Secondary Steel Making - Ahindra Ghosh

Principles and Applications

Ahindra Ghosh, Sc.D.AICTE Emeritus FellowProfessor (Retired)Indian Institute of Technology, KanpurDepartment of Materials and Metallurgical Engineering

SECONDARYSTEELMAKING

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Ghosh, AhindraSecondary Steelmaking : Principles and Applications

p. cm.Includes bibliographical references and index.ISBN 0-8493-0264-1 1. Steel. I. Title.

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Dedication

toDr. G. P. Ghosh

(Late) Prof. T. B. King(Late) Prof. A. K. Seal


Preface

With the passage of time, customers who buy steel are becoming more and more quality conscious.In view of this, steelmakers are attempting to improve steel quality as a continuing endeavor. Theproduct of steelmaking is liquid steel, which is then cast primarily via the continuous casting route.Liquid steel of superior quality should have a minimum of harmful impurities and nonmetallicinclusions, the desired alloying element content and casting temperature, and good homogeneity.

The primary steelmaking furnaces, such as the basic oxygen furnace and electric arc furnace,are not capable of meeting quality demands. This has led to the growth of what is known assecondary steelmaking, which is concerned with further refining and processing of liquid steel afterit is tapped into the ladle from the primary steelmaking furnace. Secondary steelmaking is a majorthrust area in modern steelmaking technology and has witnessed significant advances in the last30 years. Its scope is wide and includes deoxidation, degassing, desulfurization, homogenization,temperature control, removal, and modifications of inclusions, etc.

This text consists of 11 chapters. The first chapter provides a brief overview of secondarysteelmaking. Chapters 2 through 4 briefly review relevant scientific fundamentals, viz., thermody-namics, fluid flow, mixing, mass transfer, and kinetics relevant to secondary steelmaking. Chapters5 through 10 deal with reactions, phenomena, and processes that are of concern in secondarysteelmaking.

Since some topics do not justify a full chapter for each, a chapter on miscellaneous topics(Chapter 8) provides coverage of these issues. The technology to manufacture what is known asclean steel calls for a variety of measures at different processing stages. An attempt has been madeto present an integrated picture of this in Chapter 10.

Mathematical modeling is an important component of process research nowadays. The basicsas relevant to secondary steelmaking, along with application examples, are presented in Chapter 11.

Although the present text deals primarily with principles and applications for the secondarysteelmaking processes, it contains brief information on the processes and modern technologicaladvances as well. Synthesis of science with technology is one of the objectives. The textbook styleof writing has been adopted. Some examples and their solutions also have been included. Referenceshave been included at the end of each chapter. Hence, the author hopes that this text will be founduseful not only by students and teachers, but also by steelmakers and research and developmentengineers interested in the field.

Ahindra Ghosh


Acknowledgments

The author gratefully acknowledges the contribution of his colleague Dr. D. Mazumdar, who wroteChapter 11 and provided help in other aspects, and assistance provided by Dr. S. K. Choudhary,Dr. T. K. Roy, Mr. K. Deo, Mr. A. Sharma, and Ms. S. Ghosh at certain stages of preparation ofthe manuscript. Thanks are due to Mr. B. D. Biswas and Mr. J. L. Kuril for careful typing of themanuscript, Mr. A. K. Ganguly for tracing figures, and Dr. M.N. Mungole for helping withphotographs. Financial assistance from the Centre for Development of Technical Education, IndianInstitute of Technology, Kanpur, is gratefully acknowledged. Lastly, the work would not have beenpossible without the patience and cooperation of author’s wife Radha and other members of hisfamily.


About the Author

Professor Ahindra Ghosh was born at Howrah, West Bengal, India, in1937. He studied for his B.E. degree in Metallurgical Engineering atBengal Engineering College and received the degree from CalcuttaUniversity in 1958. Subsequently, he received his Sc.D. degree fromthe Massachusetts Institute of Technology in 1963, specializing inextractive metallurgy. He served as Research Associate at Ohio StateUniversity, U.S.A., from 1963–64. Since 1964, he has been with theDepartment of Materials and Metallurgical Engineering, Indian Insti-tute of Technology, Kanpur, where he retired as Professor in June,2000, and is currently an Emeritus Fellow of All India Council ofTechnical Education. During this period, he also has spent short periodsat the Imperial College, London, as well as the Massachusetts Institute

of Technology as a visiting scientist; and at Metallurgical and Engineering Consultants, Ranchi,and Tata Research Development and Design Centre, Pune, as an advisor.

Professor Ghosh has guided many research students and scholars. He has to his credit 2 booksand about 75 original research publications in reviewed journals. He also has delivered invitedlectures at many conferences and has published several review papers in conference proceedings,etc. For the last three decades, his principal interest has been in the theory of metallurgical processesin ironmaking and steelmaking, with specific emphasis on sponge ironmaking, secondary steel-making, ingot casting, and continuous casting. In these endeavors, Professor Ghosh also hadsignificant interaction with industry in addition to his work with metallurgical fundamentals. Heis also involved in basic research in solidification of metals and high-temperature oxidation of alloys.

Professor Ghosh has served as an editor of the Transactions of the Indian Institute of Metalsand as a member or advisor for many professional activities. In recognition, he has been elected aFellow of the Indian National Academy of Engineering for his distinguished contribution toengineering.


Contents

Preface

About the Author

List of Symbols with Units

Chapter 1 Introduction

1.1 History of Secondary Steelmaking1.2 Trends in Steel Quality Demands1.3 Scientific Fundamentals1.4 Process ControlReferences

Chapter 2 Thermodynamic Fundamentals

2.1 Introduction2.2 First and Second Laws of Thermodynamics2.3 Chemical Equilibrium2.4 ∆G0 for Oxide Systems2.5 Activity–Composition Relationships: Concentrated Solutions2.6 Activity–Composition Relationships: Dilute Solutions2.7 Chemical Potential and Equilibrium2.8 Slag Basicity and CapacitiesReferences

Appendix 2.1Appendix 2.2Appendix 2.3Appendix 2.4

Chapter 3 Flow Fundamentals

3.1 Basics of Fluid Flow3.2 Fluid Flow in Steel Melts in Gas-Stirred LadlesReferences

Appendix 3.1

Chapter 4 Mixing, Mass Transfer, and Kinetics

4.1 Introduction4.2 Mixing in Steel Melts in Gas-Stirred Ladles4.3 Kinetics of Reactions among Phases

4.4 Mass Transfer in a Gas-Stirred Ladle4.5 Mixing vs. Mass Transfer Control


References

Appendix 4.1

Chapter 5 Deoxidation of Liquid Steel

5.1 Thermodynamics of Deoxidation of Molten Steel5.2 Kinetics of the Deoxidation of Molten Steel5.3 Deoxidation in IndustryReferences

Appendix 5.1

Chapter 6 Degassing and Decarburization of Liquid Steel

6.1 Introduction6.2 Thermodynamics of Reactions in Vacuum Degassing6.3 Fluid Flow and Mixing in Vacuum Degassing6.4 Rates of Vacuum Degassing and Decarburization6.5 Decarburization for Ultra-Low Carbon (ULC) and Stainless SteelReferences

Chapter 7 Desulfurization in Secondary Steelmaking

7.1 Introduction7.2 Thermodynamic Aspects7.3 Desulfurization with Only Top Slag7.4 Injection Metallurgy for DesulfurizationReferences

Chapter 8 Miscellaneous Topics

8.1 Introduction8.2 Gas Absorption during Tapping and Teeming from Surrounding Atmosphere8.3 Temperature Changes of Molten Steel during Secondary Steelmaking8.4 Phosphorus Control in Secondary Steelmaking8.5 Nitrogen Control in Steelmaking8.6 Application of MagnetohydrodynamicsReferences

Chapter 9 Inclusions and Inclusion Modification

9.1 Introduction9.2 Influence of Inclusions on the Mechanical Properties of Steel9.3 Inclusion Identification and Cleanliness Assessment9.4 Origin of Nonmetallic Inclusions9.5 Formation of Inclusions during Solidification9.6 Inclusion ModificationReferences

Chapter 10 Clean Steel Technology

10.1 Introduction

10.2 Summary of Earlier Chapters10.3 Refractories for Secondary Steelmaking


10.4 Tundish Metallurgy for Clean SteelReferences

Chapter 11 Modeling of Secondary Steelmaking Processes

Dipak Mazumdar, Ph.D.11.1 Introduction11.2 Modeling Techniques11.3 Modeling Turbulent Fluid Flow Phenomena11.4 Modeling of Material and Thermal Mixing Phenomena11.5 Modeling of Heat and Mass Transfer between Solid Additions and Liquid Steel11.6 Numerical Considerations11.7 Concluding RemarksReferences


List of Symbols with Units*

a specific surface area m–1

acceleration vector ms–2

A area m2

ai activity of component i in a solution —

Bi Biot number —

C specific heat Jmol–1K–1, Jkg–1K–1

CD drag coefficient —

Ci concentration of component i in solution kg m–3

slag capacity for component i —

d diameter m

Di molecular diffusivity of species i m2 s–1

Dt turbulent diffusivity m2 s–1

E internal energy, activation energy Jmol–1

energy input in a gas-stirred bath J

first-order interaction coefficient describing influence of solute j on fi —

Eu Euler number —

F view factor —

F, force, force vector N

FD drag force N

fi activity coefficient of solute i in a solution in 1 wt.pct. standard state —

Fr Froude number —

Frm modified Froude number —

g acceleration due to gravity ms–2

G Gibbs free energy Jmol–1, J

GO Gibbs free energy at standard state Jmol–1, J

∆G, ∆GO finite change in G, GO Jmol–1, J

partial molar Gibbs free energy of component i in solution Jmol–1

partial molar Gibbs free energy of mixing of component i in solution J mol–1

Gr Grasshof number —

H enthalpy J mol–1, J

height of liquid bath m

hi activity of solute i in a solution in 1 wt.% standard state —

* — indicates a dimensionless quantity, mol means gram · mole.

a

eij

F

Gi

Gim

I

intensity of turbulence —

i,

j

tensor arrays —


Ji,x flux of species i along x-coordinate mol · m–2 s–1

k turbulent kinetic energy per unit mass of fluid Jkg–1

kc specific chemical rate constant ms–1, etc.

ki empirical rate constant for first-order process ms–1

km,i mass transfer coefficient for species i ms–1

K equilibrium constant —

KM deoxidation constant for deoxidizer M —

equilibrium constant involving metal M —

l a length parameter m

Li partition coefficient of species i between two phases —

m, M mass kg

rate of change of mass kg · s–1

mi mass fraction of component i —

Mi molecular/atomic mass of species i g · mol–1

Mo Morton number —

Nu Nusselt number —

P pressure atm, Nm–2

pi partial pressure of component i in a gas mixture atm

Pe Peclet number —

Pr Prandtl number —

q quantity of heat J

Q volumetric gas flow rate m3 s–1

activity quotient —

heat flow rate W

r radial coordinate m

reaction rate mol · s–1

R universal gas constant Jmol–1 K–1, m3 atm mol–1 K–1

vessel radius m

circulation rate of metal in vacuum degassing kg s–1

degree of desulfurization —

S entropy Jmol–1 K–1, JK–1

Danckwerts surface renewal factor s–1

source term in differential equation as applicable

Sc Schmidt number —

Sh Sherwood number —

t time s

m M,

tc circulation time s

te exposure time s


tmix mixing time s

tr residence time s

T temperature K

u, velocity, velocity vector ms–1

ux velocity along x-coordinate ms–1

V volume m3

w quantity of work done J

We Weber number —

Wi weight percent of component i in a solution —

x, y, z rectangular coordinates m

Xi mole/atom fraction of component i in solution —

Y degree of mixing —

slag rate in desulfurization kgt–1

Greek Symbols

α volume fraction of gas in gas-liquid mixture —

α i a-function for component i in a solution —

Pauling electronegativity —

γi activity coefficient of component i in a solution —

Henry’s law constant for solute i in binary solution —

Γ general symbol for diffusivity of heat, mass, momentum m2s–1

δ partial differential

∆ finite change of a quantity as applicable

δc,eff effective concentration boundary layer thickness m

δu,eff effective velocity boundary layer thickness m

ε rate of dissipation of energy W

emissivity of surface —

εm rate of dissipation of energy per unit mass Wkg–1

θ angle degree, radian

λ geometrical scale factor —

λt turbulent thermal conductivity W m–1 s–1

Λ optical basicity —

µ viscosity N sm–2

µ i chemical potential of component i in a solution J mol–1

ν kinematic viscosity m2s–1

ρ density kg m–3

u

γio

1 Introduction

1.1 HISTORY OF SECONDARY STEELMAKING

Prior to 1950 or so, after steel was made in furnaces such as open hearths, converters, and electricfurnaces, its treatment in a ladle was limited in scope and consisted of deoxidation, carburizationby addition of coke or ferrocoke as required, and some minor alloying. However, more stringentdemands on steel quality and consistency in its properties require controls that are beyond thecapability of the steelmaking furnaces. This is especially true for superior-quality steel products insophisticated applications. This requirement has led to the development of various kinds of treat-ments of liquid steel in ladles, besides deoxidation. These have witnessed massive growth and, asa result, have come to be variously known as secondary steelmaking, ladle metallurgy, secondaryprocessing of liquid steel, or secondary refining of liquid steel. However, the name secondarysteelmaking has more or less received widest acceptance and hence has been adopted here.

Secondary steelmaking has become an integral feature of modern steel plants. The advent ofthe continuous casting process, which requires more stringent quality control, is an added reasonfor the growth of secondary steelmaking. Steelmaking in furnaces, also redesignated now as primarysteelmaking, is therefore increasingly employed only for speedy scrap melting and gross refining,leaving further refining and control to secondary steelmaking. There are processes, such as vacuumarc refining (VAR) and electroslag remelting (ESR), that also perform some secondary refining.However, they start with solidified steel and remelt it. Hence, by convention, these are not includedin secondary steelmaking.

Harmful impurities in steel are sulfur, phosphorus, oxygen, hydrogen, and nitrogen. Theyoccupy interstitial sites in an iron lattice and hence are known as interstitials. The principal effectsof these impurities in steel are loss of ductility, impact strength, and corrosion resistance. When itcomes to detailed consideration, each element has its own characteristic influence on steel proper-ties. These will be briefly mentioned in subsequent chapters associated with them. Oxygen andsulfur are also constituents of nonmetallic particles in steel, known as inclusions. These particlesare also harmful to properties of steel and should be removed as much as possible. Carbon is alsopresent as interstitial in iron lattice. However, unlike the other interstitials, it is generally notconsidered to be harmful impurity and should be present in steel as per specification. But, today,there are grades of steel in which carbon also should be as low as possible.

Historically, the Perrin process, invented in 1933, is the forerunner of modern secondarysteelmaking. Treatment of molten steel with synthetic slag was the approach. Vacuum degassing(VD) processes came in the decade of 1950–1960. The initial objective was to lower the hydrogencontent of liquid steel to prevent cracks in large forging-quality ingots. Later on, its objective alsoincluded lowering of nitrogen and oxygen contents. Purging with inert gas (Ar) in a ladle usingporous bricks or tuyeres (IGP) came later. Its primary objective was stirring, with consequenthomogenization of temperature and composition of melt. It offered the additional advantage offaster floating out of nonmetallic particles. It was also found possible to lower carbon to a verylow value in stainless steel by treatment of the melt with oxygen under vacuum or along with an


argon stream. This led to development of

vacuum-oxygen decarburization (VOD)

and

argon-oxygendecarburization (AOD).


Synthetic slag treatment and powder injection processes of molten steel in a ladle were startedin late 1960s and early 1970s with the objective of lowering the sulfur content of steel to the verylow level demanded by many applications. This led to the development of what is known as injectionmetallurgy (IM). Injection of powders of calcium bearing reagents, typically calcium silicide, wasalso found to prevent nozzle clogging by Al2O3 and lead to inclusion modification, which are ofcrucial importance in continuous casting as well as for improved properties.

The growth of secondary steelmaking is intimately associated with that of continuous castingof steel. Up to the decade of the 1960s, ingot casting was dominant. Now, most of world’s steel iscast via the continuous casting route. The tolerance levels of interstitial impurities and inclusionsare lower in continuous casting than in ingot casting, and this has made secondary refining moreimportant. For good quality finished steel, proper macrostructure of the casting is also important,in addition to the impurity level. This requires close control of the temperature of molten steelprior to teeming into the continuous casting mold.

In traditional pitside practice, without ladle metallurgical operations, the temperature drop ofmolten steel from furnace to mold is around 20–40°C. An additional temperature drop of about30–50°C occurs during secondary steelmaking. Continuous casting uses pouring through a tundish,causing some further drop of 10–15°C. Therefore, provisions for heating and temperature adjust-ment during secondary steelmaking are very desirable. This has led to the development of specialfurnaces such as the vacuum arc degasser (VAD), ladle furnace (LF), and ASEA-SKF ladle furnace.These are very versatile units, capable of performing various operations. There have been furtherdevelopments in this direction recently. Efforts are being made to install one unit only and eventhen achieve a flexible manufacturing program.

Table 1.1 summarizes the features of various processes.1 It shows the capabilities of each.However, it is to be borne in mind that some versatile units of today are really combinations ofseveral processes. For example, some modern vacuum degassers have provisions for oxygen blowingand powder injection. Hence, good desulfurization and decarburization also can be attained in them.It ought to be noted here that a significant fraction of sulfur in blast furnace hot metal is removedby pretreatment in a ladle during transfer to steelmaking shop. Similarly, phosphorus is removedprimarily in a basic oxygen furnace and to some extent during pretreatment of hot metal. Shima2

has reviewed the development of steelmaking technology in Japan, dealing broadly with these.

1.2 TRENDS IN STEEL QUALITY DEMANDS

The world steel market was somewhat stagnant and did not witness significant growth during thedecade of the 1980s. Scholey3 has discussed this with special emphasis on Europe. Table 1.2presents world consumption of steel products in 1990 and predictions of the same for A.D. 2000 asper statistics prepared by the International Iron and Steel Institute (IISI).4

Table 1.2 shows that predicted growth of consumption is large in Asia but either insignificantor negative in other countries. However, according to IISI, lack of tonnage growth does not indicatestagnancy. With continuous improvement in quality, less and less quantity of steel is being consumedfor the same applications. If this point is taken into consideration, then there has been remarkableprogress in steel technology on the quality front, and also improved yield. Figure 1.1 shows thechange in product mix in the U.S.A. from 1925 to 1990, as compiled by Stubble.5 It demonstratesa massive shift in favor of sheet and strip; so much so that, in 1990, more than 50% of the productwas in this shape, as compared to about 20% in 1925. This is the worldwide trend also. It is to berecognized that this shift was technologically possible to a large extent due to improvement in steelquality through secondary steelmaking. Near net shape casting, which is commercially expectedin the near future, will require even more stringent control of impurities and inclusions.


With the passage of time, customers are demanding better and better quality steels, which means

1. fewer impurities2. more cleanliness (i.e., lower inclusion content)3. more stringent quality control, i.e., less variation from cast to cast4. microalloying to impart better properties (for plain carbon and low alloy steels)5. better surface quality and homogeneity

The above demands, combined with other requirements such as (a) the need for cost reduction inview of competition from polymers etc., (b) environmental pollution control, and (c) a relativelystagnant world steel market, pose enormous challenge to the steelmaking community. Before any

TABLE 1.1Various Secondary Steelmaking Processes and Their Capabilities

Processes

Item VD VOD IGP IM VAD LF ASEA-SKF

Desulfurization minor minor minor yes yes yes yes

Deoxidation yes yes yes yes yes yes yes

Decarburization minor yes no no no no yes

Heating no/yes yes* no no yes yes yes

Alloying minor yes minor minor yes yes yes

Degassing yes yes no no yes no yes

Homogenization yes yes yes yes yes yes yes

Achieving more cleanliness (i.e., less inclusions) yes yes yes yes yes yes yes

Inclusion modification no no minor yes yes yes yes

*chemical heating only

Source: data primarily from Ref. 1.

FIGURE 1.1 Product mix in the United States of America: 1925 vs. 19805 (reprinted by permission of Iron& Steel Society, Warrendale, PA, U.S.A.).

TABLE 1.2World Steel Consumption


secondary steelmaking treatment, the lowest levels of impurities attainable with present-day prac-tices, including a metal pretreatment facility, would be approximately as follows:

sulfur: 100 ppmphosphorus: 20 ppmnitrogen: 40 ppmhydrogen: 5 ppmcarbon: 400 ppmoxygen: variable

Upon traditional deoxidation in a ladle, oxygen can be brought down to lower than 30 ppm. Thus,the minimum total of S + O + P + N would be about 200 ppm, and including carbon about 600 ppm.

Changing demands on quality may be illustrated with the example of line pipe steel for NorthSea gas.6

Ramaswamy6 has reviewed the subject and has outlined some of the quality requirements ofline pipe steel for sour gas applications, steels for offshore platforms, bearing steels, steel for therod and wire industry, and for power plant rotors. Figure 1.2 shows the trends in residuals attainedby Japanese Steel Works.7 A special mention may be made of a recent spurt in demand for ultra-low carbon steel (C < 30 ppm or so) for the manufacture of thin sheets by cold rolling withcontinuous annealing for automobiles. These steels not only have ultra-low C but have otherresiduals also at ultra-low levels, e.g., N < 15 ppm, S < 10 ppm, P < 15 ppm, H < 2 ppm. Inaddition, inclusion contents are also drastically lower as compared to regular steels. An expansion

Millions of Metric Tonnes of Steel Products

1990 (actual) 2000 (predicted)

North America 96.5 99

European Community 115.5 117

Japan 92.6 85

Latin America 22.3 35

P. R. China 54.9 80

Other Asian countries 78.6 120

Africa 8.6 9

Former USSR and Eastern Europe 148.5 100

Others 36.4 41

Total 653.9 686

Source: data from Ref. 4.

Maximum ppm in Steel, by Element

Year C S P H N O

1983 400–600 20 150 – 100 –

1990 10 15 – 35 20

Long-term S + O + P + N = 45 ppm


of the market for fine steels by approximately a factor of three has been predicted from 1985 toyear 2000 by Japan’s fine steel study group.7

As shown in Table 1.1, all kinds of secondary steelmaking operations are capable of yieldingsteels with more cleanliness. Inclusions are generally harmful to the mechanical properties andcorrosion resistance of steels. The choice of deoxidation practice combined with proper stirring isone of the measures to remove inclusions. However, a more serious source of harmful inclusions(i.e., larger sizes) is erosion of refractory lining. In addition, reaction of lining with the melt is asource of impurity at such low impurity levels. Therefore, the success of secondary steelmakingprocesses is intimately linked with the development or use of newer refractory materials such asthose high in alumina, zircon, magnesia, dolomite, etc.

The cleanliness consciousness has increased to such an extent that trials are going on for filteringmolten steel through ceramic filters to remove nonmetallic inclusions. The technique is still in theexperimental stages.

Inclusion modification is one of the techniques to render inclusions less harmful to the propertiesof steel. Injection of calcium into the melt is done for this purpose. Sometimes, rare earths are alsoemployed.

1.3 SCIENTIFIC FUNDAMENTALS

The application of scientific fundamentals is an important contributing factor to the progress ofsecondary steelmaking technology. This has been possible due to growth of applied sciences,including metallurgical sciences, and their application.

The laws of thermodynamics had been well laid out by the turn of the 19th century. However,their application to high-temperature systems had to wait because of a lack of thermochemical data.Collection of such data had started on a modest scale by the beginning of this century. The paceaccelerated as years went by, and it began on a really massive scale after the 1940s. By about 1970,fairly reliable data were available on most of the systems and reactions of interest in pyrometallurgy.

Equilibrium process calculations call for experimental data on activity vs. composition rela-tionships in liquids that may be broadly grouped into metallic solutions, SiO2-based slag solutions,etc. Most of these solutions are multicomponent ones. The development of metallurgical thermo-dynamics called for new techniques to handle them. The participation of renowned physical chemistsother than metallurgists made these possible.

FIGURE 1.2 Minimum residual levels in steel in Japan.7

Kinetics is a late comer as compared to the thermodynamics of pyrometallurgical reactions.Scientific investigations were started after 1950. However, they picked up quickly and, for the last


three decades, the field has been pursued vigorously. As a result, kinetics of pyrometallurgicalreactions and processes is a subject of engineering science in its own right. Knowledge alreadyavailable in chemical engineering has been instrumental in its development.

It had been recognized several decades back that lack of proper mixing in the liquid bathadversely affects the efficiency of steelmaking processes. Many investigations have been carriedout on mixing, especially in the last two decades. Again, mixing, mass transfer, and phase disper-sions depend on fluid flow in the bath. Such a flow is turbulent in steelmaking processes. Turbulenceis a very complex phenomenon. Scientists and engineers in a variety of disciplines are concernedwith the solution of problems involving turbulent flow.

Experimental investigations on fluid flow and mixing at steelmaking temperatures are difficult.In this connection, water modeling (i.e., cold modeling or physical modeling) has contributedsignificantly to our understanding of these aspects. Here, water typically simulates liquid metal.Transparent perspex or glass vessels allow flow visualization. Similarity criteria have been employedto various extents.

A quantitative approach in the area of fluid flow, mixing, and mass transfer is based on fluidmechanics—especially as related to turbulent flow. Such computations involve computer-orientednumerical methods. Considerable advances have been made in this direction—so much so thatthese are being employed for interpretation of results, design, and process prediction.

1.4 PROCESS CONTROL

A variety of process control measures must be adopted if desirable benefits are to be obtained fromsecondary steelmaking. It is neither possible nor necessary to list all these. Only some will bebriefly mentioned below in view of their special significance.

1.4.1 IMMERSION OXYGEN SENSOR

Dissolved oxygen in molten steel is a key scientific as well as quality parameter in secondarysteelmaking. Its measurement has been possible due to development of immersion oxygen sensorover the last two decades or so. It is actually an oxygen concentration cell with a solid electrolyte(typically ZrO2 + MgO or ZrO2 + CaO variety). The EMF of the cell allows estimation of dissolvedoxygen content through thermodynamic relations. Since the signal is electrical and obtained within15 s of immersion, it is widely used to measure and control oxygen in molten steel. Throughthermodynamic relations, it allows us also to know the soluble aluminum content of steel, whichagain is another valuable piece of information that steelmakers desire.

An immersion oxygen sensor has also been widely employed in a variety of scientific andtechnological investigations related to deoxidation reactions and behavior of oxygen at differentstages of steelmaking. The pioneering contribution of Kiukkola and Wagner (1956), who first setup such a cell for thermodynamic measurements in laboratory, is to be recognized. Iwase andMcLean8 have reviewed sensors for iron and steelmaking. It may be noted that immersion electro-chemical sensors for other elements, such as silicon and phosphorus, are being developed but areessentially based on oxygen sensors.

1.4.2 SOME OTHER PROCESS CONTROL MEASURES

Gases such as oxygen and nitrogen are picked up from surrounding air during teeming and pouring.This can significantly increase gas contents in liquid steel. Unless this is prevented, most secondarysteelmaking operations will not provide any benefit. For continuous casting, the use of either asubmerged nozzle or shrouding of the nozzle by inert gas is the solution. For ingot casting, this isdifficult to practice; in this case, management of teeming stream is the strategy.

For efficient deoxidation, synthetic slag treatment, and injection processes, it is essential toprevent too much slag from primary steelmaking furnaces from being carried over into ladles. All


steelmakers know the associated difficulties if we wish to avoid lots of metal being left out untapped.Therefore, through considerable efforts, significant advances have been made in techniques oftapping with a very low quantity of slag. It is then modified by suitable additions for furtherprocessing.

In traditional ladles, refractory lined stoppers were employed for flow control during teemingthrough the nozzle. A major development has been slide gate, which is superior as a flow controldevice.

The traditional method of addition of aluminum to liquid steel as ingots or shots makes theefficiency of aluminum deoxidation poor as well as irreproducible, leading to serious controlproblems. The technology of mechanized feeding of aluminum wire is a significant improvementin this connection. Today, many plants have facilities for feeding wires consisting of Ca or CaSipowders clad in steel as well. This is an alternative to the injection of these powders into the meltby injection metallurgy techniques.

Fruehan9 has reviewed some of these topics in a concise fashion. Of course, advances ininstrumentation as well as the use of computers have contributed significantly, as in all other fields.The modern installations employ extensive computer control. Increasing efforts are being made toemploy software based on mathematical models, as well as expert control systems by applicationof artificial intelligence techniques. The review by Bozenhardt and Shafer provides some informa-tion.10

Good process control is not possible without fast and reliable chemical analysis techniques.There have been considerable advances in this direction. Emphasis is also being given to in-situanalysis without the need of transferring samples to a separate analytical unit. These advances arebeing utilized not only in secondary steelmaking but in other areas as well.

Stirring is an integral part of secondary steelmaking. It is done primarily by gas purging.However, electromagnetic stirring is an alternative. Electromagnetic (EM) stirring during inductionfurnace melting of steel has been known from the beginning of 20th century. A major applicationof EM stirring from the 1970s was in continuous casting. EM devices are also being employedincreasingly in recent years in the secondary steelmaking area not only for stirring, but also forflow control, slag control, etc. This offers many advantages, including flexibility in the nature andintensity of fluid motion.

REFERENCES

1. Srinivasan, C.R., in Proc. of National Seminar on Secondary Steelmaking, Tata Steel and Ind. Inst.Metals, Jamshedpur, 1989, p. 15.

2. Shima, T., in Proc. of the 6th Iron and Steel Cong., the Iron and Steel Institute Japan, Nagoya, 1990,Vol. 3, p. 1.

3. Scholey, R., in Proc. 69th Steelmaking Conference, ISS-AIME, Washington, D.C. 1986, p. V.4. McAloon, T.P., Iron and Steelmaker, Dec. 1992.5. Stubbles, J.R., in Steelmaking Conference Proceedings, ISS–AIME, vol. 75, 1992, p. 132.6. Ramaswamy, V., in Srinivasan, p. 71.7. Y. Adachi, in Shima, Vol. 5, p. 248. 8. Iwase, M., and, McLean, A., in Shima, Vol. 1, p. 521.9. Fruehan, R.J., Ladle Metallurgy, ISS-AIME, Warrendale, PA, U.S.A., 1985.

10. Bozenhardt, H.F., and Shafer, J.D., Iron and Steel Engineer, June 1993, p. 41.

σ surface/interfacial tension N m–1

Stefan–Boltzmann constant W m–2 K–4


τ shear stress N m–2

dimensionless residence time —

φ general symbol for dependent variable in differential equation as applicable

Other Symbols

[ ] metal phase

( ) slag/oxide phase

gradient of a scalar quantity

Some Physical Constants

acceleration due to gravity (g) = 9.81 ms–2

atmospheric pressure, 1 atm = 760 mm Hg

= 1.013 × 105 Nm–2

= 1.013 bar

gas constant (R) = 8.314 × J · mol–1 k–1

= 82.06 × 10–6 m3 · atm · mol–1 k–1

∇

2 Thermodynamic Fundamentals

2.1 INTRODUCTION

Metallurgical thermodynamics belongs to the field of chemical thermodynamics, which is employedto predict whether a chemical reaction is feasible. It also allows quantitative calculation of the stateof equilibrium of a system in terms of composition, pressure, and temperature, as well as determi-nation of heat effects of reactions and processes. Laws of thermodynamics are exact. Therefore,calculations based on them are, in principle, sound and reliable. There are standard books dealingwith the basics of chemical-cum-metallurgical thermodynamics.1,2 The following is a very briefreview only, with special emphasis on topics of relevance to secondary steel making.

All reactions and processes tend towards the thermodynamic equilibrium. If sufficient time isallowed, then attainment of equilibrium is possible. Steelmaking reactions and processes are veryfast due to their high temperatures. As a result, some of these have been found to approachequilibrium closely within the short processing time. Examples of this in secondary steelmakingare provided in subsequent chapters. Therefore, a full knowledge of thermodynamics is requiredfor the understanding, control, design, and development of metallurgical processes.

A discussion of thermodynamics requires precise definitions of some terms. For example, asystem is defined as any portion of the universe selected for consideration. The rest of the universeoutside the system is known as surroundings. An open system exchanges both matter and energy,a closed system exchanges only energy, and an isolated system exchanges nothing with the ambient.The state of a system is defined at any instant by specifying all state variables and properties suchas temperature, pressure, volume, surface tension, viscosity, etc. A complete listing of all theproperties of a state is superfluous, because many of them are often mutually interdependent.

Pressure (P), volume (V), and temperature (T) are the most common state variables. When astate is described by such variables, assumptions are made implicitly or explicitly. For example, ifthere is no mention of magnetic field intensity, then it implies that the magnetic effect is insignificant.Similarly, if surface tension forces are ignored, then there is the underlying assumption that surfaceenergy is negligible. Again P, V and T are interrelated. For example, for an ideal gas,

(2.1)

where n is the number of moles occupying volume V. In general, for a thermodynamic substance,if V/n = v, where v is molar volume, then

(2.2)

where the R.H.S. of Eq. (2.2) denotes some appropriate function of P and T. Therefore, the stateof a thermodynamic substance can be defined by any two of the above three variables, providedthat the only work done is against pressure.

PV nRT=

v f P T,( )=


It should be noted that, among these variables,

V

is a property that depends on the amount ofsubstance under question. On the other hand,

P

and

T

are not dependent on mass. A variable such


as volume, which depends on the amount of substance in the system, is known as an extensivevariable. Variables such as temperature, pressure, etc., which do not depend on mass, are knownas intensive variables. It goes without saying that, if an equation contains a variable denoting anextensive property, then there must also be a term denoting mass or mol as in Eq. (2.1). If the latteris missing, there is an implicit assumption that the extensive property is per mass/mol, such as v,in Eq. (2.2), which becomes an intensive property. Thermodynamic relations among intensiveproperties are of more general validity.

A state can be characterized by state variables only when the system has come to equilibriumwith respect to those variables. Then and only then can the state be correctly defined in terms ofthese variables. This also implies that the magnitudes of related intensive properties throughout thesystem are the same.

Thermodynamic equilibrium necessarily requires the attainment of mechanical, thermal, andchemical equilibria. Mechanical interaction of a system with the surroundings is most commonlyin the form of pressure. Therefore, in the absence of a field of force, mechanical equilibriumgenerally means pressure equilibrium, i.e., uniform pressure throughout the system. Similarly,thermal equilibrium implies uniformity of temperature, and chemical equilibrium, in a broad sense,means uniformity of chemical potential for all species in the system. At chemical equilibrium, thereis no tendency for further reaction.

It is possible that the system is at equilibrium with respect to some variables but not someothers. This is known as partial equilibrium, and thermodynamics is capable of handling this aswell. However, a precondition for handling any chemical equilibrium is the establishment ofmechanical and thermal equilibria.

2.2 FIRST AND SECOND LAWS OF THERMODYNAMICS

2.2.1 STATEMENT OF THE FIRST LAW

(2.3)

where dE = an infinitesimal change in the internal energy (E) of the systemδq = an infinitesimal quantity of heat absorbed by the systemδw = an infinitesimal quantity of work done by the system

For a finite change,

(2.4)

The first law of thermodynamics is nothing but a statement of the law of conservation of energy.Careful experiments have revealed that q is not equal to w for many processes, apparently violatingthe law of conservation of energy. To make these findings conform to the law of conservation ofenergy, the concept of internal energy (E) was proposed. Internal energy is the energy stored inthe system. In chemical thermodynamics, E is taken as the energy of atoms and molecules.

Experiments have proved that E is a state property. Ignoring other fields of forces, and for aclosed system,

(2.5)

dE δq δw, for an infinitesimal change–=

∆E q w–=

E f P T,( )=

Again, we do not know or cannot measure the absolute value of

E

. All we can measure are changesin

E

(

∆

E

for a finite change,

dE

for an infinitesimal change).


2.2.2 ENTHALPY AND SPECIFIC HEAT

Every substance, in a given state at a certain temperature, has a characteristic value of heat contentor enthalpy (H).

By definition,

(2.6)

and hence is a state property. Differentiating,

(2.7)

at constant P, dP = 0

and therefore, dH = δq (2.8)

or, ∆H = q (2.9)

Therefore, at constant P, q is related to the change of state property (H) and hence can be calculatedfrom the initial and final states only. We do not have to consider the path.

This is a great simplification. Most of the processes are carried out approximately at constantpressure. Even though the pressure fluctuates, it does not introduce any significant error if q istaken as ∆H. Molar ∆H (i.e., ∆H per mole) values for a variety of processes have been determinedexperimentally and are available in thermodynamic data books. Using them, heat requirements ofprocesses can be calculated, and process heat balances can be worked out.

The molar specific heat of a substance is the heat required to raise temperature of one mole ofa substance by 1 Kelvin. Specific heat at a constant pressure is given by

(2.10)

Experimental Cp values are expressed as functions of temperature as

(2.11)

where T is temperature in Kelvins, and a, b, and c are empirical constants. Values of Cp may befound in standard thermodynamic data books. Table 2.1 presents values of Cp and enthalpies oftransformations for iron.

2.2.3 STATEMENT OF THE SECOND LAW

The second law of thermodynamics is based on universal experience. It may be stated in a varietyof ways. For the purpose of the ensuing discussions, the following statement would be useful:“Spontaneous processes, i.e., processes taking place without any outside intervention, such asdiffusion, free expansion of a gas, heat flow, etc., are not thermodynamically reversible.”

H E PV+=

dH dE P dV+( ) V dP+ δq Vdp+= =

C p∂q∂T-------

p

∂H∂T-------

p

= =

C p a bTc

T 2-----+ +=

TABLE 2.1Specific Heats and Enthalpies of Transformation for Iron


2.2.4 REVERSIBLE PROCESSES

Heat and work are not properties of state. They are energy in transition, and thus the magnitudeof q and w would depend on the path that the process takes in going from an initial to the finalstate. That is why δq and δw rather than dq and dw have been employed in Eq. (2.3). This is agreat mathematical limitation. Hence, considerable effort has been made by thermodynamicists toexamine under what conditions δw and δq can be related to state properties. Obviously, the pathhas to be defined. This is where the concept of reversible processes has assumed importance.

In a reversible process, the system is displaced from equilibrium infinitesimally and then allowedto attain a new equilibrium, then again displaced infinitesimally and so on. Thus, it may be definedas “the hypothetical passage of a system through a series of equilibrium states.” A reversible processis very slow and impractical. No practical process is reversible in strict sense. However, the conceptis very useful and a key one in thermodynamics. The term reversible has been coined because sucha process can be reversed along the same path without leaving any permanent change in the systemor its surrounding.

2.2.5 ENTROPY (S)

A system may go from an initial to the final state by any of the innumerable paths available to it.These paths would be mostly irreversible. Some of them, however, would be or can be treated asreversible. It can be proved on the basis of Carnot’s Cycle that the quantity δqrev/T is dependentonly on the initial and final states, where δqrev refers to δq along a reversible path. The followingrelationship has been thereby proposed.

(2.12)

or, in differential form,

(2.13)

where A and B designate the initial and final states respectively, and S is a state function (i.e. stateproperty) known as entropy.

Transformation Reaction Temperature (K) Specific heat (Cp) (Jmol–1 k–1)Enthalpy change

(∆Η) (J mol–1)

Feα →Feβ 1033 Feα = 17.49 + 24.769 × 10–3 T + 5105

Feβ →Fe 1187 Feβ = 37.66 + 670

Feγ →Feδ 1665 Feγ = 7.70 + 19.5 × 10–3 T + 837

Feδ →Feliq 1809 Feδ = 28.284 +7.53 × 10–3 T +13807

Feliq = 35.4 + 3.74 × 10–3 T

Source: F.R. DeBoer, R. Boom, W.C.M. Mattens, A.R. Miedema, and A.K. Niessen, Cohesion in Metals—TransitionMetal Alloys, Cohesion and Structure Series, North-Holland, Amsterdam (l988).

δqrev

T-----------

A B→∑ SB SA– ∆S= =

δqrev

T----------- dS=

According to the third law of thermodynamics, the entropy of a substance at zero Kelvins (i.e.,absolute zero), and at complete internal equilibrium, is zero if there is perfect order in that state,


e.g., in perfectly crystalline solids, but not in metastable vitreous phases. This allows evaluation ofabsolute values of entropy, which are also tabulated in the thermodynamic data books.

Example 2.1

Calculate (a) entropy (So) of 1 mole of liquid iron at 2000 K, and (b) enthalpy change in heating 1 mole of iron from 298 to 2000 K. Note that

Solution

(a) Entropy of liquid iron at 2000 K, i.e.

(E1.1)

Substituting the values of Cp and ∆H for various transformations from Table 2.1.

(b) Enthalpy change in heating 1 mole of iron from 298 to 2000 K

(E1.2)

Substituting the values of Cp and ∆H from Table 2.1,

∆H°2000 ∆H°298–( )

S°( 298 α Fe–( ) 27.15J mol 1– K 1– )=

S2000o l( ) S298

o α Fe–( )C p α( )

T--------------- Td

298

1033

∫∆Ha B→

1033------------------

C p β( )T

---------------1033

1187

∫ dT∆HB γ→

1187------------------ + + + + +=

C p γ( )T

--------------1187

1665

∫ dT∆Hγ δ→

1665------------------

C p δ( )T

--------------1665

1809

∫ dT∆Hm

1809------------

C p l( )T

-------------1809

2000

∫ dT+ + + +

S2000 l( )o 27.15 17.49

T------------- 24.769 10 3–×+

298

1033

∫ dT51051033------------++=

37.66

T-------------

1033

1187

∫ dT6701187------------ 7.7

T------- 19.5 10 3–×+

1187

1665

∫ dT8371665------------++ ++

28.284T

---------------- 7.531 10 3–×+1665

1809

∫ dT138071809--------------- 35.4

T---------- 3.745 10 3–×+

1809

2000

∫ dT+ ++

105.5 J mol 1– K 1– (Ans.)=

H2000 l( )o H298 s( )

o– C p α( ) Td298

1033

∫ ∆Hα b→ C p β( ) Td ∆Hβ γ→+( )1033

1187

∫+ +=

C p γ( ) Td1187

1665

∫ ∆Hγ δ→ C p δ( ) Td1665

1809

∫ ∆Hm C p l( ) Td1809

2000

∫+ + + + +

H2000 l( )o H298 s( )

o– 17.49 24.769 10 3– T×+[ ] Td 5105 37.66 Td

1187

∫ 670+ + +1033

∫=


2.2.6 COMBINED EXPRESSIONS OF FIRST AND SECOND LAWS

For a reversible process and a closed system, if the only work done is against pressure, thencombining the Eqs. (2.3) and (2.13) we obtain Eq. (2.14), i.e.,

dE = T dS – P dV (2.14)

again,

dH = dE + P dV + V dP (2.15)

Combining Eqs. (2.8) and (2.14),

dH = T dS + V dP (2.16)

2.3 CHEMICAL EQUILIBRIUM

2.3.1 FREE ENERGY AND CRITERION OF EQUILIBRIUM

In Eq. (2.14), internal energy E is expressed as a function of entropy S and volume V, both of whichare independent state variables. Experimental control of temperature and pressure is easier. Gibbs,therefore, defined a new function G, where

G = E + PV – TS = H – TS (2.17)

G is known as Gibbs free energy, which is a state property from the definition of G. DifferentiatingEq. (2.17),

dG = dE + P dV + V dP – T dS – S dT (2.18)

1033298

7.7 19.5 10 3– T×+[ ] Td 837+1187

1665

∫+

28.284 7.531 10 3– T×+[ ] Td 13807+1665

1809

∫+

35.4 3.745 10 3– T×+[ ] Td1809

2000

∫+

(Ans.)

24971 5105 5800 670 16972 837 5957 13807 7489+ + + + + + + += 821788 J mol 1–=

For a closed system, and for a reversible process (or at equilibrium), if the only work done isagainst pressure, then combining Eqs. (2.14) and (2.18),


dG = V dP – S dT (2.19)

at equilibrium, under constant temperature and pressure,

(dG)P,T = 0, i.e. (∆G)P,T = 0, for a finite process (2.20)

For an irreversible (spontaneous) process, it can be shown that

dG < V dP – SdT (2.21)

Therefore, at constant temperature and pressure, a spontaneous, (i.e., natural or irreversible) processwould occur if

(dG)P,T < 0, i.e. (∆G)P,T < 0, for a finite process (2.22)

Thus, the Gibbs free energy provides us with a criterion to predict equilibrium or possibility ofoccurrence of a spontaneous process at constant T and P.

2.3.2 ACTIVITY, EQUILIBRIUM CONSTANT

Consider the following isothermal reaction, which occurs at a temperature T.

aA + bB = lL + mM (2.23)

Here A, B, L, and M are general symbols of chemical species and a, b, l, and m denote the numberof moles of each. The word isothermal implies that the initial temperature at the beginning of thereaction and the final temperature (when equilibrium is reached) are the same. It is not necessarythat the temperature remain unchanged throughout the progress of the reaction.

The free energy change for reaction represented by Eq. (2.23) may be expressed as

(2.24)

where is the partial molar free energy of the species i. The standard state is the stablest stateof the pure substance at the same temperature (T) and at a pressure of 1 atmosphere. The standardstate could thus be a pure solid or liquid or ideal gas at 1 atmosphere of pressure. The magnitudeof a variable for any standard state is indicated by a superscript o.

It can be shown that

(2.25)

where, = free energy of species i at its standard state

= activity of species i at partial molar free energy

fi = the fugacity of i at the state under consideration

= the fugacity at its standard state

∆G 1GL mGM+( ) aGA bGB+( )–=

Gi

Gi Gio– RT ln ai=

Gio

ai

f i

f io

-----= Gi

f io

For ideal gases, fugacity equals partial pressure, expressed in atm (i.e., standard atmosphere =760 mm Hg).


By definition, activity ai is 1 when species i is at its standard state. If all reactants and productsare at their standard states, then for the reaction of Eq. (2.23),

(2.26)

where is the standard free energy change of reaction represented by Eq. (2.23) at temperatureT. Combining Eqs. (2.24) through (2.26),

(2.27)

or,

(2.28)

where

(2.29)

Q is called the activity quotient. Equation (2.27) has been derived assuming an isothermal condition, i.e., the same temperature

for reactants and products. If it is further assumed that the reaction is isobaric, i.e., the initial andfinal pressures are the same, and also that thermodynamic equilibrium prevails, then ∆(G)P,T = 0from Eq. (2.20). Combining this with Eq. (2.28),

∆Go = –RT ln[Q]e = –RT ln K (2.30)

where K is the value of the activity quotient at equilibrium. K is known as the equilibrium constant. Equation (2.27) is the basis for prediction of the feasibility of reactions. A reaction is sponta-

neous or feasible if ∆(G)p,T is negative. It is impossible when ∆(G)p,T is positive. Equation (2.30)is used to calculate the equilibrium condition of a reaction.

Thermodynamic predictions and calculations can be made if the following conditions aresatisfied:

1. The process should take place isothermally (i.e., the initial and final temperature shouldbe the same) and the temperature should be known.

2. The standard free energy change of reaction (∆Go) should be available. 3. Activity versus composition relations for all species involved should be known.

Since changes in pressure as encountered in metallurgy do not affect thermodynamic propertiessignificantly, the condition that P should be constant is of no importance in situations we normallyencounter. Hence, P = constant restriction shall be omitted from here on.

∆Go lGLo mGM

o+( ) aGAo bGB

o+( )–=

∆Go

∆G ∆Go RT ln aL

1 aMm⋅

aAa aB

b⋅---------------+=

∆G ∆Go RT ln Q+=

QaL

1 aMm⋅

aAa aB

b⋅----------------=

2.4 ∆G0 FOR OXIDE SYSTEMS


In secondary steelmaking, we primarily encounter formation or decomposition of inorganic oxides.Therefore, a brief write-up is presented on free energies of oxide systems.

The standard free energies of formation reactions, representing formation of compounds fromthe elements, are now known for all inorganic compounds of interest in secondary steelmaking.These are called standard free energies of formation . A number of books carry compilationsof such data.3–6 Some values of for compounds of interest in secondary steelmaking arepresented in Appendix 2.1.

Consider formation of an oxide from the elements represented by the following general reaction:

(2.31)

where M denotes a metal. X and Y are general symbols for oxide stoichiometry. Traditionally, freeenergy data shown in diagrams would be for a reaction such as Eq. (2.31), where the formationreaction involves only one mole of oxygen. This would make it convenient to compare the datafor different oxides.

If the metal, oxygen and oxide are in their standard states, then the free energy change is relatedto temperature as

(2.32)

where and are standard heat and entropy of formation, respectively.

According to Kirchoff’s law, in the absence of any phase transformation between T and T1,

(2.33)

(2.34)

where and are standard heat and standard entropy of formation at temperature T, and is the difference of specific heats of products and reactants at standard states. The values

of are generally very small and, therefore, one may assume that and areessentially independent of temperature. This allows us to express dependence of on tem-perature as:

(2.35)

where A and B are constants.Equation (2.35) is an approximate one. A more precise representation of as a function of T is

(2.36)

However, data at steelmaking temperatures in standard compilations are available in the form ofEq. (2.35), for the limited temperature range of steelmaking.

∆G fo( )

∆G fo

2XY

-------M O2+ g( ) 2Y---MXOY=

∆G fo ∆H f

o T∆S fo–=

∆H fo ∆S f

o

∆H fo ∆H f

o at T1( ) ∆C po

T 1

T

∫ dT+=

∆S fo ∆S f

o at T1( )∆C p

o

T----------

T 1

T

∫ dT+=

∆H fo ∆S f

o

∆C po

∆C po ∆H f

o ∆S fo

∆G fo

∆G fo A BT+=

∆G fo

∆G fo A BT CT Tln+ +=

Appendix 2.1 provides values of A and B for oxides as well as some other compounds ofimportance in secondary steelmaking. Figure 2.1 presents a diagram for oxides. values are∆G f

o


per gm mol of O2. This normalization allows us to compare stabilities of oxides directly from suchfigures. For example, Al2O3 is stabler than SiO2, since the free energy of formation of the formeris more negative as compared to that of the latter.

Quantitatively speaking, we are interested in the following reaction:

(2.37)

∆Go [for the reaction of Eq. (2.37)] = (2/3Al2O3) – (SiO2) is a negative quantity, andhence the reaction is feasible if all reactants and products are at their respective standard states(i.e., pure substances) in accordance with free energy criteria [Eq. (2.22)]. However, if they are notpure (e.g., present as solution in molten iron or slag), then ∆Go does not provide a correct guideline,and we have to find out ∆G by using Eq. (2.27). These will require knowledge of activity as afunction of composition.

FIGURE 2.1 Standard free energy of formation for some oxides.

43---Al SiO2+

23---A12O3 Si+=

∆G fo

2.5 ACTIVITY–COMPOSITION RELATIONSHIPS: CONCENTRATED SOLUTIONS


Crudely speaking, activity is a measure of “free” concentration in a solution, i.e., concentrationthat is available for chemical reaction. Also, by definition, activity is dimensionless. In metallurgicalprocessing, the gases behave as ideal, and molecules are free. Hence, activity of a component i ina gas mixture is equal to its concentration. Numerically, by convention, ai = pi, where pi is partialpressure of i in atmosphere.

The composition of a solution can be altered significantly during processing only if mixingand mass transfer are rapid. Solid state diffusion is very slow. Hence, during the short processingtime, its composition does not change. For example, a particle of CaO will remain CaO as long asit does not dissolve in slag. It may get coated by another solid such as Ca2SiO4 or CaS during steelprocessing. Here, solid CaO remains pure and its activity, by definition, is 1, since this is its standardstate.

However, liquid steel contains variable concentrations of impurities and alloying elements.Molten slag is also a solution of oxides with a variety of compositions. Hence, activity versuscomposition relationships are required here for equilibrium calculations.

As already stated, a pure element or compound constitutes its conventional standard state. Forexample, pure Fe is the conventional standard state for liquid steel, and aFe = 1 for pure iron.Similarly, pure SiO2 is the standard state for a slag containing silica. In the conventional standardstate, an ideal solution obeys Raoult’s law, which states,

ai = Xi (2.38)

where Xi is mole fraction of solute i in the solution. For example, let liquid steel contain chromiumand nickel. Then, XCr is to be calculated from weight percent composition as follows.

(2.39)

where Wi denotes weight percent and Mi molecular mass of species i.Most real solutions do not obey Raoult’s law. They either exhibit positive or negative departures

from it. For a binary solution (i.e., containing two species such as Fe + Ni or CaO + SiO2), this isillustrated in Figure 2.2. For example, molten Fe-Mn, Fe-Ni, FeO-MnO solutions are ideal. MoltenFe-Si, CaO-SiO2, FeO-SiO2, MnO-SiO2, etc. show negative departures. Liquid Fe-Cu exhibitspositive departure.

Departures from Raoult’s law are quantified using a parameter, known as the activity coefficient(γ), which is defined as:

(2.40)

Activities in slag systems use conventional standard states as reference. However, industrial slagsare multicomponent systems. Hence, presentation of activity versus composition diagrams is morecomplex and different from that of a binary solution.

Figure 2.3 shows values of activity of SiO2 in CaO-SiO2-Al2O3 ternary system at 1550°C (1823K).4 These are in the form of isoactivity lines for SiO2. Similarly, there would be diagrams presentingisoactivity lines for CaO and Al2O3. The liquid field is bounded by liquidus lines. In this diagram,Al2O3 has been written as AlO1.5. This is because molecular mass of CaO, SiO2, and AlO1.5 are

XCr

W Cr

MCr

---------

W Cr

MCr

---------W Ni

MNi

---------W Fe

MFe

---------+ +------------------------------------------=

γi ai/xi=


FIGURE 2.2 Raoult’s law and real systems showing positive and negative deviations.

FIGURE 2.3 Activity of SiO2 in CaO-SiO2 – Al2O3 ternary system at 1823 K; the liquid at various locationson liquidus is saturated with compounds as shown.4

close, being equal to 56, 60, and 51, respectively. Therefore, the mole fraction scale is approximatelythe same as the weight fraction scale. Slag activity data are available from several sources, but the


most comprehensive is the Slag Atlas.7 However, this is quite unsatisfactory, since

1. slags are multicomponent and not ternary, and2. thermodynamic calculations can be performed properly if the activity vs. composition

relationship can be expressed by equations. This allows easier interpolations and extrap-olations of laboratory experimental data in a composition regime.

Example 2.2

Solid iron is in contact with a liquid FeO-CaO-SiO2 slag and gas containing CO and CO2 at 1300°C.The activity of FeO in slag is 0.45, and the ratio in gas is 20/1. Predict whether it ispossible to oxidize iron. Also, calculate equilibrium value of ratio in gas.

Solution

We are to consider the following reaction:

Fe(s) + CO2 (g) = (FeO) + CO(g) (E2.1)

For the reaction of Eq. (E2.1),

(E2.2)

The standard state for FeO is solid pure FeO, since its melting point is 1368°C. With the help of Appendix 2.1,

∆Go at 1300°C (1573 K) = –249.8 – 161.3 + 395.7= –15.38 kJ mol–1 = –15.38 × 103 J mol–1

(a) From Eq. (2.27),

(E2.3)

As discussed earlier, solid iron would remain essentially pure in a limited time period. So, aFe

may be taken as 1. Going through the calculations,

∆G = + 13.36 kJ mol–1

Since ∆G is positive, oxidation of Fe is not possible.

(b) At equilibrium,

∆Go = –RT ln K (2.30)

where

pCO/ pCO2

pCO/ pCO2

∆Go ∆G fo CO g( )[ ] ∆ G f

o FeO s( )[ ] ∆ G fo CO2 g( )[ ]–+=

∆G ∆G0 R T× ln+pCO aFeO( )×aFe[ ] pCO2

×-----------------------------=

K lnpCO aFeo( )×aFe[ ] pCO2

×-----------------------------

at equilibrium

=

Using the value of , the ratio at equilibrium with Fe and the slag turns out to be 7.20.(Note that R = 8.314 J mol–1 K–1.)

∆Go pCO PCO2⁄


2.5.1 A NOTE ON SOLUTION MODELS FOR MOLTEN SLAGS

Whitley8 made the earliest effort in this direction. He assumed the slag to consist of 2CaO · SiO2,3CaO · P2O5, etc. to estimate “free CaO” in slag as an index of aCaO. However, slags are reallyionic liquids, and compounds like CaO, SiO2, etc. do not exist as such. In contrast to these models,the other group of models has been termed as ionic models, where some kind of ionic structure isassumed.

The first ionic model of salt melts is that of Temkin (1945), who assumed ideal mixing (i.e.,ideal solution) among cations and ideal mixing among anions but no interaction between cationsand anions. The last assumption is too simplistic and has not been accepted. However, the firstassumption, namely, ideal mixing among cations and among anions separately, constituted the basisfor some later models.

Flood et al.9 utilized it for reaction of sulfur between liquid steel and slag and obtained theanalytical relation for the equilibrium constant as follows:

(2.41)

where Kh,S denotes the equilibrium constant for sulfur reaction between metal and slag containingseveral cations. i denotes a cation. is an electrically equivalent fraction of i among all cations.

is the equilibrium constant if i is the only cation in slag. This is a useful equation. It allowscalculation of Kh,S in slag from knowledge of of various cations. Hence, this approach waslater extended to the reaction of phosphorus as well.

Slag modeling for thermodynamic calculations is of considerable interest to steelmaking. Somerecent studies10 indicate efforts to apply the approach of Flood et al. with refinements. Of course,thermodynamic predictions are independent of structural considerations. This provides anotherapproach. Analytical relations based on a regular solution model have proved to be the most popularamong structure-independent predictions.

For a binary solution, the regular solution model predicts

(2.42)

where X2 is the mole fraction of component 2 in the binary 1–2, and α is a constant. For amulticomponent solution, the general form of the equation for the regular solution model is10

(2.43)

where α values are constants, known as interaction energies between subscripted solutes. Ban-ya11 has recently summarized mathematical expression of slag-metal reactions in steel-

making processes by quadratic formalism based on regular solution model. If the melt is not astrictly regular solution, then for a real solution,

(2.44)

where I has been termed the conversion factor of the activity coefficient from the hypotheticalregular solution to the real solution.

Klog h S, X ′ ii

∑ Klog h ,Si=

X ′ i

Kh ,Si

Kh ,Si

RT lnγ1 α X22=

RT lnγi α X2ij jj∑ α ij α ik α jk–+( )k∑j∑ X jXk+=

RT lnγi α X2ij jj∑ α ij α ik α jk–+( )k∑j∑ X jXk I++=

Experimental data of various slag-metal and slag-gas equilibria for many slag compositionswere statistically fitted with Eq. (2.44). These have yielded some values of α ij and I.11


Example 2.3

Calculate γi in a multicomponent solution of slag at 1873 K. Composition of slag in weight percentis as follows:

MnO = 4, CaO = 50, Al2O3 = 35, SiO2 = 8, FeO = 3

Take MnO as species i.

Solution

From Eq (2.39):Mole fractions of various species in slag are

Interaction energies between various cations are11

αMn-Ca = –92050, αMn-Al = –83680, αMn-Si = –75310,

αMn-Fe = 7110, αCa-Al = –154810, αCa-Si = –133890,

αCa-Fe = –31380, αAl-Si = –127610, αAl-Fe = –41000,

αSi-Fe = –41840

For reaction MnO(s) = MnO (regular solution),

I = –32470 + 26.14T, J

Performing calculations on the basis of Eq. (2.44) and using the above data, γMnO = 0.163 (Ans.).

2.6 ACTIVITY–COMPOSITION RELATIONSHIPS: DILUTE SOLUTIONS

2.6.1 ACTIVITIES WITH ONE WEIGHT PERCENT STANDARD STATE

Liquid steel comes primarily in the category of dilute solution, where concentration of solutes(carbon, oxygen etc.) are mostly below 1 wt.% or so except for high alloy steels. Solutes in dilutebinary solutions obey Henry’s law, which is stated as follows:

(2.45)

where is a constant. Deviation from Henry’s law occurs when the solute concentration increases.Therefore, activities of dissolved elements in liquid steel are expressed with reference to Henry’s

law and not Raoult’s law. Since we are interested in finding values directly in weight percent, thecomposition scale is weight percent, not mole fraction. With these modifications, in dilute solutionof species i in liquid iron,

XMnO 0.0384, XCaO 0.6058, X Al2O30.2339,XSiO2

0.091, XFeO 0.0284= = = = =

ai γioXi=

γio

1. If Henry’s law is obeyed by species i, then


hi = Wi (2.46)

2. If Henry’s law is not obeyed by species i, then

hi = fi Wi (2.47)

hi is activity and fi is the activity coefficient in the so-called one weight percent standard state. Thisis because, at 1 wt.%, hi = 1, if Henry’s law is obeyed.

Again, it can be shown that fi is related to Raoultian activity coefficient γi as:

(2.48)

It is to be noted that the standard free energy change for reaction is not going to be the sameif the standard state is changed. For example, at 1600°C,

(2.49)

with pure liquid silicon as standard state. However, for the 1 wt.% standard state of Si dissolvedin liquid iron,

* (2.50)

and are related to each other as

(2.51)

(2.52)

where is known as the partial molar free energy of mixing of solute i into a solution.Again, from Eq. (2.25),

(2.53)

(2.54)

With reference to Eq. (2.39), in Fe-Si binary,

(2.55)

* Note: Si dissolved in liquid metal is denoted either as [Si] or Si, SiO2 dissolved in slag is indicated by (SiO2).

f iγi

γio

-----=

Si 1( ) 02 g( )+ SiO2 s( ); ∆G49o 571.5– kJ mol 1–= =

Si[ ] wt.pct. 02 g( )+ SiO2 s( ); ∆G50o –406.4 kJ mol 1–= =

∆G49o ∆G50

o

∆G50o ∆G49

o GSi G– Sio+[ ] at 1 wt. pct. std. state for Si in liquid iron–=

∆G49o= GSi

m[ ] at 1 wt. pct. std. state for Si in liquid iron–

Gim

Gi Gio

–=

GSim

RT ln aSi[ ] at 1 wt. pct. std. state Si in liquid iron=

RT ln γSio XSi[ ] at 1 wt. pct.=

XSi

W Si

MSi

--------

W Si

MSi

--------W Fe

MFe

---------+-------------------------=

On the basis of Eq. (2.55), XSi = 0.02 at WSi = 1. Noting that = 1.25 × 10–3, the value of in Eq. (2.50) was obtained.

γSio ∆G50

o


Appendix 2.2 presents values of for some solute in liquid iron.

2.6.2 SOLUTE–SOLUTE INTERACTIONS IN DILUTE MULTICOMPONENT SOLUTIONS

It has been found that solutes in a multicomponent solution interact with one another and thusinfluence activities of other solutes. Figure 2.4 illustrates this for activity of carbon and oxygen inliquid iron at 1833 K. In the Henry’s law region of Fe-C binary (i.e., without any other addedelement), fC = 1, i.e., log fC = 0. In the presence of a third element in liquid iron solution, fC keepschanging systematically.

It has been derived that if, in a dilute multicomponent solution, A is solvent (Fe in case ofliquid steel), and B, C,..., i, j, etc. are solutes, then

(2.56)

where e values are constants. is called the interaction coefficient, describing the influence ofsolute j on fi, which is defined as

(2.57)

Gim

0.10

0.05

-0.05

0

0 1 2 3 4 5

C

P

TeAs Al

Sb Cu

Co

Ti

VMn Mo

Cr

Se

S (< 4 % )Sn (< 4 % )

Ni

W

Si

ALLOYING ELEMENT, mass% j

LOG

fNj

FIGURE 2.4 Influence of alloying elements on the activity coefficient of nitrogen dissolved in molten ironat 1823 K.

f ilog eiB W B ei

CW C … eiiW i ei

jW j ……+ + + + +⋅=

eij

eij ∂ f ilog( )

∂W j

---------------------W j O→

=

is known as the self interaction coefficient and has a non-zero value only if Fe-i binary deviatesfrom Henry’s law. Again, ei

i


(2.58)

Appendix 2.3 presents values of interaction coefficient for some common elements dissolved inliquid iron.

Equation (2.56) contains only first-order interaction coefficients. It is, in general, all right fordilute solutions of liquid iron. However, sometimes, even here, second-order interaction coefficients

are to be employed. On the other hand, if solute–solute interactions are not significant, log fivs. weight percent of the added element exhibit good linear behavior over a long range. This isdemonstrated by Figure 2.4 for nitrogen dissolved in liquid iron. The figure is based on severaldata sources and taken from the review by Iguchi.12 In such cases, Eq. (2.56) may be fairly all rightup to reasonably high concentrations of solutes. Iguchi12 has recently reviewed the subject, espe-cially the work of Ban-ya and his coworkers, who had been active in this field for about twodecades. The following two approaches have been seriously explored. The first approach is appli-cation of quadratic formalism, originally proposed by Darken and applied to several binary systemsby Turkdogan and Darken.10 Ban-ya examined its use in Fe-C-j ternary melts.

The second approach is application of the interstitial solution model originally proposed byChipman.13 Elements P, C, S, N, etc. may be treated as interstitial atoms, and this model has beenapplied to ternary iron alloys containing these elements to high concentrations. It predicts linearitybetween log ψ with Yj, where ψi is a modified activity coefficient of i, and Yj is atom ratio of j ina ternary containing i and j. Figure 2.5 shows its application to the effect of iron on the activitycoefficient of nitrogen in Cr-Fe-N ternary melts. Good linear relation up to a high concentrationof iron may be noted.

Example 2.4

Liquid steel is being degassed by argon purging in a ladle at 1873 K (1600°C). The gas bubblescoming out of the bath have 10 percent CO, 5 percent N2, 5 percent H2, and the rest Ar. Assumingthese to be at equilibrium with molten steel, calculate the hydrogen, nitrogen, and oxygen concen-trations in steel in parts per million (ppm). The steel contains 1 percent carbon, 2 percent manganese,and 0.5 percent silicon. The total gas pressure may be taken as 1 atm.

Solution

(a) For hydrogen, the reaction may be written as

(E4.1)

for which

(E4.2)

Again, at equilibrium,

(E4.3)

e ji ∂ f jlog( )

∂W i

---------------------Wi O→

eij M j

Mi

------- 0.434 10 2–×Mi M j–

Mi

-------------------+⋅= =

rij( )

H[ ] wt.pct.12---H2 g( )=

KHlog 1905T

------------ 1.591+=

KH

pH2

1 2⁄

hH[ ]----------=


Now,

= 0.05 atm, and KH = 405.58 at 1873 K

So,

hH at equilibrium = 5.513 × 10–4 = fH · WH

Again,

(E4.4)

Assume interactions of dissolved H, N, and O on fH as negligible. This is justified in view of theirvery small concentrations. Taking values of from Appendix 2.3,

log fH = 0.06 × 1 – 0.002 × 2 + 0.027 × 0.5

putting in values,

WH = 4.69 × 10–4 percent = 4.69 ppm (Ans.)

FIGURE 2.5 Effect of iron on the activity coefficient of nitrogen in liquid chromium.13

pH2

log f H eHC W C eH

Mn W Mn eHSi W Si⋅+⋅+⋅=

eij

(b) For nitrogen, the reaction may be written as


(E4.5)

for which

(E4.6)

Proceeding as for hydrogen,

[hN] = 0.01, in 1 weight percent standard state

Now,

hN = fN · WN (E4.7)

and

(E4.8)

Proceeding as before,

WN = 0.0077 wt.% = 77 ppm (Ans.)

(c) For oxygen, the reaction may be written as

[C]wt.%. + [O]wt.%. = CO(g) (E4.9)

for which

(E4.10)

Again, at equilibrium,

(E4.11)

hC = fC · WC = fC · 1

(E4.12)

(As in previous cases, assume interactions of H, N, and O on fC as negligible.) Putting in values, fC = 1.82, and hC = 1.82. So,

N[ ] wt.pct.12---N2 g( )=

K Nlog 518T

--------- 1.063+=

f Nlog eNC W C eN

Mn W Mn eNSi W Si⋅+⋅+⋅=

KOlog 1160T

------------ 2.003+=

KOPCO

hC[ ] hO[ ]---------------------=

f Clog eCC W C eC

Mn W⋅ Mn eCSi W Si⋅+ +⋅=

hOPCO

KO[ ] hC[ ]----------------------- 0.1

419 1.82×------------------------- 1.31 10 4–×= = =

Again,


WO = hO/fO

and,

(E4.13)

Putting in values (taking = –0.421),

WO = 4.1 × 10–4 wt.% = 4.1 ppm (Ans.)

2.7 CHEMICAL POTENTIAL AND EQUILIBRIUM

So far, we have followed the approach in which the overall free energy change had been employedas the criterion for assessing the feasibility of a process. There is an alternative approach based onchemical potential.

Suppose that an element i is to be transferred from phase I to phase II. Then, we say that, forthe transfer to be feasible thermodynamically,

µ i (I) > µ i (II) (2.59)

and for equilibrium,

µ i (I) = µ i (II) (2.60)

where µ i (I) and µ i (II) denote the chemical potential of species i in phases I and II, respectively. µ i is identical with partial molar free energy of solute i in a solution . On the basis of

Eq. (2.25),

µ i (I) = (I) + RT ln ai (I) (2.61)

µ i (II) = (II) + RT ln ai (II) (2.62)

where denotes the chemical potential of i at its standard state. If the standard state of i is thesame in both the phases, then

(I) = (II) (2.63)

so, ai(I) > ai(II), for transfer from phase (I) to (II), and,

ai(I) = ai(II), for equilibrium (2.64)

The chemical potential approach has the following advantages:

1. We can visualize a process better because of the similarity of the concept to some commonphysical processes. Just as heat flows from a higher heat potential (temperature) to alower heat potential, and electricity flows from a higher electrical potential to a lower

f Olog eOC W C eO

Mn W Mn eOSi W Si⋅+⋅+⋅=

eOC

Gi( )

µiO

µiO

µiO

µiO µi

O

one, in the same way a chemical species i is transferred spontaneously from higher µ i

to a lower µ i.


2. It is not necessary to bother about the overall reaction; it is sufficient to find out thechemical potential of the species concerned only. Suppose we know µ i(I). If anotherphase II is brought in contact with it, all we have to do is to calculate µ i(II) to find outdirection of transfer of i.

2.7.1 CHEMICAL POTENTIAL OF OXYGEN

In refining processes, we are primarily concerned about the transfer of oxygen. For the reductionof a metal from its oxide, the reaction environment must have a lower chemical potential thanoxygen. Similarly, if impurities in a metal are to be preferentially oxidized in refining, then theenvironment must have a higher chemical potential than oxygen as compared to that in the impuremetal. The chemical potential of oxygen (O2) is expressed as

(2.65)

Since may be equated to for ideal gas, and is set equal to zero, then

(2.66)

Calculation of the oxygen potential in a gas phase is relatively simple. For liquid metals, one shouldconsider the reaction O2(g) = 2[O]. For this,

(2.67)

Hence,

(2.68)

For liquid slag in ironmaking, we consider the reaction

(2.69)

(2.70)

where is partial pressure of O2 in equilibrium with [Fe] and (FeO).Since aFe ≈ 1 in ironmaking and steelmaking,

(2.71)

If slag-metal equilibrium does not exist, Eq. (2.71) gives the in slag, because it is not dependenton the composition of iron. If slag-metal equilibrium exists, then it is in both slag and metal.

µO2µO2

o RT aO2ln+ µO2

o RT pO2ln+= =

aO2pO2

µO2

o

µO2RT pln O2

=

∆Gho RT ln

hO[ ] 2

pO2

------------– 2RT ln– hO[ ] RT pln O2+= =

µO2metal( ) ∆Gh

o 2RT ln hO[ ]+=

2 Fe[ ] O2 g( )+ 2 FeO( ); ∆G69o=

∆G69o RT Kln 69– RT

aFeO( )2

aFe[ ] 2 pO2

----------------------ln–= =

pO2

µO2slag( ) RT pln O2

∆G69O 2RT aFeO( )ln+= =

µO2

µO2

Of course, primary steelmaking slags contain Fe2O3 (i.e., Fe3+ ions) also. There is determinedmore by the following reaction:

µO2


4 (FeO) + O2(g) = 2(Fe2O3) (2.72)

However, in secondary steelmaking, Eq. (2.71) is applicable, since the FeO concentration is low.The above analysis does not mean that oxygen is present as O2 in the slag or metal. As a matter

of fact, it is far from being so, because oxygen exists as ions in slag and as dissociated atoms inmetal. But, for thermodynamic calculations and concepts, this is unimportant.

Example 2.5

Calculate the chemical potential of oxygen in a CO/CO2 gas mixture and slag as given in Example2.2, and the chemical potential of nitrogen as per Example 2.4.

Solution

(a) Calculation of in CO/CO2 gas mixture for the problem in Example 2.2:

Consider the reaction,

(E5.1)

where is in equilibrium with CO and CO2.

Since

(E5.2)

At 1300°C (1573 K), for the reaction of Eq. (E5.1),*

(E5.3)

= 2[(–396.46 + 0.08 × 10–3 × 1573) + (118.0 + 84.35 × 10–3 × 1573)] = –291.32 kJ mol–1

Substituting in Eq. (E5.2),

(Ans.) (E5.4)

* From data in Appendix 2.1.

µO2

2CO g( ) O2 g( )+ 2CO2 g( )=

∆Go RTpCO2

2

pCO2 pO2

×-----------------------

equilibrium

ln–=

RT pO2( )

eln 2RT

pCO2

pCO

----------ln–=

pO2( )

e

pCO

pCO2

----------201------, µo2

RT ln pO2( )

e∆Go 2RT ln

120------

+= = =

∆Go 2 ∆G f CO2,o ∆G f ,CO

o–[ ]=

µO2369.67 kJ mol 1– O2–=

(b) Calculation of in FeO-CaO-SiO2 slag for the problem in Example 2.2:µO2


Consider the reaction

(E5.5)

Since aFe = 1, aFeO = 0.45 (given), from Eq. (2.71),

(E5.6)

From Appendix 2.1,

At 1573 K,

Therefore, from Eq. (E5.6),

(in slag) = –341.46 kJ/mol–1 O2 (Ans.)

in slag is different from in gas, because they are not at equilibrium.

(c) Calculation of for Example 2.4:

Since = 0.05 atm in Example 2.4,

= RT ln = RT ln (0.05)

At T = 1873 K,

= –46.65 kJ mol–1 N2 (Ans.)

Since liquid steel and nitrogen in exit gas are at equilibrium, in liquid steel also shall be thesame.

2.8 SLAG BASICITY AND CAPACITIES

Basicity of a slag increases with increased percentages of basic oxides in it. It is an importantparameter governing refining. Steelmakers had always paid attention to it. In the early days, thenumerical value of basicity was taken as the CaO/SiO2 ratio, modified ratio, or excess base.

2Fe(s) O2(g)+ 2 FeO( )=

µO22∆GFeO 1( )

o 2RT ln 0.45( )+=

∆GFeO 1( )o 238.07 49.45 1× 0 3– T kJ mol 1–+–=

2∆GFeO l( )o 320.57 – kJ mol 1–=

µO2

µO2µO2

µN2

pN2

pN2pN2

µN2

µN2

Since a basic oxide (e.g., CaO) tends to dissociate into a cation and oxygen ion (e.g., Ca2+, O2–),the concentration of free O2– increases with increasing basicity. Therefore, from a thermodynamic


viewpoint, the activity of oxygen ion may be taken as an appropriate measure of the basicityof slag. However, there is no method available for experimental determination of .

2.8.1 OPTICAL BASICITY

A breakthrough came with the development of the concept of optical basicity (Λ) in the field ofglass chemistry by Duffy and Ingram14 in 1975–76. It was applied to metallurgical slags first byDuffy, Ingram, and Somerville.15 From then on, numerous investigators have applied it to metal-lurgical slags for a variety of correlations.

Experimental measurements of optical basicity in transparent media such as transparent glassand aqueous solutions were carried out employing Pb2+ as the probe ion. In an oxide medium,electron donation by oxygen brings about a reduction in the 6s–6p energy gap, and this in turnproduces a shift in frequency in UV spectral band.

(2.73)

where υfree, υCaO and υsample are frequencies at peak for free Pb2+, Pb2+ in CaO, and Pb2+ in a sample,respectively. Therefore, Λ = 1 for pure CaO by definition. Hence, Λ is an expression for limecharacter, even though there may not be any CaO in sample.

Based on experimental measurements, the following empirical correlation was proposed byDuffy et al.14,15

(2.74)

where α i is Pauling electronegativity of the cation in a single oxide i. This relationship has allowedestimation of Λi for a variety of oxides where experimental data are not available from the valuesof α i. The estimated Λi is known as theoretical optical basicity (Λth.i).

For a multicomponent system such as slag or glass.

Λth (for slag/glass) = Σ Λth.i (2.75)

where = equivalent cation fraction of oxide i. Slags are opaque. The same is true of glasses containing oxides of transition metals. Hence, Λ

is to be estimated for slags. The most widely employed method of estimation is on the basis ofEqs. (2.74) and (2.75). Other, lesser-known methods also have been employed.16

Optical basicity of individual oxides was estimated from Eq. (2.74), where experimental datawere not available. This was tantamount to suggesting that each oxide is characterized by a uniquevalue of Λi, irrespective of medium and temperature. However, it has not been accepted by recentinvestigators. Moreover, assignment of correct values of Λth to transition metal oxides such as FeO,MnO is controversial, since Eq. (2.74) is not applicable for these from theoretical considerations.Differing findings and opinions have been published in the literature. Estimated values of Λi havebeen questioned, and other methods of estimation based on refractive index, electronic polarizability,and electron density have been employed besides Pauling’s electronegativity.17–19 Some metallur-gical slags contain fluorides or chlorides. Here, fluoride or chloride ions also ought to be considered,in addition to oxygen, for their contribution toward basicity. Considerable efforts have been madeto evaluate Λi for common fluorides such as CaF2.

aO

2 –( )a

O2 –( )

Λυ free υsample–υ free υCaO–

-----------------------------=

1Λ i

----- 1.35 α i 0.26–( )=

Xi ′

Xi ′

One important problem facing application of the optical basicity concept has been differingvalues of Λi proposed by different investigators, especially for transition metal oxides such as FeO,


MnO, TiO2, and others. The present status is shown in Appendix 2.4. The values of optical basicityrecommended by Duffy and coworkers18,20 were on the basis of electronegativity, electronic polar-izability, and refractive index, whereas those by Nakamura et al.21 were estimated from averageelectron density. It may be noted that there is both agreement as well as disagreement amongvarious investigators. It is not presently possible to recommend one set over another.

Example 2.6

Calculate the optical basicity of a slag of composition same as in Example 2.3.

Solution

= 2 × 0.0384 + 2 × 0.6058 + 3 × 0.2339 + 4 × 0.091 + 2 × 0.0284 = 2.414, for Example 2.3.Equivalent cation fractions of species are:

Optical basicity of various species (considering data of Nakamura et al.21; Appendix 2.4):

Substituting the values of and Λi in Eq. (2.75),

Λth,slag = 0.82 (Ans.)

2.8.2 SLAG CAPACITIES

Along with basicity, another concept, namely that of slag capacity, has evolved, and its use hasbecome quite widespread. Richardson and Fincham10 in 1954 defined sulfide capacity (Cs) as thepotential capacity of a melt to hold sulfur as sulfide. Mathematically,

(2.76)

where are partial pressures of O2 and S2 in the gas at equilibrium with slag. Noting thatthe reaction is

1/2 S2 (g) + (O2–) = 1/2 O2 (g) + (S2–) (2.77)

it can be shown that

(2.78)

X ′ i

X ′Mn

2 +2 0.0384×

2.414------------------------- 0.031= = X ′

Cn2 +

2 0.6058×2.414

------------------------- 0.504= =

X ′Si

4 +4 0.091×

2.414---------------------- 0.151= =X ′

Al3 +

3 0.2339×2.414

------------------------- 0.291= =

X ′Fe

2 +2 0.028×

2.414---------------------- 0.023= =

ΛMnO 0.95, ΛCaO 1.0, ΛAl2O30.66, ΛSiO2

0.47, ΛFeO 0.94= = = = =

Xi ′

Cs wt. % S2 –( ) pO2

1 2⁄ pS2

1 2⁄⁄⋅=

pO2pS2

⋅

Cs

K77 aO

2 –⋅φS2 –

------------------------=

where K77 is the equilibrium constant for the reaction of Eq. (2.77) and is the activity coefficientof S2– in slag in an appropriate scale.

