinetics of reactions between slag and molten iron with gas injection in steel refining 1. Apparatus processes have become of increasing interest to the Figure 1 shows a schematic diagram of the experi- metallurgists. Previously studies were made by mental apparatus. A 13 kW SiC furnace, fitted with Richardson and co-workers on elucidating the funda- a mullite reaction tube (O.D. 145 mm, I.D. 130 mm, mental relation between slag-metal reaction rate and and 740 mm long) was used. The slag-metal melt gas injection stirring conditions with using model was held in an alumina crucible. Temperature was reaction systems at low temperatures, i.e., aqueous measured with a Pt-Pt 13 %Rh thermocouple located solution-amalgam system"3,4) and molten salt-molten at the bottom of the crucible. lead system.2-4~ From the practical viewpoint, model The injection nozzle consisted of a mullite tube studies have been made frequently with using organic (I.D. 1 mm, O.D. 3 mm and 400 mm long) was solvent-water systems.5~ A considerable amount of located at the center of the crucible bottom. The information has been obtained from these fundamental distance between the nozzle tip and the crucible and practical model studies at low temperatures. bottom was 5 mm. The frequency of bubble forma- But the experimental results are not adequate to give tion was measured by using a pressure pulse tech- a clear picture on the rate of slag-metal reactions nique.8) A pressure transducer connected to a syn- with gas stirring because of the limited experimental chroscope was used to detect the pressure pulse in the conditions covered in these studies. Furthermore the gas supply train, which was produced from bubble large difference in physical properties between in the formation at the nozzle tip. The injected Ar gas slag-molten iron system at high temperature and in flow rate was metered with a capillary flowmeter the model reaction system at low temperature is calibrated by means of a soap film meter. needed to be examined. However, the difficulties inherently involved in the experiments for a slag- 2. Procedure molten iron system at high temperature prevent them The explored reaction between slag and metal is
* Manuscript received on September 18, 1986; accepted in the final form on December 12, 1986. © 1987 ISIJ ** Department of Metallurgy, Faculty of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464. *** Formerly Graduate School, Nagoya University. Now at Oita Works, Nippon Steel Corporation, Oaza Nishinosu, Oita 870. **** Formerly Graduate School, Nagoya University. Now at Engineering Department, Nachi-Fujikoshi Corporation, Ishigane, Toyama 930. ***** Graduate School, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464.
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III. Results and Discussion 1. Frequencyof Bubble Formation and Bubble Diameter Figures 2 and 3 show examples of the pressure pulses produced by bubble formation. Gas flow rates of injected Ar, Vg, are 18 cm3/s and 90 cm3/s (at 1250°C and at 1 atm pressure) at Figs. 2 and 3, respectively. Each decaying pulse recorded in the two figures corresponds to single bubble formation at the nozzle. Figure 2 shows that bubbles were formed very regularly at low gas flow rates. At higher gas flow rates, shown in Fig. 3, long and short time intervals between two adjacent maximum peaks are observed alternately. In this case, a " pair " of bubbles (large and small) forms at the nozzle.9~ Since the formation of paired bubbles has been observed at Vg> 40 cm3/s, the measurement of the frequency of bubble forma- tion was made at Vg<40 cm3/s in the present study. With increasing Vg from 3 to 40 cm3/s, the fre- quency of bubble formation increased from 13 to 31 bubbles/s. The bubble diameter, dB, was deter- mined by using the following equation: '6 Vg 1/3 U B = ...... (2) 2tfB Si (in Cu)+2FeO (in slag) = Si02 (in slag) +2Fe (in Cu) ...... (1) Figure 4 shows the relation between the bubble size, dB, and the gas flow rate, Vg. In the figure the data The Cu-Si alloy contained 0.1 % of Si initially. are compared with the values calculated from Eq. The primary slag had a nominal composition of (3) which had been derived by Sano and Mori.8~ Li2028%-Si0258%-A120314%. The charged slag consisted of 91 % primary slag and 9 % FeO. The dB = 6d0 )2+o.o242vd0o.867}116 (2n)...... (3) quantities of the metal and the slag used in each experiment were varied, respectively, as l30-'2 100 g where, do°: outer diameter of nozzle (cm) and 2.4'- 160 g according to the experimental condi- g: acceleration of gravity (cm/s2), tion. In the authors' previous studies,6'7~it has been where the surface tension, a, and the density, p, of clarified that the rate of the reaction (1) is controlled pure Cu (6=1 320 dyn/cm,1D) p = 7.8 g/cm311)) have by Si transport in the metal phase when the initial been used because of low content of Si in the Cu-Si concentrations of Si, [%Si]o, and FeO, (%FeO)o, alloy used in the present study. From the figure, it are 0.1 and 9 %, respectively. is seen that the results of the calculation are in close A weighed Cu-Si alloy and Li20-Si02-A1203 slag agreement with experimental data of dB. The were melted in an alumina crucible under a flow of observed value of dB ranges from 0.7 to 1.4 cm when Ar gas at 1 250°C. A predetermined amount of FeO Vg=340 cm3/s. was added to the slag to initiate the reaction. During On the assumption that the bubble rises with the the experiment, the slag-metal bath was stirred by free-rising velocity of a bubble, v= (0.5dBg)"2, bubbles Ar gas injected through the nozzle. The flow rate with diameter dB=0.7~ 1.4 cm are calculated to rise of injected Ar was kept constant throughout the a distance of dB in 0.040.05 s. From the data of experiment. At intervals small amount (~ 5 g) of frequency of bubble formation, f B, the bubble forma- sample of Cu phase was withdrawn, using a quartz tion time is given by f'=0.03'-.'0.07B s, which is near tube, for analysis of Si in Cu phase. The method of to the above bubble rising time. From this, the analysis of Si in Cu was a reduced molybdosilicate bubbles releasing succeedingly from the nozzle are spectrophotometric method. 6,7) The frequency of considered to form a single bubble stream. bubble formation was measured during the experi- ment at intervals. 2. Variation in Si Concentrationwith Time The experimental conditions were varied as The variation in the concentration of Si in the follows : (1) gas flow rate of injected Ar, Vg= 180' metal phase with time is given by Eq. (4) when the 6 000 cm3/min, * (2) metal depth, hM= 2.4 N 6.0 cm, rate of the slag-metal reaction represented by Eq. (3) crucible diameter, d~=3, 4 and 7.5 cm. The slag (1) is controlled by Si transport in the metal phase.6,7~ depth, hs1, was mainly hs1=1.6 ~ 1.7 cm ('-.constant). Some experiments were carried out with h1= 1.2 cm. [%Sj] -k' A t
* In the following , in this paper, the flow rate, Vg, is expressed at the conditions of 1 250°C and 1 atm pressure.
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Fig. 2. Variation of pressure in gas supply train during bubble formation. (Vg= 18 cm'/s)
Fig. 5. Typical relation between log [%Si] and time.
some approximation is necessary to evaluate the value of A. Brimacombe and Richardson,3~ in the study of mass transfer between a fused salt and molten lead with Ar gas injection stirring, have observed that the Ar bubbles were stopped momentarily at the interface before being pushed through by succeeding bubbles. Similar behavior of bubbles is presumed to occur at the slag-Cu interface in the present study. Except the experiments with very high gas flow rate Fig. 3. Variation of pressure in gas supply train during (Vg> 80 ' 90 cm3/s), single bubbles were observed to bubble formation. (Vg 90 cm'/s) appear succeedingly at the surface of the slag phase during the reaction. According to visual observa- tion, the frequency of bubble appearance at the sur- face of the slag was approximately equal to that of bubble formation at the nozzle. From these observa- tions, the number of the bubbles staying at the interface may be assumed to be no more than one. Presumably, the existence of one bubble at the slag- metal interface decreases the interfacial area. The extent of the decrease in the interfacial area by the existence of one bubble is represented at most by the ratio of the largest cross sectional area of the bubble to the cross sectional area of the crucible, (dB/d~), where the latter nearly equals to the interfacial area under static conditions. When d~= 4 cm, the ratio
