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Densities and Viscosities of Slags – Modeling and Experimental Investigations Mikael Persson Licentiate Thesis School of Industrial Engineering and Management Division of Materials Process Science Royal Institute of Technology SE-100 44 Stockholm Sweden Akademisk avhandling som med tillstånd av Kungliga Tekniska Högskolan i Stockholm, framlägges för offentlig granskning för avläggande av Teknologie licentiatexamen, fredagen den 28 april 2006, kl. 14.00 i sal B3, Brinellvägen 23, Kungliga Tekniska Högskolan, Stockholm ISRN KTH/MSE--06/23--SE+THMETU/AVH ISBN 91-7178-336-9

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Page 1: Densities and Viscosities of Slags – Modeling and ...10040/FULLTEXT01.pdf · Densities and Viscosities of slags – Modeling and Experimental Investigations ... of molar volume

Densities and Viscosities of Slags – Modeling and Experimental Investigations

Mikael Persson

Licentiate Thesis

School of Industrial Engineering and Management Division of Materials Process Science

Royal Institute of Technology SE-100 44 Stockholm

Sweden

Akademisk avhandling som med tillstånd av Kungliga Tekniska Högskolan i Stockholm, framlägges för offentlig granskning för avläggande av Teknologie licentiatexamen, fredagen den 28 april 2006, kl. 14.00 i sal B3, Brinellvägen 23,

Kungliga Tekniska Högskolan, Stockholm

ISRN KTH/MSE--06/23--SE+THMETU/AVH ISBN 91-7178-336-9

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Mikael Persson. Densities and Viscosities of slags – Modeling and Experimental Investigations KTH School of Industrial Engineering and Management Division of Materials Process Science Royal Institute of Technology SE-100 44 Stockholm Sweden ISRN KTH/MSE--06/23--SE+THMETU/AVH ISBN 91-7178-336-9 © The Author

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ABSTRACT

The present dissertation describes part of the efforts directed towards the development of computational tools to support process modeling. This work is also a further development of the Thermoslag® software developed in the Division of Materials Process Science, KTH. The essential parts of the thesis are a) development of a semi-empirical model for the estimation of the molar volumes/densities of multicomponent slags with a view to incorporate the same in the model for viscosities and b) further development of the viscosity model for application towards fluorid- containing slags, as for example, mould flux slags. The model for the estimation of molar volume is based on a correlation between the relative integral molar volume of a slag system and the relative integral molar enthalpies of mixing of the same system. The integral molar enthalpies of the relevant systems could be evaluated from the Gibbs energy data available in the Thermoslag® software. The binary parameters were evaluated from experimental measurements of the molar volumes. Satisfactory correlations were obtained in the case of the binary silicate and aluminate systems. The model was extended to ternary and multi component systems by computing the molar volumes using the binary parameters. The model predictions showed agreements with the molar volume data available in literature. The model was used to estimate the molar volumes of industrial slags as well as to trace the trends in molar volume due to compositional variations. The advantage of the present approach is that it would

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enable prediction of molar volumes of slags that are compatible with the thermodynamic data available. With a view to extend the existing model for viscosities to F--containing slags, the viscosities of mould flux slags for continues casting in steel production have been investigated in the present work. The measurements were carried out utilizing the rotating cylinder method. Seven mould fluxes used in the Swedish steel industry and the impact of Al2O3 pick up by mould flux slags on viscosities were included in the study. The results showed that even relatively small additions of Al2O3 are related with a significant increase in viscosity. Keywords: density, molar volume, thermodynamics, enthalpies, model, slags, oxide

melts, viscosity, mould flux, continuous casting

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ACKNOWLEDGMENTS

I would like to express my sincere gratitude and appreciation to my supervisor Professor Seshadri Seetharaman for his guidance and constant support as well as constructive criticism during the work of this licentiate thesis. I am grateful to Associate Professor Ragnhild E. Aune, for every day help with both technical and theoretical concerns during this project. Dr. Mårten Görnerup is gratefully acknowledged, especially for bringing practical and industrial aspects to light. I am very thankful to Professor Jiayun Zhang for giving me the opportunity to come and complete some of the work at USTB, University of Science and Technology Beijing. Her guidance and interesting discussions have been most helpful in carrying out this work.

A special thank to M. Sc. Mikael Ersson for fruitful discussions, valuable comments, and other not so life dependent matters. Thanks to Mr. Peter Kling for valuable help and assistance with experimental equipment. The author also would also like to thank all of the colleagues and friends at the Division of Metallurgy. Financial support from Jernkontoret and traveling grants from the Axel Hultgren Fund is also acknowledged. Finally, I would also like to thank my family for their support. I am especially grateful to my wife, Sara, for her never-ending support and encouragement. Mikael Persson Stockholm, April 2006

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SUPPLEMENTS

This thesis is based on the following supplements:

Supplement 1: “Estimation of Molar Volumes of Some Binary Slags from Enthalpies of Mixings”

M. Persson, T. Matsushita, J. Zhang and S. Seetharaman

Submitted to Steel Research, 2006

Supplement 2: “A Thermodynamic Approach to a Density Model for Oxide Melts”

M. Persson, J. Zhang and S. Seetharaman

Submitted to Steel Research, 2006

Supplement 3: “Viscosities of some Mould Flux Slags” M. Persson, M. Görnerup and S. Seetharaman

Submitted to Metallurgical and Materials Transactions B, 2006

The contributions by the author to the different supplements of the thesis:

1. Literature survey, major part of the calculations, major part of the writing.

2. Literature survey, calculations, major part of the writing.

3. Literature survey, experimental work, major part of the writing.

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CONTENTS 1 Introduction 1

1.1. Project Objectives 2

2 General Aspects 5 2.1. Molten Slags 5 2.2. Densities 5 2.3. Viscosities 6 2.4. Mould Fluxes 7

3 Density Model 9 3.1. Model Considerations 9 3.2. Experimental data 14

4 Experimental Work 17 4.1. Materials and Sample preparations 17 4.2. Apparatus 17 4.3. Procedure 19

5 Result and Discussion 21 5.1. Density Model Applications 21

5.1.1. Binary Systems 21 5.1.2. Ternary Systems 26 5.1.3. Quaternary systems 34 5.1.4. Industrial Applications 38

5.2. Viscosity Measurements 39

6 Summary and Conclusions 49

7 Future Work 51

References 53

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Contents

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1

Chapter 1

INTRODUCTION

Steel making practice today is extremely complex in view of the optimization of the various unit processes with respect to the chemistry of the process, the technological aspect, process economy as well as environmental considerations. In the modeling of steel making processes, it is very important to have the optimum slag practice, which, in turn, needs a clear understanding of the properties of slags. The slag properties are commonly divided into two parts, viz. the thermochemical properties and the thermophysical properties. The former comprises of the integral molar properties like enthalpies and integral molar Gibbs energies as well as partial molar properties like the activities of the slag components. On the other hand, the physical properties include, among others, viscosities, thermal diffusivities and surface tensions. Molar volumes, which can be classified under thermochemical properties, come under the physical properties as densities. The specific heats are common to both the categories. Both these types of data are necessary for process optimization, for thermochemical modeling, heat and mass transfer calculations as well as Computerized Fluid Dynamics (CFD) computations. The classification of the properties into the above-mentioned two categories is some what ambiguous as both these are structure-related and consequently, must be related to each other. Thus, the properties should be mutually consistent. This is an essential condition in process modeling as mutually inconsistent data regarding the properties of the same slag necessitates the introduction of empirical coefficients in order to achieve convergence. The Division of Materials Process Science at KTH has been involved in the investigations of the thermochemical and thermophysical properties of metallurgical slags, with special emphasis on iron- and steelmaking. The aim has been to generate accurate data by careful experimentation and modeling of the

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Introduction

2

properties in order to extrapolate the data reliably as functions of temperature and composition. These efforts are supported by the Swedish Steel Producers Association in a project aiming at development of a toolbox towards process optimization. Inter property correlation has been the focus point in this project. The division has earlier linked the viscosities of binary metallic systems to the Gibbs energies of mixing. The activation energies of binary silicate systems were combined with the Gibbs energies of Mixing in order to estimate the activation energies for viscous flow n ternary silicates. Liquidus temperatures were estimated from the activation energies of viscous flow. The present work is expected to widen this approach to other properties.

1.1 Project Objectives The general aim of this project is to develop computational tools for slag properties that could provide reliable and mutually consistent data for the benefit of the Swdish Steel Industry. More specifically, the project aims at the modeling of the densities/molar volmes of multicomponent slags and deploying this in the already existing viscosity model, referred to as the KTH-model. The model has been incorporated in a commercial software developed in the division, Thermoslag®. This software, in the present version consists of three different modules, viz. viscosity module, sulphide capacity module and the activity module. The basic description of the silicate slag is based on the Temkin-Lumsden approach, wherein the anions and cations are classified into separate subgroupings in order to calculate the entropies of mixing. Silicate ions which have complicated structure are “split” into Si4+ and O2- ions and these ions are placed in the respective subgroupings. The viscosity description is based on the Eyring equation which involves the estimation of the densities of slags. At the present stage, the model approximates the densities of slags by linearization. The present works aims at incorporating a more rigorous description of the slag densities. The molar volume (which is in fact the reciprocal of density multiplied by the mol mass) is also a thermodynamic property. Thus, it should be possible to establish a correlation between molar volume and thermodynamic properties, which would enable the exploitation of the abundance of thermodynamic data towards the estimation of slag densities. This will also enable generation of mutually consistent thermodynamic and density data for complex slags.

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Chapter 1

3

Thus, the present thesis work is intended to trace the following flow diagram.

Molar Volumes Flouride Slags and

Sulphide Capacities

Thermodynamic Activities

Viscosities

Slag Model Temkin-Lumsden

Mould Fluxes

Approch

Figure 1.1-The flow sheet of the planned extension of the slag model at the

division. The slag model optimizes the existing experimental data to the model parameters. In the case of densities, it was aimed to arrive at reasonable descriptions of densities of multi component slags from the data corresponding to binary systems. In the case of the viscosity models, the present description had been found to have certain limitations. The slags containing CaF2 have not been included in the present slag model. This is very important with respect to the investigations regarding mould fluxes, used for continuous casting. Inclusion of fluoride containing species would necessitate generation of viscosity data with respect to mould flux compositions. This is also attempted as part of the present work. Viscosity measurements have been carried out in the case of some proprietary mould fluxes. The effect of alumina addition was also examined.

