interfacial area in top blown oxygen steelmaking€¦ · interfacial area in top blown oxygen...

INTERFACIAL AREA IN TOP BLOWN OXYGEN STEELMAKING

Subagyo G.A. Brooks

and K.S. Coley

Steel Research Centre McMaster University

1280 Main Street West Hamilton, Ontario. Canada L8S 4L7

[email protected]

Key Words: interfacial area; emulsion; multi-phase reactions; gas top blowing; oxygen steelmaking; steelmaking.

INTRODUCTION

The overall rate of chemical reactions is critical in achieving an efficient steelmaking process. Generally, multiphase reactions occur during oxygen steelmaking and the most important of these are presented in Table I. As pointed out by Levenspiel f!J, for multi-phase reaction, the requirements are (i) the reactants must contact or meet each other, and (ii) both mass transfer and chemical reaction rate determine the overall rate of reaction.

The phase contact area of reactants or reacting interface is called the interfacial area. Due to the importance of the contact area in the steelmaking process, this has been the subject of several investigations 12-31. Considering the major reactions in oxygen steelmaking presented in Table I, we will concentrate on the dissolution of oxygen into the metal from 02 gas or FeO (I and 2), decarburization through dissolved oxygen (5), and oxidation of Fe, Si, Mn, and P (6-9). These seven reactions are the most important to the overall steelmaking kinetics.

These reactions take place in three distinct regions within a top blown oxygen steelmaking vesseL

Region 1, Metal-Oxygen. This is the region where oxygen, injected at supersonic speeds. is in direct contact with the molten metal. In this region oxygen pick up is via reaction (1), and reactions (5) to (9) follow from this initial pick-up of oxygen. The size of this impact region is a function of flowrate. lance height, and lance geometry 121• The size of the cavity formed in the metal bath is a function of these parameters and also the physical properties of the slag and metal. By assuming that the droplets generated from the impact of oxygen

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injection are thrown out in a radial direction and do not make significant contact with the oxygen jet from above, it can be estimated that the interfacial area between the oxygen jet and the metal bath is about 2 m2 for a "typical" top blown oxygen steelmaking vessel. Moreover, during this process it is also possible that the oxygen gas is dispersed in the fonn of gas bubbles in the metal around the jet impact area. Another phenomenon in this area, the intense stirring from the gas jet will also enhance reactions (5) to (9).

Table I. The major reactions in oxygen steelmaking.

Oxygen pick up by the metal: 02(g) = 20

(FeO) =Fe+ 0 (Fe203) = 2(Fe0) + 0 C02(g) = CO(g) + 0

Oxidation of elements in the metal: C + 0 = CO(g) Fe+ 0 = (FeO)

Si + 20 = (Si02) Mn+O=(MnO) 2:f + 50 = (P20s)

Oxidation of compounds in the slag: 2(Fe0) + Y202(g) = (Fe203)

2(Fe0) + C02(g) = (Fe203) + CO Flux Reactions:

Gas Reactions:

Note:

MgO(s) = (MgO) CaO(s) = (CaO)

CO(g) + 'llOz(g):::: C02

"-" metal phase and "( )" slag phase.

(1) (2) (3) (4)

(5) (6) (7)

(8) (9)

(10) (11)

(12) (13)

(14)

Region 2. Slag-Metal. This is the region where the stirred bath of metal is in direct contact with emulsified slag above. In this region, oxygen for reactions (5) to (9) is supplied from two sources, (i) the oxygen dissolved at the oxygen metal interface and subsequently transferred to the slag-metal interface by the intense stirring in the metal bath and (ii) oxygen transferred from the emulsified slag through reaction (2). The interfacial area for this region is largely decided by the geometry of the furnace, though disturbance of the interface through the intense stirring of the system complicates this calculation. If we take a "typical" 200t converter to have an internal diameter of 3.0m, assuln.e flat bath geometry and deduct the impact region from the calculation, we can estimate the interfacial area for the slag-metal region to be 5.1 m2• Region 3. Slag-Metal-Gas Emulsion. In this region, an FeO rich slag is in contact with droplets of molten metal. Gas generated from decarburization below from both the metal-oxygen and slag-metal region, as well as gas generated from decarburization in the emulsion, results in a highly stirred system with significant quantities of gas "held up" in the emulsion. In this region, oxidation of the metal occurs via reaction (6) before the various oxidation reactions, reactions (5) to (9), take place. Based on the surface area of the metal droplets dispersed in this emulsion phase, a very large interfacial area, about 2100 m2 [41, is available for the reactions. The aim of the present paper is to critically review what is known about interfacial area from plant data and physical modeling studies, addressing the connection between theory and practice, as well as identifying

