Secondary Steelmaking: Principles and Applications

SECONDARY STEELMAKING Principles and Applications Ahindra Ghosh, Sc.D. AICTE Emeritus Fellow Professor (Retired) Indian...

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SECONDARY STEELMAKING Principles and Applications

Ahindra Ghosh, Sc.D. AICTE Emeritus Fellow Professor (Retired) Indian Institute of Technology, Kanpur Department of Materials and Metallurgical Engineering

CRC Press Boca Raton London New York Washington, D.C.

©2001 CRC Press LLC

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Library of Congress Cataloging-in-Publication Data Ghosh, Ahindra Secondary Steelmaking : Principles and Applications p. cm. Includes bibliographical references and index. ISBN 0-8493-0264-1 1. Steel. I. Title. TN730 .G48 2000 672—dc21

00-060865

This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage or retrieval system, without prior permission in writing from the publisher. The consent of CRC Press LLC does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific permission must be obtained in writing from CRC Press LLC for such copying. Direct all inquiries to CRC Press LLC, 2000 N.W. Corporate Blvd., Boca Raton, Florida 33431. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation, without intent to infringe.

© 2001 by CRC Press LLC No claim to original U.S. Government works International Standard Book Number 0-8493-0264-1 Library of Congress Card Number 00-060865 Printed in the United States of America 1 2 3 4 5 6 7 8 9 0 Printed on acid-free paper

©2001 CRC Press LLC

Dedication to Dr. G. P. Ghosh (Late) Prof. T. B. King (Late) Prof. A. K. Seal

©2001 CRC Press LLC

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. The product 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 nonmetallic inclusions, 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 as secondary steelmaking, which is concerned with further refining and processing of liquid steel after it is tapped into the ladle from the primary steelmaking furnace. Secondary steelmaking is a major thrust area in modern steelmaking technology and has witnessed significant advances in the last 30 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 secondary steelmaking. Chapters 2 through 4 briefly review relevant scientific fundamentals, viz., thermodynamics, fluid flow, mixing, mass transfer, and kinetics relevant to secondary steelmaking. Chapters 5 through 10 deal with reactions, phenomena, and processes that are of concern in secondary steelmaking. 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 as clean steel calls for a variety of measures at different processing stages. An attempt has been made to present an integrated picture of this in Chapter 10. Mathematical modeling is an important component of process research nowadays. The basics as 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 secondary steelmaking processes, it contains brief information on the processes and modern technological advances as well. Synthesis of science with technology is one of the objectives. The textbook style of writing has been adopted. Some examples and their solutions also have been included. References have been included at the end of each chapter. Hence, the author hopes that this text will be found useful not only by students and teachers, but also by steelmakers and research and development engineers interested in the field. Ahindra Ghosh

©2001 CRC Press LLC

Acknowledgments The author gratefully acknowledges the contribution of his colleague Dr. D. Mazumdar, who wrote Chapter 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 of the manuscript. Thanks are due to Mr. B. D. Biswas and Mr. J. L. Kuril for careful typing of the manuscript, Mr. A. K. Ganguly for tracing figures, and Dr. M.N. Mungole for helping with photographs. Financial assistance from the Centre for Development of Technical Education, Indian Institute of Technology, Kanpur, is gratefully acknowledged. Lastly, the work would not have been possible without the patience and cooperation of author’s wife Radha and other members of his family.

©2001 CRC Press LLC

About the Author Professor Ahindra Ghosh was born at Howrah, West Bengal, India, in 1937. He studied for his B.E. degree in Metallurgical Engineering at Bengal Engineering College and received the degree from Calcutta University in 1958. Subsequently, he received his Sc.D. degree from the Massachusetts Institute of Technology in 1963, specializing in extractive metallurgy. He served as Research Associate at Ohio State University, U.S.A., from 1963–64. Since 1964, he has been with the Department of Materials and Metallurgical Engineering, Indian Institute of Technology, Kanpur, where he retired as Professor in June, 2000, and is currently an Emeritus Fellow of All India Council of Technical Education. During this period, he also has spent short periods at 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 books and about 75 original research publications in reviewed journals. He also has delivered invited lectures 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 processes in ironmaking and steelmaking, with specific emphasis on sponge ironmaking, secondary steelmaking, ingot casting, and continuous casting. In these endeavors, Professor Ghosh also had significant interaction with industry in addition to his work with metallurgical fundamentals. He is 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 Metals and as a member or advisor for many professional activities. In recognition, he has been elected a Fellow of the Indian National Academy of Engineering for his distinguished contribution to engineering.

©2001 CRC Press LLC

Contents

Preface About the Author List of Symbols with Units Chapter 1

Introduction

1.1 History of Secondary Steelmaking 1.2 Trends in Steel Quality Demands 1.3 Scientific Fundamentals 1.4 Process Control References Chapter 2

Thermodynamic Fundamentals

2.1 Introduction 2.2 First and Second Laws of Thermodynamics 2.3 Chemical Equilibrium 2.4 ∆G0 for Oxide Systems 2.5 Activity–Composition Relationships: Concentrated Solutions 2.6 Activity–Composition Relationships: Dilute Solutions 2.7 Chemical Potential and Equilibrium 2.8 Slag Basicity and Capacities References Appendix Appendix Appendix Appendix

2.1 2.2 2.3 2.4

Chapter 3

Flow Fundamentals

3.1 Basics of Fluid Flow 3.2 Fluid Flow in Steel Melts in Gas-Stirred Ladles References Appendix 3.1 Chapter 4 4.1 4.2 4.3

Mixing, Mass Transfer, and Kinetics

Introduction Mixing in Steel Melts in Gas-Stirred Ladles Kinetics of Reactions among Phases

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4.4 Mass Transfer in a Gas-Stirred Ladle 4.5 Mixing vs. Mass Transfer Control References Appendix 4.1 Chapter 5

Deoxidation of Liquid Steel

5.1 Thermodynamics of Deoxidation of Molten Steel 5.2 Kinetics of the Deoxidation of Molten Steel 5.3 Deoxidation in Industry References Appendix 5.1 Chapter 6

Degassing and Decarburization of Liquid Steel

6.1 Introduction 6.2 Thermodynamics of Reactions in Vacuum Degassing 6.3 Fluid Flow and Mixing in Vacuum Degassing 6.4 Rates of Vacuum Degassing and Decarburization 6.5 Decarburization for Ultra-Low Carbon (ULC) and Stainless Steel References Chapter 7

Desulfurization in Secondary Steelmaking

7.1 Introduction 7.2 Thermodynamic Aspects 7.3 Desulfurization with Only Top Slag 7.4 Injection Metallurgy for Desulfurization References Chapter 8

Miscellaneous Topics

8.1 Introduction 8.2 Gas Absorption during Tapping and Teeming from Surrounding Atmosphere 8.3 Temperature Changes of Molten Steel during Secondary Steelmaking 8.4 Phosphorus Control in Secondary Steelmaking 8.5 Nitrogen Control in Steelmaking 8.6 Application of Magnetohydrodynamics References Chapter 9

Inclusions and Inclusion Modification

9.1 Introduction 9.2 Influence of Inclusions on the Mechanical Properties of Steel 9.3 Inclusion Identification and Cleanliness Assessment 9.4 Origin of Nonmetallic Inclusions 9.5 Formation of Inclusions during Solidification 9.6 Inclusion Modification References Chapter 10

Clean Steel Technology

10.1 Introduction ©2001 CRC Press LLC

10.2 Summary of Earlier Chapters 10.3 Refractories for Secondary Steelmaking 10.4 Tundish Metallurgy for Clean Steel References Chapter 11 Modeling of Secondary Steelmaking Processes Dipak Mazumdar, Ph.D. 11.1 Introduction 11.2 Modeling Techniques 11.3 Modeling Turbulent Fluid Flow Phenomena 11.4 Modeling of Material and Thermal Mixing Phenomena 11.5 Modeling of Heat and Mass Transfer between Solid Additions and Liquid Steel 11.6 Numerical Considerations 11.7 Concluding Remarks References

©2001 CRC Press LLC

List of Symbols with Units* a

specific surface area

m–1

a

acceleration vector

ms–2

A

area

m2

ai

activity of component i in a solution

—

Bi

Biot number

C

specific heat

CD

drag coefficient

Ci

concentration of component i in solution

— –1

–1

–1

Jmol K , Jkg K–1 — kg m–3

slag capacity for component i d

—

diameter

m

Di

molecular diffusivity of species i

m s–1

Dt

turbulent diffusivity

m2 s–1

E

internal energy, activation energy

Jmol–1

energy input in a gas-stirred bath

J

e

j i

Eu F F, F FD fi Fr Frm

2

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

—

Euler number

—

view factor

—

force, force vector

N

drag force

N

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

—

Froude number

—

modified Froude number

— ms–2

g

acceleration due to gravity

G

Gibbs free energy

Jmol–1, J

Gibbs free energy at standard state

Jmol–1, J

finite change in G, GO

Jmol–1, J

GO ∆G, ∆GO Gi m

partial molar Gibbs free energy of component i in solution

Gi

partial molar Gibbs free energy of mixing of component i in solution

Gr

Grasshof number

H hi

enthalpy

Jmol–1 J mol–1 — J mol–1, J

height of liquid bath

m

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

—

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

©2001 CRC Press LLC

I

intensity of turbulence

—

i, j

tensor arrays

—

Ji,x

flux of species i along x-coordinate

mol · m–2 s–1 Jkg–1

k

turbulent kinetic energy per unit mass of fluid

kc

specific chemical rate constant

ki

empirical rate constant for first-order process

ms–1

mass transfer coefficient for species i

ms–1

km,i K KM l Li m, M m˙ , M˙

ms–1, etc.

equilibrium constant

—

deoxidation constant for deoxidizer M

—

equilibrium constant involving metal M

—

a length parameter

m

partition coefficient of species i between two phases

—

mass

kg

rate of change of mass

mi

mass fraction of component i

Mi

molecular/atomic mass of species i

kg · s–1 — g · mol–1

Mo

Morton number

—

Nu

Nusselt number

—

P

pressure

pi

partial pressure of component i in a gas mixture

atm, Nm–2 atm

Pe

Peclet number

—

Pr

Prandtl number

—

q

quantity of heat

Q

r

volumetric gas flow rate

m s

—

heat flow rate

W

radial coordinate

m

universal gas constant vessel radius circulation rate of metal in vacuum degassing degree of desulfurization

S

–1

activity quotient

reaction rate R

J 3

entropy

mol · s–1 Jmol–1 K–1, m3 atm mol–1 K–1 m kg s–1 — 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

©2001 CRC Press LLC

s

tc

circulation time

s

te

exposure time

s

mixing time

s

tr

residence time

s

T

temperature

tmix

K

velocity, velocity vector

ms–1

ux

velocity along x-coordinate

ms–1

V

volume

w

quantity of work done

u, u

m3 J

We

Weber number

—

Wi

weight percent of component i in a solution

—

rectangular coordinates

m

Xi

mole/atom fraction of component i in solution

—

Y

degree of mixing

—

x, y, z

slag rate in desulfurization

kgt–1

Greek Symbols α

volume fraction of gas in gas-liquid mixture

—

αi

a-function for component i in a solution

—

Pauling electronegativity

—

γi

activity coefficient of component i in a solution

—

o i

Henry’s law constant for solute i in binary solution

γ

Γ

general symbol for diffusivity of heat, mass, momentum

δ

partial differential

∆

finite change of a quantity

— 2 –1

ms

as applicable

δc,eff

effective concentration boundary layer thickness

m

δu,eff

effective velocity boundary layer thickness

m

rate of dissipation of energy

W

emissivity of surface

—

ε εm

rate of dissipation of energy per unit mass

Wkg–1

θ

angle

λ

geometrical scale factor

λt

turbulent thermal conductivity

Λ

optical basicity

µ

viscosity

N sm –2

µi

chemical potential of component i in a solution

J mol–1

ν

kinematic viscosity

ρ

density

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degree, radian — W m–1 s–1 —

m2s–1 kg m–3

σ

surface/interfacial tension Stefan–Boltzmann constant

τ

general symbol for dependent variable in differential equation

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

©2001 CRC Press LLC

W m–2 K–4 N m–2

shear stress dimensionless residence time

φ

N m–1

— as applicable

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 electric furnaces, its treatment in a ladle was limited in scope and consisted of deoxidation, carburization by addition of coke or ferrocoke as required, and some minor alloying. However, more stringent demands on steel quality and consistency in its properties require controls that are beyond the capability of the steelmaking furnaces. This is especially true for superior-quality steel products in sophisticated applications. This requirement has led to the development of various kinds of treatments of liquid steel in ladles, besides deoxidation. These have witnessed massive growth and, as a result, have come to be variously known as secondary steelmaking, ladle metallurgy, secondary processing of liquid steel, or secondary refining of liquid steel. However, the name secondary steelmaking 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 of the continuous casting process, which requires more stringent quality control, is an added reason for the growth of secondary steelmaking. Steelmaking in furnaces, also redesignated now as primary steelmaking, 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 vacuum arc 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 included in secondary steelmaking. Harmful impurities in steel are sulfur, phosphorus, oxygen, hydrogen, and nitrogen. They occupy interstitial sites in an iron lattice and hence are known as interstitials. The principal effects of these impurities in steel are loss of ductility, impact strength, and corrosion resistance. When it comes to detailed consideration, each element has its own characteristic influence on steel properties. These will be briefly mentioned in subsequent chapters associated with them. Oxygen and sulfur are also constituents of nonmetallic particles in steel, known as inclusions. These particles are also harmful to properties of steel and should be removed as much as possible. Carbon is also present as interstitial in iron lattice. However, unlike the other interstitials, it is generally not considered 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 secondary steelmaking. 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 hydrogen content of liquid steel to prevent cracks in large forging-quality ingots. Later on, its objective also included lowering of nitrogen and oxygen contents. Purging with inert gas (Ar) in a ladle using porous bricks or tuyeres (IGP) came later. Its primary objective was stirring, with consequent homogenization of temperature and composition of melt. It offered the additional advantage of faster floating out of nonmetallic particles. It was also found possible to lower carbon to a very low value in stainless steel by treatment of the melt with oxygen under vacuum or along with an

©2001 CRC Press LLC

argon stream. This led to development of vacuum-oxygen decarburization (VOD) and argon-oxygen decarburization (AOD). Synthetic slag treatment and powder injection processes of molten steel in a ladle were started in late 1960s and early 1970s with the objective of lowering the sulfur content of steel to the very low level demanded by many applications. This led to the development of what is known as injection metallurgy (IM). Injection of powders of calcium bearing reagents, typically calcium silicide, was also found to prevent nozzle clogging by Al2O3 and lead to inclusion modification, which are of crucial importance in continuous casting as well as for improved properties. The growth of secondary steelmaking is intimately associated with that of continuous casting of steel. Up to the decade of the 1960s, ingot casting was dominant. Now, most of world’s steel is cast via the continuous casting route. The tolerance levels of interstitial impurities and inclusions are lower in continuous casting than in ingot casting, and this has made secondary refining more important. 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 steel prior to teeming into the continuous casting mold. In traditional pitside practice, without ladle metallurgical operations, the temperature drop of molten steel from furnace to mold is around 20–40°C. An additional temperature drop of about 30–50°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 adjustment during secondary steelmaking are very desirable. This has led to the development of special furnaces 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 further developments in this direction recently. Efforts are being made to install one unit only and even then 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 of several processes. For example, some modern vacuum degassers have provisions for oxygen blowing and 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 removed by pretreatment in a ladle during transfer to steelmaking shop. Similarly, phosphorus is removed primarily 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 the decade of the 1980s. Scholey3 has discussed this with special emphasis on Europe. Table 1.2 presents world consumption of steel products in 1990 and predictions of the same for A.D. 2000 as per 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 insignificant or negative in other countries. However, according to IISI, lack of tonnage growth does not indicate stagnancy. With continuous improvement in quality, less and less quantity of steel is being consumed for the same applications. If this point is taken into consideration, then there has been remarkable progress in steel technology on the quality front, and also improved yield. Figure 1.1 shows the change in product mix in the U.S.A. from 1925 to 1990, as compiled by Stubble.5 It demonstrates a massive shift in favor of sheet and strip; so much so that, in 1990, more than 50% of the product was in this shape, as compared to about 20% in 1925. This is the worldwide trend also. It is to be recognized that this shift was technologically possible to a large extent due to improvement in steel quality through secondary steelmaking. Near net shape casting, which is commercially expected in the near future, will require even more stringent control of impurities and inclusions. ©2001 CRC Press LLC

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 1.1 Various Secondary Steelmaking Processes and Their Capabilities Processes Item Desulfurization Deoxidation

VD

VOD

IGP

IM

VAD

LF

ASEA-SKF

minor

minor

minor

yes

yes

yes

yes

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.

With the passage of time, customers are demanding better and better quality steels, which means 1. 2. 3. 4. 5.

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

The above demands, combined with other requirements such as (a) the need for cost reduction in view of competition from polymers etc., (b) environmental pollution control, and (c) a relatively stagnant world steel market, pose enormous challenge to the steelmaking community. Before any ©2001 CRC Press LLC

TABLE 1.2 World Steel Consumption Millions of Metric Tonnes of Steel Products 1990 (actual) North America

2000 (predicted)

96.5

99

115.5

117

Japan

92.6

85

Latin America

22.3

35

P. R. China

54.9

80

Other Asian countries

78.6

120

European Community

Africa Former USSR and Eastern Europe Others Total

8.6

9

148.5

100

36.4

41

653.9

686

Source: data from Ref. 4.

secondary steelmaking treatment, the lowest levels of impurities attainable with present-day practices, including a metal pretreatment facility, would be approximately as follows: sulfur: phosphorus: nitrogen: hydrogen: carbon: oxygen:

100 ppm 20 ppm 40 ppm 5 ppm 400 ppm 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 North Sea gas.6 Maximum ppm in Steel, by Element Year 1983 1990 Long-term

C

S

P

H

N

O

400–600

20

150

–

100

–

10

15

–

35

20

S + O + P + N = 45 ppm

Ramaswamy6 has reviewed the subject and has outlined some of the quality requirements of line pipe steel for sour gas applications, steels for offshore platforms, bearing steels, steel for the rod and wire industry, and for power plant rotors. Figure 1.2 shows the trends in residuals attained by Japanese Steel Works.7 A special mention may be made of a recent spurt in demand for ultralow carbon steel (C < 30 ppm or so) for the manufacture of thin sheets by cold rolling with continuous annealing for automobiles. These steels not only have ultra-low C but have other residuals also at ultra-low levels, e.g., N < 15 ppm, S < 10 ppm, P < 15 ppm, H < 2 ppm. In addition, inclusion contents are also drastically lower as compared to regular steels. An expansion ©2001 CRC Press LLC

FIGURE 1.2 Minimum residual levels in steel in Japan.7

of the market for fine steels by approximately a factor of three has been predicted from 1985 to year 2000 by Japan’s fine steel study group.7 As shown in Table 1.1, all kinds of secondary steelmaking operations are capable of yielding steels with more cleanliness. Inclusions are generally harmful to the mechanical properties and corrosion resistance of steels. The choice of deoxidation practice combined with proper stirring is one 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 a source of impurity at such low impurity levels. Therefore, the success of secondary steelmaking processes is intimately linked with the development or use of newer refractory materials such as those high in alumina, zircon, magnesia, dolomite, etc. The cleanliness consciousness has increased to such an extent that trials are going on for filtering molten steel through ceramic filters to remove nonmetallic inclusions. The technique is still in the experimental stages. Inclusion modification is one of the techniques to render inclusions less harmful to the properties of steel. Injection of calcium into the melt is done for this purpose. Sometimes, rare earths are also employed.

1.3 SCIENTIFIC FUNDAMENTALS The application of scientific fundamentals is an important contributing factor to the progress of secondary 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 pace accelerated 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 relationships 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 thermodynamics called for new techniques to handle them. The participation of renowned physical chemists other than metallurgists made these possible. ©2001 CRC Press LLC

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 pyrometallurgical reactions and processes is a subject of engineering science in its own right. Knowledge already available in chemical engineering has been instrumental in its development. It had been recognized several decades back that lack of proper mixing in the liquid bath adversely affects the efficiency of steelmaking processes. Many investigations have been carried out on mixing, especially in the last two decades. Again, mixing, mass transfer, and phase dispersions depend on fluid flow in the bath. Such a flow is turbulent in steelmaking processes. Turbulence is a very complex phenomenon. Scientists and engineers in a variety of disciplines are concerned with 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 contributed significantly to our understanding of these aspects. Here, water typically simulates liquid metal. Transparent perspex or glass vessels allow flow visualization. Similarity criteria have been employed to various extents. A quantitative approach in the area of fluid flow, mixing, and mass transfer is based on fluid mechanics—especially as related to turbulent flow. Such computations involve computer-oriented numerical methods. Considerable advances have been made in this direction—so much so that these 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 from secondary steelmaking. It is neither possible nor necessary to list all these. Only some will be briefly 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 secondary steelmaking. Its measurement has been possible due to development of immersion oxygen sensor over 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 dissolved oxygen content through thermodynamic relations. Since the signal is electrical and obtained within 15 s of immersion, it is widely used to measure and control oxygen in molten steel. Through thermodynamic relations, it allows us also to know the soluble aluminum content of steel, which again is another valuable piece of information that steelmakers desire. An immersion oxygen sensor has also been widely employed in a variety of scientific and technological investigations related to deoxidation reactions and behavior of oxygen at different stages of steelmaking. The pioneering contribution of Kiukkola and Wagner (1956), who first set up such a cell for thermodynamic measurements in laboratory, is to be recognized. Iwase and McLean8 have reviewed sensors for iron and steelmaking. It may be noted that immersion electrochemical sensors for other elements, such as silicon and phosphorus, are being developed but are essentially 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 secondary steelmaking operations will not provide any benefit. For continuous casting, the use of either a submerged nozzle or shrouding of the nozzle by inert gas is the solution. For ingot casting, this is difficult to practice; in this case, management of teeming stream is the strategy. ©2001 CRC Press LLC

For efficient deoxidation, synthetic slag treatment, and injection processes, it is essential to prevent 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 of tapping with a very low quantity of slag. It is then modified by suitable additions for further processing. In traditional ladles, refractory lined stoppers were employed for flow control during teeming through the nozzle. A major development has been slide gate, which is superior as a flow control device. The traditional method of addition of aluminum to liquid steel as ingots or shots makes the efficiency of aluminum deoxidation poor as well as irreproducible, leading to serious control problems. The technology of mechanized feeding of aluminum wire is a significant improvement in this connection. Today, many plants have facilities for feeding wires consisting of Ca or CaSi powders clad in steel as well. This is an alternative to the injection of these powders into the melt by injection metallurgy techniques. Fruehan9 has reviewed some of these topics in a concise fashion. Of course, advances in instrumentation 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 to employ software based on mathematical models, as well as expert control systems by application of artificial intelligence techniques. The review by Bozenhardt and Shafer provides some information.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-situ analysis without the need of transferring samples to a separate analytical unit. These advances are being 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 induction furnace melting of steel has been known from the beginning of 20th century. A major application of EM stirring from the 1970s was in continuous casting. EM devices are also being employed increasingly in recent years in the secondary steelmaking area not only for stirring, but also for flow control, slag control, etc. This offers many advantages, including flexibility in the nature and intensity 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.

©2001 CRC Press LLC

2

Thermodynamic Fundamentals

2.1 INTRODUCTION Metallurgical thermodynamics belongs to the field of chemical thermodynamics, which is employed to predict whether a chemical reaction is feasible. It also allows quantitative calculation of the state of equilibrium of a system in terms of composition, pressure, and temperature, as well as determination 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 dealing with the basics of chemical-cum-metallurgical thermodynamics.1,2 The following is a very brief review only, with special emphasis on topics of relevance to secondary steel making. All reactions and processes tend towards the thermodynamic equilibrium. If sufficient time is allowed, then attainment of equilibrium is possible. Steelmaking reactions and processes are very fast due to their high temperatures. As a result, some of these have been found to approach equilibrium closely within the short processing time. Examples of this in secondary steelmaking are provided in subsequent chapters. Therefore, a full knowledge of thermodynamics is required for the understanding, control, design, and development of metallurgical processes. A discussion of thermodynamics requires precise definitions of some terms. For example, a system is defined as any portion of the universe selected for consideration. The rest of the universe outside 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 such as temperature, pressure, volume, surface tension, viscosity, etc. A complete listing of all the properties 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 a state is described by such variables, assumptions are made implicitly or explicitly. For example, if there 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 surface energy is negligible. Again P, V and T are interrelated. For example, for an ideal gas, PV = nRT

(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 v = f ( P, T )

(2.2)

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

©2001 CRC Press LLC

It should be noted that, among these variables, V is a property that depends on the amount of substance 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 extensive variable. Variables such as temperature, pressure, etc., which do not depend on mass, are known as intensive variables. It goes without saying that, if an equation contains a variable denoting an extensive property, then there must also be a term denoting mass or mol as in Eq. (2.1). If the latter is 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 intensive properties are of more general validity. A state can be characterized by state variables only when the system has come to equilibrium with respect to those variables. Then and only then can the state be correctly defined in terms of these variables. This also implies that the magnitudes of related intensive properties throughout the system are the same. Thermodynamic equilibrium necessarily requires the attainment of mechanical, thermal, and chemical equilibria. Mechanical interaction of a system with the surroundings is most commonly in the form of pressure. Therefore, in the absence of a field of force, mechanical equilibrium generally 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, there is no tendency for further reaction. It is possible that the system is at equilibrium with respect to some variables but not some others. This is known as partial equilibrium, and thermodynamics is capable of handling this as well. However, a precondition for handling any chemical equilibrium is the establishment of mechanical and thermal equilibria.

2.2 FIRST AND SECOND LAWS OF THERMODYNAMICS 2.2.1

STATEMENT

OF THE

FIRST LAW

dE = δq – δw, for an infinitesimal change where

(2.3)

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

For a finite change, ∆E = q – w

(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 violating the law of conservation of energy. To make these findings conform to the law of conservation of energy, the concept of internal energy (E) was proposed. Internal energy is the energy stored in the 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 a closed system, E = f ( P, T ) ©2001 CRC Press LLC

(2.5)

Again, we do not know or cannot measure the absolute value of E. All we can measure are changes in 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 content or enthalpy (H). By definition, H = E + PV

(2.6)

and hence is a state property. Differentiating, dH = ( dE + P dV ) + V dP = δq + Vdp

(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 calculated from 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 constant pressure. Even though the pressure fluctuates, it does not introduce any significant error if q is taken as ∆H. Molar ∆H (i.e., ∆H per mole) values for a variety of processes have been determined experimentally and are available in thermodynamic data books. Using them, heat requirements of processes 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 of a substance by 1 Kelvin. Specific heat at a constant pressure is given by ∂q ∂H C p =  ------- =  -------  ∂T  p  ∂T  p

(2.10)

Experimental Cp values are expressed as functions of temperature as c C p = a + bT + -----2 T

(2.11)

where T is temperature in Kelvins, and a, b, and c are empirical constants. Values of Cp may be found in standard thermodynamic data books. Table 2.1 presents values of Cp and enthalpies of transformations 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 variety of 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 as diffusion, free expansion of a gas, heat flow, etc., are not thermodynamically reversible.” ©2001 CRC Press LLC

TABLE 2.1 Specific Heats and Enthalpies of Transformation for Iron 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—Transition Metal Alloys, Cohesion and Structure Series, North-Holland, Amsterdam (l988).

2.2.4

REVERSIBLE PROCESSES

Heat and work are not properties of state. They are energy in transition, and thus the magnitude of q and w would depend on the path that the process takes in going from an initial to the final state. That is why δq and δw rather than dq and dw have been employed in Eq. (2.3). This is a great mathematical limitation. Hence, considerable effort has been made by thermodynamicists to examine under what conditions δw and δq can be related to state properties. Obviously, the path has 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 allowed to attain a new equilibrium, then again displaced infinitesimally and so on. Thus, it may be defined as “the hypothetical passage of a system through a series of equilibrium states.” A reversible process is very slow and impractical. No practical process is reversible in strict sense. However, the concept is very useful and a key one in thermodynamics. The term reversible has been coined because such a process can be reversed along the same path without leaving any permanent change in the system or 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 as reversible. It can be proved on the basis of Carnot’s Cycle that the quantity δqrev/T is dependent only on the initial and final states, where δqrev refers to δq along a reversible path. The following relationship has been thereby proposed. δq

rev ----------∑ T A→B

= S B – S A = ∆S

(2.12)

or, in differential form, δq rev ----------- = dS T

(2.13)

where A and B designate the initial and final states respectively, and S is a state function (i.e. state property) known as entropy. ©2001 CRC Press LLC

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 of absolute 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 ( ∆H ° 2000 – ∆H ° 298 ) in heating 1 mole of iron from 298 to 2000 K. Note that ( S° 298 ( α – Fe ) = 27.15J mol K ) –1

–1

Solution (a) Entropy of liquid iron at 2000 K, i.e. 1033

S

o 2000

(l) = S

o 298

( α – Fe ) +

∫

C p(α) ∆H a → B --------------- dT + -----------------+ T 1033

298 1665

∫

∫

C p(β) ∆H B → γ -+ --------------- dT + ----------------1187 T

1033

C p(γ ) ∆H γ → δ -+ ------------- dT + ----------------1665 T

1187

1187

1809

∫

C p(δ) ∆H -------------- dT + -----------m- + 1809 T

1665

2000

∫

C p(l) ------------- dT T

(E1.1)

1809

Substituting the values of Cp and ∆H for various transformations from Table 2.1. 1033

S

o 2000 ( l )

= 27.15 +

17.49 5105 –3 ------------- + 24.769 × 10 dT + -----------T 1033

∫ 298

1187

+

∫

37.66 670 ------------- dT + ------------ + T 1187

1033

1665

∫

7.7 837 –3 ------- + 19.5 × 10 dT + -----------T 1665

1187

1809

+

∫

2000

28.284 13807 –3 ---------------- + 7.531 × 10 dT + --------------- + T 1809

1665

∫

35.4 –3 ---------- + 3.745 × 10 dT T

1809

–1

= 105.5 J mol K

–1

(Ans.)

(b) Enthalpy change in heating 1 mole of iron from 298 to 2000 K 1033 o

o

H 2000 ( l ) – H 298 ( s ) =

∫

1187

C p ( α ) dT + ∆H α → b +

298

1665

+

∫ 1187

∫

C p ( β ) ( dT + ∆H β → γ )

1033

1809

C p ( γ ) dT + ∆H γ → δ +

∫

2000

C p ( δ ) dT + ∆H m +

1665

Substituting the values of Cp and ∆H from Table 2.1, ©2001 CRC Press LLC

∫ 1809

C p ( l ) dT

(E1.2)

1033

H

o 2000 ( l )

–H

o 298 ( s )

∫

=

1187

[ 17.49 + 24.769 × 10 T ] dT + 5105 + –3

298

∫

37.66 dT + 670

1033

1665

+

∫

[ 7.7 + 19.5 × 10 T ] dT + 837 –3

1187

1809

+

∫

[ 28.284 + 7.531 × 10 T ] dT + 13807 –3

1665

2000

+

∫

[ 35.4 + 3.745 × 10 T ] dT –3

1809

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

–1

(Ans.)

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, then combining the Eqs. (2.3) and (2.13) we obtain Eq. (2.14), i.e., dE = T dS – P dV

(2.14)

dH = dE + P dV + V dP

(2.15)

dH = T dS + V dP

(2.16)

again,

Combining Eqs. (2.8) and (2.14),

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 which are 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. Differentiating Eq. (2.17), dG = dE + P dV + V dP – T dS – S dT ©2001 CRC Press LLC

(2.18)

For a closed system, and for a reversible process (or at equilibrium), if the only work done is against 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) process would 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 of occurrence 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 number of moles of each. The word isothermal implies that the initial temperature at the beginning of the reaction and the final temperature (when equilibrium is reached) are the same. It is not necessary that 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 ∆G = ( 1G L + mG M ) – ( aG A + bG B )

(2.24)

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

G i – G i = RT ln a i o

where, G i = free energy of species i at its standard state f a i = -----oi = activity of species i at partial molar free energy G i fi fi = the fugacity of i at the state under consideration o = the fugacity at its standard state fi ©2001 CRC Press LLC

(2.25)

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 products are at their standard states, then for the reaction of Eq. (2.23), ∆G = ( lG L + mG M ) – ( aG A + bG B ) o

o

o

o

o

(2.26)

where ∆G is the standard free energy change of reaction represented by Eq. (2.23) at temperature T. Combining Eqs. (2.24) through (2.26), o

aL ⋅ aM -------------a b a A ⋅ aB 1

∆G = ∆G + RT ln o

m

(2.27)

or, ∆G = ∆G + RT ln Q

(2.28)

aL ⋅ aM Q = --------------a b a A ⋅ aB

(2.29)

o

where 1

m

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 and final pressures are the same, and also that thermodynamic equilibrium prevails, then ∆(G)P,T = 0 from 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 spontaneous 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 are satisfied: 1. The process should take place isothermally (i.e., the initial and final temperature should be 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 properties significantly, the condition that P should be constant is of no importance in situations we normally encounter. Hence, P = constant restriction shall be omitted from here on. ©2001 CRC Press LLC

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 from the elements, are now known for all inorganic compounds of interest in secondary steelmaking. o These are called standard free energies of formation ( ∆G f ) . A number of books carry compilations o of such data.3–6 Some values of ∆G f for compounds of interest in secondary steelmaking are presented in Appendix 2.1. Consider formation of an oxide from the elements represented by the following general reaction: 2X 2 ------- M + O 2 ( g ) = ---M X O Y Y Y

(2.31)

where M denotes a metal. X and Y are general symbols for oxide stoichiometry. Traditionally, free energy data shown in diagrams would be for a reaction such as Eq. (2.31), where the formation reaction involves only one mole of oxygen. This would make it convenient to compare the data for different oxides. If the metal, oxygen and oxide are in their standard states, then the free energy change is related to temperature as ∆G f = ∆H f – T∆S f o

o

o

(2.32)

where ∆H f and ∆S f are standard heat and entropy of formation, respectively. o

o

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

∆H f = ∆H f ( at T 1 ) + o

o

∫ ∆C p dT o

(2.33)

T1 T

∆S f = ∆S f ( at T 1 ) + o

o

∆C p - dT ∫ --------T o

(2.34)

T1

where ∆H f and ∆S f are standard heat and standard entropy of formation at temperature T, and o ∆C p is the difference of specific heats of products and reactants at standard states. The values o o o of ∆C p are generally very small and, therefore, one may assume that ∆H f and ∆S f are o essentially independent of temperature. This allows us to express dependence of ∆G f on temperature as: o

o

∆G f = A + BT o

(2.35)

where A and B are constants. o Equation (2.35) is an approximate one. A more precise representation of ∆G f as a function of T is ∆G f = A + BT + CT ln T o

(2.36)

However, data at steelmaking temperatures in standard compilations are available in the form of Eq. (2.35), for the limited temperature range of steelmaking. ©2001 CRC Press LLC

Appendix 2.1 provides values of A and B for oxides as well as some other compounds of o importance in secondary steelmaking. Figure 2.1 presents a diagram for oxides. ∆G f values are per gm mol of O2. This normalization allows us to compare stabilities of oxides directly from such figures. For example, Al2O3 is stabler than SiO2, since the free energy of formation of the former is more negative as compared to that of the latter. Quantitatively speaking, we are interested in the following reaction: 4 2 --- Al + SiO 2 = --- A1 2 O 3 + Si 3 3

(2.37)

∆Go [for the reaction of Eq. (2.37)] = ∆G f (2/3Al2O3) – (SiO2) is a negative quantity, and hence 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 not pure (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 a function of composition. o

FIGURE 2.1 Standard free energy of formation for some oxides.

©2001 CRC Press LLC

2.5 ACTIVITY–COMPOSITION RELATIONSHIPS: CONCENTRATED SOLUTIONS Crudely speaking, activity is a measure of “free” concentration in a solution, i.e., concentration that is available for chemical reaction. Also, by definition, activity is dimensionless. In metallurgical processing, the gases behave as ideal, and molecules are free. Hence, activity of a component i in a gas mixture is equal to its concentration. Numerically, by convention, ai = pi, where pi is partial pressure of i in atmosphere. The composition of a solution can be altered significantly during processing only if mixing and mass transfer are rapid. Solid state diffusion is very slow. Hence, during the short processing time, its composition does not change. For example, a particle of CaO will remain CaO as long as it does not dissolve in slag. It may get coated by another solid such as Ca2SiO4 or CaS during steel processing. Here, solid CaO remains pure and its activity, by definition, is 1, since this is its standard state. 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 versus composition relationships are required here for equilibrium calculations. As already stated, a pure element or compound constitutes its conventional standard state. For example, 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 standard state, 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 chromium and nickel. Then, XCr is to be calculated from weight percent composition as follows.

X Cr

W Cr --------M Cr = -----------------------------------------W Cr W Ni W Fe --------+ --------- + --------M Cr M Ni M Fe

(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 is illustrated in Figure 2.2. For example, molten Fe-Mn, Fe-Ni, FeO-MnO solutions are ideal. Molten Fe-Si, CaO-SiO2, FeO-SiO2, MnO-SiO2, etc. show negative departures. Liquid Fe-Cu exhibits positive departure. Departures from Raoult’s law are quantified using a parameter, known as the activity coefficient (γ), which is defined as: γ i = a i /x i

(2.40)

Activities in slag systems use conventional standard states as reference. However, industrial slags are multicomponent systems. Hence, presentation of activity versus composition diagrams is more complex 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 (1823 4 K). These are in the form of isoactivity lines for SiO2. Similarly, there would be diagrams presenting isoactivity 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 ©2001 CRC Press LLC

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 locations on liquidus is saturated with compounds as shown.4

©2001 CRC Press LLC

close, being equal to 56, 60, and 51, respectively. Therefore, the mole fraction scale is approximately the 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, and 2. thermodynamic calculations can be performed properly if the activity vs. composition relationship can be expressed by equations. This allows easier interpolations and extrapolations 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 p CO / p CO2 ratio in gas is 20/1. Predict whether it is possible to oxidize iron. Also, calculate equilibrium value of p CO / p CO2 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), ∆G = ∆G f [ CO ( g ) ] + ∆G f [ FeO ( s ) ] – ∆G f [ CO 2 ( g ) ] o

o

o

o

(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), p CO × ( a FeO ) 0 ∆G = ∆G + R × T ln ---------------------------[ a Fe ] × p CO2

(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 p CO × ( a Feo ) K = ln ----------------------------[ a Fe ] × p CO2 ©2001 CRC Press LLC

at equilibrium

Using the value of ∆G , the p CO ⁄ P CO2 ratio at equilibrium with Fe and the slag turns out to be 7.20. (Note that R = 8.314 J mol–1 K–1.) o

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 really ionic 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 is assumed. 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 cations and anions. The last assumption is too simplistic and has not been accepted. However, the first assumption, namely, ideal mixing among cations and among anions separately, constituted the basis for some later models. Flood et al.9 utilized it for reaction of sulfur between liquid steel and slag and obtained the analytical relation for the equilibrium constant as follows: log K h, S =

∑i X′i log K h,S i

(2.41)

where Kh,S denotes the equilibrium constant for sulfur reaction between metal and slag containing several cations. i denotes a cation. X′ i is an electrically equivalent fraction of i among all cations. i K h,S is the equilibrium constant if i is the only cation in slag. This is a useful equation. It allows i calculation of Kh,S in slag from knowledge of K h,S of various cations. Hence, this approach was later extended to the reaction of phosphorus as well. Slag modeling for thermodynamic calculations is of considerable interest to steelmaking. Some recent studies10 indicate efforts to apply the approach of Flood et al. with refinements. Of course, thermodynamic predictions are independent of structural considerations. This provides another approach. Analytical relations based on a regular solution model have proved to be the most popular among structure-independent predictions. For a binary solution, the regular solution model predicts RT lnγ 1 = αX 2 2

(2.42)

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

∑ jα ijX j + ∑ j∑ k( αij + αik – α jk ) X j X k 2

(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 steelmaking processes by quadratic formalism based on regular solution model. If the melt is not a strictly regular solution, then for a real solution, RT lnγ i =

∑ jα ijX j + ∑ j∑ k( αij + αik – α jk ) X j X k + I 2

(2.44)

where I has been termed the conversion factor of the activity coefficient from the hypothetical regular solution to the real solution. ©2001 CRC Press LLC

Experimental data of various slag-metal and slag-gas equilibria for many slag compositions were statistically fitted with Eq. (2.44). These have yielded some values of αij and I.11 Example 2.3 Calculate γi in a multicomponent solution of slag at 1873 K. Composition of slag in weight percent is 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 X MnO = 0.0384, X CaO = 0.6058, X Al2 O3 = 0.2339,X SiO2 = 0.091, X FeO = 0.0284 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 dilute binary solutions obey Henry’s law, which is stated as follows: ai = γ i Xi o

(2.45)

where γ i 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, the composition scale is weight percent, not mole fraction. With these modifications, in dilute solution of species i in liquid iron, o

©2001 CRC Press LLC

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. This is 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: γ f i = -----oi γi

(2.48)

It is to be noted that the standard free energy change for reaction is not going to be the same if the standard state is changed. For example, at 1600°C, Si ( 1 ) + 0 2 ( g ) = SiO 2 ( s ); ∆G 49 = – 571.5 kJ mol o

–1

(2.49)

with pure liquid silicon as standard state. However, for the 1 wt.% standard state of Si dissolved in liquid iron, [ Si ] wt.pct. + 0 2 ( g ) = SiO 2 ( s ); ∆G 50 = –406.4 kJ mol * o

–1

(2.50)

∆G 49 and ∆G 50 are related to each other as o

o

∆G 50 = ∆G 49 – [ G Si + – G Si ] at 1 wt. pct. std. state for Si in liquid iron o

o

o

m

= ∆G 49 – [ G Si ] at 1 wt. pct. std. state for Si in liquid iron o

m

(2.51) (2.52)

o

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

G Si = RT ln [ a Si ] at 1 wt. pct. std. state Si in liquid iron = RT ln γ Si [ X Si ] at 1 wt. pct. o

(2.53) (2.54)

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

X Si

W Si -------M Si = -----------------------W Si W Fe -------- + --------M Si M Fe

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

©2001 CRC Press LLC

(2.55)

On the basis of Eq. (2.55), XSi = 0.02 at WSi = 1. Noting that γ Si = 1.25 × 10–3, the value of ∆G 50 in Eq. (2.50) was obtained. m Appendix 2.2 presents values of G i for some solute in liquid iron. o

2.6.2

SOLUTE–SOLUTE INTERACTIONS

IN

o

DILUTE MULTICOMPONENT SOLUTIONS

It has been found that solutes in a multicomponent solution interact with one another and thus influence activities of other solutes. Figure 2.4 illustrates this for activity of carbon and oxygen in liquid iron at 1833 K. In the Henry’s law region of Fe-C binary (i.e., without any other added element), fC = 1, i.e., log fC = 0. In the presence of a third element in liquid iron solution, fC keeps changing systematically. It has been derived that if, in a dilute multicomponent solution, A is solvent (Fe in case of liquid steel), and B, C,..., i, j, etc. are solutes, then log f i = e i ⋅ W B + e i W C + … + e i W i + e i W j + …… B

C

i

j

(2.56)

j

where e values are constants. e i is called the interaction coefficient, describing the influence of solute j on fi, which is defined as ∂ ( log f i ) j e i = -------------------∂W j

0.10

C

(2.57)

Wj→O

Si

P Co

0.05

Sb Cu

Te Al

Ni

LOG f

j

N

As

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

0

W Cr

Ti

-0.05

Mn

Mo

V

0

1

2

3

4

5

ALLOYING ELEMENT, mass% j

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

©2001 CRC Press LLC

i

e i is known as the self interaction coefficient and has a non-zero value only if Fe-i binary deviates from Henry’s law. Again, ∂ ( log f ) i e j = --------------------j ∂W i

Wi → O

j M –2 M i – M j = e i ⋅ -------j + 0.434 × 10 -----------------Mi Mi

(2.58)

Appendix 2.3 presents values of interaction coefficient for some common elements dissolved in liquid iron. Equation (2.56) contains only first-order interaction coefficients. It is, in general, all right for dilute solutions of liquid iron. However, sometimes, even here, second-order interaction coefficients j ( r i ) are to be employed. On the other hand, if solute–solute interactions are not significant, log fi vs. weight percent of the added element exhibit good linear behavior over a long range. This is demonstrated by Figure 2.4 for nitrogen dissolved in liquid iron. The figure is based on several data sources and taken from the review by Iguchi.12 In such cases, Eq. (2.56) may be fairly all right up to reasonably high concentrations of solutes. Iguchi12 has recently reviewed the subject, especially the work of Ban-ya and his coworkers, who had been active in this field for about two decades. The following two approaches have been seriously explored. The first approach is application of quadratic formalism, originally proposed by Darken and applied to several binary systems by 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 by Chipman.13 Elements P, C, S, N, etc. may be treated as interstitial atoms, and this model has been applied to ternary iron alloys containing these elements to high concentrations. It predicts linearity between log ψ with Yj, where ψi is a modified activity coefficient of i, and Yj is atom ratio of j in a ternary containing i and j. Figure 2.5 shows its application to the effect of iron on the activity coefficient of nitrogen in Cr-Fe-N ternary melts. Good linear relation up to a high concentration of 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 bubbles coming out of the bath have 10 percent CO, 5 percent N2, 5 percent H2, and the rest Ar. Assuming these to be at equilibrium with molten steel, calculate the hydrogen, nitrogen, and oxygen concentrations 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 1 [ H ] wt.pct. = --- H 2 ( g ) 2

(E4.1)

1905 log K H = ------------ + 1.591 T

(E4.2)

for which

Again, at equilibrium, 1⁄2

KH

©2001 CRC Press LLC

p H2 = ---------[ hH ]

(E4.3)

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

Now, p H 2 = 0.05 atm, and KH = 405.58 at 1873 K So, hH at equilibrium = 5.513 × 10–4 = fH · WH Again, log f H = e H ⋅ W C + e H ⋅ W Mn + e H ⋅ W Si C

Mn

Si

(E4.4)

Assume interactions of dissolved H, N, and O on fH as negligible. This is justified in view of their j very small concentrations. Taking values of e i 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.) ©2001 CRC Press LLC

(b) For nitrogen, the reaction may be written as 1 [ N ] wt.pct. = --- N 2 ( g ) 2

(E4.5)

518 log K N = --------- + 1.063 T

(E4.6)

for which

Proceeding as for hydrogen, [hN] = 0.01, in 1 weight percent standard state Now, hN = fN · WN

(E4.7)

and log f N = e N ⋅ W C + e N ⋅ W Mn + e N ⋅ W Si C

Mn

Si

(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)

1160 log K O = ------------ + 2.003 T

(E4.10)

P CO K O = -------------------[ hC ] [ hO ]

(E4.11)

for which

Again, at equilibrium,

hC = fC · WC = fC · 1 log f C = e C ⋅ W C + e C ⋅ W Mn + e C ⋅ W Si C

Mn

Si

(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, P CO 0.1 –4 h O = ---------------------- = ------------------------- = 1.31 × 10 [ K O ] [ hC ] 419 × 1.82 ©2001 CRC Press LLC

(E4.12)

Again, WO = hO/fO and, log f O = e O ⋅ W C + e O ⋅ W Mn + e O ⋅ W Si C

Mn

Si

(E4.13)

C

Putting in values (taking e O = –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 employed as the criterion for assessing the feasibility of a process. There is an alternative approach based on chemical potential. Suppose that an element i is to be transferred from phase I to phase II. Then, we say that, for the transfer to be feasible thermodynamically, µ i (I) > µ i (II)

(2.59)

µ i (I) = µ i (II)

(2.60)

and for equilibrium,

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 ( G i ) . On the basis of Eq. (2.25), µ i (I) = µ i (I) + RT ln ai (I)

(2.61)

µ i (II) = µ i (II) + RT ln ai (II)

(2.62)

O

O

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

µ i (I) = µ i (II) O

O

(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 common physical processes. Just as heat flows from a higher heat potential (temperature) to a lower heat potential, and electricity flows from a higher electrical potential to a lower ©2001 CRC Press LLC

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 the chemical potential of the species concerned only. Suppose we know µ i(I). If another phase II is brought in contact with it, all we have to do is to calculate µ i(II) to find out direction 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 reduction of a metal from its oxide, the reaction environment must have a lower chemical potential than oxygen. Similarly, if impurities in a metal are to be preferentially oxidized in refining, then the environment must have a higher chemical potential than oxygen as compared to that in the impure metal. The chemical potential of oxygen (O2) is expressed as µ O2 = µ O2 + RT ln a O2 = µ O2 + RT ln p O2 o

o

(2.65)

Since a O2 may be equated to p O2 for ideal gas, and µ O2 is set equal to zero, then o

µ O2 = RT ln p O2

(2.66)

Calculation of the oxygen potential in a gas phase is relatively simple. For liquid metals, one should consider the reaction O2(g) = 2[O]. For this, [ hO ] o ∆G h = – RT ln -----------= – 2RT ln [ h O ] + RT ln p O2 p O2

(2.67)

µ O2 ( metal ) = ∆G h + 2RT ln [ h O ]

(2.68)

2

Hence, o

For liquid slag in ironmaking, we consider the reaction 2 [ Fe ] + O 2 ( g ) = 2 ( FeO ); ∆G 69 o

(2.69)

( a FeO ) o ∆G 69 = – RT ln K 69 = – RT ln --------------------2 [ a Fe ] p O2 2

(2.70)

where p O2 is partial pressure of O2 in equilibrium with [Fe] and (FeO). Since aFe ≈ 1 in ironmaking and steelmaking, µ O2 ( slag ) = RT ln p O2 = ∆G 69 + 2RT ln ( a FeO ) O

(2.71)

If slag-metal equilibrium does not exist, Eq. (2.71) gives the µ O2 in slag, because it is not dependent on the composition of iron. If slag-metal equilibrium exists, then it is µ O2 in both slag and metal. ©2001 CRC Press LLC

Of course, primary steelmaking slags contain Fe2O3 (i.e., Fe3+ ions) also. There µ O2 is determined more by the following reaction: 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 in metal. 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 Example 2.2, and the chemical potential of nitrogen as per Example 2.4. Solution (a) Calculation of µ O2 in CO/CO2 gas mixture for the problem in Example 2.2: Consider the reaction, 2CO ( g ) + O 2 ( g ) = 2CO 2 ( g )

(E5.1) 2

p CO2 ∆G = – RT ln ---------------------2 p CO × p O2 o

equilibrium

p CO = RT ln ( p O2 ) e – 2RT ln ----------2 p CO where ( p O2 ) e is in equilibrium with CO and CO2. Since p CO 20 1 o --------- = ------ , µ o2 = RT ln ( p O2 ) e = ∆G + 2RT ln  ------  20 1 p CO2

(E5.2)

At 1300°C (1573 K), for the reaction of Eq. (E5.1),* ∆G = 2 [ ∆G f , CO2 – ∆G f ,CO ] o

o

o

(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), µ O2 = – 369.67 kJ mol O 2 –1

* From data in Appendix 2.1.

©2001 CRC Press LLC

(Ans.)

(E5.4)

(b) Calculation of µ O2 in FeO-CaO-SiO2 slag for the problem in Example 2.2: Consider the reaction 2Fe(s) + O 2 (g) = 2 ( FeO )

(E5.5)

Since aFe = 1, aFeO = 0.45 (given), from Eq. (2.71), µ O2 = 2∆G FeO ( 1 ) + 2RT ln ( 0.45 ) o

(E5.6)

From Appendix 2.1, ∆G FeO ( 1 ) = – 238.07 + 49.45 × 1 0 T kJ mol o

–3

–1

At 1573 K, o

2∆G FeO ( l ) = – 320.57 kJ mol

–1

Therefore, from Eq. (E5.6), µ O2 (in slag) = –341.46 kJ/mol–1 O2

(Ans.)