Fig. 4. Relation between size of b ubbles and gas flow rate. of (dB/d~) ranges from 0.03 to 0.12 with bubbles of dB= 0.7 ' 1.4 cm. In most experiments in the present study, the decrease in the interfacial area caused by where, ks1: the apparent metal-side mass transfer the bubble existence at the interface is considered to coefficient of Si be no more than 10 % of the static interfacial area. A : the interfacial area From these considerations, the interfacial area A in V: the volume of metal phase Eq. (4) is taken to be the cross sectional area t: the time. of the crucible in calculating the apparent mass Typical results of experiments are shown in Fig. 5, transfer coefficients, ks1, from the data of the kinetic where the logarithm of the Si concentration is plotted experiments. against time. The results shown in Figs. 5(a) to (c) have been obtained at different gas flow rates, Vg, 3. Relation betweenMass Transfer Coefficientand Injected metal depths, hM, and crucible diameters, d~, respec- Gas Flow Rate tively. All data of the present experiments under Figures 6~8 show the relation between the apparent various experimental conditions are represented satis- metal-side mass transfer coefficients of Si, ks1, and factorily by linear lines predicted from Eq . (4) as the gas flow rate of injected Ar, Vg, for the three shown in Figs. 5(a)' (c). From the slopes of the crucible diameters, i.e., 3, 4 and 7.5 cm. The metal linear lines one may calculate ksi with using Eq . (4) and slag depths, hM and hs1, were 3.63.7 cm and and with taking an appropriate value of the inter- 1.6 -1.7 cm, respectively. As seen from the figures, facial area, A. ks1 increases with increasing Vg, but the dependence Because the true interfacial area cannot be known, of ks1 on the gas flow rate changes at certain transi- (280) Transactions ISIJ, Vol. 27, 1987
It is to be noted that at d~= 7.5 cm, Region II covers a wide range of Vg from 5 to 50 cm3js. In the experiments in Region III, formation of a large amount of metal particles, i.e., splashes of the metal phase, was observed. This observation sug- gests that the increase in the extent of the increase in ks1 with Vg in Region III is partly due to the increase in actual interfacial area caused by formation of liquid droplets (metal and/or slag particles) at the vigorously disturbed slag-metal interface. At gas flow rates lower than Vg* (Regions I and II), production of only small amount of metal par- ticles was observed. Particularly, in Region II, Fig. 6. Relation between apparent mass transfer coefficient, the extent of the increase in ks1 with Vg is consider- ks1, and gas flow rate. (d0=3 cm). ably small. From these facts and the behavior of bubbles at the interface mentioned in III. 2, in Regions I and II the interfacial area may be repre- sented by the cross-sectional area of the crucible. Hence, ks1, which is calculated on the assumption that the interfacial area is taken to the cross sectional area of the crucible, is regarded as the metal-side mass transfer coefficient. Below, discussion is focused mainly on the relations between ks1 and gas injection stirring conditions in the Vg ranges of Regions I and II. The relation in Region I obtained in the present study, ksiocVg/2, is in agreement with the experimental results of the model studies3,4~by Richardson and co- workers at low temperature. In Region I, intensifi- Fig. 7. Relation between ks1and gas flow rate. (d~ = 4 cm) cation of stirring in the metal phase caused by the increase in Vg enhances the metal-side mass transfer. In Region II, however, the intensification of stirring affects the metal-side mass transfer apparently much less effectively than in Region I. Throughout the gas flow range of Regions I and II, with increasing gas flow rate, the stirring in the bulk metal phase itself is more intensified. Therefore, the difference in the ksi Vg relation between Regions I and I I is presumed to come from the change in the Vg dependence of hydrodynamic flow regime in the metal phase in the vicinity of the interface at the transitional gas flow rate Vg. 4. Relation between the Mass Transfer Coefficientand Metal Depth Fig. 8. Relation between ks; and gas flow rate. (d0= 7.5 cm) The dependence of the mass transfer coefficient, ks1, on metal depth, hM, has been investigated in the Vg range of Regions I and II. The