φS

2 –


Wagner22 has critically discussed the concept of basicity and various capacity parameters suchas sulfide capacity, phosphate capacity, carbonate capacity, etc. He has discussed interrelationshipsamong capacities. He also suggested use of carbonate capacity as a method of measurement ofbasicity. Many papers have been published on measurements and application of these capacities,and relationships among these.17,24

The reaction of phosphorus under oxidizing condition may be written as

(2.79)

for which the phosphate capacity of slag may be defined as

(2.80)

From Eqs. (2.79) and (2.80),

(2.81)

where K79 is the equilibrium constant for the reaction of Eq. (2.79) and is the activity coefficientof in slag in an appropriate scale.

The combination of Eqs. (2.78) and (2.81) leads to the following relation:

(2.82)

K82 is an equilibrium constant term and depends only on temperature. At a constant temperature,in the same slag system (e.g., Na2O – SiO2 system), parameter is expected to beconstant,22 Hence, a single straight line with slope of 3/2 is expected. Figure 2.6 is based on reviewby Sano et al.24 It shows agreement with the above expectation. Of course, a corollary to thisconclusion is that there is no universal correlation between log Cp and log Cs that will be applicableto all kinds of slag systems. Similar conclusions can be drawn about interrelationships of othercapacities.

Optical basicity concept is being utilized by industries as well. Equation (2.75) forms the basisof estimation of optical basicity in slags. Cs increases with increasing (i.e., increasing basicity)and hence ought to have a relation to optical basicity. Many workers have shown that

log Cs = m Λ + n (2.83)

where m and n are empirical constants. Figure 2.723 shows such an attempt for various slags at1500°C.

Young et al.18 have recently questioned applicability of a simple linear dependence of log Cs

and log Cp on Λ. Capacities have been correlated with Λ, Λ2, temperature, as well as some

12---P2 g( ) 5

4---O2 g( ) 3

2--- O2 –( )+ + PO4

3 –( )=

C p

wt. % PO43 –( )

Pp2( )1 2⁄ pO2( )5 4⁄---------------------------------------=

C p K 79

aO

2 –[ ] 3 2⁄

φPO4

3–

----------------------⋅=

φPO4

3–

PO43 –

C plog32--- Cslog Klog 82 log

φS

2 –3 2⁄

φPO4

3–

-----------+ +=

φS

2–3 2⁄( ) φPO4

3–⁄

aO

2–


composition parameters. However, it has also been shown that, at values of Cs less than 0.01,Eq. (2.83) as employed in Figure 2.723 is also all right. Since, in secondary steelmaking, Cs lies inthis range, a linear relationship as in Eq. (2.83) would be adequate for industrial uses.

REFERENCES

1. Darken, L.S. and Gurry, R.W., Physical Chemistry of Metals, McGraw-Hill Book Co., New York, 1953. 2. Gaskell, D.R., Introduction to Metallurgical Thermodynamics, 2nd Ed., McGraw-Hill Book Co., New

York, 1973. 3. Elliott, J.F. and Gleiser, M., Thermochemistry for Steelmaking, Vol. 1, Addison-Wesley Publishing

Co., Reading, Mass., USA, 1960. 4. Elliott, J.F., Gleiser, M. and Ramakrishna, V., Thermochemistry for Steelmaking, Vol. 2, Addison-

Wesley Publishing Co., Reading, Mass, USA, 1963. 5. Kubaschewski, O., Evans, E.L. and Alcock, C.B., Metallurgical Thermochemistry, 4th Ed., Pergamon

Press, Oxford, 1967. 6. Wicks, C.E. and Block, F.E., Thermodynamic Properties of 65 Elements—Their Oxides, Halides,

Carbides, and Nitrides, U.S. Bureau of Mines, United States Government Printing Office, Washington,1963.

7. Committee for Fundamental Metallurgy, Slag Atlas, Verlag Stahleisen M.B.H., Dusseldorf, 1981. 8. Whiteley, J.H., Proc. Cleveland Inst. Engrs., 59 1922–23, p. 36.9. Flood, H., Forland, T. and Grjotheim, K., in The Physical Chemistry of Melts, Inst. Mining and

Metallurgy, London, 1953. 10. Turkdogan, E.T., Physical Chemistry of High Temperature Technology, Academic Press, New York,

1980.

FIGURE 2.6 Relationship between sulfide capacities and phosphate capacities for various fluxes. Source:Sano, N., in Proceedings of the Elliott Symposium, ISS, Cambridge, Mass., reprinted by permission of theIron & Steel Society, Warrendale, PA.

2.0 Ca0 - Al203


11. Ban Ya, S., ISIJ Int., 33, 1993, p. 2. 12. Iguchi, Y., in Proc. The Elliott Symposium, ISS, Cambridge, Mass., USA, 1990, p. 132. 13. Ban Ya, S., and Chipman, J., Trans AIME, 242, 1968, p. 940. 14. Duffy, J.A. and Ingram, M.D., J. of Non-Crystalline Solids, 21, 1976, p. 373. 15. Duffy, J.A., Ingram, M.D. and Sommerville, I.D., J. Chem. Soc., Faraday Trans. 1, 74, 1978, p. 1410. 16. Bergman, A. and Gustafsson, A., in Proc. 3rd Int. Conf. on Molten Slags and Fluxes, Inst. of Metals,

London, 1989, p. 150. 17. Proc. 3rd Int. Conf. on Molten Slags and Fluxes, Inst. of Metals, London, 1989.18. Young, R.W., Duffy, J.A., Hassall, G.J. and Xu, Z., Ironmaking and Steelmaking, 19,1992, p. 201. 19. Nakamura, T., Yokoyama, T. and Toguri, J.M., ISIJ Int., 33, 1993, p. 204. 20. Duffy, J.A., Ironmaking and Steelmaking, 17, 1990, p. 410. 21. Nakamura, T., Ueda, Y. and Toguri, J.M., Trans. Japan Inst. Met., 50, 1986, p. 456. 22. Wagner, C., Metall. Trans. B, 6B, 1975, p. 405. 23. Sosinsky, D.J., Sommerville, I.D. and McLean, A., in Proc. 6th PTD Conference, ISS, Washington

D.C., 1986, p. 697. 24. Sano, N., in Proc. The Elliott Symposium, ISS, Cambridge, Mass., USA, 1990, p. 163. Table 2.1:

Specific heats and enthalpies of transformation for iron.

3.0

4.0

5.0

0.55 0.60 0.65 0.70 0.75 0.80 0.85

0PTICAL BASICITY (Λ), ( - )

T = 1500 oC

- LO

G C

S

Ca0 - AI203 - Si02

Ca0 - Mg0 - Al203

Ca0 - Si02 - B203

Ca0 - Mg0 - Si02

Ca0 - Mg0 - Al203-

Si02

Ca0 - Si02

FIGURE 2.7 Logarithm of sulfide capacity vs. optical basicity at 1823 K.23

3 Flow Fundamentals

The nature of fluid motion and the intensity of turbulence during liquid steel processing are ofconsiderable importance to the success of secondary steelmaking due to their significant influenceon mixing, mass transfer, inclusion removal, refractory lining wear, entrapment of slag, and reactionwith the atmosphere. Therefore, several studies have been carried out in the past two to three decadesor so on the subjects of fluid flow and mixing in ladles, tundishes, etc. Among these, molten steelin a ladle, stirred by argon gas, injected through porous and slit plugs located at the ladle bottom,constitutes the most commonly encountered situation in secondary steelmaking. Extensive funda-mental studies on fluid flow have been carried out on this system. Hence, this chapter first of allbriefly mentions the basics of fluid flow and then takes up flow in gas-stirred ladles.

The motion of liquid steel arises from free convection due to temperature and compositiongradient in the melt, and forced convection due to gas stirring, electromagnetic stirring, agitationby the pouring stream, and mechanical stirring. However, free convection has been found to bevery mild and can be ignored in ladle metallurgy.

3.1 BASICS OF FLUID FLOW

The fundamentals of fluid flow are available in standard texts.1–4 The following is a very briefintroductory presentation for the sake of completeness. Figure 3.1 depicts the motion of a fluidelement (dm), i.e. an infinitesimally small mass of a fluid, moving along a path. It moves underthe action of some forces acting upon it. Such forces may be classified in the following twocategories:

1. Body forces, which act throughout the volume of the fluid element. Gravitational forceis the primary body force of relevance. However, there are the following other body forces:

dFB

PATH

τ

dFS

σ

dm

FIGURE 3.1 Forces and stresses acting on a fluid element.


•

Thermal buoyancy force:

density difference due to inhomogeneity of temperature inthe fluid leads to this force, and it is expressed as

ρ

g

β

t

∆

T

,


where g = acceleration due to gravity ßt = coefficient of volume expansion of the fluid due to temperature change

∆T = overall temperature difference in the fluid

• Solutal buoyancy force: density difference due to composition inhomogeneity in thefluid leads to this force expressed as ρgβc∆C, where ßc = coefficient of volume expansion of the fluid due to concentration change

∆C = overall concentration difference of solute in the fluid

• Electromagnetic force: sometimes known as Lorentz force, is expressed as ,where J is conduction current density and B is magnetic flux density. J and B arerelated through Maxwell’s equation.

2. Surface forces, which act at the surface of the fluid element due to contact with itssurrounding. A surface force can be resolved into normal and shear forces. ApplyingNewton’s second law of motion to the fluid element,

(3.1)

where is acceleration of the element, and are, respectively, the body andsurface forces acting on it. These are all vector quantities.

Again, is nothing but the rate of change of momentum of the fluid element,dm. Force acting on a fluid element per unit area is designated as stress. There are twotypes of stresses: the one acting perpendicular to the surface of the fluid element is knownas normal stress, and the other, acting parallel to the surface of the fluid element, istermed as shear stress.

(3.2)

where is force per unit volume of fluid, is the symbol for gradient vector.

3.1.1 VISCOSITY

Unlike a solid, a fluid cannot sustain a shear stress. In other words, it is completely deformable.If a shear stress is applied, then the fluid will undergo shear deformation continuously. Newton’slaw of viscosity was the beginning of the quantification of the relationship between shear stressand shear deformation. The assumption is that shear stress is proportional to the rate of sheardeformation. Newton’s law of viscosity, which is applicable to parallel and incompressible flow,is stated as

(3.3)

With reference to Figure 3.2, denotes shear stress acting on the y-plane (i.e., a plane normalto the y-axis) along the x-direction. µ is a proportionality constant, known as coefficient of viscosityor simply viscosity. Figure 3.2 also shows the expected velocity profile in fluid adjacent to a solidsurface for parallel flow. Velocity in the x-direction is zero at the surface, since the fluid layer justat the surface cannot slip past the solid. It increases as we move along the y-coordinate.

J B×

dF dFB dFs+ a dm⋅= =

a dFB dFS

a dm⋅

Fs

V----- ∇–( )p=

Fs

V----- ∇

τ yx µ∂ux

∂y--------–=

τ yx


An alternate form of Eq. (3.3) is

(3.4)

where ρ is density of the fluid. µ/ρ is known as kinematic viscosity (ν). Flow characteristics of afluid are governed more by ν than µ. A velocity gradient in a fluid causes momentum transfer fromhigher to lower velocity due to its viscosity. Hence, shear stress in Figure 3.2 is also equal to therate of transfer of x-momentum along y-direction per unit area normal to y-direction (i.e., x-momentum flux along y).

Viscosities of gases can be estimated from the kinetic theory of gases. There are empirical rulesavailable for estimation of the same for liquids. However, for the latter, it is by and large advisableto employ experimentally determined values. Viscosity, density, and some other physical andphysicochemical properties of water, liquid iron, and some iron alloys, slags of interest in secondarysteelmaking, are presented in Appendix 3.1. It may be noted that liquid iron has a value of νcomparable to water. Hence, it is as fluid as water. On the other hand, molten slags have muchhigher values of both µ and ν.

3.1.2 FLOW CHARACTERIZATION

Fluid motion can be categorized as follows:

1. Newtonian or non-Newtonian2. Viscous or nonviscous (ideal)3. Laminar or turbulent4. Incompressible or compressible5. Steady or unsteady6. Forced or free convection

The total characterization includes specifications on each of these points as well as the flowgeometry. Liquids with high viscosity, such as viscous slags, do not have constant values of µ.Here, viscosity would be varying with the level of shear stress applied. These are known as non-Newtonian liquids. According to Eq. (3.3), viscous shear stress is proportional to µ as well as

FIGURE 3.2 Velocity profile in a fluid parallel to a flat plate.

τ yx µ∂ ρux( )

ρ∂y--------------------– ν

∂ ρux( )∂y

----------------–= =

(i.e., velocity gradient). If one of these is negligibly small, then

τ

yx

can be ignored, andthe flow may be treated as nonviscous or ideal. Otherwise, it would be considered as viscous flow.

∂ux ∂y⁄


Figure 3.3 depicts a typical velocity profile adjacent to a solid surface. Velocity of the fluidjust at the surface is zero, and it increases rapidly to a constant value (uo) within a small distance.The region where the velocity is varying with distance is known as velocity boundary layer. Outsidethe velocity boundary layer is the bulk of the fluid. As an approximate general guideline, therefore,the motion of fluid in the boundary layer may be taken as viscous, and that in the bulk as nonviscous.

As Figure 3.3 shows, the velocity profile approaches the bulk asymptotically. Hence, thethickness of the velocity boundary layer (δu) is theoretically infinity. To overcome this dilemma,δu is taken as the value of x where u = 0.99uo · δu is very small in a liquid—always less than amillimeter and even of the order of few microns. On the other hand, it is typically larger than amillimeter or even a centimeter in gases.

If a tangent is drawn to the velocity profile at the solid–fluid interface, then its slope is equalto . From this it follows that

(3.5)

τxy acting on the surface would be opposite in sign and positive. δu,eff is known as the effectivevelocity boundary layer thickness.

Laminar flow is obtained at low velocities, and turbulent flow at high velocities. The former ischaracterized by distinct streamlines with no cross mixing, whereas the latter is accompanied byextensive mixing. Suppose we are measuring the velocity of fluid at a particular location as afunction of time. Let us also assume that the flow is steady, i.e., it does not vary with time. Then,Figure 3.4 shows schematically the pattern of velocity vs. time curves to be expected in both laminarand turbulent flow.

In a steady turbulent flow, although the time-averaged velocity is constant, the instantaneousvelocity exhibits random fluctuations. Imagine the fluid element A in Figure 3.5. Under turbulentflow, its instantaneous velocity fluctuates at random. Similar random fluctuations are exhibited byits neighbors. Since, in general, fluctuations of neighboring fluid elements are not in harmony with

FIGURE 3.3 Velocity profile in a fluid parallel to a flat plate.

∂uy ∂x⁄( )x 0=

τ xy[ ] surface µ∂uy

∂x--------

–x 0=

µ–uo

δu,eff

----------= =


those of A, the latter is always receiving impacts from its neighbors, and vice versa. This occa-sionally will throw A out of its location to region B. In exchange, fluid from location B may beimagined to occupy location A.

Such a process of exchange is visualized as an eddy. These eddy-like exchanges go on atrandom in all directions, leading to extensive mixing in turbulent flow. That is why turbulent flowis preferred in engineering. Exchange of eddy elements tends to impart a whirlpool-type motion

FIGURE 3.4 (a) Schematic velocity vs. time curve illustrating the difference between laminar and turbulentflow, and (b) eddy fluctuations in water at Re = 6500, at the center of a pipe of 22 mm I.D., measured by alaser Doppler anemometer.2

B

A

FIGURE 3.5 Eddy mechanism.

in the eddy area. This is because the exchange takes place by small, jerky movements in a closedloop. Very large eddies can form even in laminar flow if the flow is disrupted. Examples are swirling


motions behind spheres and cylinders at sudden enlargements of diameter in pipe flow. Actually,the term eddy traditionally had been employed for a large, macroscopic vortex flow. However, smallones, especially those of microscopic size, can be generated only in turbulent flow.

When a fluid flows, considerable pressure differences may exist across the system. If the fluidis a gas, such pressure differences would lead to a variation of density, and under such a situationthe flow is called a compressible flow. The motion of gases at a small pressure difference, and ofliquids, is treated as incompressible. Forced convection refers to flow caused by an external agentsuch as a fan or pump. Free convection arises from thermal and solutal buoyancy forces.

The results of an analysis of fluid motion depend on the geometry of flow. Standard texts mostlydeal with the following two broad classes:

1. Flow in channel. The simplest example of this is flow through a straight circular pipe. 2. Flow around a submerged object. The simplest example of this is flow around a sphere.

In the subsequent discussions, we shall be concerned with Newtonian, viscous, incompressible,and steady fluid motion only.

3.1.3 ANALYSIS OF FLUID FLOW

Standard texts1–4 have detailed derivations. There are basically two types of analysis, viz., differentialanalysis and integral analysis. Here, only a brief outline of differential analysis is presented.

Equation of Continuity

This is nothing but differential mass balance. Figure 3.6 presents a differential volume element offluid in a rectangular coordinate system. From the principle of conservation of mass,

(3.6)

FIGURE 3.6 Region of volume ∆x∆y∆z fixed in space through which fluid is flowing.

Rate of accumulation of massin the volume element

=[Rate of flow of mass into the volume element

– Rate of flow of mass out of the volume element]

Rate of accumulation of mass in the control volume = (3.7)

∂ρ∂t------ ∆x∆y∆z( )


where t is time.

Along the x-coordinate,

(3.8)

where ux is velocity component along x-coordinate. Similar derivations can be made for rate of mass flow along y and z directions. Combining all

these, Eq. (3.6) may be mathematically expressed as

(3.9)

For an incompressible flow, ρ is constant, so Eq. (3.9) reduces to

(3.10)

where is divergence of velocity vector .

Equations (3.9) and (3.10) are known as the equation of continuity.

Equation of Motion

This is based on Newton’s second law of motion, i.e., Eq. (3.1). Let us consider the fluid elementdepicted in Figure 3.1. As it moves, its change of properties is a consequence of both change ofposition and of time. When it is considered this way, and the fluid element is followed in time andspace, then the rate of change of a property is expressed by its substantial derivative. For a velocityvector, it would be

(3.11)

Where is substantial derivative of u.

[Rate of flow of mass into the volume element – Rate of flow of mass out of the volume element]

ρux( )x ρux( )x ∆x+–[ ]∆ y∆z=

ρux( )x ρux( )x

∂ ρux( )∂x

----------------dx+

– ∆y∆z=

∂ ρux( )∂x

---------------- ∆x∆y∆z=

∂ρ∂t------

∂ ρux( )∂x

----------------∂ ρuy( )

∂y----------------

∂ ρuz( )∂z

----------------+ + + 0=

∂ux

∂x--------

∂uy

∂y--------

∂uz

∂z--------+ + div.u 0= =

div.u u

aDuDt------- ∂u

∂t------ ux

∂ux

∂x-------- uy

∂uy

∂y--------

∂uz

∂z--------+ ++= =

DuDt-------

Equation (3.1) may be restated as follows:


Rate of change of momentum of the fluid element = (body forces)+ (pressure forces) + (shear forces) acting on the fluid element (3.12)

For an incompressible fluid and per unit volume of fluid, it may be derived, on the basis of conceptsalready presented, that

(3.13)

where is body force per unit mass of the fluid. If gravitational force is taken as the only body force, then

(3.14)

where is the unit vector along the z-direction (i.e., vertical direction). is the Laplacian of. For a rectangular coordinate system, it is given as

(3.15)

Equation (3.14) is the well known Navier–Stokes equation. For laminar flow and simplesituations, analytical solutions are available in standard texts. For complex but laminar flow, resortto numerical methods. The Navier–Stokes equation, with certain modifications and empiricism, hasbeen applied for fluid flow computations in turbulent flow as well. Of course, the procedures involvelengthy computer-oriented numerical methods. The vectorial equations can be resolved into threecomponent equations along the three coordinates. These are available for the three standard co-ordinate systems, viz., rectangular, cylindrical, and spherical, in standard texts.

3.1.4 DIMENSIONLESS VARIABLES

The importance of dimensionless variables in momentum, heat, and mass transfer is well known.These are also known as dimensionless numbers and are widely employed. According to Bucking-ham’s π-theorem, the number of dimensionless variables is n – r, where n is the number of physicalvariables and r is the number of basic dimensions. In fluid flow, r = 3 (mass, length, time).

For example, in laminar flow of a fluid past a sphere, the drag force (FD) exerted by the fluidon the sphere is a function of four variables, i.e. diameter of sphere (d), bulk flow velocity of fluid(uo), viscosity, and density of fluid (µ, ρ). In other words,

FD = f(d, uo, µ, ρ) (3.16)

According to the π-theorem, the number of dimensionless variables is (5 – 3), i.e., 2. Dimensionalanalysis leads to the following formulation:

Eu = f(Re) (3.17)

where Eu is Euler number, which is equal to , and Re is the Reynolds number (= ρuod/µ).

ρa ρDuDt------- ρFB ∇ P µ∇ 2u+–= =

FB

ρa ρDuDt------- ρgk– ∇ρ µ∇ 2µ+–= =

k ∇ 2

u

∇ 2u∂2ux

∂x2----------

∂2uy

∂y2----------

∂2uz

∂z2----------+ +=

FD ρuo2d2⁄

A reduction in the number of variables is a tremendous advantage of dimensionless numbers,as it greatly simplifies the experimental data collection program. Representation of data by equa-


tions, graphs, or tables is also enormously simplified. Another advantage is that the correlationsbecome independent of the unit employed. Dimensionless numbers have physical significance aswell. They are proportional to the ratios of forces. For example,

(3.18)

Because of this, they are employed as criteria for dynamic similarity in two different flow situations. An important application of similarity criteria and dimensionless numbers is in the area of

physical modeling of processes in connection with design and development. For example, smallmodels of aircraft are tested in a wind tunnel in connection with their design. In the area ofsteelmaking, room temperature, laboratory-size models, simulating liquid steel by water (i.e., watermodels), are very popular and have advanced our understanding of steelmaking processes signifi-cantly. Extrapolation of model results to actual prototypes is more reliable, provided there is dynamicsimilarity between the two through equality of relevant dimensionless numbers. Of course, themodel and prototype have to be geometrically similar.

Which dimensionless numbers would be relevant for simulation of a flow situation woulddepend on the significance of the forces. Table 3.1 lists the numbers important in secondarysteelmaking.

3.1.5 TURBULENT FLOW AND ITS ANALYSIS

Fluid flow in metallurgical processes is turbulent in nature. As already stated in Sec. 3.1.2, the flowis characterized by random fluctuations in velocity at any location in the flow field as well as byrandom motion of eddies as a consequence. Section 3.1.2 also has discussed differences betweenlaminar and turbulent flow. Laminar flow is characterized by well developed stable streamlines.On the other hand, a turbulent flow exhibits rapid mixing and no stable streamline. This was nicelydemonstrated by Osborne Reynolds more than a century ago. When he injected some red dye in

TABLE 3.1Important Dimensionless Numbers in Secondary Steelmaking

Name Symbol Definition Force proportionality ratio Application

Reynolds number Re General fluid flow

Froude number Fr In forced convection

Modified Froude number

Frm Gas–liquid system

Weber number Wb Gas bubble formation in liquid

Morton number Mo Velocity of gas bubbles in liquid

L = characteristic length (such as diameter for a pipe or sphere)ρg = density of gas, ρl = density of liquidσ = surface tension of a liquid

Re α resultant (i.e., inertia) force

viscous force-----------------------------------------------------------------

ρuLµ

---------- inertialviscous------------------

u2

gL------

inertialgravitational------------------------------

ρgu2

ρl ρg–( )gL----------------------------

inertialgravitational------------------------------

ρµ2Lσ

-------------inertial

surface tension------------------------------------

gµ4

ρlσ3

---------- gravitational( ) viscous( )×surface-tension

----------------------------------------------------------------

laminarly flowing water in a glass tube, the dye moved along a stable streamline, which was likea red thread that did not mix with surrounding water. But, in turbulent flow, the dye mixed up with


water rapidly, thus making the entire water red. Turbulence is complex in nature and, in spite of a large number of studies, is not understood

properly. In many typical situations, such as flow through a pipe, the disturbance caused by thepresence of a solid surface in contact with the fluid causes the onset of turbulence. Laminar flowis observed at small Reynolds number values, e.g., 2100 for flow through a straight pipe. At valuesof Re larger than this critical Re, the flow is turbulent. Sometimes, a laminar-to-turbulent transitionis characterized by a transitional flow regime, as in the case of flow through a pipe. Value ofcritical Re depends on the flow geometry. For example, in a flow around a sphere, Recrit isapproximately 0.1.

Eddies exhibit a large size range. The largest one may be comparable to the size of the vesseland the smallest one less than a millimeter. The smaller an eddy, the higher is its jump frequencyand hence consequent frequency of velocity fluctuation at a point, which may be as high asapproximately 1000 per second. Large eddies derive their energy from the main flow and maycontain as much as 20% of the kinetic energy of the turbulent motion. The interaction among largereddies generates smaller eddies, and so on.

The smaller the size of an eddy, the higher its specific kinetic energy (i.e., kinetic energy perunit mass or volume). Also, smaller eddies are isotropic, whereas larger eddies tend to exhibitanisotropy. Dissipation of the kinetic energy of an eddy into heat can occur only through viscousforces. With decreasing eddy size, viscous forces increasingly resist further disintegration of eddies.The smallest eddy size (lmin) may be estimated using Kolmogorov’s equation5 as

(3.19)

where ν is kinematic viscosity and εd is the rate of total kinetic energy dissipation of the turbulentmotion. Under secondary steelmaking conditions, lmin is on the order of fraction of a millimeter.

Figure 3.7 schematically shows the eddy size distribution of a fully developed turbulent flowas a function of the inverse of eddy size (le). The size distribution in large-sized eddies dependson the flow pattern and vessel geometry. However, for a fully developed, steady turbulent motion,

lminν3

εd

-----0.25

=

FIGURE 3.7 Diagrammatic scheme of the energies of eddies of different sizes relative to the reciprocal ofthe eddy length.

the size distribution for small eddies attains equilibrium and is probabilistic. It is independent offlow conditions and is known as Universal equilibrium range.


In turbulent motion, the velocity at any instant of time (u) at a location may be considered asconsisting of three components (ux, uy, and uz) along x, y, and z coordinates, respectively.

(3.20)

where is the time-averaged (i.e., mean) velocity of the fluid, and u´ is the fluctuating componentof velocity.

Again,

(3.21)

Similarly, and may be defined. Here, to is the time over which averaging is done. is thequantity measured by ordinary instruments. As already stated, is independent of time at steadystate. u´ can be measured only by special fast-response instruments such as a hot film anemometeror a laser Doppler anemometer.

Intensity of turbulence is measured by the relative magnitudes of u´ and . Since the valueof u´ at a location fluctuates at random, some kind of averaging of u´ is required. However, by definition. Hence, intensity of turbulence (I) has been defined as:

(3.22)

For isotropic turbulence, and hence Eq. (3.22) reduces to Eq. (3.23), i.e.,

(3.23)

The numerator in Eq. (3.23) is root mean square of u´ and is a non-zero quantity. Another fundamental parameter is a set of Reynolds stresses. These are , and

. These have dimensions of stress. They can also be shown to be related to the rate ofmomentum transport by eddies along a velocity gradient, which is another physical interpretationof shear stress. Hence, Reynolds stresses have physical existence and are not just conceptualquantities.

An important quantity, commonly used for characterizing turbulent flow behavior, is turbulentkinetic energy per unit mass of fluid (k), defined as

(3.24)

For isotropic turbulence,

(3.25)

ux ux u ′ x+ ; uy uy u ′ y;+ uz uz u ′ z+= = =

u

ux1to

--- ux

o

to

∫ t( )dt=

uy uz uu

uu ′ 0=

I

13--- u ′ x

2 u ′ y2 u ′ z

2+ +( )1 2⁄

u-----------------------------------------------------=

u ′ x u ′ y u ′ z u ′= = =

Iu ′ 2[ ]

1 2⁄

u------------------=

ρu ′ xu ′ y, ρu ′ xu ′ z

ρu ′ yu ′ z

k12--- u ′ x

2 u ′ y2 u ′ z

2+ +[ ]=

k32--- u ′ 2[ ]=

Momentum transfer by eddy mechanism has one similarity to transfer by molecular mechanism.Motions of both eddies and molecules are random in all directions. Only when a velocity gradient


is present does net momentum transfer occur. Therefore, in analogy with Newton’s law of viscosity,we may write

(3.26)

µ t is called eddy viscosity or turbulent viscosity and was first introduced by Bousinesq. Therefore,in turbulent motion,

µeff = µ t + µ (3.27)

where µeff is the effective viscosity of flow. Since an eddy contains trillions or more molecules, µ t

» µ, and µ eff is approximately equal to µ t. The difficulty with the eddy viscosity concept is that µ t is not a property of the fluid but depends

on the nature and intensity of turbulence as well. Hence, for quantitative analysis, µ t is to becorrelated with measurable variables governing fluid flow. The “one equation model” based onPrandtl’s concept of mixing the length of eddies (lm) proposes the following relationship:

µ t = ρ lm k1/2 (3.28)

However, it has been found to be inadequate. Among the “two equation” models, the one by Launderand Spalding,6 popularly known as k-ε model, proposes

(3.29)

where ε is rate of dissipation of k, and CD is an empirical constant equal to 0.09. Numerical computations of turbulent flow are done by solution of the turbulent Navier–Stokes

equation with the help of the eddy viscosity concept. These are complex calculations requiringlarge computer time. The basic procedure will be presented in Chapter 11. Calculated results willbe presented in subsequent chapters wherever required.

3.2 FLUID FLOW IN STEEL MELTS IN GAS-STIRRED LADLES

Recently, Mazumdar and Guthrie7 have reviewed fluid flow, mixing, and mass transfer in gas stirredladles. Stirring may be achieved by purging the steel melt with argon and also by gases liberatedfrom the melt during processing. The latter is important for successful processing during vacuumdegassing of liquid steel, when the evolution of CO, H2, and N2 causes vigorous stirring in the meltand consequent droplet ejection into the evacuated chamber. Electromagnetic stirring is alsoemployed in secondary steelmaking.

However, the most common situation is stirring by the purging of inert gas. Hence, so far asfundamental studies on fluid flow are concerned, principal attention has been focused on turbulenceand agitation in the ladle due to argon purging. The gas is introduced into the melt mostly throughporous plugs fitted at the ladle bottom (i.e., bottom purging) or by a lance immersed vertically intothe melt from the top. Fluid motion and turbulence in both these arrangements have some similaritiesbut have differences as well.

It is the bottom purging geometry that has been most widely studied. Hence, this section isrestricted to fluid flow in liquid due to bottom purging of inert gas. Liberation of gases from the

τ yx( )t µ– t

∂ux

∂y--------=

µt CDρk2

ε--------=

melt due to reactions is ignored. In industry, small ladles are fitted with one bottom plug and largeones with two plugs. Again, these are typically not axisymmetric with the ladle but are fitted in


eccentric fashion. However, fundamental investigations have been mostly conducted in the labora-tory with transparent room-temperature water models. In these studies, mostly axisymmetric nozzleswere employed for the sake of simplicity and basic interpretations.

The presentations in this section are aimed at elucidation of fundamentals. Our understandingof the same will be better if the above background information is kept in mind. Fluid flow inindustrial situations that differ significantly in the mode of stirring and melt geometry is taken upin later sections when necessary and possible. Even there, the information contained in this sectionprovides the basics.

Table 3.2 presents some values of gas flow rates per unit volume of liquid in ladle refining ofliquid steel as well as other situations involving bottom purging.

For calculation of Qv, gas temperatures were assumed as 300 K for the water model and 1873 Kfor the steel melt. The overall range of Qv for steel melt may be taken as 10 × 10–4 to 100 × 10–4

s–1. The table also demonstrates that Qv is 2 to 3 orders of magnitude lower in ladle refining thanthat in an OBM converter. In a combined top and bottom blowing converter, the bottom gas injectionrate is few percent (say at least 2%) of the oxygen blowing rate through top lance. Hence, Qv wouldbe at least 500 × 10–4 s–1. Even then, it is a few times larger than typical values of Qv in ladle refining.

In converter steelmaking, tuyeres (i.e., nozzles) are typically employed for bottom gas injection.It is a must if oxygen is introduced, either singly or mixed with inert gas. The high velocity of gasissuing from tuyeres causes jetting flow and prevents back attack of tuyeres of molten metal. Inladle refining, on the other hand, the flow rates and velocities of gas are low. Hence, a jetting regimecannot be obtained, and porous or slit refractory plugs are more suitable than tuyeres. Moreover,bubbles are statistically smaller in size in porous plug systems than for nozzles. This enhances therefining rate due to a larger gas–liquid interfacial area.

Hammerer et al.13 have reviewed latest developments in gas-purging plugs. Figure 3.8 showssketches of them. These may be classified as

• plugs made of porous refractory material• segment-purging plugs (i.e., slit plugs) with gas flow by round channels or predominantly

straight slits in refractory shapes

Besides permeability, durability, and economy, operational safety is important. Formation andrelease of gas bubbles cause pressure fluctuations in the gas line, leading to back attack of plugsby steel melt. Plugs get damaged by penetration of liquid metal into them through back attack, aswell as by peeling at the surface in contact with the melt. Both of these are less common for slitplugs, which are therefore more popular. Porous plugs are employed for gas bubbling at moderaterates only (less than 0.01 Nm3s–1).

TABLE 3.2Gas Flow Rates (Qv) per m3 Bath Volume

SituationQv, m3 s–1 × 104per m3 of bath Reference

Ar-stirred ladle 44–1800 8

-do- 3–54 9

-do- 25–330 10

Water model 17–240 11

OBM converter 25000 12


3.2.1 GAS BUBBLES IN LIQUID

The behavior of gas bubbles in liquid has been extensively studied. Szekely1 has reviewed it andmay be referred to for more details. Growth and motion of single bubbles in liquid are reasonablywell understood. In gas flow through submerged nozzles, discrete bubbles form at a low flow rate,and gas issues at a high flow rate as a jet from the nozzle.

At low flow rates, the bubble diameter (dB), upon detachment from the nozzle, is determinedby a balance between surface tension and buoyancy force. For an air-water system, the followingcorrelations have been proposed:

(3.30)

and

(3.31)

where dn is the nozzle diameter, and other symbols are as noted in Table 3.1. The nozzle Reynoldsnumber (Ren) is given as , where un is linear velocity of gas in the nozzle.

Liquid metals are non-wetting to a refractory nozzle or plug. Hence, dn in Eqs. (3.30) and (3.31)is to be taken as the outside diameter of nozzle rather than the inside diameter. A porous plug maybe considered as a collection of fine tubes (straight or zigzag). At low gas flow rates, discretebubbles form at the plug exit, but at higher flow rates bubbles coalesce at the plug exit itself andassume a large size before detachment. Anagbo and Brimacombe,14 in their water model study,found coalescence above a flow rate of 0.4 m3 s–1 per m2 of plug area. In Table 3.2, noting that theargon stirred ladles have a 60-tonne capacity, and assuming 0.15 m as the diameter of the porousplug, the critical value of Qv turns out to be 8.3 × 10–4 m3 s–1 per m3 bath volume.

This is indeed low. Moreover, bubble detachment would be more difficult in liquid metal dueto the non-wetting nature of the liquid. Hence, it may be concluded that coalescence beforedetachment is expected. It is shown schematically in Figure 3.9, which depicts a simplified situationonly. For example, with segment-purging plugs, fine streams of gas would be issuing out throughparallel channels. There, coalescence is expected only at a higher gas flow rate. Hence, smallerbubble sizes and faster gas-liquid reaction are expected even at a higher flow rate. Moreover,

FIGURE 3.8 Kinds of purging plug systems.

dB

6dnσg ρl ρg–( )------------------------

1 3⁄

, for Re < 500=

dB 0.046dn1 2⁄ Ren

1 3⁄ , for 500 Re 2100≤ ≤=

ρgdnun µg⁄


pulsations would be much less in the absence of coalescence. This explains why there is less backattack in segment-purging plugs as compared to that in porous brick plugs.

An additional refinement in the calculation of dB has been the incorporation of the effect ofthe volume of the antechamber (Vc), which is defined as the volume between the last location fora large pressure drop (i.e., a valve) and the actual nozzle or orifice. Due to gradual rather thaninstantaneous buildup of pressure in the antechamber, the final volume of the bubble, upon detach-ment, would be larger than calculated from Eqs. (3.30) and (3.31). Sano and Mori29 have proposedan empirical correlation relating dB to dn,o´, dimensionless antechamber volume (capacitance num-ber, Nc), and other variables. Experimental measurements in liquid iron have demonstrated goodagreement with the above. Figure 3.10 shows significant dependence of dB on .

A great deal of theoretical work has been done on the rising velocity and shape of gas bubblesin liquids, and in most cases the theory is in quite good agreement with measurements. There are

Wetted

Non-wetted

Nozzle Orifice Porous plug

FIGURE 3.9 Bubble formation at wetted and nonwetted nozzle, orifice, and porous plug.

FIGURE 3.10 A comparison of experimentally measured bubble diameters in molten metals with predictionsbased on the analysis of Guthrie and Irons, demonstrating the effect of the capacitance number.15

Nc15

several dimensionless numbers controlling bubble shape.13 An important one is the bubble Reynoldsnumber, defined as


(3.32)

where uB = linear rise velocity of bubble. Small bubbles (ReB < 1) are spherical in shape. Largebubbles (ReB > 1000), under some other restrictions, are spherical cap shaped. To satisfy variousconditions, they have to be larger than 1 cm in diameter in liquids of low viscosity (e.g., water orliquid metals). Ellipsoidal and other shapes are obtained at an intermediate Reynolds number.Bubbles rise by pulsation and can be swirling, too. Considerable circulation is also present in thegas inside.

Small spherical bubbles behave like rigid spheres, and the terminal velocity (ut) is given byStokes’ law, viz.,

(3.33)

ut for spherical cap bubbles can be expressed as

(3.34)

where de is diameter of a sphere whose volume is equal to that of the bubble. Experimentalmeasurements in water as well as in molten metals indicate that a better approximation is obtainedif the coefficient is taken as 0.9 rather than 1.02 for de less than 3 cm.

In industrial situations, we are concerned with assemblages of interacting bubbles, known asbubble swarms, rather than single bubbles. In such systems, bubbles behave differently from singlebubbles, and our knowledge is much more limited due to the complexity of the situation.

An important parameter characterizing a bubble swarm is gas hold up (α), where

(3.35)

Based on this parameter, essentially three regimes may be identified.

1. Bubbling regime (α < 0.4) 2. Froth (α ≅ 0.4 – 0.6)3. Foam (α ≅ 0.9 – 0.98)

In ladle refining, we are concerned with the bubbling regime only. Almost all studies on bubble swarms have been conducted in room-temperature systems with

water or other transparent liquids. The upward velocity of a rising bubble may be considerablylarger than what Eqs. (3.33) or (3.34) would predict, because the upward motion of the liquidassists bubble motion.

3.2.2 THE PLUME IN A GAS-STIRRED LIQUID BATH

Figure 3.11 shows a sketch of a simplified situation when the gas is introduced into a cylindricalvessel containing liquid via a nozzle located at the bottom and placed along the axis of the vessel.

ReBdBuBρl

µl

----------------=

ut

dB2 g

18µl

----------- ρl ρg–( )=

ut 1.02gde

2--------

1 2⁄

=

α volume of gas in gas/liquid mixturetotal volume of mixture

-------------------------------------------------------------------------------------=


Around the axis of the vessel, there is a two-phase region consisting of gas bubbles and liquid.This is known as the plume. Upward movement of bubbles in the plume leads to circulation ofliquid in the vessel. Such a liquid motion is called recirculatory flow, and it is turbulent as well.

At low gas velocities, discrete bubbles form at the nozzle/plug tips. The resulting plume isknown as an ordinary plume. At higher velocities, a continuous gas stream issues out into the liquid.It subsequently disintegrates into discrete bubbles at a short distance after exiting from the nozzleor plug. It is called a forced plume. Henceforth, both will be referred to simply as plume.

If the plume is idealized as a truncated cone, its profile can be characterized in terms of itscone angle (θp), as shown in Figure 3.11. The plume profile and its dimensions depend on variousoperating variables. The most critical of these is the gas velocity at the nozzle tip. Measurementof the plume cone angle in liquid steel is obtained indirectly from the plume diameter as it emergesat the top surface. This is not reliable, since the profile deviates from that of a cone near the topsurface. Photographic measurements in water models have indicated a range of 20 to 30 degrees.

Krishnamurthy et al.16 made comprehensive measurements of θp as a function of gas flow rate(Q), bath height (H), vessel diameter (D), and nozzle diameter (dn). They employed an axisymmetricnozzle at bottom of the vessel and, through regression fitting of data, obtained the correlation:

(3.36)

The definition of modified Froude number (Frm) was provided in Table 3.1, where u is to be takenas the velocity of gas issuing out of the nozzle, and L means H. Xie et al.17 determined plumewidth in molten Wood’s metal at 100°C and compared this with measurements in a water modeland mercury. Statistically speaking, no difference could be obtained, indicating that we may employEq. (3.36) for estimating θp in liquid steel, of course, after incorporating the actual value of Q uponexit from the nozzle at bath temperature. Although the above discussions would provide a simpleapproach to estimation of θp, it is to be kept in mind that the plume diameter, at least near the topsurface, is likely to be larger in steel melt than in water as a result of the greater density of steeland consequently more bubble expansion.

FIGURE 3.11 Sketch of the situation in a gas-stirred melt.

θp

180--------- 0.915Frm

0.12 HD----

0.254– dn

D-----

0.441–

=

Significant experimental data have been collected on physical characteristics of the plume inwater as well as low-melting metals over the last five years. Electrical resistivity probes have been


employed to determine dispersion of gas bubbles as characterized by local time-averaged gasfraction, bubble size, bubble frequency, and bubble rise velocity. The use of hot film anemometersand laser Doppler velocimeters has allowed the measurement of liquid velocity in water models.Since all these depend on the height above the nozzle tip as well as the horizontal radial distancefrom the nozzle axis, data have been collected as a function of both.

In a horizontal section, maximum gas fraction (αmax) is obtained at axial location, i.e., at radius(r) = 0. Several investigators17,18 have suggested Gaussian distribution, i.e.,

(3.37)

where b is an empirical constant. Comprehensive measurements by Castillejos and Brimacombe19

in water and mercury have yielded the following regression-fitted empirical correlation for bottomblowing through an axisymmetric nozzle in a water model:

(3.38)

At r = r1,

Equation (3.38) demonstrates that the decay of α/αmax with increasing r is more than thatpredicted by the Gaussian curve. Data of others17,18 also seem to suggest the same, although theyhave fitted with the Gaussian curve. Castillejos and Brimacombe19 proposed further that

(3.39)

and,

αmax = 0.815 N–0.1, for N < 1.35 = 1.069 N–1, for N ≥ 1.35 (3.40)

where Qn is volumetric gas flow rate at the temperature and pressure prevailing at nozzle exit, andN is a dimensionless parameter equal to

where Z is the vertical distance from the nozzle exit. ρg is the density of gas at nozzle exit.Xie et al.17 carried out similar investigations with Wood’s metal at 100°C (ρ1 = 9.4 × 103 kg

m–3) and have proposed a Gaussian distribution of α as in Eq. (3.37). On the basis of regressionfitting of experimental data, they have proposed the following relations:

ααmax

---------- r2

b2-----–

exp=

ααmax

---------- 0.7rr1

---- 2.4

–exp=

ααmax

2----------=

r1g

Qn2

-------1 5⁄

0.275gdn

5

Qn2

--------

0.155ρ1

ρg------

0.11 Z

dn

----- 0.51

=

gdn5

Qn2

--------

0.26ρ1

ρg

-----

0.13 Zdn

----- 0.94

(3.41)b 0.28 Z Ho+( )7 12⁄ Qz2 g⁄( )1 12⁄

=


(3.42)

where Ho is the axial distance of the hypothetical origin of conical plume from the nozzle exit,given as . σ1 is the surface tension of the liquid, and Qz is the gas flow rate atpressure and temperature at a height from the nozzle exit. For Wood’s metal, σ1 is 0.46 N m–1.Figure 3.12 compares some calculated values of α as a function of r for water and Wood’s metalbased on the above equations.

Xie et al.17 also made measurements with gas blowing through eccentric nozzles, and theyproposed the following correlations:

(3.43)

and

(3.44)

where rm is the radial distance of the nozzle from the center of the vessel.It was observed that, despite the stable lateral deflection mentioned, the distribution of α was

symmetric around the axis of the nozzle. bz = 1.17br on the average, meaning that the plume wasan elliptic cross section. From measurements of α, the mean velocity of the gas stream (ug) in across section of the plume can be determined as the ratio of gas flow rate to the total gas fractionin the cross section, i.e.,

αmax 0.65 Qn2 ρ1 σ1⁄ g( )1 2⁄[ ] 1 4⁄

/ Z Ho+( )=

4.5dn1 2⁄ Qn

2 g⁄( )0.1

FIGURE 3.12 Comparison of void fraction vs. radial position data for different investigators.

α ecc,r

αmax

-----------r rm

2–

br2

-------------

–exp=

α ecc,z

αmax

-----------Z2

bz2

----- –exp=

(3.45)ug Q α AdA∫

1–=


Based on Eqs. (3.41), (3.42), and (3.45), and assuming radial symmetry of the plume around theaxis for a centric nozzle,

ug = 75.73 [Q/(Z + Ho)]1/6 (3.46)

A measure of the extent of total gas holdup may be taken as

A refers to plume cross-sectional area. It was found that this parameter was the same for centricand eccentric gas blowing.

Some measurements of time-averaged upward velocity of liquid in the plume are availablein the literature for a nozzle-fitted water model.9,10,18,20 is at maximum along the axis. Valuesranged between 0.2 and 0.3 ms–1, depending on value of Qn. Radial distribution of velocity isGaussian, with the maximum value along the axis, i.e.,

(3.47)

where bu is a constant that depends on gas flow rate, height above the nozzle, etc. Quantitativecorrelation of experimental data has been proposed by Oeters et al.10 for centric blowing of air inwater as

(3.48)

bu = 0.38 Q0.15 Z0.62 (3.49)

It shows that the axial velocity, , does not vary much with vertical distance, Z. This hasbeen corroborated by other investigators as well. This is in contrast to a free gas jet where the axialvelocity decreases rapidly as Z increases. The difference lies in the fact that the rising bubblesimpart upward momentum to the entrained liquid throughout the plume volume due to buoyancyforce, whereas the momentum of a free jet is derived solely from its momentum upon exiting fromthe nozzle.

The buoyant plume may be visualized as a pump, making the liquid flow upward. The volumetricflow rate of liquid at any horizontal section Ql may be obtained from Eqs. (3.47), (3.48), and (3.49) as

(3.50)

Oeters et al.10 also proposed that the above correlations may be employed for liquid steel aswell, provided that the gas flow rate (Qn) is calculated for the actual pressure and temperature ofgas at the nozzle exit. Moreover, a broadening of the plume in liquid steel may be taken care ofby substituting Z with Z · ψ, where

α AdA∫

u1 p( )u1 p( )

u1 p

u1 p ,max

--------------- r2– bu2⁄( )exp=

u1ρ,max 3.37Q0.25Z 0.12–=

u1 p ,max

Q1 ulp

A∫ dA 1.52Qn

0.55Z1.13= =

(3.51)ψ 1β--- 1

1 β–( )-----------------ln=


and

(3.52)

where ha = the height of liquid steel equivalent to the atmospheric pressure. However, Eqs. (3.49)through (3.52) would require verification and may be treated as approximate guidelines only.

Time-averaged bubble rise velocities in the plume have been measured in water models18–20

and Wood’s metal,17 and did not vary significantly along the axis of the nozzle. The variationwas much less in the radial direction as compared to α and . For example, was morethan 60% of its axial value in all cases, and sometimes the profile was almost flat. In water, theoverall range obtained by the investigators ranged from 0.2 to 2 ms–1 depending on Q and Z. InWood’s metal, along the axis ranged between 0.5 and 0.7 ms–1, and it was found to beproportional to ug. It has been proposed17 that Eq. (3.46) can be used to estimate as well,except that the coefficient should be 54.51 in place of 75.73.

Comparison of and in water model studies revealed that was always largerthan . This is due to bubble slip.

(3.53)

varied approximately between 0.2 and 0.4 ms–1. On the basis of their experimental data andcomprehensive analysis of the same, Sheng and Irons20 have shown that was approximatelythe same as the rise velocity of a bubble of equivalent diameter in stagnant water.

The spout region of the plume occupies only 3 to 4 percent of its total volume but is ofimportance in connection with processes occurring at melt surface, such as gas absorption, slagmetal reaction, etc. Sahajwalla et al.21 investigated this region using an electroresistivity probe ina water model. The gas fraction was at minimum at the axis and increased with radial distancefrom the axis to a value of 0.95. This is in contrast to what has been found in the rest of the plume.Photographic measurements of plume dimensions corresponded to α = 0.82 to 0.86. Variation ofspout radius (rs) with other parameters was expressed by the following relationship:

(3.54)

where

The bubble frequency ranged between 14 to 16 s–1 along the axis and decreased to 1 to 4 s–1 towardperiphery. The plume oscillation frequency was 2 to 4 s–1.

For gas-stirred industrial ladles, the purging time is often not too long. A relevant questionthere is whether the flow is unsteady (i.e., transient) or steady. One mathematical modeling work22

found that a steady state could be attained in three minutes. This was about the time required toobtain good thermal homogenization as well. It was also found that the time for homogenizationwas approximately the same regardless of whether the flow was taken as transient or steady.

As already stated, fundamental studies with gas blowing through porous plugs are limited. Twowater-model investigations14,23 have provided some information. These were porous glass-disc andnot segment-purging plugs. Gas fraction measurements by electroresistivity probe yielded thecorrelation for axial location14 as

β Zha H+----------------=

uB( )uB( )

ulp( ) uB( )

uB( )uB( )

uB( ) ulp( ) uB( )ulp( )

Time–averaged bubble slip velocity us( ) uB ulp–=

us( )us( )

rsg

Qn2

------ 1 5⁄

0.48Z* 8.3 Fr( ) 0.18–+=

Z* Z g/Qn2( )1 5⁄

=

(3.55)αmax 0.71Z

Q2/g( ) 0.2–-----------------------

0.9–=


Radial variation of α was found to obey Gaussian distribution. The mean bubble diameter showeda sudden increase with the onset of coalescence. Axial and radial velocity components of the liquidvaried along the radial direction in a similar fashion as for gas flow through the nozzle.

In the design of a water model, besides geometric similarity, the most important dimensionlessnumber considered for simulation is the modified Froude number (Frm) as defined in Table 3.1. Inconnection with a gas-purged ladle, it is to be rewritten as

(3.56)

where un is the linear velocity of gas issuing through a nozzle.For porous plugs, un does not have any meaning and cannot be determined from the gas flow

rate. For argument’s sake, let us take the example of a 60 t ladle in Table 3.2 with a porous plugdiameter of 0.15 m, and assume entire plug surface area as a nozzle. For Qv = 330 × 10–4 m3s–1 perm3 bath volume, nominal value of un would be 16 ms–1 and Frm = 0.57. This may be comparedwith Frm >10 if a tuyere was employed, and Frm >100 in bottom-blowing converters. Hence, theinertial force is too small to significantly influence the flow for a porous plug, and Frm should notbe a relevant criterion for simulation from this point of view. Mazumdar and Guthrie7 have alsoquestioned relevance of Frm in gas injection through a porous plug.

Forces that are expected to govern the nature of flow are

• buoyant force of the rising plume• inertial force due to liquid motion• surface forces at the top of the bath• viscous shear forces at ladle wall

3.2.3 FLOW FIELD IN LIQUID OUTSIDE THE PLUME

As Figure 3.11 shows, the flow induced by the plume is recirculatory in liquid outside the plume.Velocities have been measured in water models by laser Doppler velocimeter (LDV) for axisym-metric nozzles10,20 as well as porous plugs.14,23 Figure 3.13 shows a typical velocity field.20

Sahai and Guthrie24 were among the earliest to attempt characterization of the recirculatoryflow. They summarized that hydrodynamic conditions near an axisymmetric nozzle or plug are notcritical to flow recirculation in large cylindrical vessels. This view is considered to be valid evennow. This is because the flow is primarily driven by the buoyant force of rising gas bubbles. Hence,we may assume the velocity fields to be fairly similar for a porous plug as for a nozzle, providedthat other conditions (viz., gas flow rate and bath dimensions) remain the same.

Figure 3.14 shows flow patterns for air injection into water for various locations of a porousplug.25 The existence of dead zones near the bottom of vessel, especially at the bottom corners, iswell established. The main flow torus has a chance to come close to the bottom only at a high gasflow rate and with the H/D ratio ranging between 0.4 and 0.8.10 The geometry and size of the deadzone are dependent also on the gas-purging arrangement. Figure 3.15 shows this schematically forvarious arrangements.26

Figure 3.13 demonstrates considerably higher velocity in the plume region than in the bulkliquid. Velocities are very small near the wall and bottom of a vessel. Quantitatively, the axialvelocities ranged from 0 to 0.4 ms–1 and radial velocities less than 0.1 ms–1 for gas flow ratesranging from 10–4 to 10–3 Nm3 s–1, which covers the ladle refining conditions, generally speaking.

n

Frm

un2

gH-------

ρg

ρ1 ρg–( )---------------------⋅=


Measurement by LDV is also capable of determining values of RMS of the fluctuating compo-nent of velocity, i.e.,

Figure 3.16 shows a plot of this, obtained in axisymmetric blowing through the nozzle in thewater model.20 Qualitative similarity with velocity field (Figure 3.13) may be noted. Turbulentkinetic energy (k) as defined in Eq. (3.25) is another parameter of importance in characterizingturbulence. Figure 3.17 shows isopleths of k20 for the same experimental conditions as for Figures3.13 and 3.16. Very low values of k in the bulk and high values in plume region may again be noted.

A fundamental parameter characterizing turbulence is the intensity of turbulence (I) as definedin Eq. (3.23). Sheng and Irons20 found I to be approximately 0.2 for bulk flow and larger than 0.5in the plume region, and turbulence was isotropic. Ballal and Ghosh27 simulated a bottom-blownsteelmaking converter process using a water model. They were interested in stresses on the bottomand side wall due to fluid motion. Air flow rates were higher than those employed in the simulationof ladle flow by other investigators. The number of nozzles was 1, 3, 6, and 12. The single nozzlewas axisymmetric, and multinozzles were either symmetrically or asymmetrically located aroundthe vessel axis. Tiny platinum electrodes were flush mounted at various locations on the bottomand wall of the vessel.

The electrochemical technique was employed to determine saturation current density, whichyielded concentration and velocity gradients at the surface and hence wall shear stress . Speciallydesigned electronic instruments allowed the determination of both mean shear stress and RMSof a fluctuating component. It was found that, for a certain nozzle arrangement, in the entire gasflow range,

(3.57)

where C is a constant. Noting that C may be taken as I, values of I ranged from 0.33 to 0.53.

FIGURE 3.13 Flow pattern of the mean liquid velocities in the model ladle produced with the flush-mountednozzle at Q = 10–4 Nm3 s–1.20

u ′ 2( )1 2⁄

τ( )τ( )

τ′ 2( )1 2⁄

Cτ=


Mazumdar et al.28 carried out measurements of fluctuating and mean velocities of liquid atseveral locations of the bath by LDV in a water model with centric gas injection by nozzle. Theyemployed four gas flow rates and three arrangements, viz., free bath surface, surface covered by afloating wooden block, and surface covered with 15 mm thick oil layer. Averaging over the bathyielded values of the average speed of bath circulation and the averaged RMS of thefluctuating velocity component,

The I obtained by taking the ratios of these ranged between 0.2 and 0.31, with a master averagevalue of 0.25. Summarizing all these findings, it may be concluded that, under ladle refiningconditions, I may be taken as 0.3 or somewhat less in the bulk liquid, on an average.

The total energy input through gas (E) is given as

E = Eb + Ek + Eexp (3.58)

FIGURE 3.14 Different positions of porous plugs and the resulting flow patterns for bottom gas injection.25

uav( )

u ′ 2[ ] av

1 2⁄


where Eb = buoyancy energy of the gas bubble in liquid, Ek = kinetic energy of the gas at exit fromthe nozzle/plug, and Eexp = expansion energy of the bubble during its rise through the liquid.

The rate of energy input (ε) is a more relevant parameter. A modified form of Eq. (3.58) is

ε = εb + εk + εexp (3.59)

Krishnamurthy et al.11 tried to assess the contribution of εk to mixing in the bath, which isrelated to energy utilization for bath stirring. They found εb to be negligible as compared to ε atlow gas flow rates. This agrees with observations by others.29 εexp is theoretically equal to εb, and

FIGURE 3.15 Flow patterns of liquid in a bath generated by blowing gas at 2.5 × 10–4 Nm3 s–1 through aporous plug.26

FIGURE 3.16 Distribution of the RMS component of liquid velocity in a model ladle at Q = 10–4 Nm3 s–1.20


it was included in calculation of ε in the classic work of Nakanishi et al.30 However, it seems thatonly a small fraction of this is really utilized in inducing bath motion. In one of the earliest analysesof this, Bhavaraju et al.31 also ignored it.

Hence, for gas-stirred ladles and many other situations, investigators take ε = εb for the sakeof avoiding complications. It may be an approximation, but it has provided the basis for furtheradvancement in the area of process dynamics in secondary steelmaking and elsewhere. This isbecause εb can be estimated from experimental conditions easily and reliably.

In simple terms,

ε = (ρ1gH) · QM (3.60)

with ρ1gH being the buoyancy force per unit volume of gas. Due to expansion of the bubble as itrises, the value of QM is to be a mean value of volumetric gas flow rate. Bhavaraju et al.31 employeda logarithmic mean value where

(3.61)

where Q is the gas flow rate in Nm3 s–1, Po is atmospheric pressure, Tl is the temperature of liquidin Kelvins, and PM is the logarithmic mean pressure, given as

(3.62)

where

PH = Po + ρ1gH (3.63)

FIGURE 3.17 Contour map of the distribution of turbulent kinetic energy in a large vessel, produced withthe flush-mounted nozzle for Q = 10–4 Nm3 s–1.20

QM Q.Po

PM

-------.T l

298---------=

PMPH Po–

PH Po⁄( )ln---------------------------=

Combining Eqs. (3.60) through (3.63), and putting in values,


(3.64)

where εm is rate of energy input in watts per kilogram of liquid steel. M is the mass of the steel inkg, H is in meters, and Po is in bar. For water, 0.707 in Eq. (3.64) is to be replaced by

As stated in Sec. 3.1.3, there are basically two methods of analysis of fluid flow-differentialand integral. Differential analysis requires the solution of equation of continuity (Eq. 3.10) and theequation of motion, i.e., Eq. (3.13) or its simplified form, viz., the Navier–Stokes equation,Eq. (3.14). This approach is the most rigorous one and is very popular for numerical computationof fluid flow problems.

The Navier–Stokes equation was originally applied to laminar flow. Nowadays, it is employedfor turbulent flow as well. This calls for certain modification and empiricism, and it involvescomputer-oriented numerical methods. As discussed in Sec. 3.1.5, turbulent viscosity (µ t) is not aproperty of the fluid but depends on nature and intensity of turbulence as well. As already statedin this connection, the k-ε model of Launder and Spalding6 is popular [Eq. (3.29)].

Szekely and his coworkers pioneered this approach for the analysis of fluid flow in metallurgicalprocessing.32,33 One of the most recent papers is by Joo and Guthrie.34 Very useful information hasbeen obtained. However, this is a specialized topic that has been well reviewed by Szekely.11

Moreover, it will be briefly dealt with in Chapter 11 of this book. Hence, further discussion is notpresented here.

Integral analysis of flow in gas-stirred ladle was initiated by Chiang et al.9 and Sahai andGuthrie.24 One may either go for macroscopic momentum balance or macroscopic energy balance.The latter has given some useful conclusions. Integral analysis has certain limitations, the mostimportant being its inability to predict spatial variation of velocity and turbulence parameters.However, both are well suited for macroscopic predictions and understanding of phenomena andanalysis at an elementary level. Hence, it is briefly presented below.

Based on their water-model investigations, Sahai and Guthrie24 employed the correlation

(3.65)

where is the average bulk velocity of liquid, and R is the radius of the vessel.Mazumdar et al.,28 from their velocity measurements, also determined the total specific kinetic

energy of recirculating liquid. Figure 3.18 shows these as a function of a specific buoyancy inputenergy rate. It may be noted that the kinetic energy content of recirculating liquid was only afraction of the total energy input. The fraction was 0.235 for a free bath surface with a floatingwooden block. But it was only 0.12 with a slag layer. According to the authors, this was due tothe energy required to create oil-water emulsion, and it demonstrates the likelihood of a significantretarding effect of top slag on recirculatory flow of steel melt in a ladle.

This demonstrates that only 10 to 30 percent of the input energy is dissipated by turbulence inthe bulk liquid, with the rest getting lost due to bubble slippage in the plume, formation of wavesand droplets at the surface of the bath, and friction at the vessel wall. It seems that bubble slippageis the dominant one. What this means is that the plume should be treated as two-phase flow rather

εm

340QT 1

M------------------- 1 0.707+( )H /Po( )ln=

0.707ρwater

ρsteel

-------------× 0.099=

uav

up

-------. R( )1 3⁄ 0.18=

uav


than a quasi-single phase flow. Some recent papers have attempted modeling on this basis. Buteven then, the loss of energy at the free surface, especially in the presence of a slag layer, remainsa source of uncertainty in energy balance.

The average plume velocity has been correlated with other variables as follows for a watermodel:26

(3.66)

Combining Eq. (3.65) with (3.66) yields

(3.67)

Krishnamurthy et al.35 employed a modified approach taking into account bubble slip in theplume and also employed their data of plume cone angle measurement Eq. (3.36). The followingcorrelations were obtained:

(3.68)

and

Q1 = 2.81 × 10–3 ε0.625 H0.942 dn0.119 (3.69)

where is the upward average liquid velocity in plume, H is the bath height and Q1 is thevolumetric flow rate of liquid in the plume. It may be further noted that Q1 is the volumetric flow

FIGURE 3.18 Plot of total kinetic energy contained in a recirculating aqueous phase vs. energy input perunit of mass liquid for various upper phase conditions.28

up 4.5 Qn1 3⁄ H1 4⁄( )/R1 3⁄=

uav 0.79 Qn1 3⁄ H1 4⁄( )/R2 3⁄=

ulp 0.446ε0.174=

ulp

rate in bulk liquid as well, and it is a measure of rate of liquid circulation. Noting that ε ≅ 104 Q1,dn ≅ 0.01 m, and H ≅ 1 m in the water model, Eq. (3.69) agrees reasonably well with Eq. (3.50)


as proposed by Oeters et al.10

REFERENCES

1. Szekely, J., Fluid Flow Phenomena in Metals Processing, Ch. 8, Academic Press, New York, 1979,p. 305.

2. Guthrie, R.I.L., Engineering in Process Metallurgy, Oxford Science Publications, Oxford University,New York, 1989.

3. Bird, R.B., Stewart, W.E. and Lightfoot, E.N., Transport Phenomena, John Wiley & Sons Inc., NewYork, 1960.

4. Szekely, J. and Themelis, N.J., Rate Phenomena in Process Metallurgy, Wiley-Interscience, JohnWiley & Sons Inc., New York, 1971.

5. Davies, J.T., Turbulence Phenomena, Academic Press, New York, 1972. 6. Launder, B.E. and Spalding, D.B., Computer Methods in Applied Mechanics and Engineering, 3,

1974, p. 269. 7. Mazumdar, D. and Guthrie, R.I.L., ISIJ International, 35, 1995, p. 1. 8. Asai, S., Kawachi, M. and Muchi, I., SCANINJECT III, MEFOS, Lulea, Sweden, 1983, p. 12:1.9. Chiang, H.T., Lehner, T. and Kjellberg, B., Scand. J. Met., 9, 1980, p. 105.

10. Oeters, F., Plushkell, W., Steinmetz, E. and Wilhelmi, H., Steel Research, 59, 1988, p. 192. 11. Krishnamurthy, G.G., Mehrotra, S.P. and Ghosh, A., Metall. Trans., 18B, 1988, p. 839. 12. Etienne, A., CRM Rep., 43, 1975, p. 15.13. Hammerer, W., Raidl, G. and Barthel, H., Proc. Steelmaking Conf., ISS, Toronto, 75, 1992, p. 291. 14. Anagbo, P.E. and Brimacombe, J.K., Metall. Trans., 21B, 1990, p. 367. 15. Guthrie, R.I.L. and Irons, G.A., Metall. Trans., 9B, 1978, p. 101. 16. Krishnamurthy, G.G., Ghosh, A. and Mehrotra, S.P., Metall. Trans., 19B, 1988, p. 885. 17. Xie, Y., Orsten, S. and Oeters, F., ISIJ International, 32, 1992, p. 66. 18. Iguchi et al., ISIJ International, 32, 1992, p. 857. 19. Castillejos, A.H. and Brimacombe, J.K., Metall. Trans., 18B, 1987, p. 659. 20. Sheng, Y.Y. and Irons, G.A., Metall. Trans., 23B, 1992, p. 779. 21. Sahajwalla, V., Castillejos, A.H. and Brimacombe, J.K., Metall. Trans., 21B, 1990, p.71. 22. Castillejos, A.H., Salcudean, M.E. and Brimacombe, J.K., Metall. Trans., 20B, 1989, p. 603. 23. Johansen, S.T., Robertson, D.G.C., Woje, K. and Engh, T.A., Metall. Trans., 19B, 1988, p. 745. 24. Sahai, Y. and Guthrie, R.I.L., Metall. Trans., 13B, 1982, p.203. 25. Krishnamurthy, G.G. and Mehrotra, S.P., Ironmaking and Steelmaking, 19, 1992, p. 377. 26. Narita, K., Tomita, A., Hiroka, Y. and Satoh, Y., Tetsu-to-Hagane, 57, 1971, p. 1101.27. Ballal, N.B. and Ghosh, A., Metall. Trans., 12B, 1981, p. 525. 28. Mazumdar, D., Nakajima, H., and Guthrie, R.I.L., Metall. Trans., 19B, 1988, p. 507. 29. Sano, M. and Mori, K., Trans. ISIJ, 23, 1983, p. 169. 30. Nakanishi, K., Fujii, T. and Szekely, J., Ironmaking and Steelmaking, 3, 1975, p. 193. 31. Bhavaraju, S.M., Russel, T.W.F. and H.W. Blanch, H.W., AIChE J., 24, 1978, p. 454. 32. Szekely, J., Wang, H.J. and Keiser, K.M., Metall. Trans., 7B, 1976, p. 287. 33. El-Kaddah, N. and Szekely, J., SCANINJECT III, MEFOS, Lulea, Sweden, 1983, p. 3:1.34. Joo, S. and Guthrie, R.I.L., Metall. Trans., 23B, 1992, p. 765. 35. Krishnamurthy, G.G., Ghosh, A. and Mehrotra, S.P., Metall. Trans., 20B, 1989, p. 53.

4 Mixing, Mass Transfer, and Kinetics

4.1 INTRODUCTION

Since chemical reactions occur during steelmaking, the vessels are reactors according to generalterminology. Steelmaking, including secondary steelmaking, is concerned with liquid-state process-ing. The reactors are semi-batch types, with the exception of the tundish, which is close to acontinuous stirred tank reactor. In semi-batch reactors, the liquids are added and withdrawn inbatches, whereas the gases flow in and out of the reactors continuously. Solid reagents are eitheradded in batches or injected continuously as powder.

Besides chemical reactions, some physical and physico-chemical processes are of importancein secondary steelmaking, i.e., homogenization of composition and temperature, separation of non-metallic particles from steel melt, loss and gain of heat content of the melt, and dissolution ofalloying elements. The rate of processing would be governed by the rates of these processes.

The rate of processing, which includes refining of the steel melt, is controlled by one or moreof the following

• kinetics of reactions among phases• mixing in the melt• feed rate of reactants• rate of heat supply to the reaction zone

The above listing excludes external factors such as shop logistics. Temperature control is asimportant as composition control in secondary steelmaking. However, the issue of temperaturecontrol is dealt with in Chapter 8. Homogenization of temperature of the steel melt is primarilydependent on convective heat transfer, which is akin to convective mass transfer. Hence, knowledgeof one can be utilized for the other. Rates of specific reactions and processes are discussed in laterchapters.

Dissolution of alloying additions in molten steel is partly controlled by rate of heat suppliedto the cold addition. There are other minor examples. However, all other reactions in secondarysteelmaking are not limited by the rate of heat supplied to the reaction zone. Therefore, we areprimarily concerned with reaction kinetics, mixing, and the feed rate of reactants. In this connec-tion, the ternary diagram in Figure 4.1, proposed by Robertson et al.,1 in connection with powderinjection processes in a secondary steelmaking ladle, is quite illustrative. Near corner 1, reactionsare close to chemical equilibrium, and the liquid is well mixed. Hence, feeding rate of powderedreagents is going to control the process rate. Near corner 2, powder mixing and feeding are fast.Hence, control is by reaction rate, which is slower. Near corner 3, mixing is the slowest, andtherefore is rate controlling.


1


The present chapter is a brief presentation of the fundamentals of kinetics, mixing, and masstransfer with specific reference to steel melt in a ladle, stirred by inert gas through a nozzle/porousplug from the bottom. The kinetics of specific reactions and processes is dealt with in later chapters,as already stated. So far as basics are concerned, standard texts are available.2–4 Ghosh and Ray5

also have briefly presented topics relevant to extractive metallurgy.

4.2 MIXING IN STEEL MELTS IN GAS-STIRRED LADLES

4.2.1 FUNDAMENTALS OF MIXING

Section 3.2 dealt with fluid flow in steel melts in gas-stirred ladles. This section is concerned withmixing in steel melts in gas-stirred ladles. Mixing is dependent on the nature and intensity of fluidmotion and turbulence in the melt. As in Section 3.2, here also we consider only inert gas purgingby porous plugs/nozzles fitted at the bottom of the vessel. Also in the area of mixing, experimentalinvestigations with steel melts have not been done often. Fundamental investigations have been

2

3

feedingrate

controls

feeding + reaction

feeding +mixing

feeding,reaction

and mixing

mixing ratecontrols

reaction + mixing

reaction rate controls

powder dumping

Σt = tf + tr + tmix

tmix / Σ t t r / Σ t

t f / Σ t

23

1

equi

libriu

m

at

xx =

0perfectly m

ixed

FIGURE 4.1 Ternary diagram showing the influence of the three possible rate-determining processes duringpower injection refining.1

conducted mostly in laboratory water models. Again, a majority of the studies employed axisym-metric nozzles. In this section, only the fundamentals are emphasized. Mixing in various industrial


situations is presented in other sections wherever information is available.There have been numerous physical and mathematical modeling studies of mixing in the last

15 to 20 years. Some good review papers have also been published6–8 in recent years. Comprehensiveliterature is available in the chemical engineering field.9–10 In view of these considerations, thenumber of references has been kept limited.

Mixing occurs by convection (i.e., bulk flow), turbulent (i.e., eddy) diffusion, and moleculardiffusion. Experimentally, the speed of mixing is measured by pulse-tracer technique. A smallquantity of tracer is suddenly added into the liquid at some location. The concentration of the traceris monitored at some other location in the liquid using a measuring probe. In water models, aqueoussolution of KCl or HCl are popular tracers. Dissolved KCl or acid increases electrical conductivityof water. Hence, its concentration at any location can be measured as a function of time by theelectrical conductivity probe.

Imagine the sudden addition of a tracer into a liquid. Bulk motion would transport the tracer-rich liquid region, known as clump, to other regions. It also causes disintegration of the clump intosmaller and smaller eddies as it moves through the liquid. Dispersion of eddies by eddy diffusioncauses further mixing. The disintegration of clumps, however, can not continue indefinitely. Asdiscussed in Section 3.1.5, with decreasing eddy size, viscous forces increasingly resist furtherdisintegration of eddies. There is a smallest size beyond which there will be no further disintegration.At this stage, macromixing of the tracer is complete. However, the liquid is still not perfectly mixed,and concentration inhomogeneities exist on a microscopic scale. Further homogenization of com-position (i.e., micromixing) is possible by molecular diffusion only.

Molecular diffusion is an extremely slow process. Hence, micromixing is unattainable inindustrial processing as well as in studies on mixing. Therefore, perfect mixing would meancomplete macromixing only, and it occurs by a combination of bulk motion and turbulent diffusion.Equation (3.27) has defined turbulent viscosity (µ t). In an analogy with this, turbulent diffusivity(Dt) can be defined. Combining contributions of bulk flow and turbulent diffusion to mixing, thevectorial form of the equation is:

(4.1)

where Ci is concentration of tracer i at time t after tracer addition. refers to rate of change ofconcentration at a location (say, the probe location).

Figure 4.2 presents a typical recorder voltage-time curve for addition of KCl solution into acylindrical water bath stirred by blowing air from the bottom using an axisymmetric nozzle.8,11 Thechange in the concentration of KCl at the probe location was proportional to the change of recordervoltage. Hence, the curve represents the variation of concentration of KCl over time at the probelocation. Major oscillations in the recorder trace are due to recirculatory flow. The peak-to-peakinterval for major peaks is the approximate time for one recirculation (tC) and was about 8 s inFigure 4.2. The amplitude of oscillation decreases rapidly with time due to the progressive disin-tegration of clumps as the bulk liquid recirculates.

Experimentally, mixing speed is determined by measuring the mixing time (tmix) of a smallquantity of tracer added into a liquid suddenly. It is difficult to measure tmix for 100 percentmacromixing. Hence, some standardization is desirable. In this connection, degree of mixing (Y)has been defined as:

(4.2)

∂Ci

∂t-------- u ∇ Ci ∇ Dt∇ Ci( )⋅+⋅=

∂Ci

∂t--------

YCi Ci

o–

Cif Ci

o–------------------=


where is the instantaneous average concentration at any time t, is the uniform initialconcentration before tracer addition, and is the uniform final concentration at the end of mixing.

Y = 0.95 (i.e., 95 percent mixing) has been generally accepted for defining mixing time.However, Krishnamurthy et al.,11 in their fundamental investigation, employed Y = 0.995. (Figure4.2).

The statistical theory of mixing10 predicts that

tmix = a constant × log(1 – Y) (4.3)

Krishnamurthy12 has shown that, for various experiments,8,11 Equation (4.3) tends to predict asomewhat lower value of tmix than experimental measurement. It is an indication that the mixingprocess is controlled both by bulk convection and turbulent diffusion.

The higher the gas flow rate, the more intense would be stirring and consequent mixing, resultingin lower tmix. This is well established. Krishnamurthy et al.8 made comprehensive measurements oftmix at several combinations of tracer injection and probe locations in their water model and obtaineda single value of tmix under a given experimental condition.

However, several investigators6 found that tmix is dependent on tracer addition and monitoringpoint locations. Such a phenomenon was observed at relatively low specific gas flow rates, typicalof ladle metallurgy. Figure 4.3 presents mixing time vs. gas flow rate at different measuring positionsin a water model with centric bottom gas injection, showing significant dependence of tmix on probelocation.13 The degree of mixing was taken as 95 percent.

4.2.2 VARIABLES INFLUENCING MIXING

It has been already mentioned, in Section 3.2.3, that hydrodynamic conditions near the nozzle orplug are not critical to flow recirculation in large cylindrical vessels. A similar comment is applicableto mixing in the liquid bath. So, it does not matter whether one employs a nozzle or porous plug.However, the location and number of nozzles/plugs have significant influence on mixing.7,8,14 Figure4.4 presents the results of a water model study by Joo and Guthrie.14 They employed a porous plug.It shows tmix as a function of nondimensional radial coordinate (r/R), where r = 0 at center and r= R at the vessel wall. The minimum value of tmix was obtained at mid-radius (i.e., r/R = 0.5).

It is occasionally necessary to bubble an industrial ladle with two or more plugs to achievegentle but rapid mixing to promote slag-metal reaction, but to avoid explosive bubble bursting.This is achieved by employing a multiplug/multinozzle gas purging arrangement. Minimum mixing

FIGURE 4.2 A typical recorder voltage-time trace showing mixing time at two different degrees of mixing.11

Ci Cio

Cif


time with dual plugs was obtained if the two plugs were located at diametrically opposite positionsat mid-radius (Figure 4.4). Modern industrial gas-stirred ladles are fitted with plugs this way.

It was mentioned in Sec. 3.2.3 that a slag layer at the top of a steel melt is expected to causea loss of energy and slow down the recirculatory flow.15 Evidence for this has been gathered fromwater model experiments (Figure 3.18). Hence, it is expected that mixing would be slower in thepresence of top slag, in contrast to that in a bath with free surface. A significant increase of tmix

due to the presence of an oil layer on top of the water bath has been confirmed by investigators.6,16

As shown in Figure 4.3, increasing gas flow rate (Q) promotes mixing and decreases tmix. Ithas also been found that tmix decreases as bath height (H) increases, provided H/D < 2, where D isthe vessel diameter. In steel ladles, H/D < 2, and hence the above conclusion is applicable. It has

FIGURE 4.3 Mixing time vs. gas flow rate (centric nozzle, tracer addition in dead zone). 1, 2, and 3 =locations of concentration measurement.13

FIGURE 4.4 Plot of mixing time vs. radial position for a single plug for various gas flow rates.14

also been found to depend on

D

as well as nozzle diameter (

d

n

). Properties of a liquid such asviscosity, density, and surface tension are also expected to influence

t

mix

.


Under a specified condition, Qn is proportional to the rate of buoyancy energy input (εb) asgiven in Eq. (3.62). As already stated, εb has been accepted as a measure of the rate of energy inputinto the bath due to gas flow. εb per unit mass of liquid, i.e., εm, as defined by Eq. (3.64), is thepopular parameter employed.

Several quantitative relations have been proposed about the dependence of tmix on εb, H, andD. These are semi-empirical, based partly on mathematical analysis and partly on experimentaldata. Measurements in molten steel are very limited. Experimental data have been collected pri-marily in water models.

Mathematical analysis of the mixing process is based on the following models.

The Turbulence Model

This was first developed by Nakanishi, Szekely, and Chiang17 for turbulent recirculatory flow. Theassumption was that mixing was solely controlled by eddy diffusion. Besides the equations ofcontinuity and motion, another differential equation for eddy diffusion of the tracer was set up.The eddy diffusivity was set equal to eddy kinematic viscosity.

The empirical correlation of Nakanishi et al.18, fitted with measurements from an argon stirredladle, RH degasser, water model, etc., is based on the concept of a turbulence model, which tendsto suggest that tmix should depend only on εm. The correlation of Nakanishi et al. was as follows:

(4.4)

As explained in Section 3.1, εm is the rate of buoyancy energy input per unit mass of the liquid.However, Nakanishi et al.18 also included bubble expansion energy in εm, which gave a value twiceas large as that of buoyancy energy. Moreover, εm was in watts/tonne. Correcting for a factor oftwo and taking εm in watts/kilogram, Eq. (4.4) may be rewritten as

(4.5)

However, this turbulence model tended to predict that mixing time was independent of vessel size,vessel geometry, and mode of stirring. Hence it could not explain experimental observations.

Equation (4.3) may be rewritten as

1 – Y = exp(–tmix/to) (4.6)

For 95 percent mixing, 1 – Y = 0.05, and tmix/to ≈ 3. Murthy and Szekely,19 on the basis of postulationsmade by some earlier workers, argued that the energy dissipation rate due to turbulence is only afraction of εm, and they related to to H and D. Combining all these, they tried to explain thedependence of to on H and D. It was also predicted that .

Another difficulty with the turbulence models is their inability to explain the oscillating natureof concentration vs. time curves upon addition of a tracer (Figure 4.2). Again, the natures of thesecurves are dependent on probe location. Mazumdar and Guthrie20 carried out extensive mathematicaland physical modeling and arrived at the conclusion that all experimental behavior patterns can beexplained only if it is assumed that mixing is controlled by both convection and turbulent diffusion.Prediction of mixing times by numerical solution of differential equations also has been carriedout recently.14,21

tmix 800em0.4–=

tmix 38.3em0.4–=

tmixα εm1 3⁄–

Circulation Models


These models assume that the circulation rate of liquid in the bath controls mixing. Here, to is takenas equal to the time required for one circulation of the liquid (tc).

