Viscosity Studies of High-Temperature Metallurgical Slags Relevant to Ironmaking Process

Transcription

1 Viscosity Studies of High-Temperature Metallurgical Slags Relevant to Ironmaking Process Chen Han Bachelor of Engineering A thesis submitted for the degree of Doctor of Philosophy at The University of Queensland in 2017 School of Chemical Engineering

2 Abstract: Slags are molten oxides presenting in a number of high-temperature processes. In ironmaking process, the metallurgical properties of blast furnace slags are determined largely by its viscosity. Understanding and controlling the behavior of the slag phase is crucial in improving the operational and economical efficiencies. However, high-temperature viscosity measurement is practically difficult, time- and cost-consuming. There is a necessity to develop a reliable mathematical model for the viscosity prediction through the review of experimental data and fundamental theory. As foundation work, abundant viscosity measurements and models have been examined and evaluated, including over 3000 viscosity data in the CaO-MgO-Al 2 O 3 -SiO 2 system and 16 viscosity models. Over the past 10 years, there has been increasing attentions on wide composition range of slag viscosity due to the continuous consumption of complex iron ores. In addition, the impacts of eight minor elements (including F, Ti, B, Fe, Mn, Na, K, and S) on slag viscosity have been studied for practical purpose. Slag viscosity is determined by its structure, which is the theoretical base of the mathematical model. The structures of the quenched silicate slags were quantitatively investigated utilizing Raman spectroscopy. It is accepted that the application of Raman spectroscopy can disclosure the vibration units of molten slag, which can be interpreted the structural of silicate melts (amorphous glass phase). In the blast furnace operations, some solid phases such as oxide precipitates, coke or Ti(CN) can be present in the slag. In addition, the precipitation of solid particles was commonly observed in iron, steel, copper and other pyrometallurgy process. These solids can significantly increase the viscosity of the slag causing operating difficulty. There is a research gap that the solid impact on suspension was limited investigated under high-temperature condition due to uncertainty. Referring to the research gap of viscosity study of blast furnace slag, the following goals have been achieved by the Ph.D. candidate: 1. Review and evaluated the experimental methodologies, viscosity data, and models relevant to the blast furnace slag in CaO-MgO-Al 2 O 3 -SiO 2 system (Chapter 2) 2. Based on the collected data and models, an accurate viscosity model has been developed to predict the viscosity of blast furnace slag in CaO-MgO-Al 2 O 3 -SiO 2 system (Chapter 4-5)

3 3. Research on the viscosity impact of minor elements on the blast furnace final slag in CaO- MgO-Al 2 O 3 -SiO 2 based system. (Chapter 4-5) 4. Quantitative investigation of the microstructural units of silicate slag utilizing Raman spectroscopy. (Chapter 6) 5. Investigation of the solid phase impact on the viscosity of liquid slag. (Chapter 7)

4 Declaration by author This thesis is composed of my original work, and contains no material previously published or written by another person except where due reference has been made in the text. I have clearly stated the contribution by others to jointly-authored works that I have included in my thesis. I have clearly stated the contribution of others to my thesis as a whole, including statistical assistance, survey design, data analysis, significant technical procedures, and professional editorial advice, and any other original research work used or reported in my thesis. The content of my thesis is the result of work I have carried out since the commencement of my research higher degree candidature and does not include a substantial part of work that has been submitted to qualify for the award of any other degree or diploma in any university or other tertiary institution. I have clearly stated which parts of my thesis, if any, have been submitted to qualify for another award. I acknowledge that an electronic copy of my thesis must be lodged with the University Library and, subject to the General Award Rules of The University of Queensland, immediately made available for research and study in accordance with the Copyright Act I acknowledge that copyright of all material contained in my thesis resides with the copyright holder(s) of that material. Where appropriate I have obtained copyright permission from the copyright holder to reproduce material in this thesis.

5 Publications during candidature 1. Chen. Han, Mao. Chen, Weidong Zhang, Zhixing Zhao, Tim Evans, Anh V. Nguyen and Baojun. Zhao *, Viscosity Model for Iron Blast Furnace Slags in SiO 2 -Al 2 O 3 -CaO-MgO system, Steel Research International, 2015, vol.85 (6), pp Chen. Han, Mao. Chen, Weidong. Zhang, Zhixing. Zhao, Tim. Evans and Baojun. Zhao *, Evaluation of Existing Viscosity Data and Models and Developments of New Viscosity Model for Fully Liquid Slag in the SiO 2 -Al 2 O 3 -CaO-MgO System, Metallurgical and Material Transactions B, 2016, Vol 47 (5), pp Chen. Han, Mao. Chen, Ron. Rasch, Ying. Yu and Baojun. Zhao *, Structure Studies of Silicate Glasses by Raman Spectroscopy, Advances in Molten Slags, Fluxes, and Salts: Proceedings of The 10 th International Conference on Molten Slags, Fluxes and Salts, Seattle, United States, 2016, pp Chen. Han, Mao. Chen, Weidong. Zhang, Zhixing Zhao, Tim. Evans and Baojun. Zhao, Viscosity Model for Blast Furnace Slags Including Minor Elements, The 10 th CSM Steel Congress & The 6 th Baosteel Biennial Academic Conference 2015, Shanghai, China, 2015, pp Chen. Han, Mao. Chen, Weidong. Zhang, Zhixing Zhao, Tim. Evans, Anh V. Nguyen and Baojun. Zhao *, Development of viscosity model for SiO 2 -CaO-MgO-Al 2 O 3 - FeO slags in ironmaking process, High Temperature Processing Symposium, 2015, Melbourne, Australia, pp

6 Publications included in this thesis 1. Chen. Han, Mao. Chen, Weidong Zhang, Zhixing Zhao, Tim Evans, Anh V. Nguyen and Baojun. Zhao *, Viscosity Model for Iron Blast Furnace Slags in SiO 2 -Al 2 O 3 -CaO-MgO system, Steel Research International, 2015, vol.85 (6), pp incorporated as Chapter 4.1 Contributor Statement of contribution Chen Han (Candidate) Wrote the paper (100%) Baojun Zhao* Discussed and edited paper (45%) Mao Chen Discussed and edited paper (45%) Tim Evans Discussed and edited paper (5%) Anh V Nguyen Discussed and edited paper (5%) Weidong Zhang Provided industrial advices (50%) Zhixing Zhao Provided industrial advices (50%) 2. Chen. Han, Mao. Chen, Weidong. Zhang, Zhixing. Zhao, Tim. Evans and Baojun. Zhao *, Evaluation of Existing Viscosity Data and Models and Developments of New Viscosity Model for Fully Liquid Slag in the SiO 2 -Al 2 O 3 -CaO-MgO System, Metallurgical and Material Transactions B, 2016, Vol 47 (5), pp incorporated as Chapter 4.2 Contributor Statement of contribution Chen Han (Candidate) Wrote the paper (100%) Baojun Zhao* Discussed and edited paper (45%) Mao Chen Discussed and edited paper (45%) Tim Evans Discussed and edited paper (5%) Anh V Nguyen Discussed and edited paper (5%) Weidong Zhang Provided industrial advices (50%) Zhixing Zhao Provided industrial advices (50%) 3. Chen. Han, Mao. Chen, Ron. Rasch, Ying. Yu and Baojun. Zhao *, Structure Studies of Silicate Glasses by Raman Spectroscopy, Advances in Molten Slags, Fluxes, and Salts:

7 Proceedings of The 10 th International Conference on Molten Slags, Fluxes and Salts, Seattle, United States, 2016, pp incorporated as Chapter 6 Contributor Statement of contribution Chen Han (Candidate) Wrote the paper (100%) Baojun Zhao* Discussed and edited paper (45%) Mao Chen Discussed and edited paper (45%) Ron Rasch Assisted in the Raman spectra analysis (50%) Ying Yu Assisted in the Raman spectra analysis (50%) 4. Chen. Han, Mao. Chen, Weidong. Zhang, Zhixing Zhao, Tim. Evans and Baojun. Zhao, Viscosity Model for Blast Furnace Slags Including Minor Elements, The 10 th CSM Steel Congress & The 6 th Baosteel Biennial Academic Conference 2015, Shanghai, China, 2015, pp incorporated as Chapter 4.2; Contributor Statement of contribution Chen Han (Candidate) Wrote the paper (100%) Baojun Zhao* Discussed and edited paper (45%) Mao Chen Discussed and edited paper (45%) Tim Evans Discussed and edited paper (5%) Anh V Nguyen Discussed and edited paper (5%) Weidong Zhang Provided industrial advices (50%) Zhixing Zhao Provided industrial advices (50%) 5. Chen. Han, Mao. Chen, Weidong. Zhang, Zhixing Zhao, Tim. Evans, Anh V. Nguyen and Baojun. Zhao *, Development of viscosity model for SiO 2 -CaO-MgO-Al 2 O 3 - FeO slags in ironmaking process, High Temperature Processing Symposium, 2015, Melbourne, Australia, pp incorporated as Chapter 5.2 Contributor Statement of contribution Chen Han (Candidate) Wrote the paper (100%)

8 Baojun Zhao* Discussed and edited paper (45%) Mao Chen Discussed and edited paper (45%) Tim Evans Discussed and edited paper (5%) Anh V Nguyen Discussed and edited paper (5%) Weidong Zhang Provided industrial advices (50%) Zhixing Zhao Provided industrial advices (50%)

9 Contributions by others to the thesis Contributions by Professor Baojun Zhao in experiment design, concept, analysis, interpretation, drafting, and writing in the advisory capacity. Statement of parts of the thesis submitted to qualify for the award of another degree None

10 Acknowledgements I express my sincere gratitude to my advisor team Prof. Baojun Zhao (principal), Prof Anh Nguyen and Dr. Tim.Evans for their guidance and support the research projects and this thesis completion I would like to acknowledge the Beijing Shougang Co., Ltd, China and Rio Tinto Iron Ore, Australia for financial support. I thank to Dr. Mao Chen for fruitful discussions and assistance in preparing this thesis. I am very grateful to the lab assistant Ms, Jie Yu, for her help and support on the completion of experimental work.

11 Key Words Slag viscosity, viscosity modelling, blast furnace slag, Raman spectrum Australian and Newzealand Standard Research Classifications (ANZSRC) ANZSRC: Pyrometallurgy 100% Fields of Research (FoR) Classification FoR code: 0914 Resources Engineering and Extractive Metallurgy 100%

12 Table of Contents Chapter 1 : Introduction Background Introduction Research Gap Aim of the Study... 2 Chapter 2 : Literature reviews The technical review of high-temperature viscosity measurement Liquid Viscosity Definition Viscometer Rotational Viscometer Falling-Body Viscometer Oscillating Viscometer Other Viscometers Post-Experimental Analysis Composition Analysis Surface Morphology Study Internal Structure Study The review of viscosity data of sub binary, ternary of CaO-MgO-Al 2 O 3 -SiO 2 system Binary System SiO 2 -CaO SiO 2 -Al 2 O SiO 2 -MgO Ternary System SiO 2 -CaO-Al 2 O SiO 2 -Al 2 O 3 -MgO Conclusion... 33

13 2.3 Evaluation of Quaternary system CaO-MgO-Al 2 O 3 -SiO Experimental Techniques in Viscosity Measurements Data Consistency Cross Reference Comparison Summary of Experimental Data Random Network Structure Minor Element Impact FeO TiO Na 2 O and K 2 O The review and evaluation of viscosity model for silicate melts of CaO-MgO-Al 2 O 3 - SiO 2 system Bottinga Model Neural Network Model Giordano Model CSIRO Model KTH Model Urbain Model Riboud Model Kondratiev and Forsbacka Model Iida Model NPL (Mills) Model Shankar Model Hu Model Shu Model Zhang Model Gan Model... 68

14 Tang Model Ray Model Li Model Quasi-Chemical Viscosity Model Factsage Summary The viscosity study review of suspension system Effects of liquid viscosity & Solid Fraction Effects of Particle Size The review of viscosity model of suspension system Chapter 3 : Experiment Methodology High-Temperature Viscosity Measurement Room Temperature Viscosity Measurement Raman Spectroscopy Study Chapter 4 : Viscosity Model Development in CaO-MgO-Al 2 O 3 -SiO 2 System Based on Urbain Model CaO-MgO-Al 2 O 3 -SiO 2 system in blast furnace composition range Introduction Experimental Data Used for Model Development Silicate Melt Structure Description of Model Expressions of Activation Energy Model Performances Industrial Applications Conclusions Introduction Experimental Methodology

15 4.2.3 Viscosity Database Collected Reference Minor Element Impact Result & Discussion Comparisons of viscosities Viscosity Model Description Industrial Application Conclusions Chapter 5 : Viscosity Model Development Based on Probability Theorem CaO-MgO-Al 2 O 3 -SiO 2 system in full composition range Introduction Silicate melt structure Pre-Exponential Factor A Network Modifier Probability Activation Energy E A Model Performance CaO-MgO-Al 2 O 3 -SiO 2 system Viscosity Trend Prediction Sub-Ternary & Sub-Binary System Industrial Application Blast Furnace Slag Ladle Slag in Steelmaking Process Conclusions CaO-MgO-Al 2 O 3 -SiO 2 - FeO system in full composition range Introduction Model Description Silicate structure of SiO 2 -CaO-Al 2 O 3 -MgO- FeO system

16 Temperature dependence Pre-exponential Factor A Fe 2+ and Fe 3+ Determination Network Modify probability Activation Energy Model Performance Industrial Application Blast Furnace Slag Coppermaking Slag Conclusion Chapter 6 : Structure studies of silicate slag by Raman spectroscopy Introduction Methodology Sample Preparation Raman Analysis Raman Results Structure of alumina silicate system Raman Peak Shift Peak Intensity Temperature Impact Bond energy and the lattice energy Summary Thermodynamic Analysis Degree of Polymerization Density Viscosity & Activation Energy Conclusion

17 Chapter 7 : Experimental and modeling study of suspension system Introduction Methodology Calibration Viscosity Study of Suspension at Room Temperature Viscosity Study of Suspension at Smelting Temperature Results Room Temperature Smelting Temperature Effect of liquid viscosity and solid fraction Effect of particle diameter Effect of Temperature Effect of Shear Rate Model Simulation Model Review and Evaluation Model Optimization Model Application Conclusion Chapter 8 : Conclusions Chapter 9 : Reference

18 List of Table Table 1.1 Blast furnace composition range [1]... 1 Table 2.1 Category of different types of fluids... 6 Table 2.2 Summary of Reviewed Viscometers... 8 Table 2.3 Summary of post-experiment techniques Table 2.4 the assigned peaks after peak deconvolution in the region cm -1 [41] Table 2.5 Summary of viscosity study at binary system SiO 2 -CaO Table 2.6 Summary of viscosity data of SiO 2 -Al 2 O 3 system Table 2.7 Summary of viscosity data of SiO 2 -MgO system Table 2.8 Summary of SiO 2 -Al 2 O 3 -CaO viscosity study Table 2.9 Summary of viscosity study at SiO 2 -Al 2 O 3 -MgO system Table 2.10 Viscosity impact of oxide in their binary and ternary system with silica Table 2.11 The summary of existing viscosity study in CaO-MgO-Al 2 O 3 -SiO 2 system 41 Table 2.12 Summary of Brokis study of expression of SiO 2 unit at various concentration [111] Table 2.13 Summary of viscosity study at CaO-MgO-Al 2 O 3 -SiO 2 - FeO system Table 2.14 Summary of viscosity study at CaO-MgO-Al 2 O 3 -SiO 2 -TiO 2 system Table 2.15 Summary of viscosity study at CaO-MgO-Al 2 O 3 -SiO 2 -Na 2 O and K 2 O system Table 2.16 the parameter D values of Bottinga model in CaO-MgO-Al 2 O 3 -SiO 2 quaternary system [126] Table 2.17 Model parameters for Giordano [128] Table 2.18 Model parameters of Urbain Model [131] Table 2.19 Equation parameters for Iida model [136, 137] Table 2.20 Model parameters of NPL model [138] Table 2.21 The model parameters used to calculate E [145]... 67

19 Table 2.22 All possible condition in the CaO-MgO-Al 2 O 3 -SiO 2 system, only the condition 1 equations were included. The equations for other conditions is not included due to text limitation [145] Table 2.23 Model parameters of Gan model [147] Table 2.24 Model parameters of Tang model [148] Table 2.25 Model parameters of Li model [150] Table 2.26 Summary of reviewed viscosity model in CaO-MgO-Al 2 O 3 -SiO 2 system Table 2.27 Summary of applicable oxides of existing viscosity model Table 2.28 The brief review of viscosity study of suspension system at different system, viscosity and temperature range, note: the relative viscosity means the ratio of suspension viscosity to liquid viscosity Table Summary of 10 different viscosity model, f is the solid fraction within suspension Table 4.1 Parameters B used in Equation Table 4.2 Model parameters N Table 4.3 Summary of typical BF composition range Table 4.4 Model parameters to calculate E i of each minor element, the parameters of SiO 2, CaO, MgO, and Al 2 O 3 were reported in the section before Table 4.5 Optical basicity of oxide from Duffy Table 4.6 Summary of model performance in BF slag composition range Table 5.1 Electronegativity χ of basic oxide cations and network former units Table 5.2 Activation energy parameters of all involved structural units in CaO-MgO- Al 2 O 3 -SiO 2 system Table 5.3 The summary of model parameters in binary and ternary silicate system containing CaO, MgO, and Al 2 O Table 5.4 Electronegativity χ of basic oxide cations and network former units Table 5.5 Activation energy parameters of all involved structural units in CaO-MgO- Al 2 O 3 -SiO 2 system Table 5.6 The prediction deviation of viscosity models for CaO-MgO-Al 2 O 3 -SiO 2 - FeO system Table 6.2 The experiment designed condition and EPMA results

20 Table 6.3 The description of assigned peak information in Raman spectrum silicate structural units, black ball is Si and white ball is O. white ball with sign is O Table 6.4 Summary of the bond energy of each deconvoluted peaks Table 7.1 Physical properties of silicon oil in present study Table 7.2: Experimental condition of viscosity measurement at room temperature Table 7.3. Viscosity measurements of suspension of solid proportion from 0-22 vol% Table 7.4. Viscosity measurements of suspension of solid proportion from vol % Table 7.5. The elemental analysis of Baosteel and JingTang slag from EPMA analysis, where the minor element include Na 2 O, K 2 O, FeO and etc Table 7.6. Summary of optimized model

21 List of Figure Figure 1.1 Technical description of blast furnace ironmaking process... 1 Figure 2.1 Laminar shear of fluid between two plates... 5 Figure 2.2 Shear stress vs strain rate of Newtonian liquid and non-newtonian fluid... 6 Figure 2.3 Schematic diagram of rotational cylinder viscometer... 9 Figure 2.4 geometry for rotational bob, (a) cylinder, (b) cylinder, (c) cone, (d) cone, (e) parallel plate (f) parallel plate Figure 2.5 Schematic diagram of the falling sphere viscometer Figure 2.6 Counter balance viscometer [15] Figure 2.7 Schematic diagram of the oscillating piston viscometer Figure 2.8 Schematic diagram of the capillary viscometer Figure 2.9 Schematic diagram of ICP [31] Figure 2.10 Spherulite of aluminous enstalite under (a) natural and (b) polarized light after the viscosity measurements [36] Figure 2.11 Bright-field TEM image [37] Figure 2.12 Raman spectrum of silica glass [38] Figure 2.13 The Raman spectrum of SiO 2 -CaO system at different Ca/Si ratio [43] Figure 2.14 The pair distribution for the pure SiO 2. A is the experimental curve, B is the calculated curve [49] Figure 2.15 (a) left, 29 Si NMR spectra of SiO 2 -Na 2 O glasses [52] Figure 2.16 Activity of SnO plotted against mole fraction of SiO 2 for the SiO 2 -SnO system at 1100 o C. Kozuka experimental data and 1) Masson prediction, 2) Flory expression k 11 =2.55. And 3) Flory expression with k 11 =1.443 [53] Figure 2.17 isovicosity data by Licko in SiO 2 -CaO-MgO system at 1500 C at 40 wt.% and 50 wt.% SiO 2 [56](b) The viscosity data of Bockris of SiO 2 -CaO and SiO 2 - MgO system at 1750 C [54] Figure 2.18 Examples showing viscosity measured below liquidus by Machin [74] and Tang [99] Figure 2.19 Linearity comparison examples by Muratov [100], Machin[80], and Yakushev [89]... 38

22 Figure 2.20 Four sets viscosity measurement at 45 wt % SiO 2, 15 wt% Al 2 O 3, 30 wt% CaO and 10 wt% MgO by Gul tyai [83], Han [93], Kita [27] and Machin [27, 74, 83, 93] Figure 2.21 Comparison of viscosity data by the present authors (UQ), Kim et al [35] and Park et al [101] at composition of 36.5% SiO 2, 17% Al 2 O 3, 36.5% CaO and 10% MgO Figure 2.22 (a) Left, pure SiO 2 structure. (b) Right, silicate mix with other basic oxide solution Figure 2.23 FeO replaced the CaO and MgO oxide at 40 wt% SiO 2, 1500 o C for SiO 2 - CaO-FeO system, 40 wt% SiO 2, 1550 o C for SiO 2 -MgO-FeO system, by Bockris [94], Chen [115], Ji [114]and Urbain [13] Figure 2.24 The comparison between Urbain model of 1981 and 1987 version using the viscosity database of before-evaluation, after-evaluation and BF composition [131, 132] Figure 2.25 The shear stress enlarged from fully liquid system to solid/liquid system Figure 2.26 Viscosity deduced from data of van der Molten and Paterson (1979) [165]at high solid fraction (circles) and from data of Mg 3 Al 2 Si 3 O 12 by Lejeune (triangles) [162] and other values at low solid fraction (squares) by Thomas [166] Figure 2.27 Experiment data of different particle size vs model prediction [167] Figure The description of interaction between solid sphere and fluid particle Figure 3.1 Schematic diagram of furnace for viscosity measurement at high temperature Figure 3.2 Schematic diagram of crucible and spindle Figure 3.3 Schematic diagram of viscosity study at room temperature Figure 3.4 (a) left, a photograph of phase equilibrium experiment. (b) Right, a schematic diagram of a vertical tube furnace The linear relationship between E A and ln(a) Figure 4.2 Comparison of the current viscosity model with others Figure 4.3 Three model performance for 0-1 Pa.s, mean deviation for three models: present model 12.5%, Zhang model 16.4% and Urbain model (1987 version) 16.3% [131, 188] Figure 4.4 Effect of MgO on viscosity of BF slag at 15 wt% Al 2 O 3 and 1500 C predicted by the present model with comparisons to the experimental data [74].. 103

23 Figure 4.5 Effects of Al 2 O 3 concentration and temperature on slag viscosity at 40 wt% SiO 2 and 10 wt% MgO predicted by the present model with comparisons to the experimental data of Gultyai [83], Hofmann [22] and Machin [68] Figure 4.6 Comparison of viscosities for CaO-MgO-Al 2 O 3 -SiO 2 -TiO 2 slag by Park [120] and Liao [119] Figure 4.7 the model prediction vs experimental results of CaO-MgO-Al2O3-SiO2-TiO2 slag system of Park [120], Shankar [32] and present (A) left, present model and (B) right, Urbain Model (1981 version) [132] Figure 4.8 Increase of prediction deviation in CaO-MgO-Al 2 O 3 -SiO 2 -FeO system with increasing FeO concentration by Bills [64], Gorbachev [189], Higgins [190] and present study Figure 4.9 The comparison of viscosity reduction ability of 8 minor elements on BF slag viscosity Figure 4.10 Comparison of model prediction and Liao s measurements [119] Figure 5.1 Interaction among Ca 2+ cations, silica and alumina Figure 5.2 The linear relationship between E A and ln(a) Figure 5.3 The performance summary of viscosity models in, (i) full CaO-MgO-Al 2 O 3 - SiO 2 composition, (ii) BF slag composition and (iii): ladle slag composition Figure 5.4 Comparison between experimental viscosity and calculated viscosity by present model (12.5% deviation), Zhang model (19.4 deviations) [145] and Urbain model (19.3 % deviation) [131] Figure 5.5 Comparisons between model predictions and Gul tyai [65] and Hofmann [22] results, 1500 C in the system CaO-MgO-Al 2 O 3 -SiO Figure 5.6 The linear relationship between E A and ln(a) for (A): SiO 2 -Al 2 O 3 -CaO and SiO 2 -Al 2 O 3 -MgO system and Figure 5.7 Comparisons between experiment viscosity and model prediction in the systems (A) SiO 2 -Al 2 O 3 -CaO, (B) SiO 2 -Al 2 O 3 -MgO, (C) SiO 2 -CaO, (D) SiO 2 -MgO and (E) SiO 2 -Al 2 O Figure 5.8 Effects of W CaO /W SiO2 and MgO on slag viscosity at 1500 C and 15 Al 2 O 3 by the present model in comparisons with the data from Kim [122], Gul tyai [83] and Machin s [74] Figure 5.9 The model prediction of the iso-viscosity diagram at 1500 C and 15 wt.% Al 2 O 3 and experiment data of Gultyai [83], Li [150], and Machin [68, 74]

24 Figure 5.10 Effects of W CaO /W SiO2 and temperature on slag viscosity at 5 wt.% MgO and 30 wt.% Al 2 O 3 by present model in comparisons with Song s data [107] Figure 5.11 The comparison between experimental viscosity and calculated viscosity using Current, Urbain [131] and Zhang model [145] Figure wt% SiO 2, 1500 o C for SiO 2 -CaO- FeO system by Chen [193], Bockris [194] and Ji [114], 40 wt% SiO 2, 1550 o C for SiO 2 -MgO- FeO system by Chen [115], Ji [195] and Urbain [60] Figure 5.13 Comparisons of the viscosities between model predictions and experimental data for different FeO -containing slags (in wt%) by Higgins [190]; Vyaktin [84] and Machin [80] Figure 5.14 Viscosity as a function of FeO at 1250 o C, base slag 52% SiO 2, 13.3% Al 2 O 3, 29.3% CaO, 5.3% MgO by Higgins [190] Figure 6.1 Schematic diagram of equilibrium experiment settings Figure 6.2 Typical deconvolution of Raman spectrum of a 52.6 mol% SiO mol% CaO sample Figure 6.3 the Raman spectrum of SiO 2 -CaO system, which covers the CaO/SiO 2 ratio from 0.55 to Figure 6.4 the Raman spectrum of SiO 2 MgO CaO system under CaO/SiO 2 =1 and 1500 o C condition, which covers the different MgO concentrations Figure 6.5 (a) left, the Raman spectrum of SiO 2 Al 2 O 3 CaO system under CaO/SiO 2 =1 and 1500 o C condition, which covers the different Al 2 O 3 concentrations. (b) Right, the peak deconvolution outcomes of left spectra Figure 6.6 The relative area occupancy of different peaks of (a) SiO 2 -CaO-MgO system ranging of CaO/SiO 2 =1, (b) right, relative area occupancy of different peaks of SiO 2 -CaO-Al 2 O 3 system ranging of CaO/SiO 2 = Figure 6.7 Raman spectrum of 45 SiO 2-10 Al 2 O 3-45 CaO mol% sample at 1300, 1500 and 1600 o C and wollastonite [202] Figure 6.8 DP index again basicity of SiO 2 -CaO, SiO 2 -CaO-MgO, and SiO 2 -CaO-Al 2 O 3 system Figure 6.9 DP index against the estimated densities of slag samples Figure 6.10 DP index of each Raman spectrum against the activation energy Figure 7.1 Schematic diagram of room temperature measurements

25 Figure 7.2 Schematic diagram of (a) left, high-temperature viscosity measurement (b) right, equilibrium experiments Figure 7.3 The viscosity measurements of Baosteel and Jintang blast furnace slag sample Figure 7.4 The relative viscosity of oil-paraffin system at different solid fraction and liquid viscosity at 25 o C Figure 7.5 The suspension viscosity at different solid fraction and particle size at (a) top, 0.1 Pa.s liquid viscosity and (b) bottom, 1 Pa.s liquid viscosity Figure 7.6 The temperature dependence on the oil-paraffin system suspension viscosity (a) 0.05 liquid viscosity suspension at 5, 10, 15 and 20 vol% and (b) 15 vol% suspension at liquid viscosity 0.05, 0.2 and 0.5 Pa.s by Wright [163] Figure 7.7 The measured torque at different rotational speed for (a) 5% solid fraction at 0.05 and 1 Pa.s silicon oil. (b) 10, 20 and 30 % solid fraction at 0.5 Pa.s silicon oil Figure 7.8 The model prediction vs experimental results at (a) top, different models and (b) bottom, 1 Pa.s liquid viscosity Figure 7.9 The model prediction vs experimental results of (a) top JingTang slag and (b) bottom, Baosteel slag Figure 7.10 The comparison between experimental data and model predictions by Wright [163] and Wu [9] Figure 7.11 The comparison of model prediction and other researchers results at (a) room temperature by Chong [153] and Namburu [160], (b) high temperature by Louise [159] and Wright [163]

26 Chapter 1 : Introduction 1.1 Background Introduction In the iron-making process, blast furnace (BF) is still the principle technology in the production of pig iron, which contributed over 90% of pig iron [1]. As shown in Figure 1.1, the iron ore, fuels and fluxes are fed from the top, flowed down and undergo the carbothermic reduction with increasing temperature and carbonic gas. Molten pig iron and slag are tapped from the bottom of the furnace. Molten oxides, known as slag, are composed of gangue minerals and ash from fuels during the high-temperature smelting process. To achieve the optimal processing, the chemical compositions of the slags are significantly varied over a wide range. Viscosity, as one of the most important physical properties of the slag, has been intensively studied in last decades. The ideal slag should have an appropriate viscosity, which flows fluently and removes most of the gangue minerals. Figure 1.1 Technical description of blast furnace ironmaking process [1] The blast furnace slag is composed of four major components SiO 2, CaO, Al 2 O 3 and MgO [2]. The typical industrial blast furnace slag compositions are summarized in 错误! 书签自引用无效. Table 1.1 Composition range of blast furnace slag [1] 1