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unresolved issues. The study will start with information on the interfacial area in slag-metal-gas emulsions followed by an analysis of the importance of this interfacial area in the overall reaction rate.

SLAG-MET AL-GAS EMULSION

The formation of a slag-metal-gas emulsion generated by an impinging gas jet is of considerable practical importance for oxygen steelmaking. For illustration, a comparison of measured data of carbon content PI and phosphorus content 141 evaluated from metal droplets and bulk metal samples taken from a 200t top blown oxygen steelmaking furnace, is presented in Figure 1. There is a significant difference between the metal emulsified phase and the bath metal, in terms of phosphorus and carbon contents. The concentration in the bath metal from the initial to the middle stages of blowing is much higher compared to the concentration in metal emulsion. This shows that the reaction between the slag and the droplets is considerably faster than that with the bulk metal indicating that the slag-metal emulsion has a significant role in the overall reaction rates of oxygen steelmaking.

• Phosphorus in metal droplets [4} 4 1:;). 0 Phosphorus in bulk metal [4]

A ... Carbon in metal droplets [61 A Carbon in bulk metal (6]

?J?. 3

A ...., .c. 0> 2 ·-

Q) s 0

0 1:;). 1 ...

•o .&o ... 0

0 • •

0 20 40 60 80 100

Blowing time, o/o

Figure 1. Phosphorus �nd carbon contents during oxygen blowing.

Num��ous studies to investigate slag-metal emulsions in oxygen steelmaking under a variety of experimental cond1t1ons have been performed, both by means of plant measurement [4•91 and laboratory work [JO-I1J. In Table II, a summary of the studies on slag-metal emulsions in oxygen steelmaking is shown. For plant measurements, based on the source of emulsion sample being analyzed, experimental methods can be classified into two categories; (1) the sample is taken from above the slag bath (splash sampling) and (2) the sample is taken from slag bath (bath sampling). The investigation carried out by Meyer et al. lSI falls into the former category whilst investigations carried out by Schoop et al. f41, Cicutti et al. !61], Price £71, Trentini [81, and Kozakevitch f9I fall into the latter.


00 � 0

N 0 0 N t:t 0 s � ...... :::

(lq n 0 ;, � = (') (\)

� 0 (') (\) (\) Q.. ...... =

(lq '7.

Investigators

Cicutti et al. (&j

Schoop et al. 141

Meyer et al. 151

Price 1'1

Trentini 181

Kozakevitch 191

Chatteijee et al. 1171

Koch et al. 1141

Urguhart and Davenport (JQJ

Peaslee et at. 1161

Standish and He [1 1·13]

Tumerand Jahanshahi 1151

Table II. A summary of slag-metal emulsion studies in oxygen steelmaking.

Experimental technique Sampling technique Percentage of metal Droplet Interfacial area, droplet to total size, mm m2/ton total

metal,% metal in furnace Plant measurement, 200t Bath sampling. - 0.23-3.35 converter. Plant measurement, 200t Bath sampling. 1.0 0.05-2.0 8-12.5 Converter. Plant measurement, 230t BOF. Splash sampling. 6.8-78 0.15-3.36 190-250 Plant measurement, 90t Bath sampling. 1-15 1.0-2.0 -86 converter. Plant measurement. Bath sampling. 2.5-12.5 6.3-25.4 Plant measurement, basic Bath sampling. (Up to40% of Bessemer converter with emulsion) bottom blowing. Hot model, 6t converter. Bath sampling. (Droplet generation 0.3-0.5

