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Jet attrition characteristics of chemical looping oxygen carriers and CO2 sorbents Kim, Jun Young 2020

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Jet attrition characteristics of chemical looping oxygen carriers and CO2 sorbents  by  Jun Young Kim  B.A.Sc., Sungkyunkwan University, 2015 M.A.Sc., Sungkyunkwan University, 2016  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Chemical and Biological Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  August 2020  © Jun Young Kim, 2020 ii  The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, the dissertation entitled:  Jet attrition characteristics of chemical looping oxygen carriers and CO2 sorbents  submitted by Jun Young Kim in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Chemical and Biological Engineering  Examining Committee: Naoko Ellis, Chemical and Biological Engineering Research supervisor John R. Grace, Chemical and Biological Engineering Co-supervisor C. Jim Lim, Chemical and Biological Engineering Co-supervisor  Davide Elmo, Mining Engineering University Examiner  Richard Kerekes, Chemical and Biological Engineering University Examiner  Additional Supervisory Committee Members: Xiaotao Tony Bi, Chemical and Biological Engineering Supervisory Committee Member Bern Klein, Mining Engineering Supervisory Committee Member iii  Abstract  Sorption-enhanced chemical looping reforming is a process with the potential to produce synthesis gas (syngas), mostly a mixture of CO and H2, from hydrocarbon fuels, without having to separate O2 from air. In this system, particle attrition is an important consideration due to the high gas velocity and chemical reactions, affecting reactor performance, operating conditions and material loss by entrainment and elutriation. Fundamental studies on jet attrition with iron as oxygen carrier and limestone as CO2 sorbent were carried out with varying temperature, jet velocity, duration, solid species weight fraction and the presence of chemical reactions to understand how these various factors affect attrition. Experimental investigation included comparing SEM images and PSD data before and after attrition, and particle size changes with different operating conditions. Furthermore, crushing strength and breakage energy tests were determined with a compression unit to understand how material properties affect particle attrition. In addition, for in-depth fundamental attrition studies on material properties, porosity, specific surface area and pore size distributions were measured to investigate the effects of chemical reaction on attrition. Based on the experimental findings, a mechanistic jet attrition model (JAM) was developed to improve the understanding of jet attrition and predict the particle size distribution in fluidized systems, considering that particle attrition was affected by changes in various operating conditions, such as time, temperature, gas phase species concentrations, reactions and particle composition. Material property changes were considered, as well as how both fragmentation and abrasion affect fluidized bed systems. A novel mechanistic model for attrition was suggested, allowing for variations of material properties, chemical reactions, and mechanical attrition by iv  fragmentation and abrasion. With the aid of three fitted constants, the model fitted the experimental results well.  v  Lay Summary  Sorption-enhanced chemical looping reforming is a potential process to produce synthesis gas (syngas), while capturing CO2 from fuels, without having to separate O2 from air. While operating the process in the reactor, fine particles are generated from particle breakage, some leaving the system with the exhaust gas, affecting operation efficiency and causing air pollution. Particle breakage of oxygen carrier and sorbent particles was tested and successfully modeled in this project to improve the efficiency and stability of processes for reducing the impact on public health and the environment.  vi  Preface  This dissertation is an original, independent work of the author, Jun Young Kim, under the supervision of Drs. Naoko Ellis, C. Jim Lim and John R. Grace. Three papers on attrition, two published, and one submitted to a journal, are included in this thesis. All of the work was completed at the University of British Columbia, Vancouver campus, and the Korea Institute of Energy Research, Daejeon, South Korea. The particle compression tests of iron, iron oxide, limestone and lime covered in this thesis were carried out in Korea Institute of Energy Research by myself. The author designed test sections, conducted experiments, wrote Matlab coding for modeling, compiled results, analyzed the outcomes and prepared this dissertation.   Chapter 3 in this thesis has been published as follows:  Kim JY, Ellis N, Lim CJ, Grace JR. Attrition of binary solids in a jet attrition unit. Powder Technology 2019;352;445-52.  I was responsible for all the tests with a jet apparatus in the Clean Energy Research Centre, Chemical and Biological Engineering at UBC under the supervision of Drs. Ellis, Lim and Grace; SEM, XRD tests at department of Earth, Ocean and Atmospheric Science at UBC were supervised by Dr. Raudsepp; particle compression tests at the Departments of Materials Engineering and Civil Engineering at UBC were under the supervision of Drs. Chae and Zobeiry. Also, I wrote all the manuscript and published the paper as the first and corresponding author.  vii  Chapter 4 has been published as a paper: Kim JY, Ellis N, Lim CJ, Grace JR. Effect of calcination/carbonation and oxidation/reduction on attrition of binary solid species in sorption-enhanced chemical looping reforming. Fuel 2020; 271; 117665.  I conducted all the tests with the jet apparatus, gas chromatograph and BET in Chemical and Biological Engineering at UBC under the supervision of Drs. Ellis, Lim, Grace and K. Smith. SEM, XRD and mercury porosimetry tests were carried out in the Department of Earth, Ocean and Atmospheric Science at UBC under the supervision of Lai, Kato and Dr. Raudsepp. EDX was conducted in the Department of Materials Engineering under the supervision of Kabel. Compression tests were performed at the Korea Institute of Energy Research supervised by Dr. Doyeon Lee. I wrote the manuscript and submitted the paper after revision as the first and corresponding author.  Chapter 5 of this thesis corresponds to the paper:  Kim JY, Li ZJ, Ellis N, Lim CJ, Grace JR. Jet attrition model in fluidized bed for sorption-enhanced chemical looping reforming process. Submitted to Fuel Processing Technology. I conducted all the tests and CFD simulations and wrote a Matlab code for attrition modeling at UBC under the supervision of Drs. Ellis, Lim and Grace. I also conducted the compression test at the Korea Institute of Energy Research under the supervision of Dr. Doyeon Lee. viii  Table of Contents  Abstract ......................................................................................................................................... iii Lay Summary .................................................................................................................................v Preface ........................................................................................................................................... vi Table of Contents ....................................................................................................................... viii List of Tables ............................................................................................................................... xii List of Figures ............................................................................................................................. xiv List of Symbols ........................................................................................................................... xix List of Abbreviations ............................................................................................................... xxiv Acknowledgements ....................................................................................................................xxv Dedication ................................................................................................................................. xxvi Chapter 1: Introduction ................................................................................................................... 1 1.1 Overview ..................................................................................................................... 1 1.2 Chemical looping process ........................................................................................... 3 1.3 Oxygen carrier and sorbent ......................................................................................... 6 1.4 Attrition ....................................................................................................................... 7 1.5 Research objectives and principal tasks of this thesis project .................................. 13 1.6 Thesis outline ............................................................................................................ 14 Chapter 2: Experimental setup and procedures ............................................................................ 16 2.1 Jet apparatus .............................................................................................................. 16 2.2 Mastersizer ................................................................................................................ 19 ix  2.3 Compression test ....................................................................................................... 23 2.4 Thermogravimetric analyzer (TGA) ......................................................................... 26 Chapter 3: Attrition testing without reaction ................................................................................ 30 3.1 Operating conditions ................................................................................................. 30 3.2 Results and discussion .............................................................................................. 31 3.2.1 Single species attrition .......................................................................................... 31 3.2.2 Binary solid species attrition ................................................................................. 34 3.3 Conclusions ............................................................................................................... 48 Chapter 4: Effect of calcination/carbonation and oxidation/reduction on attrition of binary solid species ........................................................................................................................................... 49 4.1 Introduction ............................................................................................................... 49 4.2 Operating conditions ................................................................................................. 52 4.2.1 Jet apparatus .......................................................................................................... 52 4.2.2 TGA tests .............................................................................................................. 55 4.3 Results and discussion .............................................................................................. 56 4.3.1 Effect of reaction on attrition ................................................................................ 56 4.3.1.1 Iron oxidation ................................................................................................ 56 4.3.1.2 Hematite reduction ........................................................................................ 64 4.3.1.3 Lime carbonation .......................................................................................... 76 4.3.1.4 Limestone calcination ................................................................................... 85 4.3.2 Attrition of binary solid species ............................................................................ 92 4.4 Conclusions ............................................................................................................... 95 Chapter 5: Jet attrition model ........................................................................................................ 96 x  5.1 Introduction ............................................................................................................... 96 5.2 Jet attrition model description ................................................................................... 99 5.3 Impact velocity determination by Computational Fluid Dynamics (CFD) ............ 111 5.4 Abrasion and fragmentation modeling.................................................................... 118 5.4.1 Hardness testing for fragmentation and abrasion ................................................ 118 5.4.2 Modified particle mass exchange model ............................................................. 119 5.4.3 Modified Archard equation ................................................................................. 122 5.4.4 Parameter fitting.................................................................................................. 125 5.5 Model comparison with Ghadiri’s model and experimental results ....................... 127 5.5.1 Ghadiri’s model .................................................................................................. 127 5.5.2 Comparison of model predictions with experimental data ................................. 130 5.6 Conclusions ............................................................................................................. 136 Chapter 6: Conclusions and recommendations ........................................................................... 137 6.1 Overall conclusions for this thesis .......................................................................... 137 6.1.1 Experimental ....................................................................................................... 138 6.2 Recommendations for future work ......................................................................... 145 References ...................................................................................................................................149 Appendices ..................................................................................................................................171 Appendix A Crystal structure of solid species ................................................................ 171 Appendix B Quantitative X-ray diffraction (XRD) method ........................................... 174 Appendix C Crushing strength and specific breakage energy calculation ..................... 175 Appendix D Experimental dataset of jet apparatus unit ................................................. 177 Appendix E Efficiency of magnetic separation procedure ............................................. 182 xi  Appendix F SEM images of particle samples ................................................................. 185 Appendix G Mesh independence study .......................................................................... 188 Appendix H Matlab codes for jet attrition model ........................................................... 189 Appendix I Engineering drawings of proposed impinging jet unit: to be constructed and tested in future work ....................................................................................................... 249  xii  List of Tables  Table 2.1 Test conditions for attrition........................................................................................... 18 Table 2.2 Chemical compositions of samples............................................................................... 21 Table 2.3 Particle characteristics for each solid species. .............................................................. 25 Table 2.4 Classical models for gas-solid reaction from Nasr and Plucknett [66]. ........................ 29 Table 3.1 Umf of iron, limestone and their mixtures. .................................................................... 36 Table 4.1 Relative mean error percentage (RME%), root mean square of absolute error (RMSE) and R2 between TGA data and model for lime carbonation. ........................................................ 61 Table 4.2 Relative mean error percentage (RME%), root mean square of absolute error (RMSE) and R2 between TGA data and model for hematite reduction with CH4. ..................................... 71 Table 4.3 Specific surface area, specific crushing strength and porosity of hematite reduced at different conversions and temperatures. Hematite was reduced with 30 vol% of CH4 in N2. ...... 72 Table 4.4 Quantitative XRD analysis (wt%) of iron phases after Fe2O3 samples were reduced by 30 vol% CH4 at 700 and at 800°C for 6 h of simultaneous attrition/reaction. .............................. 74 Table 4.5 Relative mean error percentage (RME%), root mean square of absolute error (RMSE) and R2 between TGA data and model for lime carbonation. ........................................................ 80 Table 4.6 Mann-Whitney U test results for the effect of CO2 on 6 h attrition at 800°C. ............. 82 Table 4.7 Specific surface area and porosity of lime carbonated with different CO2 concentrations at 800°C for 6 h. ................................................................................................... 83 Table 4.8 Relative mean error percentage (RME%), root mean square of absolute error (RMSE) and R2 between TGA data and model for limestone calcination. ................................................. 89 Table 4.9 Specific surface area and porosity of limestone calcined at different temperatures. .... 91 xiii  Table 5.1 Reaction kinetic models for reactions, adapted from Chapter 4. ................................ 106 Table 5.2 Young’s modulus for different solid species. ............................................................. 107 Table 5.3 Constitutive equations for CFD simulation. ............................................................... 112 Table 5.4 Simulation model parameters. .................................................................................... 114 Table 5.5 Daughter particle size distribution of iron from each particle size bin after compression test in percentage by mass........................................................................................................... 120 Table 5.6 Daughter particle size distribution of hematite from each particle size bin after compression test in percentage by mass. .................................................................................... 121 Table 5.7 Daughter particle size distribution of limestone from each particle size bin after compression test in percentage by mass. .................................................................................... 121 Table 5.8 Daughter particle size distribution of lime from each particle size bin after compression test in percentage by mass. .................................................................................... 121 Table 5.9 Values of the parameters Cfatigue and Ccollision. ............................................................. 127 Table 5.10 Interfacial energies of particle species. ..................................................................... 128 Table 5.11 Values of parameters for daughter distributions in general form adapted from Diemer and Olson [208]........................................................................................................................... 129 Table 5.12 Comparison of experimental data and predictions of attrition model with two fitting parameters (Cfatigue and Ccollision). ................................................................................................. 131 Table A.1 Five crystal systems with three edge lengths and three interaxial angles [189]. ....... 172  xiv  List of Figures  Figure 1.1 Schematic diagram of amine scrubbing technology. ..................................................... 2 Figure 1.2 Schematic of chemical looping reforming concept with iron as oxygen carrier. .......... 4 Figure 1.3 Schematic of sorption-enhanced chemical looping reforming concept. ....................... 5 Figure 1.4 Three types of attrition in fluidized beds: (a) jet attrition; (b) bed attrition; and (c) cyclone attrition. ............................................................................................................................. 9 Figure 1.5 Two types of attrition modes and their effects on particle sizes. ................................ 10 Figure 2.1 Schematic of the modified ASTM experimental jet apparatus. .................................. 16 Figure 2.2 PSDs of iron after different periods of single-species attrition testing in jet apparatus at 20ºC with air flow of 149 m/s. .................................................................................................. 19 Figure 2.3 Particle size distributions of iron, iron oxide (Fe2O3), limestone and lime particles prior to attrition and compression tests. ........................................................................................ 22 Figure 2.4 Schematic diagram of FGJN compression test unit. ................................................... 24 Figure 2.5 Schematic of TGA unit. ............................................................................................... 27 Figure 3.1 Particle size distributions of (a) iron and (b) limestone particles after different periods of single-species attrition testing in jet apparatus at 20ºC with air flow of 149 m/s. ................... 33 Figure 3.2 (a) Schematic progress of fluidization in a two solid species bed; (b) fluidization curve of an iron and limestone mixture (Iron:Limestone=0.75:0.25 by mass fraction at 20ºC). ........... 35 Figure 3.3 Particle size distributions of: (a) iron particles; and (b) limestone particles for different initial mass proportions (20°C, jet velocity = 149 m/s, 6 h of attrition). ...................................... 37 Figure 3.4 SEM images of iron for initial mass proportions of: (a) 75%; (b) 50%; and (c) 25% from Iron:Limestone mixture with jet velocity = 149 m/s after 6 h of attrition at 20ºC. ............. 38 xv  Figure 3.5 Size distributions of: (a) iron; and (b) limestone particles for different gas jet velocities, beginning at Iron:Limestone = 0.5:0.5 by mass; temperature: 20°C; duration: 6 h attrition. ......................................................................................................................................... 40 Figure 3.6 Size distributions of: (a) iron; and (b) limestone particles after 6 h of attrition for different temperatures with Iron:Limestone initially 0.5:0.5 by mass, jet velocity of 149 m/s. ... 43 Figure 3.7 SEM images of iron particles at: (a) 20ºC; (b) 250ºC; and (c) 500ºC with Iron:Limestone after 6 h of attrition initially 0.5:0.5 by mass, actual flow of 149 m/s. ............... 44 Figure 3.8 SEM images of limestone at: (a) 20ºC; (b) 250ºC; and (c) 500ºC for Iron:Limestone after 6 h of attrition, initially 0.5:0.5 by mass, jet velocity of 149 m/s. ........................................ 45 Figure 3.9 SEM images of iron and limestone after 6 h of attrition from Iron:Limestone initially 0.5:0.5 by weight with different temperatures, and jet velocity of 149 m/s. ................................ 47 Figure 4.1 Iron oxidation conversion percentage with extra dry air for 60 ml/min flow rate at 700 to 800°C. ....................................................................................................................................... 58 Figure 4.2 Iron oxidation conversion percentage with 60 ml/min extra dry air and different particle size ranges at 800°C. ........................................................................................................ 58 Figure 4.3 Parabolic rate constants for Fe to Fe3O4 oxidation in air. ........................................... 59 Figure 4.4 Curve fitting of 0-63 μm iron oxidation data, and combined parabolic model and second order kinetic model at 800°C with an air flow rate of 60 ml/min. .................................... 61 Figure 4.5 Particle size distributions of iron attrition with and without reaction at 800°C for 6 h at jet velocity = 221 m/s. ............................................................................................................... 63 Figure 4.6 SEM image of cross-sectional area of a partially oxidized ~1000 μm iron particle after 6 h of heat treatment with air at 700°C. Cavities were formed at the iron/iron oxide interface. .. 64 xvi  Figure 4.7 Effect of reaction temperature on conversion of Fe2O3 to Fe (0-63 μm Fe2O3 particles reduction with 10 vol% CH4 balanced in N2, with overall flow of 60 ml/min). ........................... 65 Figure 4.8 Effect of particle size on conversion of Fe2O3 to Fe (Fe2O3 reduction with 10 vol% CH4 balanced in N2 at 800°C with an overall flow of 60 ml/min). .............................................. 66 Figure 4.9 Effect of CH4 concentration balanced by N2 on conversion of Fe2O3 to Fe (0-63 μm Fe2O3 reduction at 800°C with overall flow of 60 ml/min). ......................................................... 66 Figure 4.10 Carbon deposition in reduced hematite for different temperatures and CH4 concentrations after 5 h of exposure in the TGA. ......................................................................... 68 Figure 4.11 Activation energy of hematite reduction as a function of conversion obtained by isothermal-isoconversional method with 5 to 15 vol% CH4 for 0-63 μm particles at 800°C. ...... 69 Figure 4.12 Curve fitting of experimental 0-63 μm Fe2O3 reduction data and parallel kinetic model with 10 vol% of CH4 in N2 at 800°C, for overall 60 ml/min gas flow. ............................. 71 Figure 4.13 PSDs of hematite (Fe2O3) attrition in the presence and absence of reduction at 800°C with a jet velocity of 221 m/s. Note that pure N2 was used for the attrition/without reaction. ..... 73 Figure 4.14 PSDs of hematite after 6 h attrition with a jet velocity of 221 m/with and without reduction at 800°C, s. .................................................................................................................... 75 Figure 4.15 PSDs of hematite (Fe2O3) after 6 h of attrition accompanied by reduction with different CH4 concentrations at 800°C and jet velocity = 221 m/s. .............................................. 76 Figure 4.16 Curve fitting of experimental lime (0-63 μm) carbonation data with 60 ml/min of 50 vol% CO2 in N2, at three temperatures. ........................................................................................ 78 Figure 4.17 Curve fitting for model of Lee et al. [137] of lime (CaO) carbonation data with two CO2 concentrations. ...................................................................................................................... 79 xvii  Figure 4.18 PSDs of lime (CaO) after 6 h attrition for carbonation with different CO2 concentration at 800°C for jet velocity = 221 m/s. ....................................................................... 81 Figure 4.19 PSDs of lime (CaO) attrited/carbonated at 700 and 800°C for 6 h with 30 vol% of CO2 balanced with N2 at jet velocity = 221 m/s. .......................................................................... 84 Figure 4.20 PSDs of lime (CaO) attrition tests with and without carbonation for 6 h at jet velocity = 221 m/s. ..................................................................................................................................... 85 Figure 4.21 Curve fitting of experimental limestone (0-63 μm) calcination data with 60 ml/min of air for three temperatures. ......................................................................................................... 88 Figure 4.22 Curve fitting of experimental limestone calcination data with rate equation adopted by Escardino et al. [153] at 800°C with 60 ml/min of air. ........................................................... 88 Figure 4.23 PSDs of limestone with calcination at 700 and 800°C after simultaneous 6 h attrition/reaction at jet velocity = 221 m/s with air. ...................................................................... 90 Figure 4.24 Pore size distribution of limestone calcined at different temperatures measured by mercury porosimetry (located at Department of Earth, Ocean and Atmospheric Science at UBC)........................................................................................................................................................ 91 Figure 4.25 Size distributions of hematite (Fe2O3) from hematite alone test and hematite segregated from hematite:lime mixtures initially 0.5:0.5 by weight, after 6 h of attrition with/without reduction at 800°C. Jet velocity = 221 m/s. ............................................................ 93 Figure 4.26 Size distributions of lime (CaO) from lime-alone test and lime segregated from hematite:lime 0.5:0.5 initially by weight, with 6 h attrition with/without carbonation at 800°C with jet velocity = 221 m/s. .......................................................................................................... 94 Figure 5.1 Jet attrition model (JAM) algorithm flow chart. ....................................................... 104 Figure 5.2 Mesh design of jet apparatus. .................................................................................... 114 xviii  Figure 5.3 Average velocity profile of the Eulerian solid phase along the vertical axis on orifice hole for iron species. ................................................................................................................... 116 Figure 5.4 Empirical particle impact velocity correlation fitted based on CFD simulation work...................................................................................................................................................... 118 Figure 5.5 Linear regression of modified Archard equation with different species. .................. 125 Figure 5.6 Experimental and predicted particle size distributions of iron at 800°C with jet velocity = 221 m/s simulated with (a) Ghadiri’s model [200] and (b) jet attrition model (JAM) with two fitted parameters (Ccollision and Cfatigue). The error bars for the experimental results represent standard errors among triplicated trials. ...................................................................... 134 Figure 5.7 Cumulative particle size distributions of experimental data points and simulation prediction lines for each solid species at 800°C and 6 h attrition with reaction (jet velocity=221 m/s, iron oxidation under air, hematite reduction with 50 vol% CH4, limestone calcination with air and lime carbonation with 30% CO2). ................................................................................... 135  xix  List of Symbols  A Pre-exponential factor [s-1] Ar Archimedes number [-] C Parameter for crushing strength [-] Ccollision Collision factor, [-] CD Drag coefficient, [-] Cfatigue Overall fatigue factor, [-] c Average particle velocity fluctuation, [m/s] cb Initial molar concentration of CaCO3 in particle [kmol/m3] cg Gas concentration [vol%] ?̅?𝑝 De Brouckere mean diameter, [μm] Fc,eq Equivalent breakage force [N] Fc Particle crushing strength [N] Ea Activation energy [kJ/mol] Eb0 Breakage energy prior to collision, [J] Eb Breakage energy [J] Eloss Kinetic energy loss after collision, [J] Esp Specific breakage energy [J/g] e Restitution coefficient [-] F Force [N] F* Ratio of loading force to crushing strength [-] Fc Particle breakage force [N] xx  f(X) Differential form of mechanism function [-] g Acceleration of gravity [m/s2] g0,p Radial distribution coefficient, [-] g(X) Integral form of mechanism function [-] H Length of column [m] I Stress tensor [-] I2D Second invariant of deviatoric stress tensor [-] K Dimensionless constant from the Archard equation [-] Kgs Gas-solid momentum exchange coefficient [-] Kabr Volume specific abrasion constant [1/m3] k Rate constant [varies with different given models] kp Parabolic rate constant [g2/(cm4s)] k(T) Arrhenius rate constant at temperature [K/s] L Wear distance [m] M Total number of particle size bin [-] m0 Initial weight of sample [mg] mf Final weight of sample [mg] mi Mass of particles in ith particle size bins, [kg] mp Particle mass, [kg] m(t) Instantaneous weight of sample during reaction [mg] N Effective number of particle collisions [-] n Number of particles [-] np Number density [1/m3] xxi  P Pressure [Pa] 𝑃𝐶𝑂2𝑒𝑞 Equilibrium partial pressure of CO2 within CaCO3 [kPa] p Calculated probability from Mann Whitney U test [-] pf Number of particles produced [-] q0, q1 Daughter distribution parameter [-] R Gas constant [J/(mol K)] Re Reynolds number [-]  Rep* Particle Reynolds number for Gidaspow’s drag model [-] r0, r1 Daughter distribution parameter [-] S Surface area of particle [m2] s0, s1 Daughter distribution parameter [-] T Temperature [K] t Time [s] U Superficial gas velocity [m/s] Uff Final fluidization velocity [m/s] Uif Initial fluidization velocity [m/s] Ujet Jet velocity [m/s] Umf Minimum fluidization velocity [m/s] up Particle impact velocity [m/s] V Volume [m3] Vp Volume of particle [m3] w Weight fraction [-] w0, w1 Daughter distribution parameter [-] xxii  X Conversion [-] Xt Total conversion at time t [-] Xu Ultimate conversion of carbonated CaO [-] X∞ Equilibrium conversion [-] Y Young’s modulus [GPa] z Ratio of daughter to parent particle volume [-]  Greek Symbols α Material constant in eqn. (5-1), [-] β Euler beta function, [-] Γ Interfacial energy [J/m2] γ Heating rate [K/s] γθm Collision dissipation of energy [kg/s3m] δ Compression displacement [m] 𝛿𝑐 Maximum compression displacement [m] ε Porosity [-] εmf Porosity at minimum fluidization velocity [-] ζ Slope of ln(-ln(1-X)) vs ln(t) [-] η Constant of Hancock and Sharp analysis [-] θ Daughter particle distribution [-] θp Granular temperature [m2/s2] λp Average distance travelled by a moving particle between successive collisions [m] μb Shear viscosity, [kg/s m] xxiii  μp,col Solid collision viscosity [kg/s m] μp,fr Solid frictional viscosity, [kg/s m] μp,kin Kinetic viscosity, [kg/s m] ν Daughter distribution parameter, [-] ρp Particle density [kg/m3] 𝜎𝑐 Particle failure strength [N] τ Stress tensor, [Pa] ψ Probability density function of daughter particle sizes, [-]  Subscripts g gas mf Minimum fluidization p particle xxiv  List of Abbreviations  ASTM American Society for Testing and Materials BET Brunauer–Emmett–Teller analysis CFD Computational fluid dynamics CLR Chemical looping reforming DEM Discrete element model DPM Discrete phase model JAM Jet attrition model KTGF Kinetic theory of granular flow LPM Liters per minute PSD Particle size distribution RME Relative mean errors RMSE Root-mean-square absolute error SEM Scanning electron microscopy TGA Thermogravimetric analyzer XRD X ray powder diffraction  xxv  Acknowledgements  I would like to express my deepest gratitude to professors Naoko Ellis, Jim Lim and John Grace for their distinguished supervision, patience, invaluable guidance and financial assistance throughout the research program. Sincere thanks also to my supervisory committee, professors Xiaotao Tony Bi and Bern Klein, who offered their guidance in my research. In addition, I would like to thank the Ministry of National Defense in South Korea for allowing me to study in Canada from 2016 to 2020. Financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC) is acknowledged with gratitude. I thank the University of British Columbia and Department of Chemical and Biological Engineering, for providing two four-year fellowships and an international tuition award. Thanks to Compute Canada for the provision of mass computational sources. Thanks to my student research assistants over the years – Dalminder, Daniel, Pius, Dominik and John – without whom I could not have accomplished as much as I did experimentally. Thanks to all my friends and colleagues in the departments of Chemical and Biological Engineering, Mechanical Engineering, Materials Engineering and Statistics, who offered advice and encouraged me along the way. Thanks to my former supervisor, professor Dong Hyun Lee for emotional support and sharing with me his experience from when he studied at UBC. Special thanks are owed to my parents and sister for their invaluable emotional support and understanding. To Seong Kyeong who is always there for me with love and encouragement. Finally, to my best friend, Hyuck Joo Kim, with my deepest condolences. May he rest in peace.  