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Introduction

4

Viscosity model appears to have limitations with respect to high alumina slags. This is hoped to be remedied as a long term aim. Thus, a continuation of the present work beyond the licentiate thesis should enable the deliverance of a software package to the Swedish Steel Industry, which enables the computation of;

a) Thermodynamic activities and enthalpies of multicomponent slags b) Estimation of sulphide capacities c) Estimation of densities of multicomponent slags d) Estimation of the viscosities of multicomponent slags that cover fluoride

slags as well as high alumina slags e) Inter-property correlations.

The industrial importance of slag densities is also of great significance in various applications. Density is a parameter that influences the foaming stability of slags, vital in foaming processes as the EAF. Efforts towards zero-slag practice are taken in metallurgical process, considering energy and environmental issues, where density is an essential factor. Densities are also relevant in heat and mass transfer calculations, commonly used in modeling of high temperature processes for optimization.

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5

Chapter 2

GENERAL ASPECTS

2.1 Molten Slags

Silicate melts are ionic in nature. The structures of these molten slags are complicated due to the polymerization of silicate anions. Si atoms are tetrahedrally bonded to four oxygen atoms. In silicate slags, the SiO4

4- tetrahedra may form more complicated structures as Si2O7

6-, Si3O108-, cyclic polymers and even three

dimensional network of bridged silica tetrahedra. Increasing content of basic oxides in silicate slags will break down these polymers into smaller units. On the other hand, amophoteric oxides like Al2O3 added to the silicate slags will contribute to the chain structure. The understanding of slag structures is of great importance, as the formation of structures will be widely reflected in the thermophysical and thermodynamic properties of these melts. The Division of Materials Process Science at KTH has developed a slag model1, 2

based on the Temkin’s3 description of the entropy of ionic melts and a Lumsden’s4 formulation of the silicate structures. Lumsden’s description simplified the silicate network as a completely dissociated ionic system with Si4+ and O2- ions.

2.2 Densities

Various models to estimate the density of molten slags are described in literature. An additive method5, which has been commonly used, obtains molar volume, ,mV

from the following two equations:

ρ...+++

= kkjjiim

xMxMxMV (1)

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General Aspects

6

...+++= kkjjiim VxVxVxV (2)

where ρ is the density, and is the mole fraction respectively the molecular mass for component i. The partial molar volume,

ix iM

V , is usually assumed to be equivalent to molar volume of the pure substance, . This approximate method gives satisfactory results for ideal systems and systems that show small deviations from ideal behavior. In reality, however, slags for industrial applications, may not be treated as ideal solutions. As mentioned, silicate structures are complex, silica and alumina slags form polymerized units such as chains, rings and three dimensional network. The use of a constant value for

imV ,

2SiOV and 32OAlV may not be theoretical compatible as well, since the silicate and aluminate structures vary with composition.

A model developed by Bottinga and Weill6 used a constant value for 2SiOV and estimated values of V for several oxides. The model claimed to predict good density values within a limited silica range. Grau and Masson7 presented a model in which the partial molar volume of SiO2 varied with structure, but the method is complicated to apply on multi component system. Another model, Botting et al.8 considers composition dependency of partial molar volumes of alumina-silica melts. The model has been successful in estimating densities, but is only suitable for comparatively high contents of silica and considered complex. Mills et al.9 have developed a model where V for alumina-silica slags vary with composition. The model claims to be successfully applied to many different systems. However, in this model, the molar partial volume for each component needs to be evaluated at different temperatures. Due to the lack of experimental data in many systems, it is difficult to estimate V over wide temperature ranges.

2.3 Viscosities Viscosity is another physical property closely related to silicate structures. The viscosity of molten slags at a given temperature is dependent of structures, hence the composition. Pure SiO2 consists of three dimensional network and has a extremely high viscosity. The entering of basic oxides into the melt leads to the breakdown of the silicate network and a lowering the viscosity of the melt. The

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Chapter 2

7

majority of the metallurgical slags contain relatively high amounts of metal oxides, which exhibit lower viscosity. The viscosity of slags may also be affected by the presence of solid particles in the slag. Viscosities of two phase mixtures have been reported in literature10-12. The results have shown that a formation of a two phase mixture may lead to non-Newtonian behaviour and have a significant impact on the viscosity. Still, the presence of solid particles below a critical level may not affect the Newtonian behavior of the liquid.

2.4 Mould Fluxes

The major part of the steel produced around the world is continuously cast. Mould fluxes are added during the casting process to ensure a smooth functioning. It plays an important role in enabling better process performance and products with less defects. The mould flux main functions are13, 14;

• protect the steel from oxidation,

• lubrication at the mould/metal interface,

• provide the optimum level of horizontal heat transfer and

• absorb inclusions from the steel. The viscosity of the mould flux is a key parameter determining the optimum casting conditions. An empirical rule usually used to predict the cast conditions are based on casting speed and viscosity. A number of experimental investigations have earlier been carried out in order to determine viscosity data for mould flux slags, both industrial ones as well as synthetic slags with compositions close to industrial mould fluxes15-24. Almost all mould powders contains CaF2 as it lowers the viscosity and melting point of the fluxes. The fluorine content varies normally between 4 and 10 wt-%, but some powders can contain as high as 20 wt-% of fluoride. The CaF2 content is a problem in the view of both process as well as environmental considerations, due to the high volatility of the fluorine-containing species. The fluoride evaporation from mould flux slags could also be a problem in the case of viscosity measurements, since the flux composition varies with time during the measurements. This issue

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General Aspects

8

regarding fluoride vapor loss from mould fluxes has earlier been investigated in the Division of Material Process Science25. The fluorine volatilization is, however, not the only factor affecting the flux composition with time. It is well known that the mould flux slag is a receptor of oxide inclusions. This absorbtion of inclusions, together with the evaporation of fluoride spices is likely to affect the chemical composition of the mould flux. A change in composition may have an influence on the physical properties of the mould flux, thereby affecting its performance in the casting process. These are important aspects to consider when modeling the casting process.

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9

Chapter 3

DENSITY MODEL

As mentioned earlier, the models available in literature for estimations of slag densities are based on numerical fits of experimental data. An alternative model for density predictions have been developed, based on the logical relationship between molar volumes and thermodynamics properties of slags, which both are structure- dependent.

3.1 Model Considerations

In the case of binary metallic systems, molar volumes are related to the relative affinities between the two component metal atoms. In Figure 3.1, this is shown for the system of Ag-Sn in liquid state. It is clearly seen that the composition linked to the highest negative enthalpies of mixing also corresponds to the highest volume contraction.

Figure 3.1-Relationsship between enthalpies of mixing and volume

contraction in the case of Ag-Sn liquid alloys26.

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Density Model

10

Further addition of Sn atoms, beyond the stoichiometric composition Ag2Sn, leads to repulsive interactions leading to positive enthalpies of mixing. A tendency towards this is as well indicated in volume contraction even though experimental values are not available. In an analogous manner for silicate melts, the attractive forces between the cations and anions are expected to be reflected in both the relative integral molar enthalpies of mixing and in the molar volumes. Since both these properties directly can be correlated to the bondings between the nearest and next-nearest neighbor ions in the system, it can be expected to have a direct correlation. By examining a number of binary silicate systems, a relationship between the two properties was arrived at27, presented in equation (3):

RTH

VxV M

iimi

M

λ=∑ ,

(3)

where is the relative integral molar volume and MV ∑ imiVx , represents the average molar volume. λ is a constant, MH the relative integral molar enthalpies for mixing, R the gas constant and T is the temperature. The enthalpies of mixing can be evaluated from ThermoSlag software® developed in the Division of Materials Process Science, KTH. The software is based on a thermodynamic model developed in the division by Björkvall et al.1, 2. The equations developed for the relative molar Gibbs energy of mixing, are presented below:

MG

( ) ( )∑ ∑ ∑

−=

Ω++= +

1,1

)(,),(ln 4

mi

OCCCjCiSiCiCi

M jiyyyTfyyRTpG (4)

where the interaction variables is defined as follows: )(, OCC jiΩ

( )( )

( )( ) .....2)(,6

)(,5

)(,4

)(,3

)(,2

)(,1

)(,

+−⋅Ω+Ω

+−⋅Ω+Ω+⋅Ω+Ω=Ω

CjCiOCCOCC

CjCiOCCOCCOCCOCCOCC

yyT

yyTTjiji

jijijijiji

(5)

and the ionic fraction of cation i within the cation grouping, yCi, as:

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Chapter 3

11

∑=

= m

jCj

CiCi

N

Ny

1

(6)

It should be mentioned that the following expression is valid for in equation (3), when

),( 4+SiyTf314 ≤+Siy :

0),( 4 =+SiyTf (7)

and when 314 ≥+Siy :

( 3*),( 4 SiSiSi yyAyTf −⋅=+ ) (8)

where 31* =Siy , ( )3* 1−Δ−= SiL yGA and LGΔ is the change of Gibbs energy for fusion of silica, [J/mol] 7.53T-35600=Δ LG .

From equation (4) and Gibbs-Helmholtz equation, the enthalpies of mixing, can be calculated by the following relationship:

( )[ ]( ) ( ) ⎥

⎥⎦

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛Ω

∂+

∂= ∑ ∑

−= +=

+

1,1 ,1

)(, /11

/, 4

mi mij

OCjCiCjCi

SiM TyyTT

TyTfH (9)

The relative integral molar volume, , can be estimated when combining equation (4) and (10). The relationship between , and molar volume of pure component i can be expressed as:

MVMV

∑−==i

imimME VxVVV , (10)

where EV is the excess molar volume, ix is the mole fraction and is the molar volume of the pure component i.

imV ,

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Density Model

12

Experimental density data can also be used to obtain for molten slags by the following equation:

mV

ρ

∑= i

ii

m

MxV (11)

The λ value may be evaluated for the binary systems, using experimental density data in literature. The values for λ and the interaction variables )(, OCC jiΩ used in the calculations are summarized in table I2, 28, 29.