6.7-R kg/s) Hot model experiment; 50kg Splash sampling without slag (Droplet generation Fe-C melt. layer. -0.25 kg/s) Laboratory studies; cold and Small scale (1/50) of BOF for hot (Water in emulsion 0.1-3.0 hot model experiment. model, and oil-water system for -45%; iron in

cold model. emulsion -50%) Cold model experiment. Glycerol-Hg (Bath sample). - 0.2-3.0 Cold model experiment. Glycerine-Hg (Bath sample) and (Hg in emulsion 1-5

water model (single phase). -30%) Cold model experiment. Glycerol-Hg. (Hg in emulsion

-25%)

Based on plant measurement data reported in the literature, there is a large variation in the amount of metal in the emulsion. As shown in Table II, the value of metal droplets as a fraction of total metal in the furnace, varies over a wide range 1 p 78%, has been reported l4•9J. This large variation may be due to the method of sampling, in fact the only very large value is reported by Meyer et al. [SJ, whose experiment was based on splash sampling. Oeters (31 suggested an average value of 5% as reasonable.

Due to the hostile conditions of the process in oxygen steelmaking and also the interconnected nature of the metal and slag phases, it is hard to perform an ideal experiment on the plant. Therefore, in order to overcome this problem, many physical modeling studies are repmted in the literature {IO-I7J. He and Standish [l2J reported important results on the similarity criteria for droplet generation from model study.

Based on water and Hg-glycerine models, they proposed the "nominal Weber number", p g u

2 � , as similarity (p1gcr) 2

criterion for droplet generation through top gas blowing. As shown in Figure 2, the water model results exhibit a similar pattern to those from the Hg-glycerine model when considered in terms of this nominal Weber number value. From this evidence, these authors suggested that this number is the appropriate similarity criterion for the system. The results of He and Standish [!21 were further developed by Deo and Boom [21 into a correlation for predicting metal droplet generation in oxygen steelmaking. They related metal droplet generation per unit volwne of blown gas to the nominal Weber number by assuming a behavior is similar to cold modeling results reported b y He and Standish [Ill.

"'

36 45� � 0

40� - 32 r::::: CD 0 ...,

U) 28 350. :::J a E 24 3oj Q)

... Q) (JJ .r:. 20 2� -CD �

0 16

::J - 20CD r::::: ..., Q) Q) r+ - 12 155" c

0 ::J () 8

mercury \odel 1om 0> r+

I (1) 4 Sco

-.... (JJ 0 0

0 20 40 60 80 100 120 140

Nominal Weber Number

Figure 2. A comparison of mercury-glycerine model with water model results as function of nominal Weber Number £1lt.


SIZE DISTRIBUTION AND RESIDENCE TIME OF METAL DROPLETS

Besides the knowledge of the amount of metal droplets in the emulsion, information on size distribution and residence time is essential for further evaluation of this system [JJ. The amount and the size distribution of the metal droplets determine the interfacial area of the droplets, which in combination with residence time is required for kinetic calculations.

The diameter of droplets generated from the action of an impinging gas jet, from plant measurement and physical modeling reported in the literature, generally lies in between 0.05 to 5.0 mm.

The droplet size distnoution usually follows the Rosin-Ranunler-Sperling (RRS) distribution function 12• 3• 6• 16• 19-201 shown in Equation (15), although some physical model experiments showed a normal distribution [11• 181

. A typical size distribution of the droplets, from plant measurement and predicted with RRS distribution function, is presented in Figure 3.

(15)

Where R is the percent of the cumulative weight of droplets retained in a screen with diameter d. The parameters d' and n represent the distribution parameters. Moreover, according to Koria and Lange (191, the parameter d1 is the diameter of a screen for R=36.8% whilst the reciprocal of d' characterizes the fineness. The homogeneity of the particle size distribution is represented by parameter n. Koria and Lange [19• 201 suggested a value of 1.26 for steel production. However, plant measurement data by Cicutti et al. £61 shows that the value of n-and also d' -is a function of the gas blowing rate.