xxvi  Dedication     To the memory of  My best friend, Hyuck Joo Kim 1  Chapter 1: Introduction  1.1 Overview A clean and relatively cheap renewable energy supply replacing carbon-containing fuel is receiving close attention to alleviate economic and environmental issues. Due to industrialization and population growth, the total energy requirement for the world is projected to increase from 3.77×1011 to 7.80×1011 GJ by 2040 [1]. Although sources of renewables and nuclear energy are projected to increase by 2040, it is expected that more than 70% of energy sources will still be obtained from fossil fuel by 2040 [1,2]. Thus, coupling fossil energy conversion systems with economic capture, transportation, and safe sequestration schemes for CO2 is needed. Excessive accumulation of CO2 in the atmosphere is causing serious climate change [3]. CO2 is by far the most important greenhouse gas, accounting for up to 64% of the enhanced greenhouse effect because of its relative abundance compared with other greenhouse gases [4]. The CO2 represents ~15% of the flue gas stream from coal combustion power plants. The total amount of CO2 produced from coal-based power plants accounts for more than 40% of all anthropogenic CO2 emissions [3]. In power plants using fossil fuels, CO2 management involves three steps: 1) separation/capture and compression; 2) transportation; and 3) sequestration. Among these steps, CO2 capture is the most energy consuming process [5]. Amine scrubbing technology is already a well-established process to capture CO2 for post-combustion. Figure 1.1 shows a schematic diagram of an amine scrubbing process. In this process, the flue gas is first cooled to ~40 °C before entering an absorber where fresh amine solvent is used to absorb CO2 from the flue gas stream. The spent amine solvent with a high CO2 concentration is regenerated in a stripper at higher temperature (100-150°C), and CO2 is then 2  recovered at low pressures (1-2 bar). In this process, large amounts of high-temperature steam are required to strip the CO2 in the regeneration step, contributing to a large amount of energy required to capture CO2 [6]. There are several alternative processes, such as membrane separation or a chilled ammonia process, but these need to be further developed to be commercially viable [7].  Figure 1.1 Schematic diagram of amine scrubbing technology. Socolow and Pacala [8] suggested several alternative energy sources to replace fossil fuels for long-term energy strategy targeting low or zero carbon emissions. These includes nuclear energy and renewable energy to generate hydrogen. Hydrogen is gaining more attention as a carbon-free clean fuel for the future and it is growingly used for transportation [9]. Current production of hydrogen mostly relies on steam natural gas reforming, with product hydrogen separated from the product syngas, which is mostly a mixture of CO and H2. Steam reforming, however, operates at around 800 to 900°C and ~20 bar pressure, requiring intense energy input due to the overall endothermic reactions.  It also emits CO2 which contributes to the global warming [10]. Yildiz and Kazimi [11] claimed that the heat generated from a nuclear power plant can be used for hydrogen generation by hydrogen-producing thermochemical or high 3  temperature electrolysis plants. However, after the Fukushima nuclear disaster, nuclear energy is not considered as the best option to produce hydrogen [12]. Thus, a new process capturing CO2, as well as producing H2, could be very helpful to reduce CO2 emission. In this project, the chemical looping concept is investigated to capture CO2 while producing H2. The fundamental concept and history of chemical looping technology is considered in the next section.  1.2 Chemical looping process Chemical looping has developed as an alternative technique for improving energy efficiency. The principles of chemical looping for carbonaceous fuel conversion were first applied by industry in the early 20th century. Howard Lane [13] was the first researcher to commercialize the steam iron process for hydrogen production using the chemical looping principle. With iron redox reactions, the steam iron process generates H2 from reducing gas obtained from coal and steam through an indirect reaction scheme. Hydrogen plants based on the same principle were constructed throughout Europe, producing 2.4×107 m3 of hydrogen annually by 1913 after Lane constructed the first plant in 1904 [13]. Modern applications of looping are focused on chemical/energy conversion system and capturing CO2. Chemical looping systems are currently focused on the conversion of carbonaceous fuels, whereas CO2 separation is achieved through the reactions in the process [14–16]. For example, in chemical looping combustion processes, coal-derived syngas or natural gas reacts with a metal oxide (e.g. nickel or iron oxide) in a reducer. The reduced metal moves to an oxidizer (or combustor) where it reacts with air to oxidize. Then the metal oxide returns to the reducer. Pure CO2 leaves the reactor steam if carbonaceous fuels are completely combusted. 4  Chemical looping reforming can be achieved when the carbonaceous fuels are partially reacted, producing H2. More recently, chemical looping reforming was proposed by Mattisson and Lyngfelt [17] to produce syngas without separating N2 from the air. In this process, two reactors are required: an oxidizer and a reformer. A metal oxide is employed as oxygen carrier, transferring oxygen from oxidizer to reformer. In the oxidizer, a reduced oxygen carrier is oxidized by the oxygen, and then carried to the reformer. In the reformer, oxygen carrier provides oxygen to hydrocarbon fuels to produce syngas. Figure 1.2 is a schematic of the chemical looping reforming concept.  Figure 1.2 Schematic of chemical looping reforming concept with iron as oxygen carrier. In order to improve production and capture of CO2, sorbent-enhanced chemical looping reforming, with lime-based sorbents, has been adopted [3,9,18,19]. This process uses an oxygen carrier to produce syngas from hydrocarbons without having to separate N2 from air, whilst 5  capturing CO2 with a sorbent such as CaO-based particles. In this case, exothermic sorbent carbonation provides the heat for the endothermic reforming, while regeneration of the sorbent is driven by the heat from oxygen carrier oxidation [9]. Figure 1.3 shows a schematic of sorption enhanced chemical looping reforming process. In the oxidizer/calciner, metal is oxidized while CaCO3 is calcined by heat, emits CO2. 𝑀 + 0.5𝑂2 → 𝑀𝑂   (1-1) 𝐶𝑎𝐶𝑂3∆→ 𝐶𝑎𝑂 + 𝐶𝑂2 (1-2) Oxidized metal and CaO move to reformer/carbonator and partial oxidation and CO2 capture occur. 𝐶𝐻4 + 𝑀𝑂 → 𝐶𝑂 + 2𝐻2 + 𝑀   (1-3) 𝐶𝐻4 + 4𝑀𝑂 → 𝐶𝑂2 + 2𝐻2𝑂 + 4𝑀  (1-4) 𝐶𝑎𝑂 + 𝐶𝑂2 → 𝐶𝑎𝐶𝑂3  (1-5)   Figure 1.3 Schematic of sorption-enhanced chemical looping reforming concept. 6   1.3 Oxygen carrier and sorbent When operating a sorption-enhanced chemical looping reforming process, there are several important particle characteristics for high performance in producing H2-enriched syngas, while capturing CO2: 1) High reactivity for redox reactions and calcination/carbonation: A higher rate of reaction allows a smaller reactor to be used to achieve the same reactant conversion. A proper selection of particles and reaction conditions can enhance the reaction rate. 2) Structure maintained during multiple reaction cycles: Improving the recyclability and durability of the particles leads to a reduced spent particle purging rate and, hence, to a lower particle makeup rate. The particle recyclability can be improved by using an oxygen carrier with high chemical durability. 3) High attrition resistance: The mechanical strength of the particles is related closely to the particle composition and method of preparation. Improving particle mechanical strength may be achieved by the use of an excellent support material or by suitable synthesis procedures. 4) Limited cost: The raw material cost and the cost of synthesizing the particles are important economic considerations. 5) Environmentally benign: 7  A large volume of purged particles needs to be disposed of in the chemical looping process from particle degradation. Thus, particles with low negative health and environmental impacts are desirable. All the conditions above are related to which particle material is used. Adanez et al. [2] listed 21 different oxygen carriers to compare the equilibrium constant for H2 and CO production. Zafar et al. [20] tested four prospective oxygen carriers for chemical looping reforming. They investigated the syngas composition without steam, and the reactivity of methane reduction. They showed that iron-based oxygen carriers resulted in less deactivation from carbon deposition than for Ni-, Cu- and Mn-based oxygen carriers. Although a Ni-based oxygen carrier showed higher solid conversions, its CO2 formation was highest, indicating the tendency for CH4 to be fully oxidized; whereas, a Fe-based oxygen carrier provided the lowest CO2 formation, showing partial oxidation with methane, generating H2.  An important requirement for reactions involving sorbents and oxygen carriers is that there be sufficient resistance to particle attrition to provide high stability of the sorbent and carrier structure so that the reactivity can be maintained over many cycles of reduction and oxidation, or calcination and carbonation. The resulting decrease in particle size may cause a change in the fluidization flow regime, or excessive entrainment from the operation [21]. Based on these considerations, iron was selected as oxygen carrier and limestone as CO2 sorbent in this study.  1.4 Attrition In any fluidized bed process, the bed material is in motion, so it is inevitably subjected to mechanical stress due to inter-particle collisions, bed-to-wall impacts, and thermal stress. This 8  mechanical stress leads to gradual degradation of the particles. The main effect of attrition is usually the generation of fine particles that may entrain and escape from the system. Therefore, there is a loss of valuable material, requiring an efficient capture system to not lose the material. In catalytic chemical reactors, fresh catalyst makeup to compensate for catalyst loss by attrition can increase the operational costs [22]. Also, the particle size distribution changes as a result of attrition, which can affect reactions in fluidized beds, resulting in deterioration of the performance of the process. For these reasons, Ray et al. [23] claimed that the effect of attrition should be considered when designing fluidized bed reactors. The major interest in attrition is to reduce its extent to a minimum. An obvious approach is to use an optimum attrition-resistant bed material. Friability testing is needed to compare different types of materials in order to select the most attrition-resistant particles. Single and bulk particle compression tests are widely used in material, civil and mechanical engineering fields. However, particles can be broken, even when the impact energy is lower than the breakage energy, due to numerous collisions, affecting the material fatigue [24]. Clift [25] noted the complexity of attrition due to: 1) processing equipment; 2) individual particle properties; and 3) sub-particle phenomena such as fracture, with different time scales. Therefore, attrition differs for the various processes and even between individual regions in reactors used for the same process. Previous work indicates that attrition occurs at three locations in fluidized beds: jet attrition, bed (or bubble) attrition and cyclone attrition [26–28]. Figure 1.4 shows these three types of attrition at different locations. Jet attrition is mainly affected by the orifice gas velocity and the hole size of gas distributors or jets entering from the side or vertically (upward or downwards). Particles are entrained by jets, accelerated, and undergo impacts with the fluidized 9  bed suspension at the end of the jets, resulting in particle attrition similar to that in jet grinding processes [29].  Figure 1.4 Three types of attrition in fluidized beds: (a) jet attrition; (b) bed attrition; and (c) cyclone attrition. Bed attrition, or bubbling attrition, occurs in fluidized beds. Jet and bed attrition are often combined together since bubbles can be only generated from the supply of gas from jets, or the bed attrition is so small that if can be neglected, in which case there is no significant attrition by bubbles [30]. Pis et al. [31] estimated bed attrition by subtracting the jet attrition rate from the total attrition rate, but the resulting bed attrition was then negligible compared to the jet and cyclone attrition rates. Similar results were found by several other groups [27,32,33].  Cyclone attrition is typically reported to be dominated by abrasion [33,34]. Reppenhagen and Werther [34] suggested a model which is independent of the size, geometry, inlet design and manufacture technique of the cyclone. They determined the cyclone loss rate as a function of the number of passes through the cyclone and the cyclone efficiency as a function of the particle size. 10  Cyclone attrition normally contributes a minor proportion of the overall attrition compared to jet attrition. There are two principal modes of attrition: fragmentation and abrasion, depicted in Figure 1.5. When abrasion occurs, small asperities on the particle surface are dislodged, forming fine-particle debris from the original particles. During abrasion, the rough edges of particles are rounded off, producing smooth particle surfaces. Typically a unimodal particle size distribution (PSD) changes to a bimodal PSD due to abrasion. The second type of attrition is fragmentation, where particles split into a small number of similar-size particles, often with rough surfaces. If this is the dominant mechanism, the PSD shifts leftward and downward, but remains unimodal. Various models of the attrition have been suggested, with a view to considering their relevance to impact attrition. Some of these models were originally developed for comminution processes, while others have been adapted for attrition processes because of the similarity of the two processes [35]. Energy-based and abrasion-based models are two representative models which can be used to explain and predict attrition. Figure 1.5 Two types of attrition modes and their effects on particle sizes. 11  Energy-based model is the earliest mechanistic attrition interpretation, considering the required energy for particle breakage. Rittinger’s model [36] is based on the energy consumed, assuming that it is directly proportional to the area of new surfaces formed. Kick's model [37] on the other hand, assumes that the energy consumption is proportional to the volume of the comminuted product. Bond's model [38] is based on the assumption that the energy required for grinding is directly proportional to the length of new cracks formed. Hukki [39] noted that the breakage energy depends on the particle size. In general, attrition models tend to be oversimplified. Abrasion-based models are relatively new compared to energy-based models. These models are frequently used in mineral processing technology since avoiding fines generation is of major interest. The model of Gwyn [40] was developed to describe the attrition of silica-alumina catalysts in fluidized beds, but it has also been applied to a number of other processes. Paramanathan and Bridgwater [41] proposed another abrasion model for shear cells based on the assumption that the rate of surface grinding is proportional to the particle radius. Abrasion-based models are based on the assumption that particle attrition is caused by particle shear stress, rather than inter-particle collisions. Therefore, these models are not applicable to impact attrition of particulate solids. Furthermore, these models do not account for the actual mechanism of particle breakage. Several single-species studies of limestone, iron oxide, and iron ore attrition have been reported. Pis et al. [31] found that the attrition of amorphous materials such as limestone and coal is not affected by the initial particle size. Knight et al. [42] tested jet attrition of limestone, lime and silica-coated calcined pellets with changing temperature and initial particle size. Chen et al. [43] investigated limestone attrition in a circulating fluidized bed at temperatures of 25-12  580ºC and superficial gas velocities from 4.8 to 6.2 m/s and proposed an empirical correlation for estimating the evolution of the average particle diameter. Kang et al. [28] varied the distributor hole size and superficial gas velocity for iron ore fluidization and correlated the attrition rate with the kinetic energy entering from the orifice. The attrition of several species of lime-based sorbents and iron-based oxygen carriers has been reported without reactions occurring. For example, Knight et al. [42] tested attrition of limestone, lime and lime-based sorbent in a modified ASTM unit with changing temperature and initial particle size, but without any reaction. Scala et al. [44] tested limestone attrition in the jet region with different velocities based on an impact damage test unit. Kang et al. [28] tested iron ore with different orifice sizes and superficial gas velocities, but without reaction. Few attrition tests have been reported where there have been two or more solid species present. Kim et al. [45] investigated limestone, iron and their mixtures with varying temperature, gas flow and composition. Arena et al. [46] and Mastellone and Arena [47] investigated coal attrition in a mixture of sand. When the size of the sand particles increased while the mass in the bed remained constant, the authors observed more attrition of coal. Werther and Reppenhagen [48] reported that attrition can be exacerbated in fluidized beds containing two particle species of significantly different hardness, as the harder species will abrade the other, in addition to attrition occurring when particles strike the column walls. Attrition with reactions taking place has received much less attention than attrition without reactions. Chen et al. [43] tested limestone sulphation in a circulating fluidized bed subject to attrition for a very limited range of operating conditions (1150 ppm, 28.6 h of attrition and 2800 ppm of SO2, 10 h of attrition at 850°C). Scala et al. [49] considered limestone 13  sulphation during attrition with different jet velocities in a high-velocity impact unit which contained 1800 ppm of SO2 in an oxygen-nitrogen mixture (8.5 vol% O2, balance N2) at 850°C.  1.5 Research objectives and principal tasks of this thesis project As mentioned above, studies of attrition in fluidized beds have not paid much attention to the effect of reactions on attrition in chemical engineering industries because of its complexity and lack of feasible experimental methods. So far, the limited number of studies of the effect of reactions on attrition have mainly focused on the evolution of particle size distributions (PSDs) and the mass of fines generated due to attrition, generally leaving the change in material properties due to reaction unaccounted for. For the attrition models, previous researchers have overlooked the distinction between abrasion and fragmentation in particle attrition, and attributed all particle breakage to abrasion. As a result, previous models tend to overestimate the extent of abrasion. Rhodes [50] even reported that the Rittinger’s energy-based attrition model usually overestimates by 200-300 times the energy requirement for new broken particle formation. Thus, fundamental attrition studies were conducted first, including: (a) Single and two-species experimental attrition tests to provide a better understanding of particle interactions; and (b) Determine the effect of relevant chemical reactions on attrition. After the experimental tests were done, a mechanistic jet attrition model was developed to predict the particle size distribution (PSD) evolution of solid samples. To achieve these objectives, the principal tasks included:  Attrition tests with binary solid species mixtures, varying the species weight fractions (Iron:Limestone), as well as time, temperatures and jet velocities, without and with 14  reactions. The experimental ranges of these attrition tests are covered in Chapter 2, Experimental setup and procedures.  Perform single-particle compression tests for each species with particle size bins.  Conduct isothermal and non-isothermal TGA tests with solids species with different particle size, gas concentration and temperature to examine the solid conversion as a function of time in the presence and absence of attrition.  Test the particle porosity, BET specific surface area, pore size distribution and crushing strength after chemical reaction.  Measure abrasion with a jet apparatus between minimum fluidization velocity and the impact velocity to fragmentation.  Calculate particle impact velocity by computational fluid dynamics software (ANSYS version 19.2)  Develop and test a jet attrition model algorithm and code.  1.6 Thesis outline Chapter 1 reviews the literature on the sorption-enhanced chemical looping process and attrition, and provides an overall introduction to the work. Chapter 2 presents the detailed experimental setup and procedures. Also, particle material properties such as average diameter, density and particle crushing strength are provided. Chapter 3 explores the effect of solid species weight fraction, time duration, jet velocity and temperature. The effects of single and binary solids species are determined in this chapter. Chapter 4 tests effects of chemical reaction conversion on attrition. Attrition results were analyzed with material properties in the presence of chemical reactions. 15  Chapter 5 develops and tests a jet attrition model based on our experimental observations on attrition. Chapter 6 presents conclusions from the overall project and provides some recommendations for future studies in this area. 16  Chapter 2: Experimental setup and procedures  In this chapter, a detailed experimental setup and procedures to measure material properties are introduced.   2.1 Jet apparatus Attrition tests were performed in a jet apparatus (located in the UBC Clean Energy Research Centre, high headroom lab), modified from the ASTM D5757-11 air-jet apparatus standard [51]. This attrition standard was introduced by Gwyn [40] to estimate the robustness of catalysts, and it has been widely used for attrition testing of various materials such as FCC (fluid cracking catalysts) and steam methane reforming catalysts, as well as limestone and pumice [52–54]. Figure 2.1 presents a schematic diagram of the jet apparatus.  Figure 2.1 Schematic of the modified ASTM experimental jet apparatus. 17  The attrition column made of SS316 has an inner diameter of 35 mm and a height of 710 mm. A diverging-then-converging calming chamber is positioned above the cylindrical column. The gas distributor plate has three orifices of diameter 0.397 mm on a triangular pitch at the bottom of the column. Gas flows through the distributor into the attrition tube where the particles are located. With the three jets causing particle comminution, particles small enough to be entrained by the gas are carried over to the fines collector containing a ceramic filter (combination of aluminum oxide and zirconium oxide, pore size of 1 μm). A 750 W clamshell ceramic heater is provided as a preheater with an 1100 W clamshell ceramic fiber heater enclosing the attrition column. OMEGA CN76000 controllers are used for the heaters. Two OMEGA FMA5526 gas flow controllers control the jet velocity. The original ASTM 5757-11 test operated at 0°C, loading 50 g samples into the attrition column [51]. Air at 0°C flowed through the three orifices in the distributor plate. However, the temperature is not practical as a cooling system would be needed to cool down the air to 0°C to meet the test conditions. Besides, actual chemical looping systems of interest in this thesis operate at high temperatures, over 700°C. Another significant disadvantage of the standard ASTM procedure is the duration of each attrition test. Standard test runs last 5 h, which is not enough to find attrition trends over durations relevant to industrial chemical looping systems. According to Adanez et al., chemical looping systems have been studied up to 1016 hours, compared with over 12 h for our pilot plant [2]. In the tests, the air jet index is measured after the standard ASTM tests, based on the mass of fines entrained from the system. The air jet index is obtained by: 18  𝐴𝑖𝑟 𝑗𝑒𝑡 𝑖𝑛𝑑𝑒𝑥 =𝑀𝑎𝑠𝑠 𝑜𝑓 𝑓𝑖𝑛𝑒𝑠 𝑐𝑜𝑙𝑙𝑒𝑐𝑡𝑒𝑑 𝑑𝑜𝑤𝑛𝑠𝑡𝑟𝑒𝑎𝑚 𝑎𝑓𝑡𝑒𝑟 5 ℎ 𝑡𝑒𝑠𝑡𝑂𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑠𝑎𝑚𝑝𝑙𝑒𝑠 (2-1) However, since the air jet index only measures the amount of fines produced, fragments which are too large to be entrained by the air flowing through the system are not measured, thus causing the attrition to be underestimated. To avoid this problem, the overall particle size distribution (PSD) was measured to allow fragmentation to be fully included in this system.  Since Iron oxidizes in air if the temperature exceeds 560ºC and limestone calcines at 670ºC or more at atmospheric pressure, the temperature was set at 20, 250 and 500ºC for the attrition test without reaction; and 700 and 800ºC with reaction. Since the rate of attrition for fresh samples is high during the initial few hours when abrasion occurs, the duration of tests was set to 3, 6 and 12 hours to cover both short-term fragmentation and long-term abrasion mechanisms. Also the jet velocity was varied from 89-221 m/s to cover the superficial gas velocity range from minimum fluidization to turbulent fluidization. Table 2.1 summarizes the modified test conditions for the attrition tests. Table 2.1 Test conditions for attrition. Experimental variable Conditions Solid materials Iron, hematite, limestone and lime Temperature [ºC] 20 ± 3, 250 ± 4, 500 ± 6, 700 ± 5 and 800 ± 5°C Pressure Atmospheric Sample mass loading [g] 50.0 Test run times [h] 0, 3, 6 and 12 Jet velocity [m/s] 89 to 221 m/s   For some tests, attrition testing was conducted up to 24 hours to see if there is any significant PSD difference after 12 h of attrition. Figure 2.2 shows the PSDs of iron after different periods of single-species attrition testing in jet apparatus at 20ºC with air flow of 149 19  m/s. Here, there is no significant difference of the particle size evolution between the 12 h and 24 h. Therefore, the rest of the attrition tests were conducted up to 12 hours. Particle diameter range, [ m]0-63 63-125 125-250 250-500 500-1000 1000-2400Weight fract ion, [%]0102030400 h 3 h 6 h 12 h 24 h 149 m/s, 20CIron Figure 2.2 PSDs of iron after different periods of single-species attrition testing in jet apparatus at 20ºC with air flow of 149 m/s.  2.2 Mastersizer After each test in the jet apparatus, all particles were gathered, and the particle size distributions of both the entrained and the retained particles were measured by a Mastersizer 2000 laser diffraction system (Malvern Panalytical) with a Scirocco dry-feeding accessory (located at CHBE 518). The De Brouckere mean diameter (volume-mean diameter) was determined, in addition to the Sauter-mean diameter which is more widely reported in the literature. The Mastersizer measures volumes of particles (more specifically, the experimental unit gives the volume of the equivalent scattering spheres) thus the De Brouckere mean diameter, 20  i.e., the volume mean-diameter, is more precise than converting to Sauter mean diameter with several assumptions. Moreover, according to Rhodes [50], the energy requirement and surface created are unlikely to be related by comparing the attrition rate with the Rittinger model, [36],  one of the classical comminution models for particle size reduction, related to surface area: 𝑑𝐸𝑑(𝑑𝑝)= −𝐶1𝑑𝑝2 (2-2) Here E is the comminution energy, dp is the particle diameter and C is an empirical constant. Rhodes showed that the energy requirement to break particles in practice is usually 200-300 times that required to generate new surface area. This work established that the energy requirement and surface created are likely unrelated. Also, Knight [30] claimed that since the Sauter mean gives extra mathematical weight to small particles because of their high surface-area-to-volume ratio, it is less appropriate than the De Brouckere mean, which places a higher importance on the large particles that have significantly higher momentum in fluidized bed processes. The Sauter mean tends to overlook the presence of a few large particles because of their low surface-area-to-volume ratio, but large particles have a more significant influence in the production of smaller particles and fines, especially since their critical stress for fracturing is lower due to larger maximum crack lengths [55]. The De Brouckere mean diameter is expressed as: ?̅?𝑝 =∑ 𝑛𝑖𝑑𝑝𝑖4𝑖∑ 𝑛𝑖𝑑𝑝𝑖3𝑖=∑ 𝑚𝑖𝑑𝑝𝑖𝑖∑ 𝑚𝑖𝑖 (2-3) where ni is the number of particles of size i, mi is the mass of particles of size i, and dpi is the particle diameter of size fraction i. 21  Samples of iron powder (Pearlite) from Rio Tinto (?̅?𝑝=633 μm, ρs=7080 kg/m3), and Strasburg limestone (?̅?𝑝=316 μm, ρs=2667 kg/m3) were obtained to represent an oxygen carrier and a CO2 sorbent, respectively. For simplicity, the iron powder (pearlite) is simply referred to as ‘iron’ in this project. The Strasburg limestone was calcined for 24 h at 900°C, to ensure that lime was formed. The particles were then placed in a dry environment to avoid hydration in the atmosphere. Also, 99.9 mol% purity iron from Goodfellow Inc. was fully oxidized for 24 h at 900°C and then mechanically ground to obtain a range of 0-2400 μm for the hematite attrition tests. The chemical compositions of the samples, measured with quantitative XRD, are identified in   Table 2.2. Here, the Fe3O4 and Fe2O3 were determined by comparing characteristic peaks. For Fe3O4, 2.69 Å (311 plane) is a characteristic peak, whereas Fe2O3 has 2.53 Å. The quantitative XRD analysis were taken by Dr. Raudsepp in the Department of Earth, Ocean and Atmospheric Sciences at UBC. An explanation of quantitative XRD analysis is provided in Appendix B. The PSDs of iron, hematite, limestone and lime are presented in Figure 2.3. All the attrition tests were performed at least three times, with average weight fractions and standard errors calculated and provided on each PSD graph in this thesis. The standard error is calculated by the standard deviation divided by square root of number of attrition tests conducted with a certain condition.  Table 2.2 Chemical compositions of samples. Iron powder (“Iron”) Fe FeO Fe3O4 Fe2O3 Fe3C Other 22  mol% 36.2 13 9.6 0.9 39.7 0.6 Iron oxide composition Fe2O3 Other   mol% 99.9 0.1 Limestone (CaCO3) composition CaCO3 MgCO3 SiO2 Fe2O3 Other mol% 93.6 4.9 0.6 0.04 0.9 Lime (CaO) composition CaO MgO SiO2 Fe2O3 Other mol% 94.7 3.1 1.0 0.1 1.1  Particle diameter range, [ m]0-63 63-125 125-250 250-500 500-1000 1000-2400Weight fraction, [%]010203040IronHematite (Fe2O3)LimestoneLime Figure 2.3 Particle size distributions of iron, iron oxide (Fe2O3), limestone and lime particles prior to attrition and compression tests.  23  2.3 Compression test There are two types of compression test: multi-particle and single particle tests. Although multi-particle tests are more similar to real processes and statistically more representative in nature, they are too complex for analysis to consider such as particle rearrangement, shear stress with different packings, and the models developed for them are empirical [56]. In other words, in multi-particle tests no account is taken of fundamental physical and mechanical properties of the material which may influence attrition. Secondly, the mechanics of particle interaction in both the test device and the real process are not sufficiently well understood to maintain dynamic similarity. In contrast, single particle tests are well defined and can provide confirmation on the attrition mechanism to each particle [57]. There are three different techniques to test single particle attrition: 1) indentation [58]; 2) compression [45]; and 3) impact on a target [59]. Indentation can be used as a tool to understand the local contact since the technique measures the load and the length when a material is indented. However, because the rough edges of particles are rounded off, indentation cannot represent abrasion. Uniaxial compression is relevant to crushing the particles when breakage is dominated by fragmentation [60]. In impact tests, particles accelerated by air or gas strike a wall [61]. With several repeated collisions, particle breakage due to fatigue can be characterized. However, due to fatigue, determining particle breakage due to fragmentation is at best approximate as fatigue accumulates in particles when collisions are repeated. Therefore, compression tests were used in this project. Many different types of compression test systems have been used to determine the particle breakage force such as a simple hydraulic press [62] and an ultra-micro loading system developed by Sikong et al. [63]. Here, the material hardness of each particle species with different particle size bins was tested with an FGJN-50 (Shimpo Inc.) connected to a push-pull 24  gauge stand (FGS-50E-H), compressing particles one at a time. Figure 2.4 is a schematic diagram of the FGJN compression test unit in Korea Institute of Energy Research accessed by Dr. Doyeon Lee. In this unit, a particle is loaded between two hard parallel platens and compressed until the particle breaks. The breakage force is analyzed at the instant at which there is a sudden decrease of force, accompanied by a large increase in displacement. For these tests, the loading rate was set at 0.1 mm/s.  