Sano and Mori22 were the first to employ this approach, which explained the dependence oftmix on H and D, as observed experimentally. Krishnamurthy et al.,23 through their macroscopicenergy balance model, proposed equations for calculation of tc. Combining that with their experi-mental values of tmix (Y = 0.995), they found that

(4.7)

The above approaches could not quantitatively explain the concentration versus time curves (Figure4.2), which was attributed to existence of dead zones and different flow regimes in the vessel.Hence, these were subsequently refined by dividing the vessel into several tanks and assumingcomplete mixing within any tank. These have successfully explained the concentration versus timecurves.12,13

Several mixing time correlations have been proposed by various investigators.6 In the earlystudies, no standardized degree of mixing was employed. It is necessary to assess how the differentcorrelations compare with one another. For this, in Table 4.1 we have selected only those in whichY = 0.95 and which have been arrived at or tested against experimental data of water model withcentric gas injection through a nozzle.

Figure 4.5 presents calculated curves of tmix vs. εm by various correlations of Table 4.1 for awater model of 0.5 m diameter and 0.4 m height at a temperature of 298 K, and atmosphericpressure of 1 bar. εm was calculated by Eq. (3.64). For comparison, the empirical correlation of[Eq. (4.5)] has also been included.

Although some investigators18,21 have tried to suggest that their correlations may be appliedeven to liquid iron, others have proposed a scale factor. An examination of the literature21 tends tosuggest that experimental values of tmix in liquid steel are somewhat larger than those in a watermodel at same values of εm, D, and H. Asai et al.25 have suggested that, for design purposes, tmix

should be measured in carefully designed water models and then be multiplied by a factor of 1.9for liquid steel (i.e., [ρFe/ρw]1/3).

4.3 KINETICS OF REACTIONS AMONG PHASES

Metallurgical reactions are almost exclusively heterogeneous in nature, where reactions occuramong phases. Examples are solid–liquid reactions, slag–metal reactions, and gas–metal reactions.Consider the following reaction occurring between molten steel and molten slag:

TABLE 4.1Mixing Time Correlations for 95 Percent Degree of Mixing

Reference Correlation

Mazumdar and Guthrie20

Stapurewicz and Themelis24

Neifer, Rodi, and Sucker21

Circulation number Ci( )tmix

tc

------- f Frm, HD----,

dn

D-----

= =

tmix 12.2εm0.33– H 1.0– D1.66=

tmix 11.1εm0.39– H0.39=

tmix 3.2Q 0.38– H 0.64– D2.0=


[S] + (O2–) = (S2–) + [O] (4.8)

S and O denote sulfur and oxygen, [ ] indicates metal phase, and ( ) indicates slag phase. Sinceslag is ionic in nature, S and O are presumed to exist there as S2– and O2–, respectively.

The above exchange reaction actually takes place as a coupled electrochemical half-cell reac-tions as follows at the slag–metal interface.

[S] + 2e– = (S2–) (4.9)

(O2–) = [O] + 2e– (4.10)

Reactions (4.9) and (4.10) occur at different sites at the slag–metal interface. Electron transfer fromone site to another takes place via liquid metal, which is an electrical conductor. This is shownschematically in Figure 4.6. The overall process consists of several steps, known as kinetic steps,shown in Figure 4.6. They are as follows:

FIGURE 4.5 Comparison of tmix vs. mixing energy plots obtained from various correlations.

FIGURE 4.6 Electrochemical mechanism of slag–metal interfacial reaction.

1. Transfer of sulfur from the bulk of the metal phase to the slag-metal interface2. Transfer of O2– from bulk of the slag phase to the interface


3. Chemical reaction at the interface 4. Transfer of oxygen from the interface to the bulk metal 5. Transfer of S2– from the interface to the slag phase

Step (3) is a chemical reaction and is governed by the laws of chemical kinetics. Other steps aregoverned by laws of mass transfer.

The above kinetic steps for the reaction shown in Eq. (4.8) are all in series. If any one of themis prevented, the overall reaction ceases to occur. It is also to be noted that the slowest kinetic stepwould tend to influence the rate predominantly, and it is typically termed the rate-controlling orrate-limiting step. The conclusions drawn above would be just the reverse if the kinetic steps werein parallel, where the fastest step would influence the overall rate the most. However, it is impossibleto conceive of a process where all the steps would be in parallel. Hence, it may be concluded thatthe slowest step in the series would be the primary rate-controlling step.

From the above viewpoint, the slowest step is the most important one. A major objective of allkinetic studies is to find out what the slowest step is. Of course, other kinetic steps would alsoinfluence the overall process rate to some extent. At times, two or more steps may have comparablerates. However, owing to the complexity of the steelmaking processes, one kinetic step is oftenassumed to control the rate, and others are assumed to be infinitely fast and thus at virtualequilibrium. With this simplification, the rate of a process estimated on the basis of only the slowestkinetic step would be the highest, and larger than the actually observed rate. Such an estimatetherefore is termed as virtual maximum rate (VMR). VMR calculations often provide great insight.

4.3.1 INTERFACIAL CHEMICAL REACTION

The fundamentals of gas–metal, slag–metal, and metal–gas–slag reactions in steelmaking can bebest understood on the basis of the findings of laboratory experiments carried out over the pastseveral decades. Here, the system is isothermal and each phase is well mixed. Hence, studies haveprovided information on reaction kinetics exclusively.

The laboratory findings have been that steelmaking reactions are generally controlled by masstransfer at the phase boundary, and not by interfacial chemical reaction. This is expected fromtheoretical considerations as well. However, there are exceptions, the most notable being absorptionand desorption of nitrogen by molten steel, which is a case of mixed control kinetics, i.e., bothinterfacial reaction and mass transfer partially controlling the rate of overall reaction. With theabove background in mind, very little is written here on the kinetics of interfacial chemical reaction.The kinetics of a nitrogen reaction is discussed more elaborately in Chapter 6.

Suppose the heterogeneous reaction is

A + B = C + D (4.11)

Then, according to the law of mass action, the rate of reaction (r) may be related to concentrationsof reactants (A, B) and products (C, D) as

(4.12)

where A is area of interface of the phases involved, CA etc. denote concentrations of respectivespecies per unit volume (i.e., mol/vol or mass/vol.), kc is the chemical rate constant, and K is theequilibrium constant for Reaction (4.11).

r Akc CACB

CCDD

K--------------–

=

Equation (4.12) is the rate expression for a reversible reaction, where both forward andbackward rates are significant. For an irreversible process, the backward rate is much smaller than


the forward rate and can be ignored. Then,

r = Akc CA CB (4.13)

Actually, theoretical predictions of rate expressions are either impossible or very difficult. Hencethey are determined experimentally. For example, for Reaction (4.11), suppose the experimentallydetermined rate expression is

(4.14)

Then, α + β = the order of reaction.Again, kc increases with an increase in temperature. Experimentally, it has been found that the

following relationship holds true in a limited range of temperatures:

(4.15)

where T is temperature and A, B are empirical constants. Arrhenius attempted to explain thisobservation through his famous equation as

(4.16)

where E is known as activation energy, R is Universal gas constant, and A is a preexponential factor.Although, in principle, A and E can be estimated with the quantum mechanical approach, it is

difficult and unreliable. Hence, A and E are determined experimentally. The Arrhenius equation istheoretically also valid for other molecular transport processes such as diffusion and viscous flow.Hence, it is not restricted to chemical reactions. E has a clear-cut theoretical meaning only if onekinetic step exclusively controls the rate. Wherever that is not true, E is not the true activationenergy but is just a temperature coefficient of some sort.

4.3.2 MASS TRANSFER

Mass transfer is concerned with the transfer of a chemical species from higher to lower concen-tration. Mixing, already discussed in Section 4.2, is also a process of mass transfer. It is a questionof terminology only. By mixing, we mean mixing in the bulk fluid. By perfect mixing, onlymacromixing was meant, and molecular diffusion was ignored.

In contrast, the motion of individual atoms and molecules is our ultimate concern in masstransfer. Hence, molecular diffusion is also important. In Figure 4.6, transport of O, S, O2– and S2–

are mass transfer processes adjacent to the slag–metal interface. In general, it is known as phase-boundary mass transfer. Actually, it is these transports in connection with heterogeneous reactionsthat constitute the principal application of the subject of mass transfer in science and engineering.

The general equation for mass transfer of species i along the x-direction may be written as:

(4.17)

r AkcCAα CB

β=

kCln ABT---–=

kC AE

RT-------–

exp=

Ji x,mi x,

Ax

--------- Di

∂Ci

∂X-------- Ciux Dt

∂Ci

∂X--------–+= =

molecular

diffusion

bulk

convection

turbulent

diffusion+ +

where Ji,x = flux of species i along the x-direction

dmi


= = mass rate of transport of species i along x

Ax = area normal to the x-directionDi = molecular diffusivity of species i in the fluidCi = concentration of species i in mass per unit volume

= time-averaged fluid velocity along the x-direction

Dt = turbulent or eddy diffusivity

Phase-boundary mass transfer processes may be classified as

• Mass transfer at the solid-fluid interface• Mass transfer between two fluids

Mass Transfer at the Solid-Fluid Interface

In solids, molecular diffusion is the only mechanism of mass transfer. It is extremely slow. Hence,in steelmaking vis-a-vis extraction and refining processes in general, we ignore it and assume thecomposition of solid to be constant. On the fluid side of the interface, the existence of a velocityboundary layer has already been discussed (Figure 3.3). In a similar fashion, a concentrationboundary layer develops in the fluid adjacent to the solid surface (Figure 4.7).

Just at the interface, we may assume = 0 and, due to laminar flow, Dt = 0. This simplifiesEq. (4.17) as

(4.18)

Noting that Ax is solid surface area (A), and through the geometric construction shown in Figure 4.7,

(4.19)

mi dt---------

ux

SCi

Ci

Coi

(Solid)

x = 0

(Fluid)

Concentration profile

x

δC, eff

FIGURE 4.7 Concentration boundary layer in fluid adjacent to a solid surface during mass transfer.

ux

mi ,x

Ax

--------at x 0=

Di–∂Ci

∂x--------

x 0=

=

mi( )at interface ADi

δc eff,----------- Ci

s Ci0–( ) Akm ,i Ci

s Ci0–( )= =

δc,eff is known as the effective concentration boundary layer thickness and km,i is the mass transfercoefficient for species i . δc, eff depends on fluid flow. The more intense the flow, theDi δc, eff⁄( )


smaller is δc,eff with larger km,i and . This is how fluid flow influences rate. km,i also depends onthe transport properties of the fluid (µ, ρ, D), and the geometry and size of the system. A measureof size is characteristic length (L), which, for example, is the diameter for a pipe or sphere, asalready mentioned in Table 3.1.

To estimate mass transfer rates, km,i is to be estimated or determined. Experimental measure-ments have been carried out on a variety of systems. Dimensionless correlations are very advan-tageous, and this is how km,i is correlated with fluid flow, etc. Table 4.2 presents the dimensionlessnumbers for convective mass transfer. The symbols have already been defined in Chapter 3 inconnection with Table 3.1.

In general,

Sh = B + D Rem Scn, for forced convection (4.20)

and

Sh = B´ + D´ Grm´ Scn´, for free convection (4.21)

For fixed geometry, B, B´, D, D´, m, n, m´, and n´ are constants within ranges of Re, Sc, and Grm.

They are mostly the same for analogous heat transfer situations, and some typical mass transfercorrelations have been obtained from analogous heat transfer correlations. Prandtl’s number (Pr)should be replaced by Sc, and Nusselt’s number (Nu) by Sh for this purpose. Such dimensionlesscorrelations are available for several geometries and flow regimes in standard texts.2,3,5 They aremostly empirical.

Appendix 3.1 contains values of µ, ρ, and ν for some liquids of interest in secondary steel-making. Appendix 4.1 presents some values of the diffusion coefficient.

Mass Transfer between Two Fluids

The reaction between two fluids is exemplified by those of molten metal with molten slag, moltensalt, or gas. The boundary layer theory of convective mass transfer has been highly successful at

TABLE 4.2Common Dimensionless Numbers in Convective Mass Transfer

Dimensionless Number

Item Definition Name Symbol

Fluid flow (forced convection) Reynolds no. Re

Fluid flow (free convection) Grasshof no. Gr

Mass transfer properties Schmidt no. Sc

Mass transfer coefficient Sherwood no. Sh

Note: ν = µ/ρ = kinematic viscosity of the fluid.

mi

Luν

------

gL3

ν2-------- ∆ρ

ρo

-------

νD----

kmL D⁄

solid–fluid interfaces. Attempts have been made to extend the same to the two-fluid situation byassuming the existence of a concentration boundary layer on both sides of the interface. It is all


right in some cases. But, by and large, there is a problem. At a solid–fluid interface, the fluid layerat the interface sticks to the solid. Therefore, it is stagnant and not renewed. Moreover, turbulencecannot reach the interface.

However, these assumptions are not valid at fluid–fluid interfaces. Davies26 has dealt withvarious aspects of turbulence phenomena, behavior of eddies, and their role on mass transfer.Turbulence at the interface of two fluids tends to get damped due to the resistive action of surfacetension. The damping effect is pronounced in the direction perpendicular to the surface, but not somuch in parallel direction. Levich considered this damping and proposed the following correlation:

(4.22)

where uo is the fluctuating RMS velocity in the bulk of the liquid, and σequiv is equivalent surfacetension, defined as

(4.23)

where σ is the surface/interface tension and l is the eddy mixing length. However, the boundary layer approach is incapable of taking into account continuous renewal

of the interface layer due to fluid motion. This led to the development of the various surface renewaltheories of mass transfer between two fluids. Out of these, only two are popular. Higbie assumedthat eddies penetrate into the interfacial layer and renew the interface periodically. Each eddy isexposed for the same time before replacement by a fresh eddy arriving from the bulk. During thisperiod, mass transfer is by unsteady diffusion.

Higbie’s surface renewal theory is also applicable when the flow at the interface is laminar. Ifthe viscosity of one fluid is much larger than that of the other, then the former exhibits a negligiblevelocity gradient near the interface and flows like a rigid solid. For example, in a gas–liquid system,the liquid near the interface would flow like a rigid body, since it has a much higher viscosity ascompared to that of the gas. Similarly, in a slag–metal system, the slag would tend to flow like arigid body. In such situations, mass transfer at the interface in the high viscosity phase would beexclusively by molecular diffusion. Since the surface gets renewed continuously due to flow at theinterface, such diffusion is unsteady, and it was derived that

(4.24)

where te is the exposure time, i.e., the time spent by a fluid element at the interface. In turbulent flow also, application of Higbie’s model is straightforward, provided that we assume

the same value of te for all eddies and te is known. However, behavior of eddies is more probabilistic,and not all eddies are expected to spend the same time at the interface before replacement by afresh eddy from the bulk. Danckwerts made a more realistic assumption that a fraction of surfacerenewal in time t is equal to [1 – exp(–St)]. Figure 4.8 shows the difference between Higbie’s andDanckwerts’ models schematically.

On the basis of the above model, Danckwerts derived that

km,i = (Di S)1/2 (4.25)

S is known as surface renewal factor. It is the rate of renewal of the surface in terms of the fractionof surface renewed per second. In this model, S is to be determined experimentally and is, therefore,

km,i 0.32Di1 2⁄ uo

3 2⁄ ρ1 2⁄ σequiv1 2⁄–=

σequiv σ l2ρg 16⁄( )+=

km ,i 2Di

πte

-------

1 2⁄

=


a source of uncertainty. S varies between 5 to 25 per second for mild turbulence, and up to 500per second for violent turbulence.26

All the above models predict that km should be proportional to D1/2. This is in contrast toboundary layer theory, which predicts a dependence on D0.7–1. In chemical engineering, manyinvestigators attempted to verify validity of this for mass transfer in liquid at gas-liquid and liquid-liquid interfaces. The proportionality of km on D1/2 has been verified, and surface renewal mode isgenerally accepted now.26

In the metallurgical field, one of the earliest investigations was by Boorstein and Pehlke.27 Theymeasured dissolution rates of hydrogen and nitrogen in inductively stirred liquid iron. Stirringintensity was varied. It was found that

in quiescent melt, and

for well-stirred melts, thus indicating the applicability of boundary layer theory for the former, andsurface renewal theory for the latter. More studies in the metallurgical field will be presented later,at appropriate places. It would suffice to summarize here that surface renewal theory is generallyemployed for correlation of experimental results for a two-fluid situation.

The rate of surface renewal increases with jump frequency of eddies, which varies from a fewper second for large eddies to about 1000 per second or more for the smallest (i.e., Kolmogoroveddies). At normal and gentle turbulence, S ranges between 5 to 25 per second, and hence surfacerenewal is expected to be primarily by large (i.e., Prandtl) eddies. Visual observations also haveconfirmed this.26 This is because smaller eddies tend to get damped considerably near the interfaceunless turbulence is intense. One of the earliest attempts to determine S in a metallurgical situationwas the water model study by Kumar and Ghosh,28 who measured rate of absorption of CO2 inwater by the pH method and also estimated liquid–gas bubble surface area by a photographictechnique. They found S to range from 40 to 100 per second.

Investigations in the chemical engineering field have established that there is no significantdifference between gas–liquid and liquid–liquid mass transfer, either in basic mechanisms or evenin some quantitative relationships (e.g., in a stirred tank with one liquid stirred).26

FIGURE 4.8 Distribution of turbulence eddies on the surface according to the postulates of Higbie (1935)and Danckwerts (1951).

km H,

km N,----------

DH

DN

-------=

km H,

km N,----------

DH

DN

-------

1 2⁄

=

Robertson and Staples29 proposed the following empirical correlation for the metal-phase masstransfer coefficient for a mercury-water and molten lead-molten salt system stirred from the bottom


by inert gas:

km = 172 D1/2 Q1/2 R (4.26)

where R is the vessel radius in meter, km is in ms–1, D is in m2 s–1, and the volumetric gas flow rateQ is in m3 s–1.

Taniguchi et al.30 measured the rate of CO2 absorption at the free surface of a water bath stirredby nitrogen from the bottom and proposed the following relationship for km in the water phase:

km = 138 D1/2 Q1/2 R (4.27)

The resemblance of Eqs. (4.26) and (4.27) may be noted, although the former is for liquid–liquidand latter for liquid–gas reaction.

The presence of surface active species on the surface would retard the motion of fresh eddiescoming from the bulk liquid, as shown in Figure 4.9a. This would lead to a lowering of the valueof km as compared to that for a clean surface. A decrease of km by a factor of two for gas–liquidsituation, and even by a factor of four for liquid–liquid mass transfer, has been observed.26 A reversesituation is shown in Figure 4.9b, where fresh eddies bring surface active species from the bulk.Here, surface flow is enhanced. This is known as Marangoni effect, after Marangoni, who firstdiscovered it in the 19th century. It may even cause spontaneous interfacial turbulence. Richardsonand coworkers at the Imperial College conducted several studies on this.31,32

FIGURE 4.9 Interfacial (a) retardation or (b) enhancement of movement induced by surface pressure.

4.4 MASS TRANSFER IN A GAS-STIRRED LADLE


4.4.1 SOLID-LIQUID INTERACTIONS

The addition of lump solids or the injection of solid powders is required in ladle refining andelsewhere in secondary steelmaking. Addition of ferroalloys is an example. Melting-cum-dissolutionof these alloys is controlled by rates of heat and mass transfer. Section 4.3.2 briefly presented thebasics of mass transfer in fluid adjacent to a solid–fluid interface. The dimensionless correlationsare of the type presented in Eqs. (4.20) and (4.21).

For example, mass transfer correlation around a solid sphere in forced convection is given bythe famous Ranz–Marshall equation as follows:

Sh = 2 + 0.6 Re1/2 Sc1/3 (4.28)

where the characteristic length is the diameter of sphere (d), and the characteristic velocity is thetime-averaged bulk velocity.

For convective heat transfer around the sphere, the analogous equation is:

Nu = 2 + 0.6 (Re)1/2 (Pr)1/3 (4.29)

where Nu =

Pr =

h = surface heat transfer coefficient, analogous to kλ = thermal conductivityα = thermal diffusivityC = specific heat of the fluid

Experiments have been done by several investigators in water models of a ladle, stirred by gasfrom the bottom. Gas injections were centric. The rates of the melting of ice and the dissolutionof benzoic acid in water were studied. Solids were immersed in various locations, too. A few studiesin molten steel are also available. Mazumdar and Guthrie6 have reviewed these. In a recentinvestigation, Iguchi et al.33 employed an electrochemical technique.

Several dimensionless correlations have been proposed in the literature. Controversy existsabout their relative merits and reliability. Hence, a detailed presentation is omitted here. The firstdifficulty in the determination of a dimensionless correlation of experimental data is that there isno characteristic bulk velocity in a gas-stirred liquid. Hence, local velocity and local Reynold’snumber were employed. This requires solution of the turbulent Navier-Stokes equation to obtainthe velocity field.

It also has been established that an equation of the type of Eq. (4.20), such as Eq. (4.28) fora sphere, is obeyed provided intensity of turbulence (I) is less than 0.2 or so. At higher values ofI, these equations tend to give a better fit with experimental data by incorporating I in the co-relations. All investigators are in agreement on this.

For example, Mazumdar et al.34 measured the rates of dissolution of vertical cylinders of benzoicacid in a gas-stirred water model and proposed the following relationship:

Sh = 0.73 (Reloc,r)0.57 (I)0.32 (Sc)0.33 (4.30)

where

hLλ

------

να--- µC

λ-------=

(4.31)Reloc ,rux

2 uy2+( )

1 2⁄D⋅

------------------------------------=


and x and y are horizontal coordinates, and D is the diameter of the cylinder. On the other hand, for a sphere, Iguchi et al.33 proposed a modified version of the Ranz–Marshall

equation as follows:

Sh = 2 + 0.6 Re(0.5+0.1 I) · Sc1/3 (4.32)

For 103 < Re < 104, 0.3 < I < 0.5. At I < 0.3, Eq. (4.28) was found to be adequate. It may be furthernoted30 that Eq. (4.30) predicts that km ∝ Q0.2 approximately, where Q is the volumetric gas flowrate. This is in agreement with experimental data for dissolution of steel cylinders in carbon-saturated iron melts.35

4.4.2 LIQUID–LIQUID INTERACTIONS

Kinetic studies carried out in connection with various ladle metallurgy operations include thereaction between a gas bubble and liquid, slag–metal reactions, and absorption of gases at a freesurface and in a plume’s eye. Fundamental studies have been primarily conducted in room tem-perature models. Not all of these are discussed in this chapter. Reactions and mass transfer betweena gas bubble and liquid is dealt with in Chapter 6, on degassing. Absorption of gases at a plumesurface is taken up in connection with deoxidation kinetics and clean steel.

There have been plant studies of the kinetics of specific reactions such as desulfurization. Thesealso will be taken up in later chapters. In this section, we are briefly concerned with somefundamental laboratory investigations on mass transfer between two liquids in a vessel stirred bybubbling inert gas from bottom. Obviously, the metallurgical objective is to understand slag–metalreaction in bubble-stirred systems. Basic open hearth steelmaking, which was the dominant primarysteelmaking process up to the 1960s, constituted the principal target for early workers across theWorld. Richardson32 and Turkdogan36 have reviewed them.

A principal difficulty of fundamental study is that the actual slag–metal interfacial area (A) islarger than the geometrical surface area due to unevenness of the interface formation of slag–metalemulsion. A is a function of gas flow rate, etc. Moreover, it is a difficult task to properly determineit. Hence, experimental rate measurement yields the value of the kA parameter, where k is specificrate constant. When mass transfer is rate controlling, then k = km and we obtain the km A parameteron the basis of Eq. (4.19). km A has a dimension of (ms–1 × m2), i.e., m3 s–1. Sometimes the kmA/Vparameter of dimension s–1 is preferred, where V is the volume of the concerned liquid. However,kmA is a more fundamental parameter as compared to kmA/V.

In gas-stirred systems, broadly speaking, the kmA parameter has been found to be proportionalto Qn.Value of n has been found to be different in different ranges of gas flow rate. This isdemonstrated by the study of Kim et al.37 as shown in Figure 4.10. Inert gas was injected frombottom axisymmetrically. Oil simulated the slag phase, and water simulated the metal phase. Theequilibrium partition coefficient of thymol between oil and water is very large—somewhat like thepartition of sulfur between slag and metal. This made the kinetics unambiguously controlled bymass transfer in the metal phase.

Figure 4.10 shows three regimes in ln(kA) vs. Q curve, with different values of n. At a lowflow rate, n = 0.6. Some other investigators have also reported n = 0.529,30. Visual observations didnot reveal any perturbation in the oil layer. In the middle regime n = 2.51, and the oil layer nearthe edge of the plume eye continuously formed ligaments and disintegrated into droplets. In regimeIII, the entire oil layer was found to be dispersed in water as droplets. A lower value of n there isexplained by the large residence time of droplets in water in this regime and their consequent

ν


saturation with thymol, retarding further transfer. Since Q is proportional to εm according to Eq.(3.64), .

Formation of oil-in-water and slag-in-metal emulsion increases the liquid–liquid interfacial areaby even a factor of about 100. Consequent large enhancement in kA parameter has been wellestablished. The mechanism of drop formation is shown schematically in Figure 4.11.38 When theinertia force due to liquid circulation exceeds surface tension and buoyancy force at slag layer onplume edge, slag droplets form. Mietz et al.38 have also demonstrated an almost proportionateincrease of the mass transfer rate with the extent of slag emulsification.

An important parameter in this context is the critical (i.e., minimum) gas flow rate, Qcr, requiredfor emulsion formation. Kim et al.37, based on dimensional analysis and their experimental data,proposed the following empirical equation:

(4.33)

where H is the height of metal bath, ρs is the density of the slag (upper) phase, is the densitydifference between the two liquids, and σms is interfacial tension between metal and slag.

FIGURE 4.10 kA vs. gas flow rate for mass transfer between two liquids in a vessel stirred by axisymmetricgas injection from the bottom.37 Reprinted by permission of Iron & Steel Society, Warrendale, PA, U.S.A.

km Aαεmn

FIGURE 4.11 Principles of slag emulsification in steel ladles. (a) Scheme of the detaching process, and (b)equilibrium between inertia force Fc, buoyancy force Fg cos α, and surface force Fσ at the point of dropletdetachment. Source: from F. Oeters, Metallurgie der stahlherstellung, Verlag stahleisen, Düsseldorf, 1989.

Qcr 0.035H1.81 σms ∆ρρs

2------------------

0.35

=

∆ρ

Iguchi et al.39 have performed comprehensive cold model experiments with several liquidssimulating slag to determine the critical condition for entrapment of slag in metal, and they proposed


the following empirical correlation:

(4.34)

where,

= 1.2ur p–0.28

V = (σms g/ρs)1/4 ur = (g Qcr/Hm)1/3

p = [Qcr2/(gHm

5)]1/5

The subscripts s and m denote slag and metal, respectively. denotes critical centerline velocity.D is vessel diameter. Here also, gas injection was through a centric nozzle. Agreement with earlierinvestigators’ results was reasonable.

Sahajwalla et al.40 have reviewed some of these studies, including their own experimental work.They found that εm in watts/kilogram, as given in Eq. (3.64), ranged between 0.065 and 0.13 at Qcr

for various investigators.Attempts have been made to examine the validity of surface renewal theory for liquid–liquid

reactions in gas-stirred ladles. It has already been mentioned that Robertson et al29 and Taniguchiet al30 verified km α D1/2, and some other aspects (Section 4.3.2). Hirasawa et al41 applied thetheory of turbulent mass transfer phenomena26 to their own investigation of the reaction of silicondissolved in molten copper with molten slag containing FeO at 1250°C, as well as to the experi-mental data of Robertson et al.29 on mercury amalgam-aqueous solutions and molten lead–moltensalt systems. Figure 4.12 shows a typical vs. Q plot for a molten Cu-slag system.

Comparison of Figures 4.10 and 4.12 reveals that, in a molten Cu–slag system, region II hasa lower dependence on Q, in contrast to a room-temperature model study. This was explained withthe help of flow patterns in slag and metal (Figure 4.13). At low Q, the slag was stagnant due to

ucr ,c V⁄ 1.2 νs νm⁄( )0.068 Hs D⁄( ) 0.11–=

ucr ,c

ucr ,c

FIGURE 4.12 Relationship between apparent mass transfer coefficient ( ) and gas flow rate.41k ′ si

k ′ si


its higher viscosity. At higher Q (region II), slag flow, as shown in Figure 4.13, retarded interfacialflow of liquid metal, causing this behavior pattern. Region III, of course, was due to an increaseof the slag–metal interfacial area. Therefore, only region I could be analyzed by the turbulencetheory and dimensionless correlations developed.

Ogawa et al42 simulated a gas-stirred ladle as well as induction stirring in their water modelstudies. Using KCl and Benzoic acid as solute, they found that approximately. Figure4.14 shows as a function of εm · V–2/3, where V is bath volume. Calculation based onEq. (4.25) yielded values of S in the range of 15 to 8000 per second. While the lower value is all

FIGURE 4.13 Schematic representation of the flow patterns in a slag–metal bath.41

km ,i Di1 2⁄∝

1020

50

100

200

500

1000

2000

20 50 100 200 500 1000

Gas bubbling

Induction stirring (upward)Induction stirring (downward)

Ar bubbling (85 ton)

ASEA-SKF (85 ton)

ε V -2/3 , watt t-1 m -2

km/

Di,min-√2

FIGURE 4.14 Relationship between km/(Di)1/2 and ε V–2/3.42

km ,i Di1 2⁄∝

right, the higher values are abnormally large and not expected (Section 4.3). Presumably, these arebased on the kmA parameter, rather than km and, hence, not indicators of true values of s.


4.5 MIXING VS. MASS TRANSFER CONTROL

The pragmatic approach to kinetic calculations in steelmaking is to take the rate equation as thatof a first-order process, estimate the rate constant from experimental data, and then use it judiciously.Consider removal of an impurity element (i), dissolved in liquid steel. Then, material balance fori leads to

(4.35)

for a first-order reversible reaction. Here, V and A are the volume and interfacial area of the melt.Ci is the instantaneous concentration of i in the melt, and is the concentration in equilibriumwith the phase in contact with steel (slag or gas).

Integrating Eq. (4.35) between (i.e., initial concentration) and t = t, Ci = Ci,

(4.36)

where a = A/V = specific interfacial area

For irreversible processes, is very small, and Eq. (4.36) reduces to

(4.37)

Convective mass transfer at the phase boundary may be treated as a first-order reversible processwith , , and in Eq. (4.35). The justification for taking is theassumption that the rate of interfacial reaction is very fast and not rate controlling. Hence, chemicalequilibrium at the interface may be assumed.

The term (1 – X) in Eqs. (4.36) and (4.37) is a measure of the extent of impurity removal. Forexample when X = 0.05, 1 – X = 0.95, which means that 95% of solute i has been eliminated fromthe steel melt. Based on some literature values of kma, Ghosh43 plotted log X vs. t for a few reactionsin steelmaking (Figure 4.15). It may be noted that 95% refining required only 40 to 260 seconds,demonstrating very high rates of steelmaking reactions.

Statistical theory also treats mixing as a first-order reversible process [Eqs. (4.2) and (4.3)].Here, Cf is equivalent to the final equilibrium concentration. Y = 0.95 means a 95 percent degreeof mixing and is attained when t = tmix according to convention. A scan of the literature revealedthat tmix ranged between 50 and 500 seconds for a variety of processes in steelmaking. Inhomogeneityin the melt due to dead volumes may show mixing times as high as 103 s in some locations.

Thus, mixing time and 95 percent conversion time for mass transfer controlled reactions arein the same overall range in steelmaking processes. Since both have rate expressions as for first-order reversible processes, it is often difficult to say whether a process is controlled by slow mixingor slow mass transfer. In the context of slag–metal reaction in a gas-stirred ladle, it has beenconcluded by all that, when stirring is vigorous and slag–metal emulsion forms, mass transfer isfaster than the rate of mixing.

VdCi

dt--------– Ak Ci Ci

e–( )=

Cie

t 0, Ci Cio= =

Ci Cie–

Cio Ci

e–------------------ln 1 X– kat–= =

Cie

Ci

Cio

------ln 1 X– kat–= =

km k= Cis Ci

e= Cio Ci= Ci

s Cie=

1.0


Szekely et al.44 considered the modified Biot number (Bim), defined as

(4.38)

Their sample calculation for typical gentle stirring in a ladle yielded Bim of approximately 10–1 to10–2. This they considered as low and concluded that the desulfurization reaction would be masstransfer controlled. Mietz and Bruhl45 carried out model calculations for mass transfer with mixingmetallurgy in a ladle for sulfur removal. Their principal conclusion was that mixing would be theslower process if dead volumes are not avoided for both gentle and strong stirring.

Equations (4.36) and (4.37) have been derived by considering rate control either by interfacialchemical reaction or mass transfer in one phase only. However, there are situations when we mayhave to take into account the control of a reaction rate jointly by mass transfer in both phases. Inthat case, Eq. (4.19) is to be employed for both phases (I and II) as follows.

(4.39)

Again, assuming interfacial equilibrium,

(4.40)

where Li is the equilibrium partition coefficient of species i between phase II and phase I. Combining Eqs. (4.39) and (4.40),

(4.41)

50 100 150 200 250

TIME, sec

(Purging ladle, immersed lance)

Slag - metal reaction(LD)

H_C_ - O_reaction (BOH)

removal

0.5

0.1

0.05

0.01

Ci - Cie

Cio

- Cie

FIGURE 4.15 Estimated X vs. time plots for some steelmaking reactions.43

Bim

km A( ) H⋅Deff

------------------------=

mi mi( )at interface Akm ,iI Ci

S ,I Cio ,I–( )= =

Akm ,iII Ci

II CiS ,II–( )=

CiS ,II

CiS ,I

---------- Li=

miA

1

km ,iI

-------- 1

km ,iII Li

------------+---------------------------- Ci

o ,I Cio ,II

Li

----------– Akm ,i

I II– Cio ,I Ci

o ,II

Li

----------– = =

REFERENCES


1. Robertson, D.G.C., Ohguchi, S., Deo, B., and Willis, A., Proc. SCANINJECT III, Part 1, MEFOS,Lulea, Sweden, 1983, p. 8.1.

2. Szekely, J., and Themelis, N.J., Rate Phenomena in Process Metallurgy, Wiley-Interscience, JohnWiley & Sons Inc., New York, 1971.

3. Geiger, G.H., and Poirer, D.R., Transport Phenomena in Metallurgy, Addison-Wesley Publishing Co.,Reading, MA, 1980.

4. Levenspiel, O., Chemical Reaction Engineering, John Wiley & Sons, Inc., New York, 1962. 5. Ghosh, A., and Ray, H.S., Principles of Extractive Metallurgy, Wiley Eastern Limited, New Delhi,

1991. 6. Mazumdar, D., and Guthrie, R.I.L., ISIJ International, 35, 1995, p. 1. 7. Oeters, F., Plushkell, W., Steinmetz, E., and Wilhelmi, H., Steel Research, 59, 1988, p. 192. 8. Krishnamurthy, G.G., and Mehrotra, S.P., Ironmaking and Steelmaking, 19, 1992, p. 377. 9. Danckwerts, P.V., Applied Science Research, 3, 1953, p. 279.

10. Nagata, S., Mixing Principles and Applications, published jointly by Kodansha Ltd. Tokyo and JohnWiley & Sons Inc., New York, 1975.

11. Krishnamurthy, G.G., Mehrotra, S.P., and Ghosh, A., Metall. Trans.,19B, 1988, p. 839. 12. Krishnamurthy, G.G., ISIJ Int., 29, 1989, p.49. 13. Mietz, J., and Oeters, F., Steel Research, 59, 1988, p.52. 14. Joo, S., and Guthrie, R.I.L., Metall. Trans., 23B, 1992, p.765. 15. Mazumdar, D., Nakajima, H., and Guthrie, R.I.L., Metall. Trans., 19B, 1988, p.507. 16. Haida, O., Emi, T., Yamada, S., and Sudo, F., Proc. SCANINJECT II, MEFOS, Lulea, Sweden, 1980,

p. 20.1. 17. Nakanishi, K., Szekely, J., and Chiang, C.W., Ironmaking and Steelmaking, 3, 1975, p. 115. 18. Nakanishi, K., Fujii, T., and Szekely, J., Ironmaking and Steelmaking, 3, 1975, p. 193. 19. Murthy, A., and Szekely, J., Metall. Trans., 17B, 1986, p. 487. 20. Mazumdar, D., and Guthrie, R.I.L., Metall. Trans., 17B, 1986, p.725. 21. Neifer, M., Rodi, S., and Sucker, D., Steel Research, 64, 1993, p. 54. 22. Sano, M., and Mori, K., Trans. ISIJ, 23, 1983, p. 169. 23. Krishnamurthy, G.G., Ghosh, A., and Mehrotra, S.P., Metall. Trans., 20B, 1989, p.53. 24. Stapurewicz, T., and Themelis, N.J., Can. Met. Quarterly, 26, 1987, p. 123. 25. Asai, S., Okamoto, T., He, J., and Muchi, I., Trans ISIJ, 23, 1983, p. 43. 26. Davies, J.T., Turbulence Phenomena, Academic Press, New York, 1972. 27. Boorstein, M., and Phelke, R.D., Trans. AIME, 245, 1969, p. 1843. 28. Kumar, J., and Ghosh, A., Trans. Indian Inst. Metals, 30, 1977, p. 39. 29. Robertson, D.G.C., and Staples, B.D., Process Engg. Of Pyrometallurgy, ed. M. Jones, Inst. Min. Met.

London, 1974. 30. Taniguchi, S., Okada, Y., Sakai, A., and Kikuchi, A., Proc. 6th Int. Iron and Steel Cong., Nagoya,

1990, 1, p. 394. 31. Brimacombe, J.K., Proc. Richardson Conference, eds. J.H.E. Jeffes and R.J. Tait, Inst. of Min. and

Met., London, 1973. 32. Richardson, F.D., Physical Chemistry of Melts in Metallurgy, 2, Academic Press, London, 1974. 33. Iguchi, M., Tomida, H., Nakajima, K., and Morita, Z., ISIJ International, 33, 1993, p. 728. 34. Mazumdar, D., Kajani, S.K. and Ghosh, A., Steel Research, 61, 1990, p. 339. 35. Mazumdar, D., Verma, V., and Kumar, N., Ironmaking and Steelmaking, 19, 1992, p. 152. 36. Turkdogan, E.T., Physical Chemistry of High Temperature Technology, Academic Press, New York,

1980. 37. Kim, S.H., Fruehan, R.J., and Guthrie, R.I.L., Steelmaking Proceedings, Iron and Steel Soc., USA,

1987, p. 107. 38. Mietz, J., Schneider, S., and Oeters, F., Steel Research, 62, 1991, p. 1. 39. Iguchi, M., Sumida, Y., Okada, R., and Morita, Z., ISIJ International, 34, 1994, p. 164. 40. Sahajwalla, V., Brimacombe, J.K., and Salcudean, M.E., Steelmaking proceedings, Iron and Steel

Soc., USA, 72, 1989, p. 497. 41. Hirasawa, M., Mori, K., Sano, M., Shimatani, Y., and Okazaki, Y., Trans. ISIJ, 27, 1987, p. 277.

42. Ogawa, K., and Onoue, T., ISIJ International, 29, 1989, p. 148. 43. Ghosh, A., Tool and Alloy Steels, 25, 1991, Silver Jubilee issue, p. 65.


44. Szekely, J., Carlsson, C., and Helle, L., Ladle Metallurgy, Springer Verlag, New York, 1989.45. Mietz, J., and Bruhl, M., Steel Research, 61, 1990, p. 105.

5 Deoxidation of Liquid Steel

Steelmaking is a process of selective oxidation of impurities in molten iron. During this, however,the molten steel also dissolves some oxygen. Solubility of oxygen in solid steel is negligibly small.Therefore, during solidification of steel in ingot or continuous casting, the excess oxygen is rejectedby the solidifying metal. This excess oxygen causes defects such as blowholes and nonmetallicinclusions in castings. It also has significant influence on the structure of the cast metal.

Therefore, it is necessary to control the oxygen content in molten steel before it is teemed.Actually, the oxygen content of the bath in the furnace is high, and it is necessary to bring it downby carrying out deoxidation after primary steelmaking and before teeming the molten metal intoan ingot or continuous casting mold. This chapter is concerned with thermodynamics and kineticsof deoxidation, and finally on industrial deoxidation.

5.1 THERMODYNAMICS OF DEOXIDATION OF MOLTEN STEEL

The dissolution of oxygen in molten steel may be represented by the equation

(5.1)

where [O] denotes oxygen dissolved in the metal as atomic oxygen. For the above reaction,

(5.2)

where KO is equilibrium constant for Reaction (5.1), denotes partial pressure of oxygen in thegas phase in atmosphere, and hO is the activity of dissolved oxygen in liquid steel with referenceto the 1 wt.% standard state. KO is related to temperature as1

(5.3)

Again,

(5.4)

where WO denotes the concentration of dissolved oxygen in weight percent, and fO is the activitycoefficient of dissolved oxygen in steel in 1 wt.% standard state. In pure liquid iron,

12---O2 g( ) O[ ]=

KO

hO

pO2

1 2⁄---------

equilibrium

=

pO2

logKO6120

T------------ 0.15+=

hO f O[ ]= W O[ ]


(5.5)

log f O 0.17 W O[ ]=


The above relations would allow us to estimate WO in liquid iron at any value of with whichthe molten iron would be brought to equilibrium. This value of WO is nothing but solubility of [O]at that . However, oxygen tends to form stable oxides with iron. Therefore, molten iron becomessaturated with [O] when the oxide starts forming, i.e., when liquid iron and oxide are at equilibrium.This oxide, in its pure form, is denoted as FexO, where x is approximately 0.985 at 1600°C. Forthe sake of simplicity we shall take x equal to 1 often and designate this compound as FeO.

For the reaction FexO(1) = xFe(1) + [O]wt.%.,

(5.6)

where

(5.7)

Here, aFe = the activity of Fe in the metal phase in the Raoultian scale (approximately 1), and denotes the activity of FexO in oxide phase. If the FeO is not pure and is present in an oxide slag,then aFeO < 1, and h (i.e., solubility of [O] in equilibrium with the slag) would be less.

Example 5.1

Calculate the concentration of oxygen in molten iron at 1600°C in equilibrium with (a) pure FexO,and (b) a liquid slag of FeO-SiO2 containing 40 mol.% SiO2.

Solution

or,

(E1.1)

Again, at 1600°C, from Eq. (5.6),

log KFe = –0.672 (E1.2)

(a) In pure FeO, aFeO = 1, and hence combining Eqs. (E1.1) and (E1.2) and solving,

WO = 0.233 wt.% (Ans.)

(WO at 1550°C and 1650°C are 0.185 and 0.29 wt.%, respectively)

(b) In liquid FeO-SiO2 slag at 1600°C and at ( denotes mole fraction of SiO2

in FeO-SiO2), aFeO = 0.43.

pO2

pO2

logKFe6150

T------------– 2.604 (Ref. 1)+=

KFe

hO aFe[ ] x×[aFexO

-----------------------------

equilibrium

= (Ref. 1)

aFexO

KFehO[ ]

aFeO( )---------------

FO[ ] W O[ ]aFeO( )

-------------------------= =

0.17– logW O logaFeO–+=

logKFe log f O logW O logaFeO–+=

XSiO20.4= XSiO2

Solving Eqs. (E1.1) and (E1.2), we obtain:


WO = 0.10 wt.% (Ans.)

The traditional method of determination of oxygen in steel samples is chemical analysis byvacuum fusion or inert gas fusion apparatus. Here, a sample of solidified steel is taken in a graphitecrucible and then heated to approximately 2000°C under vacuum or under a highly purified inertatmosphere. The steel sample melts and the oxygen contained in it reacts very fast with the crucibleand generates carbon monoxide. The quantity of CO is measured by a sensitive instrument suchas an infrared analyzer, and from it the quantity of oxygen in the sample is estimated. This apparatushas been made quite accurate and reasonably fast.

Analyses of alloying elements in steel are done very quickly and conveniently using an emissionspectrometer. Commercial development of the instrument has recently been reported wherein theoptical wavelength range has been extended to the ultraviolet region, enabling the determinationof total oxygen as well. This would eliminate the need for separate sampling and analysis. However,the author is not aware of relative precision and reliability of these two techniques.

In industrial melts, the bath not only contains dissolved oxygen but also oxide particles.During freezing, solidifying steel rejects most of its dissolved oxygen, which forms additionaloxide particles, and these are also retained by the solid as inclusions. The above methods ofdetermination give the total oxygen content, which is the sum of dissolved O and oxygen ininclusions. This hampered progress of our understanding about the behavior of oxygen in steel-making and deoxidation until the development of immersion oxygen sensors based on ZrO2 anddoped with CaO or MgO during the decade of the 1960s. Thereafter, this has become quite apopular tool for the measurement of dissolved oxygen content in molten steel, both in thelaboratory and in industry. Excellent reviews are available in the literature on the principles anddetails of such sensors.2–5

For the sake of illustration, Figure 5.1 shows the sensor employed by Fruehan et al.3 schemat-ically. The ZrO2 (CaO) or ThO2 (Y2O2) disk served as the solid electrolyte, and at high temperatureit is an ionic conductor with O2– as the only mobile ionic species. The Cr + Cr2O3 mixture is the

FIGURE 5.1 Sketch of an oxygen sensor.3

reference electrode. This assembly is immersed into liquid steel. Molten steel constitutes the otherelectrode. A molybdenum-Al

2

O

3

cermet was dipped into it, and the electrical circuit was completed


by platinum lead wires connected to the measuring circuit. These sensors can be used only once,i.e., they are a disposable type. Immersion time required is less than a minute. Efforts are goingon to develop sensors that can be continuously immersed in liquid steel for a longer period.Laboratory successes have been reported.

Such sensors behave as reversible galvanic cells. Since the solid electrolyte conducts oxygenions only, the cell electromotive force (EMF) is related only to the difference of the chemicalpotentials of oxygen at the two electrodes.

(5.8)

where designates the chemical potential of oxygen, F is Faraday’s constant, Z is valence (4,here) and E is cell EMF.

The galvanic cell in Figure 5.1 may be represented as

(5.9)

With reference to Section 2.7,

(5.10)

and

(5.11)

Combining the above equations,

(5.12)

Therefore, knowing (Cr2O3) and KO from the literature, the cell EMF allows us to calculate [hO].With reference to Section 2.6.2, [fO] can be estimated from chemical analysis of steel. Therefore,the content of dissolved oxygen (i.e., WO) can be obtained from Eq. (5.4).

Several designs of commercial oxygen sensors are now on the market. A popular one is CELOX,marketed by Electro-Nite n.v., Belgium. It has been jointly developed by CRM, Belgium, andHoogovens Ijmuiden B.V., along with Electro-Nite.6 The cell is

(5.13)

The solid electrolyte is in the form of a tube with one end closed.

µO2(liquid steel) µO2

(reference)– Z– FE=

µO2

(reference) (solid electrolyte)

Cr s( ) Cr2O3 s( )+ ZrO2 CaO+ O[ ] (in liquid steel)

∆G fo for formation of Cr2O3 s( ) per mole O2=

µO2(reference) RT pO2

ln (reference)=

23---∆G f

o Cr2O3( )=

µO2 (liq. steel) RT pO2

ln (in equlibrium with liq. steel)=

2RThO

KO

-------ln (from Eq. 5.2)=

2RThO

KO

-------ln23---∆G f

o Cr2O3( )– 4FE–=

Mo Cr Cr2O3+ ZrO2 MgO( ) liq. steel Fe

All such sensors also contain immersion thermocouples as well so that the temperature ofmolten steel is also recorded simultaneously. At steelmaking temperatures, the solid electrolyte


exhibits partial electronic conduction, especially at a low level of dissolved oxygen. The measuredcell voltage of the cell of type illustrated by Expression (5.13) would also include thermo-EMFdue to use of dissimilar leads, viz., Mo and Fe. The manufacturer provides correction terms for it.

In pure liquid iron, the solubility of oxygen is governed by either Eq. (5.2) or (5.7). However,in molten steel, there are other more reactive alloying elements such as C, Si, and Mn. The oxygensolubility is governed by reaction with one or more of these elements. It has been well establishedthat the carbon content of steel has a considerable influence on bath oxygen content at the end ofheat in steelmaking furnaces. The reaction is

(5.14)

The value of equilibrium constant (KCO) is given as.1

(5.15)

Figure 5.2 shows the relationship between dissolved carbon and dissolved oxygen in a moltensteel bath in a 100 kVA induction furnace. The equilibrium line corresponds to pCO = 1 atm at1600°C. Dissolved oxygen contents were measured by a solid electrolyte oxygen sensor with twotypes of reference electrodes.

5.1.1 THERMODYNAMICS OF SIMPLE DEOXIDATION

Deoxidation of liquid steel is carried out mostly via ladle, tundish, and mold. Even in a furnace,deoxidizers are often added directly into the metal bath. In all these cases, the product of deoxi-dation, which is an oxide or a solution of more than one oxide, forms as precipitates.

Deoxidation never occurs at a constant temperature. The temperature of molten steel keepsdropping from furnace to mold. The addition of a deoxidizer also causes some temperature changedue to heat of reaction. However, we shall consider it as isothermal. This will not affect our

C[ ] O[ ]+ CO g( ); KCOpCO

hc[ ] ho[ ]--------------------= =

logKCO1160

T------------ 2.003+=

FIGURE 5.2 Dissolved oxygen content of liquid iron as a function of bath carbon at 1873 K in a 100 kVAinduction furnace.4

considerations of deoxidation equilibria, since only the final temperature at which the equilibriumis supposed to be attained is of importance. Thermodynamically, it would not make any difference


if the process were presumed to take place at that temperature. Deoxidation may be carried out by addition of one deoxidizer only. This is known as simple

deoxidation. In contrast, we may use more than one deoxidizer simultaneously and, in that case,it will be termed a complex deoxidation. In this section, we will discuss simple deoxidation. Adeoxidation reaction may be represented as

x[M] + y[O] = (MxOy) (5.16)

where M denotes the deoxidizer, and MxOy is the deoxidation product. The equilibrium constant( ) for reaction (5.16) is given as

(5.17)

Again, on the basis of Eq. (2.46), hM = fM · WM and hO = fO · WO.If the deoxidation product is pure, then = 1. Also, in very dilute solutions, fM and fO may

be taken as 1. Hence, Eq. (5.17) may be rewritten as

(5.18)

where KM is known as deoxidation constant.Obviously, WM and WO, as already understood, are weight percentages of [M] and [O], respec-

tively, at equilibrium with pure oxide. It may be noted that KM is like the solubility product in anaqueous solution. It is a measure of solubility of the compound MxOy in molten steel at thetemperature under consideration.

As in Eq. (5.6), variation of KM with temperature may be represented by an equation of the type:

(5.19)

where A and B are constants. Equation (5.19) shows that as T increases, log KM and hence KM alsoincrease. In other words, the solubility of MxOy in molten steel increases with temperature. Since,in deoxidation, we are interested in lowering the concentration of oxygen with the addition of aslittle deoxidizer as possible, an increase in temperature would adversely affect the thermodynamicsof the process.

Experimental determination as well as thermodynamic estimation of KM for various deoxidizershave been going on for the last four or five decades. With advancements in science and technology,more accurate values are being found with the passage of time. This has led to a number ofcompilations, some old and some new, where efforts have been made to record the most acceptablevalues. The exercise is still going on, and discrepancies still exist, especially with more reactiveelements such as Al, Zr, Ce, Ca, etc. Appendix 5.1 presents such a compilation taken from that ofthe 19th Steelmaking Committee of the Japan Society for Promotion of Science,1 as well as fromother sources.7–9

It may be noted that all oxide products are definite compounds except for deoxidation bymanganese, where the product is either a solid or a liquid solution of FeO-MnO of variablecomposition. The underlying reason for this behavior is the fact that manganese is a weak deoxidizer,

K ′ M

K ′ M

aMxOy( )

hM[ ] x hO[ ] y--------------------------

equilibrium

=

aMxOy

W M[ ] x W O[ ] y 1K ′ M

--------- K M= =

logK MAT--- B+–=

since the stability of MnO, although greater than that of FeO, is not drastically different from thatof the latter (Figure 2.1).


For deoxidation by Mn, it is in a way more appropriate to consider the reaction

(MnO) + [Fe] = [Mn] + (FeO) (5.20)

Fe and Mn form an ideal solution (i.e., one that obeys Raoult’s law). The same is true of theMnO-FeO slag. Therefore, aMnO = XMnO, aFeO = XFeO, and hMn = WMn. Noting that aFe = 1, theequilibrium constant for Reaction (5.20) is

(5.21)

where X denotes mole fraction. Equation (5.21) shows that in the deoxidation productwould be proportional to WMn at constant temperature. Figure 5.3 shows the relationship. The oxideproduct is liquid at low and solid at high values.

Example 5.2

Consider deoxidation by addition of ferromanganese (60 percent Mn) to molten steel at 1600°C.The initial oxygen content is 0.04 wt.%. It has to be brought down to 0.02 wt.%. Calculate thequantity of ferromanganese required per tonne of steel. The manganese content of steel beforedeoxidation is 0.1 wt.%.

Solution

Consider the following reaction:

(MnO) = [Mn] + [O]; KMn = (E2.1)

K Mn Fe–hMn[ ] aFeO( )×

aMnO( )-----------------------------------

W Mn[ ] XFeO( )XMnO( )

--------------------------------= =

XMnO XFeO⁄

FIGURE 5.3 Composition of liquid or solid FeO-MnO solution in equilibrium with liquid iron containingmanganese and oxygen.9

hMn[ ] ho[ ]aMnO( )

-----------------------

As noted earlier, hMn may be taken as WMn, and aMnO as XMnO. Assuming also that hO = WO,


(E2.2)

From Appendix 5.1,

i.e., at 1600°C (1873 K), KMn = 0.041.Noting that the final WO = 0.02 wt.%,

(E2.3)

Now from Eq. (5.21),

(E2.4)

From Appendix 5.1,

that is, at 1873 K,

KMn-Fe = 0.15

Therefore, combining Eqs. (E2.3) and (E2.4),

or,

or,

Now, the total quantity of Mn required = Mn required to form MnO

+ Mn required to increase the Mn-content of bath

from 0.1 to 1.90 wt.%

W Mn[ ]XMnO( )

-----------------K Mn

W O[ ]-------------=

logK Mn–11070

T------------------ 4.536+=

W Mn[ ]aMnO( )

---------------- 2.05=

W Mn[ ]XMnO( )

-----------------K Mn Fe–

XFeO( )-----------------=

logK Mn Fe–6980

T------------ 2.91+– (assuming the product to be solid MnO – FeO)=

XFeO 0.073=

XMnO 1 XFeO– 0.927= =

W Mn 1.90 wt.%=

Now, the Mn required to form MnO per tonnne of steel


The Mn required to increase the Mn content of bath = (1.90 – 0.1) × 10–2 × 103 = 23.7 kg/t steel.

Total Mn required = 18.64 kg.

Total ferromanganese required . (Ans.)

From Figure 5.3, it is confirmed that the assumption of solid FeO-MnO as the deoxidationproduct is correct.

Taking the activity coefficients, viz., fO and fM, as 1, one would be able to calculate therelationship between [WM] and [WO] using Eq. (5.18) and Appendix 5.1 for many deoxidizers. Suchcalculations would be all right at very low values of WM. At higher ranges, it would give approximatevalues only, since fM and fO (especially fO) may deviate somewhat from 1. For more precisecalculations, therefore, first-order interaction coefficients are to be considered. The rela-tionship between activity coefficients and interaction coefficients follow from Chapter 2 and are asnoted below.

(5.22)

(5.23)

where j denotes all the alloying elements present in liquid steel. For example, if the steel containsC and Mn, then

(5.24)

Some values of interaction coefficients are tabulated in Appendix 2.3.Taking the logarithm of Eq. (5.18), we have

(5.25)

In a log WO vs. log WM plot, Eq. (5.25) would yield a straight line with a slope of –x/y. However,such linearities are not always expected if rigorous equations such as Eqs. (5.16), (5.17), (5.22),and (5.23) are employed. Calculated log WO vs. log WM curves for various deoxidizers in Figure5.4 demonstrate such nonlinearities.

Immersion oxygen sensors are nowadays widely employed in oxygen control during secondarysteelmaking, especially for deoxidation control. An associated use is estimation of dissolved alu-

Quantity of oxygen removed per tonne of steelAtomic mass of oxygen

---------------------------------------------------------------------------------------------------------------- XMnO Atomic mass of Mn××=

0.04 0.02–( ) 10 2– 103 0.927 55××××16

----------------------------------------------------------------------------------------------=

0.64 kg/t=

18.6410060---------×= 31.1 kg/ton steel=

eMj W j⋅

log f M eMj

j∑ W j⋅=

log f O eOj

j∑ W j⋅=

log f O eOO W O eO

C W C eOMn W Mn⋅+⋅+⋅=

logW O1y---logK M

xy--logW M–=


minum in molten steel.4,6 Since residual dissolved aluminum content is very low (0.005 to 0.05%),its determination by an emission spectrometer was unreliable in view of interference from Al2O3

inclusions. The analysis is time consuming, too. However, today’s commercially available spec-trometers are useful for the determination of dissolved aluminum content in steel. Measurementsare made on several spots of the sample. The minimum value is assumed to be from an inclusion-free spot and, in principle, acceptable as a measure of dissolved aluminum content.

The principle of the determination of [Al] using an oxygen sensor follows from the equilibriumof the following reaction, viz.,

Al2O3(s) = 2[Al] + 3[O] (5.26)

(5.27)

i.e.,

log KAl = 2 log hAl + 3 log hO (5.28)

With the value of log KAl from Appendix 5.1, and measured hO, the value of hAl can be obtained.Evaluation of fAl on the basis of Eq. (5.22) allows the determination of WAl.

Example 5.3

Consider the determination of dissolved oxygen in liquid steel using an oxygen sensor with a Cr-Cr2O3 reference electrode at 1600°C. What would be the value of hO if the EMF of the cell is–153 mV? Also calculate dissolved aluminum content. Ignore solute–solute interactions.

Solution

Combining Eqs. (5.8), (5.10), and (5.11),

FIGURE 5.4 Deoxidation equilibria in liquid iron at 1873 K.9

K Al hAl[ ] 2 hO[ ] 3, since aAl2O31= =

(E3.1)∆G fO 2

3---Cr2O3

, 2RThO

KO

-------ln– ZFE–=


From Appendix 2.1, at 1600°C (1873 K)

with R = 8.314 J mol–1K–1, Z = 4, F = 96,500 J volt–1 gm. equiv.–1, E = –0.153 V, from Eq. (5.3),KO = 2615 at 1873 K. Putting in the values and solving, hO = 0.0005.

From Appendix 5.1,

For 2Al + 3O = Al2O3(s); KAl = 2.51 × 10–14 = [WAl]2 [WO]3

WO is nothing but hO in the above equation, since solute–solute interactions have been ignoredin arriving at it.

Putting in the values in Eq. (5.12) and solving,

WAl = 0.0141 wt.% (Ans.)

Figure 5.4 shows that Mn is the weakest deoxidizer of all, and Al, Zr, etc. are very powerful.Deviation from the straight line for Mn deoxidation is caused by the variable composition of thedeoxidation product as well as the fact that the liquid FeO-MnO changes to solid FeO-MnO withhigher manganese content. Deoxidizers such as Al, Ti, Zr, etc. exhibit a minimum in the solubilityof oxygen. This behavior is due to the large negative value of (see Appendix 2.3) for theseelements. The situation has been analyzed by several authors, such as Ghosh and Murty,9 and suchminima have been quantitatively explained.

Differentiating Eq. (5.28) with regard to WAl,

(5.29)

or,

(5.30)

or,

(5.31)

Now,

(5.32)

(5.33)

∆G fO Cr2O3( ) 422.7 103×– J/mol; O2=

eCM

2d loghAl( )

dW Al

-----------------------d loghO( )

dW Al

----------------------+d logK Al( )

dW Al

------------------------ 0= =

2d logW Al log f Al+( )

dW Al

----------------------------------------------- 3d logW O log f O+( )

dW Al

---------------------------------------------+ 0=

22.303------------- 1

W Al

---------3

2.303------------- 1

W O

--------dW O

dW Al

------------ 2d log f Al( )

dW Al

----------------------- 3d log f O( )

dW Al

----------------------+ +⋅+⋅ 0=

log f Al eAlAl W Al eAl

O W O⋅+⋅=

log f O eOAl W Al eO

O W O⋅+⋅=

Substituting these in Eq. (5.31) and noting that interaction coefficients are constant,


(5.34)

At minimum oxygen solubility,

Hence,

(5.35)

where = WAl at oxygen minimum.

Equation (5.35) provides a simple relationship between WAl at oxygen minimum and theinteraction coefficients. As Appendix 2.3 shows, has a large negative value. This makes positive and small in magnitude and substantiates the statement made above that large negativevalues of are responsible for these minima.

On the basis of their exercise, the following analytical equation was proposed by Ghosh andMurty9 to describe the curves:

(5.36)

where is the second-order interaction coefficient.

Unlike conventional deoxidizers, the alkaline earths, viz., Ca and Mg, are gaseous at steelmakingtemperatures (pMg = 25 atm, and pCa = 1.8 atm at 1600°C). Moreover, they are sparingly solublein molten steel. The solubility of Mg is 0.1 wt.% at pMg = 25 atm, and that of Ca is 0.032 wt.%at pCa = 1.8 atm at 1600°C. As a result of poor solubility, as well as the extremely reactive natureof these elements, the equilibrium relationships between them and dissolved oxygen are difficultto determine experimentally, and there are uncertainties. Experimental measurements and assess-ment exercises of data are still continuing.10,11

Example 5.4

Consider deoxidation of molten steel by aluminum at 1600°C. The bath contains 1% Mn and0.1% C. The final oxygen content is to be brought down to 0.001 wt.%. Calculate the residualaluminum content of molten steel assuming that [Al] – [O] – Al2O3 equilibrium is attained. Alsotake into account all interaction coefficients.

Solution

log KAl = 2 log hAl + 3 log hO (5.28)

(E4.1)

dW O

dW A1

-------------

22.303------------- 1

W A1

---------- 2eAlAl 3eO

Al+ +⋅

32.303------------- 1

W O

-------- 2eAlO 3eO

O+ +⋅-------------------------------------------------------------–=

dW O

dW Al

------------ 0=

W Al•

1

2.303 eAlAl 3

2---eO

Al+

------------------------------------------–=

W Al•

eOAl W Al

•

eOM

logK M x logW M eMM W M⋅+( ) y logW O eO

M W M rOM W M

2⋅+⋅+( )+=

rOM

3 logW O eOMn W Mn eO

A1 W A1 eOC W C eO

O W O×+×+×+×+[ ]+

2 logW Al eA1Mn W Mn eA1

C W C eA1O W O eA1

A1 W A1×+×+×+×+[ ]=

Noting that WMn = 1, WC = 0.1, and WO = 0.001, and substituting the values in Eq. (E4.1) and takingKAl value from Appendix 5.1 and values of e from Appendix 2.3, we obtain


log [2.5 × 10–14] = 2 log WAl + 3 log 0.001 – 3.42 WAl – 0.06 (E4.2)

Taking a first guess as WAl = 0.01, a trial-and-error solution yields

WAl = 5.36 × 10-3 wt.% as the residual aluminum in the bath (Ans.)

5.1.2 THERMODYNAMICS OF COMPLEX DEOXIDATION

As already stated, if more than one deoxidizer is added to the molten steel simultaneously, it isknown as complex deoxidation. Some important complex deoxidizers are Si-Mn, Ca-Si, Ca-Si-Al,etc. Complex deoxidation offers the following advantages and is being employed increasingly fora better quality product.

1. The dissolved oxygen content is lower in complex deoxidation as compared to simpledeoxidation from equilibrium considerations. Consider deoxidation by silicon.

(5.37)

If only ferrosilicon is added, then the product is pure SiO2, i.e., = 1. On the otherhand, simultaneous addition of ferrosilicon and ferromanganese in a suitable ratio leadsto the formation of liquid MnO-SiO2. Consequently, is less than 1, and hence [WSi][WO]2 is less than that obtained by simple ferrosilicon addition. At a fixed value of WSi,therefore, WO, would be less in complex deoxidation.

2. The deoxidation product, if liquid, agglomerates easily into larger sizes and consequentlyfloats up faster, making the steel cleaner. This is what happens in many complex deox-idation such as in the example presented above.

3. Properties of inclusions remaining in solidified steel can be made better by complexdeoxidation, thus yielding a steel of superior quality. This will be discussed again later,in an appropriate place.

Equilibrium calculations involving complex deoxidation require data on activity vs. compositionrelationships in the binary or ternary oxide systems of interest, besides values of KM and . Theseare available for many systems.12 Figure 5.5 presents the activity-composition data for a MnO-SiO2

system. The activities are in Raoultian scale, whereas the composition has been expressed in termsof weight percent of SiO2. Figure 2.3 has presented isoactivity lines for silica in the ternary CaO-SiO2-Al2O3 system at 1550°C. Figure 5.6 shows the same for CaO and Al2O3. The activities weredetermined in the liquid slag region only.

For activity in oxide (i.e., slag) systems, the general discussions in Chapter 2 may be consulted.For complex deoxidation, the desired product should be within this liquid field. Thermodynamiccalculations involving complex deoxidation should aim at the following:

• Estimation of weight percentages of deoxidizing elements and oxygen remaining inmolten steel when equilibrium is attained

• Estimation of the composition of the deoxidation product in equilibrium with the above

Rigorous calculations pose difficulties for two reasons. First of all, the activity vs. compositiondata in oxide systems are not available in the form of equations. Secondly, interaction of more than

KSi

hSi[ ] hO[ ] 2

aSiO2( )

------------------------W Si[ ] W O[ ] 2

aSiO2( )

-----------------------------= =

aSiO2

aSiO2

eij


FIGURE 5.5 Activity vs. composition relationship in MnO-SiO2 melts; standard state are pure solid MnOand pure β-crystobalite. Source: Elliott et al., Ref. 4 of Chapter 2.

FIGURE 5.6 Activities of CaO and Al2O1.5 in CaO-Al2O3-SiO2 system at 1823 K. Source: Elliott et al., Ref.4 of Chapter 2.

one deoxidizer calls for an iterative procedure for the solution of Eqs. (5.22) and (5.23). Therefore,it is necessary to use a computer-oriented method. A major challenge is the minimization of


calculation errors. Turkdogan13 has carried out thermodynamic analysis for complex deoxidationby Si-Mn. Bagaria, Deo, and Ghosh14 have carried out thermodynamic analysis of simultaneousdeoxidation by Mn-Si-Al. Ghosh and Naik15 have done the same for deoxidation systems: Ca-Si-Al and Mg-Si-Al. Readers may refer to those works for details. Some salient findings by Ghoshand Naik are presented below.

Calculations were performed in the range where the deoxidation product is liquid CaO-SiO2-Al2O3 slag in the ternary diagram (Figure 2.3) at two temperatures. Figure 5.7 presents some resultsof calculations for a Ca-Si-Al system as log WO vs. log WM (M = Si or Al) curves for threecompositions of liquid deoxidation products. The dotted curves are based on rigorous calculations,taking into consideration all interaction coefficients. For the solid curves, h values were taken tobe the same as weight percent, i.e., the interaction coefficients were ignored. The two curves differby about 20%. Thermodynamically, the complex deoxidizer was found to be, at most, an order ofmagnitude more powerful than simple deoxidation by Al or Si.

The above exercise is important from the point of view of industrial application. Ignoring ofinteractions, i.e., taking hi = Wi, simplifies the calculation procedure in a significant way. The aboveanalysis shows that the kind of error one may encounter is tolerable for many applications. It isalso possible to predict thermodynamically the sequence of precipitation of deoxidation product,provided the process is treated as reversible. This issue is pertinent for deoxidation, where theproduct composition varies with time. An example of this approach is the work by Wilson et al.16

on a Fe-O-S-Ca system. Another is the analysis of a Fe-O-Ca-Al system by Faulring et al.17 Here,the hCa/hAl ratio in liquid iron determined the nature of the deoxidation product. This topic is takenup in Chapter 9 again in connection with inclusion modification.

Example 5.5

Consider deoxidation of molten steel by the simultaneous addition of ferromanganese and ferro-silicon at 1600°C. If the residual WO and WSi are, respectively, 0.01 and 0.1 wt.%, determine thecomposition of the deoxidation product and WMn in steel at equilibrium with the above conditions.Ignore interactions among elements in molten steel.

FIGURE 5.7 Some [wt.% O] vs. [wt.% M] and [hO] vs. [hM] relationships for [Al]-[O]-(Al2O3) and [Si]-[O]-(SiO2) equilibria for deoxidation by Ca-Si-Al at 1873 K.15

Solution

Consider deoxidation by Si (Eq. 5.37). Now,


KSi = 2.11 × 10–5 at 1600°C (Appendix 5.1), WSi = 0.1, and WO = 0.01

This yields .Assuming the deoxidation product as MnO-SiO2 and using Figure 5.5, the weight percent of

SiO2 in the deoxidation product is 41%, and therefore, MnO content is 59%. Also, aMnO is approx-imately 0.25.

Again, consider the reaction of Mn as in Example 5.2.

Substituting values for aMnO and WO, WMn becomes 1.33 wt.%. Therefore,

• The deoxidation product contains 41 wt.% SiO2 and 59 wt.% MnO.• The weight percent of Mn in steel = 1.33. (Ans.)

5.2 KINETICS OF THE DEOXIDATION OF MOLTEN STEEL

In Section 5.1, we were concerned with dissolved oxygen only. However, in industrial deoxidationpractice, dissolved and total oxygen both are of importance. Even if the former is low, the presenceof entrapped deoxidation products gives rise to inclusions in solidified steel. The products ofdeoxidation should be separated out from the molten steel before the latter solidifies, if a cleansteel is desired. Therefore, the subject of deoxidation kinetics is concerned with deoxidation reactionas well as separation of deoxidation products.

Studies of deoxidation kinetics started seriously in 196018 and are still continuing. Factorscontrolling the rates have been established reasonably well from theoretical considerations as wellas from experiments conducted in laboratories and plants. The availability of new equipment andtechniques has been of considerable help. In almost all studies prior to 1970, only total oxygencould be determined by sampling and vacuum or inert gas fusion analysis. Later investigators alsoemployed immersion oxygen sensors for the determination of dissolved oxygen in molten steel.The advent of electron probe microanalyzers allowed the rapid and easy determination of chemicalcompositions of inclusions in steel. Development of the Quantimet brought about a method forrapid determination of inclusion size, number, etc. By 1970, and even earlier, thermodynamicparameters for important deoxidation reactions were available that could provide a fair degree ofconfidence.

The basic behavior pattern of oxygen and inclusions from a furnace to solidification duringsteelmaking may be visualized with the help of Figure 5.8 from Plockinger and Wahlster.18 Thedissolved oxygen content decreases rapidly upon deoxidation in the ladle and keeps on decreasingall the way. Inclusion content in liquid steel becomes quite high in the ladle upon deoxidation,followed by decrease due to separation of the deoxidation product. Since steel has negligiblesolubility for oxygen, the dissolved oxygen in liquid steel also, upon solidification, could give riseto more inclusions. Therefore, the expected inclusion content in steel would always be higher inthe solid than in the liquid in a mold. To gain a greater understanding of the factors influencingthe rates, a number of fundamental investigations have been carried out from 1960 onward. Thesehave been done mostly in the laboratory under controlled conditions. Therefore, we shall firstdiscuss the findings of laboratory experiments.

Laboratory investigations have been carried out mostly with a small melt (on the order of afew kilograms of steel) and under inert atmosphere. High-frequency induction furnaces were

aSiO20.47=

K Mn 0.053W Mn[ ] W O[ ]

aMnO( )-----------------------------= =


normally employed for maintaining steel molten at the desired temperature. If the steel is directlyheated by a high-frequency power source, then an eddy current flows through it. This eddy currentand the magnetic field of the induction coil generate force, which causes the flow and circulationof molten steel. This is known as induction stirring. On the other hand, if the ceramic cruciblecontaining the steel is surrounded by a hollow cylinder of graphite or molybdenum, then the eddycurrent flows primarily through the latter and heats it up. Then, the steel is heated up indirectly byradiative and convective heat transfer from the hot cylinder. In this case, induction stirring of moltensteel may be made negligibly small, and the bath would be a quiet one.

Discussions of deoxidation kinetics as conducted in the laboratory may be subdivided into:

1. kinetics of deoxidation reaction2. kinetics of elimination of deoxidation products from liquid steel

5.2.1 KINETICS OF DEOXIDATION REACTION

The kinetics of a deoxidation reaction consists of the following steps (or stages):

1. dissolution of deoxidizer into molten steel 2. chemical reaction between dissolved oxygen and deoxidizing element at phase boundary

or homogeneously 3. nucleation of deoxidation product 4. growth of nuclei, principally by diffusion

Rates of deoxidation reaction have been followed by many investigators13,19 by monitoring thechange in the dissolved oxygen content of molten steel over time. Figure 5.9 shows dissolved [O]as well as total oxygen content of molten steel as a function of time for deoxidation by electrolytic

FIGURE 5.8 Change of oxygen and inclusion content of steel from furnace to ingot.


manganese. It shows that the dissolved [O] decreases much more rapidly than the total oxygen.This behavior pattern has been found by all investigators. Turkdogan et al13 found deoxidationreaction with Si to be complete more or less within two minutes. Recent investigations by Kunduet al.20 and Patil et al.21 have demonstrated that Si-O-SiO2 equilibrium is attained within five minutesof the addition of ferrosilicon into an induction stirred laboratory melt. But it takes almost 20minutes for the total oxygen content to achieve a steady state.21 Olette et al.19 carried out deoxidationby the addition of aluminum shots as well as by the injection of liquid aluminum (Figure 5.10)and found most of the reaction to be complete within one minute.

FIGURE 5.9 Change of oxygen content of molten steel following the addition of manganese.19

FIGURE 5.10 Effect of the method of introduction of aluminum on dissolved oxygen in molten steel.19

Scrutiny of Figures 5.9 and 5.10 grossly reveals two stages. Initially, the dissolved [O] decreasesrapidly in first 30 s or so. This is followed by the second stage, which exhibits a much slower rate


in the decrease of [O]. This behavior pattern has been explained resulting from the very high speedof three kinetic steps 2, 3, and 4 as listed above, which is responsible for the rapid initial rate, andreasonably high speed of step 1.

Let us now try to present the supporting logic as well as experimental evidence for the aboveexplanation. The reaction

x[M] + y[O] = (MxOy) (5.16)

would take place mostly either on the surface of the added deoxidizer or on the surfaces of (MxOy)particles. Therefore, it is primarily a phase-boundary reaction. No one has been able to determinethe rate of the actual phase boundary reaction step (step 2). However, at high temperatures, it ismostly very fast and has been assumed to be so here. Homogeneous reactions, of course, are evenfaster.

The mechanism of the dissolution of deoxidizer would depend on its melting point. The commondeoxidizers, viz., ferromanganese, ferrosilicon and aluminum, all melt below 1500°C. Therefore,they melt and dissolve. The melting rate depends on the heat requirement as well as rate of heattransfer to the deoxidizer. Dissolution of ferromanganese is endothermic. On the other hand,dissolution of ferrosilicon is slightly exothermic, but its melting point is higher than that offerromanganese. Therefore, on overall count, both would perhaps melt at about the same rate.Aluminum is expected to melt faster due to its much lower melting point.

Guthrie22 has reviewed addition kinetics in steelmaking. As soon as a cold solid addition suchas ferroalloy or aluminum is made, a layer of steel freezes around it and forms a solid crust. Fromthen on, the mechanism of dissolution would depend on the melting point of the addition. If it islower than that of steel, it may become molten, with the crust of solid steel intact as an extremecase. If the melting point of the addition is higher than that of steel, such as ferrotungsten, thenthe crust of steel will remelt, exposing the alloy to the melt and leading to its dissolution bysimultaneous heat and mass transfer. The effect of the formation of a steel shell was illustratedthrough sample calculation for melting 10 cm dia. ferrosilicon sphere under some assumed condi-tions. Melting time was estimated as 1200 seconds if we consider the formation of a steel shell,but only 45 seconds if no shell is formed. Similarly, for Al, it was also the melting of the frozenshell that took most of the time.

Factors that govern the rate of dissolution are bath hydrodynamics, density, melting point andthermal conductivity of the addition, size of the addition, and melt superheat. Of course, as statedearlier, if the addition is a deoxidizer, then the heat effect of the reaction is also important. Approx-imations point out a time of melting of at least 1 minute or so22 due to formation of the solid crust.Therefore, addition of liquid aluminum would enhance the rate of deoxidation as compared to thatfor solid. This is borne out by Figure 5.10. A detailed mathematical treatment is available.23,24

After melting, the dissolution of the deoxidizer requires its mixing and homogenization in themolten steel bath. This would depend on intensity of the fluid convection due to density differences(free convection) as well as stirring from other sources (such as induction stirring). However, thewhole process of dissolution may be delayed if tenacious oxide films form around the dissolvingdeoxidant.

Some observed slowness in the deoxidation reaction may be attributed to formation of stableoxide films formed on the interface of regions with a high content of deoxidizing agent and a highcontent of oxygen. Grethen and Phillippe25 have presented a photomicrograph of such a film ofMnO · Al2O3 in a deoxidation system: Al-Fe-Mn.

Deoxidation involves the formation of a new phase (i.e., the deoxidation product) as a resultof Reaction (5.16). New phases form by what are known as processes of nucleation and growth.Nucleation refers to formation of a small embryo of the new phase that is capable of growth. Such

an embryo (also called a critical nucleus) consists of a small number of molecules and has adimension on the order of 10 Å or so. Again, two mechanisms of nucleation are possible:


1. homogeneous nucleation, which occurs in the matrix as such2. heterogeneous nucleation, which occurs with the aid of a substrate

According to the classical theory, the work required to form a spherical nucleus homogeneously is

(5.38)

where σ = interfacial tension between liquid steel and deoxidation productr = radius of the nucleus

∆G = change in free energy for Reaction (5.16) per molev = molar volume of the deoxidation product (i.e., the new phase)

σ is positive, whereas ∆G is negative. This results in the type of ω vs. r curve shown in Figure 5.11. At r > r*, the nucleus grows

spontaneously, and hence r* is the radius of the critical nucleus.At ,

(5.39)


ω* = (16 πσ3v2)/3(∆G)2 (5.40)

The rate of formation of the nucleus in terms of number of critical nuclei per unit volume persecond ( ) is

(5.41)

where kB is Boltzmann’s constant (i.e., R/NO, where NO is Avogadro’s number), and n is the numberof atoms in a critical nucleus.

ω 4πrσ 43---πr3 ∆G v⁄( )+=

FIGURE 5.11 Energy barrier for homogeneous nucleation.

r r*=

dωdr------- 0, and hence, r*

2σv∆G----------–= =

N

N Aexpω*–

nkBT------------

=

increases if ω* decreases, which again happens if (∆G)2 increases [Eq. (5.40)]. ∆G, i.e., thefree energy of reaction, would actually have to be negative for the deoxidation reaction to proceed

N


in the forward direction. Therefore, an increase in (∆G)2 actually means that ∆G becomes moreand more negative.

Now,

(5.42)

From Eq. 2.8,

(5.43)

For pure deoxidation product, in accordance with Eq. (5.18), we may write

(5.44)

Since ∆G is negative, . The inverse of (i.e., ) is known as the super-saturation ratio (X) and is larger than 1. The more negative ∆G is, the higher X is.

Therefore, for higher rate of nucleation, the supersaturation is also going to be higher. Bogdandyet al.,26 Turpin and Elliott,27 and Turkdogan28 tried to estimate supersaturations required for areasonable rate of nucleation for common deoxidation systems. Turpin and Elliott took nucleus/cm3/s as a reasonable rate, whereas Turkdogan took nuclei/cm3/s. However, ithardly matters, since the supersaturation changes very little with a change of , even by severalorders of magnitude, due to the nature of the equations already presented. For estimation purposes,the value of A was taken as approximately 1027 cm–3 s–1, which is the maximum theoretical collisionfrequency. Values of interfacial tension, σ, were not known that precisely and therefore constituteda source of uncertainty.

Values of this critical supersaturation as estimated by different workers ranged from 103 to 108

for strong deoxidizers (Al, Zr, and Ti), 500 to 4000 for manganese silicate, and 200 to 20,000 forsilica. However, a reexamination of these calculations is called for. Such supersaturations areattainable in the initial stages of deoxidation by strong deoxidizers, but not so much with weakdeoxidizers.