27 Major Constituents Mass% Minor Constituents Mass% SiO TiO CaO Na 2 O Al 2 O K 2 O MgO 5-10 CaO/SiO Research Gap During the BF operation, slag viscosity plays a significant role in controlling the process, which has a direct impact on the metal/slag separation efficiency and other operation benefits. Understanding and controlling slag viscosity at different compositions and temperatures will assist in improving operation efficiency and minimizing the energy usage. Abundant studies have been conducted on the viscosity measurements and model simulation in the past century for variable oxide systems. The viscosity measurement techniques were continuously developed [3]. It was found that improper selection of crucible/spindle material would significantly increase the measurement uncertainty and confirmed that use of graphite crucible cannot report reliable viscosity data at high temperature [3]. Nowadays, the Mo material replaced the graphite crucible to hold the molten sample. It is necessary to evaluate the published viscosity data and mathematical models for fundamental study and industrial application. The reliability of viscosity data from early publications (around 1950s) should be critically reviewed to establish the database and determine the appropriate prediction range of the existing viscosity models. Different characterization techniques were utilized to determine the chemical and physical properties of slags. The application of Raman spectroscopy can disclosure the vibration units of molten slag, which can be interpreted the structure of silicate melts (amorphous glass phase). Kim reported a mathematical correlation between the peak area of Raman peak and the external physical properties, including density and viscosity [4]. However, the role of Al 2 O 3 was not well studied, which is necessary to utilize the Raman spectrum on the SiO 2 - CaO-MgO-Al 2 O 3 based slag (blast furnace slag) to investigate the silicate structure units. In the blast furnace operations, some solid phases such as oxide precipitates, coke or Ti(CN) can be present in the slag. In addition, the precipitation of solid particles was commonly 2

28 observed in iron, steel, copper and other pyrometallurgy process [5]. These solids can significantly increase the viscosity of the slag causing operating difficulty. There is a research gap that the solid impact on suspension was limited investigated under high-temperature condition due to uncertainty. 1.3 Aim of the Study There is an increasing focus on process optimization and energy usage efficiency of blast furnace ironmaking. During the operation, slag viscosity plays a significant role in controlling the process, which has a direct impact on the metal/slag efficiency. Understanding and controlling slag viscosity at different compositions and temperatures will assist in improving operation production, efficiency, minimizing energy usage. Referring to the research gap, the aims of the study include: 1. Review the experimental methodologies, viscosity data, and models relevant to the blast furnace slag in CaO-MgO-Al 2 O 3 -SiO 2 system 2. Based on collected data and models, establish an accurate viscosity model to predict the viscosity of blast furnace slag in CaO-MgO-Al 2 O 3 -SiO 2 system 3. Research on the viscosity impact of minor elements on the blast furnace final slag in CaO-MgO-Al 2 O 3 -SiO 2 based system. 4. To improve the fundamental understanding of silicate structure, utilized the Raman techniques to study the SiO 2 -CaO based system and determine its correlation with external physical properties. 5. Study the solid impact on suspension systems under room and smelting temperature regions. 3

29 Chapter 2 : Literature reviews This section would introduce the reviewed literature, which includes the following sections. The Section 2.1 introduced the viscosity measurement techniques under high temperature condition, which would be utilized to evaluate the existing viscosity data to develop the viscosity database of CaO-MgO-Al 2 O 3 -SiO 2 system in Section 2.3. Section 2.4 is the mathematical model review and evaluations for the slag of CaO-MgO-Al 2 O 3 -SiO 2 system. From section , it should be noted that the scoping of the viscosity study is fully liquid slag at high temperature. The viscosity study of solid containing slag will be reviewed in the Section The technical review of high-temperature viscosity measurement 2. The review of viscosity study of sub binary and ternary of SiO 2 -Al 2 O 3 -CaO-MgO system 3. The evaluation of the viscosity data of CaO-MgO-Al 2 O 3 -SiO 2 system 4. The review and evaluation of existing viscosity model for CaO-MgO-Al 2 O 3 -SiO 2 system 5. The review of experimental data and mathematical model of suspension system 2.1 The technical review of high-temperature viscosity measurement Viscosity, one of the most important physiochemical properties of slag, has been theoretically and experimentally investigated by abundant researchers over the last decades. The proper measurement techniques could directly determine the measurements reliability. Therefore, in the present section, the measurement techniques would be discussed for the preparation of viscosity data evaluation in Section Liquid Viscosity Definition In fully liquid, the viscosity is an internal property, which is defined as the internal friction of a fluid. For example, as Figure 2.1 shown, assuming a liquid between two closely spaced parallel plates, a force (F) is applied to top plate causes the fluid dragged in the direction of F [6]. The applied force is communicated to neighboring layers of fluid, however, with diminishing magnitude, the fluid motion will progressive decrease as further away from the upper plate. In this system, the dynamic viscosity Ƞ of fluid can be determined using Equation

30 Figure 2.1 Laminar shear of fluid between two plates Equation 2-1: Dynamic Viscosity Calculation Formula Ƞ = τ du x du z Where τ is an applied shear force and dux/duz is the velocity decreasing gradient (also called strain rate). There are two major categories, Newtonian and Non-Newtonian fluid, which is differently in the ratio of applied shear force and dux/duz [7]. The details of each category and example were summarized in Table 2.1. It is known that the Newtonian fluid behavior linear proportional relationship between shear stress and strain rate at a constant temperature, which reported a fixed viscosity for that fluid as shown in Figure 2.2. Other fluids, called non- Newtonian fluid, have a polynomial relation between shear stress and strain rate, which indicated that the viscosity is a variable parameter based on the shear rate. 5

31 Figure 2.2 Shear stress vs strain rate of Newtonian liquid and non-newtonian fluid Table 2.1 Category of different types of fluids Category Description Example Newtonian Fluid Liquid whose viscosity keep constants with the rate of the shear strain Molten slag Water Non-Newtonian Fluid Shear Thinning Liquids whose viscosity increase Modern paints Fluid with the rate of shear strain Ketchup Shear Thickening Fluid Liquids whose viscosity decreases with the rate of shear strain Corn starch Silica nanoparticles in polyethylene glycol Bingham Plastics Behave as a solid at low stresses Mayonnaise but flow as a viscous fluid at high Toothpaste stresses 6

32 A fully liquid slag belongs to the Newtonian fluid at constant condition (pressure, temperature and etc) [8]. This characteristic had been practically confirmed by researchers through the calculation of viscosity at the different shear rate. However, the solid containing slag was reported a different fluidic rheology. For silicate melts, at high-temperature condition, Wu discovered that the slag will become shear thinning fluid above 15% solid fraction [9]. The viscosity of suspension system will be reviewed in Section Viscometer The viscometer is an instrument for measuring liquid viscosity under steady flow condition. At high temperatures, it is practically difficult to examine and observe the relevant rheology property of slag/matte. In pyro-metallurgical field, generally, the velocity of liquid slag and matte is slow and steady, which can be assumed as an ideal flow. At high-temperature condition, a technique that could accurately measure the viscosity at wide slag composition is still a challenging area in the pyro-metallurgy field. In this section, the common methods of viscosity measurement technique of molten slag will be reviewed and compared. From the existing literature, the following viscometers are often used in viscosity measurement of molten slag, which are: Rotational Spindle Viscometer Falling Viscometer Oscillating Viscometer Two extra viscometers were reviewed, which is specifically to the certain liquid system: Capillary Viscometer Ultrasonic Viscometer The major features of above viscometer were summarized in Table

33 Table 2.2 The Summary of Reviewed Viscometers Viscometer Section Description Disadvantage Rotational A wide viscosity measurement ranges cover Pa.s. It require high accuracy torque measurements, hard to clean thick fluids The major disadvantage is the interaction between rotational cylinder and crucible wall, which will reduce the measured torque accuracy [10]. Falling Body A wide viscosity measurement ranges cover Pa.s, simple, good for high temperature and pressure, not good for viscoelastic fluids. The major disadvantage is the thermal expansion of falling ball. And it required a certain distance to achieve freefalling, which is practically difficult at high-temperature condition [11]. Oscillating A wide viscosity measurement ranges covers Pa.s, good for low viscosity liquid, need constant and steady instrument The major disadvantage is similar as falling ball viscometer shown above [11]. Capillary Simple, very high shears and range, but very inhomogeneous shear. The capillary viscometer is often utilized for high viscous and non-newtonian fluid. The capillary viscometer could not control the P O2 during viscosity measurement, which is not suitable for high-temperature condition [12]. Ultrasonic Good for high viscosity fluids, small sample volume, gives shear and volume viscosity, and elastic property data. 8 The ultrasonic viscometer could not provide accurate and precise measurements at high-temperature condition [18].

34 Rotational Viscometer The rotational viscometer is the most widely used viscometer in nowadays research. The basic schematic diagram is shown in Figure 2.3. The bob located in the central position of the crucible and rotated at a constant rate. The resistance force from fluid was recorded as torque. The torque at known rotation rate was measured to calculate liquid viscosity as Equation 2-2. Equation 2-2: Viscosity calculation using data from rotational viscometer [13] Ƞ = τ γ K Where Ƞ is the slag viscosity, τ is the measured torque, γ is the rotational speed and K is the instrument parameter. Figure 2.3 Schematic diagram of rotational cylinder viscometer It has found that reactive force from the bob rotation, called edge effect, reduce the reliability of the measured torque, which causes that the calculated viscosity data inconsistent with shear rate [14]. Different shapes of bobs were designed to minimize the interaction, which improve the measured torque for accurate viscosity measurements. The most common cylinder shape includes the cylinder, disc, cone, spindle and etc., which were demonstrated in Figure 2.4. Other shapes were developed, such as spindle and thin disc to minimize the wall edge effect [13]. 9

35 Figure 2.4 geometry for rotational bob, (a) cylinder, (b) cylinder, (c) cone, (d) cone, (e) parallel plate (f) parallel plate In summary, it is widely accepted that rotational viscometer is mostly used and reliable viscometer, which covers a wide range from 10-4 to 10 7 Pa.s. The major physical uncertainty of rotational viscometer is the edge effect causing by the settings of container and bob, which has been considered and minimized from Chen s research [13]. And the major chemical uncertainty generally is from the reaction among molten slag, crucible, spindle, and atmosphere. The post-experimental analysis is significantly necessary to ensure the viscosity measurement reliability, such as examine the slag sample concentration and container/sensor condition Falling-Body Viscometer Falling-Ball viscometer The falling-ball viscometer is one of the earliest developed methods to determine the viscosity of a Newtonian fluid. In this method, as Figure 2.5 shown, a sphere is allowed to fall freely a measured distance through a viscous liquid medium and its velocity is measured. The viscosity can be measured directly through the falling velocity as Equation 2-3 shown. Equation 2-3: Viscosity Formula of Falling Sphere Method [11] Ƞ = 2gr 2 (ρ s ρ l ) 9U Where Ƞ is the slag viscosity, g is the specific gravity, r is the effective radius of the falling sphere, ρ s is the density of sphere, ρ l is the density of liquid and U is the falling velocity. 10

36 Figure 2.5 Schematic diagram of the falling sphere viscometer Counter-balanced Viscometer The working mechanisms of counter-balance viscometer are similar as the falling-ball viscometer. As Figure 2.6 shown, a standard weight is put on one arm of balance and crucible containing liquid slag is set in another arm inside the furnace. The viscosity of liquid slag is calculated from the movement of weight through a certain fixed distance. The improvement from counter-balanced viscometer is that the flexible control of settling rate of falling items, which improve the measurements reliability comparing to falling ball viscometer [15]. Figure 2.6 Counter balance viscometer [15] 11

37 There are several disadvantages involved using falling body viscometer at the hightemperature condition. The falling item requires a certain distance to reach a constant speed, called free falling velocity. However, the hot zone of the furnace is generally too short for freefalling of the ball, which could not determine the reliable velocity. It practically increased the difficulty of crucible settings to reach steady position and temperature. Another major disadvantage is that the thermal expansion of the ball materials. Riebling determined that the thermal expansion of the falling ball is able to cause Pa.s uncertainty in viscosity measurements, which is dependent on the ball material and settle length [11] Oscillating Viscometer The oscillating viscometer is another technique used to measure the slag viscosity of the small sample. As Figure 2.7 shown, when the piston is contained within the fully liquid vessel and oscillated about its vertical axis, the motion of piston will cause a gradual damping. The damping effects arise as a result of the viscous coupling of the liquid to the piston. From observations of the amplitudes and time periods of the oscillations, a viscosity of the liquid can be calculated. The oscillating method is best suited for use with low values of viscosity within the range of 10-5 Pa.s to 10-2 Pa.s [16]. The closed design has made this design popular on measuring low viscosity liquid, such as pure metals. Figure 2.7 Schematic diagram of the oscillating piston viscometer 12

38 Other Viscometers Capillary Viscometer The capillary viscometer is based on the fully developed laminar tube flow theory (Hagen- Poiseuille flow) and is shown in Figure 2.8. The capillary tube length is much larger than its diameter; therefore, the impact of entrance flow on viscosity measurement can be neglect. The shear stress and strain rate can be measured from mathematical expression of tube diameter and length, which used to calculate liquid viscosity as Equation 2-4. The main advantage of capillary over rotational viscometers is low cost and the ability to achieve high shear rates, even with high viscosity samples. The main disadvantage is high residence time and variation of shear across the flow, which might change the structure of complex test fluids. In addition, because of its long tubes, capillary viscometer does not suit viscosity measurement of high-temperature melts [15]. Equation 2-4. Viscosity Formula of Capillary Viscometer [17] n = τ γ = P D4 π 128QL Where P, D, Q, and L are pressure, tube diameter, fluid volume flow and tube length respectively. Figure 2.8 Schematic diagram of the capillary viscometer 13

39 Ultrasonic viscometer The ultrasonic viscometer is a newly developed technique to measure viscosity based on wave absorption of liquid. Liquid viscosity plays an important role in the absorption of energy of an acoustic wave traveling through a liquid. The mechanical vibrations in a piezoelectric are generated and go through the liquid sample and will be received by another similar transducer in the end. The decay rate and amplitude of wave will be analyzed to calculate fluid viscosity. Ultrasonic methods have not been and are not likely to become the mainstay of fluid viscosity determination because they are more technically complicated than conventional viscometry techniques [18]. Ultrasonic absorption measurements play a unique role in the study of volume viscosity as providing volume viscosity data Post-Experimental Analysis The experimental method used to characterize the internal structures of silicate melts can be classified in terms of a) Composition analysis, b) Surface morphology and c) internal structure. Table 2.3 provides a summary of several experimental techniques that have been used to study the complex silicate system (molten slag). The methods described in Chapter are commonly used to determine the composition of silicate. Chapter outline the methods for surface morphology study. Chapter introduce the techniques for internal structure analysis of silicate. Table 2.3 Summary of post-experiment techniques Chapter Method Exciting Radiation EDS Focus beam of electron Application Obtain the composition of metal element EPMA-WDS Focus beam of electron Obtain the composition of most elements except [O] ICP-MS Pulse from magnetic field Obtain the composition of most elements after calibration of that 14

40 element SEM Focus beam of electron Surface morphology TEM Focus beam of electron Surface morphology Crystal information and etc Raman & FTIR Laser light Stretch and vibration of internal structure XRD X-ray Crystal structure determination NMR Pulse from magnetic field Magnetic properties of atomic nuclei. Order-disorder Composition Analysis The composition analysis of post-experimental sample confirmed the reliability of viscosity data. Three techniques were widely used: a) EDS, b) EPMA and c) ICP. Energy Dispersive X-ray Spectroscopy (EDS) EDS is an analytical technique used for the elemental analysis of metals or chemical characterization of a sample [19]. During operation, a high-energy beam of charged is focused into the sample, which excites the ground state electrons. The excited electrons at inner shell may eject from the shell while creating an electron-hole where the electron was. An electron from an outer, higher energy shell then fills the hole, and the energy difference between electrons may be released in the form of an X-ray. The number and energy of the X- rays can be measured by an energy dispersive spectrometer and recorded. The quantitative analysis can be performed by counting the x-rays at the characteristic energy levels for each element. The accuracy of EDS spectrum can be affected by various factors. There are several common issues of X-ray techniques. These X-rays are emitted in any direction, and so they may not all escape the sample. The likelihood of an X-ray escaping the specimen, and thus being 15

41 available to detect and measure, depends on the energy of X-ray and the amount and density of material it has passed through, which reduced accuracy in inhomogeneous and rough samples. For major elements, it is usually possible to obtain a statistical precision of 3% relative error [20]. In the review of viscosity study of CaO-MgO-Al 2 O 3 -SiO 2, 7 authors reported the composition analysis utilizing EDS [21-27]. EPMA-WDS The Electron Probe Micro Analyser (hereinafter, EPMA ) is an instrument to for elemental analysis, by irradiating electron beams onto the substance surface and measuring the characteristic of X-ray [28]. In the operation, the electrons emitted from the electron source are accelerated at a certain accelerating voltage and collimated through electron lenses. When accelerated electrons hit a specimen, in addition to the X-rays, particles and electromagnetic waves carrying various kinds of information are emitted, which is also called wavelengthdispersive X-ray spectroscopy (WDS). With EPMA, signals such as the characteristic-x-rays, secondary electrons, backscattered electrons, etc. are detected by the appropriate detectors and that information is utilized to find the area of interest on a specimen, and for analysis. Quantitatively, EPMA-WDS report more accuracy elemental analysis than EDS [20]. Comparing their energy resolution, a Si Ca X-ray line on an EDS system will typically be between 160 ev wide. On a WDS system, this same X-ray line will only be about 15 ev wide. This means that the amount of overlap between peaks of similar energies is much smaller on the WDS system. Therefore, the reliability and accuracy of WDS are overwhelming the EDS as from pure to multi-component system. Another major problem with EDS systems is their low court rates. Typically, a WDS system will have a count rate that 10 times of an EDS system. In the review of viscosity study of CaO-MgO-Al 2 O 3 -SiO 2, only 2 authors reported the composition analysis utilizing EPM--WDS technique [29, 30]. Inductively Coupled Plasma Mass Spectrometry (ICP) The inductively coupled plasma mass spectrometry, known as ICP, is a type of mass spectrometry which is capable of detecting metals and several non-metals at concentrations as low as (limited series) [31]. As Figure 2.9 shown, when plasma energy is given to an analysis sample from outside, the component elements (atoms) are excited. When the excited 16

42 atoms return to low energy position, emission rays (spectrum rays) are released and the emission rays that correspond to the photon wavelength are measured. The element type is determined based on the position of the photon rays, and the content of each element is determined based on the wave intensity. To generate plasma, first, argon gas is supplied to torch coil, and high-frequency electric current is applied to the work coil at the tip of the torch tube. Using the electromagnetic field created in the torch tube by the high-frequency current, argon gas is ionized and plasma is generated. This plasma has high electron density and temperature (10000K) and this energy is used in the excitation-emission of the sample. Solution samples are introduced into the plasma in an atomized state through the narrow tube in the center of the torch tube. In the review of viscosity study of CaO-MgO-Al 2 O 3 -SiO 2, only 4 authors reported the composition analysis utilizing ICP technique [32-35]. Figure 2.9 Schematic diagram of ICP [31] Surface Morphology Study The surface morphology provides a visible information on the structure of the silicates. Two most common techniques are SEM and TEM. Scanning Electron Microscope A scanning electron microscope (SEM) is a type of electron microscope that produces images of a sample by scanning it with a focused beam of electrons. The electrons interact with atoms in the sample, producing various signals that contain information about the sample's surface topography and composition. The electron beam is generally scanned in a raster 17

43 scan pattern, and the beam's position is combined with the detected signal to produce an image. SEM can achieve resolution better than 1 nanometer. The common application of SEM is to examine the surface of post-experiment sample. In the viscosity study of fully liquid slag, it is expected that only one phase existing, which could be confirmed by SEM image. Different phase can be observed with the application of different light. In the study of alumina silicate melts, as an example, the application of polarized light exposure the crystal part within samples as Figure 2.10 shown. The crystals appear as wellrounded and homogeneously distributed, which have nearly the same size [36]. Figure 2.10 Spherulite of aluminous enstalite under (a) natural and (b) polarized light after the viscosity measurements [36] 18

44 Transmission Electron Microscope Transmission electron microscopy (TEM) is a microscopy technique in which a beam of electrons is transmitted through an ultra-thin specimen, interacting with the specimen as it passes through it. An image is formed from the interaction of the electrons transmitted through the specimen. The image of TEM is formed as electrons went through the sample, which can obtain many characteristics of the sample, such as morphology, crystallization, and stress. On the other hand, SEM shows only the morphology of samples. In Vail study, the microstructure of various polymer-organically modified layered silicate hybrids, synthesized via static polymer melt intercalation, is examined with transmission electron microscopy [37]. As Figure 2.11 shown, in these hybrids, individual silicate layers are observed near the edge, whereas small coherent layer packets separated by polymer-filled gaps are prevalent toward the interior of the primary particle. In general, the features of the local microstructure from TEM give useful detail to the overall picture and enhance the understanding of various thermodynamic and kinetic issues. However, few study was constructed on the glass form of silicate melts. Figure 2.11 Bright-field TEM image [37] 19

45 Internal Structure Study In the past decades, abundant experimental and theoretical studies have been carried out so far on the determination of silicate structure, thermodynamic and mechanical properties. Many spectroscopic methods have been developed to determine the structure of slags and distinctively identify the ionic structural units composing them. However, due to amorphous properties, novel methods continue to evolve to elucidate the structure of the ionic slag structure for metallurgical slag, many well-proven spectroscopic methods has been developed and are now widely applied to correlate the viscous behavior with structure melts at high temperature. These methods include Raman spectroscopy, NMR, and XRD, which will be reviewed in the present section. Based on the spectroscopic results, the network structure theory was proposed, developed and mostly accepted by present researchers to describe the silicate slag structure. Raman Spectroscopy Raman spectroscopy is a spectroscopic technique used to observe vibrational, rotational, and other low-frequency modes in a system. It relies on inelastic scattering, or Raman scattering, of visible laser light near infrared range. The laser light interacts with molecular vibrations other excitations in the system, resulting in the energy of the laser photons being shifted up or down. The shift in energy gives information about the vibrational modes in the system. Although, the silicate glass is an amorphous state; it is becoming popular to utilize Raman to disclosure the structural information of molten slag of a multi-component system. The Raman investigation had been constructed for pure silica glass, CaO-SiO 2, CaO-Al 2 O 3 -SiO 2 and other multicomponent system by researchers. Several bands were detected by Raman Spectrum in the fused silica glass (amorphous phase) in the shift range of cm -1 as Figure 2.12 shown. The two major bands located in the region of cm -1 and cm -1. Sharp peaks appear in the position of 390, 420, 510, 560 and 590 cm respectively. The peaks in the cm -1 was generally assigned to Si-O-Si bond-bending vibration and formed the silicate network referring to its area. Galeener and co-workers proposed another theory by applying the energy minimization argument method [38]. The bond angle referring to peak D1 and D2 were calculated and 20

46 suggested that the 606 and 495 peak can be assigned to 3-fold and a 4-fold ring of tetrahedral SiO 4 respectively [38]. The ring structure were mentioned and discussed by later researchers [39-41]. However, there is limited experimental evidence for this theory. Figure 2.12 Raman spectrum of silica glass [38] The Raman spectrum of CaO-SiO 2 system was investigated to understand the impact of CaO addition into amorphous SiO 2 [42, 43]. Comparing the spectrum of pure SiO 2 glass (Figure 2.12) and CaO-SiO 2 system (Figure 2.13), the peaks located at 500 cm -1 shrinks and cm -1 enlarged, which indicated the broken of silica tetrahedral network. The addition of CaO would break SiO 4 tetrahedral network and form different [Ca] 2+ [44] - combinations, which can be assigned to the peaks at cm -1. For Raman spectrum region of 800 to 1200 cm -1, the bands were deconvoluted to several peaks for analysis, which reflects different silicate-oxide units [43]. As Figure 2.13 shown, with the decreasing of Ca/Si ratio from 1.4 to 0.5, the intensity of peak M shrinks and peak C significantly enlarged. Through analysis multi-components, four peaks were assigned and summarized in the Table 2.4. After the peak deconvolution, the structural can be qualitatively determined by the ratio of non-bridging oxygen/si (NBO/Si). 21

47 Figure 2.13 The Raman spectrum of SiO 2 -CaO system at different Ca/Si ratio [43] The structure of silicate glasses was continually investigated utilizing Raman spectra [41, 43, 45-48]. Park proposed a research of quantitative structural information such as the relative abundance of silicate discrete anions (Q n units) and the concentration of three types of oxygens, viz. free-, bridging- and non-bridging oxygen can be obtained from micro-raman spectra of the quenched CaO-SiO 2 -MgO glass samples [41]. Various transport properties such as viscosity, density, and electrical conductivity can be expected as a simple linear function of ln (Q3/Q2), indicating that these physical properties are strongly dependent on a degree of polymerization of silicate melts [41]. Table 2.4 the assigned peaks after peak deconvolution in the region cm -1 [41] Peak Raman Structural NBO/Si Structural Shift Description Units (cm -1 ) 22

48 Q SiO 4 with zero bridging oxygen Q Si 2 O 5 with one bridging oxygen Q Si 2 O 6 with 2 bridging oxygen 4 Monomer 3 Dimer 2 Chain Q Si 2 O 7 with three bridging oxygen 1 Sheet X-ray diffraction X-ray crystallography is a technique used for determining the atomic and molecular structure of a crystal, in which the crystalline atoms cause a beam of incident X-rays to diffract into many specific directions. By measuring the angles and intensities of these diffracted beams, a crystallographer can produce a three-dimensional picture of the density of electrons within the crystal. From this electron density, the mean positions of the atoms in the crystal can be determined, as well as their chemical bonds, their disorder, and various other information. On 1968, Mozzi utilized x-ray diffraction to analysis the vitreous silica and reported that the Si-O distance is around 1.62 A; while the Si-O-Si angle is approximately 144 o [49]. As Figure 2.14 shown, the calculated spectrum agreed with the experimental values for the first three peaks. 23

49 Figure 2.14 The pair distribution for the pure SiO 2. A is the experimental curve, B is the calculated curve [49] A high-temperature XRD technique has been carried by Waseda and Toguri for in-situ XRD measurements, which confirm the similarity of the melts structure to the corresponding glasses [50]. However, because of the amorphous materials, it is difficult to gather useful information from CaO-MgO-Al 2 O 3 -SiO 2 system. A limited study was performed in the fully liquid system. Nuclear Magnetic Resonance Spectroscopy Nuclear magnetic resonance spectroscopy, most commonly known as NMR spectroscopy, is a research technique that exploits the magnetic properties of certain atomic nuclei. This type of spectroscopy determines the physical and chemical properties of atoms or the molecules in which they are contained. It relies on the phenomenon of nuclear magnetic resonance and can provide detailed information about the structure, dynamics, reaction state, and chemical environment of molecules. The intramolecular magnetic field around an atom in a molecule changes the resonance frequency, thus giving access to details of the electronic structure of a molecule and its individual functional groups. MMR spectroscopy has been used extensively, similar to Raman spectroscopy in the identification of silicate melts structure. 29Si and 27 Al elements were selected for analysis of silicate melt slag. Most of the binary silicate based slag were investigated using 29 Si NMR. In the structural investigation of the SiO 2 -Na 2 O system by Maekawa, as shown, the peak deconvolution was utilized to quantitatively analysis the correlation between structures and composition, which theoretically determined that the modify ability decreased as Li + >Na + >K + 24

50 at the same basic oxide concentration [51]. As shown in Figure 2.15, this theoretical discovery was confirmed from the experimental measurement by Kim in the CaO-MgO- Al 2 O 3 -SiO 2 -Na 2 O/K 2 O system [52]. Figure 2.15 (a) left, 29 Si NMR spectra of SiO 2 -Na 2 O glasses [52] On 1970, Masson utilizes polymer theory to estimate the molecular size in binary silicate melts [53]. As Figure 2.16 shown, the derived results were in good agreement with experimental spectrum over the entire range of compositions up to the maximum degree of poly utilized NMR to obtain the polymerization degree allowed by the theory in the SiO 2 - SnO binary system. 25

51 Figure 2.16 Activity of SnO plotted against mole fraction of SiO 2 for the SiO 2 -SnO system at 1100 o C. Kozuka experimental data and 1) Masson prediction, 2) Flory expression k 11 =2.55. And 3) Flory expression with k 11 =1.443 [53] 2.2 The review of viscosity data of sub binary, ternary of CaO-MgO-Al 2 O 3 -SiO 2 system A critical review of viscosity data is important for industrial application and fundamental research. In the present section, a careful review of experimental method and viscosity data will be demonstrated first for the binary and ternary of SiO 2 -CaO-Al 2 O 3 -MgO system in section and respectively. In Section 2.2.3, the viscosity study of the minor element on blast furnace slag, which includes TiO 2, CaF 2, MnO, FeO and etc, were reviewed as well. Please note, only the quaternary system viscosity data of CaO-MgO-Al 2 O 3 -SiO 2 were carefully reviewed and evaluated in the Section 2.3. The viscosity data of other systems were collected and utilized as supporting information of the viscosity database, which improved the understanding of the viscosity impact of oxide on silicate network.. In the Section 2.2.4, the evaluation criteria will be introduced and utilized to select reliable data for the SiO 2 -CaO- Al 2 O 3 -MgO system Binary System SiO 2 -CaO SiO 2 and CaO are the two major components for CaO-MgO-Al 2 O 3 -SiO 2 ironmaking slags, which have been investigated by 5 researchers on a wide composition and temperature ranges, which is summarized in Table

52 Table 2.5 Summary of viscosity study at binary system SiO 2 -CaO Composition Viscosity Temperature Methodology Description (wt%) (Pa.s) o C Bockris [54] 45-75% SiO % CaO Hofmaier [22] 45-75% SiO % CaO Kozakevitch [55] 55-75% SiO % CaO Licko [56] 56-63% SiO Rotational viscometer Graphite crucible Rotational viscometer Ar atmosphere Rotational viscometer Ar atmosphere Falling ball viscometer 37-44% CaO Urbain [57] 45-75% SiO % CaO Rotational viscometer Mo crucible and bob Ar atmosphere SiO 2 -Al 2 O 3 For SiO 2 -Al 2 O 3 system, the addition of Al 2 O 3 also reduced the viscosity compared to pure SiO 2. However, the reduction ability of Al 2 O 3 is lower than CaO and MgO content. 3 types of research of viscosity measurements on this system have been constructed. The methodology and viscosity ranges are shown in Table 2.6. Table 2.6 Summary of viscosity data of SiO 2 -Al 2 O 3 system Composition Viscosity Temperature Methodology Description (wt%) (Pa.s) o C 27