Figure 2.4 Schematic diagram of FGJN compression test unit. Five particle size bins were used, with size intervals of 63-125, 125-250, 250-500, 500-1000 and 1000-2400 μm. The 0-63 μm particle bin could not be tested because the device used was unable to measure how much each small particle had compressed when it broke. An average of 30 test particles per sample were crushed to determine the particle failure strength. The particle crushing strength, defined as the maximum normal compression force that particle 25  withstood, was measured when particles started to break when compressed by the punch. The specific breakage energy for each species in different particle-size bins was calculated by dividing the breakage energy by the mass of a volume-equivalent sphere. The breakage energy and specific breakage energy can be calculated [62,64] as: 𝐸𝑏 = ∫ 𝐹𝑑𝛿𝛿𝑐0 (2-4) 𝐸𝑠𝑝 =6𝐸𝑐𝜋𝑑𝑝3𝜌𝑝 (2-5) where δ is the displacement, and δc is the maximum compression displacement. More explanation and an example are provided in Appendix C. The particle characteristics for each solid species, including De Brouckere mean diameter, density, porosity, average crushing strength and specific breakage, are listed in Table 2.3. Standard deviations are given on each crushing strength. Note that the unit of crushing strength is N, as commonly used in material engineering [62,64,134]. Table 2.3 Particle characteristics for each solid species. Solid species Iron Iron oxide Limestone Lime Manufacturer Rio Tinto Goodfellow Greymont Greymont Particle density [kg/m3] 7105 4403 2667 2666 De Brouckere mean diameter [μm] 633 705 316 316 Porosity, p [-] 0.046 0.170 0.338 0.201 Specific breakage energy [J/g] 63-125 μm 290.6 261.1 13.0 6.57 125-250 μm 27.0 23.7 12.1 6.64 250-500 μm 17.6 15.2 1.30 0.74 500-1000 μm 3.08 2.91 1.10 0.22 1000-2400 μm 0.26 0.26 0.49 0.14 Average crushing strength of particles with different size bins [N] 63-125 μm 4.7±0.5 3.2±0.5 0.2±0.1 0.3±0.1 125-250 μm 5.7±1.2 4.2±1.4 1.6±0.8 1.2±0.5 26  250-500 μm 18.4±2.0 12.3±1.4 2.1±0.6 1.6±0.4 500-1000 μm 30.8±3.5 21.5±1.7 5.3±1.1 3.5±0.4 1000-2400 μm 45.8±2.7 33.0±3.2 26.4±2.3 14.5±1.1  The actual breakage energy of the particles in the jet apparatus is less than the observed value because: (1) Compression testing generally overestimates Young’s modulus compared to impact loading since the deformation from the impact loading is not recoverable upon sudden impact which leads to particle breakage [65]; and (2) Fatigue accumulates, contributing to particle breakage [24]. Rozenblat et al. [59] tested both particle breakage in a compression unit and due to impact. They found a linear empirical dimensional relationship on a log-log scale: ln(𝐹𝑐,𝑒𝑞) = 𝐶1 + 𝐶2 ln(𝑑𝑝3.3𝑈𝑗𝑒𝑡) (2-6) where Fc,eq is the equivalent particle breakage force by impact and compression, Ujet is the impact velocity, and C1 and C2 are fitting parameters.  2.4 Thermogravimetric analyzer (TGA) TGA tests were conducted with a SDT-600 (TA Instruments) located in CHBE 518. Schematic diagram of TGA unit is in Figure 2.5. N2 enters the reaction chamber from the side, keeping the balance in an inert environment. For the isothermal and non-isothermal tests, ~10 mg of iron, iron oxide (Fe2O3), limestone and lime samples were heated in a ceramic pan up to 900°C, with three different ramping rate (5, 10 and 20°C/min). For the iron oxide reduction tests, 10, 30 or 50 vol% of CH4 balanced with N2, for a total flow rate of 60 ml/min. 99.999% purity N2 was flushed for 75 min before each test. 60 ml/min of air was used to oxidize iron and calcine CaCO3. In addition, 10, 30 and 50 vol% of CO2 concentration, balanced with N2, (total flow rate of 60 ml/min) were used to carbonate the CaO up to 900 °C. 27   Figure 2.5 Schematic of TGA unit.  An initial equilibrium hold was at 105°C for 15 minutes; then the temperature was raised by 20°C/min to a final temperature for the isothermal test. The samples were preheated under an inert (N2) gas to the test temperature. After the temperature reached the test temperature, the reaction gas was switched, and the temperature was held constant for up to 300 minutes. For the gas mixture, an OMEGA FMA5526 gas flow controller was connected to the secondary gas line. The extent of the reaction (or conversion) was calculated as: X =𝑚0 − 𝑚(𝑡)𝑚0 − 𝑚𝑓 (2-7) where m0 and mf are the initial and final weights of the oxygen carrier or sorbent, respectively, and m(t) is the instantaneous weight of the solid during the reaction. For the reaction kinetics under isothermal conditions and constant gas flow rate, the conversion rate can be expressed as: 𝑑𝑋𝑑𝑡= 𝑘(𝑇)𝑓(𝑋) (2-8) 28  where t is time, T is temperature, X is the extent of conversion, f(X) is the differential form of the mechanism function and k(T) is the Arrhenius rate constant, assumed to be given by: 𝑘(𝑇) = 𝐴 𝑒𝑥𝑝 (−𝐸𝑎𝑅𝑇) (2-9) where R is the gas constant, A is a pre-exponential factor and Ea is the apparent activation energy. For the isothermal condition test, eqn. (2-8) can also be expressed as: 𝑔(𝑋) = ∫𝑑𝑋𝑓(𝑋)= 𝑘(𝑇)𝑡𝑋0= 𝐴 𝑒𝑥𝑝 (−𝐸𝑎𝑅𝑇) (2-10) where g(X) denotes an integral expression related to the mechanism of the solid phase reactions. In the non-isothermal condition tests, a constant heating rate (γ) is defined by: 𝑑𝑡 = 𝑑𝑇/𝛾 (2-11) Substituting eqn. (2-11) into eqns. (2-8) and (2-9), 𝑑𝑋𝑓(𝑋)=𝐴𝛽𝑒𝑥𝑝 (−𝐸𝑎𝑅𝑇)𝑑𝑇 (2-12) The Coats-Redfern method was used to estimate the activation energy and pre-exponential factor. Integrating eqn. (2-12) with X=0 and T=T0 at time 0 gives: 𝑔(𝑋) = ∫𝑑𝑋𝑓(𝑋)=𝑋0∫𝐴𝛽𝑒𝑥𝑝 (−𝐸𝑎𝑅𝑇)𝑑𝑇𝑇𝑇0 (2-13) Cauchy’s rule is applied to estimate the integral, i.e., ∫𝐴𝛽𝑒𝑥𝑝 (−𝐸𝑎𝑅𝑇)𝑑𝑇𝑇𝑇0≅𝐴𝑅𝑇2𝛽𝐸(1 −2𝑅𝑇𝐸𝑎) 𝑒𝑥𝑝(−𝑅𝑇𝐸𝑎) (2-14) Since 2RT/Ea<<1, eqn. (2-14) can be expressed as: ln𝑔(𝑋)𝑇2= ln(𝐴𝑅𝛽𝐸𝑎(1 −2𝑅𝑇𝐸𝑎)) −𝐸𝑎𝑅𝑇= ln (𝐴𝑅𝛽𝐸𝑎) −𝐸𝑎𝑅𝑇 (2-15) 29  Note that f(X) is a mathematical function and g(X) is an integral expression form related to the mechanism of solid phase reactions listed in Table 2.4, adopted from Nasr and Plucknett [66]. Here, ζ  is a constant to determine the reaction mechanism proposed by Hancock and Sharp [67]. The Hancock and Sharp equation is: ln(− ln(1 − 𝑋)) = 𝜁 ln 𝑡 + ln 𝜂 (2-16) where t is time and η is a constant for the system.  Table 2.4 Classical models for gas-solid reaction from Nasr and Plucknett [66]. No. Model f(X) g(X) ζ  Power law models 1  4𝑋3/4 𝑋1/4 1 2  3𝑋2/3 𝑋1/3  3  2𝑋1/2 𝑋1/2  4  2/3𝑋−1/2 𝑋3/2  Geometrical contraction models 5 0th order 1 𝑋  6 2D 2(1 − 𝑋)1/2 1 − (1 − 𝑋)1/2 1.11 7 3D 3(1 − 𝑋)2/3 1 − (1 − 𝑋)1/3 1.07 Diffusion models 8 1D 1/(2𝑋) 𝑋2  9 2D [−ln(1 − 𝑋)]−1 𝑋 + (1 − 𝑋)ln(1 − 𝑋) 0.57 10 3D (Jander) 3/2(1 − 𝑋)2/3[1 − (1 − 𝑋)1/3]−1 [1 − (1 − 𝑋)1/3]2 0.54 11 3D (Ginstling) [−ln (1 − 𝑋)]−1 (1 − 2/3𝑋) − (1 − 𝑋)2/3  Reaction-order models 12 1st order 1 − 𝑋 − ln(1 − 𝑋)  13 3/2 order (1 − 𝑋)3/2 2[(1 − 𝑋)−1/2 − 1]  14 2nd order (1 − 𝑋)2 (1 − 𝑋)−1 − 1  15 3rd order (1 − 𝑋)3 0.5[(1 − 𝑋)−2 − 1]  Nucleation models 16 n = 1.5 2/3(1 − 𝑋)[−ln(1 − 𝑋)]1/3 [−ln(1 − 𝑋)]2/3  17 n = 2 2(1 − 𝑋)[−ln(1 − 𝑋)]1/2 [−ln(1 − 𝑋)]1/2 2 18 n = 3 3(1 − 𝑋)[−ln(1 − 𝑋)]2/3 [−ln(1 − 𝑋)]1/3 3 19 n = 4 4(1 − 𝑋)[−ln(1 − 𝑋)]3/4 [−ln(1 − 𝑋)]1/4  30  Chapter 3: Attrition testing without reaction  This chapter presents studies of two-species attrition to provide better understanding of particle interactions. Iron and limestone were selected as a typical oxygen carrier and a common CO2 sorbent, respectively. Attrition tests were conducted with binary solid species mixtures, varying the species weight fractions, as well as the duration, temperature and jet velocity.  3.1 Operating conditions An air-jet apparatus based on ASTM D5757 with several improvements was used to test attrition with varying duration (3, 6 and 12 h), temperature (20, 250 and 500˚C), jet velocity (89, 119 and 149 m/s) and particle mixture compositions (Iron:Limestone mass ratios=1:0, 0.75:0.25, 0.5:0.5, 0.25:0.75 and 0:1). Here, iron refers to iron powder (pearlite), as explained in Chapter 2. The particle loading was fixed at 50 g, in accordance with the ASTM standard [51]. The jet tests were based on a jet velocity of 149 m/s at 250 and 500°C. In addition, 89 and 119 m/s at 20°C were tested to determine the effect of gas velocity on the attrition of binary solid species at room temperature. All experimental datasets tested with the jet apparatus are listed in Appendix D. After each test, all particles were gathered, and the particle size distributions (PSDs) of entrained and retained particles were measured by a Mastersizer 2000 laser diffraction system (Malvern Panalytical) with a Scirocco dry-feeding accessory. All attrition tests were performed at least three times, with average weight fractions and standard errors given on each PSD graph. To find the influence of the mixture composition on the attrition rate, the iron was separated from the limestone by magnetic separation, allowing the PSD of each of the two species in each 31  sample to be determined. In detail, water was added into a sampling bottle where the samples were collected, and dispersed with a sonicator to segregate iron from the mixtures with a magnet, repeated several times. The segregated samples were dehydrated first with filtration by filter paper and then dried in the oven at 40°C for 12 h. To confirm the particle segregation, the segregated iron species was put into sulfuric acid, to make sure that iron was all reacted and observe whether there was any sediment, i.e., whether CaSO4, formed. Results of qualitative and quantitative methods evaluating and confirming the efficiency of the magnetic separation method are provided in Appendix E.  3.2 Results and discussion 3.2.1 Single species attrition The particle size distributions of single-species (a) iron and (b) limestone, at room temperature after different attrition times are shown in Figure 3.1. Both the iron and limestone show a leftward shift in PSD over time. The weight fraction of < 250 μm iron increased with attrition time, whereas only the 0 to 63 μm fraction increased with increasing time for the limestone. Portnikov et al. [62], Austin [68] and Rahimian et al. [69] reported that the stress required to break smaller particles is greater than that needed to break larger particles. Although the attrition resistance of both iron and limestone particles was higher for smaller particles, there was sufficient gas flow to break the limestone particles. However, 149 m/s was not enough jet velocity to break iron particles smaller than 250 μm. Therefore, as the particle breakage energy decreased with increasing particle size, particle resistance to attrition was less than for the smaller particles, so that more breakage occurred. 32  The weight fractions of iron particles < 250 μm and limestone < 63 μm increased with increasing attrition time. One possible mechanism affecting the breakage of relatively coarse particles was a ‘cushioning effect’ as suggested by Forsythe and Hertwig [70], who postulated that the presence of fines reduces the degradation of larger particles in jet attrition tests. In other words, fines appear to limit collision impacts and thus constrain the breakage of coarse particles. Arena et al. [46] and Ray et al. [23] also observed decreases of particle attrition when fines were present due to cushioning. Assuming that particle breakage energy is shared across the entire material surface, fine particles have greater total surface area than an equal mass of coarse particles, affecting the surface energy available for attrition. In Figure 3.1(a), the percentage of 0-63 μm particles remaining in the attrition column decreased with increasing attrition time. Also, the effect of fragmentation is noticeable for the 12 h attrition test, with a decrease in the 1000-2400 μm weight fraction, whereas the proportion of the other size fractions increased. As the weight percentage of fines decreased with increasing attrition time due to entrainment, iron particles > 63 μm may have had more opportunities to collide with and break each other. 33   Figure 3.1 Particle size distributions of (a) iron and (b) limestone particles after different periods of single-species attrition testing in jet apparatus at 20ºC with air flow of 149 m/s.  34  3.2.2 Binary solid species attrition To analyze the attrition test with two solid species, U/Umf was calculated for our system. Figure 3.2 shows (a) schematics of the progress of fluidization in a two-solid-species bed; and (b) the fluidization curve for an iron/limestone mixture (Iron:Limestone=0.75:0.25 by mass fractions, 20°C) as a typical example. Uff is the superficial gas velocity for final fluidization, at which the heavier jetsam (iron) particles began to fluidize. When the superficial gas velocity > Uff, all particles should be fluidized in the system. Uif is defined as the superficial gas velocity for initial fluidization at which the lighter flotsam particles started to fluidize. These fluidization velocities have commonly been adopted for two species fluidization studies to characterize the minimum fluidization velocity by previous researchers [71–73].  As shown in Figure 3.2 (b), the mixture minimum fluidization velocity, Umf, is determined in the conventional manner at the intersection of the fixed bed curve with the horizontal line representing the suspended state. Since the iron and limestone in this system do not mix perfectly as the iron particles are significantly larger and denser than the limestone particles, Umf does not correspond to where all particles in the bed started to fluidize. Instead, when the superficial gas velocity was set at Umf, all the flotsam particles and some jetsam particles underwent fluidization, while some jetsam particles sunk and formed a defluidized layer. This was visually confirmed by testing the fluidization behaviour in an acrylic column of the same cylindrical diameter. The Umf of iron, limestone and their mixtures were listed in Table 3.1. 35   Figure 3.2 (a) Schematic progress of fluidization in a two solid species bed; (b) fluidization curve of an iron and limestone mixture (Iron:Limestone=0.75:0.25 by mass fraction at 20ºC). 36  Table 3.1 Umf of iron, limestone and their mixtures.  Umf [mm/s] Iron 199.4 Iron:Limestone=0.75:0.25 by mass 86.3 Iron:Limestone=0.5:0.5 by mass 85.9 Iron:Limestone=0.25:0.75 by mass 83.4 Limestone 82.6  The particle size distributions for (a) iron and (b) limestone for different initial particle mass fractions at 20˚C with an air jet velocity of 149 m/s and 6 h attrition time are shown in  Figure 3.3. The proportion of iron particles 1000-2400 μm after a binary mixture attrition test was less than for the corresponding single-solid-species attrition test (see Figure 3.1a)). The mass fraction of 63-125 μm and 125-250 μm bins also decreased, whereas the 250-500 μm and 500-1000 μm bins decreased with increasing mass fraction of iron. Because U/Umf for each solid mixtures was greater than 1, whereas U/Umf for pure iron < 1, the mixtures were partially fluidized during the attrition tests. Moreover, the presence of fines reduced the degradation of particles in jet attrition tests, likely by cushioning collision impacts. The attrition of iron with different initial mass fractions of iron and limestone is well illustrated in the SEM images of Figure 3.4. SEM images of attrition of limestone with different initial mass fractions of iron and limestone appear in Appendix F. 37    Figure 3.3 Particle size distributions of: (a) iron particles; and (b) limestone particles for different initial mass proportions (20°C, jet velocity = 149 m/s, 6 h of attrition). 38   Figure 3.4 SEM images of iron for initial mass proportions of: (a) 75%; (b) 50%; and (c) 25% from Iron:Limestone mixture with jet velocity = 149 m/s after 6 h of attrition at 20ºC. 39  In  Figure 3.3(b), fines generation by the limestone component was greater for all weight fractions than for the single species (Figure 3.1), presumably because the denser and harder iron particles struck limestone particles, promoting attrition. As the size and density of the iron particles were both greater than for the limestone particles, particle segregation may have occurred regardless of how well mixed the particles were at the outset of the tests (see Figure 3.2(a)). Since some of the relatively lighter and smaller iron particles were carried up and down with the limestone due to drag forces at a given gas velocity, iron-limestone collisions possibly did not result in much exchange of kinetic energy compared to inter-particle collisions in a single-species system. When the weight percentage of iron increased, the total weight of fluidized iron particles also increased, augmenting the attrition of limestone, while also increasing fines generation for the 0-63 μm bin, compared to the limestone-alone attrition for 6 h. Figure 3.5 plots the particle size distributions of iron and limestone after 6 h of attrition at different jet velocities (Iron:Limestone = 0.5:0.5 by mass at 20ºC). In general, the gas velocity directly affected the particle velocity, one of the most significant factors affecting inter-particle collisions [49]. Werther and Reppenhagen [27] found that fines generation increased linearly with increasing excess superficial gas velocity, (U-Umf). Moon et al. [74] recently explained that the attrition rate increased with increasing particle momentum based on tests with different temperatures and pressures. When the jet velocity increased, more fines were generated for both the iron and limestone, possibly for different reasons. For the iron, when the jet velocity increased, more particles began to fluidize, resulting in greater upwards and downwards motion, leading to more collisions with other particles. For the limestone, as the superficial gas velocity exceeds Umf, and limestone is more attritable than iron, the weight percentage of limestone 40  particles in the 0-63 μm bin increased, while that of the other bins decreased with increasing jet velocity.  Figure 3.5 Size distributions of: (a) iron; and (b) limestone particles for different gas jet velocities, beginning at Iron:Limestone = 0.5:0.5 by mass; temperature: 20°C; duration: 6 h attrition. 41  The particle size distribution of the species after attrition at an air jet velocity of 149 m/s for 6 h at different temperatures for 0.5:0.5 by weight Iron:Limestone is reported in Figure 3.6. With increasing gas temperature, the attrition rate has been found to decrease in previous work [61,74]. At first when the relative particle Reynolds number (based on particle diameter and relative gas velocity, Rep=dp|up-ug|ρg/μg) is higher around the orifice, the gas density affects the particle momentum more significantly than the gas viscosity. However, when the Reynolds number based on the difference of the gas and particle velocities decreases as particles are entrained in the jets, the gas viscosity may play a more important role, bringing the particle velocity up to the impact value. The drag ultimately becomes more dependent on viscous drag than inertial (high Re) drag if there is enough height. Thus, gas density is initially more important, but, if there is enough height in the fluidized vessel, the gas viscosity will become more significant than the gas density. Note that gas density decreases with increasing gas temperature, whereas gas viscosity increases with increasing temperature. Hence, increasing temperature can result in an increase or a decrease in attrition.  The effect of temperature on attrition rate was previously studied by a number of researchers. For example, Moon et al. [74] tested with a CO2 sorbent (KPM1-SU) at varying temperatures (100-400°C) using ASTM D5757 jet apparatus and reported that the attrition rate decreased with increasing temperature, mainly affected by gas density. Chen et al. [61] tested with an impact tester having 0.012 m diameter and 1 m length with limestone at 25 to 580°C and found that increasing temperature decreased the particle impact velocity. Lee et al. [75] used two types of lime sorbent at 20 to 180°C and reported that the attrition rate decreased with increasing temperature. Knight et al. [42] tested 4 different types of Ca-based sorbents in a jet attrition unit and found that increasing temperature decreased the attrition rate. However, there are a few 42  contradictory results found in literature. Lin and Wey [76] tested silica sand with a temperature range of 20 to 900°C in a bubbling fluidized bed reactor, with a porous plate distributor having 15% open area to minimize the effect of jets. They reported that the attrition rate increased with increasing temperature. Vaux and Keairns [77] found that the particle breakage rate increased with increasing temperature, tested in pilot scale fluidized bed combustor. These results may explain that the effect of gas viscosity may increase the attrition, given that the effect of jet is minimized. Although gas density and gas viscosity have opposite effects on particle velocity, the contribution of their effects varies along the height of the column, which is likely to be the reason for the contradictory results in the literature. In Figure 3.6 (a), the 0-63 μm bin range shows more iron fines generated with increasing temperature. For particles 1000-2400 μm, particle breakage was reduced with increasing temperature. For iron particle bins between 0 and 500 μm at 20°C after 6 h, attrition increased with increasing gas flow, providing sufficient energy for particles to undergo fragmentation. Fines production was increased with increasing temperature, showing the reduced effect of fragmentation and increased effect of abrasion. 43   Figure 3.6 Size distributions of: (a) iron; and (b) limestone particles after 6 h of attrition for different temperatures with Iron:Limestone initially 0.5:0.5 by mass, jet velocity of 149 m/s. 44  Figure 3.7 shows SEM images of iron at (a) 20ºC, (b) 250ºC and (c) 500ºC with Iron:Limestone initially 0.5:0.5 by weight and jet velocity of 149 m/s after 6 h of attrition. As expected from Figure 3.6(a), the diameter of the coarse particles increased with increasing temperature, showing that the particle momentum decreased and thereafter, the kinetic energy of the particles was insufficient to break the particles into fines.  Figure 3.7 SEM images of iron particles at: (a) 20ºC; (b) 250ºC; and (c) 500ºC with Iron:Limestone after 6 h of attrition initially 0.5:0.5 by mass, actual flow of 149 m/s. In Figure 3.6(b), the weight percentage of 0-63 μm limestone particles decreased, whereas those of the 63-125 and 125-250 μm fractions increased with increasing temperature. As smaller particles have greater specific breakage energy, 63-125 and 125-250 μm limestone particles underwent both fragmentation and abrasion at 20ºC. When the temperature increased, 45  the decreased gas density decreased the momentum so that the kinetic energies of the particles were not enough to cause fragmentation, as shown in Figure 3.8. The SEM images show smoother surfaces of the coarse particles with increasing temperature.   Figure 3.8 SEM images of limestone at: (a) 20ºC; (b) 250ºC; and (c) 500ºC for Iron:Limestone after 6 h of attrition, initially 0.5:0.5 by mass, jet velocity of 149 m/s. Similar results were reported by Knight et al. [42] who identified three effects related to the rate of fines production: 1) initial abrasion of the rough particle surfaces; 2) abrasion of newly-generated particle surfaces which resulted from fragmentation; and 3) production of fines from the fragmentation of small particles. In our case, effects 2 and 3 were reduced with increasing temperature. To verify this result, surfaces of 250-500 μm iron and limestone particles 46  were magnified and observed with SEM, as shown in Figure 3.9. Both the iron and limestone surfaces became smoother with increasing temperature, showing enhanced abrasion and reduced fragmentation.   47   20ºC 250ºC 500ºC Iron    Limestone    Figure 3.9 SEM images of iron and limestone after 6 h of attrition from Iron:Limestone initially 0.5:0.5 by weight with different temperatures, and jet velocity of 149 m/s.48  3.3 Conclusions Binary solids (iron/limestone) mixture attrition tests were carried out varying attrition time, solid species mass fraction ratio, temperature and jet velocity. Both iron and limestone attrition increased overall when the two species were mixed together. However, the attrition of iron increased with increasing mass fraction of iron, whereas limestone showed no significant change for a jet velocity of 149 m/s, at which the iron particles were only partially fluidized, while the limestone was fully fluidized. As expected, attrition of both iron and limestone in mixtures increased with increasing gas jet velocity. Higher temperature affected the gas and particle kinetic energy, as well as the material properties of the particles, leading to reduced fragmentation and more fines generation of iron, while there was less fragmentation of limestone at higher temperature. 49  Chapter 4: Effect of calcination/carbonation and oxidation/reduction on attrition of binary solid species  4.1 Introduction Fluidized bed reactors have been used for many different industrial processes, such as coal-burning power plants, fluid catalytic cracking and gasification, with such advantages as large processing capacity, good solids mixing and high heat transfer compared to fixed bed and moving bed reactors, e.g. [23,78–82]. Due to the high gas velocity in most fluidized bed reactors, particle attrition is an important consideration, negatively affecting reactor performance, operating conditions and material loss by entrainment and elutriation [83]. Some efforts have been made to consider attrition in fluidized beds with ASTM D5757 [51] at 0ºC or 20ºC based on material friability tests. However, these tests are not fully applicable since temperature affects the attrition. Also, chemical reactions, strongly influenced by temperature, affect the rate of attrition [46,84,85]. Despite the significant impact of reactions on the extent of attrition in fluidized beds, studies of attrition in fluidized beds have not paid much attention to the effect of reactions on attrition in the chemical industries because of its complexity and lack of feasible experimental methods [86–90]. So far, the limited number of studies of the effect of reactions on attrition have mainly focused on the evolution of particle size distributions (PSDs) and the mass of fines generated due to attrition, generally leaving the change in material properties due to reaction unaccounted for. For example, Chen et al. [43] tested limestone sulphation in a circulating fluidized bed subject to attrition for very limited operating conditions (28.6 h of attrition with 50  1150 ppm of SO2 and 10 h with 2800 ppm of SO2 at 850°C), but only mentioned that sulphation may reduce the attrition. They did not compare the particle size distribution data with those without sulphation. Arena et al. [91] tested attrition of char-sand mixtures during char combustion, but only focused on how the ash, produced from the char, affected the attrition with sand, not how the combustion affected the material properties. However, material properties are known to significantly affect particle attrition as well [92]. In the field of metallurgy, it is more common to study the breakage behaviour of individual or bulk granules due to compression, based on image analysis, instead of PSDs and measuring the mass of fines generated [35,62,64,65,93]. In these studies, granules, after reacting chemically, were compressed by a mechanical testing machine to measure mechanical properties, such as crushing strength, yield stress and Young’s modulus [63,94–97]. These tests provide information on the influence of material properties under static compression conditions, whereas attrition in fluidized beds is influenced by dynamic compression; particles, due to the motion of gas, collide with other particles and with the reactor wall. Ideally, perspectives from both chemical engineering and metallurgical findings may give more comprehensive understanding on attrition in fluidized beds. In fluidized beds, attrition and reaction usually occur simultaneously in the reactor. However, there are very few ways to measure the instantaneous material properties. Alonso et al. [98] even claimed that there was no feasible method to measure the instantaneous material properties to study the attrition mechanisms when reactions accompany attrition. To overcome this hurdle, Lee et al. [75] suggested to measure the variance of material properties, such as size, surface area, porosity, hardness and breakage energy of particles in fluidized beds at atmospheric temperature after attrition/reactions have occurred since those properties do not differ 51  significantly from data measured when attrition/reactions are taking place at high temperature. This chapter presents measurements of a limited number of material properties, including BET specific surface area, porosity, pore size distribution, particle breakage energy, and particle size distributions to investigate how the chemical conversion of particle species affects the attrition in specific single-species, and two-species environments. Chemical reaction kinetics can be relevant in the study of attrition because the formation of a product layer in a solid particle alters the mechanical properties of particles, while also affecting mass transfer and hence reaction rates. Some reaction kinetic models are used to fit TGA data in this chapter since these models attempt to explain the reaction mechanism related to crystal structure changes, affecting particle breakage energy and porosity. Data with changes of temperature, particle size and gas concentration were obtained to indicate how these parameters affect the reactions, and to further investigate how they affect attrition. Iron, hematite (Fe2O3), limestone and lime were selected as oxygen carriers and CO2 sorbents in sorption-enhanced chemical looping reforming processes. Two reversible reactions (four one-way reactions: iron oxidation, hematite reduction, limestone calcination and lime carbonation) are considered in this chapter. Again, “iron” in this chapter refers to iron powder (pearlite) as in Chapters 2 and 3. Attrition tests were conducted with particles of a single species and with binary solid mixtures, for different temperatures, different gas species and ranges of gas concentrations, affecting the reactions. An ASTM jet apparatus was again used to measure the extent of attrition. PSDs were analyzed to determine the combined effects of reactions and attrition.  52  4.2 Operating conditions 4.2.1 Jet apparatus A modified jet apparatus based on ASTM D575716 was again used to test particle attrition. Details of this unit are provided in Figure 2.1. Samples of iron from Rio Tinto (?̅?𝑝=633 μm, ρs=7080 kg/m3), and Strasburg limestone ( ?̅?𝑝 =316 μm, ρs=2667 kg/m3) served as the oxygen carrier and CO2 sorbent, respectively. Properties of these materials are provided in Chapter 2. The Strasburg limestone was calcined for 24 h at 900°C to ensure that the limestone were completely calcined to lime, and then held under dry conditions until testing. 99.9 mol% purity elemental iron from Goodfellow Inc. was fully oxidized for 24 h at 900°C to hematite (Fe2O3) and then mechanically ground to be in the range of 0-2400 μm for hematite attrition tests. The compositions and key characteristics of samples and their initial PSDs appear in Table 2.3. The chemical compositions of the samples are identified in Table 2.2. The PSDs of iron, hematite, limestone and lime are plotted in Figure 2.2. All experimental data from the jet apparatus tests are listed in Appendix D. After each attrition test, all particles were gathered, and the PSDs of both the entrained and retained particles were determined by a Mastersizer 2000 laser diffraction system (Malvern Panalytical) with a Scirocco dry-feeding accessory.  As in Chapter 2, De Brouckere (volume-mean) diameters were calculated, since the Sauter mean tends to overlook the presence of a few large particles because of their low surface-area-to-volume ratio, although large particles have a more significant influence in producing smaller particles and fines, especially since their critical stress for fracturing is lower due to larger maximum crack lengths [55]. Note that the particle size of each solid species did not change prior to attrition. 53  To find the influence of the binary species mixture and reactions on attrition, iron-based particles were separated from the lime-based particles by magnetic separation, allowing the PSD of each species in each sample to be determined and facilitating the analysis of the extent of conversion. Details of the magnetic separation method are provided in Chapter 3 and Appendix E. The specific crushing strength by compression of each particle species in different particle size bins was tested with an FGJN-50 (Shimpo Inc.) connected to a push-pull gauge stand (FGS-50E-H), compressing particles one at a time. Five particle size bins were used, with size intervals of 63-125, 125-250, 250-500, 500-1000 and 1000-2400 μm. The 0-63 μm particle bin could not be tested because the device was unable to measure how much such small particles were compressed when they broke. 30 tests per sample were conducted to determine the particle failure strength. The particle crushing strength was determined at the instant when particles started to break when compressed by the punch. The specific breakage energy for each species in different particle-size bins was then calculated by dividing the breakage energy by the mass of a volume-equivalent sphere. The breakage energy and specific breakage energy can be calculated [62,64] as: 𝐸𝐵 = ∫ 𝐹𝑑𝛿𝛿𝑐0 (4-1) 𝐸𝑠𝑝 =6𝐸𝐵𝜋𝑑𝑝3𝜌𝑝 (4-2) where δ is the displacement, and δc is the maximum compression displacement. The average crushing strength and specific breakage energy of each species in each particle bin are listed in Table 2.3. The actual breakage energy of the particles in the jet apparatus is less than the 54  observed value because: (1) Compression tests generally over-estimate Young’s modulus compared to impact loading [65]; (2) The breakage force due to impact is less than the breakage force due to compression [59]; and (3) Fatigue accumulates, contributing to particle breakage [24]. Rozenblat et al. [59] tested particle breakage both in a compression unit and impact tester. They found an empirical linear relationship on a log-log scale: ln(𝐹𝑐,𝑖𝑚𝑝𝑎𝑐𝑡) = 𝐶1 + 𝐶2 ln(𝑑𝑝3.3𝑈𝑗𝑒𝑡) (4-3) where Fc,impact is the particle crushing strength by impact (N), Ujet is the impact velocity (m/s), and C1 and C2 are constant fitting parameters (dimensionless). The specific surface area of particles in the presence and absence of reaction was determined with N2 absorption single-point BET (Brunauer, Emmett and Teller) analysis in the Department of Chemical and Biological Engineering at UBC. All samples subjected to BET testing and to attrition testing below the minimum fluidization velocity, were handled carefully to ensure that no particles were attrited. The particle porosity and pore diameter were measured with mercury porosimetry using a Micrometrics Autopore IV in the UBC Department of Earth, Ocean and Atmospheric Sciences. X-ray powder diffraction (XRD) analysis in the Department of Earth, Ocean and Atmospheric Science at UBC was conducted with Bruker D8 Advanced diffractometers for the characterization of samples from the powders, with CoKα radiation over a 2 range of 10-140°. To obtain quantitative XRD analyses, each sample was crushed dry in a mortar and top-mounted agate. The experimental temperatures for the attrition tests were 700±5 and 800±5˚C with 95% confidence intervals. The particle loading was fixed at 50 g, in accordance with the ASTM standard [51]. Jet tests were based on an actual jet velocity of 221 m/s. 99.9 vol% N2 was used 55  for the attrition tests without reaction. Air was used for the iron oxidation and limestone calcination, while 10, 30, 50 and 70 vol% CO2, and 10, 30 and 50 vol% CH4 were used to carbonate lime and reduce the iron oxide, respectively. All attrition tests were performed at least three times, with average weight fractions and standard errors calculated and provided on each PSD graph. Mann-Whitney U tests [99] were performed to confirm the effect of reaction on attrition. This test evaluates the correlation of the variable (reaction) and covariable (PSD) where the deviation of the covariable does not follow a normal distribution and the degree of freedom is low [99–101]. The p value calculated from the Mann-Whitney U test represents the probability at which there is no statistically significant correlation between reactions and the resultant PSDs. Generally, the significance level is set to 0.05, indicating a 95% confidence level to conclude that the variable and covariable are dependent. If the calculated p < 0.05, reaction has a statistically significant effect on the PSDs, and vice versa if p > 0.05 [99].  