According to Sano et al.,30 rapid homogeneous nucleation is possible during the initial stageof deoxidation even by Mn and Si. Moreover, in the melt, exogenous oxide particles are likely tobe present in all cases. These particles would serve as substrates for heterogeneous nucleation,which is easier because less energy is required.

Anyway, to sum up the situation, it has been concluded by various researchers that rapidnucleation of deoxidation product is possible when the deoxidizer is added. This has made therapid initial decrease of dissolved oxygen content possible. However, as a result of reaction, thesupersaturation in the melt also comes down drastically. Therefore, nucleation eventually ceases.

Growth of deoxidation products occurs by a number of mechanism. However, growth bydiffusion alone can contribute to the reaction and consequent lowering of dissolved oxygen. It hasbeen analyzed by Turkdogan,28 Sano et al.,29 and Lindberg and Torsell.30 The essential conclusion

QK ′ M

---------aMxOy

( )

hM[ ] x ho[ ] y

aMxOy( )

hM[ ] x ho[ ] y-------------------------

equilibrium

--------------------------------------------------

--------------------------------------------------=

∆G ∆Go RT Qln+ RT K ′ Mln– RT Qln+ RTQ

K ′ M

---------ln= = =

QK ′ M

---------W M[ ] x W O[ ] y[ ]W M[ ] x W O[ ] y

------------------------------------ equilibrium=

Q K ′ M⁄ 1< Q K ′ M⁄ K ′ M Q⁄

N 1=N 103=

N

is that growth by diffusion also is expected to be extremely rapid, taking barely a few seconds forcompletion. This is in view of very large number of nuclei formed—of the order of 105 to 107


nuclei/cm3 of melt.From the above discussions, it is evident that the deoxidation reaction accompanied by simul-

taneous nucleation and growth should be complete, the attainment of equilibrium is expected withina few seconds, and dissolution and homogenization of the deoxidizer are also instantaneous. Thisis not expected if dissolved oxygen decreases more slowly (Figures 5.9 and 5.10). Dissolution isperhaps more or less complete during the initial stage, but the mixing and homogenization, evenin laboratory experiments, take a few minutes, and this seems to be the primary cause for a slowdecrease in dissolved oxygen content during the second stage—although dissolution of the solidmay have some role to play here as well (Figures 5.9 and 5.10).

Example 5.6

Calculate the absolute maximum size of the deoxidation product as a result of the growth of criticalnuclei by diffusion alone. Assume the deoxidation product to be silica and the number of criticalnuclei (z) per cm3 to be 106. Initially, the melt contains 0.15 wt.% silicon and 0.03 wt.% oxygen.The temperature = 1800 K. Ignore all interaction coefficients.

Solution

The absolute maximum size would be obtained only if a very long time is allowed and the systemattains equilibrium.

For SiO2(s) = [Si]wt.% + 2[O]wt.% and = 1,

(E6.1)

From reaction stoichiometry,

(E6.2)

where = 0.15 wt.% and = 0.03 wt.%

or,

WSi = 0.875 WO + 0.124 (E6.3)

Substituting WSi from Eq. (E6.1) into Eq. (E6.3) and solving by iteration, WO = 0.007 wt.% (Ans.).

Material Balance for Oxygen

Oxygen in 106 nuclei + residual oxygen in 1 cm3 of melt = initial oxygen in 1 cm3 of melt, i.e.,

(E6.4)

where V is the volume of one particle of SiO2, 25 is the molar volume of SiO2 in cm3, and 7.16 isthe density of liquid iron in gm cm–3.

Solving Eq. (E6.4) for V and assuming the particle to be spherical, the radius of the particle isequal to 6.7 × 10–4 cm, i.e., 6.7 microns. Since growth by diffusion takes places for a short time,the actual radius will be less than this.

aSiO2

KSi W Si[ ] W O[ ] 2 4.7 10 6–×= =

W Si W Sio–

2832------ W O W O

o–( )=

W Sio W O

o

106 V3225------ 7.16 0.007 10 2–××+×× 7.16 0.03 10 2–××=

5.2.2 KINETICS OF DEOXIDATION PRODUCT REMOVAL FROM MOLTEN STEEL


As Figure 5.9 shows, the total oxygen content of molten steel decreases more slowly than thedissolved oxygen content. This has been well established by several researchers. It may take 10 to15 minutes, even in laboratory melts, to remove the total oxygen adequately. This behavior patterndemonstrates that the removal of deoxidation products from the melt is a slow process and is reallythe most important kinetic step controlling steel cleanliness.

Growth by diffusion is expected to be complete essentially in seconds. Sample calculations31

demonstrate that the deoxidation products can assume a size of 1 to 2 microns at best. This isbecause there are too many nuclei in the melt and, hence, each one has limited growth. In contrast,microscopic observations of solidified steel reveal presence of a large number of inclusions of asize even above 50 microns. Therefore, other mechanisms of growth play an important role.

The kinetics of removing deoxidation products from molten steel consists of the following steps:

1. growth 2. movement through molten steel to the surface or crucible wall 3. floating out to the surface or adhesion to the crucible wall

Sano et al.29 and Lindberg and Torsell30 carried out fundamental investigations with laboratorymelts. Out of these, the latter have received wide acceptance because their theoretical analyseswere supported by inclusion counting and size analysis. In addition to diffusion, they consideredthe following additional mechanisms of growth.

Ostwald Ripening (i.e., Diffusion-Coalescence)

According to this mechanism, larger particles of deoxidation product grow at the cost of smallerones. However, this mechanism does not make any significant contribution to the growth ofdeoxidation product.

Stokes Collision

In a quiet fluid and at low Reynold’s number (i.e., laminar flow), a spherical particle of solid, atsteady state, moves according to the Stokes’ Law of Settling, and its terminal velocity (v) is given as

(5.45)

where g is acceleration due to gravity, d is diameter of the particle, µ is viscosity of the fluid, ρs

and ρf are densities of solid and fluid, respectively. This equation may be applied even to the motionof gas bubbles and liquid droplets, provided that these are small in size (less than a millimeter orso). Since deoxidation products are lighter than molten steel, they move upward. Equation (5.45)shows that , other factors remaining constant. Therefore, particles of different sizes wouldmove at different speeds. During this process, many of them are likely to collide with one another.Lindberg and Torsell30 assumed that they would coalesce and form one particle as soon as theycollide. This is the mechanism of growth by Stokes collision.

Gradient Collision

Suppose the melt is not quiet, and there is some stirring and consequent turbulent flow, and randommotion of eddies. The the minimum size of such an eddy under conditions of Torsell’s experimentswas estimated as 300 microns.30 Since inclusion sizes were much smaller than this, it was assumed

utgd2 ρs ρ f–( )

18µ------------------------------=

ut d2∝

that any oxide particle would move along with the eddy in which it is contained. Since differenteddies have different velocities both in magnitude and direction, they would continuously collide,


enhancing the chances of the collision of deoxidation products and leading to their coalescenceand growth.

Example 5.7

Liquid steel is being deoxidized by the addition of ferrosilicon at 1600°C. The deoxidation productis globular silica. Calculate the time required for particles of 5 and 50 microns diameter to floatup through a depth of 10 cm and 2 m.

Given

Densities of liquid steel and silica are 7.16 × 103 and 2.2 × 103 kg m–3, respectively. The viscosityof liquid steel = 6.1 × 10–3 kg m–1 s–1, g = 9.81 m s–2.

Solution

Assume that the particles have a steady, terminal velocity given by Stokes law from the beginning.Then,

(E7.1)

If d is expressed in microns (10–6 m) and time in minutes, then

(E7.2)

Calculations yield:

These theoretical expectations were confirmed by laboratory experiments30 as shown by Figure5.12 for silicon deoxidation. Very little oxygen (total) is removed in the first stage, because theparticles are small, and they do not float out rapidly. Then, particles grow rapidly due to collisionsand start floating out, giving rise to rapid oxygen removal in the second stage. Since most largeparticles float out at this stage, further flotation and removal in the third stage is slow.

Based on their work, Lindborg and Torsell30 proposed a schematic diagram of average particleradius vs. time for deoxidation by silicon (Figure 5.13). The decrease in average size after the peakis due to preferential removal of larger particles by flotation.

It has been well established that stirring helps in the removal of deoxidation products.19,29,31

Stirring contributes to faster growth of oxide particles and hence helps in the removal of deoxidationproduct. Some researchers are of the view that a recirculatory motion of bath, such as in inductionstirring, actually makes the floating out of inclusions difficult,25 but Miyashita et al.,31 on the otherhand, have shown that, even in induction stirring, the rate of the floating out of inclusions is muchhigher than predicted by Stokes’ law ( Figure 5.14).

Slow flotation of smaller inclusions (<10 µm) and consequent dif ficulties in eliminating themis of concern in connection with production of ultra-clean steels. Hirasawa et al.32 carried out

Time to float up t( ) Depth of steel H( )ut

-----------------------------------------------18µ

g ρl ρs–( )----------------------- H

d2-----×= =

t18 6.1 10 3– 1012×××

9.81 7.16 2.22–( ) 103 60×××--------------------------------------------------------------------------- H

d2-----× 3.6 104 H

d2----- min××= =

H (in m) = 0.1 0.1 2 2

d (in microns) = 5 50 5 50

t (in min) = 150 1.5 3 103× 30


laboratory experiments on transfer of small (<10 µm) SiO2 inclusions from molten copper to slagin a resistance furnace under argon atmosphere. Two kinds of stirring were employed. Increasingthe RPM of the mechanical stirrer from 100 to 350 did not significantly enhance the rate of decreaseof total oxygen content ([WO]T) in copper. On the other hand, when the stirring was by argonbubbling from the bottom, the rate constant (kO), as defined by

(5.46)

was found to increase significantly with increasing gas flow rate. The above investigators also measured bubble frequency (f) by a pressure pulse technique.

Bubble diameters (dB) thus could be calculated from experimental data. These dB values matchedwell with those predicted by the correlation earlier proposed by Sano and Mori.33 From these, kO

FIGURE 5.12 Total inclusion content vs. time, calculated and experimental.30

FIGURE 5.13 Average radius of silica particles as a function of time upon deoxidation by silicon.30

d W O[ ] T

dt-------------------– ko W o[ ] T=


was found to vary linearly with f · A (Figure 5.15), where A is the surface area of a single bubble(assumed spherical). The above findings led Hirasawa et al.32 to conclude that the principal reasonfor the effectiveness of bubble stirring over mechanical stirring was the attachment of bubbles toinclusion particles and consequent faster floating out of small inclusions. It worth noting that theprocess of froth flotation in mineral processing is based on this principle.

In 1960, E. Plockinger et al.18 demonstrated that, contrary to the ideas of the time, primaryinclusions rich in alumina could be eliminated several times more quickly than silicates of com-parable size. It was subsequently shown by some other investigators that the chemical nature ofthe deoxidation product has a significant influence on its removal. Since the particle can interactchemically with the melt at the interface only, it was apparent that interfacial phenomena cannotbe ignored. One of the most decisive experiments was by Nogi et al.,34 who found that the addition

FIGURE 5.14 Change of total oxygen content in a stirred iron melt upon deoxidation by silicon.31

FIGURE 5.15 Empirical relationship of deoxidation rate constant with the rate of bubble surface areacreation.32

of a little surface active agent such as tellurium to molten steel accelerated the elimination of oxideinclusions (alumina, mullite, and zirconia).


Interfacial phenomena can influence all stages, viz., growth, movement, and floatingout/removal of deoxidation products. Previously, it was believed that only a liquid deoxidationproduct is capable of growing to a large size, since they coalesce together upon collision. Thediscovery of large, coral-like alumina clusters disproves this contention.35 Some investigators19,35

have claimed that small alumina particles coalesce upon collision due to the fact that molten irondoes not “wet” alumina. Therefore, an alumina–alumina interface has considerably less energy ascompared to an alumina–iron interface. Some other investigators also have supported this viewbroadly and provided evidence. Singh36 explained nozzle blockage in aluminum deoxidized meltsby a mechanism similar to that found by Olette et al.19

Of course, this view has been questioned by some others who are of the opinion that theseclusters may form in the melt during solidification in interdendritic space. Lindborg37 tried to explainthese observations as well as the multiplicity of forms assumed by inclusions. Al2O3 inclusionshave been found to assume different forms (Figure 5.16) depending on oxygen concentration.Comparable series of inclusion configurations have also been found in Mn-Si-O and Fe-Mn-Sinclusions. The concentration field near a growing inclusion, and its fluctuation, decide the shapeand size of the growing crystal. Variation of the field with time causes variation in growth. Theregularity or irregularity of the forms appears to be connected with fluctuations in mass flux. Thesame fluctuations during solidification may also cause random as well as abnormal growths.

Agglomeration of inclusions occurs by flocculation (i.e., establishing contact) and coalescence.Lindborg and Torsell30 assumed these to be instantaneous. Kozakevitch and Olette35 have tried toelucidate the mechanism. First of all, contact is established at some points. Coalescence takes placeby drainage of molten steel out of the region between the two particles due to capillary forces.Coalescence is easy in case of liquid deoxidation product. For solid particles, it happens bysintering.34

It was recognized quite some time ago that the oxide particles may come up almost to the freesurface of molten steel. However, it is likely to take a little more time or face difficulties in actuallyfloating out on the surface if the interfacial forces are not favorable. Similarly, a particle may comein contact with the crucible wall but may face difficulties in actually getting stuck on to the cruciblewall if interfacial forces are not favorable. This is especially important for stirred melts, since theparticles are not likely to stay long near the free surface or crucible wall and are likely to be sweptback into the melt. Therefore, a number of workers studied these aspects.25

Kozakevitch et al.35 have elucidated the fundamental considerations for emergence at the freesurface of the melt and at slag–metal interface. Emergence at a free surface can take place if

FIGURE 5.16 Some shapes of Al2O3 inclusions in steel.37

∆G < 0, where ∆G = σp – σm – σpm (5.47)


Where σp is surface tension of the deoxidation product, σm is the surface tension of molten steel,and σpm is interfacial tension between the deoxidation product and molten steel. On the other hand,if there is a slag layer on metal surface, then the condition for emergence is

∆G´ < 0, where ∆G´ = σps – σms – σpm (5.48)

where σps and σms are interfacial tensions at particle–slag and metal–slag interfaces, respectively.If calculations are carried out, it is found that ∆G is mostly negative for all systems. Actually, it isa question of how strongly negative it is. The more negative ∆G, the easier is emergence and henceremoval of the oxide particles. Since slags would wet the deoxidation product, ∆G´ is alwaysexpected to be more negative as compared to ∆G. Therefore, a slag cover on molten steel oughtto help in the removal of deoxidation product, and experimental findings support this.38

Nakanishi et al.39 deoxidized liquid iron containing 300 ppm of oxygen by aluminum in alaboratory high-frequency induction furnace using crucibles of different materials. Extremely lowconcentrations of oxygen (12 to 14 ppm) were obtained with SiO2 and CaO crucibles, whereasoxygen was higher (34 to 42 ppm) for Al2O3, ZrO2, and MgO crucibles. X-ray microanalysis ofSiO2 and CaO crucibles after deoxidation revealed an increase of Al2O3 concentration on theirsurfaces. These observations have been corroborated by some other investigators and are causedby interfacial forces.

To sum up, for production of clean steels upon deoxidation with low oxygen content,

1. The deoxidation product should be chemically very stable and, preferably, should beliquid.

2. The melt should be stirred.3. The interfacial forces should be favorable for the elimination of the oxide particles.

It also noteworthy that extensive investigations have been carried out on particle size distributionand the nature and morphology of inclusions in steel as affected by deoxidation practice. However,inclusions also arise during teeming and solidification. Also, inclusions arise from extraneoussources such as refractory erosion and entrapped slag particles. These topics are covered furtherin Chapters 9 and 10.

5.3 DEOXIDATION IN INDUSTRY

Deoxidation is carried out in industry in furnaces, ladles, runners, and even in molds. It is beyondthe scope of this book to describe all of these. The fundamentals of deoxidation thermodynamicsand kinetics as established through laboratory experiments apply to industrial situations as well.However, the conditions in the latter are different from those of the laboratory in a number of waysand are much more complex. Here, it is intended to discuss these very briefly.

An industrial vessel is much larger in size as compared to a laboratory crucible. Therefore,

1. The deoxidation products take a much longer time to float up or to come in contact withthe lining.

2. Mixing and homogenization of bath are much more difficult as compared to a laboratorysituation.

In addition to the above, the following have to be kept in mind:

1. An industrial melt is contaminated by the presence of exogenous oxide particles comingfrom refractory linings and slag.

2. There is a layer of slag covering the free surface of the metal. 3. Controlled laboratory experiments are conducted under argon atmosphere, whereas it is


not necessarily so in industry.

As discussed earlier, stirring assists in faster growth of oxide particles through gradient collision.It also helps in the faster rise of the oxide particles. Hence, for the production of cleaner steel,stirring of molten metal in the bath by inert gas purging has been widely adopted. Suzuki et al.40

have reported results of investigations on deoxidation in a 150 tonne ladle furnace (LF) at MurorauPlant of Japan Steel Works. Figure 5.17 presents some of their findings. The degree of deoxidationreached a maximum with an increase of stirring energy input into the melt. Thereafter, it decreasedsomewhat. Authors have explained this decrease to either erosion of refractory lining or entrapmentof top slag into steel. Similar findings have been reported by some others, and it has been establishedthat stirring should be optimized for best results.

Ghosh and Choudhary8 carried out deoxidation by ferromanganese and ferrosilicon in 6t and1t electric arc furnaces. Their findings point out that deoxidation equilibria could be attained within10 minutes after the addition of deoxidizers if only stirring of the bath by CO evolution werereasonable. One strategy is to obtain a liquid deoxidation product by proper sequence of the additionof Si, Mn, and Al. Liquid deoxidation products tend to coalesce and grow rapidly upon collisionand hence are eliminated faster.

Many experimental and plant studies have shown that the rate of separation of deoxidationproducts in stirred melts can be represented by an equation of the form

Ct = Ci exp(–kt) (5.49)

where Ci is the initial concentration of inclusions, Ct is the concentration of inclusions at time t,and k is the apparent separation constant. The value of k obviously would depend on stirring.

However, Eq. (5.49) should be taken only as an approximate guide. For example, Suzuki etal.40 measured total oxygen content as a function of time in a ladle stirred by argon. Their data arepresented in Figure 5.18. The mean curve is also superimposed on the data. Employment of Eq.(5.49) on their data at stirring times of 4 and 10 minutes yielded values of k equal to 2.7 × 10–3

FIGURE 5.17 The effect of stirring on the degree of deoxidation.40


s–1 and 1.7 × 10–3 s–1, respectively. These are significantly different. It is to be borne in mind thatthe total oxygen content of liquid steel also includes dissolved oxygen content in addition to oxideparticles. Moreover, some re-entrainment of particles also occurs. So, even after prolonged stirring,a steady value of oxygen content remains in the melt.

From the above considerations, a more appropriate equation is

[∆WO]T = [∆WO]T,i exp (–kOt) (5.50)

where [∆(WO]T is difference in wt.% total oxygen at time t after stirring and at steady state, i.e.,

[∆WO]T = [∆WO]T,i – [∆WO]T,s (5.51)

where [WO]T, [WO]T,s and [WO]T,s are total oxygen content at time t, at steady state, and initially,respectively. Equation (5.50) is thus a modified version of Eq. (5.46).

In Figure 5.18, if the steady value is taken as approximately 30 ppm, the values of kO evaluatedat stirring times of 4 and 10 min are 4.9 × 10–3 s–1 and 4.2 × 10–3 s–1, respectively. These are muchcloser to one another.

The steady level of oxygen content during ladle deoxidation is a consequence of the fact thatsimultaneous reoxidation also goes on during this period. The sources of oxygen pickup areatmosphere, oxidizing slag, and oxides from refractory lining. The value of steady-state oxygencontent is obtained when the rate of deoxidation and rate of reoxidation are equal.

Lehner41 reported reoxidation experiments in argon purged ladles in a pilot plant scale. He triedto ascertain the role of carryover slag from the steelmaking furnace and found that reoxidation bythe top slag was significant. The steady-state total oxygen content was 26 ppm for a slag containing5.6% FeO and 2.4% MnO, whereas it was 92 ppm for the slag with 6.5% FeO and 8.1% MnO. Itwas also found that the top slag gets deoxidized by added deoxidizers slowly. Hence, it is advisableto deoxidize any remaining furnace slag before addition of synthetic slag.

Kim et al.42 conducted water model experiments with an NaOH solution. Argon was bubbledthrough the bottom centrally. An atmosphere of CO2 was maintained at the top of the bath.Significant absorption of CO2 was observed, demonstrating that the rising argon bubbles wereincapable of preventing absorption of CO2. It was also found that the rate of absorption increasedwith increasing argon purge rate. The rate of absorption decreased significantly when an oil layer,

FIGURE 5.18 Total oxygen content of molten steel as a function of time in an argon stirred ladle.40

simulating top slag, was present on the water. In this case, the absorption was through the plumeeye only.


A NaOH solution-CO2 system had been investigated widely earlier, and it had been establishedthat the absorption rate of CO2 was basically controlled by mass transfer in aqueous solution, unlessone operates in a regime of very high mass transfer rates. Kim et al.42 also assumed water phasemass transfer control. In Chapter 4, Section 4.3, we also presented the findings of Taniguchi et al.on the rate of absorption of CO2 at the free surface of water, stirred by injection of nitrogen fromthe bottom, along with their mass transfer correlation.

Section 5.2.2 presented a brief discussion on the difficulties in flotation of small inclusionparticles and the beneficial role of gas bubbling. Attachment of particles to rising gas bubbles andconsequent faster float out explained experimental observations of Hirasawa et al.32 Kikuchi et al.43

have presented some information on the NK-PERM process. The melt in a ladle is subjected tosome nitrogen pressure so as to raise its dissolved nitrogen content to about 100 to 150 ppm. Thepressure of N2 is subsequently lowered drastically by a factor of 25 to 100. This leads to thegeneration of nitrogen bubbles throughout the melt, promoting faster flotation of fine inclusionparticles. Figure 5.19 compares the deoxidation rate constants for this method with those for Arbubbling. Enhancement of kO by a factor of few may be noted. The authors also attempted aquantitative analysis of this phenomenon.

Earlier, deoxidation was carried out in an open teeming ladle as a single-stage process. Theaddition of deoxidizers used to be done primarily during tapping. With developments in secondaryrefining technology, it is generally practiced in two or three stages. The first stage is the traditionalone during tapping. The ladle has a facility for the bottom purging of argon. After tapping, theladle is taken to an argon purging station. During this transfer, we may also resort to some gasstirring using a lance immersed from the top into molten steel.

The objective of the final deoxidation during argon purging is to accomplish precise control ofdissolved oxygen by the addition of more deoxidizers. Additional objectives are the removal ofinclusions, temperature and composition adjustments, plus additional refining such as desulfuriza-

0.50

0.20

0.10

0.05

0.02

0.01

0.005

0.002

0.001

20 50 100 200 500 1000 2000 5000

New method

Gasbubbling

1.5kg VIF

70kg VIF

50TVOD

Carbon steelSUS

ε x 103,Wkg-1

K0,m

in-

1

FIGURE 5.19 Relation between the apparent deoxidation rate constant and stirring energy.43

tion. A ladle furnace (LF), as shown in Figure 5.20, is widely employed for this purpose. Here,argon purging is done from the bottom. A cover is put on the top of the ladle. Heating is by electric


arc, for which graphite electrodes are introduced through the top cover. It is provided with facilitiesfor additions as well as sampling and temperature measurement. In some new LF units (e.g., LTV,Indiana Harbour plant), induction stirring has been adopted in place of gas stirring.

For grades of steel that also require degassing, the second stage of deoxidation is carried outnot in ladle furnace but in a vacuum degassing unit such as a vacuum arc degasser (VAD).

A low recovery of aluminum and silicon (added to the ladle while furnace tapping the steel),as well as the phenomenon of phosphorus reversion from the tap slag into the steel, have long beenknown consequences of the reaction of the liquid steel with the slag carried over from the furnace.Turkdogan44,45 has reported findings of a comprehensive investigation. Percentages of utilizationof the ladle additions for low carbon heats were 85 to 95% for Mn, 60 to 70% for Si, and 35 to65% Al. Vaporization of Mn was held as the primary cause of its loss. So far as Al is concerned,

[WAl] (added) = [WAl] (dissolved) + [WAl] (for deoxidation)

+ [WAl] (oxidized by furnace slag and fallen converter skull)

+ [WAl] (oxidized by entrained air bubble) (5.52)

Since oxygen pickup from air bubbles entrained by the tapping stream does not exceed 20 ppm orso, it is not a significant source of aluminum loss. A similar conclusion can be drawn for Si.

FIGURE 5.20 Sketch of a ladle furnace.

The reaction of Al and Si with FeO and MnO of carryover slag is of the general form


(Fe, Mn)Ox + [Al, Si] → [Fe, Mn] + (Al,Si)Oy (5.53)

Turkdogan assumed the converter skull to consist of Fe3O4. Material balance yielded the followingapproximate relation:

[WAl + WSi]sl = 1.1 × 10–6 · ∆(WFeO(T) + WMnO) Wfs + 11 × 10–5 Wsk (5.54)

where Wfs = mass of furnace carryover slag, kgWsk = mass of fallen converter skull, kg

∆(WFeO(T) + WMnO) = decrease in oxide contents of furnace slag during tapping[WAl + WSi]sl = percent Al and Si (as percent of mass of steel) lost by reaction with slag

and skull

Another consequence of slag carryover is phosphorus reversion, especially in Al-killed steels.From change of phosphorus content of steel, phosphorus balance allowed estimation of furnacecarryover slag.44 It was found to range between 1 to 3.5 tonnes for a 200t BOF heat. Figure 5.21shows that both [WAl +WSi]sl, as well as the extent of phosphorus reversion, increased with thequantity of carryover slag. It also demonstrates that slag is a major source of loss of Al and Si.

The above adverse effects of carryover slag have prompted industries to tap liquid steel fromthe furnace without slag, i.e., “slag-free tapping.” However, complete prevention of carryover slagis quite difficult. Also, some top slag in the ladle is desirable, since it slows down heat loss fromthe melt and provides protection against oxidation by atmospheric air. As pointed out in Section5.2.2, the top slag aids in the elimination of inclusions as well. Hence, the objective of slag-freetapping may be stated as minimization of carryover slag.

Formation of a funnel-shaped air core during the emptying of liquid from a vessel by drainageis a common experience, such as we can observe in a kitchen sink. During the tapping of steelmelt from a converter, or teeming of a ladle or tundish through a nozzle, such a funnel allows theslag to flow out as well. Some fundamental studies have been conducted in water models.

Shankarnarayanan and Guthrie46 have reviewed their own as well as earlier studies. The slag-entraining funnels have been classified into the following two types:

• The vortexing funnel, for rotational flow (Figure 5.22a)• The draining funnel, for irrotational flow (Figure 5.22b)

FIGURE 5.21 Relation of phosphorus reversion during the tapping of a 200t basic oxygen furnace (BOF)heat to the extent of reaction of [Si] and [Al] of steel with ladle carryover slag and fallen converter skull.44


The critical limiting height (HCr), below which such a funnel would reach down to the drainageopening, is of technological importance. In industrial processes, rotational (i.e., tangential) flow isvery likely to be present and, hence, HCr for a vortexing funnel (HCr,v) is of importance. The findingsmay be stated as

(5.55)

where D = vessel diameterQ = discharge flow rateg = acceleration due to gravity

The scatter of the data did not allow further quantification, but n was approximately 2. HCr,v /Dranged between 1 and 50 in their experiments. For a draining funnel, data of various investigatorsshowed wide discrepancies. However, HCr,d /D was found to be in a range from 0.1 to 2. Hence,HCr,d constitutes the lower limit and HCr,v the upper limit of drainage height.

In further studies, Shankarnarayan and Guthrie47 refined the correlation of Eq. (5.55) further.Since vortexing funnels are undesirable in terms of the cleanliness of steel, they designed “vortexbusters” both for a water model and plant studies and carried out experiments. The object was toprevent vortexing. They have reported a significant decrease of HCr,V in the water model as well asimproved steel cleanliness in plant studies by use of these vortex busters.

Steffen48 has reported studies on flow phenomena related to slag carryover in water models aswell as in 300t basic oxygen furnace (BOF) vessel. In ladles, drain sink occurred if the volumeflow of the open channel at the ladle bottom was less than the corresponding out let capacity.Critical liquid height was not significantly dependent on the location of the bottom nozzle (centricor eccentric). Also, HCr was found to be proportional to the nozzle diameter (dn).

Water model investigations by Mazumdar et al.49 demonstrated a significant decrease in entrain-ment of the upper liquid phase if its viscosity was larger. Increased waiting time after the blow

nozzle ouflow nozzle outflow

drainagenozzle

drainagenozzle

primaryliquid

primaryliquid

Hcr,d

Hcr,v

d d

Vθ,I = 0

Vθ,i>=Vθ,cr>0

(a) (b)

FIGURE 5.22 (a) Vortexing funnel and (b) draining funnel during the pouring of liquid through a bottomnozzle.45 Reprinted by permission of Iron & Steel Society, Warrendale, PA.

HCr ,v

D------------

Q

gD5( )1 2⁄--------------------- n

=

from 15 to 180 s also lowered the drainage of the upper liquid phase by a factor of 4 to 5. Thiscan be explained as due to the decay of vortexing flow. Dubke and Schwerdtfeger50 dropped balls


of various sizes and densities into the draining liquid. Entrainment of the lighter liquid was foundto decrease by a factor of 4 to 5 due to the presence of the ball. A ball density that allows partialimmersion of the ball into the heavier liquid was found to be very effective. The ball settles intothe mouth of the vortexing funnel and thus prevents the lighter liquid from flowing out.

The studies on entrainment phenomena have enabled industries to control slag carryover duringtapping with varying degrees of success. The devices are plugs of various shapes, e.g., as nailshaped. Fruehan51 has briefly discussed about devices for slag-free tapping. In electric arc furnaces,eccentric bottom tapping allows considerable reduction in the quantity of carryover slag. The useof slide gates decreases vortexing as compared to stoppers. As far as the BOF is concerned, theplugs are composites of refractory materials and iron, so the density is in between that of slag andof metal. If everything works right, the plug falls into the tap hole and blocks it before the slagflows through it. A teapot-type spout for tapping should be quite effective, too.

Another device that is useful in reducing the amount of slag carryover is an electromagneticsensor, which is placed around the tap hole. When slag starts coming out through the hole, thenature of the signal changes significantly due to differences in electromagnetic induction for slagand metal. The device is superior to visual detection. Poferl and Eysn52 have reported on plant trialswith 130/140t converters at Linz and obtained the following average slag rates (kg/tonne steel):

Besides the use of a slag stopper in a BOF, further deslagging by slag raking seems to bepracticed in some modern plants. During this even electromagnetic stirring is being employed topush the BOF slag towards the front of the ladle for quick and efficient removal.

In secondary refining, a slag of CaO-Al2O3-SiO2-CaF2 with a high content of CaO and sub-stantial percentage of Al2O3 is aimed at for better deoxidation, desulfurization, etc., as well as forcontrolling dissolved Al in molten steel. This requires the addition of CaO, CaF2, etc., anddeoxidizers to modify the carryover slag during tapping of steel as well as during the subsequentstage. The average slag composition in a ladle furnace after arc reheating is 50 to 56% CaO, 7 to9% MgO, 6 to 12% SiO2, 20 to 25% Al2O3, 1 to 2%(FeO+MnO), and 0.3% TiO2, with smallamounts of S and P.45 An already prepared synthetic slag speeds up refining. The concept is notnew. In the Perrin process of early 1930s, steel was tapped onto a molten calcium (magnesium)aluminosilicate slag placed at the ladle bottom. Lime-alumina–based premelted synthetic slags areon the market now.

Turkdogan44 has reported the findings of some plant experiments in which, during sometappings, only ferromanganese was added to the ladle, whereas for some others ferromanganeseand calcium aluminate slag were added. Figure 5.23 presents the findings. Si and Al were less than0.003% each. The figure demonstrates significant improvement in deoxidation upon use of slag.Of course, the extent of improvement depends on the steel grade. For Si-Mn killed or Al-killedsteels, the difference would be less. Section 5.1.2 has already provided the necessary thermodynamicbackground for this. Turkdogan has also tried to show that reactions approached thermodynamicequilibria approximately. This was attributed to the strong stirring and mixing action of the tappingstream. These agree with the findings by Choudhary and Ghosh8 in EAF, reported earlier in thissection.

Section 5.2.1 has already presented a brief discussion on melting-cum-dissolution of ferroalloys,aluminum, and other alloying additions. In industrial processing, it is desirable that the solidadditions remain submerged in liquid steel long enough for completion of melting-cum-dissolution.

Without slag stopper 10–15

With slag stopper 4.45

With slag stopper and slag indication system 3.5


Heavy ferroalloys, such as ferrotungsten, shall remain submerged. However, additions of lowerdensity, such as Al, ferromanganese, etc., would tend to float up and react with slag and atmosphericoxygen. This problem is especially serious with aluminum. Guthrie22 has reviewed the subject andreported findings based on mathematical modeling, cold modeling, and actual plant trials.

There have been subsequent mathematical exercises on the same subject, as well as water modelexperiments.53 Since additions are made primarily during the tapping of steel, the same situationwas simulated. Attention was paid to the subsurface trajectories of buoyant (i.e., lighter than liquidbath) additions, and total immersion times were found to range between 0.1 and 40 s. Someguidelines for optimum particle size, location, and timing of the addition have been proposed.However, plant trials are a must since, besides the flow hydrodynamics caused by the tappingstream, there are several variables affecting alloy recovery, as discussed earlier. Moreover, signif-icant improvements in the utilization of deoxidizers during tapping would be possible only withmajor investments. Baldzicki et al.54 have reported significant improvement in Al recovery by wireinjection in Al-killed grades.

Rapid mixing and homogenization of the bath, as well as metal-slag mass transfer, are verydesirable for success. During tapping, stirring is effected by the tapping stream. Some limitedcontrol of the process is possible.

During argon purging, the flow rate of argon is a key variable. Chapter 3 presented details offundamental studies on fluid flow in gas-stirred ladles. Chapter 4 discussed mixing and mass transferin gas-stirred ladles. These are being utilized for industrial process control, design, and optimizationto some extent. Figure 4.4 illustrates that, for a ladle with a single porous plug, minimum mixingtime is obtained if the plug is located at mid-radius. Accordingly, in smaller ladles with singleplugs, the plug location is at mid-radius. For dual plugs, the two plugs at mid-radius are locatedin diametric opposition. Zhu et al.55 have reported their findings from water model and mathematicalmodel work for mixing in a gas-purged ladle with multiple tuyeres at the bottom, and they arrivedat the same conclusion.

Nippon Steel Corporation of Japan has developed the CAS (composition adjustments by sealedargon bubbling) process. With an additional facility for oxygen blowing, it is known as CAS-OBand seems to be catching up as alternative to ladle furnaces. The features of CAS-OB have beenpresented by S. Audebert et al.56 Figure 5.24 illustrates the features of the process. Since it doesnot involve elaborate top and arc heating arrangements as does LF, capital cost is low. The high-

FIGURE 5.23 Deoxidation by ferromanganese with and without calcium aluminate ladle slag in furnacetaping of low-Si, low-Al steel.44

Raising temperature of steel5. O2 blowing into snorkel á


alumina refractory snorkel had a life of about 60 heats. Deoxidizers and other alloying elementsare added inside the snorkel during argon purging. This significantly prevents their oxidation lossdue to reaction with atmosphere and slag.

As mentioned in Section 4.2, stirring is most intense in the plume region, leading to fastermelting and dissolution of additions. Temperature adjustment, as required, is done by feedingaluminum wire and oxygen blowing inside the snorkel. The oxidation of Al provides the necessaryheat input. This way, heating is more rapid (7 C/min or so) and cheaper as well. However, thecontrol of residual dissolved aluminum calls for good process control measures. Nilsson et al.57

have reported the performance of CAS-OB, commissioned at the SSAB Tunnplat AB, Lulea Worksin 1993. They have claimed a reduction in total production cost as well as improvement of productquality.

Section 5.1 has briefly discussed the principles and importance of an immersion oxygen sensor,which measures dissolved oxygen content of molten steel. The use of this to monitor bath oxygenlevels in steelmaking furnaces and ladles is a must for scientific purposes and improved deoxidationcontrol. Many investigators have reported extensive trials and the results achieved. For example,Anderson and Zimmerman58 have reported findings of trials at Republic Steel’s Warren BOF shop.The [Wc] · [Wo] product, before tapping of the BOF, was determined to be 0.0029, in comparisonto 0.0020, the equilibrium deoxidation constant at 1593°C.

Maximum vessel oxygen was found to provide a superior control criterion of the bath oxygenlevel rather than the traditional one, i.e., minimum tap carbon.58 This vessel oxygen level was alsoemployed for BOF charge calculation, deoxidizer additions in ladles, and decisions about thedeoxidation schedule. Significant improvements were found, including improved rimming action,improved yield of semi-killed grades, and an improved aluminum addition schedule. However, alack of reproducibility in aluminum recovery was still a major problem.

REFERENCES

1. Steelmaking Data Sourcebook: The Japan Soc. for The Promotion of Science, The 19th Committeeon Steelmaking (revised ed.), Gordon and Breach Science Publishers, New York, 1988.

2. Subbarao, E.C., ed. Solid Electrolytes and Their Applications, Plenum Press, New York, 1980. 3. Fruehan, R.J., Martonik, L.J., and Turkdogan, E.T., Trans. AIME, 245, 1969, p. 1501.

Low running cost and investment1. Simple equipment & operation

2. Alloy addition Ar atmosphere

4. Ar stirring into snorkel

3. Slag off for prevention of slag- metal reaction

Fumeextraction

AlloyingC, Si, Mn, Aletc.

O2 blowing

Slag

Moltensteel

Snorkel

Ladle

Porous plug

ArN2

gas}

ááááá

ááá

Quick treating andlow temperature drop

Low reoxidationHigh yieldPrecise composition adjustment

Effective removal of oxidesNo disturbance of slag layerQuick homogeneity

FIGURE 5.24 Features of the CAS-OB process.56

4. Saeki, T., Nisugi, T., Ishikura, K., Igaki, Y., and Hiromoto, T., Trans. ISIJ, 18, 1978, p. 501. 5. Plushkell, W., Stahl ûnd Eisen, 96, 1976, p. 657.


6. Nilles, P., Defays, J., Cure, O., and Surinx, H., CRM Report, No. 51, Oct. 1977, p. 31. 7. Jacquemot, A., Gatellier, C., and Olette, M., IRSIDE RE 289, 1975, also ref.19, p. 50. 8. Ghosh, A. and Chaudhary, P.N., Trans. IIM, 38, 1985, p. 31.9. Ghosh, A. and Murty, G.V.R., Trans. ISIJ, 26, 1986, p. 629.

10. Qiyong Han, Proc. 6th Int. Iron and Steel Cong., Nagoya, Vol. 1, 1990, p. 166.11. Kimura, T. and Suito, H., Metall. Trans. B., 25B, 1994, p. 33.12. Verein Deutscher Eisenhuttenleute, Slag Atlas, Verlag Sthalisen mbH, 1981. 13. Turkdogan, E.T., in Chemical Metallurgy of Iron and Steel, Iron and Steel Inst., London, 1973, p. 153.14. Bagaria, A.K., Brahma, Deo, and Ghosh, A., Proc. Int. Symp. Modern Developments in Steelmaking,

Chatterjee, Amit and Singh, B.N., ed., Jamshedpur, 1981, 8.1.1. 15. Ghosh, A. and Naik, V., Tool and Alloy Steels, 17, 1983, p. 239. 16. Wilson, W.G., Kay, D.A.R., and Vahed, A., J. Metals, 26, 1974, p. 14.17. Faulring, G.M., and Ramalingam, S., Metall. Trans. B, 11B, 1980, p. 125. 18. .Plockinger, E. and Wahlster, M., Stahl Eisen, 80, 1960, p. 659. 19. Olette, M. and Gatellier, C., in Information Symposium on Casting and Solidification of Steel, IPC

Science and Technology Press Ltd., Guildford, U.K., 1977, p. 8. 20. Kundu, A.L., Gupt, K.M., and Krishna Rao, P., Ironmaking and Steelmaking, 13, 1986, p. 9. 21. Patil, B.V. and Pal, U.B., Metall. Trans. B, 18B, 1987, p. 583. 22. Guthrie, R.I.L., Electric Furnace Proceedings, AIME, 1977, p. 30. 23. Engh, T.A., Principles of Metal Refining, Oxford University Press, Oxford, 1992, Ch. 8. 24. Argyropoulos, S.A. and Guthrie, R.I.L., in Heat and Mass Transfer in Metallurgical Systems, ed.

Spalding, D.B. and Afgan, N.H., Hemisphere Publishing Corp., London, 1981, p. 159. 25. Grethen, E. and Phillippe, L., in Production and Application of Clean Steels, Iron and Steel Inst.,

London, 1972. 26. Von Bogdandy, L., et al., Arch. Eisenhuttenleute, 32, 1961, p. 451.27. Turpin, M.L. and Elliott, J.F., JISI, 204, 1966, p. 217.28. Turkdogan, E.T., JISI, 204, 1966, p. 14. 29. Sano, N., Shiomi, S., and Matsushita, Y., Trans. ISIJ, 7, 1967, p. 244. 30. Lindborg, U. and Torsell, K., Trans. AIME, 242, 1968, p. 94. 31. Miyashita, Y. et al., in Proceedings 2nd Japan-USSR Joint Symposium on Physical Chemistry of

Metallurgical Processes, Iron and Steel Inst., Tokyo, 1969, p. 101.32. Hirasawa, M., Okumura, K., Sano, M., and Mori, K., in Ref. 10, Vol. 3, p. 568. 33. Mori, K., Hirasawa, M., Shinkai, M., and Hatamaka, A., Tetsu-to-Hagane, 71, 1985, p. 1110. 34. Nogi, K. and Ogino, K., Canad Met. Qtly., 22, No. 1, 1983, p. 19.35. Kozakevitch, P. and Olette, M., in Production and Application of Clean Steels, Iron and Steel Inst.,

London, 1972, p. 42. 36. Singh, S.N., Metall. Trans., 2, 1971, p. 3248.37. Lindborg, U., in Ref. 19, Vol. 2, 85. 38. Bziva, K.P. and Averin, V.V., in Proceedings 2nd Japan-USSR Joint Symposium on Physical Chemistry

of Metallurgical Processes, Iron and Steel Inst., Tokyo, 1969, p. 113. 39. Nakanishi, K. et al., in Proceedings 2nd Japan-USSR Joint Symposium on Physical Chemistry of

Metallurgical Processes, Iron and Steel Inst., Tokyo, 1969, p. 50. 40. Suzuki, K., Kitamura, K., Takenouchi, T., Funazaki, M., and Iwanami, Y., Ironmaking and Steelmaking,

1982, p. 33. 41. Lehner, T., Canad Met. Qtly., 20, No. 1, 1981, p. 163. 42. Kim, S.H., Fruehan, R.J. and Guthrie, R.I.L., Steelmaking Proceedings, Iron and Steel Soc., USA,

1987, p. 107. 43. Kikuchi, Y., et al., in Ref.10, Vol. 3, p. 532. 44. Turkdogan, E.T., Ironmaking and Steelmaking, 15, 1988, p. 311.45. Shankarnarayanan, R. and Guthrie, R.I.L., Steelmaking Proceedings, Iron and Steel Soc., USA, 1992,

p. 655. 46. Steffen, R., in Int. Conf. Secondary Metallurgy (English preprints), Verein Deutscher Eisenhuttenleute,

Verlag Stahleisen mBH, Dusseldorf, 1987, p. 97.

47. Mazumdar, S., Pradhan, N., Bhor, P.K., and Jagannathan, K.P., ISIJ Int., 35, 1995, p.92. 48. Dubke, M. and Schwerdtfeger, K., Ironmaking and Steelmaking, 15, 1990, p. 184.


49. Fruehan, R.J., Ladle Metallurgy Principle and Practices, Iron and Steel Soc., Warrendale, PA, USA,1985, p. 655.

50. Poferl, G. and Eysn, M., in Ref. 46, p. 137.51. Tanaka, M., Mazumdar, D. and Guthrie, R.I.L., Metall. Trans. B, 24B, 1993, p. 639. 52. Baldzicki, E.J., Tomazin, C.E. and Turacy, D.L., in Ref. 48, p. 129. 53. Zhu, M.Y., Inomoto, T., Sawada, I., and Hsiao, T.C., ISIJ Int., 35, 1995, p. 472.54. Audebert, S., Gugliarmina, P., Reboul, J.P., and Sauermann, M., MPT, 1989, p. 26.55. Anderson, E.D. and Zimmerman, E., in Ref. 48, p. 79.

6 Degassing and Decarburization of Liquid Steel

6.1 INTRODUCTION

As stated in Chapter 1, the degassing of steel melts by subjecting them to vacuum treatment wasintroduced in the decade of the 1950s. The primary objective was to lower the hydrogen contentin forging quality steels. The gases—hydrogen, nitrogen, and oxygen—dissolve as atomic H, N,and O, respectively, in molten steel. However, their solubilities in solid steel are very low. Chapter5 has already dealt with oxygen. Solubilities of H and N in pure iron at 1 atm pressure of therespective gases are shown in Figure 6.1 to demonstrate this point.

When liquid steel is solidified, excess nitrogen may form stable nitrides such as nitrides ofaluminum, silicon, and chromium. However, hydrides are thermodynamically unstable. Therefore,the excess hydrogen in solid steel tends to form H2 gas in pores and also diffuses out to theatmosphere. H has a very high diffusivity even in solid steel due to its low atomic mass. In relativelythin sections, such as those manufactured by rolling, diffusion is fairly rapid. Hence, excesshydrogen is less, reducing the tendency toward development of high gas pressure in pinholes. Also,the bulk of the rolled products in the ingot route belong to rimming and semi-killed grades. Here,liquid steel tends to contain less hydrogen due to a flushing action by the evolution of CO gas.

However, diffusion is not that efficient in forgings, due to their large sizes. Moreover, liquidsteel in forging grades contains more hydrogen too, since these are killed steels. As a consequence

FIGURE 6.1 Effect of temperature on the solubilities of nitrogen and hydrogen in iron at 1 atm pressurefor each gas.


of this, H rejected by solid steel accumulates in blowholes and pinholes. The gas pressure developedinside the latter tends to be high. During forging, the combination of hot working stresses and high


gas pressure in pinholes near the surface tends to cause fine cracks in the surface region. Effortsto avoid these cracks led to commercial development of vacuum degassing processes.

Hydrogen also causes a loss of ductility of steel. Hence, low H is a necessity for superior gradesof steel with high strength and impact resistance. These considerations have led to hydrogenconsciousness in rolled products as well for several grades of steel.

The need to control the oxygen content of steel melt and deoxidation has been discussed inChapter 5. The use of deoxidizers leads to the formation of deoxidation products affecting thecleanliness of steel. Vacuum treatment of liquid steel promotes a carbon-oxygen reaction andremoval of oxygen as CO. This is clean deoxidation. Recognizing this, steelmakers also madedeoxidation a target of vacuum treatment. This simultaneously lowers carbon as well and constitutesthe basis for vacuum decarburization.

Nitrogen affects toughness and aging characteristics of steel as well as enhancing the tendencytoward stress corrosion cracking. Nitrogen is by and large considered to be harmful for propertiesof steel. Its strain hardening effect does not allow extensive cold working without intermittentannealing. Low nitrogen is essential for deep drawing quality steel. Very low nitrogen levels havebecome extremely important for ultra-low carbon, cold rolled steels with high formability for theautomotive industry, subjected to continuous annealing.

However, it is worth mentioning that there are applications where nitrogen has beneficial effectson the properties of steel.1 The grain refinement action of fine precipitates of aluminum nitride(AlN), and consequent beneficial effects on properties, have been known for a long time. Solidsolution hardening and precipitation strengthening effects are utilized in high-strength steels. Nitro-gen additions are also particularly beneficial for stability and pitting resistance of austenitic stainlesssteel grades. Precipitates of nitrides or carbonitrides of several alloying elements, such as aluminum,boron, chromium, niobium, etc., have been reported.2

Hydrogen is picked up by the steel melt during primary steelmaking from moisture and waterassociated with raw materials and atmosphere. Nitrogen, of course, is picked up from the air.Steelmakers endeavor to lower the extent of such pickup as well as to flush out these gases fromthe melt using various strategies. All of this is beyond the scope of discussion here, since we areconcerned with secondary steelmaking. However, in this connection, it may be mentioned thatnitrogen is to be largely controlled in the primary steelmaking and tapping stage. In Chapter 8,there is a discussion of this topic in connection with gas absorption from the atmosphere duringtapping and teeming.

As discussed in Section 5.1, total oxygen in steel is determined by inert gas fusion apparatus.A similar method is employed for determining the nitrogen and hydrogen content of steel. Thesample is melted in graphite crucible under a flow of pure argon. N and H evolve as N2 and H2 inthe gas stream, whose total quantity is determined spectroscopically. More recently, emissionspectrometers have come on the market and are in wide use for the analysis of nitrogen and otheralloying elements, as for oxygen in steel.

Peerless and Clay2 have reported development of the “Nitris” system by Heraus Electro-Nite.It has been derived directly from the Hydris technique for the determination of hydrogen in liquidsteel. It employs a disposable immersion lance. Through some pumping arrangement, the gas inequilibrium with the melt is collected. The partial pressures of N2 or H2 directly give values of thenitrogen or hydrogen contents of molten steel. This method does not require the collection of solidsample and handling of the same for subsequent analysis, and hence it is more rapid.

6.1.1 VACUUM DEGASSING PROCESSES

Review articles and monographs have been published on general features.3,4,5 Vacuum degassingprocesses are traditionally classified into the following categories:

1. ladle degassing processes 2. stream degassing processes


3. circulation degassing processes (DH and RH)

As stated in Chapter 1, an additional temperature drop of 20 to 40°C occurs during secondaryprocessing of liquid steel. Temperature control is very important for proper casting, especiallycontinuous casting. Therefore, provisions for heating and temperature adjustment during secondarysteelmaking are very desirable. In vacuum processing, a successful commercial development in thedecade of the 1960s was vacuum arc degassing (VAD), where arc heating is undertaken. Provisionfor heating is provided in an RH degasser as well.

Stainless steels contain a high percentage of chromium. A cheap source of Cr is high-carbonferrochrome. However, its addition raises the carbon content of the melt to about 1%, which is tobe lowered to less than 0.03% in subsequent processing. Oxygen lancing has already been foundto promote C–O reaction in preference to Cr–O reaction, and it has been practiced commercially.The use of a vacuum is of further help and led to the development of vacuum-oxygen decarburization(VOD) process for stainless steels in the decade of the 1960s. Some oxygen blowing is nowadaysresorted to in vacuum degassers for the production of ultra-low carbon steels as well. The RH-OBprocess is an example.

In vacuum degassing, the total pressure in the chamber is lowered, whereas, in degassing byargon purging, the total pressure above the melt is essentially atmospheric. Even then, degassingis effected. This is because partial pressures of H2, N2, and CO are essentially zero in the incomingargon gas. Therefore, degassing by bubbling argon through the melt without vacuum is possible inprinciple. But consumption and cost of argon would be high, and the processing time would belengthy. Hence, it is not practiced for ordinary steels. However, decarburization of stainless steelmelts by the argon-oxygen decarburization (AOD) process is still popular.

Besides degassing, modern vacuum degassers are used to carry out various other functions suchas desulfurization, decarburization, heating, alloying, and homogenization, thereby achieving morecleanliness as well as inclusion modification. Adaptation of vacuum processes to produce ultra-lowcarbon steels is an important development direction.

It is to be recognized that not all of these functions are equally important. A plant’s managementhas to fix its targets and accordingly has to decide priorities. These in turn dictate the choice ofprocess, facilities required, and operating practices. Some broad guidelines are noted below3.

1. The treatment time in vacuum degassing should be short enough to logistically matchwith the converter steelmaking on the one hand and continuous casting on the other. Thisis one of the challenges. Higher pumping capacity for the vacuum systems is a prereq-uisite. For a modern 200t VD unit, a capacity higher than 500 kg of air/hr at 1 torr iscommon (1 torr = 1 mm Hg).

2. Injection of argon below the melt is a must for good homogenization, mass transfer, andinclusion removal. Design and location of tuyeres for such injection play an importantrole toward achievement of the targeted goals. Some plants have even adopted powderblowing with the gas for desulfurization, as in injection metallurgy.

3. In early vacuum degassers, deoxidation by carbon was one of the objectives. Nowadays,it is carried out principally by deoxidizers such as ferrosilicon, aluminum, and calciumsilicide, either in the ladle prior to degassing or in the VD unit itself during degassing.The carbon-oxygen reaction is promoted in vacuum degassing either for deep decarbur-ization in ultra-low carbon steels, for enhancing rates of removal of nitrogen and hydro-gen, or for both.

4. The carryover slag from a steelmaking converter poses problems during secondarysteelmaking and has to be considered. Its modification by additions such as deoxidizersand CaO is to be included in the refining program for achieving defined objectives.

Figure 6.2 shows the various degassing processes schematically. Sales trends for the period1981–91 are presented in Figure 6.3, showing the dominant processes in the international market


during that period. The situation has not changed. One dominant process is RH (Ruhrstahl Heraus)and its variants, such as RH-OB. These come under the category of circulation degassing processes.Another dominant process is vacuum degassing in the ladle (VD), and its variants, VAD, VOD, etc.

FIGURE 6.2 Some degassing processes.

FIGURE 6.3 Share of various degassing processes in the world market, 1981–1991. Courtesy of MessoMetallurgie.

Figure 6.4 shows the RH process schematically. Molten steel is contained in the ladle. The twolegs of the vacuum chamber (known as snorkels) are immersed into the melt. Argon is injected


into the upleg. Rising argon bubbles have a pumping action and lift the liquid into the vacuumchamber, where it is degassed and comes down through the downleg snorkel. The entire vacuumchamber is refractory lined. There is provision for argon injection from the bottom, heating, alloyaddition, sampling, and sighting of the interior of the vacuum chamber.

Figure 6.5 shows the VAD process schematically. Heating is by arc with graphite electrodes,as in an electric arc furnace (EAF). Heating, degassing, slag treatment, and alloy adjustment aredone without interruption of the vacuum.

Even in late 19th century, vacuum treatment of steel melt was advocated. A major constraintwas the availability of large-capacity industrial vacuum generating systems. Comprehensive dis-cussions on this subject are available in the early publications on vacuum metallurgy.6 Figure 6.6shows a typical system. Mechanical booster pumps remove the bulk of the air and gas. However,they are not capable of lowering vacuum chamber pressure to as low as approximately 1 torr (1mm Hg). This is achieved by the use of steam ejector pumps in conjunction with mechanical pumps.

12

3

4

5

6

7

89

10

11

12

13

14

FIGURE 6.4 RH degasser. Courtesy of Messo Metallurgie.

1. Vacuum connection2. Television camera3. Sightglass with rotor4. Alloying hopper5. Alloying feeder6. Heating transformer7. Graphite rod vacuum vessel8. Upper part9. Middle part

10. Lower part11. Lifting gas connection12. Upleg snorkel13. Downleg snorkel14. Teeming ladle

1


Ejector pumps work on the principle of the diffusion pump. A jet of steam issues through a nozzleat high velocity and drags surrounding gas along with it (known as entrainment). Dusts comingout of the vacuum chamber, including condensed particles of volatile matters, settle down withcondensed steam and are removed as sludge from time to time.

6.2 THERMODYNAMICS OF REACTIONS IN VACUUM DEGASSING

6.2.1 PRINCIPAL REACTIONS

Chapter 2 reviewed the basics of metallurgical thermodynamics relevant to secondary refining ofliquid steel. Appendix 2.1 through 2.4 presented tables for important thermochemical data. Table6.1, therefore, contains equilibrium data pertaining to the principal degassing reactions only, viz.,

2

3

45

6

7

8

9

10

11

12

13

14

15

16

FIGURE 6.5 VAD unit. Courtesy of Messo Metallurgie.

1. Temperature and sampling lance

2. Telescopic tubes for vacuum-tight electrode sealing

3. Bus tube supporting arms

4. Secondary bus5. Water-cooled

flexible high-

current cable6. Electrode

tensioning device7. Vacuum hopper for

alloying agents8. Guide column for electrode

control9. Sight glass with rotor

10. Sampling valve and hopper11. Heat shield12. Vacuum connection13. Vacuum treatment vessel14. Teeming ladle with steel15. Porous inert gas bubbler16. Diaphragm for steel outlet at

ladle breakout


(6.1)

(6.2)

(6.3)

TABLE 6.1Equilibrium Relations of Degassing Reactions7

SL.No. Reaction

Equilibrium relation Unit of h K vs. T relation

Values of h at 1600°C

and 1 mm Hg

1. ppm 0.77

2. ppm 14.1

3. wt.pct 4.7 × 10−4∗

ppm 0.47∗

*At hC – 0.05 wt.%, i.e. 500 ppm. Note: 1 mm Hg = 1 torr = 1.315 × 10–3 atm.

FIGURE 6.6 Vacuum generating system.

H[ ] 12---H2 g( )=

N[ ] 12---N2 g( )=

C[ ] O[ ]+ CO g( )=

H[ ] 12---H2 g( )= hH[ ] KH pH2

1 2⁄⋅= logKH1905

T------------– 2.409+=

N[ ] 12---N2 g( )= hN[ ] K N pH2

1 2⁄⋅= logK N518T

---------– 2.937+=

C[ ] O[ ] = CO g( )+ hC[ ] hO[ ] = KCO pCO⋅ logKCO1160

T------------–

2.00–=

logKCO1160

T------------–

6.00–=

In Table 6.1,

T

is temperature in Kelvins,

h

denotes activity of solute dissolved in molten steel,and

p

is partial pressure of the concerned gas in atmosphere. In the binary iron alloys Fe-H, Fe-N,


h may be taken as equal to concentration of H and N, respectively, in parts per million. This isbecause concentrations of H and N are small and lie in the Henry’s law region. Hence, the activitycoefficient (fi) may be taken as 1 (Section 2.6). This approximation is quite valid for ordinary low-carbon and even microalloyed steels. However, the influence of alloying elements on hH and hN

would be significant for high-carbon and high-alloy steels, and solute–solute interactions are to betaken into account. Calculations have already been illustrated in the solved Example 2.4 in Chapter 2.

The above comments are applicable for carbon-oxygen reaction also. However, in this case,some departures from Henrian behavior are possible even in a simple Fe-C-O ternary melt, depend-ing on the concentrations of carbon and oxygen.

Dissolved oxygen cannot be removed from the melt as gaseous O2. A sample calculation onthe basis of Eqs. (5.2) and (5.3), and assuming that hO = WO, shows that, at atmosphereand 1600°C, WO is 26 wt.%. This demonstrates the impossibility of the removal of dissolved oxygenas O2.

Table 6.1 also shows that it is possible to obtain very low and completely satisfactory levelsof H, N, and O in the melt from a thermodynamic point of view. The C–O reaction constitutes thebasis for vacuum decarburization as well. For example, at 1600°C and 1 torr* pressure of CO, ifthe oxygen content in liquid steel (= hO) is 25 ppm, then the carbon content (= hC) would be equalto 7.1 ppm only, which is indeed very low. However, such low values are not obtained in practice.This is due to kinetic limitations.

6.2.2 SIDE REACTIONS

In addition to the principal degassing reactions discussed above, several other reactions occur duringvacuum degassing to a minor extent. A brief discussion of some of these is presented below.

Decomposition of Inclusions

Suppose that the inclusion is a nitride (such as AlN). Its decomposition is given by

AlN (s) = Al + N (6.4)

Under vacuum, N decreases, thus favoring decomposition of AlN. Oxide inclusions can be decomposed, in principle, by reduction with carbon. For example,

SiO2 (s) + 2C = Si + 2CO(g) (6.5)

A lowering of the CO pressure helps this reaction to proceed in the forward direction.Thermodynamic predictions about inclusion decomposition can be made only through calcu-

lations under specific conditions. It would depend on the stability of the oxide. For example, Al2O3

would be more difficult to decompose than SiO2. There have been a number of investigations ofthe breakdown of nonmetallic inclusions upon vacuum treatment of steel, and decreases have beenfound.8

Reaction of Liquid Steel with the Refractory Lining

Besides the above reactions, which are encouraged by lowering the chamber pressure, some moreare illustrated with examples below.

* 1 torr = 1.315 × 10–3 atm.

pO210 3–=

SiO

2

(s) + C = SiO (g) + CO (g) (6.6)


MgO (s) = Mg (g) + O (6.7)

CaO (s) = Ca (g) + O (6.8)

MgO (s) + C = Mg (g) + CO (g) (6.9)

In all these reactions, one or more gaseous species are generated. Therefore, the lowering of pressuretends to lead them to the forward direction as shown. SiO is a gas. Mg and Ca are stable gases atsteelmaking temperatures. They also have negligible solubility in liquid steel. Some data indicatethat melt-refractory reactions do occur in industrial vacuum degassing.

Example 6.1

In a vacuum degassing process, MgO is being used as ladle lining and the temperature is 1850 K.Make a thermodynamic assessment of reaction of MgO with molten steel containing 0.2 wt.% Cand 0.001 wt.% O. Ignore interaction coefficients.

Given

MgO(s) = Mg(g) + O2 (g) (E1.1)

= 6.085 × 105 + 1.005 T log T – 112.84T J/mole

Solution

1. Consider Reaction (6.7). This reaction is a combination of Reaction (E1.1) and Eq. (5.1).

(5.1)

So,

(E1.2)

Carrying out the calculations,

at 1850 K = 2.94 × 105 J mole–1 = –RT ln K7 = –RT ln

since aMgO = 1 and hO = WO, because interaction coefficients are ignored. Hence, KMgO = pMg × WO

= 0.5 × 10–8. Since WO = 10–3, pMg = 0.5 × 10–8/10–3 = 0.5 × 10–5 atm.Thermodynamically, Reaction (6.7) would occur only if pressure on the ladle wall is less than

10–5 atm. This is not achievable in vacuum degassing.

2. Consider the alternate reaction, i.e., Eq. (6.9). This reaction is the sum of Reactions (6.7) and(6.3). So,

K9 = K7 × K3 (E1.3)

12---

∆G01

12---O2 g( ) O; ∆G

O

o 117.3 103 2.889 T, J/mole+×= =

∆G7o ∆G1

o ∆GOo+=

∆G7o ρMg ho[ ]×

aMgO

-------------------------

RT ln – pMg x W O[ ]×( )=

At 1850 K,

–8


K3 = 500 and K7 = 0.5 × 10

Hence,

K9 = 250 × 10–8 = (E1.4)

Noting that

WC = 0.2, pMg × pCO = 0.5 × 10–6,

toward the top of the melt, pCO may be taken as 10–3 atm. Then, pMg = 0.5 × 10–3 atm and hencethe extent of this reaction would be appreciable. But at a depth, pCO is close to 1 atm. So pMg wouldbe very low, and as such this reaction should be negligible.

Volatilization

Many elements have high vapor pressures and therefore are expected to be distilled off to someextent during vacuum treatment. An idea can be obtained if some calculations of vapor pressures(pi) are carried out for Fe-i binary solution.

(6.10)

where = vapor pressure of pure element i at temperature under consideration

ai = activity of element i dissolved in liquid ironXi = mole fraction of i in liquid ironγi = activity coefficient (Raoultian) of i in liquid iron

Mi = molecular mass of element i

For a dilute binary solution in iron, wFe ≈ 100, and γi = constant = (Henry’s Law constant).Hence Eq. (6.10) may be simplified as

(6.11)

Table 6.2 shows some sample calculations based on Eq. (6.11). Again, the temperature dependenceof is given by the Clausius–Clapeyron equation, viz.,

(6.12)

where ∆Hv = enthalpy of vaporization of the element per mol∆Sv = entropy of vaporization of the element per mol

R = universal gas constant = 8.314 J/mol/K

pMg PCO×W C

------------------------

pi pio ai⋅ pi

o γiXi⋅ pio γi

W i

Mi

------

W i

Mi

------W Fe

MFe

---------+-----------------------⋅ ⋅= = =

pio

γio

pi pioγi

o W iMFe

100Mi

----------------⋅=

pio

log pio (atm)

∆Hv

2.303 RT-----------------------

∆Sv

2.303 R-------------------+–=

TABLE 6.2Equilibrium Vapor Pressures of Some Elements Dissolved in Molten Iron at 1600°C


Table 6.2 indicates that volatilization of Mn should be the most predominant, followed by thatof Fe. This agrees with observations. Significant loss of Mn occurs during vacuum treatment. Thedust collected at the exit of the vacuum chamber shows that it consists primarily of Fe and Mn.Tix11 reported that the flue dust in a ladle degassing installation consisted of (in weight percent)the following: FeO, 17.9; MnO, 47.0; Zn, 1.4; Cu, 2.6; Sn, 0.2; and Pb, 1.0. Olette12 reported theresults of extensive investigation carried out at IRSID, France, on vacuum distillation of minorelements from liquid iron alloys. Experiments had been carried out in a laboratory induction furnace.They found phosphorus to remain constant, and As, S, Sn, Cu, Mn, and Pb exhibited increasingelimination in the order given. Mn evaporated at such a velocity that its elimination could beconsidered as a degassing process.

The above observations are qualitatively in line with Table 6.2. S and P are gaseous atsteelmaking temperatures. Several gaseous compounds of these elements have been identified, e.g.,S, S2, S4, S6, and S8 for sulfur, and P, P2, and P4 for phosphorus. Therefore, their total vapor pressuresare really the sum of all the gaseous components. However, the calculations in Table 6.2 have beenperformed assuming S2 and .

According to Table 6.2, the vaporization of Al and Si should be negligible. However, Olette12

reported much higher vaporization rates for these elements. These were explained by the formationof volatile suboxides, SiO and Al2O. This is in line with studies on the characterization of high-temperature vapors where various other volatile suboxides such as SnO, AlO, and ZrO have beenidentified. Sehgal13 and others found that there was an appreciable loss of silicon from liquid steelunder vacuum only if the latter contained sulfur. The results were interpreted by the formation ofa volatile species, SiS.

Ohno14 has reviewed the kinetics of evaporation in detail. He has shown how the formation ofvolatile compounds like SiS, CS, CS2, SO, SO2, etc. enhances the rate of elimination of S undervacuum. Deoxidation by Si was also helped thermodynamically and kinetically under vacuum orargon atmosphere due to the formation and removal of volatile SiO.

The above findings are based on laboratory/bench-scale studies employing shallow melts, andsomewhat leisurely experiments. In principle, they are applicable to industrial degassing processes,too. However, the author has little information on their quantitative significance.

Element(i) Mi

at 1600°C,milliatmosphere

(approx.) (Ref. 9) at 1600°C(Ref. 10)

, milliatmosphere (calculated)

@ Wi = 0.05 @ Wi = 1

Al 27.0 2.66 0.029 8.0 × 10–5 1.6 × 10–3

Cu 63.5 1.2 8.6 4.5 × 10–3 0.09

Mn 54.9 665 1.3 0.44 8.8

Si 28.1 0.027 0.0013 0.35 × 10–6 6.9 × 10–6

Sn 118.7 2.66 2.8 1.7 × 10–3 0.035

Fe 55.85 0.76 – – –

S* 32.1 – – 10–5 –

P* 31.0 – – 10–9 –

*Method of calculation discussed in text.

pio

γio

pI

P2

6.3 FLUID FLOW AND MIXING IN VACUUM DEGASSING


The nature of fluid motion and the turbulence intensity during vacuum treatment of liquid steel areof considerable importance due to their significant influence on mixing, mass transfer, inclusionremoval, refractory lining wear, entrapment of slag, and reaction with the atmosphere. Rising gasbubbles are either the only source or the principal source of stirring. The bubbles are gases evolveddue to degassing (CO, N2, and H2) as well as injected argon gas. As stated earlier, argon injectionthrough submerged tuyeres or porous plugs is a must for a successful process.

The basics of fluid flow and flow in a gas-stirred liquid bath were discussed in Chapter 3. Invacuum degassing, the chamber pressure is very small as compared to the ferrostatic head of theliquid in a vessel. As a consequence, the bubbles expand enormously when they rise to a freesurface. This causes the phenomenon known as bubble bursting, as a result of which liquid metaldroplets are ejected into the vacuum chamber in large numbers.

For the purpose of understanding, the situations prevalent in vacuum degassing may be sim-plified into two categories. The first category basically is a ladle stirred by argon gas from bottom.Chapter 3, Section 3.2 presented discussions on fluid flow in steel melts in gas-stirred ladles. Briefpresentations have been made on the following:

• Growth and motion of single bubbles• Bubble size and shapes• Gas holdup and dynamics in bubble swarms• Characteristics of the rising plume, viz., gas holdup, bubble size, and bubble frequency

distributions• Flow field in the liquid bath outside the plume-isopleths of velocity, turbulent kinetic

energy, etc.• Rate of energy input per unit mass (ε), importance of buoyancy and εb

6.3.1 FLUID FLOW IN LADLE DEGASSING

Generally speaking, the above are basically applicable to flow in the melt during ladle degassing,since here also argon is introduced through purging plugs located at the ladle bottom. However,the situation would differ from that in Chapter 3 in the following ways:

1. The gas pressure above the melt is close to zero.2. The argon bubbles pick up CO, N2, and H2 as they rise through the melt.

Both these factors are expected to lead to massive volumetric expansions of the bubbles,especially when they approach the top surface of the melt. Let us consider the issue of reducedgas pressure above the melt. From Boyles law,

Pn Vb,n = PVb (6.13)

where P, Vb are pressure on the bubble and the volume of the bubble, respectively, at any depthbelow the free surface. The subscript n denotes the condition existing at nozzle exit at bottom. Letatmospheric pressure = 0. Then, P = ρlgz, where ρl is liquid density and z is the depth below thefree surface. Taking z = 2 m at the nozzle exit, and considering the size of the bubble at z = 0.1 m,Vb/Vb,n = 20, indicating a 20× expansion in volume. At z = 0.02 m, Vb/Vb,n = 100.

Szekely and Martins15 argued that rapid radial expansion of the gas bubble in vacuum processingwould impart a radial velocity to the surrounding fluid. The corresponding radial accelerationrequires a radial pressure gradient. For this pressure gradient to be maintained, the pressure in thebubble must be higher than the pressure in the bulk of the liquid at the level of the bubble. Rapid

expansion also would not allow instantaneous attainment of terminal velocity at a location, and itcalls for modification of the drag coefficient relation. Quantitative predictions of bubble radius as


a function of z agreed reasonably well with experimental data on growth of an n-pentane bubblein n-tetradecane at room temperature for a freeboard pressure of 1 mm Hg, as shown in Figure6.7.16 Such bubble expansion recently has been observed in a silicon oil room-temperature model.17

The bubble shape also changed from oval to spherical-cap. Mixing time tended to be constant,independent of the stirring power of gas per unit bath volume in low vessel pressure, presumablydue to the dissipation of most of the expansion energy.

In a buoyant plume of rising gas-liquid mixture, bubbles may be emerging as single ones fromthe nozzle. But, at a short distance above, they coalesce and disintegrate, exhibiting a spectrum ofsizes. Such a phenomenon will occur here also, thus rendering theoretical predictions of the situationextremely difficult. It is possible to state with fair confidence that the plume characteristics, as wellas the flow field in the liquid outside the plume, can be assumed to be the same as in an ordinarygas-stirred ladle situation toward the bottom part of the liquid. However, toward the top, somedeparture is expected.

Splashing of liquid droplets above the bath by rising gas bubbles is a common experience. Theextent of such splashing increases with an increase in the gas purge rate. It also increases withincreasing bubble size. This phenomenon occurs in the traditional open-hearth steelmaking processand is held to be responsible for fast transfer of oxygen from the gas phase to the bath. Rimmingphenomena during solidification of steel ingot provide another example. Visual observations duringdegassing of liquid steel also show droplet ejection in the vacuum chamber on an extensive scale.

Richardson18 has reviewed fundamental studies on bubble bursting, carried out on water andmercury at room temperature. A film of liquid tends to stick to the bubble due to surface tensioneffects while the bubble tries to emerge from the bath. The rupture of this film is responsible forejection of droplets. If a layer of slag is present at the top of the melt, such droplets cause theformation of a slag-metal emulsion. Chapter 4, Section 4.4.2, reviewed this.

FIGURE 6.7 Plot of bubble radius against height for the growth of n-pentane bubble in n-tetradecane at afreeboard pressure of 1 mm Hg.16

6.3.2 FLUID FLOW AND CIRCULATION RATE IN RH DEGASSING


In modern RH degassers, argon is also bubbled through bottom purging plugs in the ladle for bettermixing. However, theoretical computations of the flow field in the vessel have been carried out ona traditional RH degasser without gas purging from bottom. Figure 6.8 shows the flow pattern ofthe melt schematically. One of the latest studies is by Kato et al.,19 who also carried out watermodel and plant studies. The computed flow pattern (i.e., velocity distribution) is shown in Figure6.9. It agreed reasonably with experimental observations in water model. Figure 6.10 shows acomparison of calculated and measured liquid velocity at a location in the water model.

The speed of degassing in an RH unit increases with an increased rate of circulation (R) ofliquid steel through the vacuum chamber. R ranges between 10 and 100 tonnes/min and has beena subject of study for some time. Circulation velocity increases with an increasing argon flow ratein the upleg of the degasser. Recently, Kuwabara et al.20 have reported extensive measurements ofcirculation rates in several RH degassers in Japan. They also computed R from the energy balanceby considering buoyant force on bubbles and frictional dissipation in uplegs and downlegs of thevacuum chamber. This yielded the equation

R = A X (6.14)

where A = a constant

and

X = Q1/3 d4/3 {ln (P1/P2)} (6.15)

where Q = argon injection rate, Nm3/sd = I.D. of leg, m

P1 = pressure at base of downlegP2 = pressure in vacuum chamberR = circulation rate, kg/s

A plot of R vs. X (Figure 6.11) yielded a straight line, confirming Eqs. (6.14) and (6.15). The valueof A was obtained as 7.42 × 103.

FIGURE 6.8 Schematic flow pattern in the melt in an RH degasser.

0.3 m s —1


Circulation rates had been estimated from radio tracer data in a 150t RH degasser.21 Data ofKuwabara et al. have been collected in a water model. Recently, Hanna et al.22 also reported anextensive water model investigation on circulation rate. They have also discussed the limitationsof water models, since these cannot properly simulate bubble expansion due to temperature andpressure changes. Hence, they are approximate guides only. However, they have proven to be quiteeffective toward evolving more efficient degassers.

FIGURE 6.9 Computed velocity field for a water model of an RH degasser.19

FIGURE 6.10 Comparison of computed and experimentally measured velocities in liquid for a water modelof an RH degasser.19


Hanna et al.22 also investigated the influence of other variables, such as the location and numberof argon injection ports in the upleg and the depth of immersion of the legs into the bath liquid,on circulation rate. These have minor influences (at most 25% or so) but are important for moreefficient design.

6.3.3 MIXING IN DEGASSER VESSELS

In both ladle and RH degassing, the vessel containing molten steel is a ladle, and the followingdiscussions pertain to it. Chapter 3 presented a brief review about the rate of stirring energy input(ε). Chapter 4 reviewed the fundamentals of mixing phenomena and the relationship of mixingtime (tmix) with ε for gas-purged ladles. Hence, the discussions here will be very brief and restrictedto ladle and RH degassers only.

In ladle degassing, mixing is due to agitation by rising gas bubbles, both argon as well as CO,N2, and H2. As already stated in Section 3.2.3, ε due to buoyancy, i.e., εb, has been accepted as ameasure of the rate of energy input into the bath due to gas flow. εb per unit mass of liquid, i.e.,εm, as defined by Eq. (3.64), is the popular parameter employed. Hence, in ladle degassing also,we can employ the tmix vs. εm correlations recommended in Section 4.2.2. This can constitute thebasis of design and process control. It is difficult to quantitatively take into account the influenceof other gases on εm and tmix. Nor is it justified in view of the uncertainty.

So far as an RH degasser is concerned, very little data are available on tmix. Nakanishi et al.21

injected a radio tracer at the base of the upleg in a 150t RH unit. Tracer intensity was monitoredat the bottom of the downleg. Theoretical computations with the aid of a two-dimensional turbulentNavier–Stokes equation were performed. Experimental data approximately matched the assump-tions that the melt inside the vacuum chamber was perfectly mixed, with eddy diffusivity rangingbetween 100 and 500 × 10–4 m2/s, depending on the argon injection rate. Tracer additions made atthe bottom of the ladle were found to be uniformly dispersed in 8 to 10 min, whereas additions invicinity of upleg were dispersed in 4 to 5 min.

In another paper,23 Nakanishi et al. suggested that the tmix vs. εm correlation proposed by them[i.e., (Eq. 4.4)] may be employed for the RH ladle with

(6.16)

FIGURE 6.11 Variation of the circulation rate (R) with the gas flow rate parameter (X) in RH degasser.

εm12---U2R/M=

where U is the linear velocity of metal in the downleg in meters per second, M is the total massof steel in kilograms, and εm is in watts per kilogram.


Kato et al.19 carried out a numerical analysis of fluid flow in an RH vessel to calculate the rateof carbon removal. They also collected samples from several depths of 240t and 300t degasserladles to determine the average carbon removal rate. A comparison of the two approaches showedthat the experimental rate was somewhat lower than the perfectly mixed assumption and somewhathigher than the plug flow assumption, demonstrating that the actual flow was nonideal. Carbonconcentration in the vertical direction was found to be rather uniform. According to them, no deadzone existed.

6.4 RATES OF VACUUM DEGASSING AND DECARBURIZATION

6.4.1 BEHAVIOR OF GASES IN INDUSTRIAL VACUUM DEGASSING

The hydrogen content can be lowered to levels of 1 to 2.5 ppm by nearly every method, independentof the time of treatment and quality of steel.24 It has also been found that the results obtained onkilled steels agree well with the theoretical equilibria derived from Sieverts’ law for the hydrogencontent of steels if the results are related to the total pressures employed in the vacuum-treatmentprocess. In degassing of semikilled or rimming steels, lower final hydrogen levels than found inkilled steels usually may be obtained by most processes. The reason for this phenomenon is thatthe hydrogen partial pressure of semikilled or rimming steels is lower at the same total pressuredue to carbon monoxide given off by these steels. Figure 6.12 presents some data.

FIGURE 6.12 Influence of total pressure on hydrogen removal from molten steel in vacuum degassingprocesses.24

In vacuum arc remelting, the nitrogen content can be lowered to 5 to 10 ppm. Sometimes thislevel can be achieved in vacuum induction melting as well. However, typically, the nitrogen content


is brought down to 25 to 30 ppm at the most in all vacuum degassing processes. This is somewhatinsensitive to processing details. A sample calculation based on Table 6.1 shows that, at = 0.1,1, and 4 milliatmospheres (matm), the equilibrium nitrogen content of steel would be 4.3 ppm, 14ppm, and 28 ppm, respectively, at 1600°C.

Since the total pressure in the vacuum chamber during degassing lies in the range of 1 to10 matm, and the exit gas contains anywhere between 10% to 50% ranges between 0.1and 5 matm. Therefore, the nitrogen content of molten steel either attains equilibrium with exit gasor may be somewhat higher during vacuum degassing. Suzuki et al.25 have put extent of nitrogenremoval as 10 to 35%. The slowness of nitrogen removal may be ascribed to a lower value ofdiffusion coefficient as compared to that of hydrogen, and additional retardation by dissolvedoxygen and sulfur as will be discussed later. It is also possible that the somewhat higher value ofN may be due to stable nitride inclusions, such as AlN.

Figure 6.1324 shows the C vs. O relationship after vacuum degassing and compares it with C– O equilibrium in molten steel at various values of pCO. At low carbon, the oxygen contentcorresponds to pCO = 100 torr (131.5 matm). At high carbon, value of O is lower. However, itcorresponds to pCO close to 1 atm. Therefore, the C – O relationship is far off from equilibrium invacuum degassing. Such a behavior pattern may be ascribed to the following causes.

1. The oxygen content indicated in Figure 6.13 is total oxygen content. The dissolved O issomewhat lower. This reduces the difference with the equilibrium curve somewhat.

pN2

N 224, p

N2

FIGURE 6.13 Influence of carbon content on ultimate total oxygen content of the steel melt in vacuumdegassing processes.24

2. The diffusivity of oxygen in liquid steel is an order of magnitude lower as compared tothat of hydrogen.


3. The equilibrium value of dissolved oxygen is really negligible. This also has a magnifyingeffect on the discrepancy between the actual value and the equilibrium value of O.