53 Elyutin [58] 93-68% SiO % Al 2 O Rotational viscometer Ar atmosphere Kozakevitch [59] 45-55% SiO % Al 2 O Rotational viscometer Ar atmosphere Urbain [57] 23-91% SiO % Al 2 O Rotational viscometer SiO 2 -MgO In the SiO 2 -MgO system, similar to SiO 2 -CaO system, the addition of MgO significantly reduced the slag viscosity compared to pure SiO 2. In addition, by comparing of CaO and MgO at same condition, it is found that CaO has stronger reduction ability than MgO. At 1800 o C, the viscosity of SiO 2 -MgO is slightly higher than SiO 2 -CaO system at various silica concentration, which indicated that the modify ability of CaO is stronger than MgO at fixed condition [60]. 3 types of research of viscosity measurements on this system have been constructed. The methodology and viscosity ranges are shown in Table 2.7. Table 2.7 Summary of viscosity data of SiO 2 -MgO system Composition Viscosity Temperature Methodology Description (wt%) (Pa.s) o C Bockris [54] 55-62% SiO % MgO Hofmaier [61] 56% SiO 2 44% MgO Rotational viscometer Ar atmosphere Rotational viscometer Ar atmosphere 28

54 Urbain [60] 55-65% SiO % MgO Rotational viscometer Mo crucible Ar atmosphere Review of the viscosity measurements in SiO 2 -CaO-MgO ternary system by Licko shows that the replacement of CaO by MgO will reduce the slag viscosity as shown in Figure 2.17 (a). At 1500 C, 40 and 50 wt% SiO 2 condition, the replacement of MgO by CaO can cause server viscosity reduction, which indicated the CaO has stronger network modify ability than MgO. The viscosity measurements by Brokris of SiO 2 -CaO and SiO 2 -MgO binary system support this conclusion as Figure 2.17 (b) shown. Under same basic oxide concentration, the viscosity of SiO 2 -CaO system is larger than the SiO 2 -MgO system at 1850 o C. The viscosity different between SiO 2- CaO and SiO 2 -MgO system decreased above 50 wt% basic oxide concentration; because the viscosity impact of CaO reduced at high concentration. Figure 2.17 isovicosity data by Licko in SiO 2 -CaO-MgO system at 1500 C at 40 wt.% and 50 wt.% SiO 2 [56](b) The viscosity data of Bockris of SiO 2 -CaO and SiO 2 -MgO system at 1750 C [54] Ternary System SiO 2 -CaO-Al 2 O 3 SiO 2 -Al 2 O 3 -CaO ternary system is one of the pseudo-quaternary system; such as CaO-MgO- Al 2 O 3 -SiO 2 and SiO 2 -Al 2 O 3 -CaO-FeO. The study of this ternary system directly supports the quaternary phase study of ironmaking slag. 29

55 The role of Al 2 O 3 in silicate melts is amphoteric. From Saito, at SiO 2 /CaO=0.3, the addition of Al 2 O 3 has a negative impact on the slag viscosity at 1800 o C [62]. However, by Leiba s study, it has been found that at the low SiO 2 /CaO ratio, the addition of Al 2 O 3 has a positive impact on the viscosity and vice versa [63]. At different SiO 2 /CaO ratio, the amphoteric behavior of Al 2 O 3 was studied in terms of its structure unit [AlO 4 ]. The silicate structure details will be reviewed in the later section. 15 researchers of viscosity measurements on this system have been constructed. The methodology and viscosity ranges are shown in Table 2.8. Table 2.8 Summary of SiO 2 -Al 2 O 3 -CaO viscosity study Composition (wt%) Viscosity (Pa.s) Temperature o C Bills [64] 40-50% SiO % Al 2 O % CaO Hofmaier [61] 20-70% SiO % Al 2 O % CaO Urbain [60] 20-70% SiO % Al 2 O % CaO Gultyai [65] 30-55% SiO % Al 2 O % CaO Johannsen [66] 50-70% SiO % Al 2 O 3 30

56 10-30% CaO Kato [67] 32-57% SiO % Al 2 O % CaO Kita [27] 35-50% SiO % Al 2 O % CaO Kozakevitch [59] 10-60% SiO % Al 2 O % CaO Leiba [63] 30-32% SiO % Al 2 O % CaO Machin [68] 30-70% SiO % Al 2 O % CaO Rossin [69] 27% SiO % Al 2 O 3 43% CaO Saito [62] 30-70% SiO % Al 2 O % CaO Scarfe [70] 43% SiO % Al 2 O 3 31

57 20% CaO Solvang [71] 25-47% SiO * % Al 2 O % CaO Taniguchi [72] 43% SiO * % Al 2 O 3 20% CaO SiO 2 -Al 2 O 3 -MgO Similar to Al 2 O 3 -CaO-SiO 2 ternary system, SiO 2 -Al 2 O 3 -MgO is another important pseudoquaternary, which supports viscosity study of the quaternary system. The Al 2 O 3 will contribute a positive impact on the viscosity at the low SiO 2 /MgO ratio and vice versa. 8 researchers of viscosity measurements on this system have been constructed. The methodology and viscosity ranges are shown in Table 2.9. Table 2.9 Summary of viscosity study at SiO 2 -Al 2 O 3 -MgO system Composition (wt%) Viscosity (Pa.s) Temperature o C Hofmaier [61] 20-70% SiO % Al 2 O % MgO Johannsen [66] 65-68% SiO % Al 2 O % MgO Lyutikov [73] 50-60% SiO

58 10-35% Al 2 O % MgO Machin [74] 60-65% SiO % Al 2 O % MgO Mizoguchi [75] 50-65% SiO % Al 2 O % MgO Riebling [76] 43-71% SiO % Al 2 O % MgO Toplis [77] 45-73% SiO % Al 2 O % MgO Urbain [60] 20-71% SiO % Al 2 O % MgO Zhilo [78] 47-56% SiO % Al 2 O % MgO Conclusion The viscosity data of binary and ternary system were utilized as the supporting information for the SiO 2 -CaO-Al 2 O 3 -MgO system. The role of metals oxide can be empirically determined from the collected viscosity data at constant condition (temperature and pressure), 33

59 which is summarized in Table The network theory would be demonstrated in the section 2.3.4, which explains the fundamental mechanisms of oxide impact on pure silica. Table 2.10 Viscosity impact of oxide in their binary and ternary system with silica Viscosity Impact Binary Ternary SiO 2 Positive Positive Al 2 O 3 Positive Negative at low (CaO+MgO) content Positive at high (CaO+MgO) content CaO Negative Negative MgO Negative Negative 2.3 Evaluation of Quaternary system CaO-MgO-Al 2 O 3 -SiO 2 The CaO-MgO-Al 2 O 3 -SiO 2 quaternary system is the four major components of blast furnace final slag viscosity data for 607 compositions in this system have been collected from 37 publications and critically reviewed in this section, which covers composition range of wt% SiO 2, 0-40 wt% Al 2 O 3, 0-60 wt% CaO, 0-38 wt% MgO and temperature between 1350 and 1550 C [12, 21, 24-27, 30, 32, 34, 52, 65, 67, 68, 70, 72, 74, 79-99]. Techniques for the measurement of slag viscosity at high temperatures are difficult and have the potential for large uncertainties in the results. The 37 publications of viscosity study were published from 1940s to 2010s crossing 70 years. In present study, three sequential steps were used to evaluate the data, which check: the review experimental techniques the data self-consistency the cross reference comparison 34

60 In addition, the viscosity impacts of the minor element, including FeO, TiO 2, Na 2 O and K 2 O, were reviewed in the section Experimental Techniques in Viscosity Measurements The proper selection and setting of viscometer will reduce measurement uncertainty. Three types of viscometer were used: rotational viscometer (27 publications), oscillation plate viscometer (7 publications) and falling-body viscometer (2 publications). It is widely accepted that the rotational viscometer is a more reliable viscosity measurement technique compared to other viscometers. For rotational viscometer, one uncertainty is the edge-effect from the crucible wall at high rotational speed; limited researchers reported the setting parameters of crucible/spindle: spindle weight, distances between the spindle and crucible, and thermal expansion, which have studied and reported as uncertainty factor by Chen [13]. The oscillating plate viscometer suits better for low values of viscosity within the range of 10-5 to 10-2 Pa.s, such as pure liquid metal system. For falling-ball viscometer, it has been found that the thermal expansion of the sensor (ball) significantly increases viscosity measurement uncertainty, ranges from 1 to 100 Pa.s, which depends on the temperature and the falling ball material. The falling-ball viscometer results were rejected because of potential uncertainty. From 1997 to 1999, K.C Mills constructed the globe project Round Robin, which determine the accuracy and reliability of various experimental techniques from different labs using the referenced materials. Altogether 21 participants measured the referenced materials and provide valuable information for the crucible and spindle materials. Mill et al reported that the graphite container/sensor materials can cause significant uncertainty (>50%) in the high temperature viscosity measurement. Under graphite crucible condition, Bockris et al reported that graphite material may reduce the SiO 2 and form SiC particles on the crucible wall at high temperature, which may change slag composition and contribute to experimental uncertainties [54]. Software Factsage 6.2 was used to estimate the reaction temperature between SiO 2 and graphite. The graphite container/sensor data were carefully reviewed, and high-temperature sets were rejected (>1520 C ). In the contrast, the uncertainty of viscosity measurements by Mo crucible is under 10%, which is confirmed as the reliable materials. At high temperatures ( C) conditions, the aggressive molten slags may react with the container and sensor materials leading to changes in slag composition or container/sensor geometry [14]. Pt, Pt/Rh alloy, Fe, Mo, and graphite, are major materials for containers and sensors utilized in the reviewed studies. Most of the researchers (18) use N 2, CO or Ar gas to 35

61 prevent potential oxidation reaction between crucible/spindle. Air atmosphere was only utilized in experiments with Pt sensor/container. Despite the chemical reactions, the geometry of container/sensor can be physically changed at high temperatures due to thermal expansion and softening. The hardness of metal keeps reducing when the temperature approaches the melting point. The melting temperature of pure Fe and Pt is 1500 and 1700 C respectively. Therefore, these viscosity measurements, which are taken from improper container/sensor materials and temperature, are not reliable and will not be accepted for model evaluation. In 37 publications, three publications reported non-equilibrium viscosity measurements, in which the viscosity data were recorded during the continuous cooling process. The viscosity and internal structure of the molten slag do not correspond to the recorded temperature when the furnace is continuous-cooling. For same composition slag sample, the viscosity measured on continuous cooling is shown to be lower than the viscosity measured at the steady condition at the same temperature. Therefore, non-equilibrium viscosity measurements are not the actual slag viscosity at designed temperature and they will not be accepted in the database. Some of the viscosity measurements were constructed below the liquidus temperature with the given composition. However, the slag compositions, the presence of solid and container/sensor geometry changes can only be examined by post-experimental technology. However, none of the slag samples was immediately quenched after viscosity measurements in all 37 publications. Therefore, the viscosity measurements require further investigations for removal or not. In summary, the reported methodology is not sufficient to filter out the reliable results. The self and cross consistency of viscosity data should be checked Data Consistency Liquidus temperature is an important indicator to discover inappropriate measurements of the viscosity. The phase diagram of CaO-MgO-Al 2 O 3 -SiO 2 has been well studied. Software Factsage 6.2 is utilized to predict the liquidus temperature of slag. The viscosity of bulk slag with solid precipitated significantly increased. For example, in Figure 2.18, the viscosity measurements were reported by Tang et al and Machin. Only the last points of two sets were rejected because of dramatic increasing. The second last point of Tang s was accepted. To prevent the prediction error of liquidus temperature, the viscosities taken below liquidus 36

62 temperature have been critically reviewed and abnormal ones were removed from the database. Figure 2.18 Examples showing viscosity measured below liquidus by Machin [74] and Tang [99] It is accepted that the slag viscosity and temperature follow the Arrhenius-type equation. According to the Equation 2-5, the natural logarithm of viscosity has a linear correlation to reciprocal of absolute temperature. Figure 2.19 shows an example of viscosity measurements with high and low consistency. Clearly, the data from Muratov and Yakushev et al have low reliability and they are excluded from the database [98, 100]. In Yakushev s data, the last three points dramatically increased, which were taken under liquidus temperature[98]. Due to insufficient information of post-experiment analysis from published paper, the reasons for other non-linear results are not clear. Data linearity is a good indication to evaluate the measurements reliability in the absence of enough experimental conditions. Equation 2-5 Logarithm form of Arrhenius equation ln(η) = ln(a) + E T Where η is viscosity, A is the pre-exponential factor, E is the activation energy of system and T is the absolute temperature (K) 37

63 Figure 2.19 Linearity comparison examples by Muratov [100], Machin[80], and Yakushev [89] Cross Reference Comparison For CaO-MgO-Al 2 O 3 -SiO 2 slag system, the experimental measurements and modelling focus on the blast furnace composition range. The viscosities measured from different researchers at close compositions were carefully compared to cross check the reliability of the data. As shown in Figure 2.20, there were four sets of viscosity measurements in the same composition and three sets of data are close. Data from Kita are excluded from the database as they are significantly different from others. Figure 2.20 Four sets viscosity measurement at 45 wt % SiO 2, 15 wt% Al 2 O 3, 30 wt% CaO and 10 wt% MgO by Gul tyai [83], Han [93], Kita [27] and Machin [27, 74, 83, 93] 38

64 In case the available viscosity data are not consistent and the information reported is not enough for the evaluation, the viscosities at this composition were measured by the present authors using a recently developed technique at the University of Queensland. Figure 2.21 is an example, where it can be seen that the results of Park et al are confirmed by the author's measurements and Kim et all s data are not accepted. The methodology was detailed discussed in a previous publication. The main feature of this technique is the possibility of quenching the slag sample immediately after the viscosity measurement. Electron probe X- ray microanalysis (EPMA) with wave spectrometers was used for microstructural and elemental analyses of the quenched samples. In addition, the possible errors associated with the high-temperature viscosity measurements have been analyzed and significantly minimized, which include effects of bob weight, distances to the crucible and thermal expansion during rotational viscometer measurements. Figure 2.21 Comparison of viscosity data by the present authors (UQ), Kim et al [35] and Park et al [101] at composition of 36.5% SiO 2, 17% Al 2 O 3, 36.5% CaO and 10% MgO Summary of Experimental Data 3135 viscosity data for 607 compositions in this system have been collected from 37 publications, critically reviewed and summarized in Table The viscosity measurements taken at graphite crucibles, such as Gul tyai and Gupta were mostly rejected [83, 87]. The data of three authors, Kim, Sheludyakov, and Tsybulnikov, were fully rejected because measurements were carried out at non-equilibrium condition [35, 86, 88]. The viscosity data of Kato and Taniguchi were also fully rejected because of large uncertainty at the falling ball 39

65 viscometer. Over 50% of Machin s data were rejected, due to most of measuring temperatures were under liquidus temperature of slag for more than 50 o C. The rejection reasons include: Lower than liquidus temperature (436 data) Use of graphite crucible at high temperature condition (273 data) Non-equilibrium measurement (252 data) Low linearity with unknown reasons (197 data) Conflict with other authors results at same composition (82 data) Extreme large or small viscosity data, >40 Pa.s or <0.01 Pa.s (68 data) Only 2 viscosity points at one composition (36 data) In summary, 1760 viscosity measurements were accepted and utilized for viscosity model development in CaO-MgO-Al 2 O 3 -SiO 2 system. 40

66 Table 2.11 The summary of existing viscosity study in CaO-MgO-Al 2 O 3 -SiO 2 system Sources Method Atmosphere Container Sensor Temperature ( C) Post Experiment Techniques Viscosity (Pa.s) No of Data Accepted Forsbacka [21] RB Ar+5%CO Mo Mo EDS Gao [30] RB CO C Mo XRD FT-IR Gul'tyai [83] RB N 2 C C N/A Gupta [87] RB Ar C C N/A Han [93] RB Ar C Pt-10Rh N/A Hofmann [82] RB Air Pt Pt EDS Hofmann [61] RB n/a C N/A EDS Johannsen [24] RB n/a Pt/20Rh Pt/20Rh EDS Kawai [79] RB n/a C C N/A

67 Kim [102] RB Ar C N/A XRF Kim [103] RB Ar Pt-10Rh Pt-10Rh N/A Kim [35] RB Ar Pt/10Rh Pt/10Rh ICP Koshida [25] RB N/a N/a N/a EDS Li [104] RB Ar Mo Mo FT-IR Lee [91] RB Ar Pt/10Rh Fe N/A Lee [105] RB Ar Pt/10Rh Fe XRF FT-IR Mishra [90] RB N 2 C n/a N/A Muratov [100] RB n/a Mo Mo N/A Nakamoto [26] RB Ar Fe Fe EDS XRD Park [106] RB Ar Pt-10Rh Pt-10Rh FT-IR Raman

68 Saito [95] RB Ar Pt-20Rh Pt-20Rh N/A Scarfe [70] RB Air Pt Pt/10Rh N/A Shankar [32] RB Ar Mo Mo ICP Song [107] RB Ar Mo Mo SEM-EDS Tang [99] RB Ar Mo Mo N/A Vyatkin [84] RB n/a C C N/A Yao [82] RB Ar C Mo XRF Kita [27] OP n/a Pt Pt EDS Machin [68] OP Air Pt Pt-alloy X-ray Machin [74] OP Air Pt Pt-alloy X-ray Machin [80] OP Air Pt Pt-alloy X-ray Sheludyakov [108] OP n/a Pt Pt N/A Tsybulnikov [88] OP n/a Mo Mo N/A

69 Yakushev [98] OP n/a Mo Mo N/A Kato [67] FB Air Pt Pt N/A Taniguchi [72] FB n/a Pt Pt N/A

70 2.3.5 Random Network Structure Zachariasen firstly proposed the ideas of the network structure of the binary system of silicate slags [109]. The binary system was continuously developed and extended to the multi-component system. In the CaO-MgO-Al 2 O 3 -SiO 2 system, they can be categorized into three groups, which are the acidic oxide (SiO 2 ), basic oxide (CaO and MgO) and amphoteric oxide (Al 2 O 3 ). As Figure 2.22 shown, pure SiO 2 forms a network structure using (SiO 4 ) tetrahedral units, which contribute for viscosity ascending. When the basic oxides are added, the O 2- (free oxygen) from basic oxide will bind with O 0 (bridging oxygen) to break the silicate network and reduce the viscosity [111]. Al 2 O 3 can behaviour as either acidic or basic oxide. When there are sufficient basic oxides, excess cations (Ca 2+ and Mg 2+ ) balance the (AlO 4 ) 5- charges, the Al 2 O 3 acts as an acidic oxide, Al 3+ can form tetrahedron structure (AlO 4) 5- as (SiO 4 ) 4- and incorporate into the silicate network. In the case of insufficient basic oxides, Al 2 O 3 will behaviour as Ca 2+ or Mg 2+ to break the (SiO 4 ) 4- network. Figure 2.22 (a) Left, pure SiO 2 structure. (b) Right, silicate mix with other basic oxide solution Although, the network model is widely accepted as the best structural model of the silicate melts. The applicability to the multi-component alkali and alkaline is much 45

71 more questionable, such as TiO 2 and CaF 2. The random network model has been optimized for certain alkaline glass system. However, limited literatures discussed the possible structural units between silicate network and basic oxides; because the present techniques could not determine the structural units at smelting temperature conditions. Most of theories were the estimation based on the experimental measurements and post sample analysis. For example, Bockris and co-workers proposed a theory of the structure units of CaO-SiO 2 system by assuming the coexisting form of silicate with basic oxide for binary slag system. The summary of structure description of silicates is given in Table 2.12 [111]. Table 2.12 Summary of Brokis study of expression of SiO 2 unit at various concentration [111] SiO 2 concentration (wt %) Type of silicate units 0-33 [SiO 4 ]O 2- ions Chains of general form Si n O 3n Mixture of discrete polyamines based on Si 3 O 10 and Si 6 O Discrete silicate polyamines based upon a six-membered ring Si 6 O Essentially SiO 4 network with number of broken bonds approximately equal to number of added O atoms from MeO and a fraction SiO 2 molecules and radicals containing Me 100 Continuous networks of SiO 4 tetrahedral with some thermal bonds 46

72 2.3.5 Minor Element Impact In the ironmaking process, the four major components, SiO 2, Al 2 O 3, CaO, and MgO occupied over 96% of the final slag. The rest 4% were contributed by the other metal oxides, including FeO, F, S, and Cu2O, which is called minor elements. A limited study was constructed on the viscosity impact of minor elements, which will be reviewed in the present study FeO There are two different slags on the CaO-MgO-Al 2 O 3 -SiO 2 - FeO system, one is ironmaking final slag and another is copper-making slag. In the present study, only the ironmaking final slag will be studied according to the scoping, as a summary in Table Only 2 researchers constructed the viscosity study of CaO-MgO-Al 2 O 3 - SiO 2 - FeO system in the composition range of ironmaking slag, which report wt% SiO 2, wt% CaO, wt% Al 2 O 3, 0-10 wt% MgO and 0-5 wt% FeO. Iron saturation is always considered by researchers, which control the oxidation status of Fe element. In conclusion, the FeO addition has a negative impact on the slag viscosity. Table 2.13 Summary of viscosity study at CaO-MgO-Al 2 O 3 -SiO 2 - FeO system Composition Viscosity Temperature Methodology Description (Pa.s) ( o C) Tang [112] %SiO %Al 2 O %CaO Rotational viscometer Mo crucible and bob Ar atmosphere %MgO 0-1 %FeO 47

73 Kim [94] %SiO %Al 2 O %CaO Rotational viscometer Mo crucible and bob Ar atmosphere %MgO 1-5 %FeO It is confirmed that the addition of FeO content will reduce the slag viscosity [113]. In addition, the modify ability of FeO content could be determined from viscosity measurement. Kim proposed that, if the SiO 2 and Al 2 O 3 content kept constant, the replacement of either CaO or MgO by FeO content will increase the slag viscosity, which indicated that the viscosity reduction ability of FeO is weaker than the CaO and MgO [94]. As Figure 2.23 shown, the viscosity firstly decreased and then increased with the replacement of both CaO and MgO by FeO at fixed temperature condition. Figure 2.23 FeO replaced the CaO and MgO oxide at 40 wt% SiO 2, 1500 o C for SiO 2 -CaO-FeO system, 40 wt% SiO 2, 1550 o C for SiO 2 -MgO-FeO system, by Bockris [94], Chen [115], Ji [114]and Urbain [13] 48

74 TiO 2 TiO 2 is a gangue mineral containing in the iron ore, which is removed in the slag phase. In the ironmaking process, there are two types of slag containing TiO 2 ; normal blast furnace slag contain <1 wt% TiO 2 and another in PanSteel could achieve 30 wt% TiO 2. The PanSteel from Panzhihua of China reported final slag containing large amounts of TiO 2 due to vanadium-titanium magnetite ore in that region, which would achieve over 30% TiO 2 in the slag. The viscosity study of slag is completed by Chinese researchers. Also, extra TiO 2 were added in the recent ironmaking process. Because, the formation of Ti(C, N) fill the defect spot inside the furnace wall, which can extend the usage life of blast furnace. The viscosity study of two types of TiO 2 slag is summarized in Table Table 2.14 Summary of viscosity study at CaO-MgO-Al 2 O 3 -SiO 2 -TiO 2 system Composition Viscosity Temperature Methodology Description (Pa.s) ( o C) Handfield %SiO Rotational viscometer [116] %Al 2 O Pt crucible and bob %CaO Air atmosphere %MgO 5-26 %TiO 2 Van [117] %SiO %Al 2 O %CaO %MgO Rotational viscometer Mo crucible and bob Ar atmosphere %TiO 2 49

75 Saito [62] %SiO %Al 2 O %CaO 5-10 %MgO Rotational viscometer Graphite crucible and bob Ar atmosphere %TiO 2 Xie [118] %SiO %Al 2 O %CaO 7-16 %MgO Rotational viscometer Graphite crucible and bob Ar atmosphere %TiO 2 Shankar %SiO Rotational viscometer [32] %Al 2 O Graphite crucible and bob %CaO Ar atmosphere 2-5 %MgO %TiO 2 Liao [119] %SiO 2 12 %Al 2 O %CaO 7 %MgO Rotational viscometer Graphite crucible and bob Ar atmosphere %TiO 2 Park %SiO Rotational viscometer [120] 17 %Al 2 O Mo crucible and bob %CaO Ar atmosphere 10 %MgO 50

76 5-10 %TiO 2 In terms of the viscosity impact of TiO 2, there are two contradictive opinions. Liao believed that the TiO 2 has a similar structural unit as SiO 2, which positively increase the slag viscosity (TiO 2 >20wt%) [119]. When the TiO 2 concentration decreased, in Park s viscosity measurement, it has been found the addition of TiO 2 reduce the slag viscosity of blast furnace type slag [121] Na 2 O and K 2 O The viscosity impact of Na 2 O and K 2 O is different, which is negative and positive respectively. Most of the basic oxides were reported a negative impact on the slag viscosity, such as CaO, MgO, FeO, CuO and etc. However, it is found that the addition of K 2 O would increase the slag viscosity in CaO-MgO-Al 2 O 3 -SiO 2 system. The mechanism of viscosity increasing is not fully explained. Both Kim and Park estimated that the K + has a strong combination with AlO 4 and form KAlO 4 units, and hence increase the slag viscosity by network formation. The reviewed publications were summarized in Table Table 2.15 Summary of viscosity study at CaO-MgO-Al 2 O 3 -SiO 2 -Na 2 O and K 2 O system Composition Viscosity Temperature Methodology Description (Pa.s) ( o C) Na 2 O Kim [122] %SiO %Al 2 O Rotational viscometer Pt crucible and bob 51

77 20-40 %CaO Ar atmosphere 5-10 %MgO %Na 2 O Kim [123] %SiO %Al 2 O %CaO Rotational viscometer Pt crucible and bob Air atmosphere 4-8 %MgO 1-10 %Na 2 O Takahira [124] % SiO %Al 2 O %CaO 5-10 %MgO 1-5 %Na 2 O Rotational viscometer Mo crucible and bob Ar atmosphere K 2 O Kim [122] %SiO %Al 2 O %CaO Rotational viscometer Pt crucible and bob Ar atmosphere 3-15 %MgO 1-5 %K 2 O Wu [125] %SiO %Al 2 O %CaO Rotational viscometer Mo crucible and bob Ar atmosphere 5-15 %MgO 3-10 %K 2 O 52

78 2.4 The review and evaluation of viscosity model for silicate melts of CaO-MgO- Al 2 O 3 -SiO 2 system Abundant viscosity models were developed to predict the viscosity of molten slag at various systems. In the present sections, the models, which covered CaO-MgO-Al 2 O 3 - SiO 2, will be reviewed. Some models only release the equations and did not include parameters, which is not capable of calculating the slag viscosity. These models were reviewed from section to The other models, suitable for CaO-MgO-Al 2 O 3 - SiO 2 system, were reviewed from section to In addition, the prediction performance of each model will be shown in the section , which utilized the evaluated viscosity database in the CaO-MgO-Al 2 O 3 -SiO 2 system Bottinga Model The Bottinga model has been developed for magmatic silicate liquid of geological interest [126]. Authors used a total of 2440 observations, which span the temperature range 1100 to 1800 o C and the composition range 35 to 91 mol% SiO 2 for D parameters optimization. The Equation 2-6 were proposed to calculate the viscosity utilizing parameter D and slag composition. Equation 2-6. Bottinga model Equation [126] log(η) = X i D i Where η viscosity in Poise, X i is the weight fraction of metal oxides and D i are the model parameters, which are constant over restricted composition and temperature range. An example of parameter D value of CaO-MgO-Al 2 O 3 -SiO 2 system is shown in Table 2.16 below, it can be seen that the temperature gap between two values is large and 53

79 cause deviations on viscosity predictions. In addition, the four components CaO, MgO, Al 2 O 3 and SiO 2 in different molar fractions has new sets parameters, which altogether report 470 model parameters. Table 2.16 the parameter D values of Bottinga model in CaO-MgO-Al 2 O 3 -SiO 2 quaternary system [126] When X SiO2 is from Component 1400 o C 1450 o C 1500 o C 1550 o C SiO CaAl 2 O MgAl 2 O CaO MgO Neural Network Model Hanao used neural networks theory to describe viscosity of blast furnace-type slags [127]. The neural network is a typical fully computer-based models without any consideration of silicate structure. The neural network model did not report a set of equations or parameters for viscosity calculation. The software will compare the input variable with existing database and calculate the viscosity value. The input includes molar fraction SiO 2, Al 2 O 3, CaO, MgO, Temperature, and basicity. This theory can apply in any other fields with large quantity of database [127] Giordano Model The Giordano model is a purely empirical models, which is developed based on Vogel-Fulcher-Tamman equation to describe slag viscosity [128]. The VFT equation 54

80 is shown below, where A, B, and C are model parameters. Model parameters were fitted to each slag compositions as Equation 2-7 shown. Therefore, the model reports an outstanding agreement with entire database (5% relative error) but is limited to use for un-fitted composition. Equation 2-7. VFT model equation [128] log(η) = A + B T C Where η is the viscosity of Poise, T is the temperature in K, A, B and C is the parameters given by Giordano shown in Table Table 2.17 Model parameters for Giordano [128] A B C Relative Error Slag Sample Slag Sample Slag Sample Slag Sample CSIRO Model Zhang proposed a structurally-based model to predicate the viscosity of a large silicate melts system, including, pure oxides SiO 2, Al 2 O 3, CaO, MgO, Na 2 O K 2 O and binary systems SiO 2 Al 2 O 3, SiO 2 CaO, SiO 2 MgO, SiO 2 Na 2 O, SiO 2 K 2 O, Al 2 O 3 CaO, Al 2 O 3 MgO, Al 2 O 3 Na 2 O, Al 2 O 3 K 2 O, as a fundamental study for the system SiO 2 Al 2 O 3 CaO MgO [129]. The completed model reported a good agreement between experimental data and calculated viscosity using only one set of model parameters. The critical model parameters were calculated using the concentration of different oxygen species, which were obtained by the cell model formalism. However, 55