µ O2 in slag is different from µ O2 in gas, because they are not at equilibrium. (c) Calculation of µ N2 for Example 2.4: Since p N2 = 0.05 atm in Example 2.4, p N2 = RT ln p N 2 = RT ln (0.05) At T = 1873 K, µ N2 = –46.65 kJ mol–1 N2 (Ans.) Since liquid steel and nitrogen in exit gas are at equilibrium, µ N2 in liquid steel also shall be the same.

2.8 SLAG BASICITY AND CAPACITIES Basicity of a slag increases with increased percentages of basic oxides in it. It is an important parameter governing refining. Steelmakers had always paid attention to it. In the early days, the numerical value of basicity was taken as the CaO/SiO2 ratio, modified ratio, or excess base. ©2001 CRC Press LLC

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 ( a O2 – ) may be taken as an appropriate measure of the basicity of slag. However, there is no method available for experimental determination of ( a O2 – ) .

2.8.1

OPTICAL BASICITY

A breakthrough came with the development of the concept of optical basicity (Λ) in the field of glass chemistry by Duffy and Ingram14 in 1975–76. It was applied to metallurgical slags first by Duffy, Ingram, and Somerville.15 From then on, numerous investigators have applied it to metallurgical slags for a variety of correlations. Experimental measurements of optical basicity in transparent media such as transparent glass and 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 turn produces a shift in frequency in UV spectral band. υ free – υ sample Λ = ---------------------------υ free – υ CaO

(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 lime character, even though there may not be any CaO in sample. Based on experimental measurements, the following empirical correlation was proposed by Duffy et al.14,15 1 ----- = 1.35 ( α i – 0.26 ) Λi

(2.74)

where αi is Pauling electronegativity of the cation in a single oxide i. This relationship has allowed estimation of Λi for a variety of oxides where experimental data are not available from the values of αi. 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 X i ′ Λth.i

(2.75)

where X i ′ = 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 of Eqs. (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 data were not available. This was tantamount to suggesting that each oxide is characterized by a unique value of Λi, irrespective of medium and temperature. However, it has not been accepted by recent investigators. 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 have been 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 metallurgical 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 made to evaluate Λi for common fluorides such as CaF2. ©2001 CRC Press LLC

One important problem facing application of the optical basicity concept has been differing values 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 basicity recommended by Duffy and coworkers18,20 were on the basis of electronegativity, electronic polarizability, and refractive index, whereas those by Nakamura et al.21 were estimated from average electron density. It may be noted that there is both agreement as well as disagreement among various 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 X′ i = 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: 2 × 0.0384 X′ Mn2 + = ------------------------- = 0.031 2.414

2 × 0.6058 X′ Cn2 + = ------------------------- = 0.504 2.414

3 × 0.2339 X′ Al3 + = ------------------------- = 0.291 2.414

4 × 0.091 X′ Si4 + = ---------------------- = 0.151 2.414

2 × 0.028 X′ Fe2 + = ---------------------- = 0.023 2.414 Optical basicity of various species (considering data of Nakamura et al.21; Appendix 2.4): Λ MnO = 0.95, Λ CaO = 1.0, Λ Al2 O3 = 0.66, Λ SiO2 = 0.47, Λ FeO = 0.94 Substituting the values of X i ′ 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 has become quite widespread. Richardson and Fincham10 in 1954 defined sulfide capacity (Cs) as the potential capacity of a melt to hold sulfur as sulfide. Mathematically, C s = ( wt. % S

2–

1⁄2

1⁄2

) ⋅ p O2 ⁄ p S2

(2.76)

where p O2 ⋅ p S2 are partial pressures of O2 and S2 in the gas at equilibrium with slag. Noting that the reaction is 1/2 S2 (g) + (O2–) = 1/2 O2 (g) + (S2–)

(2.77)

K 77 ⋅ a O2 – C s = ----------------------φ S2 –

(2.78)

it can be shown that

©2001 CRC Press LLC

where K77 is the equilibrium constant for the reaction of Eq. (2.77) and φ S2 – is the activity coefficient of S2– in slag in an appropriate scale. Wagner22 has critically discussed the concept of basicity and various capacity parameters such as sulfide capacity, phosphate capacity, carbonate capacity, etc. He has discussed interrelationships among capacities. He also suggested use of carbonate capacity as a method of measurement of basicity. 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 1 5 3 2– 3– --- P 2 ( g ) + --- O 2 ( g ) + --- ( O ) = ( PO 4 ) 2 4 2

(2.79)

for which the phosphate capacity of slag may be defined as ( wt. % PO 4 ) C p = -------------------------------------1⁄2 5⁄4 ( P p2 ) ( p O2 ) 3–

(2.80)

From Eqs. (2.79) and (2.80), 3⁄2

[ a O2 – ] C p = K 79 ⋅ --------------------φ PO3–

(2.81)

4

where K79 is the equilibrium constant for the reaction of Eq. (2.79) and φ PO3– is the activity coefficient 3– 4 of PO 4 in slag in an appropriate scale. The combination of Eqs. (2.78) and (2.81) leads to the following relation: 3⁄2

φ S2 – 3 log C p = --- log C s + log K 82 + log ---------φ PO3– 2

(2.82)

4

K82 is an equilibrium constant term and depends only on temperature. At a constant temperature, 3⁄2 in the same slag system (e.g., Na2O – SiO2 system), ( φ S2– ) ⁄ φPO3– parameter is expected to be 4 22 constant, Hence, a single straight line with slope of 3/2 is expected. Figure 2.6 is based on review by Sano et al.24 It shows agreement with the above expectation. Of course, a corollary to this conclusion is that there is no universal correlation between log Cp and log Cs that will be applicable to all kinds of slag systems. Similar conclusions can be drawn about interrelationships of other capacities. Optical basicity concept is being utilized by industries as well. Equation (2.75) forms the basis of estimation of optical basicity in slags. Cs increases with increasing a O2– (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 at 1500°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 ©2001 CRC Press LLC

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 the Iron & Steel Society, Warrendale, PA.

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 in this 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, AddisonWesley 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. ©2001 CRC Press LLC

2.0

- LOG CS

3.0

Ca0 - Al203 Ca0 - Si02 Ca0 - AI203 - Si02 Ca0 - Mg0 - Al203 Ca0 - Si02 - B203 Ca0 - Mg0 - Si02 Ca0 - Mg0 - Al203Si02

4.0

5.0

0.55

o

T = 1500 C

0.60

0.65

0.70

0.75

0.80

0.85

0PTICAL BASICITY (Λ), ( - ) FIGURE 2.7 Logarithm of sulfide capacity vs. optical basicity at 1823 K.23 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24.

Ban Ya, S., ISIJ Int., 33, 1993, p. 2. Iguchi, Y., in Proc. The Elliott Symposium, ISS, Cambridge, Mass., USA, 1990, p. 132. Ban Ya, S., and Chipman, J., Trans AIME, 242, 1968, p. 940. Duffy, J.A. and Ingram, M.D., J. of Non-Crystalline Solids, 21, 1976, p. 373. Duffy, J.A., Ingram, M.D. and Sommerville, I.D., J. Chem. Soc., Faraday Trans. 1, 74, 1978, p. 1410. Bergman, A. and Gustafsson, A., in Proc. 3rd Int. Conf. on Molten Slags and Fluxes, Inst. of Metals, London, 1989, p. 150. Proc. 3rd Int. Conf. on Molten Slags and Fluxes, Inst. of Metals, London, 1989. Young, R.W., Duffy, J.A., Hassall, G.J. and Xu, Z., Ironmaking and Steelmaking, 19,1992, p. 201. Nakamura, T., Yokoyama, T. and Toguri, J.M., ISIJ Int., 33, 1993, p. 204. Duffy, J.A., Ironmaking and Steelmaking, 17, 1990, p. 410. Nakamura, T., Ueda, Y. and Toguri, J.M., Trans. Japan Inst. Met., 50, 1986, p. 456. Wagner, C., Metall. Trans. B, 6B, 1975, p. 405. Sosinsky, D.J., Sommerville, I.D. and McLean, A., in Proc. 6th PTD Conference, ISS, Washington D.C., 1986, p. 697. 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.

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3

Flow Fundamentals

The nature of fluid motion and the intensity of turbulence during liquid steel processing are of considerable importance to the success of secondary steelmaking due to their significant influence on mixing, mass transfer, inclusion removal, refractory lining wear, entrapment of slag, and reaction with the atmosphere. Therefore, several studies have been carried out in the past two to three decades or so on the subjects of fluid flow and mixing in ladles, tundishes, etc. Among these, molten steel in 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 fundamental studies on fluid flow have been carried out on this system. Hence, this chapter first of all briefly 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 composition gradient in the melt, and forced convection due to gas stirring, electromagnetic stirring, agitation by the pouring stream, and mechanical stirring. However, free convection has been found to be very 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 brief introductory presentation for the sake of completeness. Figure 3.1 depicts the motion of a fluid element (dm), i.e. an infinitesimally small mass of a fluid, moving along a path. It moves under the action of some forces acting upon it. Such forces may be classified in the following two categories: 1. Body forces, which act throughout the volume of the fluid element. Gravitational force is the primary body force of relevance. However, there are the following other body forces:

dFB PATH

τ

dm dFS

σ

FIGURE 3.1 Forces and stresses acting on a fluid element.

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• Thermal buoyancy force: density difference due to inhomogeneity of temperature in the fluid leads to this force, and it is expressed as ρgβt∆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 the fluid 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 J × B , where J is conduction current density and B is magnetic flux density. J and B are related through Maxwell’s equation. 2. Surface forces, which act at the surface of the fluid element due to contact with its surrounding. A surface force can be resolved into normal and shear forces. Applying Newton’s second law of motion to the fluid element, dF = dF B + dF s = a ⋅ dm

(3.1)

where a is acceleration of the element, dF B and dF S are, respectively, the body and surface forces acting on it. These are all vector quantities. Again, a ⋅ dm 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 two types of stresses: the one acting perpendicular to the surface of the fluid element is known as normal stress, and the other, acting parallel to the surface of the fluid element, is termed as shear stress. Fs ----- = ( – ∇ )p V

(3.2)

F where -----s is force per unit volume of fluid, ∇ is the symbol for gradient vector. V

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’s law of viscosity was the beginning of the quantification of the relationship between shear stress and shear deformation. The assumption is that shear stress is proportional to the rate of shear deformation. Newton’s law of viscosity, which is applicable to parallel and incompressible flow, is stated as ∂u τ yx = – µ --------x ∂y

(3.3)

With reference to Figure 3.2, τ yx denotes shear stress acting on the y-plane (i.e., a plane normal to the y-axis) along the x-direction. µ is a proportionality constant, known as coefficient of viscosity or simply viscosity. Figure 3.2 also shows the expected velocity profile in fluid adjacent to a solid surface for parallel flow. Velocity in the x-direction is zero at the surface, since the fluid layer just at the surface cannot slip past the solid. It increases as we move along the y-coordinate. ©2001 CRC Press LLC

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

An alternate form of Eq. (3.3) is µ∂ ( ρu x ) ∂ ( ρu x ) - = – ν ---------------τ yx = – ------------------ρ∂y ∂y

(3.4)

where ρ is density of the fluid. µ/ρ is known as kinematic viscosity (ν). Flow characteristics of a fluid are governed more by ν than µ. A velocity gradient in a fluid causes momentum transfer from higher to lower velocity due to its viscosity. Hence, shear stress in Figure 3.2 is also equal to the rate of transfer of x-momentum along y-direction per unit area normal to y-direction (i.e., xmomentum flux along y). Viscosities of gases can be estimated from the kinetic theory of gases. There are empirical rules available for estimation of the same for liquids. However, for the latter, it is by and large advisable to employ experimentally determined values. Viscosity, density, and some other physical and physicochemical properties of water, liquid iron, and some iron alloys, slags of interest in secondary steelmaking, are presented in Appendix 3.1. It may be noted that liquid iron has a value of ν comparable to water. Hence, it is as fluid as water. On the other hand, molten slags have much higher values of both µ and ν.

3.1.2

FLOW CHARACTERIZATION

Fluid motion can be categorized as follows: 1. 2. 3. 4. 5. 6.

Newtonian or non-Newtonian Viscous or nonviscous (ideal) Laminar or turbulent Incompressible or compressible Steady or unsteady Forced or free convection

The total characterization includes specifications on each of these points as well as the flow geometry. 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 nonNewtonian liquids. According to Eq. (3.3), viscous shear stress is proportional to µ as well as ©2001 CRC Press LLC

∂u x ⁄ ∂y (i.e., velocity gradient). If one of these is negligibly small, then τyx can be ignored, and the flow may be treated as nonviscous or ideal. Otherwise, it would be considered as viscous flow. Figure 3.3 depicts a typical velocity profile adjacent to a solid surface. Velocity of the fluid just 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. Outside the 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, the thickness 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 a millimeter and even of the order of few microns. On the other hand, it is typically larger than a millimeter or even a centimeter in gases. If a tangent is drawn to the velocity profile at the solid–fluid interface, then its slope is equal to ( ∂u y ⁄ ∂x ) x = 0 . From this it follows that ∂u uo [ τ xy ] surface = – µ  --------y = – µ -------- ∂x  x = 0 δ u,eff

(3.5)

τxy acting on the surface would be opposite in sign and positive. δu,eff is known as the effective velocity boundary layer thickness. Laminar flow is obtained at low velocities, and turbulent flow at high velocities. The former is characterized by distinct streamlines with no cross mixing, whereas the latter is accompanied by extensive mixing. Suppose we are measuring the velocity of fluid at a particular location as a function 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 laminar and turbulent flow. In a steady turbulent flow, although the time-averaged velocity is constant, the instantaneous velocity exhibits random fluctuations. Imagine the fluid element A in Figure 3.5. Under turbulent flow, its instantaneous velocity fluctuates at random. Similar random fluctuations are exhibited by its 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.

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

B

A FIGURE 3.5 Eddy mechanism.

those of A, the latter is always receiving impacts from its neighbors, and vice versa. This occasionally will throw A out of its location to region B. In exchange, fluid from location B may be imagined to occupy location A. Such a process of exchange is visualized as an eddy. These eddy-like exchanges go on at random in all directions, leading to extensive mixing in turbulent flow. That is why turbulent flow is preferred in engineering. Exchange of eddy elements tends to impart a whirlpool-type motion ©2001 CRC Press LLC

in the eddy area. This is because the exchange takes place by small, jerky movements in a closed loop. 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, small ones, 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 fluid is a gas, such pressure differences would lead to a variation of density, and under such a situation the flow is called a compressible flow. The motion of gases at a small pressure difference, and of liquids, is treated as incompressible. Forced convection refers to flow caused by an external agent such 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 mostly deal 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., differential analysis 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 of fluid in a rectangular coordinate system. From the principle of conservation of mass,

Rate of accumulation of mass in the volume element

=

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

(3.6)

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

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∂ρ Rate of accumulation of mass in the control volume = ------ ( ∆x∆y∆z ) ∂t

(3.7)

where t is time. Along the x-coordinate, [Rate of flow of mass into the volume element – Rate of flow of mass out of the volume element]

= [ ( ρu x ) x – ( ρu x ) x + ∆x ]∆y∆z  ∂ ( ρu x )  = ( ρu x ) x –  ( ρu x ) x + ----------------dx  ∆y∆z ∂x   ∂ ( ρu x ) = ---------------∆x∆y∆z ∂x

(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 ∂ρ ∂ ( ρu x ) ∂ ( ρu y ) ∂ ( ρu z ) ------ + ---------------- + ---------------- + ---------------- = 0 ∂t ∂x ∂y ∂z

(3.9)

For an incompressible flow, ρ is constant, so Eq. (3.9) reduces to ∂u ∂u ∂u --------x + --------y + --------z = div.u = 0 ∂x ∂y ∂z

(3.10)

where div.u is divergence of velocity vector u . 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 element depicted in Figure 3.1. As it moves, its change of properties is a consequence of both change of position and of time. When it is considered this way, and the fluid element is followed in time and space, then the rate of change of a property is expressed by its substantial derivative. For a velocity vector, it would be ∂u ∂u ∂u Du ∂u a = ------- = ------ + u x --------x + u y --------y + --------z ∂x ∂y ∂z Dt ∂t Du Where ------- is substantial derivative of u. Dt ©2001 CRC Press LLC

(3.11)

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 concepts already presented, that Du 2 ρa = ρ ------- = ρF B – ∇P + µ∇ u Dt

(3.13)

where F B is body force per unit mass of the fluid. If gravitational force is taken as the only body force, then Du 2 ρa = ρ ------- = – ρgk – ∇ρ + µ∇ µ Dt

(3.14)

where k is the unit vector along the z-direction (i.e., vertical direction). ∇ is the Laplacian of u . For a rectangular coordinate system, it is given as 2

∂ u ∂ u ∂ u 2 ∇ u = ---------2-x + ---------2-y + ---------2-z ∂x ∂y ∂z 2

2

2

(3.15)

Equation (3.14) is the well known Navier–Stokes equation. For laminar flow and simple situations, analytical solutions are available in standard texts. For complex but laminar flow, resort to numerical methods. The Navier–Stokes equation, with certain modifications and empiricism, has been applied for fluid flow computations in turbulent flow as well. Of course, the procedures involve lengthy computer-oriented numerical methods. The vectorial equations can be resolved into three component equations along the three coordinates. These are available for the three standard coordinate 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 Buckingham’s π-theorem, the number of dimensionless variables is n – r, where n is the number of physical variables 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 fluid on 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. Dimensional analysis leads to the following formulation: Eu = f(Re)

(3.17)

where Eu is Euler number, which is equal to F D ⁄ ρu o d , and Re is the Reynolds number (= ρuod/µ). 2

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2

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 equations, graphs, or tables is also enormously simplified. Another advantage is that the correlations become independent of the unit employed. Dimensionless numbers have physical significance as well. They are proportional to the ratios of forces. For example, resultant (i.e., inertia) force Re α ----------------------------------------------------------------viscous force

(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, small models of aircraft are tested in a wind tunnel in connection with their design. In the area of steelmaking, room temperature, laboratory-size models, simulating liquid steel by water (i.e., water models), are very popular and have advanced our understanding of steelmaking processes significantly. Extrapolation of model results to actual prototypes is more reliable, provided there is dynamic similarity between the two through equality of relevant dimensionless numbers. Of course, the model and prototype have to be geometrically similar. Which dimensionless numbers would be relevant for simulation of a flow situation would depend on the significance of the forces. Table 3.1 lists the numbers important in secondary steelmaking. TABLE 3.1 Important Dimensionless Numbers in Secondary Steelmaking Name

Symbol

Definition

Force proportionality ratio

Reynolds number

Re

ρuL ---------µ

inertial -----------------viscous

Froude number

Fr

u -----gL

Modified Froude number

Frm

Weber number

Morton number

2

Application General fluid flow

inertial -----------------------------gravitational

In forced convection

ρg u --------------------------( ρ l – ρ g )gL

inertial -----------------------------gravitational

Gas–liquid system

Wb

ρµ L ------------σ

inertial -----------------------------------surface tension

Mo

gµ ----------3 ρl σ

2

2

4

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

Gas bubble formation in liquid

Velocity of gas bubbles in liquid

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

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 flow is characterized by random fluctuations in velocity at any location in the flow field as well as by random motion of eddies as a consequence. Section 3.1.2 also has discussed differences between laminar 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 nicely demonstrated by Osborne Reynolds more than a century ago. When he injected some red dye in ©2001 CRC Press LLC

laminarly flowing water in a glass tube, the dye moved along a stable streamline, which was like a 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 the presence of a solid surface in contact with the fluid causes the onset of turbulence. Laminar flow is observed at small Reynolds number values, e.g., 2100 for flow through a straight pipe. At values of Re larger than this critical Re, the flow is turbulent. Sometimes, a laminar-to-turbulent transition is characterized by a transitional flow regime, as in the case of flow through a pipe. Value of critical Re depends on the flow geometry. For example, in a flow around a sphere, Recrit is approximately 0.1. Eddies exhibit a large size range. The largest one may be comparable to the size of the vessel and the smallest one less than a millimeter. The smaller an eddy, the higher is its jump frequency and hence consequent frequency of velocity fluctuation at a point, which may be as high as approximately 1000 per second. Large eddies derive their energy from the main flow and may contain as much as 20% of the kinetic energy of the turbulent motion. The interaction among larger eddies generates smaller eddies, and so on. The smaller the size of an eddy, the higher its specific kinetic energy (i.e., kinetic energy per unit mass or volume). Also, smaller eddies are isotropic, whereas larger eddies tend to exhibit anisotropy. Dissipation of the kinetic energy of an eddy into heat can occur only through viscous forces. 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 ν l min = ----εd

3 0.25

(3.19)

where ν is kinematic viscosity and εd is the rate of total kinetic energy dissipation of the turbulent motion. 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 flow as a function of the inverse of eddy size (le). The size distribution in large-sized eddies depends on the flow pattern and vessel geometry. However, for a fully developed, steady turbulent motion,

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

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the size distribution for small eddies attains equilibrium and is probabilistic. It is independent of flow 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 as consisting of three components (ux, uy, and uz) along x, y, and z coordinates, respectively. u x = u x + u′ x ; u y = u y + u′ y ; u z = u z + u′ z

(3.20)

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

1 u x = --- ∫ u x ( t )dt to

(3.21)

o

Similarly, u y and u z may be defined. Here, to is the time over which averaging is done. u is the quantity measured by ordinary instruments. As already stated, u is independent of time at steady state. u´ can be measured only by special fast-response instruments such as a hot film anemometer or a laser Doppler anemometer. Intensity of turbulence is measured by the relative magnitudes of u´ and u . Since the value of u´ at a location fluctuates at random, some kind of averaging of u´ is required. However, u′ = 0 by definition. Hence, intensity of turbulence (I) has been defined as: 1⁄2 1 2 2 2 --- ( u′ x + u′ y + u′ z ) 3 I = ----------------------------------------------------u

(3.22)

For isotropic turbulence, u′ x = u′ y = u′ z = u′ and hence Eq. (3.22) reduces to Eq. (3.23), i.e., 2 1⁄2

[ u′ ] I = -----------------u

(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 ρu′ x u′ y , ρu′ x u′ z , and ρu′ y u′ z . These have dimensions of stress. They can also be shown to be related to the rate of momentum transport by eddies along a velocity gradient, which is another physical interpretation of shear stress. Hence, Reynolds stresses have physical existence and are not just conceptual quantities. An important quantity, commonly used for characterizing turbulent flow behavior, is turbulent kinetic energy per unit mass of fluid (k), defined as 1 2 2 2 k = --- [ u′ x + u′ y + u′ z ] 2

(3.24)

3 2 k = --- [ u′ ] 2

(3.25)

For isotropic turbulence,

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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 ∂u ( τ yx ) t = – µ t --------x ∂y

(3.26)

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

(3.27)

where µ eff 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 be correlated with measurable variables governing fluid flow. The “one equation model” based on Prandtl’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 Launder and Spalding,6 popularly known as k-ε model, proposes ρk µ t = C D -------ε 2

(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 requiring large computer time. The basic procedure will be presented in Chapter 11. Calculated results will be 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 stirred ladles. Stirring may be achieved by purging the steel melt with argon and also by gases liberated from the melt during processing. The latter is important for successful processing during vacuum degassing of liquid steel, when the evolution of CO, H2, and N2 causes vigorous stirring in the melt and consequent droplet ejection into the evacuated chamber. Electromagnetic stirring is also employed in secondary steelmaking. However, the most common situation is stirring by the purging of inert gas. Hence, so far as fundamental studies on fluid flow are concerned, principal attention has been focused on turbulence and agitation in the ladle due to argon purging. The gas is introduced into the melt mostly through porous plugs fitted at the ladle bottom (i.e., bottom purging) or by a lance immersed vertically into the melt from the top. Fluid motion and turbulence in both these arrangements have some similarities but have differences as well. It is the bottom purging geometry that has been most widely studied. Hence, this section is restricted to fluid flow in liquid due to bottom purging of inert gas. Liberation of gases from the ©2001 CRC Press LLC

melt due to reactions is ignored. In industry, small ladles are fitted with one bottom plug and large ones 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 laboratory with transparent room-temperature water models. In these studies, mostly axisymmetric nozzles were employed for the sake of simplicity and basic interpretations. The presentations in this section are aimed at elucidation of fundamentals. Our understanding of the same will be better if the above background information is kept in mind. Fluid flow in industrial situations that differ significantly in the mode of stirring and melt geometry is taken up in later sections when necessary and possible. Even there, the information contained in this section provides the basics. Table 3.2 presents some values of gas flow rates per unit volume of liquid in ladle refining of liquid steel as well as other situations involving bottom purging. TABLE 3.2 Gas Flow Rates (Qv) per m3 Bath Volume Situation Ar-stirred ladle

Qv , m3 s–1 × 104 per m3 of bath

Reference

44–1800

8

-do-

3–54

9

-do-

25–330

10

Water model

17–240

11

OBM converter

25000

12

For calculation of Qv, gas temperatures were assumed as 300 K for the water model and 1873 K for 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 than that in an OBM converter. In a combined top and bottom blowing converter, the bottom gas injection rate is few percent (say at least 2%) of the oxygen blowing rate through top lance. Hence, Qv would be 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 gas issuing from tuyeres causes jetting flow and prevents back attack of tuyeres of molten metal. In ladle refining, on the other hand, the flow rates and velocities of gas are low. Hence, a jetting regime cannot 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 the refining rate due to a larger gas–liquid interfacial area. Hammerer et al.13 have reviewed latest developments in gas-purging plugs. Figure 3.8 shows sketches 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 and release of gas bubbles cause pressure fluctuations in the gas line, leading to back attack of plugs by steel melt. Plugs get damaged by penetration of liquid metal into them through back attack, as well as by peeling at the surface in contact with the melt. Both of these are less common for slit plugs, which are therefore more popular. Porous plugs are employed for gas bubbling at moderate rates only (less than 0.01 Nm3s–1). ©2001 CRC Press LLC

FIGURE 3.8 Kinds of purging plug systems.

3.2.1

GAS BUBBLES

IN

LIQUID

The behavior of gas bubbles in liquid has been extensively studied. Szekely1 has reviewed it and may be referred to for more details. Growth and motion of single bubbles in liquid are reasonably well 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 determined by a balance between surface tension and buoyancy force. For an air-water system, the following correlations have been proposed: 6d n σ d B = ----------------------g ( ρl – ρg )

1⁄3

, for Re < 500

(3.30)

and 1⁄2

1⁄3

d B = 0.046d n Re n , for 500 ≤ Re ≤ 2100

(3.31)

where dn is the nozzle diameter, and other symbols are as noted in Table 3.1. The nozzle Reynolds number (Ren) is given as ρ g d n u n ⁄ µ g , 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 may be considered as a collection of fine tubes (straight or zigzag). At low gas flow rates, discrete bubbles form at the plug exit, but at higher flow rates bubbles coalesce at the plug exit itself and assume 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 the argon stirred ladles have a 60-tonne capacity, and assuming 0.15 m as the diameter of the porous plug, 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 due to the non-wetting nature of the liquid. Hence, it may be concluded that coalescence before detachment is expected. It is shown schematically in Figure 3.9, which depicts a simplified situation only. For example, with segment-purging plugs, fine streams of gas would be issuing out through parallel channels. There, coalescence is expected only at a higher gas flow rate. Hence, smaller bubble sizes and faster gas-liquid reaction are expected even at a higher flow rate. Moreover, ©2001 CRC Press LLC

Wetted

Non-wetted Nozzle

Orifice

Porous plug

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

pulsations would be much less in the absence of coalescence. This explains why there is less back attack 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 of the volume of the antechamber (Vc), which is defined as the volume between the last location for a large pressure drop (i.e., a valve) and the actual nozzle or orifice. Due to gradual rather than instantaneous buildup of pressure in the antechamber, the final volume of the bubble, upon detachment, would be larger than calculated from Eqs. (3.30) and (3.31). Sano and Mori29 have proposed an empirical correlation relating dB to dn,o´, dimensionless antechamber volume (capacitance number, Nc), and other variables. Experimental measurements in liquid iron have demonstrated good 15 agreement with the above. Figure 3.10 shows significant dependence of dB on N c . A great deal of theoretical work has been done on the rising velocity and shape of gas bubbles in liquids, and in most cases the theory is in quite good agreement with measurements. There are

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

©2001 CRC Press LLC

several dimensionless numbers controlling bubble shape.13 An important one is the bubble Reynolds number, defined as d B uB ρl Re B = --------------µl

(3.32)

where uB = linear rise velocity of bubble. Small bubbles (ReB < 1) are spherical in shape. Large bubbles (ReB > 1000), under some other restrictions, are spherical cap shaped. To satisfy various conditions, they have to be larger than 1 cm in diameter in liquids of low viscosity (e.g., water or liquid 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 the gas inside. Small spherical bubbles behave like rigid spheres, and the terminal velocity (ut ) is given by Stokes’ law, viz., 2

dBg - ( ρ – ρg ) u t = ---------18µ l l

(3.33)

ut for spherical cap bubbles can be expressed as gd u t = 1.02 --------e 2

1⁄2

(3.34)

where de is diameter of a sphere whose volume is equal to that of the bubble. Experimental measurements in water as well as in molten metals indicate that a better approximation is obtained if 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 as bubble swarms, rather than single bubbles. In such systems, bubbles behave differently from single bubbles, 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 volume of gas in gas/liquid mixture α = ------------------------------------------------------------------------------------total volume of mixture

(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 considerably larger than what Eqs. (3.33) or (3.34) would predict, because the upward motion of the liquid assists 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 cylindrical vessel containing liquid via a nozzle located at the bottom and placed along the axis of the vessel. ©2001 CRC Press LLC

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

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 of liquid 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 is known 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 nozzle or 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 its cone angle (θp), as shown in Figure 3.11. The plume profile and its dimensions depend on various operating variables. The most critical of these is the gas velocity at the nozzle tip. Measurement of the plume cone angle in liquid steel is obtained indirectly from the plume diameter as it emerges at the top surface. This is not reliable, since the profile deviates from that of a cone near the top surface. 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 axisymmetric nozzle at bottom of the vessel and, through regression fitting of data, obtained the correlation: – 0.441 – 0.254 θp 0.12 H  d-----n -------- = 0.915Fr m  ----  D  D 180

(3.36)

The definition of modified Froude number (Frm) was provided in Table 3.1, where u is to be taken as the velocity of gas issuing out of the nozzle, and L means H. Xie et al.17 determined plume width in molten Wood’s metal at 100°C and compared this with measurements in a water model and mercury. Statistically speaking, no difference could be obtained, indicating that we may employ Eq. (3.36) for estimating θp in liquid steel, of course, after incorporating the actual value of Q upon exit from the nozzle at bath temperature. Although the above discussions would provide a simple approach to estimation of θp, it is to be kept in mind that the plume diameter, at least near the top surface, is likely to be larger in steel melt than in water as a result of the greater density of steel and consequently more bubble expansion. ©2001 CRC Press LLC

Significant experimental data have been collected on physical characteristics of the plume in water 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 gas fraction, bubble size, bubble frequency, and bubble rise velocity. The use of hot film anemometers and 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 distance from 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., r α ---------- = exp  – -----2  b α max 2

(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 bottom blowing through an axisymmetric nozzle in a water model: r 2.4 α ---------- = exp – 0.7  ----  r 1 α max

(3.38)

At r = r1, α max α = --------2 Equation (3.38) demonstrates that the decay of α/αmax with increasing r is more than that predicted by the Gaussian curve. Data of others17,18 also seem to suggest the same, although they have fitted with the Gaussian curve. Castillejos and Brimacombe19 proposed further that g r 1 ------2 Qn

1⁄5

 gd 5 = 0.275  -------2-n  Qn 

0.155

ρ1   ---- ρg

0.11

Z  --- d n

0.51

(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, and N is a dimensionless parameter equal to  gd 5n  -------2-  Qn 

0.26

ρ -----1  ρ g

0.13

Z  --- d n

0.94

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 –3 m ) and have proposed a Gaussian distribution of α as in Eq. (3.37). On the basis of regression fitting of experimental data, they have proposed the following relations: ©2001 CRC Press LLC

b = 0.28 ( Z + H o )

7 ⁄ 12

( Qz ⁄ g )

α max = 0.65 [ Q n ( ρ 1 ⁄ σ 1 g ) 2

2

1⁄2 1⁄4

]

1 ⁄ 12

/( Z + H o)

(3.41) (3.42)

where Ho is the axial distance of the hypothetical origin of conical plume from the nozzle exit, 0.1 1⁄2 2 given as 4.5d n ( Q n ⁄ g ) . σ1 is the surface tension of the liquid, and Qz is the gas flow rate at pressure 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 metal based on the above equations. Xie et al.17 also made measurements with gas blowing through eccentric nozzles, and they proposed the following correlations:  r – r 2m α ecc,r ----------- = exp –  ------------2  α max  br 

(3.43)

2 α ecc,z Z ----------- = exp –  ----2- b  α max z

(3.44)

and

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 was an elliptic cross section. From measurements of α, the mean velocity of the gas stream (ug) in a cross section of the plume can be determined as the ratio of gas flow rate to the total gas fraction in the cross section, i.e.,

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

©2001 CRC Press LLC

–1 u g = Q  ∫ α d A  

(3.45)

A

Based on Eqs. (3.41), (3.42), and (3.45), and assuming radial symmetry of the plume around the axis 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 α d A A refers to plume cross-sectional area. It was found that this parameter was the same for centric and eccentric gas blowing. Some measurements of time-averaged upward velocity of liquid in the plume ( u 1 p ) are available in the literature for a nozzle-fitted water model.9,10,18,20 ( u 1 p ) is at maximum along the axis. Values ranged between 0.2 and 0.3 ms–1, depending on value of Qn. Radial distribution of velocity is Gaussian, with the maximum value along the axis, i.e., u1 p 2 2 --------------= exp ( – r ⁄ b u ) u 1 p,max

(3.47)

where bu is a constant that depends on gas flow rate, height above the nozzle, etc. Quantitative correlation of experimental data has been proposed by Oeters et al.10 for centric blowing of air in water as – 0.12

(3.48)

bu = 0.38 Q0.15 Z0.62

(3.49)

u 1ρ,max = 3.37Q

0.25

Z

It shows that the axial velocity, u 1 p,max , does not vary much with vertical distance, Z. This has been corroborated by other investigators as well. This is in contrast to a free gas jet where the axial velocity decreases rapidly as Z increases. The difference lies in the fact that the rising bubbles impart upward momentum to the entrained liquid throughout the plume volume due to buoyancy force, whereas the momentum of a free jet is derived solely from its momentum upon exiting from the nozzle. The buoyant plume may be visualized as a pump, making the liquid flow upward. The volumetric flow rate of liquid at any horizontal section Ql may be obtained from Eqs. (3.47), (3.48), and (3.49) as Q1 =

∫A ulp dA

0.55

= 1.52Q n Z

1.13

(3.50)

Oeters et al.10 also proposed that the above correlations may be employed for liquid steel as well, provided that the gas flow rate (Qn) is calculated for the actual pressure and temperature of gas at the nozzle exit. Moreover, a broadening of the plume in liquid steel may be taken care of by substituting Z with Z · ψ, where ©2001 CRC Press LLC

1 1 ψ = --- ln ----------------β (1 – β)

(3.51)

Z β = ---------------ha + H

(3.52)

and

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 ( u B ) have been measured in water models18–20 and Wood’s metal,17 and ( u B ) did not vary significantly along the axis of the nozzle. The variation was much less in the radial direction as compared to α and ( u lp ) . For example, ( u B ) was more than 60% of its axial value in all cases, and sometimes the profile was almost flat. In water, the overall range obtained by the investigators ranged from 0.2 to 2 ms–1 depending on Q and Z. In Wood’s metal, ( u B ) along the axis ranged between 0.5 and 0.7 ms–1, and it was found to be proportional to ug. It has been proposed17 that Eq. (3.46) can be used to estimate ( u B ) as well, except that the coefficient should be 54.51 in place of 75.73. Comparison of ( u B ) and ( u lp ) in water model studies revealed that ( u B ) was always larger than ( u lp ) . This is due to bubble slip. Time–averaged bubble slip velocity ( u s ) = u B – u lp

(3.53)

( u s ) varied approximately between 0.2 and 0.4 ms–1. On the basis of their experimental data and comprehensive analysis of the same, Sheng and Irons20 have shown that ( u s ) was approximately the 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 of importance in connection with processes occurring at melt surface, such as gas absorption, slag metal reaction, etc. Sahajwalla et al.21 investigated this region using an electroresistivity probe in a water model. The gas fraction was at minimum at the axis and increased with radial distance from 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 of spout radius (rs) with other parameters was expressed by the following relationship: g r s  ------2 Q  n

1⁄5

= 0.48Z + 8.3 ( Fr ) *

– 0.18

(3.54)

2 1⁄5

where Z = Z ( g/Q n ) *

The bubble frequency ranged between 14 to 16 s–1 along the axis and decreased to 1 to 4 s–1 toward periphery. 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 question there 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 to obtain good thermal homogenization as well. It was also found that the time for homogenization was 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. Two water-model investigations14,23 have provided some information. These were porous glass-disc and not segment-purging plugs. Gas fraction measurements by electroresistivity probe yielded the correlation for axial location14 as ©2001 CRC Press LLC

Z α max = 0.71 ---------------------– 0.2 2 ( Q n /g )

– 0.9

(3.55)

Radial variation of α was found to obey Gaussian distribution. The mean bubble diameter showed a sudden increase with the onset of coalescence. Axial and radial velocity components of the liquid varied 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 dimensionless number considered for simulation is the modified Froude number (Frm) as defined in Table 3.1. In connection with a gas-purged ladle, it is to be rewritten as un ρg Fr m = ------⋅ -------------------gH ( ρ 1 – ρ g ) 2

(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 plug diameter of 0.15 m, and assume entire plug surface area as a nozzle. For Qv = 330 × 10–4 m3s–1 per m3 bath volume, nominal value of un would be 16 ms–1 and Frm = 0.57. This may be compared with Frm >10 if a tuyere was employed, and Frm >100 in bottom-blowing converters. Hence, the inertial force is too small to significantly influence the flow for a porous plug, and Frm should not be a relevant criterion for simulation from this point of view. Mazumdar and Guthrie7 have also questioned relevance of Frm in gas injection through a porous plug. Forces that are expected to govern the nature of flow are • • • •

3.2.3

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

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 axisymmetric 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 recirculatory flow. They summarized that hydrodynamic conditions near an axisymmetric nozzle or plug are not critical to flow recirculation in large cylindrical vessels. This view is considered to be valid even now. 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, provided that 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 porous plug.25 The existence of dead zones near the bottom of vessel, especially at the bottom corners, is well established. The main flow torus has a chance to come close to the bottom only at a high gas flow rate and with the H/D ratio ranging between 0.4 and 0.8.10 The geometry and size of the dead zone are dependent also on the gas-purging arrangement. Figure 3.15 shows this schematically for various arrangements.26 Figure 3.13 demonstrates considerably higher velocity in the plume region than in the bulk liquid. Velocities are very small near the wall and bottom of a vessel. Quantitatively, the axial velocities ranged from 0 to 0.4 ms–1 and radial velocities less than 0.1 ms–1 for gas flow rates ranging from 10–4 to 10–3 Nm3 s–1, which covers the ladle refining conditions, generally speaking. ©2001 CRC Press LLC

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

Measurement by LDV is also capable of determining values of RMS of the fluctuating component of velocity, i.e., 2 1⁄2

( u′ )

Figure 3.16 shows a plot of this, obtained in axisymmetric blowing through the nozzle in the water model.20 Qualitative similarity with velocity field (Figure 3.13) may be noted. Turbulent kinetic energy (k) as defined in Eq. (3.25) is another parameter of importance in characterizing turbulence. Figure 3.17 shows isopleths of k20 for the same experimental conditions as for Figures 3.13 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 defined in Eq. (3.23). Sheng and Irons20 found I to be approximately 0.2 for bulk flow and larger than 0.5 in the plume region, and turbulence was isotropic. Ballal and Ghosh27 simulated a bottom-blown steelmaking converter process using a water model. They were interested in stresses on the bottom and side wall due to fluid motion. Air flow rates were higher than those employed in the simulation of ladle flow by other investigators. The number of nozzles was 1, 3, 6, and 12. The single nozzle was axisymmetric, and multinozzles were either symmetrically or asymmetrically located around the vessel axis. Tiny platinum electrodes were flush mounted at various locations on the bottom and wall of the vessel. The electrochemical technique was employed to determine saturation current density, which yielded concentration and velocity gradients at the surface and hence wall shear stress ( τ ) . Specially designed electronic instruments allowed the determination of both mean shear stress ( τ ) and RMS of a fluctuating component. It was found that, for a certain nozzle arrangement, in the entire gas flow range, 2 1⁄2

( τ′ )

= Cτ

(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. ©2001 CRC Press LLC

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

Mazumdar et al.28 carried out measurements of fluctuating and mean velocities of liquid at several locations of the bath by LDV in a water model with centric gas injection by nozzle. They employed four gas flow rates and three arrangements, viz., free bath surface, surface covered by a floating wooden block, and surface covered with 15 mm thick oil layer. Averaging over the bath yielded values of the average speed of bath circulation ( u av ) and the averaged RMS of the fluctuating velocity component, 2 1⁄2

[ u′ ] av

The I obtained by taking the ratios of these ranged between 0.2 and 0.31, with a master average value of 0.25. Summarizing all these findings, it may be concluded that, under ladle refining conditions, 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 ©2001 CRC Press LLC

(3.58)

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

where Eb = buoyancy energy of the gas bubble in liquid, Ek = kinetic energy of the gas at exit from the 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 is related to energy utilization for bath stirring. They found εb to be negligible as compared to ε at low gas flow rates. This agrees with observations by others.29 εexp is theoretically equal to εb, and ©2001 CRC Press LLC

FIGURE 3.17 Contour map of the distribution of turbulent kinetic energy in a large vessel, produced with the flush-mounted nozzle for 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 that only a small fraction of this is really utilized in inducing bath motion. In one of the earliest analyses of this, Bhavaraju et al.31 also ignored it. Hence, for gas-stirred ladles and many other situations, investigators take ε = εb for the sake of avoiding complications. It may be an approximation, but it has provided the basis for further advancement in the area of process dynamics in secondary steelmaking and elsewhere. This is because 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 it rises, the value of QM is to be a mean value of volumetric gas flow rate. Bhavaraju et al.31 employed a logarithmic mean value where P Tl Q M = Q. ------o- . -------P M 298

(3.61)

where Q is the gas flow rate in Nm3 s–1, Po is atmospheric pressure, Tl is the temperature of liquid in Kelvins, and PM is the logarithmic mean pressure, given as PH – Po P M = -------------------------ln ( P H ⁄ P o )

(3.62)

PH = Po + ρ1gH

(3.63)

where

©2001 CRC Press LLC

Combining Eqs. (3.60) through (3.63), and putting in values, 340QT ε m = -------------------1 ln ( ( 1 + 0.707 )H /P o ) M

(3.64)

where εm is rate of energy input in watts per kilogram of liquid steel. M is the mass of the steel in kg, H is in meters, and Po is in bar. For water, 0.707 in Eq. (3.64) is to be replaced by ρ water - = 0.099 0.707 × -----------ρ steel As stated in Sec. 3.1.3, there are basically two methods of analysis of fluid flow-differential and integral. Differential analysis requires the solution of equation of continuity (Eq. 3.10) and the equation 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 computation of fluid flow problems. The Navier–Stokes equation was originally applied to laminar flow. Nowadays, it is employed for turbulent flow as well. This calls for certain modification and empiricism, and it involves computer-oriented numerical methods. As discussed in Sec. 3.1.5, turbulent viscosity (µ t) is not a property of the fluid but depends on nature and intensity of turbulence as well. As already stated in 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 metallurgical processing.32,33 One of the most recent papers is by Joo and Guthrie.34 Very useful information has been 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 not presented here. Integral analysis of flow in gas-stirred ladle was initiated by Chiang et al.9 and Sahai and Guthrie.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 most important being its inability to predict spatial variation of velocity and turbulence parameters. However, both are well suited for macroscopic predictions and understanding of phenomena and analysis at an elementary level. Hence, it is briefly presented below. Based on their water-model investigations, Sahai and Guthrie24 employed the correlation u av 1⁄3 ------- . ( R ) = 0.18 up

(3.65)

where u av 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 input energy rate. It may be noted that the kinetic energy content of recirculating liquid was only a fraction of the total energy input. The fraction was 0.235 for a free bath surface with a floating wooden block. But it was only 0.12 with a slag layer. According to the authors, this was due to the energy required to create oil-water emulsion, and it demonstrates the likelihood of a significant retarding 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 in the bulk liquid, with the rest getting lost due to bubble slippage in the plume, formation of waves and droplets at the surface of the bath, and friction at the vessel wall. It seems that bubble slippage is the dominant one. What this means is that the plume should be treated as two-phase flow rather ©2001 CRC Press LLC

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

than a quasi-single phase flow. Some recent papers have attempted modeling on this basis. But even then, the loss of energy at the free surface, especially in the presence of a slag layer, remains a source of uncertainty in energy balance. The average plume velocity has been correlated with other variables as follows for a water model:26 1⁄3

u p = 4.5 ( Q n H

1⁄4

)/R

1⁄3

(3.66)

Combining Eq. (3.65) with (3.66) yields 1⁄3

u av = 0.79 ( Q n H

1⁄4

)/R

2⁄3

(3.67)

Krishnamurthy et al.35 employed a modified approach taking into account bubble slip in the plume and also employed their data of plume cone angle measurement Eq. (3.36). The following correlations were obtained: u lp = 0.446ε

0.174

(3.68)

and Q1 = 2.81 × 10–3 ε0.625 H0.942 dn0.119

(3.69)

where u lp is the upward average liquid velocity in plume, H is the bath height and Q1 is the volumetric flow rate of liquid in the plume. It may be further noted that Q1 is the volumetric flow ©2001 CRC Press LLC

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., New York, 1960. 4. Szekely, J. and Themelis, N.J., Rate Phenomena in Process Metallurgy, Wiley-Interscience, John Wiley & 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.

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4

Mixing, Mass Transfer, and Kinetics

4.1 INTRODUCTION Since chemical reactions occur during steelmaking, the vessels are reactors according to general terminology. Steelmaking, including secondary steelmaking, is concerned with liquid-state processing. The reactors are semi-batch types, with the exception of the tundish, which is close to a continuous stirred tank reactor. In semi-batch reactors, the liquids are added and withdrawn in batches, whereas the gases flow in and out of the reactors continuously. Solid reagents are either added in batches or injected continuously as powder. Besides chemical reactions, some physical and physico-chemical processes are of importance in secondary steelmaking, i.e., homogenization of composition and temperature, separation of nonmetallic particles from steel melt, loss and gain of heat content of the melt, and dissolution of alloying 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 more of 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 as important as composition control in secondary steelmaking. However, the issue of temperature control is dealt with in Chapter 8. Homogenization of temperature of the steel melt is primarily dependent on convective heat transfer, which is akin to convective mass transfer. Hence, knowledge of one can be utilized for the other. Rates of specific reactions and processes are discussed in later chapters. Dissolution of alloying additions in molten steel is partly controlled by rate of heat supplied to the cold addition. There are other minor examples. However, all other reactions in secondary steelmaking are not limited by the rate of heat supplied to the reaction zone. Therefore, we are primarily concerned with reaction kinetics, mixing, and the feed rate of reactants. In this connection, the ternary diagram in Figure 4.1, proposed by Robertson et al.,1 in connection with powder injection processes in a secondary steelmaking ladle, is quite illustrative. Near corner 1, reactions are close to chemical equilibrium, and the liquid is well mixed. Hence, feeding rate of powdered reagents 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, and therefore is rate controlling.