Table 3.1−Binary λ values and interactions variables used in the calculations.

System Interaction variable )(, OCC jiΩ λ

Al2O3-CaO ( ) ( )2CaAlCaAl y-y44390-y-y6594.66125997- + [2] -0,061

Al2O3-FeO ( ) ( )2FeAlFeAl y-y0284.9y-yT11.686 - 7091.4- − ⋅ [2] 0,035

Al2O3-MgO ( )MgAl y-y30313.22-T4.30-7049.76- ⋅ [2] 0,04 Al2O3-MnO ( ) ( )2

MnAlMnAl y-y13408y-y13054.522165.1- ++ [2] 0,033

Al2O3-SiO2 ( ) ( )2SiAlSiAl y-y10811.9-y-y27248.210256.9- + [2] 0,029

CaO-FeO ( ) ( )2FeCaFeCa y-y5804.6y-y1081945175.2- ++ [2] 0,01

CaO-MgO 80961.3- [2] 0,042 CaO-MnO 2

MnCaMnCa )y-5804.6(y)y-10819(y45175.2- ++ [2] 0,053

CaO-SiO2( )

( ) ( )2SiCaSiCa y-y37739-y-y

T145.133414694-T113.356-42988.5- ⋅⋅++⋅ [2]

0,055

FeO-MgO 5173.66 [28] 0,056 FeO-MnO 0 [2] - FeO-SiO2 ( ) ( )22650410264 - 29830- SiFeSiFe yyyy − + − [29] 0,11 MgO-MnO 0 [2] - MgO-SiO2 ( ) ( )2

SiMgSiMg y-y28086.2-y-y79099.6-126521- [2] 0,057

MnO-SiO2( )

( )2SiMn

SiMn

y-y43013.3

y-y35278.3-T10.57489638.2- +⋅+ [2]

0,04

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Chapter 3

13

In the present model, the systems FeO-MnO and MgO-MnO are both approximated to behave as ideal solutions. Hence, the interactions between the Fe2+-Mn2+ and Mg2+-Mn2+ ions are not considered. As described earlier, the addition of metal oxides has a strong impact on the physical properties of silicate melts. The effect of cations on the structure is commonly related to the charge of the cations as well as the radius. Consequently, the molar volume is linked to the cation. It is common practice to use different approaches in order to estimate the effect of different cations. Normally used relationships are rz or 2rz where z is the valance and r the cation radius. In Figure 3.2, the difference in ratio between the cationic charge and square of average radius has been plotted as function of λ. The correlation is fairly good for most binaries and 2

rz shows a proportional trend to λ value. An exception, however, is the negative λ for the Al2O3-CaO system that shows a different behavior compared to the other binary systems.

-0,0800

-0,0600

-0,0400

-0,0200

0,0000

0,0200

0,0400

0,0600

0,0800

0,1000

0,1200

0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45 0,5 0,55 0,6

(1+ Δz)/ (average r)^2

λ

Figure 3.2−Ratio between difference in valance and average radius

as function of λ. The parameters of the corresponding binary subsystems have been used for the estimations of molar volumes in higher orders systems. The following relationship describes λ in ternary and higher order of slag systems:

.........

........

kjkjkiji

kj

kikjkiji

kiji

kjkiji

ji

yyyyyyyy

yyyyyyyy

yyyyyyyy

−−

⋅+⋅+⋅

+⋅+⋅+⋅

⋅+

⋅+⋅+⋅

⋅=

λ

λλλ (12)

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Density Model

14

3.2 Experimental Data

The density measurements available in literature are generally related to discrepancies. This is usually attributed to the experimental difficulties associated with the experimental techniques adopted. Various methods have been used to carry out density measurements and the experimental uncertainties associated with these methods are usually in the range of 2 %5. It should be pointed out that the diversity among different density measurements is larger and most commonly encountered in the case of FeO-containing slags. In FeO-containing slag systems, Fe exists as Fe2+, Fe3+ as well as free iron. The Fe distribution between these spices is evidently dependent on the oxygen potential and the temperature. This makes density measurement of FeO slags complicated, due to the difficulty controlling the composition of the melt. Consequently, most liquid FeO slags contains of a significant amount of Fe3+ ions. The presences of Fe3+ will generally decrease the density in systems containing FeO 30. The best approach to evaluate λ and to verify the model would be to use density data obtained from the same research group or at least the same measuring technique. However, this is not possible. The lack of experimental data is obvious in most systems, and usually the system has only been investigated in one or couple of studies, if it has been studied at all. Basically, one has to use the data available without regarding the measuring technique or the research group. Still, as expected, it was clearly seen that, whenever it was possible to evaluate the binary and ternary system with data form the same investigation, the model predictions correlated very well to the experimental data. The density data used to evaluate λ and to verify the model predictions have mainly been determined using the Archimedes method, maximum bubble pressure method and the sessile drop method. In the case of some systems, there have been widely different sets of experimental values reported. The choice of the value of λ was based on the compatibility of the value with ternary systems. All λ values are positive with the exception for the Al2O3-CaO system where λ has been evaluated to a negative value. No data at all has been obtained for binary or higher order systems containing both Al2O3 and MnO. This difficulty could be overcome by means of a correlation between λ and the ratio of cationic charge difference to square of average radius presented in the Figure 3.2. This relationship can be used to estimate the λ constant in the Al2O3-MnO system, which is one of the approximations in the model.

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Chapter 3

15

There have also been some difficulties in retrieving reliable density data of pure oxides from literature. Densities for pure molten Al2O3 and SiO2 have been investigated by Mitin and Nagibin31, and Bacon et al32, respectively. The data for the density of pure CaO, FeO, MgO, MnO at liquid state (supercooled) have not been found in literature. Molar volume for MgO and MnO had been estimated by Mills9. Molar volume for CaO and FeO has been estimated by extrapolation from binary system33.

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Density Model

16

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17

Chapter 4

EXPERIMENTAL WORK

4.1 Materials and Sample Preparation

The mould powders were decarburized by using a muffle furnace at 1073 K for 48 h. The decarburized powders were pre-melted in an induction furnace. A graphite crucible was heated to 1673 K and approximately 300 g of mould powder was added. The melting time was in range of 15-20 minutes to ensure a completely melted slag. The slag was poured in to an iron crucible and solidified. This was later used in the viscosity measurement. Alumina was added to four of the mould powders. The Al2O3 used was of 99.7 % purity supplied by Sigma Aldrich Chemie. The Al2O3 powder was thoroughly mixed with the mould powder before pre-melting. Argon gas was used both during the melting of the mould flux slag and subsequent solidification. The argon gas used during viscosity measurements and pre-melting was 99.998 % pure and supplied by AGA Gas (Stockholm, Sweden).

4.2 Apparatus

The viscosity measurements were carried out using the rotating cylinder method, with a Brookfield digital viscometer (Model RVDV-III, full-scale torque 7.187×10-4 Nm). The viscometer was rigidly mounted on a movable platform above the furnace so that it can be adjusted to be aligned to the crucible. A high temperature furnace system, supplied by Thermal Technology Inc (Laboratory Furnace Group 1000 series) with a maximum temperature limit of 2573 K was used and controlled by an Eurotherm (Model 818) controller as well as an optical pyrometer. The temperature was monitored by high temperature thermocouple, type B (Pt-30%Rh/Pt-6%Rh), during the experiments. The thermocouple was mounted just below the crucible. The experimental setup for viscosity measurements is shown in Figure 4.1.

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Experimental Work

18

Figure 4.1-Experimental setup for viscosity measurements.

To minimize the risk of crucible oxidation and sample contamination, a gas purifying system was connected to the experimental setup. As shown in Figure 4.2, the gas was passed through silica gel and Mg(ClO4)2 for removal of moisture. The CO2 content in the argon gas was lowered by passing the gas through a column of ascarite. Oxygen impurity in the argon gas was removed by using columns of copper turnings kept at 973 K and magnesium turnings at 773 K.

Figure 4.2-Illustration of the gas cleaning system connected to the furnace.

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Chapter 4

19

4.3 Procedure The crucible along with the pre-melted slag was placed in even temperature zone of the furnace. The spindle was then mounted on the iron transducer lowered into alumina tube. The crucible and spindle dimensions are shown in Table 4.1.

Table 4.1-Dimensions of iron crucible and spindles. Crucible (pure iron-Armco iron)

Internal diameter, mm 40 Inner depth, mm 95 Height, mm 103 Base thickness, mm 8 Wall thickness, mm 2

Spindle (pure iron-Armco iron) Bob diameter, mm 16 Length of bob, mm 27 Shaft diameter, mm 4 Length diameter, mm 54 Degree of taper 45

To avoid oxidation of iron components and contamination of the sample, the system was purged with argon gas for approximately one hour before starting the heating procedure. A heating rate of 5 K/min was employed during all the experiments and the gas flow was kept at 0.2 Nl/min. The furnace was heated up to 1673 K and left for one hour to completely melt the slag and stabilize the temperature. The spindle was then carefully lowered into the slag, the tip being kept about 2 cm above the crucible base and about 1 cm of the shaft immersed in the slag. Five rotation rates were used at each temperature for evaluation of the slag viscosity, in order to ensure that the molten slag showed a Newtonian behavior. The rotating speeds used in the measurement varied between 8 to 70 rpm. The equilibrium time for viscosity measurements at each speed was estimated to be 120 seconds. The temperature was kept constant for 30 minutes before each measurement. This was to assure that thermal equilibrium was established at each measuring point. Most of the measurements were carried out during cooling cycles, but some measurements were also performed during heating sequences in order to verify the reproducibility of the measurements. A second viscosity measurement with a new slag sample was also carried out for a couple of the slags, in order to confirm the reproducibility of the results. The viscometer was calibrated using mineral oil standards with viscosities of 0.097 and 0.057 Pa s at 298 K.

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Experimental Work

20

In view of the possibility of the fluorine volatilization during the experiments, samples were taken at two different stages of the experimental sequence, viz. after premelting as well as after the viscosity measurements. Special consideration was also taken in order to ascertain that the slags were homogenous and there were no concentration gradients along the height of the crucible. Three samples from the solidified slag mass after furnace cooling were chemically analyzed viz. one sample 1 cm below the surface, one in the middle, and one 1 cm above the bottom of the crucible. The oxide contents were analyzed using X-ray fluorescence spectroscopy and the fluorine contents by electrode spectrometry after dissolving in NaOH solution.