4.2.2 TGA tests TGA tests were conducted with an SDT-600 instrument manufactured by TA Instruments. Gas enters the reaction chamber from the side, keeping the balance in an inert environment. For  isothermal and non-isothermal tests, ~10 mg iron, iron oxide (Fe2O3), limestone and lime samples were heated in a ceramic pan up to 900°C, at three ramping rates (5, 10 and 20 °C/min). For the iron oxide reduction tests, 10, 30 or 50 vol% of CH4 balanced with N2, for a total flow rate of 60 ml/min. 99.999% purity N2 was flushed through the sample for 75 min before each test. Also, 10, 30 or 50 vol % of CO2 concentration, balanced with N2 (total flow rate of 60 ml/min) was used to carbonate the CaO at temperatures up to 900°C. 60 ml/min of air 56  was used to oxidize iron and calcine CaCO3. Note that 100 vol% CO2 was used to provide an inert environment for isothermal testing of CaCO3 calcination. The temperature was held at 105°C for 15 minutes, and then the temperature was raised by 20°C/min to the final temperature for the isothermal tests. The samples were preheated under an inert gas (N2) to the test temperature. After the temperature reached the designated test value, the reaction gas was quickly switched, and the temperature was held constant for up to 300 minutes. For gas mixtures, an OMEGA FMA5526 gas flow controller was connected to the secondary gas line. Figure 2.5 provides a schematic of the TGA unit.  4.3 Results and discussion 4.3.1 Effect of reaction on attrition 4.3.1.1 Iron oxidation Most attrition tests on iron in fluidized beds focus on iron Fischer-Tropsch catalysts, assuming no iron oxidation [102,103]. Some attrition tests where iron acts as an oxygen carrier have also been reported, but oxidation was not considered or discussed [104,105]. Metallurgists and mineralogists have studied how oxidation affects micro-cracks on iron surfaces, or changes in porosity and Young’s modulus [89,106,107]. Thus, in our work, PSDs and material properties were investigated with air oxidation, varying temperature and particle size in the ASTM attrition unit. Also, TGA tests were performed and fitted with previously suggested chemical reaction models from other researchers [108–115] since the material properties depend heavily on the reaction, for example, whether particles react homogeneously or the reaction starts at the outer surface and then proceeds to the core. 57  Iron oxidation initiates reaction at the surface. Further reaction occurs when: (1) iron cations diffuse through the oxide layer to react with oxygen from the air contacting the surface/oxide interface; or (2) oxygen diffuses through the oxide layer to react at the iron/iron oxide interface. Two assumptions are commonly adopted to explain iron oxidation [116]. For the initial reaction, iron cation diffusion is predominant, so that the rate of outward diffusion is faster than the reaction rate at the surface. Following the initial reaction, inward oxygen anion diffusion is of predominant importance, with the oxygen diffusion rate being slower than the reaction rate inside the particles. In our work, iron oxidation was conducted in a TGA under isothermal conditions at 700-800°C and with particles of diameter 0-63, 125-250 and 500-1000 μm. Figure 4.1 and 4.2 show the iron oxidation conversion with air for an overall flow rate of 60 ml/min at 700 to 800°C and different particle sizes at 800°C. The results indicate that the oxidation initially proceeds rapidly, before giving way to a gradual increase in oxidation until the sample is fully oxidized. Since the crystal structure of the iron, wustite (FeO) and magnetite (Fe3O4) is cubic, whereas hematite (Fe2O3) is rhombohedral, the reaction mechanism can change [66] (see details of crystal structure of solid species in Appendix A). The horizontal lines are theoretical oxidation conversion percentages of each iron oxide phase. The theoretical weight increase corresponding to the complete transformation of Fe to FeO (wustite) is 72.4%; the increase for transformation of Fe to Fe3O4 (magnetite) is 77.8% and Fe to Fe2O3 (hematite) is 100%, respectively. A theoretical magnetite conversion line is considered to demarcate different reaction regimes, whether the diffusion of iron cations through the oxide layer to react with oxygen on the surface/oxide interface is predominant, or oxygen diffusion through the layer to react at the iron/iron oxide interface is predominant. 58  Time, [s]0 5000 10000 15000 20000 25000Oxidation conversion percentage, [%]020406080100700C 750C 800C FeOFe3O4Fe2O3 Figure 4.1 Iron oxidation conversion percentage with extra dry air for 60 ml/min flow rate at 700 to 800°C. Time, [s]0 5000 10000 15000 20000Oxidation conversion percentage, [%]0204060801000-63 m125-250 m500-1000 mFeOFe3O4Fe2O3 Figure 4.2 Iron oxidation conversion percentage with 60 ml/min extra dry air and different particle size ranges at 800°C. 59  For the ferrous iron oxidation by air, a parabolic law, assuming that the oxide growth process is governed by the diffusion of ions or electrons, using a Pilling-Bedworth type equation: (𝑚(𝑡) − 𝑚0𝑆)2= 𝑘𝑝𝑡 (4-4) is generally used [108–114], where S is the surface area of the sample and kp is a parabolic rate constant with units of g2/(cm4s). Chen and Yuen [117] suggested an empirical equation for the parabolic rate constant over the 700 to 1250°C range: 𝑘𝑝 = 3.047𝑒𝑥𝑝 (−157539𝑅𝑇) (4-5) Parabolic rate constants for Fe to Fe3O4 oxidation in air, plotting some data, including the test results obtained in this study and an empirical correlation of the results from other researchers, are depicted in Figure 4.3. As shown, this empirical correlation fits our data and previous research data well, with R2=0.982. 10000/T [K]6 7 8 9 10 11log10kp, [g2/(cm4s)]-9-8-7-6-5-4 This work, dp=0-63 mPaidassi (1958)Davies et al. (1951)Schmahl et al. (1958) Empirical correlation from Chen and Yuen (2003) Figure 4.3 Parabolic rate constants for Fe to Fe3O4 oxidation in air. 60  Fitting eqns. (4-4) and (4-5) with the data before the conversion rate reached the theoretical Fe3O4 line gave R2=0.983, 0.994 and 0.990 for 700, 750 and 800°C respectively. However, after the data crossed the theoretical Fe3O4 line, they no longer followed the parabolic model. Monsen et al. [115] and Monazam et al. [118] tested a second order reaction for Fe3O4 oxidation, which agreed well with their TGA data for the diffusion control regime. Here, the activation energy of the Fe3O4 to Fe2O3 reaction is 116.9 kJ/mol, which is similar to 100 kJ/mol from Monsen et al. [115], based on spherical particles in the temperature range of 600 to 850°C. The fitted rate equation for Fe3O4 oxidation is: 𝑘 = 2.33 × 103𝑒𝑥𝑝(−1.17 × 105/𝑅𝑇) (4-6) where the unit of k is 1/s. The combination of a parabolic model for initial iron oxidation (Fe to Fe3O4 oxidation) and a second order kinetic model for Fe3O4 to Fe2O3 oxidation at 800°C are fitted in Figure 4.4, resulting in R2 = 0.977. Note that the De Brouckere mean diameter (?̅?𝑝=31.5 μm, average bin size of 0-63 μm) is adopted in the model and the impurities (inert materials, such as SiO2) are excluded in this figure.  R2, RME%, and RMSE for different variables are listed in Table 4.1. 61   Figure 4.4 Curve fitting of 0-63 μm iron oxidation data, and combined parabolic model and second order kinetic model at 800°C with an air flow rate of 60 ml/min.  Table 4.1 Relative mean error percentage (RME%), root mean square of absolute error (RMSE) and R2 between TGA data and model for lime carbonation. Reaction Chemical reaction model fitted T [°C] dp [μm] Reactive gas cg [%] R2 RME% RMSE Iron oxidation 𝐹𝑒 + 𝑂2→ Fex𝑂𝑦 Parabolic model for Fe to Fe3O4 oxidation [108–114] + Second order kinetic model for Fe3O4 to Fe2O3 oxidation [115] 700 0-63 O2 in air 21.0 0.977 4.14 0.117 750 0-63 0.976 4.28 0.094 800 0-63 0.977 1.66 0.107 700 125-250 0.983 3.37 0.090 700 500-1000 0.941 5.80 0.076 𝑅𝑀𝐸% =100𝑁∑ |𝑋𝑚𝑜𝑑𝑒𝑙,𝑖−𝑋𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙,𝑖𝑋𝑚𝑜𝑑𝑒𝑙,𝑖|𝑁𝑖=1   𝑅𝑀𝑆𝐸 = √1𝑁∑(𝑋𝑚𝑜𝑑𝑒𝑙,𝑖 − 𝑋𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙,𝑖𝑋𝑚𝑜𝑑𝑒𝑙,𝑖)2𝑁𝑖=1 62  Size distributions of particles after 6 h of iron attrition with and without oxidation at 800°C, with a jet velocity of 221 m/s, are plotted in Figure 4.5. For the iron without reaction during the attrition, solid material properties such as Young’s modulus change as the temperature increases, which may further reduce the attrition. Schaller [119] observed a brittle to ductile transition of alumina, zirconia and silicon nitride, at 300 to 1000°C and explained that particle crushing strength, which is related to the breakage resistance, increases with increasing temperature. When oxidation occurs, iron cations diffuse through the outer surface of the particle, generating an iron oxide layer on the surface [116]. During this oxidation, cavities are formed, generating porous iron oxide, which reduces the particle crushing strength [120]. Here, both fragmentation and abrasion were shown, given that the fractions of particle size bins of 500-1000 and 1000-2400 μm are increased; whereas, the weight fraction of the 0-63 μm bin is increased when iron is oxidized. 63  Particle diameter range, [ m]0-63 63-125 125-250 250-500 500-1000 1000-2400Weight  fraction, [%]010203040Unattrited and unreacted ironIron: attrition but no reaction at 800C with N2Iron: attrition with oxidation at 800C by air Figure 4.5 Particle size distributions of iron attrition with and without reaction at 800°C for 6 h at jet velocity = 221 m/s. Figure 4.6 provides a SEM image of a cross-sectional area of partially oxidized iron particle of diameter ~1000 μm after 6 h of heat treatment at 700°C using air in the attrition unit, showing cavities generated between the oxidized iron/ferrous iron interface during oxidation. Similar results are shown in Appendix F, with different iron particle sizes and heat treatment durations. As the oxide scale thickens, the resultant stress at the iron/iron oxide interface increases, and eventually fractures the oxide layer parallel to the interface, or tensile fracture occurs through the layer [121]. Thus, the particle crushing strength is reduced by formation of cavities when iron is oxidized. Since the iron oxidation conversion increases with increasing temperature, the average crushing strength of the particles decreased, making the particles more fragile, even when increasing the temperature reduced the particle momentum.  64   Figure 4.6 SEM image of cross-sectional area of a partially oxidized ~1000 μm iron particle after 6 h of heat treatment with air at 700°C. Cavities were formed at the iron/iron oxide interface.  4.3.1.2 Hematite reduction No previous research could be found on hematite attrition in fluidized beds during reduction. Monazam et al. [105] recently tested hematite attrition in a jet cup without considering reduction. However, their results are not applicable to jet attrition since they assumed that only abrasion occurs when hematite undergoes attrition. Therefore, the TGA and attrition unit were used to test the effect of hematite reduction on attrition, varying temperature and CH4 concentrations. The hematite reduction model of Monazam et al. [122] is fitted with the TGA results to explain the influence of attrition on material properties undergoing reduction. Hematite was reduced in the TGA under isothermal conditions at temperatures from 700-800°C, varying CH4 concentrations in N2 (5, 10 and 15 vol%) and particle diameter ranges (0-63, 125-250 and 500-1000 μm). Experimental conversions are plotted in Figures 4.7 to 4.9. Although there was enough time to reduce the iron oxide, Fe2O3 was not fully reduced all the 65  way to Fe by CH4. Increasing the reaction temperature and the CH4 concentration, as well as decreasing the particle diameter, are seen to have increased the reaction rate. Time, [s]0 5000 10000 15000 20000Reduction conver sion percentage, [%]0102030405060700C 750C800CFe3O4FeO Figure 4.7 Effect of reaction temperature on conversion of Fe2O3 to Fe (0-63 μm Fe2O3 particles reduction with 10 vol% CH4 balanced in N2, with overall flow of 60 ml/min). 66  Time, [s]0 5000 10000 15000 20000Reduction conversion percentage, [%]01020304050600-63 m125-250 m500-1000 mFe3O4FeO Figure 4.8 Effect of particle size on conversion of Fe2O3 to Fe (Fe2O3 reduction with 10 vol% CH4 balanced in N2 at 800°C with an overall flow of 60 ml/min). Time, [s]0 5000 10000 15000 20000Reduct ion conv ersion percentage, [%]01020304050605 vol% CH410 vol% CH415 vol% CH4Fe3O4FeO Figure 4.9 Effect of CH4 concentration balanced by N2 on conversion of Fe2O3 to Fe (0-63 μm Fe2O3 reduction at 800°C with overall flow of 60 ml/min). 67  In a manner similar to the iron oxidation reaction, hematite reduction with CH4 also has two different reaction kinetic steps as the crystal structure changes with reduction. When hematite (Fe2O3) is reduced by CH4, CH4 molecules adsorb onto Fe sites and are dehydrated, providing hydrogen molecules on the Fe surface, while the methyl group (CH3–) preferably adsorbs on oxygen vacancy sites, slowing down further reaction on the surface of the oxygen vacancy sites [123]. After all C–H bonds are cleaved, carbon is deposited on the surface, causing Fe surface deactivation. Carbon formation at different temperatures for three CH4 inlet concentrations is analyzed in Figure 4.10. The particles after reduction by CH4 are treated in air at 900°C to oxidize the deposited carbon. The total mass of the resulting CO2 was measured by a gas chromatograph (GC) to quantify the amount of deposited carbon. In Figure 4.10, the carbon deposition, on the ordinate axis, is expressed as a ratio of the deposited mass of carbon to the initial mass of Fe2O3. The carbon deposition increased as the CH4 inlet concentration increased from 5 to 15 vol%. Monazam et al. [122] showed the carbon content in reduced Fe2O3 for different temperatures and CH4 concentrations. They explained that a small amount of carbon always remains deposited on the reduced Fe2O3 due to the Boudouard reaction, potentially forming carbon on the reduced Fe2O3 surface. As a result, CH4 cannot fully reduce Fe2O3 to Fe at temperatures from 700 to 850°C with 5 to 20 vol% CH4. 68  Temperature, [C]650 700 750 800 850Carbon deposited to the carbon fed, [%]024685 vol% CH410 vol% CH415 vol% CH4 Figure 4.10 Carbon deposition in reduced hematite for different temperatures and CH4 concentrations after 5 h of exposure in the TGA. After hematite on the surface was reduced by adsorption of CH4, the lattice oxygen in the subsurface diffused toward oxygen vacancies on the surface, and iron oxide was further reduced by CH4 on the surface [123]. Monazam et al. [122] tested hematite reduction with 5 to 20 vol% CH4 and suggested a two-step kinetics model, considering initial reduction on the surface and outward oxygen diffusion for further reduction. They used an isothermal-isoconversional method [124] to confirm the two-step reaction mechanisms: if the activation energy is independent of conversion, X, the process is described as single-step reaction kinetics; on the other hand, if the activation energy varies with X, the process is described as having 69  multi-step kinetics [122,124,125]. Activation energies as a function of X, obtained by the isothermal-isoconversional method [124] with 5 to 15 vol% CH4, are plotted in Figure 4.11. The error bars here correspond to the standard errors of three hematite reduction tests with 10 vol% methane. It is seen that the activation energy did not change significantly with varying CH4 concentration, in agreement with Monazam et al. [122], confirming that the CH4 concentration does not significantly influence the hematite reduction. Thus, the two-step model of Monazam et al. [122] is used in this case. Conversion (X), [-]0.00 0.05 0.10 0.15 0.20 0.25 0.30Ea, [kJ/mol]04080120160200Fe2O3 reduction with 5 vol% CH4Fe2O3 reduction with 10 vol% CH4Fe2O3 reduction with 15 vol% CH4 Figure 4.11 Activation energy of hematite reduction as a function of conversion obtained by isothermal-isoconversional method with 5 to 15 vol% CH4 for 0-63 μm particles at 800°C.  For the initial hematite reduction (Fe2O3 to Fe3O4), a first order reaction is generally assumed [66,122,125,126]. The later stage (Fe3O4 to Fe) is modelled as a 3D slab having a 70  diffusion reaction mechanism [126]. Monazam et al. [122] fitted their TGA results with a 3D model with two fitting constants, pre-exponential factor (k0) and activation energy (Ea), and found R2=0.97. The curve fitting of the experimental reduction data and kinetic model combining first order reaction for Fe2O3 to Fe3O4 reduction and the 3D Jander diffusion model [127] for Fe3O4 reduction with 10 vol% of CH4 at 800°C is shown in Figure 4.12, as an example. This model fits well, showing R2=0.999, with a relative mean error percentage of 2.06% and a root-mean-square absolute error of 0.058. Go et al. [126] also fitted their data with a first order reaction for Fe2O3 to Fe3O4 reduction [66] and then applied a 3D diffusion model (Jander equation) [127] from 800 to 900°C. Their experimental data again showed good agreement of their TGA data with the two-step hematite reduction model. Details of the model fitting with R2, RME% and RMSE with varying temperature, particle size and CH4 concentrations are provided in Table 4.2. 71  Time, [s]0 5000 10000 15000 20000Reduction conversion percentage, [%]0102030405060800CFirst order kinetics + 3D diffusion modelFe3O4FeO Figure 4.12 Curve fitting of experimental 0-63 μm Fe2O3 reduction data and parallel kinetic model with 10 vol% of CH4 in N2 at 800°C, for overall 60 ml/min gas flow. Table 4.2 Relative mean error percentage (RME%), root mean square of absolute error (RMSE) and R2 between TGA data and model for hematite reduction with CH4. Reaction Chemical reaction model fitted T [°C] dp [μm] Reactive gas cg [%] R2 RME% RMSE [-] Hematite reduction 𝐹𝑒2𝑂3 + 𝐶𝐻4→ 𝐹𝑒𝑥𝑂𝑦 Monazam et al. [122] 700 0-63 CH4 10 0.998 2.66 0.066 750 0-63 10 0.999 2.09 0.042 800 0-63 10 0.999 2.06 0.058 800 0-63 5 0.996 12.8 0.153 800 0-63 15 0.998 10.1 0.105 800 125-250 10 0.996 2.91 0.045 800 500-1000 10 0.985 6.43 0.100  As mentioned above, during hematite reduction, physical properties change as the crystal structure changes when hematite is reduced, while oxygen diffuses outward to the surface. The BET specific surface area, porosity and specific crushing strength with different conversion 72  and temperatures are listed in Table 4.3. Here, the specific crushing strengths were measured after the reduction at 20°C. PSDs of hematite attrited/reduced with time at 800°C are plotted in Figure 4.13 to see the effect of the reduction on attrition. As reduction proceeded, the specific surface area and porosity increased. Yu et al. [128] observed that micro pores were generated when hematite was reduced with 20 vol% CO/80 vol% CO2. They explained that the formation of micro pores results from crystal structure differences between the hematite, having a trigonal (or hexagonal closed-packed) crystal structure, and magnetite, which has a cubic structure. When the reduction time was fixed at 6 h, while the temperature increased, the specific surface area and porosity were not significantly changed. However, when the conversion was fixed at approximately 4.7%, increasing the temperature decreased the porosity due to sintering. Several studies [129–131] showed similar results, indicating that the sintering temperature has a strong influence on the porosity of iron oxide compounds. An interesting result is that although the porosity increased with hematite reduction, the specific crushing strength increased because the reduced iron species, which have higher crushing strength compare to hematite [135], form from the outer layer of the surface. Quantitative XRD result of iron phases reduced from hematite with 30 vol% of CH4 at 700 and 800°C after 6 h of attrition is listed in Table 4.4 to support that the reduction conversion proceeds more with higher temperature.  Table 4.3 Specific surface area, specific crushing strength and porosity of hematite reduced at different conversions and temperatures. Hematite was reduced with 30 vol% of CH4 in N2.  Conditions Conversion [%] BETN2 [m2/g] Porosity Specific crushing strength of 250-500 μm particles [MPa] Hematite, no heat treatment 0 1.1 ± 0.5 0.170 101±11.5 73  Hematite reduction for 6 h at 700°C 4.7 2.0 ± 0.3 0.311 108±4.9 Hematite reduction for 1 h at 800°C 4.9 1.7 ± 0.3 0.193 111±4.9 Hematite reduction for 3 h at 800°C 9.1 2.1 ± 0.4 0.255 123±5.8 Hematite reduction for 6 h at 800°C 11.0 2.3 ± 0.4 0.320 126±7.4  Particle diameter range, [ m]0-63 63-125 125-250 250-500 500-1000 1000-2400Weight  fraction, [%]010203040Fe2O3, no reaction, 1h attritionFe2O3 reduction/attrition with 30 vol% CH4 in N2 for 1h, X=4.9%Fe2O3, no reaction, 3h attritionFe2O3 reduction/attrition with 30 vol% CH4 in N2 for 3h, X=9.1%Fe2O3, no reaction, 6h attritionFe2O3 reduction/attrition with 30 vol% CH4 in N2 for 6h, X=11.0% Figure 4.13 PSDs of hematite (Fe2O3) attrition in the presence and absence of reduction at 800°C with a jet velocity of 221 m/s. Note that pure N2 was used for the attrition/without reaction. 74   Table 4.4 Quantitative XRD analysis (wt%) of iron phases after Fe2O3 samples were reduced by 30 vol% CH4 at 700 and at 800°C for 6 h of simultaneous attrition/reaction.  700°C 800°C Fe2O3 79.0 76.3 Fe3O4 14.2 17.5 FeO 3.55 3.29 Fe3C 0.23 0.66 Fe 3.02 2.26  PSDs for 6 h attrition of hematite with and without reduction at 800°C, with a jet velocity of 221 m/s are depicted in Figure 4.14. As mentioned above, the surface area and porosity did not significantly influence the attrition. Instead, the reduction increased the crushing strength: the intrinsic crushing strength of reduced iron oxides, including magnetite, wustite and ferrous iron, reduced the attrition. Also, formation of Fe3C led to higher breakage energy than for any other iron oxide phases [89,120,132,133], ultimately reducing attrition.  75  Particle diameter range, [ m]0-63 63-125 125-250 250-500 500-1000 1000-2400Weight f raction, [%]010203040Unattrited and unreacted Fe2O3Fe2O3: no reaction at 800C, with airFe2O3: reduction at 800C with 30 vol% of CH4 Figure 4.14 PSDs of hematite after 6 h attrition with a jet velocity of 221 m/with and without reduction at 800°C, s. The PSDs of hematite (Fe2O3) after 6 h of attrition accompanied by reduction at different CH4 concentrations at 800°C are shown in Figure 4.15. The weight fractions of 500-1000 and 1000-2400 μm particles increased with increasing CH4 concentration; on the other hand, the weight fractions of 125-250 and 250-500 μm particles were lower as the CH4 concentration increased, indicating that the effect of fragmentation was reduced. During hematite reduction, ferrous iron (Fe) is generated on the surface with higher specific breakage energy than hematite, as observed by Taniguchi and Ohmi [134]. Also, with reduced ferrous iron exposed to CH4, iron carburization starts to generate Fe3C and to consume carbon with syngas reaction by the Boudouard reaction [135]. The proportion of Fe3C increases with increasing CH4 concentration, reducing attrition, since hematite reduction and formation of Fe3C lead to higher breakage energy 76  than any other iron oxide phases, as proven by previous researchers [89,120,132,133] who tested the effect of carbon content and oxide layer on mechanical properties. Particle diameter range, [ m]0-63 63-125 125-250 250-500 500-1000 1000-2400Weight fraction, [%]010203040Unattrited and unreacted Fe2O3 for reference0 vol% CH4Reduction with 30 vol% CH4Reduction with 50 vol% CH4Reduction with 70 vol% CH4 Figure 4.15 PSDs of hematite (Fe2O3) after 6 h of attrition accompanied by reduction with different CH4 concentrations at 800°C and jet velocity = 221 m/s.  4.3.1.3 Lime carbonation Similar to the previous sections, research on lime focused only on attrition rate and PSDs [98,136], without material properties variance at different CO2 concentrations. In this section, lime (CaO) was carbonated in a TGA under isothermal conditions in the 700-800°C temperature range, varying the CO2 concentration in N2 (30 and 50 vol%) and particle diameter 77  (0-63, 125-250 and 500-1000 μm, obtained by screening) to understand how lime carbonation affects key material properties and further attrition. Reaction kinetics were studied to determine whether the crushing strength changes from the outer layer or homogeneously throughout the particles during the carbonation. There are two rate-controlling regimes for the CO2-CaO reaction. For the initial stage of reaction, reaction occurs rapidly by heterogeneous surface chemical reaction kinetics [137]. After this stage, a layer of CaCO3 forms on the surface, leading to a substantial diffusion limitation through this layer. To explain this phenomenon, an unreacted core kinetic model is widely used [138], with 𝑡𝜏= 1 − (1 − 𝑋)1/3      (for kinetic rate control) (4-7) 𝑡𝜏= 1 − 3(1 − 𝑋)23 + 2(1 − 𝑋)  (for control by diffusion through a porous shell) (4-8) Here, t is time, X is conversion of CaO and τ is the time required to completely convert unreacted CaO into CaCO3. However, since the model assumes complete conversion (X=1) at t=τ, this model cannot describe actual kinetic behaviour. It has been reported that the reaction does not proceed to complete carbonation, with ultimate conversions in the range of 70-80% [78,137–142]. Lee et al. [137] proposed a practical apparent kinetic model, which showed good agreement with the data of Bhatia and Perlmutter [142] and Gupta and Fan [143] obtained at 550°C with CO2 concentrations from 2 to 100 vol%. The rate of conversion was expressed as: dXdt= 𝑘 (1 −𝑋𝑋𝑢)2 (4-9) where Xu is the ultimate conversion considering utilization decay [144] and k is a rate constant. After integration, the carbonation conversion can be expressed as: 78  𝑋 =𝑋𝑢𝑡(𝑋𝑢/𝑘) + 𝑡 (4-10) The lime carbonation at different temperatures is plotted versus time in Figure 4.16. As mentioned above, the chemical reaction is rate-controlling at low conversions, followed by diffusion control at higher conversions. As the temperature decreases, the rate of carbonation becomes more dependent on the diffusion limitation, deviating from chemical reaction control at lower conversions. Time, [s]0 5000 10000 15000 20000Conversion, [X]0.00.20.40.60.81.0Lime 0-63 m carbonated at 750C with 50 vol% CO2 in N2Lime 0-63 m carbonated at 700C with 50 vol% CO2 in N2Lime 0-63 m carbonated at 650C with 50 vol% CO2 in N2 Figure 4.16 Curve fitting of experimental lime (0-63 μm) carbonation data with 60 ml/min of 50 vol% CO2 in N2, at three temperatures. The apparent kinetic model from Lee et al. [137] does not include a CO2 concentration term. Dedman and Owen [145] reported that the reaction rate was zeroth order with respect to CO2 partial pressures and concentrations. Bhatia and Perlmutter [142] also found that the CO2 concentration did not affect the rate of carbonation. Figure 4.17 shows curve fitting of lime (CaO) carbonation data for different CO2 concentrations and the model adopted by Lee et al. 79  [137], with two fitted constants, a pre-exponential factor (k0) and an activation energy (Ea). The R2 for 30 vol% CO2 and the model from Lee et al. [137], and 50 vol% CO2 and the model are 0.996 and 0.997, respectively, indicating that the interdependence between the carbonation conversion and CO2 concentration is minor. Relative mean error percentages (RME%) and root mean squares of absolute error (RMSE) for different variables are presented in Table 4.5. Time, [s]0 5000 10000 15000 20000Conv ersion, [X]0.00.20.40.60.81.0Lime 0-63 m carbonated at 650C with 30 vol% CO2 in N2Lime 0-63 m carbonated at 650C with 50 vol% CO2 in N2Model from Lee et al. [79] Figure 4.17 Curve fitting for model of Lee et al. [137] of lime (CaO) carbonation data with two CO2 concentrations.    80  Table 4.5 Relative mean error percentage (RME%), root mean square of absolute error (RMSE) and R2 between TGA data and model for lime carbonation. Reaction Chemical reaction model fitted T [°C] dp [μm] Reactive gas cg [%] R2 RME% RMSE [-] Lime carbonation 𝐶𝑎𝑂 + 𝐶𝑂2→ 𝐶𝑎𝐶𝑂3 Lee et al. [137] 700 0-63 CO2 50 0.992 5.49 0.083 750 0-63 50 0.999 3.92 0.047 800 0-63 50 0.996 4.13 0.085 800 0-63 30 0.997 3.59 0.094 800 125-250 50 0.997 3.82 0.088 800 500-1000 50 0.996 6.08 0.105  PSDs of lime (CaO) after 6 h attrition with carbonation at different CO2 concentrations at 800°C are shown in Figure 4.18. The proportion of fines (0-63 μm) decreased with increasing CO2 concentration, whereas the other particle size bins did not show substantial differences. Since the Mann-Whitney U test can compare differences between two independent groups (different CO2 concentrations) when the dependent variable (PSD) is not normally distributed [99], this test is appropriate to assess the effect of CO2 concentrations on particle size distribution, rather than using the student T test or χ2 test, which assume that the dependent variable is normally distributed. Table 4.6 gives the results of the Mann-Whitney U test with unequal variances between the lime attrition without CO2 and the attrition test with different CO2 concentrations. Here, the p value from the Mann-Whitney U test, comparing the PSD of lime without CO2 and the PSD of lime carbonated with 10 vol% CO2, was 0.226, indicating that there is no statistically significant correlation between these two PSDs. Since 10 vol% CO2 is not enough to carbonate the lime at 800°C, the particle crushing strength did not change significantly. The lime carbonation equilibrium equation with partial pressure of CO2 [144] is: 𝑃𝐶𝑂2𝑒𝑞 = 1.87 × 109𝑒−19697/𝑇 (4-11) 81  where 𝑃𝐶𝑂2𝑒𝑞 is the equilibrium partial pressure of CO2 in CaCO3. An interesting result here is that the lime particle crushing strength did not significantly change, even though the CO2 concentration exceeded the equilibrium value, since the CaCO3 forms at the surface. Particle diameter range, [ m]0-63 63-125 125-250 250-500 500-1000 1000-2400Weight fraction, [%]0102030400 vol% CO2 Carbonation with 10 vol% CO2 Carbonation with 30 vol% CO2Carbonation with 50 vol% CO2 Carbonation with 70 vol% CO2  Figure 4.18 PSDs of lime (CaO) after 6 h attrition for carbonation with different CO2 concentration at 800°C for jet velocity = 221 m/s.    82  Table 4.6 Mann-Whitney U test results for the effect of CO2 on 6 h attrition at 800°C.  Mean [μm] Standard deviation [μm] skewness p value Lime attrition without CO2 276.8 251.5 0.798  Lime attrition/carbonation with 10 vol% CO2 289.8 269.5 1.148 0.226 Lime attrition/carbonation with 30 vol% CO2 283.3 262.7 1.117 0.334 Lime attrition/carbonation with 50 vol% CO2 283.1 253.7 0.908 0.223 Lime attrition/carbonation with 70 vol% CO2 284.3 254.7 1.041 0.159  Although the CO2 concentration did not significantly affect attrition, it was found that sintering by CO2 can change the particle crushing strength, possibly affecting fines (0-63 μm) generation. Table 4.7 shows the specific surface area, porosity and specific crushing strength with different CO2 concentrations at 800°C for 6 h. Specific crushing strengths were measured after carbonation. The BET surface area and porosity were slightly reduced with increasing CO2 concentration. As the CO2 concentration affects the sintering of CaO [146], the porosity decreased with increasing CO2 concentration. Similar results were obtained by Chen et al. [147]. The porosity also affect the particle breakage energy. Aqida et al. [106] showed the effect of the porosity on particle strength with a Mg-Al alloy. They claimed that the porosity increased particle crack formation, as well as decreasing the Young’s modulus. Thus, the fines generation was slightly reduced with increasing CO2 concentration, as sintering decreased the BET surface area of the particle (see Figure 4.19 and Table 4.7).     83   Table 4.7 Specific surface area and porosity of lime carbonated with different CO2 concentrations at 800°C for 6 h.   BETN2 [m2/g] Porosity Specific crushing strength of 250-500 μm particles [MPa] Uncalcined limestone 8.9 ± 0.4 0.201 21.7 ± 5.4 Lime carbonated with 30 vol% CO2 for 6 h 6.1 ± 0.6 0.171 24.5 ± 2.7 Lime carbonated with 50 vol% CO2 for 6 h 5.2 ± 0.5 0.153 27.2 ± 2.7 Lime carbonated with 70 vol% CO2 for 6 h 4.9 ± 0.5 0.142 27.2 ± 4.1  PSDs after 6 h of attrition/carbonation of lime (CaO) at 700 and 800°C, and PSDs of lime with 6 h of attrition for a jet velocity of 221 m/s with and without carbonation at 800°C are plotted in Figures 4.19 and 4.20. Several factors affected the attrition. First, as the temperature increased, the extent of lime sintering increased [144], reducing the porosity, which increased the particle breakage energy. As mentioned above, decreasing porosity by sintering increases the particle crushing strength [70,148,149]. Also, increasing the temperature reduces the gas density and reduces the particle momentum, leading to less attrition [74]. Higher ductility by increasing the temperature also reduces particle attrition, as proven by several researchers [32,148,150]. In addition, CO2 can affect attrition. Since CO2 reacts with lime, CaCO3 is generated at the surface of the particle, increasing the particle crushing strength as the breakage energy of limestone is higher than that of lime. Fines generation declined with increasing temperature, but coarse 84  particles in the size ranges 500-1000 and 1000-2400 μm did not significantly change because lime carbonation is slower with increasing particle size. Particle diameter range, [ m]0-63 63-125 125-250 250-500 500-1000 1000-2400Wei ght fraction, [ %]010203040Unattrited and unreacted limeLime: after carbonation at 700C with 30 vol% CO2 Lime: after carbonation at 800C with 30 vol% CO2 Figure 4.19 PSDs of lime (CaO) attrited/carbonated at 700 and 800°C for 6 h with 30 vol% of CO2 balanced with N2 at jet velocity = 221 m/s. 85  Particle diameter range, [ m]0-63 63-125 125-250 250-500 500-1000 1000-2400Weight fraction, [%]010203040Unattrited and unreacted limeLime: no reaction at 800C with N2Lime: carbonation at 800C with 30 vol% CO2 Figure 4.20 PSDs of lime (CaO) attrition tests with and without carbonation for 6 h at jet velocity = 221 m/s.  4.3.1.4 Limestone calcination Jia et al. [151] tested attrition when calcining limestone in a circulating fluidized bed reactor at 810±20°C. They found that the PSD changed, but did not explain how calcination affected the attrition. Gonzalez et al. [92] also tested sorbent attrition with calcination in a pilot plant, but there was no consideration of the variation of mechanical properties with calcination.  In general, most researchers [43,92,151,152] who studied limestone attrition during calcination in fluidized beds only measured PSDs; none of them investigated how the degree of calcination affected the PSD results. Although many researchers [43,44,52,92,98,151,152] mentioned that 86  calcination may affect attrition, there is little or no evidence of how. Thus, our attrition tests were analyzed not only to obtain PSD data, but also to determine the porosity, specific surface area and pore size distributions in order to find the effects of calcination on attrition. The TGA tests were also fitted with previously suggested chemical reaction models from previous research [153]. In this study, limestone was calcined in extra dry air in a TGA under isothermal conditions in the 700-800°C temperature range for particle diameters of 0-63, 125-250 and 500-1000 μm. The experimental data are plotted for each series of experiments in Figures 4.21 and 4.22 below, as limestone calcination conversion (X) versus time. As expected, the slope of the experimental data increased with increasing temperature. In Figure 4.22, the slope of the graph of the experimental X versus time decreased as the particle diameter increased. This suggests that CO2 diffusion through the particle structure, without or with chemical reaction, influenced the process kinetics in this temperature range. This behaviour indicates that the conversion was influenced by CO2 diffusion, whether by intergrain diffusion alone or together with the chemical reaction step. Escardino et al. [153] derived a rate equation for limestone calcination, based on a grainy pellet model, which adopted the following assumptions: 1) Internal temperature gradients in each grain are negligible during calcination under isothermal conditions. 