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1

2 3

tf /Σt

1

0 =

reaction + mixing

d

at

mixing rate controls

xe

feeding feeding + + reaction mixing feeding, reaction and mixing

mi

eq uil ibr ium

y

xx

ctl

rfe

pe

feeding rate controls

reaction rate controls

3

2

tmix / Σ t

powder

dumping

tr / Σt

Σt = tf + tr + tmix

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

The present chapter is a brief presentation of the fundamentals of kinetics, mixing, and mass transfer with specific reference to steel melt in a ladle, stirred by inert gas through a nozzle/porous plug 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 4.2.1

MIXING IN STEEL MELTS IN GAS-STIRRED LADLES FUNDAMENTALS

OF

MIXING

Section 3.2 dealt with fluid flow in steel melts in gas-stirred ladles. This section is concerned with mixing in steel melts in gas-stirred ladles. Mixing is dependent on the nature and intensity of fluid motion and turbulence in the melt. As in Section 3.2, here also we consider only inert gas purging by porous plugs/nozzles fitted at the bottom of the vessel. Also in the area of mixing, experimental investigations with steel melts have not been done often. Fundamental investigations have been ©2001 CRC Press LLC

conducted mostly in laboratory water models. Again, a majority of the studies employed axisymmetric 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. Comprehensive literature is available in the chemical engineering field.9–10 In view of these considerations, the number of references has been kept limited. Mixing occurs by convection (i.e., bulk flow), turbulent (i.e., eddy) diffusion, and molecular diffusion. Experimentally, the speed of mixing is measured by pulse-tracer technique. A small quantity of tracer is suddenly added into the liquid at some location. The concentration of the tracer is monitored at some other location in the liquid using a measuring probe. In water models, aqueous solution of KCl or HCl are popular tracers. Dissolved KCl or acid increases electrical conductivity of water. Hence, its concentration at any location can be measured as a function of time by the electrical conductivity probe. Imagine the sudden addition of a tracer into a liquid. Bulk motion would transport the tracerrich liquid region, known as clump, to other regions. It also causes disintegration of the clump into smaller and smaller eddies as it moves through the liquid. Dispersion of eddies by eddy diffusion causes further mixing. The disintegration of clumps, however, can not continue indefinitely. As discussed in Section 3.1.5, with decreasing eddy size, viscous forces increasingly resist further disintegration 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 composition (i.e., micromixing) is possible by molecular diffusion only. Molecular diffusion is an extremely slow process. Hence, micromixing is unattainable in industrial processing as well as in studies on mixing. Therefore, perfect mixing would mean complete 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, the vectorial form of the equation is: ∂C i -------- = u ⋅ ∇C i + ∇ ⋅ ( D t ∇C i ) ∂t

(4.1)

∂C where Ci is concentration of tracer i at time t after tracer addition. --------i refers to rate of change of ∂t concentration at a location (say, the probe location). Figure 4.2 presents a typical recorder voltage-time curve for addition of KCl solution into a cylindrical water bath stirred by blowing air from the bottom using an axisymmetric nozzle.8,11 The change in the concentration of KCl at the probe location was proportional to the change of recorder voltage. Hence, the curve represents the variation of concentration of KCl over time at the probe location. Major oscillations in the recorder trace are due to recirculatory flow. The peak-to-peak interval for major peaks is the approximate time for one recirculation (tC) and was about 8 s in Figure 4.2. The amplitude of oscillation decreases rapidly with time due to the progressive disintegration of clumps as the bulk liquid recirculates. Experimentally, mixing speed is determined by measuring the mixing time (tmix) of a small quantity of tracer added into a liquid suddenly. It is difficult to measure tmix for 100 percent macromixing. Hence, some standardization is desirable. In this connection, degree of mixing (Y) has been defined as: o

Ci – Ci Y = -----------------o f Ci – Ci ©2001 CRC Press LLC

(4.2)

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

where C i is the instantaneous average concentration at any time t, C i is the uniform initial f concentration before tracer addition, and C i 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. (Figure 4.2). 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 a somewhat lower value of tmix than experimental measurement. It is an indication that the mixing process is controlled both by bulk convection and turbulent diffusion. The higher the gas flow rate, the more intense would be stirring and consequent mixing, resulting in lower tmix. This is well established. Krishnamurthy et al.8 made comprehensive measurements of tmix at several combinations of tracer injection and probe locations in their water model and obtained a single value of tmix under a given experimental condition. However, several investigators6 found that tmix is dependent on tracer addition and monitoring point locations. Such a phenomenon was observed at relatively low specific gas flow rates, typical of ladle metallurgy. Figure 4.3 presents mixing time vs. gas flow rate at different measuring positions in a water model with centric bottom gas injection, showing significant dependence of tmix on probe location.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 or plug are not critical to flow recirculation in large cylindrical vessels. A similar comment is applicable to 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 Figure 4.4 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 achieve gentle 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 ©2001 CRC Press LLC

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

time with dual plugs was obtained if the two plugs were located at diametrically opposite positions at 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 cause a loss of energy and slow down the recirculatory flow.15 Evidence for this has been gathered from water model experiments (Figure 3.18). Hence, it is expected that mixing would be slower in the presence 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. It has also been found that tmix decreases as bath height (H) increases, provided H/D < 2, where D is the vessel diameter. In steel ladles, H/D < 2, and hence the above conclusion is applicable. It has ©2001 CRC Press LLC

also been found to depend on D as well as nozzle diameter (dn). Properties of a liquid such as viscosity, density, and surface tension are also expected to influence tmix. Under a specified condition, Qn is proportional to the rate of buoyancy energy input (εb) as given in Eq. (3.62). As already stated, εb has been accepted as a measure 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. Several quantitative relations have been proposed about the dependence of tmix on εb, H, and D. These are semi-empirical, based partly on mathematical analysis and partly on experimental data. Measurements in molten steel are very limited. Experimental data have been collected primarily 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. The assumption was that mixing was solely controlled by eddy diffusion. Besides the equations of continuity 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 stirred ladle, RH degasser, water model, etc., is based on the concept of a turbulence model, which tends to suggest that tmix should depend only on εm. The correlation of Nakanishi et al. was as follows: – 0.4

t mix = 800e m

(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 twice as large as that of buoyancy energy. Moreover, εm was in watts/tonne. Correcting for a factor of two and taking εm in watts/kilogram, Eq. (4.4) may be rewritten as – 0.4

t mix = 38.3e m

(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 postulations made by some earlier workers, argued that the energy dissipation rate due to turbulence is only a fraction of εm, and they related to to H and D. Combining all these, they tried to explain the –1 ⁄ 3 dependence of to on H and D. It was also predicted that t mix α ε m . Another difficulty with the turbulence models is their inability to explain the oscillating nature of concentration vs. time curves upon addition of a tracer (Figure 4.2). Again, the natures of these curves are dependent on probe location. Mazumdar and Guthrie20 carried out extensive mathematical and physical modeling and arrived at the conclusion that all experimental behavior patterns can be explained 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 carried out recently.14,21 ©2001 CRC Press LLC

Circulation Models These models assume that the circulation rate of liquid in the bath controls mixing. Here, to is taken as 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 of tmix on H and D, as observed experimentally. Krishnamurthy et al.,23 through their macroscopic energy balance model, proposed equations for calculation of tc. Combining that with their experimental values of tmix (Y = 0.995), they found that t mix H d = f  Fr m , ----, -----n Circulation number ( C i ) = ------ D D tc

(4.7)

The above approaches could not quantitatively explain the concentration versus time curves (Figure 4.2), 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 assuming complete mixing within any tank. These have successfully explained the concentration versus time curves.12,13 Several mixing time correlations have been proposed by various investigators.6 In the early studies, no standardized degree of mixing was employed. It is necessary to assess how the different correlations compare with one another. For this, in Table 4.1 we have selected only those in which Y = 0.95 and which have been arrived at or tested against experimental data of water model with centric gas injection through a nozzle. TABLE 4.1 Mixing Time Correlations for 95 Percent Degree of Mixing Reference Mazumdar and Guthrie20 Stapurewicz and Themelis24 Neifer, Rodi, and Sucker21

Correlation – 0.33

t mix = 12.2ε m

H

– 1.0

– 0.39

t mix = 11.1ε m t mix = 3.2Q

– 0.38

H

H

D

1.66

0.39

– 0.64

D

2.0

Figure 4.5 presents calculated curves of tmix vs. εm by various correlations of Table 4.1 for a water model of 0.5 m diameter and 0.4 m height at a temperature of 298 K, and atmospheric pressure 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 applied even to liquid iron, others have proposed a scale factor. An examination of the literature21 tends to suggest that experimental values of tmix in liquid steel are somewhat larger than those in a water model 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 1.9 for 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 occur among phases. Examples are solid–liquid reactions, slag–metal reactions, and gas–metal reactions. Consider the following reaction occurring between molten steel and molten slag: ©2001 CRC Press LLC

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

[S] + (O2–) = (S2–) + [O]

(4.8)

S and O denote sulfur and oxygen, [ ] indicates metal phase, and ( ) indicates slag phase. Since slag 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 reactions 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 from one site to another takes place via liquid metal, which is an electrical conductor. This is shown schematically 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 4.6 Electrochemical mechanism of slag–metal interfacial reaction.

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1. 2. 3. 4. 5.

Transfer of sulfur from the bulk of the metal phase to the slag-metal interface Transfer of O2– from bulk of the slag phase to the interface Chemical reaction at the interface Transfer of oxygen from the interface to the bulk metal 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 are governed 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 them is prevented, the overall reaction ceases to occur. It is also to be noted that the slowest kinetic step would tend to influence the rate predominantly, and it is typically termed the rate-controlling or rate-limiting step. The conclusions drawn above would be just the reverse if the kinetic steps were in parallel, where the fastest step would influence the overall rate the most. However, it is impossible to conceive of a process where all the steps would be in parallel. Hence, it may be concluded that the 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 all kinetic studies is to find out what the slowest step is. Of course, other kinetic steps would also influence the overall process rate to some extent. At times, two or more steps may have comparable rates. However, owing to the complexity of the steelmaking processes, one kinetic step is often assumed to control the rate, and others are assumed to be infinitely fast and thus at virtual equilibrium. With this simplification, the rate of a process estimated on the basis of only the slowest kinetic step would be the highest, and larger than the actually observed rate. Such an estimate therefore 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 be best understood on the basis of the findings of laboratory experiments carried out over the past several decades. Here, the system is isothermal and each phase is well mixed. Hence, studies have provided information on reaction kinetics exclusively. The laboratory findings have been that steelmaking reactions are generally controlled by mass transfer at the phase boundary, and not by interfacial chemical reaction. This is expected from theoretical considerations as well. However, there are exceptions, the most notable being absorption and desorption of nitrogen by molten steel, which is a case of mixed control kinetics, i.e., both interfacial reaction and mass transfer partially controlling the rate of overall reaction. With the above 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 concentrations of reactants (A, B) and products (C, D) as C C D D r = Ak c  C A C B – ------------ K 

(4.12)

where A is area of interface of the phases involved, CA etc. denote concentrations of respective species per unit volume (i.e., mol/vol or mass/vol.), kc is the chemical rate constant, and K is the equilibrium constant for Reaction (4.11). ©2001 CRC Press LLC

Equation (4.12) is the rate expression for a reversible reaction, where both forward and backward 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. Hence they are determined experimentally. For example, for Reaction (4.11), suppose the experimentally determined rate expression is α

β

r = Ak c C A C B

(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: B ln k C = A – --T

(4.15)

where T is temperature and A, B are empirical constants. Arrhenius attempted to explain this observation through his famous equation as E k C = A exp  – -------  RT 

(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 is theoretically 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 one kinetic step exclusively controls the rate. Wherever that is not true, E is not the true activation energy 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 concentration. Mixing, already discussed in Section 4.2, is also a process of mass transfer. It is a question of terminology only. By mixing, we mean mixing in the bulk fluid. By perfect mixing, only macromixing was meant, and molecular diffusion was ignored. In contrast, the motion of individual atoms and molecules is our ultimate concern in mass transfer. 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 phaseboundary mass transfer. Actually, it is these transports in connection with heterogeneous reactions that 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: ∂C ∂C m˙ i, x J i, x = -------- = D i --------i + C i u x – D t --------i ∂X ∂X Ax molecular + bulk + turbulent diffusion convection diffusion

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(4.17)

where

Ji,x = flux of species i along the x-direction dm m˙ i = ---------i = mass rate of transport of species i along x dt Ax = area normal to the x-direction Di = molecular diffusivity of species i in the fluid Ci = concentration of species i in mass per unit volume u x = 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 the composition of solid to be constant. On the fluid side of the interface, the existence of a velocity boundary layer has already been discussed (Figure 3.3). In a similar fashion, a concentration boundary layer develops in the fluid adjacent to the solid surface (Figure 4.7). Just at the interface, we may assume u x = 0 and, due to laminar flow, Dt = 0. This simplifies Eq. (4.17) as m˙ i, x -------Ax

at x = 0

∂C = – D i  --------i  ∂x  x = 0

(4.18)

Noting that Ax is solid surface area (A), and through the geometric construction shown in Figure 4.7, Di s 0 s 0 - ( C – C i ) = Ak m,i ( C i – C i ) ( m˙ i ) at interface = A ---------δ c, eff i

S Ci

(Fluid) (Solid)

Ci

Concentration profile

o

Ci

δC, eff x=0

x

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

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(4.19)

δc,eff is known as the effective concentration boundary layer thickness and km,i is the mass transfer coefficient for species i ( D i ⁄ δ c, eff ) . δc, eff depends on fluid flow. The more intense the flow, the smaller is δc,eff with larger km,i and m˙ i . This is how fluid flow influences rate. km,i also depends on the transport properties of the fluid (µ, ρ, D), and the geometry and size of the system. A measure of size is characteristic length (L), which, for example, is the diameter for a pipe or sphere, as already mentioned in Table 3.1. To estimate mass transfer rates, km,i is to be estimated or determined. Experimental measurements have been carried out on a variety of systems. Dimensionless correlations are very advantageous, and this is how km,i is correlated with fluid flow, etc. Table 4.2 presents the dimensionless numbers for convective mass transfer. The symbols have already been defined in Chapter 3 in connection with Table 3.1. TABLE 4.2 Common Dimensionless Numbers in Convective Mass Transfer Dimensionless Number Item

Definition

Name

Symbol

Lu -----ν

Reynolds no.

Re

gL ∆ρ -------2 ------ν ρo

3

Grasshof no.

Gr

Mass transfer properties

ν ---D

Schmidt no.

Sc

Mass transfer coefficient

kmL ⁄ D

Sherwood no.

Sh

Fluid flow (forced convection)

Fluid flow (free convection)

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

In general, Sh = B + D Rem Scn, for forced convection

(4.20)

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

(4.21)

and

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 transfer correlations 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 dimensionless correlations are available for several geometries and flow regimes in standard texts.2,3,5 They are mostly empirical. Appendix 3.1 contains values of µ, ρ, and ν for some liquids of interest in secondary steelmaking. 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, molten salt, or gas. The boundary layer theory of convective mass transfer has been highly successful at ©2001 CRC Press LLC

solid–fluid interfaces. Attempts have been made to extend the same to the two-fluid situation by assuming 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 layer at the interface sticks to the solid. Therefore, it is stagnant and not renewed. Moreover, turbulence cannot reach the interface. However, these assumptions are not valid at fluid–fluid interfaces. Davies26 has dealt with various 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 surface tension. The damping effect is pronounced in the direction perpendicular to the surface, but not so much in parallel direction. Levich considered this damping and proposed the following correlation: 1⁄2 3⁄2

k m,i = 0.32D i u o ρ

1⁄2

–1 ⁄ 2

σ equiv

(4.22)

where uo is the fluctuating RMS velocity in the bulk of the liquid, and σequiv is equivalent surface tension, defined as σ equiv = σ + ( l ρg ⁄ 16 ) 2

(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 renewal theories of mass transfer between two fluids. Out of these, only two are popular. Higbie assumed that eddies penetrate into the interfacial layer and renew the interface periodically. Each eddy is exposed for the same time before replacement by a fresh eddy arriving from the bulk. During this period, mass transfer is by unsteady diffusion. Higbie’s surface renewal theory is also applicable when the flow at the interface is laminar. If the viscosity of one fluid is much larger than that of the other, then the former exhibits a negligible velocity 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 as compared to that of the gas. Similarly, in a slag–metal system, the slag would tend to flow like a rigid body. In such situations, mass transfer at the interface in the high viscosity phase would be exclusively by molecular diffusion. Since the surface gets renewed continuously due to flow at the interface, such diffusion is unsteady, and it was derived that D 1⁄2 k m,i = 2  -------i   πt e

(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 a fresh eddy from the bulk. Danckwerts made a more realistic assumption that a fraction of surface renewal in time t is equal to [1 – exp(–St)]. Figure 4.8 shows the difference between Higbie’s and Danckwerts’ 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 fraction of surface renewed per second. In this model, S is to be determined experimentally and is, therefore, ©2001 CRC Press LLC

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

a source of uncertainty. S varies between 5 to 25 per second for mild turbulence, and up to 500 per second for violent turbulence.26 All the above models predict that km should be proportional to D1/2. This is in contrast to boundary layer theory, which predicts a dependence on D0.7–1. In chemical engineering, many investigators attempted to verify validity of this for mass transfer in liquid at gas-liquid and liquidliquid interfaces. The proportionality of km on D1/2 has been verified, and surface renewal mode is generally accepted now.26 In the metallurgical field, one of the earliest investigations was by Boorstein and Pehlke.27 They measured dissolution rates of hydrogen and nitrogen in inductively stirred liquid iron. Stirring intensity was varied. It was found that k m, H D ---------- = ------Hk m, N DN in quiescent melt, and D 1⁄2 k m, H ---------- =  ------H-  D N k m, N for well-stirred melts, thus indicating the applicability of boundary layer theory for the former, and surface 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 generally employed 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 few per second for large eddies to about 1000 per second or more for the smallest (i.e., Kolmogorov eddies). At normal and gentle turbulence, S ranges between 5 to 25 per second, and hence surface renewal is expected to be primarily by large (i.e., Prandtl) eddies. Visual observations also have confirmed this.26 This is because smaller eddies tend to get damped considerably near the interface unless turbulence is intense. One of the earliest attempts to determine S in a metallurgical situation was the water model study by Kumar and Ghosh,28 who measured rate of absorption of CO2 in water by the pH method and also estimated liquid–gas bubble surface area by a photographic technique. They found S to range from 40 to 100 per second. Investigations in the chemical engineering field have established that there is no significant difference between gas–liquid and liquid–liquid mass transfer, either in basic mechanisms or even in some quantitative relationships (e.g., in a stirred tank with one liquid stirred).26 ©2001 CRC Press LLC

Robertson and Staples29 proposed the following empirical correlation for the metal-phase mass transfer 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 rate Q is in m3 s–1. Taniguchi et al.30 measured the rate of CO2 absorption at the free surface of a water bath stirred by 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–liquid and latter for liquid–gas reaction. The presence of surface active species on the surface would retard the motion of fresh eddies coming from the bulk liquid, as shown in Figure 4.9a. This would lead to a lowering of the value of km as compared to that for a clean surface. A decrease of km by a factor of two for gas–liquid situation, and even by a factor of four for liquid–liquid mass transfer, has been observed.26 A reverse situation 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 first discovered it in the 19th century. It may even cause spontaneous interfacial turbulence. Richardson and 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.

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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 and elsewhere in secondary steelmaking. Addition of ferroalloys is an example. Melting-cum-dissolution of these alloys is controlled by rates of heat and mass transfer. Section 4.3.2 briefly presented the basics of mass transfer in fluid adjacent to a solid–fluid interface. The dimensionless correlations are 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 by the 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 the time-averaged bulk velocity. For convective heat transfer around the sphere, the analogous equation is: Nu = 2 + 0.6 (Re)1/2 (Pr)1/3 where

(4.29)

hL Nu = -----λ ν µC Pr = --- = ------α λ h = surface heat transfer coefficient, analogous to k λ = thermal conductivity α = thermal diffusivity C = specific heat of the fluid

Experiments have been done by several investigators in water models of a ladle, stirred by gas from the bottom. Gas injections were centric. The rates of the melting of ice and the dissolution of benzoic acid in water were studied. Solids were immersed in various locations, too. A few studies in molten steel are also available. Mazumdar and Guthrie6 have reviewed these. In a recent investigation, Iguchi et al.33 employed an electrochemical technique. Several dimensionless correlations have been proposed in the literature. Controversy exists about their relative merits and reliability. Hence, a detailed presentation is omitted here. The first difficulty in the determination of a dimensionless correlation of experimental data is that there is no characteristic bulk velocity in a gas-stirred liquid. Hence, local velocity and local Reynold’s number were employed. This requires solution of the turbulent Navier-Stokes equation to obtain the velocity field. It also has been established that an equation of the type of Eq. (4.20), such as Eq. (4.28) for a sphere, is obeyed provided intensity of turbulence (I) is less than 0.2 or so. At higher values of I, these equations tend to give a better fit with experimental data by incorporating I in the corelations. All investigators are in agreement on this. For example, Mazumdar et al.34 measured the rates of dissolution of vertical cylinders of benzoic acid in a gas-stirred water model and proposed the following relationship: Sh = 0.73 (Reloc,r)0.57 (I)0.32 (Sc)0.33 where ©2001 CRC Press LLC

(4.30)

2

Re loc,r

2 1⁄2

( ux + uy ) ⋅ D = ----------------------------------ν

(4.31)

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 further noted30 that Eq. (4.30) predicts that km ∝ Q0.2 approximately, where Q is the volumetric gas flow rate. This is in agreement with experimental data for dissolution of steel cylinders in carbonsaturated iron melts.35

4.4.2

LIQUID–LIQUID INTERACTIONS

Kinetic studies carried out in connection with various ladle metallurgy operations include the reaction between a gas bubble and liquid, slag–metal reactions, and absorption of gases at a free surface and in a plume’s eye. Fundamental studies have been primarily conducted in room temperature models. Not all of these are discussed in this chapter. Reactions and mass transfer between a gas bubble and liquid is dealt with in Chapter 6, on degassing. Absorption of gases at a plume surface 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. These also will be taken up in later chapters. In this section, we are briefly concerned with some fundamental laboratory investigations on mass transfer between two liquids in a vessel stirred by bubbling inert gas from bottom. Obviously, the metallurgical objective is to understand slag–metal reaction in bubble-stirred systems. Basic open hearth steelmaking, which was the dominant primary steelmaking process up to the 1960s, constituted the principal target for early workers across the World. Richardson32 and Turkdogan36 have reviewed them. A principal difficulty of fundamental study is that the actual slag–metal interfacial area (A) is larger than the geometrical surface area due to unevenness of the interface formation of slag–metal emulsion. A is a function of gas flow rate, etc. Moreover, it is a difficult task to properly determine it. Hence, experimental rate measurement yields the value of the kA parameter, where k is specific rate constant. When mass transfer is rate controlling, then k = km and we obtain the km A parameter on the basis of Eq. (4.19). km A has a dimension of (ms–1 × m2), i.e., m3 s–1. Sometimes the kmA/V parameter 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 proportional to Qn.Value of n has been found to be different in different ranges of gas flow rate. This is demonstrated by the study of Kim et al.37 as shown in Figure 4.10. Inert gas was injected from bottom axisymmetrically. Oil simulated the slag phase, and water simulated the metal phase. The equilibrium partition coefficient of thymol between oil and water is very large—somewhat like the partition of sulfur between slag and metal. This made the kinetics unambiguously controlled by mass transfer in the metal phase. Figure 4.10 shows three regimes in ln(kA) vs. Q curve, with different values of n. At a low flow rate, n = 0.6. Some other investigators have also reported n = 0.529,30. Visual observations did not reveal any perturbation in the oil layer. In the middle regime n = 2.51, and the oil layer near the edge of the plume eye continuously formed ligaments and disintegrated into droplets. In regime III, the entire oil layer was found to be dispersed in water as droplets. A lower value of n there is explained by the large residence time of droplets in water in this regime and their consequent ©2001 CRC Press LLC

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

saturation with thymol, retarding further transfer. Since Q is proportional to εm according to Eq. n (3.64), k m Aαε m . Formation of oil-in-water and slag-in-metal emulsion increases the liquid–liquid interfacial area by even a factor of about 100. Consequent large enhancement in kA parameter has been well established. The mechanism of drop formation is shown schematically in Figure 4.11.38 When the inertia force due to liquid circulation exceeds surface tension and buoyancy force at slag layer on plume edge, slag droplets form. Mietz et al.38 have also demonstrated an almost proportionate increase 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, required for emulsion formation. Kim et al.37, based on dimensional analysis and their experimental data, proposed the following empirical equation: Q cr = 0.035H

1.81

0.35 ms ∆ρ  σ -----------------2  ρ 

(4.33)

s

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

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 droplet detachment. Source: from F. Oeters, Metallurgie der stahlherstellung, Verlag stahleisen, Düsseldorf, 1989.

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Iguchi et al.39 have performed comprehensive cold model experiments with several liquids simulating slag to determine the critical condition for entrapment of slag in metal, and they proposed the following empirical correlation: u cr ,c ⁄ V = 1.2 ( ν s ⁄ ν m )

0.068

(Hs ⁄ D)

– 0.11

(4.34)

where, u cr ,c = 1.2ur p–0.28 V = (σms g/ρs)1/4 ur = (g Qcr/Hm)1/3 p = [Qcr2/(gHm5)]1/5 The subscripts s and m denote slag and metal, respectively. u cr ,c denotes critical centerline velocity. D is vessel diameter. Here also, gas injection was through a centric nozzle. Agreement with earlier investigators’ 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 Taniguchi et al30 verified km α D1/2, and some other aspects (Section 4.3.2). Hirasawa et al41 applied the theory of turbulent mass transfer phenomena26 to their own investigation of the reaction of silicon dissolved in molten copper with molten slag containing FeO at 1250°C, as well as to the experimental data of Robertson et al.29 on mercury amalgam-aqueous solutions and molten lead–molten salt systems. Figure 4.12 shows a typical k′ si 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 has a lower dependence on Q, in contrast to a room-temperature model study. This was explained with the help of flow patterns in slag and metal (Figure 4.13). At low Q, the slag was stagnant due to

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

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

its higher viscosity. At higher Q (region II), slag flow, as shown in Figure 4.13, retarded interfacial flow of liquid metal, causing this behavior pattern. Region III, of course, was due to an increase of the slag–metal interfacial area. Therefore, only region I could be analyzed by the turbulence theory and dimensionless correlations developed. Ogawa et al42 simulated a gas-stirred ladle as well as induction stirring in their water model 1⁄2 studies. Using KCl and Benzoic acid as solute, they found that k m,i ∝ D i approximately. Figure 1⁄2 –2/3 4.14 shows k m,i ∝ D i as a function of εm · V , where V is bath volume. Calculation based on Eq. (4.25) yielded values of S in the range of 15 to 8000 per second. While the lower value is all

km/

Di, min

√

- 2

Gas bubbling

2000 1000

Induction stirring (upward) Induction stirring (downward)

Ar bubbling (85 ton)

500

200

ASEA-SKF (85 ton)

100 50

20 10

20

50

ε

100

500 1000

V -2/3 , watt t-1 m -2

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

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200

right, the higher values are abnormally large and not expected (Section 4.3). Presumably, these are based 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 that of 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 for i leads to dC e – V --------i = Ak ( C i – C i ) dt

(4.35)

for a first-order reversible reaction. Here, V and A are the volume and interfacial area of the melt. e Ci is the instantaneous concentration of i in the melt, and C i is the concentration in equilibrium with the phase in contact with steel (slag or gas). o Integrating Eq. (4.35) between t = 0, C i = C i (i.e., initial concentration) and t = t, Ci = Ci, e

Ci – Ci -e = 1 – X = – kat ln ----------------o Ci – Ci

(4.36)

where a = A/V = specific interfacial area e

For irreversible processes, C i is very small, and Eq. (4.36) reduces to C ln ------oi = 1 – X = – kat Ci

(4.37)

Convective mass transfer at the phase boundary may be treated as a first-order reversible process s e o s e with k m = k , C i = C i , and C i = C i in Eq. (4.35). The justification for taking C i = C i is the assumption that the rate of interfacial reaction is very fast and not rate controlling. Hence, chemical equilibrium 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. For example when X = 0.05, 1 – X = 0.95, which means that 95% of solute i has been eliminated from the steel melt. Based on some literature values of kma, Ghosh43 plotted log X vs. t for a few reactions in 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 degree of mixing and is attained when t = tmix according to convention. A scan of the literature revealed that tmix ranged between 50 and 500 seconds for a variety of processes in steelmaking. Inhomogeneity in 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 are in the same overall range in steelmaking processes. Since both have rate expressions as for firstorder reversible processes, it is often difficult to say whether a process is controlled by slow mixing or slow mass transfer. In the context of slag–metal reaction in a gas-stirred ladle, it has been concluded by all that, when stirring is vigorous and slag–metal emulsion forms, mass transfer is faster than the rate of mixing. ©2001 CRC Press LLC

1.0 0.5

Slag - metal reaction (LD)

e

C _-O _ reaction (BOH)

Ci - Ci

o e Ci - Ci 0.1

0.05

0.01

H _ removal (Purging ladle, immersed lance)

50

100

150

200

250

TIME, sec

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

Szekely et al.44 considered the modified Biot number (Bim), defined as (km A) ⋅ H Bi m = ----------------------D eff

(4.38)

Their sample calculation for typical gentle stirring in a ladle yielded Bim of approximately 10–1 to 10–2. This they considered as low and concluded that the desulfurization reaction would be mass transfer controlled. Mietz and Bruhl45 carried out model calculations for mass transfer with mixing metallurgy in a ladle for sulfur removal. Their principal conclusion was that mixing would be the slower 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 interfacial chemical reaction or mass transfer in one phase only. However, there are situations when we may have to take into account the control of a reaction rate jointly by mass transfer in both phases. In that case, Eq. (4.19) is to be employed for both phases (I and II) as follows. m˙ i = ( m˙ i ) at interface = Ak m,i ( C i – C i ) I

S,I

o,I

= Ak m,i ( C i – C i ) II

II

S,II

(4.39)

Again, assuming interfacial equilibrium, S,II

Ci --------- = Li S,I Ci

(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), o,II

o,II

Ci  Ci  A o,I I – II o,I m˙ i = ----------------------------  C i – --------- = Ak m,i  C i – --------   1 1 Li Li  ------+ -----------I II k m,i k m,i L i ©2001 CRC Press LLC

(4.41)

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, John Wiley & 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 John Wiley & 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. ©2001 CRC Press LLC

42. 43. 44. 45.

Ogawa, K., and Onoue, T., ISIJ International, 29, 1989, p. 148. Ghosh, A., Tool and Alloy Steels, 25, 1991, Silver Jubilee issue, p. 65. Szekely, J., Carlsson, C., and Helle, L., Ladle Metallurgy, Springer Verlag, New York, 1989. Mietz, J., and Bruhl, M., Steel Research, 61, 1990, p. 105.

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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 rejected by the solidifying metal. This excess oxygen causes defects such as blowholes and nonmetallic inclusions 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 down by carrying out deoxidation after primary steelmaking and before teeming the molten metal into an ingot or continuous casting mold. This chapter is concerned with thermodynamics and kinetics of 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 1 --- O 2 ( g ) = [ O ] 2

(5.1)

where [O] denotes oxygen dissolved in the metal as atomic oxygen. For the above reaction,  hO  K O =  --------1 ⁄ 2  p O2 

(5.2) equilibrium

where KO is equilibrium constant for Reaction (5.1), p O2 denotes partial pressure of oxygen in the gas phase in atmosphere, and hO is the activity of dissolved oxygen in liquid steel with reference to the 1 wt.% standard state. KO is related to temperature as1 6120 logK O = ------------ + 0.15 T

(5.3)

hO = [ f O ] [ W O ]

(5.4)

Again,

where WO denotes the concentration of dissolved oxygen in weight percent, and fO is the activity coefficient of dissolved oxygen in steel in 1 wt.% standard state. In pure liquid iron,

©2001 CRC Press LLC

log f O = 0.17 [ W O ]

(5.5)

The above relations would allow us to estimate WO in liquid iron at any value of p O2 with which the molten iron would be brought to equilibrium. This value of WO is nothing but solubility of [O] at that p O2 . However, oxygen tends to form stable oxides with iron. Therefore, molten iron becomes saturated 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. For the 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.%., 6150 logK Fe = – ------------ + 2.604 T

(Ref. 1)

(5.6)

where  [ h O × [ a Fe ] x  - K Fe =  ---------------------------a Fe x O   equilibrium

(Ref. 1)

(5.7)

Here, aFe = the activity of Fe in the metal phase in the Raoultian scale (approximately 1), and a F e x O 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 [ hO ] [FO][W O] K Fe = -------------- = -----------------------( a FeO ) ( a FeO ) or, logK Fe = log f O + logW O – loga FeO = – 0.17 + logW O – loga FeO

(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 X SiO2 = 0.4 ( X SiO2 denotes mole fraction of SiO2 in FeO-SiO2), aFeO = 0.43. ©2001 CRC Press LLC

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 by vacuum fusion or inert gas fusion apparatus. Here, a sample of solidified steel is taken in a graphite crucible and then heated to approximately 2000°C under vacuum or under a highly purified inert atmosphere. The steel sample melts and the oxygen contained in it reacts very fast with the crucible and generates carbon monoxide. The quantity of CO is measured by a sensitive instrument such as an infrared analyzer, and from it the quantity of oxygen in the sample is estimated. This apparatus has been made quite accurate and reasonably fast. Analyses of alloying elements in steel are done very quickly and conveniently using an emission spectrometer. Commercial development of the instrument has recently been reported wherein the optical wavelength range has been extended to the ultraviolet region, enabling the determination of 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 additional oxide particles, and these are also retained by the solid as inclusions. The above methods of determination give the total oxygen content, which is the sum of dissolved O and oxygen in inclusions. This hampered progress of our understanding about the behavior of oxygen in steelmaking and deoxidation until the development of immersion oxygen sensors based on ZrO2 and doped with CaO or MgO during the decade of the 1960s. Thereafter, this has become quite a popular tool for the measurement of dissolved oxygen content in molten steel, both in the laboratory and in industry. Excellent reviews are available in the literature on the principles and details of such sensors.2–5 For the sake of illustration, Figure 5.1 shows the sensor employed by Fruehan et al.3 schematically. The ZrO2 (CaO) or ThO2 (Y2O2) disk served as the solid electrolyte, and at high temperature it 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

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reference electrode. This assembly is immersed into liquid steel. Molten steel constitutes the other electrode. A molybdenum-Al2O3 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 going on 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 oxygen ions only, the cell electromotive force (EMF) is related only to the difference of the chemical potentials of oxygen at the two electrodes. µ O2 (liquid steel) – µ O2 (reference) = – Z FE

(5.8)

where µ O2 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 Cr ( s ) + Cr 2 O 3 ( s ) ZrO 2 + CaO [ O ] (reference)

(in liquid steel)

(solid electrolyte)

(5.9)

With reference to Section 2.7, µ O2 (reference) = RT ln p O2 (reference) = ∆G f for formation of Cr 2 O 3 ( s ) per mole O 2 o

2 o = --- ∆G f ( Cr 2 O 3 ) 3

(5.10)

and µ O2 (liq. steel) = RT ln p O2 (in equlibrium with liq. steel) hO - (from Eq. 5.2) = 2RT ln -----KO

(5.11)

Combining the above equations, hO 2 o - – --- ∆G f ( Cr 2 O 3 ) = – 4FE 2RT ln -----KO 3

(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, and Hoogovens Ijmuiden B.V., along with Electro-Nite.6 The cell is Mo Cr + Cr 2 O 3 ZrO 2 ( MgO ) liq. steel Fe The solid electrolyte is in the form of a tube with one end closed. ©2001 CRC Press LLC

(5.13)

All such sensors also contain immersion thermocouples as well so that the temperature of molten steel is also recorded simultaneously. At steelmaking temperatures, the solid electrolyte exhibits partial electronic conduction, especially at a low level of dissolved oxygen. The measured cell voltage of the cell of type illustrated by Expression (5.13) would also include thermo-EMF due 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 oxygen solubility is governed by reaction with one or more of these elements. It has been well established that the carbon content of steel has a considerable influence on bath oxygen content at the end of heat in steelmaking furnaces. The reaction is p CO [ C ] + [ O ] = CO ( g ); K CO = ------------------[ hc ] [ ho ]

(5.14)

The value of equilibrium constant (KCO) is given as.1 1160 logK CO = ------------ + 2.003 T

(5.15)

Figure 5.2 shows the relationship between dissolved carbon and dissolved oxygen in a molten steel bath in a 100 kVA induction furnace. The equilibrium line corresponds to pCO = 1 atm at 1600°C. Dissolved oxygen contents were measured by a solid electrolyte oxygen sensor with two types 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 deoxidation, 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 keeps dropping from furnace to mold. The addition of a deoxidizer also causes some temperature change due to heat of reaction. However, we shall consider it as isothermal. This will not affect our

FIGURE 5.2 Dissolved oxygen content of liquid iron as a function of bath carbon at 1873 K in a 100 kVA induction furnace.4

©2001 CRC Press LLC

considerations of deoxidation equilibria, since only the final temperature at which the equilibrium is 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. A deoxidation 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 ( K′ M ) for reaction (5.16) is given as  ( a M x Oy )  -y  K′ M =  ------------------------x  [ h M ] [ h O ] equilibrium

(5.17)

Again, on the basis of Eq. (2.46), hM = fM · WM and hO = fO · WO. If the deoxidation product is pure, then a M x O y = 1. Also, in very dilute solutions, fM and fO may be taken as 1. Hence, Eq. (5.17) may be rewritten as 1 x y [ W M ] [ W O ] = --------- = K M K′ M

(5.18)

where KM is known as deoxidation constant. Obviously, WM and WO, as already understood, are weight percentages of [M] and [O], respectively, at equilibrium with pure oxide. It may be noted that KM is like the solubility product in an aqueous solution. It is a measure of solubility of the compound MxOy in molten steel at the temperature under consideration. As in Eq. (5.6), variation of KM with temperature may be represented by an equation of the type: A logK M = – --- + B T

(5.19)

where A and B are constants. Equation (5.19) shows that as T increases, log KM and hence KM also increase. 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 as little deoxidizer as possible, an increase in temperature would adversely affect the thermodynamics of the process. Experimental determination as well as thermodynamic estimation of KM for various deoxidizers have 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 of compilations, some old and some new, where efforts have been made to record the most acceptable values. The exercise is still going on, and discrepancies still exist, especially with more reactive elements such as Al, Zr, Ce, Ca, etc. Appendix 5.1 presents such a compilation taken from that of the 19th Steelmaking Committee of the Japan Society for Promotion of Science,1 as well as from other sources.7–9 It may be noted that all oxide products are definite compounds except for deoxidation by manganese, where the product is either a solid or a liquid solution of FeO-MnO of variable composition. The underlying reason for this behavior is the fact that manganese is a weak deoxidizer, ©2001 CRC Press LLC

since the stability of MnO, although greater than that of FeO, is not drastically different from that of 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 the MnO-FeO slag. Therefore, aMnO = XMnO, aFeO = XFeO, and hMn = WMn. Noting that aFe = 1, the equilibrium constant for Reaction (5.20) is [ h Mn ] × ( a FeO ) [ W Mn ] ( X FeO ) K Mn – Fe = ---------------------------------- = ------------------------------( a MnO ) ( X MnO )

(5.21)

where X denotes mole fraction. Equation (5.21) shows that X MnO ⁄ X FeO in the deoxidation product would be proportional to WMn at constant temperature. Figure 5.3 shows the relationship. The oxide product 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 the quantity of ferromanganese required per tonne of steel. The manganese content of steel before deoxidation is 0.1 wt.%. Solution Consider the following reaction: [ h Mn ] [ h o ] (MnO) = [Mn] + [O]; KMn = ---------------------( a MnO )

(E2.1)

FIGURE 5.3 Composition of liquid or solid FeO-MnO solution in equilibrium with liquid iron containing manganese and oxygen.9

©2001 CRC Press LLC

As noted earlier, hMn may be taken as WMn, and aMnO as XMnO. Assuming also that hO = WO, K Mn [ W Mn ] ---------------- = -----------( X MnO ) [W O]

(E2.2)

From Appendix 5.1, –11070 logK Mn = ------------------ + 4.536 T i.e., at 1600°C (1873 K), KMn = 0.041. Noting that the final WO = 0.02 wt.%, [ W Mn ] --------------- = 2.05 ( a MnO )

(E2.3)

K Mn – Fe [ W Mn ] ---------------- = ----------------( X MnO ) ( X FeO )

(E2.4)

Now from Eq. (5.21),

From Appendix 5.1, 6980 logK Mn – Fe = – ------------ + 2.91 (assuming the product to be solid MnO – FeO) T that is, at 1873 K, KMn-Fe = 0.15 Therefore, combining Eqs. (E2.3) and (E2.4), X FeO = 0.073 or, X MnO = 1 – X FeO = 0.927 or, W Mn = 1.90 wt.% 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.% ©2001 CRC Press LLC

Now, the Mn required to form MnO per tonnne of steel Quantity of oxygen removed per tonne of steel = ---------------------------------------------------------------------------------------------------------------- × X MnO × Atomic mass of Mn Atomic mass of oxygen ( 0.04 – 0.02 ) × 10 × 10 × 0.927 × 55 = ---------------------------------------------------------------------------------------------16 –2

3

= 0.64 kg/t 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. 100 Total ferromanganese required = 18.64 × --------- = 31.1 kg/ton steel . 60

(Ans.)

From Figure 5.3, it is confirmed that the assumption of solid FeO-MnO as the deoxidation product is correct. Taking the activity coefficients, viz., fO and fM, as 1, one would be able to calculate the relationship between [WM] and [WO] using Eq. (5.18) and Appendix 5.1 for many deoxidizers. Such calculations would be all right at very low values of WM. At higher ranges, it would give approximate values only, since fM and fO (especially fO) may deviate somewhat from 1. For more precise j calculations, therefore, first-order interaction coefficients e M ⋅ W j are to be considered. The relationship between activity coefficients and interaction coefficients follow from Chapter 2 and are as noted below. log f M =

∑j e M ⋅ W j

(5.22)

log f O =

∑j eO ⋅ W j

(5.23)

j

j

where j denotes all the alloying elements present in liquid steel. For example, if the steel contains C and Mn, then log f O = e O ⋅ W O + e O ⋅ W C + e O ⋅ W Mn O

C

Mn

(5.24)

Some values of interaction coefficients are tabulated in Appendix 2.3. Taking the logarithm of Eq. (5.18), we have 1 x logW O = --- logK M – --logW M y y

(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 Figure 5.4 demonstrate such nonlinearities. Immersion oxygen sensors are nowadays widely employed in oxygen control during secondary steelmaking, especially for deoxidation control. An associated use is estimation of dissolved alu©2001 CRC Press LLC

FIGURE 5.4 Deoxidation equilibria in liquid iron at 1873 K.9

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 spectrometers are useful for the determination of dissolved aluminum content in steel. Measurements are made on several spots of the sample. The minimum value is assumed to be from an inclusionfree 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 equilibrium of the following reaction, viz., Al2O3(s) = 2[Al] + 3[O]

(5.26)

K Al = [ h Al ] [ h O ] , since a Al2 O3 = 1

(5.27)

log KAl = 2 log hAl + 3 log hO

(5.28)

2

3

i.e.,

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 CrCr2O3 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), ©2001 CRC Press LLC

hO O 2 ∆G f  --- Cr 2 O 3 , – 2RT ln ------ = – ZFE 3  KO

(E3.1)

From Appendix 2.1, at 1600°C (1873 K) ∆G f ( Cr 2 O 3 ) = – 422.7 × 10 J/mol; O 2 O

3

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 ignored in 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 the deoxidation product as well as the fact that the liquid FeO-MnO changes to solid FeO-MnO with higher manganese content. Deoxidizers such as Al, Ti, Zr, etc. exhibit a minimum in the solubility M of oxygen. This behavior is due to the large negative value of e C (see Appendix 2.3) for these elements. The situation has been analyzed by several authors, such as Ghosh and Murty,9 and such minima have been quantitatively explained. Differentiating Eq. (5.28) with regard to WAl, d ( logh Al ) d ( logh O ) d ( logK Al ) - + ---------------------- = ----------------------2 ---------------------- = 0 dW Al dW Al dW Al

(5.29)

d ( logW O + log f O ) d ( logW Al + log f Al ) - + 3 -------------------------------------------- = 0 2 ---------------------------------------------dW Al dW Al

(5.30)

d ( log f Al ) d ( log f O ) 2 3 1 dW O 1 ------------- ⋅ --------- + ------------- ⋅ -------- ------------ = 0 + 2 ----------------------+ 3 --------------------2.303 W Al 2.303 W O dW Al dW Al dW Al

(5.31)

log f Al = e Al ⋅ W Al + e Al ⋅ W O

(5.32)

log f O = e O ⋅ W Al + e O ⋅ W O

(5.33)

or,

or,

Now, Al

Al

©2001 CRC Press LLC

O

O

Substituting these in Eq. (5.31) and noting that interaction coefficients are constant, 2 1 Al Al ------------- ⋅ ---------- + 2e Al + 3e O 2.303 W A1 dW O ------------- = – ------------------------------------------------------------dW A1 3 1 O O ------------- ⋅ -------- + 2e Al + 3e O 2.303 W O

(5.34)

dW O = 0 At minimum oxygen solubility, -----------dW Al Hence, 1 • W Al = – -----------------------------------------3 Al Al 2.303  e Al + --- e O   2 

(5.35)

•

where W Al = WAl at oxygen minimum. Equation (5.35) provides a simple relationship between WAl at oxygen minimum and the Al • interaction coefficients. As Appendix 2.3 shows, e O has a large negative value. This makes W Al positive and small in magnitude and substantiates the statement made above that large negative M values of e O are responsible for these minima. On the basis of their exercise, the following analytical equation was proposed by Ghosh and Murty9 to describe the curves: logK M = x ( logW M + e M ⋅ W M ) + y ( logW O + e O ⋅ W M + r O ⋅ W M ) M

M

M

2

(5.36)

M

where r O is the second-order interaction coefficient. Unlike conventional deoxidizers, the alkaline earths, viz., Ca and Mg, are gaseous at steelmaking temperatures (pMg = 25 atm, and pCa = 1.8 atm at 1600°C). Moreover, they are sparingly soluble in 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 nature of these elements, the equilibrium relationships between them and dissolved oxygen are difficult to determine experimentally, and there are uncertainties. Experimental measurements and assessment 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 and 0.1% C. The final oxygen content is to be brought down to 0.001 wt.%. Calculate the residual aluminum content of molten steel assuming that [Al] – [O] – Al2O3 equilibrium is attained. Also take into account all interaction coefficients. Solution log KAl = 2 log hAl + 3 log hO

(5.28)

= 2 [ logW Al + e A1 × W Mn + e A1 × W C + e A1 × W O + e A1 × W A1 ] Mn

C

O

A1

+ 3 [ logW O + e O × W Mn + e O × W A1 + e O × W C + e O × W O ] Mn

©2001 CRC Press LLC

A1

C

O

(E4.1)

Noting that WMn = 1, WC = 0.1, and WO = 0.001, and substituting the values in Eq. (E4.1) and taking KAl 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 is known 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 for a better quality product. 1. The dissolved oxygen content is lower in complex deoxidation as compared to simple deoxidation from equilibrium considerations. Consider deoxidation by silicon. [ h Si ] [ h O ] [ W Si ] [ W O ] - = ---------------------------K Si = ----------------------( a SiO2 ) ( a SiO2 ) 2

2

(5.37)

If only ferrosilicon is added, then the product is pure SiO2, i.e., a SiO2 = 1. On the other hand, simultaneous addition of ferrosilicon and ferromanganese in a suitable ratio leads to the formation of liquid MnO-SiO2. Consequently, a SiO2 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 consequently floats up faster, making the steel cleaner. This is what happens in many complex deoxidation such as in the example presented above. 3. Properties of inclusions remaining in solidified steel can be made better by complex deoxidation, 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. composition j relationships in the binary or ternary oxide systems of interest, besides values of KM and e i . These are 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 terms of weight percent of SiO2. Figure 2.3 has presented isoactivity lines for silica in the ternary CaOSiO2-Al2O3 system at 1550°C. Figure 5.6 shows the same for CaO and Al2O3. The activities were determined 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. Thermodynamic calculations involving complex deoxidation should aim at the following: • Estimation of weight percentages of deoxidizing elements and oxygen remaining in molten 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. composition data in oxide systems are not available in the form of equations. Secondly, interaction of more than ©2001 CRC Press LLC

FIGURE 5.5 Activity vs. composition relationship in MnO-SiO2 melts; standard state are pure solid MnO and 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.

©2001 CRC Press LLC

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 deoxidation by Si-Mn. Bagaria, Deo, and Ghosh14 have carried out thermodynamic analysis of simultaneous deoxidation by Mn-Si-Al. Ghosh and Naik15 have done the same for deoxidation systems: Ca-SiAl and Mg-Si-Al. Readers may refer to those works for details. Some salient findings by Ghosh and Naik are presented below. Calculations were performed in the range where the deoxidation product is liquid CaO-SiO2Al2O3 slag in the ternary diagram (Figure 2.3) at two temperatures. Figure 5.7 presents some results of calculations for a Ca-Si-Al system as log WO vs. log WM (M = Si or Al) curves for three compositions 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 to be the same as weight percent, i.e., the interaction coefficients were ignored. The two curves differ by about 20%. Thermodynamically, the complex deoxidizer was found to be, at most, an order of magnitude more powerful than simple deoxidation by Al or Si. The above exercise is important from the point of view of industrial application. Ignoring of interactions, i.e., taking hi = Wi, simplifies the calculation procedure in a significant way. The above analysis shows that the kind of error one may encounter is tolerable for many applications. It is also 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 the product 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 taken up in Chapter 9 again in connection with inclusion modification. Example 5.5 Consider deoxidation of molten steel by the simultaneous addition of ferromanganese and ferrosilicon at 1600°C. If the residual WO and WSi are, respectively, 0.01 and 0.1 wt.%, determine the composition 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

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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 a SiO2 = 0.47 . 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 approximately 0.25. Again, consider the reaction of Mn as in Example 5.2. [ W Mn ] [ W O ] K Mn = 0.053 = ---------------------------( a MnO ) 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 deoxidation practice, dissolved and total oxygen both are of importance. Even if the former is low, the presence of entrapped deoxidation products gives rise to inclusions in solidified steel. The products of deoxidation should be separated out from the molten steel before the latter solidifies, if a clean steel is desired. Therefore, the subject of deoxidation kinetics is concerned with deoxidation reaction as well as separation of deoxidation products. Studies of deoxidation kinetics started seriously in 196018 and are still continuing. Factors controlling the rates have been established reasonably well from theoretical considerations as well as from experiments conducted in laboratories and plants. The availability of new equipment and techniques has been of considerable help. In almost all studies prior to 1970, only total oxygen could be determined by sampling and vacuum or inert gas fusion analysis. Later investigators also employed 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 chemical compositions of inclusions in steel. Development of the Quantimet brought about a method for rapid determination of inclusion size, number, etc. By 1970, and even earlier, thermodynamic parameters for important deoxidation reactions were available that could provide a fair degree of confidence. The basic behavior pattern of oxygen and inclusions from a furnace to solidification during steelmaking may be visualized with the help of Figure 5.8 from Plockinger and Wahlster.18 The dissolved oxygen content decreases rapidly upon deoxidation in the ladle and keeps on decreasing all 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 negligible solubility for oxygen, the dissolved oxygen in liquid steel also, upon solidification, could give rise to more inclusions. Therefore, the expected inclusion content in steel would always be higher in the solid than in the liquid in a mold. To gain a greater understanding of the factors influencing the rates, a number of fundamental investigations have been carried out from 1960 onward. These have been done mostly in the laboratory under controlled conditions. Therefore, we shall first discuss the findings of laboratory experiments. Laboratory investigations have been carried out mostly with a small melt (on the order of a few kilograms of steel) and under inert atmosphere. High-frequency induction furnaces were ©2001 CRC Press LLC

FIGURE 5.8 Change of oxygen and inclusion content of steel from furnace to ingot.

normally employed for maintaining steel molten at the desired temperature. If the steel is directly heated by a high-frequency power source, then an eddy current flows through it. This eddy current and the magnetic field of the induction coil generate force, which causes the flow and circulation of molten steel. This is known as induction stirring. On the other hand, if the ceramic crucible containing the steel is surrounded by a hollow cylinder of graphite or molybdenum, then the eddy current flows primarily through the latter and heats it up. Then, the steel is heated up indirectly by radiative and convective heat transfer from the hot cylinder. In this case, induction stirring of molten steel 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 reaction 2. 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 the change 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 ©2001 CRC Press LLC

FIGURE 5.9 Change of oxygen content of molten steel following the addition of manganese.19

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 deoxidation reaction with Si to be complete more or less within two minutes. Recent investigations by Kundu et al.20 and Patil et al.21 have demonstrated that Si-O-SiO2 equilibrium is attained within five minutes of the addition of ferrosilicon into an induction stirred laboratory melt. But it takes almost 20 minutes for the total oxygen content to achieve a steady state.21 Olette et al.19 carried out deoxidation by 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 5.10 Effect of the method of introduction of aluminum on dissolved oxygen in molten steel.19

©2001 CRC Press LLC

Scrutiny of Figures 5.9 and 5.10 grossly reveals two stages. Initially, the dissolved [O] decreases rapidly 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 speed of three kinetic steps 2, 3, and 4 as listed above, which is responsible for the rapid initial rate, and reasonably high speed of step 1. Let us now try to present the supporting logic as well as experimental evidence for the above explanation. 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 determine the rate of the actual phase boundary reaction step (step 2). However, at high temperatures, it is mostly very fast and has been assumed to be so here. Homogeneous reactions, of course, are even faster. The mechanism of the dissolution of deoxidizer would depend on its melting point. The common deoxidizers, 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 heat transfer 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 of ferromanganese. 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 such as ferroalloy or aluminum is made, a layer of steel freezes around it and forms a solid crust. From then on, the mechanism of dissolution would depend on the melting point of the addition. If it is lower than that of steel, it may become molten, with the crust of solid steel intact as an extreme case. If the melting point of the addition is higher than that of steel, such as ferrotungsten, then the crust of steel will remelt, exposing the alloy to the melt and leading to its dissolution by simultaneous heat and mass transfer. The effect of the formation of a steel shell was illustrated through sample calculation for melting 10 cm dia. ferrosilicon sphere under some assumed conditions. 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 frozen shell that took most of the time. Factors that govern the rate of dissolution are bath hydrodynamics, density, melting point and thermal conductivity of the addition, size of the addition, and melt superheat. Of course, as stated earlier, if the addition is a deoxidizer, then the heat effect of the reaction is also important. Approximations 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 that for 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 the molten 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, the whole process of dissolution may be delayed if tenacious oxide films form around the dissolving deoxidant. Some observed slowness in the deoxidation reaction may be attributed to formation of stable oxide films formed on the interface of regions with a high content of deoxidizing agent and a high content of oxygen. Grethen and Phillippe25 have presented a photomicrograph of such a film of MnO · Al2O3 in a deoxidation system: Al-Fe-Mn. Deoxidation involves the formation of a new phase (i.e., the deoxidation product) as a result of 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 ©2001 CRC Press LLC

an embryo (also called a critical nucleus) consists of a small number of molecules and has a dimension on the order of 10 Å or so. Again, two mechanisms of nucleation are possible: 1. homogeneous nucleation, which occurs in the matrix as such 2. 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 4 3 ω = 4πrσ + --- πr ( ∆G ⁄ v ) 3 where

σ r ∆G v

= = = =

(5.38)

interfacial tension between liquid steel and deoxidation product radius of the nucleus change in free energy for Reaction (5.16) per mole 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 r = r , 2σv dω * ------- = 0, and hence, r = – ---------∆G dr

(5.39)

Combining Eqs. (5.38) and (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 per second ( N˙ ) is –ω N˙ = Aexp  ------------  nk B T  *

(5.41)

where kB is Boltzmann’s constant (i.e., R/NO, where NO is Avogadro’s number), and n is the number of atoms in a critical nucleus.