81 the model parameters were not published. Only the equation can be reviewed, as shown in Equation 2-8. Equation 2-8 CSIRO model equation [129] η = A W T exp ( Ew η RT ) Where η is the viscosity, T is the temperature in (K), R is the gas constant, A W and E w n are the pre-exponential term and the activation energy, respectively. E w η = a + b(n O 0) 3 + c(n O 0) 2 + d(n O 2) Where a, b, c and d are fitting parameters optimized against experimental data. The values of N O and N O2- were obtained by the Cell model formalism. ln(a W ) = a + b E w η Where a and b are fitting parameters in the publications [129] KTH Model The KTH viscosity model was developed on the basis of the Erying equation, which is based on the absolute reaction rate theory for the description of flow processes [130]. The completed model reported a good agreement between experimental data and calculated viscosity using as a function of temperature and composition. However, the model parameters were not published. Only the equation can be reviewed, as shown in Equation 2-9. Equation 2-9 Model equation of KTH model [130] η = hnρ exp ( G M RT ) 56

82 Where η is the viscosity, T is temperature in (K), R is the gas constant, h is Planck s constant, N is Avogadro's number, ρ is average density and G is the gibbs energy of activation per mole Urbain Model Urbain s model is one of the most widely used slag viscosity models and based on the Weymann-Frenkel liquid viscosity model [131]. Urbain proposed two versions models on 1981 and 1987 respectively. The application range of Urbain model include the oxide CaO, MgO, SiO 2, S and F containing slag, which covers most of slag system. Although, the Urbain model covers wide range of slag system; the prediction deviations is large in the particular slag system. Another disadvantage of Urbain model is the consideration of amphoteric oxide, which regarded Al 2 O 3 as positive terms to slag viscosity without correlation with basic oxide concentration. Therefore, in the conditions of low abundance of basic oxide slag, Urbain model reported a high variance of viscosity prediction. For the Urbain model 1981 and 1987 version, the mathematical equations and parameters were similar except the calculation of individual B parameters. The development Urbain model was based on the CaO-Al 2 O 3 -SiO 2 system and classified the slag components into three categories: glass former; modifier and amphoteric [132]. In the CaO-MgO-Al 2 O 3 -SiO 2 system, the X G, X M and X A were calculated as follows. The X G* was obtained by division of (1+X CaF2 +0.5X FeO1.5 +X ZrO2 ). For example, the X G* =X G / (1+X CaF2 +0.5X FeO1.5 +X ZrO2 ). Equation 2-10 Urbain Model Equation [132] X G = X SiO2 + X M = X CaO + X MgO + X A = X Al2 O 3 + X Fe2 O 3 + X B2 O 3 57

83 X G X G = 1 + X CaF X FeO1.5 + X ZrO2 η = A T exp ( 1000B T ) ln(a) = 0.29 B Where X A is the molar composition of that component, η is the viscosity in poise, T is the temperature in K, A and B are model parameters. The X A were fitted into a third order polynomial equation to calculate the parameter B. Parameter B in Urbain model equalled to the role of activation energy of Arrhenius equation. The parameters B were expressed by third order polynomial equation of 4 model terms B 0-3 as equation shown. Equation 2-11 Urbain Model Equation [132] B 0 = α α 2 B 1 = α α 2 B 2 = α α 2 B 3 = α α 2 B = B 0 + B 1 (X G) 3 + B 2 (X G) 2 + B 3 (X G) 3 X M α = X A +X M Where X A and X M is the molar composition of that component On 1987, Urbain suggested a different method to determine the individual parameter B of B Ca and B Mg ; and then determined the mean B as Equation 2-12 shown. The modified equations of B improve the prediction accuracy CaO, MgO and MnO including system, especially CaO-MgO-Al 2 O 3 -SiO 2. The B of Ca, Mg and Mn (if necessary) was calculated individually, which combine to the final B. The required model equations and parameters were shown in Table

84 Equation Urbain model equation [131] B = M Ca B Ca + M Mg B Mg + M Mn B Mn M Ca + M Mg + M Mn 0 B i(i=ca,mg) = B i(i=ca,mg) 1 + B i(i=ca,mg) 2 + B i(i=ca,mg) 0,1,2 B i (i=ca,mg) = B 0,Ca + B 1,Ca R + B 2,Ca R 2 M Ca + M Mg Basicity index (R) = M Ca + M Mg + M Al Table 2.18 Model parameters of Urbain Model [131] Constant B 1 * α B 2 * α 2 CaO CaO MgO MnO CaO MgO MnO MgO MnO The Urbain model of 1987 version is more suitable for the viscosity prediction of CaO-MgO-Al 2 O 3 -SiO 2 system. As Figure 2.24 shown, the 1987 Urbain models reported smaller prediction deviation comparing to the 1981 version, due to Urbain optimization on the parameter calculations. Please note, the quantity of viscosity measurements of before-evaluation group is 3105, which was the original viscosity data without evaluation process in Section 2.3. The quantity of viscosity measurements of after-evaluation group is

85 Figure 2.24 The comparison between Urbain model of 1981 [132] and 1987 version [131] using the viscosity database of before-evaluation, after-evaluation and BF composition Riboud Model Riboud optimized the Urbain model to estimate the viscosity in mould fluxes [133]. Riboud simplified the Urbain s expression of B term, the model term A is not dependent on B, which was calculated using slag composition. As Equation 2-14 shown, the network modifiers parameter, CaO, and MgO have the same contribution (value=1.73) to the viscosity, which did not obey their network modify ability. It is accepted that different basic oxide has various ability to break silicate network. Equation Riboud model equation [133] η = A T exp ( 1000B T ) lna = (X CaO + X MgO ) 35.76X Al2O3 B = (X CaO + X MgO ) X Al2O3 Where η is the viscosity of Poise, A and B is the parameters, T is the temperature in K, X Ca and X Mg are the molar composition of slag system 60

86 Kondratiev and Forsbacka Model The modified-urbain viscosity model was also constructed at the University of Queensland by Kondratiev and Forsbacka for the viscosity prediction of coal ash slag [134, 135]. Kondratieve first proposed the model for viscosity prediction of coal ash slag of CaO-FeO-Al 2 O 3 -SiO 2 system [134]. Later, Forsbacka optimized the parameters using excel-solver and extend the prediction range to MgO, CrO and Cr 2 O 3 containing system [135]. The proposed model reported similar mathematical structure as Urbain model, which changed the equations and parameters of B calculation. The model was able to describe the viscosity of complex slags reasonably well in most experimental cases, which agreed well with experimental measurements in the Round Robin project [135] Iida Model Iida proposed the mathematical model to estimate the slag viscosity, which is based on Arrhenius type of equation and slag basicity property [136, 137]. The core parameters A,μ 0 E are determined based on temperature as Equation 2-15 shown. B i was defined as slag basicity. In the CaO-MgO-Al 2 O 3 -SiO 2 system, it is accepted that (wt% CaO/SiO 2 ) slag basicity is an indication of the ironmaking operation performance. Referring to the viscosity, a high basicity slag would report a low viscosity. Iida considered and encountered the amphoteric oxide Al 2 O 3 and regarded it as a network former, which will reduce the slag basicity. Iida reported that the viscosity predictions closely fit with the experimental data for a large number of blast furnace type slags. The relevant equations and parameters are shown in 错误! 未找到 引用源 and Table 2.19 respectively. Equation Iida Model Equations [136, 137] η = A μ 0 exp ( E Bi ) 61

87 A = T T 2 Bi = a CaO W CaO + a MgO W MgO a Al2O3 W Al2O3 + a SiO2 W SiO2 μ 0 = μ 0i X i M μ 0i = i (T m ) 0.5 i ( (V m ) 2/3 H i exp ( i R (T m ) 0.5 ) i ) H i = 5.1 (T m ) 1.2 i E = T Where M i is the formula weight of i component, T mi is the melting temperature, R is gas constant, H i melting enthalpy of i component, B i is the slag basicity, W is the wt% of each oxide, a oxide is the model parameters, E is the enthalpy of slag. Table 2.19 Equation parameters for Iida model [136, 137] SiO 2 Al 2 O 3 CaO MgO A Temperature Μ o C SiO 2 Al 2 O 3 CaO MgO /

88 2.4.8 NPL (Mills) Model Mills viscosity model (also called NPL) is based on optical basicity parameter, which is firstly determined and named by Duffy J.A [138, 139]. The metal oxides were reported various peak intensity under UV light. Assume CaO is 1, the other oxides basicity were determined and demonstrated by Duffy [139, 140]. The NPL model was developed based on the Arrhenius-type equation. As Equation 2-16 shown, the A OP, Mills calculated the slag basicity with insertion of oxide composition*optical basicity. The A OP term were directly linked to the parameter A and B for viscosity calculation. The predictions of NPL model were in reasonable agreement with experimental data for reported multicomponent system. Equation NPL (Mills) model equation [138] η = A exp ( B T ) B = Exp ( ) 1000 Aop ln(a) = A op (A op ) 2 A op = γ SiO2 M SiO2 + γ Al2O3 M Al2O3 + γ CaO M CaO + γ MgO M MgO 2 M SiO2 + 3 M Al2O3 + M CaO + M MgO Where η is the viscosity in Pa.s, T is the temperature in K, M i is the molar composition of slag system and all other parameters are shown in Table Table 2.20 Model parameters of NPL model [138] SiO 2 Al 2 O 3 CaO MgO Optical Basicity

89 2.4.9 Shankar Model Based on Mills work on the optical basicity, Shankar did a doctoral thesis work on the studies on high alumina blast furnace slags, which investigate the viscosities data and improve the model prediction accuracy on blast furnace slag system [141]. The model equations were shown as Equation Shankar has different calculations on the A OP comparing to the NPL model. The basicity of basic oxide and acid oxide were normalized first; then calculated the slag basicity. The model predictions report satisfactory agreement with experimental data. Equation Shankar model equations [141] 1000 E η = A exp ( ) T ln(a) = A op B = A op A op = ( γ CaO M CaO + γ MgO M MgO )/ ( γ SiO2 M SiO2 + γ Al2O3 M Al2O3 ) M CaO + M MgO 2 M SiO2 + 3 M Al2O3 Where η is the viscosity of poise, T is the temperature in K, M i is the molar composition of slag system and all other optical basicity parameters are the same as Table 2.20 shown Hu Model Hu did a similar work as Shankar that optimized the Mill s model towards the blast furnace slag field [142]. Comparing the model from Mills and Shankar, Hu consider the alumina charge compensation effect by the CaO, which is noted from his equation. However, the equation structure can only apply on the M CaO >M Al2O3 condition, which is a typical blast furnace composition range. The model prediction fits well with experiment data in the SiO 2 -Al 2 O 3 -CaO, CaO-MgO-Al 2 O 3 -SiO 2 and CaO-MgO- 64

90 Al 2 O 3 -SiO 2 -TiO 2 system, with the mean deviation less than 25%. The model equations were shown as Equation Equation Hu model equations [142] 1000 E η = A exp ( ) T ln(a) = A op B = A op A corr = M SiO M Al2O3 + (M CaO M Al2O3 ) M MgO 2 M SiO2 + 3 M Al2O3 + (M CaO M Al2O3 ) + M MgO Where η is the viscosity of poise, T is the temperature in K, M i is the molar composition of slag system and all other optical basicity parameters are the same as Table 2.20 shown Shu Model There are two versions of Shu s viscosity model, which published at 2009 and 2015 [143, 144]. In the present study, only the latest version (2015) were reviewed and evaluated. Shu pointed that viscosity of CaO-MgO-Al 2 O 3 -SiO 2 quaternary system is composed of two sub ternary systems ideal mixing, which is SiO 2 -Al 2 O 3 -CaO and SiO 2 -Al 2 O 3 -MgO. This assumption has benefits that ternary system involved parameters and consideration are less than the quaternary system. For example, Ca and Mg cations are required to charge compensate (AlO 4 ) 5- structure. This assumption avoids the consideration of the priority of Ca and Mg cations with AlO 4. The normalized molar fraction formula is used to combine two sub-ternary systems to a quaternary variable, and then use Arrhenius equation to calculate the final viscosity. Shu s model considers the equilibrium between three types oxygen: O (bridging oxygen), O - (non-bridging oxygen) and O 2- (free oxygen). Shu utilizes the Ottonello s 65

91 work on the equilibrium constant K, which established a link between the optical basicity and silicate polymerization [144]. A good agreement between calculated and measured viscosity with a mean deviation of less than 25% was achieved. Equation Shu model equations [143, 144] lnη = lna + E/RT ln(a) = m E R + n E = X Al E Al + (1 X Al )(X O 2 E O 2 X O (y Si E O (Si O ) + y Al E O (Al O )) + X O 0 (y Si E O 0(Si O 0 ) + y Al E O 0(Al O 0 ))) Where η is the viscosity of poise, T is the temperature in K, X i is the molar composition of slag system and E parameters shown in publication [143, 144] Zhang Model Zhang proposed a mathematical model to describe the viscosity behavior of the multicomponent system, which is based on different oxygen ions present in molten slag [145]. The three oxygen ions are bridging oxygen [O], non-bridging oxygen [O - ], and free oxygen [O 2- ]. With the consideration of possible structural units, Zhang specifies the oxygen ions between Al, Ca and Mg cations. For example, the charge compensated oxygen between Ca and Al etc. The concentrations of these different oxygen ions are calculated on the basis of Zhang s assumptions, then, Zhang uses Arrhenius type equation to calculate the slag viscosity and reported an outstanding agreement with experimental data. The utilized equation and model parameters were included in the Equation 2-20 and Table 2.21 respectively. As shown in Table 2.21 and Table 2.22, the major features of Zhang s model are the assumptions based calculations. The calculated structural units would be utilized to determine the 66

92 activation energy of that composition slag, and hence determine the viscosity at fixed temperature. Equation Zhang model equations [145] lnη = lna + E/RT Where η is the viscosity of poise, E is the activation energy term, T is the temperature in K, R is the gas constant lna = k(e ) k = (x i k i )/ (x i ) i,i SiO2 i,i SiO E = n OSi + a 2 n O Where n OSi is the number of oxygens bridging with silicate, the n O is the number of other types of oxygen except bridging oxygens n OSi. The calculation of these parameters were shown in the Table 2.22 Table 2.21 The model parameters used to calculate E [145] k Mg a Mg a Si Mg a Al,Mg a Mg Al,Mg * k Ca a Ca a Si Ca a Al,Ca a Mg Al,Mg * k Al a Al a Mg Al,Ca *

93 Table 2.22 All possible condition in the CaO-MgO-Al 2 O 3 -SiO 2 system, only the condition 1 equations were included. The equations for other conditions is not included due to text limitation [145]. Condition I. x CaO + x MgO < x Al2 O 3 η OSi = 2x SiO2 η OAl = 3(x Al2 O 3 x CaO x MgO ) η OAl,Ca = 4x CaO η OSi,Mg = 4x MgO II. x CaO < x Al2 O 3, x CaO + x MgO < x Al2 O 3 and x CaO + x MgO x Al2 O 3 < 2(x SiO2 + 2x Al2 O 3 ) III. x CaO > x Al2 O 3 and x CaO + x MgO x Al2 O 3 < 2(x SiO2 + 2x Al2 O 3 ) IV. x CaO > x Al2 O 3 and x CaO + x MgO x Al2 O 3 > 2(x SiO2 + 2x Al2 O 3 ) V. x CaO < x Al2 O 3 and x CaO + x MgO x Al2 O 3 > 2(x SiO2 + 2x Al2 O 3 ) [145, 146] [145, 146] [145, 146] [145, 146] Gan Model Gan developed blast furnace viscosity model based on Vogel-Fulcher-Tammann Equation 2-21, which has successfully applied to magmatic liquids before [147]. It is a linear relation between the slag composition and model parameter (B, C). Gan reported that model can accurately predict the viscosity of blast furnace slag with a relative average error of A slight modification of this model can also predict the glass transition temperature of blast furnace slag satisfactorily. Equation Gan model equations, A is -3.1, the parameters of b i and c i were shown in Table 2.23 [147] η = A + B T C 68

94 B = b i x i C = c i x i Where η is the viscosity in Pa.s, T is the temperature in K, X i are the molar composition of slag system Table 2.23 Model parameters of Gan model [147] b i c i SiO Al 2 O CaO MgO Tang Model Tang proposed viscosity model utilizing a ratio of non-bridging oxygen to tetrahedral metal (NBO/T) [148] as Equation 2-22 shown. Tang s expression is similar to Iida s basicity equation with additional concerning of alumina-silicate structure. In round robin project, the model predictions have an outstanding agreement with experimental data, which reported smaller deviations than Iida model in CaO-MgO- Al 2 O 3 -SiO 2 -R 2 O (K 2 O or Na 2 O) system. Equation Tang model equations [148] η = exp ( ( NBO + T ) ( NBO ) T ) T NBO T = 2 (a MgO X MgO + a CaO (X CaO X Al2O3 )) b Al2O3 X Al2O3 + X SiO2 69

95 Where η is the viscosity in Pa.s, T is the temperature in K, X i are the molar composition of slag system and all other parameters are given by Shankar, other model parameters are shown in Table 2.24 Table 2.24 Model parameters of Tang model [148] a i b i Ca 1 1 Mg Ray Model Based on the Urbain model, Ray proposed a new mathematical model, which is capable of calculating the viscosity based on slag composition, temperature and optical basicity [149] as Equation 2-23 shown. The model proposed is applicable to homogeneous fluid melts only. The mathematical equations of Ray model are similar to Mill model, which were shown as below: Equation Ray model equations [149] η = A exp ( B T ) B = (A op ) A op ln(a) = B A op = γ SiO2 M SiO2 + γ Al2O3 M Al2O3 + γ CaO M CaO + γ MgO M MgO 2 M SiO2 + 3 M Al2O3 + M CaO + M MgO Where η is the viscosity of Poise, T is the temperature in K, M i is the molar composition of slag system and all other optical basicity parameters are the same as Table 2.20 shown. 70

96 Li Model Li proposed a novel viscosity model based on the flow mechanism involving the concept of cut-off points proposed by Nakamoto [150]. The non-bridging oxygen and free oxygen have large mobility because there are cut-off points near nonbridging oxygen linkage Si-O-Ca and free oxygen. These cut-off points constantly move and break the networks to produce new cut-off points when shear stress is applied to the silicate melts. Thus, the movement of cut-off points results in viscous flow. The concept of cut-off from Li and Nakamoto is similar to the hole theory in the other silicate melts structure. The model equations and parameters have been summarized in the Equation 2-24 and Table Equation 2-24 Li model equations [150] η = A W exp ( E RT ) ln(a W ) = a + b E a = a ix i x i b = b ix i x i Where η is the viscosity of Poise, A and B is the parameters calculating from equation, T is the temperature in K Table 2.25 Model parameters of Li model [150] A b CaO-SiO MgO-SiO Al 2 O 3 -SiO

97 Quasi-Chemical Viscosity Model Alex, Suzuki and Jak developed multicomponent slag viscosity model, which is called quasi-chemical viscosity model (QCV) [151], as Equation 2-25 shown. QCV is based on Erying liquid viscosity model, which assumes molten slag has quasi-crystalline structure. In molten slag, the molecules oscillate from equilibrium position to a neighboring one when their energy momentarily is equal or larger than the height of the potential barrier. Therefore, QCV model links the oscillation molecules (also called bond fraction) to slag viscosity. The potential oscillated molecules are subdivided into cationic molecular structures (also called bond fraction). For example, bond fraction parameters of alumina include Al-O-Al, Al-O-Si, Al-O-Mg and Al-O- Ca. These bond fractions of each metal oxide can only be calculated from FactSage software. In addition, second nearest neighbor bond (SNNB), which defines as the impact from neighboring structure, is introduced to improve the model prediction accuracy. As shown, QCV model includes calculations of each minor structure of four aspects, which are mass, volume, and activation and vaporization energy term. Equation QCV model equations [151] η = 2 RT (2πkm SUT) 0.5 E 2 V 3 v SU exp ( E a RT ) Factsage model links the viscosities of silicate melts to their thermodynamic properties, which is described by the quasi-chemical theory. It utilized Q-pairs (similar as a bond fraction in QCV model) to determine the E parameters and hence viscosity. Therefore, the QCV models highly rely on the FactSage software to calculate the critical parameters Q-pair. When FactSage updated from 6.2 to 6.4, the model parameters require optimization to suit the changes of Q-pair. 72

98 Factsage 7.0 Factsage is one of the largest fully integrated database computing systems in the chemical thermodynamics field of pyro-metallurgy study, which focus on the study of thermodynamic prediction, such as equilibrium, viscosity, and chemical reaction. Viscosity is one of the features of Factsage and the latest version is 7.0. Although the mathematical formulas for Factsage are uncertain, it is still a useful and convenient tool for viscosity prediction with input of temperature and slag composition as Equation 2-26, which covered most of the slag system and temperature ranges. Equation Factsage model requirements η = input (slag composition, Temperature) Where η is the slag viscosity, the input is the required information from user Summary Abundant mathematical models were developed to predict the viscosity of the molten slag. In the present study, altogether 20 models, which is capable of predicting the CaO-MgO-Al 2 O 3 -SiO 2 system, were critically reviewed. In summary, there are several common features within 18 models: 1. Most of the model utilize Arrhenius type equation to express and calculated slag viscosity. Arrhenius equation is a formula for the temperature dependence of reaction rates. Viscosity, as physical properties, was reported an outstanding agreement using Arrhenius-type equation (Equation 2-27). Equation Arrhenius equation η = A exp ( E T ) 73

99 Where η is the viscosity of Poise, A is the pre-exponential factor and B is the activation energy of reaction, T is the temperature in K 2. Another interesting feature is the linear correlation between pre-exponential factor A and activation energy B. From the publications different authors in various systems, there is a strong linear relationship between A and B, which was utilized in the model development. Fundamentally, in the Arrhenius equation, the A was regarded as a frequency factor, which indicated the rate of collision between reactants. B is activation energy the energy gap required to initial chemical reaction. The linear relationship was never reported between A and B in reaction kinetics field. As Equation 2-28 shown, the linear relationship between A and B was widely utilized and demonstrate a linear relationship at existing viscosity data, including Hu, Shankar, Urbain and Shu model [131, 142, 143]. Equation 2-28 the linear correlation between ln(a) and b ln(a) = m b + n Where A and B are the parameters required for Arrhenius model calculation, m and b is generally given by authors It is widely accepted that molten slag viscosity is determined by its internal structure. In CaO-MgO-Al 2 O 3 -SiO 2 system, (SiO 4 ) tetrahedral forms the slag network, hence increases viscosity. The CaO and MgO perform as network modifiers, which reduce the slag viscosity. Al 3+ can form (AlO 4 ) - tetrahedral structure similar to SiO 4 (network former). However, AlO 5-4 requires Mg and Ca cations to balance the electrical charge. With an insufficient amount of Ca and Mg cations, AlO 5-4 tetrahedral structure will break and behavior as network modifier (same as Mg 2+ and Ca 2+ ). 74

100 The reviewed models can be categorized based on model structure, parameters, and consideration of the silicate structures. In different stages of the viscosity development, understanding of alumina-silicate structure was different: (I) Al 2 O 3 as an amorphous oxide was not considered in model development, including Gan models. (II) Consider Al 2 O 3 as network former and introduce into the viscosity model. This includes Urbain, Riboud, Iida, Mill, Shankar, Hu, Ray, Tang, Li, Suzuki and Factsage, models. (III) If basic oxides e.g. CaO are insufficient, the excess Al 2 O 3 will behavior as basic oxides. This was considered by Shu and Zhang models. In the pyro-metallurgy field, the fundmental equation from other field were often utilzed for the viscosity model development. The most popular equation was the Arrhenius-type equation and its modified equations, which was utilized by Urban, Mill, Shankar, Hu, Li, Zhang, Li, Ray, Riboud, and Shu (10 authors, Equation 2-29). Equation 2-29 General form of Arrhenius-type equation η = A T X e E A RT Where η is viscosity in (Pa.s), T is temperature in K; and A is pre-exponential factor, R is gas constant, X can be 0 (Ray, Shu, Mills, Shankar, Zhang, and Li), 0.5 (Suzuki) and 1 (Riboud, Hu, and Urbain) from different researchers. Vogel-Fulcher-Tammann (VFT) is an equation for glass-forming liquid (Equation 2-30), which was firstly proposed by Gan to predict slag viscosity of molten slag of the CaO-MgO-Al 2 O 3 -SiO 2 system. Equation 2-30 VFT equation log(η) = A + B T C 75

101 Where η is viscosity in (Pa.s), T is the temperature in K; and A, B, C are model parameters. Another general equation is the basicity calculation of slag, which is the ratio of basic oxide to acidic oxide. Researchers proposed different mathematical formulas to correlate the slag structures with compositions. Urbain uses a weight ratio of (W CaO +W MgO )/ (W Al2O3 ) to describe the basicity of slag and predict viscosity. Afterward, Iida and Mills proposed viscosity models using the ratio of (W CaO +W MgO )/ (W SiO2 +W Al2O3 ), with the multiplication of basicity of each oxide. Based on optical basicity and Mills model, Shankar Ray and Hu revised the model structures and parameters to improve the precision and accuracy on blast furnace slags containing minor elements. Shu and Zhang's models established viscosity model with consideration of three type s oxygen O, O - and O -2. However, the calculation of oxygen concentration is a lack of theory support and relies on assumption. The features of the existing viscosity models are summarized in Table 2.26 and Table structural models were reviewed are evaluated in the present study using the accepted viscosity database of CaO-MgO-Al 2 O 3 -SiO 2 slag system. Equation 2-31 is used to calculate the difference between the measured and the calculated viscosity values. The evaluation results have been summarized in Table 2.26 and Table Equation 2-31 Error deviation calculation Δ = 1 n η Calc η Exp η Exp 100% Where Δthe mean deviation, n is is the total number of simulations, η Calc is the model viscosity and η Exp is the experimental viscosity. 76

102 Table 2.26 Summary of reviewed viscosity model in CaO-MgO-Al 2 O 3 -SiO 2 system Error Sources Structure Related Equation Model Features Deviation (%) Based on Frenkel-Weymann liquid viscosity model, Urbain Urbain [131] W CaO + W MgO W Al2O3 theoretically approved the linear correlation between A and B in the Arrhenius-type equation Riboud [133] A = e (a (M CaO+M MgO ) b M Al2O3 +c) B = a (M CaO + M MgO ) b M Al2O3 + c Based on Urbain model, Riboud simplify the model equations and optimize the model parameters using viscosity data of blast furnace slag 61.0 Iida [136, 137] W CaO a + W MgO b W Al2O3 c + W SiO2 d Iida s model was developed based on slag basicity and own optimized parameters Mill [138] M CaO a + M MgO b M Al2O3 c + M SiO2 d Mill s model was developed based on the oxides optical basicity, which was reported by Duffy and Ingram 70.4 Shankar [141] W CaO a + W MgO b W CaO + W MgO M Al2O3 c + M SiO2 d M Al2O3 + M SiO2 Shankar optimized the model parameters and equation based on Mill s work

103 Ray [149] M CaO a + M MgO b M Al2O3 c + M SiO2 d Ray optimized the model parameters based on Mill s work Hu [142] M CaO M Al2O3 + M MgO b + 2M SiO2 c M MgO + M CaO M Al2O3 + M Al2O3 c + 2M SiO2 Hu also optimized the model parameters and equations based on Mill s work 44.3 Gan first proposed Vogel-Fulcher-Tammann-type equation in Gan [147] B = b MO M MO C = c MO M MO CaO-MgO-Al 2 O 3 -SiO 2 field, which can also predict the glass transition temperature the blast furnace slag with slight modification Tang [148] Non brdging oxygen SiO 4 Tang proposed the viscosity model using the ratio of non-bridging oxygen to silica content Suzuki developed the viscosity model based on a bond fraction, QCV [151] E a = E a,si Si M Si Si + E a,si Me M Si Me + E a,me Me M Me Me which was calculated by Factsage software. Suzuki s model contains large number of equations and parameters (>50 equations and parameters for CaO-MgO-Al 2 O 3 -SiO 2 quaternary system, 35.1 more for higher order system) FactSage N/A N/A 37.7 Shu [143, E = E SiO2 M SiO2 + E M2SiO4 M M2SiO4 + E Mo M Mo Shu developed the viscosity models based on compositions of

104 144] three types of oxygen, which was calculated from optical basicity values. Zhang developed the viscosity models based on compositions of Zhang [145] E a = E a,bridging M bridging + E a,non bridging M non bridging + E a,free M free three types of oxygen, which was calculated from assumptions of [AlO 4 ] binding with Ca 2+ and Mg 2+ in CaO-MgO-Al 2 O 3 -SiO 2 system Table 2.27 Summary of applicable oxides of existing viscosity model Sources Bottinga [126] Giordano [128] Gupta Application SiO 2, Al 2 O 3, CaO, MgO, TiO 2, FeO, MnO, SrO, BaO, Li 2 O, Na 2 O and K 2 O SiO 2, Al 2 O 3, CaO, MgO, Na 2 O and K 2 O SiO 2, Al 2 O 3, CaO, MgO, Na 2 O, K 2 O, MnO and FeO Neutral [127] Network SiO 2, Al 2 O 3, CaO and MgO Urbain [131] SiO 2, Al 2 O 3, CaO, MgO, B 2 O 3, MnO, FeO and PbO 79

105 Riboud [133] Iida [136, 137] Mill [138] SiO 2, Al 2 O 3, CaO and MgO SiO 2, Al 2 O 3, CaO and MgO SiO 2, Al 2 O 3, CaO, MgO, Na 2 O, TiO 2, B 2 O 3, MnO, FeO, PbO and CaF 2 Shankar [141] SiO 2, Al 2 O 3, CaO, MgO and TiO 2 Ray [149] SiO 2, Al 2 O 3, CaO, MgO and TiO 2 Hu [142] Gan [147] SiO 2, Al 2 O 3, CaO and MgO SiO 2, Al 2 O 3, CaO, MgO, N 2 O and K 2 O Tang [148] SiO 2, Al 2 O 3, CaO, MgO, N 2 O, K 2 O, FeO and Fe 2 O 3 QCV [151] FactSage Shu [143, 144] SiO 2, Al 2 O 3, B 2 O 3, MgO, CaO, MnO, FeO, ZnO and CuO All oxides SiO 2, Al 2 O 3, CaO and MgO 80

