Computational fluid dynamics analysis and design of flash ironmaking reactors

A novel flash ironmaking technology is being developed at the University of Utah aimed at producing iron directly from magnetite concentrate (< 100 μm) using natural gas in a flash ironmaking reactor in the temperature range of 1150-1600 °C. In this process, natural gas is partially oxidized by oxygen to generate a reducing gas mixture of H2 and CO as well as providing the heat required for the reduction of iron oxide concentrate. Computational Fluid Dynamics (CFD) models, coupled with experimental results, were first used to accurately evaluate the kinetic parameters of iron oxide particle reduction by H2, CO, and H2+CO mixtures. The nucleation and growth rate expressions were found to best describe the reaction kinetics of the concentrate particles in the interested temperature range. The reduction rate was also found to be inversely proportional to the particle size for the higher temperature range, while no particle size effect for the lower temperature range was found. The rate equations for reduction by the H2+CO mixtures were also developed using the rate expressions by individual component gases. An enhancement factor which is a function of temperature and partial pressures of component gases was introduced to account for the synergistic effects due to the presence of CO. A three-dimensional CFD model was developed to simulate the gas particle flow pattern, heat transfer, and chemical reactions inside a laboratory scale flash. The obtained rate expressions from the first stage of this work were used and verified in the CFD iv simulation. The temperature profiles and the reduction degrees obtained from the simulation results satisfactorily agreed with the experimental measurements. As an intermediate step to the full industrial-scale flash ironmaking reactor, the design of a pilot-scale flash reactor was investigated in this work. The verified rate expressions and CFD models were used for the design of a reactor with a capacity of 100,000 tons/yr of metallic iron. The CFD simulation provided information such as temperature and species distribution, gas and particle flow patterns that are essential for the proper design of reactor design

COMPUTATIONAL FLUID DYNAMICS ANALYSIS AND DESIGN OF FLASH IRONMAKING REACTORS by Deqiu Fan A dissertation submitted to the faculty of The University of Utah in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Metallurgical Engineering The University of Utah August 2019 Copyright © Deqiu Fan 2019 All Rights Reserved The University of Utah Graduate School STATEMENT OF DISSERTATION APPROVAL The dissertation of Deqiu Fan has been approved by the following supervisory committee members: , Chair Hong Yong Sohn 1/15/2019 Date Approved , Member Michael F. Simpson 1/15/2019 Date Approved , Member Milind Deo 1/15/2019 Date Approved , Member Eric G. Eddings 1/15/2019 Date Approved , Member York R. Smith 1/15/2019 Date Approved and by Michael F. Simpson the Department/College/School of , Chair/Dean of Metallurgical Engineering and by David B. Kieda, Dean of The Graduate School. ABSTRACT A novel flash ironmaking technology is being developed at the University of Utah aimed at producing iron directly from magnetite concentrate (< 100 µm) using natural gas in a flash ironmaking reactor in the temperature range of 1150-1600 °C. In this process, natural gas is partially oxidized by oxygen to generate a reducing gas mixture of H2 and CO as well as providing the heat required for the reduction of iron oxide concentrate. Computational Fluid Dynamics (CFD) models, coupled with experimental results, were first used to accurately evaluate the kinetic parameters of iron oxide particle reduction by H2, CO, and H2+CO mixtures. The nucleation and growth rate expressions were found to best describe the reaction kinetics of the concentrate particles in the interested temperature range. The reduction rate was also found to be inversely proportional to the particle size for the higher temperature range, while no particle size effect for the lower temperature range was found. The rate equations for reduction by the H2+CO mixtures were also developed using the rate expressions by individual component gases. An enhancement factor which is a function of temperature and partial pressures of component gases was introduced to account for the synergistic effects due to the presence of CO. A three-dimensional CFD model was developed to simulate the gas particle flow pattern, heat transfer, and chemical reactions inside a laboratory scale flash. The obtained rate expressions from the first stage of this work were used and verified in the CFD simulation. The temperature profiles and the reduction degrees obtained from the simulation results satisfactorily agreed with the experimental measurements. As an intermediate step to the full industrial-scale flash ironmaking reactor, the design of a pilot-scale flash reactor was investigated in this work. The verified rate expressions and CFD models were used for the design of a reactor with a capacity of 100,000 tons/yr of metallic iron. The CFD simulation provided information such as temperature and species distribution, gas and particle flow patterns that are essential for the proper design of reactor design. iv To Mom & Dad Yanan Thank you all. TABLE OF CONTENTS ABSTRACT ....................................................................................................................... iii LIST OF TABLES .............................................................................................................. x LIST OF FIGURES .......................................................................................................... xii ACKNOWLEDGMENTS .............................................................................................. xvii Chapters 1. INTRODUCTION .......................................................................................................... 1 2. RATE ANALYSIS OF MAGNETITE CONCENTRATE PARTICLE REDUCTION: PART I: ANALYSIS OF THE HYDROGEN REDUCTION RATE OF MAGNETITE CONCENTRATE PARTICLES IN A DROP-TUBE REACTOR THROUGH CFD MODELING ....................................................................................................................... 3 2.1 Abstract ................................................................................................................ 3 2.2 Introduction .......................................................................................................... 4 2.3 Approach to Rate Analysis in This Work ............................................................ 6 2.4 Experimental Work .............................................................................................. 8 2.5 Mathematical Work ........................................................................................... 10 2.6 Numerical Procedure ......................................................................................... 13 2.7 Results and Discussion ...................................................................................... 14 2.7.1 Modeling Results ................................................................................... 14 2.7.2. Kinetics Analysis .................................................................................. 16 2.7.3. Complete Expression ............................................................................ 19 2.8. Conclusions ....................................................................................................... 20 2.9. Acknowledgments............................................................................................. 21 2.10. Nomenclature .................................................................................................. 22 2.11. References ....................................................................................................... 23 2.12. Appendix: Complete Experimental Data (Excess H2 > 500%) ..................... 25 3. RATE ANALYSIS OF MAGNETITE CONCENTRATE PARTICLE REDUCTION: PART II: THE KINETICS OF HYDROGEN REDUCTION OF MOLTEN MAGNETITE CONCENTRATE ..................................................................................... 36 3.1. Abstract ............................................................................................................. 36 3.2. Introduction ....................................................................................................... 37 3.3. Experimental Work ........................................................................................... 40 3.4. Rate Analysis Without CFD ............................................................................. 41 3.4.1. Reaction Model ..................................................................................... 42 3.4.2. Reaction Order ...................................................................................... 43 3.4.3. Particle Size Effect ................................................................................ 43 3.4.4. Activation Energy ................................................................................. 44 3.5. CFD Refinement of Rate Parameters ................................................................ 44 3.6. Complete Rate Expression ................................................................................ 46 3.7. Conclusions ....................................................................................................... 48 3.8. Acknowledgments............................................................................................. 48 3.9. References ......................................................................................................... 48 4. RATE ANALYSIS OF MAGNETITE CONCENTRATE PARTICLE REDUCTION: PART III: THE KINETICS OF CARBON MONOXIDE REDUCTION OF MAGNETITE CONCENTRATE PARTICLES THROUGH CFD MODELING .......... 58 4.1. Abstract ............................................................................................................. 58 4.2 Introduction ........................................................................................................ 59 4.3 Experimental Work ............................................................................................ 63 4.4. Approach to Rate Analysis ............................................................................... 65 4.5 Mathematical Modeling ..................................................................................... 67 4.6. Results and Discussion ..................................................................................... 68 4.6.1. Reaction Model ..................................................................................... 68 4.6.2. Reaction Order ...................................................................................... 68 4.6.3. Particle Size Effect ................................................................................ 69 4.6.4. Activation Energy ................................................................................. 70 4.6.5. CFD Refinement ................................................................................... 70 4.6.6. Complete Expressions ........................................................................... 71 4.7. Conclusions ....................................................................................................... 74 4.8 Acknowledgments.............................................................................................. 75 4.9. Nomenclature .................................................................................................... 75 4.10. References ....................................................................................................... 76 4.11. Appendix: Cold Model Experiment ................................................................ 77 5. RATE ANALYSIS OF MAGNETITE CONCENTRATE PARTICLE REDUCTION: PART IV: KINETICS OF MAGNETITE CONCENTRATE PARTICLES REDUCTION BY H2+CO MIXTURES THROUGH CFD MODELING ...................... 89 5.1. Abstract ............................................................................................................. 89 5.2 Introduction ........................................................................................................ 90 5.3. Experimental Work ........................................................................................... 94 5.4. Mathematical Model ......................................................................................... 95 5.5. Results and Discussion ..................................................................................... 98 5.5.1 Results .................................................................................................... 98 5.5.2. Complete Rate Expressions ................................................................ 100 5.6. Conclusions ..................................................................................................... 101 5.7. Acknowledgments........................................................................................... 101 5.8. Nomenclature .................................................................................................. 102 vii 5.9. References ....................................................................................................... 102 6. CFD SIMULATION OF LABORATORY FLASH REACTOR: PART I: CFD SIMULATION OF THE HYDROGEN REDUCTION OF MAGNETITE CONCENTRATE ........................................................................................................... 111 6.1 Abstract ............................................................................................................ 111 6.2. Introduction ..................................................................................................... 112 6.3. Mathematical Model ....................................................................................... 114 6.3.1. Physical Model.................................................................................... 114 6.3.2. Fluid Flow ........................................................................................... 115 6.3.3. Heat Transfer ...................................................................................... 116 6.3.4. Species Transport ................................................................................ 118 6.3.5. Combustion Mechanism ..................................................................... 119 6.3.6. Particle Tracking ................................................................................. 119 6.3.7. Boundary Conditions .......................................................................... 121 6.4. Numerical Details ........................................................................................... 122 6.5. Results and Discussion ................................................................................... 123 6.5.1. Model Validation ................................................................................ 123 6.5.2. Velocity Field...................................................................................... 126 6.5.3. Temperature Distribution .................................................................... 126 6.5.4. Species Distribution ............................................................................ 127 6.5.5. Particle Residence Time ..................................................................... 128 6.6. Conclusions ..................................................................................................... 129 6.7. Acknowledgments........................................................................................... 129 6.8. Nomenclature .................................................................................................. 130 6.9. References ....................................................................................................... 131 6.10. Appendix A: Physical Properties of the Particle and Equilibrium Constant 133 6.11. Appendix B: Experimental and Simulation Results of Different Runs in the Laboratory Flash Reactor ....................................................................................... 135 7. CFD SIMULATION OF LABORATORY FLASH REACTOR: PART II: EXPERIMENTAL INVESTIGATION AND CFD SIMULATION OF MAGNETITE CONCENTRATE REDUCTION USING METHANE- OXYGEN FLAME............... 144 7.1 Abstract ............................................................................................................ 144 7.2. Introduction ..................................................................................................... 145 7.3. Experimental Work ......................................................................................... 148 7.3.1. Materials ............................................................................................. 148 7.3.2. Apparatus ............................................................................................ 148 7.3.3. Experimental Procedure ...................................................................... 149 7.3.4. Definition of Parameters ..................................................................... 151 7.4. Mathematical Model ....................................................................................... 153 7.4.1 Governing Equations ........................................................................... 153 7.4.2. Combustion Mechanism ..................................................................... 155 7.5. Results and Discussion ................................................................................... 156 7.5.1. Experimental Results .......................................................................... 156 viii 7.5.2. CFD Results ........................................................................................ 158 7.6. Concluding Remarks ....................................................................................... 161 7.7. Acknowledgments........................................................................................... 162 7.8. Nomenclature .................................................................................................. 162 7.9. References ....................................................................................................... 163 8. DESIGN OF PILOT FLASH IRONMAKING REACTORS USING COMPUTATIONAL FLUID DYNAMICS MODELING ............................................. 178 8.1 Introduction ...................................................................................................... 178 8.2. Geometries and Dimensions ........................................................................... 179 8.3. Operating Conditions ...................................................................................... 180 8.4. Meshing and Mathematical Model ................................................................. 181 8.5. Results and Discussion ................................................................................... 182 8.5.1. One-burner Design .............................................................................. 182 8.5.2. Four-burner Design ............................................................................. 184 8.6. Concluding Remarks ....................................................................................... 186 ix LIST OF TABLES Tables 2.1. Governing Equations of Gas Phase............................................................................ 27 2.2. Searching Range and Optimized Values of the Kinetics Parameters in Eq. (2.21) ... 27 3.1. Searching Ranges and Optimized Values of the Kinetics Parameters ....................... 51 4.1. Commonly Used Conversion Functions .................................................................... 79 4.2. Solid Phase Governing Equations .............................................................................. 79 4.3. Searching Ranges and Optimized Values of the Kinetics Parameters ....................... 79 4.4. Apparent Activation Energy from Literature for the Reduction of Fine Iron Oxide Particles. ............................................................................................................................ 80 5.1. Solid Phase Governing Equations ............................................................................ 105 5.2. Kinetic Parameters for Reduction by Individual Component Gases[11, 15, 16] ........... 105 5.3. Comparison of the Reaction Rate at Different Temperatures with X=0.5 for Magnetite Reduction by CO and H2 Individually ........................................................... 105 5.4. Optimum Values for a and b .................................................................................... 105 6.1. H2-O2 Partial Combustion Mechanism .................................................................... 135 6.2. Kinetics Parameters ................................................................................................. 135 6.3. Chemical Composition of Magnetite Concentrate Used in This Work ................... 136 7.1. Chemical Composition of Magnetite Concentrate Particles .................................... 166 7.2. Summary of the Experimental Conditions ............................................................... 167 7.3. Summary of the Kinetic Parameters ........................................................................ 167 7.4. CH4-O2 Partial Combustion Mechanism ................................................................. 167 8.1. Dimension of Pilot Reactors under One-burner Design .......................................... 187 8.2. Wall Material Properties .......................................................................................... 187 8.3. Operating Conditions for Solid Product with Input Gases Preheated to 600 °C ..... 187 8.4. Operating Conditions for Solid Product with Input Gases Preheated to 1000 °C ... 187 8.5. Operating Conditions for Molten Product with Input Gases Preheated to 1000 °C 188 8.6. Product Temperature in Each Run ........................................................................... 188 8.7. Heat Loss and Heat Generated from Partial Combustion ........................................ 188 xi LIST OF FIGURES Figures 2.1. A block diagram of the algorithm for kinetics parameter optimization..................... 28 2.2. Comparison of the measured and calculated temperature profiles along the drop-tube reactor axis ........................................................................................................................ 28 2.3. Schematic representation of the drop-tube reactor system. ....................................... 29 2.4. Schematic representation of the reactor: (a) computational domain, (b) mesh for computational domain. ...................................................................................................... 30 2.5. Particle temperature and velocity profile along the centerline of the reactor for Tiso=1573 K ....................................................................................................................... 31 2.6. Gas velocity vector near the top part region of the reactor for Tiso=1573 K.............. 32 2.7. Particle temperature profile and unreacted fraction in the top part region of the reactor for Tiso = 1423 K ................................................................................................... 33 2.8 Particle temperature profile and unreacted fraction in the top part region of the reactor for Tiso =1623 K ................................................................................................................ 33 2.9. Calculated profiles of particle temperature and unreacted fraction along the reactor length................................................................................................................................. 34 2.10. Reduction degrees for different size particles at 1623 K (1350 ºC), pH2=0.2 atm .. 34 2.11. Comparisons between the calculated reduction degrees vs. experimental results of all runs (n=2, m=0.5). ....................................................................................................... 35 2.12. Comparisons between the calculated reduction degrees vs. experimental results of all runs (n=1, m=1) ........................................................................................................... 35 3.1. SEM micrographs (a) magnetite ore and (b) particles after reduction ....................... 51 3.2. Schematic representation of the high temperature drop-tube reactor (DTR) ............ 52 3.3 Cross-sectional view of a partially reduced particle ................................................... 53 3.4. Relationship between k app and f(pH2 , pH2 O )avg ....................................................... 54 3.5. Effect of particle size on the reduction degree at different temperatures .................. 55 3.6. Ln(k) vs 104/T for reduction by H2. ........................................................................... 56 3.7. Calculated profiles of particle temperature and unreacted fractions along the reactor centerline ........................................................................................................................... 56 3.8. Comparisons between the calculated reduction degrees vs. experimental results. .... 57 4.1. SEM micrograph for particles reduced at T = 1846 K (1573 °C) under pCO =0.3 atm, Reduction degree = 0.62 ................................................................................................... 80 4.2. SEM micrograph for particles reduced at T = 1558 K (1285 °C) under pCO =0.85 atm, Reduction degree = 0.27. .................................................................................................. 81 4.3. Schematic representation of the high temperature drop-tube reactor (DTR) ............ 81 4.4. The powder feeder system: (a) components and, (b) working mechanism. .............. 82 4.5. A block diagram of the algorithm for kinetics parameter optimization..................... 82 4.6. SEM micrographs of samples with different reduction degrees at average isothermal temperature of 1512 K (1239 °C) and 1558 K (1285 °C). ................................................ 83 4.7. Relationship between k app and f(pCO , pCO2 )avg for reduction by CO in the lower temperature range.............................................................................................................. 83 4.8. Relationship between k app andf(pCO , pCO2 )avg for reduction by CO in the higher temperature range.............................................................................................................. 84 4.9. Effect of particle size in the lower temperature range. .............................................. 85 4.10. Effect of particle size in the higher temperature range. ........................................... 85 4.11. Ln(k) vs 104/T for reduction by CO: (a) lower temperature range, (b) higher temperature range.............................................................................................................. 86 4.12. Calculated profiles of particle temperature and unreacted fractions along the reactor length in the lower temperature range .............................................................................. 86 4.13. Calculated profiles of particle temperature and unreacted fractions along the reactor length in the higher temperature range ............................................................................. 87 4.14. Comparisons between the calculated reduction degrees vs. experimental results ... 87 xiii 4.A.1. Schematic representation of the cold model system. ............................................. 88 4.A.2. Image of particle dispersion inside the cold model of DTR. ................................. 88 5.1. Comparisons between the calculated reduction degrees vs. experimental results ... 106 5.2. Calculated profiles of particle temperature and unreacted fraction along the reactor length in the lower temperature range ............................................................................ 107 5.3. Calculated profiles of particle temperature and unreacted fraction along the reactor length in the higher temperature range ........................................................................... 108 5.4. CO contribution to overall reduction at 1512 K: pCO = 0.4 atm, pH2 = 0.2 atm, gas flow rates: CO: 1.6 L/min, H2: 0.8 L/min, N2: 1.0 L/min. .............................................. 109 5.5. CO contribution to overall reduction at 1512 K: pCO = 0.2 atm, pH2 = 0.1 atm, gas flow rates: CO: 1.6 L/min, H2: 3.2 L/min, N2: 8.8 L/min, dp = 35 µm. .......................... 109 5.6. Comparisons between the calculated reduction degrees vs. experimental results by H2 + CO mixtures in the lower temperature range ............................................................... 110 5.7. Comparisons between the calculated reduction degrees vs. experimental results by H2 + CO mixtures in the higher temperature range.............................................................. 110 6.1. Schematic representation of the laboratory flash ironmaking reactor (inner diameter 0.19 m and length 2.13 m) .............................................................................................. 136 6.2. The positions of injection ports: (a) injection ports plane (A-A section), (b) top view of the reactor ................................................................................................................... 137 6.3. Measured wall temperature profiles of the laboratory flash reactor ........................ 137 6.4. Geometry and meshing of the Utah Flash Reactor (UFR) and burner .................... 138 6.5. Gas phase temperature along the centerline of the reactor ...................................... 139 6.6. Comparison between the calculated reduction degrees vs. experimental results .... 139 6.7. Velocity fields: (a) streamlines, (b) velocity vector for H2 flow rate 3600 L/h, O2 flow rate 579 L/h with H-O-H configuration .................................................................. 140 6.8. Representative particle trajectories for H2 flow rate 3600 L/h, O2 flow rate 579 L/h with H-O-H flame configuration .................................................................................... 141 6.9. Temperature distribution for H2 flow rate 2400 L/h, O2 flow rate 384 L/h ............. 142 6.10. Species distribution: (a) H2O mole fraction, (b) H2 mole fraction (c) EDF distribution for H2 flow rate 3600 L/h, O2 flow rate 579 L/h with H-O-H flame configuration ................................................................................................................... 143 xiv 7.1. X-ray diffraction pattern of the magnetite concentrate ............................................ 168 7.2. SEM micrograph for the magnetite concentrate particles........................................ 168 7.3. Schematic representation of the laboratory flash ironmaking reactor ..................... 169 7.4. Schematic diagram the nonpremixed burner ........................................................... 170 7.5. Powder feeding modes ............................................................................................. 171 7.6. SEM micrographs for samples collected from experiments with 60 L/min H2 and 9.65 L/min O2 and EDF = 0.5 ......................................................................................... 171 7.7. Effect of EDF on reduction degree under different feeding modes and flame configurations ................................................................................................................. 172 7.8. SEM micrograph of samples under the O-F-O flame configuration with burner feeding at EDF = 1; gas flow rates: CH4 = 5 L/min, H2 =2 L/min, O2 = 4 L/min. ......... 172 7.9. SEM micrograph of sample under F-O-F flame configuration with two-side feeding at EDF = 1; gas flow rates: CH4 = 5 L/min, H2 =2 L/min, O2 = 4 L/min. ...................... 173 7.10. Velocity fields: (a) Streamlines, (b) velocity vector for CH4 = 5 L/min, H2 =2 L/min and O2 = 4 L/min with O-F-O configuration .................................................................. 174 7.11. Temperature distribution for CH4 = 5 L/min, H2 =2 L/min and O2 = 4 L/min ...... 175 7.12. Comparison of calculated gas phase temperature and the measured values along the centerline of the reactor .................................................................................................. 176 7.13. Species distribution: (a) H2 mole fraction, (b) H2O mole fraction, (c) CO mole fraction, and (d) CO2 mole fraction distribution for CH4 = 10 L/min, H2 =2 L/min and O2 = 8.2 L/min with O-F-O flame configuration and two-side feeding mode. .................... 177 8.1 Schematic representations of pilot flash ironmaking reactors .................................. 189 8.2 Distribution of the powder feeding ports on the roof of the reactor. ........................ 189 8.3 Burner configuration. ................................................................................................ 