FIGURE 5.11 Energy barrier for homogeneous nucleation.

©2001 CRC Press LLC

N˙ increases if ω* decreases, which again happens if (∆G)2 increases [Eq. (5.40)]. ∆G, i.e., the free energy of reaction, would actually have to be negative for the deoxidation reaction to proceed in the forward direction. Therefore, an increase in (∆G)2 actually means that ∆G becomes more and more negative. Now, ( a M x Oy ) Q --------- = ------------------------------------------------y x K′ M [ hM ] [ ho ] ------------------------------------------------- ( a M x Oy )  -y   -----------------------x  [ h M ] [ h o ] equilibrium

(5.42)

From Eq. 2.8, Q o ∆G = ∆G + RT ln Q = – RT ln K′ M + RT ln Q = RT ln --------K′ M

(5.43)

For pure deoxidation product, in accordance with Eq. (5.18), we may write [[W M ] [W O] ] Q - equilibrium --------- = ----------------------------------x y K′ M [W M ] [W O] x

y

(5.44)

Since ∆G is negative, Q ⁄ K′ M < 1 . The inverse of Q ⁄ K′ M (i.e., K′ M ⁄ Q ) is known as the supersaturation 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. Bogdandy et al.,26 Turpin and Elliott,27 and Turkdogan28 tried to estimate supersaturations required for a reasonable rate of nucleation for common deoxidation systems. Turpin and Elliott took N˙ = 1 3 nucleus/cm3/s as a reasonable rate, whereas Turkdogan took N˙ = 10 nuclei/cm3/s. However, it hardly matters, since the supersaturation changes very little with a change of N˙ , even by several orders 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 collision frequency. Values of interfacial tension, σ, were not known that precisely and therefore constituted a 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 for silica. However, a reexamination of these calculations is called for. Such supersaturations are attainable in the initial stages of deoxidation by strong deoxidizers, but not so much with weak deoxidizers. According to Sano et al.,30 rapid homogeneous nucleation is possible during the initial stage of deoxidation even by Mn and Si. Moreover, in the melt, exogenous oxide particles are likely to be 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 rapid nucleation of deoxidation product is possible when the deoxidizer is added. This has made the rapid initial decrease of dissolved oxygen content possible. However, as a result of reaction, the supersaturation in the melt also comes down drastically. Therefore, nucleation eventually ceases. Growth of deoxidation products occurs by a number of mechanism. However, growth by diffusion alone can contribute to the reaction and consequent lowering of dissolved oxygen. It has been analyzed by Turkdogan,28 Sano et al.,29 and Lindberg and Torsell.30 The essential conclusion ©2001 CRC Press LLC

is that growth by diffusion also is expected to be extremely rapid, taking barely a few seconds for completion. 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 simultaneous nucleation and growth should be complete, the attainment of equilibrium is expected within a few seconds, and dissolution and homogenization of the deoxidizer are also instantaneous. This is not expected if dissolved oxygen decreases more slowly (Figures 5.9 and 5.10). Dissolution is perhaps more or less complete during the initial stage, but the mixing and homogenization, even in laboratory experiments, take a few minutes, and this seems to be the primary cause for a slow decrease in dissolved oxygen content during the second stage—although dissolution of the solid may 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 critical nuclei by diffusion alone. Assume the deoxidation product to be silica and the number of critical nuclei (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 system attains equilibrium. For SiO2(s) = [Si]wt.% + 2[O]wt.% and a SiO2 = 1, K Si = [ W Si ] [ W O ] = 4.7 × 10 2

–6

(E6.1)

From reaction stoichiometry, 28 o o W Si – W Si = ------ ( W O – W O ) 32 o

(E6.2)

o

where W Si = 0.15 wt.% and W O = 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., 32 6 –2 –2 10 × V × ------ + 7.16 × 0.007 × 10 = 7.16 × 0.03 × 10 25

(E6.4)

where V is the volume of one particle of SiO2, 25 is the molar volume of SiO2 in cm3, and 7.16 is the 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 is equal 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. ©2001 CRC Press LLC

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 the dissolved oxygen content. This has been well established by several researchers. It may take 10 to 15 minutes, even in laboratory melts, to remove the total oxygen adequately. This behavior pattern demonstrates that the removal of deoxidation products from the melt is a slow process and is really the 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 is because 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 a size 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 laboratory melts. Out of these, the latter have received wide acceptance because their theoretical analyses were supported by inclusion counting and size analysis. In addition to diffusion, they considered the 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 smaller ones. However, this mechanism does not make any significant contribution to the growth of deoxidation product. Stokes Collision In a quiet fluid and at low Reynold’s number (i.e., laminar flow), a spherical particle of solid, at steady state, moves according to the Stokes’ Law of Settling, and its terminal velocity (v) is given as gd ( ρ s – ρ f ) u t = ----------------------------18µ 2

(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 motion of gas bubbles and liquid droplets, provided that these are small in size (less than a millimeter or so). Since deoxidation products are lighter than molten steel, they move upward. Equation (5.45) 2 shows that u t ∝ d , other factors remaining constant. Therefore, particles of different sizes would move 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 they collide. 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 random motion of eddies. The the minimum size of such an eddy under conditions of Torsell’s experiments was estimated as 300 microns.30 Since inclusion sizes were much smaller than this, it was assumed ©2001 CRC Press LLC

that any oxide particle would move along with the eddy in which it is contained. Since different eddies 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 coalescence and growth. Example 5.7 Liquid steel is being deoxidized by the addition of ferrosilicon at 1600°C. The deoxidation product is globular silica. Calculate the time required for particles of 5 and 50 microns diameter to float up 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 viscosity of 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, 18µ H Depth of steel ( H ) Time to float up ( t ) = ----------------------------------------------- = ----------------------- × -----2 g ( ρl – ρs ) d ut

(E7.1)

If d is expressed in microns (10–6 m) and time in minutes, then 18 × 6.1 × 10 × 10 H H 4 - × -----2 = 3.6 × 10 × -----2 min t = -------------------------------------------------------------------------3 9.81 × ( 7.16 – 2.22 ) × 10 × 60 d d –3

12

(E7.2)

Calculations yield: H (in m) = 0.1 d (in microns) = 5 t (in min)

0.1 50

2 5

= 150 1.5 3 × 10

2 50 3

30

These theoretical expectations were confirmed by laboratory experiments30 as shown by Figure 5.12 for silicon deoxidation. Very little oxygen (total) is removed in the first stage, because the particles are small, and they do not float out rapidly. Then, particles grow rapidly due to collisions and start floating out, giving rise to rapid oxygen removal in the second stage. Since most large particles 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 particle radius vs. time for deoxidation by silicon (Figure 5.13). The decrease in average size after the peak is 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 deoxidation product. Some researchers are of the view that a recirculatory motion of bath, such as in induction stirring, actually makes the floating out of inclusions difficult,25 but Miyashita et al.,31 on the other hand, have shown that, even in induction stirring, the rate of the floating out of inclusions is much higher than predicted by Stokes’ law ( Figure 5.14). Slow flotation of smaller inclusions (<10 µm) and consequent dif ficulties in eliminating them is of concern in connection with production of ultra-clean steels. Hirasawa et al.32 carried out ©2001 CRC Press LLC

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

laboratory experiments on transfer of small (<10 µm) SiO 2 inclusions from molten copper to slag in a resistance furnace under argon atmosphere. Two kinds of stirring were employed. Increasing the RPM of the mechanical stirrer from 100 to 350 did not significantly enhance the rate of decrease of total oxygen content ([WO]T) in copper. On the other hand, when the stirring was by argon bubbling from the bottom, the rate constant (kO), as defined by d[W O] – ------------------T- = k o [ W o ] T dt

(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 matched well with those predicted by the correlation earlier proposed by Sano and Mori.33 From these, kO ©2001 CRC Press LLC

FIGURE 5.14 Change of total oxygen content in a stirred iron melt upon deoxidation by silicon.31

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 reason for the effectiveness of bubble stirring over mechanical stirring was the attachment of bubbles to inclusion particles and consequent faster floating out of small inclusions. It worth noting that the process 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, primary inclusions rich in alumina could be eliminated several times more quickly than silicates of comparable size. It was subsequently shown by some other investigators that the chemical nature of the deoxidation product has a significant influence on its removal. Since the particle can interact chemically with the melt at the interface only, it was apparent that interfacial phenomena cannot be ignored. One of the most decisive experiments was by Nogi et al.,34 who found that the addition

FIGURE 5.15 Empirical relationship of deoxidation rate constant with the rate of bubble surface area creation.32

©2001 CRC Press LLC

of a little surface active agent such as tellurium to molten steel accelerated the elimination of oxide inclusions (alumina, mullite, and zirconia). Interfacial phenomena can influence all stages, viz., growth, movement, and floating out/removal of deoxidation products. Previously, it was believed that only a liquid deoxidation product is capable of growing to a large size, since they coalesce together upon collision. The discovery 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 iron does not “wet” alumina. Therefore, an alumina–alumina interface has considerably less energy as compared to an alumina–iron interface. Some other investigators also have supported this view broadly and provided evidence. Singh36 explained nozzle blockage in aluminum deoxidized melts by 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 these clusters may form in the melt during solidification in interdendritic space. Lindborg37 tried to explain these observations as well as the multiplicity of forms assumed by inclusions. Al2O3 inclusions have 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-S inclusions. The concentration field near a growing inclusion, and its fluctuation, decide the shape and size of the growing crystal. Variation of the field with time causes variation in growth. The regularity or irregularity of the forms appears to be connected with fluctuations in mass flux. The same 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 to elucidate the mechanism. First of all, contact is established at some points. Coalescence takes place by 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 by sintering.34 It was recognized quite some time ago that the oxide particles may come up almost to the free surface of molten steel. However, it is likely to take a little more time or face difficulties in actually floating out on the surface if the interfacial forces are not favorable. Similarly, a particle may come in contact with the crucible wall but may face difficulties in actually getting stuck on to the crucible wall if interfacial forces are not favorable. This is especially important for stirred melts, since the particles are not likely to stay long near the free surface or crucible wall and are likely to be swept back 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 free surface 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

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∆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 is a question of how strongly negative it is. The more negative ∆G, the easier is emergence and hence removal of the oxide particles. Since slags would wet the deoxidation product, ∆G´ is always expected to be more negative as compared to ∆G. Therefore, a slag cover on molten steel ought to 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 a laboratory high-frequency induction furnace using crucibles of different materials. Extremely low concentrations of oxygen (12 to 14 ppm) were obtained with SiO2 and CaO crucibles, whereas oxygen was higher (34 to 42 ppm) for Al2O3, ZrO2, and MgO crucibles. X-ray microanalysis of SiO2 and CaO crucibles after deoxidation revealed an increase of Al2O3 concentration on their surfaces. These observations have been corroborated by some other investigators and are caused by 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 be liquid. 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 distribution and 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 extraneous sources such as refractory erosion and entrapped slag particles. These topics are covered further in 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 beyond the scope of this book to describe all of these. The fundamentals of deoxidation thermodynamics and 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 ways and 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 with the lining. 2. Mixing and homogenization of bath are much more difficult as compared to a laboratory situation. 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 coming from refractory linings and slag. ©2001 CRC Press LLC

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 Murorau Plant of Japan Steel Works. Figure 5.17 presents some of their findings. The degree of deoxidation reached a maximum with an increase of stirring energy input into the melt. Thereafter, it decreased somewhat. Authors have explained this decrease to either erosion of refractory lining or entrapment of top slag into steel. Similar findings have been reported by some others, and it has been established that stirring should be optimized for best results. Ghosh and Choudhary8 carried out deoxidation by ferromanganese and ferrosilicon in 6t and 1t electric arc furnaces. Their findings point out that deoxidation equilibria could be attained within 10 minutes after the addition of deoxidizers if only stirring of the bath by CO evolution were reasonable. One strategy is to obtain a liquid deoxidation product by proper sequence of the addition of Si, Mn, and Al. Liquid deoxidation products tend to coalesce and grow rapidly upon collision and hence are eliminated faster. Many experimental and plant studies have shown that the rate of separation of deoxidation products 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 et al.40 measured total oxygen content as a function of time in a ladle stirred by argon. Their data are presented 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 ©2001 CRC Press LLC

FIGURE 5.18 Total oxygen content of molten steel as a function of time in an argon stirred ladle.40

s–1 and 1.7 × 10–3 s–1, respectively. These are significantly different. It is to be borne in mind that the total oxygen content of liquid steel also includes dissolved oxygen content in addition to oxide particles. 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 evaluated at stirring times of 4 and 10 min are 4.9 × 10–3 s–1 and 4.2 × 10–3 s–1, respectively. These are much closer to one another. The steady level of oxygen content during ladle deoxidation is a consequence of the fact that simultaneous reoxidation also goes on during this period. The sources of oxygen pickup are atmosphere, oxidizing slag, and oxides from refractory lining. The value of steady-state oxygen content 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 tried to ascertain the role of carryover slag from the steelmaking furnace and found that reoxidation by the top slag was significant. The steady-state total oxygen content was 26 ppm for a slag containing 5.6% FeO and 2.4% MnO, whereas it was 92 ppm for the slag with 6.5% FeO and 8.1% MnO. It was also found that the top slag gets deoxidized by added deoxidizers slowly. Hence, it is advisable to deoxidize any remaining furnace slag before addition of synthetic slag. Kim et al.42 conducted water model experiments with an NaOH solution. Argon was bubbled through 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 were incapable of preventing absorption of CO2. It was also found that the rate of absorption increased with increasing argon purge rate. The rate of absorption decreased significantly when an oil layer, ©2001 CRC Press LLC

simulating top slag, was present on the water. In this case, the absorption was through the plume eye only. A NaOH solution-CO2 system had been investigated widely earlier, and it had been established that the absorption rate of CO2 was basically controlled by mass transfer in aqueous solution, unless one operates in a regime of very high mass transfer rates. Kim et al.42 also assumed water phase mass 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 from the bottom, along with their mass transfer correlation. Section 5.2.2 presented a brief discussion on the difficulties in flotation of small inclusion particles and the beneficial role of gas bubbling. Attachment of particles to rising gas bubbles and consequent 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 to some nitrogen pressure so as to raise its dissolved nitrogen content to about 100 to 150 ppm. The pressure of N2 is subsequently lowered drastically by a factor of 25 to 100. This leads to the generation of nitrogen bubbles throughout the melt, promoting faster flotation of fine inclusion particles. Figure 5.19 compares the deoxidation rate constants for this method with those for Ar bubbling. Enhancement of kO by a factor of few may be noted. The authors also attempted a quantitative analysis of this phenomenon. Earlier, deoxidation was carried out in an open teeming ladle as a single-stage process. The addition of deoxidizers used to be done primarily during tapping. With developments in secondary refining technology, it is generally practiced in two or three stages. The first stage is the traditional one during tapping. The ladle has a facility for the bottom purging of argon. After tapping, the ladle is taken to an argon purging station. During this transfer, we may also resort to some gas stirring using a lance immersed from the top into molten steel. The objective of the final deoxidation during argon purging is to accomplish precise control of dissolved oxygen by the addition of more deoxidizers. Additional objectives are the removal of inclusions, temperature and composition adjustments, plus additional refining such as desulfuriza-

0.50

0.20

K0,min

-1

0.10 0.05 0.02 0.01

New method

0.005

Gas bubbling

1.5kg VIF 70kg VIF 50T Carbon steel VOD SUS

0.002 0.001 20

50

100

500 1000 2000

200

5000

ε x 10 ,Wkg 3

-1

FIGURE 5.19 Relation between the apparent deoxidation rate constant and stirring energy.43

©2001 CRC Press LLC

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 facilities for 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 out not 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 been known 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 utilization of the ladle additions for low carbon heats were 85 to 95% for Mn, 60 to 70% for Si, and 35 to 65% 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 or so, 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.

©2001 CRC Press LLC

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 following approximate 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, kg Wsk = 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 furnace carryover slag.44 It was found to range between 1 to 3.5 tonnes for a 200t BOF heat. Figure 5.21 shows that both [WAl +WSi]sl, as well as the extent of phosphorus reversion, increased with the quantity 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 from the furnace without slag, i.e., “slag-free tapping.” However, complete prevention of carryover slag is quite difficult. Also, some top slag in the ladle is desirable, since it slows down heat loss from the melt and provides protection against oxidation by atmospheric air. As pointed out in Section 5.2.2, the top slag aids in the elimination of inclusions as well. Hence, the objective of slag-free tapping may be stated as minimization of carryover slag. Formation of a funnel-shaped air core during the emptying of liquid from a vessel by drainage is a common experience, such as we can observe in a kitchen sink. During the tapping of steel melt from a converter, or teeming of a ladle or tundish through a nozzle, such a funnel allows the slag 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 slagentraining 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

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Vθ,i>=Vθ,cr>0

Hcr,v Vθ,I = 0 Hcr,d d

d drainage nozzle

drainage nozzle

primary liquid

primary liquid nozzle ouflow (a)

nozzle outflow (b)

FIGURE 5.22 (a) Vortexing funnel and (b) draining funnel during the pouring of liquid through a bottom nozzle.45 Reprinted by permission of Iron & Steel Society, Warrendale, PA.

The critical limiting height (HCr), below which such a funnel would reach down to the drainage opening, is of technological importance. In industrial processes, rotational (i.e., tangential) flow is very likely to be present and, hence, HCr for a vortexing funnel (HCr,v) is of importance. The findings may be stated as H Cr ,v Q n ----------- =  -------------------5 1⁄2  D ( gD ) 

(5.55)

where D = vessel diameter Q = discharge flow rate g = acceleration due to gravity The scatter of the data did not allow further quantification, but n was approximately 2. HCr,v /D ranged between 1 and 50 in their experiments. For a draining funnel, data of various investigators showed 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 “vortex busters” both for a water model and plant studies and carried out experiments. The object was to prevent vortexing. They have reported a significant decrease of HCr,V in the water model as well as improved 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 as well as in 300t basic oxygen furnace (BOF) vessel. In ladles, drain sink occurred if the volume flow 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 (centric or 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 entrainment of the upper liquid phase if its viscosity was larger. Increased waiting time after the blow ©2001 CRC Press LLC

from 15 to 180 s also lowered the drainage of the upper liquid phase by a factor of 4 to 5. This can 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 found to decrease by a factor of 4 to 5 due to the presence of the ball. A ball density that allows partial immersion of the ball into the heavier liquid was found to be very effective. The ball settles into the 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 during tapping with varying degrees of success. The devices are plugs of various shapes, e.g., as nail shaped. 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 use of slide gates decreases vortexing as compared to stoppers. As far as the BOF is concerned, the plugs are composites of refractory materials and iron, so the density is in between that of slag and of metal. If everything works right, the plug falls into the tap hole and blocks it before the slag flows 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 electromagnetic sensor, which is placed around the tap hole. When slag starts coming out through the hole, the nature of the signal changes significantly due to differences in electromagnetic induction for slag and metal. The device is superior to visual detection. Poferl and Eysn52 have reported on plant trials with 130/140t converters at Linz and obtained the following average slag rates (kg/tonne steel): Without slag stopper

10–15

With slag stopper

4.45

With slag stopper and slag indication system

3.5

Besides the use of a slag stopper in a BOF, further deslagging by slag raking seems to be practiced in some modern plants. During this even electromagnetic stirring is being employed to push 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 substantial percentage of Al2O3 is aimed at for better deoxidation, desulfurization, etc., as well as for controlling dissolved Al in molten steel. This requires the addition of CaO, CaF2, etc., and deoxidizers to modify the carryover slag during tapping of steel as well as during the subsequent stage. The average slag composition in a ladle furnace after arc reheating is 50 to 56% CaO, 7 to 9% MgO, 6 to 12% SiO2, 20 to 25% Al2O3, 1 to 2%(FeO+MnO), and 0.3% TiO2, with small amounts of S and P.45 An already prepared synthetic slag speeds up refining. The concept is not new. 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 are on the market now. Turkdogan44 has reported the findings of some plant experiments in which, during some tappings, only ferromanganese was added to the ladle, whereas for some others ferromanganese and calcium aluminate slag were added. Figure 5.23 presents the findings. Si and Al were less than 0.003% 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-killed steels, the difference would be less. Section 5.1.2 has already provided the necessary thermodynamic background for this. Turkdogan has also tried to show that reactions approached thermodynamic equilibria approximately. This was attributed to the strong stirring and mixing action of the tapping stream. These agree with the findings by Choudhary and Ghosh8 in EAF, reported earlier in this section. 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 solid additions remain submerged in liquid steel long enough for completion of melting-cum-dissolution. ©2001 CRC Press LLC

FIGURE 5.23 Deoxidation by ferromanganese with and without calcium aluminate ladle slag in furnace taping of low-Si, low-Al steel.44

Heavy ferroalloys, such as ferrotungsten, shall remain submerged. However, additions of lower density, such as Al, ferromanganese, etc., would tend to float up and react with slag and atmospheric oxygen. This problem is especially serious with aluminum. Guthrie22 has reviewed the subject and reported 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 model experiments.53 Since additions are made primarily during the tapping of steel, the same situation was simulated. Attention was paid to the subsurface trajectories of buoyant (i.e., lighter than liquid bath) additions, and total immersion times were found to range between 0.1 and 40 s. Some guidelines 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 tapping stream, there are several variables affecting alloy recovery, as discussed earlier. Moreover, significant improvements in the utilization of deoxidizers during tapping would be possible only with major investments. Baldzicki et al.54 have reported significant improvement in Al recovery by wire injection in Al-killed grades. Rapid mixing and homogenization of the bath, as well as metal-slag mass transfer, are very desirable for success. During tapping, stirring is effected by the tapping stream. Some limited control of the process is possible. During argon purging, the flow rate of argon is a key variable. Chapter 3 presented details of fundamental studies on fluid flow in gas-stirred ladles. Chapter 4 discussed mixing and mass transfer in gas-stirred ladles. These are being utilized for industrial process control, design, and optimization to some extent. Figure 4.4 illustrates that, for a ladle with a single porous plug, minimum mixing time is obtained if the plug is located at mid-radius. Accordingly, in smaller ladles with single plugs, the plug location is at mid-radius. For dual plugs, the two plugs at mid-radius are located in diametric opposition. Zhu et al.55 have reported their findings from water model and mathematical model work for mixing in a gas-purged ladle with multiple tuyeres at the bottom, and they arrived at the same conclusion. Nippon Steel Corporation of Japan has developed the CAS (composition adjustments by sealed argon bubbling) process. With an additional facility for oxygen blowing, it is known as CAS-OB and seems to be catching up as alternative to ladle furnaces. The features of CAS-OB have been presented by S. Audebert et al.56 Figure 5.24 illustrates the features of the process. Since it does not involve elaborate top and arc heating arrangements as does LF, capital cost is low. The high©2001 CRC Press LLC

5. O2 blowing into snorkel 1. Simple equipment & operation

Fume extraction O2 blowing Alloying C, Si, Mn, Al etc.

2. Alloy addition Ar atmosphere

á áá

Raising temperature of steel Low running cost and investment Quick treating and low temperature drop

áá á

Low reoxidation High yield Precise composition adjustment

áá á

Effective removal of oxides No disturbance of slag layer Quick homogeneity

3. Slag off for prevention of slagmetal reaction

Slag Molten steel

Snorkel 4. Ar stirring into snorkel

Ladle Porous plug Ar N2

} gas

FIGURE 5.24 Features of the CAS-OB process.56

alumina refractory snorkel had a life of about 60 heats. Deoxidizers and other alloying elements are added inside the snorkel during argon purging. This significantly prevents their oxidation loss due to reaction with atmosphere and slag. As mentioned in Section 4.2, stirring is most intense in the plume region, leading to faster melting and dissolution of additions. Temperature adjustment, as required, is done by feeding aluminum wire and oxygen blowing inside the snorkel. The oxidation of Al provides the necessary heat input. This way, heating is more rapid (7 C/min or so) and cheaper as well. However, the control 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 Works in 1993. They have claimed a reduction in total production cost as well as improvement of product quality. 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 oxygen levels in steelmaking furnaces and ladles is a must for scientific purposes and improved deoxidation control. 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 comparison to 0.0020, the equilibrium deoxidation constant at 1593°C. Maximum vessel oxygen was found to provide a superior control criterion of the bath oxygen level rather than the traditional one, i.e., minimum tap carbon.58 This vessel oxygen level was also employed for BOF charge calculation, deoxidizer additions in ladles, and decisions about the deoxidation schedule. Significant improvements were found, including improved rimming action, improved yield of semi-killed grades, and an improved aluminum addition schedule. However, a lack 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 Committee on 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. ©2001 CRC Press LLC

4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46.

Saeki, T., Nisugi, T., Ishikura, K., Igaki, Y., and Hiromoto, T., Trans. ISIJ, 18, 1978, p. 501. Plushkell, W., Stahl ûnd Eisen, 96, 1976, p. 657. Nilles, P., Defays, J., Cure, O., and Surinx, H., CRM Report, No. 51, Oct. 1977, p. 31. Jacquemot, A., Gatellier, C., and Olette, M., IRSIDE RE 289, 1975, also ref.19, p. 50. Ghosh, A. and Chaudhary, P.N., Trans. IIM, 38, 1985, p. 31. Ghosh, A. and Murty, G.V.R., Trans. ISIJ, 26, 1986, p. 629. Qiyong Han, Proc. 6th Int. Iron and Steel Cong., Nagoya, Vol. 1, 1990, p. 166. Kimura, T. and Suito, H., Metall. Trans. B., 25B, 1994, p. 33. Verein Deutscher Eisenhuttenleute, Slag Atlas, Verlag Sthalisen mbH, 1981. Turkdogan, E.T., in Chemical Metallurgy of Iron and Steel, Iron and Steel Inst., London, 1973, p. 153. 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. Ghosh, A. and Naik, V., Tool and Alloy Steels, 17, 1983, p. 239. Wilson, W.G., Kay, D.A.R., and Vahed, A., J. Metals, 26, 1974, p. 14. Faulring, G.M., and Ramalingam, S., Metall. Trans. B, 11B, 1980, p. 125. .Plockinger, E. and Wahlster, M., Stahl Eisen, 80, 1960, p. 659. 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. Kundu, A.L., Gupt, K.M., and Krishna Rao, P., Ironmaking and Steelmaking, 13, 1986, p. 9. Patil, B.V. and Pal, U.B., Metall. Trans. B, 18B, 1987, p. 583. Guthrie, R.I.L., Electric Furnace Proceedings, AIME, 1977, p. 30. Engh, T.A., Principles of Metal Refining, Oxford University Press, Oxford, 1992, Ch. 8. 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. Grethen, E. and Phillippe, L., in Production and Application of Clean Steels, Iron and Steel Inst., London, 1972. Von Bogdandy, L., et al., Arch. Eisenhuttenleute, 32, 1961, p. 451. Turpin, M.L. and Elliott, J.F., JISI, 204, 1966, p. 217. Turkdogan, E.T., JISI, 204, 1966, p. 14. Sano, N., Shiomi, S., and Matsushita, Y., Trans. ISIJ, 7, 1967, p. 244. Lindborg, U. and Torsell, K., Trans. AIME, 242, 1968, p. 94. 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. Hirasawa, M., Okumura, K., Sano, M., and Mori, K., in Ref. 10, Vol. 3, p. 568. Mori, K., Hirasawa, M., Shinkai, M., and Hatamaka, A., Tetsu-to-Hagane, 71, 1985, p. 1110. Nogi, K. and Ogino, K., Canad Met. Qtly., 22, No. 1, 1983, p. 19. Kozakevitch, P. and Olette, M., in Production and Application of Clean Steels, Iron and Steel Inst., London, 1972, p. 42. Singh, S.N., Metall. Trans., 2, 1971, p. 3248. Lindborg, U., in Ref. 19, Vol. 2, 85. 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. 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. Suzuki, K., Kitamura, K., Takenouchi, T., Funazaki, M., and Iwanami, Y., Ironmaking and Steelmaking, 1982, p. 33. Lehner, T., Canad Met. Qtly., 20, No. 1, 1981, p. 163. Kim, S.H., Fruehan, R.J. and Guthrie, R.I.L., Steelmaking Proceedings, Iron and Steel Soc., USA, 1987, p. 107. Kikuchi, Y., et al., in Ref.10, Vol. 3, p. 532. Turkdogan, E.T., Ironmaking and Steelmaking, 15, 1988, p. 311. Shankarnarayanan, R. and Guthrie, R.I.L., Steelmaking Proceedings, Iron and Steel Soc., USA, 1992, p. 655. Steffen, R., in Int. Conf. Secondary Metallurgy (English preprints), Verein Deutscher Eisenhuttenleute, Verlag Stahleisen mBH, Dusseldorf, 1987, p. 97.

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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.

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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 was introduced in the decade of the 1950s. The primary objective was to lower the hydrogen content in 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. Chapter 5 has already dealt with oxygen. Solubilities of H and N in pure iron at 1 atm pressure of the respective 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 of aluminum, 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 the atmosphere. H has a very high diffusivity even in solid steel due to its low atomic mass. In relatively thin sections, such as those manufactured by rolling, diffusion is fairly rapid. Hence, excess hydrogen 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, liquid steel 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 pressure for each gas.

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of this, H rejected by solid steel accumulates in blowholes and pinholes. The gas pressure developed inside 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. Efforts to 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 grades of steel with high strength and impact resistance. These considerations have led to hydrogen consciousness 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 in Chapter 5. The use of deoxidizers leads to the formation of deoxidation products affecting the cleanliness of steel. Vacuum treatment of liquid steel promotes a carbon-oxygen reaction and removal of oxygen as CO. This is clean deoxidation. Recognizing this, steelmakers also made deoxidation a target of vacuum treatment. This simultaneously lowers carbon as well and constitutes the basis for vacuum decarburization. Nitrogen affects toughness and aging characteristics of steel as well as enhancing the tendency toward stress corrosion cracking. Nitrogen is by and large considered to be harmful for properties of steel. Its strain hardening effect does not allow extensive cold working without intermittent annealing. Low nitrogen is essential for deep drawing quality steel. Very low nitrogen levels have become extremely important for ultra-low carbon, cold rolled steels with high formability for the automotive industry, subjected to continuous annealing. However, it is worth mentioning that there are applications where nitrogen has beneficial effects on 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. Solid solution hardening and precipitation strengthening effects are utilized in high-strength steels. Nitrogen additions are also particularly beneficial for stability and pitting resistance of austenitic stainless steel 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 water associated 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 from the melt using various strategies. All of this is beyond the scope of discussion here, since we are concerned with secondary steelmaking. However, in this connection, it may be mentioned that nitrogen 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 during tapping 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. The sample is melted in graphite crucible under a flow of pure argon. N and H evolve as N2 and H2 in the gas stream, whose total quantity is determined spectroscopically. More recently, emission spectrometers have come on the market and are in wide use for the analysis of nitrogen and other alloying 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 liquid steel. It employs a disposable immersion lance. Through some pumping arrangement, the gas in equilibrium with the melt is collected. The partial pressures of N2 or H2 directly give values of the nitrogen or hydrogen contents of molten steel. This method does not require the collection of solid sample 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 degassing processes are traditionally classified into the following categories: ©2001 CRC Press LLC

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 secondary processing of liquid steel. Temperature control is very important for proper casting, especially continuous casting. Therefore, provisions for heating and temperature adjustment during secondary steelmaking are very desirable. In vacuum processing, a successful commercial development in the decade of the 1960s was vacuum arc degassing (VAD), where arc heating is undertaken. Provision for heating is provided in an RH degasser as well. Stainless steels contain a high percentage of chromium. A cheap source of Cr is high-carbon ferrochrome. However, its addition raises the carbon content of the melt to about 1%, which is to be lowered to less than 0.03% in subsequent processing. Oxygen lancing has already been found to 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 nowadays resorted to in vacuum degassers for the production of ultra-low carbon steels as well. The RH-OB process is an example. In vacuum degassing, the total pressure in the chamber is lowered, whereas, in degassing by argon purging, the total pressure above the melt is essentially atmospheric. Even then, degassing is effected. This is because partial pressures of H2, N2, and CO are essentially zero in the incoming argon gas. Therefore, degassing by bubbling argon through the melt without vacuum is possible in principle. But consumption and cost of argon would be high, and the processing time would be lengthy. Hence, it is not practiced for ordinary steels. However, decarburization of stainless steel melts by the argon-oxygen decarburization (AOD) process is still popular. Besides degassing, modern vacuum degassers are used to carry out various other functions such as desulfurization, decarburization, heating, alloying, and homogenization, thereby achieving more cleanliness as well as inclusion modification. Adaptation of vacuum processes to produce ultra-low carbon steels is an important development direction. It is to be recognized that not all of these functions are equally important. A plant’s management has to fix its targets and accordingly has to decide priorities. These in turn dictate the choice of process, facilities required, and operating practices. Some broad guidelines are noted below3. 1. The treatment time in vacuum degassing should be short enough to logistically match with the converter steelmaking on the one hand and continuous casting on the other. This is one of the challenges. Higher pumping capacity for the vacuum systems is a prerequisite. For a modern 200t VD unit, a capacity higher than 500 kg of air/hr at 1 torr is common (1 torr = 1 mm Hg). 2. Injection of argon below the melt is a must for good homogenization, mass transfer, and inclusion removal. Design and location of tuyeres for such injection play an important role toward achievement of the targeted goals. Some plants have even adopted powder blowing 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 calcium silicide, 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 decarburization in ultra-low carbon steels, for enhancing rates of removal of nitrogen and hydrogen, or for both. 4. The carryover slag from a steelmaking converter poses problems during secondary steelmaking and has to be considered. Its modification by additions such as deoxidizers and CaO is to be included in the refining program for achieving defined objectives. ©2001 CRC Press LLC

Figure 6.2 shows the various degassing processes schematically. Sales trends for the period 1981–91 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 Messo Metallurgie.

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Figure 6.4 shows the RH process schematically. Molten steel is contained in the ladle. The two legs 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 vacuum chamber, where it is degassed and comes down through the downleg snorkel. The entire vacuum chamber is refractory lined. There is provision for argon injection from the bottom, heating, alloy addition, 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 are done without interruption of the vacuum. Even in late 19th century, vacuum treatment of steel melt was advocated. A major constraint was the availability of large-capacity industrial vacuum generating systems. Comprehensive discussions on this subject are available in the early publications on vacuum metallurgy.6 Figure 6.6 shows 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 (1 mm Hg). This is achieved by the use of steam ejector pumps in conjunction with mechanical pumps.

1 2 3 4

5 6

7

8 9 10

11

12 13

14

FIGURE 6.4 RH degasser. Courtesy of Messo Metallurgie.

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1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

Vacuum connection Television camera Sightglass with rotor Alloying hopper Alloying feeder Heating transformer Graphite rod vacuum vessel Upper part Middle part Lower part Lifting gas connection Upleg snorkel Downleg snorkel Teeming ladle

1 2 3 4 5 6 7

1. Temperature and sampling lance 2. Telescopic tubes for vacuum-tight electrode sealing 3. Bus tube supporting arms 4. Secondary bus 5. Water-cooled flexible highcurrent cable 6. Electrode tensioning device 7. Vacuum hopper for alloying agents 8. Guide column for electrode control 9. Sight glass with rotor 10. Sampling valve and hopper 11. Heat shield 12. Vacuum connection 13. Vacuum treatment vessel 14. Teeming ladle with steel 15. Porous inert gas bubbler 16. Diaphragm for steel outlet at ladle breakout

8

9

10 11 12

13 14 15

16

FIGURE 6.5 VAD unit. Courtesy of Messo Metallurgie.

Ejector pumps work on the principle of the diffusion pump. A jet of steam issues through a nozzle at high velocity and drags surrounding gas along with it (known as entrainment). Dusts coming out of the vacuum chamber, including condensed particles of volatile matters, settle down with condensed 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 of liquid steel. Appendix 2.1 through 2.4 presented tables for important thermochemical data. Table 6.1, therefore, contains equilibrium data pertaining to the principal degassing reactions only, viz., ©2001 CRC Press LLC

FIGURE 6.6 Vacuum generating system.

1 [ H ] = --- H 2 ( g ) 2

(6.1)

1 [ N ] = --- N 2 ( g ) 2

(6.2)

[ C ] + [ O ] = CO ( g )

(6.3)

TABLE 6.1 Equilibrium Relations of Degassing Reactions7 SL. No.

Reaction

Equilibrium relation

1.

1 [ H ] = --- H 2 ( g ) 2

[ h H ] = K H ⋅ p H2

2.

1 [ N ] = --- N 2 ( g ) 2

3.

[ C ] + [ O ] = CO ( g )

Unit of h

K vs. T relation

ppm

1905 logK H = – ------------ + 2.409 T

0.77

[ h N ] = K N ⋅ p H2

ppm

518 logK N = – --------- + 2.937 T

14.1

[ h C ] [ h O ] = K CO ⋅ p CO

wt.pct

1160 logK CO =  – ------------ – 2.00  T 

4.7 × 10−4∗

ppm

1160 logK CO =  – ------------ – 6.00  T 

0.47∗

1⁄2

1⁄2

At hC – 0.05 wt.%, i.e. 500 ppm. Note: 1 mm Hg = 1 torr = 1.315 × 10–3 atm.

*

©2001 CRC Press LLC

Values of h at 1600°C and 1 mm Hg

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 is because concentrations of H and N are small and lie in the Henry’s law region. Hence, the activity coefficient (fi) may be taken as 1 (Section 2.6). This approximation is quite valid for ordinary lowcarbon 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 be taken 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, depending on the concentrations of carbon and oxygen. Dissolved oxygen cannot be removed from the melt as gaseous O2. A sample calculation on –3 the basis of Eqs. (5.2) and (5.3), and assuming that hO = WO, shows that, at p O2 = 10 atmosphere and 1600°C, WO is 26 wt.%. This demonstrates the impossibility of the removal of dissolved oxygen as O2. Table 6.1 also shows that it is possible to obtain very low and completely satisfactory levels of H, N, and O in the melt from a thermodynamic point of view. The C–O reaction constitutes the basis for vacuum decarburization as well. For example, at 1600°C and 1 torr* pressure of CO, if the oxygen content in liquid steel (= hO) is 25 ppm, then the carbon content (= hC) would be equal to 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 during vacuum 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 calculations 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 of the breakdown of nonmetallic inclusions upon vacuum treatment of steel, and decreases have been found.8 Reaction of Liquid Steel with the Refractory Lining Besides the above reactions, which are encouraged by lowering the chamber pressure, some more are illustrated with examples below. * 1 torr = 1.315 ×10–3 atm.

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SiO2 (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 pressure tends to lead them to the forward direction as shown. SiO is a gas. Mg and Ca are stable gases at steelmaking temperatures. They also have negligible solubility in liquid steel. Some data indicate that 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.% C and 0.001 wt.% O. Ignore interaction coefficients. Given 1 MgO(s) = Mg(g) + --- O2 (g) 2 ∆G

0 1

= 6.085 × 105 + 1.005 T log T – 112.84T

(E1.1)

J/mole

Solution 1. Consider Reaction (6.7). This reaction is a combination of Reaction (E1.1) and Eq. (5.1). 1 3 o --- O 2 ( g ) = O; ∆G O = 117.3 × 10 + 2.889 T, 2

J/mole

(5.1)

So, ∆G 7 = ∆G 1 + ∆G O o

o

o

(E1.2)

Carrying out the calculations, ρ Mg × [ h o ] o ∆G 7 at 1850 K = 2.94 × 105 J mole–1 = –RT ln K7 = –RT ln -----------------------a MgO = – RT ln ( p Mg × x [ W O ] ) 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 ©2001 CRC Press LLC

(E1.3)

At 1850 K, K3 = 500 and K7 = 0.5 × 10–8 Hence, p Mg × P CO K9 = 250 × 10–8 = ----------------------WC

(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 hence the extent of this reaction would be appreciable. But at a depth, pCO is close to 1 atm. So pMg would be 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 some extent during vacuum treatment. An idea can be obtained if some calculations of vapor pressures (pi) are carried out for Fe-i binary solution. Wi -----Mi ---------------------pi = p ⋅ ai = p ⋅ γ i X i = p ⋅ γ i ⋅ W i W Fe ------ + --------M i M Fe o i

where

o

pi = ai = Xi = γi = Mi =

o i

o i

(6.10)

vapor pressure of pure element i at temperature under consideration activity of element i dissolved in liquid iron mole fraction of i in liquid iron activity coefficient (Raoultian) of i in liquid iron molecular mass of element i

For a dilute binary solution in iron, wFe ≈ 100, and γi = constant = γ i (Henry’s Law constant). Hence Eq. (6.10) may be simplified as o

o o W i M Fe p i = p i γ i ⋅ ---------------100M i

(6.11)

Table 6.2 shows some sample calculations based on Eq. (6.11). Again, the temperature dependence o of p i is given by the Clausius–Clapeyron equation, viz., ∆H v ∆S v o log p i (atm) = – ---------------------- + -----------------2.303 RT 2.303 R 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 ©2001 CRC Press LLC

(6.12)

TABLE 6.2 Equilibrium Vapor Pressures of Some Elements Dissolved in Molten Iron at 1600°C o

Element (i)

Mi

at 1600°C, milliatmosphere (approx.) (Ref. 9)

Al

27.0

2.66

Cu

63.5

1.2

Mn

54.9

Si

28.1

0.027

Sn

118.7

pi

γi

o

p I , milliatmosphere (calculated) at 1600°C (Ref. 10)

@ Wi = 0.05

@ Wi = 1

0.029

8.0 × 10–5

1.6 × 10–3

8.6

4.5 × 10–3

0.09

1.3

0.44

8.8

0.0013

0.35 × 10–6

6.9 × 10–6

2.66

2.8

1.7 × 10–3

0.035

665

Fe

55.85

0.76

–

–

–

S*

32.1

–

–

10–5

–

P*

31.0

–

–

10–9

–

*

Method of calculation discussed in text.

Table 6.2 indicates that volatilization of Mn should be the most predominant, followed by that of Fe. This agrees with observations. Significant loss of Mn occurs during vacuum treatment. The dust 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 the results of extensive investigation carried out at IRSID, France, on vacuum distillation of minor elements 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 increasing elimination in the order given. Mn evaporated at such a velocity that its elimination could be considered as a degassing process. The above observations are qualitatively in line with Table 6.2. S and P are gaseous at steelmaking 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 pressures are really the sum of all the gaseous components. However, the calculations in Table 6.2 have been performed assuming S2 and P 2 . 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 formation of volatile suboxides, SiO and Al2O. This is in line with studies on the characterization of hightemperature vapors where various other volatile suboxides such as SnO, AlO, and ZrO have been identified. Sehgal13 and others found that there was an appreciable loss of silicon from liquid steel under vacuum only if the latter contained sulfur. The results were interpreted by the formation of a volatile species, SiS. Ohno14 has reviewed the kinetics of evaporation in detail. He has shown how the formation of volatile compounds like SiS, CS, CS2, SO, SO2, etc. enhances the rate of elimination of S under vacuum. Deoxidation by Si was also helped thermodynamically and kinetically under vacuum or argon atmosphere due to the formation and removal of volatile SiO. The above findings are based on laboratory/bench-scale studies employing shallow melts, and somewhat leisurely experiments. In principle, they are applicable to industrial degassing processes, too. However, the author has little information on their quantitative significance. ©2001 CRC Press LLC

6.3 FLUID FLOW AND MIXING IN VACUUM DEGASSING The nature of fluid motion and the turbulence intensity during vacuum treatment of liquid steel are of considerable importance due to their significant influence on mixing, mass transfer, inclusion removal, refractory lining wear, entrapment of slag, and reaction with the atmosphere. Rising gas bubbles are either the only source or the principal source of stirring. The bubbles are gases evolved due to degassing (CO, N2, and H2) as well as injected argon gas. As stated earlier, argon injection through 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. In vacuum degassing, the chamber pressure is very small as compared to the ferrostatic head of the liquid in a vessel. As a consequence, the bubbles expand enormously when they rise to a free surface. This causes the phenomenon known as bubble bursting, as a result of which liquid metal droplets are ejected into the vacuum chamber in large numbers. For the purpose of understanding, the situations prevalent in vacuum degassing may be simplified 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. Brief presentations 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 reduced gas 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 depth below the free surface. The subscript n denotes the condition existing at nozzle exit at bottom. Let atmospheric pressure = 0. Then, P = ρlgz, where ρl is liquid density and z is the depth below the free 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 processing would impart a radial velocity to the surrounding fluid. The corresponding radial acceleration requires a radial pressure gradient. For this pressure gradient to be maintained, the pressure in the bubble must be higher than the pressure in the bulk of the liquid at the level of the bubble. Rapid ©2001 CRC Press LLC

expansion also would not allow instantaneous attainment of terminal velocity at a location, and it calls 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 bubble in n-tetradecane at room temperature for a freeboard pressure of 1 mm Hg, as shown in Figure 6.7.16 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, presumably due 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 from the nozzle. But, at a short distance above, they coalesce and disintegrate, exhibiting a spectrum of sizes. Such a phenomenon will occur here also, thus rendering theoretical predictions of the situation extremely difficult. It is possible to state with fair confidence that the plume characteristics, as well as the flow field in the liquid outside the plume, can be assumed to be the same as in an ordinary gas-stirred ladle situation toward the bottom part of the liquid. However, toward the top, some departure is expected. Splashing of liquid droplets above the bath by rising gas bubbles is a common experience. The extent of such splashing increases with an increase in the gas purge rate. It also increases with increasing bubble size. This phenomenon occurs in the traditional open-hearth steelmaking process and is held to be responsible for fast transfer of oxygen from the gas phase to the bath. Rimming phenomena during solidification of steel ingot provide another example. Visual observations during degassing 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 and mercury at room temperature. A film of liquid tends to stick to the bubble due to surface tension effects while the bubble tries to emerge from the bath. The rupture of this film is responsible for ejection of droplets. If a layer of slag is present at the top of the melt, such droplets cause the formation 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 a freeboard pressure of 1 mm Hg.16

©2001 CRC Press LLC

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 better mixing. However, theoretical computations of the flow field in the vessel have been carried out on a traditional RH degasser without gas purging from bottom. Figure 6.8 shows the flow pattern of the melt schematically. One of the latest studies is by Kato et al.,19 who also carried out water model and plant studies. The computed flow pattern (i.e., velocity distribution) is shown in Figure 6.9. It agreed reasonably with experimental observations in water model. Figure 6.10 shows a comparison 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) of liquid steel through the vacuum chamber. R ranges between 10 and 100 tonnes/min and has been a subject of study for some time. Circulation velocity increases with an increasing argon flow rate in the upleg of the degasser. Recently, Kuwabara et al.20 have reported extensive measurements of circulation rates in several RH degassers in Japan. They also computed R from the energy balance by considering buoyant force on bubbles and frictional dissipation in uplegs and downlegs of the vacuum chamber. This yielded the equation

where

R = AX

(6.14)

X = Q1/3 d4/3 {ln (P1/P2)}

(6.15)

A = a constant

and

where

Q d P1 P2 R

= = = = =

argon injection rate, Nm3/s I.D. of leg, m pressure at base of downleg pressure in vacuum chamber 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 value of A was obtained as 7.42 × 103.

FIGURE 6.8 Schematic flow pattern in the melt in an RH degasser.

©2001 CRC Press LLC

0.3 m s

—1

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 model of an RH degasser.19

Circulation rates had been estimated from radio tracer data in a 150t RH degasser.21 Data of Kuwabara et al. have been collected in a water model. Recently, Hanna et al.22 also reported an extensive water model investigation on circulation rate. They have also discussed the limitations of water models, since these cannot properly simulate bubble expansion due to temperature and pressure changes. Hence, they are approximate guides only. However, they have proven to be quite effective toward evolving more efficient degassers. ©2001 CRC Press LLC

FIGURE 6.11 Variation of the circulation rate (R) with the gas flow rate parameter (X) in RH degasser.

Hanna et al.22 also investigated the influence of other variables, such as the location and number of 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 more efficient design.

6.3.3

MIXING

IN

DEGASSER VESSELS

In both ladle and RH degassing, the vessel containing molten steel is a ladle, and the following discussions 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 mixing time (tmix) with ε for gas-purged ladles. Hence, the discussions here will be very brief and restricted to 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 a measure 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 the basis of design and process control. It is difficult to quantitatively take into account the influence of 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 monitored at the bottom of the downleg. Theoretical computations with the aid of a two-dimensional turbulent Navier–Stokes equation were performed. Experimental data approximately matched the assumptions that the melt inside the vacuum chamber was perfectly mixed, with eddy diffusivity ranging between 100 and 500 × 10–4 m2/s, depending on the argon injection rate. Tracer additions made at the bottom of the ladle were found to be uniformly dispersed in 8 to 10 min, whereas additions in vicinity 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 1 2 ε m = --- U R/M 2 ©2001 CRC Press LLC

(6.16)

where U is the linear velocity of metal in the downleg in meters per second, M is the total mass of 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 rate of carbon removal. They also collected samples from several depths of 240t and 300t degasser ladles to determine the average carbon removal rate. A comparison of the two approaches showed that the experimental rate was somewhat lower than the perfectly mixed assumption and somewhat higher than the plug flow assumption, demonstrating that the actual flow was nonideal. Carbon concentration in the vertical direction was found to be rather uniform. According to them, no dead zone 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, independent of the time of treatment and quality of steel.24 It has also been found that the results obtained on killed steels agree well with the theoretical equilibria derived from Sieverts’ law for the hydrogen content of steels if the results are related to the total pressures employed in the vacuum-treatment process. In degassing of semikilled or rimming steels, lower final hydrogen levels than found in killed steels usually may be obtained by most processes. The reason for this phenomenon is that the hydrogen partial pressure of semikilled or rimming steels is lower at the same total pressure due 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 degassing processes.24

©2001 CRC Press LLC

In vacuum arc remelting, the nitrogen content can be lowered to 5 to 10 ppm. Sometimes this level 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 somewhat insensitive to processing details. A sample calculation based on Table 6.1 shows that, at p N 2 = 0.1, 1, and 4 milliatmospheres (matm), the equilibrium nitrogen content of steel would be 4.3 ppm, 14 ppm, and 28 ppm, respectively, at 1600°C. Since the total pressure in the vacuum chamber during degassing lies in the range of 1 to 24 10 matm, and the exit gas contains anywhere between 10% to 50% N 2 , p N ranges between 0.1 2 and 5 matm. Therefore, the nitrogen content of molten steel either attains equilibrium with exit gas or may be somewhat higher during vacuum degassing. Suzuki et al.25 have put extent of nitrogen removal as 10 to 35%. The slowness of nitrogen removal may be ascribed to a lower value of diffusion coefficient as compared to that of hydrogen, and additional retardation by dissolved oxygen and sulfur as will be discussed later. It is also possible that the somewhat higher value of N 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 content corresponds to pCO = 100 torr (131.5 matm). At high carbon, value of O is lower. However, it corresponds to pCO close to 1 atm. Therefore, the C – O relationship is far off from equilibrium in vacuum 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 is somewhat lower. This reduces the difference with the equilibrium curve somewhat.