4. The reaction between melt and oxide refractory, as discussed in Section 6.2, also hasbeen attributed to this behavior pattern.

6.4.2 RATES OF REVERSIBLE DEGASSING PROCESSES

The degassing processes are unit processes. The ladle or the degassing chamber is a reactor inaccordance with the terminology adopted in chemical engineering. In metallurgical engineering,we can profit greatly by exploiting some of the concepts and mathematical techniques that havealready been developed by chemical engineers and subsequently extended to metallurgical engi-neering. Considerable progress has been made in the last two decades in this direction.

Degassing processes, such as ladle degassing, cycling and circulation degassing (DH and RH),and argon purging in a ladle may be classified as semi-batch processes. The liquid metal is takenout only after the batch processing is over. But the gases are introduced/removed continuously. Instream degassing, however, the metal is introduced into the vacuum chamber continuously, andgases are withdrawn continuously as well. Therefore, it may be classified as a continuous stirredtank reactor (CSTR).

The rates of these processes theoretically may be estimated by performing calculations based on

• materials and heat balance• reaction equilibria• reaction kinetics and mass transfer

In our present state of knowledge, this can be accomplished by making some simplifying assump-tions. However, a lot more experimental data are required to do a better job. Major uncertaintiesrelate to fluid flow, mixing, and phase dispersions. We shall present a brief discussion of these later.

Under the circumstances, it is often advisable to carry out a considerably simplified mathemat-ical analysis for evaluating the process rates. For this, the process may be treated as isothermal andisobaric. Moreover, it may be assumed that mass transfer and reaction kinetics are extremely fast.This is not a bad assumption for many steelmaking reactions because of the high temperature andintense agitation. This allows rapid attainment of equilibrium. Therefore, for problem solving, weassume the process to be thermodynamically reversible, i.e., equilibrium is established rapidly atevery stage instantaneously. Also, the melt is well mixed. In other words, at any instant of time,equilibrium is assumed to exist among reactants and products. This is illustrated through Example6.2 on RH degassing.

Example 6.2

Calculate the rate of circulation of molten steel through the vacuum chamber in the RH degassingprocess to lower the hydrogen content of steel from 4 to 1.5 ppm in 15 min. Assume that the moltensteel attains equilibrium with respect to hydrogen inside the vacuum chamber.

Given

1. Temperature = 1577°C, weight of steel in the ladle = 50 tonnes, pressure inside thevacuum chamber = 0.1 milliatmosphere

2. Composition of molten steel: C, 0.05%,; Cr, 5%; Ti, 0.5%; Ni, 2%, remainder Fe

3. eHC 0.04,eH

Cr+ 0.005,eHTi 0.22–= = =

Solution


1. Hydrogen balance:

Rate of removal of hydrogen from steel (g/min)

= rate at which hydrogen is transferred to vacuum (g/min) (E2.1)

Now,

(E2.2)

where W is the weight of steel in tonnes, t is time in minutes, and [ppmH] denotes concentrationof H in parts per million at any instant in time. Again,

(E2.3)

where R is the circulation rate of liquid steel through the vacuum chamber in tonnes/min, and[ppmH]eq. denotes [ppmH] in equilibrium with in the vacuum chamber (as assumed in problem).Equating Eqs. (E2.2) and (E2.3),

(E2.4)

Integrating Eq. (E2.4) within limits t = 0, [ppmH]initial and t = tf, [ppmH] = [ppmH]final,

(E2.5)

For calculation of [ppmH]eq, assume that the gas in the vacuum chamber is primarily H2 (nota bad assumption, since it is a killed steel). So = 0.1 × 10–3 atm.

From Table 6.1, hH = 0.623. Again, from Eq. (2.56).Substituting values, fH = 0.851. So,

Or, from Eq. (E2.5),

R = 4.82 tonnes/min (Ans.)

6.4.3 KINETICS OF DEGASSING AND DECARBURIZATION GENERAL FEATURES

Degassing and decarburization reactions involve two phases: molten steel and gas. The overallreaction consists of the following kinetic steps:

1. Transfer of dissolved gas-forming elements H, N, C, and O from the interior (i.e., bulk)of the liquid to the gas/liquid interface

2. Chemical reactions [i.e., Reactions (6.1) to (6.3)] at the gas–liquid interface

m1( )m2( )

m1 W 106 d ppmH[ ] 10 6–×dt

---------------------------------------××– Wd ppmH[ ]

dt-----------------------×–= =

m2 R 106 ppmH[ ] ppmH[ ] eq.–( )×× 10 6–× R ppmH[ ] ppmH[ ] eq.–( )= =

pH2

d ppmH[ ]ppmH[ ] ppmH[ ] eq–

-------------------------------------------------RW-----dt=

RWt f

-----ppmH[ ] initial ppmH[ ] eq–ppmH[ ] final ppmH[ ] eq–

----------------------------------------------------------ln5015------

4 ppmH[ ] eq–1.5 ppmH[ ] eq–-------------------------------------ln= =

pH2

log f H eHC W C eH

Cr W Cr eHTi W Ti×+×+×=

ppmH[ ] eq0.6230.851------------- 0.73= =

3. Transfer of gaseous species H2, N2, and CO from the interface to the bulk gas4. Nucleation, growth, and escape of gas bubbles


5. Mixing in the bulk liquid6. Mixing in the bulk gas

From our knowledge of reaction kinetics here as well as in similar situations, it has been takenas established that steps 4 and 6, i.e., mass transfer and mixing in the gas phase, are very fast andare not rate controlling, even partially.

Chapter 5, Section 5.2.1 has reviewed the fundamentals of nucleation in connection with theformation of deoxidation products. Equation (5.39) gives the relationship between critical radiusof nucleus (r*) with other variables for homogeneous nucleation, i.e.,

(5.39)

For the equilibrium of the gas bubble with the liquid at constant temperature,

dG = 0 = VdP + (dG)chemical (6.17)

So,

(6.18)

and hence,

(6.19)

where ∆P* = excess pressure inside the gas bubble with radius r*

The gas law for the critical nucleus may be written as

(6.20)

Here,

with and in atm and m3 respectively, N is the Avogadro number, and n* is the number of

molecules in the critical nucleus (assume 100). Combinations of Eqs. (6.19) and (6.20) yield

(6.21)

where σ = 1.6 Nm–1 for molten steel. Taking T = 1850 K, Eq. (6.21) gives a value of ∆P* as 7.2× 104 atm.

r* 2σ∆G/V( )

-------------------–=

∆GV

--------

chemical

∆GV

--------

in Eq.(5.39)

∆P*–= =

r* 2σ∆P*-----------=

pb* V b

*⋅ n*N------

RT⋅=

∆P* Pb*≅ V b

*, 43---π r*3= R, 82.06 10 6–× m3 K

1– mol 1–=

Pb* V b

*

Pex* atm( ) 1.54 106× σ3

T-----

1 2⁄

=

It is impossible to generate such high excess pressure via the steelmaking reactions. In con-nection with the basic open hearth (BOH) process of steelmaking, this issue had been investigated,


and it was concluded that nucleation of gas bubbles is not required. They grow on existing gas-containing cavities in the refractory lining of the hearth.26 Nucleation of gas bubbles is not at alla problem, as it appears from several other studies, including carefully conducted cold modelstudies.25,27

In the early days, ladles for degassing were not fitted with gas purging arrangements. It wasfound that, initially, there was vigorous evolution of gas bubbles. After a time, when gas evolutionceased, degassing rates were very slow. The need for some stirring was sensed. This was achievedby electromagnetic stirring in ASEA-SKF ladles. Here, stirring helped mass transfer. Now, ladleshave argon purging facilities. As a result, nucleation and growth are not required, as H2, N2, andCO either would be picked up by argon bubbles or would escape into vacuum chamber directly atthe stirred top surface.

It has been established that the rates of nitrogen absorption and desorption by molten iron andsteel are partially controlled by slow surface reaction. This will be discussed separately later. Forthe time being, surface reaction is assumed to be fast. Hence, kinetic steps 1 and 5, viz., masstransfer and mixing in the liquid, have been generally considered to be slow and rate controlling,either singly or jointly.

Section 4.5, in Chapter 4, discussed the issue of mixing vs. mass transfer control in steelmaking.It presented an analysis by Ghosh28 that tried to show that the mixing times for 95% mixing are inthe same overall range as the 95% conversion times for mass transfer controlled reactions for somesteelmaking processes. Since both have rate expressions as for first-order reversible processes, itis often difficult to say whether a process is controlled by slow mixing or slow mass transfer.

For mass transfer between a gas and a liquid, surface renewal theory is to be applied. Section4.3.2 has reviewed it. It predicts that km,i should be proportional to , where km,i is the masstransfer coefficient, and Di is diffusivity of solute i. It was also pointed out in Section 4.4.2 that,in view of uncertainties in the surface area of the melt, experimental rate data generally allowdetermination of the lumped parameter ka with the help of Eq. (4.36) or (4.37).

If it is desired to further generalize the empirically determined rate without attributing it tomass transfer or mixing, it is better to define the empirical (i.e., experimentally determined) rateconstant as

(6.22)

Takemura et al.29 determined values of ki,emp parameters for the removal of carbon and hydrogenin RH injection process. Figure 6.14 presents these as a function of argon gas flow rate. It may benoted that there is virtually little difference between them, i.e., ki,emp parameters were approximatelythe same for both carbon and hydrogen.

DC = 7.2 × 10–9 m2 s–1 and DH = 10–7 m2 s–1 at 1600°C. Hence, if mass transfer were ratecontrolling, then from Eq.(4.25),

Since this is not the case, it may be concluded that mass transfer was not rate controlling. On theother hand, rate control by mixing theoretically predicts same value of ki,emp for both carbon andhydrogen.

Bauer et al.30 measured rates of removal of hydrogen, oxygen, sulfur, and nitrogen in a 185tVOD unit. Quantitative comparison of ki,emp parameters was not possible on the basis of their data.

Di1 2⁄

dW i

dt----------– ki ,emp W i W i

e–( )=

kH ,emp

kC ,emp

--------------10 7–

7.2 10 9–×-----------------------

1 2⁄

3.73= =


But they indicated behavior similar to that obtained by Takemura et al.29 Therefore, it does notseem to be correct to assume mass transfer control for degassing processes.

6.4.4 IMPORTANCE OF THE akm PARAMETER

Regardless of whether the mass transfer is rate controlling, the degassing rate can be speeded uponly if the ak parameter is large. Assuming that k = km, k can be increased by enhanced stirring.But there is a limit to it. As discussed in Section 4.3.2, k m,i = (DiS)1/2 in turbulent flow. S isDanckwerts’ surface renewal factor. S has been found to range between 5 and 25 s–1 in mildturbulence, going up to 500 s–1 in high turbulence. This gives the maximum ratio of

In contrast to this, the specific surface area (a) can be increased by a factor of even 104 by thecreation of small gas bubbles and metal droplets ejected into the gas space.31 Hence, for fastdegassing, a large value of specific surface area is a prerequisite. It can be achieved only if a largenumber of gas bubbles are present in the melt during processing or if the molten steel is dispersedinto the gas phase as fine droplets. Let us examine the various degassing processes from this pointof view.

1. In ladle degassing, as soon as the chamber is evacuated, rapid growth and evolution ofbubbles occur due to the initially large thermodynamic supersaturation. Rapid evolutionof bubbles also causes ejection of fine droplets of liquid steel into the empty space ofthe vacuum chamber, causing a further rate increase. However, after few minutes, bubbleevolution ceases, and rate of degassing decreases drastically unless there is argon purgefrom the bottom.

2. In stream degassing, the steel is introduced continuously into the vacuum chamber as astream. Rapid formation and bursting of gas bubbles in the stream cause the latter todisintegrate into fine droplets. Hence, degassing is fast throughout the processing.

FIGURE 6.14 ki,emp vs. argon flow rate for carbon and hydrogen in the RH-injection process.29

km ,i( )high turbulence

km ,i( )low tubulence

------------------------------------5005

---------

1 2⁄

10= =

3. In the DH process, molten steel is drawn into the vacuum chamber as a shallow pool.Again, rapid gas evolution and droplet ejection lead to fast degassing of the melt inside


the chamber.4. In RH process, steel is continuously drawn into the vacuum chamber by both the vacuum

action and the lifting effect of rising argon bubbles. These argon bubbles expand andburst out of the melt in a vacuum chamber, thus assisting in the creation of drops andbubbles and assuring a fast rate of degassing throughout the processing.

6.4.5 KINETICS OF DESORPTION AND ABSORPTION OF NITROGEN BY LIQUID IRON

It has already been mentioned that degassing of nitrogen has to be considered separately, since itskinetics includes some special features. Pehlke and Elliott,32 in their pioneering study, measuredthe rate of absorption and desorption of nitrogen by a clean liquid iron surface in an inductivelyheated melt in a modified Sieverts apparatus. They derived the following important findings.

1. Absorption and desorption were first-order reversible processes with approximately thesame rate constant. Rate (r) of desorption was given by

r = AkN ([WN] – [WN]e) (6.23)

where A = liquid-gas interfacial area[WN], [WN]e = weight percent of dissolved nitrogen in iron respectively at that

instant and at equilibrium with the partial pressure of nitrogenabove the melt

kN = first-order rate constant

2. The increase in oxygen content of the liquid iron decreased the rate drastically. Figure6.15 presents a typical behavior pattern, which shows that .

Several investigators measured the surface tension (σ) of liquid iron with variable concentrationsof oxygen dissolved in it. Figure 6.1633 shows the variation of σ with ln[WO] at 1550°C. FromGibbs Adsorption Isotherm,

(6.24)

where ΓO = excess oxygen at surfaceµO = chemical potential of oxygen dissolved in liquid iron

Noting that aO ∝ WO, from Figure 6.16, it was inferred on the basis of the above equation thatΓO is positive. In other words, oxygen is surface active in liquid iron and prefers to stay at thesurface. Darken and Turkdogan34 critically reviewed this inference. Theoretical calculations revealedthat most of the surface would be covered by oxygen atoms at WO = 0.05 wt.% at 1550°C. Figure6.17 shows the fraction of surface covered (θ) as a function of WO.

On the basis of the above, Pehlke and Elliott32 quantitatively explained the dependence of kN

on WO by assuming that the rate was controlled by slow surface reaction, and that adsorbed oxygenatoms acted as barriers to it, consequently retarding the rate. Sulfur is also surface active in liquidiron. It also has been found to retard nitrogen absorption/desorption rates. This phenomenon hasbeen well established in laboratory as well as in industry through numerous subsequent studies.As an example, Figure 6.18 shows influence of sulfur on removal of nitrogen from molten steel

kN W O[ ]∝

ΓOdσdµO

---------– dσRTd ao[ ]ln( )-------------------------------–= =


during degassing in a 185t ladle.30 Hence, the melt should be well deoxidized and desulfurizedbefore attempting to remove nitrogen.

Although Pehlke and Elliott claimed the kinetics to be exclusively controlled by slow surfacereaction, this view was not accepted by all. In view of its importance, there have been severalfundamental laboratory investigations in the last two decades. The current view may be summarizedas follows.

• The rate is primarily controlled by mass transfer in liquid iron at low oxygen and sulfurlevels.

• At normal oxygen and sulfur levels in liquid iron, partial rate control by slow interfacialreaction is also exhibited. Some investigators even considered mass transfer of N2 in gasphase as well.

• It has also been concluded by several investigators that the interfacial reaction is a second-order process, i.e., the rate of interfacial chemical reaction (rC) is given by

FIGURE 6.15 Influence of oxygen content on the absorption rate of nitrogen by liquid iron at 1823 K.32

FIGURE 6.16 Variation in the surface tension of liquid iron with its oxygen content at 1823 K.34 Reprintedby permission from American Chemical Society.


(6.25)

where kC = chemical rate constant

A quantitative correlation of rate with oxygen and sulfur content of steel has been proposedby Fruehan and Martonik35 at constant temperature as

(6.26)

where kN is the actual first-order rate constant and is less than the mass transfer coefficient fornitrogen in liquid steel (km,N), and a and b are empirical constants.

FIGURE 6.17 Fraction of surface covered (θ) vs. [WO] for liquid iron at 1823 K (estimated).34

FIGURE 6.18 Influence of sulfur content of liquid steel on the extent of nitrogen removal during ladledegassing.30

rC AkC W N[ ] 2 W N[ ] e2–( )=

kN

km ,N

1 a W O[ ] b W S[ ]+ +------------------------------------------------=

Evaluation of kC based on Eq. (6.25) requires the elimination of mass transfer effects fromactual rates through theoretical analysis. It has been done by several investigators. Harada and


Janke36 have summarized their own findings as well as those of some other recent studies. KC wascorrelated with variables at 1600°C by an equation of the following type:

(6.27)

where a, b, and c are empirical constants. Figure 6.19 presents the results of some investigations.36

It may be noted that data obtained at reduced pressures (curve 1 and data points of Ref. 36)corresponding to vacuum degassing conditions do not agree with those obtained at normal pressures(curves 3, 4, and 5). There was no satisfactory explanation for this. Formation and evolution oftiny gas bubbles at reduced pressures, causing surface flows in melt, may be responsible for sucha discrepancy.

It was stated in Section 4.3.2 that the presence of surface-active species on the surface of aliquid would retard the motion of fresh eddies coming from the bulk of the liquid (Figure 4.9a),resulting in a smaller value of km as compared to that for a clean surface. Richardson37 suggestedthat this may, in principle, explain the retardation of rate in the presence of oxygen and sulfurwhere mass transfer is occurring in a turbulent flow situation. This alternative mechanism has notbeen seriously considered yet.

As discussed in Section 6.4.1, industrial vacuum degassing is not very efficient in the removalof nitrogen. Suzuki et al.25 suggested the extent of removal to be 10 to 35%. To a significant extent,the retarding influence of oxygen and sulfur is responsible for this, as well as for the irreproduciblenature of removal. However, as stated earlier, it has been possible to achieve fairly low nitrogenlevels in a well desulfurized and well deoxidized melt. Of course, even then, vacuum degassingalone is not enough. Nitrogen is picked up by molten steel at all stages of processing, viz., primarysteelmaking, tapping, and teeming, due to contact with N2 in an air/gaseous environment. A low-nitrogen steel can be produced (WN < 20 ppm) only if precaution is taken at all stages to preventits absorption. Chapter 8 offers further discussion on this subject.

kCaφ f N( )

1 b hO[ ] c hS[ ]+ +------------------------------------------=

FIGURE 6.19 Variation of kC for nitrogen desorption with dissolved oxygen and sulfur content of moltensteel at 1873 K.36

6.4.6 KINETIC CONSIDERATIONS FOR INDUSTRIAL VACUUM DEGASSING AND DECARBURIZATION


In industrial vacuum degassing, as already mentioned in Section 6.1.1, the treatment time shouldbe short enough to logistically match with converter steelmaking on the one hand and withcontinuous casting on the other hand. To achieve this, in addition to the proper choice and designof the process, the principal variables are:

• pumping rate of vacuum equipment (also known as exhaust rate)• rate of injection of argon below the melt

Increasing the Ar flow rate increases the rate of degassing and gas evolution. This tends to raisechamber pressure and requires a higher exhaust rate. The dynamic balance between the two determinesthe chamber pressure. This is illustrated for ladle degassing by Figure 6.20.38 In the initial stage, gasevolution is much faster, leading to higher chamber pressure. Predeoxidation is helpful, since it lowersthe extent of CO evolution, thus allowing quicker attainment of a steady vacuum. The need foroptimization has been illustrated by Soejima et al.39 (Figure 6.21) theoretically. The figure shows that,for an RH degasser, below a certain exhaust rate, the argon flow had no effect on rate constant k. Noris there any advantage in having a high pumping rate if Ar flow rate is not adequate.

Reaction sites are as follows:

• argon bubble/melt interface • free surface of the melt• surfaces of ejected liquid metal droplets• separately formed gas bubbles through growth inside the melt

Argon bubbling as such is ineffective without vacuum. This can be illustrated by analyzing thedehydrogenation of steel melt by argon purging, assuming it to be a thermodynamically reversibleprocess. It is based on:

1. Hydrogen balance, viz., the rate of removal of hydrogen from molten steel = the rate atwhich hydrogen is going out with the exit gas

2. The assumption that the argon leaving the ladle is in equilibrium with the molten steelat that instant

FIGURE 6.20 Variation of chamber pressure with treatment time for ladle degassing.38


This analysis would predict the highest possible rate of hydrogen removal by simple argonpurging from the bottom. Going through the derivation steps, the following equation was derived:31

(6.28)

where M is the mass of steel in tonnes and V is the volume of Ar (in Nm3) to be passed for loweringH from [ppmH]o to [ppmH].

Assuming [ppmH]o = 4, [ppmH] = 2, T = 1873 K, and fH = 1, calculations show that 1.67 Nm3

of argon would be required per tonne of steel. It is indeed a very high and uneconomical consump-tion of argon.

As discussed in Section 6.3.1, argon bubbles would expand enormously as they approach thetop surface of melt in the vacuum chamber. Hence, the dominant volume would be present onlybelow the top surface, and this is the region where bubbles pick up large quantities of H2, CO, andN2. Bannenberg et al.40 have illustrated this through their mathematical modeling exercise for aladle degasser.

Yano et al.41 have developed a dynamic model in connection with improvement of the RHprocess for production of ultra-low-carbon and low-nitrogen steel. They have not considered ejecteddroplets separately but have taken them as part of the free surface. Higbie’s surface renewal theory(Section 4.3) was employed for calculation of rate constants at each site. Steel in the reaction vesselwas assumed to be perfectly mixed in agreement with that by Kato et al.19 The chamber pressurewas calculated by balancing the gas exhaust rate and the gas forming rate. Effective reaction surfacearea was estimated by fitting the calculated rate with measured values.

Figure 6.22 shows some calculated results of Yano et al.41 The process was divided into twostages. Stage I was characterized by the rapid generation of gases (principally CO). Hence, thereaction inside the melt had a dominant share in decarburization. In stage II, this subsided due toa lowering of the contents of C, H, and N in the melt. Then, the free surface (including ejecteddroplets) was found to play the most dominant role, followed by the argon bubble/melt interface.We may assume that this pattern would be valid only qualitatively. Quantitatively, the ratios areexpected to exhibit a range depending on the assumptions in model formulation and the nature ofplant data.

Yamaguchi et al.42 carried out kinetic studies in an RH degasser of Kawasaki Steel Corporationin connection with production of ultra-low carbon steel. The mechanism was assumed to be rate

FIGURE 6.21 Influence of pumping rate and argon flow on decarburization rate constant in RH degasser.39

M ppmHKH

2

f H2 ppmH[ ]

--------------------------+

ppmH[ ] oKH

2

f H2 ppmH[ ] o

----------------------------+

–103

11.2----------V=

controlled jointly by the mass transfer of carbon and oxygen in the molten steel in the vacuumvessel. In the low carbon range (<200 ppm), the oxygen content of the melt did not have significant


influence on the rate of decarburization. In the ultra-low carbon range (<50 ppm), the Akm parameter(m3s–1) (also known as the capacity coefficient) for decarburization was correlated with othervariables through regression analysis of plant data as follows:

(6.29)

where AV = cross-sectional area of RH vacuum vesselR = circulation flow rate of liquid metalC = carbon concentration of melt in vacuum vessel in parts per million

The dependence of Akm on carbon concentration is very significant. The authors have explainedit as due to the predominance of the surface of ejected droplets as site for decarburization. Theextent of droplet ejection depended on both CO evolution as well as the argon flow rate.

The injection of argon gas is responsible for the circulation of melt through the vacuum vesselin an RH degasser. Degassing rate increases with an increasing circulation rate in RH. This is wellestablished.25,41 For the situation in Figure 6.22, it is expected that the exhaust rate would havesignificant influence on rate of decarburization in stage I, in view of the large rate of generationof gases, but not in Stage II. Yano et al.41 verified this from their plant data as well. Therefore, theattainment of ultra-low carbon is possible by having a high exhaust rate and low/moderate argonflow rate in stage I (i.e., left region of Figure 6.22) and a moderate exhaust rate and relatively highargon flow rate for stage II (i.e., right region of Figure 6.22).

Akm AV0.32 R1.17 C1.48⋅ ⋅∝

FIGURE 6.22 Typical results of calculations by Yano et al.41 for decarburization in an RH degasser, showingkinetic behaviors in different stages: (a) low exhaust rate and (b) high exhaust rate.

The primary focus nowadays is to speed up the rate of decarburization under vacuum so as toproduce ultra-low-carbon steel (WC < 20 ppm) in a short treatment time. However, the findings


therein are broadly applicable to removal of nitrogen and hydrogen as well. For example, the rateof nitrogen removal has been shown to depend on the rate of decarburization41 as follows:

AkC [in Eq. (6.25)] = 0.29 + 8900 VC (6.30)

where AkC is in units of (% · s)–1 and VC is the rate of decarburization in %C per second.Macroscopic liquid flow in a gas-stirred ladle is recirculatory in nature. Chapter 3 presented

elaborate discussions on the subject, and hence it need not be repeated. Nakanishi et al.43 carriedout experimental measurements in a 50t VOD vessel. A Co tracer was employed for collecting dataon mixing behavior. Deoxidation was carried out by aluminum addition. From the variation ofradio-tracer intensity at a location of the melt as a function of time, the circulation rate of metalwas determined. It ranged between 15 to 56t/min, depending on argon purging rate. The deoxidationrate constant (kO) ∝ R ∝ Q1/2.

Bauer et al.30 and some others have employed the circulation concept in a ladle degasser. Theydefined R as ratio of (treatment time/mixing time). Actually, it should not be called a rate. It issimply a measure of the number of circulations. From a fundamental point of view, it seems to besuperior to simply using time, since the former brings the mixing criterion into consideration.

Argon injection enhances the rate of vacuum degassing and decarburization by

• imparting stirring to the melt• causing circulation of liquid metal• enhancing gas–metal interfacial area through the generation of bubbles and drops

Hence, rate constants for degassing and decarburization would increase with an increasingvolumetric flow rate of argon. In general, it may be stated that k ∝ Qn, where 0 < n < 1. For asimple situation, such as a gas-stirred melt in ladles without vacuum, ν may lie between 1/3 and1/2, depending on whether mixing or mass transfer controls the rate (see Chapter 4).

Such a simplistic approach would not be applicable to vacuum degassing, due to complexitiesarising out of bubble expansion and droplet ejection, design of the RH vessel, generation of CO,etc. In addition, the role of argon injection would depend on which stage is under consideration(see Figures 6.20 and 6.22). For an RH degasser, the experimental data of Taemura et al.29 indicatedthat ν ranged between 1/3 and 1/2. Data of Yano et al.41 indicate κ ∝ Ρ1/3 approximately for StageI. Again, Ρ ∝ Q1/3 [Eq. (6.15)]. This means that k ∝ Q1/9 approximately. This corresponds to thelow exhaust rate in Figure 6.21. However, in the ultra-low carbon range, as Eq. (6.29) indicates, nis approximately 1/2. Hence, it tentatively may be concluded that n will be less than 1/2 in vacuumdegassing. Kleimt and Kohle44 have developed a dynamic model of RH decarburization. It has beenverified by plant data, which included waste gas analysis and gas flow rate measurement. Thephysics and thermodynamics of the process constituted the basis.

6.5 DECARBURIZATION FOR ULTRA-LOW CARBON (ULC) AND STAINLESS STEEL

For stainless steelmaking, before the advent of secondary steelmaking, decarburization of steel wascarried out in primary steelmaking furnaces only. High-carbon ferrochrome is much cheaper thanlow-carbon ferrochrome for alloying during the manufacture of stainless steels in an electric arcfurnace. However, it raises the carbon content of the melt. This is undesirable, since stainless steelgrades demand carbon content less than 0.03% or so. Since Cr also forms stable oxides, removalof carbon by oxidation to CO is associated with the problem of simultaneous bath chromiumoxidation.

Thermodynamic measurements revealed that the higher the temperature of the bath, the greaterthe tendency for preferential oxidation of carbon over chromium. This led to the practice of oxygen


lancing in an electric arc furnace (EAF) for oxidation as well as for raising bath temperature. Sincea decrease of partial pressure of CO would assist preferential decarburization further, vacuum-oxygen decarburization (VOD) and argon-oxygen decarburization (AOD) processes were inventedfor stainless steelmaking. Oxygen is blown into the steel melt either under vacuum or along withargon in these processes, respectively. This made the EAF simply a melting unit and transferredthe job of decarburization to VOD or AOD vessels. Now, decarburization under vacuum is practicedfor carbon steels and also for ULC, for which oxygen injection facilities are provided in RH (RH-OB) and ladle degassers. For large scale production of stainless steel, the use of an LD converterin place of an EAF is cheaper. A combination of converter and VOD has led to development ofthe VODC (i.e., vacuum-oxygen decarburization converter).

Choulet et al.45 have reviewed the status of stainless steel refining. Demand for stainless steelwas projected to grow at an annual rate of 4 to 6% over the next decade and may reach a worldproduction of 18 million tonnes in A.D. 2000. More remarkable is the growth of ferritic stainlesssteel, whose share was about 22 to 30% of total stainless steel production in North America, Europe,and Japan. The advent of ultra-low carbon and nitrogen containing ferritic grades for automobileexhaust systems is worth mentioning. A variety of refining processes have been patented, as shownin Figure 6.23.45 Even then, the AOD process accounted for 75.6% of total stainless steel productionin western countries in 1991. This, of course, includes variants of AOD in which top blowing isalso employed.

Shinkai et al.46 carried out a kinetic analysis of plant data of VOD processes for stainless steelrefining at Yawata works and concluded as follows:

1. The nitrogen desorption reaction mainly occurs at the surface of CO bubbles, whenstrong CO gas formation in the bath occurs in the early stage of the operation.

2. About 70% of the nitrogen desorption reaction occurs at the bath surface, and 30% atthe surface of the injected Ar gas bubble when CO gas formation decreases.

3. The decarburization reaction by the CO gas formation in the bath is predominant at theearly stage of operation.

The above conclusions are qualitatively in agreement with those of Yano et al.41

(a) AOD(b) RH-OB / KTB (c) VOD (d) VODC / AOD-VCR

(e) K-BOP (f) CLU (g) LD / MRP

FIGURE 6.23 Secondary steelmaking processes for stainless steelmaking.45 Reprinted by permission of Iron& Steel Society, Warrendale, PA, U.S.A.

6.5.1 PRODUCTION OF ULTRA-LOW CARBON STEEL BY RH-OB PROCESS


To meet increasing demand for cold-rolled steel sheets with improved mechanical properties, andto cope with the change from batch-type to continuous annealing, the production of ULC steel(C < 20 ppm) is increasing. A major problem in the conventional RH process is that the timerequired to achieve such low carbon is so long that carbon content at BOF tapping should belowered. However, this is accompanied by excessive oxidation of molten steel and loss of ironoxide in the slag. It adversely affects surface the quality of sheet as well.

Hence, decarburization in RH degasser is to be speeded up. This is achieved by some oxygenblowing (OB) during degassing. The RH-OB process, which uses an oxygen blowing facility duringdegassing, was originally developed for decarburization of stainless steel by Nippon Steel Corp.,Japan, in 1972. Subsequently, it was employed for the manufacture of ULC steels. The popularityof RH-OB can be noted from Figure 6.3. The present thrust is to decrease carbon content fromsomething like 300 ppm to 10 or 20 ppm within 10 min.

In line with the general trend of making secondary refining units versatile for all purposes,viz., degassing, decarburization, desulfurization, removal of inclusions, and temperature and com-position adjustments, powder injection facilities were subsequently added to RH-OB. Obana47 hasreviewed these developments. Figure 6.24 shows the RH-injection (RH-PB) process schematically.In the Oita steelmaking plant of Nippon Steel, two units have been installed for treating as muchas 90% of BOF heats. During oxygen blowing, aluminum is also added. Aluminum finally deox-idizes the melt. Oxidation of aluminum also generates heat and raises the temperature of the melt.Al consumption of 1 kg/t raises steel temperature by 30°C, thus countering the temperature drop.A heating rate of 10°C/min was achieved at an oxygen flow rate of 0.2 Nm3/min · t.47

It seems that, in RH-OB, RH-PB, stirring and oxygen/powder injection are being done in someplants through tuyeres located below the melt in the ladle. However, oxygen spraying by top lanceand injection by immersed lance seem to be more common. Turkdogan48 has discussed the role ofladle slag in RH degassing. He has concluded that slag FeO reacts with dissolved carbon in steelabove about 200 ppm carbon. The higher the initial carbon content, the greater the tendency forreaction with slag FeO.

FIGURE 6.24 The RH injection process.

It may be noted from Section 6.4.6 that most of the current investigations on kinetics andmechanisms of degassing were undertaken in connection with the manufacture of ULC steel in RH


degassers, i.e., RH-OB or its variants such as Kawasaki top blowing (KTB).Inoue et al.49 of NKK Corporation, Japan, have reported attempts to accelerate decarburization

in an RH degasser. Based on room-temperature model work, they introduced eight additional nozzlesinto the vacuum vessel of the degasser for argon purging. These were located just above the snorkellevel, into the vessel lining for side-blowing argon into the melt. The gas flow rate into the snorkelfor circulation was 2.5 Nm3/min and into vacuum vessel at 0.8 Nm3/min. The latter enhanced therate by a factor of 1.6 on the average and enabled a lowering of carbon content from 200 ppm to10 ppm within 10 min. It demonstrates the effect of design modification on rate. Another exampleis a doubling of the decarburization rate in an RH degasser at Kawasaki Steel Corporation, Japan,by enlarging the snorkel diameters by 50%, thus avoiding an increase in pumping capacity, whichis costly.50

As stated in Section 6.4.6, Yamaguchi et al.42 did not find any significant influence of the oxygencontent of liquid steel on the decarburization rate in the ULC range. However, at a carbon contentof more than 200 ppm, an increase in dissolved oxygen content due to concurrent oxygen blowingenhanced the decarburization rate almost proportionately. It indicated that oxygen blowing waseffective in the high-carbon range only.

6.5.2 THERMODYNAMICS OF DECARBURIZATION OF HIGH-CHROMIUM STEEL MELTS

Like iron, chromium exhibits two valences, viz., Cr2+ and Cr3+, when it is oxidized. An issue onwhich controversies have persisted for a long time, and perhaps persist now, is whether Cr is presentin slag as CrO or Cr2O3 or something else. From investigations over years, the picture that emergesis as follows. Cr is capable of exhibiting a variable Cr2+/Cr3+ ratio in slag like iron, depending onthe oxygen potential and basicity. In reducing slags or acid slags, CrO is the dominant oxide. Inoxidizing or basic slags, Cr2O3 is dominant. During the oxidizing period of VOD or AOD, the slagmay be assumed to be saturated with chromium oxide in view of the very low quantity of slag pertonne of metal. Appendix 5.1 shows that Cr3O4 is the stable deoxidation product if the Cr contentof iron is above 8%. Toker et al.51 determined the phase relations and thermodynamics of a Cr-Osystem. They found Cr3O4 coexisting in equilibrium with the liquid oxide in the temperature rangeof 1650 to 1705°C.

Hence, the reaction for the process is written as

Cr3O4(s) + 4C = 4CO(g) + 3Cr (6.31)

The equilibrium constant for the above reaction is

(6.32)

since the activity of Cr3O4 is 1. Eq. (6.32) may be rewritten as

4 log hC = 3 log hCr + 4 log pCO – log K31 (6.33)

i.e.,

4 log WC + 4 log fC = 3 log WCr + 3 log fCr + 4 log pCO – log K31 (6.34)

K 31pCO{ } 4 hCr[ ] 3×

hC[ ] 4--------------------------------------=

The terms fC and fCr are functions of temperature and composition. K31 is a function oftemperature. All of these make the resulting equation somewhat cumbersome to use. Hilty and


Kaveney52 simplified it as

log [WCr/WC] = –13800/T + 8.76 –0.925 pCO (6.35)

Figure 6.25 shows this relationship at 1 atm CO pressure. It demonstrates that a very high temper-ature is required if we wish to obtain less than 0.04% C at above 15% Cr. Lowering pCO allows usto achieve that at a much lower temperature (Figure 6.26).52

Since nickel dissolved in liquid iron has a small but significant influence on the thermodynamicactivities of carbon and oxygen., Eq. (6.35) was modified as

log [WCr/WC] = –13800/[T + 4.21 WNi] + 8.76 – 0.925 pCO (6.36)

For the reduction of chromium oxide from slag by ferrosilicon during the last stage ofVOD/AOD operation, Hilty et al.52 assumed the following reaction:

Cr3O4(s) + 2Si = 3Cr + 2(SiO2) (6.37)

(6.38)

Noting that and in slag are functions of slag basicity, an equilibrium relation wasarrived at from Eq. (6.38). However, for practical uses, statistically fitted empirical coefficients arerecommended as follows:

log(WCr)slag = 1.283 log[WCr] – 0.748 log[WSi] – 1.709 log V – 0.923 (6.39)

where V = slag basicity = (CaO + MgO)/SiO2

FIGURE 6.25 Chromium-carbon-temperature relationship in oxygen-saturated steel melt.52 Reprinted bypermission of Iron & Steel Society, Warrendale, PA, U.S.A.

K37

hCr[ ] 3 aSiO2( )2

hSi[ ] 2 aCr3O4( )

--------------------------------=

aSiO2aCr3O4


6.5.3 ARGON-OXYGEN DECARBURIZATION

Figure 6.23 presents a sketch of the reactors. In conventional argon-oxygen decarburization (AOD),there was no top blowing. However, current AOD vessels are mostly fitted with a concurrent facilityfor top blowing of oxygen like an LD converter. The Ar + O2 mixture is blown through the immersedside tuyere. Initially, when the carbon content of the melt is high, blowing through a top lancedominates. Even the gas mixture through side tuyere has a high percentage of O2. However, asdecarburization proceeds, O2 blowing is cut down in stages, and Ar blowing is increased. Some stainlesssteel grades contain nitrogen as a part of the specification. There, N2 is employed in place of Ar.

Choulet et al.45 have reviewed the practice. Figure 6.27 illustrates a mixed gas-blowing program.Use of a supersonic top lance like LD allows post-combustion of evolved CO gas with a consequentminimization of toxic carbon monoxide in the exit gas as well as utilization of the fuel value ofCO to raise the bath temperature. It has been reported that 75 to 90% of the available energy fromthe combustion reaction is transferred to the molten bath.

Toward the end, when the carbon content is very low and meets specifications, only argon isblown to effect mixing and promote a slag–metal reaction. At this stage, ferrosilicon and otheradditions are made. Silicon reduces chromium oxide from slag. If extra-low sulfur content isrequired, the first slag is removed, and a fresh reducing one is built up with Ar stirring. The purposesof other additions include both alloying and bath cooling, since the bath temperature goes above1700°C due to oxidation reactions.

Another recent trend is to carry out further secondary refining of the melt after processing inan AOD converter in another treatment facility (e.g., ladle furnaces and vacuum systems). Thepurpose of this is to reduce the cycle time for the AOD and to improve quality. Vacuum units assistin achieving ultra-low carbon and low nitrogen levels for ferritic stainless steels. Shinkai et al.53

have reported a development along this line at Daido Steel Japan. The AOD vessel was revampedto a vacuum tight structure. A significant lowering of final carbon (<50 ppm) and nitrogen couldbe obtained by applying vacuum in the final stage.

FIGURE 6.26 Influence of pressure and temperature on the retention of chromium by oxygen-saturated steelmelt at 0.05% carbon.49 Reprinted by permission of Iron & Steel Society, Warrendale, PA, U.S.A.


Ladle furnace treatment with typical addition of lime, spar, etc. is meant for a general improve-ment in quality. The use of CO2 as replacement for argon is also being advocated,54 as CO2 behaveslike an inert in conjunction with O2 in the AOD situation, and it is much cheaper than Ar.

Figueira and Szekely55 have reported findings of experimental measurements on fluid flow andturbulence in a water model of the AOD with only side blowing of gas. Local heat transfer rateswere also determined from melting rates of immersed ice samples. They found the velocity fieldsand distribution of turbulent kinetic energy to be quite uniform. In addition, dead zones could notbe located. Figure 6.28 shows a typical experimentally measured velocity profile. The outline ofthe plume is shown by the dotted curves. The high gas flow rate and the large size of the plumedue to side blowing give rise to such uniformity.

Tsujino et al.56 investigated the decarburization behavior of Fe-18% Cr molten steel in a 6tAOD vessel with combined blowing. They correlated the ratio of chromium loss to carbon lossfrom the metal during refining with some indices containing parameters such as oxygen flow rate,mixing time, rate of energy dissipation, slag composition, slag volume, and temperature. Interestedreaders may consult the original paper for details.

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FIGURE 6.27 An example of a mixed gas blowing program in stainless steelmaking by an AOD converter.45

Reprinted by permission of Iron & Steel Society, Warrendale, PA, U.S.A.


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NOZZLE

20 cm/s

FIGURE 6.28 Experimentally measured velocity field in jet plane and plane perpendicular to jet plane, fora water model of an AOD converter.51

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& Steel Inst, Japan, 1974, p. 121.44. Kleimt, B. and Kohle, S., in Proc. 14th Process Technology Conference, Iron and Steel Soc., U.S.A.,

1996, p. 123.45. Choulet, R.J. and Masterson, I.F., Iron & Steelmaker, 20, May 1993, p. 45.46. Shinkai, A., Katsuhiko, K., and Sugano, H., in Proc. 14th Process Technology Conference, Iron and

Steel Soc., U.S.A., 1996, p. 13.47. Obana, Y., in Int.Symp. on Quality steelmaking (preprints), Indian Inst. Metals, Ranchi, 1991, p. 123.48. Turkdogan, E.T., Fundamentals of Steelmaking, Inst. of Materials, London, 1996, p.282.49. Inoue, S., Furuno, Y., Usui, T., and Miyahara, S., ISIJ Int., 32, 1992, p. 120.50. Takashiba, N., Okamoto, H., and Aizawa, K., in Ref. 41, p. 127.51. Toker, N.Y., Darken, L.S., and Muan, A., Metall Trans. B., 22B, 1991, p. 225.52. Hilty, D.C. and Kaveney, T.F., in Electric Furnace Steelmaking, C.R. Taylor ed., Iron & Steel Soc.,

U.S.A., 1985, Ch. 3.53. Shinkai, M., Inagaki, Y., Tsuno, and Nagatani, A., in Proc. 14th Process Technology Conference, p. 37.54. Hornby-Anderson, S., and Rockwell, D., Iron & Steelmaker, 20, Feb. 1993, p. 27.55. Figueira, R.M. and Szekely, J., Metall Trans B, 16B, 1985, p. 67. 56. Tsujino, R., Hirata, H., Nakao, R., and Mizoguchi, S., 10th PTD, Conf. Proc., Iron & Steel Soc., U.S.A.

7 Desulfurization in Secondary Steelmaking

7.1 INTRODUCTION

Except in free-cutting steels, sulfur is considered to be a harmful impurity, since it causes hotshortness in steels. Some decades back, for common grades of steel cast through the ingot route,the maximum permissible sulfur content was 0.04%. In the continuous casting route, it should be0.02%. In special steel plates, the normal specification for sulfur is 0.005% these days, but thereis a demand for ultra-low-sulfur (ULS) steel with as low as 10 ppm (0.001%), e.g., in line pipe,HIC resistive steels, and alloyed steel forgings.1

Sulfur comes into iron principally through coke ash. It is effectively removed from molten ironby slag in a reducing environment only. Hence, traditionally, sulfur control used to be done duringironmaking in a blast furnace. Very little sulfur removal is possible in primary steelmaking due tothe oxidizing environment. An exception is the electric arc furnace (EAF), where low-sulfur steelsare produced through two-stage refining.

In view of the consistent demand for lower-sulfur steel and the incapability of the blast furnaceto achieve it, external desulfurization of liquid iron in a ladle during transfer to the steelmakingshop was developed. The process is capable of lowering sulfur content to 0.01% or so and is anessential feature of a modern integrated steel plant.

Content below 0.01% must be accomplished in secondary steelmaking. There are now pro-cesses, such as the MPE process of Mannesman and the EXOSLAG process of U.S. Steel,2 wheredesulfurization is achieved to some extent during tapping by using synthetic slag and utilizing thekinetic energy of the tapping stream. Desulfurization by treatment with synthetic slag on top ofmolten steel and gas stirring (either in an ordinary ladle, in a ladle furnace or VAD, or duringvacuum degassing) are also being practiced.

However, only the injection of a powder such as calcium silicide into the melt is capable ofproducing ULS steel. ULS can be achieved only if the dissolved oxygen is also very low. Gasstirring is required, so deep desulfurization is associated with deep deoxidation. The use of alumi-num in combination with calcium or rare earth (RE) metals achieves both. In addition, injectionprocesses are capable of inclusion modification for further improvement of the properties of steel.

Section 6.4.5 of this book has already stated that oxygen and sulfur dissolved in liquid steelretard the nitrogen desorption rate from steel in vacuum degassing. A low nitrogen level has beenachieved in low-sulfur and low-oxygen steels. This is an additional benefit if deep desulfurizationis done before or during vacuum treatment.

Furnace slags contain oxides such as FeO, SiO2, P2O5, and MnO. These oxides are unstable inthe presence of a deoxidized steel, especially when the slag and steel are intimately mixed. As aresult, some reversion of phosphorus into the steel occurs. This slag also partly consumes addeddeoxidizers, so it does not allow proper utilization of them for steel deoxidation. The slag alsocauses wear on the ladle lining.


Although these have been known for a long time, very little physicochemical investigation hasbeen conducted on these effects. Turkdogan

2

has considered some aspects of the reaction of liquid


steel with slag during furnace tapping. This has already been discussed in Section 5.3. It is best ifslags from primary steelmaking furnaces are not allowed into the secondary steelmaking ladle.However, this is difficult to implement. In addition, some slag is required for desulfurization duringsecondary steelmaking and other beneficial effects. Therefore, control of furnace carryover slagaims at the twin strategy, viz., (a) minimization of furnace carryover slag, and (b) modification ofcarryover slag by the addition of fluxes (principally CaO, but also Al, SiO2, Al2O3, and CaF2 tosome extent) to render desirable properties to it. Section 5.3 discussed the minimization of slagcarryover, so this information need not be repeated here.

7.2 THERMODYNAMIC ASPECTS

7.2.1 SOLUTION OF SULFUR IN LIQUID STEEL

At steelmaking temperatures, sulfur is a stable gas, with the most predominant molecule being S2.The dissolution of sulfur in molten steel may be represented by the following equation:

1/2 S2 (g) = S (7.1)

For the above reaction,

(7.2)

where K1 is the equilibrium constant for Reaction (7.1), denotes partial pressure of sulfur inthe gas phase in atmosphere, and hS is the activity of dissolved sulfur in steel with reference to1 wt.% standard state.

Again,

log K1 = – 0.964 (Ref. 5) (7.3)

Equation (7.3) gives a little differing value from that based on Appendix 2.2 (335 and 348,respectively, at 1600°C).

The interaction coefficients describing the influence of some common solutes (j) in liquid steelon the activity coefficient of sulfur (fS) dissolved in liquid steel (i.e., ) at 1600°C are given inAppendix 2.3, where hS = fS · WS, WS being the weight percent of sulfur in steel. It may be notedfurther that the solubility of sulfur in molten steel is very high.

7.2.2 REACTION EQUILIBRIA OF SULFUR

Appendix 2.1 provides a compilation of the standard free energy of formation of some oxides andsulfides. Ca and Ba form CaS and BaS, respectively, upon reaction with sulfur, whereas ceriumforms several sulfides7 out of which CeS is the stablest one under steelmaking conditions. Ce alsoforms an oxysulfide, Ce2O2S. All of these compounds are solids at steelmaking temperatures. Itmay be noted, from thermodynamic data on these compounds in any standard text, that all these

K 1

hS[ ]pS2

1 2⁄---------

equilibrium

=

pS2

6535T

------------

esj

elements form very stable sulfides as well as oxides. Therefore, they are both strong deoxidizersas well as desulfurizers and would form both oxides and sulfides.


Again, these compounds would not necessarily be present in a pure form. For example, additionof Ca-Si leads to the formation of a CaO-SiO2-type deoxidation product as discussed earlier inSection 5.2. However, we do not propose to get involved in these complexities and consider theoverall reaction to be

S + (MO) = O + (MS) (7.4)

For the limiting case of unit activities of MO and MS (i.e., assuming pure MO and pure MS), theequilibrium constant (KMS) for Reaction (7.4) is

(7.5)

The values of KMS for different systems can be calculated from the free energy of reaction. Figure7.1, reproduced from Turkdogan,8 shows the pattern. Ba is the strongest desulfurizer and Mg theweakest, with Ca and Ce lying in between.

Holappa1 has reviewed the theoretical basis for sulfur removal in ladle treatment by slag–metalreaction. If the MO and MS are not pure, then it is better to utilize the general ionic form ofdesulfurization reaction, viz.,

[S] + (O2–) = (S2–) + [O] (7.6)

K MShO[ ]hS[ ]

----------W O[ ]W S[ ]

-------------= = (at equilibrium)

FIGURE 7.1 Oxygen/sulfur activity ratio in liquid iron for some sulfide-oxide equilibria at 1873 K.9

K 6

aS

2–( ) hO[ ]hS[ ] a

o2–( )

------------------------=

or,


(7.7)

If we replace with weight percent sulfur in slag (i.e., WS), then we may use a modifiedvalue of K6 (let it be ). Then,

(7.8)

where is known as the modified sulfide capacity.As discussed in Section 2.8, the sulfide capacity of slag (CS), i.e., the ability of a slag to absorb

sulfur, was originally defined by Richardson9 as

(7.9)

where (WS) is the weight percent sulfur in the slag in equilibrium with a gas having partial pressuresof oxygen and sulfur as and . Its usefulness stems from the fact that CS is a property ofslag, and at a fixed temperature it is determined solely by slag composition. The higher the valueof CS, the better the desulfurizing ability of the slag. Figure 7.2 shows CS values for some typicalslag systems of interest in secondary steelmaking.9 The superiority of CaO-CaF2 slag is obvious.Values of CS for various slags are available in Slag Atlas.10

CS is determined by equilibrating the slag with a gas mixture having known oxygen and sulfurpotential. However, it is the slag–metal equilibrium that is of interest. This requires the use of amodified CS (viz., ) as defined in Eq. (7.8).

The relationship between CS and is

(7.10)

At 1600°C, = 7.5 CS.

K6( ) ao

2–( )a

s2–( ) hO[ ]hS[ ]

-----------------------=

as

2–

K ′ 6

K ′ 6 ao

2–( )W S ]( ) hO[ ]

hS[ ]-------------------------- C ′ S= =

C ′ S

CS W S( ) pO2/ pS2

( )1 2⁄=

pO2pS2

FIGURE 7.2 Sulfide capacities of some slags at 1873 K.9

C ′ S

C ′ S

log CS log C ′ S936T

--------- 1.375–+=

C ′ S

Another parameter of interest is the equilibrium

sulfur partition ratio

between slag and metal(

L

S

), where

L

S

= (

W

S

)/[

W

S

]. From Eq. (7.8), if [

h

S

] is taken as [

W

S

], then, at

slag–metal sulfur


equilibrium,

(7.11)

hO in liquid steel is typically determined by the presence of a deoxidizer, especially dissolvedaluminum. One may relate hO to the FeO content of slag as well. However, it has been found moreappropriate to relate it to the former. Figure 7.3 shows LS as a function of the CaO content of slagand aluminum content of metal for CaO-Al2O3 slag.8 Therefore, for good desulfurization, Al contentof more than 0.020% is generally recommended.1

7.2.3 TEMPERATURE AND COMPOSITION DEPENDENCE OF CS

A simplified approach to this issue is to recognize that the CaO in slag is the predominantdesulfurizer. For the reaction,

CaO(s) + S = CaS(s) + O (7.12)

With the data on free energies in Appendices 2.1 and 2.2,

(7.13)

K12 is the equilibrium constant for Reaction (7.12) and is same as KMS for a CaO-CaS reaction. At1600°C (1873 K), Eq. (7.13) gives K12 as 0.013, whereas KMS from Figure 7.1 is approximately 0.03.

Carlsson et al.11 have proposed an alternate correlation, viz.,

(7.14)

LSW S( )W S[ ]

------------C ′ S

hO[ ]----------= =

FIGURE 7.3 Equilibrium sulfur partition ratio between liquid iron with dissolved Al and CaO-Al2O3 slags.8

logK 125140

T------------– 0.961+=

logK 125304

T------------– 1.191+=

This yields a value of K12 at 1600°C of 0.028, matching Figure 7.1. The compilation of Zhang andToguri12 yields a value of 0.06. Equation (7.14) is recommended for use. If CaO and CaS are not


pure, but in solution in slag, then

(7.15)

Proceeding similarly as in the derivation of Eq. (7.8),

(7.16)

where m is a constant of proportionality. Combining Eqs. (7.10), (7.14), and (7.16),

logCS = logm + log(aCaO) – (7.17)

Figures 7.4, 7.5, and 7.6 present activity vs. composition relations in CaO-Al2O3, CaO-SiO2,and CaO-SiO2-Al2O3 systems at 1500 to 1600°C13. At 50 wt.% CaO, aCaO = 0.33 in CaO-Al2O3

slag and only 0.01 in CaO-SiO2 slag (approximately). To generalize, aCaO is 10 to 20 times largerin CaO-Al2O3 than in CaO-SiO2 in the composition ranges that are of interest in ladle refining.Hence, CaO-Al2O3 slag is far superior to CaO-SiO2 slag for desulfurization. This is reflected in theCS values of Figure 7.2.

Figure 7.6 gives values of CS in a ternary CaO-Al2O3-SiO2 system at 1600°C. In the limitedtemperature range of secondary steelmaking, it seems good enough to assume aCaO to be independentof temperature at a fixed slag composition. Therefore, if CS is known at one temperature from adiagram such as Figure 7.2, it can be estimated at any other temperature. Further refinement onthis can be made by invoking a regular solution assumption for aCaO.

K 12aCaOS( ) hO[ ]aCaO( ) hS[ ]

-----------------------------=

mK12 aCaO( ) W S( )hO[ ]hS[ ]

----------⋅ C ′ S= =

4204T

------------ 0.184–

FIGURE 7.4 Activity vs. composition diagram for CaO-Al2O3 system at 1773 to 1873 K.13


For determining values of CS or , using diagrams as in Figure 7.2 is somewhat inconvenient.Therefore, attempts are underway to analytically represent CS as a function of slag composition. Tsaoet al.14 performed equilibrium measurements. With the help of their own data, and those of others,they have proposed the following correlation by data fitting through statistical regression analysis.

log CS = 3.44 (XCaO + 0.1 XMgO – 0.8 (7.18)

FIGURE 7.5 Activity vs. composition diagram for CaO-SiO2 system at 1873 K.13

FIGURE 7.6 Sulfide capacities and CaO-saturated liquidus (broken line) for CaF2-CaO-Al2O3 system at1773 K.18

C ′ S

X Al2O3XSiO2

)– 9894T

------------– 2.05+

This may be useful for prediction purposes within a factor of 2 to 3. Also, it is not applicable toCaF2-bearing slags. Gaye et al.15 employed the following correlation, arrived at by Duffy et al.16


on the basis of the optical basicity index (see Chapter 2, Section 2.8):

(7.19)

Combining with Eq. (7.10),

(7.20)

where B = 5.62 WCaO + 4.15 WMgO – 1.15

D = WCaO + 1.39 WMgO + 1.87

The conclusion drawn by the above mentioned authors is that the domains of liquid slag compo-sitions leading to high LS are rather limited, and the efficiency of a sulfur removal treatment willrely on the ability to reach these domains. The aimed compositions should be close to CaOsaturation. The authors also recommend that, in using Eq. (7.19), calcium present as CaF2 shouldbe subtracted in slag analysis.

7.2.4 TEMPERATURE AND COMPOSITION DEPENDENCE OF LS

For good desulfurization, a large value of LS is required. This can be achieved not only by a largevalue of CS (i.e., ), but also by a low value of hO. Here, aluminum is superior to silicon, sinceit allows deeper deoxidation. The thermodynamic relationship between LS with other parametersfor deoxidation by aluminum may be derived as described below.

From Eqs. (7.10) and (7.11),

(7.21)

Again,

(Al2O3) = 2[Al] + 3[O] (7.22)

For which

(at equilibrium) (7.23)

From Appendix 5.1,

(7.24)

or, if it is assumed that hAl = WAl,

(7.25)

logC ′ SBD---- 2.82 13300

T---------------–+=

logCSBD---- 1.445 12364

T---------------–+=

W SiO21.46W Al2O3

+

W SiO21.65W Al2O3

+

C ′ S

LSlog logC ′ S loghO– logCS936T

--------- 1.375 loghO–+–= =

K AlhAl[ ] 2 hO[ ] 3

aAl2O3( )

---------------------------=

logK Al64000

T---------------– 20.57+=

loghO13--- 64000

T---------------– 20.57 2 logW Al log aAl2O3

( )+–+=



(7.26)

An important issue is variation of LS with temperature at a fixed slag composition. In additionto Eq. (7.26), we should also know how CS varies with temperature.

Example 7.1

Figure 7.2 presents values of sulfur capacity for some slags at 1600°C. Compare these withpredictions based on Eqs. (7.18) and (7.20) at a mole fraction of CaO of 0.6 for CaO-SiO2 andCaO-Al2O3 systems.

Solution

Values of CS as read from Figure 7.2 are noted below. As for calculation from Eq. (7.18), XCaO =0.6 in all cases. = 0.4 for CaO-SiO2 slag, and = 0.4 for CaO-Al2O3 slag.

In CaO-SiO2 at 0.6 mole fraction CaO,

or,

= 100 – 58.3 = 41.7%

In CaO-Al2O3 at 0.6 mole fraction CaO,

or,

= 100 – 45 = 55%

Hence, Figure 7.2 and Eq. (7.18) give differing values. But Eq. (7.20) matches reasonably with Figure7.2.

Example 7.2

At 1600°C and for CaO-Al2O3 slag with a mole fraction of CaO equal to 0.6,

1. Calculate desulfurization efficiency of slag (i.e., [WO]/[WS] ratio).2. Compare the above with that of pure CaO.3. Calculate the value of LS if liquid steel contains 0.01 wt.% Al, and compare with Figure 7.3.4. Calculate the weight percent sulfur in metal.

Values of Cs

Fig. 7.2 Eq. (7.18) Eq. (7.20)

CaO−SiO2 5.0 × 10–4 2.85 × 10–3 7.89 × 10–4

CaO−Al2O3 2.7 × 10–3 5.38 × 10–3 1.99 × 10–3

logLS logCS 13---– log aAl2O3

( ) 23--- logW Al

20397T

--------------- 5.482–+ +=

XSiO2XAl2O3

W CaO 1000.6 56×

0.6 56 0.4 102×+×-------------------------------------------------× 58.3%==

W SiO2

W CaO 1000.6 56×

0.6 56 0.4 102×+×-------------------------------------------------× 45%==

W Al2O3

Assume slag–metal equilibrium and sulfur in slag as 1 wt.%. Ignore the interactions of othersolute elements.


Solution

(a) From Eq. (7.11), and taking hO = WO in metal phase,

(E1.1)

Now, (WS) = 1, and CS = 2.7 × 10–3 (Figure 7.2). From Eq. (7.10) at 1600°C, = 7.5 CS. Puttingin these values,

(b) From Figure 7.1, for a CaO-CaS system at 1600°C,

Therefore, the slag with 1% sulfur is as powerful a desulfurizer as pure CaO.

(c) The composition of slag corresponds to 45 wt.% CaO and 55 wt.% Al2O3. From Figure 7.4,. Putting in other values, i.e., CS = 2.7 × 10–3, WAl = 0.01, and T = 1873 K in Eq. (7.26),

log LS = 1.64, i.e., LS = 43.6

Figure 7.3 gives LS approximately equal to 30 for 45 wt.% CaO and at 1600°C.For comparison, LS is to be estimated at 1650°C (1923 K) with the help of Eq. (7.26). But

before that, CS is to be estimated at 1650°C using Eq. (7.17).From Eq. (7.17),

log(CS)1923 – log(CS)1873 = –4208 = 0.0585 (E1.2)

log(CS)1923 = log(2.7 × 10–3) + 0.0585 = –2.510

Putting values into Eq. (7.26),

Assuming that the activity of Al2O3 is independent of temperature, LS at 1923 K (1650°C) = 28.8.The value of LS in Figure 7.3 is approximately 20.

(d) From (c),

Since (WS) = 1, [WS] = = 0.023% at equilibrium.

hO[ ]W S[ ]

------------W O[ ]W S[ ]

-------------C ′ S

W S( )------------= =

C ′ S

W O[ ]W S[ ]

------------- 2.03 10 2–×=

W O[ ]W S[ ]

------------- 2.5 10 2–×=

aAl2O30.4=

11923------------ 1

1873------------–

log LS( )1923 2.510–23---log0.01 20397

1923--------------- 5.482

13--- 0.4log––+ + 1.46= =

LS

W S( )W S[ ]

------------ 43.6= =

1 43.6⁄

7.2.5 SOME COMMENTS ON LS

15


As Example 7.1 shows, the correlation by Gaye et al. gave a better match with Figure 7.2. FromExample 7.2, the following conclusions may be drawn:

• A slag that is not saturated with CaO is not an effective desulfurizer.• Pure CaO is also not an effective desulfurizer.

Let us consider a slag of CaO-Al2O3-SiO2-MgO with 5 wt.% SiO2 and 3 wt.% MgO. At limesaturation, WCaO is 60 and is 32 (Figure 7.6). From Eqs. (7.20) and (7.26), and taking = 0.1, LS is calculated as 220 at T = 1873 K and WAl = 0.01. If WAl = 0.04 wt.%, then, fromEq. (7.26), LS = 555. According to Gaye et al.15 even a value of 1000 is possible in CaO-Al2O3-SiO2. A still larger value of LS can be obtained if some CaF2 is present in the slag due to a highervalue of CS (Figure 7.2). This way, it is possible to obtain a value of LS larger than 1000. Literaturereports show that such large values are indeed obtained in industrial practices.17

Interest in CaF2-containing slags originated from electroslag remelting processes. Richardson9

and Davies18 have reviewed the thermodynamic properties of these slags, including sulfide capacity.CaF2 dissolves oxides significantly. But it is a stable, neutral compound. Hence, activity coefficientsof oxides tend to be high in comparison to those in slags. For example, at comparable CaOconcentration, aCaO in a CaF2-CaO slag is much higher than those in Al2O3-CaO and SiO2-CaOsystems. This results in higher values of CS in CaF2-containing slags. Figure 7.6 presents sulfidecapacities in CaF2-CaO-Al2O3 ternary at 1500°C as determined by Kor and Richardson.19

The importance of LS can be demonstrated as follows.The sulfur balance is

1000[WS]o + MS1(WS)o = 1000[WS] + MS1(WS) (7.27)

where MS1 = weight of slag in kg/tonne steel and the subscript o indicates initial values.Assuming the attainment of slag–metal equilibrium and also that (WS)o = 0, and combining

Eq. (7.27) with Eq. (7.11),

degree of desulfurization (R) = (7.28)

Figure 7.7 presents some calculated curves based on Eq. (7.28). It shows the necessity of high LS

for good desulfurization. Rewriting Eq. (7.28) we obtain,

(7.29)

where Y = LS · MS1/1000

7.3 DESULFURIZATION WITH ONLY TOP SLAG

7.3.1 INTRODUCTORY REMARKS

As mentioned in Section 7.1, powder injection is done to achieve an ultra-low sulfur level (S < 10to 20 ppm) only. Otherwise, desulfurization by treatment with synthetic slag on top of molten steelin an ordinary ladle, ladle furnace, or during vacuum treatment is quite all right. Principal additionsare as follows:

W Al2O3aAl2O3

1W S[ ]W S[ ] O

---------------– LS MS1⋅

1000 LS MS1⋅+--------------------------------------

=

RY

1 Y+-------------=


1. CaO. This is for the formation of a highly limy slag, either saturated with CaO orunsaturated.

2. Al. This is for reaction with dissolved oxygen in molten steel and to form Al2O3, whichjoins the slag phase. This reaction is exothermic and raises the temperature of steel aswell. Al also reacts with the SiO2 of slag to some extent.

3. CaF2,SiO2,Al2O3. Use this as required for slag formation.

Additions are made partly during tapping of the metal from the steelmaking furnace into theladle. The tapping stream causes violent stirring, and during this process some slag–metal reactionand desulfurization will occur. To make it more effective, the practice of synthetic slag additionalso exists, as for example, the MPE process of Mannesman and the EXOSLAG process of U.S.Steel Corp. As a consequence of these additions, the metal gets well deoxidized by aluminum, anda molten top slag forms, consisting dominantly of CaO and Al2O3 with some CaF2,SiO2. This isthe beginning of the second stage of the slag–metal desulfurization reaction. Stirring by argonintroduced through porous bottom plugs is a must for speeding up mixing and mass transfer.

If the slag–metal sulfur equilibrium is attained at the end of the process, the extent of desulfu-rization can be predicted by following the procedure mentioned in Section 7.2.5. However, aprincipal question is whether such an equilibrium gets established in industrial processing. As faras literature reports are concerned, the slag–metal equilibrium for sulfur reaction is sometimesattained and sometimes not.

This topic shall be taken up again later. For the time being, it will suffice to state that thereaction comes close to equilibrium if

• The equilibrium partition coefficient (LS) is not too large.• There are no disturbing side reactions going on, such as dissolution of the refractory

lining into slag and a consequent change of slag composition, and/or absorption of oxygenfrom the atmosphere.

As far as disturbing side reactions are concerned, a vacuum ladle degasser is least affected.Figure 7.8 presents some data.20 The degree of CaO saturation simply means the ratio of WCaO inactual slag to that in CaO-saturated slag. The highest sulfur partition was obtained in the CaO-

FIGURE 7.7 Desulfurization degree for different sulfur distributions as a function of specific slag amount.


saturated slag. Thermodynamic limitations were held responsible for lower partition in unsaturatedslags. The lower values in supersaturated slags were attributed to kinetic factors. These slags containsolid particles of CaO and hence tend to have higher viscosity with consequent retarding influenceon mixing and mass transfer in slag phase.

In Figure 7.8, the maximum value of the

parameter is about 25000 at a saturation degree of 1. At WAl = 0.04, this corresponds to an effectivepartition coefficient of 2920. From discussions in Section 7.2.5, it is evident that it is quite a largevalue, perhaps indicating a close attainment of equilibrium. However, as stated earlier, nonattain-ment of equilibrium also seems to be a common feature. Moreover, there is a worldwide effort tospeed up the refining process. Hence, the kinetics of desulfurization are of considerable relevance.

7.3.2 KINETICS OF DESULFURIZATION REACTION WITH TOP SLAG

General Features

Chapter 4 briefly reviewed mass transfer between two liquids as well as mixing and mass transferin gas-stirred ladles. Several studies reported therein were in the context of the reaction of sulfurbetween slag and metal. Chapter 6 presented the special features of flow, circulation in vacuumdegassing of steel, and their influence on mixing of liquid as well as gas–metal reaction kinetics.Hence, there is no need to repeat this material, and discussions here are limited to a few additionalremarks.

The overall desulfurization reaction consists of the following kinetic steps:

1. Transfer of sulfur dissolved in liquid iron to slag–metal interface2. Transfer of O2– from the bulk of the slag to the slag–metal interface3. Chemical reaction at the interface, i.e.,

[S] + (O2–) = (S2–) + [O] (7.6)

FIGURE 7.8 Sulfide capacity vs. CaO-saturation degree of slag in ladle desulfurization of steel.20 Reprintedby permission of Iron & Steel Society, Warrendale, PA, U.S.A.

W S( )W S[ ]

------------ 1

W Al[ ] 2 3⁄--------------------×

4. Transfer of S2– from the interface into bulk slag5. Transfer of [O] from the interface into the bulk metal phase


6. Mixing in slag phase7. Mixing in metal phase

Section 4.3 reviewed reaction kinetics among phases. As stated there, reactions at high tem-peratures, especially at steelmaking temperatures, are mostly controlled by mass transfer ratherthan interfacial chemical reaction in a laboratory situation (i.e., melts well mixed and in anisothermal zone). Several laboratory investigations have been conducted on the reaction of sulfur,especially in the ironmaking situation. It was established that the content of oxygen dissolved inliquid iron, which is a product of Reaction (7.6), has to be considerably lowered through its reactionwith C, Si, Al etc. of liquid iron if a good desulfurization is desired.

The desulfurization reaction has been found to behave approximately as a first-order reversibleprocess with respect to concentration of sulfur in metal. In an analogy with Eq. (6.22) in connectionwith vacuum degassing and decarburization, we may write

(7.30)

where kS,emp is an empirical rate constant in s–1

This as such does not point to any particular rate-controlling step, since mass transfer, mixing,and interfacial reaction can all be expressed as a first-order reversible process. Since concentrationsof solutes in slag are much larger as compared to those in metal, mass transfer in the slag phase(steps 2 and 4) are expected to be faster as compared to those in metal.

Of course, Eq. (7.30) would be valid even if the transfer of sulfur in metal and slag jointlycontrol rate. In that case, kS,emp would be the parameter of Eq. (4.41), where solute iwould stand for sulfur, phase I for liquid steel, and phase II for slag. Slag volume is much smalleras compared to that of the metal. Moreover, as will be seen later, the top slag gets violently churnedand even emulsified due to gas stirring. Hence, mixing in the slag phase (step 6) is also expectedto be fast. Transfer of oxygen in the metal phase (step 5) is also likely to be fast, due to the factthat the reaction

2[Al] + 3[O] = (Al2O3) (7.31)

would occur in the metal phase close to the slag–metal interface in the metal itself. This wouldincrease the mass transfer rate of [O] significantly due to the phenomenon of reaction-enhancedboundary layer mass transfer.21

Another way to consider this issue can be derived from the classic work of King et al.22 on themechanism of slag–metal sulfur transfer. They found that the rate of sulfur transfer from metal toslag was always equal to the sum of the rates of oxidation of Fe, C, Si, etc. Figure 7.9 presentsthe data of one of their laboratory experiments. The increase of sulfur in slag was numericallyequal to the sum of CO generated, and Fe + Si transferred to the slag. As such, the result is notsurprising. But what was puzzling was the temporary overshoot of Fe and Si transfer to slag beyondequilibrium during the course of the reaction.

This was explained by invoking the electrochemical mechanism of slag–metal reaction. Thereactions have been summarized in Table 7.1. It shows that there are several electrochemicalreactions occurring simultaneously. The sum of the rate of all cathodic reactions would be equalto that of all anodic reactions in all cases. Moreover, there will be a common electrical potentialat the interface, known as corrosion potential. In the initial stages, the cathodic reactions of sulfur

d W S[ ]dt

---------------– kS ,emp= W S[ ]W S( )LS

------------–

A V⁄( )km ,iI-II


altered this potential to a value that led to a shifting of the equilibrium of Fe/Fe2+ and Si/Si4+

couples. In later stages, these returned to equilibrium values. In the context of desulfurization insecondary steelmaking, therefore, we may think of the transfer of Al from metal to slag rather thanoxygen from slag to metal. The concentration of Al being larger, its transfer would be faster thanthat of sulfur.

Investigators tried to ascertain whether the interfacial chemical reaction could be slow and ratecontrolling. No clear-cut evidence was available. Perhaps, in stagnant laboratory melts, this wasthe situation.23,24 However, the general conclusion was that the reaction was mass transfer con-trolled.25 Of course, as later investigators concluded (Section 4.5), sometimes it may be bulk mixingrather than phase boundary mass transfer that seems to be slow and rate controlling. Of course,mixing is not a problem in small laboratory melts.

If the backward reaction is ignored in Eq. (7.30), then integration of Eq. (7.31) is simplifiedas follows, if ks,emp is taken as independent of t:

TABLE 7.1Reactions Occurring during Sulfur Transfer from Liquid Iron to Slag

Type Initial Stages Later Stages

Cathodic

Anodic

FIGURE 7.9 Increase of sulfur in slag and equivalents of Fe, Si, and CO transferred or evolved in laboratoryexperiments of Ramachandran and King.23

S[ ] 2e–+ S2–( )= S[ ] 2e–+ S2–( )=

Fe2 +( ) 2e_+ Fe[ ]=

1 2⁄ Si4 +( ) 2e_+ 1 2⁄( ) Si[ ]=

2 3⁄ Al3 +( ) 2e_+ 2 3⁄ Al[ ]=

C[ ] O2 –( )+ CO 2e_+=

Fe[ ] Fe2 +( ) 2e_+=

1 2⁄ Si[ ] 1 2⁄ Si4 +( ) 2e_+=

2 3⁄ Al[ ] 2 3⁄ Al3 +( ) 2e_+=

C[ ] O2 –( )+ CO 2e_+=

2 3⁄ Al[ ] 2 3⁄ Al3 +( ) 2e_+=

(7.32)W S[ ] 0

W S[ ]--------------

ln kS ,emp t⋅=


Figure 7.10 is plotted accordingly and is taken from an investigation by Ohma et al.26 in a 35 tonneladle furnace. The slopes gave values of kS,emp.

The values of kS,emp increase with increasing volumetric gas flow rate (Q). Section 4.4.2 has abrief discussion on this issue, from mass transfer between two liquids in a gas-stirred vessel. Itwas noted there that, in general, kmA ∝ Qn. Since Q is proportional to the rate of buoyancy energyinput per unit mass of the bath liquid (εm), kmA ∝ varies over a wide range. Asai et al.27 havereviewed mass transfer in ladle refining processes. They have compiled the k vs. ε relationshipobtained by several investigators in cold models and at high temperatures. These show a range ofn from 0.33 to 3.0.

Table 7.2 presents a summary of the behavior pattern of k vs. εm. It is primarily based on thecompilation by Asai et al.27 It may be noted from Table 7.2 that, in cases where investigators mademeasurements over a large range of gas flow rate, log k vs. log εm curves exhibited kinks, and nshowed a much larger value in the high flow rate range. Several subsequent investigators alsoreported similar observation (see Section 4.4.2). Figure 4.10 shows an example of such behaviorin a water-oil system. Figure 7.11 presents a similar behavior for desulfurization in a gas-stirredladle of pilot plant size.28

Slag–Metal Emulsion and Reaction Rate

It has been established through water-model studies that this phenomenon is due to onset ofemulsification of top liquid (slag, oil, etc.) into the bath liquid (steel, water, etc.). Emulsificationleads to an increase of the interfacial area and hence the kmA parameter. Technologically importantissues are as follows:

1. Critical value of Q or εm at which emulsification begins [QCr or εm(Cr)]2. Change of the mass transfer coefficient (km) due to emulsification3. Enhancement of the interface area (A) as a result of emulsification

FIGURE 7.10 Rate of desulfurization of steel by slag refining and powder injection for (WCaO + WMgO/WSiO2– WAl2O3

) = 2 – 4.26 Reprinted by permission of Iron & Steel Society, Warrendale, PA, U.S.A.

εmn n⋅

TABLE 7.2Correlation of Mass Transfer in Liquid–Liquid System27


Some discussions, data, and references have already been presented in Section 4.4.2 on item 1above. QCr depends on several variables. An important one is interfacial tension between slag andmetal. A more fundamental parameter is the critical liquid velocity at the interface (uCr,i). Oeters29

has presented an elaborate theoretical analysis for the conditions of drop formation that sets on theemulsification process. The analysis leads to the correlation expressed in Eq. (7.33).

System Stirring Reaction Correlation Remarks

Slag–steel Ar gas Desulfurization 2.5t converter

Water–Hg N2 gas Reduction of quinone

Slag–steel Ar gas, mechanical stirring

Dephosphorization

Slag–steel Ar gas

Slag–steel Desulfurization

Oil–water

Amalgams–aqueous sol.

= (amal)

(aq.)

n–hexane– N2 gas

Aqueous sol.

Amalgams–aqueous sol.Lead–molten salt

Slag–steel O2 gas Dephosphorization

Liquid paraffin–water

Tetraline–aqueous sol. Air

Q(1/min · t) ∝ ε is assumedK: capacity coefficient of mass transfer = akε: mixing power density (W/t)φ: fraction of slagt: tonne

K ε0.25∝

ε 60w/t<

K ε2.1∝

ε 60w/t<

Q 150 1/min. t<

150 Q 240< <

K ε0.3 0.4∼∝ Q 58<

φ 0.22=

K ε0.6∝ 30 Q 160< <

Cu Cu( )→ K ε0.27∝ Q 100<

K ε1.0∝

K ε0.33∝

In[ ] 3 Fe3 +( )+

I n3 +( ) 3 Fe2 +( )+

K ε0.33∝

K ε0.42∝

Q 10<

φ 0.5=

I2 2OH–+ IO–= K ε0.72∝ 200 Q 994< <

+I– H2O+

31O– 103– 21–+=

φ 0.5=

K ε0.5∝ Q 130<

φ 0.5=

K ε0.54∝ 50 Q 80< <

K ε0.36∝

K ε3.0∝

30 Q 80< <

80 Q 200< <

φ 0.17=

K ε0.36∝

K ε1.0∝

Q 150<

150 Q 650< <

φ 0.1=


(7.33)

where ρ denotes density, σ denotes interfacial tension, s and m stand for slag and metal, g isacceleration due to gravity, and α is the angle at the slag–metal interface. Equation (7.33) showsthat uCr,i ∝ σ1/4. Hence, QCr would increase with increase in σ.

σsm values for a steel-slag system are much larger as compared to those for room temperaturesystems. Hence, εm(Cr) is expected to be larger as compared to those for cold models. However,the value of interfacial tension has been found to exhibit a significant decrease (even by an orderof magnitude) during the transfer of a species across a phase boundary. It has been reported forsulfur transfer from metal to slag as well.23 It is only appropriate, therefore, to consider this dynamicvalue of σsm in Eq. (7.33). Unfortunately, these are not available. Sahajwalla et al. (Section 4.4.2)reviewed this and found it to range between 0.065 and 0.13 W/kg. Literature data on desulfurizationrates in ladles indicate that kS,emp lies in the range of (0.5 to 3) × 10–3 s–1 for a low gas flow rateand (3 to 15) × 10–3 s–1 for emulsified slag.

No directly determined data are available about the change of km upon emulsification. However,some approximate estimation is possible. Extensive measurements have been made in chemicalengineering on mass transfer from a liquid droplet moving through another liquid. Correlations areavailable in standard texts such as the ones already cited.9.29 The droplet would rise or fall throughthe liquid, depending on the densities of the two liquids. Larger drops would have larger rise orfall velocities. In the case of slag–metal emulsion in a gas-stirred vessel, the rising bubbles ejectdroplets of liquid metal into the slag. Then, metal drops fall through the slag phase.

The exact relationship among the dimensionless numbers would depend on the nature of theflow and surface renewal near the droplet-bulk liquid interface. These in turn would depend ondrop size, the density difference of the two liquids, and the interfacial tension. Again, droplets ina slag–metal emulsion exhibit a spectrum of sizes.

In view of so many uncertainties, it is desirable to use one representative mass transfercorrelation. This is what Mietz et al.30 did and estimated km theoretically by employing the followingrelationship:

FIGURE 7.11 Effect of gas flow rate on kmA parameter (capacity coefficient) for desulfurization reaction.27

uCr ,i8ρ---

s

1 2⁄

2 3⁄ σsmg ρm ρs–( ) cos α[ ] 1 4⁄=

Sh = 2.0 + 0.0511 Re0.724 Sc0.70 (7.34)


where the dimensionless numbers are as defined in Table 4.2.Mietz et al.30 carried out mass transfer measurements in a model where water and cyclohexane

simulated steel and slag, respectively. Iodine dissolved in water was transferred to cyclohexane.Variation in the concentration of iodine in water as a function of time was measured by samplingand analysis. Employing Eq. (7.34) and a theoretical equation derived by Oeters29 correlatingdimensionless iodine concentration with other parameters, they calculated average residence timeof droplets for each experiment. Furthermore, values of were also calculated employinganother procedure involving energy balance. Good agreement was obtained between these two setsof values, and was found to range between 24 and 123 s for these experiments.