experimental tional gas flow rates denoted by Vg and Vg. The results are shown in Fig. 9. The crucible diameters whole range of the gas flow rate is divided into three at Figs. 9(a) and (b) are 4, 3 and 7.5 cm, respec- regions according to the dependence of Ic on the tively. The slag depth, hs1,was equal to 1.6-' 1.7 cm. gas flow rate : The figure shows that ks1 increases with hM below Region I (Vg< Vg) where ks1 varies as the square a transitional depth, hM,indicated with arrow, while root of Vg, it becomes independent of hMabove hM. The transi- Region II (Vg < Vg< Vg*) where the effect of the tional depth hM tends to decrease with increasing increase in gas flow rate on ks1 is con- Vg. Richardson et a1.4~found from mass transfer siderably smaller than in Region I, and studies in an aqueous solution-amalgam system that Region III (Vg> Vg*) where the extent of the the metal phase mass transfer coefficient increases increase in ks1 with Vg increases again. when hM is increased from 2.34 to 5.8 cm. They It is evident from Figs. 6'--8 that the transitional gas classified the conditions of metal depth into two groups, flow rate Vg varies with d~, while the transitional gas that is, " low depth " and " high depth ".4) Richard- flow rate Vg* is independent of d~ (Vg* _, 50 cm3/s). son and co-workers concluded that the extent in the Transactions ISIJ, Vol. 27, 1987 (281)
Fig. 9. Relation between ks1 and metal depth, hM. Fig. 10. Relation between ks1 and Vg for different metal depths. development of liquid circulation in the bulk metal phase influences the mass transfer coefficient, kM. According to them, under the " low depth " condi- tions, the liquid circulation was not fully developed, leading to low kM. At " high depth " fully developed liquid circulation brought about kM higher than at " low depth " and independent of metal depth . The features of these results by Richardson et al. in the effect of metal depth on mass transfer coefficient are similar to that obtained in the present study. Further discussions are to be made analytically in the next paper12~ to present comparisons between the results of aqueous solution-Hg system3,4>and slag-Cu system of the present study. Figure 10 shows the relation between ks1 and Vg Fig. 11. Relation between ks1 and Vg for different slag in Regions I and II at various hM,d and hs1 being depths. 4 and 1.6 cm, respectively. The symbols •, 0 and 0 in Fig. 10 represent results for three metal depth, that is, hM> hM,hM = 3.0 cm (hM< hM) and hM= 3.6 cm. the flow in the metal phase is considered to influence As far as hM=3.6 cm (0) in Fig. 10 is concerned, hM the metal-side mass transfer, while in Region II both is larger than h at Vg> 25 cm3/s, while at Vg< 25 the flow in the metal phase and that in the slag phase cm3/s hMis smaller than hM (Fig. 9). Figure 10 shows possibly determine the metal-side mass transfer. that the transitional gas flow rate Vg is independent of hMwithin experimental uncertainty. This suggests 6. The Change in the Mass Transfer Coefficientwith that the change in the flow in the metal phase caused CrucibleDiameter by the change in hMdoes not influence Vg. The Vg Richardson et a1.4~and Robertson and Staples3~ is presumed to be affected by the slag flow as de- made model studies on slag-metal mass transfer with scribed later. aqueous solution-amalgam systems and molten salt- molten lead system. They obtained the following 5. Relation betweenthe Mass Transfer Coefficientand Slag correlation equation Depth Experiments have been performed with a lowered k x - (BDxVg\"2d2 ...... (5) slag depth, hs1. The experimental conditions were as follows: d~=4 cm, hM=3.43.6 cm (constant), where, kx: the mass transfer coefficient of solute x h1= 1.2 cm. The results are shown in Fig. 11 together in either the " slag " (aqueous solution, with the data with h81=1.6 cm shown in Fig. 7. At molten salt) phase or the metal (amal- gas flow rates shown in Fig. 11, metal depth is smal- gam, lead) phase ler than the transitional depth, that is, hM