FIGURE 6.13 Influence of carbon content on ultimate total oxygen content of the steel melt in vacuum degassing processes.24

©2001 CRC Press LLC

2. The diffusivity of oxygen in liquid steel is an order of magnitude lower as compared to that of hydrogen. 3. The equilibrium value of dissolved oxygen is really negligible. This also has a magnifying effect 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 has been 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 in accordance with the terminology adopted in chemical engineering. In metallurgical engineering, we can profit greatly by exploiting some of the concepts and mathematical techniques that have already been developed by chemical engineers and subsequently extended to metallurgical engineering. 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 taken out only after the batch processing is over. But the gases are introduced/removed continuously. In stream degassing, however, the metal is introduced into the vacuum chamber continuously, and gases are withdrawn continuously as well. Therefore, it may be classified as a continuous stirred tank 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 assumptions. However, a lot more experimental data are required to do a better job. Major uncertainties relate 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 mathematical analysis for evaluating the process rates. For this, the process may be treated as isothermal and isobaric. 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 and intense agitation. This allows rapid attainment of equilibrium. Therefore, for problem solving, we assume the process to be thermodynamically reversible, i.e., equilibrium is established rapidly at every 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 Example 6.2 on RH degassing. Example 6.2 Calculate the rate of circulation of molten steel through the vacuum chamber in the RH degassing process to lower the hydrogen content of steel from 4 to 1.5 ppm in 15 min. Assume that the molten steel 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 the vacuum chamber = 0.1 milliatmosphere 2. Composition of molten steel: C, 0.05%,; Cr, 5%; Ti, 0.5%; Ni, 2%, remainder Fe C

Cr

Ti

3. e H = + 0.04,e H = 0.005,e H = – 0.22 ©2001 CRC Press LLC

Solution 1. Hydrogen balance: Rate of removal of hydrogen from steel (g/min) ( m˙ 1 ) = rate at which hydrogen is transferred to vacuum (g/min) ( m˙ 2 )

(E2.1)

d [ ppmH ] × 10 d [ ppmH ] 6 m˙ 1 = – W × 10 × --------------------------------------- = – W × ----------------------dt dt

(E2.2)

Now, –6

where W is the weight of steel in tonnes, t is time in minutes, and [ppmH] denotes concentration of H in parts per million at any instant in time. Again, m˙ 2 = R × 10 × ( [ ppmH ] – [ ppmH ] eq. ) × 10 6

–6

= R ( [ ppmH ] – [ ppmH ] eq. )

(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 p H2 in the vacuum chamber (as assumed in problem). Equating Eqs. (E2.2) and (E2.3), R d [ ppmH ] ------------------------------------------------- = ----- dt W [ ppmH ] – [ ppmH ] eq

(E2.4)

Integrating Eq. (E2.4) within limits t = 0, [ppmH]initial and t = tf, [ppmH] = [ppmH]final, W [ ppmH ] initial – [ ppmH ] eq 50 4 – [ ppmH ] eq R = ----- ln --------------------------------------------------------- = ------ ln -----------------------------------t f [ ppmH ] final – [ ppmH ] eq 15 1.5 – [ ppmH ] eq

(E2.5)

For calculation of [ppmH]eq, assume that the gas in the vacuum chamber is primarily H2 (not a bad assumption, since it is a killed steel). So p H 2 = 0.1 × 10–3 atm. C Cr Ti From Table 6.1, hH = 0.623. Again, log f H = e H × W C + e H × W Cr + e H × W Ti from Eq. (2.56). Substituting values, fH = 0.851. So, 0.623 [ ppmH ] eq = ------------- = 0.73 0.851 Or, from Eq. (E2.5), R = 4.82 tonnes/min

6.4.3

KINETICS

OF

DEGASSING

AND

(Ans.)

DECARBURIZATION GENERAL FEATURES

Degassing and decarburization reactions involve two phases: molten steel and gas. The overall reaction 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 ©2001 CRC Press LLC

3. 4. 5. 6.

Transfer of gaseous species H2, N2, and CO from the interface to the bulk gas Nucleation, growth, and escape of gas bubbles Mixing in the bulk liquid Mixing in the bulk gas

From our knowledge of reaction kinetics here as well as in similar situations, it has been taken as established that steps 4 and 6, i.e., mass transfer and mixing in the gas phase, are very fast and are not rate controlling, even partially. Chapter 5, Section 5.2.1 has reviewed the fundamentals of nucleation in connection with the formation of deoxidation products. Equation (5.39) gives the relationship between critical radius of nucleus (r*) with other variables for homogeneous nucleation, i.e., 2σ r* = – ------------------( ∆G/V )

(5.39)

For the equilibrium of the gas bubble with the liquid at constant temperature, dG = 0 = VdP + (dG)chemical

(6.17)

∆G *  ∆G -------- =  -------- = – ∆P  V  chemical  V  in Eq.(5.39)

(6.18)

2σ r* = ----------∆P*

(6.19)

So,

and hence,

where ∆P* = excess pressure inside the gas bubble with radius r* The gas law for the critical nucleus may be written as n* * * p b ⋅ V b =  ------ ⋅ RT N

(6.20)

Here, ∆P* ≅ P b, *

*

4 *3 * V b = --- π r , 3

R = 82.06 × 10

–6

3

–1

m K mol

–1

*

with P b and V b 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 3 1⁄2

6 σ * P ex ( atm ) = 1.54 × 10  ----- T

(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. ©2001 CRC Press LLC

It is impossible to generate such high excess pressure via the steelmaking reactions. In connection 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 gascontaining cavities in the refractory lining of the hearth.26 Nucleation of gas bubbles is not at all a problem, as it appears from several other studies, including carefully conducted cold model studies.25,27 In the early days, ladles for degassing were not fitted with gas purging arrangements. It was found that, initially, there was vigorous evolution of gas bubbles. After a time, when gas evolution ceased, degassing rates were very slow. The need for some stirring was sensed. This was achieved by electromagnetic stirring in ASEA-SKF ladles. Here, stirring helped mass transfer. Now, ladles have argon purging facilities. As a result, nucleation and growth are not required, as H2, N2, and CO either would be picked up by argon bubbles or would escape into vacuum chamber directly at the stirred top surface. It has been established that the rates of nitrogen absorption and desorption by molten iron and steel are partially controlled by slow surface reaction. This will be discussed separately later. For the time being, surface reaction is assumed to be fast. Hence, kinetic steps 1 and 5, viz., mass transfer 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 in the same overall range as the 95% conversion times for mass transfer controlled reactions for some 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 mixing or slow mass transfer. For mass transfer between a gas and a liquid, surface renewal theory is to be applied. Section 1⁄2 4.3.2 has reviewed it. It predicts that km,i should be proportional to D i , where km,i is the mass transfer 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 allow determination 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 to mass transfer or mixing, it is better to define the empirical (i.e., experimentally determined) rate constant as dW e – ----------i = k i,emp ( W i – W i ) dt

(6.22)

Takemura et al.29 determined values of ki,emp parameters for the removal of carbon and hydrogen in RH injection process. Figure 6.14 presents these as a function of argon gas flow rate. It may be noted that there is virtually little difference between them, i.e., ki,emp parameters were approximately the 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 rate controlling, then from Eq.(4.25), –7 1⁄2 k H ,emp 10  ------------- =  ----------------------= 3.73 – 9  7.2 × 10  k C,emp

Since this is not the case, it may be concluded that mass transfer was not rate controlling. On the other hand, rate control by mixing theoretically predicts same value of ki,emp for both carbon and hydrogen. Bauer et al.30 measured rates of removal of hydrogen, oxygen, sulfur, and nitrogen in a 185t VOD unit. Quantitative comparison of ki,emp parameters was not possible on the basis of their data. ©2001 CRC Press LLC

FIGURE 6.14 ki,emp vs. argon flow rate for carbon and hydrogen in the RH-injection process.29

But they indicated behavior similar to that obtained by Takemura et al.29 Therefore, it does not seem 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 up only 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 is Danckwerts’ surface renewal factor. S has been found to range between 5 and 25 s–1 in mild turbulence, going up to 500 s–1 in high turbulence. This gives the maximum ratio of ( k m,i ) high turbulence 500 1 ⁄ 2 ------------------------------------ =  --------- = 10  5  ( k m,i ) low tubulence In contrast to this, the specific surface area (a) can be increased by a factor of even 104 by the creation of small gas bubbles and metal droplets ejected into the gas space.31 Hence, for fast degassing, a large value of specific surface area is a prerequisite. It can be achieved only if a large number of gas bubbles are present in the melt during processing or if the molten steel is dispersed into the gas phase as fine droplets. Let us examine the various degassing processes from this point of view. 1. In ladle degassing, as soon as the chamber is evacuated, rapid growth and evolution of bubbles occur due to the initially large thermodynamic supersaturation. Rapid evolution of bubbles also causes ejection of fine droplets of liquid steel into the empty space of the vacuum chamber, causing a further rate increase. However, after few minutes, bubble evolution ceases, and rate of degassing decreases drastically unless there is argon purge from the bottom. 2. In stream degassing, the steel is introduced continuously into the vacuum chamber as a stream. Rapid formation and bursting of gas bubbles in the stream cause the latter to disintegrate into fine droplets. Hence, degassing is fast throughout the processing. ©2001 CRC Press LLC

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 and burst out of the melt in a vacuum chamber, thus assisting in the creation of drops and bubbles 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 its kinetics includes some special features. Pehlke and Elliott,32 in their pioneering study, measured the rate of absorption and desorption of nitrogen by a clean liquid iron surface in an inductively heated melt in a modified Sieverts apparatus. They derived the following important findings. 1. Absorption and desorption were first-order reversible processes with approximately the same rate constant. Rate (r) of desorption was given by r = AkN ([WN] – [WN]e) where

(6.23)

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 nitrogen above the melt kN = first-order rate constant

2. The increase in oxygen content of the liquid iron decreased the rate drastically. Figure 6.15 presents a typical behavior pattern, which shows that k N ∝ [ W O ] . Several investigators measured the surface tension (σ) of liquid iron with variable concentrations of oxygen dissolved in it. Figure 6.1633 shows the variation of σ with ln[WO] at 1550°C. From Gibbs Adsorption Isotherm, dσ dσ Γ O = – --------- = – ------------------------------dµ O RTd ( ln [ a o ] ) where

(6.24)

ΓO = excess oxygen at surface µ O = 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 that ΓO is positive. In other words, oxygen is surface active in liquid iron and prefers to stay at the surface. Darken and Turkdogan34 critically reviewed this inference. Theoretical calculations revealed that most of the surface would be covered by oxygen atoms at WO = 0.05 wt.% at 1550°C. Figure 6.17 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 oxygen atoms acted as barriers to it, consequently retarding the rate. Sulfur is also surface active in liquid iron. It also has been found to retard nitrogen absorption/desorption rates. This phenomenon has been 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 ©2001 CRC Press LLC

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 Reprinted by permission from American Chemical Society.

during degassing in a 185t ladle.30 Hence, the melt should be well deoxidized and desulfurized before attempting to remove nitrogen. Although Pehlke and Elliott claimed the kinetics to be exclusively controlled by slow surface reaction, this view was not accepted by all. In view of its importance, there have been several fundamental laboratory investigations in the last two decades. The current view may be summarized as follows. • The rate is primarily controlled by mass transfer in liquid iron at low oxygen and sulfur levels. • At normal oxygen and sulfur levels in liquid iron, partial rate control by slow interfacial reaction is also exhibited. Some investigators even considered mass transfer of N2 in gas phase as well. • It has also been concluded by several investigators that the interfacial reaction is a secondorder process, i.e., the rate of interfacial chemical reaction (rC) is given by ©2001 CRC Press LLC

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 ladle degassing.30

r C = Ak C ( [ W N ] – [ W N ] e ) 2

where

2

(6.25)

kC = chemical rate constant

A quantitative correlation of rate with oxygen and sulfur content of steel has been proposed by Fruehan and Martonik35 at constant temperature as k m,N k N = ----------------------------------------------1 + a[W O] + b[W S]

(6.26)

where kN is the actual first-order rate constant and is less than the mass transfer coefficient for nitrogen in liquid steel (km,N), and a and b are empirical constants. ©2001 CRC Press LLC

Evaluation of kC based on Eq. (6.25) requires the elimination of mass transfer effects from actual 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 was correlated with variables at 1600°C by an equation of the following type: aφ ( f N ) k C = -----------------------------------------1 + b [ hO ] + c [ hS ]

(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 of tiny gas bubbles at reduced pressures, causing surface flows in melt, may be responsible for such a discrepancy. It was stated in Section 4.3.2 that the presence of surface-active species on the surface of a liquid 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 suggested that this may, in principle, explain the retardation of rate in the presence of oxygen and sulfur where mass transfer is occurring in a turbulent flow situation. This alternative mechanism has not been seriously considered yet. As discussed in Section 6.4.1, industrial vacuum degassing is not very efficient in the removal of 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 irreproducible nature of removal. However, as stated earlier, it has been possible to achieve fairly low nitrogen levels in a well desulfurized and well deoxidized melt. Of course, even then, vacuum degassing alone is not enough. Nitrogen is picked up by molten steel at all stages of processing, viz., primary steelmaking, tapping, and teeming, due to contact with N2 in an air/gaseous environment. A lownitrogen steel can be produced (WN < 20 ppm) only if precaution is taken at all stages to prevent its absorption. Chapter 8 offers further discussion on this subject.

FIGURE 6.19 Variation of kC for nitrogen desorption with dissolved oxygen and sulfur content of molten steel at 1873 K.36

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6.4.6

KINETIC CONSIDERATIONS DECARBURIZATION

FOR INDUSTRIAL

VACUUM DEGASSING

AND

In industrial vacuum degassing, as already mentioned in Section 6.1.1, the treatment time should be short enough to logistically match with converter steelmaking on the one hand and with continuous casting on the other hand. To achieve this, in addition to the proper choice and design of 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 raise chamber pressure and requires a higher exhaust rate. The dynamic balance between the two determines the chamber pressure. This is illustrated for ladle degassing by Figure 6.20.38 In the initial stage, gas evolution is much faster, leading to higher chamber pressure. Predeoxidation is helpful, since it lowers the extent of CO evolution, thus allowing quicker attainment of a steady vacuum. The need for optimization 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. Nor is 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 the dehydrogenation of steel melt by argon purging, assuming it to be a thermodynamically reversible process. It is based on: 1. Hydrogen balance, viz., the rate of removal of hydrogen from molten steel = the rate at which hydrogen is going out with the exit gas 2. The assumption that the argon leaving the ladle is in equilibrium with the molten steel at that instant

FIGURE 6.20 Variation of chamber pressure with treatment time for ladle degassing.38

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FIGURE 6.21 Influence of pumping rate and argon flow on decarburization rate constant in RH degasser.39

This analysis would predict the highest possible rate of hydrogen removal by simple argon purging from the bottom. Going through the derivation steps, the following equation was derived:31 2 2 3     KH KH 10 ---------V = M  ppmH + ------------------------+ ---------------------------[ ppmH ] –    o 2 2 11.2 f H [ ppmH ]  f H [ ppmH ] o   

(6.28)

where M is the mass of steel in tonnes and V is the volume of Ar (in Nm3) to be passed for lowering H 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 consumption of argon. As discussed in Section 6.3.1, argon bubbles would expand enormously as they approach the top surface of melt in the vacuum chamber. Hence, the dominant volume would be present only below the top surface, and this is the region where bubbles pick up large quantities of H2, CO, and N2. Bannenberg et al.40 have illustrated this through their mathematical modeling exercise for a ladle degasser. Yano et al.41 have developed a dynamic model in connection with improvement of the RH process for production of ultra-low-carbon and low-nitrogen steel. They have not considered ejected droplets 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 vessel was assumed to be perfectly mixed in agreement with that by Kato et al.19 The chamber pressure was calculated by balancing the gas exhaust rate and the gas forming rate. Effective reaction surface area 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 two stages. Stage I was characterized by the rapid generation of gases (principally CO). Hence, the reaction inside the melt had a dominant share in decarburization. In stage II, this subsided due to a lowering of the contents of C, H, and N in the melt. Then, the free surface (including ejected droplets) 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 are expected to exhibit a range depending on the assumptions in model formulation and the nature of plant data. Yamaguchi et al.42 carried out kinetic studies in an RH degasser of Kawasaki Steel Corporation in connection with production of ultra-low carbon steel. The mechanism was assumed to be rate ©2001 CRC Press LLC

controlled jointly by the mass transfer of carbon and oxygen in the molten steel in the vacuum vessel. 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 other variables through regression analysis of plant data as follows: Ak m ∝ A V ⋅ R 0.32

where

1.17

⋅C

1.48

(6.29)

AV = cross-sectional area of RH vacuum vessel R = circulation flow rate of liquid metal C = carbon concentration of melt in vacuum vessel in parts per million

The dependence of Akm on carbon concentration is very significant. The authors have explained it as due to the predominance of the surface of ejected droplets as site for decarburization. The extent 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 vessel in an RH degasser. Degassing rate increases with an increasing circulation rate in RH. This is well established.25,41 For the situation in Figure 6.22, it is expected that the exhaust rate would have significant influence on rate of decarburization in stage I, in view of the large rate of generation of gases, but not in Stage II. Yano et al.41 verified this from their plant data as well. Therefore, the attainment of ultra-low carbon is possible by having a high exhaust rate and low/moderate argon flow rate in stage I (i.e., left region of Figure 6.22) and a moderate exhaust rate and relatively high argon flow rate for stage II (i.e., right region of Figure 6.22).

FIGURE 6.22 Typical results of calculations by Yano et al.41 for decarburization in an RH degasser, showing kinetic behaviors in different stages: (a) low exhaust rate and (b) high exhaust rate.

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The primary focus nowadays is to speed up the rate of decarburization under vacuum so as to produce 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 rate of 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 carried out experimental measurements in a 50t VOD vessel. A Co tracer was employed for collecting data on mixing behavior. Deoxidation was carried out by aluminum addition. From the variation of radio-tracer intensity at a location of the melt as a function of time, the circulation rate of metal was determined. It ranged between 15 to 56t/min, depending on argon purging rate. The deoxidation rate constant (kO) ∝ R ∝ Q1/2. Bauer et al.30 and some others have employed the circulation concept in a ladle degasser. They defined R as ratio of (treatment time/mixing time). Actually, it should not be called a rate. It is simply a measure of the number of circulations. From a fundamental point of view, it seems to be superior 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 increasing volumetric flow rate of argon. In general, it may be stated that k ∝ Qn, where 0 < n < 1. For a simple situation, such as a gas-stirred melt in ladles without vacuum, ν may lie between 1/3 and 1/2, 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 complexities arising 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 indicated that ν ranged between 1/3 and 1/2. Data of Yano et al.41 indicate κ ∝ Ρ1/3 approximately for Stage I. Again, Ρ ∝ Q1/3 [Eq. (6.15)]. This means that k ∝ Q1/9 approximately. This corresponds to the low exhaust rate in Figure 6.21. However, in the ultra-low carbon range, as Eq. (6.29) indicates, n is approximately 1/2. Hence, it tentatively may be concluded that n will be less than 1/2 in vacuum degassing. Kleimt and Kohle44 have developed a dynamic model of RH decarburization. It has been verified by plant data, which included waste gas analysis and gas flow rate measurement. The physics 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 was carried out in primary steelmaking furnaces only. High-carbon ferrochrome is much cheaper than low-carbon ferrochrome for alloying during the manufacture of stainless steels in an electric arc furnace. However, it raises the carbon content of the melt. This is undesirable, since stainless steel grades demand carbon content less than 0.03% or so. Since Cr also forms stable oxides, removal of carbon by oxidation to CO is associated with the problem of simultaneous bath chromium oxidation. ©2001 CRC Press LLC

Thermodynamic measurements revealed that the higher the temperature of the bath, the greater the 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. Since a decrease of partial pressure of CO would assist preferential decarburization further, vacuumoxygen decarburization (VOD) and argon-oxygen decarburization (AOD) processes were invented for stainless steelmaking. Oxygen is blown into the steel melt either under vacuum or along with argon in these processes, respectively. This made the EAF simply a melting unit and transferred the job of decarburization to VOD or AOD vessels. Now, decarburization under vacuum is practiced for carbon steels and also for ULC, for which oxygen injection facilities are provided in RH (RHOB) and ladle degassers. For large scale production of stainless steel, the use of an LD converter in place of an EAF is cheaper. A combination of converter and VOD has led to development of the VODC (i.e., vacuum-oxygen decarburization converter). Choulet et al.45 have reviewed the status of stainless steel refining. Demand for stainless steel was projected to grow at an annual rate of 4 to 6% over the next decade and may reach a world production of 18 million tonnes in A.D. 2000. More remarkable is the growth of ferritic stainless steel, 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 automobile exhaust systems is worth mentioning. A variety of refining processes have been patented, as shown in Figure 6.23.45 Even then, the AOD process accounted for 75.6% of total stainless steel production in western countries in 1991. This, of course, includes variants of AOD in which top blowing is also employed. Shinkai et al.46 carried out a kinetic analysis of plant data of VOD processes for stainless steel refining at Yawata works and concluded as follows: 1. The nitrogen desorption reaction mainly occurs at the surface of CO bubbles, when strong 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% at the 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 the early stage of operation. The above conclusions are qualitatively in agreement with those of Yano et al.41

(a) AOD

(b) RH-OB / KTB

(e) K-BOP

(c) VOD

(f) CLU

(d) VODC / AOD-VCR

(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.

©2001 CRC Press LLC

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, and to 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 time required to achieve such low carbon is so long that carbon content at BOF tapping should be lowered. However, this is accompanied by excessive oxidation of molten steel and loss of iron oxide 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 oxygen blowing (OB) during degassing. The RH-OB process, which uses an oxygen blowing facility during degassing, 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 popularity of RH-OB can be noted from Figure 6.3. The present thrust is to decrease carbon content from something 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 composition adjustments, powder injection facilities were subsequently added to RH-OB. Obana47 has reviewed 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 much as 90% of BOF heats. During oxygen blowing, aluminum is also added. Aluminum finally deoxidizes 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 some plants through tuyeres located below the melt in the ladle. However, oxygen spraying by top lance and injection by immersed lance seem to be more common. Turkdogan48 has discussed the role of ladle slag in RH degassing. He has concluded that slag FeO reacts with dissolved carbon in steel above about 200 ppm carbon. The higher the initial carbon content, the greater the tendency for reaction with slag FeO.

FIGURE 6.24 The RH injection process.

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It may be noted from Section 6.4.6 that most of the current investigations on kinetics and mechanisms 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 nozzles into the vacuum vessel of the degasser for argon purging. These were located just above the snorkel level, into the vessel lining for side-blowing argon into the melt. The gas flow rate into the snorkel for circulation was 2.5 Nm3/min and into vacuum vessel at 0.8 Nm3/min. The latter enhanced the rate by a factor of 1.6 on the average and enabled a lowering of carbon content from 200 ppm to 10 ppm within 10 min. It demonstrates the effect of design modification on rate. Another example is 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, which is costly.50 As stated in Section 6.4.6, Yamaguchi et al.42 did not find any significant influence of the oxygen content of liquid steel on the decarburization rate in the ULC range. However, at a carbon content of more than 200 ppm, an increase in dissolved oxygen content due to concurrent oxygen blowing enhanced the decarburization rate almost proportionately. It indicated that oxygen blowing was effective in the high-carbon range only.

6.5.2

THERMODYNAMICS MELTS

OF

DECARBURIZATION

OF

HIGH-CHROMIUM STEEL

Like iron, chromium exhibits two valences, viz., Cr2+ and Cr3+, when it is oxidized. An issue on which controversies have persisted for a long time, and perhaps persist now, is whether Cr is present in slag as CrO or Cr2O3 or something else. From investigations over years, the picture that emerges is as follows. Cr is capable of exhibiting a variable Cr2+/Cr3+ ratio in slag like iron, depending on the oxygen potential and basicity. In reducing slags or acid slags, CrO is the dominant oxide. In oxidizing or basic slags, Cr2O3 is dominant. During the oxidizing period of VOD or AOD, the slag may be assumed to be saturated with chromium oxide in view of the very low quantity of slag per tonne of metal. Appendix 5.1 shows that Cr3O4 is the stable deoxidation product if the Cr content of iron is above 8%. Toker et al.51 determined the phase relations and thermodynamics of a Cr-O system. They found Cr3O4 coexisting in equilibrium with the liquid oxide in the temperature range of 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 { p CO } × [ h Cr ] K 31 = ------------------------------------4 [ hC ] 4

3

(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)

4 log WC + 4 log fC = 3 log WCr + 3 log fCr + 4 log pCO – log K31

(6.34)

i.e.,

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The terms fC and fCr are functions of temperature and composition. K31 is a function of temperature. 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 temperature is required if we wish to obtain less than 0.04% C at above 15% Cr. Lowering pCO allows us to 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 thermodynamic activities 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 of VOD/AOD operation, Hilty et al.52 assumed the following reaction: Cr3O4(s) + 2Si = 3Cr + 2(SiO2)

(6.37)

[ h Cr ] ( a SiO2 ) K 37 = -------------------------------2 [ h Si ] ( a Cr 3 O4 )

(6.38)

3

2

Noting that a SiO2 and a Cr 3 O4 in slag are functions of slag basicity, an equilibrium relation was arrived at from Eq. (6.38). However, for practical uses, statistically fitted empirical coefficients are recommended 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 by permission of Iron & Steel Society, Warrendale, PA, U.S.A.

©2001 CRC Press LLC

FIGURE 6.26 Influence of pressure and temperature on the retention of chromium by oxygen-saturated steel melt at 0.05% carbon.49 Reprinted by permission of Iron & Steel Society, Warrendale, PA, U.S.A.

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 facility for top blowing of oxygen like an LD converter. The Ar + O2 mixture is blown through the immersed side tuyere. Initially, when the carbon content of the melt is high, blowing through a top lance dominates. Even the gas mixture through side tuyere has a high percentage of O2. However, as decarburization proceeds, O2 blowing is cut down in stages, and Ar blowing is increased. Some stainless steel 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 consequent minimization of toxic carbon monoxide in the exit gas as well as utilization of the fuel value of CO to raise the bath temperature. It has been reported that 75 to 90% of the available energy from the combustion reaction is transferred to the molten bath. Toward the end, when the carbon content is very low and meets specifications, only argon is blown to effect mixing and promote a slag–metal reaction. At this stage, ferrosilicon and other additions are made. Silicon reduces chromium oxide from slag. If extra-low sulfur content is required, the first slag is removed, and a fresh reducing one is built up with Ar stirring. The purposes of other additions include both alloying and bath cooling, since the bath temperature goes above 1700°C due to oxidation reactions. Another recent trend is to carry out further secondary refining of the melt after processing in an AOD converter in another treatment facility (e.g., ladle furnaces and vacuum systems). The purpose of this is to reduce the cycle time for the AOD and to improve quality. Vacuum units assist in 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 revamped to a vacuum tight structure. A significant lowering of final carbon (<50 ppm) and nitrogen could be obtained by applying vacuum in the final stage. ©2001 CRC Press LLC

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.

Ladle furnace treatment with typical addition of lime, spar, etc. is meant for a general improvement in quality. The use of CO2 as replacement for argon is also being advocated,54 as CO2 behaves like 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 and turbulence in a water model of the AOD with only side blowing of gas. Local heat transfer rates were also determined from melting rates of immersed ice samples. They found the velocity fields and distribution of turbulent kinetic energy to be quite uniform. In addition, dead zones could not be located. Figure 6.28 shows a typical experimentally measured velocity profile. The outline of the plume is shown by the dotted curves. The high gas flow rate and the large size of the plume due to side blowing give rise to such uniformity. Tsujino et al.56 investigated the decarburization behavior of Fe-18% Cr molten steel in a 6t AOD vessel with combined blowing. They correlated the ratio of chromium loss to carbon loss from 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. Interested readers may consult the original paper for details.

REFERENCES 1. Llewellyn, D.T., Ironmaking and Steelmaking, 20, 1993, p. 35. 2. Peerless, J. and Clay, W., Ironmaking and Steelmaking, 20, 1993, p. 312. 3. Verein Deutsher Eisenhuttenleute., preprints of Int.Conf on Secondary Metallurgy, Verlag Stahleisen mbH, Dusseldorf, Germany, 1987. ©2001 CRC Press LLC

NOZZLE

20 cm/s

FIGURE 6.28 Experimentally measured velocity field in jet plane and plane perpendicular to jet plane, for a water model of an AOD converter.51 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30.

Bergmann, W., Holtermann, H., Ellebrecht, C.and Wahlster, M., MPT, 1979, No. 6, p. 46. Fruehan, R.J., Vacuum Degassing of Steel, Iron & Steel Soc., U.S.A., 1990. Bunshah, R.F., ed, Vacuum Metallurgy, Reinhold Publishing Corp., New York, 1958. The Japan Society for the Promotion of Science, the 19th Committee Steelmaking Data Source book, revised ed., Gordon & Breach Science Publishers, Tokyo, 1988. Akshoy, A.M., in Ref. 6, p. 59. Elliott, J.F. and Gleiser. M., Thermochemistry for Steelmaking, Vol. 1, Addison-Wesley Publishing Co., Reading, Mass, U.S.A., 1960. Ref. 9, Vol. 2 (with V. Ramakrishna), 1963. Tix, A., J. Metals, 8, 1956, p. 420. Ollette, M., in Physical Chemistry of Process Metallurgy, G.R. St. Pierre, ed., Interscience Publishers, New York, 1961, Part 2, p. 1045. Sehgal, V.D., JISI, 207, 1969, p. 95. Ohno, R., in Liquid Metals-Chemistry and Physics, S.Z. Beer ed., Marcel Dekker Inc., New York, 1972, Ch. 2. Szekely, J. and Martins, G.P., Trans. AIME, 245, 1969, p. 629. Szekely, J., Fluid Flow Phenomena in Metals Processing, Academic Press, New York, 1979, Ch. 8. Tatsuoka, T., Kamata, C. and Ito, K., ISIJ Int., 37, 1997, p. 557. Richardson, F.D., Physical Chemistry of Melts in Metallurgy, Academic Press, London, Vol. 2, 1974, Chs. 13, 14. Kato, Y., Nakato, H., Fujii, T., Ohmiya, S., and Takatori, S., ISIJ Int, 33, 1993, p. 1088. Kuwabara, T., Umeza, K., Mori, K., and Watanabe, H., Trans. ISIJ, 28, 1988, p. 305. Nakanishi, K., Szekely, J., and Chang, C.W., Ironmaking & Steelmaking, 2, 1975, p. 115. Hanna, R.K., Jones, T., Blake, R.I., and Millman, M.S., Ironmaking & Steelmaking, 21, 1994, p. 37. Nakanishi, K., Fujii, T., and Szekely, J., Ironmaking & Steelmaking, 2, 1975, p. 193. Ruttinger, K., in Vacuum Metallurgy, O. Winkler, and R. Bakish, ed., Elsevier Publishing Co., Amsterdam, 1971, Ch. 4. Suzuki, Y. and Kuwabara, T., in Secondary Steelmaking, Book 190, Metals Soc., London, 1978, p. 32. Ward, R.G., An Introduction to Physical Chemistry of Iron and Steelmaking, Edwin and Arnolds, London, 1962, p. 91. Dharwadkar, H.N. and Ghosh, A., Metall. Trans., 17B, 1986, 553. Ghosh, A., Tool & Alloy Steels, 25, 1991, Silver jubilee issue, p. 65. Takemura, Y., Inaba, A., Yamamoto, T., Nagata, S., Takamoto, H., and Endoh, K., in Ref. 3, p. 244. Bauer, K.H. and Wagner, H., in Ref. 3, p. 256.

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31. Ghosh, A. and Ray, H.S., Principles of Extractive Metallurgy, Wiley Eastern Ltd. (Publishers), New Delhi, 1991, Ch. 9. 32. Pehlke, R.D. and Elliott, J.F., Trans. AIME, 227, 1963, p 844. 33. Holden, F.A. and Kingery, W.D., J. Phys. Chem., 59, 1955, p. 557. 34. Darken, L.S. and Turkdogan, E.T., in Heterogeneous Kinetics at Elevated Temperature, Belton,G.R., and Worrell, W.D., ed., Plenum Press, New York, 1970. 35. Fruehan, R.J. and Martonik, L.J., Metall Trans B, 11B, 1980, p. 615. 36. Harada, T. and Janke, D., Steel Research, 60, 1989, p. 337. 37. Richardson, F.D., Trans. ISIJ, 14, 1974, p. 1. 38. Nolle, D., Eulenburg, U., Jahns, A., and Miska, H., in Ref. 3., p. 269. 39. Soejima, T., et al., Trans. ISIJ, 27, 1987, B-146. 40. Bannenberg, N., Bergman, B., Wagner, H., and Gaye, H., Proc. 6th Iron & Steel Cong, Nagoya, 1990, Vol. 3, p. 603. 41. Yano, M., Kitamura, S., Harashima, K., Azuma, K., Ishiwata, N., and Obana, Y., Steelmaking Conf. Proc., Iron and Steel Soc., Chicago, Vol. 77, 1994, p. 117. 42. Yamaguchi, K., Kishimoto, Y., Sakuraya, T., Fujii, T., Aratani, M., and Nishikawa, H., ISIJ Int., 32, 1992, p. 126. 43. Nakanishi, K., Fujii, T., Ooi, H., Mihara, Y., and Iwaska, S., Proc. 4th Int.Conf. on Vacuum Met., Iron & 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.

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7

Desulfurization in Secondary Steelmaking

7.1 INTRODUCTION Except in free-cutting steels, sulfur is considered to be a harmful impurity, since it causes hot shortness 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 be 0.02%. In special steel plates, the normal specification for sulfur is 0.005% these days, but there is 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 iron by slag in a reducing environment only. Hence, traditionally, sulfur control used to be done during ironmaking in a blast furnace. Very little sulfur removal is possible in primary steelmaking due to the oxidizing environment. An exception is the electric arc furnace (EAF), where low-sulfur steels are produced through two-stage refining. In view of the consistent demand for lower-sulfur steel and the incapability of the blast furnace to achieve it, external desulfurization of liquid iron in a ladle during transfer to the steelmaking shop was developed. The process is capable of lowering sulfur content to 0.01% or so and is an essential feature of a modern integrated steel plant. Content below 0.01% must be accomplished in secondary steelmaking. There are now processes, such as the MPE process of Mannesman and the EXOSLAG process of U.S. Steel,2 where desulfurization is achieved to some extent during tapping by using synthetic slag and utilizing the kinetic energy of the tapping stream. Desulfurization by treatment with synthetic slag on top of molten steel and gas stirring (either in an ordinary ladle, in a ladle furnace or VAD, or during vacuum degassing) are also being practiced. However, only the injection of a powder such as calcium silicide into the melt is capable of producing ULS steel. ULS can be achieved only if the dissolved oxygen is also very low. Gas stirring is required, so deep desulfurization is associated with deep deoxidation. The use of aluminum in combination with calcium or rare earth (RE) metals achieves both. In addition, injection processes 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 steel retard the nitrogen desorption rate from steel in vacuum degassing. A low nitrogen level has been achieved in low-sulfur and low-oxygen steels. This is an additional benefit if deep desulfurization is done before or during vacuum treatment. Furnace slags contain oxides such as FeO, SiO2, P2O5, and MnO. These oxides are unstable in the presence of a deoxidized steel, especially when the slag and steel are intimately mixed. As a result, some reversion of phosphorus into the steel occurs. This slag also partly consumes added deoxidizers, so it does not allow proper utilization of them for steel deoxidation. The slag also causes wear on the ladle lining.

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Although these have been known for a long time, very little physicochemical investigation has been conducted on these effects. Turkdogan2 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 if slags 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 during secondary steelmaking and other beneficial effects. Therefore, control of furnace carryover slag aims at the twin strategy, viz., (a) minimization of furnace carryover slag, and (b) modification of carryover slag by the addition of fluxes (principally CaO, but also Al, SiO2, Al2O3, and CaF2 to some extent) to render desirable properties to it. Section 5.3 discussed the minimization of slag carryover, 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, [ hS ] K 1 = --------1⁄2 p S2

(7.2) equilibrium

where K1 is the equilibrium constant for Reaction (7.1), p S2 denotes partial pressure of sulfur in the gas phase in atmosphere, and hS is the activity of dissolved sulfur in steel with reference to 1 wt.% standard state. Again, 6535 log K1 = ------------ – 0.964 T

(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 steel j on the activity coefficient of sulfur (fS) dissolved in liquid steel (i.e., e s ) at 1600°C are given in Appendix 2.3, where hS = fS · WS, WS being the weight percent of sulfur in steel. It may be noted further 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 and sulfides. Ca and Ba form CaS and BaS, respectively, upon reaction with sulfur, whereas cerium forms several sulfides7 out of which CeS is the stablest one under steelmaking conditions. Ce also forms an oxysulfide, Ce2O2S. All of these compounds are solids at steelmaking temperatures. It may be noted, from thermodynamic data on these compounds in any standard text, that all these ©2001 CRC Press LLC

elements form very stable sulfides as well as oxides. Therefore, they are both strong deoxidizers as well as desulfurizers and would form both oxides and sulfides. Again, these compounds would not necessarily be present in a pure form. For example, addition of Ca-Si leads to the formation of a CaO-SiO2-type deoxidation product as discussed earlier in Section 5.2. However, we do not propose to get involved in these complexities and consider the overall 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), the equilibrium constant (KMS) for Reaction (7.4) is [ hO ] [ W O ] - = ------------- (at equilibrium) K MS = --------[ hS ] [ W S ]

(7.5)

The values of KMS for different systems can be calculated from the free energy of reaction. Figure 7.1, reproduced from Turkdogan,8 shows the pattern. Ba is the strongest desulfurizer and Mg the weakest, with Ca and Ce lying in between. Holappa1 has reviewed the theoretical basis for sulfur removal in ladle treatment by slag–metal reaction. If the MO and MS are not pure, then it is better to utilize the general ionic form of desulfurization reaction, viz., [S] + (O2–) = (S2–) + [O] ( a S2– ) [ h O ] K 6 = ----------------------[ h S ] ( a o2– )

FIGURE 7.1 Oxygen/sulfur activity ratio in liquid iron for some sulfide-oxide equilibria at 1873 K.9

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(7.6)

or, ( a s2– ) [ h O ] ( K 6 ) ( a o2– ) = ---------------------[ hS ]

(7.7)

If we replace a s2– with weight percent sulfur in slag (i.e., WS), then we may use a modified value of K6 (let it be K′ 6 ). Then, ( W S ] ) [ hO ] K′ 6 ( a o2– ) = ------------------------- = C′ S [ hS ]

(7.8)

where C′ S 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 C S = ( W S ) ( p O2 / p S2 )

1⁄2

(7.9)

where (WS) is the weight percent sulfur in the slag in equilibrium with a gas having partial pressures of oxygen and sulfur as p O2 and p S2 . Its usefulness stems from the fact that CS is a property of slag, and at a fixed temperature it is determined solely by slag composition. The higher the value of CS, the better the desulfurizing ability of the slag. Figure 7.2 shows CS values for some typical slag 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 sulfur potential. However, it is the slag–metal equilibrium that is of interest. This requires the use of a modified CS (viz., C′ S ) as defined in Eq. (7.8). The relationship between CS and C′ S is 936 log C S = log C′ S + --------- – 1.375 T At 1600°C, C′ S = 7.5 CS.

FIGURE 7.2 Sulfide capacities of some slags at 1873 K.9

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(7.10)

Another parameter of interest is the equilibrium sulfur partition ratio between slag and metal (LS), where LS = (WS)/[WS]. From Eq. (7.8), if [hS] is taken as [WS], then, at slag–metal sulfur equilibrium, (W S) C′ L S = ----------- = ---------S[W S] [ hO ]

(7.11)

hO in liquid steel is typically determined by the presence of a deoxidizer, especially dissolved aluminum. One may relate hO to the FeO content of slag as well. However, it has been found more appropriate to relate it to the former. Figure 7.3 shows LS as a function of the CaO content of slag and aluminum content of metal for CaO-Al2O3 slag.8 Therefore, for good desulfurization, Al content of 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 predominant desulfurizer. For the reaction, CaO(s) + S = CaS(s) + O

(7.12)

With the data on free energies in Appendices 2.1 and 2.2, 5140 logK 12 = – ------------ + 0.961 T

(7.13)

K12 is the equilibrium constant for Reaction (7.12) and is same as KMS for a CaO-CaS reaction. At 1600°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., 5304 logK 12 = – ------------ + 1.191 T

(7.14)

FIGURE 7.3 Equilibrium sulfur partition ratio between liquid iron with dissolved Al and CaO-Al2O3 slags.8

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This yields a value of K12 at 1600°C of 0.028, matching Figure 7.1. The compilation of Zhang and Toguri12 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 ( a CaOS ) [ h O ] K 12 = ---------------------------( a CaO ) [ h S ]

(7.15)

Proceeding similarly as in the derivation of Eq. (7.8), [ hO ] - = C′ S mK 12 ( a CaO ) = ( W S ) ⋅ --------[ hS ]

(7.16)

where m is a constant of proportionality. Combining Eqs. (7.10), (7.14), and (7.16), 4204 logCS = logm + log(aCaO) – ------------ – 0.184 T

(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 larger in 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 the CS values of Figure 7.2. Figure 7.6 gives values of CS in a ternary CaO-Al2O3-SiO2 system at 1600°C. In the limited temperature range of secondary steelmaking, it seems good enough to assume aCaO to be independent of temperature at a fixed slag composition. Therefore, if CS is known at one temperature from a diagram such as Figure 7.2, it can be estimated at any other temperature. Further refinement on this can be made by invoking a regular solution assumption for aCaO.

FIGURE 7.4 Activity vs. composition diagram for CaO-Al2O3 system at 1773 to 1873 K.13

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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 at 1773 K.18

For determining values of CS or C′ S , using diagrams as in Figure 7.2 is somewhat inconvenient. Therefore, attempts are underway to analytically represent CS as a function of slag composition. Tsao et 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. 9894 log CS = 3.44 (XCaO + 0.1 XMgO – 0.8 X Al2 O3 – X SiO2 ) – ------------ + 2.05 T ©2001 CRC Press LLC

(7.18)

This may be useful for prediction purposes within a factor of 2 to 3. Also, it is not applicable to CaF2-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): B 13300 logC′ S = ---- + 2.82 – --------------D T

(7.19)

B 12364 logC S = ---- + 1.445 – --------------D T

(7.20)

Combining with Eq. (7.10),

where

B = 5.62 WCaO + 4.15 WMgO – 1.15 W SiO2 + 1.46W Al2 O3 D = WCaO + 1.39 WMgO + 1.87 W SiO2 + 1.65W Al2 O3

The conclusion drawn by the above mentioned authors is that the domains of liquid slag compositions leading to high LS are rather limited, and the efficiency of a sulfur removal treatment will rely on the ability to reach these domains. The aimed compositions should be close to CaO saturation. The authors also recommend that, in using Eq. (7.19), calcium present as CaF2 should be 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 large value of CS (i.e., C′ S ), but also by a low value of hO. Here, aluminum is superior to silicon, since it allows deeper deoxidation. The thermodynamic relationship between LS with other parameters for deoxidation by aluminum may be derived as described below. From Eqs. (7.10) and (7.11), 936 log L S = logC′ S – logh O = logC S – --------- + 1.375 – logh O T

(7.21)

(Al2O3) = 2[Al] + 3[O]

(7.22)

Again,

For which [ h Al ] [ h O ] K Al = -------------------------( a Al2 O3 ) 2

3

(at equilibrium)

(7.23)

From Appendix 5.1, 64000 logK Al = – --------------- + 20.57 T

(7.24)

or, if it is assumed that hAl = WAl, 1 64000 logh O = --- – --------------- + 20.57 – 2 logW Al + log ( a Al2 O3 ) 3 T

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(7.25)

Combining Eqs. (7.21) and (7.25), 1 2 20397 logL S = logC S – --- log ( a Al2 O3 ) + --- logW Al + --------------- – 5.482 3 3 T

(7.26)

An important issue is variation of LS with temperature at a fixed slag composition. In addition to 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 with predictions based on Eqs. (7.18) and (7.20) at a mole fraction of CaO of 0.6 for CaO-SiO2 and CaO-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. X SiO2 = 0.4 for CaO-SiO2 slag, and X Al2 O3 = 0.4 for CaO-Al2O3 slag. In CaO-SiO2 at 0.6 mole fraction CaO, 0.6 × 56 W CaO = 100 × ------------------------------------------------- = 58.3% 0.6 × 56 + 0.4 × 102 or, W SiO2 = 100 – 58.3 = 41.7% In CaO-Al2O3 at 0.6 mole fraction CaO, 0.6 × 56 W CaO = 100 × ------------------------------------------------- = 45% 0.6 × 56 + 0.4 × 102 or, W Al2 O3 = 100 – 45 = 55% Values of Cs Fig. 7.2

Eq. (7.18)

Eq. (7.20)

–3

CaO−SiO2

5.0 × 10

2.85 × 10

7.89 × 10–4

CaO−Al2O3

2.7 × 10–3

5.38 × 10–3

1.99 × 10–3

–4

Hence, Figure 7.2 and Eq. (7.18) give differing values. But Eq. (7.20) matches reasonably with Figure 7.2. Example 7.2 At 1600°C and for CaO-Al2O3 slag with a mole fraction of CaO equal to 0.6, 1. 2. 3. 4.

Calculate desulfurization efficiency of slag (i.e., [WO]/[WS] ratio). Compare the above with that of pure CaO. Calculate the value of LS if liquid steel contains 0.01 wt.% Al, and compare with Figure 7.3. Calculate the weight percent sulfur in metal.

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Assume slag–metal equilibrium and sulfur in slag as 1 wt.%. Ignore the interactions of other solute elements. Solution (a) From Eq. (7.11), and taking hO = WO in metal phase, [ hO ] [W O] C′ S ----------- = ------------ = ----------[W S] [W S] (W S)

(E1.1)

Now, (WS) = 1, and CS = 2.7 × 10–3 (Figure 7.2). From Eq. (7.10) at 1600°C, C′ S = 7.5 CS. Putting in these values, [W O] –2 ------------- = 2.03 × 10 [W S] (b) From Figure 7.1, for a CaO-CaS system at 1600°C, [W O] –2 ------------- = 2.5 × 10 [W S] 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, a Al2 O3 = 0.4 . 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), 1 1 log(CS)1923 – log(CS)1873 = –4208  ------------ – ------------ = 0.0585  1923 1873

(E1.2)

log(CS)1923 = log(2.7 × 10–3) + 0.0585 = –2.510 Putting values into Eq. (7.26), 2 1 20397 log ( L S ) 1923 = – 2.510 + --- log0.01 + --------------- – 5.482 – --- log 0.4 = 1.46 3 3 1923 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),

(W S) L S = ----------- = 43.6 [W S]

Since (WS) = 1, [WS] = 1 ⁄ 43.6 = 0.023% at equilibrium. ©2001 CRC Press LLC

7.2.5

SOME COMMENTS

ON

LS

As Example 7.1 shows, the correlation by Gaye et al.15 gave a better match with Figure 7.2. From Example 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 lime saturation, WCaO is 60 and W Al2 O3 is 32 (Figure 7.6). From Eqs. (7.20) and (7.26), and taking a Al2 O3 = 0.1, LS is calculated as 220 at T = 1873 K and WAl = 0.01. If WAl = 0.04 wt.%, then, from Eq. (7.26), LS = 555. According to Gaye et al.15 even a value of 1000 is possible in CaO-Al2O3SiO2. A still larger value of LS can be obtained if some CaF2 is present in the slag due to a higher value of CS (Figure 7.2). This way, it is possible to obtain a value of LS larger than 1000. Literature reports 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 coefficients of oxides tend to be high in comparison to those in slags. For example, at comparable CaO concentration, aCaO in a CaF2-CaO slag is much higher than those in Al2O3-CaO and SiO2-CaO systems. This results in higher values of CS in CaF2-containing slags. Figure 7.6 presents sulfide capacities 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),    L S ⋅ M S1 [W S]  - -  =  ------------------------------------degree of desulfurization (R) =  1 – -------------1000 + L ⋅ M [ ] W S S1 S O    

(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, Y R = ------------1+Y where

(7.29)

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 < 10 to 20 ppm) only. Otherwise, desulfurization by treatment with synthetic slag on top of molten steel in an ordinary ladle, ladle furnace, or during vacuum treatment is quite all right. Principal additions are as follows: ©2001 CRC Press LLC

FIGURE 7.7 Desulfurization degree for different sulfur distributions as a function of specific slag amount.

1. CaO. This is for the formation of a highly limy slag, either saturated with CaO or unsaturated. 2. Al. This is for reaction with dissolved oxygen in molten steel and to form Al2O3, which joins the slag phase. This reaction is exothermic and raises the temperature of steel as well. 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 the ladle. The tapping stream causes violent stirring, and during this process some slag–metal reaction and desulfurization will occur. To make it more effective, the practice of synthetic slag addition also 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, and a molten top slag forms, consisting dominantly of CaO and Al2O3 with some CaF2,SiO2. This is the beginning of the second stage of the slag–metal desulfurization reaction. Stirring by argon introduced 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 desulfurization can be predicted by following the procedure mentioned in Section 7.2.5. However, a principal question is whether such an equilibrium gets established in industrial processing. As far as literature reports are concerned, the slag–metal equilibrium for sulfur reaction is sometimes attained and sometimes not. This topic shall be taken up again later. For the time being, it will suffice to state that the reaction 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 oxygen from 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 in actual slag to that in CaO-saturated slag. The highest sulfur partition was obtained in the CaO©2001 CRC Press LLC

FIGURE 7.8 Sulfide capacity vs. CaO-saturation degree of slag in ladle desulfurization of steel.20 Reprinted by permission of Iron & Steel Society, Warrendale, PA, U.S.A.

saturated slag. Thermodynamic limitations were held responsible for lower partition in unsaturated slags. The lower values in supersaturated slags were attributed to kinetic factors. These slags contain solid particles of CaO and hence tend to have higher viscosity with consequent retarding influence on mixing and mass transfer in slag phase. In Figure 7.8, the maximum value of the (W S) 1 ------------ × ------------------[ W S ] [ W Al ] 2 ⁄ 3 parameter is about 25000 at a saturation degree of 1. At WAl = 0.04, this corresponds to an effective partition coefficient of 2920. From discussions in Section 7.2.5, it is evident that it is quite a large value, perhaps indicating a close attainment of equilibrium. However, as stated earlier, nonattainment of equilibrium also seems to be a common feature. Moreover, there is a worldwide effort to speed 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 transfer in gas-stirred ladles. Several studies reported therein were in the context of the reaction of sulfur between slag and metal. Chapter 6 presented the special features of flow, circulation in vacuum degassing 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 additional remarks. The overall desulfurization reaction consists of the following kinetic steps: 1. Transfer of sulfur dissolved in liquid iron to slag–metal interface 2. Transfer of O2– from the bulk of the slag to the slag–metal interface 3. Chemical reaction at the interface, i.e., [S] + (O2–) = (S2–) + [O] ©2001 CRC Press LLC

(7.6)

4. 5. 6. 7.