106 2.5 The viscosity study review of suspension system The viscosity of suspensions is of interest in many disciplines of engineering, for example, food science, wastewater treatment and etc. The suspension viscosity η sus primarily depends on (1) the solid fraction, (2) shape and size of particles, and (3) the suspending Newtonian liquid, which will be reviewed in the section and respectively. A large number of studies have been carried experimentally and theoretically at room temperature condition. There is a research gap that the solid impact on suspension was rarely studied in a high-temperature region. It is known that the precipitation of solid particles in molten slag was commonly observed in iron, steel, copper and other pyrometallurgy processes. It is necessary to explore and compare the suspension viscosity by the systematic variation of the parameters at both room and smelting temperature conditions. Table 2.28 summarized the experiment measurements of suspension viscosity at different systems. Table 2.28 The brief review of viscosity study of suspension system at different system, viscosity and temperature range, note: the relative viscosity means the ratio of suspension viscosity to liquid viscosity Author Solid/Liquid System Viscosity Range (Pa.s) Temperature Range ( o C) Bibbo [152] Fiber Relative Viscosity 25 Water Chong [153] Glass beads Polyisobutylene (PIB) Darton [154] Silica sand Water Fan [155] Fiber Relative Viscosity 25 Water

107 Joung [156] Fiber Relative Viscosity 25 Water Kwon [157] Magnetic particle Ethylene glycol Konjin [158] Glycerine polymethylmethacrylate Marshall [159] Silica sols Cis/transdecahydronaphthalene, (Decalin) Namburu [160] SiO 2 nanoparticle 60% ethyleneglycol 40% water Tsuchiya [161] Glass beads Water Wu [9] Paraffin Oil CaO-MgO-Al 2 O 3 -SiO Lejeune [162] CaO-MgO-Al 2 O 3 -SiO Wright [163] CaO-MgO-Al 2 O 3 -SiO Effects of liquid viscosity & Solid Fraction Liquid viscosity and solid fraction are the two most critical factors in the experimental study of suspension viscosity, which was also approved in the model simulation work. Einstein first 82

108 proposed a mathematical expression to predict the suspension viscosity η sus using liquid viscosity η Liq and solid fraction f. The mathematical expression was accepted and optimized by other researchers to improve the prediction accuracy of Einstein Model [164]. From the model view, the mathematical expression η sus = η liq η rela were utilized for the model development of suspension viscosity prediction, where n rela is expressed by solid fraction as shown in Equation Equation 2-32 Definition of relative viscosity η sus η liq = η rela = f(f) Where η sus is suspension viscosity, η liq is the liquid viscosity. f (f) is a mathematical function of solid fraction. From the existing viscosity results, it is accepted that both liquid viscosity and solid fraction has a positive proportional impact on the suspension viscosity at a temperature ranging from - 40 to 1500 o C. When a force applied, the shear stress of liquid is enlarged when the solid exist within liquid comparing to the pure liquid condition. As Figure 2.25 shown, with the appearance of the solid particle, the smooth molecular distribution of fully liquid was converted to the rigid distribution of solid/liquid system; hence increased the gradient (viscosity). Also, the increase in viscosity with solids concentrations was attributed to the increased frequency of particle-particle interactions. Figure 2.25 The shear stress enlarged from fully liquid system to solid/liquid system 83

109 For the solid fraction ranging from 0-1, the solid proportion and liquid viscosity have a positive proportional impact on the suspension viscosity. In the low melt fraction regime, the solid particles have a predominant role until the solid-like behavior is exhibited as solid fraction achieving 1. As Figure 2.26 shown, with the increasing of solid particles, the viscosity moderately increases but when a critical solid content is reached, the viscosity increases so rapidly that over a short range. Upon critical point, the viscosity slowly increased, which is known as solid-like behavior. Figure 2.26 Viscosity deduced from data of van der Molten and Paterson (1979) [165]at high solid fraction (circles) and from data of Mg 3 Al 2 Si 3 O 12 by Lejeune (triangles) [162] and other values at low solid fraction (squares) by Thomas [166] Effects of Particle Size There is a contradiction discussion about the impact of particle size on the suspension viscosity. As Figure 2.27 shown, Wu construct a series study of paraffin/silicon oil system under room temperature condition. The particle size ranges from 150 um to 450 um reported similar results, which is only slightly derivate 1.2% [9]. Konijn constructs viscosity measurement of glycerine/polymethylmethacrylate system and also reported that the particle size did not impact on the suspension viscosity [167]. 84

110 Figure 2.27 Experiment data of different particle size vs model prediction [167] However, in Gust s study, utilizing silica sand/water system, he proposed that the apparent viscosity increased with particle size at the different pseudo shear rate [168]. The particles of greater size possess more inertia such that on interaction with rotational bob, which will momently stop and accelerate during rotation. In both these stages, their inertia affects the amount of energy required. This dissipation of energy appears as extra viscosity. In Bruijn's study of glycerine and polymethylmethacrylate system, for particles with diameters less than 1 to 10 microns, colloid-chemical forces become important causing that the relative viscosity increase as particle size decreasing [169]. For particles larger than 1 to 10 microns, de Bruijn believes that inertial effects due to the restoration of particle rotation after collision result in an additional energy dissipation and consequent that viscosity increased with increasing particle diameter, which reports similar conclusion as Gust study [169]. Most of the viscosity models assumed that the particle shape is sphere for the estimation of volume impact of solid particle. However, the experimental results demonstrated that different particle shape could have significantly impact on the suspension viscosity. Nawab observed experimentally that Nylon fibre suspensions could produce a measured viscosity three times of the theoretical predictions [170]. This difference might be a result of fibre curvature. By comparison of suspension viscosity of different particle shapes, at same condition, it can be ranked that spherical particle reported the smallest suspension viscosity [170]. 85

111 2.5.3 The review of viscosity model of suspension system On 1905, Einstein proposed the mathematical equations to estimate the viscosity of the suspension system, which related the viscosity of the two-phase mixture to the volume fraction of solid particles and liquid viscosity [173]. The Einstein model was developed using Stoke law under the assumption of no interaction between the solid particles. Also, he assumed that at very low particle fraction, the energy dissipation during laminar shear flow increase due to the perturbation of the streamline by particles. Because the interactions between solid particles are not considered, the equation can only be applied to the dilute solution system [173]. Although Einstein model has a limited prediction range, the basic mathematical expression of viscosity model of suspension system was accepted and utilized by other researchers, which the suspension viscosity dependent on a constant liquid viscosity and solid volume fraction. Other researchers accepted the basic expression of relative viscosity [ η sus η liq = η rela ] and developed own mathematical models to express the relative viscosity with high particle fractions. There are two major branches of model development: 1) Extension of Einstein model and 2) Cell model theory. It is known that Einstein model assumed that no interaction occurred between solid particles. Part of researchers focuses on the study by considering the possible interaction between two or more particles interactions and derives the mathematical equations to predict the suspension viscosity with a high solid fraction. For example, KD assume three flow pattern of nearby particles including rotating independently, rotate as dumb-bell and rigid flow pattern; hence derive the equation. The development of Cell model based on the assumption that solid sphere of radius of R o is surrounded by liquid out to a radius R as shown in Figure Suitable boundary conditions and Stoke equation were applied at this outer boundary layer. For example, Brady assumed that the velocity field on the outer sphere is precisely that of externally imposed flow [171]. Happel assumes that the shear stresses on the outer sphere are those of the imposed flow [172]. 86

112 Figure The description of interaction between solid sphere and fluid particle In the present study, altogether 11 models were collected and evaluated using experimental data. The model features and its equations were summarized in Table 2.29 below. 87

113 Model Einstein [173] Kunitz [174] Krieger-Dougherty [175] Probstein [176] Toda [177] Happel [178] Table Summary of 10 different viscosity model, f is the solid fraction within suspension Features Einstein model is suitable for diluted sphere particles suspension under the assumption of no interaction between solid particles. Kunitz modifies Einstein model in one of the deviation steps and empirical optimal the parameters from (1-f) 2 to (1-f) 4. Assume three flow pattern of nearby particles including rotate independently, rotate as dumb-bell and rigid flow pattern; hence derive the equation. A polydisperse suspension with a particle size distribution from submicrometer to hundreds of micrometers is simulated and treated as bimodal. Based on Einstein theory, Toda model further derives the equation on the calculation of dissipation of mechanical energy into heat in the dispersion. Based on the cell model theory, Happel assumes that the shear stresses on the outer sphere are those of the imposed flow; then derive the equations on the steady-state Stokes-Navier equations of motion omitting inertia terms. Model Equation η rela = η rela = (1 + η sus η liq = η rela = ( f) η rela = f (1 f) 4 η rela = (1 f ) η rela = ( f f ) f ( f) f (1 ( f) f) 2 (1 f) f (22 f f 2 3) 10 (1 f f (1 f 4 3)) Thomas [179] Thomas model largely concerned with the transport characteristics of non-newtonian suspensions (sphere particle) by consideration of inertial force and measuring instrument wall effects. Thomas model reported an average 25% deviations for sets of existing viscosity data 88 η rela = f f e 16.6f

114 Roscoe [180] Mooney [181] Batchelor [182] Bergenholtz [183] using different size sphere particles and containers. Einstein expression is re-evaluated and optimized to improve the prediction of existing viscosity data. Roscoe model reported a good agreement with different sizes of sphere particles suspension, which ranges from solid%. Mooney developed a model based on Einstein approach and reported a good agreement with experimental data. Cell model theory Cell model theory η rela = (1 f) 2.5 η rela = e 2.5f f η rela = ( f f2 ) η rela = ( f f2 ) 89

115 Chapter 3 : Experiment Methodology This chapter describes the experimental methodology utilized in the present study, which include: 1. High-temperature viscosity measurements for fully liquid slag, which is established by the Dr. Chen 2. Room temperature viscosity measurements for suspension, which ranges from 0-30 wt% solid. 3. The Raman spectroscopy study 3.1 High-Temperature Viscosity Measurement The viscosity measurement techniques of high-temperature viscosity measurements have been detailed studied by Dr. Chen in his Ph.D. Thesis [184]. A digital rotational rheometer (model LVDV III Ultra; Brookfield Engineering Laboratories, Middle-boro, MA) controlled by a personal computer was used in the current study. The acquisition of the torque measured by the rheometer was simultaneously collected by Rheocalc software provided by Brookfield Engineering Laboratories. A Pyrox furnace with lanthanum chromite heating elements (maximum temperature 1923 K (1650 o C) was employed. The rheometer placed on a movable platform was enclosed in a gas-tight steel chamber. There were two independent gas flow circuits (one through the chamber, and another through the furnace) to suppress heat to the chamber and protect the rheometer from high temperature. The rheometer rotated coaxially the alumina driving shaft with the cylindrical spindle. The schematic diagram of experimental set up is shown in the Figure

116 Figure 3.1 Schematic diagram of furnace for viscosity measurement at high temperature Figure 3.2 provide dimensional details of the cylindrical crucible and spindle used during viscosity measurements. The viscosity measurements included 3 major steps: 1. the calibration of one set of equipment under room temperature, including Al 2 O 3 rod, crucible and spindles, 2. High temperature viscosity measurement using the calibrated equipment and 3: elemental analysis of quenched sample using EPMA. Figure 3.2 Schematic diagram of crucible and spindle 91

117 3.2 Room Temperature Viscosity Measurement The viscosity of suspension was measured using rotational viscometer as Figure 3.3. The viscosities of solid-containing liquid at room temperature are measured by A Brookfield digital rotational rheometer (model LVDV III Ultra) controlled by a PC with the standard spindle provided by the same company. The acquisition of the torque measured by the rheometer can be simultaneously collected by Rheocalc software provided by Brookfield Company. A thermostatic water bath will be used to control and maintain the temperatures at low-temperature ranges from o C. A transparent crucible will be submerged in the water Figure 3.3 Schematic diagram of viscosity study at room temperature 3.3 Raman Spectroscopy Study The Raman spectroscopy study was carried into two steps, the first step is to obtain the quenched sample, which is completed using phase equilibrium experiment. The phase equilibrium experiments were carried out in the vertical tube furnace by stabilizing the synthetic sample in the hot zone for a period of time at Ar gas atmosphere. After the sample achieves equilibrium, it will be quenched directly into the water bucket, which maintains the high-temperature structure for Ramen analysis. The quenched sample will be crashed and mounted to stabilize in the resin for Raman analysis. 92

118 The photograph of the furnace below is vertical tube furnace. The schematic diagram is shown in Figure 3.4. The detailed description of the experimental procedures and conditions were demonstrated in the Chapter 6: Structural studies of Silicate using Raman Spectroscopy. Figure 3.4 (a) left, a photograph of phase equilibrium experiment. (b) Right, a schematic diagram of a vertical tube furnace 93

119 Chapter 4 : Viscosity Model Development in CaO-MgO-Al 2 O 3 -SiO 2 System Based on Urbain Model The Urbain model was optimized in the present study by introducing the concept of optical basicity to describe the correlation between slag composition and viscosity. The optimized version significantly improves the prediction accuracy of CaO-MgO-Al 2 O 3 -SiO 2 system of blast furnace slag; also the parameters in the present model are 14 comparing to 22 parameters in the Urbain model (1987 version). In chapter 4, the optimized Urbain model was presented in section 4.1. In addition, the optimized model can be extended to calculate the viscosity of blast furnace slag including 8 common minor elements, including Fe, Ti, F, S, Na, K, B and Mn, which was reported in section CaO-MgO-Al 2 O 3 -SiO 2 system in blast furnace composition range Introduction Development of a reliable viscosity model for the CaO-MgO-Al 2 O 3 -SiO 2 systems over a wide range of compositions and temperatures is important for iron and steel making processes. A blast furnace (BF) slag with proper viscosity leads to (a) fluent flowing in the tapping process, (b) easy separation from hot metal and coke, (c) efficient desulphurisation process and (d) less accretion formation on the BF wall [1]. High-temperature viscosity measurement is practically difficult and, costing considerable time and money. Therefore, it is necessary to establish a reliable model to predict slag viscosity to provide accurate information for efficient blast furnace operation. A number of viscosity models have been developed to predict the viscosity in the CaO-MgO- Al 2 O 3 -SiO 2 (typical BF slag components) system over the last decades as reviewed in Section 2.4. These viscosity models can be generally classified into two groups, empirical models, and structural models. The empirical models correlate slag viscosity as a function of temperatures and bulk compositions directly using experimental data. The structural models consider the profound internal structure of silicate melts, which are more accurate and flexible than empirical models. Urbain model is one of the structural viscosity models for viscosity prediction covering a wide range of multi-component system. Several authors 94

120 chosen Urbain model for optimization due to its flexibility. Riboud and Forsbacka optimized the Urbain model for mould fluxes and coal ash slag respectively, which both reported an outstanding agreement with that slag system [134, 135]. Urbain proposed the model on 1981 for viscosity prediction of complex slag system, including CaO, MgO, FeO, SiO 2, K 2 O and etc [132]. From , Urbain focus on the viscosity experiment study of CaO-MgO- Al 2 O 3 -SiO 2 slag system and published the outcomes [60, 185]. Later on 1987, Urbain modify the model equations and parameters for CaO-MgO-Al 2 O 3 -SiO 2 system, which were demonstrated in Section [131]. The 1987 version of Urbain model demonstrated superior performance on the CaO-MgO-Al 2 O 3 -SiO 2 slag system. In the present study, due to high flexibility, the Urbain model (1987 version) was selected as basement to developed a new viscosity model for the CaO-MgO-Al 2 O 3 -SiO 2 system in the blast furnace slag composition range [131] Experimental Data Used for Model Development Accurate viscosity data are essential for successful development of a reliable viscosity model. The viscosity measurements in the CaO-MgO-Al 2 O 3 -SiO 2 system have been collected from 37 publications and critically reviewed in the Section 2.3. These data covers the composition ranges of wt% SiO 2, 1-40 wt% Al 2 O 3, 1-60 wt% CaO and 1-38 wt% MgO. The reliability of viscosity data directly impacts on the model prediction performance. The quality of data was carefully examined. Three sequential steps were undertaken to evaluate the data: a) Review experimental techniques, b) Check data self-consistency, and c) Cross reference comparisons. The evaluation details and examples have been demonstrated in the Section out of 3125 viscosity data in the CaO-MgO-Al 2 O 3 -SiO 2 system were accepted for model development in the present study Silicate Melt Structure The viscosity of molten slag is closely related to its structure, which is dependent on its composition and temperature. The final blast furnace slag has four major components, SiO 2, Al 2 O 3, CaO and MgO that can be categorized into three groups, acidic oxide (SiO 2 ), basic oxide (CaO and MgO) and amphoteric oxide (Al 2 O 3 ). SiO 2 forms a network structure through (SiO 4 ) 4- tetrahedral units to increase viscosity. The basic oxides Ca 2+ and Mg 2+ tend to break the network and reduce slag viscosity. Al 2 O 3 can behave as either an acidic oxide or basic oxide depending on the concentrations of other components. If sufficient basic oxides Ca 2+ and Mg 2+ are present to balance the (AlO 4 ) 5-95

121 charges, the Al 2 O 3 acts as an acidic oxide, which is incorporated into the silicate network as (AlO 4) 5- form. In the case of insufficient basic oxides, Al 2 O 3 will behave the same as Ca 2+ or Mg 2+ to break the (SiO 4 ) 4- network. In typical BF composition ranges, where (CaO+MgO)/SiO 2 is high, the Al 2 O 3 component is considered to act as an acidic oxide and requires charge compensation of CaO and MgO Description of Model The Urbain model is a structure-based model for the slag viscosity prediction, which has been optimized for other multi-component systems by various researchers. Urbain firstly proposed the model on 1981 and modified it to improve the performance in CaO-MgO-Al 2 O 3 -SiO 2 system on As comparison in the literature review, the Urbain model (1987) version is more suitable for the viscosity prediction of CaO-MgO-Al 2 O 3 -SiO 2 system. Present study select the Urbain model (1987 version) as a basement for the model development due to its high flexibility. The comparisons of two Urbain models were introduced in the Section Viscosity is generally a function of temperature and chemical composition of molten slag. Urbain considered Weymann s expression of the temperature dependence of viscosity, which is the modified Arrhenius-type equation [186] (Equation 4-1). Equation 4-1 Arrhenius-type equation η = A T exp ( 1000B T ) Where η is viscosity in Pa.s, T is the absolute temperature (K), A is the pre-exponent factor and B represents the integral activation energy. In the modelling study by Urbain, the pre-exponent factor A and activation energy B was reported to have a relationship as Equation 4-2 shown. The linear correlation were accepted and utilized in other researchers viscosity models, such as the Shankar [32], Shu [187] and Hu [142]. In the current study, a similar relationship between ln(a) and B is confirmed for the CaO-MgO-Al 2 O 3 -SiO 2 system using the accepted viscosity data. ln(a) and B has a strong linear correlation (R 2 =0.948) and is used in the construction of current viscosity model. The values of m and n in the present model are determined to be and respectively optimized from the evaluated measurements in the CaO-MgO-Al 2 O 3 -SiO 2 system (Section 2.3). 96

122 Equation 4-2 the linear relationship between A and B lna = mb n Where A the pre-exponential factor and B is the activation energy from Equation 4-3. m and n is the model parameters are and respectively. They are close to that reported by Hu (0.508 and 7.28) but different from that reported by Urbain (0.29 and 11.57) [142]. Because, both Urbain and present study utilized the equation ln(n/t)=ln(a)+1000b/t to determine the value of B; however Hu model utilized the ln(n)=ln(a)+1000b/t. Both equations reported the linear relationship as Figure 4.1 shown. lna = mb n Figure 4.1 The linear relationship between E A and ln(a) Expressions of Activation Energy In the tradition Arrhenius equation, B is defined as the term activation energy. It is known that the viscous flow is driven by thermally activated process. According to the network theory, there are silicate network, broken network and free-moving components in the molten slag. The activation energy term described the sum of required energy for these components movement, which overcome the potential barrier to reach another equilibrium positions. In the present study, the integral activation energy can be expressed as Equation 4-3 shown. The contribution of the broken and free-moving components were individually calculated and 97

123 normalized based on molar composition. The contribution of silicate network is constant, which is derived from the pure silica. Equation 4-3 Parameter B calculation B = M CaO B CaO + M MgO B MgO + M Al2 O 3 B Al2 O 3 M CaO + M MgO + M Al2 O B Si Where M is a molar fraction of oxide, B i is partial activation energy calculated by Equation 4-4 to Equation 4-6. A constant value of is used forb 0 Si, which is derived from the pure SiO 2. The partial activation energy B i of each oxide is expressed as the third order polynomial equation Equation 4-4 shown. Equation 4-4 Partial activation energy B i calculation, for Equation 4-3 B Ca = B 1 Ca + B 2 Ca N + B 3 Ca N B Mg = B Mg + B Mg N + B Mg N 2 B Al = B 1 Al + B 2 Al N + B 3 Al N 2 Where N represents the effective optical basicity of the slag and B i 1, B i 2 and B i 3 are model parameters of each metal oxide. The parameters B 1, B 2 and B 3 for the present model were optimized from the viscosity measurements as shown in Table 4.1. The parameter optimizations were constructed from calculated activation energy and molar composition of oxides. The activation energy B and pre-exponential factor A can be determined from plotting ln ( η 1000B ) = ln(a) +. With T T known B and Equation 4-3, the range of B CaO, B MgO, B Al2O3 and B SiO2 can be estimated within a certain range for all compositions, which are B CaO = (-30)~ (-250), B MgO = (-45)~(-180), B Al2O3 = (-15)~(+10) and B SiO2 = around 60. It can be noted that at low basic oxide conditions, the Al 2 O 3 has a negative contribution on the silicate network due to its amphoteric property. The parameters of B 1, B 2 and B 3 were \optimized based on the oxide contribution ranges. 98

124 The experiment measurements confirmed that CaO and MgO negatively contributed to the activation energies, which represent the network breaking and reduce the slag viscosity. In contrast, the Al 2 O 3 and SiO 2 positively contributed to the activation energy, which represents the network-forming effect and improve the slag viscosity. Table 4.1 Parameters B used in Equation 4-4 B CaO MgO Al 2 O The effective optical basicity of the slag N can be calculated by Equation 4-5 using the optical basicity of CaO, MgO, Al 2 O 3, (SiO 4 ) 4- and (AlO 4 ) 5-. The optical basicity of each component represents their ability for network-breaking or network-forming. The values of optical basicity of CaO, MgO, and Al 2 O 3 are adopted from Duffy. The new parameters Λ Opt i, which represent the optical basicity of (SiO 4 ) 4- and (AlO 4 ) 5- were derived from the viscosity data. The optical basicity values were shown in Table 4.2. Equation 4-5 Slag basicity N calculation, for Equation 4-4 N = Λ CaO M CaO + Λ MgO M MgO Λ Al2 O 3 M Al2 O 3 Opt M (AlO4 ) 5 + Λ Opt (SiO 4 ) 4 M (SiO4 ) 4 Λ (AlO4 ) 5 Where M is a molar fraction of metal oxide, Λ i is the effectiveness of basic oxides and Λ i Opt is the effectiveness of acidic oxide. Note: M AlO4 = 2*M Al2O3. Table 4.2 Model parameters N CaO MgO Al 2 O 3 99

125 Λ (SiO 4 ) 4- (AlO 4 ) 5- Λ Opt Model Performances The revised Urbain model has been constructed in the present study to predict the viscosity for BF slags. This optimized model has a reduced number of equations (from 14 to 7) and parameters (from 22 to 14) compared to the Urbain model (1987 version). The prediction performance was evaluated by comparison of other models using the accepted viscosity measurements in the CaO-MgO-Al 2 O 3 -SiO 2 slag system. In order to provide a full view of the comparison, the evaluation of the model performance was carried out for two different composition ranges: a) all data in the CaO-MgO-Al 2 O 3 -SiO 2 system; b) data in the typical BF slag composition range wt% SiO 2, wt% Al 2 O 3, wt% CaO and 5-10 wt% MgO. Each viscosity model was examined and compared using the above data classifications to test its accuracy. The mean deviation Δ is calculated using Equation 4-6 described as follows. Equation 4-6 the viscosity prediction deviation calculation Δ = 1 n η Calc η Exp η Exp 100% Where Δthe mean deviation, n is is the total number of simulations, η Calc is the model viscosity and η Exp is the experimental viscosity. The results for model comparison are shown in Figure 4.2. It can be seen that the present model has the lowest deviation in both composition ranges, with 29.5% in the full composition range and 13.5% in the BF slag composition range. The relative deviations reported by other models are all above 30% in the full composition range and 20% in the BF slag composition range. 100

126 Figure 4.2 Comparison of the current viscosity model with others A detailed comparison of the viscosity model performance is constructed using the three most accurate models: present model, Zhang model [188] and Urbain model [131] in the viscosity range 0-1 Pa.s, which is typical for BF slags. As Figure 4.3 shown, the present model has superior performance than both Zhang and Urbain models. The mean deviation is an average of the absolute deviation which may underestimate the model prediction accuracy. For the viscosity measurements between 0-1 Pa.s, as Figure 4.3 shown, the mean deviation is 12.5%, 16.4% and 16.3% for the present model, Zhang model, and Urbain model respectively. However, for a given experimental viscosity, the maximum predicted deviations can be 0.3 Pa.s for Urbain model, 0.37 Pa.s for Zhang model that are much higher than the present model (0.06 Pa.s). 101

127 Figure 4.3 Three model performance for 0-1 Pa.s, mean deviation for three models: present model 12.5%, Zhang model 16.4% and Urbain model (1987 version) 16.3% [131, 188] Industrial Applications Examples of the applications in the prediction of BF slag viscosity are shown in this section using the present viscosity model. Figure 4.4 shows the effect of MgO on the viscosity of BF slag at 15 wt% Al 2 O 3 and 1500 C. It can be seen that the calculated viscosities by the present model agree very well with Machin s measurements. At a given CaO/SiO 2 ratio and Al 2 O 3 concentration, replace of (CaO+SiO 2 ) by MgO decreases the slag viscosity. On the other hand, the BF slag viscosity increases with decreasing MgO. In the ironmaking process, sulphur removal of hot metal directly related to the slag viscosity. The higher viscosity of the slag could increase the sulphur content in the hot metal. To balance the viscosity raised by decreasing MgO, the CaO/SiO 2 ratio in the slag can increase according to the predictions shown in Figure 4.4. It also can be seen that at CaO/SiO 2 ratio of 1.30, 15 wt% Al 2 O 3 and 1500 C, the viscosities of the BF slag are below 0.5 Pa.s even the MgO concentration in the slag is as low as 2 wt%. This indicates that low MgO in slag does not have a significant effect on slag tapping. 102

128 Figure 4.4 Effect of MgO on viscosity of BF slag at 15 wt% Al 2 O 3 and 1500 C predicted by the present model with comparisons to the experimental data [74] Figure 4.5 shows the effects of Al 2 O 3 concentration and temperature on slag viscosity at 40 wt% SiO 2 and 10 wt% MgO. It can be seen that the calculated viscosities by the present model agree very well with the reported measurements. At fixed SiO 2 concentration and temperature, the viscosity increases with increasing Al 2 O 3 concentration and the increment is more significant at lower temperatures. For example, the viscosity is increased by approximately 0.4 Pa.s at 1500 o C and 0.65 Pa.s at 1450 o C when the Al 2 O 3 concentration in the slag is increased from 10 to 20 wt%. On the other hand, the viscosity is more sensitive to temperature for the slag containing higher Al 2 O 3. Decrease of temperature from 1500 to 1450 o C increases the viscosity by 0.1 Pa.s for 10 wt% Al 2 O 3 slag and 0.35 Pa.s for 20 wt% Al 2 O 3 slag. This indicates that increased Al 2 O 3 concentration in BF slag not only increases viscosity directly but also decreases the thermal stability of the slag. 103

129 Figure 4.5 Effects of Al 2 O 3 concentration and temperature on slag viscosity at 40 wt% SiO 2 and 10 wt% MgO predicted by the present model with comparisons to the experimental data of Gultyai [83], Hofmann [22] and Machin [68] Conclusions A novel viscosity model has been developed based on Urbain model (1987 version) in the CaO-MgO-Al 2 O 3 -SiO 2 system. The present model improved the viscosity prediction for the blast furnace slag. The present model shows superior performance to the existing viscosity models, which reduce the prediction deviation from 22% (Urbain model) to 14% (present model). Also, the parameters in the present model are 14 compared to 22 in the original Urbain model. Present model can provide accurate viscosity prediction of CaO-MgO-Al 2 O 3 - SiO 2 system, which occupied 97% of blast furnace slag. In recent study, the impact of minor element was addressed, which report the significant impact on the final slag viscosity. The present model was further investigated and developed for the viscosity prediction of minor element within the blast furnace slag, which would be demonstrated in the Section CaO-MgO-Al 2 O 3 -SiO 2 system containing 8 minor elements Introduction Slag viscosity is one of the important properties in ironmaking process, which significantly influences operation and fuel efficiency. Viscosities of the CaO-MgO-Al 2 O 3 -SiO 2 system (97 wt% of slag) have been well studied in last decades. Because of gradual consumption of highgrade iron ore, in view of operation cost and energy efficiency, the low-grade materials and pulverized coal injection were used in the blast furnace (BF) operation. This results in 104