On the basis of the above exercise, calculations were performed with regard to the increase ofslag–metal interfacial area due to emulsification for a 120t molten steel in a ladle under a particularset of conditions. was assumed to 60 s and mean drop size as 0.4 mm. It was found that, whereasthe geometrical surface area was 6.6 m2, in emulsion it was 608 m2, indicating about a hundred-fold increase in area. These were then applied to desulfurization data obtained in the 120t ladle.Figure 7.12 presents both the measured and calculated dimensionless concentration of sulfur

as a function of time.31

It may be noted that the measured desulfurization data agreed very well with calculationsassuming emulsification. Calculations assuming no emulsification showed much slower desulfur-ization, demonstrating the importance of emulsion. However, it ought to be taken only as anapproximate guide. First of all, there are some unverified assumptions in the procedure of Mietzet al.30 Second, at high rates of desulfurization with an emulsified slag, mixing rather than phase-boundary mass transfer is expected to limit the rate, as will be discussed shortly.

Hence, the above studies indicate only that emulsification led to an increase of slag–metalinterface area and a consequent rate increase. It is also expected that this increase would dependon the degree of slag emulsification. Water-model studies indicated that the rate constant (kS,emp)increased approximately proportionately with the degree of emulsification. Hence, it may beconcluded that emulsification enhances interface area and kS,emp by one to two orders of magnitude.

The issue related to mixing vs. mass transfer in steelmaking was briefly discussed in Section4.5. Arguments there were partly general, partly specific. The time for 95% mixing provides onlyan approximate indication for slag–metal reaction. The best approach is to actually measure

tr( ) tr

tr

tr

FIGURE 7.12 Desulfurization in a 120t ladle; comparison of calculated values, with and without consider-ation of the emulsification of slag droplets.

i.e., W S[ ] W S[ ] O⁄( )

concentration homogeneity in the bath while the reaction is in progress. The present author hasnot been able to locate any such study in the literature.


However, there have been some efforts to throw light on this issue through mathematicalmodeling with the help of some experimental rate data. Section 4.5 has mentioned studies bySzekely and coworkers.32 The basic differential equation is

(7.35)

with the symbols as defined in Chapter 4. Variable r is the rate of reaction per unit volume of liquidsteel, and Deff = effective diffusivity = Dt + Di. Since the turbulent diffusivity (Dt) is orders ofmagnitude larger than the molecular diffusivity (Di), Deff ≈ Dt.

The analysis was actually carried out for powder injection. At the slag–metal interface, chemicalequilibrium was assumed. Figure 7.13 shows variation of as a function of theh/H parameter during desulfurization in a 40t ladle. ∆[WS] is the difference of WS between thebottom and top of the ladle. [WS]b is the weight percent of sulfur at the ladle bottom. h is the depthof lance immersion and H is the melt height. A bottom-stirred ladle corresponds to h/H = 1 andhence ≈ 0.05 from Figure 7.13. However, it is expected to be higher if no powderinjection is employed. Hence, this analysis indicates the possibility of significant nonhomogeneityin the bath during desulfurization.

As noted in Section 4.5, Szekely et al.32 proposed the modified Biot’s number (Bim) criterionfor comparison of the rate of mass transfer with that of mixing. Their order of magnitude calculationrevealed that Bim would be approximately 10–1 to 10–2 for gentle stirring (i.e., no emulsification).Under this situation, mass transfer would be relatively slow and rate controlling in comparison tomixing. However, with vigorous stirring and slag–metal emulsion, kmA and hence Bim would beabout two orders of magnitude larger, and so mixing would tend to control rate.

The model calculations of Mietz and Bruhl33 indicate that inhomogeneities can be avoided fordesulfurization in gas-stirred ladles with top slag even when slag is emulsified, provided dead zonesare eliminated. This can be somewhat accomplished by proper location of porous plugs. As notedin Section 4.2, use of eccentric plugs lowered the mixing time as compared to centric plugs.However, this also has been found to retard slag emulsification and hence lower the reaction rate.30

Moreover, it would be incapable of minimizing dead zone. Hence, a correct solution is to have atleast two eccentric plugs for a reasonable ladle size.

δCi

δt-------- u ∇ Ci⋅+ ∇ Deff ∇ Ci⋅( )⋅ r+=

∆ W S[ ]( ) W S[ ] b⁄

∆ W S[ ]( ) W S[ ] b⁄

FIGURE 7.13 Sulfur segregation in molten iron bath during desulfurization by powder injection.32

Rate Equations


With a low gas flow rate and nonemulsified slag, the slag–metal interfacial area may be taken asthe geometric one. Even there, it is an approximation, since some perturbations will be present.Section 4.4.2 discussed mass transfer correlations for this situation. Table 7.2 shows that n variesfrom 0.3 to 0.7. Higbie’s surface renewal theory leads to the following equation:

(4.24)

For centric gas stirring, the exposure time for an element of molten steel in contact with theslag is approximated as

(7.36)

where R is the inner radius of the ladle and uo is a characteristic melt velocity. uo again may betaken as Q/A, where A is the interface area of slag and metal. Combining Eqs. (4.24) and (7.36)suggests that km,i ∝ (Q/A)1/2, giving a value of n as 1/2.

Gaye et al.15 employed Eq. (7.30) as the basis of their kinetic analysis. Assuming mass transfercontrol,

(7.37)

On the basis of Eqs. (4.24) and (7.36), km,S was correlated as

km,S = β(DS · Q/A)1/2 (7.38)

From ladle desulfurization data of their own, as well as those of Usui et al.,34 a value of β =500 m–1/2 was arrived at. Q is the actual volumetric gas flow rate in m3 s–1.

It may be noted that, with progress of desulfurization, sulfur content in the slag keeps increasing.Considering this and neglecting the initial sulfur content in the slag, the following equation can bearrived at by combining Eqs. (7.11), (7.27), and (7.30):

(7.39)

integrating between limits, t = o, [WS] = [WS]O, and t = t, [WS] = [WS],

(7.40)

where B = kS,emp · t

On the basis of Eq. (7.40), Figure 7.14, adapted from Gaye et al.,15 is a set of iso-R plots with Bas x-axis and Y as y-axis.

km ,i 2Di

πte

-------

1 2⁄

=

teRuo

----- RQ A⁄( )

-----------------∝ ∝

kS ,emp km ,SAV----⋅=

d W S[ ]dt

--------------- kS ,emp– W S[ ] 1 1Y---+

W S[ ] O

Y---------------–

=

RW S[ ] O W S[ ]–

W S[ ] O

--------------------------------- 1 exp– B– BY---–

/ 1 1Y---+

= =


This equation can also be applied to emulsified slag. In that case, the slag–metal interface areawill be much larger, as discussed earlier.29

Concluding Remarks on Industrial Desulfurization by Top Slag

Industrial desulfurization kinetics is intimately linked with slag formation kinetics as well as otherdisturbing side reactions.17,20 The slag consists of the following components:

• slag carried over from the BOF vessel• deoxidation products• worn ladle lining• remaining slag from the previous heat• added slag-forming components such as lime, limestone, dolomite, and fluorspar

Figure 7.1517 shows the evolution of slag composition in CaO-SiO2-Al2O3 ternary due to theaddition of Al and CaO. If the starting carryover slag is at A, oxidation of Al with formation ofAl2O3 would take it to some composition such as A´. Dissolution of added CaO would finally takeit to A´´. If the starting point is B, then it would be something like B–B´–B´´.

Figure 7.1620 shows the MgO content of the slag in a magnesia-lined ladle after vacuumtreatment. It is strongly dependent on the CaO slag saturation degree, which not only controls theMgO content of the final slag but also the refractory lining life.

As stated in Section 7.2.5, one function of CaF2 addition is to increase LS. CaO-saturated slagis viscous and delays slag formation and sulfur removal. CaF2 makes the slag fluid and speeds upslag formation as well.

FIGURE 7.14 Iso-R plots with as x-axis and as the y-axis. Adapted from Ref.15.

B ( ks emp, t )⋅= Ls Msl 1000⁄⋅


7.4 INJECTION METALLURGY FOR DESULFURIZATION

7.4.1 INTRODUCTION

The injection process was introduced in the 1970s. The primary objective was more efficientdesulfurization of hot metal (i.e., impure liquid iron) and/or liquid steel. Here, discussions willemphasize desulfurization of steel melt in a ladle in secondary steelmaking. However, the followingdiscussions will reveal that there are many features common to all ladle-injection processes, andliterature dealing with either hot metal or steel will be cited, depending on availability. Broadly, itmay be classified into the following two categories:

• Continuous injection of solid powdered reagents inside molten steel along with a streamof gas (generally argon)

• Continuous injection (i.e., feeding) of reagents in wire form inside molten steel

The addition of calcium metal into the melt led to deep deoxidation, deep desulfurization, andmodification of inclusions for desirable properties. Extensive deposits of natural gas were discovered

FIGURE 7.15 Ladle slag formation in the system CaO-Al2O3-SiO2.17 Reprinted by permission of Iron &Steel Society, Warrendale, PA, U.S.A.

FIGURE 7.16 Refractory wear in a vacuum degasser ladle as a function of CaO slag saturation degree.20

Reprinted by permission of Iron & Steel Society, Warrendale, PA, U.S.A.

in the cold Arctic regions such as Alaska. The line pipe material for transporting gas over a longdistance has to withstand high pressure, corrosion from H2S in gas, and subzero temperatures and


the consequent tendency toward brittle fracture. The steel for this purpose required treatment bycalcium.

The properties of calcium and its alloys have been reviewed by Ototani.35 The typical reagentis Ca-Si alloy containing about 30% Ca and 60% Si, and rest Al, etc. It melts at around 1050 to1150°C.

Calcium is a gas at steelmaking temperatures. The vapor pressure-temperature relationship forpure calcium is36

(7.41)

At 1600°C (1873 K), = 1.81 atm. This is quite high and is likely to lead to instant, violentvapor formation. Very little Ca would get chance to react with the melt if it were added as such.In Ca-Si alloy,

(7.42)

where aCa is activity of Ca in Ca-Si alloy. Figure 7.17 presents the estimated activity vs. molefraction of Ca at 1600°C.36

For 33 wt.% Ca-67 wt.% Si alloy, XCa = 0.254. From Figure 7.17, aCa < 0.1, and hence thevapor pressure is below 1 atm. As such, top addition should have been all right. However, thesolubility of calcium in liquid iron is very low (0.025 ± 0.008 wt.% at 1600°C). Therefore, siliconis expected to dissolve into the melt much faster than calcium. So, shortly after addition, the liquidCa-Si alloy would get depleted in silicon, consequently raising pCa and leading to instant vapor-ization and loss of calcium.

The problem was satisfactorily solved by injecting CaSi alloy at a depth of at least 1 to 1.5 minside the melt so as to prevent vapor formation due to the ferrostatic pressure. This allowed thecalcium to react with the oxygen and sulfur of steel. Even then, some losses occurred.

The TN process, developed by Thyssen Niederrhein, Germany, was the first commercial powderinjection process. It was followed by Scandinavian Lancers (SL) after a few years. Their success

plog Cao (in atm) 8920

T------------– 1.39 logT 9.569+–=

pCao

pCa pCao aCa×=

1.0

0.8

0.6

0.4

0.2

1.0 0.8 0.6 0.40

MOLE FRACTION CALCIUM

CA

LCIU

M A

CT

IVIT

Y

FIGURE 7.17 Estimated calcium activity in Ca-Si alloys at 1873 K.

led to its application to some other grades of steel and for other purposes such as dephosphorization,alloying, and clean steel. Injection processes are also being widely employed for desulfurization


of hot metal in the ladle. This is done before primary steelmaking. Various reagents have beenemployed, depending on the objective. As a result, many steel companies worldwide have installedthis facility, and a large number of patented processes subsequently have been developed. Moltensteel is contained in a covered ladle. Solid powders along with Ar or N2 are injected through arefractory-lined lance tube whose position can be adjusted. A powder dispenser is employed tointroduce the powders into the gas stream in a fluidized state.

Figure 7.18 presents a sketch of the TN process.1,32 A characteristic of this method is that thedispenser and lance constitute an integrated unit capable of moving up and down a vertical stand.On the other hand, the SL process has a separate dispenser connected by a flexible hose to thelance tube (Figure 7.19). Powder and gas are mixed in the dispenser for pneumatic transport.Usually, the powder is fluidized in the container and then expelled by the top pressure of thecontainer through an adjustable orifice. A part of the carrier gas is introduced as an ejector gas justbeneath the dispenser or at a later stage. The feeding rate of the powder and the gas/solid ratio arecontrolled by the top and ejector pressures, as well as by the dimensions of the orifice.

The powder is fed into the molten steel through a lance, consisting of a metallic tube with arefractory lining of tubular bricks or a cast coating. The design and dimensions of the lance outletnozzle are important for maintaining proper feed rate. Typical outlet shapes are shown in Figure7.20. It is either a single hole or a T-outlet, or a multihole unit. Clogging of the nozzle throughpenetration of steel is a problem that occurs when there is too much pressure fluctuation in thepneumatic transport system. Proper nozzle design can significantly reduce the occurrence of clogging.

The cost of the lance depends on lance life, which again depends on the refractory material.This is a major expense item. In view of this, attention has been paid to developing alternativemodes of injection through the bottom or side wall of the ladle. Notable among such systems is

FIGURE 7.18 Principle of TN injection equipment with a moving powder dispenser.1

bunkers


lance stand

control

runnerfor ladleadditions

powderdispenser

FIGURE 7.19 Principle of SL injection equipment with a stationary powder dispenser unit.1

MULTIPORT STRAIGHT

T SHAPE SWEPT SINGLE PORT

FIGURE 7.20 Sketch of injection nozzle.

the Injectall Side Injection System (ISID) developed in the United Kingdom. The system uses amultiorifice mechanism fitted to the side wall. The refractory plug of the nozzle is removed at the


start of injection by a hydraulic device. It is again plugged in after injection. However, it seemsthat lance tubes are even now being primarily employed.

The choice of refractory lining material is important, too. High alumina or basic lining, i.e.,burned dolomite, chrome magnesia or magnesia, are in vogue. These influence a degree of des-ulfurization as well.

Another advantage of the injection process is the enhanced reaction rate. Figure 7.10 showsthe findings of a plant study on desulfurization. For the injection process, kS,emp was about five timeslarger as compared to that for top slag alone. In view of all of these, the process attracted worldwideattention of steelmakers in the 1970s and 1980s. This is reflected in several International Confer-ences on this topic. Specific mention may be made of the SCANINJECT series held at Lulea,Sweden. There have been other reviews and monographs as well.1,3,32

Injection metallurgy will be coming into the picture in later chapters, also in connection withclean steel, etc. In this section, discussions will be specifically restricted to the reaction of sulfur.It will also be restricted to powder injection. Toward the end, a comparison will be made betweenpowder injection and wire feeding. Table 7.3 shows the common desulfurizing agents. It is possiblethat some other reagents are being used in scattered applications. For example, in low silicon steels,injection of CaO-CaF2 flux along with Al powder is an alternative. Desulfurization occurs by thecombined action of powder feeding and the reaction of molten steel with top slag. Prevention orminimization of carryover slag is of utmost importance. It has been dealt with in Chapter 5 andSection 7.1. Detailed descriptions are also available elsewhere.32

7.4.2 THE REACTOR MODEL

The reactor model was originally proposed by Lehner.37 In view of extensive discussions on thekinetic and dynamic aspects of gas-stirred ladles, a simplified version of the model, as presentedin Figure 7.21, is adequate for further discussions.

As Figure 7.21 shows, injected gas and powder rise up through the melt. The gas is the sourceof stirring, which is essential for the success of the process. Broadly speaking, the reaction occursin the following three zones:

1. In the transitory contact zone, the rising solid powders react during their passage throughthe melt.

2. The permanent contact zone is a consequence of the presence of a top slag. The reactionis between slag and metal.

3. The breakthrough zone is created where the gas bubbles penetrate the slag layer andescape into the atmosphere. In this zone, liquid metal is also dragged up and broughtinto contact with the atmosphere with which it reacts, leading to some reoxidation andnitrogen pickup of the melt. This tendency is enhanced by the ejection of droplets intothe atmosphere, since a large gas–metal interfacial area is created. Reactions in thebreakthrough zone are undesirable.

TABLE 7.3Desulfurizing Agents for Powder Injection in Secondary Steelmaking

Agent Composition, wt.% Injected amount, kg/tonne

Ca-Si alloy Ca-30, Si-62, Al-8 2–4

CaO-CaF2 CaO-90, CaF2-10 3–6

CaO-Al2O3-CaF2 CaO-70, Al2O3-20, CaF2-10 2–5


In addition to the above, the ladle lining also tends to react with slag, melt, and powder, causingsome reoxidation. Dolomite lining is stable and has been found to be the best for desulfurizationas well (less than 0.004%). With fireclay and silica linings, dissolved Ca and Al in melt react withSiO2, with the consequent effects as mentioned above. In practical process conditions, differentreoxidation sources may be limiting the final cleanness.

The simplest analysis of the process is based on the assumption that there are no kinetic andmixing limitations, i.e., the process is thermodynamically reversible. This kind of analysis has beendemonstrated in Ch. 6 in connection with vacuum and argon degassing.

For desulfurization by slag injection and transitory contact zone, the situation would be as inthe top corner of Figure 4.1, i.e., the feed rate of the powder would be rate controlling. Sulfurbalance leads to the relation

(7.43)

where is the rate of slag powder injection in kilograms per tonne of liquid steel per second,and t is the time from the beginning of injection.

Integrating Eq. (7.43) from t = 0, [WS] = [WS]O, and t = t, [WS] = [WS],

(7.44)

For a permanent contact zone, from Eq. (7.29),

(7.45)

Example 7.3

Compare the predictions of for LS = 102, 5 × 102 and the equilibrium value ofExample 7.2 for slag, and MSl = 5 and 10, assuming both the transitory contact and permanentcontact models.

FIGURE 7.21 Zones in the ladle injection process.

1000d W S[ ]

dt---------------– MSlLS W S[ ]=

MSl

W S[ ]W S[ ] O

--------------- expMSlLSt1000

----------------– MSlLS

1000--------------–

exp Y–( )exp= = =

W S[ ]W S[ ] O

--------------- 11 Y+-------------=

W S[ ] W S[ ] O⁄

Solution


This calculation reveals that sulfur removal efficiencies are comparable for transitory and permanentcontact at lower values of LS, but transitory contact is much more efficient at larger values of LS.However, a better conclusion of transitory and permanent contact zones is possible only when weconsider kinetics as well, which will be dealt with in the following section.

7.4.3 KINETIC CONSIDERATIONS

As noted in Section 7.3.2, a slag–metal emulsion forms at a high gas stirring rate and, as aconsequence, kS,emp has been found to increase by a factor of 5 to 10. Figure 7.10 shows a similarincrease in the rate for powder injection of slag as compared to top slag treatment alone. Hence,creation of a slag–metal emulsion would give about the same rate of desulfurization as comparedto the powder injection of slag at a low gas flow rate (i.e., nonemulsified top slag). This has beenthe conclusion in the literature as well.32

Ying et al.39 carried out a cold-model study with water simulating liquid steel and a mineraloil simulating slag. Transfer rates of benzene-carboxylic acid dissolved in oil, to water, weremeasured. In one set of experiments, oil was used as top slag. In another set, oil droplets weresprayed (i.e., injected) inside water. Figure 7.22 shows the time required to achieve equilibriumpartitioning of the acid between oil and water. It demonstrates that, at a low gas flow rate, sprayingallowed faster attainment of equilibrium as compared to gas-stirred permanent contact. However,at a high gas flow rate, there was no difference.

LS = 102 LS = 5 × 102 LS = 1.6 × 103 (φ)

MSl Y Y Y

Trans.contact

Perm.contact

Trans.contact

Perm.contact

Trans.contact

Perm.contact

5 0.5 0.6 0.67 2.5 0.082 0.29 8.0 3.4 × 10–4 0.11

10 1.0 0.37 0.5 5.0 6.7 × 10–3 0.17 16.0 1.1 × 10–7 0.06

(φ) = equilibrium value for slag in Example 7.2.

W S[ ] / W S[ ] O W S[ ] / W S[ ] O W S[ ] / W S[ ] O

FIGURE 7.22 Comparison of time to attain equilibrium partitioning of solute between water and oil forspraying (i.e., injection) of oil droplets and oil-water bulk phases with gas stirring.39

In older injection practice, high argon flow rates of about 6 × 10–4 Nm3 s–1 per tonne of steelwere employed. With reference to Table 3.2, this is equivalent to a QV of about (120–140) × 10–4 m3


s–1 per m3 of bath. In modern practice, it is an order of magnitude lower.3,32.40 It leads to considerablesavings in argon. It also helps to maintain the compactness of the slag layer, preventing formation ofa breakthrough zone and consequent undesirable reactions of the melt with atmospheric oxygen andnitrogen. A low rate also cuts down on the extent of undesirable reactions with the refractory lining.

Taking the value as 6 × 10–5 Nm3 s–1 per tonne of steel, with temperature = 1900 K and heightof the melt in ladle as 3 m, Eq. (3.64) yields the value of the specific rate of input of stirring energy(εM) as 0.006 W kg–1. This is much lower than the range of 0.065 to 0.13 W kg–1, which is theminimum required for formation of slag–metal emulsion (Section 4.4.2).

Hence, it may be concluded that the gas flow rate in modern injection metallurgy is such thatslag–metal emulsion does not form. As discussed in Section 7.3.2, the rate of desulfurization fortop slag treatment is likely to be controlled by mass transfer at the slag–metal boundary, and thegeometrical interfacial area may be taken for calculation.

Rate Equations

Rate equations for permanent contact, i.e., reaction with top slag, have already been derived[Eqs. (7.39) and (7.40)]. For phase boundary mass transfer control, the general rate equation isgiven by Eq. (4.41). Combining the above,

(7.46)

where Vm = volume of metal, and I and II refer to metal and slag, respectively. Equation (7.46) isanalogous to Eq. (7.37) but has been derived from theory, whereas Eq. (7.37) is more empirical innature.

Engell et al.40 considered the influence of carryover slag on the reaction. They assumed thefollowing:

1. Steel is at equilibrium with carryover slag, i.e., at t = 0,

(WS)O = LS · [WS]O

2. The value of LS is same for carryover slag and final slag.

With the above assumptions, Eq. (7.27) is modified as

1000 [WS]O + MSl · S · LS [WS]O = 1000 [WS] + MSl (1 + S) (WS) (7.47)

where S is the ratio of carryover slag to added slag (i.e., MSl). Combining Eqs. (7.39), (7.46), and (7.47),

(7.48)

Integrating from t = 0 to t = t,

(7.49)

kS ,empA

V m

------- km ,sI–II⋅ k= =

d W S[ ]dt

--------------- k W S[ ] 1 1Y 1 S+( )---------------------+

W S[ ] O1

Y 1 S+( )--------------------- S

1 S+------------+

––=

W S[ ]W S[ ] O

---------------1

1 1Y 1 S+( )---------------------+

------------------------------- 1Y 1 S+( )--------------------- S

1 S+------------

11 S+------------

B 1 1Y 1 S+( )---------------------+

–exp⋅+ +

⋅=

For transitory contact, Eq. (7.43) is to be modified to take mass transfer into account as follows:


(7.50)

Combining Eq. (7.50) with Eqs. (7.30) and (7.46) and assuming that (WS)O = 0,

(7.51)

Integrating from t = 0 to t = trp,

(7.52)

where Ap = surface area of individual particle,

trp = residence time of a particle in molten steel before it goes to the top

For a spherical particle,

(7.53)

where dp = diameter of the particle

When desulfurization takes place both in the transitory contact zone and permanent contactzone, then

(7.54)

where P and T refer to permanent and transitory contact, respectively.

It may be noted that would have different values for the two zones. Residence time for aparticle in the melt is difficult to predict theoretically. Trp was taken as 20 s40 on the basis of literaturedata. This value assumes that the particle circulates a few times in the melt before coming out.Assuming values of k for both permanent and transitory contact as 10–3 s–1 and 10–2 s–1, numericalcalculations were performed on the basis of Eqs. (7.48), (7.51), and (7.54).40 Calculated variationsof [Ws]/[WS]O with time are presented in Figures 7.23 and 7.24 for two values of slag carryover andtwo values of k. These again demonstrate that rate of desulfurization is much faster with injectionas compared to that without injection at k = 10–3 s–1. However, at k = 10–2 s–1, which is the case foran emulsified slag, both are comparable. A significant influence on the amount of slag carryover isalso evident. The more carryover slag, the less desulfurization. The rise in the sulfur content of steelafter stopping the injection is due to a further reaction toward equilibrium with top slag.

1000–d W S[ ]

dt--------------- MSl W S( ) W S( )O–[ ]=

d W S[ ]dt

---------------k p W S[ ]

11000k p

MS1 LS⋅-------------------+

----------------------------------–=

W S[ ]W S[ ] o

-------------- trp

11000k p

MSl LS⋅------------------+

----------------------------–exp=

k p

Ap

V p

------ km ,sI–II( )p⋅=

Ap

V p

------ 6d p

-----=

d W S[ ]dt

---------------d W S[ ]

dt---------------

p

d W S[ ]dt

---------------

T

+=

km S,I–II

Injection Stop Tapping


In general, only a fraction of the injected particles go into the melt. The rest remain attachedto the bubbles and hence are only partially exposed to the melt. Chiang et al.41 did mathematicalmodeling considering this. Their predictions are shown in Figure 7.25. kS,emp for desulfurization ofhot metal in a three-tonne ladle is also presented. Calcium carbide was injected as a solid. Theargon flow rate was 2.5 × 10–3 Nm3 s–1. The figure shows that experimental data approximatelymatched with predictions for a situation where the fraction of solid in the melt is 30%. The findingon a 60 kg laboratory melt was similar.

0 2000.00

k = 1.10-3

k = 1.10-2

k = 1.10-3

(k in s-1)

0.25

0.50

0.75

1.00

400 600 800

Carry-Over Slag 1kg/tInjected or Added Slag 20 kg/t

Injection and Top Slag Reaction

Top SlagReaction only

Injection only

[ Ws

] / [

Ws

] 0

TIME, s

FIGURE 7.23 Change of concentration of sulfur in a steel or hot metal melt by top slag reaction and/orreaction with injected particles; carryover slag 1 kg/t.40

FIGURE 7.24 Change of concentration of sulfur in a steel or hot metal melt by top slag reaction and/orreaction with injected particles; carryover slag 10 kg/t.40


Deo and Boom42 have presented a detailed analysis of this based on their own work43 as wellas that of others. They considered the reaction of particles in a melt and particles attached to bubblesseparately and arrived at the following correlations:

(7.55)

where,

a = Ak, due to permanent contact (7.56)

(7.57)

and is due to particles in the melt. f is the fraction of particles in the melt, and ρS is the density ofthe solid.

(7.58)

and is due to the contribution of particles attached to bubbles toward desulfurization. DB is bubblediameter, Q is gas flow rate in Nm3 s–1.

Equations (7.55) through (7.58) were applied to desulfurization during the injection of calciumcarbide for a 300-tonne hot metal in a torpedo vessel.42 Values of certain parameters were assumed.Contribution due to a, b, c to desulfurization turned out to be approximately 30, 40, and 30%,respectively. However, there are indications that the transitoric zone may not be contributing morethan 40% toward desulfurization in steel refining. Hence, a fluid top slag with high sulfide capacityshould be employed.

FIGURE 7.25 Desulfurization rate constant as a function of the flow rate of solids for calcium carbideinjection into hot metal in a ladle; solid lines are predictions.41 Reprinted by permission of Iron & SteelSociety, Warrendale, PA, U.S.A.

W S[ ] o

W S[ ]--------------ln a b c+ +( ) t

V----

m⋅=

b 1000LSMS1 f 1 6k ptrp

d pLS

--------------– exp–⋅=

C1000LSMS1

ρS

--------------------------- 1 f–( ) 1 2.38dB

----------– mT

298---------

kgtrbQρS

1000MS1 1 f–( )LS

--------------------------------------------⋅ ⋅ ⋅ exp–=

7.4.4 MELT–PARTICLE PHYSICAL INTERACTION


This interaction was studied by several investigators. Among them, the most comprehensive inves-tigations have been carried out by Irons and coworkers.44,45 For effective participation of the particlesin the desulfurization reaction, they should become detached from the argon bubbles and comeinto the liquid soon after emerging from the lance nozzle. This is best achieved if the particles arecoarse and have low interfacial tension with liquid steel (i.e., wetting). Coarse particles have highmomentum, which leads to their easy detachment from the bubbles. The nature of wetting assistsit further. The solid:gas ratio is an important variable.

Another important issue is the behavior of the gas-particle mixture as it emerges from thenozzle. The high velocity of gas from the nozzle causes jetting flow and prevents back-attack ofthe nozzle by molten metal and consequent nozzle clogging (Chapter 3, Section 3.2). This is incontrast to the bubbling regime at lower gas velocities. In the gas-particle mixture, even at samegas flow rate, one can obtain either a jetting or bubbling regime. Fine particles tend to be in thegas phase. Since particles have orders of magnitude higher density than that of the gas, they increasejet momentum significantly and lead to jetting. More solid loading in the gas has the same effect.Figure 7.26, taken from Irons,44 demonstrates this. It includes operational data from several sources.

In the early days of injection metallurgy, particle sizes used to be in the range of 1 to 3 mm1.Nowadays, it is typically 0.1 mm or less, the maximum upper limit being 1 mm.32 The use of fineparticles (<0.1 mm) offers the following advantages:

• Jetting flow and hence less lance clogging• Powder injection at a low gas flow rate because of easier fluidization and conveying of

the solid particles in the dispenser-lance assembly• A large specific surface area compensating for lower particle-melt contact in connection

with the reaction rate

The orientation of the lance has little effect on the flow regime immediately adjacent to thelance but, of course, has a dramatic effect on the particle and gas trajectory. A mathematical modelwas developed to predict the penetration length of the jet into the liquid.45 Calculated dimensionless

FIGURE 7.26 Flow regimes in powder injection systems.44

penetration length (length/lance diameter) agreed well with experimental measurements. It is animportant design and operational parameter. The lance tip is to be located such that mixing in the


bath is good, and transitoric reactions are efficient. On the other hand, solid particles should notimpinge on the refractory lining to ensure longer lining life.

As has already been stated, modern injection refining of molten steel is carried out in a gasflow rate where mixing is more rapid as compared to mass transfer at the top slag–metal interface.A mathematical model exercise has shown that mixing offers negligible resistance to reaction withpowder injection.45 This is because injection causes much more rapid mixing as compared to thatfor only gas purging, for the following reasons:

1. Transitoric reaction is dispersed in the melt and thus partially eliminates bulk inhomo-geneities in sulfur concentration.

2. As already mentioned, the gas-particle jet has much higher momentum as compared toa simple gas jet. This leads to larger penetration of the jet into the melt and increasesthe effective rise depth of a gas bubble, which in turn increases εm [Eq. (3.64)] and lowersthe mixing time even if immersion depth is low. This is illustrated in Figure 7.27 for a240t torpedo ladle.45

As far as fluid flow and mixing during injection are concerned, the general features may betaken as those for a gas-stirred ladle. These have been sufficiently discussed in Chapters 3 and 4.In addition, Section 7.3 presented brief discussions on fluid flow, mixing, and mass transfermodeling by Szekely and coworkers.32 It has been stated there that it covered lance injection aswell. Some other studies have also been cited.42 Hence, no further deliberations on these will beincluded here.

7.4.5 COMMENTS ON INDUSTRIAL INJECTION PROCESSES

Powder Delivery and Preparation

Szekely et al.32 have reviewed this subject. A brief description is contained in Section 7.4.1. Littlemore elaboration is included here. When a gas is blown vertically upward through a packed bedof solids, the bed starts to expand at a critical gas velocity, known as minimum fluidization velocity.A further velocity increase leads to a fluidized bed in which solid particles remain suspended inthe gas stream in the bed. If velocity is increased further, another critical point is reached when

FIGURE 7.27 Mixing time (for 95% mixing) in a model of a torpedo ladle as a function of lance immersiondepth.45 Gas flow rate = 1.67 × 10–3 Nm3 s–1 and the solid flow rate = 5 × 10–3 kg s–1.

the linear velocity of the gas equals the terminal settling velocity of the particle. This is known asthe elutriation velocity. A further increase in velocity leads to the escape of the particles from the


bed with the gas stream, i.e., pneumatic conveying.An increase of the velocity of gas (u) means an increase in gas flow rate (Q). It is possible only

by an increase of pressure difference across the bed (∆P). For pneumatic conveying along a horizontalpipe, a minimum u is required for a given set of conditions (conduit size, solid/gas ratio, etc.) toprevent saltation (i.e., settling) of the solid particles in the pipe. In vertical pneumatic conveying,the concept of choking is somewhat analogous to saltation. Again, a minimum velocity is requiredto prevent choking. Dimensionless quantitative correlations are available in the literature.32

As stated in the previous section, solid particle size is typically less than 0.1 mm. Typicalinjection time is 10 min. Hence, the feed rate for a 130t melt would range from 20 to 60 kg/min.Fine powders are very reactive. They easily react with air during storage and handling. Oxidationof a metal/alloy powder, such as calcium silicide, may be so rapid as to raise its temperature abovethe ignition point, resulting in spontaneous combustion due to exothermic heat generation. This isa safety hazard. Lime and lime-based fluxes readily react with moisture. Hence, efforts are requiredto prevent contact of the powder with the atmosphere. Powders should flow easily. For this, a roundshape is best. A moisture-free surface also is very desirable. Hence, to summarize, much care isrequired for preparation, storage, and handling of powders.

Side Reactions

Various side reactions occur during injection refining of steel melt. Some of them are undesirable.For the manufacture of steels with a very low content of objectionable impurities and goodcleanliness, these side reactions often pose serious difficulties and thus must be tackled satisfactorily.Considerable attention has therefore been paid to them. Holappa1 and Helle46 have extensivelyreviewed them, and their conclusions may be summarized as follows. (There will be more discus-sions in subsequent chapters.)

1. The injected powder should be dry and free from impurities that are likely to be difficultto eliminate.

2. The formation of a breakthrough zone is undesirable, since ejected metal droplets thencome into contact with the atmosphere above and pick up oxygen and nitrogen. Thisproblem, by and large, has been overcome in the modern processes, since the argon flowrate is low, and breakthrough zone is not significant.

3. Reaction of the melt with ladle refractory lining is to be controlled in all secondarysteelmaking processes. The choice of refractory material in this context is crucial. Goodsteel cannot be made without good quality refractory. In view of the importance of thetopic, it will be taken up again in Chapter 10. A very brief discussion is included here,specifically relevant to desulfurization.

Silica-containing acid refractory lining is unstable. The decomposition of SiO2 leads to anincrease in the oxygen content of the melt, since the melt is highly deoxidized by aluminum orcalcium. This prevents the attainment of ultra-low sulfur level. A dolomite lining or high aluminalining is much better. The former has allowed attainment of as low as 0.004% (40 ppm) or lesssulfur in steel. Figure 7.28, redrawn by Holappa1 from other sources, is presented to show thebeneficial effect of dolomite lining on desulfurization.

Typical Recommended Practice for Ultra-Low-Sulfur Steel

• Dolomite ladle lining is to be employed.• Carryover slag should be as low as possible; its quantity should be determined as well.

A maximum of 5 kg/tonne of steel is acceptable.


• Steel is to be killed primarily by aluminum.• Additions for making synthetic top slag with high sulfide capacity and good fluidity are

to be made during tapping or later.• Injection of calcium silicide is required for 8 to 10 minutes at a solid flow rate of about

0.1 to 0.3 kg/tonne of steel per minute and an argon flow rate of 0.001 to 0.003 Nm3/min.• Measurement of dissolved oxygen by an immersion oxygen sensor is very helpful.• After injection, a gentle stirring by argon for a few minutes helps in homogenization

and removal of inclusions.• A multihole lance is better than single-hole lance; the depth of immersion should be at

least 1.5 m.

For stainless steel, Sumitomo Metal Industry has developed a new refining method, VOD-PBfor a 50t VOD. It can produce ULC (<10 ppm), ULN (<20 ppm), ULH (<1 ppm), ULS (<10 ppm).Ultra-low S was achieved by blowing CaO-based flux powder with argon under vacuum. Also, thevacuum Kimitsu Injection process is capable of giving sulfur <5 ppm in 10 min.

Powder Injection vs. Wire Feeding of CaSi

The relative merits and demerits of these two methods for injection of CaSi have been evaluated.38,47

By powder injection, an efficient combined desulfurization and inclusion modification can beachieved. In wire feeding, CaSi powder is encased in steel, and the entire composite is in the formof wire. With wire feeding, primarily only inclusion modification can be achieved. However, itgives a higher recovery and better alloying precision, provided proper metallurgical preconditionsprevail. Nowadays, many steel plants maintain provisions for both and are carrying on powderinjection and wire feeding, depending on the specific situation.

REFERENCES

1. Holappa, L.E.K., Int. Met. Reviews, 27, 1982, p. 53.2. Turkdogan, E.T., Ironmaking and Steelmaking, 15, 1988, p. 311.3. Fruehan, R.J., Ladle Metallurgy principles and Practices, Iron & Steel Soc., U.S.A., 1985, Chs. 2,

3, and 5.4. Renkens, H.J., in Int.Symp. on Quality Steelmaking—Emerging Trends, Ind. Inst. Metals, Ranchi,

India, 1991, p. 107.

FIGURE 7.28 The influence of ladle refractory on desulfurization efficiency.

5. The Japan Soc. for Promotion of Science, the 19th Committee on Steelmaking, Steelmaking DataSourcebook, Gordon & Breach Science Pub., Tokyo, revised ed. 1984.


6. Sigworth, G.K. and Elliott, J.F., Metal Science, 8, 1974, p. 298.7. Vahed, A. and Kay, D.A.R., Met. Trans. B., 7B, 1976, p. 375.8. Turkdogan, E.T., Arch. Eisenhuttenwesen, 54, 1983, p. 4.9. Fincham, C.J.B. and Richardson, F.D., Proc. Royal Soc., A223, 1954, p. 40.

10. Verein Deutscher Eisenhuttenleute, Slag Atlas, Verlag Stahleisen mBH, Dusseldorf, 1981.11. Carlsson, G., Dong, Y.Y., and Jorgensen, D., Scand. J. Met., 16, 1987, p. 50.12. Zhang, X.F. and Toguri, J.M., Canad. Met. Qtly., 26, 1987, p. 117.13. Elliott, J.F., Gleiser, M. and Ramakrishna, V., Thermochemistry for Steelmaking, Addison-Wesley Pub.

Co., Reading, Mass, U.S.A., Vol. 2, 1963.14. Tsao, T. and Katayama, H.G., Trans. ISIJ, 26, 1986, p. 717.15. Gaye, H., Riboud, P.V. and Welfringer, J., in Proc. PTD, 5th Int. Iron & Steel Cong., Washington

D.C., Vol. 6, 1986, p. 631.16. Duffy, J.A., Ingram, M.D., and Somerville, I.D., Trans. Far. Soc. I., 74, 1978, p. 1410.17. Bannenberg, N., Lachmud, H., and Prothmaun, B., Steelmaking Conf. Proc., Chicago, 77, 1994, p. 135.18. Davies, M.W., Chem. Met. of Iron & Steel, Iron & Steel Inst., London, 1973, p. 43.19. Kor, G.J.W. and Richardson, F.D., Trans. AIME, 245, 1969, 319.20. Humbert, J.C. and Blossey, R.G., The Elliott Symposium, Iron & Steel Soc., U.S.A., 1990, p. 427.21. Bird, R.B., Stewart, W.E., and Lightfoot, E.L., Transport Phenomena, J. Wiley & Sons., New York,

1960, Ch. 19.22. King, T.B. and Ramachandran, S., in Physical Chemistry of Steelmaking, J.F. Elliott, ed., MIT Press,

Cambridge, Mass, U.S.A., 1958, p. 128.23. Richardson, F.D., Physical Chemistry of Melts in Metallurgy, Academic Press, London, Vol. 2, 1974,

Ch. 14.24. Kapoor, M.L. and Frohberg, M.G., in Ref. 18, p. 17.25. Ward, R.G., The Physical Chemistry of Iron and Steelmaking, Edwin Arnold, London 1962, Ch. 10.26. Ohma, M., Nakata, H., Morii, K., and Yajima, T., in Ref. 15, p. 327. 27. Asai, S., Kawachi, M., and Muchi, I., preprints Scaninject III, MEFOS, Lulea, Sweden. Part 1, 1983,

Paper 12.28. Sundberg, Y., Scand. J. Met., 7, 1978, p. 81.29. Oeters, F., Metallurgy of Steelmaking, Stahl Eisen, English Version, 1994, Ch. 5 and 6.30. Mietz, J., Schneider, S. and Oeters, F., Steel Res., 62, 1991, p. 1.31. Mietz, J., Schneider, S. and Oeters, F., Steel Res., 62, 1991, p. 10.32. Szekely, J., Carlsson, G., and Helle, L., Ladle Metallurgy, Springer-Verlag, New York, 1989.33. Mietz, J. and Bruhl, M., Steel Res., 61, 1990, p. 105.34. Usui, T., Yamada, K., Miyashita, Y., Tanabe, H., Hanmyo, M., and Taguchi, K., preprints SCANINJECT

II, MEFOS, Lulea, Sweden, 1980, Paper 12.35. Ototani, T., Calcium Clean Steel, Springer-Verlag, Heidelberg, 1986, Ch. 1.36. Mellberg, P.O. and Gustafsson, S., Proc. Symp. on Injection Metallurgy, Shanghai, P.R. China, 1982.37. Lehner, T., preprint SCANINJECT I, MEFOS, Lulea, Sweden, 1977, Paper 1.38. Tivelius, B., Gustafsson, S., and Mao, YU. De., preprint Seminar on Secondary Steelmaking, Ind.

Inst. Metals, Jamshedpur, India, 1989, p. 189.39. Ying, Q., Yun, L., and Liu, L., in Ref. 27, Paper 21.40. Engell, H.J., Janke, D., and Hammerschmid, P., preprints Int. Conf. Secondary Metallurgy, Verein

Deutscher Eisenhuttenleute, Verlag Stahleisen mBH, Dusseldorf 1987, p. 19.41. Chiang, L.K., Irons, G.A., Lu, W.K., and Cameron. I.A., Trans. ISS, Jan. 1990, p. 35.42. Deo, B. and Boom, R., Fundamentals of Steelmaking Metallurgy, Prentice Hall International, London,

1993, Ch. 8.43. Robertson, D.G.C.,Ohguchi, S., Deo, B., and Willis, A., in Ref. 27, Paper 8.44. Irons, G.A., in preprints SCANINJECT IV, MEFOS, Lulea, Sweden 1986, Paper 3.45. Irons, G.A., in Proc. Savard/Lee Int. Symp. on Bath Smelting, J.K. Brimacombe et al., ed., Minerals

Metals & Materials Soc., 1992, p. 494.46. Helle, L., in Ref. 32, Ch. 3.47. Sengupta, S. and Basu, S., in Ref. 38, p. 199.

8 Miscellaneous Topics

8.1 INTRODUCTION

Each of the previous chapters had one broad but specific topic as its theme. However, there aresubjects that are important in secondary steelmaking but do not justify coverage as full chapterswithin the scope of the present text. Also, they are somewhat disparate in nature. Hence, they arebeing presented here as miscellaneous topics.

The topics covered in this chapter are

1. Gas absorption during tapping and teeming from the surrounding atmosphere2. Changes in temperature of molten steel during secondary steelmaking3. Phosphorus control in secondary steelmaking4. Nitrogen control in steelmaking5. Application of magnetohydrodynamics in secondary steelmaking

8.2 GAS ABSORPTION DURING TAPPING AND TEEMING FROM SURROUNDING ATMOSPHERE

It was known as early as 1950 that oxygen is absorbed by molten steel during teeming from thesurrounding air. From then on, many investigators have reported the phenomenon. Heaslip, McLean,and Sommerville1 reviewed this. Since the oxygen is picked up just before casting, the resultinginclusions do not get separated well and lead to additional dirtiness in the solidified steel. Theproblem is more serious in continuous casting because of faster freezing and consequently lesstime available for inclusions to float up. It is of relevance to ingot casting as well, if we wish toproduce clean steel.

It has been found that the product of such reoxidation generally forms macroinclusions (above100 microns or so), which are harmful to the properties of steel. Also, they are generally richer iniron and manganese oxides. The extent of oxygen absorption during tapping is of the order of 10to 20 ppm2, whereas it exhibits a wide range of 10 to 1000 ppm (i.e., 0.001 to 0.1%) during teeming,depending on conditions.

Therefore, it has been widely accepted that, if we really desire clean steel, especially incontinuous casting, the teeming stream ought to be shielded from the surrounding air either by aninert gas or by the use of a submerged nozzle. This is known as stream protection, and it is a widelyadopted practice in continuous casting. However, it is rarely practiced for ingot casting because ofthe adverse cost-to-benefit ratio. It is important to understand the mechanism of such absorptionand the variables that influence it so as to minimize it in industrial practices.

Nitrogen pickup is much slower than oxygen pickup but is also significant. During tapping,nitrogen pickup may be as large as 40 ppm3, and during teeming it may go up to 150 ppm.4 Somereoxidation also takes place from the ferrous oxide/silicate slag coating on ladle refractory lining.This has already been discussed in Chapter 5, Section 5.3.


8.2.1 G

ENERAL

C

OMMENTS

ON

M

ECHANISM

l


Geometrically speaking, this is a case of a liquid stream falling freely into a pool of the same liquidthrough a gaseous atmosphere. As shown schematically in Figure 8.1, the absorption of gas cantake place5

• through the surface of the falling stream• at the surface of the pool • via entrainment as bubbles inside the molten pool

Theoretical analysis and experimental work with water models have shown that the last mech-anism, viz., absorption via entrainment, is the predominant one. Szekely6 theoretically estimatedthe extent of oxygen absorption by a stream of molten steel from air during teeming. He assumedthe stream to be laminar and smooth and that the air gets dragged into the pool of liquid steel byfrictional drag at the stream surface. The entrained air forms bubbles inside the liquid metal pool,and all the oxygen from such bubbles are absorbed by the metal. Szekely calculated the extent ofoxygen absorption (∆O). For laminar streams, these agreed well with the reported value of 26.5ppm from some industrial data.

However, many investigators4 found very large quantities of oxygen pickup, and these wereascribed to turbulence and the rough surface of the stream. Therefore, here we have a situationwhere the physical characteristics of the stream are of considerable importance. In addition, it wasfound that, under certain circumstances, the stream becomes unstable and breaks up into droplets.Such droplets increase the specific surface area of liquid metal enormously and lead to significantabsorption of gas, even before the teeming stream plunges into the liquid metal pool. Kumar andGhosh5 carried out a cold model experiment in which water simulated liquid metal and CO2

simulated air. They found that the rate of absorption of CO2 by water increased by an order ofmagnitude when the falling water stream disintegrated before plunging into the pool of water.

FIGURE 8.1 Mechanism of gas absorption by liquid from surrounding atmosphere during pouring.

Extensive oxygen and nitrogen pickup in the fraction of a second during the free fall of dropletsof liquid iron has been experimentally measured.

4


Meaningful experiments for understanding the mechanism are very difficult with liquid steel.Therefore, investigators carried out experiments with water models.5,7 In such experiments, visu-alizations of the stream and the pool were done using still as well as movie photography. In addition,the rates of entrainment of air as well as the rates of gas absorption have been determined.

8.2.2 STREAM BREAKUP

Since gas absorption increases very significantly if the stream breaks up as droplets, prediction ofthe conditions under which the stream is expected to break up before plunging is an importantissue. It has been observed that, if at all, it breaks up only at some distance from the nozzle exit.This distance may be designated as stream breakup length (lb). Actual breakup takes place if H >lb, where H is the height of the nozzle exit from the surface of liquid pool. It has been establishedthat lb depends on nozzle geometry (i.e., length/diameter ratio of the nozzle, etc.), teeming rate,and motion of fluid in the tank.

Actually, the stream displays some perturbation when it comes out of the nozzle. This pertur-bation gets accentuated during its free fall and eventually leads to breakup. Perturbation theoryhas been used to analyze the situation,8 and one of the relations proposed, in combination withexperimental data, is

lb/dn = BWe2/5 Fr–1/7 (8.1)

where dn = nozzle diameterB = a constant

We = Weber number = (8.2)

In the equation, un is the velocity of the liquid stream at the nozzle exit, and ρ and σ are the densityand surface tension of the liquid, respectively.

Fr = Froude number = (8.3)

where g = acceleration due to gravity

Simplification of Eq. (8.1) yields

(8.4)

where C is an empirical constant that depends on nozzle geometry, fluid motion in the tank, etc.A very important conclusion is that a thinner stream at low velocity tends to break up most

easily, i.e., it is characterized by a low value of lb. Experimental observations confirm this. However,the conclusions should not be generalized, as the data have been obtained over a limited range ofconditions. Actually, lb is expected to vary with jet velocity as shown in Figure 8.2.8 The investigatorsclaimed to have worked in region I, whereas in reality they had turbulent flow, which is generallyencountered in industrial tapping and teeming of molten steel.

un2ρdn

σ--------------

un2

dng--------

lb Cd3 2⁄ un1 2⁄≅


8.2.3 MECHANISM OF GAS ENTRAINMENT BY ROUGH AND TURBULENT STREAMS

A number of water-model studies directed their attention to the mechanism of gas entrainment byrough and turbulent streams,7 and a general picture has emerged. With increasing stream velocity,the stream Reynolds number (Res = ) increases. Above a certain value of Res, the streamstarts to exhibit turbulence. The turbulence intensity of the stream is one of the key factors. It hasbeen proposed that there are four distinct mechanisms as follows:1,4

1. At a very low Res, there is a smooth, laminar stream as Szekely assumed.6

2. At a higher Res, the stream surface becomes rough, but the surface of the pool remainsreasonably smooth with a nice vortex at plunge point.

3. At still a higher Res, both the stream and pool surface become rough, and the inductiontrumpet (Figure 8.1), i.e., the cavity around the plunge point, has a violent, boil-like motion.

4. At a still higher Res, the stream breakup takes place.

It has also been established that the wavy nature of the stream surface roughness drags gaspockets along with it. Mechanical interaction at the plunge point on the liquid pool surface leadsto entrainment. The rate of entrainment becomes one or two orders of magnitude higher under thiscondition. It has been found that the rate of entrainment increases with increasing un and H, andit depends on nozzle geometry, etc.

Iwata et al.8 have proposed the following empirical relationship based on their model workwith water, ethanol, glycerin-water, and liquid tin:

(8.5)

where Qg is the volumetric rate of entrainment of gas, Ql is the volumetric flow rate of liquid, Rc

is the radius of vortex cavity, r is the stream radius at the plunge point, and rn is the stream radiusat the nozzle exit.

8.2.4 QUANTITATIVE PREDICTIONS OF OXYGEN AND NITROGEN ABSORPTION DURING TAPPING AND TEEMING

Assuming 100% absorption of gas from entrained bubble, the fractional increase of gas content inliquid (∆[G]) is given as

FIGURE 8.2 Shape of breakup curve for a liquid jet falling freely through the atmosphere (schematic).

dnρun( ) µ⁄

Qg

Ql

------ 0.02 Rc r–( )/rn[ ] 3=

(8.6)

∆ G[ ]ρgQg

ρlQl

------------=


where ρg and ρl are densities of gas and liquid, respectively.Choh et al.2,3 applied the above equations for estimating oxygen absorption during teeming as

well as tapping from a converter. For this purpose, they used the theoretical analysis and experi-mental results.8 They prepared nomographs for predicting oxygen absorption during teeming andtapping. They have also shown that these are in reasonable agreement with the experimental dataof some other investigators.

Regarding nitrogen absorption during tapping and teeming, it was mentioned in Section 6.4.5that the rates are retarded significantly if the melt contains dissolved oxygen and/or sulfur. Therefore,nitrogen pickup during tapping and teeming is expected to be higher in deoxidized and desulfurizedmelts. This has been confirmed by other data.3,4 Sommerville4 found nitrogen pickup during thefree fall of droplets of molten steel through a nitrogen atmosphere to decrease with increasingweight percent of S in the melt. Figure 8.3 shows the increase of nitrogen content in steel ∆([N])during tapping from an 80t converter. Again, the retarding effect of oxygen is evident. The calculatedvalues assuming 100% absorption were 40 ppm, which matched with converter data at very lowoxygen content, but not in heats containing a higher weight percent of oxygen.

Very little information is available about the influence of physicochemical processes occurringinside molten steel on mass transfer controlled absorption during pouring of liquid, except thatfrom Kumar and Ghosh.5 It is also likely that presence of strong oxide and nitride forming elementssuch as Al and Ti would increase the quantity of absorption.

Not much information about absorption of hydrogen from atmosphere during teeming couldbe located in the literature. Hydrogen pickup occurs presumably from atmospheric moisture viathe reaction

H2O(g) = 2H + O (8.7)

Therefore, the extent of hydrogen absorption would increase with an increase in the partial pressureof moisture in the atmosphere as well as a decrease of O in the melt.

FIGURE 8.3 Dependence of nitrogen pickup by molten steel on dissolved oxygen content during tappingfrom an 80t converter. The curves show estimations at different assumed mass transfer coefficients.3

8.3 TEMPERATURE CHANGES OF MOLTEN STEEL DURING SECONDARY STEELMAKING


8.3.1 GENERAL FEATURES

For obtaining the desired cast structure as well as eliminating serious casting defects, the temper-ature of liquid steel should be controlled within a suitable range before it is teemed into the mold.Good continuous casting practice demands even more stringent temperature control as comparedto that for steel ingot casting. Therefore, this topic is of considerable importance in steelmaking.

The temperature of molten steel drops from furnace to mold due to heat losses during tapping,ladle holding or purging, and teeming. In old pitside practice, before the advent of secondarysteelmaking, the overall loss of temperature used to be 20 to 40°C. Secondary steelmaking processesinvolve prolonged treatment of the melt in a ladle, leading to temperature drop even as high as100°C. One way to compensate for this is to tap the metal from the primary steelmaking furnaceat a higher temperature. However, this has adverse side effects such as faster lining wear, lowerphosphorus removal, less scrap charge, and more prolonged furnace operation.

Hence, as already noted in Chapters 5, 6, and 7, secondary steelmaking units such as the ladlefurnace, VAD, and RH have provisions for heating the melt. This eliminates the need for tappingat too high a temperature. Moreover, much better and more flexible temperature control of steel ispossible. More alloy additions also can be made. Arc heating is most common, followed by chemicalheating, plasma arc, or induction heating. Chemical heating requires the addition of aluminum,which reacts with dissolved oxygen and liberates heat, thus raising temperature. Compared to archeating, its advantage is lower capital cost and faster heating of the melt (up to 10oC/min).Disadvantages are higher operating costs and less flexible temperature control, as well as dissolvedaluminum.

Steel plants keep temperature records at various stages. The traditional quantitative approachto process control and predictions is statistical correlation of data through multiple regressionanalysis.

The overall temperature change from furnace to mold (∆Tov) is the sum total of the following:

• Temperature loss from tapping and teeming stream by radiation and convection• Temperature loss during holding or purging in the ladle due to conduction into the ladle

wall and radiation from the top surface of the melt• Temperature loss or gain due to endothermic or exothermic dissolution of deoxidants

added at room temperature (e.g., dissolution of high-grade ferrosilicon is exothermic,whereas that of low-grade ferrosilicon or ferromanganese is endothermic)

• Temperature gain due to exothermic deoxidation (also, atmospheric reoxidation) reac-tions

• Temperature gain due to heating

Very few systematic investigations on such temperature changes could be found in the literaturefor traditional pitside practice. An extensive study was reported by Samways et al.9 who mademeasurements of temperatures in the plant, carried out statistical regression analysis, and madesome thermochemical calculations for both BOH and BOF heats. They listed 11 broad categoriesof variables that affect ∆Tov. For their study, however, they considered seven only, viz., bathtemperature, tapping time, ladle addition, ladle refractory temperature, holding time, teeming time,and teeming temperature.

The temperature gain or loss due to heat effects associated with ladle additions and deoxidationreactions (∆Tr) were computed theoretically by carrying out heat balance exercises with the helpof available thermochemical data. The linear equation based on statistical analysis may be writtenas follows:

∆Tov – ∆Tr = K + kttt + khth + kptp (8.8)


where tt, th and tp are tapping, holding, and teeming times, respectively. K terms are statisticallyfitted coefficients.

The rate of heat loss from a ladle depends on ladle size. Molten steel in a smaller ladle ischaracterized by higher surface-to-volume ratio and hence a faster rate of heat loss. In a large ladle(say 200 tonnes), the temperature loss rates of steel are approximately as follows:

In addition to these, a temperature drop of 5 to 15°C occurs upon tapping, as the ladle refractorylining absorbs quite a bit of heat initially, since it is at a lower temperature. For a smaller ladle of50 tonnes, powder injection would give a loss rate of about 3 to 5°C/min.

Preheating of the ladle lining is a must to prevent excessive cooling of the melt. It also prolongslining life, since thermal shock due to heating and cooling is less. The lower the porosity of thebrick, the higher its resistance to corrosion and erosion by liquid slag and metal. However, itsthermal conductivity will be higher as compared to a porous brick, and hence it will cause a greatertemperature drop of the melt. Moreover, a denser brick has lower thermal shock resistance ascompared to a porous one. Since there will be some discussion on refractories in Chapter 10, onlya brief mention is made here. An open-top traditional ladle is associated with higher heat loss ascompared to a covered ladle. Therefore, in modern secondary steelmaking practice, ladles haverefractory-lined top covers except during the tapping stage.

Today, most steel is cast via a continuous casting route where control of teeming rate requiresthe use of a tundish. Details of tundish metallurgy will be taken up in Chapter 10. It may be simplystated here that a tundish has a shallow pool of flowing liquid steel and hence causes a temperaturedrop of as much as 10 to 15°C. Therefore, much attention is given to its thermal aspects. It includesuse of slag and a cover, as well as heating of the melt by plasma torches or induction current.

Figure 8.4 shows temperature changes in liquid steel from a BOF to a continuous casting moldfor a typical ladle furnace treatment cycle.10 It may be noted that the overall temperature loss was

Temperature Loss Rate, °C/min

Ladle holding 0.5–1

Gas purging 1–2

Powder injection 2–3.5

Circulation degassing 0.7–1.5

FIGURE 8.4 Temperature changes in steel melt from furnace to tundish via ladle furnace.10

more than 75°C in spite of heating in an LF. Casting from the ladle took about 50 min. Duringthis period, the loss of melt temperature was about 7°C. This is another control problem and is a


consequence of continuous heat loss from the teeming ladle. Another consequence of heat loss isthe development of nonuniformities in liquid steel held in the ladle. This is known as temperaturestratification.

In view of the importance of temperature control, several theoretical analyses and mathematicalmodeling exercises have been reported in recent literature. Rather than relying only on statisticalanalyses of data, many plants around the world have resorted to mathematical modeling based onheat balance, the laws of heat transfer, and temperature measurements in the plant. They are usingthese for prediction and control of steel temperature. Some successes have been reported in theliterature. Some of these will be mentioned later. However, further discussions will be brief andconcentrate on topics that provide help in understanding the basics.

8.3.2 TEMPERATURE CHANGE DUE TO THE ADDITION OF DEOXIDIZERS

Assuming the ladle to be an adiabatic system, the heat balance equation may be written as

–∆Hex = (HT – H298) + ∆Hen + NsCs (∆Ts) (8.9)

where –∆Hex = heat evolved due to exothermic reactions/processesHT – H298 = sensible heat required to bring the deoxidizers to the temperature of molten steel

∆Hen = heat absorbed due to endothermic reactions/processes

Ns,Cs, and ∆Ts are the number of moles, specific heat, and rise of temperature, respectively, ofmolten steel (i.e., molten iron, approximately speaking). Some salient data are given below.11

• Cs = 44 J mol–1 K–1

• heat of fusion of molten iron = 15.5 kJ mol–1 at 1873 K• HT – H298 of elements (kJ mol–1)

• Heats of solution of elements in liquid iron at 1873 K (kJ mol–1)

Al(l): – 43.1, Si(l): – 119.3, C(s): 21.35, Mn(l): 0

• Heats of reaction (kJ mol–1) at 1873 K

2Al (wt.%) + 3 O (wt.%) = Al2O3(s); ∆H = –1242.4

Si (wt.%) + 20 (wt.%) = SiO2 (s); ∆H = –594.6

Mn (wt.%) + 0 (wt.%) = MnO(l); ∆H = –244.5

Example 8.1

Calculate ∆Ts if 45 kg of silicon is added to 50t of molten steel in a ladle at 1873 K. Assume thathalf of the silicon added reacts with dissolved oxygen and the rest simply remains dissolved in steel.

Temperature, K Al C Fe Si Mn

1800 54.10 30.65 58.25 31.9 77.8

1873 56.24 32.45 76.94 33.5 81.16

1900 57.03 33.15 78.12 34.1 82.4

Solution


45 kg silicon = , i.e., 1608 mol

150 tonnes of steel = , i.e., 26.88 × 105 mol.

Since half of the silicon reacts,

HT – H298 = 1608 × 33.5 = 5.4 × 104 kJ

∆Hen (due to dissolution of Si) = 1608 × (–119.3) = –13.17 × 104 kJ

(Actually it is exothermic, which is why the sign of ∆Hen is negative.)

Ns = 26.88 × 105, Cs = 44 J mol–1 K–1 = 44 × 10–3 kJ mol–1 K–1

Inserting in these values into Eq. (8.8),

∆Ts = +5.8°C (Ans.)

So, the temperature of molten steel will rise by 5.8°C.

For ferroalloys, calculating the of dissolution heats and sensible heats would require someadditional information. In the literature, there are some handy guides to temperature changes ofliquid iron due to addition of cold ferroalloys, etc.11,12,13 Figure 8.5 presents some estimates.Turkdogan12 has provided the following estimates at 1630°C steel temperature.

Additions Decrease in Steel Temperature in a Tap Ladle, °C

(a) Addition for 1% alloying element in steel at 100% recovery

Coke 65

HC: Fe/50% Cr 41

LC: Fe/70% Cr 24

HC: Fe/Mn 30

Fe/50%Si 0

(b) For 1 kg flux per tonne of steel

SiO2 2.59

CaF2 3.37

CaO 2.16

CaCO3 3.47

CaO.Al2O3 2.39

45 103×28

--------------------

50 106×55.8

--------------------

∆Hex–1608

2------------ 594.6–( )×– 47.7 104 kJ×= =


8.3.3 HEAT LOSS FROM TAPPING/TEEMING STREAM

Prabhakar and Ghosh14 carried out experiments and heat transfer analysis of temperature loss duringteeming of molten lead at 650°C in the laboratory. Important mechanisms of heat loss or gain wereidentified as

1. Temperature loss due to heat transfer from the surface of the teeming stream by convec-tion and radiation (∆T1)

2. Temperature loss due to entrainment of cold air by the molten stream (∆T2)3. Temperature gain due to heat of oxidation of molten metal by oxygen absorbed from

entrained air (∆T3)

Assuming that all entrained oxygen gets dissolved in liquid steel, ∆T2 and ∆T3 are opposite insign, and hence they are likely to somewhat cancel each other.

For item 1,

∆T1 = ∆T1 (due to convection) + ∆T1 (due to radiation) (8.10)

However, the convective heat loss from the stream heats up the air around it, which in anyevent gets entrained back in the liquid metal pool below. Also, it can be shown following theprocedure of Prabhakar and Ghosh14 that radiation heat loss is one to two orders of magnitudelarger as compared to the convective one.

Therefore, we may simplify Eq. (8.9) as

∆T1 = ∆T1 (radiation) (8.11)

Now,

(8.12)

FIGURE 8.5 Temperature loss resulting from cold alloy additions. Ferroalloy compositions refer to Mn orCr. No heat loss from the bath is assumed.11

Qrad Aσε T s4 T o

4–( )=

where Qrad = rate of loss of heat due to radiationA = stream surface area


σ = Stefan–Boltzmann constant = 5.667 × 10–8 Wm–2 K–4

ε = emissivity of the stream surface ≈ 0.8 (assumed) Ts, To = temperatures at the stream surface and in the surrounding atmosphere,

respectively, in K

Again, from heat balance,

(8.13)

where and Cs are the mass rate of pouring and specific heat, respectively, for molten steel.Combining Eqs. (8.12) and (8.13),

(8.14)

Taking stream diameter = 0.05 m, stream length = 1.25 m, ms = 75 kgs–1, Ts = 1850 K, and To =300 K, Cs = 788 Jkg–1 K–1, Eq. (8.13) yields a value of 2°C.

In modern practice, teeming is either done through a submerged refractory nozzle or the streamis shielded by argon. In either case, radiation loss would be insignificant. It is only during tappingthat some temperature loss occurs. As the above calculations show, it is at most a few degrees andtherefore may be ignored.

8.3.4 HEAT LOSS AND THERMAL STRATIFICATION IN A LADLE

The principal heat loss of liquid steel occurs in the ladle through conduction of heat through thewall and bottom of the ladle and as radiation from the top of the melt.

Conduction through the lining is unsteady in nature. With some simplifying assumptions,Szekely and Themelis15 solved the basic differential equation for one-dimensional case, viz.,

(8.15)

where α = thermal diffusivity and y is distance. The solution is

(8.16)

where ∆H is amount of heat transferred from liquid steel by conduction in time te after pouring itinto the ladle, A is the ladle wall area, λ is the thermal conductivity of refractory lining, Ts is thetemperature of steel, and Ti is the initial uniform wall temperature.

Again,

∆H = mscs (Ts,i – Ts,f) (8.17)

where subscripts i and f denote “initial” and “final.” From Eqs. (8.16) and (8.17), one may obtainthe mean rate of loss of temperature due to conduction. Lange16 has suggested a universal correlation

Qrad msCsDT 1=

ms

∆T 1Aσε T s

4 T o4–( )

msCs

---------------------------------=

α δ2T

δy2--------- δT

δt-------= =

∆H 2Aλ T S T I–( )te

πα-------

1 2⁄

=

that grossly predicts the heat flow rate (Qcond) across the refractory for sand and dolomitic liningsapplicable for steel ladles, viz.,


Qcond = AG (Ts – To)/t1/2 (8.18)

where To is the ambient temperature around the ladle and G is an empirical constant. G ~ 1100 forsand and 1700 for dolomite lining, in Js–1/2 m–2 K–1.

Equation (8.16) was derived with several simplifying assumptions, some of which are

1. The heat flow through the lining is one-dimensional.2. The lining consists of one homogeneous layer of refractory material.3. The initial temperature of the lining, before the pouring of liquid steel, is uniform

throughout.

These are gross approximations. The heat flow is, in reality, two-dimensional in view of endlosses at the top and the presence of bottom lining in addition to side lining. The lining consistsof several refractory materials located in different zones. For example, adjacent to the outer steelshell, there is a layer of insulating firebrick. The facing brick is mostly dolomite. The initialtemperature of the lining also is not uniform.

Some later investigators therefore removed the simplifying assumptions and solved the 2-Ddifferential equation numerically. Out of these, extensive work by Austin et al.,17 and Olika andBjorkman18 are referenced here. In their mathematical modeling exercise, they also considered ladlecycling, drying and preheating practices, ladle lid practice, etc. Many unknown parameters areinvolved in formulating the model, such as convective heat transfer coefficients, emissivities, initialrefractory moisture content, etc. Therefore, the model was calibrated with the help of data collectedand then employed for predictions. Figure 8.618 presents the predicted temperature profiles in therefractory wall of a ladle for some ladle preheating schedules. It also shows that measured tem-peratures are higher than calculated ones.

Besides heat loss through the wall and bottom, loss through the top surface of the melt is tobe considered. At steelmaking temperatures, it would occur predominantly by radiation. The heatbalance equation is

(8.19)

FIGURE 8.6 Calculated and measured temperature profiles in ladle lining (0 mm corresponds to the outsideof the ladle).18

mscs–dTdt------- AFσ T s

4 T o4–( )=

where ms is mass of steel in ladle, A is the top surface area, and F is the master view factor. Example8.2 presents a sample calculation illustrating the use of Eq. (8.19). It has been assumed that the


open top surface is slag free and that there is no gas purging. Although emissivity of liquid steelis quite low, there will be always a layer of oxide at the top however thin it may be. For this, ε hasbeen taken as 0.8 in the example. The calculated value of the rate of temperature loss in Example8.2 is 1.16°C/min, which is quite large.

Example 8.2

One hundred fifty tonnes of liquid steel at 1900 K is contained in a refractory-lined ladle thatis open at the top. The ladle may be considered as cylindrical in shape with internal diameter of2.5 m. The height of the empty space in the ladle above the surface of the liquid metal is 2 m.Assuming that the heat loss is principally by radiation at the open top, calculate the rate oftemperature drop of the molten steel. Also assume that there is almost no slag on top.

Solution

Equation (8.19) is to be employed for the solution. For this, the values are as follows:

A = 4.91m2, ms = 150 × 103 kg, Ts = 1900 KTo = temperature at the open mouth of the ladle = 500 K (assumed)Cs = 44 J mol–1 K–1 = 788 J kg–1 K–1

For the calculation of F, formulae and data from standard texts15 are to be employed. The firststep is to estimate FB (i.e., the geometric view factor for black bodies). Noting that radiationexchange between the top surface of the melt and the converter mouth can be considered as twoparallel disks, FB turns out to be 0.55.

Since the converter wall around the open space above the melt is refractory lined, its influenceis to be estimated by the formula

(E2.1)

Here, A2/A1 = the ratio of the two disks = 1, and hence FBR = 0.775.The master view factor (F) is related to FBR as follows:

(E2.2)

where ε1 = emissivity of the steel surfaceε2 = emissivity of the converter mouth

A clean liquid steel surface has an emissivity less than 0.1. However, a thin layer of slag oroxide would raise its emissivity and, hence ε1 is assumed to be 0.8. Since an open surface can bemathematically treated as a black surface, ε2 = 1. Inserting the above values into Eq. (E2.2), F =0.635. This yields

= 0.0193 Ks–1 = 1.16 K/min (Ans.)

FBRA2 A1⁄( ) FB

2–1 A2 A1⁄( ) 2FB–+----------------------------------------------=

F1

1FBR

-------- 1ε1

---- 1– A1

A2

------ 1ε2

---- 1– + +

-------------------------------------------------------------------=

dTdt-------–

It may be noted that there is an uncertainty in the temperature at the mouth of the converter.However, that is not going to affect calculations significantly, since To < Ts, and .T o

4‹‹T s4


In Eq. (8.19), , provided other factors are constant. Usually, there is a slag layer of afew centimeters thickness on top. If it is thin, the slag will be molten. Since it is semi-transparent,heat flow through it would be both by conduction and radiation. For a thick slag layer, the top partwould be frozen, since its temperature would be below its freezing point. In Eq. (8.19), Ts actuallymeans top surface temperature and would be lower in the presence of slag. For argument’s sake,if Ts is taken as 1700 K and 1500 K, then in Example 8.2 becomes 0.74 and 0.45oC/min,respectively.

Szekely and Lee19 carried out a mathematical analysis and found that the heat loss rate wasnegligible for a slag thickness of 5 cm or more. Hence, depending on the specific situation, wemay sometimes ignore the top loss if the melt is not stirred. However, in the presence of gas purging,the slag layer is disrupted, exposing the molten steel. Moreover, the effective top surface areaincreases as a result of wave and droplet formations. This is the reason for enhanced heat loss ina gas-purged ladle (Section 8.3.1). Simple heat balance calculation indicates that the heating ofargon from room temperature to liquid steel temperature requires only a negligible quantity of heatand can be ignored.

Through their predictive models, Austin et al.17 have assessed the role of the ladle cover duringmetal holding, teeming, and on an empty hot ladle of 275t capacity. Their conclusions were asfollows:

1. During holding, when the slag was removed from the top of the melt, the cast mid-pointtemperature of the steel was about 15°C lower with lid on and 40°C lower without the lid.

2. Use of a lid during casting did not make any difference for the first few heats on theladle but, with subsequent recycling, the presence of a lid gave about a 4°C higher steeltemperature.

3. The ladle in between casts is held empty, sometimes for a prolonged period. For 100 minof empty ladle holding, use of lid gave about 10°C higher steel temperature.

In Example 8.2, the cooling rate of melt for a 150t ladle without top slag was 1.16oC/min. Fora 27t ladle, it would be less than 1°C/min. The cast midpoint time was about 40 min. Hence, a40°C lower temperature means about 1°C/min temperature loss, which agrees approximately withEx. 8.2.

With a lid, To would mean the inside face temperature of the ladle cover (Tlid). Taking the datafrom (1) above, and using Eq. (8.19),

and hence Tlid would be approximately 1700 K.Several mathematical modeling studies have been reported on thermal stratification in the ladle

during holding as well as during teeming.20,21 Even a slow purging eliminates stratification. In staticmelt, heat losses induce temperature gradients in the melt. This consequently generates a freeconvective flow. However, the intensity of flow is not enough to eliminate thermal stratification,which has the adverse effect that the steel temperature decreases with the progress of casting, thuscreating a control problem. An insulated top, achieved approximately by a thick slag and/or a ladlecover, decreases this stratification considerably and reduces the temperature variation of the teemingstream from the beginning to end of casting. Figure 8.7, prepared on the basis of the work byChakraborty and Sahai,20 illustrates this.

T o4 T s

4«

dT dt⁄[ ]–

T s4 T lid

4–

T s4

-------------------- 1540------=


8.3.5 CONCLUDING REMARKS ON STEEL TEMPERATURE CONTROL IN INDUSTRY

As already noted in Sections 8.3.1 and 8.3.4, many steel plants have developed elaborate programsto control the temperature of liquid steel for proper casting.16,17,21,22 These are based on mathematicalmodeling and calibration of the model from plant data. They include the influence of variousvariables and various aspects of plant practice such as ladle drying and preheating, ladle cycling,melt holding, teeming, etc. In addition to temperature measurements of liquid steel at various stages,special temperature measurements in various parts of the ladle lining were made. A principal issueis agreement of predicted temperature with measured values. Olika et al.18 claimed a predictabilityof ±3°C at the casting station. Verhoog et al.23 have reported a value of about ±5°C. Zoryk et al.22

obtained it within ±7°C for 92% heats in slab casting but about 65% for bloom and billet casting.Zoryk et al.22 also carried out an assessment of multiple tundish temperature measurements by

immersion thermocouple to determine the expected error associated with steel temperature mea-surements in the tundish. The analysis showed that the typical error associated will be approximately±7°C. As mentioned in Section 8.3.1, a tundish has a shallow and flowing liquid steel bath. Thiscauses a higher rate of steel temperature drop here than in the ladle. Temperature inhomogeneityalso develops. This is responsible for such a large error band in the measurement of liquid steeltemperature in the tundish.

Recently, Deb et al.24 developed a comprehensive flow and thermal model from tapping toteeming into a tundish of molten steel via the ladle furnace route. A flow model was validated fromwater-model experimental data in the literature.

Choudhary and Ghosh25 carried out studies on macrosegregation of continuously cast steelbillets. They determined the columnar-to-equiaxed transition (CET) in samples collected from theplant. Correlation of these with the conjugate heat transfer-fluid flow model of solidification byChoudhary and Mazumdar26 required values of the teeming stream temperature. Since data wereavailable only on immersion thermocouple measurements in a tundish, a correction was called for.From elaborate plant data and correlations of Robertson and Perkins27 on temperature inhomoge-neities in a tundish, the stream temperature was taken to be 10°C lower than the measured tundishmetal temperature. This led to a better match of theoretically predicted and measured CET.25 Asstated in Section 8.3.1, a reduction of temperature loss and stratification in the tundish is verydesirable for lowering the error band in the end temperature.

FIGURE 8.7 Calculated temperature variations of the teeming stream from the ladle for insulated andnoninsulated top, teeming commences 20 min after the end of inert gas stirring.20

8.4 PHOSPHORUS CONTROL IN SECONDARY STEELMAKING


8.4.1 LOW-ALLOY STEELS

For most grades of steel, no attention is paid to phosphorus in secondary steelmaking. The metaltapped from the primary steelmaking furnaces has a phosphorus content of 0.01% (100 ppm) oreven less. During secondary steelmaking, some phosphorus is picked up by the liquid steel fromthe carryover slag, leading to a marginal increase of phosphorus in steel. This is known asphosphorus reversion.

Even with some reversion, the phosphorus content of the final product is satisfactory for mostgrades of steel. However, some superior grades demand ultra-low phosphorus (less than 40 ppm).This can be achieved in any one of the following ways:

1. Dephosphorization of hot metal in the ladle before feeding it into the basic oxygensteelmaking furnace

2. Dephosphorization treatment during secondary steelmaking, if required in occasionalsituations

In the ladle, phosphorus removal can be accomplished either by addition of reagents at the topor by the injection of powders. The latter is more common. Large additions may cause too muchof a temperature drop, which is to be compensated by arc heating.

Section 2.8 reviewed slag basicity and capacities. Reaction of phosphorus between slag andmetal under oxidizing conditions is noted in Eq. (2.79). The phosphorus capacity of slag (Cp) hasbeen defined by Eq. (2.80). Values of Cp are available in the literature. Figure 2.6 presented acompilation of the log Cp vs. log CS relation for several slags.

Equilibrium partitioning of phosphorus between slag and metal is important, and the partitioncoefficient is given as

(8.20)

Finally, Lp can be expressed by a relation of the following form:

log Lp = log Cp + log fp + φ (T) + (8.21)

where fp is the activity coefficient of phosphorus in steel, and B is a constant. Cp is determined bythe slag composition and fp by the metal composition. At fixed compositions and temperature,Eq. (8.21) may be simplified as

(8.22)

where B´ is the lumped value of the constant.An alternate approach is to consider the equilibrium constant (K) for the phosphorus reaction

[Eq. (2.79)]. K depends on the composition of the slag and temperature. Analytical correlations areuseful for calculation. The issue was discussed in Ch. 2, Section 2.5.1, and the regular solutionmodel utilized by Ban-Ya and coworkers for multicomponent slag systems was briefly presented.By utilizing this approach, and on the basis of experimental data of several investigators, Iguchi28

has proposed the following correlation:

Lp

W p( )W p[ ]

------------wt%P

O43 –( )

W p[ ]----------------------------∝=

54--- pO2

log B+

Lplog logC p54---+ log po2

B ′+=

log Kp = 17060/T – 8.510 (8.23)


where Kp is the equilibrium constant for the reaction

P + 2.5 O = (PO2.5) (8.24)

i.e.,

(8.25)

In a recent study on highly basic CaO-FeOt based slags, Zou and Holappa29 considered theequilibrium constant for the reaction

2P + 5(FeO) = (P2O5) + Fe (8.26)

and proposed the following correlation:

(8.27)

at 1600°C. This brings out the significant influence of CaF2 and Na2O on phosphorus equilibrium.From Eqs. (8.21) and (8.22), it may be noted that Lp increases with an increase in , i.e.,

oxygen potential. Hence, for efficient removal of phosphorus from molten iron or steel, oxidizingconditions as prevail during primary steelmaking are a must. A lower temperature helps phosphorusremoval, too.

The oxygen potential in blast furnace hot metal is several orders of magnitude lower ascompared to those in primary steelmaking. So, in the normal course of things, hot metal dephos-phorization is not possible. However, technology has been developed in which the injection of slagalong with oxygen raises the transient value of Lp to a sufficiently large magnitude, enablingdephosphorization of hot metal. The typical slag is CaO-SiO2-FeOt.

There are many published papers on the topic. However, since hot metal treatment is not a partof secondary steelmaking, a detailed presentation is avoided here. A recent review by Wijk30

summarizes the current status. Lower temperature of hot metal and enhancement of fp due topresence of carbon in hot metal have helped the process. Even so, it requires a slag of high Cp anda nonequibrium phenomenon for the system as a whole. If the slag is kept in contact with metalfor a longer time, phosphorus reversion will occur.

Figure 8.8 presents log Cp as a function of log .31 Soda ash presents anenvironmental problem, so its use is not recommended. BaO and BaF2 are costly. This restricts theindustry’s use of CaO as the principal dephosphorizing agent in CaO-CaF2-FeOt flux. CaF2 enhancesaCaO in slag and consequently Cp in comparison to SiO2, and so it is preferred. High silicon in hotmetal does not allow proper dephosphorization. Therefore, the silicon content first needs to bebrought down to <0.1%. The extent of dephosphorization depends on both Lp and msl (quantity ofslag per tonne of metal). With Lp = 100 and msl = 10 kg/t, 50% metal phosphorus theoretically canbe removed. Up to 70% dephosphorization has been commercially achieved.

Dephosphorization is principally carried out in basic oxygen furnaces (BOFs), which have thecapability of achieving a phosphorus content of steel at turndown to a value that is an order ofmagnitude lower than that of the original hot metal phosphorus content.