190 8.4 Reactor wall structure (unit in m). ............................................................................ 190 8.5. Typical mesh for the pilot reactor, total number of cells 250,996: (a) 3D view, (b) Cross-section view. ......................................................................................................... 191 8.6. Velocity vector field in the plane that passes through the center of two powder feeding ports.................................................................................................................... 192 xv 8.7. Velocity vector field in the plane that passes through the center of two powder feeding ports.................................................................................................................... 192 8.8. Velocity vector field in the plane that passes through the center of two powder feeding ports.................................................................................................................... 193 8.9. Particle number density (particles/cm3) in the plane that passes through the center of two powder feeding ports................................................................................................ 193 8.10. Particle number density (particles/cm3) in the plane that passes through the center of two powder feeding ports................................................................................................ 194 8.11. Particle number density (particles/cm3) in the plane that passes through the center of two powder feeding ports................................................................................................ 194 8.12. Temperature distribution in the plane that passes through the center of two powder feeding ports.................................................................................................................... 195 8.13. Temperature distribution in the plane that passes through the center of two powder feeding ports.................................................................................................................... 195 8.14. Temperature distribution in the plane that passes through the center of two powder feeding ports.................................................................................................................... 196 8.15. Species distribution in the plane that passes through the center of two powder feeding ports of run # 5 ................................................................................................... 196 8.16. Species distribution in the plane that passes through the center of two powder feeding ports of run # 6 ................................................................................................... 197 8.17 Distribution of the burners on the roof of the reactor. ............................................ 197 8.18. Burner configuration and dimension ..................................................................... 198 8.19. Vector field in the plane that passes through (a) the center of two burners, (b) the center of two powder feeder ports (unit in m/s). ............................................................. 198 8.20. Particle number density (particles/cm3) in the plane that passes through the center of two powder feeding ports................................................................................................ 199 8.21. Velocity vector field in the plane that passes through (a) the center of two burners, (b) the center of two powder feeder ports (unit in m/s). ................................................. 199 8.22. Species distribution in the plane that passes through the center of two burners: (a) H2, (b) H2O...................................................................................................................... 200 8.23. Species distribution in the plane that passes through the center of two burners: (a) CO, (b) CO2 .................................................................................................................... 200 xvi ACKNOWLEDGMENTS I would like to express my sincere gratitude to my supervisor, Professor H. Y. Sohn, for his help and mentoring during my PhD study. For his generous help and accurate perception and innumerable discussions, the author is most grateful. I would give my appreciation to the excellent supervisory committee members, Professors Michael F. Simpson, Miland Deo, Eric G. Eddings and York R. Smith, for their time and efforts in reviewing my dissertation and attending my defense. I am very grateful to Dr. Y. Mohassab and Dr. M. Olivas-Martinez for their help and supervision during the first three-year study. Dr. Y. Mohassab has been a great project manager and his insightful advice helped in shaping my career. On the personal side, he has been my older brother and I will be always grateful for his support. I would give my thanks other members of Prof. Sohn research group who have helped me a lot during this work: Mohamed Elzohiery, A. Mohamed, R. Sarkar, S. Roy, and A. Murali. The financial support of the Department of Energy and American Iron and Steel Institute is sincerely acknowledged. I want to give my thanks to my loving wife, Yanan Fang, for her endless help and encouragement. She has always been supportive in all the decisions I make. I want to give my thanks to my parents for their love and generous support through my whole life. They are the most wonderful parents in this world. CHAPTER 1 INTRODUCTION Iron is the fourth most common element in the earth’s crust. Magnetite (Fe3O4) and hematite (Fe2O3) are the most common minerals used for the production of metallic iron. More than 90% of iron in the world is currently produced through the blast furnace (BF) process with the rest being produced by the direct reduction (DR) processes. The blast furnace process is the major process in ironmaking. In the BF process, concentrate ore is first agglomerated to produce pellets and sinters of a diameter of 1 - 4 cm. Then they are charged into BF together with coke and limestone from the top part of the reactor. Coke is typically made in a separate coke-making step by heating coal to remove volatile organics and tar. Coke contains mostly carbon and some ash components. The roles coke plays in a modern BF are multifold. It first provides the fuel and reducing agent needed for the reduction of iron ore. It also acts as the main support of the materials in the lower part of furnace and increases the permeability to allow the gas to pass through the solid or semimolten materials countercurrently up from the bottom to top. Molten iron is produced and collected in the BF hearth at around 1500 °C. The blast furnace process suffers from drawbacks which are mainly the energy consumption and the large infrastructure cost. The needs for sintering/pelletizing of the ore and high-grade coking coal cannot be avoided. 2 Several DRI process have been developed aimed at replacing the traditional BF process. Most of these processes, such as MIDREX, Energiron, etc., are not sufficiently intensive to replace BF as they cannot be operated at high temperatures due to the sticking and fusion of particles. Especially, the shaft furnace processes, being dominant types among others, require pelletization of iron ore concentrate, and also suffer from pellet disintegration problems. Thus, a novel flash ironmaking technology has been developed at the University of Utah. In this process, iron is produced from fine iron oxide concentrate particles in a flash reactor, utilizing hydrogen, natural gas, or coal gas as the reducing agent as well as the fuel. The direct use of iron oxide concentrate in this flash ironmaking process bypasses the pelletization/sintering and cokemaking steps in the blast furnace process, which will significantly reduce the energy consumption and CO2 emission. CHAPTER 2 RATE ANALYSIS OF MAGNETITE CONCENTRATE PARTICLE REDUCTION: PART I: ANALYSIS OF THE HYDROGEN REDUCTION RATE OF MAGNETITE CONCENTRATE PARTICLES IN A DROP-TUBE REACTOR THROUGH CFD MODELING De-Qiu Fan, Yousef Mohassab, Mohamed Elzohiery, and H. Y. Sohn Department of Metallurgical Engineering, University of Utah, Salt Lake City, Utah 84112, USA Published in Metallurgical and Materials Transactions B, Vol. 47 (3), 2016 2.1 Abstract A computational fluid dynamics (CFD) approach, coupled with experimental results, was developed to accurately evaluate the kinetic parameters of iron oxide particle reduction. Hydrogen reduction of magnetite concentrate particles was used as a sample case. A detailed evaluation of the particle residence time and temperature profile inside the reactor is presented. This approach eliminates the errors associated with assumptions like constant particle temperature and velocity while the particles travel down a drop-tube 4 reactor. The gas phase was treated as a continuum in the Eulerian frame of reference, and the particles were tracked using a Lagrangian approach in which the trajectory and velocity were determined by integrating the equation of particle motion. In addition, a heat balance on the particle that relates the particle temperature to convection and radiation was also applied. An iterative algorithm that numerically solved the governing coupled ordinary differential equations was developed to determine the pre-exponential factor and activation energy that best fit the experimental data. Keywords: Flash reduction, Drop-tube reactor, DTR, CFD, Kinetics, Ironmaking 2.2 Introduction The blast furnace process currently produces more than 90% of primary iron, with the balance by alternate processes such as direct-reduced iron (DRI) and smelting reduction. Although the blast furnace has a high production rate and other advantages, it suffers from high energy consumption and CO2 emissions. A novel ironmaking technology is under development at the University of Utah.[1-9] In this process, iron is produced from fine iron oxide concentrate particles in a flash process, utilizing hydrogen, natural gas, or coal gas as the reducing agent as well as a fuel. These reducing gases offer high reactivity and eliminate or decrease carbon dioxide emissions during ironmaking. Flash ironmaking also allows the direct use of concentrate to bypass the problematic pelletization/sintering and cokemaking steps in the blast furnace process. Traditional thermogravimetric analysis (TGA) system and drop-tube reactor (DTR) are two experimental apparatuses used in the study of kinetics of gas-solid reaction. TGA is typically used when the gas-solid reaction time is in the order of 5 minutes or longer[10-12]. The DTR system is useful for fast reactions that take only several seconds, like flash process and fast pyrolysis of biomass, coal and other fuels. Sohn and coworkers[6, 8, 9] have investigated the gaseous reduction of iron oxide concentrate particles under various experimental conditions using a DTR aimed at generating a database to be used for the design of a flash ironmaking reactor. The residence time in their work was calculated by considering the length of the reaction zone, the linear velocity of the gas and the terminal falling velocity of particles under the assumption of constant particle velocity and temperature. Qu[13] has conducted a series of experiments on the reduction kinetics of fine hematite ore particle at different temperature ranging from 1550 K to 1750 K (1277 to 1477 ºC) with different reaction time (210–2020 ms) in a high temperature DTR. Particle residence time was calculated by iteratively solving the particle motion equation under constant particle temperature assumption in their work. In situ particle temperature measurement and real-time tracking of particles inside the DTR would require sophisticated and intrusive experimental techniques, e.g., particle image velocimetry (PIV) and optical access to the DTR interior.[14-17] Moreover the use of H2 atmosphere at high temperature adds an extra layer of complexity to use these techniques. Furthermore, temperature measurements in the reactor during the experiments in this work as well as CFD simulations found that there was a narrow, lowtemperature region near the tip of the water-cooled tube through which the carrier gas and particles were injected at room temperature. The presence of this region affects the temperature and flow history of the particles. The use of CFD to incorporate such details allows realistic calculations of particle temperature and residence time as functions of position and improves the accuracy of kinetic analysis. Several efforts of using CFD as 6 an effective tool to investigate the kinetics of fast pyrolysis of biomass and other fuels have been reported in the literature. Brown et al.[18] used CFD approach to predict an accurate time-temperature profile in an entrained flow reactor to study biomass pyrolysis. Simone et al.[19] developed a procedure coupling experimental results and CFD to evaluate the global biomass devolatilization kinetics in a DTR. Little work has been reported on the CFD simulation of a DTR in the investigation of the kinetics of metal oxide reduction. Experimental results in this work and previous work done by Sohn and coworkers[6, 8, 9] indicate that iron oxide concentrate particles can be reduced to a high reduction degree within a few seconds of residence time available in a flash process. The goal of this research was to develop an accurate kinetics expression of iron oxide concentrate reduction that will be used to design ironmaking flash reactors. In this work, detailed description of the particle movement and heat and mass transfer were obtained by simulating the high temperature DTR using CFD. 2.3 Approach to Rate Analysis in This Work The algorithm used in this study is shown in Figure 2.1. Detailed thermal and velocity profiles in the gas phase under each set of experimental conditions were first obtained via CFD simulations. Despite great efforts made to form a uniform temperature zone inside the reactor, there are still temperature variations, particularly in the top and bottom parts of the reactor. Gas stream temperature was measured experimentally only along the centerline over the reaction region. As the wall temperatures of the drop-tube reactor (DTR) were 7 not known but essential for setting up boundary conditions in the CFD simulations, preliminary CFD runs were carried out to calculate the suitable wall temperature profiles for different target temperatures using the measured centerline temperature profiles. The wall temperature profiles were first optimized until the calculated gas stream temperature profile agreed with the measured profiles in the isothermal zone and bottom part along the reactor axis. The optimized wall temperature, from the top to near the end of the reactor, was essentially the same as the target gas temperature because the gas comes into the reactor preheated to that temperature by the honeycomb. Toward the bottom, there was some heat loss and thus the wall temperature had to be lowered to reproduce the decreasing temperature. A comparison of the measured and calculated temperature profiles are presented in Figure 2.2. Simone[19] also used the same approach for setting up the boundary conditions in their DTR simulation work. The particles are mostly concentrated in the center of the reactor, which has been proved by optical measurement in a similar DTR by Lehto[20] who used a 12 mm × 16 mm glass pane as an image window for a high speed camera. The camera was placed in a proper position so that it focused on a region along the reactor center. He found that on average 75% of the particles were closer than 1 mm (reactor diameter 12 mm) to the centerline and over 94% of the particles were located within 2 mm of the centerline. Avila et al.[16] also used a similar optical system to investigate the dispersion of particles in a similar DTR and found that most particles traveled within a narrow region around the centerline. Therefore, the central velocity and temperature of gas phase from the CFD results were used to track the particle in this work. Error analysis of using centerline velocity is 8 further performed below. The kinetics parameters for magnetite reduction by hydrogen, namely, the preexponential factor (ko) and activation energy (E), are both inputs for the model as well as unknowns to be determined. The procedure used in this study for estimating ko and E using the experimental data is as follows: Step 1: Predetermine sufficiently broad ranges of values for ko and E that contain the actual values for the hydrogen reduction of magnetite and discretize the range into pairs of ko and E with a specified activation energy increment. Step 2: The discretized pairs of ko and E are then used to predict the reduction degree of magnetite particles under each set of experimental conditions. Step 3: The deviation between each of the predicted reduction degree and the corresponding experimental value is computed. And a summation over all the deviations is performed to calculate the mean of the squared errors f (defined by Eq. 2.22). Step 4: Pick the combination of ko and E that gives the minimum mean of squared error. The increments of ko and E close to the optimized values were both < 1% of the adjacent values. 2.4 Experimental Work The high temperature drop-tube reactor (DTR) used in this research is schematically shown in Figure 2.3.[8, 9] It consisted of pneumatic powder feeding system, gas delivering system, cooling system and powder collection system. The reactor was made up of a vertical split tube furnace with a maximum working temperature of 1813 K (1540 ˚C) and a cylindrical alumina tube with an inner diameter of 5.6 cm and 193 cm in 9 length. The isothermal zone of all the experiments was maintained at a temperature between 1423 K (1150 ˚C) to 1623 K (1350 ˚C) by bar-type SiC heating elements. Although the setup used in this experiment was the same as the system used in the work of Wang[6] and Chen,[8] some heating elements were replaced as part of a frequent maintenance of the furnace. Replacing heating elements caused some variation in the temperature profile. In general, the typical temperature profile exhibits a wide isothermal range and with short lower temperature zones at two ends. (See the temperature profiles presented in Figure 2.2 for 1423 K (1150 ˚C) and 1623 K (1350 ˚C).) The particles together with N2 as carrier gas were fed from the center of the water-cooled powder feeding tube. A cylindrical porous alumina honeycomb was inserted at the top part of the reactor. H2 was fed from the gas inlet, shown in Figure 2.3, then through a mullite honeycomb to enter the reaction zone. The main purpose of the honeycomb was to straighten gas flow and improve the heating of the reducing gas before it entered the reaction zone. The entire experimental data of magnetite reduction by H2 obtained under various conditions are listed in the Appendix. Dried and screened magnetite concentrate particles of size fractions 20 - 25, 32 - 38, or 45 - 53 µm were delivered continuously with a carrier gas (N2 or N2 and H2 mixture) at a constant flow rate. In the flash ironmaking process, the particle residence time in the reactor is expected to be between 2 ~ 10 seconds. The gas flow rates were adjusted in this work to provide these residence times while allowing desired reduction degrees depending on other experimental conditions such as temperature and gas composition. During the experiment, the particle feeding rate was controlled from 30~100 mg min-1. The mass ratio of particle to gas was usually kept at ≤ 0.05. The reacted powder was collected in a powder collector at the 10 bottom of the reactor. The reduction degree of magnetite concentrate particles to metallic iron was defined in terms of removable oxygen, as follows: Degree(%) of reduction = 𝑚𝑂(0) −𝑚𝑂(𝑡) 𝑚𝑂(0) × 100 𝑚 2 𝑚𝑂(0) = (𝑇𝐹𝑒) × (𝑂)0 0 𝑚 2 𝑚𝑂(𝑡) = 𝑚2 − 𝑚1 − (𝑇𝐹𝑒) × [100 − (𝑇𝐹𝑒)0 − (𝑂)0 ] 0 (2.1) (2.2) (2.3) where mO (0) is the mass of the removable oxygen in the sample before reduction; mO (t) is the mass of the removable oxygen after time t; m1 is the mass of reduced sample used in the ICP analysis; m2 the mass of total iron in the reduced sample used in the ICP analysis; (TFe)0 is the mass percentage of total iron in the sample before reduction; (O)0 is the mass percentage of removable oxygen in the sample before reduction. 2.5 Mathematical Work The realizable k-ε model[21] was chosen for simulating the spread of the carrier gas jet. Radiation was taken into account using the discrete ordinate (DO) model.[22] During the drop-tube experiment, the bulk flow of the gas mixture consisted of H2, N2 and H2O. But reducing gas H2 was usually in more than 500% excess of the minimum required amount of H2 and the amount of water vapor generated in the reduction process only accounted for around 2%.[8] In this scenario, species H2O is excluded from the gas mixture in this simulation. The governing equations of momentum, thermal energy and mass transfer in the gas phase are listed in Table 2.1. As the volume fraction of the solid phase in the reactor is in the order of 10-6, the flow is categorized as a very dilute flow. Thus, the interparticle collisions were neglected. 11 2 Also, the dimensionless Stokes number defined as Stk   p d p u /18 g D is less than 0.1 which indicates that the particles will closely follow the gas stream. The particles are heated mainly by the radiation from the wall of reactor tube in addition to the heat transferred from the gas phase by convection. The energy needed to heat the particle phase is much smaller than the amount of heat carried by the gas phase in this dilute system (usually ≤ 5 wt.%), and thus the addition of particles into the reactor does not significantly affect the gas phase temperature. This was confirmed experimentally by measuring the temperature profiles with and without particle feeding. The temperature profiles were similar in both cases. Similarly, the particle addition at this low level does not significantly affect the gas phase velocity profile.[23] Therefore, the gas phase temperature and velocity profiles calculated in the absence of particles were used even in the presence of particles. This simplified approach was used to minimize the computational time since a full CFD simulation of the entire experimental data set that considers coupling between the discrete and continuous phase would have taken a prohibitive amount of computational time. The flow inside the reactor is a fully developed laminar flow except in the initial part of the reactor where particle laden jet exists. Although most of the particles were believed to flow along the centerline, an error analysis was performed by Choi.[24] It has been found that even if the particles were spread over half of the radius of the cross section, the averaged residence time increased only about 10%, a difference that is tolerable. Therefore, using the centerline velocity and temperature of the gas phase is reasonable. The concentrate particle is treated as a discrete phase. It was assumed that there 12 were only three main forces exerting on the particle: drag, gravitational and buoyancy forces; other external forces like thermophoretic force are negligible compared with them. The particle motion written in a Lagrangian reference frame is described as: 𝑑𝑢𝑝 𝑑𝑡 = 𝐹𝐷 (𝑢 ⃗ −𝑢 ⃗ 𝑝) + 𝑔⃗(𝜌𝑝 −𝜌) (2.12) 𝜌𝑝 where, 𝐹𝐷 (𝑢 ⃗ −𝑢 ⃗ 𝑝 ) is the drag force per unit particle mass, and 𝐹𝐷 was calculated as: 18𝜇 𝐶𝐷 𝑅𝑒 𝐹𝐷 = 𝜌 2 𝑝 𝑑𝑝 (2.13) 24 The concentrate particle was assumed as solid sphere, and the drag coefficient was calculated as:[25] 0.44, 𝐶𝐷 = { 24 (1 𝑅𝑒 + 0.15𝑅𝑒 𝑅𝑒 > 1000 𝑅𝑒 ≤ 1000 0.678 ), (2.14) A heat balance on the particle that relates the particle temperature to convection and radiation was also applied. The particle thermal energy equation is expressed as: 𝑚𝑝 𝑐𝑝,𝑑 𝑑𝑇𝑝 𝑑𝑡 = ℎ𝐴𝑝 (𝑇 − 𝑇𝑝 ) − 𝑓ℎ 𝑑𝑚𝑝 𝑑𝑡 ∆𝑟 𝐻𝑟𝑒𝑎𝑐 + 𝜀𝑝 𝐴𝑝 𝜎(𝑇𝑠4 − 𝑇𝑝4 ) (2.15) in which, the term dmp/dt was related to particle chemical reaction rate, which is given by:[6, 8] 𝑑𝑋 𝑑𝑡 𝑝𝐻2 𝑂 𝑚 𝐸 = 𝑛 ⋅ 𝑘0 exp (− 𝑅𝑇) [𝑝𝐻𝑚2 − ( 𝐾𝑒 1 ) ] 𝑑𝑝𝑠 ⋅ (1 − 𝑋)[−𝐿𝑛(1 − 𝑋)]1−𝑛 (2.16) The particle heat transfer coefficient was evaluated using the correlation of Ranz and Marshall.[26] 𝑁𝑢 = ℎ𝑑𝑝 𝑘𝑔 1/2 = 2.0 + 0.6 𝑅𝑒𝑑 𝑃𝑟 1/3 A value of 0.8 was chosen as the particle emissivity (2.17)  p , recommended by Hahn and Sohn.[27] The particle specific heat was calculated as a mass fraction average of iron and 13 magnetite during the reduction process. 𝑐𝑝,𝑑 = 𝑋 ⋅ 𝑐𝑝,𝐹𝑒 + (1 − 𝑋) ⋅ 𝑐𝑝,𝐹𝑒3 𝑂4 (2.18) The size of the particles before and after an experiment stays almost the same as SEM micrographs taken in this work revealed (not shown here). The solid particle density equals the particle instantaneous mass divided by the initial particle volume (before reaction) as: 𝜌𝑝 = 𝜌𝑝,0 (1 − 𝜔𝑂0 𝑋) (2.19) 2.6 Numerical Procedure The computational domain includes a section of the injection tube long enough to establish the correct velocity profile at the tube exit (z = 1.2 m) and a schematic representation of this is shown in Figure 2.4 (a). The mesh was generated using ICEMCFD ANSYS with a total of 150,288 hexahedral cells as shown in Figure 2.4 (b). Mesh independence was confirmed by halving and doubling the number of cells with the same results. A mass flow rate boundary condition was imposed at the inlet of powder injection tube and reactor tube. The operating pressure was kept at 0.85 atm (the barometric pressure at Salt Lake City; 1 atm = 101.32 kPa). A nonslip condition was applied to the reactor wall for the gas flow inside the reactor. At the outlet, the flow was assumed to be fully developed and the gradients for all variables in the exit direction were zero. The temperatures of the gases at their inlets were given a constant room temperature of 298 K (25 ºC). The wall temperature profile along the longitudinal direction of the reactor to be used as a boundary condition was obtained by the method described in Section 2.3. It is 14 worth mentioning, however, that the water-cooled powder injection tube [see Figure 2.4 (a)] was not installed during the temperature profile measurement due to experimental difficulties. In the CFD simulation of an actual run, the water-cooled powder injection tube and the cold carrier gas were taken into consideration. Although the wall temperature profile as a boundary condition was optimized to match the measured centerline temperature in the absence of the carrier gas, its amount was typically less than 10% of the total gas input. Thus, its effect on wall boundary condition was neglected. The inner walls were assumed to be gray and diffuse, and a constant value of 0.4 was chosen for the emissivity of the alumina tube wall.[28] The gas phase governing equations (2.4) ~ (2.9) were discretized and solved using the commercial CFD software package ANSYS FLUENT 15.0. The calculation was carried out by a steady state pressure-based solver and the SIMPLE scheme was chosen for the pressure-velocity coupling. The second-order upwind scheme was chosen for momentum, species transport and energy equation discretization. A separate program was developed in MATLAB for solving the Lagrangian particle governing equations (2.12), (2.15) and (2.16) using 4th order Runge–Kutta method. 2.7 Results and Discussion 2.7.1 Modeling Results From the computed gas phase temperature inside the drop-tube reactor (DTR) under all sets of experimental conditions, it is clear that a low temperature region does exist adjacent to the water-cooled injection tube in the initial stage of the reactor. The length of this region increases and becomes narrower as the total gas flow rate increases. 15 The typical calculated particle temperature profile within the DTR is shown in Figure 2.5. The position where the particle temperature rises to the temperature of the isothermal zone, marked by the first dashed line on the left in Figure 2.5, is 0.205 m from the tip of the particle injector, which accounts for nearly 17% of the whole reaction zone length in this case. This length can be larger or smaller depending on specific experimental conditions. Within the water-cooled injection tube, temperature remains close to room temperature, and thus no reaction is considered there. It can be seen from Figure 2.5 that the particle temperature stays at the isothermal temperature 1573 ± 20 K (1300 ± 20 ºC) for some distance (until the second dashed line on the right in Figure 2.5) and then starts to decrease in the bottom part of the reactor. For all cases studied, the gas flow in most of the reactor tube is a fully developed laminar flow except in the region where the carrier gas with the solid particles exits a 2-mm diameter injection tube and forms a jet. The jet spreads and loses its momentum while traveling downward as demonstrated by the velocity profiles of the gas and particles in Figure 2.5. The velocity vectors shown in Figure 2.6 demonstrate that the gas travels mostly downward along the reactor longitudinal axis and the whole flow transits to laminar flow within a short distance (in the case shown around 0.1 m). The radial velocity was too small to disperse the particles. A similar feature was also computed by other researchers (e.g., Simone[19]) and was observed with particle tracking velocimetry and optical measurement by Lehto[20] and Avila et al.[16] in their study of a DTR. Since some reaction occurs in the upper low temperature region, a certain amount of error may occur if this lower temperature zone is ignored. The thermal history and reduction degree of the particles in the upper low temperature region for Tiso=1423 K (1150 16 ºC) and Tiso=1623 K (1350 ºC) are presented in Figures 2.7 and 2.8, respectively. As expected, a lower particle reduction degree is achieved in this region when the target temperature is lower. The length of this zone also affects the reduction degree achieved as can be seen in both figures as the gas flow rate increases. Typical calculated particle reduction degrees along the reactor length are shown in Figure 2.9 together with particle temperature profiles and the corresponding experimental final values. 2.7.2. Kinetics Analysis Previous work of Chen et al.[8, 9] demonstrates that the reduction behavior of iron oxide concentrate particle was affected by the partial pressure of gaseous reducing agents, particle size, particle residence time in the reaction zone and temperature. The nucleation and growth model was proved to best describe the reduction process of hematite and magnetite concentrate particles by H2 or CO. In the nucleation and growth kinetics, the reducing agent adsorbs on active sites on the surface and then reacts with oxygen and produces Fe nuclei that grow with time. For small particles, the period of the formation and growth of nuclei occupies essentially the entire conversion range. The reduction of hematite (Fe2O3) or magnetite (Fe3O4) to iron in the temperature range of 1423 K (1150 ˚C) to 1623 K (1350 ˚C) goes through a stepwise procedure, in which intermediate products like Fe3O4 and Fe0.947O will be formed. H2 or CO (fast) Fe2 O3 → H2 or CO (fast) Fe3 O4 → H2 or CO (slow) Fe0.947 O → Fe (2.20) However, it is extremely difficult to measure the intrinsic kinetics involving the formation of Fe3O4 or Fe0.947O for small particles going through a rapid reduction. In 17 addition, different parts of a small irregular iron oxide particle react at different rates and thus different oxide phases coexist in the particle at any time. Thus, the following global nucleation and growth rate expression for the overall reduction process was used in this work: 𝐸 𝑝𝑝,𝑔 𝑚 𝑚 [−𝐿𝑛(1 − 𝑋)]1/𝑛 = 𝑘0 exp (− ) [𝑝𝑟,𝑔 −( 𝑅𝑇 𝐾 ) ] 𝑑𝑝−𝑠 ⋅ 𝑡 (2.21) where pr , g and p p , g are the partial pressure of gaseous reducing agent (CO or H2) and product (CO2 or H2O), respectively; n is the Avrami parameter; and s represents the dependence of rate on the particle size. K is the equilibrium constant for the reduction of Fe0.947O [Fe0.947O + H2 = 0.947Fe + H2O]; m is the reaction order with respect to the partial pressure of gaseous reactant and product. The reaction order of the reactant and product must be equal to each other since a zero net reaction rate must be satisfied at equilibrium when K=pr,g/pp,g.