slag depth, he,, have been investigated. The results are summarized as follows : (1) ks1increases generally with increasing Vg, but the dependence of ks1 on Vg changes at transitional gas flow rates, Vg and Vg * . The explored Vg range is divided into three regions according to the depen- dence of ks, on Vg. In Region I (Vg< Vg), ksiocVgi2. In Region I I (V g < Vg < Vg*), ks, increases only slightly with increasing the gas flow rate. In Region III (Vg> Vg*), the extent of increase in ks1 with Vg increases again. (2) The transitional gas flow rate Vg varies with crucible diameter and slag depth. The transitional gas flow rate, v:*, is constant, irrespectively of the crucible diameter. (3) In Region III, the increase in actual inter- Fig. 12. Relation between ks1 and (Vgld~). facial area caused by formation of liquid droplets is considered to be reflected on the increase of ks1 at 1/2 in Region I. This indicates that the high Vg. In Regions I and II, gas injection does not present data fit Eq. (5), independent of d~ and Vg. affect markedly the interfacial area, so that ks; can For the data in Region I, the value of the propor- be regarded approximately as the metal-side mass tionality constant B in Eq. (5) is calculated to be transfer coefficient. 41 cm-1, * This value of B is considerably smaller (4) In Regions I and II, ks1 increases with hM than that reported previously for amalgam phase in below a transitional depth, hM. Above hM, ks1 be- aqueous solution-amalgam system4~(80 cm-1 for " low comes independent of hM. The transitional depth hM depth " and 120 cm-1 for " high depth ") and for tends to decrease as Vg increases. molten lead phase in molten salt-Pb system4) (B= (5) Slag depth, hs1, has no influence on ks; in 110 cm-1). The discrepancy between the present Region I. In Region I, ks, is proportional to slag-Cu system and model systems at low tempera- (Vg/d)'/', when hM>hM. In Region II, ks; is sug- tures is considered to be due to the large difference in gested to decrease with decreasing hs1. the physical properties. REFERENCES 7. Summarizing Remarks 1) W. F. Porter, F. D. Richardson and K. N. Subramanian: As mentioned above, metal-side mass transfer Heat and Mass Transfer in Process Metallurgy, ed, by A. W. coefficient is affected complicatedly by the gas injec- Hills, Inst. Min. Met., London, (1967), 79. tion stirring conditions (i.e., gas flow rate, metal 2) J. K. Brimacombe and F. D. Richardson : Trans. Inst. Min. depth, crucible diameter, slag depth). In this report, Met. [C], 82 (1973), C63. the experimental results have been reported phenome- 3) D.G.C. Robertson and B. B. Staples: Process Engineering nologically and only qualitative explanations have of Pyrometallurgy, ed. by M. J. Jones, Inst. Min. Met., been made on the results. In the next report,12) London, (1974), 51. mass transfer phenomena in the metal-side of slag- 4) F. D. Richardson, D.G.C. Robertson and B. B. Staples: Proceedings Darken Conference on Physical Chemistry in metal interface with gas injection stirring is to be Metallurgy, US Steel Corp. Research Lab., Monroeville, handled theoretically on the basis of a hydrodynamic (1976), 25. theory. From this, the experimental results obtained 5) S. Asai: The 100th-lOlst Nishiyama Memorial Seminar, in the present study will be analyzed quantitatively. ed, by ISIJ, ISIJ, Tokyo, (1984), 65. 6) K. Mori, M. Hirasawa, M. Shinkai and A. Hatanaka : Iv. Conclusion Tetsu-to-Hagane, 71 (1985), 1110. Model studies have been made on the role of gas 7) M. Hirasawa, M. Matsu-ura and K. Mori : J. Japan Inst. injection stirring in slag-metal reactions. The slag- Metals, 50 (1986), 796. molten Cu reaction system of oxidation of Si in Cu 8) M. Sano and K. Mori: Trans. JIM, 17 (1976), 344. by FeO in slag, taking place under the condition of 9) M. Sano, K. Mori and Y. Fujita: Tetsu-to-Hagane, 65 rate-controlling by Si transport in the metal phase, (1979), 1140. 10) K. Nogi, K. Ogino, A. McLean and W. A. Miller: Met. was selected as the model system. Kinetic experi- Trans., 17B (1986), 163. ments were done at 1 250°C. The relations between 11) J. F. Elliot, M. Gleiser and V. Ramakrishna: Thermo- apparent metal side mass transfer coefficient, ks,, and chemistry for Steelmaking, I, Addison-Wesley, Mass., (1960). the gas injection stirring conditions, i.e., gas flow 12) M. Hirasawa, K. Mori, M. Sano, Y. Shimatani and Y. rate, Vg, metal depth, hM,crucible diameter, d~, and Okazaki : Trans. ISIJ, 27 (1987), 283.
* In the calculation , the diffusion coefficie nt Dsi =6.4x 10.5 cm2/s7) is used.
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