K p

γPO2.5( )hp[ ] ho[ ]

--------------------, at equilibrium=

K ′ p( )

K ′ plog 0.181 W CaO 0.3W MgO 1.2W CaF22.1W Na2O+ + +( ) 11.73–=

pO2

XNa2O XBaO XCaO+ +( )


As already stated, ladle dephosphorization in secondary steelmaking is not commonly practicedbut is done in occasional cases. The first requirement is to prevent carryover slag as much aspossible, since it already contains a lot of P2O5. The Cp of this slag is raised by the addition ofCaO and CaF2. The oxygen potential of steelmaking slag is controlled by the reaction

2(FeO) = 2[Fe] + O2 (g) (8.28)

(8.29)

Since aFe is approximately 1, . Hence, high Lp can be achieved not only with ahigh slag Cp but a concurrently high value of , i.e., with an appreciable FeO content of slag.However, increasing FeO dilutes the CaO-content of slag and also tends to raise the Fe2O3 contentof slag as follows:

3(FeO) = [Fe] + (Fe2O3) (8.30)

FIGURE 8.8 Phosphate capacities in slags for refining hot metal.31 Reprinted by permission of Iron & SteelSociety, Warrendale, PA, U.S.A.

K 28

aFe( )2 pO2×

aFeO( )2----------------------------

equil

=

pO2aFeO( )2∝

pO2

Fe2O3 is more acidic in nature and tends to form calcium ferrite, thus further decreasing aCaO

and hence producing a lower Cp.


The two opposing effects of FeO thus give rise to an optimum FeO-content of slag for maximumLp for a fixed CaO/SiO2 ratio, as originally found by Baljiva et al.32 (Figure 8.9).

To sum up, a slag primarily consisting of CaO-SiO2-CaF2-FeOt with high CaO-content isrequired. This allows attainment of Lp values in excess of 200. Taking msl = 10 kg/t, 60 to 70%dephosphorization is thermodynamically possible. However, gas stirring is a must for speeding upthe reaction.

A high FeOt slag will raise the dissolved oxygen content of molten steel (Chapter 5, Section5.1). Further deoxidation of steel would require removal of this slag to avoid phosphorus reversion.Without deoxidation, further desulfurization is also not possible. This is a technological problemof ladle dephosphorization, since it increases the handling cost of the melt.

8.4.2 STAINLESS STEELS

Decarburization of stainless steel melts was discussed in Chapter 6, Section 6.5. It was discussedthere that high-carbon ferrochrome is cheaper than the low-carbon variety, and the use of the formercalls for extensive decarburization of the melt by AOD/VOD/VODC. HC ferrochrome also containsa significant quantity of phosphorus. Again, improved corrosion resistance of stainless steels canbe achieved only with an ultra-low phosphorus content (less than 0.015 wt.%). No commerciallyviable process is available for removal of phosphorus from ferrochrome. Therefore, it has to beachieved by dephosphorization treatment of the stainless steel melt. Two commercial routes areavailable, viz.,

1. treatment under oxidizing conditions2. treatment under reducing conditions

FIGURE 8.9 Effect of FeO content in steelmaking slags on phosphorus distribution between slag and metalat 1958 K.32

Dephosphorization under Oxidizing Conditions

30


Wijk has reviewed the fundamentals of the process. Chromium oxide is more stable than P2O5

and iron oxides. Consequently, any attempt to oxidize phosphorus would tend to cause large-scaleoxidation of chromium. Figure 8.1030 sums up the thermodynamic requirements for the treatmentof crude SS melt with 4% C and 18% Cr at 1400°C. It should be at around 10–14 atm, which islower than that required to form Cr2O3. Another problem is that Cr decreases the activity coefficientof phosphorus in the steel melt ( = – 0.018), thus making phosphorus removal more difficult.

The shaded area in Figure 8.10 shows conditions under which most laboratory investigationswere carried out. Figure 8.11, compiled by Wijk,30 summarizes findings on dephosphorizationefficiency by several investigators in the laboratory. Carbon increases the activity coefficient ofphosphorus in the steel melt ( = + 0.13), thus helping dephosphorization. The lower the tem-perature, the more efficient the phosphorus oxidation, although it is applicable to chromium aswell. Of course, lower temperature is generally beneficial to the operation in terms of refractorywear, energy consumption, etc.

For these reasons, industrial dephosphorization treatment is carried out before decarburizationof the melt. Figure 8.11 shows that fluxes containing BaO and CaO-NaF are most effective.However, due to cost considerations, it seems that CaO and CaF2 are the common fluxing reagents.

Phosphorus Removal under Reducing Conditions

There have been many investigations on the subject of phosphorus removal under reducing condi-tions.30 Phosphorus can be removed to the slag as phosphides by addition of Ca, Mg, or rare earthmetals under reducing conditions. The most suitable element investigated so far is Ca, because itis commercially available at a reasonable price in the form of CaC2.

The reaction of Ca with P may be written in various ways, such as:

3 Ca(l) + 2 P = (Ca3P2) (8.31)

FIGURE 8.10 Equilibrium partition ratios between slag and crude stainless steel at different oxygen poten-tials and phosphate capacities at 1673 K. The shaded area indicates conditions in most published studies.30

epCr

epC


For Reaction (8.31), two values of ∆Go are available in the literature.33 These are

∆Go = –430.13 + 0.2778 T, kJ mol–1, and∆Go = –339.25 + 0.1332 T, kJ mol–1

Thermodynamic predictions based on them differ by about a factor of 2.Masumitsu et al.33 carried out thermodynamic measurements on dephosphorization by Ca+Ca-

halide mixtures. Metallic calcium dissolves in CaF2 and CaCl2 liquids. The use of halide allowsattainment of slag fluidity as well as lower vaporization of Ca, vapor pressure of pure Ca at 1600°Cbeing 1.8 atm. CaF2 being less volatile than CaCl2, it is preferred. At 18% Cr, attainment of a

FIGURE 8.11 Results from laboratory studies presented in the literature on crude stainless steel refining(normalized to 100 kg flux/tonne of metal).30

partition ratio of 20 is achievable. This can allow about 50% phosphorus removal, which is adequatein many situations. Nickel has no significant effect on calculated values.


Sano31 has discussed relative stabilities of calcium phosphide versus calcium phosphate in basicslags as a function of temperature and . In a CaO-Al2O3 slag at 1550°C in equilibrium with afixed partial pressure of P2, the changeover from phosphide to phosphate occurred at of 10–18

–10–17 atm, exhibiting a minimum at the transition point. In other words, the lower the , thehigher the phosphide capacity of slag under reducing conditions.

The problem of calcium addition due to its high vapor pressure was discussed in Chapter 7,Section 7.4. Injection well below the melt is the only way to solve it. CaC2 is more convenientthis way, and it can be added from the top as well. It is cheaper, too. A mixture of CaC2 andCaF2 is employed for the formation of a fluid slag.30,33,34 The phenomena and reactions are asfollows:

1. Generation of metallic calcium due to the decomposition of CaC2 (see Appendix 2.1 for∆Go values).

2. Consumption of generated Ca by– oxidation by slag, refractory and atmosphere– vaporization– reaction with phosphorus

Trials demonstrated that about 50% removal of P from an initial value of 0.03% P is achievable.Also, the treatment removes other objectionable impurities such as N, S, As, Sb, and even Sn, andPb. But a significant quantity of calcium gets lost. Decomposition of CaC2 increases carbon in themelt. –∆[P]/∆[C] was found to be as low as 0.025 in some trials, indicating very poor utilizationof Ca in dephosphorization and the requirement of about 25 kg CaC2 per tonne of steel. Moreover,furnace slag should be removed before treatment. Another serious problem is safe disposal of CaC2-containing slag, since it reacts with moisture to generate phosphine, a toxic gas.

8.5 NITROGEN CONTROL IN STEELMAKING

Chapter 6 presented discussions of the influence of nitrogen on steel properties. It has beenmentioned that, generally speaking, nitrogen is harmful and should be low. For most applications,lower than 60 ppm is satisfactory, but there are grades of steel demanding N < 30 ppm. Thermo-dynamic and kinetic aspects of absorption and desorption of nitrogen in molten steel, as well asits behavior in industrial degassing processes, were dealt with in Section 6.4.5. It was mentionedthat, at best, about 35% of the initial nitrogen in a steel melt can be removed by vacuum degassing.This, along with the fact that molten steel absorbs and desorbs nitrogen in other stages of thesteelmaking route, makes nitrogen removal and control a difficult task.

The purpose of this section is not to repeat materials presented in Chapter 6 and Section 8.2but very briefly to make an integrated assessment of nitrogen control for the entire steelmakingprocess.

Liquid steel has a large solubility for nitrogen. On the basis of Table 6.1, solubilities at =1 atm are 450, 458, and 465 ppm, respectively, at 1550°C, 1600°C, and 1650°C. The nitrogencontent of steel is far lower than these values. Hence, the kinetics of absorption and desorptiongovern the ultimate nitrogen level. The strategy for achievement of a low level is to minimizeabsorption and maximize desorption.

As elaborately discussed earlier, oxygen and sulfur dissolved in liquid steel retard rates of bothabsorption and desorption equally. So, absorption prevention is more effective at high O and S levels.On the other hand, desorption should be enhanced, and low levels of O and S in steel are desirablefor this. In a situation where both absorption and desorption are occurring simultaneously, the relative

pO2

pO2

pO2

pN2

rates would depend on the relative magnitudes of surface areas for absorption and desorption.Flushing by bubbles of other gases is the common strategy for enhancing the desorption rate.


8.5.1 NITROGEN CONTROL IN A BASIC OXYGEN FURNACE

Here, simultaneous absorption and desorption of nitrogen occur. But in modern converter practice,desorption is greater than absorption, thus leading to a lowering of N at turndown. Both the materialscharged into the converter, and blowing conditions influence turndown nitrogen content. Mariqueet al.35 and Normanton36 have presented detailed investigation reports, and they have reviewed someother studies.

The nitrogen content of hot metal can be decreased by treating it with reagents based oncarbonates and oxidants such as CaCO3 and iron ore. CaCO3 decomposes, and the resulting CO2

further reacts with carbon of hot metal to form CO. Iron ore reacts with carbon to generate CO.Removal of nitrogen from hot metal is due to the flushing action of CO bubbles. The extent ofremoval can be up to 50%. However, it does not help much. A decrease of 10 ppm nitrogen in hotmetal was found to decrease converter turndown nitrogen by barely 1 ppm.

More scrap usage increases turndown nitrogen. More scrap means less hot metal and thus lessC–O reaction, and consequently less removal of nitrogen by CO bubbles. Lowering of scrap from250 to 100 kg/t steel was found to decrease turndown nitrogen by about 10 ppm for LD–HCconverter.35 A third important input parameter is nitrogen content in oxygen, employed for blowing.Ten to 15 years ago, oxygen was less pure than it is now. At the SIDMAR plant, lowering thenitrogen content of oxygen gas from 250 ppm to 20 ppm led to a drop of turndown nitrogen by 5to 8 ppm.

As far as blowing practice is concerned, the following are important:

• composition of bottom stirring gas• switchover to only argon for bottom purging during the blow• reblowing• hard vs. soft blow

Bottom purging gas in combined top and bottom blowing converters may be N2, Ar, O2, orCO2. The use of N2 in place of other gases was found to increase the turndown nitrogen of steelby as much as 15to 20 ppm.35 N2 is the most common stirring gas due to its low cost and easyavailability. For lowering nitrogen in steel, it is a must that N2 be replaced by Ar sometime beforethe end of the blow. The sooner the switchover, the lower the nitrogen in steel will be. For example,a switchover at 50% blow yielded 8 to 10 ppm less N as compared to that at 95% blow.36

During reblow, bath carbon content is low, and there is no vigorous C–O reaction to flush outthe nitrogen. Hence, reblowing is harmful and can cause an increase of nitrogen content by asmuch as 30 ppm. Reblowing time is important and nitrogen pickup is proportional to time. A hardblow causes more vigorous C–O reaction and leads to a lowering of N.

With improper operation of the BOF, turndown nitrogen in steel may be as high as 60 to70 ppm. However, in modern converter practice, it generally ranges from 20 to 40 ppm. With specialefforts, it may be as low as 10 ppm.35 However, that involves a compromise on other technologicalparameters such as the use of less scrap, more iron ore, and more argon, which can increaseproduction costs.

8.5.2 NITROGEN CONTROL IN AN ELECTRIC ARC FURNACE

In an EAF, turndown nitrogen in steel is a consequence of absorption from the atmosphere andfrom input materials, and desorption due to flushing by CO bubbles. The nitrogen content of EAFsteel produced entirely from scrap is much higher than that for a BOF and ranges between 60 and100 ppm. This is due to

• less CO evolution• nitrogen containing scrap melting late in the process


• dissociation of nitrogen molecules by the arc, and consequent faster pickup by moltensteel

The nitrogen content of steel can be lowered significantly by the following measures:

1. One can open the bath at (e.g.) 0.5% higher carbon, which would require promotion ofa C–O reaction.

2. It can be accomplished by the charging of DRI, which again has higher carbon and lowernitrogen as compared to those in scrap. Continuous charging of DRI is better, since itprovides a flushing action throughout the refining period.

3. We can also use foaming slag, which shields the arc from the surrounding air.

It has been claimed that, with some or all of these measures, turndown nitrogen in EAF steel canbe lowered to 30 to 40 ppm.37

8.5.3 NITROGEN ABSORPTION DURING TAPPING AND TEEMING FROM SURROUNDING AIR

The mechanism of absorption during tapping and teeming was discussed in Section 8.2. The extentof nitrogen pickup varies over a large range, depending on the nature of the stream as well asdissolved oxygen and sulfur in the melt. It may be as large as 40 ppm during tapping, and higherduring teeming.

In continuous casting, teeming has two stages: ladle → tundish, and tundish → mold. For aslab and bloom caster, submerged refractory nozzles are commonly employed. These nozzles neednot be fixed to the ladle or tundish, since adequate protection of the stream from surrounding aircan be achieved by argon shrouding at gaps. For a billet caster, the use of submerged nozzles ismore difficult for tundish → mold due to the small cross section of the mold. But some plants havebeen able to implement it.35

With stream protection as outlined above, nitrogen pickup by the teeming streams has beenreduced drastically and is no more than a few parts per million. However, considerable pickup(about 20 ppm) may still occur at the tundish, since the flowing metal comes in contact with theatmosphere. With protection like the use of flux to prevent contact with air, it has been reportedthat nitrogen absorption of less than 10 ppm in the tundish was achieved.35

The use of a submerged nozzle is not possible in top pouring of the ingot. Of course, since atundish is not involved, the extent of nitrogen pickup will be much less than that in continuouscasting. The stream must be smooth and compact. Absorption, again, is expected to be negligiblefor rimming ingots for the following reasons:

1. high oxygen content of steel and consequent retardation in absorption rate2. flushing action due to the evolution of CO

For killed steel, the extent of nitrogen absorption would be more. However, the author doesnot have any information on the subject.

As far as tapping is concerned, stream protection as practiced during teeming is not possible.Two strategies can be adopted and are being employed in steel plants to a varied extent. Lessaluminum addition during tapping keeps the oxygen content of the molten metal somewhat higher.The consequent decrease of nitrogen pickup is at the most about 10 ppm.3,35,37 However, deoxidationpractice is related to other downstream processing such as desulfurization. So, it may be difficultto avoid aluminum addition completely during tapping.

Gruner and Loscher38 carried out extensive plant trials on an alternative strategy. It consistedof the addition of CaCO3 into the ladle during tapping. Decomposition of CaCO3 and consequent


evolution of CO2 expelled air from the surroundings of the tapping stream, thus preventing nitrogenpickup. For a 220t heat and a tapping time of about 5 min, the CaCO3 addition rate of 15 kg · min–1

reduced nitrogen absorption from 20 ppm to 14 ppm. More addition did not produce much morebenefit. With reference to Figure 8.1, shielding of the plunge point is the most effective method.The authors also carried out elaborate mathematical modeling. However, it is being omitted for thesake of conciseness.

8.5.4 NITROGEN ABSORPTION DURING LADLE PROCESSING

While the melt is held in the ladle, the thick, partially frozen slag at the top prevents contact withair. Nitrogen absorption is negligible. Argon purging in a ladle furnace is theoretically able toprevent contact with air and should also be able to remove some nitrogen. However, this requiresa good seal of the top cover and a high argon flow rate. Otherwise, there is a net increase ofnitrogen in steel of 5 to 10 ppm. The addition of CaCO3 throughout ladle processing has beenfound to be quite beneficial. Figure 8.12 presents the influence of CaCO3 addition at all stages ofsecondary steelmaking beginning with tapping.38 A substantial decrease in final nitrogen contentis evident.

Starting in the last decade, the possibility of nitrogen removal by synthetic slag treatment duringladle processing of molten steel has been under consideration, and some investigations have beencarried out. It has been known for a long time that slags have some solubility for nitrogen.

In a basic slag, nitrogen dissolves as N3– according to the following reaction:39,40

(8.32)

The nitride capacity of slag may be expressed as

(8.33)

For slag–metal reaction, Eq. (8.32) is modified as

(8.34)

The equilibrium partition coefficient for nitrogen between slag and metal (LN) is related to CN as

(8.35)

where fN is the activity coefficient of N in steel, and KO and KN are equilibrium constants for thefollowing reactions:

O2 (g) = O (wt.%) (8.36)

12---N2 g( ) 3

2--- O2 –( )+ N3 –( ) 3

4---O2 g( )+=

CN W N( )pO2

3 4⁄

pN2

1 2⁄---------⋅=

N wt.%( ) 32--- O2 –( )+ N3 –( ) 3

2---O wt.%( )+=

LNW N( )W N[ ]

-------------f N KO

3 2⁄⋅hO

3 2⁄ K N⋅--------------------- CN⋅= =

12---

N2 (g) = N (wt.%) (8.37)12---


Calcium aluminate type slag is preferred in secondary steelmaking, as discussed in Chapters5 and 7. Several investigators measured CN for these slags.41 At 1600°C and in the basic range, i.e.,

> 1

CN ranges between 10–13 and 3 × 10–13. Aluminum dissolved in liquid steel and the Al2O3 contentof slag determine hO and thus influence LN. Figure 8.13 shows LN as a function of these variables.41

It may be noted that calcium aluminate type slag has a low value of LN and is not expected tobe effective in nitrogen removal. However, laboratory measurements have found that CN can beincreased by two orders of magnitude if the slag contains appreciable quantities of BaO and TiO2

and therefore has a potential to remove some nitrogen from liquid steel during argon purging.37

This application would be governed by other technological and cost considerations.Figure 8.12 shows some calculations for iron-chromium alloy melts.33 Figure 8.13 shows the

variation of equilibrium partition coefficient for nitrogen.

8.6 APPLICATION OF MAGNETOHYDRODYNAMICS

The field of magnetohydrodynamics (MHD) deals with the motion of an electrically conductingliquid under the simultaneous action of a magnetic field and electric current through the liquid.The driving force is the Lorentz force, given by

(8.38)

W CaO W MgO+W Al2O3

---------------------------------

FIGURE 8.12 Variation of nitrogen content of steel melt after tapping. Solid lines are calculated curves forCaCO3 addition. (Curves 1 and 2 are based on different assumptions).38 Reprinted by permission of Iron &Steel Society, Warrendale, PA, U.S.A.

F i B×=


where is the applied magnetic field and is the current. The direction of is normal to both and . In the metallurgical field, the existence of such fluid motion (induction stirring) duringinduction melting of iron and steel has been known for more than 60 years. On a large scale, it wasemployed in an ASEA-SKF ladle furnace. Electromagnetic stirring (EMS) in continuous casting isa major application today.

Considerable advances in MHD took place in connection with fusion research and astrophysics.An awareness of importance of fluid flow in liquid metal processing led to fundamental theoreticalanalysis and experimental studies of MHD in liquid metals. For typical metallurgical systems,theoretical analyses by Szekely and coworkers are worth mentioning. That there is considerablecurrent interest in this field in steelmaking circles is evident from many recent papers on thesubject.42

Garnier43 has reviewed the topic. If the magnetic field is dc, then a dc current is to be passedthrough the liquid separately to generate motion. On the other hand, an ac magnetic field interactswith its own induced current. The first effect produced is induction heating. Moreover, two mechan-ical effects are induced that result in electromagnetic pressure and electromagnetic stirring. Theforce can be divided into an irrotational part and a rotational part. The first one results in magneticpressure, and the second one is the driving force for stirring motion in the liquid.

The major disadvantage in the use of an ac field for EMS purposes is the power losses due toJoule heating in the liquid. This can be reduced considerably by going for a very low-frequencysupply (2 to 10 Hz) for large steel melts. Rotational forces concentrate in regions where the magneticfield intensity undergoes spatial variations in the direction of the applied magnetic field. The relativeintensity of rotational forces compared to irrotational forces increases as the electromagnetic skindepth increases. Again, skin depth increases as frequency decreases. Therefore, a low-frequencysupply promotes fluid motion as well.

A travelling or rotating magnetic field induces mechanical effects in the liquid metal with betterefficiency than an alternating magnetic field. Induced currents result from the relative velocity ofthe liquid and the magnetic field. For example, Sakuraya et al.44 developed an intensively stirred5t ladle furnace with a rotating electromagnetic stirrer. With this device, they claimed to have

FIGURE 8.13 Variation of equilibrium partition coefficient for nitrogen with dissolved Al in steel and Al2O3

content of calcium aluminate slag at 1600°C.41 Reprinted by permission of Iron & Steel Society, Warrendale,PA, U.S.A.

B i F iB

obtained a maximum mixing energy of 14 kW per tonne of steel, which is 10 to 100 times as largeas that obtained by argon stirring and in the ASEA-SKF ladle. They also carried out experiments


on desulfurization and deoxidation and could obtain a significantly higher rates. Mixing time wasalso much lower than those in an RH and ladle degasser.

As stated in Section 5.3, some new LF installations are fitted with only induction stirring forbetter and flexible flow control. This gives a relatively uniform velocity field (0.5 to 1 m/s). EMstirrers are suspended from retractable, hydraulically operated trolleys that position the stirreragainst the ladle when processing. EM stirring is also employed to assist slag raking in deslaggingstations as well as for distribution of synthetic slag uniformly. Disturbance to arc heating is less.

In continuous steel casting, control of the teeming rate of steel from the tundish to the moldis carried out by changing the cross-sectional area of the flow channel by means of a stopper orslide gate. However, nozzle clogging or air suction occasionally occurs, thus affecting the teemingrate. The development and successful application of an electromagnetic flow control device, usedalong with the conventional stopper or slide gate, has been reported. The device consists of aninduction coil installed around the nozzle. Two approaches are under examination. In the firstapproach, the coil is designed to make irrotational force significant, thus inducing an upwardmagnetic pressure. It opposes the gravity force on the liquid and thus retards the flow. Control iseffected by variation of current through coil. The second approach is to have a rotating EM stirreraround the nozzle, which induces a rotary motion in the liquid inside the nozzle, thus retardingflow.45

The advantages of EM devices are noted below.

1. As stated above, it is capable of delivering much higher mixing energy as compared togas stirring, with a consequent speeding up of rates of homogenization.

2. The flow pattern and intensity can be varied flexibly to achieve specific objectives.3. No free board space is required in the processing vessel, which is in contrast to gas

stirring.4. It selectively induces force in the metal and not in the slag. This feature is being utilized

to prevent the flow of carryover slag during tapping and to push out slag during theaddition of alloying elements into the ladle. It also has been employed to detect the entryof slag into the tapping and teeming nozzle, thus helping in slag-free tapping or teeming.

Therefore, it seems that MHD is going to play an important role in the production of fine qualitysteel.

REFERENCES

1. Heaslip, L.J., McLean, A. and Somerville, I.D., Continuous Casting, Vol. I, Chemical and PhysicalInteractions During Transfer Operations, Iron & Steel Soc., U.S.A., 1983.

2. Choh, T., Iwata, K., and Inouye, M., Trans. ISIJ, 23, 1983, p. 598. 3. Choh, T., Iwata, K., and Inouye, M., Trans. ISIJ, 23, 1983, p. 680.4. McLean, A. and Somerville, I.D., in Proc. Int. Symp. on Modern Developments in Steelmaking,

Chatterjee, A. and Singh, B.N., ed., Jamshedpur, 1981, p. 739.5. Kumar, J. and Ghosh, A., Trans. Ind. Inst. Metals, 30, 1977, 39. 6. Szekely, J., Trans. AIME, 245, 1969, p. 341.7. McCarthy, M.J., Henderson, J., and Molloy, N.A., Met. Trans., 1, 1970, p.2657.8. Iwata, K., Choh, T. and Inouye, M., Trans. ISIJ, 23, 1983, 218. 9. Samways, N.L., Dancy, T.E., Li, K., and Halapatz, J., in Physical Chemistry of Process Metallurgy,

G.R. St. Pierre ed., Part 2, Interscience Publishers, New York, 1961, p. 1029.10. Mellinghoff, H., in Int.Symp.on Quality Steelmaking, Ind. Inst. of Metals, Ranchi, 1991, p. 144.11. Elliott, J.F., Gleiser, M., and Ramakrishna, V., Thermochemistry for Steelmaking, Addison Wesley,

MA, U.S.A., Vol. I, 1960, Vol. II, 1963.

12. Turkdogan, E.T., Fundamentals of Steelmaking, The Inst. of Materials, London, 1996, p. 255.13. Chipman, J. and Elliott, J.F., in Electric Furnace Steelmaking, Interscience Publishers, New York,


1963, Ch. 6. 14. Prabhakar, S.R. and Ghosh, A., Trans. Ind. Inst. Metals, 34, 1981, p. 441.15. Szekely, J. and Themelis, N.J., Rate Phenomena in Process Metallurgy, Wiley Interscience, New York,

1971, p. 169.16. Lange, K.W., Int. Mat. Review, 33, 1988, p. 53.17. Austin, P.R., Rourke, S.L.O., He, Q.L., and Rex, A.J., Steelmaking Proceedings, Vol. 75, Iron & Steel

Soc., U.S.A., 1992, p. 317.18. Olika, B. and Bjorkman, B., Scand. J. Met., 22, 1993, p. 213.19. Szekely, J. and Lee, R.G., Trans. AIME, 242, 1968, p. 961.20. Chakraborty, S. and Sahai, Y., Met. Trans. B., 23B, 1992, p. 135.21. Ilegbusi, O.J. and Szekely, J., ISIJ Int., 27, 1987, 563. 22. Zoryk, A. and Reid, P.M., Trans. ISS, June 1993, p. 21.23. Verhoog, H.M., Rosier, S., Hartog, H.W. den., Snoeyer, A.B., and Kreyger, P.J., Hoogovens Tech.

Report, July 1995, p. 114.24. Deb, P., Mukhopadhyay, A., Ghosh, A., Basu, B., Paul, S., Mishra, G., and Mukhopadhyay, P.K., Tata

Search, Tata Steel, Jamshedpur, India, 1999, p. 47.25. Choudhary, S.K. and Ghosh, A., ISIJ Int., 34, 1994, p. 338.26. Choudhary, S.K. and Mazumdar, D., ISIJ Int., 34, 1994, p. 584.27. Robertson, T. and Perkins, A., Ironmaking and Steelmaking, 13, 1986, p. 301.28. Iguchi, Y., in The Elliott Symposium, Iron and Steel Soc., U.S.A., Cambridge, 1990, p. 132.29. Zou, Z. and Holappa, L., Proc. 6th Int. Iron and Steel Cong., Nagoya 1990, Vol. 1, p. 296.30. Wijk, O., Scand J. Met., 22, 1993, p. 130.31. Sano, N., in Ref. 26, p. 163.32. Baljiva, K., Quarrell, A.G., and Vajragupta, P., J. Iron and Steel Inst., 153, 1946, p. 115.33. Nakamura, Y., Bull. Jap. Inst. Metals, 15, 1976, p. 387.34. Katayama, H., Kajioka, H., Inatomi, M., and Harashima, K., Tetsu-to-Hagane, 65, 1979, p. 1167.35. Marique, C., Beyne, E., and Palmaers, A., Ironmaking and Steelmaking, 15, 1988, p. 38.36. Normanton, A.S., Ironmaking and Steelmaking, 15, 1988, p. 33.37. Sasagawa, M., Ozturk, B. and Fruehan, R.J., Trans. ISS, Dec. 1990, p. 51.38. Gruner, H. and Loscher, W., Proc. 5th Int. Iron and Steel Cong., Vol. 6, Iron and Steel Soc., Washington

D.C., 1986, p. 307.39. Min, D.J. and Fruehan, R.J., Met. Trans. B., 21B, 1990, p. 1025.40. Martinez R, E. and Sano, N., Met. Trans. B., 21B, 1990, p. 97.41. Ozturk, B. and Fruehan, R.J., in Proc. Philbrook Memorial Symp., Iron and Steel Soc., U.S.A., 1988,

p. 119.42. Moffat, H.K. and Proctor, M.R.E., ed. Metallurgical Applications of Magnetohydrodynamics, Metals

Soc., London, 1982.43. Garnier, M., in Proc. 6th Int. Iron and Steel Cong., Nagoya, 1990, Vol. 4, p. 226.44. Sakuraya, T., Sumita, N., Fujii, T., and Fukui, Y., in Ref. 41, Vol. 3, p. 576.45. Ayata, K. and Fujimoto, T., in Ref. 41, p. 347.

9 Inclusions and Inclusion Modification

9.1 INTRODUCTION

Inclusions are nonmetallic particles embedded in the matrix of metals and alloys. In this chapter,we are specifically concerned with inclusions in steel. In view of the influence of inclusions on theproperties of steel, extensive investigations have been and are being carried out. A vast body ofliterature is available, as will be evident from the classic book by Kiessling and Lange,1 which hasa comprehensive presentation of the structure, properties, and origin of a wide variety of inclusionsfound in steel. In this chapter, an attempt is made to outline the salient features of the theory aswell as important findings and conclusions for a general comprehension of the subject.

As a generalization, inclusions have been found to be harmful to the mechanical properties andcorrosion resistance of steel. This is more so for high-strength steels for critical applications. As aresult, there is a move to produce clean steel. However, no steel can be totally free from inclusions.The number of inclusions has been variously estimated to range between 1010 and 1015 per tonneof steel. Again, the yardstick for cleanliness depends on how one assesses it. For example, mostof the inclusions are submicroscopic. Therefore, a microscopic examination cannot faithfully assesscleanliness.

The above considerations lead to the conclusion that cleanliness is a vague and relative term.Which steel is clean and which steel is dirty can be determined only when we know the intendedapplications and consequent property requirements, after which we can understand the correspond-ing limiting size, frequency of occurrence, and properties of inclusions. Therefore, it is necessaryto have a broad understanding of how inclusions affect the properties of steel. Herein, we restrictourselves to mechanical properties only.

9.2 INFLUENCE OF INCLUSIONS ON THE MECHANICAL PROPERTIES OF STEEL

Discussions on this subject are available from many sources. Only a few are referenced here.1–6

The properties that are adversely affected are fracture toughness, impact properties, fatigue strength,and hot workability. The factors responsible for these may be classified as follows:

1. Geometrical factors: size, shape (may be designated as the ratio of major axis to minoraxis), size distribution, and total volume fraction of inclusions

2. Property factors: deformability and modulus of elasticity at various temperatures, coef-ficient of thermal expansion

From a fundamental point of view, an inclusion/matrix interface has a mismatch. This causeslocal stress concentration around it. Application of external forces during working or service can


augment it. If the local stress becomes high, then microcracks develop. The propagation of micro-cracks leads to fracture. Investigations have established that only large inclusions are capable of


doing this kind of damage, and this led Kiessling1 to develop the idea of critical size. In practice,it is customary to divide inclusions by size into macroinclusions and microinclusions. Macroinclu-sions ought to be eliminated because of their harmful effects. However, the presence of microin-clusions can be tolerated, since they do not necessarily have a harmful effect on the properties ofsteel and can even be beneficial. They can, for example, restrict grain growth, increase yield strengthand hardness, and act as nuclei for the precipitation of carbides, nitrides, etc.

The critical inclusion size is not fixed but depends on many factors, including service requirements.Broadly speaking, it is in the range of 5 to 500 µm (5 × 10–3 to 0.5 mm). It decreases with an increasein yield stress. In high-strength steels, its size will be very small. Kiessling advocated the use offracture mechanics concepts for theoretical estimation of the critical size for a specific situation.

The objective, therefore, should be to produce steel that does not contain any macroinclusion(i.e., above the critical size). Technologically, this is difficult to achieve without escalating the costto a high level. Therefore, we have to put up with some macroinclusions, and in this context wehave to determine how to reduce their harmful effects by controlling their size, shape, and properties.This is known as inclusion modification, and to carry it out, we first have to know how variousfactors connected with inclusions affect the properties of steel.

To sum up the effects, the following statements may be made:

1. Impact properties are adversely affected with an increase in volume fraction as well asinclusion length; spherical inclusions are better. Brittle inclusions or inclusions that havelow bond strength with the matrix break up early during straining, with the initiation ofvoids at the inclusion/matrix interface.

2. The fatigue strength of high-strength steel is reduced by surface and subsurface inclu-sions, especially those that have lower coefficients of thermal expansion than steel. Theseset up stresses in the matrix and are primarily responsible for fatigue failure.

3. The hot workability of steel is affected by the low deformability of inclusions (i.e., morebrittleness at hot working temperatures).

4. Anisotropy of a property is caused by orientation of elongated inclusions along thedirection of working or the elongation of inclusions during working.

5. Macroinclusions of sulfides are desirable for better steel machining properties.

Therefore, if we have to put up with macroinclusions, their sizes and numbers should be as lowas possible. In addition, they preferably should be spherical, with good deformability under stress.

The great majority of oxide inclusions belong to the pseudo-ternary system: AO-SiO2-B2O3,where A is Ca, Fe(II), Mg, and Mn, and B is Al, Cr, and Fe(III). The sulfide inclusions are usuallyMnS or solid solutions of the (Mn, Me) (S, X) type. Other elements such as Ti, Zr, rare earths,Nb, V, etc. usually appear as solid solutions in existing inclusion phases. There are great similaritiesin the morphology and physical and chemical properties of isostructural phases, and therefore thisclassification has been advantageous to the metallographer who has to determine the inclusion types.

From the point of view of deformability, the following classifications are useful:

1. Al2O3 and Ca-aluminates that are undeformable at all temperatures of interest in steel-making

2. Double oxides of the spinel type (AO-B2O3), which are undeformable at current steel-forming temperatures but would be deformable at higher temperatures (above 1200°C)

3. Silicates that are not deformable at room temperature but are deformable in a highertemperature range, the extent of which depends on their chemical composition

4. FeO, MnO, and (Fe, Mn)O, which are plastic at room temperature but start losingplasticity above 400°C

5. MnS, which is highly deformable up to 1000

o

C but not so much above 1000°C6. Pure silica, which is not deformable up to 1300°C


9.3 INCLUSION IDENTIFICATION AND CLEANLINESS ASSESSMENT

Inclusion identification refers to the determination of chemical composition and identification ofits phase. The routine plant procedure employed the microscopic method. From the shape of theinclusion and a knowledge of the steelmaking process in the plant, it is inferred as to whether itis a silica/silicate/aluminate or sulfide inclusion. Standard charts are available as aids. The chartsoriginally were prepared from decades of investigation by metallurgists using the laborious methodof extracting inclusions and analyzing them chemically.

The advent of the electron probe microanalyzer (EPMA) in late 1950s, which can determinethe chemical composition of individual inclusions in-situ and with reasonable speed, allowedrapid progress in inclusion identification. Kiessling and his coworkers in the Swedish Institute ofMetals Research, as well as others elsewhere, carried out extensive investigations on inclusionidentification using this instrument as well as with optical microscopy. Since the inclusions aresmall in size, phase identification in-situ by x-ray diffraction is not possible. This was done onsynthetic slags using standard x-ray powder pattern indices for synthetic minerals. All of thesehave been compiled by Kiessling and Lange1 and provide us with valuable information on variousinclusion types; their compositions, phases, and properties; and their appearance under an opticalmicroscope. The invention of the scanning electron microscope (SEM) has added a new dimensionto inclusion identification, since much higher magnification is possible than with optical micros-copy.The energy dispersive x-ray analysis (EDX) attachment for an SEM allows quantitativechemical analysis of inclusions in-situ as well as qualitative mapping of distribution of variouselements in and around the inclusions. These have proved to be very valuable tools for inclusionidentification.

Cleanliness assessment refers to determination of size, size distribution, number, and volumefraction of inclusions in steel. Again, the traditional microscopic method is available. But it islaborious and unreliable. The field of view in a microscope is of the order of 1 mm2. This is toosmall a sample to be representative, because inclusion distribution in steel is nonuniform. Therefore,the microscopic method requires examination at several locations. Even then, it is insufficient.

A significant development since the 1960s has been in the field of instrumentation and auto-mation of quantitative microscopy, and its application to cleanliness assessment. The best knowninstrument is Quantimet, pioneered by Metals Research Ltd., U.K. It has an optical microscopefitted with video screen and associated microprocessor-based instrumentation. It can scan thespecimen very quickly and provide a variety of information such as inclusion size distribution,number, volume fraction, etc. Therefore, a much larger area can be scanned in a shorter time, andthe assessment is more reliable.

The total oxide inclusion content of steel can be determined from the analysis of oxygen bysampling and the use of vacuum/inert gas fusion apparatus. Again, to what extent a small samplewould be representative of the whole is an open question. Moreover, samples are usually takenfrom molten steel. This may not properly reflect the oxygen content in the finished product.However, special techniques have been developed recently to obtain reliable analysis.

Radioactive tracers, although they are not employed in routine assessment, have helped enor-mously in inclusions research to understand the origin of inclusions, inclusion distributions, etc.Therefore, it is imperative that any statement about cleanliness also indicate how the informationwas derived. Recently, attempts have been made for tracing of Al2O3-bearing inclusions by lantha-num. In this technique, small quantity of La is added after Al addition for deoxidation. La formsLa2O3 and becomes incorporated in Al2O3.

9.4 ORIGIN OF NONMETALLIC INCLUSIONS

8


Sims and Forgeng briefly reviewed the subject in the early 1960s. He classified the sources ofinclusions into the following:

1. Precipitation due to reaction from molten steel or during freezing2. Mechanical and chemical erosion of refractories and other materials that come in contact

with molten steel 3. Oxygen pickup by teeming stream and consequent oxide formation

Inclusions arising out of item 1 are known as endogenous, and those arising out of items 2 and3 are exogenous. Usually, these groups can be differentiated reasonably well on the basis of size,composition, and distribution. The endogenous inclusions are small, numerous, and rather uniformlydistributed, and they are typical of the steel in which they occur. Exogenous inclusions are large,scarce, and haphazard in occurrence. Nonmetallic inclusions can be oxides, sulfides, nitrides,carbides, etc., with oxides and sulfides being the more predominant ones. Inclusions that are solidduring formation exhibit variety of shapes. Inclusions that form as liquids are globular if they ariseat an early stage. Those (e.g., FeS) that form at a very low temperature in the thin residualinterdendritic liquid spread in between the grains.

Kiessling1 emphasizes the point that the division into exogenous and endogenous types accordingto the above classification is too simplistic. It is well established that precipitation of oxides/sulfidestakes place on exogenous inclusions. Moreover, the exogenous inclusions may undergo reactionsand change in composition. Silicates, for example, would react with dissolved aluminum. As a matterof fact, EPMA and SEM/EDX analyses have revealed that most real inclusions are non-uniform incomposition. Very often, the core would consist of one compound and the outside layer of someother compound.6 Examples are sequential formation of alumina, galaxite, and manganese alumino-silicate by reoxidation of aluminum-killed steel,9 or a coating of CaS on calcium aluminate in Ca-treated Al-killed steel.10 Silicate inclusions may vary in composition widely from center to periphery.2

Kiessling and Lange1 have presented comprehensive information on varieties of exogenousinclusions that form during steelmaking. Table 9.1 summarizes possible inclusion sources. It providesan idea as to inclusions’ sources and key elements. Pickering11 conducted extensive investigationson inclusions that are present at different stages, from furnace to mold, during manufacture of steelby electric and open hearth furnace. The influence of basic processing variations at various stageswere also ascertained. Based on their studies, they found the approximate pattern noted in Table 9.2.

Table 9.2 shows that, for Pickering’s investigation, erosion of silicate refractories followed byprimary deoxidation products gave rise to most of the troublesome inclusions. McLean andSomerville9 also cited the erosion of refractory linings of nozzles, stoppers, runners, etc. as a serioussource of large inclusions. Also, they quoted several investigators who found that macroinclusionslarger than 100 µm also originate from reoxidation of the steel stream during teeming. In one study,60 to 65% of inclusions were eliminated by argon shielding. Reoxidation products tend to forminclusions that are richer in weaker oxides (e.g., FeO, MnO). This has been observed by manyinvestigators.12

Sims and Forgeng8 discussed some of the common formation mechanisms of exogenous inclu-sions and concluded that mechanical erosion is not serious. The most serious damage to refractories,and the most potent source of exogeneous inclusions, is a combination of chemical attack andmechanical erosion. The presence of CaO in inclusions is a common finding, and exogeneous slagparticles are responsible for it. It is common knowledge that nozzles are attacked by liquid steelduring pouring. Chemical reactions, such as fluxing by slag, loosen particles of refractory, whichare detached by the flow of liquid steel. For example, Pickering11 found the maximum diameter ofinclusions to increase with time after tapping (Figure 9.1). This is presumably due to the fact thatthe more the nozzle is in contact with steel, the more serious the effect of chemical attack.

TABLE 9.1Possible Inclusion Sources

1


9.5 FORMATION OF INCLUSIONS DURING SOLIDIFICATION

Inclusions form during solidification by chemical reactions. Oxides, sulfides, and some oxysulfidesare typical products. Even nitrides and carbides have been found to form.6 The driving force issupersaturation of solutes leading to precipitation of reaction products. Section 5.2.1 containsdiscussions on formation of deoxidation products in molten steel by nucleation and growth.Although the present text is not concerned with phenomena that occur during freezing, it is necessaryto briefly discuss the topic so as to obtain a better understanding of inclusion control and modifi-cation.

Source Key elements

Furnace Furnace slagsFurnace refractoriesFerroalloys

CaCa

Cr, Al, Si

Tapping Launder refractoriesOxidation

Mg, Ti, KFeO

Ladle DeoxidationLadle slagLadle refractories

Ca, MgMg, Ti, K

Teeming Stopper and nozzle refractoriesOxidationDeoxidation

Mg, Ti, KFeO

Ingot mold RefractoriesDeoxidation

Mg, Ti, K

Heat treatment and rolling Surface oxidationSurface sulfurizationInner oxidationHot shortness

FeOFeSSiO2

FeS

Welding Welding slagsElectrode coatingsSteel inclusionsHot tearing

Ca, TiTi, V

S

TABLE 9.2Average Sizes and Relative Abundance of Inclusions11

Type of inclusion Diameter, µm Approx. relative volume

1. Alumina spinel, and CaO · 6Al2O3 (other than clusters) 5 1

2. Other calcium aluminates 27 160

3. Secondary deoxidation products (Si-killed steel)

32 260

4. Primary deoxidation products (Si-killed steel)

49 940

5. Erosion of silicates (Al-killed steel)

64 2100

6. Erosion of silicates (Si-killed steel)

107 9800


The cause of supersaturation in a ladle is the addition of deoxidizers to the bath. However, thatis not the situation in the mold. Here, the supersaturation arises for the following reasons:

1. The decrease in the temperature of liquid steel in the mold during freezing shifts thereaction equilibria in favor of the formation of oxides and sulfides. This can be generallyunderstood from the Ellingham diagrams (e.g., Figure 2.1). We may consider the specificcase of deoxidation of steel by aluminum, viz.,

2 Al + 3 O = Al2O3 (s) (9.1)

From Appendix 5.1, the values of the deoxidation constant (KAl) are 2.51 × 10–14 at1600°C and 2.97 × 10–16 at 1500°C. Suppose the melt is poured at 1600°C, and after atime in the mold, its temperature is 1500°C. Then, the supersaturation ratio as definedon the basis of Eq. (5.44) would be

, i.e., 84.5

2. Solid metals and alloys have lower solubilities for solutes as compared to those forliquids. This causes rejection of solutes by the solidifying material into the melt at thesolid-liquid interface and leads to nonuniform chemical composition in the cast material.The phenomenon is known as segregation, which is one of the casting defects.

Quantitative estimates of segregation for many situations are available. For example,Turkdogan12 carried out some calculations for solidification of plain, low-carbon steelingot. Concentrations of solutes in the liquid as a function of percent solidification areshown in Figure 9.2. The assumptions were as follows:• Segregation of elements in interdendritic liquid according to Scheil’s equation for Si,

Mn, and O, and equilibrium solidification for H, C, and N

FIGURE 9.1 Variation of maximum size of erosion silicates during teeming.11

2.51 10 14–×2.97 10 16–×----------------------------


• Complete mixing in bulk liquid• No reaction among solutes

3. Some oxygen is invariably picked up during teeming. Also, the occasional addition ofdeoxidizers, such as aluminum shots, into the mold is practiced.

As far as the kinetics of inclusion formation is concerned, most experimental observationsindicate that an abundance of nonmetallic particles are always present, and subsequent reactionsduring solidification occur on them.12,13 As a consequence, nucleation is not required, and the growthof inclusions occurs without the need for appreciable supersaturation. This assumption constitutesthe basis for thermodynamic analysis of inclusion formation. Figure 9.3 presents calculations byTurkdogan12 for the situation in Figure 9.2, except that deoxidation by Si and Mn have now beenconsidered. It shows how deoxidation reactions set in when Si and Mn are present. Phase diagrams

FIGURE 9.2 Solute enrichment in solidifying liquid steel if no reaction occurs between the solutes.12

FIGURE 9.3 Change in oxygen content of entrapped liquid during the freezing of steel.12

have also been utilized for qualitative predictions of inclusion formation. Examples are those offormation of FeS, MnS, and Fe-S-O type inclusions.

2,8


9.6 INCLUSION MODIFICATION

Inclusion control in industry falls into the following two categories:

1. Minimizing the occurrence of inclusions, primarily macroinclusions (This is the themeof Chapter 10, “Clean Steel Technology.”)

2. Modifying the inclusions to impart globular shape and desirable properties. (This isknown as inclusion modification and is dealt with in this section.)

In most applications, the requirements for steel quality demand sufficient attention to bothoptions above. There is no unique way to achieve that goal. Cost-to-benefit ratio is important. Avariety of process options are available in secondary steelmaking for lowering inclusion contentas well as modifying inclusions. The following discussion on inclusion modification is primarilyconcerned with principles.

9.6.1 INCLUSION MODIFICATION BY TREATMENT OF LIQUID STEEL WITH CALCIUM

This approach is practiced widely for continuously cast steel. Calcium is introduced into moltensteel as a Ca-Si based alloy powder, either by powder injection or by feeding through hollowmetallic tubes. Chapter 7, Section 7.4, presented elaborate discussions on the technology. Ototani14

has extensively reviewed the science and technology of calcium treatment of liquid steel. Compre-hensive data on structure and properties are available in standard text.1

Thermodynamics related to the deoxidation of molten steel was discussed in Chapter 5, Section5.1.2. It was noted there that calcium is a more powerful deoxidizer than silicon or aluminum. Theadvantages of complex deoxidation have also been discussed. Deoxidation by Ca-Si alloy, with orwithout Al, is capable of forming a liquid deoxidation product of CaO-SiO2 type or CaO-SiO2-Al2O3 type (Figure 5.7) with all the attendant advantages. If Si is very low and some dissolved Alis present in liquid steel, calcium treatment would produce a CaO-Al2O3 type deoxidation product.Treatment by Ca or Ca-Si based alloys is able to lower oxygen content of the melt to a very lowvalue. Calcium is a powerful desulfurizer as well. Therefore, it is employed in elemental form oras CaO in secondary steelmaking to bring the sulfur content of steel down to a very low value (seeChapter 7).

One of the defects associated with continuous casting is the formation of subsurface pinholesdue to the presence of dissolved gases. Therefore, the oxygen content of the melt should be keptvery low. This used to be achieved by maintaining a certain minimum level of dissolved aluminumin the melt. This gave rise to the problem of nozzle clogging. Alumina clusters (see Section 5.2.2)were found to be sticking to the inner wall of the nozzle,10,15 thus leading to nozzle blockage. Calciumtreatment at the final stage in a ladle or tundish was found to eliminate this, because the deoxidationproduct is a liquid consisting of CaO and Al2O3, occasionally with SiO2. Figure 9.4 shows the effectof Ca addition on the flow of an aluminum-killed steel melt through a tundish nozzle.16

Several recent papers deal with thermodynamic analysis for the prediction of inclusion com-position upon calcium treatment.17–23 Broadly speaking, two phases are formed. The oxide phaseconsists of one or more of the compounds in a CaO-Al2O3 system. The sulfide phase consists ofa solution of CaS and MnS [i.e., (Ca, Mn)S]. Various possible compounds, along with their meltingpoints, are listed in Table 9.3.

The phase diagram for the CaS-MnS system is available.24 The sulfide reaction may be repre-sented as

(MnS) + Ca = (CaS) + Mn (9.2)


(9.3)

Values of hMn and hCa can be calculated from the weight percent of Mn and Ca in liquid steel andappropriate interaction coefficients as available (see Chapter 2). Lu et al.17 calculated aCaS and aMnS

in a CaS-MnS system at steelmaking temperatures. The liquid solution was assumed to be idealand the solid solution to be a regular one. The authors claim that the calculated values are compatiblewith the liquidus. Gatellier et al.22 employed experimental data of activities in a CaS-MnS-FeSsystem from an unpublished work of Castro.

Figure 9.5 presents the CaO-Al2O3 phase diagram.25 It indicates the various compounds. Thereaction upon calcium treatment, for Al-killed steel, may be generalized as

Ca (l) = Ca (g) (9.4)

TABLE 9.3Theoretical Compositions and Melting Points of Oxide and Sulfide Phases

Composition, wt.%

Phase Code CaO Al2O3 Mn Ca S Melting point, °C

CaO · 6 Al2O3 CA6 8 92 ~1850

CaO · 2 Al2O3 CA2 22 78 ~1750

CaO · Al2O3 CA 35 65 1605

12 CaO · 7 Al2O3 C12A7 48 52 1455

3 CaO · Al2O3 C3A 62 38 1535

MnS 63 – 37 1610

CaS – 55 45 >2000

Source: from Ref. 14, Chapter 5.

FIGURE 9.4 Influence of dissolved calcium on the flow of an aluminum-killed steel melt through the tundishnozzle.16

K 2aCaS( ) hMn[ ]aMnS( ) hCa[ ]

----------------------------=


Ca (g) = Ca (9.5)

Ca + O = (CaO) (9.6)

3 (CaO) + 2 Al + 3 S = 3 (CaS) + (Al2O3) (9.7)

Ultimately, it is reaction (9.7) that is of importance for inclusion-steel equilibrium.

(9.8)

Equation (9.7) can be arrived at by combining Eqs. (7.12) and (7.22), and K7 can thus beobtained by combining Eqs. (7.13) and (7.24). This yields

(9.9)

If, on the other hand, Eq. (7.24) is combined with Eq. (7.14), then

FIGURE 9.5 CaO-Al2O3 phase diagram.25

K 7

aCaS( )3 aAl2O3( )

aCaO( )3 hAl[ ] 2 hs[ ] 3--------------------------------------------=

K 7log 3 5304T

------------– 0.961+ 64000

T---------------–

48088T

--------------- 17.687–=–=

(9.10)K 7log 48580T

--------------- 16.997–=


This may be compared with the value given by Kor,18 viz.,

(10.11)

Values of K7 at various temperatures are as follows:

If may be noted that the predictions of Eq. (9.10) are fairly close to that of Eq. (9.11). On theother hand, Eq. (9.9) gives an order of magnitude lower value. Hence, Eq. (9.10) or Eq. (9.11) isrecommended for use. This is consistent with the recommendation in Chapter 7 to employ Eq.(7.14) rather than Eq. (7.13).

Figures 7.5 and 7.6 presented values of activities of CaO and Al2O3 in CaO-Al2O3 binary meltat 1500°C and 1600°C, as well as in ternary CaO-Al2O3-SiO2 liquid at 1600°C. We would like tosee the formation of a liquid deoxidation product upon calcium treatment. However, upon coolingin the mold, solid oxides such as CA2,CA6 and so on would precipitate. Here, C means CaO andA means Al2O3. To carry out thermodynamic calculations, free energies of formation of thesecompounds from solid CaO and solid Al2O3 are required. Fujisawa et al.23 have compared the dataof some investigators.

CaO-Al2O3 melt has some solubility for CaS. The sulfide phase starts to separate out eitherwhen concentration of CaS is high or when CaS-MnS phase starts forming, or upon cooling. Asimplified analysis assumes CaS to be a pure, separate phase (i.e., aCaS = 1).18,21 Fruehan26 hasbriefly reviewed the salient features of inclusion modification. Figure 9.6 shows some calculated

Temperature, °C → 1500 1600 1700

K7 (Eq. 9.9) → 2.7 × 109 9.7 × 107 4.9 × 106

K7 (EQ. 9.10) → 2.5 × 1010 8.7 × 108 2.5 × 107

K7 (EQ. 9.11) → 2.2 × 1010 9.1 × 108 5.2 × 107

K7log 45959T

--------------- 15.579–=

FIGURE 9.6 Equilibrium inclusions predicted for calcium-treated steels as a function of its Al and S contentat 1823 K.26 Reprinted by permission of Iron & Steel Society, Warrendale, PA, U.S.A.

values of critical sulfur and aluminum contents of an Al-killed and Ca-treated steel for someinclusion types at 1550°C.26 The calculations will be modified if the sulfide phase consists of a


CaS-MnS solid solution. Figure 9.7 presents some calculated results at 1470°C.22 The y-axis refersto weight percent CaS in CaS-MnS phase. The x-axis indicates [Ws]/[Wo] in steel. For example,CA2 is the stable oxide phase at around [Ws/Wo] = 1.0.

As mentioned earlier, thermodynamic predictions are expected to be valuable, since nucleationand consequent melt supersaturation are not required. But, to the author’s knowledge, there is notmuch experimental verification of predictions, with some exceptions such as by Holappa et al.,21

where laboratory experiments were conducted and inclusions characterized by EPMA. In that case,experimental data were compared with predictions, and satisfactory agreement was observed. Itmay also be noted that all added calcium is not utilized for reaction (Section 7.4).

Recently, Cicutti et al.27 reported the use of their thermodynamic model to predict the formationof microinclusions in calcium-treated, aluminum-killed steels. Basic data required for this aretemperature and chemical analysis of steel. The model was applied to analyze different situationsin practice, such as calcium attack on aluminous ladles and tundish refractories, nozzle cloggingby either high alumina calcium aluminates or calcium sulfide, and inclusions in the final product.Model predictions showed approximate agreement with the results of chemical analyses of nozzledeposits and inclusions.

It is also worth noting that the solubility of calcium in liquid iron is very low. It also lowersequilibrium oxygen and sulfur content of iron to very low values. Equilibration, melt homogeni-zation, sampling, and analysis pose enormous difficulties in laboratory thermodynamic measure-ments. As a consequence, experimental data suffer from scatter and irreproducibility, and variousinvestigators have proposed widely differing equilibrium constants for reaction of Ca with S andO. The same is true for values of interaction coefficients . Recently, Han28 reported acritical and extensive compilation of the thermodynamic behavior of rare earth and alkaline earthelements in molten iron and nickel, which explicitly demonstrates these. Reported values of range from –62 to –535. However, the value is more consistent and may be taken as –105.

Extensive discussions are available on the properties of inclusions upon calcium treatment.5,14,22

It is not our intent to deal with them here. Fruehan26 has summarized this information briefly foreasy qualitative understanding. It is presented in Figure 9.8, which shows the superiority of duplexinclusion where C12A7 constitutes the core and CaS-MnS the ring. It is round in shape with gooddeformability. Encapsulation of CaO-Al2O3 by sulfide has been reported by many investigators.10,29

However, according to Kitamura et al.,30 it is not always true. CaS has been found dispersedthroughout the oxide matrix as well. Depending on concentration levels of the elements, thefollowing four types of inclusions were obtained by them:

FIGURE 9.7 Influence of the (%S:%O) ratio in composite inclusion on the nature of the oxide and on theCaS content of the sulfide at equilibrium (calculated).22 Reprinted by permission of Iron & Steel Society,Warrendale, PA, U.S.A.

eoCa, es

Ca

eoCa

esCa


A-type: oxysulfide containing Ca, Al, O, and S distributed throughout the inclusion B-type: CaO-Al2O3 having a ring of CaS around it C-type: CaO-Al2O3

D-type: CaS

Many micrographs, scanning electron micrographs, and SEM/EDX elemental maps are avail-able in the literature. Just as an example, Figure 9.9 shows some for calcium treatment of Al-killedsteel.

9.6.2 INCLUSION MODIFICATION BY RARE EARTH TREATMENT OF STEEL

Rare earths (REs) consist of 14 elements having almost identical chemical properties: 50% cerium,25% lanthanum, and others. Commercially, a rare earth is available as Mischmetall. Rare earthsare strong deoxidizers and desulfurizers like calcium. They also can modify an inclusion, especiallysulfide shape. However, they are not as commonly used as calcium.

Kiessling and Lange1 have presented the structure and properties of some inclusions obtainedfrom RE additions. Significant informations are available elsewhere.2,31 Fruehan26 has briefly dis-cussed the salient features. Fundamental thermochemical investigations have been conducted mostlyfor cerium. Some data are available on lanthanum and niobium as well.28 However, there is verylittle difference in their thermochemical properties. Hence, it is common practice to use data relatedto cerium for RE, with the correction that [WRe] = 2[WCe].

Compounds of cerium are solids at steelmaking temperatures. Important ones are CeO2, Ce2O3,CeS, Ce2O2S, and Ce2S3. ∆Go for the formation of CeO2 and Ce2O3 has been included in Appendix2.1. As far as the solution and reaction of Ce in liquid steel are concerned, there have been severalinvestigations. However, as in the case of calcium, wide discrepancies exist among various inves-tigators.28,32 Recommended values of interaction coefficients are28

Equilibrium constants for deoxidation and desulfurization in liquid steel at 1600°C, as recom-mended by Han,27 are noted in Table 9.4.

FIGURE 9.8 Schematic diagram of inclusions in aluminum-killed steels.26 Reprinted by permission of Iron& Steel Society, Warrendale, PA, U.S.A.

eoCe 12.1, – es

Ce 2.36– , ecCe 0.037–= = =


Figure 9.10 shows the stability diagram for phases in equilibrium with liquid steel, constructedon the basis of Table 9.4. If S and O are assumed to obey Henry’s law, then hs and ho can bereplaced by the respective weight percent. Very low values of hs and ho obtained by RE additionmay be noted.

Unlike calcium, molten steel has good solubility for RE. The latter does not vaporize as well.Hence, it tends to react with refractory lining, atmospheric air, etc. because of the reactive nature

TABLE 9.4Equilibrium Constants for Reaction of Cerium in Liquid Steel at 1600°C28

Reaction Equilibrium constant

7.94 × 10–10

4.90 × 10–18

6.20 × 10–17

2.70 × 10–6

4.27 × 10–12

FIGURE 9.9 Microprobe x-ray images of glassy-type calcium aluminate inclusions.2 Reprinted by permis-sion of Iron & Steel Society, Warrendale, PA, U.S.A.

CeO2 s( ) Ce[ ] 2 O[ ]+=

Ce2O3 s( ) 2 Ce[ ] 3 O[ ]+=

Ce2O2 s( ) 2 Ce[ ] 2 O[ ] S[ ]+ +=

CeS s( ) Ce[ ] S[ ]+=

Ce2S3 s( ) 2 Ce[ ] S[ ]+=


of RE. Moreover, RE inclusions have densities close to that of liquid steel (5000 to 6000 kgm–3).Hence, they do not float out easily. All these tend to make the steel dirty unless extensive precautionsare taken, such as use of very good quality basic refractory lining for the ladle (very low FeO andMnO and relatively low SiO2 content) and prevention of atmospheric oxidation.

If the sulfur and oxygen contents of steel are not too low, hard nondeformable and fine REoxysulfide inclusions precipitate continuously during cooling. This is not desirable. It has beenfound that, for adequate sulfide shape control, the following criterion should be observed:

On the basis of this, Figure 9.11 has been constructed.26 These conditions can be satisfied only if[Ws] < 0.01.

9.6.3 USE OF TELLURIUM AND SELENIUM FOR INCLUSION MODIFICATION

Kor18 has reviewed this topic. The use of selenium or tellurium, particularly the latter, for improvingthe machinability of sulfur-containing steels has been in practice for several years. The basic effectof Te or Se is to globularize the inclusions, leading to better deformation characteristics during hotworking of steel. The ratio [WTe]/[Ws] has been found to be important. Too much Te affects hotworkability. However, a [WTe]/[Ws] ratio larger than 1 has been found to improve the deformabilityindex of the inclusion due to formation of a film of liquid around it, rich in Te. However, thereseems to be little benefit of using a high [WTe]/[Ws] ratio. Good hot workability has been found ata ratio less than 0.1.

Thermodynamic data for formation of sulfotelluride phases seems to be scanty. Kor18 tried tomake some theoretical estimates for the reaction as follows:

MnS + [X] = MnX + [S] (10.12)

where X denotes Te or Se.

FIGURE 9.10 Phase stability diagram for Ce-O-S system.26 Reprinted by permission of Iron & Steel Society,Warrendale, PA, U.S.A.

W Re[ ]W s[ ]

-------------- 3, W RE[ ] W s[ ] 4 10 4–×<>


REFERENCES

1. Kiessling, R. and Lange, N., Non-Metallic Inclusions in Steel, Parts I-IV, The Metals Soc., London,1978.

2. Hilty, D.C. and Kay, D.A.R., in Electric Furnace Steelmaking, C.R. Taylor ed., ISS of AIME, U.S.A.,1985, Ch. 18.

3. VanVlack, L.H., ed. Oxide Inclusions in Steel, Review 220, International Metal Reviews, The MetalSoc., London, 1977.

4. Pompey, G. and Trentini, B., in Production and Application of Clean Steels, Iron & Steel Inst., London,1972, p. 1.

5. Gladman, T., Ironmaking and Steelmaking, 19, 1992, p. 457.6. Takamura, J. and Mizoguchi, S., Proc. 6th Iron and Steel Cong., ISIJ, Nagoya, 1990, Vol. 1, p. 591.7. Session on Assessment of Cleanness, in Ref. 4.8. Sims, C.E. and Forgeng, W.D., in Electric Furnace Steelmaking, Vol. II, Sims, C.E., ed., AIME,

U.S.A., 1963.9. McLean, A. and Somerville, I.D., in Proc. Int. Symp. on Modern Developments in Steelmaking,

Chatterjee, A. and Singh, B.N., ed., National Metallurgical Lab, Jamshedpur, 1981, p. 739.10. Tatinen, K. and Vainola, R., in Ref. 9, p. 673.11. Pickering, F.B., in Ref. 4, p. 75.12. Turkdogan, E.T., in Proc. Int. Symp. on Chemical Metallurgy of Iron and Steel, Iron and Steel Inst.,

London, 1973, p. 153; also Proc. 5th Int. Iron and Steel Cong., Washington D.C., 1986, p. 767.13. Mackawa, S., Nakagawa, Y., Fukumoto, M., and Taniguchi, K., in Proc. 2nd Japan–USSR Symp. on

Physical Chemistry of Metallurgical Processes, ISI Japan, 1969, p. 247.14. Ototani, T., Calcium Clean Steel, Springer Verlag, Tokyo, 1986.15. Saxena, S.K., in SCANINJECT I, Lulea, Sweden, 1977, also in Ref. 9, p. 633.16. Faulring, G.M., Farrell, J.W., and Hilty, D.C., Iron & Steelmaker, 7, 1980, p. 14.17. Lu, D.-Z., Irons, G.A., and Lu, W.-K., Ironmaking and Steelmaking, 18, 1991, p. 342.18. Kor, G.J.W., in The Elliott Symposium, ISS-AIME, Warrendale, PA, U.S.A., 1990, p. 400.19. Presern, V., Korousic, B., and Hastie, J.W., Steel Res, 62, 1991, p. 289.20. Yamada, W. and Matsumiya, T., in Ref. 6, p. 618.21. Holappa, L.E.K. and Ylonen, H.Y.S., Proc. Steelmaking Conf., ISS-AIME, Washington D.C., 69, 1986,

p. 277.

FIGURE 9.11 Criterion for critical sulfur and rare earth contents for sulfide shape control and avoidinginverse cone segregation.26 Reprinted by permission of Iron & Steel Society, Warrendale, PA, U.S.A.

22. Gatellier, C., Gaye, H., Lehmann, J., Pontoire, J.N., and Castro, F., Steelmaking Conf. Proc., ISS-AIME, 1991, p. 827.


23. Fujisawa, T., Yamauchi, C., and Sakao, H., in Ref. 6, p. 201.24. Leung, C.H. and Van Vlack, L.H., J. Am. Ceram. Soc., 62, 1979, p. 613.25. Muan, A. and Osborn, E.F., Phase Diagram for Ceramists, AISI Publication 43, Addison Wesley and

Pergamon Press, 1965.26. Fruehan, R.J., Ladle Metallurgy, ISS-AIME, 1985, Chs. 2 and 7.27. Cicutti, C.E., Madias, J. and Gonzalez, J-C., Ironmaking and Steelmaking, 24, 1997, p. 155.28. Han, Q., in Ref. 6, p. 166.29. Lange, N., in Ref. 1, II-43 to II-44.30. Kitamura, M., Soejima, T., Kawasaki, S., and Koyama, S., in Proc. 63rd Steelmaking Conf., ISS-

AIME, Washington D.C., 1980, p. 154.31. Desulfurization of Iron and Steel and Sulfide Shape Control, ISS-AIME, Warrendale, PA, U.S.A., 1980.32. Ghosh, D., Apte, P., and Kay, D.A.R., in NOH-BOS AIME Conf., Chicago, 1978, 6–1.

10 Clean Steel Technology

10.1 INTRODUCTION

It was mentioned in Chapter 1 that

1. The manufacture of cleaner steels is a thrust area in steelmaking in view of more stringentcustomer demands, especially for plates and sheets.

2. Achievement of good cleanliness is possible only if attention is paid to this goal at allstages of secondary steelmaking, from furnace to mold.

The term clean steel should mean a steel free of inclusions. However, as Chapter 9 pointed out,no steel can be free from all inclusions. Macroinclusions are the primary harmful ones. Hence, aclean steel means a cleaner steel, i.e., one containing a much lower level of harmful macroinclusions.

Chapter 9 also dealt with some details of inclusions, their origin, and modifications. Chapter5 and Chapter 8 contain discussions related to the science and technology of clean steel. However,this information is somewhat scattered. Also, not all aspects of clean steel production have beentouched upon.

In view of the importance of the topic, this chapter looks at clean steel technology in anintegrated manner and it contains

• a summary of points discussed in earlier chapters• information about refractories in secondary steelmaking, with special emphasis on clean

steel technology• a discussion of tundish metallurgy for clean steel

10.2 SUMMARY OF EARLIER CHAPTERS

10.2.1 DEOXIDATION PRACTICE

With reference to Chapter 5, better cleanliness and removal of deoxidation products can be achievedif the following points are kept in mind:

1. Carryover slag from the furnace into the ladle does not directly cause “dirtiness” in steel.However, it should be deoxidized well. Otherwise, FeO and MnO, and to some extentSiO2 present in it, will keep transferring oxygen into the melt. It is especially seriousfor aluminum-killed grades for the continuous casting route. Besides lowering aluminumyield, the slag also requires the addition of CaO and CaF2 for proper desulfurization (seeChapter 7). Hence, in modern steelmaking practice, as much attention as possible is paidtoward the prevention of slag carryover.


2. Deoxidation product should be chemically stable. Otherwise, it tends to decompose andtransfer oxygen into liquid steel. Moreover, it should be liquid for its faster growth and


removal by flotation. The use of more than one deoxidizer (i.e., complex deoxidation)helps to achieve both of these objectives satisfactorily. For ingot casting of rimming andsemi-killed grades, deoxidation by Si+Mn is adequate. But, for killed grades, and forcontinuous casting, aluminum is the principal deoxidizer. The addition of some calciumas Ca-Si alloy in addition to the aluminum tends to improve cleanliness besides inclusionmodification (see Chapters 7 and 9).

3. It is important to properly sequence and locate deoxidizer additions for maximum benefit.Some broad guidelines are available from a theoretical point of view. However, optimalpractice can be established only through plant trials.

4. Stirring of the melt in the ladle is a must for mixing and homogenization, faster growth,and flotation of deoxidation products. All modern steelworks are equipped with sec-ondary steelmaking facilities in the form of a ladle furnace or CAS–OB or vacuumdegasser. Argon purging through porous/slit plugs, located at the ladle bottom, is thestandard mode of stirring. In addition, arrangements exist for argon purging, with orwithout the injection of solid powders, through a lance immersed into the melt fromthe top.

Broadly speaking, deoxidizers are added in two stages. First, they are added duringtapping into the ladle when stirring is by the tapping stream. The second addition is inthe LF or CAS-OB or vacuum degasser, as the case may be. Here, a gentle flow of argonis enough for good deoxidation. But a much higher flow rate is required for efficientdesulfurization. The latter is not desirable from a cleanliness point of view, since it causesre-entrainment of slag particles into molten steel as well as more erosion of refractorylining. A high gas flow rate also exposes liquid steel to the atmosphere above, and someconsequent oxidation if the sealing of the top cover is not perfect, as in an LF. Fordeoxidation in a vacuum vessel, this is not a problem. The remedy is to have a high gasflow rate during most of the processing, but a gentle purging toward the end.

5. Subsequent to processing in the LF/CAS-OB/vacuum degasser and/or injection treatment,the liquid steel is held in the ladle for 30 to 60 min before and during teeming. Largernonmetallic particles get plenty of time to float up. The presence of a well deoxidizedtop slag does not allow much atmospheric reoxidation. Since there is no gas purging,the use of a superior quality ladle lining does not cause much lining erosion or meltreoxidation.

For most grades of steels, this is quite satisfactory as far as cleanliness is concerned.However, particles of finer sizes would still be present in the melt in large numbers. If,for certain grades, these also ought to be lowered, then an additional process step suchas the NK-PERM (see Chapter 5) seems to be of help. Here, fine gas bubbles are generatedthroughout the melt. Some nonmetallic particles get attached to these and thus float outat a larger rise velocity. However, the author is not aware as to what extent it is practicedcommercially.

10.2.2 TEEMING PRACTICE

As discussed in Chapters 8 and 9, oxygen and exogenous nonmetallic particles are picked up byliquid steel during teeming via the following mechanisms:

1. Absorption of atmospheric oxygen via entrainment by the teeming stream has been foundto increase total oxygen content of the melt by as much as 40 to 1000 ppm, dependingon the nature of the stream. This leads to formation of macroinclusions rich in FeO andMnO. Moreover, it increases dissolved oxygen content and causes more generation of

inclusions by reaction during solidification. The use of shrouded and submerged nozzleshas eliminated this problem as far as continuous casting of blooms and slabs are concerned.


Submerged nozzles also tend to introduce inclusions and impurities into steel byreaction and interaction with the melt. For billet casting, submerged entry nozzle (SEN)for tundish-to-mold pouring is generally not (and may not be not at all) practiced, dueto engineering difficulties. The same is true for ingot casting. Ensuring that the streamis smooth and laminar is the best way to minimize oxygen pickup.

2. Slag entrainment due to vortexing during teeming is responsible for slag particle inclu-sions (see Section 5.3). This can be minimized by• not emptying the ladle completely• employing a refractory float on the vortex• using an electromagnetic sensor around the nozzle that gives a signal when entrained

slag starts flowing out through the nozzle along with the metal3. Erosion of the teeming nozzle and the consequent increase in exogenous inclusions can

be curtailed primarily by use of proper nozzle refractory. This will be discussed in thenext section, dealing with refractories for secondary steelmaking.

10.3 REFRACTORIES FOR SECONDARY STEELMAKING

10.3.1 GENERAL ASPECTS

The importance of refractories to steelmaking processes is well known to all steelmakers and needsno elaboration. The success or failure of the processes is closely linked with development and/orchoice of proper refractories for lining furnaces, ladles, etc. Hence, it is only proper to devote asection to it. However, it must be recognized that the subject is complex. Optimization of refractorypractice in a shop is achieved with continuous operating experience and trials. This is why thereis a large body of information in the literature on refractories for steelmaking. But most of it dealswith shop floor experience and related developmental work detailing successful practices. Since itis neither possible nor desirable within the purview of the present text to get into such details, thebrief discussions here will be restricted to some salient features only. Special emphasis is given tothe influence of refractory lining on steel cleanliness. At the outset, some general references thatthe reader might require include Refs. 1 through 6.

Until about 1970, secondary steelmaking was not making much headway. Refractories for ladlelining used to be fire clay with some variations. Scientists and technologists were carrying ondevelopment work in connection with primary steelmaking only. The life of the lining was ofprimary concern, and it is principally governed by corrosion/erosion. Corrosion refers to chemicalattack. In primary steelmaking, the highly oxidizing slag containing FeO and Fe2O3 is the principalcorroding agent. Erosion refers to spalling and detachment of grains and pieces of refractoriescaused by abrasion and impact. Corrosion and consequent loosening of refractory surface speedup erosion. Bath turbulence causes impact. Thermal shock is an additional factor aggravating thespalling tendency.

In an LD converter, the refractory material is burnt dolomite or magnesite (popularly knownas dolomite and magnesite) or a mixture of the two in some proportion. Bonding is by tar or pitch.The practice varies from country to country. Dolomite is cheaper than magnesite but tends to wearfaster. Burnt dolomite is CaO · MgO. Iron oxide in slag can form liquid product by reaction withCaO, but solid product by reaction with MgO at these temperatures. This makes MgO more resistantto slag attack in comparison to burnt dolomite. Again, SiO2 and other impurities are harmful. Puremagnesia, manufactured from sea water, has proved to be superior to natural magnesite but is morecostly as well.

The tar or pitch constitutes the bonding agent that, upon heating to a moderately high temper-ature, leaves carbon as residue. This also retards slag attack in the following ways:

1. Slag does not wet carbon.2. Carbon reduces iron oxide in slag, which is the principal corroding constituent.


Therefore, until the surface layer of refractory gets decarburized, significant slag attack does notoccur. It has also been established that increasing carbon content in brick lowers lining wear.

In addition to the chemical composition of refractory lining, its porosity is an important factorin slag corrosion and lining wear. A porous brick offers more surface area, speeding up slag attack.From this point of view, graphite is better than tar or pitch, since the former is denser than thecarbon residue of the latter. Moreover, graphite is more crystalline than the residue. More crystal-linity means fewer defects and hence more resistance to chemical attack. However, here again, theissue of cost comes into the picture. Dense materials are more costly.

It has been long recognized that other factors govern the lining life of steelmaking vessels, such as

• bonding and brickmaking technique• bricklaying technique• vessel design• operating conditions • lining maintenance

In contrast to primary steelmaking, the slag in secondary steelmaking is deoxidized and containsa high proportion of CaO and Al2O3. Again, in primary steelmaking, the choice and design ofrefractory lining is governed by lining life and its impact on overall steelmaking cost. However, insecondary steelmaking, we are additionally concerned with its effect on steel quality, cost of ladleheating, etc., as summarized by the following discussions.

1. Table 9.2 presents the findings of Pickering that products of the erosion of silicaterefractory contribute most significantly to harmful inclusions of large size. This behaviorpattern has been widely recognized. In Section 9.6.2, it was mentioned that, withoutgood quality refractory, not much benefit can be obtained from inclusion modification.

2. Refractory lining should be stable as well as inert to liquid steel. Otherwise, it will tendto introduce undesirable impurities into the metal. Such tendencies are aggravated byuse of vacuum and higher temperature and are specially important for superior qualitysteel. This issue has been briefly and sporadically discussed in earlier chapters and willbe taken up further in this section. For example, Chapter 7, Section 7.4.5, mentions theimportance of ladle lining material for desulfurization and that dolomite is superior tofireclay and silica (see also Figure 7.28).

3. Secondary steelmaking and continuous casting cause additional temperature loss inmolten steel. Hence, somewhat higher tapping temperatures are required. This enhancesthe tendency for lining wear.

4. A low thermal conductivity in ladle lining is desirable to prevent heat loss by conductionthrough the wall. Again, a low thermal conductivity tends to enhance spalling by thermalshock at the hot face. An interesting development is the use of a higher percentage ofgraphite (10% or more), which allows continuity throughout the carbon phase, thusincreasing thermal conductivity. The conductivity again can be made directional byproper brickmaking technique and by use of flake graphite.8 In that case, heat will floweasily in a direction parallel to the hot face, thus reducing the tendency of spalling. Onthe other hand, thermal conductivity in a direction perpendicular to the hot face wouldbe low.

5. Ladles require preheating. The heat requirement can be cut down if the heat capacity ofthe lining is less. A large heat capacity also cools the steel more upon pouring and causesmore temperature loss.

6. Porous ceramic plugs are employed for argon purging in ladles. In these applications,besides wear resistance and stability, permeability is an important issue. Permeability


can be increased by increasing pore diameter and porosity. But then the tendency ofthe penetration of molten steel and consequent clogging is aggravated. In-situ sinteringof particles is undesirable, as it leads to densification and loss of permeability. Okawaet al.9 have presented some fundamental considerations for the development of improvedpermeable ceramics. However, as mentioned in Section 3.2, refractory plugs withoriented channels are superior to porous plugs in performance and are preferred inindustry.

7. Erosion of the lining by phenomena 1 and 2 above is most severe in the case of thenozzle, because the liquid metal flows through it at a high velocity. This not only affectsquality but also teeming rate by progressive enlargement of nozzle diameter over time.Chapter 5, Section 5.2.2, mentioned that products of deoxidation get attached to thesurface of the vessel lining in contact with the melt if there is chemical affinity betweenthem. This phenomenon leads to nozzle clogging, the well known case being that causedby alumina clusters present in liquid steel. Nozzle refractory is also subjected to highthermal shock.

8. The ladle lining is a composite. The zone in contact with the top slag should resist slagattack well. Since the slag is rich in CaO, dolomite is superior to magnesite. Mag-chromeis also a good refractory. For the zone in contact with liquid steel, the influence on steelquality and lining life is an important consideration. To reduce weight, expense, and totalheat capacity of the refractory system, a fireclay backup lining is provided.

9. The lining design would, of course, depend on the process under consideration. Gasstirring causes faster corrosion/erosion of lining. In a vacuum vessel, bubbles expandconsiderably at the top of the melt, leading to more vigorous stirring of the top slag andhence more corrosion by slag. In AOD/VOD vessels, oxygen is also blown, raising theoxygen potential of the melt and generating iron oxide.

10. The design of refractory lining is a specialized task. Optimization is called for, whichshould take into consideration• process requirements including steel quality• cost and availability• lining life

11. It is to be remembered that steel cleanliness is related to interaction between liquid steeland the refractory lining. Erosion of the lining increases exogenous nonmetallic particles,whereas corrosion causes a change in the composition of steel such as increase in oxygencontent. This, in turn, tends to generate more deoxidation products during the freezingof steel in the mold (Section 9.5).

10.3.2 THERMODYNAMIC CONSIDERATIONS OF REFRACTORY STABILITY AND INERTNESS

Figure 2.1 presents the standard free energies of formation of oxides as a function of temperature.This is a guide to the stabilities of oxides. It shows that, at steelmaking temperatures, CaO is stablerthan Al2O3 and so on. The stability of an oxide can be improved further if it is present as a doublecompound. An example is MgCr2O4, which forms according to the reaction

MgO + Cr2O3 = MgCr2O4 (10.1)

Since ∆Go for this reaction is negative, MgCr2O4 is stabler than MgO. The displacement of thefree energy curve as a consequence is illustrated in Figure 10.1.4


The displacement would be in the reverse direction if the oxide came in contact with therespective element dissolved in liquid steel, as illustrated by the curve Si–SiO2 in Figure 10.1. Inother words, it is easier for SiO2 to dissociate as follows:

SiO2 (s) = Si + 2 O (10.2)

as compared to dissociation into pure silicon and oxygen.Thermodynamic considerations tell us that dissociation would occur if [WSi][WO]2 (in melt) <

[WSi][WO]2 (equilibrium), i.e., [WSi][WO]2 < KSi (i.e., the deoxidation constant for Si) (see Section5.1).