100

80 R,%=100 Exp(-(dfd')")

/

'#. 60

a:: 40

20

0 0 0.0 0_5 1.0 1.5 2.0 2.5 3.0 3.5

Particle diameter, mm

Figure 3. A typical metal droplet size distribution ((;].


Although knowledge of the droplet residence time is of considerable importance, due to the difficulty in measuring this value experimentally, little information has been reported in the literature 1131• This condition is mainly due to the interconnected condition of slag-metal emulsion in oxygen steelmaking. Therefore, a direct measurement of the residence time of the metal droplet in the slag-metal emulsion phase is difficult. As a result, studies of the residence time are carried out indirectly. Due to the difference in evaluation methods, the values reported in the literature are subject to some variation. As shown in Table III, the average residence time reported lie between 0.25 and 120s.

Although the exact value of the residence time of metal droplets in the slag could not be directly detennined using their cold model, He and Standish [I3J suggested using the value of 60s as the average value in oxygen steehnaking. This suggestion is also consistent with values suggested by Oeters 1211 and Jahanshahi and Belton 1221 in their work on the chemical kinetics of oxygen steelmaking.

Table III. A summary of residence time studies of metal droplets in the slag in oxygen steelmaking.

Investigators Schoop et al. tal

Price PJ

Kozakevitch 191

Urguhart and Davenport [IOJ He and Standish fiJJ

Methods Indirect plant measurement, residence time is calculated based on chemical analysis and kinetics model. Plant measurement with radioactive gold isotope tracer technique. Prediction based on the carbon and phosphorus content in metal droplet from plant measurement. Prediction based on cold model experiment.

Cold model experiment, Hg�glycerine system.

Residence time, s. -59.9

120 ± 30

60-120

0.25

60 (Cold model: 2-40)

INTERFACIAL AREA OF REACTIONS IN OXYGEN STEELMAKING Up to this point, our discussion about interfacial area in oxygen steelmaking has mainly concerned the interfacial area of metal droplets in the slag-metal emulsion. This interfacial area has been believed to be the main factor for promoting the rapid reaction in oxygen steelmaking [J-Sl. The significance of this interfacial area on the overall performance of oxygen steelmaking is addressed in the following analysis.

Model for entrained metal droplets

A schematic diagram of the metal flow is presented in Figure 4. By employing the principle of mass conservation on the slag phase for time t = t to t = t + dt , the following equations can be developed l23l;

dV -=R -R dt 8 D

with the boundary condition:

at t=O, V=O

at t � tss, V = V"'

(16)

(17)

(18)

For a constant value of droplet birth rate, R8, and with assumption that, for t < tss , the droplet death rate, R0, is proportional to their concentration (or mass) in emulsion, the solution for equations (16) to (18) is f23l:


For 0 < t < tss, V = R8-r(l-Exp(-th))

v = voo

(19)

(20)

and Voo = RB't (21)

The constant value of't is the mean residence time of the droplets in the slag (or emulsion) [231. Moreover, from the population balance theory and settling (sedimentation) theory 1241, the value steady state time, tss, is equal to the longest residence time or the residence time of the smallest droplet.

SLAG PHASE

V,kg

Rn, kgls

,,

L,kg

METAL PHASE

Figure 4. A schematic diagram of metal flow in oxygen steelmaking.

By using equations (19) to (21), the value of the droplets' birth rate, Re, the weight of metal droplets in the emulsion at steady state, V ""'and the average residence time, 't, can be determined based on the droplets' weight in the emulsion as function of time.

In order to get figures for the droplet birth rate and average residence time in oxygen steelmaking, the data of Schoop et al. £4] is used. This measured data is taken from a 200t converter with a constant top blowing flowrate (525 Nm3/min) and adjusted lance height to ensure a good foaming slag. This calculation gives results on the value ofRs, V oo, and 't equal to 11.0 kg/s, 1708 kg, and 156s, respectively.

Comparison of the predicted values from entrained metal droplets model [lJJ with measured profile taken from Schoop et al. f41, presented in Figure 5, demonstrates fairly good agreement. The deviation between the predicted and the measured data may be due to the fact that the measured data is not taken from a constant value of droplet generation as required by the model. This non-constant droplet generation is primarily due to the variation of the lance height during the experiment.