2) CO2 intragrain diffusion (CO2 diffusion into each limestone grain) is assumed to not influence the overall process rate, because it develops more quickly than the chemical reaction and intergrain diffusion steps, given the very small size of the grains. 3) The reaction interface is assumed to be the CaCO3/CaO boundary in every limestone grain. 87  4) The concentration gradient responsible for CO2 diffusion through the particle pores is assumed to remain constant. 5) CO2 transfer from the outer surface of the particle to the bulk gas phase is assumed to take place instantaneously, i.e. there is negligible external mass transfer resistance. The calcination conversion is expressed as proposed by Escardino et al. [153]: 1 − (1 − 𝑋)23 =23𝑆𝑉𝑝𝑘𝑐𝐵−2/3𝑡 (4-12) where S and Vp are the surface area and volume of particles, respectively, k is a rate constant of the calcination, and cB is the initial molar concentration of CaCO3 inside the particle.  The activation energy of the limestone in this test was 190.9 ± 8.7 kJ/mol, a value similar to values proposed by several previous researchers [154–156]. Eqn. (4-12) is fitted with our TGA data in Figure 4.22 for limestone calcination at 800°C. Details of the relative mean error percentage (RME%) and root mean square of absolute error (RMSE) for different variables are listed in Table 4.8. 88  Time, [s]0 1000 2000 3000 4000 5000Calcination conversion percentage, [%]020406080100700 C 750 C 800 C  Figure 4.21 Curve fitting of experimental limestone (0-63 μm) calcination data with 60 ml/min of air for three temperatures.  Figure 4.22 Curve fitting of experimental limestone calcination data with rate equation adopted by Escardino et al. [153] at 800°C with 60 ml/min of air. 89  Table 4.8 Relative mean error percentage (RME%), root mean square of absolute error (RMSE) and R2 between TGA data and model for limestone calcination. Reaction Chemical reaction model fitted T [°C] dp [μm] Reactive gas cg [%] R2 RME% RMSE [-] Limestone calcination 𝐶𝑎𝐶𝑂3→ CaO + CO2 Escardino et al. [153] 700 0-63 - - 0.976 3.67 0.167 750 0-63 0.974 1.21 0.098 800 0-63 0.971 0.46 0.060 800 125-250 0.918 3.99 0.233 800 500-1000 0.913 15.9 0.466  In general, increasing the temperature affects the density and viscosity of the gas, which then influences the particle velocity and hence attrition as well. Moon et al. [157] tested high-temperature attrition and claimed that the gas density contributes the major change in inertia force compared to the viscosity at the particle Reynolds number of 21. In our work, the reduced gas density with increasing temperature lowered the particle momentum, consequently reducing attrition [74]. Figure 4.23 plots the PSDs of limestone with calcination at 700 and 800°C after 6 h of simultaneous attrition/reaction at a jet velocity of 221 m/s with air as the gas. However, the attrition increased with increasing temperature, as the calcination rate increased with increasing temperature. Here, the material properties changed at higher temperature, which may affect the attrition. Several previous researchers [70,148,149] have reported a relationship between the porosity of the particle and crushing strength, confirming that increasing porosity decreases particle crushing strength.  Table 4.9 gives the BET specific surface area and the porosity of limestone calcined at 700 to 800°C for 6 hours. It is seen that the particle porosity increased when calcination occurred. Since the porosity of calcined limestone after 6 h at 700°C is less than that calcined at 800°C, the specific crushing strength also decreased with increasing temperature. Abanadez and Alvarez 90  [158] and Borgwardt [159] observed that sintering causes a rapid change in particle morphology and a decrease in surface area. In this work, the specific BET surface area of limestone dropped from 16.9 to 5.3 m2/g after 6 h of calcination at 800°C. Sintering also affected the pore size distribution, as shown in Figure 4.24. The micro pores (1-10 μm) of limestone decreased, whereas the meso pores (10-100 μm) increased due to sintering. To summarize, although the surface area pore size and the gas density change due to temperature have previously been found to affect attrition, these material properties did not significantly affect the attrition in this work. Rather, the porosity and specific crushing strength affected the attrition.  Figure 4.23 PSDs of limestone with calcination at 700 and 800°C after simultaneous 6 h attrition/reaction at jet velocity = 221 m/s with air. 91  Table 4.9 Specific surface area and porosity of limestone calcined at different temperatures.  BETN2 [m2/g] Porosity Specific crushing strength of 250-500 μm particles [MPa] Uncalcined limestone 16.9 ± 0.4 0.338 28.5 ± 8.2 Limestone calcined at 700°C for 6 h 9.2 ± 0.5 0.521 21.7 ± 4.1 Limestone calcined at 800°C for 6 h 5.3 ± 0.3 0.540 14.9 ± 4.1 Pore mean diameter, [nm]0.1 1 10 100Incremental  por e volume, [ml/g]0.000.010.020.030.040.05Uncalcined limestoneCalcined limestone at 700C for 6hCalcined limestone at 800C for 6h Figure 4.24 Pore size distribution of limestone calcined at different temperatures measured by mercury porosimetry (located at Department of Earth, Ocean and Atmospheric Science at UBC).  92  4.3.2 Attrition of binary solid species Since limestone calcines at temperatures ≥700°C by thermal decomposition at atmospheric pressure [144], only binary mixtures of hematite (Fe2O3) and lime (CaO) particles were tested to find how the chemical conversion of particle species affect the attrition in a two-solid-species environment. The size distributions of hematite (Fe2O3) from a hematite alone test and the hematite segregated from hematite:lime mixture initially 0.5:0.5 by weight are shown in Figure 4.25. The attrition lasted 6 h with/without reaction at 800°C. Compared to the results for hematite alone undergoing attrition without reduction and PSDs of hematite alone, attrition increased in the presence of lime. Since U/Umf for the separated hematite was 4.75, which is higher than 2.11 for hematite alone, particle collisions increased when the hematite and lime were mixed together. This was confirmed by Buffiere and Moletta [160], who tested particle collision frequency vs solid holdup ratio. Particle fatigue due to the cumulative particle collisions with time can reduce particle crushing strength [161]. Attrition decreased when reduction occurred for both the hematite alone test and for hematite:lime 0.5:0.5 by weight mixtures. The proportion of particles in the 0-63 μm size fraction increased in the presence of lime, indicating less fragmentation and increased abrasion. 93  Particle diameter range, [ m]0-63 63-125 125-250 250-500 500-1000 1000-2400Weight fraction, [%]010203040Fe2O3, unattrited, unreacted Fe2O3, alone, no reaction, conveyed by N2Fe2O3, alone, reduction with 30 vol% CH450% Fe2O3, no reaction, conveyed by N250% Fe2O3, reduction with 30 vol% CH4 Figure 4.25 Size distributions of hematite (Fe2O3) from hematite alone test and hematite segregated from hematite:lime mixtures initially 0.5:0.5 by weight, after 6 h of attrition with/without reduction at 800°C. Jet velocity = 221 m/s. The size distributions of lime (CaO) from the lime-alone test and the lime segregated from an 0.5:0.5 by weight hematite:lime mixture, after 6 h of attrition with/without reaction at 800°C are plotted in Figure 4.26. Attrition, including fines generation, was greater in the presence of hematite, because the hematite particles, with a higher specific breakage energy than lime, struck lime particles, promoting breakage. Also, since lime carbonation starts from the outer surface of the particle, attrition of lime was reduced in the presence of carbonation compared to uncarbonated lime. 94  Particle diameter range, [ m]0-63 63-125 125-250 250-500 500-1000 1000-2400Weight f raction, [ %]01020304050Lime, unattrited, unreacted Lime, alone, no reaction, conveyed by N2Lime, alone, carbonation with 30 vol% CO250% lime, no reaction, conveyed by N250% lime, carbonation with 30 vol% CO2 Figure 4.26 Size distributions of lime (CaO) from lime-alone test and lime segregated from hematite:lime 0.5:0.5 initially by weight, with 6 h attrition with/without carbonation at 800°C with jet velocity = 221 m/s.  95  4.4 Conclusions Attrition tests accompanied by specific reactions were studied, combined with measurements of both PSDs and relevant material properties to investigate how chemical conversion of particle species affect attrition in fluidized beds. The material properties measured included BET specific surface area, porosity, pore size distribution and particle breakage energy, in addition to particle size distributions. Chemical reaction kinetics were also investigated because of their relationship with mechanical properties of the particles. Attrition tests were conducted with both particles of a single species and binary solid mixtures. Oxidation decreased the particle crushing strength of iron particle, forming a porous iron oxide layer on the surface. Change in porosity and surface area did not significantly affect the attrition when hematite was reduced. Instead, the proportions of reduced iron oxides, such as magnetite, wustite and ferrous iron, increased the intrinsic crushing strength on the surface when hematite was reduced with CH4, reducing attrition. For limestone, calcination increased the attrition due to a decrease in the intrinsic particle specific crushing strength. With increasing temperature, attrition increased as the porosity increased and the particle specific crushing strength decreased. Lime carbonation reduced attrition due to the changes in material properties, increasing ductility and sintering, as well as the formation of a limestone surface layer of carbonate. Particle attrition increased when two solid species were mixed together, due to the increasing frequency of inter-particle collisions. 96  Chapter 5: Jet attrition model 5.1 Introduction Attrition occurs during particulate solid handling and processing in the chemical, energy and other industries. In processes involving fluidized beds, particles are damaged by attrition over repeated cycles of reactions and particle transport, increasing the operating cost [116,123,162,163]. Fines generated from attrition are entrained, some leaving the system with the exhaust gas, affecting downstream unit operations and reducing the operation efficiency. Furthermore, the entrained dust can cause particulate matter air pollution, affecting public health. Thus, monitoring and predicting how much fines are generated in fluidized bed reactors are important. Several approaches have been adopted by previous authors to model attrition in fluidized beds in order to predict how much fines are generated. Chen et al. [83] developed a model for limestone impact attrition at temperatures between 25 and 580°C and particle impact velocities from 9 to 64 m/s. They assumed that mass loss from different particle size bins follows a first order rate law, with the rate constant expressed as a function of temperature by an Arrhenius-type equation, as well as being proportional to the square of particle velocity. Ray et al. [23] presented a population balance model to predict the overall particle size distributions (PSDs) of limestone undergoing both attrition and reaction, assuming that limestone calcination follows a zeroth order reaction model, with only abrasion causing the attrition. Jiang et al. [164] proposed an attrition model for quartzite particles in fluidized beds, with particle size ranging from 2.18 to 2.75 mm, and temperatures from 750 to 950°C. They assumed that only abrasion is responsible for fluidized bed attrition and that this attrition is proportional to time. Wang et al. [165] proposed a population balance model for coal particles in circulating fluidized bed reactors, 97  assuming that the coal particles follow a shrinking core model, with the attrition rate being independent of time. Previous researchers have overlooked the distinction between abrasion and fragmentation in particle attrition, and attributed all particle breakage to abrasion. As a result, previous models tend to overestimate the extent of abrasion. These models also generally assume that all particles follow a shrinking core model when reactions occur [23,164–166]. Moreover, most attrition models for fluidized beds omit material properties, such as elastic modulus (Young’s modulus) and particle crushing strength, although particle attrition clearly depends on material properties, such as particle size, particle density and modes of failure [42,74,167]. Another significant factor to consider when developing an attrition model is the location where the attrition occurs, which has also been neglected in previous models. There are three main locations of attrition in fluidized beds, these being related to jets, bubbles and cyclones. Jet attrition is usually considered as the major source of fragmentation, compared to the attrition from other locations [30]. Despite the importance of jet attrition in fluidized beds, jet attrition has received only limited attention by researchers because of its complexity in determining the attrition mode, i.e. the distinction between fragmentation and abrasion. Jet attrition has been investigated by a few researchers. Moon et al. [74] tested a CO2 sorbent (KPM1-SU) varying the static bed height, temperature, pressure, gas velocity and humidity. They reported that the attrition rate increased with increasing pressure and gas velocity, but decreased with increasing temperature. Xiao et al. [53] tested limestone, varying several particle size bins and time in an ASTM D5757 unit, and suggested an empirical equation to estimate the attrition rate. Kang et al. [28] tested different types of distributors to test the effects of jet velocities and distributor hole size on the attrition rate of iron ore. However, the attrition 98  tests above by Moon et al. [74], Xiao et al. [53] and Kang et al. [28] did not consider the attrition mode, nor the impact of chemical reactions on attrition. In this chapter, a mechanistic fluidized bed jet attrition model (JAM) is developed to improve the understanding of jet attrition and to predict the particle size distribution for various operating conditions, considering how both fragmentation and abrasion affect particle size distributions in fluidized bed systems. A universal algorithm for attrition is suggested, dependent on material properties, as well as chemical reactions, with mechanical attrition by both fragmentation and abrasion. Material properties, such as Young’s modulus, particle density and breakage energy, change when chemical reaction occurs. Thus, the solid conversion vs. time with solid reactions are applied to estimate the particle mechanical properties by conversion-weighted average properties of the particle species. Overall, four chemical reactions are considered for comparison with the data presented in Chapters 3 and 4 of this thesis (iron oxidation in air, hematite reduction with CH4, limestone calcination and lime carbonation with CO2). Mechanical attrition by fragmentation and abrasion is also considered after estimating the material properties change. Since the crushing force by compression with ductile material does not significantly changes when it is under plastic deformation, such as strain hardening and structure change, the force-based model is considered not suitable. Therefore, the energy-based model, which comprises the overall material characteristics by compression for both ductile and brittle materials, is used to develop the jet attrition model. To distinguish the attrition modes by fragmentation and abrasion, the particle breakage energy was calculated and compared with the kinetic energy loss after particle collision. The particle breakage energy was measured with the 99  compression unit, described in Chapter 4. Also, the particle impact velocity was calculated by the empirical equation, simulated with Eulerian-Eulerian computational fluid dynamics (CFD). Fragmentation is considered to follow the particle mass exchange steps suggested by Chen et al. [83]. For the abrasion, a modified Archard equation, which attributes particle abrasion to shear, is adopted. Also, the fatigue of materials due to repeated collisions is considered when predicting the particle size distribution of solid species resulting from both fragmentation and abrasion. The predicted attrition of single and binary solid species are also compared with experimental results from the data provided in Chapters 3 and 4.  5.2 Jet attrition model description As explained in the Introduction, previous models [23,83,164,165] did not determine separately the abrasion and fragmentation in particle attrition. Although the necessity of distinguishing different modes of attrition has been emphasized by several researchers [27,28,42,56], most studies have determined the attrition mode by observing particle size distributions, without any further mathematical or mechanistic approaches. In a jet attrition model, fragmentation and abrasion are determined by comparing the particle breakage energy (Eb) and the energy loss after collision (Eloss). In the model developed in this chapter, the particle breakage energy is defined as the energy required for fragmentation, measured by the compression unit described in Chapter 2. Thus, the breakage energy is fixed for different solid species and particle sizes. At the same time, the energy beyond that lost in collisions (Eloss) is assumed to be available to break particles when a particle collides with other particles. Therefore, the energy loss after collision changes with the relative particle velocity of two different particles colliding with each other. 100  The relative particle velocity before a collision is calculated by measuring/estimating the impact velocity of two particles colliding with each other. There are several ways to determine the particle velocity experimentally. First, optical fiber probes can measure the velocity of particles moving at a constant speed in the direction connecting two receiving fibers [168]. However, since the particle impact velocity is the maximum velocity when particles are accelerated by a jet and collide with other particles, optical fiber probes were not useful for the particles accelerating by the jet in this thesis project. Another measuring method is to mark a single particle with a radioactive tracer and track the motion of this particle in fluidized beds [41]. However, the radioactive particle tracking method requires data collection over a long time [169]. Also, the data collected in the radioactive particle tracking method are time-averaged information, such as axial and radial velocities and granular temperature. Thus, these experimental methods are not suitable for measuring the particle impact velocity in fluidized beds, where particles may break via attrition. Rather, a suitable simulation method is developed to estimate the particle impact velocity in fluidized beds, providing estimates of particle velocity before collisions with other particles. Computational fluid dynamics (CFD) simulation is used to estimate the particle impact velocity. Generally, there are two representative methodologies of multiphase modeling in CFD simulation – Eulerian- and Lagrangian-based methods. In the Eulerian-Eulerian overlapping continuum approach, the portion of volume occupied by each phase is given by the volume fraction [170]. Because the volume of each phase cannot be occupied by other phases, the concept of phase volume fraction is introduced [171]. In other words, individual particles are not identified. Instead, a control volume is defined for each phase. Thus, the velocity calculated from 101  the Eulerian-Eulerian approach predicts the velocity of the granular phase at a particular location of interest at a particular time.  The Eulerian-Lagrangian approach, which adopts an Eulerian approach for the gas flow and a Lagrangian approach for the particle flow, can also be used to estimate the particle velocity. Unlike the Eulerian-Eulerian approach, individual particles are ‘marked’ and followed, predicting their positions and velocities as functions of time in the Eulerian-Lagrangian approach. The Discrete Element Method (DEM) is one of the representative models using the Lagrangian approach. Despite the advantages of predicting position vectors and velocity vectors at each time instant for each of the marked particles, the Lagrangian method is less often used in fluidized beds because of the higher amount of computational resources required. Several researchers have recommended constraining the number of particles to less than 200k in the simulation system [172,173]. Cengel and Cimbala [174] claimed that tracking with the Lagrangian approach is not suitable for fluidized beds systems because there are too many particles to track. DEM can only be used in very limited conditions, especially constraining the particle numbers for attrition system because particles are instantaneously formed during attrition which is hard to track [175]. Therefore, the Eulerian-Eulerian approach was used in this work to estimate the particle impact velocity. After the kinetic energy loss (Eloss) and breakage energy of particles (Eb) have been estimated and measured respectively, particle breakage is determined by either fragmentation or abrasion. If Eloss≤Eb, abrasion is assumed to occur; otherwise, i.e., for Eloss>Eb, fragmentation is assumed. Two fitting parameters representing material fatigue and repeated collisions are introduced here. The details of the energy loss after the collision are described after outlining the assumptions adopted in this model. 102  Another advantage of the model proposed in this chapter is flexibility – with potential applicability to any attrition system. The attrition algorithm is developed to consider how the material properties change with chemical reactions, as well as with temperature. Furthermore, the algorithm distinguishes between fragmentation and abrasion, using an approach which can be applied at any attrition location, modifying the particle velocity calculation.  Figure 5.1 presents the Jet Attrition Model (JAM) algorithm flow chart. This model is based on several simplifying assumptions: 1) Temperature is constant in time and spatially uniform. 2) Particles are brittle; they break without significant plastic deformation when subjected to stress. 3) Each solid species shows a linear relationship between stress and strain. 4) Particles are spherical, but with relatively small asperities on their surfaces before breakage. 5) Collisions occur when particles are rising. Particles that are falling are not considered in this simulation since the Eulerian model cannot track individual particles. 6) The particle collision frequency model is derived by applying the kinetic theory of gases to particle motion, assuming a Maxwellian distribution of particle velocities [176]. This representation has been found to be applicable experimentally by several researchers [160,164,177,178] fitting well for solid holdups up to 0.42. 7) All particles of the same species in the same bin are uniform in terms of size, composition, impact velocity, etc. 103  8) For the fragmentation, a “mass exchange step” is applied to calculate the breakage of particles. The general mass exchange step has been used previously by Chen et al. [83] and Uzi et al. [179] who tested particle breakage due to impacts. 9) The abrasion rate is calculated by a modified Archard equation [180] (see Section 5.3.3). The modified Archard equation [180] is tested with the experimental jet apparatus, for superficial gas velocities between the minimum fluidization velocity of particles and the particle crushing velocity. 10) Fine particles (defined here as having dp <63 μm) cannot be attrited and are not effective in breaking other particles. 11) When reactions occur, particle mechanical properties are estimated by the conversion-weighted average of the properties of the constituent particulate species, assuming a homogenous distribution of the materials inside each particle. 104   Figure 5.1 Jet attrition model (JAM) algorithm flow chart. 105  As noted in Chapters 3 and 4, material properties can play a significant role in understanding and predicting particle attrition behaviour, particularly when chemical reactions occur. Based on our previous findings, the jet attrition model was developed, considering that particle attrition rates depend on operating time, temperature, gas phase species concentrations, reaction and particle compositions. Four solid species, iron, hematite, limestone and lime, were chosen to represent both oxygen carrier and CO2 sorbents in sorption-enhanced chemical looping processes. Also, four chemical reactions are included in this model: iron oxidation, hematite reduction, limestone calcination and lime carbonation. Suitable reaction kinetics were selected to estimate the change in material properties with chemical reactions. Young’s modulus and particle crushing strength were selected as representative material properties.  Table 5.1 provides a list of reaction kinetic models adopted from Chapter 4. Chapter 4 showed that the particle species reaction rate in the jet apparatus was 1/4 of the TGA result because: 1) The orifices only covered 3.6% of the total open area, resulting in limited solid-gas contact; and 2) The reaction atmosphere in the ASTM unit contained more product gases and less reactant gases due to a relatively low gas feed rate, reducing the reaction driving force [181]. The incremental reaction conversions of all species were calculated by the respective differential rate equations over the specified time step, ∆t. After estimating the solid reaction conversion, material properties, such as Young’s modulus and particle crushing strength, were estimated based on the revised compositions of the particles.   106  Table 5.1 Reaction kinetic models for reactions, adapted from Chapter 4. Reaction Reactive gas Simplified chemical equation References for reaction kinetic model Hematite reduction CH4 𝐹𝑒2𝑂3 + 𝑎𝐶𝐻4 → 𝐹𝑒𝑥𝑂𝑦 + 2𝑎𝐻2 + 𝑏𝐶 + (𝑎 − 𝑏)𝐶𝑂 Monazam et al. [122] Iron oxidation O2 in air 𝐹𝑒 + 𝑂2 → 𝐹𝑒𝑥𝑂𝑦 Parabolic model for Fe to Fe3O4 oxidation [108–114] + Second order kinetic model for Fe3O4 to Fe2O3 oxidation [115] Limestone calcination - 𝐶𝑎𝐶𝑂3 → 𝐶𝑎𝑂 + 𝐶𝑂2 Escardino et al. [153] Lime carbonation CO2 𝐶𝑎𝑂 + 𝐶𝑂2 → 𝐶𝑎𝐶𝑂3 Lee et al. [137]  Young’s modulus has been determined previously [86,120,182,183] as a function of temperature and material porosity. The Young’s moduli of different particle species used in this model were adopted from literature values, and they were corrected with the particle porosity. Several researchers [86,184–187] have shown that Young’s modulus as a linear function of temperature for various porous and non-porous solid species between 400 and 900°C [86,120,183]. Spriggs [182] proposed an empirical model of Young’s modulus as a function of internal porosity: 𝑌 = 𝑌𝑜𝑒𝑥𝑝(−𝛼𝑝) (5-1) where Y0 is the Young’s modulus without porosity, p is internal porosity and α is a material constant. Based on eqn. (5-1), Young’s modulus of the same materials with different porosities can be calculated [149], leading to the following equation at a given temperature: 𝑌2𝑌1= 𝑒𝑥𝑝(−𝛼(𝑝2 − 𝑝1)) (5-2) 107  Here Y1 and Y2 are the measured Young’s moduli of the same materials with different porosities, p1 and p2, respectively. Assuming that the porosity of each material remains constant over a temperature range, 𝑒𝑥𝑝(−𝛼(𝑝2 − 𝑝1)) is a constant correction factor correlating the Young’s moduli of two materials in this temperature range. Therefore, the literature Young’s modulus can be corrected to account for the difference in the material porosity. In order to determine this correction factor, the ratio of the experimental Young’s modulus data and literature values at room temperature, Yexp, RT /Ylit, RT, were calculated, as listed in Table 5.2. Table 5.2 Young’s modulus for different solid species. Species  Young’s modulus [GPa] Reference Correction factor, Yexp, RT /Ylit, RT [-] Iron  Y=-0.267T+281 [187] 0.837 Hematite  Y=-0.043T+221 [86] 0.523 Limestone  Y=-0.066T+56.8 [184] 4.418 Lime  Y=-0.007T+80.3 [186] 0.413  The average particle impact velocity was estimated from a dimensionless empirical correlation of results from a CFD simulation, as detailed in Section 5.2. All particles in the same size bin are assumed to have the same impact velocity because of the limitation of Eulerian-Eulerian CFD simulation – the velocity calculated from the Eulerian-Eulerian approach shows the velocity of the granular phase at a particular location of interest at a particular time. Particle collision frequency also affects the attrition. Martin [176] suggested a model for the collision frequency of particles, depending on the average distance travelled by a particle between successive collisions and the average fluctuation velocity of particles in a fluidized bed: 𝜆𝑝 =1√2𝜋𝑑𝑝2𝑛𝑝=𝑑𝑝6√2(1 − 𝜀𝑚𝑓)𝜀 − 𝜀𝑚𝑓1 − 𝜀 (5-3) 108  𝑐 = √𝑔𝑑𝑝5(1 − 𝜀𝑚𝑓)𝜀 − 𝜀𝑚𝑓1 − 𝜀 (5-4) 𝑓𝑐 =𝑐𝜆𝑝 (5-5) where λp is average distance travelled by a particle between successive collisions, c is the average particle velocity fluctuation, np [1/m3] is the number density, and fc is the collision frequency. Rearranging to give the collision frequency as a function of number density and particle size, we obtain: 𝑓𝑐 = 2𝑑𝑝√0.6𝜋𝑔𝑛𝑝 (5-6) The collision frequency of particles of different sizes or composed of different materials is approximated using the geometric average. Jiang et al. [164] assumed that the kinetic energy loss after an inter-particle collision is considered to be the energy available to potentially break particles. This kinetic energy loss is estimated based on an equation from Senior and Grace [188]: 𝐸𝑙𝑜𝑠𝑠 =𝑚𝑝,1𝑚𝑝,22(𝑚𝑝,1 + 𝑚𝑝,2)(1 − 𝑒2)|𝑢𝑝,1 − 𝑢𝑝,2|2 (5-7) where subscripts 1 and 2 represent the two particles, mp is the particle mass, up the particle velocity and e is the coefficient of restitution. Eqn. (5-7) is based on a typical collision between two spherical particles. Particle breakage can be considered to occur by three loading modes: static loading, impact loading and cyclic loading [189]. The static loading particle breakage energy, estimated based on the results from the compression test unit (see Table 2.3), is generally used for attrition testing due to its simplicity, despite the fact that the impact loading is likely to be more 109  appropriate for attrition in fluidized beds. Efforts have been made by Han et al. [161] and Rozenblat et al. [59] to correlate the particle impact loading strength and cyclic loading strength with its static loading strength. Particle breakage energy is calculated based on Young’s modulus and particle diameter: 𝐸𝑏0 =2𝐹𝑐2𝜋𝑌𝑑𝑝 (5-8) where Fc is the particle crushing strength prior to collision measured by the compression test. It is also important to consider the effect of the particle collisions on material properties over many cycles, since cyclic impact over an extended time period may cause material fatigue, lowering the breakage energy. Fatigue causes time-dependent growth of subcritical cracks under cyclic (repeated) loading/unloading. The cyclic stresses and collisions result in a degradation of material resistance, leading to micro-cracks in the material. As the micro-cracks propagate over repeated impact cycles, the particle breakage energy decreases, thus particles can break at lower loading intensities. Han et al. [161] suggested an empirical correlation for the breakage force of particles subject to fatigue: 𝐹𝑏𝐹𝑏0= {1 +𝑃1exp [𝑃3 − 𝑃2(𝐹∗)1/3]}−3/2𝑁 (5-9) where Fb is the breakage force of particles with fatigue, Fb0 is the breakage force of particles before loading, F* is the ratio of the impact force in each collision to the initial particle crushing strength, P1 is the translational degree of freedom of the activated complex along the reaction coordinate, P2 and P3 describe the theoretical strength and initial strength of the particles, respectively, and N is the number of collisions of each particle [161]. Since P1, P2 and P3 are 110  material properties of a micro-material structure, which cannot be easily measured, an overall fatigue factor, Cfatigue, is adopted to incorporate all the material properties: 𝐶𝑓𝑎𝑡𝑖𝑔𝑢𝑒 =𝑃1exp [𝑃3 − 𝑃2(𝐹∗)1/3] (5-10) The parameter N in eqn. (5-9) represents the number of cycles in which a particle was ejected and collided at right angles with a fixed target [161]. This is not identical to the particle behaviour in a fluidized bed where particles may be affected by tribocharging and turbulence. The Han et al. model [161] assumed one-dimensional collisions, which again is not precise in a fluidized bed. Besides, only collisions in the jet region are considered here to cause jet attrition, which is only a portion of the total collision frequency predicted by eqn. (5-6). To account for these factors, N is calculated as a function of collision frequency, fc: 𝑁 = 𝐶𝑐𝑜𝑙𝑙𝑖𝑠𝑖𝑜𝑛 ∙ 𝑓𝑐 ∙ ∆𝑡 (5-11) where ∆t is the time step for which the number of collisions is calculated and Ccollision is the particle collision factor, accounting for the difference between the assumptions of the Han et al. [161] and Martin models [176] and the experimental conditions. By rearranging eqns. (5-8) to (5-11), the particle fatigue behaviour is characterized in terms of energy by 𝐸𝑏𝐸𝑏0= (1 + 𝐶𝑓𝑎𝑡𝑖𝑔𝑢𝑒)−3𝐶𝑐𝑜𝑙𝑙𝑖𝑠𝑖𝑜𝑛𝑓𝑐𝑡 (5-12) given that Young’s modulus is an intrinsic material property [189]. Here Eb is the breakage energy of particles subject to fatigue, and Eb0 is breakage energy of particles without fatigue. Cfatigue and Ccollision are parameters to be fitted, as described in Section 5.3. After the kinetic energy loss (Eloss) and breakage energy of particles (Eb) have been calculated, particle breakage is determined by either fragmentation or abrasion. If Eloss≤Eb, 111  abrasion is assumed to occur; otherwise, i.e., for Eloss>Eb, fragmentation is assumed. When particles are determined to be abraded, the mass of abraded particles is calculated from a modified Archard equation (see Section 5.3.3). When particles are found to be fragmented, a new particle mass exchange model, similar to that of Chen et al. [83] and Uzi et al. [179], is adopted. Both abrasion and fragmentation modeling are explained in detail in Section 5.3.  5.3 Impact velocity determination by Computational Fluid Dynamics (CFD) Particle impact velocity was estimated by simulating particle attrition in the jet apparatus using CFD software, ANSYS Fluent 19.2, solving the governing equations of mass, momentum and energy conservation. In this simulation, mass and momentum balances were applied to both the gas and solid particles phases: 𝜕𝜕𝑡(𝜀𝑔𝜌𝑔) + ∇(𝜀𝑔𝜌𝑔𝑢𝑔) = 0 (5-13) 𝜕𝜕𝑡(𝜀𝑝𝜌𝑝) + ∇(𝜀𝑝𝜌𝑝𝑢𝑝) = 0 (5-14) 𝜕𝜕𝑡(𝜀𝑔𝜌𝑔𝑢𝑔) + ∇(𝜀𝑔𝜌𝑔𝑢𝑔2) = −𝜀𝑔∇𝑃𝑔 − ∇(𝜀𝑔𝜏𝑔) + 𝜀𝑔𝜌𝑔𝑔 + 𝐾𝑔𝑠(𝑢𝑝 − 𝑢𝑔) (5-15) 𝜕𝜕𝑡(𝜀𝑝𝜌𝑝𝑢𝑝) + ∇(𝜀𝑝𝜌𝑝𝑢𝑝2) = −𝜀𝑝∇𝑃𝑝 − ∇(𝜀𝑝𝜏𝑝) + 𝜀𝑝𝜌𝑝𝑔 + 𝐾𝑔𝑠(𝑢𝑔 − 𝑢𝑝) (5-16) where eqns. (5-13)-(5-16) are mass and momentum conservation equations for gas (g) and solid (p) phases. Kgs, the gas-solid momentum exchange coefficient, is calculated from the Gidaspow drag model [190]: 𝐾𝑔𝑠 =34𝐶𝐷𝜀𝑝𝜀𝑔𝜌𝑔|𝑢𝑔 − 𝑢𝑝|𝑑𝑠𝜀𝑔−2.65   for 𝜀𝑔 > 0.8 (5-17) 112  Kgs = 150𝜀𝑠2𝜇𝑔𝜀𝑔𝑑𝑝2   for 𝜀𝑔 ≤ 0.8 (5-18) where 𝐶𝐷 =24𝜀𝑔𝑅𝑒𝑝[1 + 0.15(𝜀𝑔𝑅𝑒𝑝∗)0.687] (5-19) and 𝑅𝑒𝑝∗ =𝜌𝑔𝑑𝑝|𝑢𝑔 − 𝑢𝑝|𝜇𝑔 (5-20) Other constitutive equations are listed in Table 5.3. An Eulerian multi-fluid model is coupled with the kinetic theory of granular flow (KTGF) to calculate the governing equations [190].  Table 5.3 Constitutive equations for CFD simulation. Name Equations Solid phase stress tensor τ = 𝜀𝑔𝜇𝑝(∇?⃗? 𝑝 + ∇?⃗? 𝑝𝑇) + 𝜀𝑝 (𝜇𝑏,𝑝 −23𝜇𝑝)∇?⃗? 