130 increases of impurities, such as Na 2 O, K 2 O, MnO and TiO 2 in the slags. CaF 2 and B 2 O 3 are fluxes used in BF maintenance stage to remove the accretion formed inside the furnace wall, which will also affect the final slag composition. A typical blast furnace slag compositions including minor elements are summarized in Table 4.3. Table 4.3 Summary of typical BF composition range Component Composition (wt%) SiO Al 2 O CaO MgO 5-10 CaO/SiO F, S, MnO, FeO, B 2 O 3, Na 2 O, K 2 O, TiO In the present study, the impacts of 8 minor elements on slag viscosity were individually and systemically studied. Previous viscosity data relevant to the BF slag with minor elements were also collected and reviewed. A series of viscosity measurements of 6 minor elements (Na 2 O, K 2 O, S, MnO, FeO, TiO 2, CaF 2 and B 2 O 3 ) was conducted at the University Of Queensland (UQ). The viscosity model was developed for the prediction of CaO-MgO- Al 2 O 3 -SiO 2 slag system containing minor elements Experimental Methodology A series of high-temperature viscosity measurements were carried out to investigate the effects of TiO 2, MnO, FeO, B 2 O 3, CaS, CaF 2 on the BF slag. The apparatus and methodologies of the viscosity measurements have been reported in previous studies [13] and section 3.1. The viscosity measurements were carried out from high temperature to low temperature in 50 C interval. The sample was kept for long enough time after temperature decreasing to achieve the equilibrium. The lowest measuring temperatures of the slags were predicted by FactSage 6.2 to ensure the molten slag status. After measurements have been 105

131 completed, the sample was directly quenched into the water to convert the liquid into the glass. The quenched samples were sectioned, mounted, polished and elementally analyzed by electron probe X-ray micro-analysis (EPMA). In the present study, S is recalculated to CaS, and F is recalculated to CaF 2 for presentation purpose. The samples containing B 2 O 3 and CaS were also sent for Inductively Coupled Plasma (ICP) analysis. The compositions of B 2 O 3 and CaS measured by ICP were very close to those measured by EPMA Viscosity Database Collected Reference The viscosity database was established by collecting reliable viscosity measurements from literature and present measurements. After a critical literature review, very limited viscosity data in systems of CaO-MgO-Al 2 O 3 -SiO 2 -B 2 O 3 and CaO-MgO-Al 2 O 3 -SiO 2 -Na 2 O (K 2 O) were found, which were reviewed in the Section More researchers studied the impact of FeO and TiO 2 additives on BF slag viscosity, which were reported in the section Only one publication in each system was collected for MnO, Na 2 O, and K 2 O containing BF slag system. According to the measurement techniques and conditions, the viscosity data were carefully examined and evaluated. For example, the data obtained at a temperature significantly below the liquidus temperature (e.g. 50 C ), which is not accepted in the present study Minor Element Impact In the CaO-MgO-Al 2 O 3 -SiO 2 slag system, the role of four major components CaO, MgO, Al 2 O 3 and SiO 2 had been explained before in the Section The viscosity of molten slag is closely related to its structure, which is dependent on its composition and temperature. The final BF slag has four major components, SiO 2, Al 2 O 3, CaO and MgO that can be categorized into three groups, acidic oxide (SiO 2 ), basic oxide (CaO and MgO) and amphoteric oxide (Al 2 O 3 ). SiO 2 forms a network structure through (SiO 4 ) 4- tetrahedral units to increase viscosity. The basic oxides Ca 2+ and Mg 2+ tend to break the network and reduce slag viscosity. The silicate structure is composed of connected silicate, broken network and free-moving component. According to the network theory, the minor elements can be classified into 3 categories: network former, network modifier and amphoteric oxide. The elements of F, S, Na, Fe, Mn belong to the network modify group, which reduce the slag viscosity. According to Kim s viscosity study of K 2 O containing system, K 2 O is the network former, which 106

132 increased the slag viscosity within composition range 1-10 wt%. In terms of the viscosity impact of TiO 2, there are two contradictive opinions. Liao believed that the TiO 2 has a similar structural unit as SiO 2, which positively increase the slag viscosity (TiO 2 >20wt%) [119]. When the TiO 2 concentration decreased, in Park s viscosity measurement, it has been found the addition of TiO 2 reduce the slag viscosity of blast furnace type slag [121] Result & Discussion Comparisons of viscosities The viscosities of 8 synthetic slags with minor elements (B 2 O 3, F, S, MnO, FeO, Na 2 O, K 2 O, and TiO 2 ) were measured. The viscosity data from both present study and literatures indicated that the additions of minor elements B 2 O 3, F, S, MnO, FeO, TiO 2 and Na 2 O reduce the viscosity. In addition, the viscosity reduction effect of CaF 2 additive is stronger than other minor elements. Kim et al reported that addition of K 2 O in CaO-MgO-Al 2 O 3 -SiO 2 system increased the viscosity. Figure 4.6 shows the comparison between the present viscosity measurements and data from Liao et al [119] and Park [120] in the close composition in the CaO-MgO-Al 2 O 3 -SiO 2 -TiO 2 system. It can be seen that the present measurements generally agree with Park s data. The comparison of viscosity data at a different TiO 2 concentration in close CaO/SiO 2 ratio, Al 2 O 3 content, and MgO content shows that the addition of TiO 2 into the system keeps decreasing the viscosity. Figure 4.6 Comparison of viscosities for CaO-MgO-Al 2 O 3 -SiO 2 -TiO 2 slag by Park [120] and Liao [119] 107

133 Viscosity Model Description A viscosity model on CaO-MgO-Al 2 O 3 -SiO 2 system has been proposed by the present authors in the Section 4.1. In the present study, the model is extended to predict the effects of Na 2 O, K 2 O, MnO, FeO, TiO 2, B 2 O 3, CaF 2 and CaS additions on the viscosity of blast furnace slags. The details of model developments had been introduced in the Section 4.1. The following section will focus on the extension part of addition of minor element. The temperature dependence of viscosity can be described by the Arrhenius-like equation as shown in Equation 4-7. Equation 4-7 the modified equation from Frenkel-Weymann equation (Equation 4-1) η = A T exp ( E A T ) Where η is viscosity in Pa.s, T is the temperature in K, E A is viscous activation energy in kj/mol, and A is the pre-exponential factor. lna = m E A n Where A the pre-exponential factor and B is the activation energy from Equation 4-3. m and n is the model parameters are and respectively. This correlation has been widely used by many researchers in the development of viscosity models, such as the Shankar, Shu, and Hu. The values of m and n in the present model are determined to be and respectively, which is the same as shown in section As shown in Equation 4-8, the activation energy B in the present model is expressed by the sum of all metal oxides multiplied with their partial activation energies E i (i =SiO 2, FeO, CaO, MgO, Al 2 O 3, CaF 2, B 2 O 3, TiO 2, Na 2 O, K 2 O, MnO, and CaS). Equation 4-8 Activation energy equation E A = (M i *E i ) Where M i and E i are molar fractions and partial energy of each metals oxides respectively. 108

134 Please note, the equation and parameters of SiO 2, CaO, MgO, and Al 2 O 3 were reported in the section before. In Equation 4-9, the partial activation energy Ei of each metallic oxide can be expressed using the following polynomial equation. The model parameters were reported in Table 4.4. Equation 4-9 Partial activation energy E i calculation, for Equation 4-8 E i = E i 0 + E i 1 *B + E i 2 *B 2 Where B is optical basicity ratio, B i 0, B i 1 and B i 2 are model parameters of each metal oxide. From the experiment measurements, the contributions of minor elements could be estimated within a range using the calculated activation energy and its molar composition. And B i 1-3 can be determined, which is summarized in the Table 4-4. A large negative numbers were reported for the model parameters of CaF 2 and B 2 O 3, which significantly reduce the slag viscosity. In contrast, the K 2 O positively contributed to the activation energy, which represents the network-forming effect and improve the slag viscosity. Table 4.4 Model parameters to calculate E i of each minor element, the parameters of SiO 2, CaO, MgO, and Al 2 O 3 were reported in the section before E CaF 2 FeO TiO 2 B 2 O 3 CaS MnO Na 2 O K 2 O As Equation 4-10 shown, the structural of different silica composition is indicated by parameter basicity B, which was calculated using optical basicity and molar composition of oxide. Equation 4-10 Slag basicity B calculation, for Equation 4-9 B = i=ca,mg,andetc B i*m i -B Al2O3 M Al2O3 i=si&al A i *M i 109

135 Where M is molar fraction of cations and anions, B i is optical basicity of basic oxides (CaO, MgO, Na 2 O, K 2 O, MnO, CaS, CaF 2, MnO, B 2 O 3, FeO, and TiO 2 ) and A i is optical basicity of acidic oxide (SiO 2 and Al 2 O 3 ) from the optical basicity of Duffy as shown in Table 4.5. Table 4.5 Optical basicity of oxide from Duffy Optical Basicity CaF 2 FeO TiO 2 B 2 O 3 CaS MnO Na 2 O K 2 O The present model performance is evaluated using Equation 4-6 by comparison between the predicted viscosity and experimental data. In the present study, only the measurements ranging within blast furnace slag composition were selected for evaluation, which is CaO/SiO 2 =1-1.3, 1-10 wt.% MgO, wt.% Al 2 O 3 and 1-5 wt.% minor element. In addition, the Urbain model (1981 version) was utilized as the comparison with present model. The outcomes were summarized in Table 4.6. Present model reported a low deviation within BF slag composition ranges comparing to the Urbain model (1981 version). From the equations and parameters of the Urbain model, it did not encounter the CaF 2 and B 2 O 3 as a strong network modify, which report a large deviations for these two components. Also, Urbain model regarded the K2O as a network modify in the CaO-MgO-Al 2 O 3 -SiO 2 system, which did not obey the experimental measurements. In contrast, the Urbain model reported the lowest deviation for MnO containing system, because Urbain modified its models for CaO-MgO-Al 2 O 3 -SiO 2 -MnO system on Table 4.6 Summary of model performance in BF slag composition range BF slag with different minor elements Deviation (%) Present Model Urbain Model TiO B 2 O

136 CaF CaS MnO FeO Na 2 O K 2 O The performance of present model (Figure 4.7A) and Urbain (Figure 4.7B) model were further investigated in the CaO-MgO-Al2O3-SiO2- TiO2 system of the Shankar, Park and present study measurements [41]. As Figure 4.7 shown, present retained consistent performance from low to high viscosity regions. Urbain model reported the accurate prediction and under-estimate the high viscosity slag. Figure 4.7 the model prediction vs experimental results of CaO-MgO-Al2O3-SiO2-TiO2 slag system of Park [120], Shankar [32] and present (A) left, present model and (B) right, Urbain Model (1981 version) [132] At the current stage, the present model could not provide accurate predictions beyond BF slag composition range. Figure 4.8 demonstrates that the deviation of the predictions increases with increasing FeO concentration. As shown in Figure 4.8, when FeO concentration is lower than 10 wt%, the average predict deviation is around 15%. If the FeO content is increased to 111

137 30 wt% (copper slag composition range), the prediction deviation will be increased to 30%. It indicated that the present model can only provide accurate viscosity information for BF slag composition ranges. Figure 4.8 Increase of prediction deviation in CaO-MgO-Al 2 O 3 -SiO 2 -FeO system with increasing FeO concentration by Bills [64], Gorbachev [189], Higgins [190] and present study Industrial Application The viscosity reduction ability of 8 minor elements was compared through model prediction at 1500 C. The base composition is 35 wt% SiO 2, 17.4 wt% Al 2 O 3, 38.6 wt% CaO and MgO 9 wt%. The concentrations of SiO 2, Al 2 O 3, CaO and MgO proportionally decrease when the concentration of additive increases. Except for K 2 O, other additives decrease the slag viscosity. It can be seen from Figure 4.9 that, the ability of viscosity decrement by different minor elements in BF slag systems can be ranked as: CaF 2 > B 2 O 3 > CaS > Na 2 O > TiO 2 > MnO > FeO. Because of strong viscosity reduction ability, CaF 2 and B 2 O 3 minor element were often used to remove accretions on the BF wall. 112

138 Figure 4.9 The comparison of viscosity reduction ability of 8 minor elements on BF slag viscosity There are two major routes to reduce the operation cost of BF ironmaking process: 1) reduce MgO flux addition, 2) increase using high Al 2 O 3 content iron ore. Both routes will tend to increase the slag viscosity at current operation condition. The minor elements from low-grade iron ore can effectively reduce BF slag viscosity. For example, due to abundant Ti-bearing iron ore resources in western part of China, Ti-bearing iron ores were used and CaO-MgO- Al 2 O 3 -SiO 2 -TiO 2 slag was generated. The concentration of TiO 2 in final slag can be wt% in Panzhihua Iron and Steel and wt% in Hebei Iron & Steel Group. As Figure 4.10 shown, present model can provide an accurate prediction for typical slag compositions containing TiO 2 above 1450 o C and 0-20 wt% TiO 2 containing slag. The TiO 2 addition into slag can reduce slag viscosity however due to inevitable precipitation of Ti(C, N) at high temperature; the viscosity significantly increases and blast furnace operation with high TiO 2 slag is still challenging. 113

139 Figure 4.10 Comparison of model prediction and Liao s measurements [119] Conclusions In the present study, the impacts of 8 minor elements on BF slag viscosity were systemically studied, which includes Na 2 O, K 2 O, FeO, B 2 O 3, CaF 2, CaS, TiO 2, and MnO. It was found that CaF 2 has the most significant effect of BF slag viscosity reduction. Except for K 2 O, the other 7 additives decrease the slag viscosity. An existing CaO-MgO-Al 2 O 3 -SiO 2 viscosity model has been extended to predict the effects of minor elements on the viscosity of BF slags using present and collected viscosity data. The model reported the good agreements with the available experimental data within BF slag composition range. For the slag of CaO-MgO-Al 2 O 3 -SiO 2 - FeO system (copper smelting slag), the prediction deviation would increase at high concentration of FeO content. Further experimental work will be required to improve the model performance. 114

140 Chapter 5 : Viscosity Model Development Based on Probability Theorem In the existing viscosity models of the CaO-MgO-Al 2 O 3 -SiO 2 system, few researchers discussed the distribution of cations (Ca 2+ or Mg 2+ ) in SiO 4 and AlO 4 network structure. A new term probability was proposed to describe the probability of Ca 2+ (or Mg 2+ ) cations to connect with SiO 4 and AlO 4 tetrahedra unit by considering the ionic electronegativity and radius. The proposed model demonstrated superior performance in the viscosity prediction of full composition range of CaO-MgO-Al 2 O 3 -SiO 2 system; as well as its sub binary, ternary system, blast furnace composition and ladle furnace range. In chapter 5, the novel developed model was presented in Section 5.1. In addition, the present model can be extended to calculate the viscosity of CaO-MgO-Al 2 O 3 -SiO 2 - FeO, which was reported in Section CaO-MgO-Al 2 O 3 -SiO 2 system in full composition range Introduction Slag viscosity is critically important to various pyrometallurgical operations, which is necessary for process optimization and reducing the operating costs. Critical data evaluation and model assessments have been carried out in Section viscosity data in the CaO-MgO-Al 2 O 3 -SiO 2 system, which covers wide composition and temperature ranges, were collected and examined based on experimental techniques, data consistency, and cross-reference comparisons. The data related to the compositions of ironmaking and steelmaking slags were also selected for evaluation. Using the accepted data above, a new viscosity model is proposed for the CaO-MgO- Al 2 O 3 -SiO 2 system and the performance of this model is compared with other existing models. In addition, the present model can also be used to predict the low orders silicate systems containing CaO, MgO, and Al 2 O Silicate melt structure The viscosity of molten slag closely related to its structure, which is dependent on composition and temperature. The components of the quaternary system CaO-MgO- Al 2 O 3 -SiO 2 can be categorized into three groups: acidic oxide (SiO 2 ), basic oxide 115

141 (CaO and MgO) and amphoteric oxide (Al 2 O 3 ). SiO 2 forms a network structure through (SiO 4 ) tetrahedral units. The addition of basic oxide, either CaO or MgO, will break the [SiO 4 ] network. It is widely accepted that O 2- from basic oxides tends to break the Si-O-Si bond in silicate network and forms Si-O - intermediate, which require cations (Ca 2+ or Mg 2+ ) charge compensation. Also, amphoteric oxide Al 2 O 3 can form AlO 4 unit to connect with the [SiO 4 ] network, which requires cations (Ca 2+ or Mg 2+) charge compensation as well. As shown in Figure 5.1, the insertion of O 2- into SiO 4 network tends to break covalent bond between Si and [O] and Ca 2+ will compensate the O - charge. This intermediate Ca(Mg)-SiO 4 structure unit has one free positive charge, which is able to break another SiO 4 or compensate the AlO 4 charges. Figure 5.1 Interaction among Ca 2+ cations, silica and alumina Al 2 O 3 can behave as either acidic oxide or basic oxide depending on the concentrations of basic oxides. If sufficient Ca 2+ and Mg 2+ cations are present to balance the (AlO 4 ) - charges, the Al 2 O 3 acts as an acidic oxide which is incorporated into the silicate network in tetrahedron coordination. In the case of insufficient basic oxides, Al 3+ will behave the same as Ca 2+ or Mg 2+ to break the (SiO 4 ) network. In CaO-MgO-Al 2 O 3 -SiO 2 system, the major roles of Ca 2+ /Mg 2+ are to compensate the Si-[O] - charge and [AlO 4 ] 5-. Due to electrical force between charges, it is accepted that when the Ca 2+ /Mg 2+ concentration is low, they have higher priority to balance the AlO 4 charges than breaking the Si-O covalent bond Pre-Exponential Factor A The temperature dependence of viscosity can be described by the Arrhenius-type equation (Equation 5-1). 116

142 Equation 5-1 Arrhenius type equation η = A exp ( 1000 E A ) T Where η is viscosity in Pa.s, T is the absolute temperature (K), A is the preexponential factor, EA represents the integral activation energy in J/mol. As shown in Equation 5-2, a linear relationship between pre-exponent factor A and activation energy E A was proposed by Urbain [131]. The activation energy E A and pre-exponential factor A can be determined by plotting ln(η) against 1/T under the same composition. Equation 5-2 the linear relationship between A and B lna = m E A n Where A the pre-exponential factor and E A is the activation energy from Equation 4-3. m and n is the model parameters are and respectively. This linear correlation has been widely applied in different viscosity models, such as the Shankar s and Hu s model [141, 142]. In the present study, from 604 compositions of accepted viscosity data, the linear correlation is confirmed as shown in Figure 5.2, ln(a) and E A has a linear relationship with R 2 =0.948, which will be used in the construction of the present viscosity model. m and n values in Equation 5-2 are and respectively. 117

143 Figure 5.2 The linear relationship between E A and ln(a) Network Modifier Probability In the existing viscosity models of the CaO-MgO-Al 2 O 3 -SiO 2 system, few researchers discussed the distribution of cations (Ca 2+ or Mg 2+ ) in SiO 4 and AlO 4 network structure except Zhang model [188]. Zhang et al calculated the concentration of three types oxygen (O 2-, O - and O 0 ) by several assumptions; for example, the full amount of CaO first compensate the Al 2 O 3 then break silicate network; then MgO will break the rest of silicate network, which did not consider equilibrium condition within the quaternary system. With the study of silicate based mineralogy, Ramberg suggests that the silicate structure (polymerized level of the SiO 4 network) is dependent on basic oxide concentrations, atomic radius and electronegativity [191]. In the present study, a new term probability (P) is introduced to describe the probability of Ca 2+ (or Mg 2+ ) cations to connect with SiO 4 and AlO 4 tetrahedral unit. P Ca and P Mg. The Equation 5-3 are proposed to be the probability of Ca 2+ or Mg 2+ connecting to the Si-O network respectively. Ca 2+ and Mg 2+ cations were also required for (AlO 4 ) - charge compensation. Therefore, the (1-P Ca ) are the probability of cations to connect with AlO 4. It is known that Ca 2+ and Mg 2+ have a higher priority to compensate the AlO 4 charges. At low concentration of CaO/MgO, there is a high probability of compensating the (AlO 4 ) - charges. When the concentration of CaO/MgO increases, the probability of breaking Si-O will raise. 118

144 Equation 5-3 the probability calculation of cations Ca and Mg for Equation 5-6 χ Ca 2+M Ca 2+ P Ca = χ (SiO4 ) 4 M (SiO4 ) 4 + χ (AlO 4 ) 5 M (AlO4 ) 5 χ Mg 2+M Mg 2+ P Mg = χ (SiO4 ) 4 M (SiO4 ) 4 + χ (AlO 4 ) 5 M (AlO4 ) 5 Where M is a molar fraction of a metal oxide; X is electronegativity of structure units in slag system. The electronegativity of Ca 2+, Mg 2+, AlO 4 and SiO 4 units are determined using Mulliken equation, as shown in Equation 5-4, which is derived from 1 st ionization energy and electron affinity of the atom. The values of electronegativity are shown in Table 5.1. Equation 5-4 Mulliken equation χ = I + E 2 Where I is the ionization energy (kj/mol) and E is electron affinity (kj/mol) Table 5.1 Electronegativity χ of basic oxide cations and network former units Ca 2+ Mg 2+ (AlO 4 ) (SiO 4 ) Χ Activation Energy E A In Arrhenius equation, E A is defined as the integral activation energy of silicate slag, which is composed of four metal oxides and can be expressed as Equation

145 Equation 5-5 Activation energy calculation E A = E CaO + E MgO + E Al2 O 3 + E SiO2 Where E i is activation energy of i component (i = SiO 2, Al 2 O 3, CaO, and MgO), which is calculated from Equation 5-6. In CaO-MgO-Al 2 O 3 -SiO 2 system, as a network modifier, three structure units are relevant to CaO including free oxygen O 2-, SiO 4 -Ca-SiO 4, and SiO 4 -Ca-AlO 4. As P Ca defined before, one Ca 2+ cation has probability P Ca to connect with one SiO 4 tetrahedron. Therefore, the probability of SiO 4 -Ca-SiO 4 and SiO 4 -Ca-AlO 4 can be assumed as P Ca 2 and P Ca *(1-P ca ) respectively. As Equation 5-5 shown, the integral activation energy of CaO is calculated by the sum of energy contributions of each 0 structural unit multiplied by its probability. The E Ca is the constant representing O 2- from CaO. Because of similar properties, the calculation of MgO integral energy is expressed in Equation 5-6. As an amphoteric oxide, Al 2 O 3 shows both negative and positive impacts on activation energy. There are four possible structure units for aluminum cations, those are, network modifies unit: O 2-, 3(SiO 4 )-Al and network former unit: AlO 4 -Ca-AlO 4 and AlO 4 -Mg-AlO 4. The charge balanced AlO 4 -Ca/Mg structure units give a positive contribution to the integral activation energy. The (1-P Ca ) and (1-P Ca ) are used to describe the probability of Ca 2+ /Mg 2+ participating on alumina network. One Ca 2+ /Mg 2+ cation is able to balance two (AlO 4 ) structure units; therefore the probability order is assumed to be 2. 3(SiO 4 )-Al represents the network breaking the effect of Al 3+ cation; so it gives a negative contribution to the activation energy. The probability of one alumina cation which is not charge compensated is (1-(1-P Ca )*(1- P Mg )). The probability order is assumed to be 3, because of 3 SiO 4 structure units. The E 0 Al is the constant representing free O 2- from Al 2 O 3. However, due to charge compensation, most of the O 2- contributes into AlO 4 network, which reflects small activation energy in Table 5.2. Silica has only one structure unit SiO 4. It has a positive impact on viscosity and activation energy and the parameter related is a constant shown in Table

146 The overall activation energy of all structure units is optimized from collected viscosity data in the CaO-MgO-Al 2 O 3 -SiO 2 system. From the parameters in Table 5.2, it can be seen that the major structural unit in network breaking is Si-Ca(Mg)-Si. The free O 2- and Si-Ca(Mg)-Al have less significant impacts on the activation energy. The Al 2 O 3 behaves almost the same as SiO 2 in CaO-MgO-Al 2 O 3 -SiO 2, which has strong positive impact on activation energy. In addition, the CaO has higher priority to compensate the AlO 4 charges and lower priority for SiO 4 charges, which is demonstrated by the optimized parameters. Equation 5-6 Partial activation energy calculation E Ca = E 0 Ca + E SiO4 Ca SiO 4 P 2 Ca + E SiO4 Ca AlO 4 P Ca (1 P Ca ) E Mg = E 0 2 Mg + E SiO4 Mg SiO 4 P Mg + E SiO4 Mg AlO 4 P Mg (1 P Mg ) E Al = E 0 Al + E Al 3SiO4 [1 (1 P Ca ) (1 P Mg )] 3 + E AlO4 Ca AlO 4 (1 P Ca ) 2 + E AlO4 Mg AlO 4 (1 P Mg ) 2 E Si2 = E SiO4 Where P represents the probability of Ca/Mg molecules breaking silicate network defined in Equation 5-3, and E is parameters of structure units from Table 5.2 Table 5.2 Activation energy parameters of all involved structural units in CaO-MgO- Al 2 O 3 -SiO 2 system Basic Oxide Acidic Oxide Ca 2+ Mg 2+ SiO 4 Al E Ca E 0 Mg E SiO E 0 Al E SiO4 Ca SiO E SiO4 Mg SiO E AlO4 Ca AlO E SiO4 Ca AlO E SiO4 Mg AlO E AlO4 Mg AlO

147 5.1.6 Model Performance The performance of the current model is evaluated by comparison with other models using the viscosity data in the CaO-MgO-Al 2 O 3 -SiO 2 system. The mean deviation Δ is calculated using Equation 5-7. Equation 5-7 Error deviation calculation Δ = 1 n η Calc η Exp η Exp 100% Where Δ is the mean deviation, n is the total number of data, η Calc is the model viscosity and η Exp is the experimental viscosity CaO-MgO-Al 2 O 3 -SiO 2 system The evaluation of the model performance was carried out for three different composition ranges: (i) all viscosity data in the CaO-MgO-Al 2 O 3 -SiO 2 system; (ii) data in the blast furnace slag composition range wt.% SiO 2, wt.% Al 2 O 3, wt.% CaO and 5-10 wt.% MgO and (iii) data in the ladle slag composition range wt.% SiO 2, wt.% Al 2 O 3, wt.% CaO and 5-10 wt.% MgO. The results for model comparison are shown in Figure 5.3. It can be seen that the present model performance very well in all composition ranges, with the mean deviation 21.4% in the full composition, 12.5% in the BF slag composition and 15.5 in the ladle slag composition range. 122

148 Figure 5.3 The performance summary of viscosity models in, (i) full CaO-MgO- Al 2 O 3 -SiO 2 composition, (ii) BF slag composition and (iii): ladle slag composition A detailed comparison is conducted using three most accurate models: present model, Zhang model and Urbain model at the viscosity range of 0-5 Pa.s [131, 145]. It can be seen from Figure 5.4, the present model has overall superior performance than both Zhang and Urbain models. The mean deviation is 12.5%, 19.4% and 19.3% for the present model, Zhang model, and Urbain model respectively. At high-value ranges (>2 Pa.s), the present model prediction distributed on both sides of the experiment viscosity; in contrast, the Urbain and Zhang model tend to underestimate the experimental data. On the other hand, it is clear that all models shown in Figure 5.4 can predict viscosity more accurately at viscosity range below 2 Pa.s which is usually enough for BF and steelmaking ladle slags. 123

149 Figure 5.4 Comparison between experimental viscosity and calculated viscosity by present model (12.5% deviation), Zhang model (19.4 deviations) [145] and Urbain model (19.3 % deviation) [131] Viscosity Trend Prediction The impacts of CaO and MgO on viscosity are investigated using model prediction and experimental data. At fixed SiO 2, Al 2 O 3 and temperature (1500 C), as shown in Figure 5.5, the replacement of MgO by CaO content was evaluated under two compositions: 1) high acidic oxide (44 wt.% SiO 2, 15 wt.% Al 2 O 3 ) and 2) low acidic oxide (33 wt.% SiO 2 and 5 wt.% Al 2 O 3 ). In both conditions, through CaO replacement, the slag viscosities decrease and decrement slope continuously reduced. Because of charge compensation impact of SiO 4 and AlO 4 units, the viscosity decrement is more sensitive at low acidic oxide concentrations. It is noted that at 44 wt% SiO 2 and 15 wt% Al 2 O 3, replacement of MgO by CaO first decreases and then increase viscosity. The model predictions agree well with experimental data by Gul tyai and Hofmann [22, 65]. 124

150 Figure 5.5 Comparisons between model predictions and Gul tyai [65] and Hofmann [22] results, 1500 C in the system CaO-MgO-Al 2 O 3 -SiO Sub-Ternary & Sub-Binary System The present model can also be used to predict the low-order silicate systems containing CaO, MgO, and Al 2 O 3. As shown in Figure 5.6, the linear relationship between activation energy E A and pre-exponential factor B can also be applied for lower-order systems with different m and n values (Equation 5-2). For each binary and ternary system, the individual m and n values were used to minimize the prediction deviation. The values of m, n and prediction deviation for each system are summarized in Table 5.3 below. In the lower-order system, modifications were required in Equation 5-5 to suit the actual system. For example, in SiO 2 -CaO system, both E Mg and E Al equals to 0 in SiO 2 -CaO system. Table 5.3 The summary of model parameters in binary and ternary silicate system containing CaO, MgO, and Al 2 O 3. m n Error Deviation (%) Database SiO 2 -Al 2 O 3 -CaO Hofmann, Bills, Johannsen Machin and Urbain SiO 2 -Al 2 O 3 -MgO Johannse and Lyutikov 125

151 SiO 2 -CaO Bockris and Urbain SiO 2 -MgO Bockris, Hofmann, and Urbain SiO 2 -Al 2 O Bockris and Urbain Figure 5.6 The linear relationship between E A and ln(a) for (A): SiO 2 -Al 2 O 3 -CaO and SiO 2 -Al 2 O 3 -MgO system and The experimental viscosity data for the systems of SiO 2 -Al 2 O 3 -CaO, SiO 2 -Al 2 O 3 - MgO, SiO 2 -CaO, SiO 2 -MgO and SiO 2 -Al 2 O 3 are compared with calculated values by the present model. As shown in Figure 5.7 (A~E), the predicted viscosities by the present model agree well with reported data. Higher error deviations are reported in two ternary systems indicating that current model needs to be improved to better describe the amphoteric behavior of Al 2 O 3 in extreme conditions (very high Al 2 O 3 concentration). Note that all available viscosity data in the ternary and binary systems have been used without evaluation. Evaluated data would give a better performance of the present model. 126