[29] The differential form of Eq. (2.21) is shown as Eq. (2.16) and solved simultaneously with other equations. In this rate expression, the bulk gas compositions were used based on previous analysis[6, 24] that the effects of external mass transfer and pore diffusion were negligible for this reaction system. Magnetite concentrate particles were screened to size fractions: 20 - 25, 32 - 38, and 45 - 53 µm for kinetics measurements. For each size fraction, the geometric mean size was used in the calculations. Experimental results indicated that the particle reduction degree does not have a strong dependence on the particle size within this range tested, shown in Figure 2.10. It can be seen that under the same temperature and H2 partial pressure almost the same amount of reduction degrees were achieved for different size particles. Similar results were obtained at other temperatures. There are conditions that cause small particle size effects: First, the particle is sufficiently porous and pore 18 diffusion does not affect the overall rate. Second, even for nonporous particles, if their shapes are irregular, the shortest dimension determines the reaction rate, and the shortest dimensions in larger screen size particles might not be too different from those in the smaller screen size particles. In our system, we believe that a combination of these factors resulted in the negligible effect of particle size within the range we used. Therefore, the dependence of rate on the particle size parameter s in Eq. (2.21) was taken as zero for the reduction of magnetite concentrate with hydrogen in the temperature range 1423 K (1150 ˚C) to 1623 K (1350 ˚C). The total iron of the reduced samples was measured by ICP analysis in order to determine the reduction degree. A Spectro Genesis SOP spectrometer supplied by SPECTRO Analytical Instruments Inc. (Mahwah, NJ) was used to analyze the samples in this study. As rate parameters pre-exponential factor and activation energy were unknown beforehand, a wide range of values that contain the expected values were discretized and scanned for searching an optimized value. The search ranges of activation energy and pre-exponential factor are listed in Table 2.2. The objective function used in this study was the mean of the squared errors of all experiments as: 2 𝑓𝑚𝑖𝑛 = ∑𝑖(𝑋𝑐𝑎𝑙,𝑖 − 𝑋𝑒𝑥𝑝,𝑖 ) /𝑁 (2.22) The determination of m and n will be discussed here. 2.7.2.1. Half Order Dependence First a half order dependence of the gaseous reactant partial pressure and Avrami parameter, n, of 2 was investigated. The range of activation energy searched for minimum mean of the squared errors was 59 ~ 176 kJ mol-1. And the range used for pre- 19 exponential factor was 5.7×103 ~ 2.4×108. The comparisons between the reduction degrees calculated using the optimized kinetics parameters and the values obtained experimentally are shown in Figure 2.11. 2.7.2.2. First-Order Dependence The minimum mean of squared errors obtained for first-order gas partial pressure dependence and Avrami parameter, n, of 1 occurred at an activation energy value of 196 kJ∙mol-1 and pre-exponential factor of 1.23×107. The comparisons between the reduction degrees calculated using the optimized kinetics parameters and the values obtained experimentally are shown in Figure 2.12. The optimized values obtained and the range of variables used for searching the optimum are summarized in Table 2.2. It is clear that the first-order gas partial pressure dependence and Avrami parameter of 1 gives a higher correlation coefficient between the modeled reduction degrees and the experimental results. Thus, the reaction order and Avrami parameter both of unity better represent the reaction rates in the ranges of conditions tested in this study. 2.7.3. Complete Expression Combining all the rate parameters obtained through the steps described above, the complete rate equation for the hydrogen reduction of magnetite concentrate particle in the temperature range 1423 K (1150 ˚C) to 1623 K (1350 ˚C) is given by: [−𝐿𝑛(1 − 𝑋)] = 1.23 × 107 × 𝑒 − 196,000 𝑅𝑇 𝑝𝐻2 𝑂 ⋅ [𝑝𝐻2 − ( where, R is 8.314 J∙mol-1∙K-1, p is in atm, and t is in seconds. 𝐾 )] ⋅ 𝑡 (2.23) 20 Wang and Sohn[6] developed a similar rate expression for the same reaction. There are differences in the two rate expressions in terms of the conversion function, activation energy and the dependence on gas composition. They determined that an Avrami parameter, n, of 2 and a half order dependence on hydrogen partial pressure gave the best fit of their experimental data, in contrast to n = 1 and a first-order hydrogen partial pressure obtained in this study. Their data included temperatures at which concentrate particles begin to melt at about 1623 K (1350 ˚C) due to the gangue contents, which change the reduction mechanism. To account for this factor, these authors also incorporated a large temperature effect together into the effect of particle size. These factors may have led to the different values of activation energy they obtained (463 kJ∙mol-1). Therefore, we have recognized that the reduction kinetics in the temperature range 1423 K (1150 ˚C) to 1623 K (1350 ˚C) should be analyzed separately from that at higher temperatures. This paper has treated data in this lower temperature range of the temperatures expected to be used in the flash ironmaking process. Work is continuing to obtain and analyze the kinetics of the hydrogen reduction of magnetite concentrate at the higher temperatures also considered in the flash ironmaking process. 2.8. Conclusions Non-uniform temperature regions were found in the upper part of the drop-tube reactor through CFD simulation and were taken into consideration for rate analysis in this work. The advantages of the method proposed in this paper are that it provides a full description of the momentum, heat and mass transfer of a single particle during its reduction process. This simulation provides a detailed evaluation of the particle residence 21 time and particle temperature inside the reactor. The advantage of this method becomes greater when the reaction temperature varies with position and particle residence time varies with the paths they follow. The comparisons between the reduction degrees obtained experimentally at various temperatures and partial pressures of hydrogen and the computed values showed that the nucleation and growth rate expression with an Avrami parameter n =1 and a first-order dependence on the partial pressure of hydrogen well describes the kinetics of magnetite concentrate particle reduction within the ranges and conditions of this investigation. The kinetics parameters obtained through global search provided an activation energy value of 196 kJ∙mol-1 and pre-exponential factor of 2.95×107 for the reduction of magnetite by hydrogen. 2.9. Acknowledgments Deep appreciation is owed to Dr. Baoqiang Xu, Dr. Shenqing Zhang, Dr. Kai Xie and Feng Chen in this laboratory for their helpful advice in building the model and contribution to the experimental work for the study. The support and resources from the Center for High Performance Computing at the University of Utah are gratefully acknowledged. The authors acknowledge the financial support from the U.S. Department of Energy under Award Number DE-EE0005751 with cost share by the American Iron and Steel Institute (AISI) and the University of Utah. 22 2.10. Nomenclature Ap : surface area of particle (m2) dp : geometric mean particle diameter (m) Di,m : mass diffusion coefficient for species i in the mixture (m2∙s-1) hg : sensible heat of the gas mixture (J∙kg-1) k : turbulent kinetic energy (J∙kg-1) keff : effective thermal conductivity (W∙m-1∙K-1): = kg+kt kg : gas thermal conductivity (W∙m-1∙K-1) mp : particle mass (kg) p : pressure (pa) T : gas phase temperature (K) Tiso : isothermal zone temperature (K) Tp : particle temperature (K) Ts: wall temperature (K) ui : gas phase velocity components (m∙s-1) up: particle velocity (m∙s-1) Yi: mass fraction of species i Z: axial distance from the tip of injection tube (m) [See Figure 2.4(a).]  : turbulence dissipation rate (J∙kg∙s-1)  p : particle emissivity  : gas phase viscosity (N∙m∙s-2)  : gas phase density (kg∙m-3)  p : particle density (kg∙m-3) 23 o : the initial mass fraction of iron-bonded oxygen in magnetite 2.11. References 1. M. E. Choi and H. Y. Sohn: Ironmaking Steelmaking, 2010, vol. 37 (2), pp. 81-88. 2. H. K. Pinegar, M. S. Moats and H. Y. Sohn: Steel Res. Int., 2011, vol. 82 (8), pp. 95163. 3. H. Wang: PhD. Dissertation, University of Utah, Salt Lake City, Utah, 2011. 4. M. Y. Mohassab Ahmed: PhD. Dissertation, University of Utah, Salt Lake City, Utah, 2013. 5. M. Olivas-Martinez: PhD. Dissertation, University of Utah, Salt Lake City, Utah, 2013. 6. H. Wang and H. Y. Sohn: Metall. Mater. Trans. B, 2013, vol. 44 (1), pp. 133-45. 7. M. Yousef Mohassab-Ahmed and H. Y. Sohn: Ironmaking Steelmaking, 2014, vol. 41 (9), pp. 665-75. 8. F. Chen, Y. Mohassab, T. Jiang and H. Y. Sohn: Metall. Mater. Trans. B, 2015, vol. 46 (3), pp. 1133-45. 9. F. Chen, Y. Mohassab, S. Zhang and H.Y. Sohn: Metall. Mater. Trans. B, 2015, vol. 46 (4), pp. 1716-28. 10. A. Bonalde, A. Henriquez and M. Manrique: ISIJ Int., 2005, vol. 45 (9), pp. 1255-60. 11. A. Pineau, N. Kanari and I. Gaballah: Thermochim. Acta, 2006, vol. 447 (1), pp. 89100. 12. A. Pineau, N. Kanari and I. Gaballah: Thermochim. Acta, 2007, vol. 456 (2), pp. 7588. 13. Y. Qu, Y. Yang, Z. Zou, C. Zeilstra, K. Meijer and R. Boom: ISIJ Int., 2015, vol. 55 (5), pp. 952-60. 14. Z. Lian, B. Eleanor, Q. Yu and C.-Z. Li: Energy Fuels, 2010, vol. 24 (1), pp. 29-37. 15. R. Khatami, C. Stivers, K. Joshi, Y.A. Levendis and A.F. Sarofim: Combust. Flame, 2012, vol. 159 (3), pp. 1253-71. 16. M. H. M. R. Avila, R. Raiko and A. Oksanen: J. IFRF, 2012, Article Number 201201, pp. 1-13 24 17. H. Tolvanen and R. Raiko: Fuel, 2014, vol. 124 pp. 190-201. 18. D. C. D. Alexander L. Brown, M. R. Nimlos and J. W. Daily: Energy Fuels, 2001, vol. 15 (5), pp. 1276-85. 19. M. Simone, E. Biagini, C. Galletti and L. Tognotti: Fuel, 2009, vol. 88 (10), pp. 181827. 20. J. Lehto: Fuel, 2007, vol. 86 (12–13), pp. 1656-63. 21. T.-H. Shih, W. W. Liou, A. Shabbir, Z. Yang and J. Zhu: Comput. Fluids, 1995, vol. 24 (3), pp. 227-38. 22. E. H. Chui and G. D. Raithby: Numer. Heat Tr. B-Fund., 1993, vol. 23 (3), pp. 269-88. 23. A. Y. Varaksin, Turbulent Particle-Laden Gas Flows, Springer, New York, 2007, pp. 22-23. 24. M. E. Choi: PhD. Dissertation, University of Utah, Salt Lake City, Utah, 2010. 25. R. Clift, J. R. GraceM. E. Weber, Bubbles, Drops, and Particles, Academic Press, New York, 1978. 26. W. E. Ranz and W. R. Marshall: Chem. Eng. Prog., 1952, vol. 48 (4), pp. 173–80. 27. Y. B. Hahn and H. Y. Sohn: Metall. Mater. Trans. B, 1990, vol. 21 (6), pp. 959-66. 28. T. L. Bergman, A. S. Lavine, F. P. Incropera, D. P. DeWitt, Fundamentals of Heat and Mass Transfer, 7th Edition, Wiley, USA, 2011, pp. 795-96. 29. H. Y. Sohn: Metall. Mater. Trans. B, 2014, vol. 45 (5), pp. 1600-02. 25 2.12. Appendix: Complete Experimental Data (Excess H2 > 500%.) Temp. K (˚C) K Input dp Residence pH2 (µm) Time (s) (atm) 0.6 1423 0.7645 (1150) 0.4 0.4 1473 (1200) 0.7872 0.3 0.2 0.3 1523 (1250) 0.8077 0.2 22.5 22.5 35 35 35 49 49 49 22.5 22.5 22.5 22.5 22.5 22.5 22.5 22.5 22.5 35 35 35 49 49 49 22.5 22.5 22.5 22.5 22.5 22.5 22.5 22.5 35 35 35 35 49 49 3.6 1.8 7.2 4.8 1.6 5 3 1.5 11.8 8.1 5.0 1.9 6.5 3.5 6.9 5 2.2 8.2 5.1 2.2 6.7 5.2 2 6.4 1.8 4.7 1.9 10 6.6 3.5 1.6 7.9 5.5 5.5 1.8 5.8 3.5 H2 Flow Rate (L/min) * 3 6.5 1 1.8 6.5 1 2.5 6.5 0.5 0.8 1.4 4 1 2 0.6 1 2.5 0.4 0.8 2.3 0.27 0.5 2.2 0.5 2 1.1 3 0.3 0.5 1 2.3 0.3 0.5 0.5 2 0.3 0.7 N2 Flow Rate (L/min) * 1 2.4 0.1 0.5 2.4 0.1 0.7 2.4 0.3 0.6 1.3 4.2 0.8 2 0.8 1.5 4.3 0.4 1.2 3.9 0.2 0.6 3.7 1.3 6.2 1.7 5.2 0.7 1.3 3 7.2 0.7 1.3 1.3 6.2 0.7 2 Carrier Gas N2 (L/min) * 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 X 0.79 0.56 0.92 0.81 0.46 0.87 0.71 0.43 0.79 0.73 0.58 0.29 0.82 0.69 0.80 0.69 0.33 0.84 0.75 0.46 0.68 0.57 0.35 0.64 0.21 0.92 0.60 0.93 0.87 0.69 0.37 0.92 0.63 0.63 0.32 0.70 0.58 26 Cont. Temp. (˚C) K 22.5 5.5 0.8077 0.1 22.5 3.5 22.5 1.9 22.5 4.9 0.3 22.5 2 22.5 6.4 22.5 3.4 22.5 1.8 0.2 35 3.4 1573 0.8262 (1300) 35 1.6 49 3.2 49 1.5 22.5 5.9 0.1 22.5 3.4 22.5 1.8 22.5 3 22.5 1.6 35 3.3 0.2 35 1.6 1623 0.8428 49 5.8 (1350) 49 3.4 49 1.5 22.5 5.1 0.1 22.5 3.6 *Flow rates are calculated at 298 K (25 ºC) 1523 (1250) H2 Flow N2 Flow Carrier Rate Rate Gas N2 (L/min) (L/min) (L/min) * * * 2 0.3 0.3 3.5 0.5 0.3 7.2 1 0.3 1.5 1 0.3 4.7 2.7 0.3 1.3 0.5 0.3 3 1 0.3 6.2 2 0.3 2.6 0.9 0.3 6.9 2.2 0.3 2.3 0.8 0.3 6.2 2 0.3 1.7 0.27 0.3 3.5 0.5 0.3 7.2 1 0.3 3.3 1.1 0.3 6.9 2.2 0.3 2.6 0.9 0.3 6.2 2 0.3 0.7 0.3 0.3 2.0 0.7 0.3 6.2 2 0.3 2 0.3 0.3 3.1 0.45 0.3 and 0.85 atm (1 atm = 101.32 kPa) Input dp Residence pH2 (µm) Time (s) (atm) X 0.54 0.40 0.24 0.97 0.86 0.94 0.77 0.62 0.72 0.45 0.71 0.46 0.76 0.61 0.32 0.90 0.68 0.96 0.74 0.97 0.85 0.53 0.87 0.71 27 Table 2.1. Governing Equations of Gas Phase 𝜕 Continuity: 𝜕𝑥𝑖 Momentum: 𝜕 𝜕𝑥𝑗 𝜕𝑝 𝜕 𝜕𝑢 𝜕𝑢 (2.4) (𝜌𝑢𝑖 ) = 0 2 𝜕𝑢 𝜕 (𝜌𝑢𝑖 𝑢𝑗 ) = − 𝜕𝑥 + 𝜕𝑥 [𝜇 (𝜕𝑥 𝑖 + 𝜕𝑥𝑗 − 3 𝛿𝑖𝑗 𝜕𝑥𝑙 )] + 𝜕𝑥 (−𝜌𝑢𝑖′ 𝑢𝑗′ ) + 𝜌𝑔𝑖 (2.5) 𝑖 𝑗 𝑗 𝜕 Energy: 𝜕𝑥𝑖 𝑙 𝑖 𝜕 (𝜌𝑢𝑖 ℎ𝑔 ) = 𝜕𝑥 ( 𝜕 𝜕𝑥𝑗 (𝜌𝑌𝑖 𝑢𝑗 ) = − 𝜕𝑥 𝜕 𝜕 (2.6) ) + 𝑄𝑟 𝜕𝑥𝑖 𝜕𝐽𝑗 𝑖 Species: 𝑗 𝑘𝑒𝑓𝑓 𝜕𝑇 𝜇 (2.7) 𝑗 𝜕𝑘 Turbulent kinetic energy: 𝜕𝑥 (𝜌𝑘𝑢𝑖 ) = 𝜕𝑥 [(𝜇 + 𝜎 𝑡 ) 𝜕𝑥 ] + 𝐺𝑘 + 𝐺𝑏 − 𝜌𝜀 Turbulent dissipation rate: 𝜕 𝜕𝑥𝑖 (𝜌𝜀𝑢𝑖 ) = Reynolds stress: Mass diffusion flux: 𝜕 𝜕𝑥𝑖 𝑖 𝑘 𝑖 𝜇 𝑖 𝜀2 𝜕𝜀 [(𝜇 + 𝜎𝑡 ) 𝜕𝑥 ] + 𝜌𝐶1 𝑆𝜀 − 𝜌𝐶2 𝑘+ 𝜀 𝑖 𝜕𝑢 𝜕𝑢 2 𝜀 √𝑣𝜀 + 𝐶1𝜀 𝑘 𝐶3𝜀 𝐺𝑏 𝜕𝑢 −𝜌𝑢𝑖′ 𝑢𝑗′ = 𝜇𝑡 (𝜕𝑥 𝑖 + 𝜕𝑥𝑗) − 3 (𝜌𝑘 + 𝜇𝑡 𝜕𝑥𝑙) 𝛿𝑖𝑗 𝑗 𝑙 𝑖 𝜇 𝑱𝑖 = − (−𝜌𝐷𝑖,𝑚 + 𝑆𝑐𝑡 ) ∇𝑌𝑖 − 𝐷𝑇,𝑖 𝑡 ∇𝑇 𝑇 (2.8) (2.9) (2.10) (2.11) Table 2.2. Searching Range and Optimized Values of the Kinetics Parameters in Eq. (2.21) E range (kJ mol-1) k0 range(atm-1 s-1) Optimized values n=2, m=0.5 59 ~ 176 5700 ~ 2.38×108 E=129, k0=3.93×104 n=1, m=1 96 ~ 221 131.2 ~ 4.46×106 E=196, k0=1.23×107 28 Figure 2.1. A block diagram of the algorithm for kinetics parameter optimization. Figure 2.2. Comparison of the measured and calculated temperature profiles along the drop-tube reactor axis (z=0 corresponds to the exit of particle from powder feeder injection tube, shown in Figure 2.4 (a)). ■, − − − : experimental and calculated temperature profiles for target temperature of 1623 K (1350 °C), N2 flow rate = 1 L∙min-1; ●, − ∙ − : experimental temperature and calculated profiles for target temperature of 1423 K (1150 °C), N2 flow rate = 1 L∙min-1. 29 Figure 2.3. Schematic representation of the drop-tube reactor system. 30 (a) (b) Figure 2.4. Schematic representation of the reactor: (a) Computational domain, (b) mesh for computational domain. 31 Figure 2.5. Particle temperature and velocity profile along the centerline of the reactor for Tiso=1573 K (1300 ºC), pH2 = 0.2 atm, dp = 49 µm, total gas flow rate = 8.5 L∙min-1. The two vertical dashed lines represent the beginning and the end of the isothermal zone (target temperature 1573 ± 20 K (1300 ± 20 ºC)) 32 Figure 2.6. Gas velocity vector near the top part region of the reactor for Tiso=1573 K (1300 ºC), pH2 = 0.2 atm, dp = 49 µm, total gas flow rate = 8.5 L∙min-1. 33 Figure 2.7. Particle temperature profile and unreacted fraction in the top part region of the reactor for Tiso = 1423 K (1150 ºC), pH2 = 0.6 atm, dp=35 µm, with different total gas flow rate. Figure. 2.8 Particle temperature profile and unreacted fraction in the top part region of the reactor for Tiso =1623 K (1350 ºC), pH2=0.6 atm, dp=49 µm with different total gas flow rate. 34 Figure 2.9. Calculated profiles of particle temperature and unreacted fraction along the reactor length. ───: pH2=0.6 atm, dp=35 µm, gas flow rate=1.42 L∙min-1; − ∙ −: pH2=0.2 atm, dp=22.5 µm, gas flow rate=2.13 L∙min-1; − − −: pH2=0.2 atm, dp=22.5 µm, gas flow rate=2.13 L∙min-1. Figure 2.10. Reduction degrees for different size particles at 1623 K (1350 ºC), pH2=0.2 atm 35 Figure 2.11. Comparisons between the calculated reduction degrees vs. experimental results of all runs (n=2, m=0.5). Figure 2.12. Comparisons between the calculated reduction degrees vs. experimental results of all runs (n=1, m=1) CHAPTER 3 RATE ANALYSIS OF MAGNETITE CONCENTRATE PARTICLE REDUCTION: PART II: THE KINETICS OF HYDROGEN REDUCTION OF MOLTEN MAGNETITE CONCENTRATE Mohamed Elzohiery, De-Qiu Fan, Yousef Mohassab, and H. Y. Sohn Department of Metallurgical Engineering, University of Utah, Salt Lake City, Utah 84112, USA This is Chapter 3 of the dissertation and it is a manuscript for a journal article that we will submit for publishing. 3.1. Abstract The reduction of magnetite concentrate particles by H2 has been investigated in drop-tube reactors (DTR) with the objective of obtaining a rate equation that can be applied to the design and analysis of a flash reactor. The temperature in this work was varied from 1623 K (1350 °C) to 1873 K (1600 °C), and the magnetite concentrate particles at this temperature range become molten droplets. Full reduction of the magnetite concentrate was achieved at a residence time of greater than 4 seconds with H2 partial pressure of 0.15 atm in the temperature range investigated. Although DTR is designed and operated to maintain uniform temperature and gas concentrations as 37 closely as possible, it is difficult to completely eliminate some variations at the top and bottom part of the reactor. Thus, computational fluid dynamics (CFD) analysis was used to improve the accuracy of the obtained rate expressions. The particles were tracked using a Lagrangian approach in which the trajectory and velocity were determined by integrating the equation of particle motion. The variation of particle temperature thus obtained was taken into consideration in the kinetic analysis. It was determined that the reduction of magnetite concentrate particles in the temperature range investigated can be described by the nucleation and growth model with an Avrami parameter n = 1 and a first-order dependence on the partial pressure of H2. The activation energy of reaction was determined to be 180 kJ∙mol-1. Keywords: Flash reduction, Drop-tube reactor, CFD, Kinetics, Ironmaking, Magnetite 3.2. Introduction There has been much effort devoted to reducing the emissions of Greenhouse gas (GHG) in all industries. The steel industry has been achieving significant reductions in greenhouse gas emissions during the past few decades by improving energy efficiency through technologies. According to the International Energy Association (IEA), the iron and steel industry accounts for 6.7% of the world’s CO2 emissions.[1] A novel ironmaking technology has been developed at the University of Utah.[2-18] In this process, iron is produced from fine iron oxide concentrate particles in a flash reactor, utilizing hydrogen, natural gas, or coal gas as the reducing agent as well as the fuel. The direct use of iron oxide concentrate in this flash ironmaking process bypasses the pelletization/sintering and cokemaking steps in the blast furnace process, which will 38 significantly reduce the GHG emission. The gaseous reduction kinetics of iron oxide investigated previously was mainly focused on large pellets and at temperatures lower than 1473 K (1200 ºC). There has been some work on the reduction of ore fines, but iron oxide particles used were hematite ore. Not much work was available on the reduction kinetics of magnetite concentrate particles by H2 in the temperature range of 1473 K (1200 °C) - 1873 K (1600 °C). Ezz and Wild[19] investigated the reduction of hematite particles in the size range of 50 to 260 µm by hydrogen in the temperature range of 773 K (500 °C) to1373 K (1100 °C) in a fluidized bed reactor. They found that the factors that affect the reduction were the porosity of the particles, cracking of particles during reduction, and water vapor concentration around the particles. The activation energy values obtained were 33, 37 and 40 kJ∙mol-1 for particle of 51, 110, and 167 µm, respectively. Ozawa and Tanaka[20] investigated the reduction of fine hematite powder produced from the pyrite cinder by hydrogen in a gas conveyed system in the temperature range of 1023 K (750 °C) to 1173 K (900 °C). The particle size ranged from 5 to 45 µm. More than 90% reduction was achieved within 2-3 seconds of residence time at 1223 K (950 °C). They reported that the reduction was highly affected by the water vapor produced during the reduction process. Hayashi and Iguchi[21] studied the reduction of spherical wüstite particles by H2N2 gas mixtures in a laboratory gas conveyed system from 1723K (1450 °C) to 1823 K (1550 °C). Hematite pellets were first reduced to wüstite and then crushed and screened to obtained fine wüstite particles. They were then melted in a gas conveyed system to 39 form spherical particles, which were rescreened to obtain particles of 53-63 µm size. A reduction degree of 70% was achieved with a reducing gas containing 30% H2 in less than 0.5 seconds. The cross section of the reduced particle showed that the newly formed metallic iron was entrapped inside by a wüstite shell. A rate expression was obtained by taking into account the gas phase mass transfer and chemical reaction. The activation energy obtained was 110 kJ∙mol-1. Sohn and coworkers[2-18] have systematically investigated the reduction of magnetite concentrate particles by H2, CO or H2+CO mixtures at temperatures higher than 1423 K (1150 °C). They proved that the concentrate particles can be reduced in the few seconds of residence time typically available in a flash reactor. In the most likely near-term industrial application of this flash technology, natural gas is expected to be partially oxidized with industrial oxygen in the flash reactor to provide the heat required for the chemical reaction as well as to generate reducing gas mixtures of H2 and CO. This work is a part of the kinetics study of the reduction of iron oxide concentrate in the temperature range of 1423 K (1150 °C ) to 1873 K (1600 °C) aimed at generating a database to be used for the design of industrial flash ironmaking reactors. This work was a follow-up on previous investigation[12] on the reduction of magnetite concentrate particles by H2 in solid state in a lower temperature range 1150 - 1350 °C.[12, 18 ] The purpose of this research was to determine a global rate expression for the reduction of molten magnetite concentrate particles by H2. The reason for dividing the experiments into two temperature ranges was that the magnetite concentrate particles fuse and melt at temperatures above 1623 K (1350 °C) rendering different reduction mechanisms of the particle. The rate expressions for single reducing gases (CO or H2) will then be used 40 to generate the rate expressions for reduction by H2 + CO mixtures. Despite all the efforts made to form a uniform temperature zone inside the droptube reactor (DTR), there are always some variations in H2O concentration and temperature along the reactor length, particularly near the top of the reactor where particles and carrier gas are injected at room temperature and in the bottom part of the reactor close to the exit. This paper presents the results of the kinetic analysis of magnetite concentrate reduction based on a CFD approach, following a similar approach applied to other related systems.[12] This approach improves the accuracy of the rate equation based on DTR data by eliminating the assumptions of a zone of uniform temperature and constant particle velocity needed without the application of CFD. 3.3. Experimental Work The magnetite concentrate used in this experiment was produced from Taconite ore and was provided by ArcelorMittal Company in the U.S. The magnetite concentrate particles were screened to 20-25, 32-38 and 45-53 µm size fractions. The same concentrate was used in previous publications where more information about it can be found.[12] These particles fuse and melt at temperatures above 1623 K (1350 °C), as shown in Figure 3.1, due to the presence of gangue contents. A high temperature DTR was used to investigate the reduction of the magnetite concentrate particles by H2 in the temperature range of 1623 K (1350 °C) to 1873 K (1600 °C) as shown in Figure 3.2. The reactor assembly had a pneumatic powder feeder, a gas delivery unit, a cooling device and a powder collection system. The reactor 41 consisted of a vertical tubular furnace with 8 MoSi2 heating elements and an alumina tube with an inner diameter of 8 cm and a length of 155 cm. The maximum temperature that this reactor can reach was 1650 °C. The carrier gas used in all experiments was either N2 or CO, which was maintained at a constant flow rate of 0.3 L/min. (All the flow rates in this work were calculated at 298 K (25 ºC) and 0.85 atm, the atmospheric pressure at Salt Lake City.) A water-cooled tube was used to ensure that there was no chemical reaction of the particle before entering the reactor. A cylindrical porous alumina honeycomb was inserted at the top part of the reactor to enhance the mixing and preheating of the reducing gas. The gas flow rates were adjusted in this work to provide residence times of 2 to 10 seconds typically encountered in a flash ironmking process, while allowing desired reduction degrees depending on other experimental conditions such as temperature and gas composition. During the experiment, the particle feeding rate was controlled from 30 ~ 250 mg/min. For all the experiments, the feed rate of the reducing gas (H2) was in more than 500% excess of the minimum required amount to ensure that the gaseous reactant concentration remained essentially constant over the entire reactor length. The reacted particles were collected in a powder collector at the bottom of the reactor and then were analyzed using ICP-OES to obtain the total iron content of the reduced. 3.4. Rate Analysis Without CFD The factors that affect the reduction of fine magnetite concentrate particles by hydrogen include the hydrogen partial pressure, particle size, reaction temperature, and 42 the degree of conversion. The reduction rate in the absence of gas-phase mass transfer effects can be expressed in the following general form: 𝑑𝑋 𝑑𝑡 = 𝑘 ⋅ 𝑓𝑝 (𝑝𝐻2 , 𝑝𝐻2 𝑂 ) ⋅ ℎ(𝑑𝑝 ) ⋅ 𝑓(𝑋) (3.1) The integral form of the above equation under constant temperature is: 𝑋 𝑑𝑤 𝑔(𝑋) = ∫0 𝑓(𝑤) = 𝑘 ⋅ 𝑓𝑝 (𝑝𝐻2 , 𝑝𝐻2 𝑂 ) ⋅ ℎ(𝑑𝑝 ) ⋅ 𝑡 = 𝑘𝑎𝑝𝑝 ⋅ 𝑡 (3.2) 𝐸 where k is the reaction rate constant, 𝑘 = 𝑘𝑜 exp (− 𝑅𝑇); 𝑘𝑎𝑝𝑝 is the apparent rate constant equal to 𝑘 ⋅ 𝑓𝑝 (𝑝𝐻2 , 𝑝𝐻2 𝑂 ) ⋅ ℎ(𝑑𝑝 ); 𝑓𝑝 (𝑝𝐻2 , 𝑝𝐻2 𝑂 ) represents the effects of the partial pressures H2 and H2O; ℎ(𝑑𝑝 ) represents the particle size effect; t is the particle residence time. The calculation of residence time was under the assumption of constant particle velocity and temperature profile inside the reactor, the details of which can be found in previous publications;[10,11,13] 𝑔(𝑋) represent the conversion functions of different reaction models; X is the reduction degree[10-13] defined as the ratio of the removed oxygen to the total removable oxygen in the concentrate particles. Preliminary tests showed that full reduction of the magnetite concentrate was achieved at a residence time of greater than 4 seconds with H2 partial pressure of 0.15 atm in the temperature range investigated in this work. Thus, the partial pressures used in this work were lowered to 0.05 and 0.1 atm to achieve less than complete reduction degrees for the kinetics analysis. 3.4.1. Reaction Model Different reaction models were tested in plotting g(X) vs t. It was determined that the reduction of magnetite concentrate particles by H2 in the temperature range of 43 1623 K (1350 °C) to 1873 K (1600 °C) can be described by the nucleation and nuclei growth kinetics with an Avrami parameter n of 1.0. It was observed that the freshly reduced iron quickly diffuses into the center of the particle and leaves the unreduced iron oxide exposed to the H2 constantly due to the surface energy differences of iron and iron oxides, which is seen from the cross section of a reduced sample shown in Figure 3.3. 3.4.2. Reaction Order To determine the order of reaction with respect to H2, its partial pressure was varied by using N2. It was shown previously[10] that a logarithmic or an arithmetic mean represents the average driving force, respectively, for first-order or half order dependence with respect to 𝑝𝐻2 . The 𝑝𝐻2 𝑂 value at the outlet of reactor was calculated based on the reduction degree of the particles. First-order dependence and half order dependence on H2 partial pressure were tested. The first-order dependence (m = 1) gave the best fit of the experimental data, as can be seen from Figure 3.4. 3.4.3. Particle Size Effect The particle size effect on the reduction degree in the two temperature ranges is shown in Figure 3.5. It indicates that the reduction rate was inversely proportional to the particle size. Thus, the function on particle size was ℎ(𝑑𝑝 ) = 𝑑𝑝−1 . The reduction of magnetite concentrate by H2[12,18] in the lower temperature range of 1423 K (1150 °C) to 1623 K (1350 °C) was found to have no effect on particle size. The most likely reason for this difference is that the particles in solid state experience thermal stress and 44 develop cracks of similar dimensions when rapidly heated as they are fed into the reactor. The reaction rate then depends on the dimensions of the solid between the cracks, and no longer on the original size. But when the particles melted to form spherical liquid droplets, the irregularity and cracks disappeared. Particles with a larger size melted and became droplets with a larger diameter. The reaction of a molten sphere took place at the surface of the droplet. Therefore, the reduction rate was inversely proportional to the particle size. 3.4.4. Activation Energy The activation energy and the pre-exponential factor were obtained by plotting 𝐿𝑛 𝑘 vs 1/T, as shown in Figure 3.6. The activation energy value was determined to be 170 kJ∙mol-1. The corresponding pre-exponential factor was 2.5×107 µm∙atm-1∙s-1. 3.5. CFD Refinement of Rate Parameters CFD approach was used in this work to eliminate errors caused in the kinetics analysis by the small variation in gas composition, i.e., water vapor content, due to reaction and temperature variations near the top and bottom part of the reactor. The Euler-Lagrange approach was used to model the two-phase flow, in which the gas phase was treated as a continuum in the Eulerian frame of reference while the solid phase was tracked in the Lagrangian mode. The detailed description of the mathematical model has been presented in a previous publication,[12] and thus will not be further elaborated on here. The temperature variations near the top and bottom of the reactor are expected 45 to have little influence on the rate dependence on particle size and partial pressures. Activation energy and/or pre-exponential factor, however, are expected to be affected more strongly by the temperature variation. Therefore, the refinement of rate analysis by CFD was focused on obtaining more accurate values of activation energy and corresponding pre-exponential factor. A wide range of pre-exponential factor and activation energy values around the preliminary values estimated above were discretized and scanned to search for the optimized values. The search ranges of activation energy and pre-exponential factor are listed in Table 3.1. The best-fit activation energy and pre-exponential factor values for the reduction of magnetite concentrate particles by H2 are also listed in Table 3.1. Typical calculated particle reduction degrees along the reactor centerline obtained using the optimum values of activation energy and pre-exponential factor, together with the corresponding experimental reduction degrees and temperature profiles, are shown in Figure 3.7. It is seen that the simulated reduction degree values match the experimental values very well. The results computed based on the CFD method demonstrates that a low temperature region existed adjacent to the water-cooled injection tube in the top part, and the particle temperature decreased gradually in the bottom part of the reactor. It is seen from Figure 3.7 that it takes about 0.2 m from the tip of the injection tube for the particle temperature to reach the isothermal experimental temperatures. The existence of this low temperature zone in the upper part of the drop-tube reactor affects the calculation of real particle residence time. This leads to the refinement of the values of the activation energy and pre-exponential factor. From Figure 3.7, it is also seen that 46 larger particles are heated more slowly, as expected. The comparisons between the calculated reduction degrees using the optimum values of activation energy and pre-exponential factor and the experimental values from all the runs are shown in Figure 3.8. It is noted that the optimum kinetic parameters obtained in this work predict the reduction degrees very well. 3.6. Complete Rate Expression Combining all the rate parameters obtained through the steps described above, the complete rate equations for the reduction of magnetite concentrate particles by H2 in the temperature range 1623 K (1350 °C) to 1873 K (1600 °C) are given, respectively, as: Integral form: [−𝐿n(1 − 𝑋)] = 6.07 × 107 × 𝑒 − 180,000 𝑅𝑇 𝑝𝐻2 𝑂 ∙ [𝑝𝐻2 − ( 𝐾 )] ⋅ 𝑑𝑝−1 ∙ 𝑡; Differential form: 180,000 𝑝𝐻 𝑂 𝑑𝑋 −1 = 6.07 × 107 ⋅ 𝑒 − 𝑅𝑇 ⋅ (𝑝𝐻2 − 2 ) ⋅ (𝑑𝑝 ) ⋅ (1 − 𝑋) 𝑑𝑡 𝐾 1623 K (1350 ˚C) < T < 1873 K (1600 ˚C) (3.3) where R is 8.314 J∙mol-1∙K-1, p is in atm, K is the equilibrium constant for the reduction of FeO by H2, dp is in µm, and t is in seconds. Although the use of CFD technique should in principle allow one to determine the rate expression even from experiments done under spatially varying temperature, velocity and gas concentrations, the accuracies of the developed rate equations and parameters are greatly enhanced by performing the experiments designed to keep these conditions as uniform as possible, in combination with CFD simulation to account for 47 small variations that are difficult to completely eliminate. This is the approach we used in this work. Not much work on the reduction of molten magnetite concentrate particles has been reported in the literature. The activation energy obtained in Ref. [21] was 110 kJ∙mol-1 for the reduction of wüstite by H2 in the temperature range of 1723 K (1450 °C) to 1823 K (1550 °C), which is lower than the value obtained in this work. The particles used in Ref. [21] was prepared by crushed wüstite pellets produced by reducing hematite green pellets, and then spherical particles were generated by preheating them in the same experimental system in a nitrogen flow, while the concentrate particles used in this work was mostly natural magnetite and did not go through any prereduction. The differences in the composition of particles used and morphology of the two particles may have led to the difference in the activation energy obtained. In addition, the reaction model used in Ref. [21] was different from the nucleation and growth model used in this work. In the previous publication on the reduction of solid state magnetite concentrate particles by H2,[12] the same nucleation and growth model with n = 1 was used to describe the reduction. The activation energy was determined to be 196 kJ∙mol-1. No particle size effect on the reaction rate was found in that lower temperature range. The reduction of solid state hematite concentrate particles by H2 in Ref. [15] yielded an activation energy of 218 kJ∙mol-1. That reaction was also found to be described by the nucleation and growth model with an Avrami parameter n = 1. 