Transfer of S2– from the interface into bulk slag Transfer of [O] from the interface into the bulk metal phase Mixing in slag phase Mixing in metal phase

Section 4.3 reviewed reaction kinetics among phases. As stated there, reactions at high temperatures, especially at steelmaking temperatures, are mostly controlled by mass transfer rather than interfacial chemical reaction in a laboratory situation (i.e., melts well mixed and in an isothermal 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 in liquid iron, which is a product of Reaction (7.6), has to be considerably lowered through its reaction with 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 reversible process with respect to concentration of sulfur in metal. In an analogy with Eq. (6.22) in connection with vacuum degassing and decarburization, we may write ( W S ) d[W S] – --------------= k S,emp  [ W S ] – ---------- dt LS 

(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 concentrations of 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 jointly I-II control rate. In that case, kS,emp would be the parameter ( A ⁄ V )k m,i of Eq. (4.41), where solute i would stand for sulfur, phase I for liquid steel, and phase II for slag. Slag volume is much smaller as compared to that of the metal. Moreover, as will be seen later, the top slag gets violently churned and even emulsified due to gas stirring. Hence, mixing in the slag phase (step 6) is also expected to be fast. Transfer of oxygen in the metal phase (step 5) is also likely to be fast, due to the fact that 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 would increase the mass transfer rate of [O] significantly due to the phenomenon of reaction-enhanced boundary layer mass transfer.21 Another way to consider this issue can be derived from the classic work of King et al.22 on the mechanism of slag–metal sulfur transfer. They found that the rate of sulfur transfer from metal to slag was always equal to the sum of the rates of oxidation of Fe, C, Si, etc. Figure 7.9 presents the data of one of their laboratory experiments. The increase of sulfur in slag was numerically equal to the sum of CO generated, and Fe + Si transferred to the slag. As such, the result is not surprising. But what was puzzling was the temporary overshoot of Fe and Si transfer to slag beyond equilibrium during the course of the reaction. This was explained by invoking the electrochemical mechanism of slag–metal reaction. The reactions have been summarized in Table 7.1. It shows that there are several electrochemical reactions occurring simultaneously. The sum of the rate of all cathodic reactions would be equal to that of all anodic reactions in all cases. Moreover, there will be a common electrical potential at the interface, known as corrosion potential. In the initial stages, the cathodic reactions of sulfur ©2001 CRC Press LLC

FIGURE 7.9 Increase of sulfur in slag and equivalents of Fe, Si, and CO transferred or evolved in laboratory experiments of Ramachandran and King.23

TABLE 7.1 Reactions Occurring during Sulfur Transfer from Liquid Iron to Slag Type

Initial Stages

Later Stages

Cathodic

[ S ] + 2e = ( S )

[ S ] + 2e = ( S )

–

2–

–

( Fe 1 ⁄ 2 ( Si

4+

2 ⁄ 3 ( Al Anodic

[C] + (O

2–

) = CO + 2e

[ Fe ] = ( Fe

2+

) + 2e

1 ⁄ 2 [ Si ] = 1 ⁄ 2 ( Si

4+

2 ⁄ 3 [ Al ] = 2 ⁄ 3 ( Al

3+

) + 2e = [ Fe ] _

) + 2e = ( 1 ⁄ 2 ) [ Si ]

3+

_

) + 2e = 2 ⁄ 3 [ Al ]

[C] + (O

_

_

2–

) = CO + 2e

2 ⁄ 3 [ Al ] = 2 ⁄ 3 ( Al

_

) + 2e

2+

2–

3+

_

) + 2e

_

_

) + 2e

_

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 in secondary steelmaking, therefore, we may think of the transfer of Al from metal to slag rather than oxygen from slag to metal. The concentration of Al being larger, its transfer would be faster than that of sulfur. Investigators tried to ascertain whether the interfacial chemical reaction could be slow and rate controlling. No clear-cut evidence was available. Perhaps, in stagnant laboratory melts, this was the situation.23,24 However, the general conclusion was that the reaction was mass transfer controlled.25 Of course, as later investigators concluded (Section 4.5), sometimes it may be bulk mixing rather 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 simplified as follows, if ks,emp is taken as independent of t: ©2001 CRC Press LLC

[W S] ln  --------------0 = k S,emp ⋅ t  [W S] 

(7.32)

Figure 7.10 is plotted accordingly and is taken from an investigation by Ohma et al.26 in a 35 tonne ladle 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 a brief discussion on this issue, from mass transfer between two liquids in a gas-stirred vessel. It was noted there that, in general, kmA ∝ Qn. Since Q is proportional to the rate of buoyancy energy n input per unit mass of the bath liquid (εm), kmA ∝ ε m ⋅ n varies over a wide range. Asai et al.27 have reviewed mass transfer in ladle refining processes. They have compiled the k vs. ε relationship obtained by several investigators in cold models and at high temperatures. These show a range of n 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 the compilation by Asai et al.27 It may be noted from Table 7.2 that, in cases where investigators made measurements over a large range of gas flow rate, log k vs. log εm curves exhibited kinks, and n showed a much larger value in the high flow rate range. Several subsequent investigators also reported similar observation (see Section 4.4.2). Figure 4.10 shows an example of such behavior in a water-oil system. Figure 7.11 presents a similar behavior for desulfurization in a gas-stirred ladle 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 of emulsification of top liquid (slag, oil, etc.) into the bath liquid (steel, water, etc.). Emulsification leads to an increase of the interfacial area and hence the kmA parameter. Technologically important issues 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 emulsification 3. 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. ©2001 CRC Press LLC

TABLE 7.2 Correlation of Mass Transfer in Liquid–Liquid System27 System Slag–steel

Stirring Ar gas

Reaction

Correlation

Desulfurization

K∝ε

0.25

ε < 60w/t K∝ε

2.1

Remarks 2.5t converter Q < 150 1/min. t 150 < Q < 240

ε < 60w/t Water–Hg

N2 gas

Reduction of quinone

K∝ε

0.3 ∼ 0.4

Q < 58 φ = 0.22

Slag–steel

Ar gas, mechanical stirring

Slag–steel

Ar gas

Slag–steel

n–hexane–

Desulfurization

K∝ε

(I n

3+

3+

) + 3(F e –

) = )

2+

I 2 + 2OH = IO

–

0.33

0.33

K∝ε

0.42

K∝ε

(amal)

Q < 10

(aq.)

φ = 0.5

0.72

–

200 < Q < 994 φ = 0.5

–

–

–

Amalgams–aqueous sol. Lead–molten salt

K∝ε

0.5

Q < 130 φ = 0.5

O2 gas

Liquid paraffin– water

Tetraline–aqueous sol.

K∝ε

1.0

+I + H 2 O 31O = 10 3 + 21

Slag–steel

Q < 100

K∝ε

[ In ] + 3 ( F e

Aqueous sol.

0.27

Cu → ( Cu )

K∝ε

N2 gas

30 < Q < 160

K∝ε

Oil–water Amalgams– aqueous sol.

0.6

Dephosphorization

Dephosphorization

K∝ε

0.54

50 < Q < 80

K∝ε

0.36

30 < Q < 80

K∝ε Air

K∝ε

3.0

φ = 0.17

0.36

K∝ε

80 < Q < 200

1.0

Q < 150 150 < Q < 650 φ = 0.1

Q(1/min · t) ∝ εis assumed K: capacity coefficient of mass transfer = ak ε: mixing power density (W/t) φ: fraction of slag t: tonne

Some discussions, data, and references have already been presented in Section 4.4.2 on item 1 above. QCr depends on several variables. An important one is interfacial tension between slag and metal. 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 the emulsification process. The analysis leads to the correlation expressed in Eq. (7.33). ©2001 CRC Press LLC

FIGURE 7.11 Effect of gas flow rate on kmA parameter (capacity coefficient) for desulfurization reaction.27

8 u Cr ,i = --ρ

1⁄2

[ 2 ⁄ 3 σ sm g ( ρ m – ρ s ) cos α ]

1⁄4

(7.33)

s

where ρ denotes density, σ denotes interfacial tension, s and m stand for slag and metal, g is acceleration due to gravity, and α is the angle at the slag–metal interface. Equation (7.33) shows that 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 temperature systems. 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 order of magnitude) during the transfer of a species across a phase boundary. It has been reported for sulfur transfer from metal to slag as well.23 It is only appropriate, therefore, to consider this dynamic value 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 desulfurization rates in ladles indicate that kS,emp lies in the range of (0.5 to 3) × 10–3 s–1 for a low gas flow rate and (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 chemical engineering on mass transfer from a liquid droplet moving through another liquid. Correlations are available in standard texts such as the ones already cited.9.29 The droplet would rise or fall through the liquid, depending on the densities of the two liquids. Larger drops would have larger rise or fall velocities. In the case of slag–metal emulsion in a gas-stirred vessel, the rising bubbles eject droplets 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 the flow and surface renewal near the droplet-bulk liquid interface. These in turn would depend on drop size, the density difference of the two liquids, and the interfacial tension. Again, droplets in a slag–metal emulsion exhibit a spectrum of sizes. In view of so many uncertainties, it is desirable to use one representative mass transfer correlation. This is what Mietz et al.30 did and estimated km theoretically by employing the following relationship: ©2001 CRC Press LLC

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 sampling and analysis. Employing Eq. (7.34) and a theoretical equation derived by Oeters29 correlating dimensionless iodine concentration with other parameters, they calculated average residence time of droplets ( t r ) for each experiment. Furthermore, values of t r were also calculated employing another procedure involving energy balance. Good agreement was obtained between these two sets of values, and t r 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 of slag–metal interfacial area due to emulsification for a 120t molten steel in a ladle under a particular set of conditions. t r was assumed to 60 s and mean drop size as 0.4 mm. It was found that, whereas the geometrical surface area was 6.6 m2, in emulsion it was 608 m2, indicating about a hundredfold 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 ( i.e., [ W S ] ⁄ [ W S ] O ) as a function of time.31 It may be noted that the measured desulfurization data agreed very well with calculations assuming emulsification. Calculations assuming no emulsification showed much slower desulfurization, demonstrating the importance of emulsion. However, it ought to be taken only as an approximate guide. First of all, there are some unverified assumptions in the procedure of Mietz et al.30 Second, at high rates of desulfurization with an emulsified slag, mixing rather than phaseboundary 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–metal interface area and a consequent rate increase. It is also expected that this increase would depend on 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 be concluded 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 Section 4.5. Arguments there were partly general, partly specific. The time for 95% mixing provides only an approximate indication for slag–metal reaction. The best approach is to actually measure

FIGURE 7.12 Desulfurization in a 120t ladle; comparison of calculated values, with and without consideration of the emulsification of slag droplets.

©2001 CRC Press LLC

concentration homogeneity in the bath while the reaction is in progress. The present author has not been able to locate any such study in the literature. However, there have been some efforts to throw light on this issue through mathematical modeling with the help of some experimental rate data. Section 4.5 has mentioned studies by Szekely and coworkers.32 The basic differential equation is δC i -------- + u ⋅ ∇C i = ∇ ⋅ ( D eff ⋅ ∇C i ) + r δt

(7.35)

with the symbols as defined in Chapter 4. Variable r is the rate of reaction per unit volume of liquid steel, and Deff = effective diffusivity = Dt + Di. Since the turbulent diffusivity (Dt) is orders of magnitude larger than the molecular diffusivity (Di), Deff ≈ Dt. The analysis was actually carried out for powder injection. At the slag–metal interface, chemical equilibrium was assumed. Figure 7.13 shows variation of ( ∆ [ W S ] ) ⁄ [ W S ] b as a function of the h/H parameter during desulfurization in a 40t ladle. ∆[WS] is the difference of WS between the bottom and top of the ladle. [WS]b is the weight percent of sulfur at the ladle bottom. h is the depth of lance immersion and H is the melt height. A bottom-stirred ladle corresponds to h/H = 1 and hence ( ∆ [ W S ] ) ⁄ [ W S ] b ≈ 0.05 from Figure 7.13. However, it is expected to be higher if no powder injection is employed. Hence, this analysis indicates the possibility of significant nonhomogeneity in the bath during desulfurization. As noted in Section 4.5, Szekely et al.32 proposed the modified Biot’s number (Bim) criterion for comparison of the rate of mass transfer with that of mixing. Their order of magnitude calculation revealed 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 to mixing. However, with vigorous stirring and slag–metal emulsion, kmA and hence Bim would be about 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 for desulfurization in gas-stirred ladles with top slag even when slag is emulsified, provided dead zones are eliminated. This can be somewhat accomplished by proper location of porous plugs. As noted in 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 at least two eccentric plugs for a reasonable ladle size.

FIGURE 7.13 Sulfur segregation in molten iron bath during desulfurization by powder injection.32

©2001 CRC Press LLC

Rate Equations With a low gas flow rate and nonemulsified slag, the slag–metal interfacial area may be taken as the 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 varies from 0.3 to 0.7. Higbie’s surface renewal theory leads to the following equation: D 1⁄2 k m,i = 2  -------i   πt e

(4.24)

For centric gas stirring, the exposure time for an element of molten steel in contact with the slag is approximated as R R t e ∝ ----- ∝ ----------------uo ( Q ⁄ A )

(7.36)

where R is the inner radius of the ladle and uo is a characteristic melt velocity. uo again may be taken 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 transfer control, A k S,emp = k m,S ⋅ ---V

(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 be arrived at by combining Eqs. (7.11), (7.27), and (7.30): [W S] d[W S] 1 --------------- = – k S,emp  [ W S ]  1 + --- – --------------O-    Y  dt Y

(7.39)

integrating between limits, t = o, [WS] = [WS]O, and t = t, [WS] = [WS], [ W S ]O – [ W S ] B 1 R = -------------------------------- = 1 – exp  – B – --- /  1 + ---  [ W S ]O Y  Y

(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 B as x-axis and Y as y-axis. ©2001 CRC Press LLC

FIGURE 7.14 Iso-R plots with B ( = k s, emp ⋅ t ) as x-axis and L s ⋅ M sl ⁄ 1000 as the y-axis. Adapted from Ref. 15.

This equation can also be applied to emulsified slag. In that case, the slag–metal interface area will 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 other disturbing 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 the addition of Al and CaO. If the starting carryover slag is at A, oxidation of Al with formation of Al2O3 would take it to some composition such as A´. Dissolution of added CaO would finally take it 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 vacuum treatment. It is strongly dependent on the CaO slag saturation degree, which not only controls the MgO 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 slag is viscous and delays slag formation and sulfur removal. CaF2 makes the slag fluid and speeds up slag formation as well. ©2001 CRC Press LLC

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.

7.4 INJECTION METALLURGY FOR DESULFURIZATION 7.4.1

INTRODUCTION

The injection process was introduced in the 1970s. The primary objective was more efficient desulfurization of hot metal (i.e., impure liquid iron) and/or liquid steel. Here, discussions will emphasize desulfurization of steel melt in a ladle in secondary steelmaking. However, the following discussions will reveal that there are many features common to all ladle-injection processes, and literature dealing with either hot metal or steel will be cited, depending on availability. Broadly, it may be classified into the following two categories: • Continuous injection of solid powdered reagents inside molten steel along with a stream of 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, and modification of inclusions for desirable properties. Extensive deposits of natural gas were discovered ©2001 CRC Press LLC

in the cold Arctic regions such as Alaska. The line pipe material for transporting gas over a long distance 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 by calcium. The properties of calcium and its alloys have been reviewed by Ototani.35 The typical reagent is Ca-Si alloy containing about 30% Ca and 60% Si, and rest Al, etc. It melts at around 1050 to 1150°C. Calcium is a gas at steelmaking temperatures. The vapor pressure-temperature relationship for pure calcium is36 8920 o log p Ca (in atm) = – ------------ – 1.39 logT + 9.569 T

(7.41)

o

At 1600°C (1873 K), p Ca = 1.81 atm. This is quite high and is likely to lead to instant, violent vapor formation. Very little Ca would get chance to react with the melt if it were added as such. In Ca-Si alloy, p Ca = p Ca × a Ca o

(7.42)

where aCa is activity of Ca in Ca-Si alloy. Figure 7.17 presents the estimated activity vs. mole fraction 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 the vapor pressure is below 1 atm. As such, top addition should have been all right. However, the solubility of calcium in liquid iron is very low (0.025 ± 0.008 wt.% at 1600°C). Therefore, silicon is expected to dissolve into the melt much faster than calcium. So, shortly after addition, the liquid Ca-Si alloy would get depleted in silicon, consequently raising pCa and leading to instant vaporization and loss of calcium. The problem was satisfactorily solved by injecting CaSi alloy at a depth of at least 1 to 1.5 m inside the melt so as to prevent vapor formation due to the ferrostatic pressure. This allowed the calcium 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 powder injection process. It was followed by Scandinavian Lancers (SL) after a few years. Their success 1.0

CALCIUM ACTIVITY

0.8

0.6

0.4

0.2

0 1.0

0.8

0.6

MOLE FRACTION CALCIUM

FIGURE 7.17 Estimated calcium activity in Ca-Si alloys at 1873 K.

©2001 CRC Press LLC

0.4

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 been employed, depending on the objective. As a result, many steel companies worldwide have installed this facility, and a large number of patented processes subsequently have been developed. Molten steel is contained in a covered ladle. Solid powders along with Ar or N2 are injected through a refractory-lined lance tube whose position can be adjusted. A powder dispenser is employed to introduce 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 the dispenser 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 the lance 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 the container through an adjustable orifice. A part of the carrier gas is introduced as an ejector gas just beneath the dispenser or at a later stage. The feeding rate of the powder and the gas/solid ratio are controlled 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 a refractory lining of tubular bricks or a cast coating. The design and dimensions of the lance outlet nozzle are important for maintaining proper feed rate. Typical outlet shapes are shown in Figure 7.20. It is either a single hole or a T-outlet, or a multihole unit. Clogging of the nozzle through penetration of steel is a problem that occurs when there is too much pressure fluctuation in the pneumatic 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 alternative modes 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

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bunkers

lance stand

control powder dispenser

runner for ladle additions

FIGURE 7.19 Principle of SL injection equipment with a stationary powder dispenser unit.1

MULTIPORT

T SHAPE

FIGURE 7.20 Sketch of injection nozzle.

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STRAIGHT

SWEPT SINGLE PORT

the Injectall Side Injection System (ISID) developed in the United Kingdom. The system uses a multiorifice 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 seems that 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 desulfurization as well. Another advantage of the injection process is the enhanced reaction rate. Figure 7.10 shows the findings of a plant study on desulfurization. For the injection process, kS,emp was about five times larger as compared to that for top slag alone. In view of all of these, the process attracted worldwide attention of steelmakers in the 1970s and 1980s. This is reflected in several International Conferences 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 with clean 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 between powder injection and wire feeding. Table 7.3 shows the common desulfurizing agents. It is possible that 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 the combined action of powder feeding and the reaction of molten steel with top slag. Prevention or minimization of carryover slag is of utmost importance. It has been dealt with in Chapter 5 and Section 7.1. Detailed descriptions are also available elsewhere.32 TABLE 7.3 Desulfurizing Agents for Powder Injection in Secondary Steelmaking Agent

7.4.2

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

THE REACTOR MODEL

The reactor model was originally proposed by Lehner.37 In view of extensive discussions on the kinetic and dynamic aspects of gas-stirred ladles, a simplified version of the model, as presented in 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 source of stirring, which is essential for the success of the process. Broadly speaking, the reaction occurs in the following three zones: 1. In the transitory contact zone, the rising solid powders react during their passage through the melt. 2. The permanent contact zone is a consequence of the presence of a top slag. The reaction is between slag and metal. 3. The breakthrough zone is created where the gas bubbles penetrate the slag layer and escape into the atmosphere. In this zone, liquid metal is also dragged up and brought into contact with the atmosphere with which it reacts, leading to some reoxidation and nitrogen pickup of the melt. This tendency is enhanced by the ejection of droplets into the atmosphere, since a large gas–metal interfacial area is created. Reactions in the breakthrough zone are undesirable. ©2001 CRC Press LLC

FIGURE 7.21 Zones in the ladle injection process.

In addition to the above, the ladle lining also tends to react with slag, melt, and powder, causing some reoxidation. Dolomite lining is stable and has been found to be the best for desulfurization as well (less than 0.004%). With fireclay and silica linings, dissolved Ca and Al in melt react with SiO2, with the consequent effects as mentioned above. In practical process conditions, different reoxidation sources may be limiting the final cleanness. The simplest analysis of the process is based on the assumption that there are no kinetic and mixing limitations, i.e., the process is thermodynamically reversible. This kind of analysis has been demonstrated in Ch. 6 in connection with vacuum and argon degassing. For desulfurization by slag injection and transitory contact zone, the situation would be as in the top corner of Figure 4.1, i.e., the feed rate of the powder would be rate controlling. Sulfur balance leads to the relation d[W S] = M˙ Sl L S [ W S ] – 1000 --------------dt

(7.43)

where M˙ Sl 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], [W S] M Sl L S M˙ Sl L S t - = exp  – -------------------------- = exp  – --------------- = exp ( – Y )   1000  1000  [ W S ]O

(7.44)

For a permanent contact zone, from Eq. (7.29), [W S] 1 -------------- = ------------[ W S ]O 1+Y

(7.45)

Example 7.3 Compare the predictions of [ W S ] ⁄ [ W S ] O for LS = 102, 5 × 102 and the equilibrium value of Example 7.2 for slag, and MSl = 5 and 10, assuming both the transitory contact and permanent contact models. ©2001 CRC Press LLC

Solution LS = 5 × 102

LS = 102 MSl

Y

[ W S ]/ [ W S ] O Trans. contact

Perm. contact

LS = 1.6 × 103 (φ)

[ W S ]/ [ W S ] O

Y

Trans. contact

Y

Perm. contact

[ W S ]/ [ W S ] O 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.

This calculation reveals that sulfur removal efficiencies are comparable for transitory and permanent contact 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 we consider 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 a consequence, kS,emp has been found to increase by a factor of 5 to 10. Figure 7.10 shows a similar increase 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 compared to the powder injection of slag at a low gas flow rate (i.e., nonemulsified top slag). This has been the conclusion in the literature as well.32 Ying et al.39 carried out a cold-model study with water simulating liquid steel and a mineral oil simulating slag. Transfer rates of benzene-carboxylic acid dissolved in oil, to water, were measured. In one set of experiments, oil was used as top slag. In another set, oil droplets were sprayed (i.e., injected) inside water. Figure 7.22 shows the time required to achieve equilibrium partitioning of the acid between oil and water. It demonstrates that, at a low gas flow rate, spraying allowed faster attainment of equilibrium as compared to gas-stirred permanent contact. However, at a high gas flow rate, there was no difference.

FIGURE 7.22 Comparison of time to attain equilibrium partitioning of solute between water and oil for spraying (i.e., injection) of oil droplets and oil-water bulk phases with gas stirring.39

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In older injection practice, high argon flow rates of about 6 × 10–4 Nm3 s–1 per tonne of steel were 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 considerable savings in argon. It also helps to maintain the compactness of the slag layer, preventing formation of a breakthrough zone and consequent undesirable reactions of the melt with atmospheric oxygen and nitrogen. 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 height of 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 the minimum 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 that slag–metal emulsion does not form. As discussed in Section 7.3.2, the rate of desulfurization for top slag treatment is likely to be controlled by mass transfer at the slag–metal boundary, and the geometrical 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 is given by Eq. (4.41). Combining the above, A I–II k S,emp = ------- ⋅ k m,s = k Vm

(7.46)

where Vm = volume of metal, and I and II refer to metal and slag, respectively. Equation (7.46) is analogous to Eq. (7.37) but has been derived from theory, whereas Eq. (7.37) is more empirical in nature. Engell et al.40 considered the influence of carryover slag on the reaction. They assumed the following: 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), d[W S] 1 1 S --------------- = – k [ W S ]  1 + --------------------- – [ W S ] O  --------------------- + ------------   Y ( 1 + S ) 1 + S dt Y ( 1 + S )

(7.48)

Integrating from t = 0 to t = t,   [W S] 1 1 1 S 1 -------------- = ------------------------------- ⋅  --------------------- + ------------ +  ------------ ⋅ exp – B  1 + ---------------------      1 1+S [ W S ]O Y (1 + S) 1 + S Y (1 + S)  1 + ---------------------  Y (1 + S) ©2001 CRC Press LLC

(7.49)

For transitory contact, Eq. (7.43) is to be modified to take mass transfer into account as follows: d[W S] = M˙ Sl [ ( W S ) – ( W S ) O ] – 1000 --------------dt

(7.50)

Combining Eq. (7.50) with Eqs. (7.30) and (7.46) and assuming that (WS)O = 0, d[W S] k p[W S] --------------- = – --------------------------------dt 1000k p   1 + ----------------- M˙ S1 ⋅ L 

(7.51)

S

Integrating from t = 0 to t = trp, t rp [W S] ------------- = exp – --------------------------1000k [ W S ]o 1 + ------------------p M˙ Sl ⋅ L S

where

(7.52)

A I–II Ap = surface area of individual particle, k p = ------p ⋅ ( k m,s ) p Vp trp = residence time of a particle in molten steel before it goes to the top

For a spherical particle, A 6 ------p = ----Vp dp

(7.53)

where dp = diameter of the particle When desulfurization takes place both in the transitory contact zone and permanent contact zone, then d [ W S ] d [ W S ] d[W S] --------------=  --------------+  --------------   dt p dt  T dt

(7.54)

where P and T refer to permanent and transitory contact, respectively. I–II

It may be noted that k m, S would have different values for the two zones. Residence time for a particle in the melt is difficult to predict theoretically. Trp was taken as 20 s40 on the basis of literature data. 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, numerical calculations were performed on the basis of Eqs. (7.48), (7.51), and (7.54).40 Calculated variations of [Ws ]/[WS]O with time are presented in Figures 7.23 and 7.24 for two values of slag carryover and two values of k. These again demonstrate that rate of desulfurization is much faster with injection as compared to that without injection at k = 10–3 s–1. However, at k = 10–2 s–1, which is the case for an emulsified slag, both are comparable. A significant influence on the amount of slag carryover is also evident. The more carryover slag, the less desulfurization. The rise in the sulfur content of steel after stopping the injection is due to a further reaction toward equilibrium with top slag. ©2001 CRC Press LLC

Injection Stop

Tapping

1.00 Carry-Over Slag 1kg/t Injected or Added Slag 20 kg/t

[ Ws ] / [ Ws ]0

0.75

0.50

Top Slag Reaction Injection and only Top Slag Reaction

0.25

200

(k in s-1) k = 1.10-2

Injection only

0.00 0

k = 1.10-3

k = 1.10-3

400

600

800

TIME, s FIGURE 7.23 Change of concentration of sulfur in a steel or hot metal melt by top slag reaction and/or reaction 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/or reaction with injected particles; carryover slag 10 kg/t.40

In general, only a fraction of the injected particles go into the melt. The rest remain attached to the bubbles and hence are only partially exposed to the melt. Chiang et al.41 did mathematical modeling considering this. Their predictions are shown in Figure 7.25. kS,emp for desulfurization of hot metal in a three-tonne ladle is also presented. Calcium carbide was injected as a solid. The argon flow rate was 2.5 × 10–3 Nm3 s–1. The figure shows that experimental data approximately matched with predictions for a situation where the fraction of solid in the melt is 30%. The finding on a 60 kg laboratory melt was similar. ©2001 CRC Press LLC

FIGURE 7.25 Desulfurization rate constant as a function of the flow rate of solids for calcium carbide injection into hot metal in a ladle; solid lines are predictions.41 Reprinted by permission of Iron & Steel Society, Warrendale, PA, U.S.A.

Deo and Boom42 have presented a detailed analysis of this based on their own work43 as well as that of others. They considered the reaction of particles in a melt and particles attached to bubbles separately and arrived at the following correlations: [W S] t ln --------------o = ( a + b + c ) ⋅ ---Vm [W S]

(7.55)

a = Ak, due to permanent contact

(7.56)

where,

6k p t rp b = 1000L S M˙ S1 ⋅ f 1 – exp  – ------------ d p LS 

(7.57)

and is due to particles in the melt. f is the fraction of particles in the melt, and ρS is the density of the solid. 1000L S M˙ S1 k g t rb Qρ S T 2.38 - C = --------------------------( 1 – f ) 1 – exp  – ---------- ⋅ m ⋅ --------- ⋅ ------------------------------------------ dB ρS 298 1000M˙ S1 ( 1 – f )L S

(7.58)

and is due to the contribution of particles attached to bubbles toward desulfurization. DB is bubble diameter, Q is gas flow rate in Nm3 s–1. Equations (7.55) through (7.58) were applied to desulfurization during the injection of calcium carbide 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 more than 40% toward desulfurization in steel refining. Hence, a fluid top slag with high sulfide capacity should be employed. ©2001 CRC Press LLC

7.4.4

MELT–PARTICLE PHYSICAL INTERACTION

This interaction was studied by several investigators. Among them, the most comprehensive investigations have been carried out by Irons and coworkers.44,45 For effective participation of the particles in the desulfurization reaction, they should become detached from the argon bubbles and come into the liquid soon after emerging from the lance nozzle. This is best achieved if the particles are coarse and have low interfacial tension with liquid steel (i.e., wetting). Coarse particles have high momentum, which leads to their easy detachment from the bubbles. The nature of wetting assists it further. The solid:gas ratio is an important variable. Another important issue is the behavior of the gas-particle mixture as it emerges from the nozzle. The high velocity of gas from the nozzle causes jetting flow and prevents back-attack of the nozzle by molten metal and consequent nozzle clogging (Chapter 3, Section 3.2). This is in contrast to the bubbling regime at lower gas velocities. In the gas-particle mixture, even at same gas flow rate, one can obtain either a jetting or bubbling regime. Fine particles tend to be in the gas phase. Since particles have orders of magnitude higher density than that of the gas, they increase jet 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 fine particles (<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 the lance but, of course, has a dramatic effect on the particle and gas trajectory. A mathematical model was 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

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penetration length (length/lance diameter) agreed well with experimental measurements. It is an important 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 not impinge 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 gas flow 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 with powder injection.45 This is because injection causes much more rapid mixing as compared to that for only gas purging, for the following reasons: 1. Transitoric reaction is dispersed in the melt and thus partially eliminates bulk inhomogeneities in sulfur concentration. 2. As already mentioned, the gas-particle jet has much higher momentum as compared to a simple gas jet. This leads to larger penetration of the jet into the melt and increases the effective rise depth of a gas bubble, which in turn increases εm [Eq. (3.64)] and lowers the mixing time even if immersion depth is low. This is illustrated in Figure 7.27 for a 240t torpedo ladle.45 As far as fluid flow and mixing during injection are concerned, the general features may be taken 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 transfer modeling by Szekely and coworkers.32 It has been stated there that it covered lance injection as well. Some other studies have also been cited.42 Hence, no further deliberations on these will be included 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. Little more elaboration is included here. When a gas is blown vertically upward through a packed bed of 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 in the 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 immersion depth.45 Gas flow rate = 1.67 × 10–3 Nm3 s–1 and the solid flow rate = 5 × 10–3 kg s–1.

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the linear velocity of the gas equals the terminal settling velocity of the particle. This is known as the 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 horizontal pipe, a minimum u is required for a given set of conditions (conduit size, solid/gas ratio, etc.) to prevent 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 required to 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. Typical injection 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. Oxidation of a metal/alloy powder, such as calcium silicide, may be so rapid as to raise its temperature above the ignition point, resulting in spontaneous combustion due to exothermic heat generation. This is a safety hazard. Lime and lime-based fluxes readily react with moisture. Hence, efforts are required to prevent contact of the powder with the atmosphere. Powders should flow easily. For this, a round shape is best. A moisture-free surface also is very desirable. Hence, to summarize, much care is required 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 good cleanliness, 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 extensively reviewed them, and their conclusions may be summarized as follows. (There will be more discussions in subsequent chapters.) 1. The injected powder should be dry and free from impurities that are likely to be difficult to eliminate. 2. The formation of a breakthrough zone is undesirable, since ejected metal droplets then come into contact with the atmosphere above and pick up oxygen and nitrogen. This problem, by and large, has been overcome in the modern processes, since the argon flow rate is low, and breakthrough zone is not significant. 3. Reaction of the melt with ladle refractory lining is to be controlled in all secondary steelmaking processes. The choice of refractory material in this context is crucial. Good steel cannot be made without good quality refractory. In view of the importance of the topic, 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 an increase in the oxygen content of the melt, since the melt is highly deoxidized by aluminum or calcium. This prevents the attainment of ultra-low sulfur level. A dolomite lining or high alumina lining is much better. The former has allowed attainment of as low as 0.004% (40 ppm) or less sulfur in steel. Figure 7.28, redrawn by Holappa1 from other sources, is presented to show the beneficial 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. ©2001 CRC Press LLC

FIGURE 7.28 The influence of ladle refractory on desulfurization efficiency.

• 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-PB for 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, the vacuum 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 be achieved. In wire feeding, CaSi powder is encased in steel, and the entire composite is in the form of wire. With wire feeding, primarily only inclusion modification can be achieved. However, it gives a higher recovery and better alloying precision, provided proper metallurgical preconditions prevail. Nowadays, many steel plants maintain provisions for both and are carrying on powder injection 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. ©2001 CRC Press LLC

5. The Japan Soc. for Promotion of Science, the 19th Committee on Steelmaking, Steelmaking Data Sourcebook, 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. ©2001 CRC Press LLC

8

Miscellaneous Topics

8.1 INTRODUCTION Each of the previous chapters had one broad but specific topic as its theme. However, there are subjects that are important in secondary steelmaking but do not justify coverage as full chapters within the scope of the present text. Also, they are somewhat disparate in nature. Hence, they are being presented here as miscellaneous topics. The topics covered in this chapter are 1. 2. 3. 4. 5.

Gas absorption during tapping and teeming from the surrounding atmosphere Changes in temperature of molten steel during secondary steelmaking Phosphorus control in secondary steelmaking Nitrogen control in steelmaking 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 the surrounding 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 resulting inclusions do not get separated well and lead to additional dirtiness in the solidified steel. The problem is more serious in continuous casting because of faster freezing and consequently less time available for inclusions to float up. It is of relevance to ingot casting as well, if we wish to produce clean steel. It has been found that the product of such reoxidation generally forms macroinclusions (above 100 microns or so), which are harmful to the properties of steel. Also, they are generally richer in iron and manganese oxides. The extent of oxygen absorption during tapping is of the order of 10 to 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 in continuous casting, the teeming stream ought to be shielded from the surrounding air either by an inert gas or by the use of a submerged nozzle. This is known as stream protection, and it is a widely adopted practice in continuous casting. However, it is rarely practiced for ingot casting because of the adverse cost-to-benefit ratio. It is important to understand the mechanism of such absorption and 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 Some reoxidation 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.

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l

8.2.1

GENERAL COMMENTS

ON

MECHANISM

Geometrically speaking, this is a case of a liquid stream falling freely into a pool of the same liquid through a gaseous atmosphere. As shown schematically in Figure 8.1, the absorption of gas can take 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 mechanism, viz., absorption via entrainment, is the predominant one. Szekely6 theoretically estimated the extent of oxygen absorption by a stream of molten steel from air during teeming. He assumed the stream to be laminar and smooth and that the air gets dragged into the pool of liquid steel by frictional 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 of oxygen absorption (∆O). For laminar streams, these agreed well with the reported value of 26.5 ppm from some industrial data. However, many investigators4 found very large quantities of oxygen pickup, and these were ascribed to turbulence and the rough surface of the stream. Therefore, here we have a situation where the physical characteristics of the stream are of considerable importance. In addition, it was found 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 significant absorption of gas, even before the teeming stream plunges into the liquid metal pool. Kumar and Ghosh5 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 of magnitude 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.

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Extensive oxygen and nitrogen pickup in the fraction of a second during the free fall of droplets of 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, visualizations 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 of the conditions under which the stream is expected to break up before plunging is an important issue. 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 established that 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 perturbation gets accentuated during its free fall and eventually leads to breakup. Perturbation theory has been used to analyze the situation,8 and one of the relations proposed, in combination with experimental data, is lb/dn = BWe2/5 Fr –1/7

(8.1)

u n ρd n We = Weber number = ------------σ

(8.2)

where dn = nozzle diameter B = a constant 2

In the equation, un is the velocity of the liquid stream at the nozzle exit, and ρ and σ are the density and surface tension of the liquid, respectively. 2

un Fr = Froude number = ------dng

(8.3)

where g = acceleration due to gravity Simplification of Eq. (8.1) yields l b ≅ Cd

3⁄2 1⁄2 n

u

(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 of conditions. Actually, lb is expected to vary with jet velocity as shown in Figure 8.2.8 The investigators claimed to have worked in region I, whereas in reality they had turbulent flow, which is generally encountered in industrial tapping and teeming of molten steel. ©2001 CRC Press LLC

FIGURE 8.2 Shape of breakup curve for a liquid jet falling freely through the atmosphere (schematic).

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 by rough and turbulent streams,7 and a general picture has emerged. With increasing stream velocity, the stream Reynolds number (Res = ( d n ρu n ) ⁄ µ ) increases. Above a certain value of Res, the stream starts to exhibit turbulence. The turbulence intensity of the stream is one of the key factors. It has been 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 remains reasonably smooth with a nice vortex at plunge point. 3. At still a higher Res, both the stream and pool surface become rough, and the induction trumpet (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 gas pockets along with it. Mechanical interaction at the plunge point on the liquid pool surface leads to entrainment. The rate of entrainment becomes one or two orders of magnitude higher under this condition. It has been found that the rate of entrainment increases with increasing un and H, and it depends on nozzle geometry, etc. Iwata et al.8 have proposed the following empirical relationship based on their model work with water, ethanol, glycerin-water, and liquid tin: Qg 3 ------ = 0.02 [ ( R c – r )/r n ] Ql

(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 radius at the nozzle exit.

8.2.4

QUANTITATIVE PREDICTIONS OF OXYGEN DURING TAPPING AND TEEMING

AND

NITROGEN ABSORPTION

Assuming 100% absorption of gas from entrained bubble, the fractional increase of gas content in liquid (∆[G]) is given as ©2001 CRC Press LLC

ρg Qg ∆ [ G ] = ----------ρl Ql

(8.6)

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 experimental results.8 They prepared nomographs for predicting oxygen absorption during teeming and tapping. They have also shown that these are in reasonable agreement with the experimental data of some other investigators. Regarding nitrogen absorption during tapping and teeming, it was mentioned in Section 6.4.5 that 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 desulfurized melts. This has been confirmed by other data.3,4 Sommerville4 found nitrogen pickup during the free fall of droplets of molten steel through a nitrogen atmosphere to decrease with increasing weight 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 calculated values assuming 100% absorption were 40 ppm, which matched with converter data at very low oxygen content, but not in heats containing a higher weight percent of oxygen. Very little information is available about the influence of physicochemical processes occurring inside molten steel on mass transfer controlled absorption during pouring of liquid, except that from Kumar and Ghosh.5 It is also likely that presence of strong oxide and nitride forming elements such as Al and Ti would increase the quantity of absorption. Not much information about absorption of hydrogen from atmosphere during teeming could be located in the literature. Hydrogen pickup occurs presumably from atmospheric moisture via the reaction H2O(g) = 2H + O

(8.7)

Therefore, the extent of hydrogen absorption would increase with an increase in the partial pressure of 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 tapping from an 80t converter. The curves show estimations at different assumed mass transfer coefficients.3

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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 temperature 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 compared to 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 secondary steelmaking, the overall loss of temperature used to be 20 to 40°C. Secondary steelmaking processes involve prolonged treatment of the melt in a ladle, leading to temperature drop even as high as 100°C. One way to compensate for this is to tap the metal from the primary steelmaking furnace at a higher temperature. However, this has adverse side effects such as faster lining wear, lower phosphorus 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 ladle furnace, VAD, and RH have provisions for heating the melt. This eliminates the need for tapping at too high a temperature. Moreover, much better and more flexible temperature control of steel is possible. More alloy additions also can be made. Arc heating is most common, followed by chemical heating, 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 arc heating, 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 dissolved aluminum. Steel plants keep temperature records at various stages. The traditional quantitative approach to process control and predictions is statistical correlation of data through multiple regression analysis. 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) reactions • Temperature gain due to heating Very few systematic investigations on such temperature changes could be found in the literature for traditional pitside practice. An extensive study was reported by Samways et al.9 who made measurements of temperatures in the plant, carried out statistical regression analysis, and made some thermochemical calculations for both BOH and BOF heats. They listed 11 broad categories of variables that affect ∆Tov. For their study, however, they considered seven only, viz., bath temperature, 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 deoxidation reactions (∆Tr) were computed theoretically by carrying out heat balance exercises with the help of available thermochemical data. The linear equation based on statistical analysis may be written as follows: ©2001 CRC Press LLC

∆Tov – ∆Tr = K + kttt + khth + kptp

(8.8)

where tt, th and tp are tapping, holding, and teeming times, respectively. K terms are statistically fitted coefficients. The rate of heat loss from a ladle depends on ladle size. Molten steel in a smaller ladle is characterized 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: Temperature Loss Rate, °C/min Ladle holding Gas purging Powder injection Circulation degassing

0.5–1 1–2 2–3.5 0.7–1.5

In addition to these, a temperature drop of 5 to 15°C occurs upon tapping, as the ladle refractory lining absorbs quite a bit of heat initially, since it is at a lower temperature. For a smaller ladle of 50 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 prolongs lining life, since thermal shock due to heating and cooling is less. The lower the porosity of the brick, the higher its resistance to corrosion and erosion by liquid slag and metal. However, its thermal conductivity will be higher as compared to a porous brick, and hence it will cause a greater temperature drop of the melt. Moreover, a denser brick has lower thermal shock resistance as compared to a porous one. Since there will be some discussion on refractories in Chapter 10, only a brief mention is made here. An open-top traditional ladle is associated with higher heat loss as compared to a covered ladle. Therefore, in modern secondary steelmaking practice, ladles have refractory-lined top covers except during the tapping stage. Today, most steel is cast via a continuous casting route where control of teeming rate requires the use of a tundish. Details of tundish metallurgy will be taken up in Chapter 10. It may be simply stated here that a tundish has a shallow pool of flowing liquid steel and hence causes a temperature drop of as much as 10 to 15°C. Therefore, much attention is given to its thermal aspects. It includes use 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 mold for a typical ladle furnace treatment cycle.10 It may be noted that the overall temperature loss was

FIGURE 8.4 Temperature changes in steel melt from furnace to tundish via ladle furnace.10

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more than 75°C in spite of heating in an LF. Casting from the ladle took about 50 min. During this 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 is the development of nonuniformities in liquid steel held in the ladle. This is known as temperature stratification. In view of the importance of temperature control, several theoretical analyses and mathematical modeling exercises have been reported in recent literature. Rather than relying only on statistical analyses of data, many plants around the world have resorted to mathematical modeling based on heat balance, the laws of heat transfer, and temperature measurements in the plant. They are using these for prediction and control of steel temperature. Some successes have been reported in the literature. Some of these will be mentioned later. However, further discussions will be brief and concentrate 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) where

(8.9)

–∆Hex = heat evolved due to exothermic reactions/processes HT – 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, of molten 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) 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

• 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 that half of the silicon added reacts with dissolved oxygen and the rest simply remains dissolved in steel. ©2001 CRC Press LLC

Solution 45 × 10 45 kg silicon = -------------------- , i.e., 1608 mol 28 3

50 × 10 150 tonnes of steel = -------------------- , i.e., 26.88 × 105 mol. 55.8 6

Since half of the silicon reacts, 1608 4 – ∆H ex = – ------------ × ( – 594.6 ) = 47.7 × 10 kJ 2 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 some additional information. In the literature, there are some handy guides to temperature changes of liquid 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

©2001 CRC Press LLC

FIGURE 8.5 Temperature loss resulting from cold alloy additions. Ferroalloy compositions refer to Mn or Cr. No heat loss from the bath is assumed.11

8.3.3

HEAT LOSS

FROM

TAPPING/TEEMING STREAM

Prabhakar and Ghosh14 carried out experiments and heat transfer analysis of temperature loss during teeming of molten lead at 650°C in the laboratory. Important mechanisms of heat loss or gain were identified as 1. Temperature loss due to heat transfer from the surface of the teeming stream by convection 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 in sign, 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 any event gets entrained back in the liquid metal pool below. Also, it can be shown following the procedure of Prabhakar and Ghosh14 that radiation heat loss is one to two orders of magnitude larger as compared to the convective one. Therefore, we may simplify Eq. (8.9) as ∆T1 = ∆T1 (radiation)

(8.11)

Q rad = Aσε ( T s – T o )

(8.12)

Now, 4

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4

where Qrad = rate of loss of heat due to radiation A = 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, Q rad = m s C s DT 1

(8.13)

where m s and Cs are the mass rate of pouring and specific heat, respectively, for molten steel. Combining Eqs. (8.12) and (8.13), Aσε ( T s – T o ) ∆T 1 = --------------------------------ms C s 4

4

(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 stream is shielded by argon. In either case, radiation loss would be insignificant. It is only during tapping that some temperature loss occurs. As the above calculations show, it is at most a few degrees and therefore 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 the wall 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., δ T δT α = --------2- = ------δt δy 2

(8.15)

where α = thermal diffusivity and y is distance. The solution is te  1 ⁄ 2 ∆H = 2 Aλ ( T S – T I )  ----- πα

(8.16)

where ∆H is amount of heat transferred from liquid steel by conduction in time te after pouring it into the ladle, A is the ladle wall area, λ is the thermal conductivity of refractory lining, Ts is the temperature 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 obtain the mean rate of loss of temperature due to conduction. Lange16 has suggested a universal correlation ©2001 CRC Press LLC

that grossly predicts the heat flow rate (Qcond) across the refractory for sand and dolomitic linings applicable 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 for sand 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 end losses at the top and the presence of bottom lining in addition to side lining. The lining consists of several refractory materials located in different zones. For example, adjacent to the outer steel shell, there is a layer of insulating firebrick. The facing brick is mostly dolomite. The initial temperature of the lining also is not uniform. Some later investigators therefore removed the simplifying assumptions and solved the 2-D differential equation numerically. Out of these, extensive work by Austin et al.,17 and Olika and Bjorkman18 are referenced here. In their mathematical modeling exercise, they also considered ladle cycling, drying and preheating practices, ladle lid practice, etc. Many unknown parameters are involved in formulating the model, such as convective heat transfer coefficients, emissivities, initial refractory moisture content, etc. Therefore, the model was calibrated with the help of data collected and then employed for predictions. Figure 8.618 presents the predicted temperature profiles in the refractory wall of a ladle for some ladle preheating schedules. It also shows that measured temperatures are higher than calculated ones. Besides heat loss through the wall and bottom, loss through the top surface of the melt is to be considered. At steelmaking temperatures, it would occur predominantly by radiation. The heat balance equation is dT 4 4 – m s c s ------- = AFσ ( T s – T o ) dt

(8.19)

FIGURE 8.6 Calculated and measured temperature profiles in ladle lining (0 mm corresponds to the outside of the ladle).18

©2001 CRC Press LLC

where ms is mass of steel in ladle, A is the top surface area, and F is the master view factor. Example 8.2 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 steel is quite low, there will be always a layer of oxide at the top however thin it may be. For this, ε has been taken as 0.8 in the example. The calculated value of the rate of temperature loss in Example 8.2 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 that is open at the top. The ladle may be considered as cylindrical in shape with internal diameter of 2.5 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 of temperature 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 K To = 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 first step is to estimate FB (i.e., the geometric view factor for black bodies). Noting that radiation exchange between the top surface of the melt and the converter mouth can be considered as two parallel disks, FB turns out to be 0.55. Since the converter wall around the open space above the melt is refractory lined, its influence is to be estimated by the formula ( A2 ⁄ A1 ) – F B F BR = --------------------------------------------1 + ( A 2 ⁄ A 1 ) – 2F B 2

(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: 1 F = ------------------------------------------------------------------A 1 1 1 -------- +  ---- – 1 + ------1  ---- – 1   A2  ε2  ε1 F BR

(E2.2)

where ε1 = emissivity of the steel surface ε2 = emissivity of the converter mouth A clean liquid steel surface has an emissivity less than 0.1. However, a thin layer of slag or oxide would raise its emissivity and, hence ε1 is assumed to be 0.8. Since an open surface can be mathematically treated as a black surface, ε2 = 1. Inserting the above values into Eq. (E2.2), F = 0.635. This yields dT – ------- = 0.0193 Ks–1 = 1.16 K/min dt ©2001 CRC Press LLC

(Ans.)

It may be noted that there is an uncertainty in the temperature at the mouth of the converter. 4 4 However, that is not going to affect calculations significantly, since To < Ts, and T o ‹‹T s . 4 4 In Eq. (8.19), T o « T s , provided other factors are constant. Usually, there is a slag layer of a few 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 part would be frozen, since its temperature would be below its freezing point. In Eq. (8.19), Ts actually means 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 – [ dT ⁄ dt ] 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 was negligible for a slag thickness of 5 cm or more. Hence, depending on the specific situation, we may 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 area increases as a result of wave and droplet formations. This is the reason for enhanced heat loss in a gas-purged ladle (Section 8.3.1). Simple heat balance calculation indicates that the heating of argon from room temperature to liquid steel temperature requires only a negligible quantity of heat and can be ignored. Through their predictive models, Austin et al.17 have assessed the role of the ladle cover during metal holding, teeming, and on an empty hot ladle of 275t capacity. Their conclusions were as follows: 1. During holding, when the slag was removed from the top of the melt, the cast mid-point temperature 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 the ladle but, with subsequent recycling, the presence of a lid gave about a 4°C higher steel temperature. 3. The ladle in between casts is held empty, sometimes for a prolonged period. For 100 min of 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. For a 27t ladle, it would be less than 1°C/min. The cast midpoint time was about 40 min. Hence, a 40°C lower temperature means about 1°C/min temperature loss, which agrees approximately with Ex. 8.2. With a lid, To would mean the inside face temperature of the ladle cover (Tlid). Taking the data from (1) above, and using Eq. (8.19), 4

4

T s – T lid 15 ------------------- = -----4 40 Ts 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 static melt, heat losses induce temperature gradients in the melt. This consequently generates a free convective 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, thus creating a control problem. An insulated top, achieved approximately by a thick slag and/or a ladle cover, decreases this stratification considerably and reduces the temperature variation of the teeming stream from the beginning to end of casting. Figure 8.7, prepared on the basis of the work by Chakraborty and Sahai,20 illustrates this. ©2001 CRC Press LLC

FIGURE 8.7 Calculated temperature variations of the teeming stream from the ladle for insulated and noninsulated top, teeming commences 20 min after the end of inert gas stirring.20

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 programs to control the temperature of liquid steel for proper casting.16,17,21,22 These are based on mathematical modeling and calibration of the model from plant data. They include the influence of various variables 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 issue is agreement of predicted temperature with measured values. Olika et al.18 claimed a predictability of ±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 measurements 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. This causes a higher rate of steel temperature drop here than in the ladle. Temperature inhomogeneity also develops. This is responsible for such a large error band in the measurement of liquid steel temperature in the tundish. Recently, Deb et al.24 developed a comprehensive flow and thermal model from tapping to teeming into a tundish of molten steel via the ladle furnace route. A flow model was validated from water-model experimental data in the literature. Choudhary and Ghosh25 carried out studies on macrosegregation of continuously cast steel billets. They determined the columnar-to-equiaxed transition (CET) in samples collected from the plant. Correlation of these with the conjugate heat transfer-fluid flow model of solidification by Choudhary and Mazumdar26 required values of the teeming stream temperature. Since data were available 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 inhomogeneities in a tundish, the stream temperature was taken to be 10°C lower than the measured tundish metal temperature. This led to a better match of theoretically predicted and measured CET.25 As stated in Section 8.3.1, a reduction of temperature loss and stratification in the tundish is very desirable for lowering the error band in the end temperature. ©2001 CRC Press LLC

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 metal tapped from the primary steelmaking furnaces has a phosphorus content of 0.01% (100 ppm) or even less. During secondary steelmaking, some phosphorus is picked up by the liquid steel from the carryover slag, leading to a marginal increase of phosphorus in steel. This is known as phosphorus reversion. Even with some reversion, the phosphorus content of the final product is satisfactory for most grades 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 oxygen steelmaking furnace 2. Dephosphorization treatment during secondary steelmaking, if required in occasional situations In the ladle, phosphorus removal can be accomplished either by addition of reagents at the top or by the injection of powders. The latter is more common. Large additions may cause too much of a temperature drop, which is to be compensated by arc heating. Section 2.8 reviewed slag basicity and capacities. Reaction of phosphorus between slag and metal under oxidizing conditions is noted in Eq. (2.79). The phosphorus capacity of slag (Cp) has been defined by Eq. (2.80). Values of Cp are available in the literature. Figure 2.6 presented a compilation of the log Cp vs. log CS relation for several slags. Equilibrium partitioning of phosphorus between slag and metal is important, and the partition coefficient is given as ( W p ) ( wt%P O34 – ) - ∝ ---------------------------L p = ----------[W p] [W p]

(8.20)

Finally, Lp can be expressed by a relation of the following form: 5 log Lp = log Cp + log fp + φ (T) + --- log p O2 + B 4

(8.21)

where fp is the activity coefficient of phosphorus in steel, and B is a constant. Cp is determined by the slag composition and fp by the metal composition. At fixed compositions and temperature, Eq. (8.21) may be simplified as 5 log L p = logC p + --- log p o2 + B′ 4

(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 are useful for calculation. The issue was discussed in Ch. 2, Section 2.5.1, and the regular solution model 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: ©2001 CRC Press LLC

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)

( γ PO2.5 ) - , at equilibrium K p = ------------------[ h p ] [ ho ]

(8.25)

i.e.,

In a recent study on highly basic CaO-FeOt based slags, Zou and Holappa29 considered the equilibrium constant ( K′ p ) for the reaction 2P + 5(FeO) = (P2O5) + Fe

(8.26)

and proposed the following correlation: log K′ p = 0.181 ( W CaO + 0.3W MgO + 1.2W CaF 2 + 2.1W Na2 O ) – 11.73

(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 p O2 , i.e., oxygen potential. Hence, for efficient removal of phosphorus from molten iron or steel, oxidizing conditions as prevail during primary steelmaking are a must. A lower temperature helps phosphorus removal, too. The oxygen potential in blast furnace hot metal is several orders of magnitude lower as compared to those in primary steelmaking. So, in the normal course of things, hot metal dephosphorization is not possible. However, technology has been developed in which the injection of slag along with oxygen raises the transient value of Lp to a sufficiently large magnitude, enabling dephosphorization 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 part of 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 to presence of carbon in hot metal have helped the process. Even so, it requires a slag of high Cp and a nonequibrium phenomenon for the system as a whole. If the slag is kept in contact with metal for a longer time, phosphorus reversion will occur. Figure 8.8 presents log Cp as a function of log ( X Na2 O + X BaO + X CaO ) .31 Soda ash presents an environmental problem, so its use is not recommended. BaO and BaF2 are costly. This restricts the industry’s use of CaO as the principal dephosphorizing agent in CaO-CaF2-FeOt flux. CaF2 enhances aCaO in slag and consequently Cp in comparison to SiO2, and so it is preferred. High silicon in hot metal does not allow proper dephosphorization. Therefore, the silicon content first needs to be brought down to <0.1%. The extent of dephosphorization depends on both Lp and msl (quantity of slag per tonne of metal). With Lp = 100 and msl = 10 kg/t, 50% metal phosphorus theoretically can be removed. Up to 70% dephosphorization has been commercially achieved. Dephosphorization is principally carried out in basic oxygen furnaces (BOFs), which have the capability of achieving a phosphorus content of steel at turndown to a value that is an order of magnitude lower than that of the original hot metal phosphorus content. ©2001 CRC Press LLC

FIGURE 8.8 Phosphate capacities in slags for refining hot metal.31 Reprinted by permission of Iron & Steel Society, Warrendale, PA, U.S.A.