152 (A) (B) 127

153 (C) (D) (E) Figure 5.7 Comparisons between experiment viscosity and model prediction in the systems (A) SiO 2 -Al 2 O 3 -CaO, (B) SiO 2 -Al 2 O 3 -MgO, (C) SiO 2 -CaO, (D) SiO 2 -MgO and (E) SiO 2 -Al 2 O Industrial Application Blast Furnace Slag Examples of the industrial applications using the developed viscosity model are demonstrated in this section. Figure 5.8 shows the effect of (W CaO /W SiO2 ) on the viscosity of blast furnace slag at 15 wt% Al 2 O 3 and various MgO concentrations at 128

154 1500 o C. It can be seen that predictions agree well with Kim, Machin and Gul tyai s data. At a given Al 2 O 3 and MgO concentration, the addition of CaO continuously decreases the slag viscosity. Also, it indicates that at a given W CaO /W SiO2, the slag viscosities decrease with increasing MgO concentration. The effect of MgO seems to be more significant at low W CaO /W SiO2. MgO is usually added in the BF operation as flux. Reduction of MgO can decrease the direct cost in material and also fuel consumptions. It can be seen from Figure 5.8 that reduced MgO will increase the slag viscosity. To keep the slag viscosity at a low-level, W CaO /W SiO2 needs to be increased. However, liquidus temperature has to be controlled to avoid the formation of solid phase at operating temperature. Figure 5.8 Effects of W CaO /W SiO2 and MgO on slag viscosity at 1500 C and 15 Al 2 O 3 by the present model in comparisons with the data from Kim [122], Gul tyai [83] and Machin s [74] The present viscosity model can only predict viscosities for single liquid phase. It is essential to make sure the slag is liquid before the viscosity is calculated by the viscosity model. It is necessary to present iso-viscosity lines on the phase diagram. As an example, the iso-viscosity lines are calculated using the present viscosity model for blast furnace slags at 1500 C and 15 wt% Al 2 O 3. In Figure 5.9, all viscosities are presented within the full-liquid region. From the Figure 5.9, the viscosity is mainly dependent on SiO 2 concentration. The iso-viscosity lines are almost parallel to the 129

155 CaO-MgO axis, which has bias down to the MgO direction. It indicated that the replacement of CaO by MgO will slightly decrease the slag viscosity at fixed SiO 2 concentration. This behaviour is consistent with the fact that the viscosity parameters of E Mg are higher than E Ca as a network modifier, which also matches the conclusion from a review of binary viscosity data of SiO 2 -CaO and SiO 2 -MgO systems. Figure 5.9 The model prediction of the iso-viscosity diagram at 1500 C and 15 wt.% Al 2 O 3 and experiment data of Gultyai [83], Li [150], and Machin [68, 74] Ladle Slag in Steelmaking Process In steelmaking process, the desired viscosity of ladle slag ( Pa.s) is lower than BF final slag ( Pa.s). Figure 5.10 shows effects of temperature and slag basicity on viscosity at 30 wt% Al 2 O 3 and 5 wt% MgO. The present model can well predict Song s data with average deviation 15%. At fixed Al 2 O 3 and MgO concentrations, the viscosities decrease significantly with increasing W CaO /W SiO2 ratio and the decrement is more significant at low temperatures. For example, the viscosity is decreased by approximately 0.13 Pa.s at 1450 C when the W CaO /W SiO2 is increased 130

156 from 3 to 5.5. At 1550 C, the decrement of the viscosity is only approximately 0.05 Pa.s when the W CaO /W SiO2 is increased from 3 to 5.5. Figure 5.10 Effects of W CaO /W SiO2 and temperature on slag viscosity at 5 wt.% MgO and 30 wt.% Al 2 O 3 by present model in comparisons with Song s data [107] Conclusions In conclusion, an accurate viscosity model has been developed in the system CaO- MgO-Al 2 O 3 -SiO 2 using a large number of critically reviewed experimental data. A new term probability based on composition and electronegativity was introduced to describe the distribution of cations within the acidic oxide. The new model can accurately predict viscosities for blast furnace slags and steel refining slags in the system CaO-MgO-Al 2 O 3 -SiO 2. The model developed also has good performance for the sub-systems SiO 2 -Al 2 O 3 -CaO, SiO 2 -Al 2 O 3 -MgO, SiO 2 -Al 2 O 3, SiO 2 -CaO, and SiO 2 -MgO. 131

157 5.2 CaO-MgO-Al 2 O 3 -SiO 2 - FeO system in full composition range Introduction As one of the important physical properties of molten slag, viscosity performs an important role in metallurgical processes. Abundant studies have been constructed by researchers to investigate the correlation among slag composition, temperature, and viscosity. There is a considerable demand for accurate viscosity data in mathematical modeling for metallurgical processes, and although viscosity of slag can be measured using the rotating cylinder method, reliable data for industrial application are limited due to the difficulty and uncertainty of viscosity measurement at high temperature. In the ironmaking process, the Blast furnace (BF) is the principal technology to produce iron. The chemistries of these slags can be described by the system SiO 2 - CaO-MgO-Al 2 O 3 - FeO. These slags have significant impacts on the gas permeability and accretion formation in a blast furnace. In addition, the five components are the major components of another smelting process, including steelmaking, mould fluxes and copper-making process. A clear understanding of viscosity changes during slag formation will help to improve the technical and economic efficiency. High-temperature viscosity measurement is practically difficult, time- and money-consuming. Therefore, it is necessary to use reliable viscosity data to develop an accurate model to predict slag viscosity for CaO-MgO-Al 2 O 3 -SiO 2 - FeO system Model Description Silicate structure of SiO 2 -CaO-Al 2 O 3 -MgO- FeO system The slag composition and temperature determined its momentary structures and viscosity. According to the experimental data and network theory, the components of the CaO-MgO-Al 2 O 3 -SiO 2 - FeO can be categorized into three groups: acidic oxide (SiO 2 ), basic oxide (CaO, MgO and FeO ) and amphoteric oxide (Al 2 O 3 ). It is widely accepted the SiO 2 forms a network structure through (SiO 4 ) tetrahedral units, which positively impact on the slag viscosity. In contrast, the basic oxide, either FeO, CaO or MgO, will break the [SiO 4 ] network, which negatively impacts on slag viscosity. The insertion of O 2- will break the covalent bond between Si-O within the 132

158 (SiO 4 ) tetrahedral unit and then balance the negative charge. This intermediate [Ca (Mg)-SiO 4 ] + structure unit has one free positive charge, which is able to break another SiO 4 or compensate the AlO 4 charges. The basic oxide FeO reported two possible cations, Fe 2+ and Fe 3+, which reported different modify ability in Wright s viscosity measurements of iron silicate slags with vary Fe 3+ /Fe 2+ ratio [192]. It concluded that the modify ability of Fe 3+ is 10-15% stronger than Fe 2+ ; because the Fe 3+ is able to compensate with 3 SiO 4 units. However, it is difficult to form Fe-3[SiO 4 ] structural units because of the space limitation. The Al 2 O 3 can behave as either acidic or basic oxide depending on the concentrations of other basic oxides. If sufficient Ca 2+, Mg 2+, and Fe 2+ cations are present to balance the (AlO 4 ) - charges, the Al 2 O 3 acts as an acidic oxide which is incorporated into the silicate network in tetrahedron coordination. In the case of insufficient basic oxides, Al 3+ will behave the same as Ca 2+ or Mg 2+ to break the (SiO 4 ) network. In summary, in molten slag, the major roles network modifies, including Ca 2+, Mg 2+ and Fe 2+ is to compensate the Si-[O] - charge and [AlO 4 ] 5-. Due to electrical force between charges, it is accepted that when cations (Ca 2+, Mg 2+, and Fe 2+ ) concentration is low, they have higher priority to balance the AlO 4 charges than breaking the Si-O covalent bond Temperature dependence The temperature dependence of viscosity can be described by the Arrhenius-type equation as Equation 5-8 shown. Equation 5-8 Arrhenius type equation 1000* EA η A*exp T Where η is the viscosity in Pa.s, T is the absolute temperature in K, A is the preexponential factor, E A represents the integral activation energy in J/mol. 133

159 Pre-exponential Factor A A linear relationship between pre-exponent factor A and activation energy E A was proposed by Urbain. The activation energy E A and pre-exponential factor A can be determined by plotting ln(η) against 1/T under the same composition. This linear correlation has been widely applied in different viscosity models, such as the Shankar s and Hu et al. s model. Equation 5-9 linear correlation between E A and pre-exponential factor A lna m E n * A Where A the pre-exponential factor and E A is the activation energy from Equation m and n are the model parameters are and respectively Fe 2+ and Fe 3+ Determination The modify ability of Fe 3+ is stronger than Fe 2+. Also, with abundant FeO existence in silicate melts, the Fe 2+ may convert to Fe 3+ through breaking SiO 4 unit. In the present study, it is necessary to calculate the concentration of Fe 3+ /Fe 2+ for the model establishment. One of the most widely used methods to estimate Fe 3+ /Fe 2+ involves the use of empirical equation relating to oxygen partial pressure to the iron redox state in quenched silicate liquid. Computer based software, FactSage, was often utilized to calculate the concentration of Fe 3+ /Fe 2+ [194] Network Modify probability With the study of silicate based mineralogy, Ramberg suggests that the silicate structure (polymerized level of the SiO 4 network) is dependent on basic oxide concentrations, atomic radius and electronegativity [191]. The electronegativity of Ca 2+, Mg 2+, Fe 2+, Fe 3+, AlO 4 and SiO 4 units are determined using Mulliken equation as Equation 5-4, which is derived from 1 st ionization energy and electron affinity of the atom. The values of electronegativity are shown in Table

160 Table 5.4 Electronegativity χ of basic oxide cations and network former units Ca 2+ Fe 2+ Fe 3+ Mg 2+ (AlO 4 ) (SiO 4 ) Χ The term probability (P) is introduced to describe the probability of Ca 2+ (or Mg 2+, Fe 2+, and Fe 3+ ) cations to connect with SiO 4 and AlO 4 tetrahedral unit as introduced in Section 5.1. The P Fe, as shown in Equation 5-10, are proposed to be the probability of Fe 2+ or Fe 3+ connecting to the Si-O network respectively. Fe 2+ and Fe 3+ cations were also required for (AlO 4 ) - charge compensation. Therefore, the (1-P Fe ) are the probability of cations to connect with AlO 4. Equation 5-10 probability calculation for Fe 3+ and Fe 2+ χ Fe 3+M Fe 3+ P Fe 3+ = χ (SiO4 ) 4 M (SiO4 ) 4 + χ (AlO 4 ) 5 M (AlO4 ) 5 χ Fe 2+M Fe 2+ P Fe 2+ = χ (SiO4 ) 4 M (SiO4 ) 4 + χ (AlO 4 ) 5 M (AlO4 ) 5 Where M is a molar fraction of a metal oxide; X is electronegativity of structure units in slag system Activation Energy In Arrhenius equation, E A is defined as the integral activation energy of silicate slag, which is composed of metal oxides and can be expressed as Equation 5-11 shown: Equation 5-11 Activation energy calculation E A = E CaO + E MgO + E FeO + E Fe2 O 3 + E Al2 O 3 + E SiO2 Where E i is the partial activation energy of i component (i = SiO 2, Al 2 O 3, CaO, MgO, and FeO) calculating from Equation

161 In CaO-MgO-Al 2 O 3 -SiO 2 - FeO system, as a network modifier, there is three possible structure units combination with Fe 2+, including free oxygen O 2-, SiO 4 -Fe- SiO 4, and SiO 4 -Fe-AlO 4. As P Fe defined before, one Fe 2+ cation has the probability of P Fe to connect with one SiO 4 tetrahedron. Therefore, the probability of SiO 4 -Fe-SiO 4 and SiO 4 -Fe-AlO 4 can be assumed as P Fe 2 and P Fe *(1-P Fe ) respectively. As Equation 5-11 shown, the integral activation energy of FeO is calculated by the sum of activation energy of each structural unit multiplied by its probability. The E 0 Fe is the constant representing O 2- from FeO. Because of similar properties, the calculation of CaO and MgO integral energy is expressed in Equation Unlike Fe 2+, the Fe 3+ is able to compensate three negative charges, which should consider 4 types of structure units as Equation 5-12 shown. The impact of cations Ca, Mg, Al and Si were detailed discussed and introduced in Section 5.1. Equation 5-12 the partial activation energy calculation E Ca = E 0 Ca + E SiO4 Ca SiO 4 P 2 Ca + E SiO4 Ca AlO 4 P Ca (1 P Ca ) E Mg = E 0 2 Mg + E SiO4 Mg SiO 4 P Mg + E SiO4 Mg AlO 4 P Mg (1 P Mg ) E Al = E 0 Al + E Al 3SiO4 [1 (1 P Ca ) (1 P Mg )] 3 + E AlO4 Ca AlO 4 (1 P Ca ) 2 + E AlO4 Mg AlO 4 (1 P Mg ) 2 + E 2AlO4 Fe 2+ (1 P Fe 2+)2 + E 3AlO4 Fe 3+ (1 P Fe 3+)2 E Fe 2+ = E 0 Fe 2+ + E SiO 4 Fe 2+ 2 SiO 4 P Fe 2+ E Fe 3+ = E 0 Fe 3+ + E 3SiO 4 Fe 3+ P 3 Fe 3+ E SiO4 Fe 3+ 2AlO 4 P Fe 3+ (1 P Fe 3+) 2 + E SiO4 Fe 2+ AlO 4 P Fe 2+ (1 P Fe 2+) + E 2SiO4 Fe 3+ 2 AlO 4 P Fe 3+ (1 P Fe 3+) + E Si2 = E SiO4 where P represents the probability of cations, Ca 2+, Mg 2+, Fe 2+ and Fe 3+ breaking silicate network and E i is parameters of structure units from Table

162 Table 5.5 Activation energy parameters of all involved structural units in CaO-MgO-Al 2 O 3 -SiO 2 system Basic Oxide Acidic Oxide Amphoteric Oxide Ca 2+ Mg 2+ Fe 2+ Fe 3+ SiO 4 Al 3+ 0 E Ca E 0 Mg E 0 Fe E0 Fe E SiO E 0 Al E SiO4 Ca SiO E SiO4 Mg SiO E SiO4 Fe 2+ SiO E 3SiO4 Fe E AlO 4 Ca AlO E SiO4 Ca AlO E SiO4 Mg AlO E SiO4 Fe 2+ AlO E 2SiO4 Fe 3+ AlO E AlO4 Mg AlO E SiO4 Fe 3+ 2AlO E 2AlO4 Fe E 3AlO4 Fe

163 5.2.3 Model Performance As Table 5.6 shown, the new model developed reported an overall 17% deviation with the viscosity data comparing with other existing models for CaO-MgO-Al 2 O 3 - SiO 2 - FeO system. As Figure 5.11 shown, the viscosity prediction accuracy was significantly improved using present model; considering the two closest Urbain and Zhang model reported 25% prediction deviations [131, 188]. Table 5.6 The prediction deviation of viscosity models for CaO-MgO-Al 2 O 3 -SiO 2 - FeO system Model Deviation (%) Present 17.1 Zhang 24.9 Urbain 25.6 Factsage 34.2 QCV 36.8 Li 42.6 Iida 50.6 Mills 64.1 A detailed comparison of the viscosity model performance is carried out using the three most accurate models: present model, Zhang model and Urbain model in the viscosity range 0-2 Pa.s. As Figure 5.11 shown, the present model has superior performance than both Zhang and Urbain models. It can be seen from Figure 5.11, the calculated viscosity from Urbain and Zhang model was an under-estimation at large viscosity region (>1 Pa.s). The experiment measurements (>1 Pa.s) was reported from Fe 2 O 3 containing slags. Because both Urbain and Zhang model assumed only FeO 138

164 existence in the molten slag and did not consider the modify ability of Fe 3+ is stronger than Fe 2+, which is included in the present model development. Figure 5.11 The comparison between experimental viscosity and calculated viscosity using Current, Urbain [131] and Zhang model [145]. Sub-ternary and quaternary system In addition, the present model can predict the viscosity of sub-ternary system of FeO containing slags. In ternary system, the network modify ability of different basic oxide can be determined. Figure 5.12 compared the viscosity of two ternary system, CaO-SiO 2 - FeO and MgO-SiO 2 - FeO. With the increasing of FeO content, at 1500 o C and CaO (MgO)/SiO 2 =1.2 conditions, the measured viscosity steadily increased for both ternary system. In addition, the viscosity of MgO-SiO2- FeO system is higher than the CaO-SiO2- FeO system at 50 o C higher temperature. The trend indicated that the modify ability of 3 basic oxides can be ranked as CaO>MgO> FeO. 139

165 Figure wt% SiO 2, 1500 o C for SiO 2 -CaO- FeO system by Chen [193], Bockris [194] and Ji [114], 40 wt% SiO 2, 1550 o C for SiO 2 -MgO- FeO system by Chen [115], Ji [195] and Urbain [60] Industrial Application Blast Furnace Slag The primary slag formed in the cohesive zone of the blast furnace contains high FeO content. The FeO concentration in the slag will decrease when the burden moves down and the reduction proceeds continuously. If initially formed primary slag is viscous and stays locally, reduction of FeO will continuously increase its viscosity making it more viscous. In the BF operation, if the primary slag forms at a lower temperature, i.e., if the top of the cohesive zone moves upward, the viscosity of the slag will be high and it may not be able to flow rapidly through the coke bed. The localized viscous slag will fill the void, which reduces the surface area for indirect reduction and also the gas permeability. It is desirable to have the primary slag formed at a higher temperature so that its viscosity is low enough to allow the slag drop quickly. As shown in Figure 5.13, the current model predictions are in very good agreement with the experimental results that cover the FeO concentration from 0 to 25 wt%. The viscosities shown in Figure 5.13 are all for fully liquid slags. The temperature impact on viscosity are more sensitive at low temperature than higher temperature condition. 140

166 Figure 5.13 Comparisons of the viscosities between model predictions and experimental data for different FeO -containing slags (in wt%) by Higgins [190]; Vyaktin [84] and Machin [80] Coppermaking Slag Figure 5.14 shows viscosity as a function of FeO at 1250 o C for a base slag 52 wt% SiO 2, 13.3 wt% Al 2 O 3, 29.3 wt% CaO and 5.3 wt% MgO, which is a typical coppermaking slag. The viscosity of the fully liquid slag continuously increases with decreasing FeO concentration in the slag. For example, it can be seen from Figure 5.14 that the viscosity of the slag with 30 wt% FeO is below 1 Pa.s. If FeO is reduced to 15 wt% the viscosity of the slag will be 3.5 Pa.s at the same temperature (1250 o C). The sensitivity of the viscosity to the FeO increases with decreasing the FeO concentration in the slag. It can be seen from Figure 5.14 that FactSage predicted viscosities are much lower than the predictions of the present model, in particular at low FeO concentrations. 141

167 Figure 5.14 Viscosity as a function of FeO at 1250 o C, base slag 52% SiO 2, 13.3% Al 2 O 3, 29.3% CaO, 5.3% MgO by Higgins [190] Conclusion In conclusion, an existing model by the present author has been optimized and extended to describe the viscous behavior of fully liquid slag in the CaO-MgO-Al 2 O 3 - SiO 2 - FeO system using a large number of reviewed experimental data. A new term probability based on composition and electronegativity was introduced to describe the distribution of cations within the acidic oxide. The new model can accurately predict viscosities for both blast furnace primary slags, steelmaking slags and copper making slags in the CaO-MgO-Al 2 O 3 -SiO 2 - FeO system. 142

168 Chapter 6 : Structure studies of silicate slag by Raman spectroscopy In the present study, Raman spectroscopy was utilized on quenched glass samples of SiO 2 -CaO, SiO 2 -CaO-Al 2 O 3, and SiO 2 -CaO-MgO system to investigate the network impact of CaO, MgO and Al 2 O 3 referring to the network theory. The Raman spectrum information, including peak location and intensity, were quantitatively analyzed correspond to the network structure of silicate glass. Various physiochemical properties such as viscosity, density, and liquidus temperature can be derived from a proposed mathematical definition called degree of polymerization (DP). The present methodology can be extended to predict the other physicochemical properties of silicate melts for metallurgical processes. 143

169 6.1 Introduction The structure and properties of amorphous slags are of widespread interest because of their importance in the process optimization of pyro-metallurgy field. Many spectroscopic methods have been developed to determine the structure of slags and distinctively identify the microstructural units within the amorphous silicate glasses [ ]. Raman spectroscopy, as an analytical technique for the study of molten slag, has been widely utilized and accepted by other researchers [41]. The microstructural information was obtained through the analysis of peak shift and intensity of Raman spectrum, which indicates the types of vibration units and its relative concentration. For CaO-MgO-Al 2 O 3 -SiO 2 slag system, the Raman spectrum study was performed by other researchers, as the summary in the Table 6.1. The alumina silicate system has been well studied; however, the focus composition range is different from the blast furnace slag composition. In addition, Different Raman spectrum will report varied results of amorphous glass phase due to instrument factors, such as intensity of laser light, which did not allow the cross-reference comparison of Raman results of amorphous glass. For silicate glass, most of the researchers focus on the high-frequency band ranging from cm -1 [199]. However, limited information was provided for the lowfrequency band ( cm -1 ), which is the critical region in the study of fused silica (amorphous phase). In the alumina silicate glass, it is accepted that the Al 2 O 3 behavior as a network former, connecting with SiO 4, was not clearly revealed in the Raman spectra of other researchers [4]. In the present study, Raman spectroscopy was utilized on quenched glass samples of SiO 2 -CaO, SiO 2 -CaO-Al 2 O 3, and SiO 2 -CaO-MgO system to identify the potential vibration units in the low-frequency region to further investigate the impact of CaO, MgO, and Al 2 O 3 on fused silica. A quantitative analysis was performed on the Raman spectroscopy to identify and estimate the abundance of silicate continuous ring and discrete anions (D n and Q n ) of silicate melts. 144

170 6.2 Methodology Sample Preparation The quenched slag samples were prepared for the SiO 2 -CaO, SiO 2 -CaO-MgO and SiO 2 -CaO-Al 2 O 3 system. The designed composition was shown in Table 6.1. Approximately 0.25g mixture was prepared for each experiment runs. The CaCO 3 (99%), SiO 2 (98%), MgO (99%) and Al 2 O 3 (99.9%) powders were weighed, mixed and grinded for 30 minutes to obtain homogeneous mixtures. The mixture melted in a graphite crucible at designed temperature for 2 hours to achieve complete fusion, homogenization and equilibrium status under Ar atmosphere condition. The schematic diagram is shown in Figure 6.1. The quenched glasses will be mounted and polished for Raman spectroscopy analysis. In addition, the electro-probe microanalysis (EPMA) were constructed for each sample to confirm the sample reliability, and the outcomes were shown in Table 6.1. Figure 6.1 Schematic diagram of equilibrium experiment settings 145

171 Table 6.1 The experiment designed condition and EPMA results Design Composition Experiment Temperature EPMA Results CaO/SiO 2 Additive o C SiO 2 CaO Mol/Mol% Mol% Mol% Mol% SiO 2 -CaO system No MgO Mol% SiO 2 -CaO-MgO system No

172 Al 2 O 3 147

173 Mol% SiO 2 -CaO-Al 2 O 3 system No

174

175 6.2.2 Raman Analysis The quenched material was mounted in epoxy resin and polished for Raman spectroscopy measurements (Company: Ranishaw; Model: invia). The Raman spectrum was recorded at room temperature in the frequency range of cm -1 using excitation wavelength of 514 nm semiconductor laser with a power of 1 mw. The instrument was calibrated in the air by utilization of electronic grade silica. The measurements were performed under ambient pressure and room temperature. There was no detectable temperature increase by laser touch to the samples. For one sample, measurements were taken on three different locations on separate pieces of quenched glasses to evaluate the consistency and stability of the instrument. The average deviations of three measurements at one sample were within 1%. The peak deconvolution is necessary for the quantitative analysis of the spectra by researchers. As Figure 6.2 shown, the baseline was firstly removed for spectra of 52.6SiO CaO system, and then the two bands were fitted by Gaussian function using software PeakFit program. Figure 6.2 Typical deconvolution of Raman spectrum of a 52.6 mol% SiO mol% CaO sample 150

176 6.3 Raman Results Structure of alumina silicate system The random network theory was accepted for the description of amorphous silicate structure. In silicate based slag of SiO 2 -CaO-Al 2 O 3 -MgO system, the SiO 2 forms a network structure by the connection of SiO 4 tetrahedral unit. The addition of basic oxide; the CaO and MgO tends to break the Si-O-Si bond. The AlO 4 from Al 2 O 3 binds with a SiO 4 unit with the existence of cations to compensate the charge, which improves the polymerization degree of silicate slag. From Raman spectrum, the interpreted microstructure units supported the development of network theory [200]. The fused glasses silica has been studied using Raman spectroscopy [201]. In the lowfrequency region, the two major peaks of glasses silica located at 495 cm -1 and 606 cm -1 in Raman spectrum. Galeener s study pointed out that the two peaks can be assigned to 4 and 3-folded rings respectively through the calculation of bond angle using the energy minimization method [38]. The structure of fused silica can be estimated as the combination of 4-3 folded rings due to the fact that the angel between O-Si-O is approximately 133 o. The required energy of 2-fold ring is >5eV comparing to 3-fold=0.51 ev and 4-fold ring=0.16 ev; while 2-fold planar rings are not possibly excepted since they require an unreasonably large amount strain energy for the bond angle=60 o [38]. In SiO 2 -CaO glasses, with the addition of basic oxide, a board band appears in the spectra ranging cm -1 shift. The addition of Ca 2+ and O - polarize the discrete anions, which was expected as the breaking silicate planar ring and form 4 different discrete anions with O 2-, according to the SiO 4 structural unit. After the peak deconvolution, 4 peaks were reported and assigned in the high-frequency region. The description of microstructure units and assigned peak location were summarized in Table 6.2. The peak Q 4 indicated the initiation of network breakage, which polymerize of non-bridging oxygen [O] -. As the continues addition O 2- from basic oxide, the abundance of [O] - will increased upon to 4 and become individual unit, which did not support the formation of network. 151

177 Table 6.2 The description of assigned peak information in Raman spectrum silicate structural units, black ball is Si and white ball is O. white ball with sign is O - Peak Raman Shift Structural Drawing Ref D 2 4-fold ring [SiO 4 ] D 3 3-fold ring [SiO 4 ] Q 1 Individual SiO 4 tetrahedral unit [SiO 4 ] 4-152

178 Q 2 Si 2 O 7 dimer (O)O - -Si-2O-Si-2O - Q 3 Si 2 O 6 chain (O)O - -Si-2O-Si-2O - Q 4 Si 2 O 6 sheet SiO 4 -Si-O - (O) 153

179 Raman Peak Shift In SiO 2 -CaO system, the increasing CaO content indicated the degradation of silicate network, which means the polymerization degree of silicate network decreased. The Raman spectrum of glasses with the composition different CaO/SiO 2 is shown in Figure 6.3. In Figure 6.3, as the green and red dot line indication, the low-frequency band shift from left to right, and the high-frequency band shifts from right to left. In the low-frequency region, as the discussion before, the low-frequency band (D n ) represented the silicate planar ring. The addition of CaO tends to break the silicate network, which degraded the 4 folded to 3 folded ring. The high-frequency band (Q n ) represented the broken silicate units with cations ions Ca 2+. The 2-fold rings possibly exist in SiO 2 -CaO system and show a dominantly strong polarized Raman line at (ring-stretch) frequencies around 1100 cm -1 under low CaO content condition. At high CaO/SiO 2 ratio, the breakage of silicate network potentially forms the individual SiO 4 unit, which reported the Raman peak shift from right to left. From the view of vibration units, the insertion of CaO not only changed the silicate structure but also vary the vibration modes from bending vibration to stretching vibration. The attachment of CaO onto silicate will form [SiO 4 -x CaO] structural units, which initial the stretching vibration and form the bands at 1000 cm -1 region. In high-frequency region, as Figure 6.3 shown, the peak shifted to left due to the decreasing of electrons density from Park s study, which might be referred to degradation of silicate polymerization network. From the study of McMillan, the doubly charged cations M 2+ of the large ionic radius and small ionization potential (small Z/r 2 ) should preferentially occupy the Q 3 (sheet) sites [4]. The Z/r 2 of Ca 2+ (=2) is much smaller than Mg 2+ (=3.9). Therefore, due to the cations size difference, the Ca 2+ ion would charge compensate two open O - ions because of the large size of the [CaO 6 ], whereas the Mg 2+ is balanced with two adjacent corner-shared O - ions because of the small size the [MgO 6 ]. The substitution of Ca 2+ by Mg 2+ will slightly increase the polymerization degree of silicate network, which is also shown in the viscosity study of SiO 2 - CaO-MgO system [56, 57, 202]. 154

180 Figure 6.3 the Raman spectrum of SiO 2 -CaO system, which covers the CaO/SiO 2 ratio from 0.55 to 1.1 From the network theory and experiment viscosity data, it is known that MgO has a similar impact as CaO, which modify and reduce the polymerization degree of silicate network. The Raman spectrum of SiO 2 -CaO based with different MgO content is shown in Figure 6.4. As the green and red dot line indication, the low-frequency band shift from left to right, and the high-frequency band shifts from right to left. The peak shifting become steady comparing to Figure 6.3, which indicate that the internal micro-structure of molten slag approaches equilibrium status. Also, it can be noted that the intensity of peak at approximate 800 cm -1 significantly increased from 5mol % MgO to 20 mol% MgO, which will be discussed in the later section. Figure 6.4 the Raman spectrum of SiO 2 MgO CaO system under CaO/SiO 2 =1 and 1500 o C condition, which covers the different MgO concentrations. From the network theory, it is known that Al 2 O 3 would be converted to [AlO 4 ] -, which binds with SiO 4 units and form the silicate network. As amphoteric oxide Al 2 O 3, its role was 155