In the event of such dissociation occurring, the melt will pick up silicon and oxygen. Thepickup may not cause a serious composition change for Si, but it may do so for oxygen if it is adeoxidized melt. SiO2 may further react with Al, C, Cr, etc. dissolved in liquid steel. The possibilitiesand extent of such reactions may be estimated with the help of data and procedures outlined inSection 5.1 under deoxidation thermodynamics. Broadly speaking, a low oxygen potential in themelt would enhance a tendency toward such reactions.

Harki et al.10 examined the stability of refractory materials against deoxidized steels. Equilib-rium calculations were performed. Laboratory investigations were carried out by simulation testsat 200 g and 50 kg scales. An oxygen sensor was used to monitor changes in dissolved oxygen inthe melt due to reaction with refractory materials. Figure 10.2 shows the calculated equilibriumoxygen content for four steel grades and different refractory materials. Laboratory tests alsodemonstrated the importance of thermodynamic stability and the flow rate of steel. The morestirring, the more melt-refractory interaction. Figure 10.3 shows the influence of refractory materialson the change of soluble aluminum with time at 1600°C for a 50 kg induction furnace.11 Thesignificant decrease of Al dissolved in steel for high-Al2O3, MgO-Cr2O3, and ZrO2-SiO2 refractoriesis due to the reaction of Al with SiO2 and Cr2O3. This is undesirable, since it poses the problemof the control and yield of aluminum.

FIGURE 10.1 ∆G vs. temperature for some metal–metal oxide systems (P = 1 atm).4 Reprinted by permissionof Iron & Steel Society, Warrendale, PA, U.S.A.


In connection with vacuum treatment of steel, vaporization phenomena require considerations.The vapor pressures of refractory oxides are quite low and need not cause any worry. Howeverreactions such as

MgO(s) = Mg(g) + O (10.3)

CaO(s) = Ca(g) + O (10.4)

MgO(s) + C = Mg(g) + CO(g) (10.5)

would be favored at low pressures and hence may lead to an objectionable quantity of oxygenpickup by the melt. Since it was dealt with in Ch. 6, no further discussion is given here.

10.3.3 REFRACTORIES FOR SECONDARY STEELMAKING

With the background information provided so far, it is now appropriate to briefly mention refrac-tories employed in secondary steelmaking. Fireclay, which has been the traditional ladle refractorymaterial, is relatively inexpensive, possesses a low bulk heat capacity, and goes through a nonre-versible expansion on heating that helps form tight fitting joints. However, SiO2 in fireclay isunstable with respect to aluminum-killed steel as well as basic top slag. The refractory materials

FIGURE 10.2 Dissolved oxygen contents in some steel melts at equilibrium with different oxides at 1873 K.10


of present-day secondary steelmaking are high alumina (70 to 80% Al2O3), dolomite, mag-chrome,MgO, and zircon. Bonding is by tar or pitch. Direct bonding by firing at a high temperature is alsopracticed. As compared to fireclay, high alumina and dolomite linings lead to more temperatureloss in melt due to their higher bulk heat capacity.

Ritza et al.2 have discussed the recent steel ladle practices at Algoma’s no. 2 steelmaking shop.They used fireclay up to 1984 then changed over to high alumina. However, they later switchedover to zircon, with ladle life of almost 100 campaigns. Masood et al., of Inland Steel,2 testedvarious refractory materials in the laboratory. Their data are presented in Table 10.1. Bose3 hassummarized the refractory linings used for secondary steelmaking in some countries (Table 10.2).It is likely that there have been some changes since the table was created. However, the it providesa glimpse of the practice in broad terms.

Raw dolomite of high purity is widely available in Europe. In view of this, as well as otheradvantages, dolomite ladle lining is the most popular one in Europe for secondary steelmaking.This trend has been picked up in North America as well.2 Chatillon et al.6 have made a compre-hensive review. For clean steel, the total impurity in calcined dolomite should not exceed 3%.

The material is a mixture of fine grains of lime and periclase (MgO). Both of these can reactwith the ambient atmosphere to form hydrates and carbonates. The lime component, however, ismuch more reactive than periclase, and it determines the speed of hydrate formation in dolomitebricks. Formation of the hydrate is accompanied by a volume increase of over 100%, disintegratingthe brick.

Therefore, hydration of dolomite bricks should be prevented during manufacture, storage, andtransportation. Bonding by tar or pitch considerably retards hydration and makes it commerciallyusable. But tar or pitch bonding is causing environmental pollution. For this, as well as to makesuperior quality bricks for ladle lining so as to have cleaner steel, the recent trend is direct bondingby firing at high temperature without use of carbonaceous matter. Hydration can be prevented bywax impregnation and/or storing the brick in a sealed container.

Both CaO and MgO are stabler oxides than Al2O3 at steelmaking temperatures. Hence, dolomitelining gives lower oxygen and sulfur content after secondary steelmaking as compared to Al2O3

lining. Figure 10.3 has illustrated this in terms of aluminum loss. These have been established by

FIGURE 10.3 Change of dissolved aluminum content of steel melt over time for some refractory linings at1873 K (50 kg induction furnace).6

TABLE 10.1Chemical and Physical Properties of Refractories Evaluated

2


several investigators in the laboratory and plant.6 Natural dolomite has been found to be superiorto MgO, since the former contains CaO, which is a more powerful desulfurizer that MgO12 (alsosee Chapter 7). Table 10.3 presents the advantages and disadvantages of some standard refractorymaterial for secondary steelmaking, according to Chatillon et al.6

Ladle covers are typically lined with high-alumina refractory (above 85% Al2O3). Porous plugsare made of high alumina or magnesia. Slide gate parts are the most highly stressed ones of thesystem. They are generally made from high-alumina material. Carbon-bonded alumina, magnesia-based materials, and sintered zirconia also are employed.

10.3.4 CHOICE OF NOZZLE REFRACTORY

For clean steel, refractory linings of teeming nozzles are of considerable importance, since thereis high probability that any inclusions and impurities introduced at this stage will not be eliminated.Here, erosion/corrosion is more severe due to high flow velocity of liquid steel through it. However,it is the thermal shock resistance that is one of the important property requirements. Good thermalshock resistance requires a low coefficient of thermal expansion. As Table 10.1 shows, zircon isbetter than alumina, which is better than basic bricks in this respect. Fused silica and mullite areeven better.

However, silica should be avoided due to its reaction with liquid steel. As a result, ZrO2-basedmaterials are increasingly employed. Figure 10.4 shows that increasing the ZrO2 content of thelining significantly decreases enlargement of the nozzle diameter by liquid steel flow, as summarizedfrom experimental data.13 However, ZrO2 is costly. Hence, insertable ZrO2-rich sleeves have beendeveloped as inner protective layer over an Al2O3-C-SiC nozzle.

Recently, some fundamental investigations were carried out on the mechanism of reaction andinteraction of nozzle refractory with molten steel. Sasai and Mizukami14 made some kinetic studies

Chemistry (wt.%)

Resin-bonded

dolomite

Tar-bondeddolomite

Direct bonded

mag-chrome Zircon70%

alumina

Tar-bonded

magnesiteA B

Al2O3 0.4 <1.0 0.4 11.1 3.4 70.0 0.5

SiO2 0.6 <1.5 1.8 1.8 33.4 26.0 1.0

MgO 41.0 36.0 60.6 60.6 – 0.3 95.0

CaO 57.0 61.0 57.0 0.7 – 0.25 2.5

ZrO2 – – – – 61.3 – –

Fe2O3 1.0 <1.0 1.0 9.2 – 1.3 0.5

Cr2O3 – – – 16.4 – – –

Bulk density (kg/m3) 2900 2900 2950 3100 3600 2600 3100

Porosity (as shipped) (%) 6 8 8 15.5 19 17 5.1

Thermal expansion @ 1200°C (%)

1.4 1.6 1.6 1.3 0.5 0.8 1.7

Thermal conductivity @ 1000°C (W/mK)

2.4 2.4 2.5 2.8 2.4 2.0 4.5

Specific heat @ 1425°C (J/kg.K)

1050 1050 1040 1050 760 1068 1175

Source: Ritrza et al., in Refractories for Modern Steelmaking Systems, ISS–Aime, 1987, reprinted with permission fromIron and &Steel Society, Warrendale PA, U.S.A.

TABLE 10.2Examples of Refractory Lining for Secondary Steelmaking in Some Countries (Ref.


in the laboratory on the reaction between a silica-containing alumina-graphite refractory and low-carbon molten steel. In one set of experiments, the refractory was simply heated to 1100 to 1600°C.It showed a significant loss of mass with an accompanied increase of porosity. In the second setof experiments, the refractory was immersed in molten steel at 1600°C. The course of reaction wasfollowed by sampling and analysis of the melt at various time intervals. Microstructures wereexamined by an optical microscope and EPMA.

3, Page 48)

Country and plant Capacity (t)Process route Bottom

Side wall

Slag line

Lining life (heats)

West Germany

Plant–1 110 EAF/LF PB Dol PB Dol 12% Mag–C 45–50

Plant–2 60 EAF/LF DB Dol PB Dol PB Mag 50–55

Plant–3 110 EAF/LF Cr Mag PB Dol PB Mag 30–33

Plant–4 60 EAF/LF PB Dol PB Dol RB Mag 45–50

Great Britain

Plant–1 90 EAF/LF 80% Al2O3 DB Dol RB Mag 28

Plant–2 105 EAF/APC DB Dol DB Dol DB Dol 30

France

Plant–1 30 EAF/APC PB Dol PB Dol RB Mag 15

Plant–2 105 EAF/APC 80% Al2O3 PB Dol DB Dol 30–35

Italy

Plant–1 60 EAF/LF PB Dol PB Dol DB Dol 45

Plant–2 90 EAF/LF Dol Carbon PB DOL DOL Carbon 45

Sweden 60 EAF/LF DB Dol DB Dol DB Dol 45

Denmark 120 EAF/LF PB Dol PB Dol PB Dol 30–35

Note: PB = pitch bonded, DB = direct bonded, RB = resin bonded.

TABLE 10.3Comparison of Advantages and Disadvantages of Various Steel Plant Refractories

Property

RefractoryInertness to steel Pollution

Hydration resistance

Thermal shock resistance

Basic slag resistance Price

Silica sand ✗ ❖ ✔ ✔ ✗ ✔

Zircon ✗ ❖ ✔ ✔ ✗ ✔

High alumina ❖ ✔ ✔ ✔ ✗ ✔

Magnesite (unfired) ✔ ❖ ✔ ✗ ✔ ✗

Magnesite–carbon ❖ ❖ ✔ ✔ ✔ ✗

Magnesite–chrome ❖ ✗ ✔ ❖ ✗ ✗

Synthetic dolomite ✔ ✔ ✗ ❖ ✔ ✗

Natural dolomite ✔ ✔ ✗ ❖ ✔ ✔

Note: ✗ = bad, ❖ = medium, ✔ = good.


Mass loss during heating experiments was explained by the reaction

SiO2(s) + C(s) = SiO(g) + CO(g) (10.6)

The results of the immersion experiments were explained by reactions such as

3SiO(g) + 2[Al] = Al2O3(s) + 3[Si] (10.7)

3CO(g) + 2[Al] = Al2O3(s) + 3[C] (10.8)

The silicon and carbon content of the melt increased with time. The Al2O3 layer deposited onthe refractory was porous. On the basis of the above mechanisms, rate equations were derivedassuming that the diffusion of SiO gas and CO gas through pores in the refractory is rate controlling.However, the actual rates were lower. Hence, it was concluded that diffusion of SiO and CO throughthe pores of Al2O3 film is rate controlling.

Tsujino et al.15 conducted laboratory experiments to understand the mechanism of nozzleclogging for ZrO2-CaO-C refractory lining. They invoked the mechanism of Sasai et al.14 butconsidered the possibility of the formation of gaseous Al2O, ZrO, and AlO in addition to SiO. Theresults of their equilibrium calculations are presented in Figure 10.5. It shows that SiO is the onlydominant gaseous species. Again, it is the SiO2 content of the refractory that is primarily responsiblefor the reaction. In steels containing higher aluminum, a reaction of [Al] with ZrO2 was alsodetected. The oxide layer formed at the melt–refractory interface was both Al2O3, CaO-Al2O3, andCaO-Al2O3-ZrO2. Since it is porous, it traps nonmetallic particles of steel melt, leading to clogging.

A layer of liquid slag originating from the mold flux floats on top of liquid steel in the continuouscasting mold. It causes local corrosion of the nozzle lining at the slag level. Mukai et al.16 conductedlaboratory experiments to understand this mechanism for alumina-graphite (AG), zirconia-graphite(ZG), and some other materials. According to them, the corrosion is a two-stage phenomenon. Itis schematically shown in Figure 10.6.

In stage (a), the oxide is exposed, so the slag wets it due to favorable interfacial tension. Ondissolution of the oxide of the refractory, the graphite particles come in contact with the melt. Sinceliquid steel wets graphite preferentially, stage (b) sets in. On dissolution of the graphite into steel,

FIGURE 10.4 Relation between enlargement of nozzle diameter upon teeming vs. ZrO2 content of nozzlerefractory.13


oxide particles become exposed, and stage (a) comes back. Since dissolution of graphite into steelis fast, stage (b) is undesirable. Hence, good corrosion resistance is achieved if it is mostly in stage(a), i.e., dissolution of oxide in slag is slow. This is why the ZG nozzle corrodes more slowly atslag level than does the AG nozzle.

FIGURE 10.5 Equilibrium partial pressures of SiO, Al2O3, ZrO, and AlO for different oxide materials dueto reaction with carbon.15

FIGURE 10.6 Mechanism of corrosion in oxide-graphite composite submerged entry nozzles in a continuouscasting mold.16

10.4 TUNDISH METALLURGY FOR CLEAN STEEL


10.4.1 GENERAL

The tundish is a shallow, refractory-lined vessel that is located in between the ladle and thecontinuous casting mold. Its shape is rectangular. The liquid metal flows from the ladle into thetundish and from the tundish into the mold. It is a must for continuous casting, for proper regulationof the rate of teeming into the mold. A tundish can simultaneously feed up to six molds.

Figure 10.7 schematically shows the longitudinal section of a tundish feeding two molds. Thedams and weirs are optional features. These are not present in a plain tundish. The capacity ofmodern tundishes ranges from approximately 10 to 80 tonnes of steel. A tundish is a continuouslyoperated vessel. When one ladle has been emptied, it is replaced by a filled ladle. During thischangeover, the reservoir of liquid metal in the tundish keeps feeding the molds.

Proper control of steel superheat is crucial to the success of continuous casting. However, whenthe liquid flows through the tundish, it looses some temperature. In a multistrand tundish, if theoutlets to the molds are not equidistant from the inlet stream, then some difference of temperatureexists from mold to mold, and it should be minimized by proper tundish design and operation.

The flowing metal also interacts with the tundish lining and picks up oxygen, nitrogen, andhydrogen from atmospheric air. These are sources of additional inclusions besides the nonmetallicparticles that come from the ladle. For clean steel, therefore, efforts are required to

• prevent reaction and interaction with air and refractory lining• provide opportunities for inclusions to float up

For operational convenience, either refractory castables or prefabricated boards are employedas tundish lining. Ease of lining and cost are important considerations. Various mixtures consistingof silica, silicates, alumina, zircon, and magnesia have been employed and seem to be in use evennow. However, MgO-based working lining in contact with the melt has gained in popularity fromthe point of view of steel quality.

FIGURE 10.7 Schematic diagram of a tundish with dams and weirs.

Prevention of heat loss from the liquid steel in the tundish leads to better temperature controland uniformity in the molds. The use of a refractory-lined tundish cover has been of considerable


help. Moreover, insulating powders are added at the top surface of molten steel. Absorption ofgases, principally oxygen, from air is lowered by having a molten slag floating on the steel.Therefore, the top additions have to serve the dual purpose of preventing heat loss and oxygenabsorption. There have been several investigations17–20 dealing with the choice of additions, so thisis covered below as a separate subsection.

10.4.2 CHOICE OF TUNDISH COVERING POWDER

Figure 10.8 schematically shows the different zones in covering powder and slag in a tundish.17

There is a steep temperature gradient across it from the molten steel surface to the atmosphere. Asa consequence, the bottom zone is a liquid slag, and top zone has solid powder. Sintered andsoftened powders constitute the intermediate zones. Thermal insulation is primarily provided bythe solid powder. Rice husk ash, which is almost pure SiO2, is a popular material. Fly ash is analternative. The use of 5 to 10% carbon along with rice husk ash and fly ash has also beenrecommended.17 An alternative is to employ the rice husk itself, which contains some carbonaceousmatter in addition to SiO2. Carbon reacts with atmospheric oxygen, forming CO and CO2 and thushelps to prevent oxygen infiltration.

The purpose of the molten slag layer is twofold.

1. To act as an barrier between air and the liquid steel to prevent reoxidation2. To assimilate the inclusions that separate from the steel in the tundish

Assimilation of inclusions by the slag causes a decrease of total oxygen content in the steel.Investigators in tundish metallurgy area have referred to it as deoxidation, although it is not thecorrect terminology.

(10.9)

Bessho et al.18 conducted plant trials with tundish fluxes in a range of CaO/SiO2 ratios of 0.83to 22.2. They came to the conclusion that a high-basicity slag (CaO/SiO2 > 11.0) is superior to alow-basicity one with CaO/SiO2 = 0.83 in preventing atmospheric reoxidation of steel. Other recentinvestigators17,19,20 have also recommended use of high-basicity slags. Oxidation of Fe, Mn leads

FIGURE 10.8 Different zones in covering powder and slag in tundish (schematic).17

∆O[ ] tot ∆O[ ] reox ∆O[ ] deox–=

to the formation FeO, MnO much more easily in an acid slag due to lower activity of FeO, MnO,and it speeds up oxygen transfer through the slag. Wettability of for Al2O3 inclusions is more in a


basic slag than in an acid slag, thus assisting easier assimilation of inclusions into the slag. A fluid slag attacks refractory lining more and hence is harmful. It also leads to faster oxygen

transfer and more reoxidation. On the other hand, some fluidity is desired for inclusion assimilation.This calls for optimization of slag viscosity. The temperature of liquid steel in the tundish is around1550°C. Straight CaO-Al2O3 slags, although desirable to prevent reoxidation, are very viscous, sothe slag should contain some SiO2. In addition, the presence of some MgO helps prevent attackon MgO-based refractory lining.

The composition of the slag keeps changing with time. CaO and Al2O3 come as inclusionsfrom ladle slag. SiO2 comes from the top powder as well as through inclusion absorption. Erosionof the tundish lining also contributes to the change. Therefore, the strategy for controlling slagcomposition has to be evolved for individual plant practices. It has been reported that, at Hoogovens,the use of approximately 200 kg of calcium aluminate flux and 100 kg of rice husk was adoptedfor a sequence of four to seven ladles in a 65 tonne tundish.19

Stel et al.19 carried out heat transfer analysis and calculation for heat loss through slag and ricehusk layers. The effectiveness of rice husk was demonstrated for insulation. It was also predictedthat approximately 70% of the calcium aluminate would be in a molten state. A mass balancemodel, coupled with actual slag analyses in the tundish, predicted the desirability of restricting theentry of carryover into tundish slag to 25 kg or less during ladle change.

Hara et al.20 carried out studies on the reoxidation of steel during the refining and castingprocesses by ladle slag, ladle refractory, packing sand in the ladle, tundish slag, and air penetratinginto the tundish. They have recommended the improved method shown below.

With improved flux management alone, it has been found that the total oxygen of steel decreasesin the tundish.17,18 It is more so with the above-recommended practice. The anxiety to avoid SiO2

to whatever extent possible is not only for cleanliness but also to prevent the reaction

4[Al] + 3(SiO2) = 2(Al2O3) + 3[Si] (10.10)

which poses difficulties in controlling dissolved Al and Si in steel.

10.4.3 FLUID FLOW AND RESIDENCE TIME DISTRIBUTION IN TUNDISH

The nature of liquid steel flow in the tundish plays a significant role in inclusion flotation, interactionwith top slag, and refractory lining erosion, and thus in the production of clean steel. Flow regulationis effected by

1. proper choice of tundish size and shape2. fitting the tundish with flow modulation (FM) devices such as dams, weirs, and baffles3. argon purging at selected locations

Factors Improved methods

Ladle slag (FeO + MnO) = 2 to 15 percent

Ladle refractories High alumina

Tundish slag

Reoxidation by air Sealed tundish

Packing sands of ladle Non–silica

CaOSiO2----------- 6=

As far as fundamentals are concerned, it is appropriate to briefly discuss fluid flow in thetundish. The flow is turbulent and three-dimensional. Optimum design depends on the design and


operation of the continuous casting machines in a particular shop. To achieve optimum design,water model studies of the tundish have been conducted in transparent perspex vessels. The firststep is a decision about the scale of the water model—whether it should be full size or of reducedsize. For this, one has to consider the similarity criteria and must decide which dimensionlessnumbers of the actual tundish (i.e., prototype) should be kept the same in the model.

Three important dimensionless numbers in fluid flow are Froude number, Reynolds number,and Weber number. These were defined in Chapter 3. Here, u = velocity of the ladle-to-tundishstream. Some investigators have considered only the Froude number as important.21 This allowedthe use of an approximately 1/6th scale model. Kemeny et al.22 advocated use of a full-size model,which corresponded to the equality of both the Froude number and Reynolds number.

Visualization of some aspects of flow, such as surface waves and vortexing, are possible assuch. Injection of a colored dye provides a tracer and facilitates detailed observations. In additionto flow visualization, investigators also determined residence time (tR).22 The concept of tR and itscharacteristics in different types of reactors is available in standard texts.23 A small volume of fluid(fluid element) may be treated as an entity like a particle. It spends some time in the tundish. Thisis its residence time.

The flow in a reactor may be idealized into two broad categories.

1. Plug flow. This is exemplified by uniform flow through a channel. It is obvious that tR

for all fluid elements would be the same here and is given as

(10.11)

2. Backmix flow. This is the situation in a stirred tank where the fluid is entering and leavingthe tank continuously. In an ideal backmix flow, the fluid is assumed to get mixedimmediately when it comes into the tank. Therefore, tR for all elements is not the same,and there is a probabilistic residence time distribution (RTD) here. The average residencetime is given by Eq. (10.11).

Figure 10.9 schematically presents C vs. τ curves, where is known as the residencetime distribution function, where

(10.12)

Experimentally, the C vs. τ curve is determined by the pulse tracer technique. In a water model, acommon tracer is KCl solution. A small quantity of KCl solution is suddenly injected into the inletstream. The concentration of KCl in the outlet stream constitutes a measure of C, and it is monitoredcontinuously by the electrical conductivity method.

It may be noted that the flow in the tundish is neither completely a backmix flow, nor completelya plug flow but something in between. The standard technique of analyzing these curves is toconsider the entire tundish to hypothetically consist of three interconnected tanks, one havingentirely plug flow, one having entirely backmix flow, and the third one being a dead zone, i.e.,having no flow at all. The RTD curves of a reactor, including the tundish, can be analyticallyrepresented in terms of the volumes of these tanks.23

tRVolume of reactor V R( )

Volumetric flow of fluid Q( )----------------------------------------------------------------------=

tR( )

τtR

tR

---- C⋅=

C τdO

α

∫ 1=


Figure 10.9 also shows a hypothetical situation in which the entire flow is short circuited. Singhand Koria24,25 recently carried out extensive RTD measurements in a tundish water model. Theyfound both the presence and absence of short circuiting. The natures of the curves were as shownschematically in Figure 10.9.

where tR,min = minimum residence time

A large residence time allows more time for the inclusions to float up as well as for homoge-nization of liquid metal temperature and composition. This calls for such a design of the tundishthat both tR,min and tR,mean are as large as possible. This can be achieved if

• The volume of the tundish is large.• Plug flow is dominant.• Dead volume is small.• The flowlines are zig-zagged so that the path is longer.

Dimensionless correlations are useful in quantitative predictions of tR for a particular tundishsize and design. Based on their own data as well as those of other investigators, Singh and Koria24,25

arrived at some generalized correlations for τmin, , and τpeak for models without weirsand dams as well as with flow modulating devices. Figure 10.10 shows their dimensionless corre-lations for tundishes without flow modulators. Data are mostly from water models. (In Figure 10.10,M = model, P = prototype.)

The regression fitted equation is

τmin = (–0.38 + 8.64α – 44.15α2 + 67.18α3) × β–0.61 φ3.04 Fr–0.08 (10.13)

FIGURE 10.9 Residence time distribution for different flow patterns.

τmintR ,min

tR

------------=

τmean tmean tR⁄( )

P M

Kemeny et al.


Here,

where L = length of tundishW, H = width and bath height of tundish

l = inlet-to-exit distance

In addition to water model studies, mathematical modeling (i.e., numerical computations offluid flow and predictions thereof) has been done by several investigators.26–29 These have generatedvelocity fields and so forth that can be employed in tundish design.

10.4.4 DESIGN AND OPERATION OF TUNDISH FOR CLEAN STEEL

Figure 10.7 is a sketch of an optimum dam and weir arrangement arrived at through a water-modelstudy of a twin-strand caster.22 The inlet stream creates turbulence. This is not desirable, as itenhances refractory erosion and reaction with the atmosphere. Moreover, it shortens the residencetime. The weirs keep this turbulence confined to a small volume. Dams direct the flow upward.This not only increases upward flow velocity, it also increases residence time, both of which assist

van der Heiden et al.Knoepke et al.He et al.Ilegbusi et al.Lee et al.Chakraborty et al.Xintian et al.Yeh et al.Szekely et al.Present Study

0.25

0.20

0.15

0.10

0.05

00 0.05 0.10 0.15 0.20 0.25

(-0.38 + 8.64 α - 44.15 α2 + 67.18 α3). β-0.61. φ3.04

Tm

in. F

r0.08

FIGURE 10.10 Comparison of measured dimensionless minimum residence time with those calculated fromEq. (10.13). M = model, P = prototype.24

α WL-----, β H

L----, φ l

L---= = =

in flotation of nonmetallic particles. Slots in the dams encourage plug flow and do not allow theformation of dead zones at the tundish bottom. A recent practice is to have a rough refractory


surface on the tundish bottom below the inlet stream to dampen turbulence.Slotted dams are popular now, and slot design constitutes one variable. Some argon purging

with porous plugs fitted at the tundish bottom is also being practiced today. This imparts an upwardmotion to liquid steel, thus assisting further in inclusion flotation. The location and flow rate ofpurging provide further flexibility in operation. However, it is to be remembered that the rising gasbubbles and upward motion of liquid steel should have only gentle effects so as not to createturbulence at the slag–metal interface. Turbulence enhances the entrainment of slag in metal, witha resultant dirtiness of the steel.

Inclusion levels in steel may become objectionably high during the changeover from one ladleto another due to the following factors:

• More slag carryover from the ladle to the tundish occurs due to shallow metal depth inthe ladle and consequent slag entrainment by the steel stream by vortexing.

• During changeover from one ladle to another, the metal height in the tundish keepsdecreasing, and a stage may come at which the tundish slag will find its way into themold due to vortexing.

A deep pool of molten metal and a viscous slag are helpful. However, optimization is needed toensure good plant performance.

Inclusions can keep floating out as the liquid metal flows through the tundish. Semi-empiricalcorrelations as well as experimental measurements have been carried out in water models.22,30

Nakajima et al.30 have reported the use of an inclusion counting technique. Low density particlesof various diameters were employed to simulate inclusions. The authors’ experimental data maybe represented as

Nout/Nin = exp(–kut) (10.14)

where Nout/Nin is the ratio of inclusion content in the exit stream to that in inlet stream for a certainsize, ut is the terminal rise velocity of particle of that size as calculated by the Stokes law [(Eq.(5.45)], and k is an empirical constant.

Mathematically, it is a complex problem. Joo et al.31 carried out mathematical and watermodeling of inclusion behavior and heat transfer phenomena in the tundish with and without damsand weirs. Some of their salient findings were as follows:

• The residual ratio of inclusions obtained from the water model agreed reasonably withthe predictions of the mathematical model without tuning.

• Small inclusions (<40 µm) were not readily removed.• Thermal convection in molten steel tundishes gave significantly different results from

those of the water model.• A conventional trough-type tundish with flow modifiers exhibited the best inclusion

removal.

Figure 10.11 presents a computed curve from the above studies for molten steel in a tundish.It shows the residual ratio of inclusions as a function of Stokes velocity, which depends only onparticle size. The lower the residual ratio, the better the inclusion removal. Most of the results areas expected and stated earlier. The ideal plug flow is best, since it gives the largest residence time.The ideal backmix flow is the worst. The figure also demonstrates the significant influence ofnatural convection.

Bessho et al.18 adopted a simpler mathematical procedure for quantitative prediction of thechange in total oxygen content in steel from inlet to exit in a tundish. As discussed in Section


10.4.2, this change reflects a dynamic balance of reoxidation and deoxidation. The assumptionswere as follows:

1. Deoxidation by coagulation and floating up of oxide particles2. Reoxidation (i.e., contamination by Al2O3 particles) by reduction of SiO2 in slag by Al

[Eq. (10.10)] at the slag–metal interface3. Homogeneous deoxidation reaction4. Horizontal plug flow with eddy dispersion5. First-order reactions

The fundamental equation is

(10.15)

where C is the concentration of [O]T, x is the horizontal longitudinal axis, u is the linear plug flowvelocity, Dt is the eddy diffusion coefficient, and R is the net reaction rate, given as

R = Rdeox + Rreox (10.16)

Rdeox = –k C (10.17)

Rreox = α A Jo (10.18)

where k is the deoxidation rate constant, A is the cross-sectional area of metal in the tundish normalto x, Jo is the oxygen flux across slag–metal interface, and α is the contamination ratio.

Dt was obtained from earlier mixing studies of Mabuchi et al.32 in a tundish by copper tracer.This was compared with Levenspiel’s equations, etc. Combining all these, Dt was estimated as 22.4× 10–4 m2 s–1. The values of k and α were obtained by fitting with plant data in tundish. This way,k was found to lie between 1 × 10–3 to 3 × 10–3 s–1.

FIGURE 10.11 Computed residual ratios of inclusions as a function of Stokes velocity for different situa-tions.31

∂C/∂t u∂C∂x-------– Dt

∂2C

∂x2--------- R+ +=

The value of the specific rate of dissipation of energy (ε in W/kg) was determined from therelationship noted below:33


(10.19)

where is the feed rate of molten steel into the tundish in kgs–1, un is the linear velocity of theladle teeming stream in ms–1, and Ms is the mass of steel in tundish in kilograms.

Bessho et al.18 estimated ε as 20.8 × 10–3 Wkg–1 for their plant investigation. The value of k atthis ε was found to be consistent with the k versus ε relations of some other investigators in gas-stirred ladles. As stated earlier, some slag suddenly may find its way from ladle to tundish towardthe end of ladle teeming. Fundamentally, this is a pulse akin to tracer injection, and one may expecta change of total oxygen concentration with time as shown schematically in Figure 10.9. With thehelp of the above equations, this variation was predicted for a ladle change assuming differentvalues of Dt and k (Figure 10.12).18 The change is effected from the end of ts to the beginning of tM.

10.4.5 CERAMIC FILTER USE IN TUNDISH

Ceramic filters have been in use to remove inclusions from the melt for low-melting nonferrousmetals such as aluminum for more than 20 years. For steel melts, active research and developmentwork is being pursued in several countries in bench-scale and pilot plant tundishes. Plant trials arealso going on. These filters have large pore size, which often means holes of macroscopic size.They are a modified version of slotted dams, where the slots house the filters. Various designs areavailable, such as loops and foams,34–36 and circular or irregular holes in ceramic plates of largerwidth (deep bed filtering).36–38

Figure 10.13 shows some of them schematically. Since the holes are much larger than theinclusions, the mechanism of capture is not like traditional laboratory filters. The inclusions collideon the inner walls of the holes when the melt flows through the filter, stick to the wall, and becomesintered there. Proper selection and testing of the ceramic material is important, since this will have

εms un

2⋅2Ms

---------------=

ms

FIGURE 10.12 Variation of total oxygen content of steel vs. time at the tundish exit for different values ofk and Dt (calculated).18


a decisive influence on the life and cost of filter. Various refractory materials have been tried sofar, such as partially stabilized ZrO2, Al2O3, CaO, Al2O3-ZrO2, and Al2O3-SiO2. ZrO2-based filtersare finding more popularity due to their good thermal shock resistance and chemical inertness.34,36

Filtration efficiency (η) may be defined as

(10.20)

where [O]T,i and [O]T,f are the total oxygen contents of the melt before and after filtration, respec-tively. In some experiments, it has not been possible to determine η this way. There η values wereestimated from values of [O]T at the inlet and exit stream and by comparing experiments with afilter and without a filter.

It has been established that filters are effective in lowering inclusion contents of steel substan-tially. Filtration efficiencies of 20 to 80%,35 70to 90%,36 15to 60%,37 and up to 60%.38 have beenreported. Figure 10.14 presents some sample results with Al2O3 filters.38 However, to the best ofthe author’s knowledge, filters have not yet been adopted commercially.

The difficulties are due to the much higher temperatures associated with steelmaking as com-pared to low-melting nonferrous metals. The problems may be summed up as34

• incomplete priming (i.e., lack of penetration into holes) at the start of flow due to thenon-wetting nature of ceramics

• filter failure• premature filter clogging by inclusions• inadequate filter efficiency

The resistance of the filter to the flow of liquid is an important design parameter. Raiber et al.36

determined the resistance (RF) with the help of the following relationship:

FIGURE 10.13 Various ceramic filter designs employed in a tundish.

η 100O[ ] T ,i O[ ] T , f–

O[ ] T ,i

-----------------------------------×=

3

S


(10.21)

where and are mass flow rates of steel with and without a filter. Values of RF rangedbetween 0.25 and 0.6.

Uemara et al.35 determined the drag coefficient (CD) based on Bernoulli equation for a flow ofwater through their filters in water model experiments. String diameter was taken as a characteristiclength for calculation of the Reynolds number for a loop filter. It is not clear what was done for afoam filter. Figure 10.15 shows their CD vs. Re regression fitted curve. Investigators have used thisrelationship for the flow of molten steel also. The relationship is

CD = 9.68 – 80.5 Re–1/2 + 1125 Re–1 (10.22)

1

12 18 24 30

2

NUMBER OF FILTERS

IND

EX

OF

CLE

AN

LIN

ES

FIGURE 10.14 Effect of the number of filters on steel cleanliness.38

RF 1ms ,filter

ms

--------------–=

ms ,filter ms

FIGURE 10.15 Relationship between CD and Re for various filters.35

At start of the steel flow, a larger ferrostatic head is required for penetration of the liquid intothe holes of the filter due to the non-wetting nature of ceramics. It can be calculated from the


following equation by Ogino et al.:39

(10.23)

where ∆H = the ferrostatic head required to initiate flowσLG = gas-liquid interfacial energy

θ = ceramic-steel contact angleρL = density of liquidd = diameter of hole

The mechanism of deep bed filtration is shown schematically in Figure 10.16. Inclusion particlesbecome attached to the interior walls of the filter and are sintered to it. Uemara et al.36 also performeda kinetic analysis for a loop filter on the basis of the following kinetic steps:

1. Transportation of the particles from the bulk melt to the filter surface2. Attachment of the particles to the filter surface3. Solid state sintering of the particles with the filter surface

The authors assumed two mechanisms for step 1, viz.,

• Diffusion (really, Brownian motion) of particles from bulk steel to surface• Interception (i.e., collision) of particles in molten steel by the filter

On the basis of their quantitative analysis, they arrived at the following conclusions:

1. Inclusions are primarily trapped on the surface by collision.2. The attractive force between the inclusion and filter surface is so strong that the flow of

molten steel is not able to detach it.3. Transportation of inclusions to the surface is rate controlling.

∆H4σLG θcos

ρLgd------------------------=

FIGURE 10.16 Mechanism of deep bed filtration.

There are some simplifying assumptions in their quantitative analysis. Hence, it is difficult tosay anything in confirmation. Finally, there are indications that use of filters cuts down vortexing


at the tundish exit as well.36

REFERENCES

1. Chesters, J.H., Refractories for Iron and Steelmaking, The Metals Soc., London, 1974.2. Refractories for Modern Steelmaking Systems, ISS-AIME, U.S.A., 1987.3. Proc. National Seminar on Secondary Steelmaking, Tata Steel and Ind. Inst. Metals, Jamshedpur, 1989.4. Muan, A., in Electric Furnace Steelmaking, Taylor, C.R., ed., ISS-AIME, U.S.A., 1985, Ch. 24.5. 69th Steelmaking Proceedings, ISS-AIME, Washington D.C., 1986. 6. Chatillon, J.H. and Schmidt-Whitley, R.D., Proc. Int. Symp. on Refractories, Xiamgchong, Z., Jiaquan,

L. and Xingjian, Y., ed., Pergamon Press, Beijing, 1989, p. 433.7. Kappmeyer, K.K. and Hubble, D.H., in High Temperature Oxides, Academic Press, London, 1970,

Part 5–1.8. Hart, R. and Michael, D., in Ref. 5, p. 171.9. Okawa, K., Kochi, H., and Tsuchinari, A., in Ref. 5, p. 237.

10. Harkki, J., Rytila, R., Palander, M. and Sandstrom, S., Scand. J. Met., 19, 1990, p. 116.11. Kishida, T., Kitagawa, S. and Sugiura, S., Proc. 7th Japan-Germany Seminar, Verein Deutscher

Eisenhuttenleute, Dusseldorf, 1987, p. 167.12. Degawa, T., Uchida, S., and Ototani, T., in Proc. 2nd Int. Conf. on Refractories, Tokyo, 1987, p. 842.13. Jiaquan, Lu., in Ref. 6, p. 321.14. Sasai, K. and Mizukami, K., ISIJ Int., 35, 1995, p. 26.15. Tsujino, R., Tanaka, A., Imamura, A., Takahashi, D., and Mizoguchi, S., ISIJ Int., 34, 1994, p. 853.16. Mukai, K., Toguri, J.M., Stubina, N.M. and Yoshitomi, J., ISIJ Int., 29, 1989, p 469.17. Kuchar, I. and Holappa, I., Steelmaking Conf. Proc., ISS-AIME, Dallas, 76, 1993, p. 495.18. Bessho, N., Yamasaki, H., Fujii, T., Nozaki, T., and Hiwasa, S., ISIJ Int., 32, 1992, p. 157.19. Van der Stel, J., Boom, R. and Deo, B., in Ref. 17, p. 503.20. Hara, Y., Idogawa, A., Sakuraya, T., Hiwasa, S., and Nishikawa, H., Steelmaking Conf. Proc., ISS-

AIME, Toronto, 75, 1992, p. 513.21. Lai, K.Y.M., Salcudean, M., Tanaka, S., and Guthrie, R.I.L., Met. Trans., 17B, 1986, p. 449.22. Kemeny, F., Harris, D.J., McLean, A., Meadowcroft, T.R., and Young, J.D., Proc. 2nd PTD Conf.,

ISS-AIME, Chicago, 1981, p. 12.23. Szekely, J. and Themelis, N.J., Rate Phenomena in Process Metallurgy, J. Wiley & Sons, New York,

1971, Ch. 15.24. Singh, S. and Koria, S.C., ISIJ Int., 33, 1993, p. 1228.25. Koria, S.C. and Singh, S., ISIJ Int., 34, 1994, p. 784. 26. Deb Roy, T. and Sychterz, J.A., Met. Trans. B, 16B, 1985, p. 497.27. El-Kaddah, N. and Szekely, J., in Proc. Cont. Casting, 85, IMM, London, 1985, p. 491.28. He, Y. and Sahai, Y., Met. Trans. B., 18B, 1987, p. 81.29. Szekely, J. and Ilegbusi, O.J., The Physical and Mathematical Modeling of Tundish Operations,

Springer-Verlag, New York, 1989.30. Nakajima, H., Tanaka, M., Guthrie, R.I.L., Dimitron, L., and Harris, D., in Ref. 5, p. 705.31. Joo, S., Han, J.W. and Guthrie, R.I.L., Met. Trans. B., 24B, 1993, p. 767, 779.32. Mabuchi, M., Yoshii, H., Nozaki, T., Habu, Y., Sakurai, M., and Moriwaki, S., Kawasaki Steel Giho,

17, 1985, p. 23.33. Asai, S., in 100th and 101st Nishiyama Memorial Seminar, ISIJ, Tokyo, 1984, p. 75.34. Gairing, R.W. and Bosomworth, P.A., in Ref. 20, p. 823.35. Uemara, K., Takahashi, M., Koyama, S. and Nitta, M., ISIJ Int., 32, 1992, p. 150.36. Raiber, K., Hammerschmid, P. and Janke, D., ISIJ Int., 35, 1995, p. 380.37. Xintian, L., Yaohe, Z., Baolu, S., and Weiming, J., Ironmaking & Steelmaking, 19, 1992, p. 221.38. Kahn, Yu. E., Liberman, A.L., Doubrovin, I.V., and Shalimov, Al. G., in Indo-Russian Bilateral Symp.,

RDCIS, SAIL Ranchi, 1992, p. 69.39. Ogino, K., Hara, S., Miwa, T., and Kimoto, S., Trans. ISIJ, 24, 1984, p. 522.

11 Modeling of Secondary Steelmaking Processes

Dipak Mazumdar, Ph.D.Department of Materials and Metallurgical EngineeringIndian Institute of Technology

11.1 INTRODUCTION

A comprehensive study of various hydrodynamic phenomena such as fluid flow, mixing, and masstransfer in full-scale liquid steel processing vessels poses serious experimental difficulties. Highoperating temperatures, opacity of liquid steel, and the relatively large size of industrial metalprocessing units preclude direct experimental observations. Consequently, it has been customaryto study the process dynamics of steelmaking operations with the aid of physical and mathematicalmodels.

While the physical modeling of metallurgical processing operations dates back to at least theearly 1960s,1 mathematical models have come of age relatively recently (i.e., mid 1970s).2 Theprogress in mathematical modeling has been largely achieved through advances in the computingpower and speed of digital computers, which are now available at moderate cost. Concurrent withthese advances have been the numerical algorithms and special computing procedures needed tosolve transient, three-dimensional forms of the turbulent Navier–Stokes or Reynolds stress equations(Chapter 3) and their equivalent heat and mass counterparts.

It is important to stress at this point that physical and mathematical modeling are not alternativesbut most often must be pursued in a complementary fashion. This is illustrated in Figure 11.1,3

which essentially indicates that mathematical modeling, physical modeling, and actual plant-scalemeasurements may all be the ingredients of a successful investigation. Indeed, owing to thecomplexities associated with the operating conditions, several iterations may be required betweenmathematical modeling and physical measurements (i.e., this is normally termed model tuning)before the desired level of understanding finally emerges.

11.2 MODELING TECHNIQUES

11.2.1 PHYSICAL MODELING

Here, the industrial vessel is known as the prototype, and its laboratory-scale counterpart is knownas the model. Laboratory-scale modeling of various secondary steelmaking operations has mostfrequently used water as the modeling medium to represent molten steel. The most important singleproperty in this context, apart from its ubiquity, is that its kinematic viscosity (that is, molecular



viscosity/density) is essentially equivalent to that of molten steel at 1600°C (i.e., within 10%). Flowvisualization experiments in aqueous systems using dyes or other tracers have therefore proved tobe very helpful in developing a qualitative understanding of various flows. Similarly, more detailedinformation on flow characteristics has also been possible by measuring velocity fields by trackingthe motion of neutrally buoyant particles, hot wire or hot film anemometry, by laser Doppleranemometry, and, lately, by PIV (particle image velocimetry). In addition, measurements of resi-dence time distribution to characterize mixing in water model experiments using dye, acids, or KClsalt solution have proved very popular.

Having realized the advantages of using water as the representative fluid, it is now appropriateto discuss the general problem of how to physically model or characterize metallurgical processes.Although this has been addressed in Section 3.1.4 very briefly, it is important to note here that, ifthe same forms of dimensionless differential equations and boundary conditions apply to two ormore such metallurgical operations, and if an equivalence of dimensionless velocity, temperature,pressure or concentration fields, etc. also exist between the two, then one of them becomes a faithfulrepresentation of the other; i.e., one can be termed as a model of the other. This is a generalstatement of the need for similarity between a model and a prototype, which requires that there beconstant ratios between corresponding quantities.

The state of similarity between a model and a full-scale system includes geometric, mechanical,thermal, and chemical similarity. Mechanical similarity is further subdivided into static, kinematic,and dynamic similarity. However, in modeling of steelmaking operations, static similarity has norelevance. The various states of similarity are discussed in standard texts in great detail4 and aresummarized below in brief.

Two bodies are said to be geometrically similar when, for every point in one body, there existsa corresponding point in the other. Such point-to-point geometrical correspondence normally allowsa single characteristic linear dimension to be used in representing the sizes of model and prototype.For instance, a cylindrical model ladle in the laboratory can be represented by its diameter d, andcompared to its equivalent full-scale counterpart by noting its relative size or scale according to

(11.1)

FIGURE 11.1 Three essential components of a successful investigation.

λdm

d p

------=

in which

λ

is called the

geometrical scale factor.

Suffixes

m

and

p

denote model and prototype,respectively.


Dynamic similarity is concerned with the forces that accelerate or retard fluid motion in dynamicsystems. It requires that the corresponding forces acting at corresponding times and correspondinglocations in the model and prototype should also correspond. Various forces acting on a moltensteel element and of relevance to secondary steelmaking operations have already been summarizedin Table 3.1. It is instructive to note here that dynamic similarity in geometrically similar systemsautomatically entails kinematic similarity. Since the typical forces in fluid flow systems are pressure(Fp), inertial (FI), gravity (FG), viscous (Fµ) and surface tension forces (Fσ), the dynamic similarityat a given point can be expressed as

(11.2)

Rearranging in terms of appropriate grouping of forces, several identities can be obtained fromEq. (11.2) and represented as

(11.3)

In modeling heat transfer operations, thermally similar systems are those in which correspondingtemperature differences bear a constant ratio to one another at corresponding positions. When thesystems are moving, kinematic similarity is a prerequisite to any thermal similarity. Thus, the heattransfer ratio by conduction, convection, and/or radiation to a certain location in the model mustbear a fixed ratio to the corresponding rates in the full-scale system.

Finally, for chemical similarity between a model and a prototype, the dynamic and thermalsimilarity first must be satisfied. The former, since mass transfer and chemical reaction usuallyoccur by convective and diffusive processes during motion of reacting material through the system,and the latter since chemical kinetics are normally temperature dependent.

11.2.2 PHYSICAL MODELING OF FLUID FLOW IN LADLES

Studies of fluid flow in ladles containing molten steel often are not concerned with thermal andchemical similarity effects. Consequently, the equivalence between a model ladle and a prototypecan be adequately described via the geometric and the dynamic similarities.

The dynamic similarity criteria can be derived considering the force balance, which for a multi-dimensional flow situation under steady-state conditions can be expressed in compact tensorialform as*

(11.4)

* In Eq. (11.4), the subscript j can take values of 1, 2, 3, denoting the three space coordinates. When a subscript is repeatedin a term, summation of three terms is implied. For example,

F p ,m

F p , p

----------FI ,m

FI , p

---------FG ,m

FG , p

-----------Fµ ,m

Fµ , p

----------Fσ,m

Fσ, p

---------- CF= = = = =

Frm Fr p=

Rem Rep=

Eum Eup=

W em W ep=

∂∂x j

-------- ρu jui( ) ∂∂x1-------- ρu1u1( ) ∂

∂x2-------- ρu2u1( ) ∂

∂x3-------- ρu3u1( )+ +=

∂∂x j

------- ρu jui( ) ∂P∂xi

-------–∂

∂x j

------- µ∂ui

∂x j

------- Fi+ +=

The nondimensional equivalence of Eq. (11.4) is represented as


Eu = f(Re, Fr) (11.5)

It is therefore apparent that, to achieve the same ratio of pressure to specific volume kineticenergy (P/(U2) in the model (e.g., Euler number) and in the full-scale systems, the Reynolds andthe Froude number equivalence must be maintained between the two. Nevertheless, with typicallaboratory-scale water models employed in physical modeling (e.g., λ less than unity and typicallyvarying in the range of 0.1 to 0.4), it is impossible to achieve both Reynolds and Froude similaritycriteria simultaneously. Assuming flows in typical gas-stirred ladles to be dominated largely by theinertial and buoyancy forces (e.g., Froude dominated), the dynamic similarity criterion betweenthe model and full-scale ladle systems can be approximated from Eq. (11.5) as

Frm = Frp (11.6)

Mazumdar5 has shown that, for ladle metallurgy operations, the Froude number can be expressed as

(11.7)

in which is the average plume rise velocity [Eq. (3.67)]. In a recent work,6 it has been shown that, for Froude-dominated ladle flows, the following

equality must be maintained between the model and the prototype:

(11.8)

Invoking geometric similarity, namely

Eq. (11.8) can be transformed into

Qm = λ5/2 Qp (11.9)

Equation (11.9) provides the requirement for dynamic similarity between a model ladle and itscorresponding full-scale system under an isothermal situation. The validity of Eq. (11.9) has beendemonstrated experimentally by carrying out observations in various reduced-scale aqueous models.

11.2.3 MATHEMATICAL MODELING

A mathematical model is a set of equations, algebraic or differential, that may be used to representand predict certain phenomena. The term model as opposed to law implies that the relationshipsemployed may not be quite exact, and thus the predictions derived from them may be onlyapproximate.

Within the scope of the present discussion, two different types of mathematical models maybe envisaged.

1. fundamental or mechanistic models2. empirical models

Frup

2

gH-------=

up

Q2

gR5---------

m

Q2

gR5---------

p

=

Hm

H p

-------Rm

Rp

------ λ= =

Fundamental

or

mechanistic models

will be the central point of discussion in this chapter.These are based on basic physical or chemical laws such as thermodynamic equilibria; chemical


kinetics; conservation of mass, momentum, and energy; and so on. Owing to their fundamentalnature, such models tend to have sufficiently general validity. Empirical models, in contrast, arebased on direct observations of a particular system and not on fundamentals. At times, if the processunder investigation is extremely complex, there is no alternative to their use. Nevertheless, suchmodels tend to be specific to a set of operating conditions. Consequently, great care needs to beexercised if these relationships are to be extrapolated or generalized.

The general methodology of mathematical model development3 in a typical situation is illus-trated in Figure 11.2. It is seen that the first step is identification of the problem. Once the keyparameters affecting the process are identified, the next task is to express this physicochemicalpicture in mathematical form (viz., problem formulation). Following formulation, it is often desir-able to carry out scaling, scoping, and order-of-magnitude analysis, as these provide useful insightinto the behavior of the system. The next two parallel stages are computer prediction and experi-mental work, since purely analytical results or order-of-magnitude estimates will not provideadequate detail. Experimental work will be needed principally for testing the appropriateness oftheoretical predictions. Judicial synthesis of prediction and measurement is pivotal to the entireexercise and form an integral component toward successful implementation of the model.

The next logical question one may address at this point is, “How is a mathematical modelformulated?” To this end, depending on the scope of application, as a starting point one can considerthe various components or building blocks of mathematical models (instead of starting from thefirst principles and consideration of elementary control volumes). Some of these that are of relevanceto the present discussion are summarized in Table 11.1. The building blocks and system geometry

ProblemIdentification

ProblemFormulation

Scoping, ScalingAsymptotic Solutions

NumericalSolutions

Experiments

Synthesis

Implementation

FIGURE 11.2 General methodology of mathematical model development.

along with the appropriate set of boundary conditions, then allow one to put together the mathe-matical models in explicit form. In subsequent sections, mathematical model development for


various secondary steelmaking operations are outlined.

11.3 MODELING TURBULENT FLUID FLOW PHENOMENA

The chemical efficiencies of typical processing operations carried out in steelmaking reactors areintrinsically related to their hydrodynamics. Consequently, for any effective process analysis,(thermal and material mixing, melting of solids, dissolution of solids, etc.) detailed knowledge ofthe flow characteristics in the system is a prerequisite. It is to be mentioned here that, owing to thelarge size of metallurgical processing vessels and the intense stirring conditions prevalent therein,fluid flow conditions in metallurgical reactors are invariably turbulent (see also Section 3.1.5).Naturally, therefore, flow calculation in metallurgical systems is likely to entail complexity.

11.3.1 GOVERNING EQUATIONS OF FLUID FLOW

In simulating flow phenomena, the system geometry together with the dimensionality of the problemneeds to be ascertained first. Following this, a decision is to be taken whether simulation for transientor steady-state conditions is to be carried out. Once such decisions are made, the governing equationsof fluid flow can be conveniently presented in appropriate form considering the building blocks ofthe flow model outlined already.

For the present illustration, a steady-state, two-dimensional, incompressible flow situation hasbeen considered. In terms of a cylindrical coordinate system (r, θ, z), the governing flow equationsunder turbulent flow conditions can then be represented as shown below.

Equation of Continuity

(11.10)

Equation of Motion in Axial Direction

(11.11)

where

TABLE 11.1Building Blocks of Mathematical Models

Sl. No. Component Application

1 Navier–Stokes equations Fluid flow

2 Fourier’s law Heat conduction

3 Fick’s law Diffusive mass transfer

4 Convection-diffusion Heat and mass transfer in moving media

5 Maxwell’s equation Electrodynamics, MHD

6 Thermodynamics Equilibria phase diagrams

7 Kinetic law Rate prediction

∂ ρuz( )∂z

----------------1r--- ∂

∂r----- ρrur( )+ 0=

∂∂z----- ρuzuz( ) 1

r--- ∂

∂r----- ρruzur( )+ ∂P

∂z------–

∂∂z----- µeff

∂uz

∂z--------

1r--- ∂

∂r----- µeff

∂uz

∂r--------

Sz+ + +=

(11.12)Sz∂∂z----- µt

∂uz

∂z--------

1r--- ∂

∂r----- rµt

∂ur

∂z--------

Fz+ +=


Equation of Motion in Radial Direction

(11.13)

where,

(11.14)

Equations (11.10) through (11.14) are known as the turbulent Navier–Stokes equations or Reynoldsequations. The F variables are the various body forces acting on the fluid element, which mayinclude buoyancy, drag, etc. Finally, µeff is the effective viscosity (= µL + µt) and is derived froma turbulence model.

11.3.2 THE TURBULENCE MODEL

The two equation k-ε turbulence model7 has been very popular for modeling turbulent flowsencountered in metallurgical processing operations. According to the model, the conservation of k[turbulence kinetic energy = ] and ε (= –dk/dt), can be expressed in terms oftwo transport type equations in terms of the cylindrical coordinate system for steady, 2-D flowconditions as shown below.

Turbulence Kinetic Energy

(11.15)

where Sk, the net source term, can be represented as

Sk = G – ρε (11.16)

and

(11.17)

Dissipation Rate of Turbulence Energy

(11.18)

where,

∂∂z----- ρuzur( ) 1

r--- ∂

∂r----- ρrurur( )+ ∂P

∂r------

∂∂z----- µeff

∂ur

∂z--------

1r--- ∂

∂r----- rµeff

∂ur

∂r--------

Sr+ + +–=

Sv∂∂z----- µt

∂uz

∂r--------

1r--- ∂

∂r----- rµt

∂ur

∂r--------

µt

2ur

r2-------- Fr+–+=

1 2⁄( ) ux′ 2 uy

′ 2 uz′ 2+ +( )

∂∂z----- ρuzk( ) 1

r--- ∂

∂r----- ρrurk( )+

∂∂z-----

µeff

σk

------- ∂k∂z------⋅

1r--- ∂

∂r-----

rµeff

σk---------- ∂k

∂r------⋅

Sk+ +=

G µt 2∂uz

∂z--------

2 ∂ur

∂r--------

2 ur

r----

2

+ +∂uz

∂r--------

∂ur

∂z--------+

2

+

=

∂∂z----- ρuzε( ) 1

r--- ∂

∂r----- ρrurε( )+

∂∂z-----

µeff

σε-------∂ε

∂z-----

1r--- ∂

∂r----- r

µeff

σε------- ∂ε

∂r-----×

Sε+ +=

(11.19)SεC1εG

k-------------

C2ρε2

k--------------–=


The effective viscosity,

µeff = µL + µ t (11.20)

where,

(11.21)

Cµ, C1, C2, σk, and σε appearing in Eqs. (11.15), (11.18), etc. are the empirical constants of the k-ε turbulence model. The standard values of these coefficients are7 C1 = 1.43, C2 = 1.92, Cµ = 0.09,σk = 1.0m and σε = 1.30.

11.3.3 BOUNDARY CONDITIONS

The boundary conditions are problem dependent. Three kinds of boundaries are typically encoun-tered in dealing with flow simulation in metallurgical systems. These include the free surface ofliquid, the symmetry axis (if this exists for a given problem), and solid vessel walls. As far asboundary conditions for velocity components are concerned, no slip conditions are applied at thesolid walls while, across the free surface, zero shear is assumed to be transmitted. Gradients of allthe velocity components at the axis of symmetry are normally assumed to vanish. Similarly, thevalues of k and ε at the walls are usually set to zero. Meanwhile, across the symmetry plane andfree surface, zero gradients of k and ε are usually applied.

Since variations of flow properties are normally steep in the vicinity of solid walls, specialtreatments for the velocity components as well as turbulence parameters are required in theimmediate neighborhood of solid walls so as to estimate the distributions of flow variables realis-tically. These include logarithmic law for the parallel to wall flow component, local equilibriumbetween turbulence production and dissipation, etc. A detailed discussion of these is, however,beyond the scope of the present discussion. Interested readers are referred to Refs. 7 and 8 forfurther details.

11.3.4 HYDRODYNAMIC MODELING OF AXISYMMETRIC GAS INJECTION OPERATIONS IN LADLES

A schematic representation of central gas injection through a tuyere in a cylindrical-shaped ladlehas already been shown in Chapter 3 (see Figure 3.11).

To mathematically model flow and the associated phenomena in Ar/N2-stirred ladles, threedifferent types of approaches have been applied.9 Of these, quasi-single phase models have beenrelatively more popular. In this, the rising gas-liquid mixture is assumed to be a homogeneousliquid of reduced density. In general, the gas volume fraction within the plume, along with thelatter’s geometry (determined empirically), are specified a priori in the calculation procedure. Thesedata constitute important input parameters for the mathematical model. The mathematical modelfor a steady, axisymmetric gas injection configuration (in terms of r, θ, and z coordinate axes) isidentical to those presented in Sec. 11.3.1. In addition, Fz = ρLgα (e.g., the buoyancy force per unitvolume) and ρ = αρg + (1 – α)ρL are to be considered in the model equations.

The term involving the gas voidage α, considered above for the axial momentum equation (i.e.,ρLgα), is used to model the buoyancy force generated by differences in density between the bulk

µtCµρk2

ε---------------=

single-phase and the plume two-phase regions. The numerical value of α and its distribution in theflow domain are normally known a priori.


The boundary conditions used for the set of partial differential equations are

At the axis of symmetry (r = 0, 0 ≤ z ≤ H),

At the free surface (z = H, 0 < r < R),

At the side walls and bottom surface (z = 0, 0 ≤ r ≤ R and r = R, 0 ≤ z ≤ H),

uz = 0; ur = 0; k = 0, and ε = 0

As a typical example of the model’s predictive capabilities, predicted flow fields generated byargon stirring in a typical 250 tonne cylindrical ladle by a flow of 4 × 10–3 Nm3/s from a centrallylocated porous plug is shown in Figure 11.3.2 The flow field as depicted in Figure 11.3 clearlyshows a recirculating vortex located high in the ladle and displaced toward the outside wall. In a

∂k∂r------ 0=

uz 0=

∂uz

∂r-------- 0= and ∂ε

∂r----- 0=

∂k∂z------ 0=

uz 0=

∂ur

∂z-------- 0;= and ∂ε

∂z----- 0=

FIGURE 11.3 Predicted flow pattern in a 250 tonne ladle at a gas flow rate of 4 × 10–3 m3 s–1 through acentrally located porous plug.2

similar fashion, one can show the predicted variation of turbulence kinetic energy in the system.The latter parameter is of importance particularly if the objective of flow calculation is to predict


heat and mass transfer phenomena (see later).In Figure 11.4, the predicted flow pattern in a 150 tonne ladle is shown when gas is injected

through a partially submerged lance.10 Qualitatively, the flow patterns in Figures 11.3 and 11.4 areessentially identical, although the intensity of flow in the latter case is less pronounced.

In Figure 11.5, the predicted flow field in a C.A.S. (composition adjustment by sealed argonbubbling) system is shown.10 There, as seen, the placement of a baffle over the rising plumesignificantly alters the flow pattern in comparison to those shown in Figures 11.3 and 11.4. It isimportant to mention here that the characteristics of the flow considerably influence heat and masstransfer operations (such as melting and dissolution of solid additions, material and thermal mixing,etc.) carried out in ladles. The flow fields, as pointed out earlier, have to be known a priori so asto predict these “convection-diffusion” phenomena.

11.4 MODELING OF MATERIAL AND THERMAL MIXING PHENOMENA

11.4.1 GOVERNING EQUATION OF MATERIAL MIXING

Mixing phenomena in metal processing units (e.g., ladles, torpedoes, etc.) can be predicted fromthe first principles considering an appropriate species conservation equation.11 In the presence of

FIGURE 11.4 Predicted flow pattern in a 150 tonne ladle at a gas flow rate of 4 × 10–3 m3 s–1 through acentrally located partially submerged lance.9


a two-dimensional velocity field (Section 11.3.1), the mass conservation of an inert tracer i (e.g.,mi is the mass fraction of the species i) can be expressed in a cylindrical coordinate system via thefollowing convection-turbulent diffusion equation:

(11.22)

The eddy diffusivity, Dt(≈ Deff = D + Dt) and the eddy kinematic viscosity, , areconventionally taken to be numerically equal. From the viewpoint of engineering calculations, theassumption of equality (Sct = νt/Dt = 1) has proven to be reasonably adequate for a large varietyof turbulent flows. It is therefore apparent that provided the flow parameters (uz , ur, etc.) andturbulence viscosity (µ t) are known with reasonable certainty, the material mixing rate [e.g., mi (r,z, t) fields] can be fairly accurately predicted.

Since the added species cannot cross the domain boundaries, a zero flux condition across thebounding surfaces appears to be the most obvious choice for defining the boundary conditions forEq. (11.22). In addition, Eq. (11.22) would also require an appropriate initial condition of mi.

11.4.2 GOVERNING EQUATION OF THERMAL ENERGY MIXING

The conservation of thermal energy in a given two-dimensional flow domain can also be describedconveniently via a transport-type equation such as Eq. (11.22). Thus, assuming no internal gener-

FIGURE 11.5 Predicted flow pattern in a 150 tonne C.A.S. ladle at a gas flow rate of 4 × 10–3 m3 s–1 througha centrally located porous plug.9

∂∂t----- mi( ) ∂

∂z----- uzmi( ) 1

r--- ∂

∂r----- rurmi( )+ +

∂∂z----- Deff

∂mi

∂z--------

1r--- ∂

∂r----- rDeff

∂mi

∂r--------

+=

ν t =µt ρ⁄( )

ation or dissipation (ST = 0) of thermal energy, the governing equation, in terms of a cylindrical-polar coordinate system can be described as


(11.23)

In Eq. (11.23), λeff is the effective (molecular + turbulent) thermal conductivity and can beestimated from the theory of turbulence phenomena in the manner described in the precedingsection. It is, however, important to mention here that, unlike the turbulent Schmidt number, theturbulent Prandtl number (Prt = νt/α t) normally assumes a value somewhat lower than unity forliquid steel systems (about 0.7).12

Through the vessel walls and the free surface, heat will be lost from the system. Consequently,such information must be incorporated through the boundary conditions so that physically realisticthermal fields can be predicted via Eq. (11.23).

Normally, outgoing heat fluxes through vessel walls are experimentally determined and con-stitute important input parameters to the thermal energy transport equation. As an alternative to theflux boundary conditions, specified temperature boundary conditions can also be applied toEq. (11.23), provided that the time-temperature history at the bounding surfaces is known a priori.

11.4.3 MIXING IN AXISYMMETRIC LADLE REFINING OPERATIONS

A reasonable estimate of homogenization, or mixing rates, in industrial-scale operations can bemade in two ways.

1. Through direct measurements taken under typical operating conditions2. Using a theoretical approach outlined in the preceding section

As pointed out already, the most viable approach for investigating mixing phenomena in a ladlerefining operation appears to be the route based on the numerical solution of Eq. (11.22) inconjunction with an appropriate set of boundary conditions.

To demonstrate the usefulness of mixing time calculations in gas-stirred ladles, we first lookat the rate of mixing near the free surface in two different axisymmetric gas-stirring configurations,namely the normal central injection and the C.A.S. alloy addition system,11 and demonstrate thekind of inferences that can be drawn from such theoretical calculations. Thus, on the basis of anumerical solution to Eq. (11.22), predictions were made for mixing times in C.A.S. and conven-tional argon stirring operations in a 150 tonne ladle at a blowing rate of 0.0188 m3/s. Predictedmixing times are approximately 280 and 155 s, respectively. Of particular importance, however,are the rates of mixing in the vicinity of free surfaces. As shown in Figure 11.6, the rates of mixingnear the free surfaces are very different for the two situations. This essentially arises because ofthe surface baffle in the C.A.S. system, causing a sluggish rate of liquid mixing near the freesurface. It is to be noted here that this effect is a design feature to ensure minimal reaction ofdissolved solute additions with the overlying slag phase.

Now, we turn our attention to the issue arising out of the dissolution of alloying additions atvarious locations in the bath and their subsequent mixing in the C.A.S. reactor vessel. It is importantto mention here that alloying additions have widely different densities, and therefore these arelikely to melt or dissolve in specific regions in the melt (e.g., additions heavier than steel wouldalways settle at the bottom and then melt or dissolve). Computed mixing rates near the free surfacefor various types of additions in the C.A.S. system are shown in Figure 11.7 at a gas flow rate of0.0188 m3/s. As such, at this gas flow rate, about 400 seconds of bubbling is needed to dispersethe dissolved additions homogeneously throughout the bath. Furthermore, it can be seen that therate of transfer of dissolved additions from the central baffled region to the slag–metal interface

ρC∂T∂t------- ∂

∂z----- ρuzCT( ) 1

r--- ∂

∂r----- ρrurCT( )+ +

∂∂z----- λ eff

∂T∂z-------

1r--- ∂

∂r----- rλ eff

∂T∂r-------

+=


(depicted by mixing curves for region C) is extremely sluggish. Consequently, such additiontechniques have the potential for improving the recovery rates of buoyant additions.

11.5 MODELING OF HEAT AND MASS TRANSFER BETWEEN SOLID ADDITIONS AND LIQUID STEEL

The melting and/or dissolution of solid additions in liquid steel baths is an important aspect ofalloying practices in steelmaking operations. In Sections 4.3.2 and 4.4.1, fundamental aspects of

FIGURE 11.6 Predicted mixing rates in the vicinity of the free surface in a C.A.S. and conventional argonstirring operation at a gas flow rate of 0.0188 m3 s–1.10

FIGURE 11.7 Predicted mixing rates in the vicinity of the free surface in a C.A.S. ladle for various typesof alloying additions (buoyant, neutrally buoyant, nonbuoyant, etc.) at a gas flow rate of 0.0188 m3 s–1.10

solid–liquid interactions were addressed in some detail. In this section, mathematical modeling ofheat and mass transfer rates between solid and liquid steel is presented.


11.5.1 PREDICTION OF MELTING RATES

As mentioned in Section 4.4.1, estimation of heat and mass transfer rates between solid additionsand liquid steel in metal processing units requires a priori knowledge of the distribution of flowvelocities and turbulence parameters in the system. Consequently, for the prediction of meltingrates, it is assumed here that hydrodynamic conditions in the reactor vessel are known. Thus, inthe presence of a known velocity field, the principal task is to obtain an appropriate value of thesurface heat transfer coefficient (h), which then allows for the estimation of melting rates. Surfaceheat transfer coefficient can be obtained from numerous available empirical correlations. Forspherical shaped addition, the following is recommended:13

(11.24)

In Eq. (11.24), ReD is the object Reynolds number based on the diameter of the spherical addition,and µb and µo are, respectively, the viscosity of the liquid at the bulk and reference temperatures.

Under a given set of operating conditions, knowing the precise distribution of velocity (andthus the Reynolds number) fields in the immediate neighborhood of the spherical shaped additions,the Nusselt number can be readily estimated via Eq. (11.24). From this, the appropriate value ofheat transfer coefficient can also be determined. Using such heat transfer values, the completemelting time can be obtained through a simple heat balance, which can be expressed in terms ofthe following an ordinary differential equation, e.g.,

(11.25)

In Eq. (11.25), ρs is the density of the solid, ∆H is the total heat requirement (sensible + latent),and Tb and Tm are, respectively, the bulk and the melting temperature. The initial condition applicableto Eq. (11.25) is t = 0, R = Ri.

11.5.2 PREDICTION OF DISSOLUTION RATES

Additions having melting points higher than the bulk steel temperature will normally undergo nomelting and, instead, dissolve directly into liquid steel. For such additions, the dissolution or masstransfer rates from the solid can be estimated from an appropriate correlation following exactly thesimilar approach to that outlined above. Some of the available mass transfer correlations havealready been discussed in Section 4.2.2. The following is, however, recommended for sphericallyshaped additions:14

Sh = 2 + 0.6 Re(0.5+0.1I)Sc0.33 (11.26)

Equation (11.26) provides a position dependent mass transfer coefficient (Sh = Kmd/D), since Reand I (= Ret /Re), the intensity of turbulence, are local hydrodynamic variables. As pointed outalready, Re and I prevalent in the neighborhood of the solid object are to be estimated a priorifrom an appropriate turbulent flow model. The corresponding form of Eq. (11.25), valid for masstransfer from a spherical shaped solid object, assumes the form

(11.27)

Nu 2– 0.4ReD1 2⁄ 0.06ReD

2 3⁄+( )Pr0.4 µb/µo( )0.25=

dRdt-------–

hρs∆H------------- T b T m–( )=

dRdt-------– Km

Cs* Cb–ρs

------------------ =

in which Km is the mass transfer coefficient and is the equilibrium concentration of the dissolvingspecies at the solid–liquid interface.

Cs*


It is instructive to note here that estimates of heat and mass transfer rates via Eqs. (11.24)through (11.27) are likely to provide only a first-hand estimate since, in practice, the overall kineticsof alloy addition procedure is far more complex than Eqs. (11.24) through (11.27) appear to indicate.Thus, during projection of a solid addition into the steel melt, a steel shell typically forms aroundthe addition. This steel shell subsequently melts back and exposes the solid addition to bulk liquidsteel. Furthermore, the additions upon projection move subsurface for a while and, during that timeperiod, are likely to encounter varying hydrodynamic conditions (e.g., fluid velocity and turbulenceintensity). It is therefore clear that a realistic prediction for industrial-scale alloying practice canbe made only if all these diverse aspects are considered in the convective heat and mass transfermodel. In the following section, modeling of subsurface trajectory of spherically shaped additionsin steel melt is presented.

11.5.3 PREDICTION OF SUBSURFACE TRAJECTORY OF SOLID ADDITIONS

For a submerged spherical particle moving through a two-dimensional flow field (Section 11.3.4),the two relevant components of Newton’s second law of motion are as follows.

In the vertical (z) direction,

(11.28)

and in the horizontal (r) direction,

(11.29)

The two corresponding kinematic relationships are

(11.30)

and

(11.31)

The instantaneous drag coefficient, CD in Eqs. (11.28) and (11.29), is based on particles’ instanta-neous velocity and can be deduced from the appropriate CD ~ Re relationship. Furthermore, urel

and vrel are the relative velocity between the particle and the fluid in z and r directions, respectively.It is through these parameters that the fluid’s motion in the vessel influences the subsurface trajectoryof the particle [viz., calculation of subsurface trajectory via Eqs. (11.29) and (11.30) can be carriedout provided the fluid velocity in the system are known a priori]. The following set of initialconditions are applicable to Eqs. (11.29) through (11.31).

1. At t = 0 and z = 0, up = Uentry in the vertical direction.2. At t = 0 and r = rentry, vp = Ventry (= 0 for vertical entry) along the horizontal direction.

34---πRP

3 ρL CAρL+( )dup

dt-------- 4

3---πRp

3 ρp ρL–( )CD

2------- πRp

2ρLurel urel2 vrel

2+( )1 2⁄⋅–=

34---πRp

3 ρL CAρp+( )dν p

dt---------

CD

2-------– πRp

2ρLνrel urel2 νrel

2+( )1 2⁄=

dzdt----- up=

drdt----- vp=

11.5.4 DISSOLUTION OF FERRO-ALLOYS IN AXISYMMETRIC GAS-STIRRED LADLES


As a typical example of the model’s (Section 11.5.3) capabilities, numerically computed trajectoriesof four typical spherical additions (Al, Fe-Si, Fe-Mn, and Fe-Nb) in a 150 tonne ladle during C.A.S.operations are illustrated in Figure 11.8.15 These trajectories show that buoyant additions such asaluminum and ferro-silicon would almost instantaneously resurfaceand would proceed to melt within the central slag free region. Ferro-manganese and additions withsimilar densities (γ = 0.44), on the other hand, may undergo subsurface melting rather than meltingwithin the central-slag free region. Heavier additions, such as ferro-niobium or ferro-tungsten (γ >1) will settle to the bottom of the vessel and only then gradually dissolve. However, since thebottom part of the ladle’s contents is relatively quiescent, such additions will typically experienceconsiderably longer dissolution times. (Note that dissolution time is directly related to the flowvelocities.)

Complete dissolution times for 75 wt.% ferro-tungsten spheres (initial diameter 50 mm) as afunction of gas flow rates in an argon stirred 60 tonne ladle are shown in Figure 11.9. These werederived16 through the numerical solution of the appropriate turbulent Navier–Stokes equation inconjunction with the following mass transfer correlation:

Sh = 2 + 0.73(Rcloc)0.25(Ret)0.32(Sc)0.33 (11.32)

FIGURE 11.8 Predicted subsurface trajectories of four different types of alloying additions in a 150 tonneC.A.S. ladle at a gas flow rate of 0.0188 m3 s–1.14

γ( ρp ρL⁄ 0.4 or 0.6 )= =


There, complete dissolution times for 50 mm dia. Fe-W spheres appear to be on the order of15 min. It is instructive to note here that complete mixing times (Section 11.4.3) are only a smallfraction of alloy dissolution times. From such time scales, first-hand estimates of inert gas purgingtimes in ladles during alloy homogenization can be conveniently determined.

11.6 NUMERICAL CONSIDERATIONS

The general structure of the relevant differential equations describing the conservation of heat,mass, and momentum appear to indicate that all the dependent variables of interest seem to obeya generalized conservation principle. If the dependent variable is denoted by φ, the general differ-ential equation is

(11.33)

in which, Γ is the diffusion coefficient and Sφ is the corresponding source term. The quantities Γand S are specific to a particular meaning of φ.

The four terms in the general differential equation are the unsteady term, the convection term,the diffusion term, and the source term. The dependent variable φ can stand for the variety ofdifferent quantities such as the mass fraction of a chemical species, the enthalpy or the temperature,a velocity component, and so on. Accordingly, for each of these variables, an appropriate meaningwill have to be given to the diffusion coefficient Γ and the source terms S. These are summarizedin Table 11.2, in which various physical phenomena are represented mathematically as a specialcase of the general differential equation. Therefore, in principle, one is concerned with the numericalsolution of only Eq. (11.32). Thus, the concept of the general differential equation enables us toformulate a general numerical method.

The differential equations presented in earlier sections cannot be solved by analytical means,so numerical methods will have to be applied. A numerical method transforms a differential equationinto a set of algebraic equations. For a given differential equation, the resultant algebraic equationsare by no means unique and depend on the method of their derivation. The interested reader isreferred to the excellent text of Ref. 17 for a detailed discussion on the subject.

FIGURE 11.9 Predicted dissolution rates of 75 wt.% ferro-tungsten in a 60 tonne ladle as a function of gasflow rates.15

∂∂t----- ρφ( ) div ρuφ( )+ div Γ gradφ( ) Sφ+=

TABLE 11.2Various Physical Phenomena and Their Unified Mathematical Representation Via the


11.7 CONCLUDING REMARKS

This chapter has demonstrated the use and value of mathematical modeling and its application tosome typical secondary steelmaking operations. The content is introductory in nature, and thereforethe examples cited have been deliberately chosen from relatively simple and easy to understandconfigurations. Transient three-dimensional programs with two-phase capabilities are currentlyavailable for computational modeling of such fluid flow systems. In light of much more powerfulpresent-day computers and software packages, it is possible to address far more challenging andcomplex problems in the area of secondary steelmaking.

REFERENCES

1. Hills, A.W.D., Heat and Mass Transfer in Process Metallurgy, The Institute of Mining and Metallurgy,London, 1967.

2. Sahai, Y. and Guthrie, R.I.L., Advances in Transport Processes, 4, 1986, p. 1.3. Szekely, S., Metall. Trans., 19B, 1988, p. 525.4. Guthrie, R., Engineering in Process Metallurgy, Oxford Scientific Publication, Clarendon Press, 1989.5. Mazumdar, D., Metall. Trans., 21B, 1990, p. 925.6. Mazumdar, D., Kim, H.B., and Guthrie, R.I.L., Ironmaking Steelmaking (in press).7. Launder, B.E. and Spalding, D.B., Computer Methods in Mechanics and Engineering, 3, 1974, p. 269.8. Rodi, W., Turbulence Modeling in Hydrautrics—A state of the art review, Institute for Hydromechanics,

University of Karlesruhe, West Germany, 1980.9. Mazumdar, D. and Guthrie, R.I.L., Metall. Trans., 25B, 1994, p. 308.

10. Mazumdar, D. and Guthrie, R.I.L., Metall. Trans., 16B, 1985, p. 83.11. Mazumdar, D. and Guthrie, R.I.L., Ironmaking and Steelmaking, 13, 1985, p. 256.12. Asai, S. and Szekely, J., Ironmaking and Steelmaking, 3, 1975, p. 205.

General Differential Equation

Physical phenomena Governing differential equation

Meaning of φ, Γ, and S in the general differential equation

[Eq. (11.33)]

1. Steady heat conduction with no source

2. Transient heat conduction with a finite source

3. Diffusive mass transfer

4. Heat transfer in a media under motion

5. Mass transfer in a media under motion

6. Time averaged equation of motion under steady flow

7. Turbulence kinetic energy

∂∂x j

-------- k∂T∂x j

-------- 0=

φ T , Γ k , S 0 and u, 0

= == =

ρC∂T∂t------- ∂

∂x j

-------- k∂T∂x j

-------- Sr+=

φ T , Γ k /ρC , ρ 1, S ST /ρc , and u 0

= = == =

∂C∂t-------

∂∂x j

-------- D∂C∂x j

-------- =

φ C , Γ D , ρ 1, S 0, and u 0

= = == =

∂T∂t-------

∂∂x j

-------- u jT( )+k

ρC------- ∂T

∂x j

-------- =

φ T , Γ k /ρC , ρ 1, and S 0

= == =

∂ mi( )∂t

-------------∂

∂x j

-------- u jmi( )+ D∂mi

∂x j

--------- =

φ mi , Γ Dρ

,1 and S, 0

= == =

∂∂x j

-------- ρuiu j( ) ∂P∂xi

-------– ∂∂x j

--------+ µeff

∂ui

∂x j

-------- Su+= φ ui , Γ µ e , and S ∂ρ

∂xi

-------– Su+= = =

∂∂t----- ρk( ) ∂

∂x j

-------- ρu jk( )+ Γ k∂k∂x j

-------- G ε ∈–+=

φ k ,Γ Γ k , and S G ρ ∈–

= ==

13. Taniguchi S., Ohmi, M., Ishiura, S., and Yamauchi, S., Transactions of ISIJ, 23, 1983, p. 565.14. Iguchi M., Tomida, H., Nakajima, K., and Morita, Z., ISIJ International, 32, 1992, p. 857.


15. Mazumdar, D. and Guthrie, R.I.L., Metall. Trans., 24B, 1993, p. 649.16. Mazumdar, D., Kajani, S., and Ghosh, A., Steel Research, 61, 1990, p. 339.17. Patankar, S.V., Numerical Heat Transfer and fluid flow, Hemisphere Publishing Corp., New York, 1980.

Secondary Steel Making - Ahindra Ghosh

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