3000

2500

2000

C) 1500 � >-

1000

500

0 0

o Schoop et al [4] data.

-- Lin and Guthrie [24] model.

0 0 0

0 0 0

5 10 15 20

Blowing time, min.

Figure 5. A comparison of the measured data 141 of metal droplet in emulsified phase with predicted by Lin and Guthrie model 1231,

Mixing-reaction zone model

To establish equations for evaluating the reaction phenomena, the system is divided into two zones; those are reaction zone and mixing zone, as schematicaily shown in Figure 6. In this model, it is asswned that all reactions considered are taking place in the reaction zone and the conclition in mixing zone is uniform or perfectly mixed.

By employing the principle of mass conservation in the mixing zone during steady state condition of material flow and assuming a constant amount of Fe in the furnace, for time t = t to t = t + dt, the following equations can developed;

and

RE -RM = 0

dXA =

RM(Y -X ) dt � A A

IT= E+M

E RM =t'

(22)

(23)

(24)

(25)

If the value of average residence time in reaction zone, •', the amount of Fe in furnace, Ir, and the concentration of A in reaction and mixing zones are known, the value ofE can be calculated.

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An example of comparison of the measured profile of the phosphorus content 141 and the carbon content 161 in the mixing phase with the predicted values is presented in Figure 7. It is clearly demonstrated that there is a good agreement between measurement and prediction by the model. As a result, it is reasonable to use the model for further evaluation.

REACTION ZONE

E, kg Y A' kg A/kg Fe

�

RM, kgls RE, kgls

�lr

M,kg XA, kg A/kg Fe

MIXING ZONE

Figure 6. A schematic diagram of reaction zone in oxygen steelmaking.

3

2

1

e Measured PhosphonJs in metal phase [4]

-- Predicted Phosphorus in metal phase

0 Measured Carbon in metal phase [61 -- Predicted carbon in metal phase

5 10 15 20

Blowing time, min.

25

Figure 7. A typical comparison of measured values of carbon and phosphorus content in metal phase with model predictions.

By using this model, a proper value for the size of the reaction zone for the rapid reaction in oxygen steelmaking can be determined as function of the average residence of the metal in the reaction zone. The size of reaction zones for a 200t furnace and their percentage of total metal in the furnace are tabulated in Table IV.


It should be noted here that the values presented in Table N are calculated based on the same carbon and phosphorus profiles as the data used in constructing Figure 7.

DISCUSSION Due to the extremely large interfacial area of metal droplets in the emulsion, it has been concluded that this area is largely responsible for the very fast reactions in oxygen steelmaking l4• 61. Given the results of the mixingreaction zone model and entrained droplets model, it is appropriate to reexamine the interfacial area of reaction in oxygen steelmaking.

If the considered reactions are assumed to occur only in the metal droplet emulsion, all the metal in the reaction zone must be in emulsion. Moreover, the average metal residence time in the reaction zone, t', must also equal the average droplet residence time in the slag phase, 't.

Considering the result of the mixing-reaction zone model calculation, if the average residence time value suggested by Oeters [211

, 60 s, is used, from Table IV it is found that the fraction of metal in reaction zone is about 15.5% of total metal in the furnace. If we compare this value to the value suggested by Oeters [J]' which is about 5%, the result is about three times higher. Moreover, this value is also considerablr higher compared with plant measurements (see Table II) and only agrees with measured data of Meyer et al. rs. However, it should be noted here that the Meyer et al. £41 data is not analyzed directly from the emulsified phase, but from the material ejected through the furnace tap bole.

Table IV. Weight fraction of reaction zone predicted by model for 200t furnace.