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21

Chapter 5

RESULT AND DISCUSSION

5.1 Density Model Applications

Model calculations were carried out for the binary, ternary and higher order systems and the results were compared with experimental data, Figure 5.1-5.28. The model is applied successfully in the case of the most systems, with deviation within the experimental uncertainties related to density measurements

5.1.1 Binary Systems

The Al2O3-SiO2 system is one of the most successful descriptions of the molar volumes by the model. In Figure 5.1, the comparison between experimental results of Askay and Pask34 and the model prediction is presented. As seen, the experimental data is very well fitted by the model.

0,3 0,4 0,5 0,6 0,7 0,828,5

29,0

29,5

30,0

30,5

31,0

31,5

32,0

2223K Askay and Pask /36/ Calculated

V m c

m3 /m

ol

yAl

Figure 5.1−Comparison of calculated and measured molar

volume values for the Al2O3-SiO2 system.

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Result and Discussion

22

Another system than can describe the experimental data very well is the binary MnO-SiO2. The model calculations correspond well with the experimental values reported by Segers et al24 as shown in Figure 5.2.

0,35 0,40 0,45 0,5018,0

18,5

19,0

19,5

20,0

20,5

1673K Segers et al. /35/ Calculated

V m c

m3 /m

ol

ySi

Figure 5.2−Comparison of calculated and measured molar

volume values for the MnO-SiO2 system. As mentioned earlier, measurements of FeO containing system are complicated and there is a large diversity in the experimental density data available in literature. This is obvious in the FeO-SiO2 system, which is one of the most important systems in ferrous as well as non-ferrous metal processing. In Figure 5.3, the experimental data used in the evaluation of λ are presented along with the predicted densities36-41.

0,10 0,15 0,20 0,25 0,30 0,35 0,4015,5

16,0

16,5

17,0

17,5

18,0

18,5

19,0

19,5

20,0

1673K Various references

/36-41/ Calculated

V m c

m3 /m

ol

ySi

Figure 5.3−Comparison of calculated and measured molar

volume values for the FeO-SiO2 system.

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Chapter 5

23

In the MgO-SiO2 system is only one reference available in literature, Tomlinson et al42. The model predictions correspond well with the experimental values. In Figure 5.4, the calculated values are presented along with density data measured at different temperatures.

0,40 0,45 0,50 0,5519,0

19,5

20,0

20,5

21,0

21,5

22,0 1973K Tomlinson et al. /42/ 2073K Tomlinson et al. /42/ 2173K Tomlinson et al. /42/

1973K calculated 2073K calculated 2173K calculated

V m c

m3 /m

ol

yMg

Figure 5.4−Comparison of calculated and measured molar volume values for the MgO-SiO2 system.

In the Al2O3-MgO system, Figure 5.5, the calculations are in agreement with experimental data for high contents of alumina. Noticeable, however, is the deviation with lower contents. Unfortunately, in this system, just one experimental measurement of the molar volume has been reported at only one temperature, viz. 2523 K43.

0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,914

16

18

20

22

24

26

28

30

32

342523K

Elyutin et al. /43/ Calculated

V m c

m3 /m

ol

yAl

Figure 5.5−Comparison of calculated and measured molar

volume values for the Al2O3-MgO system.

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Result and Discussion

24

It should be pointed out that the phase diagram for Al2O3-MgO system with a composition above 60 mass % MgO and a temperature of 2523 K represents a two phase region44. The presence of a solid phase can explain the relatively large difference between model and density data in this area, considering that the phase diagram is accurate. Calcium oxide containing systems show marked deviations between the experimental data and model calculations. Great efforts were made to extract the molar volume values of CaO in super-cooled liquid state; but it is realized that these may not be very reliable. However, greater emphasis was taken in account towards establishing compatibility with the higher order systems. It is realized that this choice could have a serious impact on the choice of the value of λ, and consequently affect the evaluation of the densities in the case of binary systems. The model estimation is satisfactory in binary CaO-FeO system is presented in Figure 5.6. The model estimation of the molar volume is only than slightly deviating from experimental data37, 45 at compositions with higher CaO contents.

0,050,100,150,200,250,300,350,400,4515,5

16,0

16,5

17,0

17,5

18,0

18,5

19,0

1673K Ogino et al. /37/ 1773K Sumita et al. /45/ 1673K calculated 1773K calculated

V m c

m3 /m

ol

yCa

Figure 5.6−Comparison of calculated and measured molar

volume values for the CaO-FeO system. The agreement is less satisfactory between model and the experimental data in the case of the Al2O3-CaO and CaO-SiO2 systems. The diversity in the predictions are within +/- 5 % for Al2O3-CaO and within +/- 10 % CaO-SiO2 systems from the experimental data. However, the model predictions in the Al2O3-CaO system are much better than the prediction using an ideal mixture approach. Even in the case of the CaO-SiO2 system, model estimations are slightly better.

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Chapter 5

25

In Figure 5.7, the model estimation of the molar volume for the Al2O3-CaO system is compared with the experimental data from two studies46, 47. The model is reasonably well correlating to the data from Evsev et al and Dymov et al. A number of other experimental measurements have been carried out in this system32,

48-50, and they all exhibit a positive deviation from ideal behavior. Noticeable, uncertainties are reported in the thermodynamic evaluation by Björkvall2 in case of this system. This uncertainty is expected to be carried over to the model prediction in the present work. Accordingly, the diversity in the Al2O3-CaO system can be attributed to the experimental studies of both thermodynamic activities as well as densities.

0,40 0,45 0,50 0,55 0,60 0,6523

24

25

26

27

28

29

301873K

Evsev et al. /46/ Dymov et al. /47/ Calculated Ideal solution

V m c

m3 /m

ol

yAl

Figure 5.7-Comparison of calculated and measured molar

volume values for the Al2O3-CaO system. In the case of CaO-SiO2 system, one most common metallurgical slag, several experimental studies have been carried out, at temperatures between 1773K and 1973K and mole fractions of silicate in the range of 0.35-0.65 39, 41, 50-55, 6, 28, 31, 40-43. Large deviations are shown in the model estimations compared to reported density measurements, taking into account most references as presented in Figure 5.8. The reason for this deviation is not clear; but as mentioned earlier, it can be attributed to the estimation of the molar volume of super-cooled CaO. This might have a stronger impact in this system that consists of a strongly acidic and a strongly basic component. However, it should be noted the λ parameter chosen in this work enables the prediction of the molar volumes of ternary and higher order systems accurately.

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Result and Discussion

26

0,35 0,40 0,45 0,50 0,55 0,60 0,6519

20

21

22

23

24

25

26

27

28

(3)(2)(1)

V m c

m3 /m

ol

yCa

Figure 5.8−Comparison of calculated and measured molar volume values

for the CaO-SiO2 system.

5.1.2 Ternary Systems System Al2O3-CaO-MgO A couple of experimental studies have been reported in the Al2O3-CaO-MgO system for MgO contents above 5 mass %, Zielinski et al50and Bochorsihvili et al56. The experimental results of Bochorsihvili et al could be fitted very well using the present model for MgO contents above 10 mass %, as shown in Figure 5.9.

0,350 0,375 0,400 0,42520,5

21,0

21,5

22,0

22,51823K

Zielinski et al. /50/ Bochorishvili et al. /56/ Calculated Ideal solution

V m c

m3 /m

ol

yCa

Figure 5.9-Comparison of calculated and measured molar volume values for the

Al2O3-CaO-MgO system for a constant MgO content of 20 mass-%.

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Chapter 5

27

The deviation of the results of Zielinski et al is about 3 %. The deviation between experimental data and model predictions for slags containing 10 mass % MgO or less is for both references in the range of 2-3 %. System Al2O3-CaO-SiO2

Several researchers have carried out density measurement in the Al2O3-CaO-SiO2 ternary system50, 56-64, which is of importance in various high temperature processes. This is one of the most widely studied slag systems and the most thorough experimental work has been performed by Winterhager et al. In the figures 5.10-5.12, has the model also been compared to the results of Barett et al and Krinochkin et al. and the correlation between the predicted values and experimental results is found to be agreeable. In particular, the trend of the model estimation follows the experimental results, as can be seen in figure 5.10-5.11. The major part of experimental data and model predictions are within maximum 3 %, typically much less, considering all the density data available in literature. Figure 5.12 shows estimation of the model at higher temperatures and at higher contents of Al2O3. However, the model predictions are less satisfactory in the area of slags containing silica above 50 mass % and alumina below 5 mass %. The deviations from the experimental data are somewhat higher in this region, illustrated in figure 5.11, where the deviations increases with decreasing alumina content for a slag of 50 mass % CaO. This tendency could be anticipated to some extent, considering the poor agreement between molar volume data and model calculations in the case high contents of silica in the binary CaO-SiO2 system.

0,4 0,5 0,6

23

24

25

26

27 1823K Winterhager et al. /57/ Barett et al. /58/ Calculated Ideal solution

V m c

m3 /m

ol

ySi

Figure 5.10-Comparison of calculated and measured molar volume values for the

Al2O3-CaO-SiO2 system for a constant Al2O3 content of 10 mass-%.

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Result and Discussion

28

0,25 0,30 0,35 0,40 0,4522,5

23,0

23,5

24,0

24,5

1823K Winterhager et al. /57/ Calculated Ideal solution

V m c

m3 /m

ol

ySi

Figure 5.11-Comparison of calculated and measured molar volume values for the

Al2O3-CaO-SiO2 system for a constant CaO content of 50 mass-%.

0,075 0,100 0,125 0,150 0,175 0,200 0,22524,5

25,0

25,5

26,0

26,5

27,01873K

Krinochkin et al. /59/ Calculated Ideal solution

V m c

m3 /m

ol

ySi

Figure 5.12-Comparison of calculated and measured molar volume values for the

Al2O3-CaO-SiO2 system for a constant CaO content of 42 mass-%.