As already stated, ladle dephosphorization in secondary steelmaking is not commonly practiced but is done in occasional cases. The first requirement is to prevent carryover slag as much as possible, since it already contains a lot of P2O5. The Cp of this slag is raised by the addition of CaO and CaF2. The oxygen potential of steelmaking slag is controlled by the reaction 2(FeO) = 2[Fe] + O2 (g)

(8.28)

 ( a Fe ) × p O2 - K 28 =  --------------------------2  ( a FeO )  equil

(8.29)

2

Since aFe is approximately 1, p O2 ∝ ( a FeO ) . Hence, high Lp can be achieved not only with a high slag Cp but a concurrently high value of p O2 , 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 content of slag as follows: 2

3(FeO) = [Fe] + (Fe2O3) ©2001 CRC Press LLC

(8.30)

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 maximum Lp 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 is required. 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 up the reaction. A high FeOt slag will raise the dissolved oxygen content of molten steel (Chapter 5, Section 5.1). 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 problem of 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 discussed there that high-carbon ferrochrome is cheaper than the low-carbon variety, and the use of the former calls for extensive decarburization of the melt by AOD/VOD/VODC. HC ferrochrome also contains a significant quantity of phosphorus. Again, improved corrosion resistance of stainless steels can be achieved only with an ultra-low phosphorus content (less than 0.015 wt.%). No commercially viable process is available for removal of phosphorus from ferrochrome. Therefore, it has to be achieved by dephosphorization treatment of the stainless steel melt. Two commercial routes are available, viz., 1. treatment under oxidizing conditions 2. treatment under reducing conditions

FIGURE 8.9 Effect of FeO content in steelmaking slags on phosphorus distribution between slag and metal at 1958 K.32

©2001 CRC Press LLC

Dephosphorization under Oxidizing Conditions Wijk30 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-scale oxidation of chromium. Figure 8.1030 sums up the thermodynamic requirements for the treatment of crude SS melt with 4% C and 18% Cr at 1400°C. It should be at around 10–14 atm, which is lower than that required to form Cr2O3. Another problem is that Cr decreases the activity coefficient Cr of phosphorus in the steel melt ( e p = – 0.018), thus making phosphorus removal more difficult. The shaded area in Figure 8.10 shows conditions under which most laboratory investigations were carried out. Figure 8.11, compiled by Wijk,30 summarizes findings on dephosphorization efficiency by several investigators in the laboratory. Carbon increases the activity coefficient of C phosphorus in the steel melt ( e p = + 0.13), thus helping dephosphorization. The lower the temperature, the more efficient the phosphorus oxidation, although it is applicable to chromium as well. Of course, lower temperature is generally beneficial to the operation in terms of refractory wear, energy consumption, etc. For these reasons, industrial dephosphorization treatment is carried out before decarburization of 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 conditions.30 Phosphorus can be removed to the slag as phosphides by addition of Ca, Mg, or rare earth metals under reducing conditions. The most suitable element investigated so far is Ca, because it is 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 potentials and phosphate capacities at 1673 K. The shaded area indicates conditions in most published studies.30

©2001 CRC Press LLC

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

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+Cahalide mixtures. Metallic calcium dissolves in CaF2 and CaCl2 liquids. The use of halide allows attainment of slag fluidity as well as lower vaporization of Ca, vapor pressure of pure Ca at 1600°C being 1.8 atm. CaF2 being less volatile than CaCl2, it is preferred. At 18% Cr, attainment of a ©2001 CRC Press LLC

partition ratio of 20 is achievable. This can allow about 50% phosphorus removal, which is adequate in many situations. Nickel has no significant effect on calculated values. Sano31 has discussed relative stabilities of calcium phosphide versus calcium phosphate in basic slags as a function of temperature and p O2 . In a CaO-Al2O3 slag at 1550°C in equilibrium with a fixed partial pressure of P2, the changeover from phosphide to phosphate occurred at p O2 of 10–18 –10–17 atm, exhibiting a minimum at the transition point. In other words, the lower the p O2 , the higher 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 convenient this way, and it can be added from the top as well. It is cheaper, too. A mixture of CaC2 and CaF2 is employed for the formation of a fluid slag.30,33,34 The phenomena and reactions are as follows: 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, and Pb. But a significant quantity of calcium gets lost. Decomposition of CaC2 increases carbon in the melt. –∆[P]/∆[C] was found to be as low as 0.025 in some trials, indicating very poor utilization of 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 CaC2containing 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 been mentioned 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. Thermodynamic and kinetic aspects of absorption and desorption of nitrogen in molten steel, as well as its behavior in industrial degassing processes, were dealt with in Section 6.4.5. It was mentioned that, 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 the steelmaking 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 8.2 but very briefly to make an integrated assessment of nitrogen control for the entire steelmaking process. Liquid steel has a large solubility for nitrogen. On the basis of Table 6.1, solubilities at p N 2 = 1 atm are 450, 458, and 465 ppm, respectively, at 1550°C, 1600°C, and 1650°C. The nitrogen content of steel is far lower than these values. Hence, the kinetics of absorption and desorption govern the ultimate nitrogen level. The strategy for achievement of a low level is to minimize absorption and maximize desorption. As elaborately discussed earlier, oxygen and sulfur dissolved in liquid steel retard rates of both absorption 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 desirable for this. In a situation where both absorption and desorption are occurring simultaneously, the relative ©2001 CRC Press LLC

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 materials charged into the converter, and blowing conditions influence turndown nitrogen content. Marique et al.35 and Normanton36 have presented detailed investigation reports, and they have reviewed some other studies. The nitrogen content of hot metal can be decreased by treating it with reagents based on carbonates 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 of removal can be up to 50%. However, it does not help much. A decrease of 10 ppm nitrogen in hot metal 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 less C–O reaction, and consequently less removal of nitrogen by CO bubbles. Lowering of scrap from 250 to 100 kg/t steel was found to decrease turndown nitrogen by about 10 ppm for LD–HC converter.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 the nitrogen content of oxygen gas from 250 ppm to 20 ppm led to a drop of turndown nitrogen by 5 to 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, or CO2. The use of N2 in place of other gases was found to increase the turndown nitrogen of steel by as much as 15to 20 ppm.35 N2 is the most common stirring gas due to its low cost and easy availability. For lowering nitrogen in steel, it is a must that N2 be replaced by Ar sometime before the 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 out the nitrogen. Hence, reblowing is harmful and can cause an increase of nitrogen content by as much as 30 ppm. Reblowing time is important and nitrogen pickup is proportional to time. A hard blow 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 to 70 ppm. However, in modern converter practice, it generally ranges from 20 to 40 ppm. With special efforts, it may be as low as 10 ppm.35 However, that involves a compromise on other technological parameters such as the use of less scrap, more iron ore, and more argon, which can increase production 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 and from input materials, and desorption due to flushing by CO bubbles. The nitrogen content of EAF steel produced entirely from scrap is much higher than that for a BOF and ranges between 60 and 100 ppm. This is due to ©2001 CRC Press LLC

• less CO evolution • nitrogen containing scrap melting late in the process • dissociation of nitrogen molecules by the arc, and consequent faster pickup by molten steel 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 of a C–O reaction. 2. It can be accomplished by the charging of DRI, which again has higher carbon and lower nitrogen as compared to those in scrap. Continuous charging of DRI is better, since it provides 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 can be lowered to 30 to 40 ppm.37

8.5.3

NITROGEN ABSORPTION SURROUNDING AIR

DURING

TAPPING

AND

TEEMING

FROM

The mechanism of absorption during tapping and teeming was discussed in Section 8.2. The extent of nitrogen pickup varies over a large range, depending on the nature of the stream as well as dissolved oxygen and sulfur in the melt. It may be as large as 40 ppm during tapping, and higher during teeming. In continuous casting, teeming has two stages: ladle → tundish, and tundish → mold. For a slab and bloom caster, submerged refractory nozzles are commonly employed. These nozzles need not be fixed to the ladle or tundish, since adequate protection of the stream from surrounding air can be achieved by argon shrouding at gaps. For a billet caster, the use of submerged nozzles is more difficult for tundish → mold due to the small cross section of the mold. But some plants have been able to implement it.35 With stream protection as outlined above, nitrogen pickup by the teeming streams has been reduced 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 the atmosphere. With protection like the use of flux to prevent contact with air, it has been reported that 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 a tundish is not involved, the extent of nitrogen pickup will be much less than that in continuous casting. The stream must be smooth and compact. Absorption, again, is expected to be negligible for rimming ingots for the following reasons: 1. high oxygen content of steel and consequent retardation in absorption rate 2. flushing action due to the evolution of CO For killed steel, the extent of nitrogen absorption would be more. However, the author does not 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. Less aluminum 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, deoxidation practice is related to other downstream processing such as desulfurization. So, it may be difficult to avoid aluminum addition completely during tapping. ©2001 CRC Press LLC

Gruner and Loscher38 carried out extensive plant trials on an alternative strategy. It consisted of 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 nitrogen pickup. 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 more benefit. 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 the sake 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 with air. Nitrogen absorption is negligible. Argon purging in a ladle furnace is theoretically able to prevent contact with air and should also be able to remove some nitrogen. However, this requires a good seal of the top cover and a high argon flow rate. Otherwise, there is a net increase of nitrogen in steel of 5 to 10 ppm. The addition of CaCO3 throughout ladle processing has been found to be quite beneficial. Figure 8.12 presents the influence of CaCO3 addition at all stages of secondary steelmaking beginning with tapping.38 A substantial decrease in final nitrogen content is evident. Starting in the last decade, the possibility of nitrogen removal by synthetic slag treatment during ladle processing of molten steel has been under consideration, and some investigations have been carried 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 1 3 2– 3 3– --- N 2 ( g ) + --- ( O ) = ( N ) + --- O 2 ( g ) 2 2 4

(8.32)

The nitride capacity of slag may be expressed as 3⁄4

p O2 C N = ( W N ) ⋅ --------1⁄2 pN2

(8.33)

For slag–metal reaction, Eq. (8.32) is modified as 3 2– 3 3– N ( wt.% ) + --- ( O ) = ( N ) + --- O ( wt.% ) 2 2

(8.34)

The equilibrium partition coefficient for nitrogen between slag and metal (LN) is related to CN as 3⁄2

f N ⋅ KO (W N ) - ⋅ CN - = -------------------L N = -----------3⁄2 [W N ] hO ⋅ K N

(8.35)

where fN is the activity coefficient of N in steel, and KO and KN are equilibrium constants for the following reactions: 1 --- O2 (g) = O (wt.%) 2 ©2001 CRC Press LLC

(8.36)

1 --- N2 (g) = N (wt.%) 2

(8.37)

Calcium aluminate type slag is preferred in secondary steelmaking, as discussed in Chapters 5 and 7. Several investigators measured CN for these slags.41 At 1600°C and in the basic range, i.e., W CaO + W MgO --------------------------------- > 1 W Al2 O3 CN ranges between 10–13 and 3 × 10–13. Aluminum dissolved in liquid steel and the Al2O3 content of 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 to be effective in nitrogen removal. However, laboratory measurements have found that CN can be increased 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 conducting liquid under the simultaneous action of a magnetic field and electric current through the liquid. The driving force is the Lorentz force, given by F = i×B

(8.38)

FIGURE 8.12 Variation of nitrogen content of steel melt after tapping. Solid lines are calculated curves for CaCO3 addition. (Curves 1 and 2 are based on different assumptions).38 Reprinted by permission of Iron & Steel Society, Warrendale, PA, U.S.A.

©2001 CRC Press LLC

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.

where B is the applied magnetic field and i is the current. The direction of F is normal to both i and B . In the metallurgical field, the existence of such fluid motion (induction stirring) during induction melting of iron and steel has been known for more than 60 years. On a large scale, it was employed in an ASEA-SKF ladle furnace. Electromagnetic stirring (EMS) in continuous casting is a 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 theoretical analysis and experimental studies of MHD in liquid metals. For typical metallurgical systems, theoretical analyses by Szekely and coworkers are worth mentioning. That there is considerable current interest in this field in steelmaking circles is evident from many recent papers on the subject.42 Garnier43 has reviewed the topic. If the magnetic field is dc, then a dc current is to be passed through the liquid separately to generate motion. On the other hand, an ac magnetic field interacts with its own induced current. The first effect produced is induction heating. Moreover, two mechanical effects are induced that result in electromagnetic pressure and electromagnetic stirring. The force can be divided into an irrotational part and a rotational part. The first one results in magnetic pressure, 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 to Joule heating in the liquid. This can be reduced considerably by going for a very low-frequency supply (2 to 10 Hz) for large steel melts. Rotational forces concentrate in regions where the magnetic field intensity undergoes spatial variations in the direction of the applied magnetic field. The relative intensity of rotational forces compared to irrotational forces increases as the electromagnetic skin depth increases. Again, skin depth increases as frequency decreases. Therefore, a low-frequency supply promotes fluid motion as well. A travelling or rotating magnetic field induces mechanical effects in the liquid metal with better efficiency than an alternating magnetic field. Induced currents result from the relative velocity of the liquid and the magnetic field. For example, Sakuraya et al.44 developed an intensively stirred 5t ladle furnace with a rotating electromagnetic stirrer. With this device, they claimed to have ©2001 CRC Press LLC

obtained a maximum mixing energy of 14 kW per tonne of steel, which is 10 to 100 times as large as 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 was also 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 for better and flexible flow control. This gives a relatively uniform velocity field (0.5 to 1 m/s). EM stirrers are suspended from retractable, hydraulically operated trolleys that position the stirrer against the ladle when processing. EM stirring is also employed to assist slag raking in deslagging stations 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 mold is carried out by changing the cross-sectional area of the flow channel by means of a stopper or slide gate. However, nozzle clogging or air suction occasionally occurs, thus affecting the teeming rate. The development and successful application of an electromagnetic flow control device, used along with the conventional stopper or slide gate, has been reported. The device consists of an induction coil installed around the nozzle. Two approaches are under examination. In the first approach, the coil is designed to make irrotational force significant, thus inducing an upward magnetic pressure. It opposes the gravity force on the liquid and thus retards the flow. Control is effected by variation of current through coil. The second approach is to have a rotating EM stirrer around the nozzle, which induces a rotary motion in the liquid inside the nozzle, thus retarding flow.45 The advantages of EM devices are noted below. 1. As stated above, it is capable of delivering much higher mixing energy as compared to gas 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 the addition of alloying elements into the ladle. It also has been employed to detect the entry of 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 quality steel.

REFERENCES 1. Heaslip, L.J., McLean, A. and Somerville, I.D., Continuous Casting, Vol. I, Chemical and Physical Interactions 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. ©2001 CRC Press LLC

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.

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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 the properties of steel, extensive investigations have been and are being carried out. A vast body of literature is available, as will be evident from the classic book by Kiessling and Lange,1 which has a comprehensive presentation of the structure, properties, and origin of a wide variety of inclusions found in steel. In this chapter, an attempt is made to outline the salient features of the theory as well 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 and corrosion resistance of steel. This is more so for high-strength steels for critical applications. As a result, 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 tonne of steel. Again, the yardstick for cleanliness depends on how one assesses it. For example, most of the inclusions are submicroscopic. Therefore, a microscopic examination cannot faithfully assess cleanliness. 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 intended applications and consequent property requirements, after which we can understand the corresponding limiting size, frequency of occurrence, and properties of inclusions. Therefore, it is necessary to have a broad understanding of how inclusions affect the properties of steel. Herein, we restrict ourselves 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 minor axis), size distribution, and total volume fraction of inclusions 2. Property factors: deformability and modulus of elasticity at various temperatures, coefficient of thermal expansion From a fundamental point of view, an inclusion/matrix interface has a mismatch. This causes local stress concentration around it. Application of external forces during working or service can

©2001 CRC Press LLC

augment it. If the local stress becomes high, then microcracks develop. The propagation of microcracks 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. Macroinclusions ought to be eliminated because of their harmful effects. However, the presence of microinclusions can be tolerated, since they do not necessarily have a harmful effect on the properties of steel and can even be beneficial. They can, for example, restrict grain growth, increase yield strength and 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 increase in yield stress. In high-strength steels, its size will be very small. Kiessling advocated the use of fracture 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 cost to a high level. Therefore, we have to put up with some macroinclusions, and in this context we have 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 various factors 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 as inclusion length; spherical inclusions are better. Brittle inclusions or inclusions that have low bond strength with the matrix break up early during straining, with the initiation of voids at the inclusion/matrix interface. 2. The fatigue strength of high-strength steel is reduced by surface and subsurface inclusions, especially those that have lower coefficients of thermal expansion than steel. These set 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., more brittleness at hot working temperatures). 4. Anisotropy of a property is caused by orientation of elongated inclusions along the direction 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 low as 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 usually MnS 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 similarities in the morphology and physical and chemical properties of isostructural phases, and therefore this classification 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 steelmaking 2. Double oxides of the spinel type (AO-B2O3), which are undeformable at current steelforming 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 higher temperature 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 losing plasticity above 400°C ©2001 CRC Press LLC

5. MnS, which is highly deformable up to 1000oC but not so much above 1000°C 6. 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 of its phase. The routine plant procedure employed the microscopic method. From the shape of the inclusion and a knowledge of the steelmaking process in the plant, it is inferred as to whether it is a silica/silicate/aluminate or sulfide inclusion. Standard charts are available as aids. The charts originally were prepared from decades of investigation by metallurgists using the laborious method of extracting inclusions and analyzing them chemically. The advent of the electron probe microanalyzer (EPMA) in late 1950s, which can determine the chemical composition of individual inclusions in-situ and with reasonable speed, allowed rapid progress in inclusion identification. Kiessling and his coworkers in the Swedish Institute of Metals Research, as well as others elsewhere, carried out extensive investigations on inclusion identification using this instrument as well as with optical microscopy. Since the inclusions are small in size, phase identification in-situ by x-ray diffraction is not possible. This was done on synthetic slags using standard x-ray powder pattern indices for synthetic minerals. All of these have been compiled by Kiessling and Lange1 and provide us with valuable information on various inclusion types; their compositions, phases, and properties; and their appearance under an optical microscope. The invention of the scanning electron microscope (SEM) has added a new dimension to inclusion identification, since much higher magnification is possible than with optical microscopy.The energy dispersive x-ray analysis (EDX) attachment for an SEM allows quantitative chemical analysis of inclusions in-situ as well as qualitative mapping of distribution of various elements in and around the inclusions. These have proved to be very valuable tools for inclusion identification. Cleanliness assessment refers to determination of size, size distribution, number, and volume fraction of inclusions in steel. Again, the traditional microscopic method is available. But it is laborious and unreliable. The field of view in a microscope is of the order of 1 mm2. This is too small 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 automation of quantitative microscopy, and its application to cleanliness assessment. The best known instrument is Quantimet, pioneered by Metals Research Ltd., U.K. It has an optical microscope fitted with video screen and associated microprocessor-based instrumentation. It can scan the specimen 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, and the assessment is more reliable. The total oxide inclusion content of steel can be determined from the analysis of oxygen by sampling and the use of vacuum/inert gas fusion apparatus. Again, to what extent a small sample would be representative of the whole is an open question. Moreover, samples are usually taken from 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 enormously 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 information was derived. Recently, attempts have been made for tracing of Al2O3-bearing inclusions by lanthanum. In this technique, small quantity of La is added after Al addition for deoxidation. La forms La2O3 and becomes incorporated in Al2O3. ©2001 CRC Press LLC

9.4 ORIGIN OF NONMETALLIC INCLUSIONS Sims and Forgeng8 briefly reviewed the subject in the early 1960s. He classified the sources of inclusions into the following: 1. Precipitation due to reaction from molten steel or during freezing 2. 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 and 3 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 uniformly distributed, 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 solid during formation exhibit variety of shapes. Inclusions that form as liquids are globular if they arise at an early stage. Those (e.g., FeS) that form at a very low temperature in the thin residual interdendritic liquid spread in between the grains. Kiessling1 emphasizes the point that the division into exogenous and endogenous types according to the above classification is too simplistic. It is well established that precipitation of oxides/sulfides takes place on exogenous inclusions. Moreover, the exogenous inclusions may undergo reactions and change in composition. Silicates, for example, would react with dissolved aluminum. As a matter of fact, EPMA and SEM/EDX analyses have revealed that most real inclusions are non-uniform in composition. Very often, the core would consist of one compound and the outside layer of some other compound.6 Examples are sequential formation of alumina, galaxite, and manganese aluminosilicate by reoxidation of aluminum-killed steel,9 or a coating of CaS on calcium aluminate in Catreated 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 exogenous inclusions that form during steelmaking. Table 9.1 summarizes possible inclusion sources. It provides an idea as to inclusions’ sources and key elements. Pickering11 conducted extensive investigations on inclusions that are present at different stages, from furnace to mold, during manufacture of steel by electric and open hearth furnace. The influence of basic processing variations at various stages were 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 by primary deoxidation products gave rise to most of the troublesome inclusions. McLean and Somerville9 also cited the erosion of refractory linings of nozzles, stoppers, runners, etc. as a serious source of large inclusions. Also, they quoted several investigators who found that macroinclusions larger 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 form inclusions that are richer in weaker oxides (e.g., FeO, MnO). This has been observed by many investigators.12 Sims and Forgeng8 discussed some of the common formation mechanisms of exogenous inclusions 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 and mechanical erosion. The presence of CaO in inclusions is a common finding, and exogeneous slag particles are responsible for it. It is common knowledge that nozzles are attacked by liquid steel during pouring. Chemical reactions, such as fluxing by slag, loosen particles of refractory, which are detached by the flow of liquid steel. For example, Pickering11 found the maximum diameter of inclusions to increase with time after tapping (Figure 9.1). This is presumably due to the fact that the more the nozzle is in contact with steel, the more serious the effect of chemical attack. ©2001 CRC Press LLC

TABLE 9.1 Possible Inclusion Sources1 Source

Key elements

Furnace

Furnace slags Furnace refractories Ferroalloys

Ca Ca Cr, Al, Si

Tapping

Launder refractories Oxidation

Mg, Ti, K FeO

Ladle

Deoxidation Ladle slag Ladle refractories

Ca, Mg Mg, Ti, K

Teeming

Stopper and nozzle refractories Oxidation Deoxidation

Mg, Ti, K FeO

Ingot mold

Refractories Deoxidation

Mg, Ti, K

Heat treatment and rolling

Surface oxidation Surface sulfurization Inner oxidation Hot shortness

Welding

Welding slags Electrode coatings Steel inclusions Hot tearing

FeO FeS SiO2 FeS Ca, Ti Ti, V S

TABLE 9.2 Average Sizes and Relative Abundance of Inclusions11 Type of inclusion 1. Alumina spinel, and CaO · 6Al2O3 (other than clusters)

Diameter, µm

Approx. relative volume

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

9.5 FORMATION OF INCLUSIONS DURING SOLIDIFICATION Inclusions form during solidification by chemical reactions. Oxides, sulfides, and some oxysulfides are typical products. Even nitrides and carbides have been found to form.6 The driving force is supersaturation of solutes leading to precipitation of reaction products. Section 5.2.1 contains discussions 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 necessary to briefly discuss the topic so as to obtain a better understanding of inclusion control and modification. ©2001 CRC Press LLC

FIGURE 9.1 Variation of maximum size of erosion silicates during teeming.11

The cause of supersaturation in a ladle is the addition of deoxidizers to the bath. However, that is 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 the reaction equilibria in favor of the formation of oxides and sulfides. This can be generally understood from the Ellingham diagrams (e.g., Figure 2.1). We may consider the specific case 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 at 1600°C and 2.97 × 10–16 at 1500°C. Suppose the melt is poured at 1600°C, and after a time in the mold, its temperature is 1500°C. Then, the supersaturation ratio as defined on the basis of Eq. (5.44) would be 2.51 × 10 ---------------------------, i.e., 84.5 – 16 2.97 × 10 – 14

2. Solid metals and alloys have lower solubilities for solutes as compared to those for liquids. This causes rejection of solutes by the solidifying material into the melt at the solid-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 steel ingot. Concentrations of solutes in the liquid as a function of percent solidification are shown 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 ©2001 CRC Press LLC

FIGURE 9.2 Solute enrichment in solidifying liquid steel if no reaction occurs between the solutes.12

• Complete mixing in bulk liquid • No reaction among solutes 3. Some oxygen is invariably picked up during teeming. Also, the occasional addition of deoxidizers, such as aluminum shots, into the mold is practiced. As far as the kinetics of inclusion formation is concerned, most experimental observations indicate that an abundance of nonmetallic particles are always present, and subsequent reactions during solidification occur on them.12,13 As a consequence, nucleation is not required, and the growth of inclusions occurs without the need for appreciable supersaturation. This assumption constitutes the basis for thermodynamic analysis of inclusion formation. Figure 9.3 presents calculations by Turkdogan12 for the situation in Figure 9.2, except that deoxidation by Si and Mn have now been considered. It shows how deoxidation reactions set in when Si and Mn are present. Phase diagrams

FIGURE 9.3 Change in oxygen content of entrapped liquid during the freezing of steel.12

©2001 CRC Press LLC

have also been utilized for qualitative predictions of inclusion formation. Examples are those of formation 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 theme of Chapter 10, “Clean Steel Technology.”) 2. Modifying the inclusions to impart globular shape and desirable properties. (This is known as inclusion modification and is dealt with in this section.) In most applications, the requirements for steel quality demand sufficient attention to both options above. There is no unique way to achieve that goal. Cost-to-benefit ratio is important. A variety of process options are available in secondary steelmaking for lowering inclusion content as well as modifying inclusions. The following discussion on inclusion modification is primarily concerned 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 molten steel as a Ca-Si based alloy powder, either by powder injection or by feeding through hollow metallic 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. Comprehensive data on structure and properties are available in standard text.1 Thermodynamics related to the deoxidation of molten steel was discussed in Chapter 5, Section 5.1.2. It was noted there that calcium is a more powerful deoxidizer than silicon or aluminum. The advantages of complex deoxidation have also been discussed. Deoxidation by Ca-Si alloy, with or without Al, is capable of forming a liquid deoxidation product of CaO-SiO2 type or CaO-SiO2Al2O3 type (Figure 5.7) with all the attendant advantages. If Si is very low and some dissolved Al is 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 low value. Calcium is a powerful desulfurizer as well. Therefore, it is employed in elemental form or as CaO in secondary steelmaking to bring the sulfur content of steel down to a very low value (see Chapter 7). One of the defects associated with continuous casting is the formation of subsurface pinholes due to the presence of dissolved gases. Therefore, the oxygen content of the melt should be kept very low. This used to be achieved by maintaining a certain minimum level of dissolved aluminum in 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. Calcium treatment at the final stage in a ladle or tundish was found to eliminate this, because the deoxidation product is a liquid consisting of CaO and Al2O3, occasionally with SiO2. Figure 9.4 shows the effect of 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 composition upon calcium treatment.17–23 Broadly speaking, two phases are formed. The oxide phase consists of one or more of the compounds in a CaO-Al2O3 system. The sulfide phase consists of a solution of CaS and MnS [i.e., (Ca, Mn)S]. Various possible compounds, along with their melting points, are listed in Table 9.3. The phase diagram for the CaS-MnS system is available.24 The sulfide reaction may be represented as (MnS) + Ca = (CaS) + Mn ©2001 CRC Press LLC

(9.2)

FIGURE 9.4 Influence of dissolved calcium on the flow of an aluminum-killed steel melt through the tundish nozzle.16

TABLE 9.3 Theoretical Compositions and Melting Points of Oxide and Sulfide Phases Composition, wt.% Code

CaO

Al2O3

CaO · 6 Al2O3

CA6

8

92

~1850

CaO · 2 Al2O3

CA2

22

78

~1750

CaO · Al2O3

CA

35

65

1605

C12A7

48

52

1455

C3A

62

38

1535

Phase

12 CaO · 7 Al2O3 3 CaO · Al2O3

Mn

Ca

S

Melting point, °C

MnS

63

–

37

1610

CaS

–

55

45

>2000

Source: from Ref. 14, Chapter 5.

( a CaS ) [ h Mn ] K 2 = --------------------------( a MnS ) [ h Ca ]

(9.3)

Values of hMn and hCa can be calculated from the weight percent of Mn and Ca in liquid steel and appropriate 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 ideal and the solid solution to be a regular one. The authors claim that the calculated values are compatible with the liquidus. Gatellier et al.22 employed experimental data of activities in a CaS-MnS-FeS system from an unpublished work of Castro. Figure 9.5 presents the CaO-Al2O3 phase diagram.25 It indicates the various compounds. The reaction upon calcium treatment, for Al-killed steel, may be generalized as Ca (l) = Ca (g) ©2001 CRC Press LLC

(9.4)

FIGURE 9.5 CaO-Al2O3 phase diagram.25

Ca (g) = Ca Ca + O = (CaO) 3 (CaO) + 2 Al + 3 S = 3 (CaS) + (Al2O3)

(9.5) (9.6) (9.7)

Ultimately, it is reaction (9.7) that is of importance for inclusion-steel equilibrium. ( a CaS ) ( a Al2 O3 ) K 7 = -------------------------------------------3 3 2 ( a CaO ) [ h Al ] [ h s ] 3

(9.8)

Equation (9.7) can be arrived at by combining Eqs. (7.12) and (7.22), and K7 can thus be obtained by combining Eqs. (7.13) and (7.24). This yields 5304 64000 48088 log K 7 = 3  – ------------ + 0.961 –  – --------------- = --------------- – 17.687    T T  T If, on the other hand, Eq. (7.24) is combined with Eq. (7.14), then ©2001 CRC Press LLC

(9.9)

48580 log K 7 = --------------- – 16.997 T

(9.10)

This may be compared with the value given by Kor,18 viz., 45959 log K 7 = --------------- – 15.579 T

(10.11)

Values of K7 at various temperatures are as follows: 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

If may be noted that the predictions of Eq. (9.10) are fairly close to that of Eq. (9.11). On the other hand, Eq. (9.9) gives an order of magnitude lower value. Hence, Eq. (9.10) or Eq. (9.11) is recommended 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 melt at 1500°C and 1600°C, as well as in ternary CaO-Al2O3-SiO2 liquid at 1600°C. We would like to see the formation of a liquid deoxidation product upon calcium treatment. However, upon cooling in the mold, solid oxides such as CA2,CA6 and so on would precipitate. Here, C means CaO and A means Al2O3. To carry out thermodynamic calculations, free energies of formation of these compounds from solid CaO and solid Al2O3 are required. Fujisawa et al.23 have compared the data of some investigators. CaO-Al2O3 melt has some solubility for CaS. The sulfide phase starts to separate out either when concentration of CaS is high or when CaS-MnS phase starts forming, or upon cooling. A simplified analysis assumes CaS to be a pure, separate phase (i.e., aCaS = 1).18,21 Fruehan26 has briefly reviewed the salient features of inclusion modification. Figure 9.6 shows some calculated

FIGURE 9.6 Equilibrium inclusions predicted for calcium-treated steels as a function of its Al and S content at 1823 K.26 Reprinted by permission of Iron & Steel Society, Warrendale, PA, U.S.A.

©2001 CRC Press LLC

values of critical sulfur and aluminum contents of an Al-killed and Ca-treated steel for some inclusion 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 refers to 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 nucleation and consequent melt supersaturation are not required. But, to the author’s knowledge, there is not much 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. It may 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 formation of microinclusions in calcium-treated, aluminum-killed steels. Basic data required for this are temperature and chemical analysis of steel. The model was applied to analyze different situations in practice, such as calcium attack on aluminous ladles and tundish refractories, nozzle clogging by 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 nozzle deposits and inclusions. It is also worth noting that the solubility of calcium in liquid iron is very low. It also lowers equilibrium oxygen and sulfur content of iron to very low values. Equilibration, melt homogenization, sampling, and analysis pose enormous difficulties in laboratory thermodynamic measurements. As a consequence, experimental data suffer from scatter and irreproducibility, and various investigators have proposed widely differing equilibrium constants for reaction of Ca with S and Ca Ca O. The same is true for values of interaction coefficients e o , e s . Recently, Han28 reported a critical and extensive compilation of the thermodynamic behavior of rare earth and alkaline earth Ca elements in molten iron and nickel, which explicitly demonstrates these. Reported values of e o Ca range from –62 to –535. However, the e s 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 for easy qualitative understanding. It is presented in Figure 9.8, which shows the superiority of duplex inclusion where C12A7 constitutes the core and CaS-MnS the ring. It is round in shape with good deformability. 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 dispersed throughout the oxide matrix as well. Depending on concentration levels of the elements, the following 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 the CaS content of the sulfide at equilibrium (calculated).22 Reprinted by permission of Iron & Steel Society, Warrendale, PA, U.S.A.

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FIGURE 9.8 Schematic diagram of inclusions in aluminum-killed steels.26 Reprinted by permission of Iron & Steel Society, Warrendale, PA, U.S.A.

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 available in the literature. Just as an example, Figure 9.9 shows some for calcium treatment of Al-killed steel.

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 earths are strong deoxidizers and desulfurizers like calcium. They also can modify an inclusion, especially sulfide shape. However, they are not as commonly used as calcium. Kiessling and Lange1 have presented the structure and properties of some inclusions obtained from RE additions. Significant informations are available elsewhere.2,31 Fruehan26 has briefly discussed the salient features. Fundamental thermochemical investigations have been conducted mostly for cerium. Some data are available on lanthanum and niobium as well.28 However, there is very little difference in their thermochemical properties. Hence, it is common practice to use data related to 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 Appendix 2.1. As far as the solution and reaction of Ce in liquid steel are concerned, there have been several investigations. However, as in the case of calcium, wide discrepancies exist among various investigators.28,32 Recommended values of interaction coefficients are28 Ce

Ce

Ce

e o = – 12.1, e s = – 2.36 , e c = – 0.037 Equilibrium constants for deoxidation and desulfurization in liquid steel at 1600°C, as recommended by Han,27 are noted in Table 9.4. ©2001 CRC Press LLC

FIGURE 9.9 Microprobe x-ray images of glassy-type calcium aluminate inclusions.2 Reprinted by permission of Iron & Steel Society, Warrendale, PA, U.S.A.

TABLE 9.4 Equilibrium Constants for Reaction of Cerium in Liquid Steel at 1600°C28 Reaction CeO 2 ( s ) = [ Ce ] + 2 [ O ]

Equilibrium constant 7.94 × 10–10

Ce 2 O 3 ( s ) = 2 [ Ce ] + 3 [ O ]

4.90 × 10–18

Ce 2 O 2 ( s ) = 2 [ Ce ] + 2 [ O ] + [ S ]

6.20 × 10–17

CeS ( s ) = [ Ce ] + [ S ]

2.70 × 10–6

Ce 2 S 3 ( s ) = 2 [ Ce ] + [ S ]

4.27 × 10–12

Figure 9.10 shows the stability diagram for phases in equilibrium with liquid steel, constructed on the basis of Table 9.4. If S and O are assumed to obey Henry’s law, then hs and ho can be replaced by the respective weight percent. Very low values of hs and ho obtained by RE addition may 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 ©2001 CRC Press LLC

FIGURE 9.10 Phase stability diagram for Ce-O-S system.26 Reprinted by permission of Iron & Steel Society, Warrendale, PA, U.S.A.

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 precautions are taken, such as use of very good quality basic refractory lining for the ladle (very low FeO and MnO 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 RE oxysulfide inclusions precipitate continuously during cooling. This is not desirable. It has been found that, for adequate sulfide shape control, the following criterion should be observed: [ W Re ] –4 -------------> 3, [ W RE ] [ W s ] < 4 × 10 [W s] 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 improving the machinability of sulfur-containing steels has been in practice for several years. The basic effect of Te or Se is to globularize the inclusions, leading to better deformation characteristics during hot working of steel. The ratio [WTe]/[Ws] has been found to be important. Too much Te affects hot workability. However, a [WTe]/[Ws] ratio larger than 1 has been found to improve the deformability index of the inclusion due to formation of a film of liquid around it, rich in Te. However, there seems to be little benefit of using a high [WTe]/[Ws] ratio. Good hot workability has been found at a ratio less than 0.1. Thermodynamic data for formation of sulfotelluride phases seems to be scanty. Kor18 tried to make some theoretical estimates for the reaction as follows: MnS + [X] = MnX + [S] where X denotes Te or Se. ©2001 CRC Press LLC

(10.12)

FIGURE 9.11 Criterion for critical sulfur and rare earth contents for sulfide shape control and avoiding inverse cone segregation.26 Reprinted by permission of Iron & Steel Society, Warrendale, PA, U.S.A.

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 Metal Soc., 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. ©2001 CRC Press LLC

22. Gatellier, C., Gaye, H., Lehmann, J., Pontoire, J.N., and Castro, F., Steelmaking Conf. Proc., ISSAIME, 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., ISSAIME, 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.

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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 stringent customer demands, especially for plates and sheets. 2. Achievement of good cleanliness is possible only if attention is paid to this goal at all stages 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, a clean 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. Chapter 5 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 been touched upon. In view of the importance of the topic, this chapter looks at clean steel technology in an integrated 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 achieved if 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 extent SiO2 present in it, will keep transferring oxygen into the melt. It is especially serious for aluminum-killed grades for the continuous casting route. Besides lowering aluminum yield, the slag also requires the addition of CaO and CaF2 for proper desulfurization (see Chapter 7). Hence, in modern steelmaking practice, as much attention as possible is paid toward the prevention of slag carryover.

©2001 CRC Press LLC

2. Deoxidation product should be chemically stable. Otherwise, it tends to decompose and transfer 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 and semi-killed grades, deoxidation by Si+Mn is adequate. But, for killed grades, and for continuous casting, aluminum is the principal deoxidizer. The addition of some calcium as Ca-Si alloy in addition to the aluminum tends to improve cleanliness besides inclusion modification (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, optimal practice 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 secondary steelmaking facilities in the form of a ladle furnace or CAS–OB or vacuum degasser. Argon purging through porous/slit plugs, located at the ladle bottom, is the standard mode of stirring. In addition, arrangements exist for argon purging, with or without the injection of solid powders, through a lance immersed into the melt from the top. Broadly speaking, deoxidizers are added in two stages. First, they are added during tapping into the ladle when stirring is by the tapping stream. The second addition is in the LF or CAS-OB or vacuum degasser, as the case may be. Here, a gentle flow of argon is enough for good deoxidation. But a much higher flow rate is required for efficient desulfurization. The latter is not desirable from a cleanliness point of view, since it causes re-entrainment of slag particles into molten steel as well as more erosion of refractory lining. A high gas flow rate also exposes liquid steel to the atmosphere above, and some consequent oxidation if the sealing of the top cover is not perfect, as in an LF. For deoxidation in a vacuum vessel, this is not a problem. The remedy is to have a high gas flow 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. Larger nonmetallic particles get plenty of time to float up. The presence of a well deoxidized top 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 melt reoxidation. 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 such as the NK-PERM (see Chapter 5) seems to be of help. Here, fine gas bubbles are generated throughout the melt. Some nonmetallic particles get attached to these and thus float out at a larger rise velocity. However, the author is not aware as to what extent it is practiced commercially.

10.2.2 TEEMING PRACTICE As discussed in Chapters 8 and 9, oxygen and exogenous nonmetallic particles are picked up by liquid steel during teeming via the following mechanisms: 1. Absorption of atmospheric oxygen via entrainment by the teeming stream has been found to increase total oxygen content of the melt by as much as 40 to 1000 ppm, depending on the nature of the stream. This leads to formation of macroinclusions rich in FeO and MnO. Moreover, it increases dissolved oxygen content and causes more generation of ©2001 CRC Press LLC

inclusions by reaction during solidification. The use of shrouded and submerged nozzles has 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 by reaction 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, due to engineering difficulties. The same is true for ingot casting. Ensuring that the stream is smooth and laminar is the best way to minimize oxygen pickup. 2. Slag entrainment due to vortexing during teeming is responsible for slag particle inclusions (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 metal 3. 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 the next 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 needs no elaboration. The success or failure of the processes is closely linked with development and/or choice of proper refractories for lining furnaces, ladles, etc. Hence, it is only proper to devote a section to it. However, it must be recognized that the subject is complex. Optimization of refractory practice in a shop is achieved with continuous operating experience and trials. This is why there is a large body of information in the literature on refractories for steelmaking. But most of it deals with shop floor experience and related developmental work detailing successful practices. Since it is neither possible nor desirable within the purview of the present text to get into such details, the brief discussions here will be restricted to some salient features only. Special emphasis is given to the influence of refractory lining on steel cleanliness. At the outset, some general references that the reader might require include Refs. 1 through 6. Until about 1970, secondary steelmaking was not making much headway. Refractories for ladle lining used to be fire clay with some variations. Scientists and technologists were carrying on development work in connection with primary steelmaking only. The life of the lining was of primary concern, and it is principally governed by corrosion/erosion. Corrosion refers to chemical attack. In primary steelmaking, the highly oxidizing slag containing FeO and Fe2O3 is the principal corroding agent. Erosion refers to spalling and detachment of grains and pieces of refractories caused by abrasion and impact. Corrosion and consequent loosening of refractory surface speed up erosion. Bath turbulence causes impact. Thermal shock is an additional factor aggravating the spalling tendency. In an LD converter, the refractory material is burnt dolomite or magnesite (popularly known as 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 wear faster. Burnt dolomite is CaO · MgO. Iron oxide in slag can form liquid product by reaction with CaO, but solid product by reaction with MgO at these temperatures. This makes MgO more resistant to slag attack in comparison to burnt dolomite. Again, SiO2 and other impurities are harmful. Pure magnesia, manufactured from sea water, has proved to be superior to natural magnesite but is more costly as well. The tar or pitch constitutes the bonding agent that, upon heating to a moderately high temperature, leaves carbon as residue. This also retards slag attack in the following ways: ©2001 CRC Press LLC

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 not occur. 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 factor in 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 the carbon residue of the latter. Moreover, graphite is more crystalline than the residue. More crystallinity means fewer defects and hence more resistance to chemical attack. However, here again, the issue 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 contains a high proportion of CaO and Al2O3. Again, in primary steelmaking, the choice and design of refractory lining is governed by lining life and its impact on overall steelmaking cost. However, in secondary steelmaking, we are additionally concerned with its effect on steel quality, cost of ladle heating, etc., as summarized by the following discussions. 1. Table 9.2 presents the findings of Pickering that products of the erosion of silicate refractory contribute most significantly to harmful inclusions of large size. This behavior pattern has been widely recognized. In Section 9.6.2, it was mentioned that, without good 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 tend to introduce undesirable impurities into the metal. Such tendencies are aggravated by use of vacuum and higher temperature and are specially important for superior quality steel. This issue has been briefly and sporadically discussed in earlier chapters and will be taken up further in this section. For example, Chapter 7, Section 7.4.5, mentions the importance of ladle lining material for desulfurization and that dolomite is superior to fireclay and silica (see also Figure 7.28). 3. Secondary steelmaking and continuous casting cause additional temperature loss in molten steel. Hence, somewhat higher tapping temperatures are required. This enhances the tendency for lining wear. 4. A low thermal conductivity in ladle lining is desirable to prevent heat loss by conduction through the wall. Again, a low thermal conductivity tends to enhance spalling by thermal shock at the hot face. An interesting development is the use of a higher percentage of graphite (10% or more), which allows continuity throughout the carbon phase, thus increasing thermal conductivity. The conductivity again can be made directional by proper brickmaking technique and by use of flake graphite.8 In that case, heat will flow easily in a direction parallel to the hot face, thus reducing the tendency of spalling. On the other hand, thermal conductivity in a direction perpendicular to the hot face would be low. 5. Ladles require preheating. The heat requirement can be cut down if the heat capacity of the lining is less. A large heat capacity also cools the steel more upon pouring and causes more temperature loss. ©2001 CRC Press LLC

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 of the penetration of molten steel and consequent clogging is aggravated. In-situ sintering of particles is undesirable, as it leads to densification and loss of permeability. Okawa et al.9 have presented some fundamental considerations for the development of improved permeable ceramics. However, as mentioned in Section 3.2, refractory plugs with oriented channels are superior to porous plugs in performance and are preferred in industry. 7. Erosion of the lining by phenomena 1 and 2 above is most severe in the case of the nozzle, because the liquid metal flows through it at a high velocity. This not only affects quality 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 the surface of the vessel lining in contact with the melt if there is chemical affinity between them. This phenomenon leads to nozzle clogging, the well known case being that caused by alumina clusters present in liquid steel. Nozzle refractory is also subjected to high thermal shock. 8. The ladle lining is a composite. The zone in contact with the top slag should resist slag attack well. Since the slag is rich in CaO, dolomite is superior to magnesite. Mag-chrome is also a good refractory. For the zone in contact with liquid steel, the influence on steel quality and lining life is an important consideration. To reduce weight, expense, and total heat capacity of the refractory system, a fireclay backup lining is provided. 9. The lining design would, of course, depend on the process under consideration. Gas stirring causes faster corrosion/erosion of lining. In a vacuum vessel, bubbles expand considerably at the top of the melt, leading to more vigorous stirring of the top slag and hence more corrosion by slag. In AOD/VOD vessels, oxygen is also blown, raising the oxygen potential of the melt and generating iron oxide. 10. The design of refractory lining is a specialized task. Optimization is called for, which should 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 steel and 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 oxygen content. This, in turn, tends to generate more deoxidation products during the freezing of steel in the mold (Section 9.5).

10.3.2 THERMODYNAMIC CONSIDERATIONS INERTNESS

OF

REFRACTORY STABILITY

AND

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 stabler than Al2O3 and so on. The stability of an oxide can be improved further if it is present as a double compound. 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 the free energy curve as a consequence is illustrated in Figure 10.1.4 ©2001 CRC Press LLC

FIGURE 10.1 ∆G vs. temperature for some metal–metal oxide systems (P = 1 atm).4 Reprinted by permission of Iron & Steel Society, Warrendale, PA, U.S.A.