𝑝𝐼 Radial distribution function g0,ss = [1 − (𝜀𝑝𝜀𝑝,𝑚𝑎𝑥)1/3]−1 Diffusion coefficient of granular temperature (Gidaspow) k𝜃𝑝 =150𝑑𝑝𝜌𝑝√𝜃𝑝𝜋384(1 + 𝑒)𝑔0,𝑝 Collision dissipation energy γ𝜃𝑚 =12(1 − 𝑒2)𝑔0,𝑝𝑑𝑝√𝜋𝜌𝑝𝜀𝑝2𝜃𝑝3/2 Kinetic energy transfer 𝜙𝑔𝑠 = −3𝐾𝑔𝑠𝜃𝑝 Solids pressure 𝑃𝑝 = 𝜀𝑝𝜌𝑝𝜃𝑝 + 2𝜌𝑝(1 + 𝑒)𝜀𝑝2𝑔0,𝑝𝜃𝑝 Solids shear viscosity 𝜇𝑝 = 𝜇𝑝,𝑐𝑜𝑙 + 𝜇𝑝,𝑘𝑖𝑛 + 𝜇𝑝,𝑓𝑟 Solid collision viscosity 𝜇𝑝,𝑐𝑜𝑙 =45𝜀𝑝𝜌𝑝𝑑𝑝𝑔0,𝑝(1 + 𝑒)√𝜃𝑝/𝜋 Kinetic viscosity 𝜇𝑝,𝑘𝑖𝑛 =10𝜌𝑝𝑑𝑝√𝜃𝑝𝜋96𝜀𝑝(1 + 𝑒)𝑔0,𝑝[1 +45 𝑔0,𝑝𝜀𝑝(1 + 𝑒)]2 Solid frictional viscosity 𝜇𝑝,𝑓𝑟 =𝑃𝑝 sin𝜙2√𝐼2𝐷 113  Bulk viscosity 𝜇𝑏𝑢𝑙𝑘 =43𝜀𝑝𝜌𝑝𝑑𝑝𝑔0,𝑝(1 + 𝑒)√𝜃𝑝𝜋  The 3D domain was discretized by 389k tetrahedral cells, as shown in Figure 5.2. Details of a mesh independence study are provided in Appendix G. A time step of 0.001 s with 20 iterations per time step was chosen based on sensitivity analysis, ensuring that the convergence of residual error drops below 10-4. The phase-coupled SIMPLE algorithm was applied for pressure-velocity coupling. The relative error between successive iterations was specified as 0.001 as the convergence criterion. Details of the simulation model parameters are listed in Table 5.4. 114   Figure 5.2 Mesh design of jet apparatus.  Table 5.4 Simulation model parameters. Description Value Gas density* 1.225 kg/m3 at 20°C 0.675 kg/m3 at 250°C 0.457 kg/m3 at 500°C 0.363 kg/m3 at 700°C 0.329 kg/m3 at 800°C Gas viscosity* 1.789×10-5 Pa·s at 20°C 2.275×10-5 Pa·s at 250°C 115  2.547×10-5 Pa·s at 500°C 4.085×10-5 Pa·s at 700°C 4.332×10-5 Pa·s at 800°C Gas velocity 59 – 221 m/s Restitution coefficient 0.9 Initial solids packing 0.6 Inlet boundary conditions Velocity Outlet boundary conditions Pressure Wall condition Gas phase – no slip Solid phase specularity coefficient of 0.6 Time step 0.001s Maximum number of iterations 20 Convergence criteria (relative error) 0.001 *Gas density and viscosity at various temperatures were calculated from Matsoukas [191]. Restitution coefficient and initial solids packing are set as default values that generally used for particle attrition with CFD simulation [192,193]. Jet attrition is mainly affected by the orifice gas velocity. In jet attrition, particles are accelerated by the gas jet, then striking other particles suspended outside the jet region, decreasing its velocity by collision. Therefore, the maximum value of the particle velocity profile along the vertical axis above the orifice can be referred to as the “particle impact velocity”. In this CFD simulation, overall 15 vertical measurement lines were set to measure the particle impact velocity. Each line is perpendicular to the base of the column, 0.1 m in length, and on the three orifices of the jet apparatus. Five measurement lines were set above each orifice, one at the center and four evenly distributed from the center with 0.1 mm apart. The velocity of the Eulerian solid phase is exported periodically along each measurement line as a velocity profile. An average velocity profile was calculated using the arithmetic mean among all 15 measurement lines. Figure 5.3 shows an example of an average velocity profile of the Eulerian solid phase. Considering the particle velocity will reduce after collision due to kinetic energy dissipation, the 116  maximum velocity may represent the particle velocity immediately before collision. Therefore, the maximum velocity in the profile is considered as the particle impact velocity. Overall, an average particle impact velocity with each solid species was calculated and used for particle impact velocity correlation.  Figure 5.3 Average velocity profile of the Eulerian solid phase along the vertical axis on orifice hole for iron species.  With the particle impact velocity estimated from the two-fluid Eulerian-Eulerian CFD simulation, an empirical correlation is proposed to predict the particle impact velocity (up) as a function of particle size (dp), particle density (ρp), gas jet velocity (Ujet), gas density (ρg) and viscosity (μg), and diameter of orifice (dor): 𝑑𝑝𝑢𝑝𝜌𝑝/𝑑𝑜𝑟𝑈𝑗𝑒𝑡𝜌𝑔 = 0.98(ln(𝐴𝑟))2 − 12.3ln (𝐴𝑟) + 41.0     (R2 = 0.906) (5-21) 117  𝐴𝑟 =𝑑𝑝3𝜌𝑔(𝜌𝑝 − 𝜌𝑔)𝑔𝜇𝑔2 (5-22) where Ar is the Archimedes number. Figure 5.4 shows the empirical correlation fittings with the simulation result. Here, the eqn. (5-21) on the left side, dp𝑢𝑝𝜌𝑝/dor𝑈𝑗𝑒𝑡𝜌𝑔, changes with particle size, particle density and gas density. When Ar is less than 400, it is found that the gas properties affected the dp𝑢𝑝𝜌𝑝/dor𝑈𝑗𝑒𝑡𝜌𝑔. When particle size, particle density and jet velocity are fixed, increasing temperature decreased Ar as well as increasing dp𝑢𝑝𝜌𝑝/dor𝑈𝑗𝑒𝑡𝜌𝑔. However, when the Ar is higher than 400, particle diameter affected more than the effect of gas properties. The particle impact velocity did not significantly changed when the particle size is higher than 750 μm, fixed the temperature and jet velocity. Thus, when the Ar increases, having particle size >750 μm, the dp𝑢𝑝𝜌𝑝/dor𝑈𝑗𝑒𝑡𝜌𝑔 increases as well. Therefore, the empirical correlation showed a minimum point at a certain particle and gas conditions. 118  ln (Ar), [-]0 3 6 9 12 15dpupp/dorUjetp, [ -]01020304050Simulation dataEmpirical correlation of particle impact velocity (Eqn. 5.21)R2=0.906 Figure 5.4 Empirical particle impact velocity correlation fitted based on CFD simulation work.  5.4 Abrasion and fragmentation modeling 5.4.1 Hardness testing for fragmentation and abrasion  The breakage energy by fragmentation of particles of different species in different particle bins was experimentally tested with a force gauge (FGJN-50, Shimpo Inc.) connected to a push-pull gauge stand (FGS-50E-H, Shimpo Inc.), which compressed particles one at a time. Thirty tests per sample per size bin were conducted to determine their respective average particle failure strength by fragmentation.  119  The particle crushing strength was measured in a static compression test. The specific breakage energy is the integral of compression loading with respect to piston displacement. The average crushing strength and specific breakage energy of different particle species in different size bins are listed in Table 2.3. The particles after the breakage of a particle are called daughter particles. The daughter particle size distribution of each particle species from each particle size bin after compression test in percentage by mass was measured and is shown in Section 5.3.2, describing the modified particle mass exchange model for fragmentation.  Abrasion requires less energy compared to fragmentation [31]. The compression unit cannot measure abrasion energy because the brittle materials are scattered when compression loading approaches the crushing strength. Instead, the jet attrition unit, described in Figure 2.1, is used to test the effect of particle size, initial loading, jet velocity and operating time on abrasion. The jet velocities were selected between the minimum fluidization velocity and the particle breakage velocity by fragmentation. The particle breakage velocity by fragmentation was calculated from the breakage energy determined by the compression unit. These results are discussed in Section 5.3.3.  5.4.2 Modified particle mass exchange model Based on the experimental observations, particles break into several daughter particles in each compression test (see Tables 5.5-5.8). Similar results were obtained by other researchers [44,61,62,83]. Chen et al. [83] developed a particle impact-induced mass exchange step model, in which particles in larger size bins break and the daughter particles are distributed into smaller bins. In other words, particles in the ith bin are distributed into the (i-1)th, (i-2)th, … 1st bins, where bin 1 contains the smallest particles. The rate constant of mass exchange and the mass for 120  particles in each particle size bin are needed in the original Chen et al. model [83]. However, since the daughter size distributions of each particle size bin once particles are broken have been measured in the compression test, only the fraction of the particles that undergo fragmentation is needed for each bin. The differential mass exchange within a certain bin can be expressed as the summation of mass of particles transferred from other bins, after subtracting the mass of particles broken: 𝑑𝑚𝑖𝑑𝑡= −𝑥𝑖𝑚𝑖 + ∑ 𝑥𝑗𝑚𝑗𝜓𝑗,𝑖𝑖+1𝑗=𝑀 (5-23) where mi is the mass of the ith bin, xi is the fraction of the fragmented particles in the ith bin, M is the total number of bins, and ψj,i is the fraction of the fragmented jth-bin particles entering the ith bin. ψ is assumed to follow the compression test results, shown in Tables 5.5 to 5.8 for each solid species.  Table 5.5 Daughter particle size distribution of iron from each particle size bin after compression test in percentage by mass.  Parent particle size [μm] 1000-2400 500-1000 250-500 125-250 63-125 Daughter particle size distribution [μm] 0-63 0.2 6.4 4.8 0.0 100 63-125 0 0 0 100.0 - 125-250 0 0 95.2 - - 250-500 4.6 93.6 - - - 500-1000 95.2 - - - - 1000-2400 - - - - -    121  Table 5.6 Daughter particle size distribution of hematite from each particle size bin after compression test in percentage by mass.  Parent particle size [μm] 1000-2400 500-1000 250-500 125-250 63-125 Daughter particle size distribution [μm] 0-63 11.0 39.3 41.2 42.8 100 63-125 8.8 1.2 1.2 57.2 - 125-250 10.3 1.0 57.6 - - 250-500 12.0 58.5 - - - 500-1000 57.8 - - - - 1000-2400 - - - - -  Table 5.7 Daughter particle size distribution of limestone from each particle size bin after compression test in percentage by mass.  Parent particle size [μm] 1000-2400 500-1000 250-500 125-250 63-125 Daughter particle size distribution [μm] 0-63 37.4 8.5 57.1 77.3 100 63-125 10.9 19.1 0.7 22.7 - 125-250 7.7 21.3 42.2 - - 250-500 13.5 51.1 - - - 500-1000 30.4 - - - - 1000-2400 - - - - -  Table 5.8 Daughter particle size distribution of lime from each particle size bin after compression test in percentage by mass.  Parent particle size [μm] 1000-2400 500-1000 250-500 125-250 63-125 Daughter particle size distribution [μm] 0-63 27.8 76.6 94.8 99.3 100 63-125 7.3 1.1 0.0 0.7 - 125-250 12.2 0.0 5.2 - - 250-500 24.6 22.3 - - - 500-1000 28.1 - - - - 1000-2400 - - - - -  122  Six bins were used for the model, ordered from smallest to largest, with the bin boundaries defined by standard sieves with aperture openings of 63, 125, 250, 500, 750, 1000 and 2400 μm. The JAM assumes that fragmentation occurs when the energy loss due to inter-particle collisions (calculated by eqn. (5-7)) exceeds the particle breakage energy. The energy loss (Eloss) is only a function of particle species, size, and impact velocity, as depicted in Eqn. (5-7). Note that xi is a probability/selection function – when particles are fragmented, broken particles are distributed to the smaller size bins, following the fraction of xi. Hence, the following equation can be used to calculate the fraction of the fragmented particles in each bin:  𝑥𝑖 =𝑣𝑖𝑉𝑖𝑁 (5-24) Incorporating eqn. (5-11) in (5-24) and rewriting it in differential form: 𝑑𝑥𝑖𝑑𝑡=𝑣𝑖𝑉𝑖∙ 𝐶𝑐𝑜𝑙𝑙𝑖𝑠𝑖𝑜𝑛 ∙ 𝑓𝑐 (5-25) where vi is the volume of an individual particle in the particle size bin i, Vi is the total volume of all particles in the bin i, and xi is the fraction of the fragmented particles in bin i. Eqn. (5-25) can be combined with eqn. (5-23) to compute the differential mass exchange within a certain bin.   5.4.3 Modified Archard equation Abrasion is often referred to as mechanical wear in the mechanical and material engineering fields. In tribology, the Archard equation [180] is commonly used to estimate the amount of debris resulting from a single-particle shear test [194]. The original Archard equation [180] is: 𝑉𝑎𝑏𝑟 =𝐾𝑊𝐿𝐹𝑐/𝐴 (5-26) 123  where Vabr is the total volume of debris produced by abrasion, K is a dimensionless constant, W is the total normal load, L is the sliding distance to abrade particles, Fc is the crushing strength and A is the cross-sectional area of a particle. In a fluidized bed, the product of total normal load and sliding distance can be considered as the collision kinetic energy of the particle. Also, the debris from a fluidized bed is produced from the entire bed rather than a single particle. Therefore, the amount of debris should be normalized by the initial bed loading. The frequency of collisions that contribute to abrasion is considered to be a function of particle loading. The amount of debris generated also depends on attrition time. With these revisions, a modified Archard equation is proposed for a fluidized bed as: 𝑉𝑎𝑏𝑟𝑉0=𝐾𝐸𝐹𝑐/𝐴𝑝𝑓(𝑙𝑜𝑎𝑑𝑖𝑛𝑔)𝑔(𝑡) (5-27) where V0 is the volume of particles prior to abrasion, E is the particle abrasion energy, f(loading) is the frequency of collisions causing abrasion as a function of initial loading, and g(t) is a function of the time of attrition. By fitting the experimental abrasion data, the frequency and time function are determined: 𝑓(𝑙𝑜𝑎𝑑𝑖𝑛𝑔) ∝ 𝑛𝑝 (5-28) 𝑔(𝑡) ∝ 𝑙𝑛 (𝑡) (5-29) where np is the number of particles initially loaded into the bed. By rearranging eqns. (5-26)-(5-29), a new modified differential Archard equation in fluidized bed is suggested here: 1𝑉0𝑑𝑉𝑎𝑏𝑟𝑑𝑡=𝐾𝑎𝑏𝑟𝐸𝑛𝑝𝐹𝑐/𝐴 1𝑡 (5-30) where Kabr is the volume-specific abrasion constant accounting for the proportionality in eqns. (5-28) and (5-29). The modified Archard equation is fitted with experimental results, varying four variables – particle size, initial loading, jet velocity and abrasion time. The jet velocity was 124  required to be greater than the minimum fluidization velocity and lower than the particle breakage velocity by fragmentation. Thus, as mentioned above, jet velocity ranges between the minimum fluidization velocity and the particle fragmentation velocity were used to test abrasion in jet attrition unit. Experimental data were arranged in the form of Eqn. (5-30) in order to obtain the volume-specific abrasion constant, Kabr, for each species based on linear least squares regression. Figure 5.5 plots the abrasion constant for each solid species and gives the R2 value for each regression. Although the abrasion tests were designed to minimize particle fragmentation, totally eliminating the effect of fragmentation was impossible, as reported in previous papers [96,195,196]. This is because the deviation of mechanical strength in the testing samples led to inevitable fragmentation of weak particles [56,59,100,148]. Material fatigue could also reduce the particle strength over the testing period, as discussed above, resulting in further fragmentation. It was assumed that 50% of the debris generated during the abrasion test was purely from abrasion, following Zhang’s chipping mechanism [61]. Therefore, a scaling factor of 0.5 was inserted in the modified Archard equation when it was used in the JAM algorithm. A weight-average kabr was used as an approximation when a particle contained more than one species due to chemical reactions. 125   Figure 5.5 Linear regression of modified Archard equation with different species.  The modified particle mass exchange model and the modified Archard equation are then used in the JAM algorithm to predict the particle size evolution due to collision.  5.4.4 Parameter fitting As discussed in Section 5.1, fatigue is also an important factor affecting material properties in the attrition system. Here, two fitting parameters, representing fatigue by material and cyclic loading, are used in the JAM. Both the overall fatigue factor, Cfatigue, and the effective collision factor, Ccollision, are expressed in eqn. (5-12). These fitting parameters were fitted by minimizing the mean square difference between the simulation predictions and the corresponding experimental results from attrition testing. Cfatigue was assumed to be an 126  aggregated material property that depends only on the particle material. Therefore, the Cfatigue value for each solid species was assumed to be the same, regardless of testing conditions and whether there was a second solid species present. On the other hand, Ccollision was assumed to be a function of the particle material and the number of solid species present since different species would affect the hydrodynamics and attrition of fluidized beds. Therefore, the Ccollision values were fitted for each solid species combination. Overall fatigue factors (Cfatigue), for iron, hematite, limestone and lime, were first obtained by fitting the model to their respective single-species attrition experimental results [45,181]. Four overall effective collision factors (Ccollision) were also obtained for each scenario.  In the presence of binary solid species, three fitting parameters were used, namely one Cfatigue for each solid species, and a single value of Ccollision. The Cfatigue values obtained from the single species fitting were used for the respective solid species in binary mixtures since Cfatigue was considered to depend only on the solid material, and, therefore, it was not varied during the fitting process. The Ccollision value was varied to minimize the mean square error. Binary attrition tests were conducted with the iron/limestone mixture, as well as with an iron oxide/lime mixture, a typical solid combination in chemical looping reforming processes. Note that limestone undergoes major morphological changes during calcination, so the difference in material properties between the nascent limestone and the calcined limestone is far from negligible [78]. The overall fatigue coefficient (Cfatigue) was, therefore, fitted separately for the limestone tests with and without calcination. The fitted values of Ccollision and Cfatigue are summarized in Table 5.9. Because limestone calcines at 700 and 800°C at atmospheric pressure air, it was not possible to perform an iron/limestone mixture attrition test when iron is oxidized whilst limestone is not calcined [181]. Thus, Ccollision for this case is left blank. 127  Table 5.9 Values of the parameters Cfatigue and Ccollision.   Cfatigue, [-] Ccollision, [-] Single species Binary species Iron 9.66×10-5 8.63×10-4 1.15×10-3 Limestone No reaction 9.34×10-7 3.29×10-2 Calcination 3.52×10-4 4.74×10-4 - Hematite 6.30×10-5 2.57×10-3 7.34×10-3 Lime 1.94×10-4 6.76×10-4   5.5 Model comparison with Ghadiri’s model and experimental results 5.5.1 Ghadiri’s model In population balance model coupled with CFD simulation, the discrete phase model (DPM), based on the Lagrangian approach, is generally used to predict the population balance model after particle breakage. Several researchers have developed particle breakage models for fluidization [197–199]. However, most of these models are based on gas-liquid fluidized bed systems, considering bubble breakage by liquid. Unlike other models, Ghadiri’s model [200] is based on gas-solid fluidization system, designed to predict the actual particle breakage, considering material properties and particle impact conditions. Thus, a population balance model, coupled with the breakage kernel model of Ghadiri [200], was applied and compared with the jet attrition model. A general form of the population balance equation only considering particle breakage, can be expressed [192,201,202] as: 𝜕𝜕𝑡[𝑛𝑝(𝑉, 𝑡)] + 𝛻[?⃗? ∙ 𝑛𝑝(𝑉, 𝑡)] = ∫ 𝑝𝑓 ∙ 𝑑[𝐺(𝑉′) ∙ 𝜓(𝑉|𝑉′) ∙∞𝑉′=0 𝑛𝑝(𝑉′, 𝑡)] − 𝐺(𝑉) ∙ 𝑛𝑝(𝑉, 𝑡) (5-31) 128  where V’ is the dummy variable over which the integral is calculated, np(V,t) is the number density of particles of volume V at time t, G(V’) is the breakage frequency of particles of pre-breakage volume V’, ψ(V|V’) is the probability of particles breaking from volume V into particles of volume V’, and pf is number of daughter particles produced per parent. The first term on the left is the transient term, while, the second term is the convective term. The terms on the right-hand side account for particle birth and death due to breakage, respectively. In Gharidi’s model [200], the breakage frequency can be expressed as: G(V′) =𝜌𝑝𝑌2/3Γ5/3𝑢𝑝2(6𝑉′𝜋)5/9 = 𝐾𝑏𝑢𝑝2(6𝑉′𝜋)5/9 (5-32) where ρp is the particle density, Y is Young’s modulus of the particles, Γ is the interfacial energy, up is the particle impact velocity, and Kb is a breakage constant. This model treats particles with semi-brittle behaviour, and all particles are treated as being abraded when breakage occurs. The interfacial energy of each species is listed in Table 5.10. Rearrangement of eqn. (5-32) leads to deformation of the breakage energy, Kb: 𝐾𝑏 =𝜌𝑠𝑌2/3Γ5/3 (5-33)  Table 5.10 Interfacial energies of particle species. Species Interfacial energy [J/m2] Fe, Tran et al. [203] 2.5 Fe2O3, Liu et al. [204] 1.357 Fe3C, Owolabi et al. [205] 5 CaO, Arutyunyan et al. [206] 0.895 CaCO3, Arutyunyan et al. [206] 0.23  129  For the probability density function (PDF), ψ(V|V’), the generalized PDF can simulate multiple breakage following a specified daughter distribution, expressed as: 𝜓(𝑉|𝑉′) =𝜃(𝑧)𝑝𝑉′ (5-34) where z (=V/V’) is the ratio of daughter-to-parent volume of the particles, and θ(z) is the daughter distribution: 𝜃(𝑧) = ∑𝑤𝑖𝑝𝑖(𝑧)𝑞𝑖−1(1 − 𝑧)𝑟𝑖−1𝛽(𝑞𝑖 , 𝑟𝑖)1𝑖=0 (5-35) The above equation represents a two-term daughter distribution [207], where i represents volumetric ratio of particle breakage; 0 as particles without breakage and 1 as particles all broken, is the running index from 0 to 1 for either terms, wi is a weighting factor, si is the average number of daughter particles, qi and ri are exponents, and β(qi,ri) is the Euler beta function [207]. The values of these parameters, (i.e., wi, si, qi, and ri) are summarized in Table 5.11, adopted from Diemer and Olson [208]. In this study, attrition parameters in Table 5.11 are adopted with Ghadiri’s model.  Table 5.11 Values of parameters for daughter distributions in general form adapted from Diemer and Olson [208]. Type w0 s0 q0 r0 w1 s1 q1 r1 Constraints Equisized 1 P ∞ ∞ - - - - p ≥ 2 Attrition 0.5 2 ν 1 0.5 2 1 ε ν <<1 Parabolic 1 (ν+2)/ν ν 2 - - - - 0<ν<2 Uniform 1 P 1 p-1 - - - - p ≥ 2  130  5.5.2 Comparison of model predictions with experimental data To compare the attrition model with experimental data, relative mean errors (RME) for each set of attrition test condition and all experiments with two fitting parameters, Cfatigue and Ccollision, were calculated and are summarized in Table 5.12. The RME is generally less than 0.2, indicating favourable agreement between the JAM and experimental results.  The relative mean errors for lime are generally larger than those for the other species tested as the particle strength of lime particles is less than the other materials studied. In detail, since the crushing strength for lime particles is less than for the other species [181], some fragmentation may have occurred during the abrasion test, despite setting the jet velocity lower than the fragmentation velocity. Therefore, the modified Archard equation for lime carries more uncertainty compared to that of the other species.  The occurrence of reactions also tends to cause the RME to increase. This may be attributed to the change in material properties during reaction. The conversion-weighted averages of these properties used in this model only serve as approximations, unable to describe the morphological changes and inhomogeneous spatial distribution of different particle species in the same particle.  The RME of binary solid mixtures is generally greater than for single species tests. This may result from the inaccuracy in estimating inter-species collisions by using the geometric average of the single-particle collision frequencies. In Chapter 3, particle mixture compositions of limestone and iron were tested, and it was observed that the attrition of iron increased with increasing mass fraction of iron.  131  Table 5.12 Comparison of experimental data and predictions of attrition model with two fitting parameters (Cfatigue and Ccollision). Species Experimental conditions RME Jet velocity [m/s] Temperature [°C] Reaction Gas Operation time [h] Iron 98 20 - Air 3 0.181 Air 6 0.217 Air 12 0.332 221 700 - N2 3 0.071 N2 6 0.108 N2 12 0.090 221 800 - N2 3 0.084 N2 6 0.124 N2 12 0.173 221 700 Oxidation Air 3 0.083 Air 6 0.096 Air 12 0.086 221 800 Oxidation Air 3 0.067 Air 6 0.039 Air 12 0.146 Overall RME 0.126 Hematite 221 800 - N2 6 0.105 221 800 Reduction 30% CH4 6 0.075 221 800 Reduction 50% CH4 6 0.074 221 800 Reduction 70% CH4 6 0.139 Overall RME 0.098 Limestone 98 20 - Air 3 0.087 Air 6 0.059 Air 12 0.069 221 700 Calcination Air 3 0.103 Air 6 0.103 Air 12 0.249 221 800 Calcination Air 3 0.190 Air 6 0.277 132  Air 12 0.224 Overall RME 0.151 Lime 221 700 - Air 6 0.179 221 800 - Air 6 0.209 221 800 Carbonation 10% CO2 3 0.181 221 800 Carbonation 10% CO2 6 0.172 221 800 Carbonation 10% CO2 12 0.181 221 800 Carbonation 30% CO2 6 0.210 221 800 Carbonation 50% CO2 6 0.189 221 800 Carbonation 70% CO2 6 0.219 Overall RME 0.193 Iron:Limestone =3:1 (wt frac.) 98 20 - Air 6 0.098 Iron:Limestone =1:1 (wt frac.) 98 20 - Air 6 0.070 Iron:Limestone =1:3 (wt frac.) 98 20 - Air 6 0.141 Iron:Limestone =1:1 (wt frac.) 98 250 - Air 6 0.178 98 500 - Air 6 0.208 59 20 - Air 6 0.119 78 20 - Air 6 0.083 Iron+Limestone Overall RME 0.128 Hematite:Lime =1:1 (wt frac.) 221 800 - N2 6 0.186 221 800 Lime carbonation 30% CO2 6 0.194 221 800 Hematite reduction 30% CH4 6 0.206 Overall RME 0.195  Figure 5.6 plots the experimental and predicted particle size distributions of iron from: (a) Ghadiri’s model [200]; and (b) the jet attrition model, as examples. Ghadiri’s model predicted 133  severe attrition within 30 s, and thus did not predict the attrition results well. There are several reasons why Ghadiri’s model overestimates the attrition rate: (1) The model was originally developed for cubic-shaped NaCl and KCl and only considered breakage at the corners and edges, which were more prone to attrition [57]; (2) NaCl and KCl crystals are semi-brittle materials; plastic deformation precedes fracture, referred to as elastic-plastic response; and (3) They considered only abrasion as a cause of particle breakage. The favourable agreement between our experimental PSD data and predicted PSD indicates that the jet attrition model with two fitted parameters (Ccollision and Cfatigue) may provide a promising means of describing particle attrition in fluidized beds of single and binary species. 134   Figure 5.6 Experimental and predicted particle size distributions of iron at 800°C with jet velocity = 221 m/s simulated with (a) Ghadiri’s model [200] and (b) jet attrition model (JAM) with two fitted parameters (Ccollision and Cfatigue). The error bars for the experimental results represent standard errors among triplicated trials. 135  The cumulative particle size distributions of experimental data and simulation of each solid species at 800°C with reaction are plotted in Figure 5.7. These indicate good predictions from the simulation model. Particle diameter, [ m]100 1000Cumulat ive weight fract ion, [%]020406080100IronHematiteLimestoneLime200030 Figure 5.7 Cumulative particle size distributions of experimental data points and simulation prediction lines for each solid species at 800°C and 6 h attrition with reaction (jet velocity=221 m/s, iron oxidation under air, hematite reduction with 50 vol% CH4, limestone calcination with air and lime carbonation with 30% CO2).  136  5.6 Conclusions A jet attrition model has been developed for gas-solid fluidized beds and applied to four different materials, iron-based species as an oxygen carrier, calcium-based species as a CO2 sorbent, and their mixtures, at temperatures from 20 to 800°C, with chemical reactions in the atmosphere at several reactive gas concentrations and at jet velocities of 59-221 m/s, as tested in Chapters 3 and 4. The model considers both material properties affected by temperature and chemical reactions, and mechanical attrition. Reactions lead to changes in the material compositions and properties, which were applied to the attrition predictive correlations. Mechanical attrition is modeled by two different attrition modes: fragmentation with particle mass exchange model; and abrasion with a modified Archard equation. The model incorporates empirical particle impact velocity estimation based on Eulerian-Eulerian CFD simulation to determine the mode of particle attrition. A fatigue factor and a collision factor are fitted to estimate the particle size distribution after a certain duration of attrition. With two fitting parameters, Cfatigue and Ccollision, the model predictions are in favourable agreement with experimental results for iron and hematite as oxygen carriers, with limestone and lime as CO2 sorbent at temperatures from 20–800°C and jet velocities from 59 to 221 m/s, with and without reactions.  137  Chapter 6: Conclusions and recommendations 6.1 Overall conclusions for this thesis In most gas-solid fluidized bed reactors with one or more solid species, particle attrition is an important consideration due to the high gas velocity and chemical reactions, affecting reactor performance, operating conditions and material loss by entrainment and elutriation. Although jet attrition is usually considered to be the major source of attrition, it has received only limited attention in determining the attrition mode because of its complexity. In this thesis, understanding and measuring the jet attrition of single species and two-solid species particulate systems for a sorption-enhanced chemical looping process were overall objectives. A jet attrition model was developed to predict how particle size distributions change with operating conditions. Up to now, most knowledge in this area has been obtained from observing particle size distribution changes and measuring how much debris was obtained as a function of time. While valuable as guidelines for understanding attrition phenomena, such knowledge has lacked a firm scientific foundation on material properties and thus has been susceptible to misinterpretations and incorrect generalizations. In addition, attrition with reactions is rarely investigated, leaving a large gap in the fundamental knowledge in attrition studies which includes material properties with operating conditions that are essential to understand particle attrition by jets in fluidized beds. In this thesis, fundamental studies on jet attrition with iron as oxygen carrier and limestone as CO2 sorbent were carried out with varying temperature, jet velocity, duration, solid species weight fraction and the presence of chemical reactions to understand how these various factors affect attrition. Experimental investigation included comparing SEM images and PSD data before and after attrition, and particle size changes with different operating conditions. 138  Furthermore, crushing strength and breakage energy were determined with a compression unit to understand how material properties affect particle attrition. In addition, for in-depth fundamental attrition studies on material properties, porosity, specific surface area and pore size distributions were measured to help investigate the effects of chemical reaction on attrition. 6.1.1 Experimental The key experimental findings of this work are summarized as follows: Single species attrition For single species experimental jet attrition, tests with varying attrition time of both iron and limestone showed shifts towards smaller particle size distributions (PSD) over time. The effect of iron fragmentation was noticeable for a 12 h attrition test, showing a decrease in the largest (1000-2400 μm) particle weight fraction, whereas the proportion of other size fractions increased. Two-species attrition Attrition of interacting solid species was tested with several initial mass fractions, to determine whether attrition shows a trend with initial mass fraction of solid species. The particle size of iron significantly decreased with decreasing initial mass fraction of limestone. However, fines generation by limestone was greater for all weight fractions than for the single species. To understand the reason why limestone did not significantly change with initial mass fraction of iron, a cylindrical acrylic column of the same diameter was used to test the fluidization behaviour, visually confirming that these two solid mixtures did not mix homogeneously. U/Umf for various initial mass fractions of iron and limestone was then calculated to help explain the observed PSD results. Since the iron and limestone in this system segregated as the iron particles were significantly larger and denser than the limestone particles, all the flotsam particles and 139  some jetsam particles underwent fluidization, while some jetsam particles sunk, forming a defluidized layer at the bottom of the column, leading to less attrition of iron powders. For the limestone, since limestone mixed with only small portion of iron with relatively small particles, iron-limestone collisions did not result in much exchange of kinetic energy compared to inter-particle collisions in a single-species system. Therefore, the limestone size distribution did not significantly change with initial mass fraction of iron. Particle size distributions (PSDs) of iron and limestone were determined after 6 h of attrition at different jet velocities. For iron, when the jet velocity increased, more particles began to fluidize, resulting in greater upwards and downwards motion, leading to more collisions with other particles. Limestone, for which the superficial jet velocity exceeded Umf, was more attritable than iron. Therefore, the weight percentage of limestone particles in the 0-63 μm bin increased, while that in other size bins decreased with increasing jet velocity. Effect of temperature on attrition There are contradictory results in the literature on the effect of temperature on attrition. In most literature [61,66,74,209,210], an increase in operating temperature has been reported to decrease particle attrition by material softening, and lowering gas density and inertia with increasing temperature. However, others [56,75] indicate particle degradation with increasing temperature due to decrepitation. For the iron powder, the 0-63 μm bin range showed more iron fines generated with increasing temperature; however, for larger particles of diameter 1000-2400 μm, particle breakage decreased with increasing temperature, likely because the jets were not able to easily entrain the larger particles. On the other hand, fragmentation of limestone decreased with increasing temperature. Based on PSD results and SEM images, the surfaces of both iron and limestone became smoother with increasing temperature, indicating enhanced 140  abrasion and reduced fragmentation. Therefore, with increasing temperature without any chemical reactions, overall reduced attrition rates were observed for both iron and limestone species. Effect of chemical reactions on attrition - iron The limited number of previous studies of the effect of reactions on attrition have mainly focused on the evolution of PSDs and the mass of fines generated due to attrition, generally not accounting for the change in material properties due to reaction. To overcome this hurdle, variances of material properties were measured, as well as PSD evolution, to understand how the chemical conversion of particle species affects attrition in both single-species and two-species environments. Presumably, there are two factors reducing attrition at high temperatures. First, gas properties can affect the particle attrition. Low gas density at high gas temperature reduces particle momentum which reduces attrition, whereas gas viscosity increases with increasing temperature leading to higher drag and acceleration of particles, causing more attrition, especially for smaller particles.  