48 3.7. Conclusions An algorithm that takes into consideration the velocity and temperature variations in the top and bottom parts of the DTR combined with CFD simulation of the flow and heat transfer was used to analyze the kinetics of the reduction of magnetite concentrate particles by H2. The activation energy was obtained to be 180 kJ∙mol-1 after CFD refinement. The experimental results at various temperatures and partial pressures of H2 showed that the nucleation and growth rate expression with an Avrami parameter n = 1 and a first-order dependence on the partial pressure of H2 describes well the kinetics of magnetite concentrate particle reduction within the ranges of conditions of this investigation. In addition, the reduction degree also has a strong dependence on the particle size. It was found that the reduction rate was inversely proportional to the particle size with a size function of ℎ(𝑑𝑝 ) = 𝑑𝑝−1 , which can be expected for a reaction taking place on the surface of a molten spherical droplet. 3.8. Acknowledgments The support and resources from the Center for High Performance Computing at the University of Utah are gratefully acknowledged. The authors acknowledge the financial support from the U.S. Department of Energy under Award Number DEEE0005751 with cost share by the American Iron and Steel Institute (AISI) and the University of Utah. 3.9. References 1. World Steel Association, 2017. https://www.steel.org.au/resources/elibrary/resourceitems/steel-s-contribution-to-a-low-carbon-future-and-cl/ accessed October 30, 2018. 49 2. H. Y. Sohn: Steel Times Int., 2007, vol. 31, pp. 68-72. 3. H. Y. Sohn, M. E. Choi, Y. Zhang, and J. E. Ramos: AIST Trans., 2009, vol. 6 (8), pp. 158-65. 4. M. E. Choi and H. Y. Sohn: Ironmaking Steelmaking, 2010, vol. 37 (2), pp. 81-88. 5. H. K. Pinegar, M. S. Moats, and H. Y. Sohn: Steel Res. Int., 2011, vol. 82 (8), pp. 951-63. 6. H. K. Pinegar, M. S. Moats, and H. Y. Sohn: Ironmaking Steelmaking, 2012, vol. 39 (6), pp. 398-408. 7. H. K. Pinegar, M. S. Moats, and H. Y. Sohn: Ironmaking Steelmaking, 2013, vol. 40 (1), pp. 44-49. 8. H. Y. Sohn and M. Olivas-Martinez: JOM, 2014, vol. 66 (9), pp. 1557-64. 9. H. Y. Sohn and Y. Mohassab, J. Sust. Metall., 2(3), 216–227 (2016). 10. H. Wang and H. Y. Sohn: Metall. Mater. Trans. B, 2013, vol. 44 (1), pp. 133-45. 11. F. Chen, Y. Mohassab, T Jiang and H. Y. Sohn: Metall. Mater. Trans. B, 2015, vol. 46 (3), pp. 1133-45. 12. D. Fan, Y. Mohassab, M. Elzohiery and H. Y. Sohn: Metall. Mater. Trans. B, 2016, vol. 47 (3), pp. 1669-80. 13. F. Chen, Y. Mohassab, S. Zhang and H. Y. Sohn: Metall. Mater. Trans. B, 2015, vol. 46 (4), pp. 1716-28. 14. D. Fan, H. Y. Sohn, Y. Mohassab and M. Elzohiery: Metall. Mater. Trans. B, 2016, vol. 47 (6), pp 3489-500. 15. D. Fan, H. Y. Sohn and M. Elzohiery: Metall. Mater. Trans. B, 2017, vol. 48 (5), pp. 2677-84. 16. D. Fan, M. Elzohiery, Y. Mohassab and H. Y. Sohn, in 8th International Symposium on High-Temperature Metallurgical Processing, J. Y. Hwang et al. (eds.), Springer, 2017, pp 61-70. 17. H. Y. Sohn, Y. Mohassab, M. Elzohiery, D. Fan and A. Abdelghany, in Applications of Process Engineering Principles in Materials Processing, Energy and Environmental Technologies, S. Wang et al. (eds.), Springer, 2017, pp 15-23. DOI 10.1007/978-3319-51091-0_2. 18. M. Elzohiery, H. Y. Sohn, and Y. Mohassab: Steel Res. Int., 2017, vol. 88 (2). http://dx.doi.org/10.1002/srin.201600133 50 19. S. Y. M. Ezz and R. Wild: J. Iron Steel Inst., 1960, vol. 194, pp. 211-21. 20. M. Ozawa and M. Tanaka: Tetsu-to-Hagane, 1972, vol. 58 (7), pp. 821-9. 21. S. Hayashi and Y. Iguchi: ISIJ International, 1994 vol. 34 (7) pp. 555-61. 51 Table 3.1. Searching Ranges and Optimized Values of the Kinetics Parameters E range k0 range Best-fit values 150 ~ 220 kJ∙mol-1 1×104 ~ 5×109 µm∙atm-1∙s-1 E = 180 kJ∙mol-1, k0 = 6.07×107 atm-1·s-1· µm Figure 3.1. SEM micrographs (a) magnetite ore and (b) particles after reduction (T = 1646 K (1373 °C), 𝑝𝐻2 = 0.1 atm, X=0.91). 52 Figure 3.2. Schematic representation of the high temperature drop-tube reactor (DTR). 53 Figure 3.3 Cross-sectional view of a partially reduced particle. [T = 1623 K (1350 °C), 𝑝𝐻2 = 0.2 atm, X=0.94] 54 Figure 3.4. Relationship between 𝑘𝑎𝑝𝑝 and 𝑓(𝑝𝐻2 , 𝑝𝐻2 𝑂 )𝑎𝑣𝑔 ; lm stands for logarithmic mean; am stands for arithmetic mean.[10] (𝑝𝐻2 , 𝑝𝐻2 𝑂 in atm) 55 Figure 3.5. Effect of particle size on the reduction degree at different temperatures. 56 Figure 3.6. Ln(k) vs 104/T for reduction by H2. Figure 3.7. Calculated profiles of particle temperature and unreacted fractions along the reactor centerline. − − −: pH2 = 0.05 atm, gas flow rate: H2 = 0.7 L/min, N2 = 11.2 L/min, dp = 22.5 µm; − ∙ −: pCO = 0.1 atm, gas flow rate: H2 = 1.5 L/min, N2 = 11.25 L/min, dp = 35 µm; − ∙∙ −: pCO = 0.1 atm, gas flow rate: H2 = 1.5 L/min, N2 = 11.25 L/min, dp = 22.5 µm. The temperature values in the legend represent the isothermal zone temperature maintained during the experiments. 57 Figure 3.8. Comparisons between the calculated reduction degrees vs. experimental results. CHAPTER 4 RATE ANALYSIS OF MAGNETITE CONCENTRATE PARTICLE REDUCTION: PART III: THE KINETICS OF CARBON MONOXIDE REDUCTION OF MAGNETITE CONCENTRATE PARTICLES THROUGH CFD MODELING De-Qiu Fan, Mohamed Elzohiery, Yousef Mohassab, and H. Y. Sohn Department of Metallurgical Engineering, University of Utah, Salt Lake City, Utah 84112, USA This is Chapter 4 of the dissertation and it is a manuscript for a journal article that we will submit for publishing. 4.1. Abstract The kinetics of CO reduction of magnetite concentrate particles has been investigated in drop-tube reactors (DTR) with the objective of obtaining a rate equation that can be applied to the design and analysis of a flash reactor in which magnetite concentrate is reduced to iron by a mixture of hydrogen and carbon monoxide. The effect of CO partial pressure was determined by varying it from 0.1 to 0.85 atm and temperature was varied from 1473 K (1200 °C) to 1873 K (1600 °C), which is the range of operation 59 of a flash ironmaking reactor. The magnetite concentrate particles tend to fuse and melt at temperatures above 1623 K (1350 °C). Therefore, the experimental data were analyzed separately in two temperature ranges, 1473 K (1200 °C) - 1623 K (1350 °C) and 1623 K (1350 °C) - 1873 K (1600 °C). The reduction degrees achieved at experimental temperatures under 1623 K (1350 °C) in the few seconds of residence time available in a typical flash reactor were relatively low (mostly under 50%), while significant reduction degrees (higher than 85%) were achieved at temperatures above 1623 K (1350 °C). Although DTR is designed and operated to maintain uniform temperature and gas concentrations as closely as possible, it is difficult to completely eliminate some variations. Thus, computational fluid dynamics (CFD) analysis was used to improve the accuracy of the obtained rate expressions. The particles were tracked using a Lagrangian approach in which the trajectory and velocity were determined by integrating the equation of particle motion. The variation of particle temperature thus obtained were taken into consideration in the kinetic analysis. It was found that the reduction of magnetite concentrate particles in both temperature ranges can be described by the nucleation and growth kinetics. The activation energy of reaction was 451 kJ∙mol-1 and 88 kJ∙mol-1 in the two temperature ranges. Keywords: Flash reduction, Drop-tube reactor, CFD, Kinetics, Ironmaking, Magnetite 4.2 Introduction The blast furnace process accounts for more than 90% of the annual production of primary iron, according to the World Steel Association, with the balance by alternative processes such as direct-reduction and smelting reduction. Although the traditional blast 60 furnace has a high production rate and other advantages, it suffers from problems like high energy consumption and high levels of pollution and CO2 emissions. A novel ironmaking technology has been developed at the University of Utah.[1-14] In this process, iron is produced from fine iron oxide concentrate particles in a flash reactor, utilizing hydrogen, natural gas, or coal gas as the reducing agent as well as the fuel. Flash ironmaking allows the direct use of iron oxide concentrate to bypass the pelletization/sintering and cokemaking steps in the blast furnace process, which will significantly reduce the CO2 emission as well as the energy consumption.[4-8] In the most likely near-term industrial application of this technology, hot reducing gases will be generated by the partial combustion of natural gas with industrial oxygen. The gas mixture thus obtained contains reducing gases CO and H2. Sohn and coworkers[914] have investigated the gaseous reduction of iron oxide concentrate particles under various experimental conditions using a DTR aimed at generating a database to be used for the design of a flash ironmaking reactor. The gaseous reduction of iron oxide was investigated previously by many other researchers but it was mainly focused on pellets or particles larger than concentrate particles. In addition, most of the kinetics studies were performed on hematite ore with the experiments done in a thermogravimetric analyzer (TGA). Bradshaw and Matyas[15] studied the mechanism and the structural changes of hematite reduction to magnetite in CO-CO2 atmosphere with CO partial pressure varying from 0.063 to 0.5 atm in the temperature range of 773 K (500 °C) to 1373 K (1100 °C). The experiment was conducted on hematite pellets as well as thin layers made of hematite powder ranging from 45-63 µm in size produced by crushing the pellets. It was 61 determined that the gaseous diffusion through the product layer cannot be controlling the rate of reduction as it was much faster compared with the experimental results and it was postulated that the reduction rate depended on the rate of nucleation of the magnetite phase. Tsukihashi et al.[16] investigated the kinetics of reduction of molten wüstite by CO gas at temperatures 1723 K (1450 °C) and 1873 K (1600 °C) in a gas conveyed system. The molten particles had a mean size of 25 µm. It was determined that there was no effect for the mass transfer on the rate of the reaction. The activation energy of the chemical reaction was calculated to be 131 kJ∙mol-1. The product was in the form of spherical molten iron surrounded by molten iron oxide. The rate of nucleation of iron on the iron oxide surface was considered to affect the overall reaction rate. Adamian and Bustamante[17] studied the partial reduction of hematite to magnetite by CO in temperature range 828 K (555 °C) to 1123 K (850 °C). Iron concentrate ranging from 74 to 149 µm was used in the experiments in a thermo-balance. It was found that the reduction was chemically controlled in the temperature range of 828 K (555 °C) to 998 K (725 °C) based on the high activation energy value (94 ± 5 kJ∙mol-1), while in the temperature range of 1023 K (750 °C) to 1123 K (850 °C), the activation energy was (31 ± 5 kJ∙mol-1), indicating the likely effect of mass transfer. Ray and Kundu[18] studied the isothermal reduction of hematite to wüstite by CO/CO2 gas mixture in the temperature range from 1073 K (800 °C) to 1273 K (1000 °C). Fine ore powder was reduced and the kinetics was measured by a nonisothermal analysis which showed that the reaction occurred in two steps where a change in the activation energy occurred at 773 K (500 °C). The average activation energy was 90 62 kJ∙mol-1. Dutta and Ghosh[19] investigated the reduction of iron ore dust containing 95.7% hematite with the size ranging from 44 to 150 µm. Thermogravimetric analysis for the reduction of the powder in a cylindrical crucible between 1073 K (800 °C) and 1373 K (1100 °C) was performed in two stages: from hematite to wüstite in CO-CO2 mixtures and from wüstite to iron by CO-Ar mixtures. Ln kc (rate constant) vs 1/T plots did not yield straight lines, which was attributed to the morphological changes during the reduction of the bed such as sintering and swelling. Su et al.[20] investigated the reduction kinetics of hematite powders ranging from 180 to 200 µm in the temperature range of 1123 K (850 °C) to 1273 K (1000 °C) as oxygen carrier in chemical looping combustion. The reduction proceeded in two sequential stages: from Fe2O3 to Fe3O4 and from Fe3O4 to FeO. The first stage reaction was controlled by external mass transfer while the second stage was mainly controlled by chemical reaction. An activation energy value of 111 kJ∙mol-1 and a reaction order of 1.5 were obtained for the second stage reaction. The purpose of this research was to determine the rate of reduction of magnetite concentrate particles by CO and obtain the global rate expression, the rate equation for hydrogen reduction having already been established.[11] The rate expressions for single reducing gases (CO or H2) will then be used to generate rate expressions for the reduction by H2 + CO mixtures. Despite all the efforts made to form a uniform temperature zone inside reactor DTR, there are always some temperature variations, particularly near the top of the reactor where particles and carrier gas are injected at room temperature, and in the 63 bottom part of the reactor close to the exit. This paper presents the results of the kinetic analysis of magnetite concentrate reduction based on a CFD approach, following a similar approach applied to other related systems.[11, 14] This approach improves the accuracy of the rate equation based on DTR data by eliminating the assumptions of a zone of uniform temperature and constant particle velocity needed without the application of CFD. 4.3 Experimental Work The magnetite concentrate particles used in this study were the same as those used in the previous work.[9, 11, 13] These particles tend to fuse and melt at temperatures above 1623 K (1350 °C), as shown in Figure 4.1, due to the presence of gangue contents. In contrast, the particles reacted at temperatures below this temperature indicated that they remained in solid state and not fused, as can be seen in Figure 4.2. Therefore, experiments have been carried out in two different temperature ranges in two different drop-tube reactors. The lower temperature range [1423 K (1200 °C) to 1623 K (1350 °C)] experiments were conducted in the same reactor that has been detailed in our previous publications,[9-12, 14] and thus will not be further elaborated on here. The high temperature range [1623 K (1350 °C) to 1873 K (1600 °C)] experiments were conducted in a reactor that can reach 1650 °C. The reactor assembly also had a pneumatic powder feeder, a gas delivery unit, a cooling device and a powder collection system. A schematic representation of this reactor is shown in Figure 4.3. The reactor tube was made of 99.8% purity alumina. The tube had an inner diameter of 8 cm and a length of 155 cm, and was heated by eight bar-type MoSi2 heating elements to maintain a 64 temperature between 1573 K (1300 °C) and 1873 K (1600 °C). The pneumatic powder feeding system is shown in Figure 4.4. This system consisted of a syringe pump, a vibrator, carrier gas lines, and a concentrate vial. The carrier gas was first fed to the concentrate vial and carried the fluidized particles from the top part of the particle bed into the reactor through a stainless steel pipe with an ID of 1.0 mm. The vibration not only helps in the fluidization of the particles, but also makes it easier and smoother for the particles to travel inside the delivering line. The syringe pump advanced up at a preset speed, which controls the particle feeding rate. The carrier gas used in all experiments was either N2 or CO, which was maintained at a constant flow rate of 0.3 L/min. (All the flow rates in this work were calculated at 298 K (25 ºC) and 0.85 atm, the atmospheric pressure at Salt Lake City.) The same water-cooled tube was used as in the previous work[9-12, 14] through which no chemical reaction of the particle was ensured before entering the reactor. A cylindrical porous alumina honeycomb was inserted at the top part of the reactor to enhance the mixing and preheating of the reducing gas. Dried and screened magnetite concentrate particles of size fraction 20 - 25, 32 38, or 45 - 53 µm were used in the experiments. In the flash ironmaking process, the particle residence time is expected to be 2 ~ 10 seconds. The gas flow rates were adjusted in this work to provide these residence times while allowing desired reduction degrees depending on other experimental conditions such as temperature and gas composition. During the experiment, the particle feeding rate was controlled from 30 ~ 200 mg/min. The mass ratio of particle to gas was usually kept at ≤ 0.05. For all the experiments, the feed rate of the reducing gas (CO) was in more than 500% excess of the minimum 65 required amount to ensure that the gaseous reactant concentration remained essentially constant over the entire reactor length. The reacted powder was collected in a powder collector at the bottom of the reactor. 4.4. Approach to Rate Analysis The reduction rate of fine particles of magnetite by CO in the absence of gasphase mass transfer effects can be expressed in the following general form: 𝑑𝑋 𝑑𝑡 = 𝑘 ⋅ 𝑓𝑝 (𝑝𝐶𝑂 , 𝑝𝐶𝑂2 ) ⋅ ℎ(𝑑𝑝 ) ⋅ 𝑓(𝑋) (4.1) The integral form of the above equation under constant temperature is: 𝑋 𝑑𝑤 𝑔(𝑋) = ∫0 𝑓(𝑤) = 𝑘 ⋅ 𝑓𝑝 (𝑝𝐶𝑂 , 𝑝𝐶𝑂2 ) ⋅ ℎ(𝑑𝑝 ) ⋅ 𝑡 = 𝑘𝑎𝑝𝑝 ⋅ 𝑡 (4.2) 𝐸 where k is the reaction rate constant, 𝑘 = 𝑘𝑜 exp (− 𝑅𝑇); 𝑘𝑎𝑝𝑝 is the apparent rate constant defined as 𝑘 ⋅ 𝑓𝑝 (𝑝𝐶𝑂 , 𝑝𝐶𝑂2 ) ⋅ ℎ(𝑑𝑝 ); 𝑓𝑝 (𝑝𝐶𝑂 , 𝑝𝐶𝑂2 ) represents the effects of the partial pressures CO and CO2; ℎ(𝑑𝑝 ) represents the particle size effect; t is the particle residence time; 𝑔(𝑋) represent the conversion functions of different reaction models; X is the reduction degree[9-14] defined as the ratio of the removed oxygen to the total removable oxygen in the concentrate particles. We use this global reduction degree, rather than distinguishing the formation of wüstite followed by iron, due to the fact that different phases of iron oxides coexist within the individual, irregularly shaped particle and in separate particles during the reduction process resulting from varying reactivity at different sites and crystal faces. The commonly used conversion functions for particle reactions that are not controlled by pore diffusion, as was determined for the reaction of iron ore concentrate particles, are listed in Table 4.1. 66 The conversion functions listed in Table 4.1 were tested first on the experimental data to find the best-fitting equation by plotting g(X) vs t. The residence time τ was calculated under the assumption of constant particle velocity and temperature profile inside the reactor by[9] 𝜏=𝑢 𝐿 𝑔 +𝑢𝑡 (4.3) where L is the length of the isothermal zone where temperature variation remained within ±20 K; 𝑢𝑔 is the centerline gas velocity; 𝑢𝑡 = 𝑑𝑝2 𝑔(𝜌𝑝 − 𝜌𝑔 )/18𝜇 is the terminal velocity of a falling particle in laminar flow. The isothermal temperature defined as above is considered as ‘experimental temperature’ for the purpose of the preliminary rate analysis in this work. CFD is then used to refine the rate parameters by accounting for the variations of temperature and velocity in the reactor. After obtaining the empirical function, the reaction order was obtained by plotting 𝑚 𝑘𝑎𝑝𝑝 from Eq. (4.1) vs 𝑝𝐶𝑂 −( 𝑝𝐶𝑂2 𝑚 𝐾 ) , where K is the equilibrium constant for the reduction of FeO by CO. It should be noted that the partial pressure dependence on CO2 is set to be the same as the reaction order of CO. The reason for this is that the rate expression of a reaction must satisfy a zero net rate at equilibrium.[21] The effect of particle size on the reaction rate was obtained by comparing experimental results on different particle sizes. The last step is to determine primitive values for the activation energy and pre-exponential factor by plotting 𝐿𝑛 𝑘 vs 1/T. The CFD technique was then used to further refine the values of activation energy and pre-exponential factor obtained to eliminate the errors associated with the assumptions of a zone of uniform temperature and constant particle velocity. The algorithm to determine the activation energy and preexponential factor is shown in Figure 4.5, which has been detailed in previous 67 publications,[11, 14] and thus the detailed procedure will not be described here. 4.5 Mathematical Modeling The Euler-Lagrange approach was used to model the two-phase flow, in which the gas phase was treated as a continuum in the Eulerian frame of reference while the solid phase was tracked in the Lagrangian mode. For the gas phase, the realizable k-ε model[22] was chosen for simulating the spread of the carrier gas jet. Radiation from the wall was taken into account using the discrete ordinate (DO) model.[23] The general steady-state transport equation for the gas phase is given by ∇ ∙ 𝜌𝑢 ⃗ 𝜙 − ∇ ∙ Γ𝜙 ∇𝜙 = 𝑆 𝜙 (4.4) where 𝜙 represents the generic dependent variable such as temperature, species, and velocity. 𝛤𝜙 is the effective transport coefficient of the dependent variable and 𝑆 𝜙 is the source term. The readers are referred to the previous work[11] on the specific form of the governing equations of the gas phase. The effect of interparticle collision was neglected as the solid volume fraction in the rector is of the order of 10-6. The addition of particles to the gas phase at this low level does not significantly affect the gas phase velocity and temperature. Furthermore, cold model tests indicated that most of the particles traveled along the centerline, as described in the Appendix. Therefore, a one-way coupling approach was used in tracking the concentrate particles, and only the centerline velocities and temperatures of the gas phase from the CFD results were used. The governing equations for the solid phase are listed in Table 4.2. 68 4.6. Results and Discussion 4.6.1. Reaction Model By plotting g(X) vs t, it was determined that the reduction of magnetite concentrate particles in both temperature ranges can be described by the nucleation and nuclei growth kinetics with an Avrami parameter n of 0.5. The evolution of new phase in the reaction depends on the nucleation rate and the growth rate. Although the Avrami value is usually within 1-3, many researchers have reported an Avrami value less than 1 (mostly 0.5) or greater than 3. Wunderlich[24] showed that the Avrami parameter can have values ranging from less than 1 to above 6. He mentioned that the Avrami value can be less than 1 in the case of limiting growth and athermal nucleation. The Avrami parameter (n) depends on the nucleation rate and growth mechanism, and n = 0.5 was attributed to a fast nucleation rate where all the nuclei form first while the growth is diffusion-controlled in one dimension causing thickening of large plates after the edge impingement.[25-28] The SEM micrographs of the particles after reduction shown in Figure 4.6 also corroborate the selection of such a model. For small particles, the period of the formation and growth of nuclei occupies essentially the entire conversion range. The formation of FeO and Fe overlap in different parts of the particle rather than strictly following the stepwise reduction from Fe3O4 to FeO and then from FeO to Fe. 4.6.2. Reaction Order To determine the order of reaction with respect to CO, its partial pressure was varied by using N2. Although the variation of CO partial pressure is small since the excess CO in all experiments was greater than 500% based on complete reduction, the 69 small effect of CO2 generated (always less than 5% of the input CO) was corrected by the addition of the term 𝑝𝐶𝑂2 /𝐾 in the rate expression. This increases the accuracy of the term 𝑓(𝑝𝐶𝑂 , 𝑝𝐶𝑂2 ) obtained. It was shown previously[9] that a logarithmic or an arithmetic mean represents the average driving force, respectively, for first-order or half order dependence with respect to 𝑝𝐶𝑂 . The 𝑝𝐶𝑂2 at the outlet of reactor was calculated based on the reduction degree of the particles. The first-order dependence and half order dependence on CO partial pressure were tested. The first-order dependence (m = 1) gave the best fit of the experimental data, as can be seen from Figures 4.7 and 4.8. 4.6.3. Particle Size Effect The particle size effect on the reduction degree in the two temperature ranges is shown in Figures 4.9 and 4.10, respectively. It indicates that the reduction degree does not have a strong dependence on the particle size in the lower temperature range [1473 K (1200 °C) to 1623 K (1350 °C)], which was also seen in the reduction of magnetite concentrate particles by H2 in similar temperature range.[11] But in the higher temperature range, the reduction rate was found to be inversely proportional to the particle size, which was also found in the reduction of magnetite concentrate particles by H2 in similar temperature range.[29] The function of size effect function was determined to be ℎ(𝑑𝑝 ) = 1 and ℎ(𝑑𝑝 ) = 𝑑𝑝−1 in the two temperature ranges, respectively. This is consistent with the reaction of a molten sphere with the reaction taking place at the surface. 70 4.6.4. Activation Energy After obtaining the partial pressure dependence function and the particle size function, the activation energy and the pre-exponential factor were obtained by plotting 𝐿𝑛 𝑘 vs 1/T, which is shown in Figure 4.11. The activation energy values for the two temperature ranges were calculated to be 430 kJ∙mol-1 and 73 kJ∙mol-1, respectively. The corresponding pre-exponential factors were determined to be 1.21 ×1013 atm-1∙s-1 and 2.39×103 µm∙atm-1∙s-1, respectively. 4.6.5. CFD Refinement Despite the temperature variations near the top and bottom part of the reactor, its effects on the size dependence and the values for n and m are expected to be negligible. Activation energy, however, is strongly affected by temperature variations. Therefore, the refinement of rate analysis by CFD was focused on the more accurate value of activation energy and corresponding pre-exponential factor. A wide range of pre-exponential factor and activation energy values around the preliminary values above were discretized and scanned for searching the optimized values. The search ranges of activation energy and pre-exponential factor are listed in Table 4.3. The best-fit activation energy and preexponential factor for the reduction of magnetite concentrate particles by CO were 2 obtained when the least mean of the squared errors, ∑i(𝑋cal,i − 𝑋exp,i ) /𝑁 were obtained, as also listed in Table 4.3. Typical calculated particle reduction degrees along the reactor length obtained using the optimum values of activation and pre-exponential factor, together with the corresponding experimental reduction degrees and temperature profiles, are shown in 71 Figures 4.12 and 4.13. It is seen that the simulated reduction degree values match the experimental values very well. The results computed based on the CFD method demonstrates that a low temperature region existed adjacent to the water-cooled injection tube in the top part, and the particle temperature decreased gradually in the bottom part of the reactor. It is seen from Figures 4.12 and 4.13 that it takes about 0.1 m from the tip of the injection tube for the particle temperature to reach the ‘uniform’ isothermal temperatures. The existence of this low temperature zone in the upper part of the drop-tube reactor affects the calculation of real particle residence time. This leads to the refinement of the values of the activation energy and pre-exponential factor. From Figure 4.13, it is also seen that larger particles are heated more slowly. The comparisons between the calculated reduction degrees using the optimum values of activation energy and pre-exponential factor and the experimental values for all the experimental runs are shown in Figure 4.14. It is noted that the optimum kinetic parameters obtained in this work predict the reduction degrees very well as the correlation coefficients between the calculated values and corresponding experimental results are high in both cases. 4.6.6. Complete Expressions Combining all the rate parameters obtained through the steps described above, the complete rate equations for the reduction of magnetite concentrate particles by CO in the temperature range 1473 K (1200 ˚C) to 1623 K (1350 ˚C) and 1623 K (1350 °C) to 1873 K (1600 °C) are given, respectively, as: 72 Integral form: [−𝐿𝑛(1 − 𝑋)]1/0.5 = 1.07 × 1014 × 𝑒 − 451,000 𝑅𝑇 ∙ (𝑝𝐶𝑂 − 𝑝𝐶𝑂2 𝐾 ) ∙ 𝑡; Differential form: 451,000 𝑝𝐶𝑂2 𝑑𝑋 = 5.35 × 1013 ⋅ 𝑒 − 𝑅𝑇 ⋅ (𝑝𝐶𝑂 − ) ⋅ (1 − 𝑋) ⋅ [− ln(1 − 𝑋)]−1 𝑑𝑡 𝐾 1473 K (1200 ˚C) < T < 1623 K (1350 ˚C) (4.8) Integral form: [−𝐿n(1 − 𝑋)]1/0.5 = 6.45 × 103 × 𝑒 − 88,000 𝑅𝑇 ∙ [𝑝𝐶𝑂 − ( 𝑝𝐶𝑂2 𝐾 )] ⋅ 𝑑𝑝−1 ∙ 𝑡; Differential form: 88,000 𝑝𝐶𝑂2 𝑑𝑋 −1 = 3.225 × 103 ⋅ 𝑒 − 𝑅𝑇 ⋅ (𝑝𝐶𝑂 − ) ⋅ (𝑑𝑝 ) ⋅ (1 − 𝑋) ⋅ [− ln(1 − 𝑋)]−1 𝑑𝑡 𝐾 1623 K (1350 ˚C) < T < 1873 K (1600 ˚C) (4.9) where R is 8.314 J∙mol-1∙K-1, p is in atm, K is the equilibrium constant for the reduction of FeO by CO, dp is in µm, and t is in seconds. The apparent activation energy is one of the most important kinetic parameters of the iron oxide reduction. The activation energy values obtained various investigations are listed in Table 4.4. However, caution must be exercised when comparing the values considering that the value of apparent activation energy depends on the temperature range, particle morphology, particle size, and the presence of impurities. There are not too many reports on the reduction of fine iron oxide by carbon monoxide in the temperature range used in this work. Most of the work was done at temperatures lower than 1000 ˚C. The work on Fe2O3/Fe3O4 to Fe using pellets was not covered in Table 4.4 as the effect of pore diffusion was usually involved in those cases. The activation energy for the reduction of Fe2O3/Fe3O4 to FeO or Fe2O3 to Fe3O4 by CO 73 is not comparable to reduction to metallic iron since the last stage from FeO to Fe occupies the largest conversion range. The activation energy in Ref. [16] is considered somewhat unreliable as this value was obtained from only two temperatures. The temperature range in Ref. [30] ranges from the lower temperature range to the higher temperature range, thus spanning the conditions of reduction in solid state and molten phase. The value of the activation energy reported lies, perhaps as expected, in-between the two activation energy values in the two respective temperature ranges of this work. One also needs to be careful of the CO2 effect as the value of equilibrium constant in this temperature range is lower than 0.2 rendering the term 𝑝𝐶𝑂2 /𝐾 significant in a CO+CO2 atmosphere. The activation energy for the reduction of hematite concentrate particles by CO reported in Ref. [14] is lower than that of magnetite concentrate particle reduction in the same temperature range. There are several reasons leading to this difference. Firstly, the morphologies of hematite concentrate particles and magnetite concentrate particles are different, the latter being more crystalline.[32] Secondly, although both reactions were described by the nucleation and growth model, the Avrami values of these two reactions were 1.0 and 0.5, respectively.[14, 33] The Avrami constant of 0.5 in the reduction of magnetite concentrate particles indicated that the growth of the newly formed nuclei was controlled by solid-state diffusion in one dimension which caused thickening of large plates after the edge impingement.