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Chapter 5

29

System CaO-FeO-SiO2

Several studies have been carried out in order to evaluate the density in this system51, 65-72, considering the fact that this system is of great importance for almost all metallurgical processes. The calculations of molar volume correlate well with the most of the experimental data. In figures 5.13 and 5.14, the model predictions are compared with the results of Lee and Gaskell at different temperatures.

0,050,100,150,200,250,300,350,400,4520,0

20,5

21,0

21,5

22,0

22,5

23,0

23,5

24,0

1673K Lee and Gaskell /51/ Calculated Ideal solution

V m c

m3 /m

ol

yCa

Figure 5.13-Comparison of calculated and measured molar volume values for the

CaO-FeO-SiO2 system for a constant SiO2 content of 44 mole-%.

0,05 0,1018,5

19,0

19,5

20,0

20,51773K

Lee and Gaskell /65/ Calculated Ideal solution

V m c

m3 /m

ol

yCa

Figure 5.14-Comparison of calculated and measured molar volume values for the

CaO-FeO-SiO2 system for a constant SiO2 content of 30 mass-%.

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Result and Discussion

30

System CaO-MgO-SiO2

The CaO-MgO-SiO2 ternary is another system that can be very well described by the model, illustrated in Figure 5.15 and 5.16. Three references61, 73, 74 have been reported for this system and the density values are in agreement with each other. The model predictions are in line with the experimental data with the maximum deviation being about 3 % at the extreme CaO end. The later can be explained by the poor model correlation in the binary CaO-SiO2, in that composition area, as mentioned earlier.

0,35 0,40 0,45 0,50 0,5520,0

20,5

21,0

21,5

22,0

22,5

23,0

23,5

24,0

1773K Staronka et al. /74/ Calculated

Ideal solution

V m c

m3 /m

ole

yCa

Figure 5.15-Comparison of calculated and measured molar volume values for the

CaO-MgO-SiO2 system for a constant SiO2 content of 44 mass-%.

0,36 0,38 0,40 0,42 0,4420,0

20,5

21,0

21,5

22,0

22,5

23,0

(1)(2)(3)

V m c

m3 /m

ol

ySi

Figure 5.16-Comparison of calculated and measured molar volume values for the

CaO-MgO-SiO2 system for a constant CaO content of 39.6 mole-%.

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Chapter 5

31

System CaO-MnO-SiO2

The investigations of both Segers et al35 and Kekeiidze et al75 and were used to compare the molar volume estimation by the model in the CaO-MnO-SiO2, as presented in Figures 5.17 and 5.18. In this case, the diversity between the two references is significant. The model predictions are very well fitted with the measured densities by Segers et al and less-satisfactorily with the data obtained from Kekeiidze et al. It is to be pointed out that the experimental data by Segers et al was also used to determine the λ constant in the binary sub system MnO-SiO2, which, to some extent can explain the agreement with the predictions.

0,1 0,2 0,3 0,418,5

19,0

19,5

20,0

20,5

21,0

21,5

22,0

22,5

23,0

1773K Segers et al. /35/ Calculated Ideal solution

V m c

m3 /m

ol

yCa

Figure 5.17-Comparison of calculated and measured molar volume values for the

CaO-MnO-SiO2 system for a constant SiO2 content of 45 mole-%.

0,1 0,2 0,3 0,4 0,519,5

20,0

20,5

21,0

21,5

22,0

22,5

23,0

1773K Kekeiidze et al. /75/ Calculated Ideal solution

V m c

m3 /m

ol

yCa

Figure 5.18-Comparison of calculated and measured molar volume values for the

CaO-MnO-SiO2 system for a constant SiO2 content of 40 mass-%.

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Result and Discussion

32

System FeO-MgO-SiO2

A couple of experimental studies76, 77 of the densities have been carried out in the FeO-MgO-SiO2 system. As seen in Figure 5.19 and 5.20, the model fits well to density data by Bryantsev et al. The deviation in the system is lower then 3 % for all the density data obtained, but generally much less. Even the model correlation to the other experimental measurement, with lesser amounts of MgO was found to be satisfactory.

0,15 0,20 0,25 0,30 0,3518,5

19,0

19,5

20,0

20,5

21,0

21,5

22,0

22,5

1723K Bryantsev et al. /76/ Calculated Ideal solution

V m c

m3 /m

ol

yFe

Figure 5.19-Comparison of calculated and measured molar volume values for the

FeO-MgO-SiO2 system for a constant SiO2 content of 55 mass-%.

0,30 0,35 0,40 0,45 0,5017,0

17,5

18,0

18,5

19,0

19,5

20,0

20,5

21,0

21,5

22,01723K

Bryantsev et al. /76/ Calculated Ideal solution

V m c

m3 /m

ol

ySi

Figure 5.20-Comparison of calculated and measured molar volume values for the

FeO-MgO-SiO2 system for a constant MgO content of 25 mass-%.

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Chapter 5

33

System FeO-MnO-SiO2

Several measurements of densities in the FeO-MnO-SiO2 system37, 39, 68, 69 have been published. Two of these experimental results have been presented along with the model calculations in Figure 5.21 and 5.22. The model estimates lower respectively higher volumes compared to the Gaskell et al. and Solokov et al., the divergence being of the order of 5 to 6 %. These deviations are in the same range as for the results both /37/ and /68/.

0,2 0,3 0,4 0,5 0,6 0,718,0

18,5

19,0

19,5

1773K Gaskell et al. /69/

Calculated Ideal solution

V m c

m3 /m

ol

yFe

Figure 5.21-Comparison of calculated and measured molar volume values for the

FeO-MnO-SiO2 system for a constant SiO2 content of 25 mass-%.

0,2 0,3 0,4 0,5 0,617,0

17,5

18,0

18,5

19,0

19,5

20,0

20,51773K

Solokov et al. /39/ Calculated Ideal solution

V m c

m3 /m

ol

yFe

Figure 5.22-Comparison of calculated and measured molar volume values for the

FeO-MnO-SiO2 system for a constant SiO2 content of 32 mass-%.

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Result and Discussion

34

System Al2O3-FeO-SiO2

Five experimental studies have been reported in literature for the Al2O3-FeO-SiO2 system. Still, the data are limited to a few measuring points and narrow composition ranges, with FeO amounts over 60 mass % and small additions of Al2O3 67, 78-81. The model shows large deviations from the reported density data, in particular for small contents of silica. In figure 5.23, the model compared to Fadeev et al. As discussed earlier, experiments in slag systems containing FeO is complicated and associated with difficulties. This should especially be the case for large amounts of FeO and the references above contain at least 60 mass % of iron oxide. The presence of Fe3+ in the slag could be the reason to the deviation compared to the model.

0,15 0,20 0,2516,0

16,5

17,0

17,5

18,0

18,5

19,0

1573K Fadeev et al. /79/ Calculated Ideal solutionV m

cm

3 /mol

ySi

Figure 5.23-Comparison of calculated and measured molar volume values for the

Al2O3-FeO-SiO2 system for a constant FeO content of 75 mass-%.

5.1.3 Quaternary Systems The lack of experimental data is noticeable regarding quaternary systems. Only very few density measurements have been undertaken in the case of quaternary and higher order systems. Nevertheless, the model predictions are considered satisfactory for most systems.

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Chapter 5

35

System Al2O3-CaO-MgO-SiO2 In the Al2O3-CaO-MgO-SiO2 system, four references are available in literature57, 74,

82, 83. The results of Winterhager et al could be fitted very well with the model, especially for Al2O3 contents above 5 mass %, as shown in Figure 5.24. The model at 5 mass % Al2O3 and below are also well estimated. In Figure 5.25, the data at higher temperature by Komelkov et al are compared with the model with satisfactory results. The correlation between the other investigations and the model is less satisfactory, even though the trends are very well predicted, as illustrated in figure 5.26.

0,30 0,35 0,40 0,4522,0

22,5

23,0

23,5

24,0

24,5

1773K Winterhager et al /57/

Calculated Ideal solution

V m c

m3 /m

ole

ySi

Figure 5.24-Comparison of calculated and measured molar volume values for the

Al2O3-CaO-MgO-SiO2 system for a constant CaO and MgO content of 31.5 respectively 9.4 mass-%.

0,10 0,1521,5

22,0

22,5

23,01923K

Komelkov et al /82/ Calculated Ideal solution

V m c

m3 /m

ole

ySi

Figure 5.25-Comparison of calculated and measured molar volume values for the

Al2O3-CaO-MgO-SiO2 system for a constant CaO and MgO content of 55 respectively 10 mass-%.

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Result and Discussion

36

0,30 0,35 0,40 0,45 0,50 0,5519,0

19,5

20,0

20,5

21,0

21,5

22,0

22,5

23,0

23,5

24,0

24,51773K

Dzhincharadze et al /83/ Calculated

Ideal solutionV m

cm

3 /mol

e

ySi

Figure 5.26-Comparison of calculated and measured molar volume values for the

Al2O3-CaO-MgO-SiO2 system for a constant Al2O3 and MgO content of 10 respectively 15 mass-%.

System Al2O3-FeO-MgO-SiO2

In the case of the Al2O3-FeO-MgO-SiO2 system, one experimental study of the density is reported in literature76,. As seen in Figure 5.27, the density data of Bryatsev et al was very well estimated by the model. The maximum deviation is lower then 3 % for all the measuring points.

0,02 0,04 0,06 0,08 0,10 0,1218,5

19,0

19,5

20,0

20,5

21,0

21,5

22,0

1773K Bryantsev et al /76/ Calculated Ideal solution

V m c

m3 /m

ole

ySi

Figure 5.27-Comparison of calculated and measured molar volume values for the

Al2O3-FeO-MgO-SiO2 system for a base slag containing 30 FeO , 20 MgO and 50 SiO2 (mass %).

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Chapter 5

37

System CaO-FeO-MgO-SiO2

The same research group as for the previous system has also evaluated the densities in the CaO-FeO-MgO-SiO2 system76. Figure 5.28 shows a fairly good correlation between the model and the experimental data, with a deviation less then 4 %.