Residence time, s

10 17 20 30 45 60 90

120 156

Reaction zone, ton

6.0 10.0 11.6 16.5 24.0 31.0 43.0 53.0 65.0

Percentage of reaction zone to

total metal % 3.0 5.0 5.5 8.3

12.0 15.5 21.5 26.5 32.5

Conversely, if we use a percentage metal in the reaction zone of about 5%, as suggested by Oeters £211, from Table IV the average residence time is about 17s. This average residence time is much lower than commonly believed in literature {IJ, 21• 221, 60s, or the plant measurement using a radioactive gold isotope tracer technique £71, 120±30s, or the value determined by the Lin and Guthrie model 1231 based on Scboop et al !41 data, 156s.

From the above brief description, although the interfacial area of the metal droplets in emulsion has significant influence on the overall rate of reaction in oxygen steelmaking, this interfacial area should not be the only phase contact used in process analysis. This condition agrees with the conclusion of Cicutti et al. [61 and Price £4J, that less than 50% of decarburization takes place in metal droplets' emulsion. Hence, other possible phase contact or interfacial area, for example the interfacial area of the gas bubbles dispersed in the metal phase around the jet impact region, should also be considered for better understanding of oxygen steelmaking.

The residence time of metal droplets in the slag phase is essential for evaluating the significance of this interfacial area on the overall rate of reaction by using the mixing-reaction zone model. However, the value of

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the residence time used in the present evaluation is still uncertain. Therefore, there is still a need for better measurement or more study of residence times of metal droplets in slag.

Work on hot model experiment and mathematical modeling for investigating the residence time of metal droplets in slag and the generation of metal droplets is underway in the authors' laboratory at McMaster University. The hot model experiment is carried out in an induction furnace with an MgO crucible (190 mm i.d., 295 mm high) containing cast iron and calcium·aluminate slag, using nitrogen blowing gas. Details of experiments procedure and the results will be reported later, elsewhere.

CONCLUSION

A mixing-reaction zone model to evaluate the significance of the interfacial area of the metal droplets in slag on the overall reaction rate in the furnace has been developed. Due to the uncertain knowledge about the average residence time of the metal droplets in emulsion, the significance of the slag-metal·gas emulsion phase on the overall reaction rate is still unclear. However, preliminary evaluation using published common values of average residence time, indicate that this interfacial area determines less than 50% of the overall rate of reaction. Therefore, a further study on other possible interfaces in this system is needed. More study on the residence time of the metal droplets in the slag phase is also needed for better understanding of the phenomena.

E weight of Fe in the reaction zone, kg Fo flowrate of blowing gas, Nm3 g gravitational constant, m s-2 N wo

Nominal Weber number,-n constant defined in Equation (15),-

d droplet diameter, m d' constant defined in Equation (15), m h total Fe in the furnace, kg L total Fe in the metal phase, kg M total Fe in the mixing zone, kg R percent cumulative weight of the droplet, %

Notation

Re birth rate of metal droplets generated by impinging gas jet, kg s·1 Ro death rate of metal droplets departing slag phase, kg s-1 RE death rate of Fe in reaction zone, kg s-1 RM birth rate of Fe departing reaction zone, kg s-1 t time, s tss steady state time, s u velocity of gas, m s-1 V weight of metal droplets in slag phase, kg V «> weight of metal droplets in slag phase after reaching steady state time, kg XA mass fraction of A in mixing zone, kg A/kg Fe Y A mass fraction of A in reaction zone, kg A/kg Fe Pg density of gas, kg m·3 P1 density of liquid, kg m·3 cr surface tension, N m·1 't average residence time of metal droplets in emulsified phase, s 't

' average residence time of metal in reaction zone, s


References

1. 0. Levenspiel, Chemical Reaction Engineering, 2nd, John Wiley & Sons, New York, 1972, pp. 408-459.

2. B. Deo and R. Boom, Fundamentals of Steelmaking Metallurgy, Prentice Hall International, New York, 1993, pp. 106-214.

3. F. Oeters, Metallurgy of Steelmaking. Verlag Stahl Eisen mbH, DUsseldorf, 1994, pp. 343 �416.

4. J. Schaap, W. Resch, and G. Mahn, "Reactions Occurring during the Oxygen Top-Blown Process and Calculation of Metallurgical Control Parameters", lronmaking & Steelmaking, (2), 1978, 72�79.