[25-28] Although the use of CFD technique should in principle allow one to determine the rate expression even from experiments done under spatially varying temperature, velocity and gas concentrations, the accuracies of the developed rate equations and parameters are greatly enhanced by performing the experiments designed to keep these conditions as 74 uniform as possible, in combination with CFD simulation to account for small variations that are difficult to completely eliminate. This is the approach we used in this work. 4.7. Conclusions An algorithm that takes into consideration the velocity and temperature variations in the top and bottom parts of the DTR combined with CFD simulation of the flow and heat transfer was used to analyze the kinetics of the reduction of magnetite concentrate particles by CO. This work yielded activation energy values of 451 kJ∙mol-1 and 88 kJ∙mol-1, respectively, in the temperature range of 1473 K (1200 °C) - 1623 K (1350 °C) and 1623 K (1350 °C) - 1873 K (1600 °C), compared with, respectively, 430 kJ∙mol-1 and 73 kJ∙mol-1 without this refinement. The comparisons between the reduction degrees obtained experimentally at various temperatures and partial pressures of CO and the computed values showed that the nucleation and growth rate expression with an Avrami parameter n = 0.5 and a first-order dependence on the partial pressure of CO describes well the kinetics of magnetite concentrate particle reduction within the ranges of conditions of this investigation. For the temperature range of 1473 K (1200 °C) to 1623 K (1350 °C), the reduction degree does not have a strong dependence on the particle size, while in the temperature range of 1623 K (1350 °C) to 1873 K (1600 °C), the reduction rate was found to be inversely proportional to the particle size with a size function of ℎ(𝑑𝑝 ) = 𝑑𝑝−1 . 75 4.8 Acknowledgments The support and resources from the Center for High Performance Computing at the University of Utah are gratefully acknowledged. The authors acknowledge the financial support from the U.S. Department of Energy under Award Number DE-EE0005751 with cost share by the American Iron and Steel Institute (AISI) and the University of Utah. 4.9. Nomenclature Ap : surface area of particle (m2) dp : geometric mean particle diameter of a screen fraction (m) k: rate constant for reduction of magnetite concentrate particles by CO (atm-1∙s-1 or µm∙atm-1∙s-1) K: equilibrium constant mp : particle mass (kg) pi: partial pressure of species i (atm) T : gas phase temperature (K) Tp : particle temperature (K) ui : gas phase velocity components (m∙s-1) up: particle velocity (m∙s-1) X: reduction degree (fraction) εp: particle emissivity 𝜌𝑃 : particle density (kg∙m-3) σ: Stefan-Boltzmann constant (W∙m-2∙K-4) 76 4.10. References 1. H. Y. Sohn: Steel Times Int., 2007, vol. 31, pp. 68-72. 2. H. Y. Sohn, M. E. Choi, Y. Zhang, and J. E. Ramos: AIST Trans., 2009, vol. 6 (8), pp. 158-65. 3. M. E. Choi and H. Y. Sohn: Ironmaking Steelmaking, 2010, vol. 37 (2), pp. 81-88. 4. H. K. Pinegar, M. S. Moats, and H. Y. Sohn: Steel Res. Int., 2011, vol. 82 (8), pp. 95163. 5. H. K. Pinegar, M. S. Moats, and H. Y. Sohn: Ironmaking Steelmaking, 2012, vol. 39 (6), pp. 398-408. 6. H. K. Pinegar, M. S. Moats, and H. Y. Sohn: Ironmaking Steelmaking, 2013, vol. 40 (1), pp. 44-49. 7. H. Y. Sohn and M. Olivas-Martinez: JOM, 2014, vol. 66 (9), pp. 1557-64. 8. H. Y. Sohn and Y. Mohassab, J. Sust. Metall., 2(3), 216–227 (2016). 9. H. Wang and H. Y. Sohn: Metall. Mater. Trans. B, 2013, vol. 44 (1), pp. 133-45. 10. F. Chen, Y. Mohassab, T Jiang and H. Y. Sohn: Metall. Mater. Trans. B, 2015, vol. 46 (3), pp. 1133-45. 11. D. Fan, Y. Mohassab, M. Elzohiery and H. Y. Sohn: Metall. Mater. Trans. B, 2016, vol. 47 (3), pp. 1669-80. 12. F. Chen, Y. Mohassab, S. Zhang and H. Y. Sohn: Metall. Mater. Trans. B, 2015, vol. 46 (4), pp. 1716-28. 13. D. Fan, H. Y. Sohn, Y. Mohassab and M. Elzohiery: Metall. Mater. Trans. B, 2016, vol. 47 (6), pp 3489-500. 14. D. Fan, H. Y. Sohn and M. Elzohiery: Metall. Mater. Trans. B, 2017, vol. 48 (5), pp. 2677-84. 15. A. V. Bradshaw and A. G. Matyas: Metall. Mater. Trans. B, 1976, vol. 7 (1), pp. 8187. 16. F. Tsukihashi, K. Kato, K.-I. Otsuka and T. Soma: Trans. ISIJ, 1982, vol. 22 (9), pp 688-95. 17. R. Adamian and R. V. Bustamante: Congr. Anu. ABM , 1985, vol. 40 (1), pp 473-84. 18. H. S. Ray and N. Kundu: Thermochim. Acta., 1986, vol. 101, pp. 107-18. 77 19. S. K. Dutta and A. Chosh: ISIJ Int., 1993, vol. 33 (11), pp. 1168-73. 20. M. Su, J. Ma, X. Tian and H. Zhao: Fuel Process. Technol., 2017, vol. 155, pp. 16067. 21. H. Y. Sohn: Metall. Mater. Trans. B, 2014, vol. 45 (5), pp. 1600-02. 22. T.-H. Shih, W. W. Liou, A. Shabbir, Z. Yang and J. Zhu: Comput. Fluids, 1995, vol. 24 (3), pp. 227-38. 23. E. H. Chui and G. D. Raithby: Numer. Heat Trans. B-Fund., 1993, vol. 23 (3), pp. 269-88. 24. B. Wunderlich, Macromolecular Physics: Crystal Nucleation, Growth, Annealing, Academic Press, New York, 1976. 25. J. W. Christian, The Theory of Transformations in Metals and Alloys: Vol. 1, Pregamon Press, Oxford, 1975. 26. P. Altúzar and R. Valenzuela: Mater. Lett., 1991, vol. 11 (3), pp. 101-4. 27. F. L. Cumbrera, and F. Bajo: Thermochim. Acta., 1995, vol. 266, 315-30. 28. M. J. Starink: J. Mater. Sci., 1997, vol. 32 (15), pp. 4061-70. 29. M. Elzohiery, Y. Mohassab, A. Abdelghany, S. Zhang, F. Chen and H. Y. Sohn: EPD Congress, 2016, pp 41-49. 30. Y. Qu, Y. Yang, Z. Zou, C. Zeilstra, K. Meijer and R. Boom: ISIJ. Int., 2015, vol. 55, pp. 952-60. 31. W. Liu, J. Lim, M. A. Saucedo, A. H. Hayhurst, S. A. Scott and J. S. Dennis: Chem. Eng. Sci., 2014, vol 120, pp149-66. 32. A. Chatterjee, Sponge Iron Production by Direct Reduction of Iron Oxide, 2nd ed., PHI Learning Private Limited, New Delhi, 2012, pp. 65-6. 33. H. Y. Sohn, Y. Mohassab, M. Elzohiery, D. Fan and A. Abdelghany, in Applications of Process Engineering Principles in Materials Processing, Energy and Environmental Technologies, S. Wang et al. (eds.), Springer, 2017, pp 15-23. DOI 10.1007/978-3319-51091-0_2 4.11. Appendix: Cold Model Experiment A schematic representation of the cold model system is shown in Figure 4.A.1. The tube in this apparatus was a transparent acrylic tube with an ID of 8 cm. The same 78 powder feeding system and water-cooled tube as described in Section 4.3 were used. Particles were fed into the tube at a rate of 100 mg/min with N2 acting as the carrier gas. The flow rate of carrier gas in this test was maintained at 0.3 L/min. N2 at a flow rate of 8 L/min was fed to pass through a honeycomb. The particles were captured by a plastic container filled with water. A high speed camera was placed at a position within the main part of the flow to capture the dispersion of the particles inside the tube. The effective size of the image taken by the high speed camera was 8 cm × 10 cm. The particle dispersion is shown in Figure 4.A.2, indicating that the particles were mostly confined in a narrow region near the centerline in this apparatus designed to represent the conditions of DTR. 79 𝑋 𝑑𝑋 Table 4.1. Commonly Used Conversion Functions, 𝑔(𝑋) = ∫0 Reaction Model Nucleation and growth (n = 0.5 ~ 4) Contraction model (n = 1 ~ 3) Power law model (n = 1 ~ 4) Pore blocking model Reaction-order model (n = 0 ~ 3) 𝑓(𝑋) 𝑓(𝑋) 𝑔(𝑋) 𝑛 (1 − 𝑋)[− 𝐿n(1 − 𝑋)]1−1/n [− 𝐿n(1 − 𝑋)]1/n 𝑛 ⋅ (1 − 𝑋)1−1/𝑛 1 − (1 − 𝑋)1/𝑛 𝑛 ⋅ 𝑋1−1/𝑛 𝑋1/𝑛 𝜆·exp (– X/𝜆) exp ( X/𝜆)-1 (1 − 𝑋)𝑛 (𝑛 − 1)−1 [(1 − 𝑋)1−𝑛 − 1] Table 4.2. Solid Phase Governing Equations Particle Movement: Energy: Oxygen removal: 𝑑𝑢𝑝,𝑖 𝑑𝑡 𝑚𝑝 𝑐𝑝,𝑑 = 𝐹𝐷 (𝑢𝑖 − 𝑢𝑝,𝑖 ) + 𝑔𝑖 (𝜌𝑝 −𝜌) 𝜌𝑝 (4.5) 𝑑𝑇𝑝 𝑑𝑚𝑝 = ℎ𝐴𝑝 (𝑇 − 𝑇𝑝 ) − Δ𝐻𝑟𝑒𝑎𝑐 + 𝜀𝑝 𝐴𝑝 𝜎(𝑇 4 − 𝑇𝑝4 ) 𝑑𝑡 𝑑𝑡 (4.6) 𝑑𝑋 𝑑𝑡 𝑚 = 𝑘 ∙ (𝑝𝐶𝑂 −( 𝑝𝐶𝑂2 𝑚 𝐾 ) ) ∙ 𝑓(𝑋) ⋅ ℎ(𝑑𝑝) (4.7) Table 4.3. Searching Ranges and Optimized Values of the Kinetics Parameters E range k0 range Best-fit values Lower temp. range Higher temp. range 300 ~ 550 (kJ∙mol-1) 30 ~ 150 (kJ∙mol-1) 3.41×105 ~ 2.93×1015 atm-1·s-1 1000 ~ 2.5×105 atm-1·s-1· µm E = 451 kJ∙mol-1, k0=1.07×1014 atm-1·s-1 E = 88 kJ∙mol-1, k0 = 6.45×103 atm-1·s-1· µm 80 Table 4.4. Apparent Activation Energy from Literature for the Reduction of Fine Iron Oxide Particles Gas Pure CO CO+CO2 CO+N2 Reactions Ref. 555 - 725 750 - 850 1450 and 1600 1275 - 1480 700 - 900 850 - 1000 1200 - 1350 Activation Energy (kJ∙mol-1) 94±5 31±5 131 270 110±20 111 241 Fe2O3 → Fe3O4 (74 -149 µm) Fe2O3 → Fe3O4 (74 -149 µm) FeO → Fe (avg. 25 µm) Fe2O3 → Fe (45 - 53 µm) FeO → Fe (300 - 425 µm) Fe2O3 → FeO (180 - 200 µm) Fe2O3 → Fe (avg. 21µm) 1200 - 1350 451 Fe3O4 → Fe (20 - 53µm) 1350 - 1600 88 Fe3O4 → Fe (20 - 53µm) [17] [17] [16] [30] [31] [20] [14] This work This work Temperature Range (˚C) Figure 4.1. SEM micrograph for particles reduced at T = 1846 K (1573 °C) under 𝑝𝐶𝑂 = 0.3 atm. Reduction degree = 0.62 81 Figure 4.2. SEM micrograph for particles reduced at T = 1558 K (1285 °C) under 𝑝𝐶𝑂 = 0.85 atm, Reduction degree = 0.27. Figure 4.3. Schematic representation of the high temperature drop-tube reactor (DTR). 82 Figure 4.4. The powder feeder system: (a) components and, (b) working mechanism. Figure 4.5. A block diagram of the algorithm for kinetics parameter optimization. 83 Figure 4.6. SEM micrographs of samples with different reduction degrees at average isothermal temperature of 1512 K (1239 °C) and 1558 K (1285 °C). Figure 4.7. Relationship between 𝑘𝑎𝑝𝑝 and 𝑓(𝑝𝐶𝑂 , 𝑝𝐶𝑂2 )𝑎𝑣𝑔 for reduction by CO in the lower temperature range. lm stands for logarithmic mean; am stands for arithmetic mean.[9] (𝑝𝐶𝑂 , 𝑝𝐶𝑂2 in atm) 84 Figure 4.8. Relationship between 𝑘𝑎𝑝𝑝 and 𝑓(𝑝𝐶𝑂 , 𝑝𝐶𝑂2 )𝑎𝑣𝑔 for reduction by CO in the higher temperature range. lm stands for logarithmic mean; am stands for arithmetic mean.[9] (𝑝𝐶𝑂 , 𝑝𝐶𝑂2 in atm) 85 Figure 4.9. Effect of particle size in the lower temperature range. Figure 4.10. Effect of particle size in the higher temperature range. 86 Figure 4.11. Ln(k) vs 104/T for reduction by CO: (a) lower temperature range, (b) higher temperature range. Figure 4.12. Calculated profiles of particle temperature and unreacted fractions along the reactor length in the lower temperature range. − − −: pCO = 0.6 atm, gas flow rate: CO = 2.0 L/min, N2 = 0.8 L/min; − ∙ −: pCO = 0.45 atm, gas flow rate: CO = 1.0 L/min, N2 = 0.9 L/min; − ∙∙ −: pCO = 0.45 atm, gas flow rate: CO = 1 L/min, N2 = 0.9 L/min; dp = 22.5 µm for all cases. The temperature values in the legend represent the ‘experimental temperatures’. 87 Figure 4.13. Calculated profiles of particle temperature and unreacted fractions along the reactor length in the higher temperature range. − − −: pCO = 0.6 atm, gas flow rate: CO = 1.1 L/min, N2 = 0.46 L/min; − ∙ −: pCO = 0.45 atm, gas flow rate: CO = 0.8 L/min, N2 = 0.7 L/min; − ∙∙ −: pCO = 0.6 atm, gas flow rate: CO = 2.2 L/min, N2 = 0.92 L/min. The temperature values in the legend represent the ‘experimental temperatures’. Figure 4.14. Comparisons between the calculated reduction degrees vs. experimental results: (a) Lower temperature range 1473 K (1200 °C) to 1623 K (1350 °C); (b) Higher temperature range 1623 K (1350 °C) to 1873 K (1600 °C). 88 Figure 4.A.1. Schematic representation of the cold model system. Figure 4.A.2. Image of particle dispersion inside the cold model of DTR. CHAPTER 5 RATE ANALYSIS OF MAGNETITE CONCENTRATE PARTICLE REDUCTION: PART IV: KINETICS OF MAGNETITE CONCENTRATE PARTICLES REDUCTION BY H2+CO MIXTURES THROUGH CFD MODELING De-Qiu Fan, Mohamed Elzohiery, Yousef Mohassab, and H. Y. Sohn Department of Metallurgical Engineering, University of Utah, Salt Lake City, Utah 84112, USA This is Chapter 5 of the dissertation and it is a manuscript for a journal article that we will submit for publishing. 5.1. Abstract The kinetics of the reduction of magnetite concentrate particles by H2+CO mixtures has been investigated in drop-tube reactors (DTR) with the objective of obtaining rate expressions that can be applied to the design and analysis of a novel flash ironmaking reactor. The experimental temperature varied from 1423 K (1150 °C) to 1873 K (1600 °C), which is the expected operational temperature range of a flash ironmaking reactor. The H2/CO ratio was varied from 0.5 to 2, which is the typical composition range of the product gas from the partial oxidation of natural gas. The experimental data were 90 analyzed separately in two temperature ranges 1423 K (1150 °C) - 1623 K (1350 °C) and 1623 K (1350 °C) - 1873 K (1600 °C), as the magnetite concentrate particles tend to fuse and melt at temperatures above 1623 K (1350 °C) changing the reduction mechanism. Although DTR is designed and operated to maintain uniform temperature and gas concentrations as closely as possible, it is difficult to completely eliminate some variations. Thus, CFD simulations were used to more accurately account for these variations. The particles were tracked using the Lagrangian approach in which the trajectory and velocity were determined by integrating the equation of particle motion. Synergistic effects were observed in the reduction by H2+CO mixtures compared with the simple summation of contributions of the individual component gases. In order to account for this enhanced effect, an enhancement factor, which is a function of temperature and partial pressure of H2, was introduced in the rate expression. Keywords: Flash ironmaking, Drop-tube reactor, CFD, Reduction kinetics, CO+H2 mixture, Magnetite concentrate 5.2 Introduction The blast furnace process accounts for more than 90% of the annual production of primary iron, according to the World Steel Association, with the balance by alternative processes such as direct-reduction and smelting reduction. Due to high energy consumption, environmental pollution and CO2 emissions, lots of efforts have been devoted to finding an alternative low-cost process which is more environmentally friendly. Processes like direct reduction in the fluidized beds or in the shaft furnaces (MIDREX) have been successfully developed and built in the iron and steel industry. 91 These processes, however, cannot be operated at high temperatures due to the sticking and fusion of the particles. Therefore, they are not sufficiently intensive to replace the blast furnace. A novel ironmaking technology is now under development at the University of Utah.[1-16] In this process, iron is produced from fine iron oxide concentrate in a flash reduction process, utilizing hydrogen, natural gas, or coal gas as the reducing agent as well as the fuel. Flash ironmaking allows the direct use of iron oxide concentrate to bypass the pelletization/sintering and cokemaking steps in the blast furnace reactor, which will significantly decrease the CO2 emissions as well as the energy consumption. The gaseous reduction of iron oxide was investigated previously by many other researchers but such work was more often than not focused on pellets or particles larger than concentrate particles at temperatures lower than the level expected in a flash reduction process. Johnson and Davison[17] studied the reduction of taconite concentrate particles ranging in size from 5 to 45 μm in a heated cyclone. Natural gas was burned to preheat the cyclone to 1273 K (1000 °C) - 1473 K (1200 °C) prior to switching to a plasma system to maintain an average operating temperature of 1773 K (1500 °C) or higher. The iron ore concentrate particles were reduced using CO as the reducing gas, and a reduction degree of 80-95% was achieved. Kazonich et al.[18] built a prototype reactor using rocket technology in which magnetite concentrate particles (-44 µm) were completely reduced in less than 50 ms. The temperature range in their reactor was 1200 - 2500 °C, and the pressure was maintained between 12.8 and 16.8 atm. Propane (C3H8) was partially oxidized by pure oxygen to produce a reducing atmosphere that consisted of mainly of H2 and CO. 92 Takeuchi et al.[19] investigated the in-flight reduction of spherical wüstite particles ranging from 32 to 45 μm in diameter in a CH4 atmosphere. Their experimental temperature range was between 1100 and 1300 °C. At 1573 K (1300 °C), complete reduction was achieved at a residence time of less than 1 second under an 11% CH4-N2 atmosphere. The experimental results showed that the reduction degrees achieved with CH4 were higher than those obtained with either H2 or CO. They proposed that CH4 first decomposed into carbon and hydrogen, which then reduced wüstite to form the initial metallic iron shell around the particle. Then, the deposited carbon diffused through the metallic iron shell to further reduce the remaining wüstite. They concluded that the chemical reaction of diffused carbon and wüstite on the Fe-FeO was the determining step. Geassy et al.[20] investigated the reduction of Fe2O3 briquettes with H2+CO mixture in the temperature range of 973 K (700 °C) - 1373 K (1100 °C). They showed that adding H2 to CO enhanced the reduction rate. Reduction rate with pure H2 gas was faster than that with pure CO, and a mixture gave intermediate reduction rate. Moon et al.[21] studied the reduction kinetics of hematite compacts (1.78 cm in diameter and 0.78 cm in height) by H2+CO mixtures between 1073 K (800 °C) and 1223 K (950 °C) in a thermogravimetric analyzer (TGA). They reported that the reaction rate increased with an increase of H2 content in the gas mixture, and the carbon deposition decreased with temperature (from 2.94 wt.% at 1073 K (800 °C) to 0.48 wt.% at 1223 K (950 °C). The reduction rate by H2 was 2 - 3 times faster than that by CO. They also obtained the effective diffusivity values for H2 and CO, and the value of that for H2 was 3 - 4 times higher than that of CO. They determined that chemical reaction at the oxide/iron interface dominated the reaction initially, and then the reduction rate was controlled by 93 the diffusion of reducing gas through the product layer until the end of reduction. The activation energy was determined to be in the range of 19.8 - 42.1 kJ∙mol-1 depending on the CO/H2 composition. Bonalde et al.[22] investigated the reduction kinetics of hematite pellets, 1.07 and 1.24 cm in diameter, with a mixture of CO and H2 at 1123 K (850 °C). The gas composition used in the experiments was 55.7% H2, 34% CO, 6.3% CO2 and 4% CH4 by volume. The effect of external mass transfer was eliminated by using a sufficiently high gas flow rate. The grain model was used to describe the kinetics of the reduction reaction. The reduction process was mixed controlled during the first stage of the reduction, while gas diffusion dominated the last stage of the reduction. Sohn and coworkers[9-16] have investigated the gaseous reduction of iron oxide concentrate particles under various experimental conditions using a drop-tube reactor (DTR) aimed at generating a database to be used for the design of a flash ironmaking reactor. In the most likely near-term industrial application of this technology, the partial combustion of natural gas with industrial oxygen is expected to be used to produce the hot reducing gas. The gas mixture thus obtained contains reducing gases H2 and CO. In this work, the kinetics of the reduction of magnetite concentrate particles by H2+CO mixtures was investigated in drop-tube reactors (DTR). The experimental temperature was varied from 1423 K (1150 °C) to 1873 K (1600 °C), which is the expected operational temperature range of a flash ironmaking reactor. The H2/CO ratio was varied from 0.5 to 2, which is the typical composition range of the product gas from the partial oxidation of natural gas. The purpose of this work was to generate the rate expression for the reduction of magnetite concentrate particles by H2+CO mixtures based 94 on the rate expressions of reduction by individual component gases. CFD analysis was used to improve the accuracy by eliminating the effect of temperature variation of the particles encountered in the DTR. 5.3. Experimental Work The magnetite concentrate used in this work was the same as those used in our previous work.[9, 11, 13] Experiments were carried out in two different temperature ranges in two different drop-tube reactors since these particles tend to fuse and melt at temperatures above 1623 K (1350 °C) due to the presence of gangue contents. Experiments in the lower temperature range [1423 K (1200 °C) - 1623 K (1350 °C)] were conducted in the same reactor as was used in our previous publications,[9-12, 14] and the same DTR used for the reduction of magnetite concentrate particles by carbon monoxide[15] was used for the higher temperature range [1423 K (1200 °C) - 1623 K (1350 °C)]. The two reactors have been described in detail in these references and thus will not be further elaborated on here. The reactor tubes were made of 99.8% purity alumina, which had inner diameters of 5.6 cm and 8 cm, respectively, in the lower and higher temperature drop-tube reactors. The carrier gas used in all experiments was either N2 or CO, which was maintained at a constant flow rate of 0.3 L/min. (Flow rates in this work were all calculated at 298 K (25 ºC) and 0.85 atm, the atmospheric pressure at Salt Lake City.) A water-cooled tube was used so that no chemical reaction of the particle took place before entering the reactor. A cylindrical porous alumina honeycomb was inserted at the top part of the reactor to enhance the mixing and preheating of the reducing gas as well as to distribute 95 the input gas uniformly over the reactor cross-section. Dried and screened magnetite concentrate particles of size fraction 20 - 25, 32 38, or 45 - 53 µm were used in the experiments. In the flash ironmaking process, the particle residence time is expected to be 2 ~ 10 seconds. The gas flow rates were adjusted in this work to provide these residence times while allowing desired reduction degrees depending on other experimental conditions such as temperature and gas composition. During the experiment, the particle feeding rate was controlled in the range of 30 ~ 200 mg/min. The mass ratio of particles to gas was kept at ≤ 0.05. For all the experiments, the feed rates of the individual reducing gases (H2 and CO) were in more than 500% excess of the minimum required amount for complete reduction by each gas to ensure that the gaseous reactant concentration remained essentially constant over the entire reactor length. The reacted powder was collected in a powder collector at the bottom of the reactor. 5.4. Mathematical Model The Euler-Lagrange approach was used to model the two-phase flow, in which the gas phase was treated as continuum in the Eulerian frame of reference while the solid phase was tracked in the Lagrangian frame of reference. For the gas phase, the realizable k-ε model[23] was chosen, and the particles followed the gas near the centerline. Radiation from the wall was taken into account using the discrete ordinate (DO) model.[24] The general steady state transport equation is given by ∇ ∙ 𝜌𝑢 ⃗ 𝜙 − ∇ ∙ Γ𝜙 ∇𝜙 = 𝑆 𝜙 (5.1) where 𝜙 represents the generic dependent variable, like gas phase temperature and gas 96 phase velocity. 𝛤𝜙 is the effective transport coefficient of the dependent variable, and 𝑆 𝜙 is the source term. The readers are referred to previous work[11] on the specific form of the governing equations of the gas phase. The effect of interparticle collision was neglected as the solid volume fraction in the rector was of the order of 10-6. The addition of particles to the gas phase at this low level does not significantly affect the gas phase velocity and temperature. The particles were mostly concentrated in a narrow region near the reactor centerline as observed by a particle image velocimetry (PIV) system. Therefore, a one-way coupling approach was used in tracking the concentrate particles, and only the centerline velocities and temperatures of the gas phase from the CFD results were needed to track the particles. The governing equations for the solid phase are listed in Table 5.1. The kinetic parameters for the reduction of magnetite concentrate particles by each component gas are summarized in Table 5.2. The general rate expression 𝑑𝑋 𝑑𝑡 for component gases in Eq. (5.4) is: 𝑚 𝑑𝑋 𝑚𝑗 𝑝 | = 𝑘𝑗 ∙ [𝑝𝑗 𝑗 − ( 𝐾𝑗𝑂 ) 𝑑𝑡 𝑗 𝑗 −𝑠 ] ∙ 𝑛𝑗 (1 − 𝑋)[− 𝐿n(1 − 𝑋)]1−1/𝑛𝑗 ⋅ 𝑑𝑝 𝑗 ; j = H2 or CO (5.5) 𝐸 where kj is the reaction rate constant for gas j, 𝑘𝑗 = 𝑘𝑜,𝑗 exp (− 𝑅𝑇𝑗 ); Kj is the equilibrium constant for the reduction of FeO by gas j; nj is the Avrami parameter; 𝑚𝑗 is the reaction order with respect to gas j; X is the reduction degree[9-14]defined as the ratio of the removed oxygen to the total removable oxygen in the concentrate particles. We use this global reduction degree, rather than distinguishing the formation of wüstite followed by iron, due to the fact that different phases of iron oxides coexist within the individual, irregularly shaped particle and in separate particles during the reduction process resulting 97 −𝑠𝑗 from varying reactivity at different sites and crystal faces; 𝑑𝑝 is the particle size effect function. Previous work[11] has demonstrated that the reduction rates by component gases were not affected by particle size for either H2 or CO in the lower temperature range [1423 K (1150 °C) - 1623 K (1350 °C)], whereas in the higher temperature range [1623 K (1350 °C) - 1873 K (1600 °C)], they were inversely proportional to the particle size. A simple additive relationship was first assumed between the overall oxygen 𝑑𝑋 𝑑𝑋 removal rate and removal rates by its component gases as 𝑑𝑋 = | + | , the results of 𝑑𝑡 𝑑𝑡 𝑑𝑡 𝐻2 𝐶𝑂 which are shown for experiments in three representative temperatures in Figure 5.1. It is seen that there was synergistic effect under the H2+CO mixture as the experimental results were always higher than the calculated results. Therefore, in order to account for the enhanced effect, an enhancement factor was multiplied to the contribution of H2, as shown in Eq. (5.4) in Table 5.1. This is based on the reasoning that most of the reduction was done by H2 in the temperature range investigated and CO mainly enhanced the H2 reduction rate by modifying the mechanism of hydrogen reduction. The contribution by CO, being rather small, was kept the same as that from CO alone. This can be seen by comparing the reaction rates under the same reaction temperatures, partial pressures and particle sizes from the individual rate expressions for CO and H2. The ratios of the reaction rate dX/dt of the individual gas at X=0.5 are listed in Table 5.3. The reaction rate of H2 under the same experimental conditions is always more than 20 times than that of CO. This has not taken into account that the partial pressure of H2 is almost twice as much as that of CO in a real flash reactor. Moreover, it requires a much higher CO/CO2 ratio (about 3), compared with a H2/H2O ratio of about one, to overcome the equilibrium limitation for the reduction by CO in the 98 temperature range expected for the flash ironmaking process. In Eq. (5.4), 𝛼(𝑇, 𝑝𝐶𝑂 , 𝑝𝐻2 ) is the enhancement factor which is assumed to be of the form 𝛼(𝑇, 𝑝𝐶𝑂 , 𝑝𝐻2 ) = (𝑎 𝑇 + 𝑏) ⋅ 𝑝 𝑝𝐶𝑂 𝐶𝑂 +𝑝𝐻2 ; T in K (5.6) with a and b the two parameters to be determined. Different values of a and b are tested and the optimum values determined when the calculated reduction degrees most closely match the experimental values. 5.5. Results and Discussion 5.5.1 Results A wide range of a and b values were discretized and scanned for searching the optimized values. The optimum values are listed in Table 5.4. In the lower temperature range, the temperature effect on this enhancement factor is negligible, whereas in the higher temperature range, temperature has a negative effect on this factor. Given that the H2/CO ratio is between 0.5 and 2, the value of the enhancement factor is between 0.43 and 0.87 in the lower temperature range. In the high temperature range, taking T = 1673 K (1400 °C) as an example, the enhancement factor is between 0.97 and 1.95 in the same H2/CO ratio range, while this enhancement factor will drop to only 0.3 ~ 0.6 when experimental temperature is increased to 1873 K (1600 °C) . Typical calculated reduction degrees along the reactor length obtained using the optimum values listed in Table 5.4, together with the corresponding experimental reduction degrees and temperature profiles, are shown in Figures 5.2 and 5.3. It is seen that the simulated reduction degree values match the experimental values very well. 99 The results computed based on the CFD method demonstrates that a low temperature region existed adjacent to the water-cooled injection tube in the top part, and the particle temperature decreased gradually in the bottom part of the reactor. It is seen from Figures 5.2 and 5.3 that it takes about 0.1 m from the tip of the injection tube for the particle temperature to reach the ‘uniform’ isothermal temperatures. The existence of this low temperature zone in the upper part of the drop-tube reactor affects the calculation of real particle residence time. From Figure 5.3, it is also seen that larger particles are heated more slowly. Examples of the contribution of CO toward the overall reduction reaction are shown in Figures 5.4 and 5.5 for two different temperatures at the same 𝑝𝐶𝑂 /𝑝𝐻2 = 2. It is seen that the contribution of CO is less than 2% at 1512 K, while at 1746 its contribution is somewhat higher at around 6%. The numerical value of this contribution must be considered somewhat approximate because the enhancement of the overall rate due to the presence of CO was all assigned to the reaction of H2. Nonetheless, it is clear that the contribution by CO is rather small compared with that by H2, even when its partial pressure is twice that of hydrogen. The comparisons between the calculated reduction degrees using the optimum values of a and b and the experimental values are shown in Figures 5.6 and 5.7 for the reduction of magnetite concentrate particles by H2+CO mixtures in the lower temperature range [1423 K (1150 °C) - 1623 K (1350 °C)] and higher temperature range [1623 K (1350 °C) - 1873 K (1600 °C)], respectively. It is noted that the optimum values of a and b obtained predict the reduction degrees very well. Thus, the rate expression proposed as Eq. (5.4) by incorporating an enhancement factor can be used with confidence to describe 100 the reduction of magnetite concentrate particles by H2+CO mixtures. 5.5.2. Complete Rate Expressions The complete rate equations for the reduction of magnetite concentrate particles by H2+CO mixtures in the temperature ranges 1423 K (1150 ˚C) - 1623 K (1350 ˚C) and 1623 K (1350 °C) - 1873 K (1600 °C) are given, respectively, as: 𝑑𝑋 𝑑𝑡 𝑑𝑋 𝑑𝑡 = (1 + 1.3 ⋅ 𝑝 𝑝𝑐𝑜 𝑐𝑜 +𝑝𝐻2 ) ∙ = [1 + (−0.01𝑇 + 19.65) ⋅ 𝑝 𝑑𝑋 𝑑𝑡 | + 𝐻2 𝑝𝑐𝑜 𝑐𝑜 +𝑝𝐻2 ] ∙ 𝑑𝑋 1423 K < T < 1623K | 𝑑𝑡 𝐶𝑂 𝑑𝑋 𝑑𝑡 | + 𝐻2 𝑑𝑋 | 𝑑𝑡 𝐶𝑂 (5.7) 1623 K < T < 1873K (5.8) where 𝑑𝑋 | 𝑑𝑡 𝐻2 𝑑𝑋 | 𝑑𝑡 𝐻2 = 1.23 × 107 exp (− = 6.07 × 107 exp (− 196,000 )∙ 𝑅𝑇 180,000 )∙ 𝑅𝑇 (𝑝𝐻2 − (𝑝𝐻2 − 𝑝𝐻2𝑂 𝐾𝐻2 𝑝𝐻2𝑂 𝐾𝐻2 ) ∙ (1 − 𝑋) 1423 K < T < 1623K; ) ∙ (1 − 𝑋) ⋅ 𝑑𝑝−1 1623 K < T < 1873K; 𝑝𝐶𝑂2 𝑑𝑋 451,000 ) ∙ (𝑝𝐶𝑂 − ) ∙ (1 − 𝑋)[− 𝐿n(1 − 𝑋)]−1 | = 5.35 × 1013 exp (− 𝑑𝑡 𝐶𝑂 𝑅𝑇 𝐾𝐶𝑂 1423 K < T < 1623K; 𝑝𝐶𝑂2 𝑑𝑋 88,000 ) ∙ (𝑝𝐶𝑂 − ) ∙ (1 − 𝑋)[− 𝐿n(1 − 𝑋)]−1 ⋅ 𝑑𝑝−1 | = 3.225 × 103 exp (− 𝑑𝑡 𝐶𝑂 𝑅𝑇 𝐾𝐶𝑂 1623 K < T < 1873K; where R is 8.314 J∙mol-1∙K-1, p is in atm, Kj is the equilibrium constant for the reduction of FeO by gas j, dp is particle size in µm, and t is in seconds. Although the use of CFD technique should in principle allow one to determine the rate expression even from experiments done under spatially varying temperature, velocity and gas concentrations, the accuracies of the developed rate equations and parameters are greatly enhanced by performing the experiments designed to keep these conditions as 101 uniform as possible, in combination with CFD simulation to account for small variations that are difficult to completely eliminate. This is the approach we used in this work. 5.6. Conclusions A one-way coupling CFD method was used in this work to account for the effects of the small variations of particle temperature and velocity inside the reactor. Synergistic effects were observed in reduction by H2+CO mixtures compared with the simple sum of contributions by the individual component gases. In order to account for this enhanced effect, an enhancement factor which is a function of temperature and partial pressures of H2 and CO was introduced in the rate expression. The enhancement factors for the reductions in the lower and higher temperature ranges were determined to be 1.3 ⋅ 𝑝𝐶𝑂 𝑝𝐶𝑂 +𝑝𝐻2 and (−0.01𝑇 + 19.65) ⋅ 𝑝 𝑝𝑐𝑜 𝑐𝑜 +𝑝𝐻2 , respectively, which indicates that temperature has a negligible impact on this factor in the lower temperature range, whereas in the higher temperature range, this factor decreases as temperature increases. The comparisons between the reduction degrees obtained experimentally at various temperatures and partial pressures of H2 and CO and the computed values showed that the introduction of an enhancement factor can be used to describe the reduction of magnetite concentrate particles by H2+CO mixtures adequately within the ranges and conditions of this investigation. 5.7. Acknowledgments The support and resources from the Center for High Performance Computing at the University of Utah are gratefully acknowledged. The authors acknowledge the 102 financial support from the U.S. Department of Energy under Award Number DEEE0005751 with cost share by the American Iron and Steel Institute (AISI) and the University of Utah. 5.8. Nomenclature Ap : surface area of particle (m2) dp : geometric mean particle diameter (m) Ki: equilibrium constant mp : particle mass (kg) pi: partial pressure of species i (atm) T : gas phase temperature (K) Tp : particle temperature (K) ui : gas phase velocity components (m∙s-1) up: particle velocity (m∙s-1) X: reduction degree εp: particle emissivity 𝜌𝑃 : particle density (kg∙m-3) σ: Stefan-Boltzmann constant (W m-2 K-4) 5.9. References 1. H. Y. Sohn: Steel Times Int., 2007, vol. 31, pp. 68-72. 