0,00 0,02 0,04 0,06 0,0818,0

18,5

19,0

19,5

20,0

20,5

21,0

21,5

22,0

1723K Bryantsev et al /76/ Calculated Ideal solution

V m c

m3 /m

ole

yCa

Figure 5.28-Comparison of calculated and measured molar volume values for the

CaO-FeO-MgO-SiO2 system for a base slag containing 30 FeO, 20 MgO and 50 SiO2 (mass %).

Other quaternary systems In the Al2O3-CaO-FexO-SiO2 system have three density measurements been carried out in two studies84, 85, all containing low quantities of Fe2O3. The molar volume predictions are satisfying for low contents of CaO, but show a large deviation at higher amounts of CaO. It should noted that the slag for higher amounts of CaO consists of 0.82 mass % of Fe2O3, which is considered rather high. The presence of Fe2O3 is not considered in the model and can be the reason to this diversity. The situation is similar in the case of the measured density by Nelson et al. Their slag has the same amount of Fe2O3 content in the slag and the model shows a lower molar volume compared to the measured results. But the deviation in this case is much lower. The results of Kekiidze et al75 is the only study found in literature concerning density measurements in Al2O3-CaO-MnO-SiO2 system. The model predictions compared to the experimental results of Kekiidze et al show less satisfactory agreement. As mentioned earlier, the λ constant was evaluated considering the results of Segers et al in both the binary system of MnO-SiO2 and the ternary CaO-MnO-SiO2 system. The model agreement to the experimental work by Kekiidze et

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Result and Discussion

38

al in this ternary system was not considered in the λ evaluation. As a result of this, it was expected that the agreement with the results of Kekiidze et al.would be poor. The lack of experimental data makes it difficult to compare the model in the CaO-FexO-MnO-SiO2 system. Only one slag composition has been experimentally evaluated in the system and this value is not in agreement with the model predictions39.

5.1.4 Industrial Applications The advantage of the present model in industrial applications is illustrated by utilizing the model to estimate the molar volumes of six-component slags, corresponding to the various slags in iron and steel making. The composition of industrial slags widely varied depending on the processes. Some typical slag compositions relevant to the Swedish steel industries are presented in Table 2, blast furnace (BF), electric arc furnace (EAF) and ladel furnace (LF). The present model was used for predictions of the densities and molar volumes of these slags, also presented in Table 5.1. Table 5.1-Some typical slag compositions of (BF), (EAF)

and (LF) processes used in Sweden, along with predicted density and molar volume.

Oxide wt-% BF EAF LF Al2O3 13 10 33.5 CaO 32 40 53.5 FeO 2 15 0.6 MgO 17 9 6 MnO 2 5 0.4 SiO2 34 21 6 density 1873 K [g/cm3] 2.70 2.98 2.67 molar volum 1873 K [cm3/mol] 21.2 20.2 24.2

In some blast furnace practices, high alumina contents are encountered. This has been considered as detrimental to process economy due to higher energy requirements. This extra energy requirement could be due to the higher liquidus temperatures of these slags. Furthermore, if there is an increase in the slag volume due to increased alumina contents, higher energy may be required to heat the larger volume of the slag. The present model can be used to estimate the slag volumes as

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Chapter 5

39

functions of composition and temperature with relative ease, while experimental measurements of molar volumes of industrial slags often are cumbersome.. In Figure 5.29, the change of molar volume of the blast furnace slag corresponding to Table 5.1, but with varying alumina contents in the range 6 – 20 wt % alumina, as estimated by the presented model. To the knowledge of the authors, there are no experimental data available on the molar volumes of these slags. It is obviously seen that alumina addition to the blast furnace slag increases the molar volume of the slag by 4 % in this range. This will necessitate increase in the energy input, calculated per unit volume. Thus, the present model can be beneficially used to modify slag volumes enabling optimization of energy and environmental aspects of iron and steel making processes.

6 8 10 12 14 16 18 2020,50

20,75

21,00

21,25

21,50

21,75

22,00

1873 K Calaculated

V mcm

3 /mol

wt-% Al2O3

Figure 5.29-Calculated molar volume values for blast furnace slag.

5.2 Viscosity Measurements Viscosity measurements were carried out in the case of seven proprietary mould flux slags used in different Swedish steel industries. The analyses of these fluxes provided by the suppliers are presented in Table 5.2. The listed values are averages of the maximum and minimum compositions guaranteed by the supplier. Alumina was added to two of these fluxes, viz. slags A and D, Al2O3 and the corresponding viscosities were measured. The chemical analysis of the premelted slags and the samples taken at different levels in the crucible post measurement are presented in Table 5.3. The weight loss of the samples during the experiments was in the range of 0.1 to 0.5 %. Sample preparation considering decarburization and premelting, was not related to any noticeable change in chemical composition, apart from the carbon

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Result and Discussion

40

loss. This confirmed by a comparison between supplier’s analyses and the analyses after premelting. In the present study, special attention was taken to the vapor loss of fluoride. The chemical analyses, in Table 5.3, show that the change in the fluorine contents in the pre- and post measurement samples was negligible. This is further supported by the small weight loss during the measurements, mentioned above. The samples could securely be considered as homogenous as the chemical analyses of the samples taken at various levels showed negligible differences.

Table 5.2-Mould Flux composition provided by supplier, wt-%. Slag A Slag B Slag C Slag D Slag E Slag F Slag G SiO2 wt-% 28.8 35.6 32.3 34.2 32.1 23.7 25.5 CaO 36.5 40.3 29.4 27.3 32.7 22.7 MgO 1.3

38.5 2-3 1.01 1.9 0.47 0.97

Al2O3 6.5 8.8 3.25 3.92 5.0 7.4 12 TiO2 0.3 - - 0.1 < 0.4 0.34 0.46 Fe2O3 0.8 16.5 0-1 1.09 < 1.5 1.98 2.86 MnO 3.3 < 0.2 0 0.05 < 0.3 6.25 0.04 Na2O 7.2 12.8 11.5 7.53 2.62 K2O 0.1

5.3 5.5 0.37 < 0.9 0.14 1.43

LiO2 0 0 0 0 0 0 0 CaF2 F 5.9 9.3 7.5 7.95 9.3 6.48 4.42 CFree 1.5 < 1.0 4.3 3.6 4.5 4.0 17.7 CO2 8.8 3.0 - 7.9 7.9 9.9 9.4 C total - < 1.5 6 5.74 - - 20.3 Basicity (CaO/ SiO2) 1.27 1.12 1.25 0.89 0.85 1.38 0.93 Basicity (CaO+MgO/ SiO2+Al2O3)

1.07 0.87 1.20 0.80 0.82 1.07 0.63

Viscosity 1300ºC, Poise 1.1 1.5 0.96 1.1 0.9 - 13.5 Viscosity 1400ºC, Poise - 0.9 0.6 - 0.6 0.8 -

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Chapter 5

41

Table 5.3-Mould Flux composition obtained in the present work, wt-%. Slag Condition SiO2 CaO MgO Al2O3 TiO2 FeO MnO P2O5 N2O K2O Cr2O3 V2O5 C S F

As premelted 31.9 41.2 1.5 7.1 0.38 0.8 3.69 0.05 6.75 0.21 <0.02 <0.02 0.04 0.11 7.10 Top part 30.5 39.5 1.5 6.8 0.37 4.67 3.45 0.05 6.40 0.20 <0.02 <0.02 0.03 0.10 7.00 Middle part 30.6 39.8 1.5 6.8 0.36 4.57 3.48 0.05 6.36 0.20 <0.02 <0.02 0.02 0.11 6.90

Slag A

Bottom part 30.5 39.4 1.4 6.8 0.36 4.97 3.40 0.05 6.29 0.21 <0.02 <0.02 0.02 0.11 6.95

As premelted 31.0 40.4 1.5 9.3 0.37 0.8 3.51 0.05 6.63 0.20 <0.02 <0.02 0.05 0.11 7.05 Top part 30.8 39.8 1.5 9.3 0.37 1.57 3.42 0.06 6.54 0.21 <0.02 <0.02 0.04 0.10 7.00 Middle part 30.8 39.9 1.5 9.3 0.36 1.55 3.43 0.05 6.57 0.22 <0.02 <0.02 0.02 0.11 7.10

Slag A + wt-%

2.5 Al2O3

Bottom part 31.0 40.0 1.5 9.3 0.37 1.55 3.45 0.06 6.52 0.21 <0.02 <0.02 0.02 0.10 7.65

As premelted 32.0 38.0 1.4 11.4 0.36 0.76 3.29 0.05 6.23 0.23 <0.02 <0.02 0.04 0.12 6.80 Top part 29.9 37.7 1.4 11.0 0.35 1..4 3.25 0.05 6.13 0.22 <0.02 <0.02 0.02 0.10 6.85 Middle part 30.4 39.1 1.5 11.4 0.36 1.50 3.39 0.05 6.39 0.22 <0.02 <0.02 <0.01 0.11 6.75

Slag A + wt-%

5.0 Al2O3

Bottom part 31.8 38.1 1.4 11.5 0.35 1.47 3.30 0.05 6.18 0.23 <0.02 <0.02 <0.01 0.10 6.90

As premelted 37.5 31.3 0.2 2.4 0.04 12.9 0.13 0.13 6.52 0.16 <0.02 <0.02 0.01 0.03 9.30 Top part 36.8 30.6 0.2 2.4 0.03 15.5 0.14 0.14 6.30 0.15 <0.02 <0.02 0.02 0.03 9.20 Middle part 36.3 30.1 0.2 2.3 0.03 15.3 0.13 0.13 6.18 0.15 0.02 <0.02 0.02 0.03 9.25

Slag B

Bottom part 37.0 30.4 0.2 2.4 0.03 15.5 0.14 0.14 6.37 0.15 <0.02 <0.02 0.02 0.03 8.85

As premelted 35.8 44.7 2.9 4.2 0.05 0.76 <0.10 0.02 4.64 0.21 <0.02 <0.02 0.02 0.05 9.60 Top part 35.8 44.8 2.9 4.2 0.05 0.90 0.10 <0.01 4.58 0.21 <0.02 <0.02 0.01 0.04 9.80 Middle part 35.9 45.0 2.9 4.2 0.05 0.91 <0.10 <0.01 4.55 0.21 <0.02 <0.02 0.01 0.04 9.60