181 dependent on the amount of basic oxide. Large amounts of basic oxide are capable of compensating [AlO 4 ] - charges and push the Al towards the network former and vice versa. The Raman spectrum of SiO 2 -CaO- Al 2 O 3 of different Al 2 O 3 content was shown in Figure 6.5. As Figure 6.5 (a) shown, it is obvious that the addition of Al 2 O 3 increase the width of the band in the low-frequency region comparing to the Raman spectrum of SiO 2 -CaO and SiO 2 - CaO-MgO system, which evidently indicated the formation of combinations between [AlO 4 ] - and SiO 4 units. The polymerization length could not be directly identified using Raman techniques. After peak deconvolution, a novel peak was identified and recorded as D 1 at approximately 500 cm -1 regions. The bands were further deconvluted to compare the trend. As Figure 6.5 (b) shown, The addition of Al 2 O 3 shift the peaks Q 1 -Q 4 to the right, which indicates the enhancement of polymerization degree of silicate network. Figure 6.5 (a) left, the Raman spectrum of SiO 2 Al 2 O 3 CaO system under CaO/SiO 2 =1 and 1500 o C condition, which covers the different Al 2 O 3 concentrations. (b) Right, the peak deconvolution outcomes of left spectra Peak Intensity It is known that the peaks area is proportional to the abundance of the structural unit. The relative occupancy of deconvolution peak can be utilized as a supporting information to determine the viscosity impact of CaO, MgO, and Al 2 O 3 on the silicate network. Theoretically, the addition of CaO and MgO would decrease the polymerization degree of silicate network; and Al 2 O 3 is considered to be the contrary. The role of peaks can be determined within silicate through the comparison of peak area at different basicity and slag system. 156

182 The relative area occupancy of different peaks of (a) SiO 2 -CaO-MgO and (b) SiO 2 -CaO- Al 2 O 3 system were shown in Figure 6.6 under CaO/SiO 2 =1 condition. As Figure 6.6 (a), for SiO 2 -CaO-MgO system, the addition of MgO decreased the relative abundance of peak Q 4, D 2, and D 3 ; however, the concentration of Q 1, Q 2 and Q 3 increased. It is known that the role of basic oxide is to break the silicate network; therefore, the structure units of peak Q 4, D 2 and D 3 contributed to the formation of silicate network. For the SiO 2 -CaO-Al 2 O 3 system, when Al 2 O 3 content increased, Figure 6.6 (b) showed the increasing of the relative abundance of peak D 1, D 2, and Q 4 ; however, the concentration of Q 1, Q 2, Q 3 and D 3 decreased. From the analysis of peak shift and concentration of SiO 2 -CaO- Al 2 O 3 system, it should be noted that peak D 1 and D 2 is relevant to SiO 4 -AlO 4 network units; and D 3 should belong to pure SiO 4 network unit. However, both the increasing slope and decreasing slope is gently comparing to the Raman spectrum of SiO 2 -CaO and SiO 2 -CaO- MgO system; because the cations Ca 2+ or Mg 2+ was utilized for charge compensation of [AlO 4 ] - unit. Figure 6.6 The relative area occupancy of different peaks of (a) SiO 2 -CaO-MgO system ranging of CaO/SiO 2 =1, (b) right, relative area occupancy of different peaks of SiO 2 -CaO- Al 2 O 3 system ranging of CaO/SiO 2 = Temperature Impact It is accepted that the temperature will influence the silicate melts structure, which could be identified by Raman spectrum. A 45 SiO 2-10 Al 2 O 3-45 CaO mol% sample was molten at 100 o C interval from o C, which knew that the liquidus temperature is approximate 1268 o C from FactSage prediction. The target composition belongs to the wollastonite primary phase field. When the quenching temperature decreased, as Figure 6.7 shown, the high frequency region of spectra of become closer comparing to the Raman spectra of 157

183 wollastonite mineral [202]. This phenomenon can only be observed in the high frequency region of spectra; because the low frequency region is relevant to the network former unit AlO 4 and SiO 4. Figure 6.7 Raman spectrum of 45 SiO 2-10 Al 2 O 3-45 CaO mol% sample at 1300, 1500 and 1600 o C and wollastonite [202] Bond energy and the lattice energy The shift of a vibration frequency is originated from the shift of energy [203]. Assuming CaO, MgO, and Al 2 O 3 as ionic compounds in the molten slag, the bond force (energy) should be considered to explain the peak shift. Coulomb interaction [203, 204], the interacting force between static electrically charged particles, is given by the formula: Equation 6-1 Coulomb interaction calculation E = k Q 1Q 2 r 1 2 Where k is the Coulomb s constant 8.99 *10 9 Nm 2 /C 2, Q 1 =Z 1 Q e is the quantity of charge on the charge 1, Q 2 =Z 2 Q e is the quantity of charge on the charge 2, Z 1 and Z 2 is the number of electrons in the outermost energy level, Q e =1.602*10-19 C is the charge of the electron and r 1-2 is the distance between the two charges. In the case of CaO, MgO and Al 2 O 3, the nature of electrostatic forces of cations and O - are attractive. The ionic radius of Al 3+, Ca 2+, Mg 2+ and O 2- ions were 0.535Å, 0.329Å, 1.068Å, 158

184 and 1.4 Å respectively [207, 208]. The electrostatic energy was calculated for one Al-O, Ca- O and Mg-O bond according to the Coulomb interaction. The bond energy of one mole bond is given by multiplication of Avogadro s number, N A =6.022 * For one mol Al-O bond Equation 6-2 Examples of Coulomb interaction calculation E Al O = ( ) 2 ( ) = For one mole Ca-O bond = 4308 KJ/mol E Ca O = ( ) 2 ( ) = J For one mole Mg-O bond = 2251 KJ/mol E Mg O = ( ) 2 ( ) = J = 3214 KJ/mol For one mole SiO 4 tetrahedral unit by Bongiorno [209] E Si O = = 8677 KJ/mol As a result, in the SiO 2 -CaO-Al 2 O 3 system, when SiO 4 units are substituted by AlO 4, the lattice energy is weaker by an amount of 4369 (KJ/mol). The lattice energy decreases; hence the respective Raman bands shift to smaller wavenumber (shift to left). In the SiO 2 -CaO- MgO system, when Ca 2+ ions were substituted by Mg 2+ ions, the lattice energy is enlarged by an amount of 963 (KJ/mol), which cause the Raman bands shift to larger wavenumbers (shift to right) Summary From the quantitative analysis of Raman spectra of quenched slag sample of SiO 2 -CaO, SiO 2 - CaO-MgO and SiO 2 -CaO-Al 2 O 3 system, it can be concluded that: When system basicity increased, the low-frequency band ( cm -1 ) shift to right and high-frequency band ( cm -1 ) shift to left 159

185 A new peak appears at the 350 cm -1 position in the Raman spectra of SiO 2 -Al 2 O3- CaO comparing to SiO 2 -CaO system, which can be assumed as AlO 4 -SiO 4 ring structure unit. Peak D 1, D 2, D 3 and Q 4 can be classified as network former group contributing to the polymerization of silicate network. In contrast, the peak Q 1, Q 2, and Q 3 can be classified as network modify the group, which degraded the silicate network. It can be noted that when sample quenched temperature close to its liquidus temperature, the Raman spectrum is closer to its primary phase field. 6.4 Thermodynamic Analysis Degree of Polymerization The degree of polymerization (DP) is defined as the abundance of monomeric units in a polymer. In the silicate based system, DP referred to the silica tetrahedral, which can be determined from the frequency shifts and intensity changes of Raman spectra [198]. From the Raman study of SiO 2 -CaO, SiO 2 -CaO-MgO and SiO 2 -CaO-Al 2 O 3 system, the peaks can be classified into two groups. The peak D 1, D 2, D 3, and Q 4 should be classified as network formed group; because the increasing basicity will also increase these peaks intensity. And the peak Q 1, Q 2, and Q 3 should be classified as network modify group. In the present study, the ratio (high polymerized unit)/ (low polymerized unit) was used to represent the DP index for one quenched slag sample, as shown below. In silicate network, CaO, MgO, and Al 2 O 3 as ionic compounds in the molten slag, the bond force (energy) should be involved to determine the DP. The correspond bond energy was calculated using Coulomb interaction equation as Equation 6-2. The details is shown in Table 6.3. It should be noted that the distribution of Ca 2+ and Mg 2+ charge compensation is not determined, which has to assume 50% equal share. Equation 6-3 the degree of polymerization calculation DP = D 1 + D 2 + D 3 + Q 4 = High polymerized unit Q n E n C n Q 1 + Q 2 + Q 3 Low polymerized unit Q n E n C n 160

186 Where Q is the number of the structural unit within the peak n, for example, in peak D 2 (4 folded ring), there are 4 connected SiO 4 units. E n is the bond energy of structural units within the peak from D 1 to Q 4, which is calculated using Coulomb equation, C n is the relative concentration of the peak n in Raman spectrum Table 6.3 Summary of the bond energy of each deconvoluted peaks Peak Structural Unit Bond Energy (KJ/mol) D 1 AlO 4 -SiO D 2 4 [SiO 4 ] D 3 3 [SiO 4 ] Q 1 [SiO 4 ] 4- individual unit 8677 Q 2 Si 2 O 7 dimer Q 3 Si 2 O 6 chain Q 4 Si 2 O 5 sheet As Figure 6.8 shown, the proposed DP was a plot against the slag sample in the present study. It can be seen that the DP index decreased as basicity increased within SiO 2 -CaO, SiO 2 -CaO- MgO, and SiO 2 -CaO-Al 2 O 3 system. In the basicity = ranges, the DP index slightly increases as Mg 2+ ion substitutes for Ca

187 Figure 6.8 DP index again basicity of SiO 2 -CaO, SiO 2 -CaO-MgO, and SiO 2 -CaO-Al 2 O 3 system Density Density is a physical variable of molten oxides in operation optimization, which is relevant to the slag/metal separation. It is also an important thermodynamic variable for calculating critical dimensionless numbers, such as Reynolds, Prand, and Nusselts, which are used in fluid transmission and can be extended to the estimation of blast furnace operation [210]. The densities of molten slags can be simulated using the partial molar volume. The effect of the SiO 2 and Al 2 O 3 on density can be represented by empirical equation from Mill s study [211]. It should be noted that the reference temperature for calculation is 1773 K and require adjustment to other temperatures by applying a temperature coefficient of -0.01%/K [211]. The relationship between density and DP is shown in Figure 6.9. A linear equation can be proposed to estimate the slag density with Raman spectrum information. Figure 6.9 DP index against the estimated densities of slag samples 162

188 6.4.3 Viscosity & Activation Energy Viscosity is a measure of the impediment of flow. The size of the constituents present in the melt constitutes the barrier or impediment to movement. Since silicates contain different structural units with varying sizes; it is necessary to relate the viscosity to the structure of silicates. The abundance of several structural units is consistent with the activation energy of slags. Consequently, it is possible that activation energy of a composition is a mathematical function of the DP index. As Equation 6-4 shown, the Arrhenius type equation was used to determine the activation energy. The activation energy of slag samples in the current study can be determined from existing viscosity data. As Figure 6.10 shown, the calculated activation energy from experimental results has a positive relationship with DP for SiO 2 -CaO, SiO 2 -CaO-MgO, and SiO 2 -CaO-Al 2 O 3 system. A polynomial equation, as Equation 6-4 shown, can use to describe the trend. The DP index, which can be experimentally measured, can potentially be used to quantify and predict the viscosity of the melts [210]. Equation 6-4 Arrhenius-type equation η = A exp ( E A T ) E A = DP DP Figure 6.10 DP index of each Raman spectrum against the activation energy 163

189 6.5 Conclusion The structure and properties of amorphous slags are of widespread interest because of their importance in the process optimization of pyro-metallurgy field. Raman spectroscopy is an analytical technique for the study of the microstructure of molten slag of the silicate-based system. The impact of Al 2 O 3 and MgO on SiO 2 -CaO based system was investigated by utilization of Raman spectrum on quenched glasses samples. A significant correlation was determined between the quantitative information of Raman spectrum and a polymerization degree of slag sample in the present study, which supported the silicate network theory. In the present study, a quantitative analysis was performed on the Raman spectrum to estimate the degree of polymerization of silicate slag, which can extend to the relevant physiochemistry properties, such as density and chain dimensions (DP). The present methodology can be extended to predict the other physicochemical properties of silicate melts for metallurgical processes. 164

190 Chapter 7 : Experimental and modeling study of suspension system 7.1 Introduction The dynamic viscosity of suspensions is of interest in many disciplines of engineering, such as mechanical, chemical and civil engineering. The suspension viscosity η sus primarily depends on (1) the solid fraction, (2) shape and size of particles, (3) the suspending Newtonian liquid, (4) Temperature, and (5) shear rate (for non-newtonian suspension). There is a research gap that the suspension viscosity was rarely studied in high-temperature region and its correlation with room temperature data. It is known that the precipitation of solid particles in molten slag was commonly observed in iron, steel, copper and other pyrometallurgy process. Most of viscosity measurement assumed the full liquid slag system. As literature review in the Section 2.5, limited viscosity study of molten slag was constructed. With the assumption of suspension at 25 o C, the suspension viscosity model did not include the temperature information, why may not suitable for the prediction at smelting temperature (>1000 o C). It is necessary to explore and compare the suspension viscosity by the systematic variation of the parameters at both room and smelting temperature conditions. For the viscosity measurements at high temperature, the potential fault was caused from obtaining the steady viscosity values and determination of the solid proportion. In Kondratiev and Wu s study, the solid proportion of molten slag was determined using software FactSage prediction and Slag Atlas respectively [9, 213]. From the researches on phase equilibrium, the experimental results demonstrated that both tools can t provide an accurate prediction of phase mixture at a high temperature, which may cause large deviation on the determination of solid fraction. A reliable technique is required to obtain reliable viscosity values and the solid proportion of solid/liquid mixtures. The mathematical models of viscosity simulation were significant for both the fundamental development and industrial application. Early on 1909, as Equation 7-1 shown, Einstein proposed a mathematical expression to predict the suspension viscosity using liquid viscosity and solid fraction f [173]. Thomas, Roscoe and other researchers continue on the development of viscosity model through varying the mathematical expression of solid fraction f, which extend the prediction range of different suspension system [173] ]. 165

191 Equation 7-1 relative viscosity calculation η sus η liq = η rela = f(f) Where η sus is suspension viscosity in Pa.s, η liq is the liquid viscosity in Pa.s, f is the solid volume fraction in vol% The present study aims to: 1) Experimentally measure the suspension viscosity at room and smelting temperature using reliable techniques and 2) examine the applicability of the existing models and optimize them if necessary. 7.2 Methodology The viscosities of two-phase mixtures at both room and smelting temperatures were measured by rotation spindle techniques. Two model series, LV III and HB III from Brookfield, were utilized to cover the viscosity range 0-1 Pa.s and Pa.s respectively. The Rheocalc software on PC was utilized to control the rotation speed and record the torque readings. The suspension viscosity was calculated using Equation 7-2 below. The equipment constant K, a function of the spindle/crucible geometries and the rheometer, was determined using the standard silicon oil (Brookfield product) with known viscosity. Equation 7-2 Viscosity calculation η = K τ Ω Where η [Pa.s] is the viscosity of the suspension, τ [N.m -1 ] is the torque at a certain rotation speed Ω [m.s -1 ], and K is the equipment constant. The K value was calculated through calibration of standard silicon oil Calibration The equipment constant K, a constant parameter of the spindle/crucible, was determined through calibration of standard silicon oil from Brookfield Engineering. The standard silicon oil is a liquid polymerized siloxane with a certain length of polydimethylsiloxane chain, which determine the standard viscosity at 25 o C. From Brookfield Engineering, the physical 166

192 properties of silicon oil are shown in Table 7.1. In the present study, five standard silicon oil were utilized for calibration, which covering the viscosity ranges from 0.05 to 1 Pa.s. Table 7.1 Physical properties of silicon oil in present study Silicon Oil Viscosity (Pa.s) Density (kg/m 3 ) A ±4 B ±4 C ±4 D ±4 E 1 968±4 In a general run, the crucible, spindle bob, and silicon oil were kept inside the water bath (25 o C) for 30 minutes to achieve homogeneous temperature condition. The rheometer will report 70 torque at the 3-second interval at 3 different rotational speed. The overall equipment constant K was calculated using Equation 7-2 and accepted if the relative difference is within 1% from 5 standard silicon oil. The calibrated crucible, spindle, and rheometer were later used in the room-temperature, and the devices for high-temperature viscosity study were recalibrated through the same procedure Viscosity Study of Suspension at Room Temperature In the viscosity study at room temperature, the silicon oil and paraffin were employed to simulate the molten slag liquid and precipitated minerals respectively. The standard silicon oil with known viscosity at 25 o C was purchased from Brookfield Engineering. The piece of paraffin was grinded to fine particles and sieved to three group sizes: <100, μm and μm. The impact of various parameters have been systematically investigated, which include, 1) liquid viscosity, 2) solid fraction, 3) particle size and 4) temperature. The experimental conditions were shown in Table 7.2 below. Run Table 7.2: Experimental condition of viscosity measurement at room temperature Silicon Temperature Paraffin Solid Proportion Paraffin Oil ( o C) (vol %) Size 167

193 (Pa.s) , 25, (at 25 o C) 0-21 (at 10 and 40 o C) , 25, (at 25 o C) 0-21 (at 10 and 40 o C) , 25, (at 25 o C) 0-21 (at 10 and 40 o C) , 25, (at 25 o C) 0-21 (at 10 and 40 o C) , 25, (at 25 o C) 0-21 (at 10 and 40 o C) (μm) < < The experimental setup is schematically shown in Figure 7.1. A crucible having an inner diameter of 28 mm was used to hold the solution mixture. In a general run, the container with silicon oil, paraffin particle, and spindle bob was kept inside the water bath for 30 minutes, which allow the mixture achieve the designed temperature. The oil-paraffin mixtures were stirred extensively by the spindle to ensure homogenization environment. During the measurement, the Rheocale software from computer controlled and recorded the measured torque readings at three different pre-set rotation speed. 70 values were taken at 3-second interval at each rotation speed. The first part fluctuation values were ignored because the solid dispersion did not achieve equilibrium. With the known equipment constant from the calibration process, the viscosity value was calculated using Equation 7-2. The results were averaged and calculated over the measurements of 3 different rotation speeds. 168

194 Figure 7.1 Schematic diagram of room temperature measurements Viscosity Study of Suspension at Smelting Temperature The experimental of high-temperature viscosity measurement include two parts: the first part is to measure the suspension viscosity at designed temperature. Synchronously, the equilibrium experiments were constructed to determine the phase information at the temperature of solid appearing within the viscosity measurement. Electron probe X-ray microanalysis (EPMA) was used for microstructural and elemental analyses of the quenched samples, which can determine the accurate solid proportion and phase. The equipment for high-temperature viscosity measurements and equilibrium experiments were schematically shown in Figure 7.2 below. The features and description of the devices have been introduced, by the present author in a previous publication. Two industrial slag samples from blast furnace of Baosteel (BS slag) and JingTang (JT slag) were tested in the present study. 169

195 Figure 7.2 Schematic diagram of (a) left, high-temperature viscosity measurement (b) right, equilibrium experiments 7.3 Results In the viscosity study of suspension, the effect of various parameters on the suspension viscosity has been investigated. These parameters are: Liquid viscosity & solid fraction Particle diameter Temperature Shear rate Room Temperature All results were obtained by varying the shear rate (rotational speed) and measuring the corresponding shear stress. These measurements have been constructed at the five species standard silicon oil and three sizes of paraffin, which is displayed in Table 7.3. It has been found that at low solid proportion, the suspension behavior as a Newtonian fluid, which report the constant ratio of shear stress to rate. However, when the solid proportion increased above 25%, the suspension deviated to shear thinning fluid, which was separately shown in Table 7.4 at a different shear rate (rotational speed). The shear thinning fluid behavior would be discussed in the later section. 170

196 Table 7.3. Viscosity measurements of suspension of solid proportion from 0-22 vol% Viscosity (Pa.s) at different Solid Proportion (vol %) η Liq D T ( o C) (Pa.s) (um) <

197 < Table 7.4. Viscosity measurements of suspension of solid proportion from vol % Shear Stress (torque) at different rotational speed (rpm) η Liq T 26.5 vol% paraffin 29 vol% paraffin 32 % paraffin (Pa.s) ( o C) Torque / rpm Torque / rpm Torque / rpm 172

198 / / / / / 175 Average viscosity = Pa.s 34.4 / / / / / 150 Average viscosity = Pa.s 41.5 / / / / 125 Average viscosity = 0.25 Pa.s / / / / / 50 Average viscosity = Pa.s 62.3 / / / / / 250 Average viscosity = Pa.s 58.4 / / / / / 225 Average viscosity = 0.49 Pa.s / / / / / / / / / / / / 225

199 86.9 / 250 Average viscosity = 0.71 Pa.s 86.9 / 250 Average viscosity = 0.81 Pa.s 86.9 / 250 Average viscosity = 1.03 Pa.s / / / / / / / 50 Average viscosity = 1.86 Pa.s 50.9 / / / / / 40 Average viscosity = 2.14 Pa.s 16.1 / 5 32 / / / / / 30 Average viscosity = 2.56 Pa.s / / / / / 250 Average viscosity = 3.89 Pa.s / / / / / 250 Average viscosity = 4.53 Pa.s / / / / / 250 Average viscosity = 5.32 Pa.s 174

200 7.3.2 Smelting Temperature Figure 7.3 presents the viscosity of Baosteel slag and JingTang slag with a variation of temperature ranging from 1575 to 1375 o C. The viscosity information and elemental analysis from EPMA were summarized in Table 7.5. The solid fraction was calculated using matrices method with a known composition. Both of the elemental analysis results and viscosity increasing confirmed the solid precipitation when the temperature reduced to 1400 o C. The solid proportions were calculated from the composition of liquid (glass phase) and solid (melilite phase) by EPMA analysis. In addition, the FactSage (version 6.2) and phase equilibrium chart (from Slag Atlas) were utilized to compare the liquid and solid proportion and composition for these two samples, which is quite different from the EPMA results. The quantity of SiO 2 content performs a critical role in the slag fluidity. At high temperature, SiO 2 from gangue mineral integrated with CaO, formed molten slag, resulted in a good fluency of slag within blast furnace operation. As Figure 7.3 shown, the viscosity of BS slag is slightly higher than JT slag (approximate 0.05 Pa.s) in the full liquid region. The viscosity difference was enlarged as temperature decreasing, because of SiO 2. According to the elemental analysis from EPMA, in fully liquid slag, BS slag has 2 wt% SiO 2 higher than JT slag, which contributed to the higher viscosity. When temperature decreased, the melilite precipitation of BS slag occurred at a higher temperature than JT slag, which reports high solid fraction at the same temperature; hence enlarge the viscosity difference. At the same temperature, according to the results at Table 7.5, the solid proportion of BS slag is higher than JT slag, 20% > 10% at 1400 and 40 %> 27 % at 1375 o C respectively. In the present study, it has found that only small quantity of SiO 2 will impact on the viscosity of both fully liquid slag (1500 o C) and solid containing slag (1400 o C), which can become a critical issue in the low-temperature region of the smelting process. Table 7.5. The elemental analysis of Baosteel and JingTang slag from EPMA analysis, where the minor element include Na 2 O, K 2 O, FeO and etc Slag Temperature ( o C) Phase SiO 2 CaO Al 2 O 3 MgO Viscosity (Pa.s) 175

201 JT 1400 Liquid Bulk Viscosity= JT Solid 10 vol% JT 1375 Liquid Bulk Viscosity= JT Solid vol% BS 1400 Liquid Bulk Viscosity= BS Solid 20 vol% BS 1375 Liquid Bulk Viscosity= BS Solid 40 vol% Figure 7.3 The viscosity measurements of Baosteel and Jintang blast furnace slag sample 176

202 7.3.3 Effect of liquid viscosity and solid fraction It is accepted that the liquid viscosity and solid fraction are the two significant parameters for the viscosity of suspensions. From the view of model simulation (Einstein Model [9] Equation 7-3), it is expected that the relative viscosity has a proportional positive correlation with solid fraction only and not dependent on the liquid viscosity. Figure 7.4 shows that the effect of liquid viscosity and solid fraction [f] on the relative viscosity for particle diameters d= µm at 25 o C. From low (2 vol%) to high (32 vol%) solid fraction, the relative viscosity of the suspension rapidly increased upon to 5 times of the liquid viscosity. And, it can be noted that the deviations of relative viscosity among different liquid viscosity is negligible at low solid fraction range (0-15 vol%) and slightly increased to 5% at high solid fraction (15-32 vol%). It indicated that the effect of liquid viscosity is not constant and raised as a solid addition. At a high solid fraction, the liquid with large viscosity will momentarily retain and accelerate the particles. This dissipation of energy will appear as extra viscosity, which was observed in the torque measurements. Equation 7-3 Einstein equation of relative viscosity η sus η liq = η rela = ( f) 177

203 Figure 7.4 The relative viscosity of oil-paraffin system at different solid fraction and liquid viscosity at 25 o C Effect of particle diameter In the present study, the impact of particle diameter on solution viscosity was investigated using three different sizes paraffin, which was <100 µm, µm and µm. Figure 7.5 (a) and (b) demonstrate the viscosities of different particle size group at low (0.1 Pa.s) and high (1 Pa.s) liquid viscosity condition respectively. For suspensions based on a liquid with high viscosity (1 Pa.s), the effect of particle size on the suspension viscosity is negligible, which reported only 0.5% deviations. But for suspensions based on a liquid with low viscosity (0.1 Pa.s), a trend can be observed that larger particle will generate a higher suspension viscosity. At 32 vol% solid fraction, the and <100 µm reported Pa.s and 0.48 Pa.s respectively, which is approximately 8% deviations. In the low liquid viscosity condition (0.1 Pa.s), the particles of greater size possess more inertia such that on interaction with rotational bob, which will momently stop and accelerate during rotation. This energy dissipation appears as extra viscosity. However, in the high liquid viscosity condition (1 Pa.s), this inertia phenomenon occurred on all three sizes paraffin because of the increment of liquid viscosity. 178

204 Figure 7.5 The suspension viscosity at different solid fraction and particle size at (a) top, 0.1 Pa.s liquid viscosity and (b) bottom, 1 Pa.s liquid viscosity Effect of Temperature Temperature is another significant factor impacting on the viscosity, which was encounter within the calculation of liquid viscosity. It is known that temperature has a negatively proportional correlation with solution viscosity. When the temperature increase, the liquid viscosity will decrease but did not impact on the expression of a solid fraction under the assumption of thermal expansion of solid particle is negligible. Therefore, the suspension viscosity will reduce as [η sus ]= [η Liq ]*[f], which is confirmed by the viscosity measurements at room and steelmaking temperatures. 179

205 The Arrhenius type equation can express the temperature dependence of the slag viscosity as Equation 7-4 shown, which was widely utilized in the model development of liquid slag. In the present study, it has found that the applicable range of Arrhenius type equation can be extended to the dilute suspension with a solid fraction from 0-15 vol% at different liquid viscosity. The suspension viscosity follows the correlation in the form lnη = A + B, where constants B are close for present paraffin/oil study. As T Figure 7.6 (b) shown, the temperature dependence of 15 vol% suspension was confirmed at different liquid viscosity and Namburu s viscosity study {Namburu, 2007 #1976}. Equation 7-4 Arrhenius-type Equation η = A e B T Where η is the apparent viscosity Pa.s and T is the temperature K. 180

206 Figure 7.6 The temperature dependence on the oil-paraffin system suspension viscosity (a) 0.05 liquid viscosity suspension at 5, 10, 15 and 20 vol% and (b) 15 vol% suspension at liquid viscosity 0.05, 0.2 and 0.5 Pa.s by Wright [163] Effect of Shear Rate It is known that the viscosity of a fluid is correlated with the shear stress and shear rate. Figure 7.7 (a) and (b) shows the shear rate has been investigated for a various solid fraction and liquid viscosity. Figure 7.7 (a) compared that the shear rate (rotational speed) of 5% solid fraction at different liquid viscosity suspension. As the liquid viscosity increased, the suspension kept as Newtonian behavior. The R 2 value of 5% solid fraction at low viscosity suspension (0.05 Pa.s) and high viscosity liquid suspension (1 Pa.s) is and respectively, which was the Newtonian fluid behavior. The impact of liquid viscosity on fluid behavior is negligible. When the solid fraction increased, it is found that fluid slightly shifts to shear thinning behavior. Figure 7.7(b) compared that the shear rate of 0.1 Pas liquid viscosity suspension at a different solid fraction (10%, 20%, and 30%). The results indicated that at high solid proportion, the suspension slightly shifted to shear thinning solution, which can be observed from R 2 =0.997 at 10% solid fraction to R 2 =0.989 at 30% solid fraction. This behavior was also observed in Wu s viscosity study at above 15% solid suspension system. The critical point transforming the Newtonian to non-newtonian fluid could not be accurately determined, because the boundary condition between them is not quantitatively defined. In Coussot s study, he proposed that at high shear rates an increase of the suspension viscosity could occur due to secondary flow, grain-inertia effects (i.e. momentum transfer due to collisions between particles with fluctuating velocities or transition to turbulence) [215]. This phenomenon was observed in section 3.3 and 3.4 as discussed before. At high shear rates, the shear rate brought in additional rotational force and may cancel the impact of extra viscosity, which cause decreasing of shear stress and shift the fluid from Newtonian to shear-thinning type. 181

207 Figure 7.7 The measured torque at different rotational speed for (a) 5% solid fraction at 0.05 and 1 Pa.s silicon oil. (b) 10, 20 and 30 % solid fraction at 0.5 Pa.s silicon oil 7.4 Model Simulation Model Review and Evaluation 11 existing models were reviewed and evaluated in the present study using the viscosity database at room temperature condition. Equation 7-5 is used to calculate the difference between the measured and the calculated viscosity values. 182

208 Equation 7-5 error deviation calculation 1 exp Calc * n exp Where Δ is the average deviation, is the experimental viscosity, exp Calc is the calculated viscosity and n is the number of data. Figure 7.8 (a) and (b) present the comparison of viscosity deviations of existing models. Ranging from 0.05 to 5.5 Pa.s, the Kunitz model reported an outstanding agreement with experimental data with 2.95% deviations [174]. Figure 7.8 (b) also demonstrated that the Kunitz model fitted well with the experiment measurements comparing to other models. The model prediction of 0-20% solid fraction fitted with Happel model, which matches the conclusion of Wu. However, with the continues addition of solid, the suspension viscosity will shift towards to the Kunitz prediction. 183