Second, the material can soften at high temperature, reducing attrition as well. However, when iron particles were oxidized, attrition was found to increase compared to tests at the same temperature without oxidation. SEM images of cross-sectional area of partially oxidized iron showed that cavities were generated at the oxidized iron/ferrous iron interface during oxidation. Given these results, oxidation decreased the crushing strength of iron particles and increased attrition. Conversely, attrition decreased when hematite was reduced by methane. It was experimentally confirmed that the crushing strength of hematite increased with increasing extent of reduction. To determine whether porosity and specific surface area may affect the reduced hematite attrition, tests were done with mercury porosimetry and BET 141  (Brunauer, Emmett and Teller) analysis. Both porosity and BET surface area increased with increasing reduction conversion, confirming that the changes in porosity and surface area did not significantly affect attrition. This is because as hematite is reduced, reduced iron species formed from the outer layer of the surface, leading to higher crushing strength. The proportions of reduced iron oxides, such as magnetite, wustite and ferrous iron were measured with quantitative XRD (X-ray powder diffraction) analysis. As the proportions of reduced iron oxides increased with conversion rate, the crushing strength on the surface increased as well, decreasing attrition.  Effect of chemical reactions on attrition - limestone Interesting results were observed for limestone calcination: with increasing temperature, attrition increased, which was not expected from the experimental findings of attrition with varying temperature, without any chemical reaction. Because the calcination extent increased at higher temperature, as confirmed by TGA results, attrition increased with decreasing particle crushing strength. For limestone, calcination increased attrition due to a decrease in intrinsic particle crushing strength. This was further supported by the increase in porosity of limestone, contributing to decreased particle crushing strength.  For lime carbonation, attrition decreased with increasing carbonation temperature. This was contrary to the initial projection that increasing temperature would increase attrition by reducing the carbonation extent with higher temperature. Based on the TGA results, carbonation rate decreased at higher temperature, leading to less carbonation for a given period of time. As limestone displays higher intrinsic crushing strength than lime, it was speculated that surface hardness would increase through carbonation. However, as the temperature increased, the extent of lime sintering increased, reducing the porosity, while increasing the particle breakage energy. This, coupled with reduced gas density and particle momentum, led to less attrition at higher 142  temperatures. The effect of CO2 concentration (10-70 vol%) on attrition during lime carbonation was also tested and found to be insignificant, based on experimental results involving PSDs, BET surface area, porosity and crushing strength. Two-species attrition tests with reactions Since limestone calcines at temperatures ≥700°C by thermal decomposition at atmospheric pressure, only binary mixtures of hematite (Fe2O3) and lime (CaO) particles were tested with CH4, CO2 and N2 gases, representing hematite reduction, lime carbonation and no reactions, respectively. PSDs were measured to find how the chemical conversion of particle species affected attrition in a two-solid-species environment. Particle attrition increased when two solid species, hematite and lime, were mixed together, due to the increasing frequency of inter-particle collisions and their difference in crushing strength. 6.1.2 Modeling Based on the experimental findings, a mechanistic jet attrition model (JAM) was developed in Chapter 5 to improve the understanding of jet attrition and predict particle size distributions in fluidized systems, considering that particle attrition is affected by changes in various operating conditions, such as time, temperature, gas phase species concentrations, reactions and particle composition. Material property changes were considered, as well as how both fragmentation and abrasion affect fluidized bed systems. The basic assumptions of the model are as follows: The model was tested only with brittle material since all the particle species tested in this thesis were brittle. Particles are considered to be spherical, allowing us to assume that the restitution coefficient of particle is independent of collision direction. Also, because abrasion is considered in the model, particles are assumed to have relatively small asperities on spherical surfaces before breakage. Fine particles (defined 143  here as <63 μm) are assumed not to be attrited further, because the model has six bins with the bin boundaries defined by standard sieve sizes, with aperture openings of 63, 125, 250, 500, 750, 1000 and 2400 μm. Particle collisions are assumed to occur when particles are rising in the jet attrition unit. The Eulerian-Eulerian CFD approach was used, which predicts the velocity of the granular phase at a particular location of interest at a particular time. Lastly, when chemical reactions occur, particle mechanical properties, such as Young’s modulus, particle density and breakage energy, are estimated by the conversion-weighted average of the properties of the constituent particulate species because the mechanical properties of the particles undergoing reaction cannot be instantaneously measured. In light of the limited attention given by researchers to determining fragmentation and abrasion in attrition, attrition was determined by comparing the particle breakage energy (Eb) and the energy loss after collision (Eloss). The particle breakage energy is estimated as the energy required for fragmentation, measured by the compression unit in Chapter 2. Thus, Eb is fixed for each particle and its size bin. At the same time, the energy beyond that lost in collisions is assumed to be available to break particles when they collide with other particles. Therefore, the energy loss after collision changes with the relative particle velocity of two different particles colliding with each other.  The relative particle velocity after a collision is calculated by measuring/estimating the impact velocity of two particles colliding with each other, i.e., the maximum velocity when particles are accelerated by a jet and collide with another particle. Despite considering experimental methods to measure the impact velocity, these methods measure the average particle velocity, which is not suitable for the particle impact velocity. Thus, a computational fluid dynamics (CFD) simulation was used to estimate the particle impact velocity. 144   CFD simulations Although the discrete element method (DEM), one of the Lagrangian approaches in CFD simulation, has advantages of predicting position vectors and velocity vectors at each time instant for marked particles, DEM is often not suitable for fluidized beds because there are too many particles to track. Therefore, Eulerian-Eulerian CFD two-fluid model simulation was selected to estimate the particle impact velocity. With a huge computational cost, DEM-CFD could be another option to monitor particles over time. A better option for the DEM-CFD is suggested in Section 6.2 below. Fatigue is also an important factor affecting material properties in attrition systems. Fatigue depends on chemical reactions, on the material, as well as repeated collisions over time. However, particle fatigue cannot be measured with general fatigue testing systems, i.e., measuring permanent structural changes that occur in materials subjected to fluctuating stresses and strains. Hence, two fitting parameters, Cfatigue and Ccollision, ultimately affecting the particle breakage energy and energy loss after collisions, are fitted to adjust changes in material properties due to fatigue. The resulting jet attrition model (JAM) was able to predict the jet attrition successfully with the two fitting parameters, Cfatigue and Ccollision. The relative mean error (RME) was generally less than 0.2, indicating favourable agreement between the JAM and experimental results. The RMEs for lime were generally larger than for the other species tested as the particle strength of lime particles is less than for the other materials studied. This is consistent with the crushing strength for lime particles being less than for the other species. Some fragmentation might have occurred in the abrasion test, despite setting the jet velocity lower than the 145  fragmentation velocity, which is inevitable during the abrasion test. The occurrence of chemical reactions also tends to cause the RME to increase, due to changes in material properties and fatigue during reaction. This highlights one of the limitations of the investigation, i.e., the material properties, such as Young’s modulus, particle breakage energy and material fatigue, cannot be instantaneously measured during the chemical reaction/attrition. Lastly, the RME of binary solid mixtures is generally greater than for single-species tests. This may result from the inaccuracy in estimating inter-species collisions by using the geometric average of the single-particle collision frequencies. Although there are some special cases to supplement this model by additional experimental findings or simulation (see Recommendations in Section 6.2), the jet attrition model can be applied to other types of attrition in different cases, such as gas cyclones, by changing the particle impact velocities and two fitting constants, Cfatigue and Ccollision, with simple tests which are explained in section 6.2. The greatest strength of this model lies in its high flexibility, based on the mechanistic attrition algorithm, considering that material properties change with temperature and chemical reaction, and determination of attrition modes – fragmentation and abrasion– by a semi-empirical equation. Also, long-term attrition tests in fluidized beds are not needed with this model since the material properties needed for the attrition model (Eb, Eloss and Young’s modulus) can be measured with a conventional compression unit.  6.2 Recommendations for future work Based on the experimental findings and the model work, some recommendations are suggested based on the limitations highlighted in Section 6.1:  146  First, the effect of reactions on attrition in chemical processes are a great challenge due to the lack of feasible experimental methods. In particular, material properties, such as Young’s modulus and fatigue, cannot be measured instantaneously with a conventional compression unit. In this study, Young’s modulus was estimated with the conversion-weighted average of the properties of the constituent particle species in developing the jet attrition model. To improve the attrition results, as well as to understand the fundamental material properties variance for the attrition study, a single particle compression test with a modified compression unit is recommended. Furthermore, the compression unit needs to have heating systems and a compression testing section sealed from the atmospheric conditions, with gas inlet and outlet. With this modified compression unit, the material properties, at high temperature and in the presence of chemical reactions, could be measured instantaneously. Enabling this test could uncover many unknown effects of material properties on attrition accompanying chemical reactions. Second, the fatigue constants related to material properties and cyclic collisions were estimated roughly in Chapter 5 due to the limitation of the experimental methodology. Since the particles of interest are too small for fatigue tests, a non-destructive method is recommended to observe micro-cracks generated by fatigue. Comparing the images taken by differential interference contrast (DIC) microscopy with fatigue duration would help explain how the micro-cracks propagate and ultimately affect the material breakage. Particle fatigue with repeated collisions, affecting particle breakage energy decrease by propagating cracks under cyclic loadings, should be tested as well. In order to investigate the repeated collisions experimentally, an impinging jet unit is proposed in Appendix I, designed to test fatigue by collisions, with two separate inlets where heated particles are accelerated by the gas flow, colliding in the middle. By 147  repeating these tests, fatigue by collisions can be observed by measuring particle size distributions with numbers of cyclic loading. The results from this unit and SEM images for observing broken particles will be able to improve the jet attrition model by experimentally calculating the fatigue constants by collision, and correlating with crack propagation with numbers of impact cycles until breakage. Third, the jet attrition model algorithm is assumed to test only brittle materials since all the particle species tested in this thesis are brittle. Although brittle materials were generally selected for fluidized beds systems, brittle materials can be ductile at high temperatures due to the ductile-brittle transition [119]. Compression testing with temperature variance could be helpful for understanding the effect of temperature on material ductility which affects particle breakage energy. Also, the overall attrition mechanism for different material fracture types can be studied more in-depth with these results.  Lastly, particle collisions are assumed to occur in the Chapter 5 model when particles are rising. Particles that are falling are not considered in this simulation since the Eulerian model predicts the velocity of the granular phase at a particular location of interest at a particular time, and thus cannot track individual particles. As explained in Section 6.1, DEM simulation of DEM-CFD is not usually recommended for fluidized beds systems because there are too many particles to track. Instead of tracking whole particles in fluidized beds with DEM, calculating the position vectors and velocity vectors of a few particles over a long period until they undergo impact can provide an improved relative particle velocity when they collide, considering particles travelling both upwards and downwards. The jet attrition model can then be more precise when these results are applied. 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Hexagonal close packed (HCP) – The top and bottom faces of the unit cell consist of six atoms that form regular hexagons and surround a single atom in the center. Unit cells are used to describe crystal structures. Unit cells for most crystal structures are cubic or prism structures, having three sets of parallel faces. Since the unit cell represents the symmetry of the crystal structure, this is the simplest way to understand the geometry of the material crystallography.   Crystal system Because there are many different possible crystal structures, the crystal structures are divided into several groups according to unit cell configurations and/or atomic arrangements. 172  One such scheme is based on the unit cell geometry, that is, the shape of the appropriate unit cell parallelepiped without regard to the atomic positions in the cell. The unit cell geometry is completely defined in terms of six parameters: the three edge lengths a, b, and c, and the three interaxial angles α, β, and γ. There are seven different possible crystal systems – cubic, tetragonal, hexagonal, orthorhombic, rhombohedral, monoclinic and triclinic. Table A.1 shows five crystal systems with three edge lengths and three interaxial angles.  Table A.1 Five crystal systems with three edge lengths and three interaxial angles [189]. Crystal system Unit cells Cubic a = b = c α = β = γ = 90∘  Tetragonal a = b ≠ c α = β = γ = 90∘  Orthorhombic a ≠ b ≠ c α = β = γ = 90∘  Hexagonal a = b ≠ c α = β = 90∘, 𝛾 = 120∘  Rhombohedral a = b = c α = β = γ ≠ 90∘    173  Here are the lists of materials with crystal structures used in this project. Iron (α-Fe): Cubic Wustite (FeO): Cubic Magnetite (Fe3O4): Cubic, octahedral, inverse spinel – O2- ions forming a face centered cubic lattice and iron cations occupying interstitial sites. Fe3+ cations occupy tetrahedral sites and the other half of Fe2+ cations occupy octahedral sites. Hematite (Fe2O3): Trigonal. Iron carbide (Fe3C): Orthorhombic. 12 atoms of iron in the unit cell and 4 of carbon. Limestone (CaCO3): Trigonal. CaCO3 contains calcium atoms coordinated by six oxygen atoms. Lime (CaO): Cubic.   174  Appendix B  Quantitative X-ray diffraction (XRD) method  Powder X-ray diffraction (XRD) is an analytical technique generally employed for the identification of crystalline materials. Each crystalline solid has its unique characteristic X-ray powder pattern, which can be used as a ‘proof’ for identification. Quantitative analysis data is one of the way to determine the amounts of different phases in in multi-phase samples. Figure B.1 shows typical XRD results of hematite reduced with 30 vol% of CH4 in N2 for 12 h at 800°C with jet velocity=221 m/s. Here, the peak positions and areas are relate to the crystalline phases present and their concentrations. The peak width can provide the crystallite size and strain. The Rietveld method, one of the methods to find the peak positions and areas in the XRD result, is used to characterize the crystalline materials. In this project, the quantitative XRD analysis were taken by Dr. Raudsepp in the UBC Department of Earth and Ocean Science.  Figure B.1 XRD results of hematite reduced with 30 vol% of CH4 in N2 for 12 h at 800C with jet velocity=221 m/s   175  Appendix C  Crushing strength and specific breakage energy calculation The crushing strength of each particle species with different particle size bins was tested with an FGJN-50 (Shimpo Inc.) connected to a push-pull gauge stand (FGS-50E-H), compressing particles one at a time at 20°C, located in Korea Institute of Energy Research. In this unit, a particle is loaded between two hard parallel platens and compressed until the particle breaks. The breakage force is analyzed at the point at which there is a sudden decrease of force, accompanied by a large increase in displacement. For these tests, the loading rate was set at 0.1 mm/s. As an example, crushing strength and the specific breakage energy of limestone, having 250-500 μm of bin size were calculated. A force-displacement curve of a compression test with limestone (250-500 μm of bin size) are depicted in Figure C.1. The crushing strength is the highest normal compression force that particle can withstand before breakage and deformation. The breakage energy is calculated according to Eqn. (C-1) by integrating the force-displacement curve up to the breakage point. The specific breakage energy is calculated by dividing the breakage energy by the mass of a volume-equivalent sphere. The breakage energy and specific breakage energy can be calculated [62,64] as: 𝐸𝑏 = ∫ 𝐹𝑑𝛿𝛿𝑐0 (C-1) 𝐸𝑠𝑝 =6𝐸𝑏𝜋𝑑𝑝3𝜌𝑝 (C-2) where δ is the displacement, and δc is the maximum compression displacement. The crushing strength of 250-500 μm limestone is 2.1 N. The breakage energy and specific breakage energy are 9.57∙10-5 J and 1.3 J/g, respectively. 176   Figure C.1 Force-displacement curve of a compression test with limestone in the range of 250-500 μm. 177  Appendix D  Experimental dataset of jet apparatus unit Particle size distribution of each operation conditions used in Chapters 3 and 4 are listed in the table. Note that the weight percentages are listed with each particle size bins. Table D.1 Experimental dataset with operating conditions tested with jet apparatus  178  Iron N2 700 221 3 3.13 8.64 18.74 30.13 30.45 8.92Iron N2 700 221 12 3.52 7.16 16.36 29.52 32.50 10.95Iron N2 700 221 12 3.77 8.37 18.48 29.85 29.01 10.51Iron N2 700 221 6 2.78 6.57 15.92 28.20 32.38 14.14Iron N2 700 221 3 1.78 5.57 13.92 25.20 35.38 18.14Iron N2 700 221 12 3.26 7.77 18.28 29.46 30.27 10.96Iron N2 700 221 3 2.64 7.54 17.50 29.60 30.71 12.01Iron N2 700 221 6 2.85 7.58 17.38 29.31 31.18 11.69Iron N2 700 221 6 2.78 6.57 15.92 28.20 32.38 14.14Iron N2 800 221 6 2.45 7.24 16.38 31.21 32.74 9.98Iron N2 800 221 3 2.08 6.99 16.65 30.56 32.71 11.00Iron N2 800 221 3 2.55 7.15 17.03 31.27 31.55 10.45Iron N2 800 221 12 3.08 7.38 18.05 30.16 31.60 9.73Iron N2 800 221 6 2.35 7.88 18.04 31.20 31.10 9.43Iron Air 800 221 12 6.31 5.58 14.20 21.26 31.75 20.90Iron N2 800 221 12 2.82 7.18 17.55 30.98 32.75 8.72Iron Air 800 221 3 8.33 11.55 19.54 21.50 24.84 14.25Iron N2 800 221 6 2.76 7.65 16.97 29.88 32.11 10.64Iron N2 800 221 3 2.16 7.06 17.09 29.72 32.92 11.05Iron N2 800 221 12 3.65 8.25 19.09 31.47 30.35 7.19Iron Air 800 221 6 6.20 6.03 15.15 22.51 31.74 18.38Lime Air 700 221 12 39.09 6.40 12.21 26.54 15.52 0.23Lime Air 700 221 6 37.69 6.26 12.74 27.08 16.03 0.19Lime Air 700 221 3 35.09 5.98 13.55 28.63 16.69 0.06Lime 30% CO2 in N2 800 221 6 32.45 9.13 15.16 27.04 16.03 0.19Lime Air 800 221 3 31.95 8.53 14.59 27.15 17.72 0.07Lime Air 800 221 6 27.95 6.27 15.09 31.93 18.65 0.12Lime 10% CO2 in N2 800 221 6 34.73 8.79 13.86 24.51 17.31 0.80Lime 30% CO2 in N2 800 221 6 32.51 8.10 14.95 27.43 16.64 0.37Lime Air 800 221 6 34.63 8.69 13.76 24.41 17.71 0.80Lime Air 800 221 6 31.13 7.78 15.49 29.00 16.44 0.16Lime 10% CO2 in N2 800 221 6 28.05 6.37 15.19 32.03 18.25 0.12Lime Air 800 221 3 26.83 6.85 15.08 32.26 18.99 0.00Lime Air 800 221 12 33.47 9.56 15.84 24.53 16.49 0.12Lime 70% CO2 in N2 800 221 6 25.18 7.60 17.62 30.55 18.57 0.46Lime Air 800 221 3 32.19 7.28 13.80 27.30 19.22 0.22Lime Air 800 221 12 29.88 7.11 16.55 28.81 17.64 0.00Lime 50% CO2 in N2 800 221 6 27.87 6.64 16.04 31.27 18.13 0.05Lime 70% CO2 in N2 800 221 6 28.83 10.58 17.66 27.71 15.15 0.08179  Lime 10% CO2 in N2 800 221 6 31.03 7.58 15.29 28.80 17.24 0.16Lime 50% CO2 in N2 800 221 6 28.45 10.23 16.27 27.97 16.97 0.11Lime 70% CO2 in N2 800 221 6 29.51 10.42 16.90 27.77 15.40 0.00Lime 50% CO2 in N2 800 221 6 31.39 10.27 16.73 26.21 15.35 0.06Lime 30% CO2 in N2 800 221 6 27.30 8.09 16.64 29.96 17.69 0.33Lime Air 800 221 12 31.99 11.33 17.77 24.11 14.68 0.12Limestone Air 700 221 3 27.89 5.58 14.47 31.89 20.17 0.00Limestone Air 700 221 6 32.52 5.58 12.32 29.23 19.91 0.43Limestone Air 700 221 12 43.54 4.66 11.27 25.12 15.32 0.09Limestone Air 700 221 3 30.06 6.19 13.85 29.94 19.65 0.31Limestone Air 700 221 12 40.05 4.65 12.81 26.23 16.29 0.14Limestone Air 700 221 3 22.88 5.83 15.73 33.10 21.93 0.52Limestone Air 700 221 6 33.21 5.84 12.79 28.81 19.04 0.31Limestone Air 700 221 12 37.36 6.64 12.35 26.54 16.86 0.24Limestone Air 700 221 6 33.90 6.09 13.25 28.39 18.17 0.19Limestone Air 800 221 6 25.59 5.55 14.29 32.15 21.82 0.60Limestone Air 800 221 6 22.71 6.42 15.44 33.06 21.81 0.56Limestone Air 800 221 12 28.02 6.93 14.07 30.24 20.37 0.36Limestone Air 800 221 12 26.32 7.63 16.45 30.84 18.59 0.16Limestone Air 800 221 12 29.85 7.70 13.93 29.32 18.98 0.21Limestone Air 800 221 3 17.07 5.87 17.80 36.23 22.67 0.37Limestone Air 800 221 3 23.93 5.95 14.76 32.99 21.91 0.46Limestone Air 800 221 6 32.02 8.55 14.79 27.67 16.83 0.13Limestone Air 800 221 3 23.51 6.69 16.78 32.25 20.37 0.41Separated hematite (Hematite:Lime=1:1 by weight) 30% CH4 in N2 800 221 6 14.52 4.56 14.00 15.36 32.60 18.96Separated hematite (Hematite:Lime=1:1 by weight) N2 800 221 6 4.88 6.60 19.57 23.17 29.29 16.49Separated hematite (Hematite:Lime=1:1 by weight) N2 800 221 6 10.56 6.68 17.83 21.15 27.47 16.32Separated hematite (Hematite:Lime=1:1 by weight) N2 800 221 6 9.62 7.39 12.48 17.62 33.62 19.26Separated hematite (Hematite:Lime=1:1 by weight) 30% CH4 in N2 800 221 6 13.41 4.08 12.24 18.07 33.86 18.34Separated hematite (Hematite:Lime=1:1 by weight) 30% CH4 in N2 800 221 6 13.96 4.32 13.12 16.71 33.23 18.65Separated iron (Iron:Limestone=1:1 by weight) Air 20 119 3 6.70 7.25 17.52 28.92 29.88 9.73Separated iron (Iron:Limestone=1:1 by weight) Air 20 119 12 9.55 5.96 16.28 28.95 29.39 9.86Separated iron (Iron:Limestone=1:1 by weight) Air 20 119 6 3.11 5.76 16.70 33.09 33.21 8.12Separated iron (Iron:Limestone=1:1 by weight) Air 20 149 3 4.87 6.19 15.25 31.28 35.06 7.36Separated iron (Iron:Limestone=1:1 by weight) Air 20 119 12 6.62 6.88 16.45 31.31 29.50 9.24Separated iron (Iron:Limestone=1:1 by weight) Air 20 149 6 3.88 6.18 16.30 33.65 32.11 7.88Separated iron (Iron:Limestone=1:1 by weight) Air 20 119 12 7.23 7.14 18.23 31.72 29.34 6.34Separated iron (Iron:Limestone=1:1 by weight) Air 20 119 6 8.94 5.93 14.56 27.09 31.97 11.51Separated iron (Iron:Limestone=1:1 by weight) Air 20 89 6 2.00 6.77 17.51 34.66 33.22 5.85180  Separated iron (Iron:Limestone=1:1 by weight) Air 20 89 12 4.45 7.00 18.38 32.71 30.26 7.20Separated iron (Iron:Limestone=1:1 by weight) Air 20 119 3 7.12 6.06 16.47 30.43 30.56 9.36Separated iron (Iron:Limestone=1:1 by weight) Air 20 89 3 9.43 6.23 17.47 30.33 28.16 8.38Separated iron (Iron:Limestone=1:1 by weight) Air 20 89 12 10.28 5.86 14.58 29.61 31.20 8.48Separated iron (Iron:Limestone=1:1 by weight) Air 20 119 3 3.15 5.55 15.71 29.83 32.16 13.61Separated iron (Iron:Limestone=1:1 by weight) Air 20 89 12 5.72 7.04 17.89 31.98 31.53 5.84Separated iron (Iron:Limestone=1:1 by weight) Air 20 89 3 9.18 6.14 14.04 31.00 33.35 6.29Separated iron (Iron:Limestone=1:1 by weight) Air 20 89 6 2.54 6.15 17.04 33.00 32.94 8.34Separated iron (Iron:Limestone=1:1 by weight) Air 20 89 6 3.10 6.71 17.28 32.11 34.53 6.27Separated iron (Iron:Limestone=1:1 by weight) Air 20 89 3 3.58 7.07 18.68 32.62 31.43 6.62Separated iron (Iron:Limestone=1:1 by weight) Air 20 119 6 2.28 5.60 15.85 30.09 32.45 13.73Separated iron (Iron:Limestone=1:1 by weight) Air 20 149 12 5.70 8.04 19.12 32.52 29.36 5.26Separated iron (Iron:Limestone=1:1 by weight) Air 250 149 12 8.72 7.42 17.84 30.11 28.75 7.15Separated iron (Iron:Limestone=1:1 by weight) Air 250 149 3 7.88 6.77 15.26 25.96 29.19 14.93Separated iron (Iron:Limestone=1:1 by weight) Air 250 149 6 8.39 7.55 16.80 32.10 29.58 5.57Separated iron (Iron:Limestone=1:1 by weight) Air 250 149 6 2.16 6.93 18.42 34.95 31.79 5.74Separated iron (Iron:Limestone=1:1 by weight) Air 250 149 3 5.96 5.78 14.59 28.81 30.83 5.66Separated iron (Iron:Limestone=1:1 by weight) Air 250 149 12 10.73 7.95 17.29 31.94 27.81 4.29Separated iron (Iron:Limestone=1:1 by weight) Air 250 149 6 2.62 8.18 19.17 33.25 31.37 5.40Separated iron (Iron:Limestone=1:1 by weight) Air 250 149 3 8.04 6.80 15.92 27.67 28.46 13.12Separated iron (Iron:Limestone=1:1 by weight) Air 250 149 12 12.73 8.48 16.73 33.77 26.87 1.43Separated iron (Iron:Limestone=1:1 by weight) Air 500 149 12 4.73 7.42 18.33 34.00 30.15 5.37Separated iron (Iron:Limestone=1:1 by weight) Air 500 149 6 4.07 7.55 18.42 33.72 31.30 4.94Separated iron (Iron:Limestone=1:1 by weight) Air 500 149 6 4.10 7.41 18.40 32.11 29.90 8.07Separated iron (Iron:Limestone=1:1 by weight) Air 500 149 3 10.27 5.30 14.52 28.66 31.46 9.78Separated iron (Iron:Limestone=1:1 by weight) Air 500 149 12 14.29 5.65 15.32 28.80 28.36 7.59Separated iron (Iron:Limestone=1:1 by weight) Air 500 149 3 4.26 7.45 19.77 32.50 29.73 6.28Separated iron (Iron:Limestone=1:1 by weight) Air 500 149 12 12.93 6.16 15.96 31.12 29.15 4.68Separated iron (Iron:Limestone=1:1 by weight) Air 500 149 3 9.30 6.86 17.74 31.49 28.49 6.11Separated iron (Iron:Limestone=1:1 by weight) Air 500 149 6 2.24 8.49 19.53 35.02 30.54 4.18Separated iron (Iron:Limestone=1:3 by weight) Air 20 149 6 6.02 4.79 15.07 33.56 33.30 7.27Separated iron (Iron:Limestone=3:1 by weight) Air 20 149 6 4.50 6.79 17.54 31.59 31.16 8.42Separated lime (Hematite:Lime=1:1 by weight) 30% CO2 in N2 800 221 6 41.40 6.79 13.89 25.08 12.62 0.23Separated lime (Hematite:Lime=1:1 by weight) 30% CH4 in N2 800 221 6 44.73 10.69 11.69 22.26 10.42 0.21Separated lime (Hematite:Lime=1:1 by weight) 30% CO2 in N2 800 221 6 39.80 6.96 16.49 24.28 12.21 0.26Separated lime (Hematite:Lime=1:1 by weight) 30% CO2 in N2 800 221 6 43.00 6.61 11.29 25.88 13.03 0.19Separated limestone (Iron:Limestone=1:1 by weight) Air 20 149 3 25.93 6.14 15.59 31.79 20.26 0.30Separated limestone (Iron:Limestone=1:1 by weight) Air 20 89 3 23.71 4.72 31.26 37.82 2.49 0.00181    Separated limestone (Iron:Limestone=1:1 by weight) Air 20 149 12 40.93 5.13 13.69 25.65 14.46 0.13Separated limestone (Iron:Limestone=1:1 by weight) Air 20 89 12 21.31 9.27 32.75 33.72 2.95 0.00Separated limestone (Iron:Limestone=1:1 by weight) Air 20 119 3 32.71 9.42 26.19 28.43 3.25 0.00Separated limestone (Iron:Limestone=1:1 by weight) Air 20 89 12 23.61 7.49 31.02 34.79 3.09 0.00Separated limestone (Iron:Limestone=1:1 by weight) Air 20 119 6 30.75 9.73 26.88 29.30 3.34 0.00Separated limestone (Iron:Limestone=1:1 by weight) Air 20 89 3 25.81 10.63 29.38 30.74 3.44 0.00Separated limestone (Iron:Limestone=1:1 by weight) Air 20 149 6 30.09 5.96 14.96 30.04 18.73 0.22Separated limestone (Iron:Limestone=1:1 by weight) Air 20 89 3 19.90 8.69 31.27 36.60 3.55 0.00Separated limestone (Iron:Limestone=1:1 by weight) Air 20 89 6 16.36 10.80 33.33 35.56 3.95 0.00Separated limestone (Iron:Limestone=1:1 by weight) Air 20 89 6 36.29 8.70 24.78 27.14 3.09 0.00Separated limestone (Iron:Limestone=1:1 by weight) Air 20 119 12 27.80 8.85 27.02 32.52 3.82 0.00Separated limestone (Iron:Limestone=1:1 by weight) Air 20 119 6 33.36 7.88 26.45 29.73 2.57 0.00Separated limestone (Iron:Limestone=1:1 by weight) Air 20 119 3 31.41 9.43 26.58 29.22 3.35 0.00Separated limestone (Iron:Limestone=1:1 by weight) Air 20 89 6 28.68 7.67 27.00 32.78 3.87 0.00Separated limestone (Iron:Limestone=1:1 by weight) Air 20 119 12 40.57 8.21 22.77 25.51 2.94 0.00Separated limestone (Iron:Limestone=1:1 by weight) Air 20 89 12 38.17 9.02 24.51 25.45 2.86 0.00Separated limestone (Iron:Limestone=1:1 by weight) Air 20 119 12 37.83 7.97 23.72 27.31 3.17 0.00Separated limestone (Iron:Limestone=1:1 by weight) Air 20 119 6 24.06 8.81 16.66 30.52 19.96 0.00Separated limestone (Iron:Limestone=1:1 by weight) Air 20 119 3 31.28 7.05 27.49 31.26 2.92 0.00Separated limestone (Iron:Limestone=1:1 by weight) Air 250 149 3 23.98 6.57 15.18 32.92 21.19 0.15Separated limestone (Iron:Limestone=1:1 by weight) Air 250 149 3 15.15 6.74 17.21 36.23 24.30 0.37Separated limestone (Iron:Limestone=1:1 by weight) Air 250 149 6 24.01 9.35 17.59 28.68 20.23 0.15Separated limestone (Iron:Limestone=1:1 by weight) Air 250 149 12 19.81 7.65 19.91 33.76 18.70 0.17Separated limestone (Iron:Limestone=1:1 by weight) Air 250 149 12 35.82 7.20 14.71 26.68 15.49 0.09Separated limestone (Iron:Limestone=1:1 by weight) Air 250 149 6 19.63 8.28 18.22 34.28 19.55 0.04Separated limestone (Iron:Limestone=1:1 by weight) Air 250 149 6 22.39 6.42 16.95 33.07 20.91 0.26Separated limestone (Iron:Limestone=1:1 by weight) Air 250 149 3 19.56 6.66 16.20 34.58 22.74 0.26Separated limestone (Iron:Limestone=1:1 by weight) Air 250 149 12 27.82 11.43 17.31 26.22 17.10 0.13Separated limestone (Iron:Limestone=1:1 by weight) Air 500 149 12 32.85 8.37 28.74 27.80 2.24 0.00Separated limestone (Iron:Limestone=1:1 by weight) Air 500 149 6 32.14 8.33 24.30 31.36 3.86 0.00Separated limestone (Iron:Limestone=1:1 by weight) Air 500 149 12 33.55 10.42 24.56 28.15 3.32 0.00Separated limestone (Iron:Limestone=1:1 by weight) Air 500 149 12 38.37 12.29 22.64 23.99 2.72 0.00Separated limestone (Iron:Limestone=1:1 by weight) Air 500 149 3 28.44 8.97 29.11 30.72 2.75 0.00Separated limestone (Iron:Limestone=1:1 by weight) Air 500 149 6 21.89 9.16 31.15 34.70 3.11 0.00Separated limestone (Iron:Limestone=1:1 by weight) Air 500 149 6 34.22 10.14 24.78 27.91 2.96 0.00Separated limestone (Iron:Limestone=1:1 by weight) Air 500 149 3 32.01 10.64 25.35 28.65 3.35 0.00Separated limestone (Iron:Limestone=1:1 by weight) Air 500 149 3 30.48 11.81 27.34 27.34 3.03 0.00Separated limestone (Iron:Limestone=1:3 by weight) Air 20 149 6 31.22 5.54 14.04 29.94 19.00 0.26Separated limestone (Iron:Limestone=3:1 by weight) Air 20 149 6 30.53 6.28 15.05 29.83 18.10 0.21182  Appendix E  Efficiency of magnetic separation procedure To find the influence of the mixture composition on the attrition rate of iron and calcium-based particles, magnetic separation was used to separate the iron from the limestone mixture. Details of the magnetic separation method are provided in Chapter 3. Overall, two methods were used to assess the effectiveness of the separation method – chemical analysis and XRD analysis with measurement of the weight of separated samples. For the chemical analysis, 1 M of sulfuric acid was used to determine whether any Ca-based materials are left in the separated iron. 1. Put separated iron powder obtained by magnetic separation into 1 M sulfuric acid (H2SO4) at 20°C, with stirring. 2. Wait 20 to 30 minutes until the sample is ionized. 3. Put a few drops of the ionized solution into the distilled water and see whether sediments form. If there is limestone in the separated iron powder, CaSO4 sediments will form. However, since there were no Ca-based compounds in the separated iron powder, nothing sedimented because FeSO4 is soluble in water.  Sediments observed when limestone remained in the separated iron. 183   No sediments observed from the separated iron once the iron was separated appropriately. Another way to validate the magnetic separation is using XRD analysis after the particles were separated from the mixture. Typically, 4.8 wt% of iron powder and 6.4 wt% of limestone were lost during the magnetic separation. These are average percentages of weight loss after 81 iron and limestone mixture separations. These separated iron powder and limestone mixtures were analyzed with the XRD to find whether any Ca remained in the iron or Fe remained in the limestone.  Figure E.1 XRD results of separated iron powder. Coloured lines are individual diffraction patterns of all phases. 184   Figure E.2 XRD results of separated limestone. Coloured lines are individual diffraction patterns of all phases. No Ca content was found in the separated iron in Figure E.1. In the separated limestone, depicted in Figure E.2, 0.11 wt% of Fe (Siderite, FeCO3) was found, indicating that the magnetic separation was not perfect, but sufficiently effective.   185  Appendix F  SEM images of particle samples   Iron:Limestone 0.75:0.25 by weight Iron:Limestone 0.5:0.5 by weight Iron:Limestone 0.25:0.75 by weight Separated iron    Separated limestone    Figure F.1 SEM images of separated iron and limestone after 6 h of attrition from different weight fraction of Iron:Limestone mixture at 20°C, jet velocity of 149 m/s. 186   20ºC 250ºC 500ºC Separated iron    Separated limestone    Figure F.2 SEM images of iron and limestone after 6 h of attrition from Iron:Limestone initially 0.5:0.5 by weight with different temperature, jet velocity of 149 m/s. 187   Figure F.3 SEM image of cross-sectional area of a partially oxidized iron particle after 1 h of heat treatment with air at 700°C.  Figure F.4 SEM image of cross-sectional area of a partially oxidized iron particle after 3 h of heat treatment with air at 700°C.  188  Appendix G  Mesh independence study Since the gas phase equations and the inter-phase momentum exchange coefficient are determined on a volume-averaged scale, the dimension of a fluid cell should be between the scales of a particle and the bed, particle size < cell length < bed height. Liu et al. [211] suggested that a fluid cell should be of length 5 to 10 times the particle diameter. Here, based on the suggestion from Liu et al. [211], the initial number of cells was chosen to be 389 K for the mesh. After the initial mesh is chosen, the convergence of residual error was measured to be less than 10-4. Since the residual error was measured to be less than 10-5, the mesh was refined to have 522K cells. The 522K cell grid was tested as well, and the values were compared to the previous one from the 389 K cells. Since those standard deviations of residual errors at steady state are overlapping each other, 389K of cells were selected for the test.  Iterations0 2000 4000 6000 8000 10000Convergence of residual er ror1e-71e-61e-51e-41e-31e-21e-11e+0389K cells552K cells Figure G.1 Convergence of residual error of 389K and 552K cells for mesh independence test.   189  Appendix H  Matlab codes for jet attrition model  Fitting parameters (Ccollision and Cfatigue) search – lime (CaO)  clear all clc % parpool(5) casenum = [20,21,22,23,24,25]; npoint = 11; Fe_fatigue_list = linspace(1,1,npoint); %i Ca_fatigue_list = linspace(1.939481521214067e-04,1.950408049416673e-04,npoint); %j Collision_factor = linspace(6.730401007562492e-04,6.760829753919819e-04,npoint);%k  result = []; count = 1; for i=1:1     for j=1:npoint         for k=1:npoint             fprintf('moving to next parameter set No. %d \n',count)             input = [Fe_fatigue_list(i),Ca_fatigue_list(j),...                 