The displacement would be in the reverse direction if the oxide came in contact with the respective element dissolved in liquid steel, as illustrated by the curve Si–SiO2 in Figure 10.1. In other 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 Section 5.1). In the event of such dissociation occurring, the melt will pick up silicon and oxygen. The pickup may not cause a serious composition change for Si, but it may do so for oxygen if it is a deoxidized melt. SiO2 may further react with Al, C, Cr, etc. dissolved in liquid steel. The possibilities and extent of such reactions may be estimated with the help of data and procedures outlined in Section 5.1 under deoxidation thermodynamics. Broadly speaking, a low oxygen potential in the melt would enhance a tendency toward such reactions. Harki et al.10 examined the stability of refractory materials against deoxidized steels. Equilibrium calculations were performed. Laboratory investigations were carried out by simulation tests at 200 g and 50 kg scales. An oxygen sensor was used to monitor changes in dissolved oxygen in the melt due to reaction with refractory materials. Figure 10.2 shows the calculated equilibrium oxygen content for four steel grades and different refractory materials. Laboratory tests also demonstrated the importance of thermodynamic stability and the flow rate of steel. The more stirring, the more melt-refractory interaction. Figure 10.3 shows the influence of refractory materials on the change of soluble aluminum with time at 1600°C for a 50 kg induction furnace.11 The significant decrease of Al dissolved in steel for high-Al2O3, MgO-Cr2O3, and ZrO2-SiO2 refractories is due to the reaction of Al with SiO2 and Cr2O3. This is undesirable, since it poses the problem of the control and yield of aluminum. ©2001 CRC Press LLC

FIGURE 10.2 Dissolved oxygen contents in some steel melts at equilibrium with different oxides at 1873 K.10

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. However reactions 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 oxygen pickup 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 refractories employed in secondary steelmaking. Fireclay, which has been the traditional ladle refractory material, is relatively inexpensive, possesses a low bulk heat capacity, and goes through a nonreversible expansion on heating that helps form tight fitting joints. However, SiO2 in fireclay is unstable with respect to aluminum-killed steel as well as basic top slag. The refractory materials ©2001 CRC Press LLC

FIGURE 10.3 Change of dissolved aluminum content of steel melt over time for some refractory linings at 1873 K (50 kg induction furnace).6

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 also practiced. As compared to fireclay, high alumina and dolomite linings lead to more temperature loss 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 switched over to zircon, with ladle life of almost 100 campaigns. Masood et al., of Inland Steel,2 tested various refractory materials in the laboratory. Their data are presented in Table 10.1. Bose3 has summarized 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 provides a glimpse of the practice in broad terms. Raw dolomite of high purity is widely available in Europe. In view of this, as well as other advantages, 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 comprehensive 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 react with the ambient atmosphere to form hydrates and carbonates. The lime component, however, is much more reactive than periclase, and it determines the speed of hydrate formation in dolomite bricks. Formation of the hydrate is accompanied by a volume increase of over 100%, disintegrating the brick. Therefore, hydration of dolomite bricks should be prevented during manufacture, storage, and transportation. Bonding by tar or pitch considerably retards hydration and makes it commercially usable. But tar or pitch bonding is causing environmental pollution. For this, as well as to make superior quality bricks for ladle lining so as to have cleaner steel, the recent trend is direct bonding by firing at high temperature without use of carbonaceous matter. Hydration can be prevented by wax impregnation and/or storing the brick in a sealed container. Both CaO and MgO are stabler oxides than Al2O3 at steelmaking temperatures. Hence, dolomite lining 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 ©2001 CRC Press LLC

TABLE 10.1 Chemical and Physical Properties of Refractories Evaluated2

Chemistry (wt.%) Al2O3

Tar-bonded dolomite

Resinbonded dolomite

A

0.4

<1.0

B

Direct bonded mag-chrome

0.4

11.1

Zircon

70% alumina

Tarbonded magnesite

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

–

–

–

2900

2900

2950

3100

3600

2600

3100

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

1050

1050

1040

1050

760

1068

1175

3

Bulk density (kg/m ) Porosity (as shipped) (%)

Specific heat @ 1425°C (J/kg.K)

Source: Ritrza et al., in Refractories for Modern Steelmaking Systems, ISS–Aime, 1987, reprinted with permission from Iron and &Steel Society, Warrendale PA, U.S.A.

several investigators in the laboratory and plant.6 Natural dolomite has been found to be superior to MgO, since the former contains CaO, which is a more powerful desulfurizer that MgO12 (also see Chapter 7). Table 10.3 presents the advantages and disadvantages of some standard refractory material for secondary steelmaking, according to Chatillon et al.6 Ladle covers are typically lined with high-alumina refractory (above 85% Al2O3). Porous plugs are made of high alumina or magnesia. Slide gate parts are the most highly stressed ones of the system. They are generally made from high-alumina material. Carbon-bonded alumina, magnesiabased 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 there is 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 thermal shock resistance requires a low coefficient of thermal expansion. As Table 10.1 shows, zircon is better than alumina, which is better than basic bricks in this respect. Fused silica and mullite are even better. However, silica should be avoided due to its reaction with liquid steel. As a result, ZrO2-based materials are increasingly employed. Figure 10.4 shows that increasing the ZrO2 content of the lining significantly decreases enlargement of the nozzle diameter by liquid steel flow, as summarized from experimental data.13 However, ZrO2 is costly. Hence, insertable ZrO2-rich sleeves have been developed as inner protective layer over an Al2O3-C-SiC nozzle. Recently, some fundamental investigations were carried out on the mechanism of reaction and interaction of nozzle refractory with molten steel. Sasai and Mizukami14 made some kinetic studies ©2001 CRC Press LLC

TABLE 10.2 Examples of Refractory Lining for Secondary Steelmaking in Some Countries (Ref. 3, Page 48) Capacity (t)

Process route

Bottom

Side wall

Slag line

Lining life (heats)

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

Country and plant West Germany Plant–1

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

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

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

France

Italy

Note: PB = pitch bonded, DB = direct bonded, RB = resin bonded.

TABLE 10.3 Comparison of Advantages and Disadvantages of Various Steel Plant Refractories Property Refractory Silica sand

Inertness to steel

Pollution

Hydration resistance

Thermal shock resistance

Basic slag resistance

Price

✗

❖

✔

✔

✗

✔

Zircon

✗

❖

✔

✔

✗

✔

High alumina

❖

✔

✔

✔

✗

✔

Magnesite (unfired)

✔

❖

✔

✗

✔

✗

Magnesite–carbon

❖

❖

✔

✔

✔

✗

Magnesite–chrome

❖

✗

✔

❖

✗

✗

Synthetic dolomite

✔

✔

✗

❖

✔

✗

Natural dolomite

✔

✔

✗

❖

✔

✔

Note: ✗ = bad, ❖ = medium, ✔ = good.

in the laboratory on the reaction between a silica-containing alumina-graphite refractory and lowcarbon 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 set of experiments, the refractory was immersed in molten steel at 1600°C. The course of reaction was followed by sampling and analysis of the melt at various time intervals. Microstructures were examined by an optical microscope and EPMA. ©2001 CRC Press LLC

FIGURE 10.4 Relation between enlargement of nozzle diameter upon teeming vs. ZrO2 content of nozzle refractory.13

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 on the refractory was porous. On the basis of the above mechanisms, rate equations were derived assuming 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 through the pores of Al2O3 film is rate controlling. Tsujino et al.15 conducted laboratory experiments to understand the mechanism of nozzle clogging for ZrO2-CaO-C refractory lining. They invoked the mechanism of Sasai et al.14 but considered the possibility of the formation of gaseous Al2O, ZrO, and AlO in addition to SiO. The results of their equilibrium calculations are presented in Figure 10.5. It shows that SiO is the only dominant gaseous species. Again, it is the SiO2 content of the refractory that is primarily responsible for the reaction. In steels containing higher aluminum, a reaction of [Al] with ZrO2 was also detected. The oxide layer formed at the melt–refractory interface was both Al2O3, CaO-Al2O3, and CaO-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 continuous casting mold. It causes local corrosion of the nozzle lining at the slag level. Mukai et al.16 conducted laboratory 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. It is schematically shown in Figure 10.6. In stage (a), the oxide is exposed, so the slag wets it due to favorable interfacial tension. On dissolution of the oxide of the refractory, the graphite particles come in contact with the melt. Since liquid steel wets graphite preferentially, stage (b) sets in. On dissolution of the graphite into steel, ©2001 CRC Press LLC

FIGURE 10.5 Equilibrium partial pressures of SiO, Al2O3, ZrO, and AlO for different oxide materials due to reaction with carbon.15

FIGURE 10.6 Mechanism of corrosion in oxide-graphite composite submerged entry nozzles in a continuous casting mold.16

oxide particles become exposed, and stage (a) comes back. Since dissolution of graphite into steel is 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 at slag level than does the AG nozzle. ©2001 CRC Press LLC

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 the continuous casting mold. Its shape is rectangular. The liquid metal flows from the ladle into the tundish and from the tundish into the mold. It is a must for continuous casting, for proper regulation of 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. The dams and weirs are optional features. These are not present in a plain tundish. The capacity of modern tundishes ranges from approximately 10 to 80 tonnes of steel. A tundish is a continuously operated vessel. When one ladle has been emptied, it is replaced by a filled ladle. During this changeover, 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, when the liquid flows through the tundish, it looses some temperature. In a multistrand tundish, if the outlets to the molds are not equidistant from the inlet stream, then some difference of temperature exists 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, and hydrogen from atmospheric air. These are sources of additional inclusions besides the nonmetallic particles 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 employed as tundish lining. Ease of lining and cost are important considerations. Various mixtures consisting of silica, silicates, alumina, zircon, and magnesia have been employed and seem to be in use even now. However, MgO-based working lining in contact with the melt has gained in popularity from the point of view of steel quality.

FIGURE 10.7 Schematic diagram of a tundish with dams and weirs.

©2001 CRC Press LLC

Prevention of heat loss from the liquid steel in the tundish leads to better temperature control and 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 of gases, 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 oxygen absorption. There have been several investigations17–20 dealing with the choice of additions, so this is 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. As a consequence, the bottom zone is a liquid slag, and top zone has solid powder. Sintered and softened powders constitute the intermediate zones. Thermal insulation is primarily provided by the solid powder. Rice husk ash, which is almost pure SiO2, is a popular material. Fly ash is an alternative. The use of 5 to 10% carbon along with rice husk ash and fly ash has also been recommended.17 An alternative is to employ the rice husk itself, which contains some carbonaceous matter in addition to SiO2. Carbon reacts with atmospheric oxygen, forming CO and CO2 and thus helps 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 reoxidation 2. 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 the correct terminology. [ ∆O ] tot = [ ∆O ] reox – [ ∆O ] deox

(10.9)

Bessho et al.18 conducted plant trials with tundish fluxes in a range of CaO/SiO2 ratios of 0.83 to 22.2. They came to the conclusion that a high-basicity slag (CaO/SiO2 > 11.0) is superior to a low-basicity one with CaO/SiO2 = 0.83 in preventing atmospheric reoxidation of steel. Other recent investigators17,19,20 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

©2001 CRC Press LLC

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 around 1550°C. Straight CaO-Al2O3 slags, although desirable to prevent reoxidation, are very viscous, so the slag should contain some SiO2. In addition, the presence of some MgO helps prevent attack on MgO-based refractory lining. The composition of the slag keeps changing with time. CaO and Al2O3 come as inclusions from ladle slag. SiO2 comes from the top powder as well as through inclusion absorption. Erosion of the tundish lining also contributes to the change. Therefore, the strategy for controlling slag composition 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 adopted for 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 rice husk layers. The effectiveness of rice husk was demonstrated for insulation. It was also predicted that approximately 70% of the calcium aluminate would be in a molten state. A mass balance model, coupled with actual slag analyses in the tundish, predicted the desirability of restricting the entry 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 casting processes by ladle slag, ladle refractory, packing sand in the ladle, tundish slag, and air penetrating into the tundish. They have recommended the improved method shown below. Factors

Improved methods

Ladle slag

(FeO + MnO) = 2 to 15 percent

Ladle refractories

High alumina

Tundish slag

CaO ----------- = 6 SiO 2

Reoxidation by air

Sealed tundish

Packing sands of ladle

Non–silica

With improved flux management alone, it has been found that the total oxygen of steel decreases in 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, interaction with top slag, and refractory lining erosion, and thus in the production of clean steel. Flow regulation is effected by 1. proper choice of tundish size and shape 2. fitting the tundish with flow modulation (FM) devices such as dams, weirs, and baffles 3. argon purging at selected locations ©2001 CRC Press LLC

As far as fundamentals are concerned, it is appropriate to briefly discuss fluid flow in the tundish. 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 first step is a decision about the scale of the water model—whether it should be full size or of reduced size. For this, one has to consider the similarity criteria and must decide which dimensionless numbers 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-tundish stream. Some investigators have considered only the Froude number as important.21 This allowed the 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 as such. Injection of a colored dye provides a tracer and facilitates detailed observations. In addition to flow visualization, investigators also determined residence time (tR).22 The concept of tR and its characteristics 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. This is 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 Volume of reactor ( V R ) t R = --------------------------------------------------------------------Volumetric flow of fluid ( Q )

(10.11)

2. Backmix flow. This is the situation in a stirred tank where the fluid is entering and leaving the tank continuously. In an ideal backmix flow, the fluid is assumed to get mixed immediately 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 residence time ( t R ) is given by Eq. (10.11). t Figure 10.9 schematically presents C vs. τ curves, where τ = ---R- ⋅ C is known as the residence tR time distribution function, where α

∫ C dτ

= 1

(10.12)

O

Experimentally, the C vs. τ curve is determined by the pulse tracer technique. In a water model, a common tracer is KCl solution. A small quantity of KCl solution is suddenly injected into the inlet stream. The concentration of KCl in the outlet stream constitutes a measure of C, and it is monitored continuously by the electrical conductivity method. It may be noted that the flow in the tundish is neither completely a backmix flow, nor completely a plug flow but something in between. The standard technique of analyzing these curves is to consider the entire tundish to hypothetically consist of three interconnected tanks, one having entirely 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 analytically represented in terms of the volumes of these tanks.23 ©2001 CRC Press LLC

FIGURE 10.9 Residence time distribution for different flow patterns.

Figure 10.9 also shows a hypothetical situation in which the entire flow is short circuited. Singh and Koria24,25 recently carried out extensive RTD measurements in a tundish water model. They found both the presence and absence of short circuiting. The natures of the curves were as shown schematically in Figure 10.9. t R,min τ min = ----------tR where tR,min = minimum residence time A large residence time allows more time for the inclusions to float up as well as for homogenization of liquid metal temperature and composition. This calls for such a design of the tundish that 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 tundish size 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, τ mean ( t mean ⁄ t R ) , and τpeak for models without weirs and dams as well as with flow modulating devices. Figure 10.10 shows their dimensionless correlations 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 ©2001 CRC Press LLC

(10.13)

P M Kemeny et al. 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

Tmin. Fr0.08

0.20

0.15

0.10

0.05

0

0

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 FIGURE 10.10 Comparison of measured dimensionless minimum residence time with those calculated from Eq. (10.13). M = model, P = prototype.24

Here, W H l α = ----- , β = ----, φ = --L L L where

L = length of tundish W, H = width and bath height of tundish l = inlet-to-exit distance

In addition to water model studies, mathematical modeling (i.e., numerical computations of fluid flow and predictions thereof) has been done by several investigators.26–29 These have generated velocity 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-model study of a twin-strand caster.22 The inlet stream creates turbulence. This is not desirable, as it enhances refractory erosion and reaction with the atmosphere. Moreover, it shortens the residence time. 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 ©2001 CRC Press LLC

in flotation of nonmetallic particles. Slots in the dams encourage plug flow and do not allow the formation 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 upward motion to liquid steel, thus assisting further in inclusion flotation. The location and flow rate of purging provide further flexibility in operation. However, it is to be remembered that the rising gas bubbles and upward motion of liquid steel should have only gentle effects so as not to create turbulence at the slag–metal interface. Turbulence enhances the entrainment of slag in metal, with a resultant dirtiness of the steel. Inclusion levels in steel may become objectionably high during the changeover from one ladle to another due to the following factors: • More slag carryover from the ladle to the tundish occurs due to shallow metal depth in the ladle and consequent slag entrainment by the steel stream by vortexing. • During changeover from one ladle to another, the metal height in the tundish keeps decreasing, and a stage may come at which the tundish slag will find its way into the mold due to vortexing. A deep pool of molten metal and a viscous slag are helpful. However, optimization is needed to ensure good plant performance. Inclusions can keep floating out as the liquid metal flows through the tundish. Semi-empirical correlations 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 particles of various diameters were employed to simulate inclusions. The authors’ experimental data may be 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 certain size, 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 water modeling of inclusion behavior and heat transfer phenomena in the tundish with and without dams and weirs. Some of their salient findings were as follows: • The residual ratio of inclusions obtained from the water model agreed reasonably with the 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 on particle size. The lower the residual ratio, the better the inclusion removal. Most of the results are as 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 of natural convection. Bessho et al.18 adopted a simpler mathematical procedure for quantitative prediction of the change in total oxygen content in steel from inlet to exit in a tundish. As discussed in Section ©2001 CRC Press LLC

FIGURE 10.11 Computed residual ratios of inclusions as a function of Stokes velocity for different situations.31

10.4.2, this change reflects a dynamic balance of reoxidation and deoxidation. The assumptions were as follows: 1. Deoxidation by coagulation and floating up of oxide particles 2. Reoxidation (i.e., contamination by Al2O3 particles) by reduction of SiO2 in slag by Al [Eq. (10.10)] at the slag–metal interface 3. Homogeneous deoxidation reaction 4. Horizontal plug flow with eddy dispersion 5. First-order reactions The fundamental equation is ∂C ∂ C ∂C/∂t = – u ------- + D t --------2- + R ∂x ∂x 2

(10.15)

where C is the concentration of [O]T, x is the horizontal longitudinal axis, u is the linear plug flow velocity, 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 normal to 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. ©2001 CRC Press LLC

The value of the specific rate of dissipation of energy (ε in W/kg) was determined from the relationship noted below:33 ms ⋅ un ε = -------------2M s 2

(10.19)

where m s is the feed rate of molten steel into the tundish in kgs–1, un is the linear velocity of the ladle 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 at this ε was found to be consistent with the k versus ε relations of some other investigators in gasstirred ladles. As stated earlier, some slag suddenly may find its way from ladle to tundish toward the end of ladle teeming. Fundamentally, this is a pulse akin to tracer injection, and one may expect a change of total oxygen concentration with time as shown schematically in Figure 10.9. With the help of the above equations, this variation was predicted for a ladle change assuming different values 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 nonferrous metals such as aluminum for more than 20 years. For steel melts, active research and development work is being pursued in several countries in bench-scale and pilot plant tundishes. Plant trials are also 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 are available, such as loops and foams,34–36 and circular or irregular holes in ceramic plates of larger width (deep bed filtering).36–38 Figure 10.13 shows some of them schematically. Since the holes are much larger than the inclusions, the mechanism of capture is not like traditional laboratory filters. The inclusions collide on the inner walls of the holes when the melt flows through the filter, stick to the wall, and become sintered there. Proper selection and testing of the ceramic material is important, since this will have

FIGURE 10.12 Variation of total oxygen content of steel vs. time at the tundish exit for different values of k and Dt (calculated).18

©2001 CRC Press LLC

FIGURE 10.13 Various ceramic filter designs employed in a tundish.

a decisive influence on the life and cost of filter. Various refractory materials have been tried so far, such as partially stabilized ZrO2, Al2O3, CaO, Al2O3-ZrO2, and Al2O3-SiO2. ZrO2-based filters are finding more popularity due to their good thermal shock resistance and chemical inertness.34,36 Filtration efficiency (η) may be defined as [ O ] T ,i – [ O ] T , f η = 100 × ---------------------------------[ O ] T ,i

(10.20)

where [O]T,i and [O]T,f are the total oxygen contents of the melt before and after filtration, respectively. In some experiments, it has not been possible to determine η this way. There η values were estimated from values of [O]T at the inlet and exit stream and by comparing experiments with a filter and without a filter. It has been established that filters are effective in lowering inclusion contents of steel substantially. Filtration efficiencies of 20 to 80%,35 70to 90%,36 15to 60%,37 and up to 60%.38 have been reported. Figure 10.14 presents some sample results with Al2O3 filters.38 However, to the best of the author’s knowledge, filters have not yet been adopted commercially. The difficulties are due to the much higher temperatures associated with steelmaking as compared 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 the non-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: ©2001 CRC Press LLC

INDEX OF CLEANLINESS

3

2

1

12

18

24

30

NUMBER OF FILTERS

FIGURE 10.14 Effect of the number of filters on steel cleanliness.38

m˙ s,filter R F = 1 – ------------m˙ s

(10.21)

where m˙ s,filter and m˙ s are mass flow rates of steel with and without a filter. Values of RF ranged between 0.25 and 0.6. Uemara et al.35 determined the drag coefficient (CD) based on Bernoulli equation for a flow of water through their filters in water model experiments. String diameter was taken as a characteristic length for calculation of the Reynolds number for a loop filter. It is not clear what was done for a foam filter. Figure 10.15 shows their CD vs. Re regression fitted curve. Investigators have used this relationship for the flow of molten steel also. The relationship is CD = 9.68 – 80.5 Re–1/2 + 1125 Re–1

FIGURE 10.15 Relationship between CD and Re for various filters.35

©2001 CRC Press LLC

(10.22)

At start of the steel flow, a larger ferrostatic head is required for penetration of the liquid into the 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 4σ LG cos θ ∆H = ----------------------ρ L gd where ∆H σLG θ ρL d

= = = = =

(10.23)

the ferrostatic head required to initiate flow gas-liquid interfacial energy ceramic-steel contact angle density of liquid diameter of hole

The mechanism of deep bed filtration is shown schematically in Figure 10.16. Inclusion particles become attached to the interior walls of the filter and are sintered to it. Uemara et al.36 also performed a 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 surface 2. Attachment of the particles to the filter surface 3. 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.

FIGURE 10.16 Mechanism of deep bed filtration.

©2001 CRC Press LLC

There are some simplifying assumptions in their quantitative analysis. Hence, it is difficult to say anything in confirmation. Finally, there are indications that use of filters cuts down vortexing at the tundish exit as well.36

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39.

Chesters, J.H., Refractories for Iron and Steelmaking, The Metals Soc., London, 1974. Refractories for Modern Steelmaking Systems, ISS-AIME, U.S.A., 1987. Proc. National Seminar on Secondary Steelmaking, Tata Steel and Ind. Inst. Metals, Jamshedpur, 1989. Muan, A., in Electric Furnace Steelmaking, Taylor, C.R., ed., ISS-AIME, U.S.A., 1985, Ch. 24. 69th Steelmaking Proceedings, ISS-AIME, Washington D.C., 1986. 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. Kappmeyer, K.K. and Hubble, D.H., in High Temperature Oxides, Academic Press, London, 1970, Part 5–1. Hart, R. and Michael, D., in Ref. 5, p. 171. Okawa, K., Kochi, H., and Tsuchinari, A., in Ref. 5, p. 237. Harkki, J., Rytila, R., Palander, M. and Sandstrom, S., Scand. J. Met., 19, 1990, p. 116. Kishida, T., Kitagawa, S. and Sugiura, S., Proc. 7th Japan-Germany Seminar, Verein Deutscher Eisenhuttenleute, Dusseldorf, 1987, p. 167. Degawa, T., Uchida, S., and Ototani, T., in Proc. 2nd Int. Conf. on Refractories, Tokyo, 1987, p. 842. Jiaquan, Lu., in Ref. 6, p. 321. Sasai, K. and Mizukami, K., ISIJ Int., 35, 1995, p. 26. Tsujino, R., Tanaka, A., Imamura, A., Takahashi, D., and Mizoguchi, S., ISIJ Int., 34, 1994, p. 853. Mukai, K., Toguri, J.M., Stubina, N.M. and Yoshitomi, J., ISIJ Int., 29, 1989, p 469. Kuchar, I. and Holappa, I., Steelmaking Conf. Proc., ISS-AIME, Dallas, 76, 1993, p. 495. Bessho, N., Yamasaki, H., Fujii, T., Nozaki, T., and Hiwasa, S., ISIJ Int., 32, 1992, p. 157. Van der Stel, J., Boom, R. and Deo, B., in Ref. 17, p. 503. Hara, Y., Idogawa, A., Sakuraya, T., Hiwasa, S., and Nishikawa, H., Steelmaking Conf. Proc., ISSAIME, Toronto, 75, 1992, p. 513. Lai, K.Y.M., Salcudean, M., Tanaka, S., and Guthrie, R.I.L., Met. Trans., 17B, 1986, p. 449. Kemeny, F., Harris, D.J., McLean, A., Meadowcroft, T.R., and Young, J.D., Proc. 2nd PTD Conf., ISS-AIME, Chicago, 1981, p. 12. Szekely, J. and Themelis, N.J., Rate Phenomena in Process Metallurgy, J. Wiley & Sons, New York, 1971, Ch. 15. Singh, S. and Koria, S.C., ISIJ Int., 33, 1993, p. 1228. Koria, S.C. and Singh, S., ISIJ Int., 34, 1994, p. 784. Deb Roy, T. and Sychterz, J.A., Met. Trans. B, 16B, 1985, p. 497. El-Kaddah, N. and Szekely, J., in Proc. Cont. Casting, 85, IMM, London, 1985, p. 491. He, Y. and Sahai, Y., Met. Trans. B., 18B, 1987, p. 81. Szekely, J. and Ilegbusi, O.J., The Physical and Mathematical Modeling of Tundish Operations, Springer-Verlag, New York, 1989. Nakajima, H., Tanaka, M., Guthrie, R.I.L., Dimitron, L., and Harris, D., in Ref. 5, p. 705. Joo, S., Han, J.W. and Guthrie, R.I.L., Met. Trans. B., 24B, 1993, p. 767, 779. Mabuchi, M., Yoshii, H., Nozaki, T., Habu, Y., Sakurai, M., and Moriwaki, S., Kawasaki Steel Giho, 17, 1985, p. 23. Asai, S., in 100th and 101st Nishiyama Memorial Seminar, ISIJ, Tokyo, 1984, p. 75. Gairing, R.W. and Bosomworth, P.A., in Ref. 20, p. 823. Uemara, K., Takahashi, M., Koyama, S. and Nitta, M., ISIJ Int., 32, 1992, p. 150. Raiber, K., Hammerschmid, P. and Janke, D., ISIJ Int., 35, 1995, p. 380. Xintian, L., Yaohe, Z., Baolu, S., and Weiming, J., Ironmaking & Steelmaking, 19, 1992, p. 221. Kahn, Yu. E., Liberman, A.L., Doubrovin, I.V., and Shalimov, Al. G., in Indo-Russian Bilateral Symp., RDCIS, SAIL Ranchi, 1992, p. 69. Ogino, K., Hara, S., Miwa, T., and Kimoto, S., Trans. ISIJ, 24, 1984, p. 522.

©2001 CRC Press LLC

11

Modeling of Secondary Steelmaking Processes

Dipak Mazumdar, Ph.D. Department of Materials and Metallurgical Engineering Indian Institute of Technology 11.1

INTRODUCTION

A comprehensive study of various hydrodynamic phenomena such as fluid flow, mixing, and mass transfer in full-scale liquid steel processing vessels poses serious experimental difficulties. High operating temperatures, opacity of liquid steel, and the relatively large size of industrial metal processing units preclude direct experimental observations. Consequently, it has been customary to study the process dynamics of steelmaking operations with the aid of physical and mathematical models. While the physical modeling of metallurgical processing operations dates back to at least the early 1960s,1 mathematical models have come of age relatively recently (i.e., mid 1970s).2 The progress in mathematical modeling has been largely achieved through advances in the computing power and speed of digital computers, which are now available at moderate cost. Concurrent with these advances have been the numerical algorithms and special computing procedures needed to solve 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 alternatives but 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-scale measurements may all be the ingredients of a successful investigation. Indeed, owing to the complexities associated with the operating conditions, several iterations may be required between mathematical 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 known as the model. Laboratory-scale modeling of various secondary steelmaking operations has most frequently used water as the modeling medium to represent molten steel. The most important single property in this context, apart from its ubiquity, is that its kinematic viscosity (that is, molecular

©2001 CRC Press LLC

FIGURE 11.1 Three essential components of a successful investigation.

viscosity/density) is essentially equivalent to that of molten steel at 1600°C (i.e., within 10%). Flow visualization experiments in aqueous systems using dyes or other tracers have therefore proved to be very helpful in developing a qualitative understanding of various flows. Similarly, more detailed information on flow characteristics has also been possible by measuring velocity fields by tracking the motion of neutrally buoyant particles, hot wire or hot film anemometry, by laser Doppler anemometry, and, lately, by PIV (particle image velocimetry). In addition, measurements of residence time distribution to characterize mixing in water model experiments using dye, acids, or KCl salt solution have proved very popular. Having realized the advantages of using water as the representative fluid, it is now appropriate to 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, if the same forms of dimensionless differential equations and boundary conditions apply to two or more 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 faithful representation of the other; i.e., one can be termed as a model of the other. This is a general statement of the need for similarity between a model and a prototype, which requires that there be constant 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 no relevance. The various states of similarity are discussed in standard texts in great detail4 and are summarized below in brief. Two bodies are said to be geometrically similar when, for every point in one body, there exists a corresponding point in the other. Such point-to-point geometrical correspondence normally allows a 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, and compared to its equivalent full-scale counterpart by noting its relative size or scale according to d λ = -----mdp ©2001 CRC Press LLC

(11.1)

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 dynamic systems. It requires that the corresponding forces acting at corresponding times and corresponding locations in the model and prototype should also correspond. Various forces acting on a molten steel element and of relevance to secondary steelmaking operations have already been summarized in Table 3.1. It is instructive to note here that dynamic similarity in geometrically similar systems automatically 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 similarity at a given point can be expressed as F p,m F I ,m F G,m F µ,m F σ,m ---------- = -------- = ---------- = --------- = --------- = CF F p, p FI,p F G, p F µ, p F σ, p

(11.2)

Rearranging in terms of appropriate grouping of forces, several identities can be obtained from Eq. (11.2) and represented as Re m Fr m Eu m W em

= = = =

Re p Fr p Eu p W ep

(11.3)

In modeling heat transfer operations, thermally similar systems are those in which corresponding temperature differences bear a constant ratio to one another at corresponding positions. When the systems are moving, kinematic similarity is a prerequisite to any thermal similarity. Thus, the heat transfer ratio by conduction, convection, and/or radiation to a certain location in the model must bear 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 thermal similarity first must be satisfied. The former, since mass transfer and chemical reaction usually occur 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 and chemical similarity effects. Consequently, the equivalence between a model ladle and a prototype can be adequately described via the geometric and the dynamic similarities. The dynamic similarity criteria can be derived considering the force balance, which for a multidimensional flow situation under steady-state conditions can be expressed in compact tensorial form as* ∂u ∂ ∂ ∂P ------- ( ρu j u i ) = – ------- + -------  µ -------i + F i ∂x j ∂x i ∂x j  ∂x j

(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 repeated in a term, summation of three terms is implied. For example, ∂ ∂ ∂ ∂ -------- ( ρu j u i ) = -------- ( ρu 1 u 1 ) + -------- ( ρu 2 u 1 ) + -------- ( ρu 3 u 1 ) ∂xj ∂ x1 ∂ x2 ∂ x3

©2001 CRC Press LLC

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 kinetic energy (P/(U2) in the model (e.g., Euler number) and in the full-scale systems, the Reynolds and the Froude number equivalence must be maintained between the two. Nevertheless, with typical laboratory-scale water models employed in physical modeling (e.g., λ less than unity and typically varying in the range of 0.1 to 0.4), it is impossible to achieve both Reynolds and Froude similarity criteria simultaneously. Assuming flows in typical gas-stirred ladles to be dominated largely by the inertial and buoyancy forces (e.g., Froude dominated), the dynamic similarity criterion between the 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 2

up Fr = ------gH

(11.7)

in which u p 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: 2

2

Q  Q  -------- =  ---------5  gR 5 m  gR  p

(11.8)

Invoking geometric similarity, namely H R ------m- = -----m- = λ Hp Rp 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 its corresponding full-scale system under an isothermal situation. The validity of Eq. (11.9) has been demonstrated 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 represent and predict certain phenomena. The term model as opposed to law implies that the relationships employed may not be quite exact, and thus the predictions derived from them may be only approximate. Within the scope of the present discussion, two different types of mathematical models may be envisaged. 1. fundamental or mechanistic models 2. empirical models ©2001 CRC Press LLC

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 fundamental nature, such models tend to have sufficiently general validity. Empirical models, in contrast, are based on direct observations of a particular system and not on fundamentals. At times, if the process under investigation is extremely complex, there is no alternative to their use. Nevertheless, such models tend to be specific to a set of operating conditions. Consequently, great care needs to be exercised if these relationships are to be extrapolated or generalized. The general methodology of mathematical model development3 in a typical situation is illustrated in Figure 11.2. It is seen that the first step is identification of the problem. Once the key parameters affecting the process are identified, the next task is to express this physicochemical picture in mathematical form (viz., problem formulation). Following formulation, it is often desirable to carry out scaling, scoping, and order-of-magnitude analysis, as these provide useful insight into the behavior of the system. The next two parallel stages are computer prediction and experimental work, since purely analytical results or order-of-magnitude estimates will not provide adequate detail. Experimental work will be needed principally for testing the appropriateness of theoretical predictions. Judicial synthesis of prediction and measurement is pivotal to the entire exercise 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 model formulated?” To this end, depending on the scope of application, as a starting point one can consider the various components or building blocks of mathematical models (instead of starting from the first principles and consideration of elementary control volumes). Some of these that are of relevance to the present discussion are summarized in Table 11.1. The building blocks and system geometry

Problem Identification

Problem Formulation

Scoping, Scaling Asymptotic Solutions

Numerical Solutions

Experiments

Synthesis

Implementation

FIGURE 11.2 General methodology of mathematical model development. ©2001 CRC Press LLC

along with the appropriate set of boundary conditions, then allow one to put together the mathematical models in explicit form. In subsequent sections, mathematical model development for various secondary steelmaking operations are outlined. TABLE 11.1 Building Blocks of Mathematical Models

11.3

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

MODELING TURBULENT FLUID FLOW PHENOMENA

The chemical efficiencies of typical processing operations carried out in steelmaking reactors are intrinsically related to their hydrodynamics. Consequently, for any effective process analysis, (thermal and material mixing, melting of solids, dissolution of solids, etc.) detailed knowledge of the flow characteristics in the system is a prerequisite. It is to be mentioned here that, owing to the large 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 problem needs to be ascertained first. Following this, a decision is to be taken whether simulation for transient or steady-state conditions is to be carried out. Once such decisions are made, the governing equations of fluid flow can be conveniently presented in appropriate form considering the building blocks of the flow model outlined already. For the present illustration, a steady-state, two-dimensional, incompressible flow situation has been considered. In terms of a cylindrical coordinate system (r, θ, z), the governing flow equations under turbulent flow conditions can then be represented as shown below. Equation of Continuity ∂ ( ρu z ) 1 ∂ ---------------- + --- ----- ( ρru r ) = 0 r ∂r ∂z

(11.10)

Equation of Motion in Axial Direction ∂u ∂u 1∂ ∂ 1∂ ∂P ∂ ----- ( ρu z u z ) + --- ----- ( ρru z u r ) = – ------ + -----  µ eff --------z + --- -----  µ eff --------z + S z r ∂r ∂z ∂z  r ∂r  ∂r  ∂z ∂z  where ©2001 CRC Press LLC

(11.11)

∂u ∂u ∂ 1∂ S z = -----  µ t --------z + --- -----  rµ t --------r + F z ∂z  ∂z  r ∂r  ∂z 

(11.12)

Equation of Motion in Radial Direction ∂u ∂u ∂ 1∂ 1∂ ∂P ∂ ----- ( ρu z u r ) + --- ----- ( ρru r u r ) = – ------ + -----  µ eff --------r + --- -----  rµ eff --------r + S r ∂z ∂z  r ∂r  ∂r  r ∂r ∂r ∂z 

(11.13)

∂u ∂u 2u r ∂ 1∂ - + Fr S v = -----  µ t --------z + --- -----  rµ t --------r – µ t ------2 ∂z  ∂r  r ∂r  ∂r  r

(11.14)

where,

Equations (11.10) through (11.14) are known as the turbulent Navier–Stokes equations or Reynolds equations. The F variables are the various body forces acting on the fluid element, which may include buoyancy, drag, etc. Finally, µ eff is the effective viscosity (= µL + µt) and is derived from a turbulence model.

11.3.2 THE TURBULENCE MODEL The two equation k-ε turbulence model7 has been very popular for modeling turbulent flows encountered in metallurgical processing operations. According to the model, the conservation of k ′2 ′2 ′2 [turbulence kinetic energy = ( 1 ⁄ 2 ) ( u x + u y + u z ) ] and ε (= –dk/dt), can be expressed in terms of two transport type equations in terms of the cylindrical coordinate system for steady, 2-D flow conditions as shown below. Turbulence Kinetic Energy 1∂ ∂ µ eff ∂k 1 ∂  rµ eff ∂k ∂ ----- ( ρu z k ) + --- ----- ( ρru r k ) = -----  ------⋅ ------ + --- ----- ---------- ⋅ ------ + S k ∂z r ∂r ∂z  σ k ∂z r ∂r  σk ∂r 

(11.15)

where Sk, the net source term, can be represented as Sk = G – ρε

(11.16)

and  G = µt  2 

2 ∂u 2 u 2 ∂u ∂u 2   ∂u --------z +  --------r +  ----r +  --------z + --------r   ∂r  ∂z   ∂r   r ∂z  

(11.17)

Dissipation Rate of Turbulence Energy 1∂ ∂ µ eff ∂ε 1 ∂  µ eff ∂ε ∂ ----- ( ρu z ε ) + --- ----- ( ρru r ε ) = -----  ----------- + --- ----- r ------- × ----- + S ε r ∂r ∂z  σ ε ∂z r ∂r  σ ε ∂r ∂z where, ©2001 CRC Press LLC

(11.18)

2

C 1 εG C 2 ρε – -------------S ε = ------------k k

(11.19)

µ eff = µ L + µ t

(11.20)

The effective viscosity,

where, 2

C µ ρk µ t = -------------ε

(11.21)

Cµ , C1, C2, σk, and σε appearing in Eqs. (11.15), (11.18), etc. are the empirical constants of the kε 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 encountered in dealing with flow simulation in metallurgical systems. These include the free surface of liquid, the symmetry axis (if this exists for a given problem), and solid vessel walls. As far as boundary conditions for velocity components are concerned, no slip conditions are applied at the solid walls while, across the free surface, zero shear is assumed to be transmitted. Gradients of all the velocity components at the axis of symmetry are normally assumed to vanish. Similarly, the values of k and ε at the walls are usually set to zero. Meanwhile, across the symmetry plane and free surface, zero gradients of k and ε are usually applied. Since variations of flow properties are normally steep in the vicinity of solid walls, special treatments for the velocity components as well as turbulence parameters are required in the immediate neighborhood of solid walls so as to estimate the distributions of flow variables realistically. These include logarithmic law for the parallel to wall flow component, local equilibrium between 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 for further details.

11.3.4 HYDRODYNAMIC MODELING OPERATIONS IN LADLES

OF

AXISYMMETRIC GAS INJECTION

A schematic representation of central gas injection through a tuyere in a cylindrical-shaped ladle has already been shown in Chapter 3 (see Figure 3.11). To mathematically model flow and the associated phenomena in Ar/N2-stirred ladles, three different types of approaches have been applied.9 Of these, quasi-single phase models have been relatively more popular. In this, the rising gas-liquid mixture is assumed to be a homogeneous liquid of reduced density. In general, the gas volume fraction within the plume, along with the latter’s geometry (determined empirically), are specified a priori in the calculation procedure. These data constitute important input parameters for the mathematical model. The mathematical model for a steady, axisymmetric gas injection configuration (in terms of r, θ, and z coordinate axes) is identical to those presented in Sec. 11.3.1. In addition, Fz = ρLgα (e.g., the buoyancy force per unit volume) 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 ©2001 CRC Press LLC

single-phase and the plume two-phase regions. The numerical value of α and its distribution in the flow 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), uz = 0 ∂u z -------- = 0 ∂r

∂k ------ = 0 ∂r

and

∂ε ----- = 0 ∂r

and

∂ε ----- = 0 ∂z

At the free surface (z = H, 0 < r < R), uz = 0 ∂u r -------- = 0; ∂z

∂k ------ = 0 ∂z

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 by argon stirring in a typical 250 tonne cylindrical ladle by a flow of 4 × 10–3 Nm3/s from a centrally located porous plug is shown in Figure 11.3.2 The flow field as depicted in Figure 11.3 clearly shows a recirculating vortex located high in the ladle and displaced toward the outside wall. In a

FIGURE 11.3 Predicted flow pattern in a 250 tonne ladle at a gas flow rate of 4 × 10–3 m3 s–1 through a centrally located porous plug.2 ©2001 CRC Press LLC

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 are essentially 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 argon bubbling) system is shown.10 There, as seen, the placement of a baffle over the rising plume significantly alters the flow pattern in comparison to those shown in Figures 11.3 and 11.4. It is important to mention here that the characteristics of the flow considerably influence heat and mass transfer 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 as to 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 from the 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 a centrally located partially submerged lance.9 ©2001 CRC Press LLC

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 through a centrally located porous plug.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 the following convection-turbulent diffusion equation: ∂m ∂m ∂ ∂ 1∂ ∂ 1∂ ----- ( m i ) + ----- ( u z m i ) + --- ----- ( ru r m i ) = -----  D eff --------i + --- -----  rD eff --------i ∂t ∂z r ∂r ∂z  ∂z  r ∂r  ∂r 

(11.22)

The eddy diffusivity, Dt(≈ Deff = D + Dt) and the eddy kinematic viscosity, ν t ( =µ t ⁄ ρ ) , are conventionally taken to be numerically equal. From the viewpoint of engineering calculations, the assumption of equality (Sct = νt/Dt = 1) has proven to be reasonably adequate for a large variety of turbulent flows. It is therefore apparent that provided the flow parameters (uz , ur , etc.) and turbulence 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 the bounding surfaces appears to be the most obvious choice for defining the boundary conditions for Eq. (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 described conveniently via a transport-type equation such as Eq. (11.22). Thus, assuming no internal gener©2001 CRC Press LLC

ation or dissipation (ST = 0) of thermal energy, the governing equation, in terms of a cylindricalpolar coordinate system can be described as 1∂ ∂ ∂T 1∂ ∂T ∂T ∂ ρC ------- + ----- ( ρu z CT ) + --- ----- ( ρru r CT ) = -----  λ eff ------- + --- -----  rλ eff ------- r ∂r ∂z  ∂z  r ∂r  ∂r  ∂t ∂z

(11.23)

In Eq. (11.23), λeff is the effective (molecular + turbulent) thermal conductivity and can be estimated from the theory of turbulence phenomena in the manner described in the preceding section. It is, however, important to mention here that, unlike the turbulent Schmidt number, the turbulent Prandtl number (Prt = νt/αt) normally assumes a value somewhat lower than unity for liquid 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 realistic thermal fields can be predicted via Eq. (11.23). Normally, outgoing heat fluxes through vessel walls are experimentally determined and constitute important input parameters to the thermal energy transport equation. As an alternative to the flux boundary conditions, specified temperature boundary conditions can also be applied to Eq. (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 be made in two ways. 1. Through direct measurements taken under typical operating conditions 2. Using a theoretical approach outlined in the preceding section As pointed out already, the most viable approach for investigating mixing phenomena in a ladle refining operation appears to be the route based on the numerical solution of Eq. (11.22) in conjunction with an appropriate set of boundary conditions. To demonstrate the usefulness of mixing time calculations in gas-stirred ladles, we first look at 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 the kind of inferences that can be drawn from such theoretical calculations. Thus, on the basis of a numerical solution to Eq. (11.22), predictions were made for mixing times in C.A.S. and conventional argon stirring operations in a 150 tonne ladle at a blowing rate of 0.0188 m3/s. Predicted mixing 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 mixing near the free surfaces are very different for the two situations. This essentially arises because of the surface baffle in the C.A.S. system, causing a sluggish rate of liquid mixing near the free surface. It is to be noted here that this effect is a design feature to ensure minimal reaction of dissolved solute additions with the overlying slag phase. Now, we turn our attention to the issue arising out of the dissolution of alloying additions at various locations in the bath and their subsequent mixing in the C.A.S. reactor vessel. It is important to mention here that alloying additions have widely different densities, and therefore these are likely to melt or dissolve in specific regions in the melt (e.g., additions heavier than steel would always settle at the bottom and then melt or dissolve). Computed mixing rates near the free surface for various types of additions in the C.A.S. system are shown in Figure 11.7 at a gas flow rate of 0.0188 m3/s. As such, at this gas flow rate, about 400 seconds of bubbling is needed to disperse the dissolved additions homogeneously throughout the bath. Furthermore, it can be seen that the rate of transfer of dissolved additions from the central baffled region to the slag–metal interface ©2001 CRC Press LLC

FIGURE 11.6 Predicted mixing rates in the vicinity of the free surface in a C.A.S. and conventional argon stirring 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 types of alloying additions (buoyant, neutrally buoyant, nonbuoyant, etc.) at a gas flow rate of 0.0188 m3 s–1.10

(depicted by mixing curves for region C) is extremely sluggish. Consequently, such addition techniques 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 of alloying practices in steelmaking operations. In Sections 4.3.2 and 4.4.1, fundamental aspects of ©2001 CRC Press LLC

solid–liquid interactions were addressed in some detail. In this section, mathematical modeling of heat 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 additions and liquid steel in metal processing units requires a priori knowledge of the distribution of flow velocities and turbulence parameters in the system. Consequently, for the prediction of melting rates, it is assumed here that hydrodynamic conditions in the reactor vessel are known. Thus, in the presence of a known velocity field, the principal task is to obtain an appropriate value of the surface heat transfer coefficient (h), which then allows for the estimation of melting rates. Surface heat transfer coefficient can be obtained from numerous available empirical correlations. For spherical shaped addition, the following is recommended:13 1⁄2

2⁄3

0.4

N u – 2 = ( 0.4Re D + 0.06Re D )Pr ( µ b /µ o )

0.25

(11.24)

In Eq. (11.24), ReD is the object Reynolds number based on the diameter of the spherical addition, and µ b and µ o 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 (and thus 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 of heat transfer coefficient can also be determined. Using such heat transfer values, the complete melting time can be obtained through a simple heat balance, which can be expressed in terms of the following an ordinary differential equation, e.g., h dR – ------- = ------------- ( T b – T m ) ρ s ∆H dt

(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 applicable to 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 no melting and, instead, dissolve directly into liquid steel. For such additions, the dissolution or mass transfer rates from the solid can be estimated from an appropriate correlation following exactly the similar approach to that outlined above. Some of the available mass transfer correlations have already been discussed in Section 4.2.2. The following is, however, recommended for spherically shaped 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 Re and I (= Ret /Re), the intensity of turbulence, are local hydrodynamic variables. As pointed out already, Re and I prevalent in the neighborhood of the solid object are to be estimated a priori from an appropriate turbulent flow model. The corresponding form of Eq. (11.25), valid for mass transfer from a spherical shaped solid object, assumes the form *

C s – C b dR – ------- = K m  ---------------- ρs  dt ©2001 CRC Press LLC

(11.27)

*

in which Km is the mass transfer coefficient and C s is the equilibrium concentration of the dissolving species at the solid–liquid interface. 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 kinetics of 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 around the addition. This steel shell subsequently melts back and exposes the solid addition to bulk liquid steel. Furthermore, the additions upon projection move subsurface for a while and, during that time period, are likely to encounter varying hydrodynamic conditions (e.g., fluid velocity and turbulence intensity). It is therefore clear that a realistic prediction for industrial-scale alloying practice can be made only if all these diverse aspects are considered in the convective heat and mass transfer model. In the following section, modeling of subsurface trajectory of spherically shaped additions in 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, du C 4 3 3 3 2 2 2 1⁄2 --- πR P ( ρ L + C A ρ L ) --------p = --- πR p ( ρ p – ρ L ) – ------D- ⋅ πR p ρ L u rel ( u rel + v rel ) dt 3 2 4

(11.28)

and in the horizontal (r) direction, dν C 3 3 2 2 2 1⁄2 --- πR p ( ρ L + C A ρ p ) ---------p = – ------D- πR p ρ L ν rel ( u rel + ν rel ) dt 4 2

(11.29)

The two corresponding kinematic relationships are dz ----- = u p dt

(11.30)

dr ----- = v p dt

(11.31)

and

The instantaneous drag coefficient, CD in Eqs. (11.28) and (11.29), is based on particles’ instantaneous 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 trajectory of the particle [viz., calculation of subsurface trajectory via Eqs. (11.29) and (11.30) can be carried out provided the fluid velocity in the system are known a priori]. The following set of initial conditions 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. ©2001 CRC Press LLC

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 trajectories of 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 as aluminum and ferro-silicon ( γ = ρ p ⁄ ρ L = 0.4 or 0.6 ) would almost instantaneously resurface and would proceed to melt within the central slag free region. Ferro-manganese and additions with similar densities (γ = 0.44), on the other hand, may undergo subsurface melting rather than melting within 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 the bottom part of the ladle’s contents is relatively quiescent, such additions will typically experience considerably longer dissolution times. (Note that dissolution time is directly related to the flow velocities.) Complete dissolution times for 75 wt.% ferro-tungsten spheres (initial diameter 50 mm) as a function of gas flow rates in an argon stirred 60 tonne ladle are shown in Figure 11.9. These were derived16 through the numerical solution of the appropriate turbulent Navier–Stokes equation in conjunction 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 tonne C.A.S. ladle at a gas flow rate of 0.0188 m3 s–1.14 ©2001 CRC Press LLC

FIGURE 11.9 Predicted dissolution rates of 75 wt.% ferro-tungsten in a 60 tonne ladle as a function of gas flow rates.15

There, complete dissolution times for 50 mm dia. Fe-W spheres appear to be on the order of 15 min. It is instructive to note here that complete mixing times (Section 11.4.3) are only a small fraction of alloy dissolution times. From such time scales, first-hand estimates of inert gas purging times 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 obey a generalized conservation principle. If the dependent variable is denoted by φ, the general differential equation is ∂ ----- ( ρφ ) + div ( ρuφ ) = div ( Γ gradφ ) + S φ ∂t

(11.33)

in which, Γ is the diffusion coefficient and Sφ is the corresponding source term. The quantities Γ and 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 of different 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 meaning will have to be given to the diffusion coefficient Γ and the source terms S. These are summarized in Table 11.2, in which various physical phenomena are represented mathematically as a special case of the general differential equation. Therefore, in principle, one is concerned with the numerical solution of only Eq. (11.32). Thus, the concept of the general differential equation enables us to formulate 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 equation into a set of algebraic equations. For a given differential equation, the resultant algebraic equations are by no means unique and depend on the method of their derivation. The interested reader is referred to the excellent text of Ref. 17 for a detailed discussion on the subject. ©2001 CRC Press LLC

TABLE 11.2 Various Physical Phenomena and Their Unified Mathematical Representation Via the General Differential Equation Meaning of φ, Γ,and S in the general differential equation [Eq. (11.33)]

Physical phenomena

Governing differential equation

1. Steady heat conduction with no source

∂ ∂T --------  k -------- = 0 ∂ x j  ∂ x j

φ = T , Γ = k, S = 0, and u = 0

2. Transient heat conduction with a finite source

∂T ∂T ∂ ρC ------- = --------  k -------- + S r ∂t ∂ x j  ∂ x j

φ = T , Γ = k/ρC, ρ = 1, S = S T /ρc, and u = 0

∂ ∂C ∂C ------- = --------  D -------- ∂ x j  ∂ x j ∂t

φ = C, Γ = D, ρ = 1, S = 0, and u = 0

4. Heat transfer in a media under motion

k ∂T ∂ ∂T ------- + -------- ( u j T ) =  ------- --------  ρC ∂ x j ∂t ∂ x j

φ = T , Γ = k/ρC, ρ = 1, and S = 0

5. Mass transfer in a media under motion

∂m ∂ ( mi ) ∂ ------------+ -------- ( u j m i ) =  D ---------i  ∂ x j ∂xj ∂t

φ = m i , Γ = D, ρ = 1, and S = 0

3. Diffusive mass transfer

6. Time averaged equation of motion under steady flow

∂u ∂ ∂P ∂ -------- ( ρu i u j ) = – ------- + --------  µ eff --------i + S u ∂xj ∂ x i ∂ x j  ∂ x j

7. Turbulence kinetic energy

∂k ∂ ∂ ----- ( ρk ) + -------- ( ρu j k ) =  Γ k -------- + G – ε ∈  ∂ x j ∂t ∂xj

11.7

∂ρ φ = u i , Γ = µ e , and S = – ------- + S u ∂ xi φ = k,Γ = Γ k , and S = G – ρ ∈

CONCLUDING REMARKS

This chapter has demonstrated the use and value of mathematical modeling and its application to some typical secondary steelmaking operations. The content is introductory in nature, and therefore the examples cited have been deliberately chosen from relatively simple and easy to understand configurations. Transient three-dimensional programs with two-phase capabilities are currently available for computational modeling of such fluid flow systems. In light of much more powerful present-day computers and software packages, it is possible to address far more challenging and complex 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. ©2001 CRC Press LLC

13. 14. 15. 16. 17.

Taniguchi S., Ohmi, M., Ishiura, S., and Yamauchi, S., Transactions of ISIJ, 23, 1983, p. 565. Iguchi M., Tomida, H., Nakajima, K., and Morita, Z., ISIJ International, 32, 1992, p. 857. Mazumdar, D. and Guthrie, R.I.L., Metall. Trans., 24B, 1993, p. 649. Mazumdar, D., Kajani, S., and Ghosh, A., Steel Research, 61, 1990, p. 339. Patankar, S.V., Numerical Heat Transfer and fluid flow, Hemisphere Publishing Corp., New York, 1980.

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