2. H. Y. Sohn, M. E. Choi, Y. Zhang, and J. E. Ramos: AIST Trans., 2009, vol. 6 (8), pp. 158-65. 3. M. E. Choi and H. Y. Sohn: Ironmaking Steelmaking, 2010, vol. 37 (2), pp. 81-88. 103 4. H. K. Pinegar, M. S. Moats, and H. Y. Sohn: Steel Res. Int., 2011, vol. 82 (8), pp. 95163. 5. H. K. Pinegar, M. S. Moats, and H. Y. Sohn: Ironmaking Steelmaking, 2012, vol. 39 (6), pp. 398-408. 6. H. K. Pinegar, M. S. Moats, and H. Y. Sohn: Ironmaking Steelmaking, 2013, vol. 40 (1), pp. 44-49. 7. H. Y. Sohn and M. Olivas-Martinez: JOM, 2014, vol. 66 (9), pp. 1557-64. 8. H. Y. Sohn and Y. Mohassab, J. Sust. Metall., 2(3), 216–227 (2016). 9. H. Wang and H. Y. Sohn: Metall. Mater. Trans. B, 2013, vol. 44 (1), pp. 133-45. 10. F. Chen, Y. Mohassab, T Jiang and H. Y. Sohn: Metall. Mater. Trans. B, 2015, vol. 46 (3), pp. 1133-45. 11. D. Fan, Y. Mohassab, M. Elzohiery and H. Y. Sohn: Metall. Mater. Trans. B, 2016, vol. 47 (3), pp. 1669-80. 12. F. Chen, Y. Mohassab, S. Zhang and H. Y. Sohn: Metall. Mater. Trans. B, 2015, vol. 46 (4), pp. 1716-28. 13. D. Fan, H. Y. Sohn, Y. Mohassab and M. Elzohiery: Metall. Mater. Trans. B, 2016, vol. 47 (6), pp 3489-500. 14. D. Fan, H. Y. Sohn and M. Elzohiery: Metall. Mater. Trans. B, 2017, vol. 48 (5), pp. 2677-84. 15. M. Elzohiery, D. Fan, Y. Mohassab and H. Y. Sohn, The Kinetics of Hydrogen Reduction of Molten Magnetite Concentrate Particles, unpublished work, University of Utah, 2018. 16. D. Fan, M. Elzohiery, Y. Mohassab and H. Y. Sohn, The Kinetics of Carbon Monoxide Reduction of Magnetite Concentrate Particles through CFD Modeling, unpublished work, University of Utah, 2018. 17. T. Johnson and J. Davison: J. Iron Steel Inst. 1964, vol.202 (5), pp. 406-19. 18. G. Kazonich, T. Gribben, J. Walkiewicz and A. Clark: Extr. Metall. Copper, Nickel Cobalt, 1993, vol. 1, 1125-32. 19. N. Takeuchi, Y. Nomura, K.-i. Ohno, T. Maeda Nishioka, K. and M. Shimizu: Tetsuto-Hagane, 2008, vol. 94 (4), 115-20. 20. A. A. El-Geassy, K. A. Shehata and S. Y. Ezz: Trans. ISIJ, 1977, vol. 17 (11), 62935. 104 21. I. J. Moon, C-H. Rhee and D-J. Min: Steel Res. 1998, vol. 69 (8), 302-6. 22. A. Bonalde, A. Henriquez and M. Manrique: ISIJ Int. 2005, vol. 45 (9), 1255-60. 23. T.-H. Shih, W. W. Liou, A. Shabbir, Z. Yang and J. Zhu: Comput. Fluids, 1995, vol. 24 (3), pp. 227-38. 24. E. H. Chui and G. D. Raithby: Numer. Heat Tr. B-Fund., 1993, vol. 23 (3), pp. 26988. 105 Table 5.1. Solid Phase Governing Equations 𝑑𝑢𝑝,𝑖 Particle Movement: Energy: Overall Oxygen Removal: 𝑑𝑡 𝑚𝑝 𝑐𝑝,𝑑 𝑑𝑇𝑝 𝑑𝑡 𝑑𝑋 𝑑𝑡 = 𝐹𝐷 (𝑢𝑖 − 𝑢𝑝,𝑖 ) + = ℎ𝐴𝑝 (𝑇 − 𝑇𝑝 ) − 𝑑𝑚𝑝 𝑑𝑡 𝑔𝑖 (𝜌𝑝 −𝜌) (5.2) 𝜌𝑝 Δ𝐻𝑟𝑒𝑎𝑐 + 𝜀𝑝 𝐴𝑝 𝜎(𝑇 4 − 𝑇𝑝4 ) 𝑑𝑋 = [1 + 𝛼(𝑇, 𝑝𝐶𝑂 , 𝑝𝐻2 )] ⋅ | 𝑑𝑡 𝐻2 + 𝑑𝑋 (5.3) (5.4) | 𝑑𝑡 𝐶𝑂 Table 5.2. Kinetic Parameters for Reduction by Individual Component Gases[11, 15, 16] Reducing Gas H2 CO Ej (kJ∙mol-1) mj Nj sj 1.23 × 107 196 1 1 0 7 1423 - 1623 K 6.07 × 10 1.07 × 1014 180 451 1 1 1 0.5 -1 0 1623 - 1873 K 6.45 × 103 88 1 0.5 -1 Temperature Range 𝑘𝑜,𝑗 1423 - 1623 K 1623 - 1873 K Table 5.3. Comparison of the Reaction Rate at Different Temperatures with X=0.5 for Magnetite Reduction by CO and H2 Individually Temperature 𝑑𝑋 | 𝑑𝑡 𝐻2 / 𝑑𝑋 | 𝑑𝑡 𝐶𝑂 1423 K (1150 °C) 366 1523 K (1250 °C) 178 1573 K (1300 °C) 94 21 1723 K (1450 °C) 1773 K (1500 °C) 1823 K (1550 °C) 25 30 Table 5.4. Optimum Values for a and b a b Lower Temp. Range Higher Temp. Range 0 1.30 -0.01 19.65 106 𝑑𝑋 𝑑𝑋 Figure 5.1. Comparisons between the calculated reduction degrees by 𝑑𝑋 = | + | 𝑑𝑡 𝑑𝑡 𝑑𝑡 𝐻2 𝐶𝑂 vs. experimental results. − ∙ −: pCO=0.4 atm, pH2=0.2 atm, gas flow rate: CO: 1.6 L/min, H2: 0.8 L/min, N2: 1.0 L/min; − − −: pCO=0.15 atm, pH2=0.3 atm, gas flow rate: CO: 0.6 L/min, H2:1.2 L/min, N2: 1.6 L/min; − ∙∙ −: pCO=0.2 atm, pH2=0.1 atm, gas flow rate: CO: 0.6 L/min, H2: 0.3 L/min, N2: 1.6 L/min. Reactor inner diameter: 5.6 cm, dp=22.5 µm for all three cases. The temperature values in the legend represent the experimental temperatures. 107 Figure 5.2. Calculated profiles of particle temperature and unreacted fraction along the reactor length in the lower temperature range. − ∙ −: pCO=0.4 atm, pH2=0.2 atm, gas flow rate: CO: 1.6 L/min, H2: 0.8 L/min, N2: 1.0 L/min; − − −: pCO=0.15 atm, pH2=0.3 atm, gas flow rate: CO: 0.6 L/min, H2:1.2 L/min, N2: 1.6 L/min; − ∙∙ −: pCO=0.2 atm, pH2=0.1 atm, gas flow rate: CO: 0.6 L/min, H2: 0.3 L/min, N2: 1.6 L/min. Reactor inner diameter: 5.6 cm, dp=22.5 µm for all three cases. The temperature values in the legend represent the experimental temperatures. 108 Figure 5.3. Calculated profiles of particle temperature and unreacted fraction along the reactor length in the higher temperature range. − ∙ −: pCO=0.2 atm, pH2=0.1 atm, gas flow rate: CO: 1.6 L/min, H2: 3.2 L/min, N2: 8.8 L/min, dp=35 µm; − − −: pCO=0.1 atm, pH2=0.1 atm, gas flow rate: CO: 1.5 L/min, H2: 1.5 L/min, N2: 9.8 L/min, dp=49 µm; − ∙∙ −: pCO=0.1 atm, pH2=0.1 atm, gas flow rate: CO: 1.0 L/min, H2: 1.0 L/min, N2: 6.3 L/min. Reactor inner diameter: 8 cm, dp=22.5 µm. The temperature values in the legend represent the experimental temperatures. 109 Figure. 5.4. CO contribution to overall reduction at 1512 K: 𝑝𝐶𝑂 = 0.4 atm, 𝑝𝐻2 = 0.2 atm, gas flow rates: CO: 1.6 L/min, H2: 0.8 L/min, N2: 1.0 L/min. Figure. 5.5. CO contribution to overall reduction at 1512 K: 𝑝𝐶𝑂 = 0.2 atm, 𝑝𝐻2 = 0.1 atm, gas flow rates: CO: 1.6 L/min, H2: 3.2 L/min, N2: 8.8 L/min, dp = 35 µm. 110 Figure 5.6. Comparisons between the calculated reduction degrees vs. experimental results by H2 + CO mixtures in the lower temperature range Figure 5.7. Comparisons between the calculated reduction degrees vs. experimental results by H2 + CO mixtures in the higher temperature range CHAPTER 6 CFD SIMULATION OF LABORATORY FLASH REACTOR: PART I: CFD SIMULATION OF THE HYDROGEN REDUCTION OF MAGNETITE CONCENTRATE De-Qiu Fan, H. Y. Sohn, Yousef Mohassab and Mohamed Elzohiery Department of Metallurgical Engineering, University of Utah, Salt Lake City, Utah 84112, USA Published in Metallurgical and Materials Transactions B, Vol. 47 (6), 2016. 6.1 Abstract A three-dimensional computational fluid dynamics (CFD) model was developed to study the hydrogen reduction of magnetite concentrate particles in a laboratory flash reactor representing a novel flash ironmaking process. The model was used to simulate the fluid flow, heat transfer and chemical reactions involved. The governing equations for the gas phase were solved in the Eulerian frame of reference while the particles were tracked in the Lagrangian framework. The change in the particle mass was related to the chemical reaction and the particle temperature was calculated by taking into consideration the heat of reaction, convection and radiation. The stochastic trajectory model was used to describe particle dispersion due to turbulence. Partial combustion of H2 by O2 injected through a nonpremixed burner was also simulated in this study. The 112 partial combustion mechanism used in this model consisted of seven chemical reactions involving six species. The temperature profiles and reduction degrees obtained from the simulations satisfactorily agreed with the experimental measurements. Keywords: Flash reactor, CFD, Ironmaking, Hydrogen, Magnetite concentrate 6.2. Introduction A transformational technology for alternate ironmaking is under development at the University of Utah. In this novel ironmaking process, iron is produced by the direct gaseous reduction of iron oxide concentrate in a flash reduction process by utilizing hydrogen, natural gas or coal gas as the reducing agent and fuel. This process aims at significant energy saving and reduction of CO2 emissions compared with the conventional blast furnace (BF) ironmaking process. The gases used in the process undergo partial oxidation to generate the process heat while providing a reducing atmosphere for the reduction of iron oxide. A number of experimental and simulation studies relevant to this novel process have been performed by Sohn and coworkers[1-10] aimed at generating a database to be used for the design of a flash ironmaking reactor. Choi and Sohn[3] investigated the kinetic feasibility of the proposed process and proved that the H2 reduction rate of magnetite concentrate particles was fast enough to obtain 90-99% reduction within 1-7 seconds in the temperature range of 1473 K - 1773 K (1200 ºC - 1500 ºC). Process simulation and economic feasibility analysis carried out by Pinegar et al.[4,5] demonstrated that energy consumption can be reduced significantly by this novel process compared with the BF process. Detailed rate expressions of H2 and CO reduction of hematite 113 concentrate particles in the temperature range of 1423 K to 1623 K (1150 ºC to 1350 ºC) were developed by Chen et al.[8, 10] Fan et al.[9] analyzed the H2 reduction rate of magnetite concentrate particles with the aid of CFD and developed a rate expression for the H2 reduction of magnetite concentrate particles in the temperature range of 1423 K to 1623 K (1150 ºC to 1350 ºC). A CFD model was developed by Sohn and Perez-Fontes[11] to investigate the H2 partial combustion, and obtained good agreements with experimental results reported in the literature. A large pilot-scale flash reactor has been constructed[12] and its commissioning has just been completed. Along with the experimental data, CFD models are useful tools in process design and optimization of an industrial reactor. The CFD model can also be used to investigate the various transport phenomena taking place in the new process. Numerous examples of using CFD as an effective tool in industrial metallurgical furnaces have been reported in the literature. Ariyama and coworkers[13-16] developed a three-dimensional computation fluid dynamics and discrete element method (CFD-DEM) model to analyze the gas phase flow and solid movement in the blast furnace. The model was used to investigate the effect of gas injection at different shaft levels. Lekakh and Robertson[17] proposed a new approach for the analysis of the melt flow in metallurgical vessels by using CFD simulation and used it for the design and optimization of different steelmaking tundishes. Huda et al.[18, 19] developed comprehensive CFD models to investigate the fluid flow, reaction kinetics and heat transfer of the zinc slag fuming process with both top- and tuyere-blown smelting furnaces. A CFD model built by Liu et al.[20] was used to investigate the fluid flow, temperature and species concentration distributions in a pilotscale rotary hearth furnace. 114 The purpose of this work was to develop a three-dimensional CFD model to study the fluid flow, heat transfer and chemical reactions involved in a laboratory flash ironmaking reactor using the commercial software package Ansys Fluent. User-defined functions (UDFs) for particle physical properties and chemical reaction kinetics were developed and implemented. Combustion mechanism that consisted of seven chemical reactions was incorporated via a separate chemical-kinetic mechanism data[21] file. Particle information regarding residence time and reduction degree were evaluated in the Lagrangian framework. The CFD model was validated by using the experimental reduction degrees and measured temperature profiles. 6.3. Mathematical Model 6.3.1. Physical Model The laboratory flash ironmaking reactor used in this work is schematically represented in Figure 6.1. It consisted of an electric heating system, electric power control system, gas delivery system and pneumatic powder feeding system. The reactor tube was made of stainless steel 316 with 0.19 m ID and 2.13 m length. A nonpremixed burner nozzle made of Inconel with four feeding crescent-shaped inlets for the fuel (H2) and four cylindrical inlets for oxygen, shown in Figure 6.4 (b), was used as the burner. Magnetite concentrate particles were fed through the two side injection ports on the upper flange of the reactor at a constant rate with N2 as the carrier gas. The side injection ports were installed on either side of the burner with an angle of 22.5˚ from the vertical axis of the reactor tube. The specific positions of the injection ports are shown in Figure 6.2. The quench chamber and the collection bin were not included in the simulation due to the 115 negligible reactions in these regions where temperature was lower than 500 K (227 ºC). Concentrate particles were fed continuously at 100-140 g/h for about an hour in each experiment after the reactor temperature stabilizes for an hour. Therefore, the operation can be assumed to be at steady state. Only steady state conditions were simulated in this work. 6.3.2. Fluid Flow The following steady state continuity equation and the Reynolds averaged NavierStokes equation were solved: 𝜕 𝜕𝑥𝑖 𝜕 𝜕𝑥𝑗 𝜕𝑝 𝜕 𝜕𝑢 (𝜌𝑢𝑖 ) = 𝑆𝑝 𝜕𝑢 (6.1) 2 𝜕𝑢 𝜕 (𝜌𝑢𝑖 𝑢𝑗 ) = − 𝜕𝑥 + 𝜕𝑥 [𝜇 (𝜕𝑥 𝑖 + 𝜕𝑥𝑗 − 3 𝛿𝑖𝑗 𝜕𝑥𝑙 )] + 𝜕𝑥 (−𝜌𝑢𝑖′ 𝑢𝑗′ ) + 𝜌𝑔𝑖 + 𝐹𝑝,𝑖 (6.2) 𝑖 𝑗 𝑗 𝑙 𝑖 𝑗 where  is the gas mixture density, which is calculated based on each of the constitutive component (Yi represents the mass fraction of species i ), as follows 𝜌 = 𝑅𝑇 ∑ 𝑝 𝑖 𝑌𝑖 /𝑀𝑤,𝑖 (6.3) The source terms in Eq. (6.1) and Eq. (6.2) arise from interactions between gas species and solid. The source term Sp represents the net rate of mass addition to the gas phase per unit volume due to the gas-solid reaction. Fp,i represents the volumetric momentum exchange rate between the continuum phase (gas) and discrete phase (solid particles) due to the drag force exerted on the particle, which will be discussed in the next section. The flow of the gas stream in the reactor was turbulent, especially in the upper region of the reactor. A turbulence model is needed for the calculation of the Reynolds 116 stress term in Eq. (6.2);   uiuj . One of the weaknesses of the standard k-ε model lies in the model equation for the dissipation rate (ε), which causes erroneous prediction of the spread of the axisymmetric round-jet. The realizable k-ε model proposed by Shih et al.[22] was intended to address these deficiencies of traditional k-ε models by adopting a new model equation for dissipation (ε) based on the dynamic mean-square vorticity fluctuation. These authors demonstrated that this method yields better prediction of the dissipation of axisymmetric jets. Thus, the realizable k-ε model was chosen in this study to calculate the turbulent viscosity required for computing the Reynolds stress term in Eq. (6.2). 𝜕 𝜕𝑥𝑖 𝜕 𝜕𝑥𝑖 (𝜌𝑘𝑢𝑖 ) = (𝜌𝜀𝑢𝑖 ) = 𝜕 𝜕𝑥𝑖 𝜕 𝜕𝑥𝑖 𝜇 𝜕𝑘 [(𝜇 + 𝜎 𝑡 ) 𝜕𝑥 ] + 𝐺𝑘 + 𝐺𝑏 − 𝜌𝜀 − 𝑌𝑀 + 𝑆𝑘 𝑘 𝜇 𝑖 𝜕𝜀 𝜀2 𝑖 √ [(𝜇 + 𝜎𝑡 ) 𝜕𝑥 ] + 𝜌𝐶1 𝑆𝜀 − 𝜌𝐶2 𝑘+ 𝜀 𝜀 + 𝐶1𝜀 𝑘 𝐶3𝜀 𝐺𝑏 + 𝑆𝑘 𝑣𝜀 (6.4) (6.5) The k and ε obtained from the above equations are used to calculate the turbulent viscosity according to the following equation: 𝜇𝑡 = 𝜌𝐶𝜇 𝑘 2 /𝜀 (6.6) and the Reynolds stress term   uiuj in Eq. (6.2) is calculated as: 𝜕𝑢 𝜕𝑢 2 𝜕𝑢 −𝜌𝑢𝑖′ 𝑢𝑗′ = 𝜇𝑡 (𝜕𝑥 𝑖 + 𝜕𝑥𝑗 ) − 3 (𝜌𝑘 + 𝜇𝑡 𝜕𝑥𝑙) 𝛿𝑖𝑗 𝑗 𝑖 𝑙 (6.7) 6.3.3. Heat Transfer Heat transfer is of particular importance in the flash ironmaking process as the temperature distribution inside the reactor greatly affects the heating of the iron concentrate particles, which in return affects the kinetics of the particle reaction. The governing equation for the energy balance in the gas phase is given as: 117 𝜕 𝜕𝑥𝑖 𝑇 where, ℎ𝑔 = ∑𝑖 𝑌𝑖 ∫𝑇 𝑟𝑒𝑓 𝜕 (𝜌𝑢𝑖 ℎ𝑔 ) = 𝜕𝑥 ( 𝑘𝑒𝑓𝑓 𝜕𝑇 𝑖 𝜕𝑥𝑖 ) + 𝑄𝑟 + 𝑆𝑔 (6.8) 𝑐𝑝,𝑖 𝑑𝑇represents the specific enthalpy of the gas mixture. The two source terms on the right-hand side of Eq. (6.8) represent the net volumetric heat transfer by gas phase radiation and heat addition/loss to the gas phase due to the reduction reaction of iron concentrate particles by H2 per unit volume, respectively. A correct prediction of the volumetric radiation source term in Eq. (6.8) is critical in obtaining an accurate temperature distribution due to the fact that the radiation plays a significant role in heating particles. The radiative transfer equation (RTE) is as follows, in which for simplicity the gas mixture was assumed to be gray and thus the spectral dependency term is neglected: 𝑑𝐼 =𝜅 𝑑𝑠 𝑛2 𝜎𝑇 4 𝜋 𝜎𝑝 4𝜋 − 𝜅𝐼 − (𝜅𝑝 + 𝜎𝑝 )𝐼 + 𝐸𝑝 + 4𝜋 ∫0 𝐼(𝑠𝑖 ) Φ(𝑠𝑖 , 𝑠)𝑑Ω𝑖 (6.9) The most absorbing species in the relevant gas mixture is H2O and thus the contributions from other gas species were neglected. The weighted-sum-of-gray-gases model[23, 24] (WSGGM) was used to evaluate the absorptivity (  ) of the gas mixture, which is a reasonable compromise between the oversimplified gray gas model and a complete model that takes into account particular absorption bands for nongray gases. The scattering coefficient of the gas mixture was assumed zero. The existence of the particles in the gas stream adds two extra terms to Eq. (6.9) representing the attenuation and emitting effects of particles, namely the third term and the forth term on the RHS, respectively. The equivalent particulate absorption and scattering coefficients were calculated by averaging the values for all the particles contained within the control volume of interest when tracking the discrete phase, as follows: 118 1 1 1 𝑁 𝑁 𝜅𝑝 = 𝑉 ∑𝑁 𝑖=1 𝐴𝑝,𝑖 𝜀𝑝,𝑖 , 𝜎𝑝 = 𝑉 ∑𝑖=1(1 − 𝜎𝑝,𝑖 )(1 − 𝜀𝑝,𝑖 )𝐴𝑝,𝑖 , and 𝐸𝑝 = 𝑉 ∑𝑖=1 𝐴𝑝,𝑖 4 𝜀𝑝,𝑖 𝜎𝑇𝑝,𝑖 𝜋 (6.10) where N is the total number of particles existing in the control volume, Ap,i is the surface area of particle i, and V is the volume of the control volume of interest. The radiative properties of single particles will be discussed in Section 6.3.5. 6.3.4. Species Transport As multiple species were involved during the experiment, each component of the gas mixture has to be solved for individually. The mass conservation equation for each of the constitutive components in terms of mass fraction is given by: 𝜕 𝜕𝑥𝑗 𝜕𝐽 (𝜌𝑌𝑖 𝑢𝑗 ) = − 𝜕𝑥𝑗 + 𝑅𝑖 + 𝑆𝑝,𝑖 𝑗 (6.11) where Yi is the mass fraction of species i, Ri is the net rate of production of the species i by chemical reaction (detailed chemical reactions will be covered later) and Si is the net rate of mass addition to the species i from the particle phase. A simplified Fick’s-law correlation was used for the mass diffusion flux 𝑱𝑖 in Eq. (6.12), which is expressed as: 𝜇 𝑱𝑖 = − (−𝜌𝐷𝑖,𝑚 + 𝑆𝑐𝑡 ) ∇𝑌𝑖 − 𝐷𝑇,𝑖 𝑡 ∇𝑇 𝑇 (6.12) The coefficient of the first term in Eq. (6.12) combines the effects of molecular diffusion and turbulent diffusion. The turbulent Schmidt number Sct was chosen to be 0.7 in this work. The second term accounts for diffusion due to thermal gradient. 119 6.3.5. Combustion Mechanism The H2 partial combustion mechanism used in this study consists of seven chemical reactions involving six species, which are listed in Table 6.1.[11, 25] In order to take the turbulence-chemistry interaction into consideration, the eddy dissipation concept (EDC)[26] approach was adopted. The forward reaction rate constant for each of the elementary reaction is given by: 𝑘𝑓,𝑖 = 𝐴𝑇 𝛾 exp (− 𝐸𝑎,𝑖 𝑅𝑇 ) (6.13) For the reverse reactions, the backward reaction rate constants were linked to the forward reactions by the equilibrium constant: 𝑘 𝑘𝑏,𝑖 = 𝐾𝑓,𝑖 (6.14) 𝑐,𝑖 6.3.6. Particle Tracking The particle phase was treated as a discrete phase. Interparticle collisions were neglected as the volume fraction of particles in this system was lower than 10-3[27]. The force balance that equates the particle inertia with the forces (mainly gravitational force and drag force) acting on the particle is expressed in the Lagrangian frame of reference as: 𝑑𝑢𝑝,𝑖 𝑑𝑡 = 𝐹𝐷 (𝑢𝑝,𝑖 − 𝑢𝑖 ) + 𝑔𝑖 (𝜌𝑝 −𝜌) 𝜌𝑝 (6.15) The concentrate particle was assumed as solid sphere and force was evaluated with FD evaluated by: 18𝜇 𝐶𝐷 𝑅𝑒 𝐹𝐷 = 𝜌 2 𝑝 𝑑𝑝 24 and the drag coefficient used in Eq. (6.16) was calculated as:[28] (6.16) 120 0.44, 𝐶𝐷 = { 24 (1 𝑅𝑒 + 0.15𝑅𝑒 𝑅𝑒 > 1000 𝑅𝑒 ≤ 1000 0.678 ), (6.17) In order to account for the turbulent dispersion of particles, the stochastic tracking model[29] was used. A heat balance on the particle that relates the particle temperature to convection and radiation was also applied, resulting in the following equation: 𝑚𝑝 𝑐𝑝,𝑑 𝑑𝑇𝑝 𝑑𝑡 = ℎ𝐴𝑝 (𝑇 − 𝑇𝑝 ) − 𝑓ℎ 𝑑𝑚𝑝 𝑑𝑡 ∆𝑟 𝐻𝑟𝑒𝑎𝑐 + 𝜀𝑝 𝐴𝑝 𝜎(𝑇𝑠4 − 𝑇𝑝4 ) (6.18) in which the term dmp/dt was related to particle chemical reaction rate. The rate expression used in this study was a global nucleation and growth rate expression for the reduction of magnetite concentrate particle by H2 [Fe3O4 + 4H2 = 3Fe + 4H2O], the general form of which is given by:[8-10] 𝑑𝑋 𝑑𝑡 𝑝𝐻2 𝑂 𝑚 𝐸 = 𝑛 ⋅ 𝑘0 exp (− 𝑅𝑇) [𝑝𝐻𝑚2 − ( ) ] 𝑑𝑝𝑠 ⋅ (1 − 𝑋)[−𝐿𝑛(1 − 𝑋)]1−1/𝑛 𝐾𝑒 (6.19) The kinetics parameters in Eq. (6.19) used in this work are listed in Table 6.2.[9] The equation for evaluating equilibrium constant is given in Appendix A. The reduction degree X [8-10] is defined as: 𝑚𝑝 1 𝑋 = 𝜔0 (1 − 𝑚0 ) (6.20) 𝑝 𝑂 where, 𝜔𝑂0 is the initial mass fraction of iron-bonded oxygen in magnetite in a particle, and 𝑚𝑝0 and 𝑚𝑝 are the initial and remaining mass of the particle, respectively. By substituting the definition of reduction degree X into Eq. (6.19), the term dmp/dt (which is also the mass balance equation of the particle) is obtained as 𝑑𝑚𝑝 𝑑𝑡 𝐸 𝑝𝐻2 𝑂 𝑚 = −𝜔𝑂0 𝑚𝑝0 ⋅ 𝑛 ⋅ 𝑘0 exp (− 𝑅𝑇) [𝑝𝐻𝑚2 − ( 𝐾𝑒 ) ] 𝑑𝑝𝑠 ⋅ (1 − 𝑋)[−𝐿𝑛(1 − 𝑋)]1−1/𝑛 (6.21) 121 The particle heat transfer coefficient was evaluated using the following correlation of Ranz and Marshall:[30] 𝑁𝑢 = ℎ𝑑𝑝 𝑘𝑔 1/2 = 2.0 + 0.6 𝑅𝑒𝑑 𝑃𝑟 1/3 (6.22) A value of 0.8 was chosen for both the particle emissivity  p and the particle scattering coefficient  p , recommended by Hahn and Sohn.[31-33] The particle specific heat was approximated as a mass fraction average of those for iron and magnetite during the reduction process. The physical properties of the particle are presented in Appendix A. 𝑐𝑝,𝑑 = 𝑋 ⋅ 𝑐𝑝,𝐹𝑒 + (1 − 𝑋) ⋅ 𝑐𝑝,𝐹𝑒3 𝑂4 (6.23) The sizes of the particles remain essentially unchanged during an experiment as SEM micrographs revealed (not shown here). The solid particle density equals the instantaneous particle mass divided by its volume as: 𝜌𝑝 = 𝜌𝑝,0 (1 − 𝜔𝑂0 𝑋) (6.24) 6.3.7. Boundary Conditions All the boundary conditions were chosen to match the experimental conditions. 6.3.7.1. Fluid Flow A mass flow rate was imposed at the H2 and O2 inlets. The operating pressure was kept at 86.1 kPa (the barometric pressure at Salt Lake City). A nonslip condition was applied to the reactor wall for the gas flow inside the reactor. At the outlet, the flow was assumed to be fully developed where the gradient for all variables in the exit direction 122 were zero. 6.3.7.2. Heat Transfer The temperatures of the gases at the inlet were set at room temperature 298 K (25 ºC). The wall temperature along the longitudinal direction of the reactor was measured and used as a first-type boundary condition. Two typical wall temperature profiles under different experimental conditions are shown in Figure 6.3. Despite the significantly different amounts of fuel and oxygen in the two cases, the two temperature profiles were essentially the same. Thus, it was assumed that the wall temperature profiles under other experimental conditions remained the same, as the amounts of fuel and oxygen fed in most of the other cases were similar to these two cases. For simplicity, the radiative properties of all the inner walls were assumed to be gray and diffuse. The values of 0.8 and 0.4[33] were chosen for the emissivity of the heavily oxidized stainless steel tube wall of the reactor and polished stainless steel surface of the burner, respectively. 6.4. Numerical Details The gas-phase governing equations were discretized and solved using the commercial CFD software package ANSYS FLUENT 15.0. Three-dimensional mesh was generated using ICEM-CFD ANSYS with a total number of 442,364 hexahedral dominating hybrid cells. Tetrahedral mesh was used only in the top part of the reactor to capture the complex geometric configuration of the burner and powder feeding ports, which are displayed in Figure 6.4. Mesh independency was confirmed by halving and doubling the number of cells without changing the computational results. Total particle 123 streams of 10,050 were released from the injection ports to establish a statistical representation of the spread of the particles due to turbulence. The particle trajectories and velocities were determined by numerically integrating the equation of particle motion, Eq. (6.15). As the particle trajectory was computed, Eqs. (6.18) and (6.21) were integrated to obtain the particle temperature and mass at the subsequent time step under the assumption that particle temperature and mass change slowly within a single time step. The calculation was carried out by a steady state pressure-based solver. The SIMPLE scheme[34] was chosen for handling the pressure-velocity coupling. A secondorder upwind scheme was chosen for momentum, species transport and energy equation discretization for the convection term. Two-way coupling calculations of the gas and particle phases were performed. 6.5. Results and Discussion 6.5.1. Model Validation 6.5.1.1. Combustion Mechanism Validation The combustion mechanism listed in Table 6.1 was validated elsewhere.[11] The predicted temperature and concentrations of major species (H2, H2O, N2, O2) as well as intermediate radical species by CFD simulation incorporating the combustion mechanism in Table 6.1 were compared with the experimental data reported in the literature[35, 36] for nonpremixed hydrogen jet flames. Sufficiently good agreement was achieved between the predicted and the experimental values.[11] 124 6.5.1.2. Temperature Validation Temperature along the centerline of the reactor was measured using a long K-type thermocouple during the experiment. The comparison of the computed temperature profiles and corresponding experimental measurement is given in Figure 6.5. It is evident that the gas temperature first spiked due to the flame and then dropped to the isothermal temperature of the reactor. Due to experimental difficulties, the temperature in the flame region was not measured. The computed and experimental gas temperatures agree well with each other overall except for some deviations at the end of the reactor. The reason for the latter is that this part of the reactor approached the exit of the reactor tube in which the tube was not surrounded by the insulation material and was thus exposed to the ambient air directly. Despite the disagreement, it does not cause significant errors in the calculated reduction degree of the magnetite concentrate particles as the chemical reaction at temperature lower than 1273 K (1000˚C) is relatively slow according the Eq. (6.19) and the reduction degree achieved within the short residence time of particle while descending in this region was negligible. 6.5.1.3. Reduction Degree Reduced particles samples were collected at the end of the reactor tube where a stainless steel bowl together with magnets were used for collecting the powder. The weight fraction of the total iron in the reduced samples was analyzed by ICP method and compared with that in the concentrate fed to determine the averaged reduction degree.[6, 8, 10] A Spectro Genesis SOP spectrometer supplied by SPECTRO Analytical Instruments Inc. (Mahwah, NJ) was used to analyze the samples. The reduction degree of magnetite 125 concentrate particles was calculated as percent removal of the oxygen combined with iron, assuming that the other components in the concentrate remain unchanged during reduction. This assumption is justified because the gangue components are small amounts of stable oxides that are not reduced under the experimental conditions and the concentrate contains little volatile compounds, as can be seen from Table 6.3. Thus, the reduction degree was calculated by subtracting the mass of removable oxygen remaining in the reduced sample of mass mt from the mass of oxygen combined with the same mass of iron in the concentrate of mass mi to be related to mt by iron balance. The derivation of this relationship must take into consideration the presence of the gangue components. 𝑋 (𝑝𝑐𝑡) = 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑚𝑎𝑠𝑠 𝑂−𝑚𝑎𝑠𝑠 𝑂 𝑖𝑛 𝑠𝑎𝑚𝑝𝑙𝑒 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑚𝑎𝑠𝑠 𝑂 𝑚 −𝑚 𝑡 𝑖 × 100 = 𝑚 (%𝑂) × 100 /100 𝑖 𝑖 (6.25) The iron balance yields 𝑚𝑡 (%𝐹𝑒)𝑡 = 𝑚𝑖 (%𝐹𝑒)𝑖 (6.26) which relates mi to mt through the iron contents in the concentrate and the sample after reduction for time t. Combining Eqs. (6.25) and (6.26), the reduction degree is obtained from the following: 𝑋 (𝑝𝑐𝑡) = 1−(%𝐹𝑒)𝑖 /(%𝐹𝑒)𝑡 (%𝑂)𝑖 /100 × 100 (6.27) where (%𝐹𝑒)𝑖 and (%𝐹𝑒)𝑡 are, respectively, the mass percentages of total iron in the sample before and after reduction; (%𝑂)𝑖 is the mass percentage of removable oxygen in the concentrate before reduction. A comparison of the calculated reduction degrees (averaged over all particle streams) and experimental values is shown in Figure 6.6. The reduction degrees obtained from CFD simulations satisfactorily agree with the experimental values, except for some 126 scatter in the region of low reduction degree. Good prediction for higher reduction degrees is important in the future design and optimization of larger flash reactors, as this novel process is aimed at producing iron at a high reduction degree (≥ 90 %). The experimental conditions are listed in Appendix B. 6.5.2. Velocity Field Figure 6.7 shows the streamline of the velocity field with H2 flow rate of 3600 L/ h. It can be seen that recirculation zone was formed in the top part of the reactor as a result of the entrainment of high velocity particle-laden jets coming out of the injection tubes. Similar recirculation zones were also seen with other experimental conditions. After the recirculation region, the gas stream travels downward along longitudinal axis of the reactor tube. The recirculation zone played an important role in dispersing the concentrate particles and in increasing the particle residence time in the top part of the reactor, which can be seen from the particle trajectories in Figure 6.8. The effect the recirculation zone had on the temperature profile can be seen in Figure 6.9. High temperature bumps were formed in the recirculation region as gas streams at higher temperatures originated from the combustion zone recirculated upward. In this context, the recirculation enhances the temperature homogeneity in the top part of the reactor. 6.5.3. Temperature Distribution The maximum flame temperatures for different experimental conditions are presented in Appendix B. The flame configuration inside the reactor was changed in some experiments by swapping the H2 and O2 feeding ports in the burner nozzle. In the 127 flame configuration with oxygen surrounding hydrogen (designated as O-H-O), O2 was fed through the crescent-shaped inlets with H2 feed streams confined to the center. The reverse flame configuration (designated as H-O-H) had the two gas streams reversed. The values of maximum flame temperature were lower in the O-H-O flame configuration compared with the H-O-H configuration in which the same amounts of O2 were consumed for combustion. A comparison of the temperature distributions with different fuel and oxygen feeding configurations is displayed in Figure 6.9. It was found that the temperature in the top side parts of reactor was elevated in the O-H-O flame configuration. The reason for this is that with the O-H-O flame configuration, the high temperature flame region was closer to the particle-laden jets and more high temperature gas streams were entrained into the recirculation zone, and hence, a better temperature homogeneity was achieved. The consequence of this also leads to an increase in the averaged particle reduction degrees (Appendix B) in the O-H-O flame configuration runs, in which the same amounts of O2 and solid feeding rate were used, maintaining the same excess driving force (EDF) as in the H-O-H flame configuration. 6.5.4. Species Distribution The species distribution inside the reactor directly affects the local EDF and thus the local chemical reaction rate. The local EDF is an indicator of how much excess H2 exists locally compared to the gas mixture in equilibrium with iron and wüstite, and is mathematically defined by the following equation: 128 ( 𝐸𝐷𝐹𝑙𝑜𝑐𝑎𝑙 = 𝑝𝐻 𝑝𝐻 2 2 ) −( ) 𝑝𝐻 𝑂 𝑝𝐻 𝑂 2 2 𝑙𝑜𝑐𝑎𝑙 𝑒𝑞 𝑝𝐻 2 ) ( 𝑝𝐻 𝑂 2 𝑒𝑞 ( = 𝑝𝐻 1 2 ) − 𝑝𝐻 𝑂 𝐾𝑒 2 𝑙𝑜𝑐𝑎𝑙 1 𝐾𝑒 𝑝𝐻2 = 𝐾𝑒 (𝑝 𝐻2 𝑂 ) −1 (6.28) 𝑙𝑜𝑐𝑎𝑙 Figure 6.10 shows the typical species distributions and corresponding local EDF distribution. The oxidation reactions are seen to take place very fast. It is also seen that H2 and H2O were uniformly distributed in most parts of the reactor, which is also observed under other experimental conditions. The local EDF shown in Figure 6.10 (c) indicates that the local EDF in the isothermal region was around 0.6. 