Slag C

Bottom part 35.7 44.7 2.9 4.2 0.05 0.90 0.10 <0.01 4.58 0.21 <0.02 <0.02 0.02 0.04 9.50

As premelted 40.0 35.0 0.8 4.3 0.8 1.09 0.04 0.08 11.65 0.51 0.01 <0.01 0.03 0.07 7.80 Top part 39.1 34.4 0.8 4.2 0.8 3.74 <0.10 0.05 10.73 0.41 <0.02 <0.02 0.01 0.06 7.70 Middle part 39.1 34.4 0.8 4.2 0.8 3.69 <0.10 0.05 10.65 0.42 0.02 <0.02 0.02 0.06 7.70

Slag D

Bottom part 39.3 34.3 0.8 4.2 0.8 3.74 <0.10 0.05 10.77 0.41 <0.02 <0.02 0.02 0.06 7.60

As premelted 38.8 33.9 0.7 6.4 0.12 1.01 0.10 0.08 11.23 0.50 <0.02 <0.02 0.03 0.07 8.30 Top part 38.5 34.3 0.8 6.4 0.12 1.35 0.11 0.06 11.14 0.47 <0.02 <0.02 0.01 0.07 8.15 Middle part 38.6 34.3 0.8 6.4 0.13 1.35 0.11 0.05 11.06 0.48 <0.02 <0.02 0.01 0.06 8.05

Slag D + wt-%

2.5 Al2O3

Bottom part 38.4 34.3 0.8 6.4 0.12 1.35 0.11 0.05 11.07 0.47 <0.02 <0.02 0.01 0.07 8.10

As premelted 38.1 33.6 0.7 8.5 0.12 1.01 <0.10 0.08 11.01 0.49 <0.02 <0.02 0.02 0.06 8.85 Top part 37.2 33.4 0.7 8.4 0.12 1.26 <0.10 0.06 10.70 0.48 <0.02 <0.02 0.03 0.07 8.85 Middle part 37.5 32.8 0.7 8.4 0.12 1.24 <0.10 0.06 10.58 0.48 <0.02 <0.02 0.01 0.07 8.70

Slag D + wt-%

5.0 Al2O3

Bottom part 37.1 33.3 0.8 8.4 0.12 1.24 <0.10 0.06 10.64 0.48 <0.02 <0.02 <0.01 0.07 8.70

As premelted 39.0 32.8 2.2 5.9 0.13 1.18 0.18 0.06 10.74 0.38 <0.02 <0.02 0.34 0.05 10.05 Top part 38.5 31.9 2.2 6.5 0.14 1.85 0.59 0.05 11.15 0.45 <0.02 <0.02 0.02 0.05 9.70 Middle part 37.9 31.8 2.1 6.4 0.13 1.84 0.60 0.05 11.17 0.44 <0.02 <0.02 0.01 0.05 9.50

Slag E

Bottom part 38.1 31.9 2.1 6.5 0.13 1.86 0.60 0.05 11.20 0.44 <0.02 <0.02 0.01 0.05 9.70

As premelted 27.7 39.6 0.6 8.7 0.44 1.20 7.99 0.08 7.34 0.25 <0.02 <0.02 0.04 0.08 7.70 Top part 27.7 39.3 0.6 8.7 0.43 1.81 8.09 0.09 6.91 0.24 0.01 <0.01 0.03 0.07 7.60 Middle part 27.5 39.5 0.6 8.7 0.43 1.77 7.98 0.08 6.93 0.23 <0.02 <0.02 0.04 0.07 7.35

Slag F

Bottom part 27.6 39.6 0.6 8.6 0.43 1.77 7.98 0.09 6.75 0.23 <0.02 <0.02 0.05 0.07 7.75

As premelted 35.9 32.1 1.2 16.0 0.79 3.66 0.10 0.31 2.91 1.73 0.02 0.02 0.03 0.19 6.30 Top part 34.7 30.8 1.1 15.4 0.76 7.18 <0.10 0.26 2.78 1.62 0.03 0.03 0.02 0.18 6.00 Middle part 34.7 30.7 1.2 15.4 0.76 7.36 <0.10 0.26 2.73 1.61 0.03 0.03 <0.01 0.20 6.00

Slag G

Bottom part 34.3 30.6 1.1 15.3 0.76 7.94 <0.10 0.28 2.80 1.67 0.03 0.02 0.02 0.21 6.25

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Result and Discussion

42

The results in Table 5.3 show a small increase of FeO content in the slag during eight of the measurements. This is thought to be contributed by iron components. It should also be noted, a relatively large increase was apparent in three of the experiment. The cause of this is uncertain, since all the experiments were conducted under identical conditions. The crucibles were examined in all the cases after the measurements and no distinctive sign of oxidation was observed on the crucible walls. The possibility of the solubility of metallic iron in the molten slag was considered in the present work. In view of the presence of iron only in the case of specific slag compositions, there is a possibility that the solubility of iron could be higher in the case of these compositions. Further work is being carried out in this regard. The results of the viscosity measurements are presented in Table 5.4. The viscosity data in this table are the average values obtained from the results obtained using five different rotation speeds. The deviation of the experimental data from the mean value is less then one percent for all of the measurements. The slags can safely be considered to behave as Newtonian fluids in the measured temperature range. The lower temperature limit for measurements is determined by the appearance of the two-phase region as marked by the drastic increase in the viscosity values. This temperature limit is almost the same for all of the mould fluxes in the range of 1300 to 1320 K except in the case of slag G, for which the lower temperature limit was around 1400 K. The upper temperature for the measurements was restricted by the use of iron components. Repetition of the viscosity measurements of the slag A and E, showed a maximum deviation of three percent and of generally less. Considering experimental uncertainties associated with viscosity measurements, is the deviation relatively small. It should also be mentioned that the second measurements in the case of the two slags were carried out with new slag samples and new crucibles. These samples repetition experiments were not chemically analyzed. The deviations are in the case of most slags large between measured viscosities and the supplier’s viscosity data. The supplier’s viscosity data are generally not measured, just estimated by the Riboud’s formula86, at one or several fixed temperature, which is only able to predict the slag viscosities approximately. No measured information is given on the viscosity temperature dependency or crystallization temperature.

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Chapter 5

43

Table 5.4-Measured viscosity values of various slags. Sample Temperature Viscosity Sample Temperature Viscosity K dPa s K dPa s

1583 0.76 1683 0.85 1473 1.36 1578 1.41 1425 1.90 1524 1.84 1374 2.77 1479 2.58 1354 3.30 1457 2.96 1333 3.98 1445 3.25 1318 4.61 1422 3.80

A

1303 5.37 1407 4.28 1673 0.48 1395 4.71 1573 0.78 1365 6.05 1523 1.01 1351 6.88 1475 1.35 1331 8.33 1425 1.88 1318 9.51 1399 2.30

D + wt-%

2.5 Al2O3

1302 11.07 1375 2.84 1675 1.06 1349 3.50 1574 1.77

A 2

1324 4.48 1525 2.37 1671 0.67 1472 3.37 1576 1.05 1425 4.80 1524 1.41 1399 5.85 1471 1.98 1371 7.53 1424 2.82 1353 8.87 1398 3.44 1333 10.77 1371 4.35 1320 12.27 1353 5.20

D + wt-%

5.0 Al2O3

1304 14.39 1333 6.33 1670 0.87 1318 7.40 1572 1.38

A + wt-%

2.5 Al2O3

1304 8.66 1522 1.84 1676 0.75 1473 2.48 1575 1.26 1424 3.46 1523 1.72 1404 4.03 1473 2.44 1374 5.04 1421 3.61 1350 6.19 1398 4.38

E

1323 7.91 1373 5.50 1624 1.01 1353 6.77 1573 1.33 1333 8.41 1523 1.79 1320 9.84 1498 2.12

A + wt-%

5.0 Al2O3

1306 11.61 1473 2.52 1673 0.65

E 2

1448 3.04 1574 0.98 1675 0.52 1521 1.20 1575 0.81 1472 1.55 1524 1.07 1426 2.05 1473 1.47 1400 2.41 1420 2.14 1372 3.02 1373 3.09 1345 3.80 1350 3.85 1326 4.34

F

1321 5.08

B

1298 5.20 1675 2.14 1673 0.66 1628 2.90 1574 1.03 1567 4.32 1525 1.36 1523 6.02 1473 1.88 1498 7.40 1422 2.71 1471 9.42 1401 3.19 1446 11.88 1375 4.00 1422 15.31 1346 5.27

G

1395 20.64 1329 6.28

C

1305 8.29 1673 0.73 1623 0.91 1571 1.18 1547 1.35 1523 1.54 1498 1.79 1473 2.10 1448 2.48 1424 2.93 1409 3.28 1399 3.51 1380 4.07 1366 4.58 1350 5.23 1330 6.31

D

1304 8.05

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Result and Discussion

44

Several studies have been carried out to determine viscosities of mould flux slags for continuous casting15-20. The results of the measured viscosities in these works are in most cases significantly higher than those obtained in the present study. The diversity in viscosity is attributed to the differences in the chemical compositions. The mould fluxes used in literature had greater amounts of SiO2 and Al2O3; and lesser amounts of alkali oxides and CaF2. It is well-known that Al2O3 and SiO2 have an increasing effect on slag viscosities, due to the tendency to promote the formation of the silicate network. On the contrary, CaF2 and alkali oxides have the opposite effect on the viscosities due to the break down of the silicate network. Figures 5.30, 5.31 and 5.32 graphically represent the variation of viscosities with respect to temperature. As expected, the viscosity values were found to increase with the decrease in temperature. In industrial practice for clean steel production, the Al2O3 pick up has generally been observed to be about 2-4 %87. To investigate this increase in alumina, 2.5 and 5.0 wt % alumina were added to slags A and D (chemical analysis shows 2.5 and 4.6 wt % respectively 2.2 and 4.2 wt %). The results presented in Figures 5.30 and 5.31 show that viscosity increases significantly with increasing alumina content, the occurrence being more prominent at lower temperatures. A relatively large increase in viscosity, like this would affect the slag film thickness, hence the heat transfer, and the friction force acting on the solidified shell88. The present results agree well with a previous study on the effect of Al2O3 addition to mould flux slags25. It is well-known fact that alumina contributes to the silicate network, thereby causing an increase in viscosities.