5. H.W. Meyer, W.F. Porter, G.C. Smith, and J. Szekely, "Slag-Metal Emulsions and their importance in BOF Steelmaking", JOM, 20(7), 1968, 35-42.

6. C. Cicutti, M. Valdez, T. Perez, J. Petroni, A. Gomez, R. Donayo, and L. Ferro, "Study of Slag-Metal Reactions in an LD-LBE Converter", Paper Presented at Slag Conference, Stockholm, 2000.

7. D.J. Price, "L.D. Steelmaking: Significance of the Emulsion in Carbon Removal", Process Engineering of Pvrometallurgy, M.J. Jones (Ed.), The Institution of Mining and Metallurgy, London, UK, 1974, pp. 8-15.

8. B. Trentini, "Comments on Oxygen Steelmaking", Trans. Met. Soc. AIME, 242, 1968, 2377-2388.

9. P. Kozakevitch, ''Foams and Emulsions in Steelmaking", JOM, 22(7), 1969, 57-68.

10. RC. Urquhart and W.O. Davenport, "Foams and Emulsions in Oxygen Stee1making", Can. Metall. Quarterly, 12(4), 1973, 507-516.

11. N. Standish and Q.L. He, "Drop Generation due to an Impinging and the Effect of Bottom Blowing in the Steelmaking V esse)", ISIJ Int. , 29( 6), 1989, 45 5-461.

12. Q.L. He and N. Standish, "A Model Study of Droplet Generation in the BOF Steelmaking", ISIJ Int., 30(4), 1990, 305-309.

13. Q.L. He and N. Standish, "A Model Study of Residence Time of Metal Droplets in the Slag in BOF Steelmaking", ISU Int., 30(5), 1990, 356-361.

14. K. Koch, J. Falkus, and R. Brockhaus, "Hot Model Experiments of the Metal Bath Spraying Effect during the Decarburization ofFe-C Melts through Oxygen Top Blowing", Steel Res., 64(1), 1993, 15-21.

15. G. Turner and S. Jahanshahi, "A Model Investigation on Emulsification of Metal Droplets in the Basic Oxygen Steelmaking Processes", Trans. ISU, 27, 1987, 734-739.

16. K.D. Peaslee, D.K. Panda, and D.G.C. Robertson, "Physical Modeling of MetaVSlag/Gas Interactions and Reactions in Steelmaking", Proceeding of 1993 ISS Steelmaking Conference, 1993, pp. 637-644.

17. A. Chatterjee, N.O. Lindfors, and J.A. Wester, "Process Metallurgy of LD Steelmaking", Ironmaking & Steelmaking, 3(1), 1976, 21-32.

18. S.C. Koria and K.W. Lange, "Disintegration of Iron-Carbon Drop by High-Velocity Gas Jet'', Iromnaking & Steelmaking., 10(4), 1983, 160-168.

19. S.C. Karia and K.W. Lange, "A New Approach to Investigate the Drop Size Distribution in Basic Oxygen Steelmaking", Metal!. Trans., 15B, 1984, 109-116.

20. S.C. Koria and K.W. Lange, "Estimation of Drop Sizes in hnpinging Jet Steelmaking Processes", Ironmaking & Steelmaking, 13(5), 1986, 236-240.

21. F. Oeters, "Kinetic Treatment of Chemical Reactions in Emulsion Metallurgy'', Steel Res., 56(2), 1985,69-74.

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22. S. Jabanshahi and G.R. Belton, "Slag/Metal Phosphorus Equilibria and the Kinetics of Phosphorus Transfer in Oxygen Steelmaking"; Proceedings of the 6th Process Technology Conference, Vol. 6, ISS� Warrendale, 1986, pp. 641-651.

23. Z. Lin and R.I.L. Guthrie, .. Modeling of Metallurgical Emulsions", Metal!. Mater. Trans.1 25B, 1994, 85S-864.

24. A,S. Foust, L.A. Wenzel, C.W. Clump, L. Maus, and L.B. Andersen, Principles ofUnit Operations, 2nd Ed., Joh.Il Wiley & Sons, New York, 1980, pp. 611-637.

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