6.5.5. Particle Residence Time The particle residence time is one of the most important experimental parameters in the flash ironmaking process. The particle residence time in this work is controlled by varying the gas flow rate. A total number of 10,050 particle streams were released from the two side injection ports in all simulation runs to establish a statistical representation of the particle spreading due to turbulence. The average particle residence time in each of the simulation runs is calculated by averaging all the particle streams. The results are listed in Appendix B. It is noted that τiso represents the average particle residence time where the particle temperature reaches the isothermal temperature (1448 ± 25 K (1175 ± 25 oC)) of the reactor. The reduction reaction of the magnetite concentrate particles by H2 takes place mostly during τiso. Trajectory (a) in Figure 6.8 did not pass through the flame zone and thus the particle did not react much before it entered the isothermal region, while trajectory (b) crossed the flame zone and about 15% reduction degree was achieved before the particle entered the isothermal zone. 129 6.6. Conclusions A three-dimensional CFD model was developed to simulate the gas particle twophase flow, heat transfer and chemical reaction in a laboratory flash reactor. The computed values of reduction degree and centerline temperature were compared with the experimentally measured results and satisfactory agreements were obtained. A recirculation zone was formed in the top part of the reactor. After the recirculation region, the gas stream travels downward along longitudinal axis of the reactor tube. The recirculation zone played an important role in dispersing the concentrate particles and increasing the particle residence time. The values of maximum flame temperature were lower in the O-H-O flame configuration compared with the H-O-H configuration, although the same amounts of O2 were consumed in the two cases. Better temperature homogeneity was achieved in the O-H-O flame configuration. The nonmixed gaseous combustion reached equilibrium composition very fast and within a small region of the reactor tube. The values of the averaged particle residence time in the O-H-O burner configuration were larger than in the H-O-H flame configuration, other conditions being the same. 6.7. Acknowledgments The technical support and resources provided by the Center for High Performance Computing at the University of Utah are gratefully acknowledged. The authors acknowledge the financial support from the U.S. Department of Energy under Award Number DE-EE0005751 with cost share by the American Iron and Steel Institute (AISI) and the University of Utah. 130 6.8. Nomenclature Ap: surface area of a particle (m2) cp,i : specific heat of species i in the mixture (J∙kg-1∙K-1) dp: geometric mean diameter of the screened particle (m) Di,m : mass diffusion coefficient for species i in the mixture (m2∙s-1) Ep: equivalent emission due to the presence of particles (W·m−3) hg: sensible heat of the gas mixture (J∙kg-1) I: radiative intensity (W·m−2) k: turbulent kinetic energy (J∙kg-1) keff: effective thermal conductivity (W∙m-1∙K-1): = kg+kt kg: gas thermal conductivity (W∙m-1∙K-1) Mw,i: molecular weight of species i (kg∙mol-1) p: pressure (pa) SP: the net rate of mass addition to the gas phase per unit volume T: gas phase temperature (K) Tiso: isothermal zone temperature (K) Tp: particle temperature (K) ui: gas phase velocity components (m∙s-1) up: particle velocity (m∙s-1) Yi: mass fraction of species i ε: turbulence dissipation rate (J∙kg∙s-1) εp: particle emissivity κ: absorption coefficient of the gas mixture (1∙m-1) 131 κp: equivalent absorption coefficient due to the particle presence (1∙m-1) μ: gas phase viscosity (N∙m∙s-2) ρ: gas phase density (kg∙m-3) ρp: particle density (kg∙m-3) σp: equivalent particle scattering factor (1∙m-1) 6.9. 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Zhou, Principles of gas-solid flows, Cambridge University Press, UK, 1998. 30. W. E. Ranz and W.R. Marshall: Chem. Eng. Prog., 1952, vol. 48 (4), pp. 173–80. 31. Y.B. Hahn and H.Y. Sohn: Metall. Trans. B, 1990, vol. 21 (6), pp. 945-58. 32. Y.B. Hahn and H.Y. Sohn: Metall. Trans. B, 1990, vol. 21 (6), pp. 959-66. 133 33. T. L. Bergman, A. S. Lavine, F. P. Incropera and D. P. DeWitt, Fundamentals of Heat and Mass Transfer, 7th ed., Wiley, USA, 2011. 34. J. H. Ferziger and M. Peric, Computational Methods for Fluid Dynamics, SpringerVerlag, Berlin, 2002. 35. R.S. Barlow and C.D. Carter: Combust. Flame, 1994, vol. 97 (3), pp. 261-80. 36. R.S. Barlow and C.D. Carter: Combust. Flame, 1996, vol. 104 (3), pp. 288-99. 37. HSC 5.11, Chemistry for Windows, Outokumpu Research, Oy, Pori, Finland, 2002. 6.10. Appendix A: Physical Properties of the Particle and Equilibrium Constant Physical properties of particle: Density:  p,0 =5170 kg∙m-3; The specific heat for Fe3O4 and Fe are evaluated by the general expression as:[37] (J∙kg-1∙K) 1 c p ,Fe3O4 or Fe = a1  a2T /1000  100000  a3T 2  a4T 2 /1000000 The values of the coefficients of Fe3O4 are: a1= 2052.42, a2 = -3773.30, a3 = -520.52, a4 = 3458.30; a1= 215.20, a2 = 313.27, a3 = 3695.00, a4 = 0; a1= 921.59, a2 = 0, a3 = 0, 298K <T ≤ 850K 850K <T ≤ 1870K a4 = 0; 1870K <T The values of the coefficients of Fe are: a1= 355.75, a2 = 393.42, a3 = -17.79, a4 = -57.17; 100 K <T ≤ 298 K a1= 570.72, a2 = -399.89, a3 = -63.01, a4 = 717.61; 298 K <T ≤ 800 K a1= 16663.82, a2 = -25880.11, a3 = -19295.30, a4 = 12117.48; 800 K <T ≤ 1043 K a1= -241188.85, a2 = 283943.72, a3 = 523025.09, a4 = -93852.75; 1043 K <T ≤ 1185 K 134 a1= 442.58, a2 = 133.64, a3 = -30.45, a1= -190.41, a2 = 553.94, a3 = 4927.14, a1= 823.68, a2 = 0, a3 = 0, a4 = 6.58; 1185 K <T ≤ 1667 K a4 = -67.88; 1667 K <T ≤ 1881 K a4 = 0; 1881 K <T Equilibrium constant: The equilibrium constant Ke data were obtained from the HSC chemistry 5.11 software package[37] and were fit to a polynomial form as follows: 𝐾𝑒 = 𝑏1 𝑇 7 + 𝑏2 𝑇 6 + 𝑏3 𝑇 5 + 𝑏4 𝑇 4 + 𝑏5 𝑇 3 + 𝑏6 𝑇 2 + 𝑏7 𝑇 + 𝑏8 where: b1= 1.60e-21, b2 = -1.01e-17, b3 = 2.54e-14, b4 = -3.16e-11; b5= 1.90e-08, b6 = -3.37e-06, b7 = -5.88e-04, b8 = 1.74e-01; T ≤ 1649 K b1= 0, b2 = 0, b3 = 0, b4 = 0; b5= 0, b6 = 7.75e-07, b7 = -3.43e-03, b8 = 4.41; 1649 K < T ≤ 1811 K b1= 0, b2 = 0, b3 = 0, b5= 0, b6 = 8.89e-08, b7 =-6.02e-04, b4 = 0; b8 = 1.53; 1881 K <T 135 6.11. Appendix B: Experimental and Simulation Results of Different Runs in the Laboratory Flash Reactor H2 O2 Cal. Exp. Max. Powder Res. Flame Flow Flow Redn. Redn. Flame Feeding Time Config. Rate Rate Degrees Degrees Temp. τiso (s) Rate (g/h) (L/h)* (L/h)* (%) (%) (K) H-O-H 918 130 84 80 2722 5.4 109 H-O-H 918 163 63 57 2805 5.6 128 H-O-H 178 2851 5 1200 118 80 83 H-O-H 193 1200 112 78 80 2879 5.1 H-O-H 222 1200 118 51 63 2901 5.2 H-O-H 259 2400 130 91 92 2966 3.6 H-O-H 384 2400 126 75 77 3017 3.7 O-H-O 384 2400 126 80 85 2790 4.2 H-O-H 579 3600 126 72 73 3030 2.9 O-H-O 579 3600 126 76 83 2898 3.3 H-O-H 606 3600 100 70 69 3034 2.9 H-O-H 639 3600 139 62 72 3041 2.9 H-O-H 672 3600 118 54 62 3047 3 *Flow rates are calculated at 298 K (25 ºC) and 0.85 atm (1 atm = 101.32 kPa) Table 6.1. H2-O2 Partial Combustion Mechanism Reaction 1 H2+O2=OH+OH 2 H+O2=OH+O 3 OH+H2=H2O+H 4 O+H2=OH+H 5 OH+OH=H2O+O 6 H+OH=H2O+M 7 H+H=H2+M A (cm3∙mol-1∙s-1) 0.170×1014 0.142×1015 0.316×108 0.207×1015 0.550×1014 0.221×1023 0.653×1018  0.0 0.0 1.8 0.0 0.0 -2.0 -1.0 Table 6.2. Kinetics Parameters Kinetics parameter n m s ko (atm-1∙s-1) E (kJ∙mol-1) Value 1 1 0 1.23×107 196 Ea (kJ∙mol-1) 2.015×105 6.862×104 1.268×104 5.753×104 2.929×103 0.000 0.000 136 Table 6.3. Chemical Composition of Magnetite Concentrate Used in This Work Component Weight percent Total Fe 68.2 Total O 26.8 SiO2 3 Al2O3 1 MgO 0.6 CaO 0.4 Figure 6.1. Schematic representation of the laboratory flash ironmaking reactor (inner diameter 0.19 m and length 2.13 m) 137 Figure 6.2. The positions of injection ports: (a) injection ports plane (A-A section), (b) top view of the reactor. Wall Temperature (K) 1600 1400 1200 1000 H₂ flow rate: 3600 L/h H₂ flow rate: 1200 L/h 800 600 400 0 0.4 0.8 1.2 Z (m) 1.6 Figure 6.3. Measured wall temperature profiles of the laboratory flash reactor. ♦: H2 flow rate 3600 L/h, O2 flow rate 579 L/h; ● H2 flow rate: 1200 L/h, O2 flow rate: 178 L/h (Flow rates are calculated at 298 K (25 ºC) and 86.1 kPa). 138 Figure 6.4. Geometry and meshing of the Utah Flash Reactor (UFR) and burner. (a) Reactor interior, (b) Burner, (c) Burner Mesh, and (d) Hybrid Mesh for the entire reactor. 139 3100 Temperature (K) 2700 2300 1900 1500 1100 700 300 0 0.4 0.8 1.2 1.6 Z (m) Figure 6.5. Gas phase temperature along the centerline of the reactor. ○ ,−−−: experimental and calculated temperature profiles for H2 flow rate 3600 L/h, O2 flow rate 579 L/h; □,−∙−,: experimental and calculated temperature profiles for H2 flow rate 1200 L/h, O2 flow rate: 178 L/h Figure 6.6. Comparison between the calculated reduction degrees vs. experimental results. 140 Figure 6.7. Velocity fields: (a) Streamlines, (b) velocity vector for H2 flow rate 3600 L/h, O2 flow rate 579 L/h with H-O-H configuration (A-A section shown in Figure 6.2. 40% of the total reactor length shown here). The maximum velocity is 36 m/s. 141 Figure 6.8. Representative particle trajectories for H2 flow rate 3600 L/h, O2 flow rate 579 L/h with H-O-H flame configuration. The final reduction degrees in (a) and (b) are 0.53 and 0.81, respectively. 142 Figure 6.9. Temperature distribution for H2 flow rate 2400 L/h, O2 flow rate 384 L/h (a) H-O-H flame configuration and (b) O-H-O flame configuration. Temperature distribution for H2 flow rate 3600 L/h, O2 flow rate 579 L/h (c) H-O-H flame configuration and (d) OH-O flame configuration. 143 Figure 6.10. Species distribution: (a) H2O mole fraction, (b) H2 mole fraction (c) EDF distribution for H2 flow rate 3600 L/h, O2 flow rate 579 L/h with H-O-H flame configuration (A-A section, Figure 6.2). CHAPTER 7 CFD SIMULATION OF LABORATORY FLASH REACTOR: PART II: EXPERIMENTAL INVESTIGATION AND CFD SIMULATION OF MAGNETITE CONCENTRATE REDUCTION USING METHANE-OXYGEN FLAME Mohamed Elzohiery, De-Qiu Fan, Yousef Mohassab, and H. Y. Sohn Department of Metallurgical Engineering, University of Utah, Salt Lake City, Utah 84112, USA This is Chapter 7 of the dissertation and it is a manuscript for a journal article that we will submit for publishing. 7.1 Abstract An experimental investigation of the reduction of magnetite concentrate particles was conducted in a laboratory scale flash reactor representing a novel flash ironmaking process. In this reactor, methane was partially oxidized by oxygen to form a reducing H2 +CO gas mixture. The test variables in this work included the particle residence time, the extent of excess reducing gases, particle feeding mode and flame configuration. The experimental results obtained from this reactor proved that the concentrate particles can be reduced directly in a flash reactor utilizing natural gas. More than 80% reduction was 145 achieved in this reactor despite its low operating temperature (1170 ºC). In addition, a three-dimensional computational fluid dynamics (CFD) model was developed to describe the reduction of concentrate particles in this reactor. The model was used to simulate the fluid flow, heat transfer and chemical reactions involved. The gas phase was simulated in the Eulerian frame of reference while the particles were tracked in the Lagrangian framework. The partial combustion of methane by oxygen was also simulated in this study. The temperature profile obtained from the simulations satisfactorily agreed with the experimental measurements, while the calculated reduction degrees consistently over predicted the experimental values. This was attributed to the soot formation as a consequence of methane cracking due to large metal surface of the reactor. The soot formation led to a high water vapor generation in the partial combustion, which lowered the excess of hydrogen. Keywords: Flash reactor, CFD, Ironmaking, Methane, Magnetite concentrate 7.2. Introduction There has been much effort devoted to reducing the emissions of greenhouse gas (GHG) in all industries. The steel industry has been achieving significant reduction in greenhouse gas emissions during the past few decades by improving the energy efficiency through technologies. According to the International Energy Association (IEA), the iron and steel industry accounts for 6.7% of the world CO2 emissions in 2017.[1] A transformational technology for alternate ironmaking has been developed at the University of Utah aimed at greatly reducing the energy consumption and GHG emission compared with the conventional blast furnace (BF) process. In this novel ironmaking 146 process, iron is produced by the direct gaseous reduction of iron oxide concentrate in a flash reactor by utilizing hydrogen, natural gas or coal gas as the reducing agent and fuel. Little work had been done on the reduction of iron oxide in a flash process before the development effort at Utah. Themelis and Zhao[2] investigated the flash reduction of iron oxides, but it was concluded that the reaction was not amenable to the high-intensity flash process as the reaction rate was too slow. This conclusion was based on experimental results of the reduction of iron oxide particles ranging from 70 to 42000 µm in the temperature range of 873 K (600 °C) to 1273 K (1000 °C). Johnson and Davison[3] studied the reduction of taconite concentrate particles ranging in size from 5 to 45 μm in a heated cyclone. The cyclone system was preheated to 1273 K (1000 °C) - 1473 K (1200 °C) prior to switching to a plasma system to maintain an average operating temperature of 1773 K (1500 °C) or higher. The iron ore concentrate particles were reduced using CO as the reducing gas, and a reduction degree of 80-95% was achieved. Most of the experimental and simulation work on flash reaction processes were focused on the smelting and converting of sulfide concentrates. Perez-Tello et al.[4, 5] investigated the copper converting reaction in terms of converting rate, converting quality, particle size change, morphology and mineralogy in a laboratory flash rector. A three-dimensional computational fluid dynamics (CFD) model was developed to model the converting process. Reasonable agreement between the experimental results and the computed result was obtained in terms of the fractional completion of the oxidation reaction and sulfur remaining. Different experiments were conducted by Jokilaakso et al.[6] in a laboratory flash reactor aiming to treating complex copper and nickel concentrates in the Outotec flash smelting process. The work was focused on the removal 147 of arsenic and antimony from the complex copper concentrates. CFD models were also developed aimed at improving the energy efficiency of the Outotec flash smelting process and investigating the applicability of the process to complex raw material. A number of experimental and simulation studies relevant to this novel process have been performed by Sohn and coworkers[7-22] aimed at generating a database to be used for the design of a flash ironmaking reactor. They proved that the iron concentrate particles can be reduced in the few seconds of residence time typically available in a flash reactor in the temperature range of 1423 K - 1873 K (1150 ºC - 1600 ºC). Process simulation and economic feasibility analysis carried out by Pinegar et al.[10-12] demonstrated that energy consumption could be reduced significantly by this novel process compared with the BF process. Detailed rate expression of H2, CO or H2+CO mixtures reduction of magnetite concentrate particles in the temperature range of 1423 K to 1623 K (1150 ºC to 1600 ºC) was developed by Fan et al.,[17, 23-25] and a CFD model was developed by Fan et al.[19] to describe the reduction of magnetite concentrate particles with just hydrogen in the same laboratory flash reactor. The model gave satisfactory agreement between the calculated reduction degrees and temperature profiles and experimental values. A pilot-scale flash reactor has been constructed and operated on the University of Utah campus.[22] This is a follow-up paper on a previous article[19] on modeling of H2 reduction of magnetite concentrate particle in this laboratory flash reactor. Unlike the drop-tube reactor used in previous work,[17] this laboratory flash reactor had hydrodynamic conditions similar to those in an industrial flash reactor. The purpose of this work was to test different powder feeding modes and flame configurations. The CFD model was used 148 to simulate the temperature and species distributions, gas flow patterns and particle trajectory inside the reactor under different experimental conditions. 7.3. Experimental Work 7.3.1. Materials In this work, the magnetite concentrate particles used were produced from a taconite ore of the Mesabi Range in the U. S. The concentrate was provided by ArcelorMittal (East Chicago, USA). The chemical analysis of the concentrate is listed in Table 7.1. The XRD analysis of this sample performed on an RJ LEE Group (Monroeville, PA, USA) XRD instrument is shown in Figure 7.1. It is seen that the major component of the concentrate was magnetite with traces of silica, which was the main gangue content as shown in Figure 7.1. The total iron content ranged from 68 to 72%. The concentrate particle size was less than 90 µm with a mass average particle size of 32 μm. The particles were irregularly shaped, nonporous and angular, as shown in Figure 7.2. 7.3.2. Apparatus The laboratory flash reactor used in this work is shown in Figure 7.3. This apparatus was used previously for the flash reduction of magnetite concentrate by hydrogen.[19] The reactor consisted of a stainless steel tube, an electric power control system, gas delivery lines, a pneumatic powder feeding system, gas scrubber, and an offgas burner. The vertical furnace housed a 316 stainless steel tube with 19.5 cm ID and 213 cm length. This reactor was electrically heated by six SiC heating elements. The 149 power supply was controlled through two silicon rectifier power controllers. In addition to the electrical heating, a mixture of methane and hydrogen was partially combusted in the top part of the reactor for part of the heat needed. Due to the relatively large size, the temperature inside the reactor was not completely uniform. The maximum temperature that could be achieved inside the reactor was 1200 ± 10 °C at a depth of 76 cm from the top flange of the reactor. A nonpremixed burner made of Inconel with four crescent-shaped inlets (Slot 1) and four round inlets (Slot 2) was used, as shown in Figure 7.4. Two flame configurations were tested in this study by swapping the inlets for fuel (F) and oxygen (O). In the first flame configuration (designated as F-O-F), the fuel (CH4+H2) and oxygen were fed through Slots 1 and 2, respectively. In the second flame configuration (designated as OF-O), the fuel and oxygen slots were swapped so that the fuel was surrounded by the oxygen streams. The concentrate was fed into this reactor through openings in the upper flange installed on the top of the reactor tube. Two different types of feeding mode were tested, which are shown in Figure 7.5. The two side ports were bent towards the center of the tube with an angle 22.5° from the longitudinal axis to avoid powder accumulation on the inner walls of the reactor tube. 7.3.3. Experimental Procedure The reactor was first preheated under a nitrogen flow. When the temperature reached 1423 K (1150 °C) measured at a depth of 76 cm in the reactor tube from the top flange, the nitrogen flow was switched to hydrogen at a predetermined flow rate, and then 150 oxygen was introduced to the reactor to start the flame. No external igniter was needed to start the flame as the local temperature in the burner was higher than the auto ignition temperature of hydrogen. During the entire duration of experiment, the flow of nitrogen through the powder feeder lines was maintained to prevent the backflow of the gas. A Ktype thermocouple placed 2.5 cm from the side of the burner nozzle was used as a flame detector. A sudden increase of 100-200 K in this thermocouple signaled a successful flame ignition. The system was then heated by both the flame and the electrical power until the measured temperature at depth 76 cm reached 1473 K (1200 °C). Then methane gas was gradually introduced to replace most but not all of the hydrogen. At the same time, O2 was also adjusted gradually to a predetermined flow rate. H2 was kept in the fuel input to help maintain a stable flame throughout the experiment. The flame extinguished after a short time when methane alone was used as the fuel. It was found by inspecting the system when extinguishment occurred that serious soot formation was observed at the tip of burner nozzle as well as the inner wall of the reactor tube. The other reason for the addition of H2 was to mimic the H2 recycled from the off-gas in the operation of an industrial reactor. During the experiment, the electrical power was adjusted so as to maintain the measured temperature at 1200 ± 5 °C. The methane flow rate was varied in order to control the particle residence time inside the reactor, and the amount of oxygen fed was varied accordingly to achieve the desired amount of excess reducing gas for the reduction reaction. The flow rates of methane and oxygen were controlled using accurate mass flow controllers (AALBORG, Orangeburg, NY) with an accuracy of ± 1% of full scale. The hydrogen and nitrogen flow 151 rates were controlled using flow meters with an accuracy of ± 2% of full scale. After the experiment, a nitrogen flow was maintained until the system cooled down to 673 K (400 °C). The collection bin was heated by a heating plate to avoid water condensation that may wet the reduced sample during the experiment. The collected samples were weighed and analyzed for the iron content using an ICP-OES method. In order to verify the results obtained from this method, the samples collected from different locations (collection bin, quench chamber inner wall and bottom part of the reactor) of the same experiment were mixed, and an analysis of the mixed sample was also determined. The difference was found to be within ± 2% of the reduction degree of samples in the collection bin. 7.3.4. Definition of Parameters The reduction degree was obtained based on the change in the mass of oxygen combined with iron in the particles before and after reduction, calculated according to:[19] Reduction Degree X (%) = 1−(%𝐹𝑒)𝑖 /(%𝐹𝑒)𝑡 (%𝑂)𝑖 /100 × 100 (7.1) where (%Fe)i and (%Fe)t, respectively, are the weight percentages of iron in the concentrate and the sample after reduction for time t; (%O)i is the weight percentage of oxygen that is combined with iron in the concentrate before reduction. The reduction of magnetite to metallic iron proceeds through two steps where magnetite (Fe3O4) is first reduced to wüstite (Fe0.947O) and then to metallic iron (Fe). The second reaction is an equilibrium limited reaction as its equilibrium constant is around unity near the flash ironmaking temperatures. Fe3O4 (s) + 4H2 or 4CO (g) = 3Fe (s) + 4H2O or 4CO2 (g) (7.2) 152 Fe0.947O (s) + H2 or CO (g) = 0.947 Fe (s) + H2O or CO2 (g) (7.3) Based on the fact, to be discussed subsequently, that the reaction rate of H2 is much faster than that of CO in the temperature range, the excess reducing gas was defined in terms of excess H2. Excess driving force (EDF) is used to describe the excess amount of H2 expected in the off-gas compared with the equilibrium value for complete reduction of iron oxide in the concentrate, as follows: ( EDF= 𝑝𝐻 𝑝𝐻 2 ) 2 ) −( 𝑝𝐻 𝑂 𝑝𝐻 𝑂 2 2 off-gas equ. 𝑝𝐻 2 ) ( 𝑝𝐻 𝑂 2 equ. 𝑝𝐻2 = 𝐾𝐻2 (𝑝 𝐻2 𝑂 ) −1 (7.4) off-gas where 𝑝𝐻2 and 𝑝𝐻2 𝑂 are, respectively, the partial pressures of hydrogen and water vapor. HSC 5.11 thermodynamics software package[26] was used in the design of experimental conditions. The designed H2 EDF values, defined by Eq. (7.4), were first selected. The values of H2 EDF tested in this work were 0.5 and 1.0. The flow rates of input gases (H2, CH4, O2, and N2) to be used under given magnetite concentrate feeding rates were then determined such that the off-gas composition met the selected H2 EDF value. The “Equilibrium Composition” module of HSC was used to determine those flow rates iteratively. The calculation was performed for complete reduction of the concentrate particles at 1448 K (1175 °C) under a total pressure of 0.86 atm (the atmospheric pressure at Salt Lake City, Utah). A summary of the experimental conditions obtained from this method is shown in Table 7.2. The flow rates of the input gases obtained remained unchanged during the entire duration of the experiment. The temperature in the reactor was controlled by adjusting the power to the electric heating elements. The nominal residence time of the particles was another parameter that was important in the design of experimental conditions. It was calculated according to:[15] 153 𝜏=𝑢 𝐿 𝑔 +𝑢𝑡 (7.5) where L is the effective length where temperature remained within 1175±25 K, which was determined to be 68.5 cm; 𝑢𝑔 is the nominal average gas velocity based on the total gas flow rate of the product gas mixture of partial combustion according to the equilibrium calculation from HSC; 𝑢𝑡 = 𝑑𝑝2 𝑔(𝜌𝑝 − 𝜌𝑔 )/18𝜇 is the terminal velocity of a falling particle in laminar flow. 7.4. Mathematical Model 7.4.1 Governing Equations Steady state conditions were simulated in this work. The Euler-Lagrange approach was used to model the two-phase flow, in which the gas phase was treated as a continuum in the Eulerian frame of reference while the solid phase was tracked in the Lagrangian mode. A two-way coupling approach between the gas phase and solid phase was used in the simulation. The governing equations for the fluid flow, heat transfer and species transport under steady state can be generalized as: ∇ ∙ 𝜌𝑔 𝑢 ⃗ 𝑔 𝜙 − ∇ ∙ Γ𝜙 ∇𝜙 = 𝑆 𝜙 (7.6) where 𝜙 represents the generic dependent variable such as temperature, species, and velocity. 𝛤𝜙 is the effective transport coefficient of the dependent variable and 𝑆 𝜙 is the source term. The reader is referred to the previous work[19] on the specific form of the governing equations. The governing equations for the particle phase were a series of ordinary differential equations, which described the particle movement, particle temperature change and oxygen removal. Here, only the oxygen removal equation is listed, as given 154 by Eq. (7.7). The reader is referred to the same previous work on the specific form of other governing equations for the solid phase. 𝑚 𝑑𝑋 𝑚𝑗 𝑝 | = 𝑘𝑗 ∙ [𝑝𝑗 𝑗 − ( 𝐾𝑗𝑂 ) 𝑑𝑡 𝑗 𝑗 −𝑠 ] ∙ 𝑛𝑗 (1 − 𝑋)[− 𝐿n(1 − 𝑋)]1−1/𝑛𝑗 ⋅ 𝑑𝑝 𝑗 ; j = H2 or CO (7.7) 𝐸 where 𝑘𝑗 is the reaction rate constant for reducing gas j, 𝑘𝑗 = 𝑘𝑜,𝑗 exp (− 𝑅𝑇𝑗 ); Kj is the equilibrium constant for the reduction of FeO by gas j; 𝑛𝑗 is the Avrami parameter; 𝑚𝑗 is the reaction order with respect to gas j. The rate expression used for the reduction of magnetite concentrate particles by single gas H2 or CO was the global nucleation and growth rate expression. The kinetic parameters in Eq. (7.7) are listed in Table 7.3. Since the amount of O2 fed was less than the stoichiometric amount required for full combustion, a mixture of H2+CO was generated in the partial combustion. It was also found that synergistic effect occurred for the reduction of magnetite concentrate particles by H2+CO mixtures.[22] In order to account for the enhanced effect, an enhancement factor was multiplied to the contribution of H2, as shown below: 𝑑𝑋 𝑑𝑡 = [1 + 𝛼( 𝑝𝐶𝑂 , 𝑝𝐻2 )] ⋅ 𝑑𝑋 | 𝑑𝑡 𝐻2 + 𝑑𝑋 | 𝑑𝑡 𝐶𝑂 (7.8) where 𝛼(𝑝𝐶𝑂 , 𝑝𝐻2 ) is the enhancement factor that is calculated as[25] 𝛼( 𝑝𝐶𝑂 , 𝑝𝐻2 ) = 1.3 ⋅ 𝑝𝐶𝑂 𝑝𝐶𝑂 + 𝑝𝐻2 1150 °C (1423 K) < T < 1350 °C (1623 K) (7.9) 155 7.4.2. Combustion Mechanism The partial combustion of methane was described in this study by four chemical reactions involving six species that are listed in Table 7.4.[27] The eddy dissipation concept (EDC)[28] model was adopted to account for the turbulence-chemistry interaction. This model takes account of the effects of turbulent mixing as well as detailed chemical mechanisms in a turbulent combustion.[29] The chemical reactions are represented in the following general form: a A(g) + b B(g) = c C(g) +d D(g) (7.10) The forward reaction rate constant for each of the elementary reaction is given by: 𝑘𝑓,𝑖 = 𝐴𝑇 𝛾 exp (− 𝐸𝑎,𝑖 𝑅𝑇 ) (7.11) In the CH4-O2 partial combustion mechanism, the second and last reactions are treated as reversible for which the corresponding backward reaction rate constants are calculated by 𝑘𝑓,𝑖 𝑘𝑏,𝑖 = 𝐾 𝑐,𝑖 (7.12) where 𝐾𝑐,𝑖 is the equilibrium constant of reaction i based on molar concentrations, rather than on activities. The net rates are then calculated as the difference between the forward reaction rate and backward reaction rate 𝑅𝑖 = 𝑘𝑓,𝑖 𝐶𝐴𝑎 𝐶𝐵𝑏 − 𝑘𝑏,𝑖 𝐶𝐶𝑐 𝐶𝐷𝑑 . (7.13) The other two reactions are treated as irreversible reactions, and thus only forward reactions are considered. The forward reaction rate for CH4+0.5O2=CO+2H2 is calculated by 0.5 1.25 𝑅𝑖,1 = 𝑘𝑓,1 𝐶𝐶𝐻 𝐶 4 𝑂2 The forward reaction rate for H2+0.5O2=H2O is calculated by (7.14) 156 𝑅𝑖,3 = 𝑘𝑓,3 𝐶𝐻0.25 𝐶𝑂1.5 2 2 (7.15) The boundary conditions and numerical techniques used in this work were the same as in previous work.[19] Mass flow rate boundary conditions were imposed at the gas inlets. The operating pressure was kept at 86.1 kPa (the barometric pressure at Salt Lake City). The wall temperature along the axial direction of the reactor was measured and used as fixed-value thermal boundary condition. Other details of the boundary conditions can be found in a previous paper.[19] Commercial software package ANSYS Fluent was used to solve the governing equations mentioned above. The partial combustion mechanism above was prepared in a CHEMKIN[30] format and was imported into the model. The chemical reaction kinetics for the concentrate particles were implemented using the user-defined functions (UDFs). 7.5. Results and Discussion 7.5.1. Experimental Results The effect of the flame configuration on particle reduction was investigated in this work. In the F-O-F flame configuration experiments, the particles were not fed through the center of the burner as the particles tended to melt and became molten droplets when they went through the flame region (> 2000 °C), which was observed in the previous H2 reduction experiments[19] as shown in Figure 7.6. This melting lowered the reduction degree in burner feeding compared with side feeding under the same flow rates and EDF. The reason for this is that the active solid surface area for chemical reaction was decreased after melting compared with side feeding in which case the particles remained solid and retained their irregular shape and reactivity, as shown in Figures 7.8 and 7.9. 157 Therefore, burner feeding was not used in the F-O-F flame configuration experiments in this work. The values of H2 EDF tested in this work were limited to 0.5 and 1.0, which are within the range of values expected in an industrial flash ironmaking reactor. As expected, an increase in the EDF value under the same residence time and temperature led to higher reduction degrees, which is seen from Figure 7.7. It was also found that higher reduction degrees were achieved under the O-F-O flame configuration compared with that obtained under the F-O-F flame configuration. This has to do with the temperature distribution inside the reactor, which will be further discussed in the CFD results. Figure 7.8 shows the SEM micrographs for the samples collected under the O-FO flame configuration with burner feeding at EDF = 1. No melting of the particles was observed. The particles were angular, irregularly shaped and porous. The SEM micrograph for the sample collected under the F-O-F flame configuration with two-side feeding mode at EDF =1 is shown in Figure 7.9. The particles were also found to be angular, irregularly shaped and porous. The reduction degree from all the experiments were listed in Table 7.2. It is noted that the reduction degrees achieved with methane were lower than that obtained using H2 under the same H2 EDF and nominal residence time. The reason for this will be discussed subsequently. 158 7.5.2. CFD Results 7.5.2.1. Velocity Field A typical velocity field inside the reactor is shown in Figure 7.10. In the top part of the reactor, a recirculation zone was formed as a result of the entrainment of the high velocity particle-laden jets coming out of the injection tubes. This kind of recirculation zone was also observed in the simulation of H2 reduction experiments.[19] After this recirculation region, the gas stream started to travel downward along the axis of the reactor tube. The recirculation zone played an important role in the concentrate particles dispersion and in increasing the particle residence time. The effect the recirculation zone had on the temperature profile can be seen in Figure 7.11. High temperature bumps were formed in the recirculation region as gas streams at higher temperatures originated from the combustion zone recirculated upward. The recirculation enhances the temperature homogeneity in the top part of the reactor. 