1300 1350 1400 1450 1500 1550 1600 1650 17000

2

4

6

8

10

12

14

Slag A A+2.5 wt-% Al2O3

A+5.0 wt-% Al2O3

Visc

osity

[dPa

s]

Temperature [K]

Figure 5.30-Viscosties of three slags as function of temperature.

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Chapter 5

45

1300 1350 1400 1450 1500 1550 1600 1650 17000

2

4

6

8

10

12

14

Slag D D+2.5 wt-% Al2O3

D+5.0 wt-% Al2O3

Visc

osity

[dPa

s]

Temperature [K]

Figure 5.31-Viscosties of three slags as function of temperature.

Figure 5.32 shows small differences in viscosity between the slags, especially at lower temperatures, with exception for slag G, which was found to have higher viscosity. Viscosity measurements were not possible below 1400 K in this case, distinguish to the other slags. The reasons for the higher viscosities in slag G, can be contribute to its compositional differences. Slag G has a significantly lesser amount of fluoride, as well as the highest amount of Al2O3.

1300 1350 1400 1450 1500 1550 1600 1650 17000

2

4

6

8

10

12

14

16

18

20

22

Slag B C E F G

Visc

osity

[dPa

s]

Temperature [K]

Figure 5.32-Viscosties of three slags as function of temperature.

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Result and Discussion

46

The Arrhenius activation energies for viscous flow for various temperature intervals have been evaluated from the measured viscosity values, The Arrhenius activation energy at higher temperatures, where viscosity variation with temperature is not drastic could be approximated to a constant value, these are presented in Table 5.5. However, the activation energy is found to increase with decreasing temperature as the liquidus temperature was approached. Similar results have been reported by Seetharaman et al89. These authors have also reported that the second derivative of the activation energy for viscous flow with respect to temperature shows a break around the liquidus temperature of the slag. In figures 5.33-5.35, the second derivatives of the activation energies for viscous flow for some of mould flux slags carried out in the present work are plotted as functions of temperature. It is seen for slags A, D and E that the second derivatives show the break points around 1350 K for the first two mentioned and somewhat higher for slag E. The liquids temperatures obtained from the second derivative method for all slags, along with the DSC measurements, carried out at KTH, and supplier data are listed in Table 5.5. DSC measurements were not employed for all fluxes. The application and the reliability of the second derivative method for the estimation of the liquidus temperatures depend upon the number of viscosity values available at different temperature intervals. The scatter in the data also would result in uncertainties. On the contrary, the measurements of liquidus temperatures of slags by DSC method are often very difficult and unreliable in view of the considerable supercooling that the slags undergo, as indicated by lower values. DSC values, taken during heating cycles can show higher values due to compositional inhomogeneities. In this respect, the second derivative method appears to give somewhat reliable values of liquidus temperatures. The higher liquidus temperature of slag G compared to the other slags is supported by the second derivative method and the supplier data, in contrast to the DSC measurement. Table 5.5-Measured viscosity values of various slags.

Slag Ahrrenius Liqudius temperature [K] activation

energy kJ/mol

d2(Q/R)/dT2 DSC first cycle

DSC second cycle

Supplier data

A 111 1350 1400 1440 1383+/- 20 A+2.5 wt-% Al2O3 114 1350 - A+5.0 wt-% Al2O3 120 1350 - B 92 1400 1400 +/- 20 C 110 1450 1463 +/- 10 D 110 1300 1410 1450 1363 +/- 20 D+2.5 wt-% Al2O3 116 1350 - D+5.0 wt-% Al2O3 119 1350 - E 109 1370 1370 1410 1458 +/- 20 F 108 1410 1433 +/- 20 G 152 1450 1350 1380 1493 +/- 20

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Chapter 5

47

1300 1350 1400 1450 1500 1550 1600 1650 1700-50

-40

-30

-20

-10

0

10

Slag A+2.5 wt-% Al2O3

d2 (Q/R

)/dT2

Temperature [K]

Figure 5.33-The second derivative of activation energy. ( ) 22 // TRQ ∂∂ , as function of temperature for slag A+2.5 wt-% Al2O3.

1300 1350 1400 1450 1500 1550 1600 1650 1700-40

-30

-20

-10

0

10

Figure 5.34-The second derivative of activation energy. ( ) 22 // TRQ ∂∂ , as function of temperature for slag D+5.0 wt-% Al2O3.

Slag D+5.0 wt-% Al2O3

d2 (Q/R

)/dT2

Temperature [K]

Figure 5.35-The second derivative of activation nergy. ( ) 22 // TRQ ∂∂ , as function of temperature for slag E.

1300 1350 1400 1450 1500 1550 1600 1650 1700-2

-1

0

1

Slag E

d2 (Q/R

)/dT2

Temperature [K]

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Result and Discussion

48

Basicity of mould flux slag is usually in the range of 0.7 and 1.313. Higher basicity leads to a higher degree of crystallinity of the mould flux slag. The degree of crystallinity, in turn, will affect the heat flux through the slag film. Higher degree of crystallinity will lead to lesser heat transport, while the glassy phase will result in higher thermal conductivity. Further, viscosity will have a strong impact on the thickness of the slag layer between the mould and the steel.

Slag B is a mould flux particularly used in the start up phase of the casting process. As seen in Table 5.2, it has a significant higher content of Fe2O3 compared to the others and a high content of F, which gives it the features of good wetting properties respectively low melt temperature and viscosity. High contents of Fe2O3 are, however, not preferable in alumina killed steels. It is easily reduced and the mould flux properties may be altered, thus only preferable in the early stages of the casting.

Mould fluxes C, D and E are used in the casting of low alloying steels, while flux A and F in high-alloyed steel grades. The type of steel grade is the primary criterion for the selection of the of mould flux. Whether the steel will undergo the peritectic phase transformation, L+δ→γ, associated with a volume change, or not. Steel grades subjected to a strong peritectic reaction are usually related with greater risks of irregular surface quality and depressions. These steel grades require good heat flux control corresponding to insulating properties such as high melting temperature and high rate of crystallinity. The thickness of the slag layer, affected by the viscosity, is also of importance controlling the heat flux. In the case of steel grades with insignificant impact of the peritectic reaction, the mould flux friction to mould and steel is normally the controlling parameter. A less crystalline slag, lower basicity, and lower melting temperature would be generally more suitable in these cases.

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49

Chapter 6

SUMMARY AND CONCLUSIONS

The present work has been conducted to develop computational tools to apply in process modeling. The thesis consist of two parts; development of a semi-empirical model for the predictions of molar volumes/densities of multicomponent slags; viscosity measurements of mould fluxes. Both parts were undertaken with the objective for further development of the Thermoslag® software developed in the Division of Materials Process Science, KTH. The mathematical model for molar volume will be incorporated in the model for viscosities, while the viscosity measurement were carried out in strive to expand the same model towards fluoride containing slags, such as mould fluxes. The model for molar volume predictions utilizes a relationship between thermodynamic properties and densities. The relationship is based on the fact that both these properties are structure related, depending on the interactions between nearest and next-nearest neighbor ions. For verification of the calculated molar volumes, the results in binary, ternary and higher order systems have been compared with experimental data obtained from literature. In the most systems, the model estimations agree very well with reported molar volumes. Disagreements between model predictions and experimental data are obtained in a few cases. In the case of FeO-containing systems, the impact of Fe2O3 present in the slag has not been considered in the present model which leads to some deviations from experimental data. Large contents of silica, above 50 mass % in ternary and higher systems with slag composition close to the binary CaO-SiO2, is also subjected to a higher uncertainty, due to the difficulties in the evaluation of the binary parameter. Reasons for this disagreement in the binary system can either be uncertainties in experimental data or the uncertainties associated with the model parameters for enthalpy estimations obtained from experimental information, or even both.

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Summary and Conclusions

50

Despite these, the model predictions are well within the experimental uncertainties associated with density measurements in most cases. Thus, the model offers a unique possibility to generate molar volume data that are consistent with the thermodynamic properties in the case of multicomponent slag systems. The model can be used to modify slag volumes with the aim to optimize energy and environmental aspects of iron and steel making processes.

In the development of a viscosity model with the features of predicting reliable values of fluoride containing slags, experimental work is essential. The rotating cylinder method was employed in order to determine the viscosity of eleven slags, seven industrial mould fluxes and four additional measurements with increased alumina contents. Alumina additions in the range of 2.5 respectively 5.0 wt % resulted in a relatively large increase in the viscosities of mould flux slags. The added alumina content is in the same order as the inclusion pick up by mould flux slags in industrial applications. Fluoride losses during the experiments were insignificant according to the chemical analyses. The experimental results were used to calculate the Arrhenius activation energy for viscous flow and the second derivative of the activation energies for viscous flow. The former was found to increase with decreasing temperature, consistent with earlier work, carried out in the Division of Materials Process Science. The later, when plotted as function of temperature, showed break points corresponding to the liquidus temperature of the slag.

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51

Chapter 7

FUTURE WORK

A continuing development of Thermoslag® is important for modeling of slags in high temperature processes. An important step would be the implementation of fluoride spices into the slag model. This is crucial for the achievement of reliable modeling of mould flux behavior in the casting process. It is essential that the knowledge regarding the fluoride slags is systematically incorporated in the Thermoslag. This needs both thermodynamic and thermophysical information regarding these slags obtained experimentally. It is admitted that such experimentations are extremely difficult to carry out. Further, incorporation of the fluoride species needs a restructuring of the model as the data for lower order systems containing fluoride species are not available. Another important development would be to study, with the help of the thermoslag software, the possibilities of replacing a part of the fluoride content of the slag with other components, without lowering its performance. This is especially interesting from an environmental view point. Fluoride is the main environmental concern related to continuous casting of steel. In this respect, the software should have computational routines to come up with optimal compositions for defined properties. This is being considered as the next step in the development of the software. Furthermore, some uncertainties are experienced in the present viscosity model, in the case of slags with high contents of alumina. The reason for this is attributed to the lack of experimental data in this composition region and thus, the model parameter optimization is out of range. In order to solve this problem, further experimentation in the relevant compositions regions are essential. Such experiments are currently planned in the division.

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Future Work

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53

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