7.5.2.2. Temperature Field A comparison of the temperature distributions with different fuel and oxygen feeding configurations is displayed in Figure 7.11. The F-O-F feeding configuration led to higher flame temperatures. For the O-F-O feeding configuration, the burner feeding mode resulted in a slightly decrease in the flame temperature. The O-F-O flame configuration also led to elevated temperature in the top part of the reactor as the high temperature flame was more evenly distributed in the radial direction compared with that under the F-O-F flame configuration. The consequence of this also leads to an increase in the averaged particle reduction degrees in the O-F-O flame configuration runs for 159 otherwise the same operating conditions. Figure 7.11 (c) also explains the melting phenomenon encountered in Figure 7.6 where the concentrate particles were fed with the burner feeding mode under the F-O-F flame configuration. The particles in this case went through the whole flame region experiencing complete melting. In contrast, most of the particles fed in Figure 7.11 (a) did not melt although the same burner feeding mode was used. This is because in the O-F-O flame configuration, the high temperature flame region was shifted toward the edge of burner leaving the center region below the melting point of the concentrate. The reason for this shift of high temperature region is that the fuel was fed at a higher volumetric flow rates and the gases generated from the oxidation of methane generated additional volume, which pushed the gas outward. Under the same O-F-O flame configuration with the same fuel, oxygen and concentrate particles flow rates, similar reduction degrees were achieved through the burner feeding mode and twoside feeding mode, which can be seen from Figures 7.11 (a) and 7.11 (b) as the two have similar temperature distributions in the top part of the reactor. Temperature along the centerline of the reactor was measured using a long K-type thermocouple during the experiment. The comparison of the computed temperature profiles and corresponding experimental measurement is given in Figure 7.12. It is evident that the computed and experimental gas temperatures agree well with each other overall except for some deviations at the end of the reactor. The reason for the latter is that this part of the reactor close to the exit of the reactor tube was not surrounded by the insulation material and was thus exposed to the ambient air directly. Despite the disagreement, it does not cause significant errors in the calculated reduction degree of the magnetite concentrate particles as the chemical reaction at temperature lower than 1273 160 K (1000˚C) is relatively slow according the Eq. (7.7), and the reduction degree achieved within the short residence time of particles while descending in this region was negligible. 7.5.2.3. Species Distribution and Comparison of Reduction Degrees A typical species distribution inside the reactor is shown in Figure 7.13. It is seen that the conversion of methane into CO and H2 was complete and fast. Comparisons of the computed reduction degrees and the corresponding experimental values are listed in Table 7.2. The computed values of reduction degrees were found to be consistently higher than the experimental values. The reason for this is that during the experiments, soot was formed at the tip of the burner and on the inner wall of the reactor tube. The soot formation was due to the large metal surface of the reactor tube which served as a catalyst for CH4 cracking. But the combustion mechanism listed in Table 7.4 did not take into consideration of the soot formation. Therefore, the actual amount of CO generated from the partial combustion was less than the amount calculated in the CFD simulation. Furthermore, the amount of H2O generated was greater than the theoretical value as the oxygen that would have oxidized with the soot instead oxidized hydrogen, which led to a lower excess driving force. The reduction of magnetite concentrate particles was negatively affected under a lower excess driving force of H2 compared with the CFD simulation. 161 7.5.2.4. Particle Residence Time Particle residence time is one of the most important experimental parameters in the flash ironmaking process. In the design of experimental conditions, nominal residence time was used. The real particle residence times were calculated by tracking particle streams. A total number of 5,000 particle streams were released from the two side injection ports in all simulation runs to establish a statistical representation of the particle spreading due to turbulence. The average particle residence time in each of the simulation runs is calculated by averaging all the particle streams. The calculated results (designated as τ) listed in Table 7.2 represent the average particle residence time where the particle temperatures are higher than the target temperature [1448 K (1175 oC)] of the experiment. 7.6. Concluding Remarks The reduction of magnetite concentrate particles was investigated in a laboratory scale flash reactor by partially oxidizing methane with oxygen to generate a mixture of H2+CO as the reducing gases. The experimental results indicated that more than 80% reduction degrees can be achieved in this reactor despite its low maximum temperature possible. Different factors such as residence time, excess reducing gas, feeding mode and flame configuration that affect the reduction of the concentrate particles were tested. A three-dimensional CFD model was developed to simulate the gas particle twophase flow, heat transfer and chemical reaction in a laboratory flash reactor. The calculated centerline temperatures satisfactorily agreed with the measured values. However, the computed values of reduction degrees were consistently higher than the experimental values due to the soot formation. The soot formation, which was not 162 accounted for in the CFD simulation, lowered the experimental values of reduction degrees. The soot formation did not occur when then burner and the wall were lined with refractory material in another larger bench reactor, and thus is not expected to be a problem in an industrial flash reactor. Thus, the problem of soot formation was not further investigated in this work. The particles melted when passing through the flame region in the burner feeding mode with F-O-F flame configuration, which negatively affected the particle reductions as the active solid surface area decreased upon melting compared with particles remaining solid in the two-side feeding mode. The O-F-O flame configuration yielded higher reduction degrees than the F-O-F flame configuration (other conditions being the same) as better temperature homogeneity in the top part of the reactor and longer averaged particle residence time in the O-F-O were achieved. 7.7. Acknowledgments The technical support and resources provided by the Center for High Performance Computing at the University of Utah are gratefully acknowledged. The authors acknowledge the financial support from the U.S. Department of Energy under Award Number DE-EE0005751 with cost share by the American Iron and Steel Institute (AISI) and the University of Utah. 7.8. Nomenclature dp: geometric mean diameter of the screened particle (m) Kj: equilibrium constant for the reduction of FeO by gas j 163 L: effective length where temperature remained within 1175±25 K (m) p: pressure (pa) ug: gas phase velocity (m∙s-1) ut: terminal velocity of the particle (m∙s-1) X: reduction degree μ: gas phase viscosity (N∙m∙s-2) ρg: gas phase density (kg∙m-3) ρp: particle density (kg∙m-3) τ: particle residence time (s) 7.9. References 1. World Steel Association, 2017. https://www.steel.org.au/resources/elibrary/resourceitems/steel-s-contribution-to-a-low-carbon-future-and-cl/ accessed October 30, 2018. 2. N. J. Themelis and B. Zhao, in Flash Reaction Processes, T.W. Davies (eds.), Kluwer Academic Publishers: Dordrecht, Netherlands, 1995, pp 273-93. 3. T. Johnson and J. Davison: J. Iron Steel Inst. 1964, vol. 202 (5), pp. 406-19. 4. M. Perez-Tello, H. Y. Sohn, K. St. Marie and A. Jokilaakso: Metall. Mater. Trans. B., 2001, vol. 32 (5), pp. 847-68. 5. M. Perez-Tello, H. 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Chen, Y. Mohassab, T Jiang and H. Y. Sohn: Metall. Mater. Trans. B, 2015, vol. 46 (3), pp. 1133-45. 17. D. Fan, Y. Mohassab, M. Elzohiery and H. Y. Sohn: Metall. Mater. Trans. B, 2016, vol. 47 (3), pp. 1669-80. 18. F. Chen, Y. Mohassab, S. Zhang and H. Y. Sohn: Metall. Mater. Trans. B, 2015, vol. 46 (4), pp. 1716-28. 19. D. Fan, H. Y. Sohn, Y. Mohassab and M. Elzohiery: Metall. Mater. Trans. B, 2016, vol. 47 (6), pp 3489-500. 20. D. Fan, H. Y. Sohn and M. Elzohiery: Metall. Mater. Trans. B, 2017, vol. 48 (5), pp. 2677-84. 21. D. Fan, M. Elzohiery, Y. Mohassab and H. Y. Sohn, in 8th International Symposium on High-Temperature Metallurgical Processing, J. Y. Hwang et al. (eds.), Springer, 2017, pp 61-70. 22. H. Y. Sohn, Y. Mohassab, M. Elzohiery, D. Fan and A. Abdelghany, in Applications of Process Engineering Principles in Materials Processing, Energy and Environmental Technologies, S. Wang et al. (eds.), Springer, 2017, pp 15-23. DOI 10.1007/978-3-31951091-0_2. 23. M. Elzohiery, D. Fan, Y. Mohassab and H. Y. Sohn, The Kinetics of Hydrogen Reduction of Molten Magnetite Concentrate Particles, unpublished work, University of Utah, 2018. 24. D. Fan, M. Elzohiery, Y. Mohassab and H. Y. Sohn, The Kinetics of Carbon Monoxide Reduction of Magnetite Concentrate Particles through CFD Modeling, unpublished work, University of Utah, 2018. 165 25. D. Fan, M. Elzohiery, Y. Mohassab and H. Y. Sohn, Kinetics of Magnetite Concentrate Particle Reduction by H2+CO Mixtures through CFD Modeling, upublished work, University of Utah, 2018. 26. HSC 5.11, Chemistry for Windows, Outokumpu Research, Oy, Pori, Finland, 2002. 27. W. P. Jones and R. P. Lindstedt, Combust. Flame, 1988, 73(3), pp.233-249. 28. I. R. Gran and B. F. Magnussen: Combust. Sci. Technol., 1996, vol. 119 (1-6), pp. 191217. 29. Fluent Theory Guide, ANSYS Inc., Canonsburg, USA. 30. R. J. Kee, F. M. Rupley, C. Wang, and O. Adigun: CHEMKIN Collection, Release 3.6, Reaction Design, Inc., San Diego, CA, 2000. 166 Table 7.1. Chemical Composition of Magnetite Concentrate Particles Component wt.% Total Iron SiO2 Al2O3 CaO MgO MnO Cr2O3 K2O Na2O TiO2 ZrO2 P S C Sr 70.65 1.87 0.13 0.27 0.13 0.11 0.11 0.01 0.1 0.01 0.03 0.01 0.02 0.24 0.01 167 Table 7.2. Summary of the Experimental Conditions Gases Flow Rate (L/min) CH H2 O2 N2 4 Conc. Feeding Rate (g/min) Feedin g Mode Flame Confi g. H2 ED F Nominal Residenc e Time (s) τ (s) Exp. RD (%) Cal. RD (%) 5.0 2.0 4.0 2.8 2.0 SS O-F-O 1.1 10.5 7.9 83 95 5.0 2.0 4.0 2.8 2.4 SS F-O-F 1.1 10.5 7.1 76 90 5.0 2.0 4.5 2.8 2.0 SS F-O-F 0.5 10.5 6.8 64 75 5.0 2.0 4.5 2.8 1.8 SS O-F-O 0.5 10.5 7.5 72 85 5.0 2.0 4.0 2.0 1.9 B O-F-O 1.1 10.5 8.2 83 97 5.0 2.0 4.0 2.0 2.1 B O-F-O 1.0 10.5 8.2 82 96 5.0 2.0 4.5 2.0 2.2 B O-F-O 0.5 10.5 7.7 65 86 5.0 0.13 4.2 2.0 2.1 B O-F-O 0.5 11 8.3 59 89 5.0 0.13 3.75 2.0 1.9 B O-F-O 1.0 11 8.4 78 99 5.0 0.13 3.75 2.8 2.2 SS O-F-O 1.0 11 8.4 81 98 5.0 0.13 3.75 2.0 2.2 B F-O-F 1.0 11 8.0 33 92 5.0 0.13 3.75 2.0 2.4 B O-F-O 1.0 11 8.4 81 99 5.0 10. 0 0.13 4.2 2.8 2.5 SS O-F-O 0.5 11 8.0 68 87 2.0 8.2 2.8 2.0 SS O-F-O 1.1 7.6 5.6 46 83 Table 7.3. Summary of the Kinetics Parameters Reducing Gas Temperature Range (K) 𝑘𝑜,𝑗 Ej (kJ∙mol-1) mj Nj sj H2 CO 1423 -1623 1423 -1623 1.23 × 107 1.07 × 1014 196 451 1 1 1 0.5 0 0 Table 7.4. CH4-O2 Partial Combustion Mechanism Reaction 1 CH4+0.5O2=CO+2H2 2 CH4+ H2O=CO+3H2 3 H2+0.5O2=H2O 4 H2O+CO=CO2+H2 A 4.40×1014 (m2.25∙mol-0.75∙s-1) 3.00×1011 (m3∙mol-1∙s-1) 2.50×1019 (m2.25∙mol-0.75∙s-1∙K) 2.75×1012 (m3∙mol-1∙s-1) 𝜸 Ea (J∙mol-1) Kc,i at 3073 K 0.0 1.26×105 2.8×1010 0.0 1.26×105 1.6×109 -1.0 1.67×105 18 0.0 8.37×104 1.3×10-1 168 Figure 7.1. X-ray diffraction pattern of the magnetite concentrate. Figure 7.2— SEM micrograph for the magnetite concentrate particles. 169 Figure 7.3. Schematic representation of the laboratory flash ironmaking reactor. 170 Figure 7.4. Schematic diagram the nonpremixed burner: (a) configuration of the upper flange (plan view), (b) configuration of the upper flange across section A-A. 171 Figure 7.5. Powder feeding modes: (a) Burner feeding (through the center of the burner), (b) Side feeding (through two ports on opposite sides of the burner). Figure 7.6. SEM micrographs for samples collected from experiments with 60 L/min H2 and 9.65 L/min O2 and EDF = 0.5 (a) side feeding and (b) burner feeding. [X represents the fraction reduced.] 172 Figure 7.7. Effect of EDF on reduction degree under different feeding modes and flame configurations. [All flow rates are at 298 K and 86.1 kPa, the atmospheric pressure at Salt Lake City.] Figure 7.8. SEM micrograph of samples under the O-F-O flame configuration with burner feeding at EDF = 1; gas flow rates: CH4 = 5 L/min, H2 =2 L/min, O2 = 4 L/min. 173 Figure 7.9. SEM micrograph of sample under F-O-F flame configuration with two-side feeding at EDF = 1; gas flow rates: CH4 = 5 L/min, H2 =2 L/min, O2 = 4 L/min. 174 Figure 7.10. Velocity fields: (a) Streamlines, (b) velocity vector for CH4 = 5 L/min, H2 =2 L/min and O2 = 4 L/min with O-F-O configuration (A-A section shown in Figure 7.4. 40% of the total reactor length shown here). The maximum velocity is 24 m/s. [All flow rates are at 298 K and 86.1 kPa, the atmospheric pressure at Salt Lake City.] 175 Figure 7.11. Temperature distribution for CH4 = 5 L/min, H2 =2 L/min and O2 = 4 L/min (a) O-F-O flame configuration and burner feeding mode; (b) O-F-O flame configuration and two-side feeding mode; (c) F-O-F flame configuration and two-side feeding mode. 176 Figure 7.12. Comparison of calculated gas phase temperature and the measured values along the centerline of the reactor for CH4 = 5 L/min, H2 =2 L/min and O2 = 4.5 L/min with F-O-F flame configuration and two-side feeding mode. 177 Figure 7.13. Species distribution: (a) H2 mole fraction, (b) H2O mole fraction, (c) CO mole fraction, and (d) CO2 mole fraction distribution for CH4 = 10 L/min, H2 =2 L/min and O2 = 8.2 L/min with O-F-O flame configuration and two-side feeding mode. CHAPTER 8 DESIGN OF PILOT FLASH IRONMAKING REACTORS USING COMPUTATIONAL FLUID DYNAMICS MODELING 8.1 Introduction Before going to full industrial-scale flash ironmaking reactor that can produce 1 – 3 millions tons/yr of metallic iron (comparable with a modern blast furnace), the intermediate step is to build a pilot reactor with a capacity of 100,000 tons/yr of metallic iron to further test the feasibility of this novel ironmaking technology. For the proper design and scale-up of such reactors, it is essential to have information on the temperature and species distribution, gas and particle flow patterns. This information is difficult or even impossible to obtain from experiments. With computational fluid dynamics (CFD) modeling, it is possible to gain such insights on these critical parameters that are essential in reactor design. In the previous chapters, the rate expressions of the reduction of magnetite concentrate particles by H2, CO or H2+CO mixtures have been determined. These rate expressions will be incorporated into the CFD model to design such pilot flash ironmaking reactors. The product of the flash ironmaking process can be either in the solid state or in the molten state depending on the operating temperatures. In this chapter, 179 two types of pilot-scale reactors will be designed. The first type is to produce metallic iron in solid state. The typical operating temperature in this case is around 1300 °C. The solid-state product collected could be first briquetted and then charged into an electric arc furnace in the steelmaking process. The second type is to produce iron in molten state, which is typically operated at a temperature of around 1600 °C. The molten product can be directly charged into a basic oxygen furnace or an electric arc furnace without further treatment. 8.2. Geometries and Dimensions Schematic representation of the 100,000 ton-per-year flash ironmaking reactor is shown in Figure 8.1. Depending on the operating conditions, the main body of the reactor is either made up of a cylindrical part and a conical part or a cylindrical shaft only. Under solid state operating conditions, a conical part near the exit of the reactor is needed for solid particle collection. If iron is produced in molten state, a bath settler is needed below the shaft. Our focus is mainly on the shaft part of the reactor in this work as the reduction of concentrate particles mostly happens during their travel in the shaft. With the same reactor volume, the design with a large height to diameter ratio leads to a long and ‘thin’ reactor, while a small height to diameter ratio leads to a short and ‘fat’ one as shown in Figure 8.1. In this study, two typical diameters–4 m and 6 m– were tested. The diameter of the long and ‘thin’ shaped reactor was set to be 4 m. A diameter of 6 m was used for the short and ‘fat’ reactor. The number of burners to be used is also an important factor in reactor design. Reactors with one burner and four burners were tested in this work. Before deciding the number of burners to be used, the 180 optimal value for the diameter was first determined under the one-burner design. The dimensions of the pilot reactors simulated are listed in Table 8.1. The powders were fed through four feeding ports installed on the roof of the reactor. The four powder feeding ports were distributed evenly (90 degrees apart), as shown in Figure 8.2. The distance between each feeding port and the centerline of the reactor was equal to half of the radius. A nonpremixed burner with two oxygen slots and one natural gas slot was used in the simulation, which is shown in Figure 8.3. The reactor wall consisted of three layers, namely, the refractory layer, insulation layer and steel shell layer from the inner layer to the outer layer, which is shown in Figure 8.4. The thickness of the refractory layer, insulation layer and steel shell layer are kept at 0.15 m, 0.08 m and 0.0254 m, respectively. Wall materials at those thicknesses were proved to be efficient in a large bench flash ironmaking reactors constructed on the campus of University of Utah that was designed to operate from 1200 °C to 1600 °C. The properties of the wall materials are listed in Table 8.2. 8.3. Operating Conditions The fuel entering the reactor consisted of fresh natural gas and recycled H2, which were partially oxidized by oxygen to provide the heat needed for the reaction as well as the reducing gases CO and H2. The actual composition of natural gas was 96% CH4, 2% C2H6, and 2% nitrogen by volume. Natural gas was considered as 98.1% CH4 (1 mol% of C2H6 equivalent to 2.6 mol% of CH4 in heat production and 2 mol% of CH4 in hydrogen and carbon monoxide production, both for generating a representative hot gas mixture from the 181 partial combustion; thus considering these two factors, 1 mol% of C2H6 was treated as being equivalent to 2.3 mol% of CH4) and 1.9% N2 to avoid the complexity of including C2H6 in the combustion calculations. The input gases were preheated to a specified temperature before charging into the reactor to reduce the amount of input gases needed. In this work, two preheat temperatures (600 °C and 1000 °C) were investigated. The operating conditions are summarized in the following tables. The concentrate feeding rate was calculated based on 340 normal operating days in a year, 70 wt.% total iron content in the concentrate and product metallization of 95%. 8.4. Meshing and Mathematical Model The pilot reactors were designed to have either a single burner in the center or four symmetrically distributed burners with four powder feeding ports evenly distributed and have the same radial position equal to half the radius of the reactor. The symmetry of the reactor was used to decrease the computational cost by taking a quarter of the reactor as a representation of the whole reactor. This decreases the time required for simulation as the number of mesh cells decreases accordingly. The typical mesh for the pilot reactor is shown in Figure 8.5. The mesh consisted of hexahedral cells only. Steady state conditions were simulated in this work. The Euler-Lagrange approach was used to model the two-phase flow, in which the gas phase was treated as a continuum in the Eulerian frame of reference while the solid phase was tracked in the Lagrangian mode. A two-way coupling approach between the gas phase and solid phase was used in the simulation. The governing equations for the gas and solid phase have 182 already been covered in the previous chapters, which will not be repeated here. The same CH4-O2 combustion mechanism as in the last chapter was used. In a large-scale pilot reactor, efficient cooling method, such as copper stove cooling technology, is usually necessary to cool the outer surface of the reactor to an acceptable temperature. The incorporation of such cooling system significant complicated the model. For simplicity, the outer surface of reactor in this work was set to be 60 °C for all the calculations. 8.5. Results and Discussion The mass weighted average products at the exit of reactor in all the runs listed in Table 8.1 were around 95% metallization. 8.5.1. One-burner Design The vector fields in the plane that passes through the center of two powder feeding ports are shown in Figures 8.6 - 8.8. It is seen from these figures that due to the high-velocity jets erupting from the burner nozzles, recirculation zones formed in regions close to the reactor inner wall in the top part of the reactor. In runs # 1, # 2 and # 5, the particles entering the reactor may be pushed to the reactor wall by the hot, high-velocity gas coming out of the flame region as seen from Figures 8.6 (a), 8.7 (a) and 8.8 (a) . The effect of this is twofold. On the one hand, as the particles were close to the high temperature flame region, the particles may fuse and melt, which would negatively affect the reduction of those particles as observed in the laboratory scale flash reactor. On the other hand, the particles being pushed towards the wall may cause the sticking problem. The accumulation of such particles would severely affect the smooth operation of the 183 reactor. In runs # 3, # 4 and # 6, the concentrate particles were less affected due to its larger diameter. Run # 3 in this case gave better flow field. The particle distributions are shown in Figures 8.9 - 8.11. It is evident that when the reactor diameter was 4 m, the particle concentration near the wall was higher than that when the reactor diameter was increased to 6 m. Although high concentration near the wall was not completely eliminated with a larger diameter design in runs # 3 and # 4, the particles were more evenly distributed in the top part of the reactor. In run # 6, the effect of larger diameter was very obvious. The particle distribution near the wall region was significantly reduced. The temperature distributions in the same plane above are shown in Figures 8.12 8.14. It is seen that in the design with a diameter of 4 m, the particles were close to the flame region in the top part of the reactor, especially in run # 1, which may cause the particles to melt as mentioned above. For the design with a diameter of 6 m, distance between the particles laden streams were farther away from the flame region. The flame lengths in the design with 6 m diameter were longer than that in the design with 4 m diameter. The averaged product temperature and reduction degree at the exit of the reactor in each run are listed in Table 8.6. Heat loss is another criterion to look at in the reactor design. The heat loss through the walls in each run was calculated and listed in Table 8.7. In order to help us better evaluate the energy efficiency of each reactor, the percentage of the energy loss (percentage of heat loss from the heat generated from combustion plus amount of sensible energy of the input gases) is also calculated. The numbers indicated that reactors with a diameter of 6 m had a smaller value of heat loss than reactors with a diameter of 4 184 m. The reason for this is that reactors with a diameter of 6 m had smaller surface area per volume compared to reactors with a diameter of 4 m. Therefore, the geometry used in run # 6 will be used as the design of the pilot flash reactor that is operated to produce molten iron. The design of a flash reactor that operates to produce solid product will be further discussed in the next section. The species distributions in runs # 5 and # 6 are shown in Figures 8.15 and 8.16. The main component gases outside the flame region reached equilibrium quickly and were uniformly distributed. The mole fractions of H2, H2O and CO at the exit of two reactors (outside the flame region) were the same at 0.48, 0.32 and 0.13, respectively. 8.5.2. Four-burner Design The pilot flash ironmaking reactor with the one-burner design led to high particle concentration near the wall in the top part of the reactor as seen from Figures 8.9 and 8.10. In this section, the four-burner design is discussed. The distribution of the four burners on the roof of the reactor is shown in Figure 8.17. The four burners were evenly distributed on the roof; they were 90 degrees apart. The distance between the burner and the centerline of the reactor was equal to half of the radius. The powder feeder feeding ports were symmetrically placed in between two burners. The distance between the powder feeding port and the centerline of the reactor was also equal to half of the radius. The burners used in this case were different from the one used in the one-burner design. The radial velocity was eliminated by replacing the conical burner tip with straight concentric design as shown in Figure 8.18. The natural gas stream was in the middle and was surrounded by two oxygen streams. 185 The same dimension as run # 3 in Table 8.1 was used in this simulation. The reactor diameter was chosen as 6 m. The same three layers of walls were also used in this design. The operating conditions listed in Table 8.3 were used as the reactor was designed to produce metallic iron in solid state. The vector field in the plane that crosses the center of two powder feeding ports is shown in Figure 8.19. The radial velocity component near the burner was greatly reduced compared with the one in the one-burner design. The particle number density distribution is shown in Figure 8.20. The number density of the concentrate particles close to the wall was greatly reduced. Therefore, the chance for the particle sticking to the wall was greatly lowered. The temperature distributions are shown in Figure 8.21. Compared with the oneburner design, the particle stream regions in the four-burner design were not affected by the flame. The consequence of this is that melting of the concentrate particles was less likely to happen so that the reduction of the concentration particles was not affected. Better temperature homogeneity was also seen in this reactor as four burners were used. As a result, the energy generated from the partial combustion was more uniformly distributed inside the reactor. The averaged product temperature at the exit of the reactor was 1278 °C rendering a mass averaged reduction degree of the product as 93%. The heat loss of this reactor was 0.65 MW, which is a little bit greater than the heat loss in run # 3. This is expected as the high temperature region in Figure 8.21 is closer to the wall than that in Figure 8.12. The main species distribution inside the reactor is shown in Figures 8.22 and 8.23. No noticeable change in the CO and CO2 mole fractions outside the flame region was 186 seen as the reduction of magnetite concentrate particles was done by H2. The mole fractions at the exit of the reactor for H2, H2O, CO and CO2 are 0.47, 0.31, 0.13 and 0.025, respectively. 8.6. Concluding Remarks Pilot flash ironmaking reactors of different geometrical dimensions with a capacity of producing 100,000 tons/yr of metallic iron were designed. The metallization degrees of product from these reactors were sufficiently high for use in the subsequent steelmaking step. In the one-burner design, reactors with a diameter of 6 m gave better particle and temperature distributions than reactors with a diameter of 4 m. Better energy efficiency in terms of heat loss was also seen for reactors with a diameter of 6 m. But high particle number density near the wall was not completely avoided in those reactors when operated to produce metallic iron. High particle number density was not seen in the reactor in run # 6 when operated to product molten iron. Therefore, the geometry used in run # 6 was used as the design of the pilot flash reactor when operated to produce molten iron. A reactor with a diameter of 6 m and 4 burners was also simulated. The increase in burner number in this reactor led to better particle distribution. The particle distribution in this reactor showed lower probability in particle sticking compared with the reactor in run # 3 with a single burner design. 187 Table 8.1. Dimension of Pilot Reactors under One-burner Design D1 (m) D2 (m) H1 (m) H2 (m) 4.0 4.0 6.0 6.0 4.0 6.0 2.0 2.0 2.0 2.0 --- 12.0 10.0 6.0 6.0 13.0 9.0 6.0 6.0 6.3 5.0 --- Preheat Temp. (°C) 600 1000 600 1000 1000 1000 Designed Product Temp. (°C) 1300 1300 1300 1300 1600 1600 Run # 1 2 3 4 5 6 Table 8.2. Wall Material Properties Refractory Insulation Steel shell Thermal Conductivity (W·m-1·K-1) 10−6 𝑇 2 − 0.0032 𝑇 +4.5396 3 × 10−8 𝑇 2 + 4 × 10−5 𝑇 +0.1797 50 Density (kg·m-3) Specific Heat (J·kg-1 ·K-1) 2890 0.2965 T+ 362 1081 714 7850 470 Table 8.3. Operating Conditions for Solid Product with Input Gases Preheated to 600 °C Natural Gas Recycled H2 Oxygen N2 (Carry Gas) Concentrate Flow Rate (kg/s) 1.15 0.43 2.19 0.07 5.20 Preheat Temp. (°C) 600 600 600 25 25 Table 8.4. Operating Conditions for Solid Product with Input Gases preheated to 1000 °C Natural Gas Recycled H2 Oxygen N2 (Carry Gas) Concentrate Flow Rate (kg/s) 0.91 0.36 1.54 0.07 5.20 Preheat Temp. (°C) 1000 1000 1000 25 25 188 Table 8.5. Operating Conditions for Molten Product with Input Gases Preheated to 1000 °C Natural Gas Recycled H2 Oxygen N2 (Carry Gas) Concentrate Flow Rate (kg/s) 0.91 0.36 1.54 0.07 5.20 Preheat Temp. (°C) 1000 1000 1000 25 25 Table 8.6. Product Temperature in Each Run Run # 1 2 3 4 5 6 Product Temp. (°C) 1302 1285 1303 1287 1605 1590 Reduction Degree (%) 96 94 96 94 97 96 Table 8.7. Heat Loss and Heat Generated from Partial Combustion Run # 1 2 3 4 5 6 Heat Loss (MW) 0.72 0.55 0.62 0.45 0.68 0.61 Heat generated (MW) 19.26 12.31 19.26 12.31 20.58 20.58 Sensible heat of input gases (MW) 6.82 9.92 6.82 9.92 13.60 13.60 Percentage (%) 2.76 2.47 2.38 2.02 1.99 1.79 189 Figure 8.1 Schematic representations of pilot flash ironmaking reactors Figure 8.2 Distribution of the powder feeding ports on the roof of the reactor. 190 Figure 8.3 Burner configuration. Figure 8.4 Reactor wall structure (unit in m). 191 Figure 8.5. Typical mesh for the pilot reactor, total number of cells 250,996: (a) 3D view, (b) Cross-section view. 192 Figure 8.6. Velocity vector field in the plane that passes through the center of two powder feeding ports: (a) run # 1, (b) run # 3 under operating conditions listed in Table 8.3 (unit in m/s). Figure 8.7. Velocity vector field in the plane that passes through the center of two powder feeding ports: (a) run # 2, (b) run # 4 under operating conditions listed in Table 8.4 (unit in m/s). 193 Figure 8.8. Velocity vector field in the plane that passes through the center of two powder feeding ports: (a) run # 5, (b) run # 6 under operating conditions listed in Table 8.5 (unit in m/s). Figure 8.9. Particle number density (particles/cm3) in the plane that passes through the center of two powder feeding ports: (a) run # 1, (b) run # 3 under operating conditions listed in Table 8.3. 194 Figure 8.10. Particle number density (particles/cm3) in the plane that passes through the center of two powder feeding ports: (a) run # 2, (b) run # 4 under operating conditions listed in Table 8.4. Figure 8.11. Particle number density (particles/cm3) in the plane that passes through the center of two powder feeding ports: (a) run # 5, (b) run # 6 under operating conditions listed in Table 8.5. 195 Figure 8.12. Temperature distribution in the plane that passes through the center of two powder feeding ports: (a) run # 1, (b) run # 3 under operating conditions listed in Table 8.3 (unit in K). Figure 8.13. Temperature distribution in the plane that passes through the center of two powder feeding ports: (a) run # 2, (b) run # 4 under operating conditions listed in Table 8.4 (unit in K). 196 Figure 8.14. Temperature distribution in the plane that passes through the center of two powder feeding ports: (a) run # 5, (b) run # 6 under operating conditions listed in Table 8.5 (unit in K). Figure 8.15. Species distribution in the plane that passes through the center of two powder feeding ports of run # 5: (a) H2, (b) H2O, (c) CO 197 Figure 8.16. Species distribution in the plane that passes through the center of two powder feeding ports of run # 6: (a) H2, (b) H2O, (c) CO Figure 8.17 Distribution of the burners on the roof of the reactor. 198 Figure 8.18. Burner configuration and dimension Figure 8.19. Vector field in the plane that passes through (a) the center of two burners, (b) the center of two powder feeder ports (unit in m/s). 199 Figure 8.20. Particle number density (particles/cm3) in the plane that passes through the center of two powder feeding ports. Figure 8.21. Velocity vector field in the plane that passes through (a) the center of two burners, (b) the center of two powder feeder ports (unit in m/s). 200 Figure 8.22. Species distribution in the plane that passes through the center of two burners: (a) H2, (b) H2O Figure 8.23. Species distribution in the plane that passes through the center of two burners: (a) CO, (b) CO2