Collision_factor(k)];             result(count,1:3) = input;             %[cum_RME(count), ind_RME(count)]             [result(count,4),ind_MSE] = tominimize(input,casenum);             [~,b] = size(ind_MSE); 190              result(count,5:(b+4)) = ind_MSE;             count = count+1;             writematrix(result,'results\result_overallCaO7.xlsx')         end     end end result_sort = sortrows(result,4); save('results\backup_overallCaO7.mat')   191   Fitting parameters (Ccollision and Cfatigue) search – hematite (Fe2O3)  clear all clc % parpool(5) casenum = [16,17,18,19]; npoint = 21; Fe_fatigue_list = linspace(6.28e-5,6.3e-5,npoint); %i Ca_fatigue_list = linspace(-6,-4,npoint); %j Collision_factor = linspace(0.002570,0.002580,npoint);%k result = []; count = 1; for i=1:npoint     for j=1:1         for k=1:npoint             fprintf('moving to next parameter set No. %d \n',count)             input = [Fe_fatigue_list(i),Ca_fatigue_list(j),...                 Collision_factor(k)];             result(count,1:3) = input;             %[cum_RME(count), ind_RME(count)]             [result(count,4),ind_MSE] = tominimize(input,casenum);             [~,b] = size(ind_MSE);             result(count,5:(b+4)) = ind_MSE; 192              count = count+1;             writematrix(result,'results\result_overallFe2O3_5.xlsx')         end     end end result_sort = sortrows(result,4); save('results\backup_overallFe2O3_5.mat')   193   Fitting parameters (Ccollision and Cfatigue) search – hematite and lime mixture  clear all clc % parpool(5) casenum = [26,27,28]; npoint = 51; Fe_fatigue_list = 0.00006296; %i Ca_fatigue_list = 0.000194057417403433; %j Collision_factor = linspace(7.328500000000000e-04,7.407500000000000e-04,npoint);%k result = []; count = 1; for i=1:1     for j=1:1         for k=1:npoint             fprintf('moving to next parameter set No. %d \n',count)             input = [Fe_fatigue_list,Ca_fatigue_list,...                 Collision_factor(k)];             result(count,1:3) = input;             %[cum_RME(count), ind_RME(count)]             [result(count,4),ind_MSE] = tominimize(input,casenum);             [~,b] = size(ind_MSE);             result(count,5:(b+4)) = ind_MSE; 194              count = count+1;             writematrix(result,'results\result_overall_Fe2O3_CaO_3.xlsx')         end     end end result_sort = sortrows(result,4); save('results\backup_overall_Fe2O3_CaO_3.mat')   195   Optimization  % This function takes the two paraemters and compute the relative mean % error and the cumulative error between the experimental and simulation function [cum_MSE, ind_MSE] = tominimize(input,casenum) % rxn index:  %           0: no rxn %           1: iron oxidation  %           2: iron oxide reduction  %           3: limestone calcination   %           4: lime carbonation %  % fatigue_factor_Fe = 10^(input(1)); % fatigue_factor_Ca = 10^(input(2)); % collision_factor = 10^(input(3)); fatigue_factor_Fe = input(1); fatigue_factor_Ca = input(2); collision_factor = input(3); load('exp_PSD.mat'); cum_MSE = 0; ind_MSE = []; ind_count = 0; [case_num,~] = size(rxn); 196  for i = casenum     [PSD_3h,PSD_6h,PSD_12h] = grand_attrition(fatigue_factor_Fe,...         fatigue_factor_Ca,collision_factor,solid_wt(i,:),...         gas_comp(i,:),runtime(i),Temp(i),V_g(i),rxn(i));     fprintf('\t \t No. %d case is computed \n', i)     if curve_num(i) == 1         % it is the 6h single species test         ind_count = ind_count+1;         if size(PSD_6h) ~=[1,1]             %if the algorithm could converge             total_mass = sum(sum(PSD_6h));             simu_psd = sum(PSD_6h,2)/total_mass*100;             cum_error = abs(simu_psd-exp_psd(:,sum(curve_num(1:i)))).^2;             ind_MSE(ind_count) = mean(cum_error(1:6));             cum_MSE = cum_MSE+sum(cum_error(1:6));         else              ind_MSE(ind_count) = 200;             cum_MSE = cum_MSE+1200;         end     elseif curve_num(i) == 2         % it is the 6h dual species test         % processing seaparated Fe result         ind_count = ind_count+1; 197          if size(PSD_6h) ~=[1,1]             simu_psd_Fe = sum(PSD_6h(:,1:2),2)/sum(sum(PSD_6h(:,1:2)))*100;             cum_error = abs(simu_psd_Fe-exp_psd(:,sum(curve_num(1:i))-1)).^2;             ind_MSE(ind_count) = mean(cum_error(1:6));             cum_MSE = cum_MSE+sum(cum_error(1:6));         else             ind_MSE(ind_count) = 200;             cum_MSE = cum_MSE+1200;         end         % processing seaparated Ca result         ind_count = ind_count+1;                  if size(PSD_6h) ~=[1,1]             simu_psd_Ca = sum(PSD_6h(:,3:4),2)/sum(sum(PSD_6h(:,3:4)))*100;             cum_error = abs(simu_psd_Ca-exp_psd(:,sum(curve_num(1:i)))).^2;             ind_MSE(ind_count) = mean(cum_error(1:6));             cum_MSE = cum_MSE+sum(cum_error(1:6));         else              ind_MSE(ind_count) = 200;             cum_MSE = cum_MSE+1200;         end     else         % it is the 12h single species test 198  % processing 3h result         ind_count = ind_count+1; if size(PSD_3h) ~=[1,1]             simu_psd_3h = sum(PSD_3h,2)/sum(sum(PSD_3h))*100;             cum_error = abs(simu_psd_3h-exp_psd(:,sum(curve_num(1:i))-2)).^2;             ind_MSE(ind_count) = mean(cum_error(1:6));             cum_MSE = cum_MSE+sum(cum_error(1:6));         else              ind_MSE(ind_count) = 200;             cum_MSE = cum_MSE+1200;         end % processing 6h result         ind_count = ind_count+1;                 if size(PSD_6h) ~=[1,1]             simu_psd_6h = sum(PSD_6h,2)/sum(sum(PSD_6h))*100;             cum_error = abs(simu_psd_6h-exp_psd(:,sum(curve_num(1:i))-1)).^2;             ind_MSE(ind_count) = mean(cum_error(1:6));             cum_MSE = cum_MSE+sum(cum_error(1:6));         else              ind_MSE(ind_count) = 200;             cum_MSE = cum_MSE+1200;         end % processing 12h result 199          ind_count = ind_count+1;         if size(PSD_12h) ~=[1,1]             simu_psd_12h = sum(PSD_12h,2)/sum(sum(PSD_12h))*100;             cum_error = abs(simu_psd_12h-exp_psd(:,sum(curve_num(1:i)))).^2;             ind_MSE(ind_count) = mean(cum_error(1:6));             cum_MSE = cum_MSE+sum(cum_error(1:6));         else              ind_MSE(ind_count) = 200;             cum_MSE = cum_MSE+1200;         end     end end cum_MSE = cum_MSE/ind_count/6; end   200   Attrition main codes  %This function takes the fitted parameters the operating parameters, and %returns the simulated particle size distributions (PSDs) %Inputs: %       fatigue_factor_Fe: iron based species fitted fatigue factor %       fatigue_factor_Ca: Ca based species fitted fatigue facotr %       collision_factor: the fraction of the effective collision that %                         causes fragmentation  %       solid_wt: 1D array in grams, [Fe_wt, FeOx_wt, CaCO3_wt, CaO_wt] %       gas_comp= 1D array in decimals,[CH4_frac,N2_frac,Air_frac,CO2_frac] %       runtime: the total time in minutes to run the simluation for  %                in 180 min, 360 min, or 720 min %       Temp: the temperature to run the simulation at  %              in C choose from 20 250 500 700 800 %       V_g: volumetric gas velocity in the column in LPM %       rxn: =1 if there is reactions  %            =0 if not % %Outputs: %        PSD_3h: the simulated PSD after 3 hr %        PSD_6h: the simulated PSD after 6 hr %        PSD_12h: the simulated PSD after 12 hr 201   function [PSD_3h,PSD_6h,PSD_12h] = grand_attrition(fatigue_factor_Fe,...     fatigue_factor_Ca,collision_factor,solid_wt,gas_comp,runtime,Temp,...     V_g,rxn) close all  %% User Settings %number of bins where bin 1 is the smallest binnum = 6; bin_meandiameter=[31.5,94,187.5,375,750,1700]; %in um %the default time step size is 0.4s. It will be reduced iteratively if %negative mass ossurs delta_t = 0.4; % in min %converting the fatigue factor to the base the fatigue calculation fatigue_Fe = 1.0+fatigue_factor_Fe; fatigue_Ca = 1.0+fatigue_factor_Ca; COR = 0.9; %coefficient of restitution  %the supposed mass of the initial loading solidtotal_mass = 50; %check if the gas Ccmpositions sum up to 1 if sum(gas_comp)~=1     error('gas composiiton does NOT sum up to 1') end 202  %check if the loaded individual speices sum up the the supposed value % if floor(sum(solid_wt))~=solidtotal_mass %     error('the total mass entered is not 50g') % end %assign the mass values to each species Fe_wt = solid_wt(1); Fe2O3_wt = solid_wt(2); CaCO3_wt = solid_wt(3); CaO_wt = solid_wt(4); %determine the orifice gas velocity compressible fluid. Values are %calculated by hand for each volumetric gas flow rate if V_g == 10     u_orif = 148.7912841; %in m/s elseif V_g == 8     u_orif = 119.2224089; %in m/s elseif V_g == 6     u_orif = 89.46415204; %in m/s elseif V_g == 22.5     u_orif = 221.2814134; %in m/s else     error('The gas velocity entered is out of the range!') end %% Loading Parameters 203   %load fragmentation daughter particle distribution load('compression_results.mat'); %Parameters empirical = empirical_parameters; ASTM = ASTM_parameters; solid_density=[empirical.rho.Fe;empirical.rho.Fe2O3;empirical.rho.CaCO3;empirical.rho.CaO]; % Young = [];  PSD_Fe = []; PSD_Ca = []; Fe_binwt=[]; Fe2O3_binwt=[]; CaO_binwt=[]; CaCO3_binwt=[]; %to determine if its binary or single particle collision if Fe_wt + Fe2O3_wt ==0     isiron=0;     binary=0; elseif CaCO3_wt + CaO_wt == 0     isiron=1;     binary=0; else     binary=1;     isiron=2; end %Import initial PSDs PSD_original = load('Original PSDs of each species.csv'); 204   %load particle breakage energy  %column = Fe FeOx CaCO3 CaO; row = 63-125 ... 1000-2400um  specie_breakage_energy = load('particle breakage energy.csv'); specie_breakage_force = load('particle breakage force.csv'); %Calculate the initial PSD for OC and sorbent particles fractions %keep track of the wt of each species in each bin if Fe_wt + Fe2O3_wt~=0     PSD_Fe = (Fe_wt*PSD_original(:,1) + Fe2O3_wt*PSD_original(:,2))/(Fe_wt + Fe2O3_wt)/100; else     PSD_Fe = zeros(6,1); end if CaCO3_wt + CaO_wt~=0     PSD_Ca = (CaCO3_wt*PSD_original(:,3) + CaO_wt*PSD_original(:,4))/(CaCO3_wt + CaO_wt)/100; else     PSD_Ca = zeros(6,1); end Fe_binwt=PSD_original(:,1)*Fe_wt/100/1000; %in kg Fe2O3_binwt=PSD_original(:,2)*Fe2O3_wt/100/1000; %in kg CaCO3_binwt=PSD_original(:,3)*CaCO3_wt/100/1000; %in kg CaO_binwt=PSD_original(:,4)*CaO_wt/100/1000; %in kg 205   %compute the composition of each bin of Fe and Ca species bin_wtspecies = [Fe_binwt,Fe2O3_binwt,CaCO3_binwt,CaO_binwt]; %Calculate the superficial gas velocity  U_superficial = V_g/1000/60/ASTM.Ac; %Calculate Young's Modulus at Temp for all oxidized and all reduced iron %particals [E_red,E_ox,E_CaCO3,E_CaO] = Youngsmod( Temp ); % in GPa Species_Youngs = [E_red;E_ox;E_CaCO3;E_CaO]; %compute the gas proporties [rho_g_species,mu_g_species] = gas_properties(Temp); rho_g=sum(rho_g_species.*gas_comp); mu_g=sum(mu_g_species.*gas_comp); %save the original variables that will be updated in each iteration as %backup. They can be used if the step size is to be adjusted and the %simulation will be restarted wt_bkp = bin_wtspecies; E_b_bkp = specie_breakage_energy; Fc_bkp = specie_breakage_force; %initialize the output variables PSD_12h=0; PSD_6h=0; PSD_3h=0; 206   %% finite time increment solving the system over testin time if binary==0     if isiron==1 %only iron         PSD=PSD_Fe;         fatigue=fatigue_Fe;     else %only Ca particles         PSD=PSD_Ca;         fatigue=fatigue_Ca;     end end time = 0; step_red = 0; fprintf('\t\t initial time step size is %3.3e s \n',delta_t*60) %flags to save simulated results flag3h=0; flag6h=0; flag12h=0; %start time iteration while time <= runtime     time=time+delta_t;     if rxn ~= 0         %update the species composition if reactions occur.         207          bin_wtspecies = reaction(bin_wtspecies,bin_meandiameter,...             Temp,delta_t,rxn,solid_density,time);     end     if binary == 0         %use single particle attrtion function         [ bin_wtspecies,specie_breakage_energy,specie_breakage_force,error_flag] = ...             singleattrition(bin_meandiameter,bin_wtspecies, time*60,...             delta_t*60,solid_density,specie_breakage_energy,specie_breakage_force,...             u_orif,rho_g,mu_g,COR,Species_Youngs,isiron,fatigue,compressionPSD,...             U_superficial,collision_factor);     else         % binary attrition function         [ bin_wtspecies,specie_breakage_energy,specie_breakage_force,...             error_flag] = binaryattrition(bin_meandiameter, bin_wtspecies,...             time*60, delta_t*60,solid_density,specie_breakage_energy,...             specie_breakage_force,u_orif,rho_g,mu_g,COR,Species_Youngs,...             fatigue_Fe,fatigue_Ca,compressionPSD,U_superficial,...             collision_factor);     end %     bin_wtspecies     if error_flag == 1          delta_t2 = delta_t/(runtime/time)^0.5;          208          if abs(delta_t2-delta_t)/delta_t<0.15             delta_t=delta_t2/2;         else              delta_t=delta_t2;         end         fprintf('\t\t\t negative mass happens at %f min \n',time)         fprintf('\t\t\t reducing time step size to %3.3e s \n',delta_t*60)         step_red = step_red+1;         %re-initialize iterative values         time=0;         bin_wtspecies = wt_bkp;         specie_breakage_energy = E_b_bkp;         specie_breakage_force = Fc_bkp;         flag3h=0;         flag6h=0;         flag12h=0;     else         end     %to avoid overall reduce the time step: if the time step is too small     %but still unable to get positive mass, abort this set of parameters     if step_red > 3 || delta_t < 1/60         fprintf('\t\t\t Iteration aborted after %d times \n',step_red)         fprintf('\t\t\t current time step size is %f s \n',delta_t*60) 209          break     end %     if max(isnan(bin_wtspecies))~=0  %         error('NaN occurs!') %     end     if error_flag == 0         if time>2.99*60 && time<3.01*60 && flag3h==0            flag3h=1;            PSD_3h=bin_wtspecies;         end         if time>5.99*60 && time<6.01*60 && flag6h == 0            flag6h = 1;            PSD_6h=bin_wtspecies;         end         if time>11.99*60 && time<12.01*60 && flag12h == 0            flag12h = 1;            PSD_12h=bin_wtspecies;         end     end end  end   210   Reaction kinetics  function [bin_wtspecies] = reaction(bin_wtspecies,bin_meandiameter,...     Temp,delta_t,rxn,solid_density,time) delta_t = delta_t/4; time = time/4; rate_factor = 1; if rxn == 1     %iron oxidation      Fe = bin_wtspecies(:,1);     Fe2O3 = bin_wtspecies(:,2);     X = Fe2O3./(Fe2O3+Fe*159.69/112);     for i=1:6         if isnan(X(i))             dm_Fe2O3 = 0;         else             if X(i)<7/9 %parabolic law                 kp = 3.047*exp(-157539/8.314/(Temp+273.15))*rate_factor;                 V = Fe(i)/solid_density(1)+Fe2O3(i)/solid_density(2);                 S = V/((bin_meandiameter(i)*1e-6)^3*pi/6)*...                     (bin_meandiameter(i)*1e-6)^2*pi;                 dm = S*sqrt(kp/time)*delta_t;                 dm_Fe2O3 = dm*(159.69/(159.69-112)); 211              else %2nd order kinetics                 k = 2328.5*exp(-116923/8.314/(Temp+273.15))*rate_factor;                 dX = k*(1-X(i))^2*delta_t;                 dm_Fe2O3 = dX*(Fe2O3(i)+Fe(i)*159.69/112);             end         end         bin_wtspecies(i,1) = bin_wtspecies(i,1)-dm_Fe2O3*112/159.69;         bin_wtspecies(i,2) = bin_wtspecies(i,2)+dm_Fe2O3;     end    elseif rxn == 2     % iron oxide reduction     Fe = bin_wtspecies(:,1);     Fe2O3 = bin_wtspecies(:,2);     X = Fe./(Fe+Fe2O3*56*2/159.69);     for i=1:6         if isnan(X(i))             dX = 0;         else             if X(i)<1/9 % 1st order kinetics                 k = exp(-81200/8.314/(Temp+273.15)-0.7802)*rate_factor;                 dX = k*(1-X(i))*delta_t;             else % 3D diffusion                 k = exp(-166100/8.314/(Temp+273.15)+7.7802)*rate_factor; 212                  dX = k*3/2*(1-X(i))^(2/3)*(1-(1-X(i))^(1/3))^(-1)*delta_t;             end         end         dm_Fe = dX*(Fe(i)+Fe2O3(i)*56*2/159.69);         bin_wtspecies(i,1) = bin_wtspecies(i,1)+dm_Fe;         bin_wtspecies(i,2) = bin_wtspecies(i,2)-159.69/112*dm_Fe;     end  elseif rxn == 3     % limestone calcination      CaCO3 = bin_wtspecies(:,3);     CaO = bin_wtspecies(:,4);     X = CaO./(CaO+56/100*CaCO3);     for i=1:6         if isnan(X(i))             dX = 0;         else             c_B0 = 26.67; %kmol/m3             %k = 6.117*exp(-175384/8.314/(Temp+273.15));             k = 47927/60*exp(-190920/8.314/(Temp+273.15))*rate_factor;             dp = bin_meandiameter(i)*1e-6;             dX = k*6/dp*c_B0^(-2/3)*(1-X(i))^(1/3)*delta_t;         end         dm_CaO = dX*(CaO(i)+56/100*CaCO3(i)); 213          bin_wtspecies(i,3) = bin_wtspecies(i,3)-dm_CaO*100/56;         bin_wtspecies(i,4) = bin_wtspecies(i,4)+dm_CaO;     end elseif rxn == 4      % lime carbonation      CaCO3 = bin_wtspecies(:,3);     CaO = bin_wtspecies(:,4);     X = CaCO3./(CaCO3+100/56*CaO);     for i=1:6         if isnan(X(i))             dX = 0;         else             if X(i)<0.25 % reaction control                 k = exp(-81800/8.314/(Temp+273.15)+3.9815)*rate_factor;                 b = -0.0208*bin_meandiameter(i)+149.87;             else % diffusion control                 k = exp(-37099/8.314/(Temp+273.15)-2.7604)*rate_factor;                 b = -0.1135*bin_meandiameter(i)+815.6;             end             dX = k*b^2*delta_t/(b+time)^2;         end         dm_CaCO3 = dX*(CaCO3(i)+100/56*CaO(i));         bin_wtspecies(i,3) = bin_wtspecies(i,3)+dm_CaCO3; 214          bin_wtspecies(i,4) = bin_wtspecies(i,4)-dm_CaCO3*56/100;     end else     error('wrong reaction index, not defined!') end for pp=1:4     for qq=1:6         if bin_wtspecies(qq,pp)<0             bin_wtspecies(qq,pp) = 0;         end     end end end    215   Attrition with single species  %function to compute the attrition result from a previous time step in a %discretized manner for SINGLE PARTICLE ONLY %input:  %       bin_meandiameter: row vector, mean diameter of each bin %       wtcomposition_0:  weight of each bin in order of Fe Fe2O3 CaCO3 %                       CaO in columns and bin 1-6 in rows %       time:           the current time point being evaluated at. %       dt:             timestep size %       solid_desity:   column vector, density of each pecies %       specie_breakage_energy: 5*4, bin-wise breakage energy of each  %                               species %       specie_breakage_force:  5*4, bin-wise breakage force of each  %                               species %       u_orif:         gas velocity at the orifice m/s %       rho_g:          average gas density kg/m3 %       mu_g:           average gas viscocity Pa-s %       COR:            Coefficient of Restitution %       Youngs:         column vector of youngs modelus of each species %       isiron:         the flag parameter to indicate the phase of the %                       single species %       fatigue:        the particle fatigue factor 216  %       compressionPSD: tructure in the format of ~.species %                       each cell is 6*5 increase in particle size %       collision_factor: scaling the number of collisions down to a %                         reasonable value %output: PSD_1:         the PSD after this time step %        composition_1: the composition of each bin after this time step %specie_breakage_energy:new breakage energy after collision  %specie_breakage_force: new breakage force after collision % error_flag:           =1 if any volume is negative  function [ wtcomposition_1,specie_breakage_energy,...     specie_breakage_force,error_flag] = singleattrition(bin_meandiameter,...     wtcomposition_0, time, dt,solid_density,specie_breakage_energy,...     specie_breakage_force,u_orif,rho_g,mu_g, COR,Youngs,isiron,fatigue,...     compressionPSD,U_superficial,collision_factor) if min(min(wtcomposition_0))<0 || max(max(isnan(wtcomposition_0)))     fprintf('negative volume')     error_flag = 1;     wtcomposition_1 = wtcomposition_0; else %Archard abrasion constant in the order of Fe FeOx CaCO3 CaO K_abr_list = [2.7376E+05;1.4439E+06;8.5016E+06;3.4376E+07]/2; K_abr = wtcomposition_0*K_abr_list./sum(wtcomposition_0,2); %column, bin wise %volume and density of each particle bin 217  bin_volume = sum(wtcomposition_0./solid_density',2); bin_density = sum(wtcomposition_0,2)./bin_volume; %number of particles in each bin bin_number = bin_volume./((bin_meandiameter/1e6)'.^3*pi/6); %particle surface area of each bin assume spherical bin_area = (bin_meandiameter/1e6)'.^2*pi; vol_species = wtcomposition_0./solid_density'; mole = wtcomposition_0*1000./[56,159.69,100,56]; %calculate young's modulus for each bin if isiron==0     bin_conv = mole(:,4)./(mole(:,3) + mole(:,4));     bin_Young = (Youngs(4)-Youngs(3))*bin_conv+Youngs(3);     E_b = (specie_breakage_energy(:,3).*wtcomposition_0(:,3)+...         specie_breakage_energy(:,4).*wtcomposition_0(:,4))./...         (wtcomposition_0(:,4)+wtcomposition_0(:,3));     Fc = (specie_breakage_force(:,3).*wtcomposition_0(:,3)+...         specie_breakage_force(:,4).*wtcomposition_0(:,4))./...         (wtcomposition_0(:,4)+wtcomposition_0(:,3)); elseif isiron==1     bin_conv = mole(:,2)*2./(mole(:,1) + mole(:,2)*2);     bin_Young = (Youngs(2)-Youngs(1))*bin_conv+Youngs(1);     E_b = (specie_breakage_energy(:,1).*wtcomposition_0(:,1)+...         specie_breakage_energy(:,2).*wtcomposition_0(:,2))./... 218          (wtcomposition_0(:,2)+wtcomposition_0(:,1));     Fc = (specie_breakage_force(:,1).*wtcomposition_0(:,1)+...         specie_breakage_force(:,2).*wtcomposition_0(:,2))./...         (wtcomposition_0(:,1)+wtcomposition_0(:,2)); else     error('binary particle go into single particle function') end %calculate the bed volume using richardson zaki equation Density_avg = sum(sum(wtcomposition_0))/sum(bin_volume); D_debouckere = bin_meandiameter*bin_volume/sum(bin_volume)/1e6; %in m ddp = D_debouckere*(rho_g*9.8*(Density_avg-rho_g)/mu_g^2)^(1/3); uu_t=((18/ddp^2)^0.824+(0.321/ddp)^0.412)^(-1.214); U_t=uu_t/(rho_g^2/(mu_g*9.8*(Density_avg-rho_g)))^(1/3); Ar_avg = 9.8*D_debouckere^3*rho_g*(Density_avg-rho_g)/(mu_g^2); % Re_t = Ar_avg^(1/3)*((18/Ar_avg^(2/3))^0.824+(0.321/Ar_avg^(1/3))^0.412)^(-1.214); % U_t = Re_t*mu_g/Density_avg/D_debouckere; n_rz=(4.8+2.4*(0.043*Ar_avg^0.57))/((0.043*Ar_avg^0.57)+1); voidage = (U_superficial/U_t)^(1/n_rz); V_bed = sum(bin_volume)/(1-voidage); %calculate bin wise number density bin_num_dens = bin_number/V_bed; % bin_num_dens(4:end) %mass change in each bin each species in this iteration  219  mass_change = zeros(6,4); %the number of collisions experienced by each particle in each bin %(not species wise)  fatigue_collision = zeros(6,1); for i=1:6     for j=1:6 dpi = bin_meandiameter(i);         dpj = bin_meandiameter(j);         [u_pi,~] = impact_velocity(bin_density(i),rho_g,mu_g,dpi,u_orif);         [u_pj,~] = impact_velocity(bin_density(j),rho_g,mu_g,dpj,u_orif);         mi = (dpi*1e-6)^3*pi/6*bin_density(i);         mj = (dpj*1e-6)^3*pi/6*bin_density(j);         if j==1             fatigue_collision(i) = fatigue_collision(i);         else             fc_i = 2*dpi*1e-6*(0.6*9.8*bin_num_dens(i)*pi)^0.5;             fc_j = 2*dpj*1e-6*(0.6*9.8*bin_num_dens(j)*pi)^0.5;             fatigue_collision(i) = fatigue_collision(i)+sqrt(fc_i*fc_j)...                 *collision_factor;                 end E_loss_total = mi*mj/(2*(mi+mj))*(1-COR^2)*(u_pi-u_pj)^2;         E_loss = E_loss_total/2;         % as long as one party of the two particles in a collision is 220          % from 0-63um this collision causes no attrition         if i==1 || j==1             collision_num = 0;         else             fc_i = 2*dpi*1e-6*(0.6*9.8*bin_num_dens(i)*pi)^0.5;             fc_j = 2*dpj*1e-6*(0.6*9.8*bin_num_dens(j)*pi)^0.5;             collision_num = sqrt(fc_i*fc_j)*dt*collision_factor;         end         %different impact velocity  collision         %typical attrition         if E_loss >= max(E_b(i),E_b(j))             %both fragmentation %                     fprintf('1 \n')             if i==1                 %no breakage for 0-63um                 mass_change=mass_change+zeros(6,4);             else                 V_frag_i = (dpi*1e-6)^3*pi/6*collision_num;                 mass_trans_i1 = vol_species(i,1)*compressionPSD.iron(:,i-1)/...                      100/sum(vol_species(i,:))*V_frag_i*solid_density(1);                 mass_trans_i2 = vol_species(i,2)*compressionPSD.ironoxide(:,i-1)/...                      100/sum(vol_species(i,:))*V_frag_i*solid_density(2);                 mass_trans_i3 = vol_species(i,3)*compressionPSD.limestone(:,i-1)/... 221                       100/sum(vol_species(i,:))*V_frag_i*solid_density(3);                 mass_trans_i4 = vol_species(i,4)*compressionPSD.lime(:,i-1)/...                      100/sum(vol_species(i,:))*V_frag_i*solid_density(4);                 mass_change(i,:)=mass_change(i,:)-[sum(mass_trans_i1),...                      sum(mass_trans_i2),sum(mass_trans_i3),sum(mass_trans_i4)];                 mass_change(:,:)=mass_change(:,:)+[mass_trans_i1,...                      mass_trans_i2,mass_trans_i3,mass_trans_i4]; %                     if j==1 %                         %sum(mass_trans_i1)>5 || sum(mass_trans_i2)>5 || sum(mass_trans_i3)>5 || sum(mass_trans_i4)>5 %                        fprintf('i=%d \n',i) %                        [mass_trans_i1,mass_trans_i2,mass_trans_i3,mass_trans_i4] %                     end             end             if j==1                 %no breakage for 0-63um                 mass_change=mass_change+zeros(6,4);             else                 V_frag_j = (dpj*1e-6)^3*pi/6*collision_num;                 mass_trans_j1 = vol_species(j,1)*compressionPSD.iron(:,j-1)/...                      100/sum(vol_species(j,:))*V_frag_j*solid_density(1);                 mass_trans_j2 = vol_species(j,2)*compressionPSD.ironoxide(:,j-1)/...                      100/sum(vol_species(j,:))*V_frag_j*solid_density(2); 222                  mass_trans_j3 = vol_species(j,3)*compressionPSD.limestone(:,j-1)/...                      100/sum(vol_species(j,:))*V_frag_j*solid_density(3);                 mass_trans_j4 = vol_species(j,4)*compressionPSD.lime(:,j-1)/...                      100/sum(vol_species(j,:))*V_frag_j*solid_density(4);                 mass_change(j,:)=mass_change(j,:)-[sum(mass_trans_j1),...                      sum(mass_trans_j2),sum(mass_trans_j3),sum(mass_trans_j4)];                 mass_change(:,:)=mass_change(:,:)+[mass_trans_j1,...                      mass_trans_j2,mass_trans_j3,mass_trans_j4];             end         elseif E_loss < min(E_b(i),E_b(j)) %                     fprintf('2 \n')             %both abrasion              Ei = 1/2*mi*u_pi^2;             Ej = 1/2*mj*u_pj^2; %                 abr__frac_i = 0.4*K_abr(i)*Ei*bin_number(i)*dt/... %                     (Fc(i)*time^0.6/bin_area(i)); %                 abr__frac_j = 0.4*K_abr(j)*Ej*bin_number(j)*dt/... %                     (Fc(j)*time^0.6/bin_area(j));             abr__frac_i = K_abr(i)*Ei*bin_number(i)*dt/...                 (Fc(i)*time/bin_area(i));             abr__frac_j = K_abr(j)*Ej*bin_number(j)*dt/...                 (Fc(j)*time/bin_area(j));             if i==1 || j==1 223                  abr__frac_i = 0;                 abr__frac_j = 0;             end             mass_trans_i = wtcomposition_0(i,:)*abr__frac_i;             mass_trans_j = wtcomposition_0(j,:)*abr__frac_j;             mass_change(i,:) = mass_change(i,:)-mass_trans_i;             mass_change(j,:) = mass_change(j,:)-mass_trans_j;             mass_change(1,:) = mass_change(1,:)+mass_trans_i+mass_trans_j;         elseif (E_loss >= E_b(i)) && (E_loss < E_b(j))             %fragmentation in i and abrasion in j %                     fprintf('3 \n')             Ej = 1/2*mj*u_pj^2; %                 abr__frac_j = 0.4*K_abr(j)*Ej*bin_number(j)*dt/... %                     (Fc(j)*time^0.6/bin_area(j));             abr__frac_j = K_abr(j)*Ej*bin_number(j)*dt/...                 (Fc(j)*time/bin_area(j));             % no abrasion when 0-63um particles are involved             if i==1 || j==1                 abr__frac_j = 0;             end             mass_trans_j = wtcomposition_0(j,:)*abr__frac_j;             mass_change(j,:) = mass_change(j,:)-mass_trans_j;             mass_change(1,:) = mass_change(1,:)+mass_trans_j; 224              if i==1                 %no breakage for 0-63um                 mass_change=mass_change+zeros(6,4);             else                 V_frag_i = (dpi*1e-6)^3*pi/6*collision_num;                 mass_trans_i1 = vol_species(i,1)*compressionPSD.iron(:,i-1)/...                      100/sum(vol_species(i,:))*V_frag_i*solid_density(1);                 mass_trans_i2 = vol_species(i,2)*compressionPSD.ironoxide(:,i-1)/...                      100/sum(vol_species(i,:))*V_frag_i*solid_density(2);                 mass_trans_i3 = vol_species(i,3)*compressionPSD.limestone(:,i-1)/...                      100/sum(vol_species(i,:))*V_frag_i*solid_density(3);                 mass_trans_i4 = vol_species(i,4)*compressionPSD.lime(:,i-1)/...                      100/sum(vol_species(i,:))*V_frag_i*solid_density(4);                 mass_change(i,:)=mass_change(i,:)-[sum(mass_trans_i1),...                      sum(mass_trans_i2),sum(mass_trans_i3),sum(mass_trans_i4)];                 mass_change(:,:)=mass_change(:,:)+[mass_trans_i1,...                      mass_trans_i2,mass_trans_i3,mass_trans_i4];             end         else              %fragmentation in j and abrasion in i %                     fprintf('4 \n')             Ei = 1/2*mi*u_pi^2; %                 abr__frac_i = 0.4*K_abr(i)*Ei*bin_number(i)*dt/... 225  %                     (Fc(i)*time^0.6/bin_area(i));             abr__frac_i = K_abr(i)*Ei*bin_number(i)*dt/...                 (Fc(i)*time/bin_area(i));             %no abrasion if 0-63 particles are involved             if i==1 || j==1                 abr__frac_i = 0;             end             mass_trans_i = wtcomposition_0(i,:)*abr__frac_i;             mass_change(i,:) = mass_change(i,:)-mass_trans_i;             mass_change(1,:) = mass_change(1,:)+mass_trans_i;             if j==1                 %no breakage for 0-63um                 mass_change=mass_change+zeros(6,4);             else                 V_frag_j = (dpj*1e-6)^3*pi/6*collision_num;                 mass_trans_j1 = vol_species(j,1)*compressionPSD.iron(:,j-1)/...                      100/sum(vol_species(j,:))*V_frag_j*solid_density(1);                 mass_trans_j2 = vol_species(j,2)*compressionPSD.ironoxide(:,j-1)/...                      100/sum(vol_species(j,:))*V_frag_j*solid_density(2);                 mass_trans_j3 = vol_species(j,3)*compressionPSD.limestone(:,j-1)/...                      100/sum(vol_species(j,:))*V_frag_j*solid_density(3);                 mass_trans_j4 = vol_species(j,4)*compressionPSD.lime(:,j-1)/...                      100/sum(vol_species(j,:))*V_frag_j*solid_density(4); 226                  mass_change(j,:)=mass_change(j,:)-[sum(mass_trans_j1),...                      sum(mass_trans_j2),sum(mass_trans_j3),sum(mass_trans_j4)];                 mass_change(:,:)=mass_change(:,:)+[mass_trans_j1,...                      mass_trans_j2,mass_trans_j3,mass_trans_j4];             end         end                                                  end end wtcomposition_1 = wtcomposition_0+mass_change; %reduce specie_breakage_energy due to fatigue  %E_b=E_b0*fatigue^(-3*collision_frequency*dt) %Fc=Fc0*fatigue^(-1.5*collision_frequency*dt) specie_breakage_energy = specie_breakage_energy.*(fatigue.^...     (-3*fatigue_collision*dt)); % specie_breakage_energy(2:end,:) specie_breakage_force = specie_breakage_force.*(fatigue.^...     (-1.5*fatigue_collision*dt)); % specie_breakage_force(2:end,:) error_flag = 0; end end   227   Attrition with binary solid species  %function to compute the attrition result from a previous time step in a %discretized manner for binary PARTICLE  %input:  %       bin_meandiameter: row vector, mean diameter of each bin %       wtcomposition_0:  weight of each bin in order of Fe Fe2O3 CaCO3 %                       CaO in columns and bin 1-6 in rows %       time:           the current time point being evaluated at. %       dt:             timestep size %       solid_desity:   column vector, density of each pecies %       specie_breakage_energy: 5*4, bin-wise breakage energy of each  %                               species %       specie_breakage_force:  5*4, bin-wise breakage force of each  %                               species %       u_orif:         gas velocity at the orifice m/s %       rho_g:          average gas density kg/m3 %       mu_g:           average gas viscocity Pa-s %       COR:            Coefficient of Restitution %       Youngs:         column vector of youngs modelus of each species %       fatigue_Fe:     iron based particle fatigue factor %       fatigue_Ca:     Ca based particle fatigue factor %       compressionPSD: tructure in the format of ~.species 228  %                       each cell is 6*5 increase in particle size %       U_superficial:  superficial gas velocity %       collision_factor: scaling the number of collisions down to a %                         reasonable value %output:  %wtcomposition_1:       the composition of each bin after this time step %specie_breakage_energy:new breakage energy after collision  %specie_breakage_force: new breakage force after collision % error_flag:           =1 if any volume is negative  function [ wtcomposition_1,specie_breakage_energy,...     specie_breakage_force,error_flag] = binaryattrition(bin_meandiameter,...     wtcomposition_0, time, dt,solid_density,specie_breakage_energy,...     specie_breakage_force,u_orif,rho_g,mu_g, COR,Youngs,fatigue_Fe,...     fatigue_Ca,compressionPSD,U_superficial,collision_factor) %jump out of this function if negative valume occur if min(min(wtcomposition_0))<0 || max(max(isnan(wtcomposition_0)))     fprintf('negative volume')     error_flag = 1;     wtcomposition_1 = wtcomposition_0; else %Archard abrasion constant in the order of Fe FeOx CaCO3 CaO %column, species wise %K_abr_list = [7.68244E+04;4.47179E+05;2.63211E+06;1.06351E+07];  229  K_abr_list = [2.7376E+05;1.4439E+06;8.5016E+06;3.4376E+07]/2; K_abr_Fe = wtcomposition_0(:,1:2)*K_abr_list(1:2,1)./...     sum(wtcomposition_0(:,1:2),2);  K_abr_Ca = wtcomposition_0(:,3:4)*K_abr_list(3:4,1)./...     sum(wtcomposition_0(:,3:4),2);  %volume and density of each particle bin vol_species = wtcomposition_0./solid_density'; bin_volume_Fe = sum(vol_species(:,1:2),2); bin_volume_Ca = sum(vol_species(:,3:4),2); bin_density_Fe = sum(wtcomposition_0(:,1:2),2)./bin_volume_Fe; bin_density_Ca = sum(wtcomposition_0(:,3:4),2)./bin_volume_Ca; %number of particles in each bin bin_number_Fe = bin_volume_Fe./((bin_meandiameter/1e6)'.^3*pi/6); bin_number_Ca = bin_volume_Ca./((bin_meandiameter/1e6)'.^3*pi/6); %particle surface area of each bin assume spherical bin_area = (bin_meandiameter/1e6)'.^2*pi; mole = wtcomposition_0*1000./[56,159.69,100,56]; %calculate young's modulus (Young) and breakage energu (E_b) for each bin %and each species bin_conv_Ca = mole(:,4)./(mole(:,3) + mole(:,4)); bin_Young_Ca = (Youngs(4)-Youngs(3))*bin_conv_Ca+Youngs(3); E_b_Ca = (specie_breakage_energy(:,3).*wtcomposition_0(:,3)+...     specie_breakage_energy(:,4).*wtcomposition_0(:,4))./... 230      (wtcomposition_0(:,4)+wtcomposition_0(:,3)); Fc_Ca = (specie_breakage_force(:,3).*wtcomposition_0(:,3)+...         specie_breakage_force(:,4).*wtcomposition_0(:,4))./...         (wtcomposition_0(:,4)+wtcomposition_0(:,3)); bin_conv_Fe = mole(:,2)*2./(mole(:,1) + mole(:,2)*2); bin_Young_Fe = (Youngs(2)-Youngs(1))*bin_conv_Fe+Youngs(1); E_b_Fe = (specie_breakage_energy(:,1).*wtcomposition_0(:,1)+...     specie_breakage_energy(:,2).*wtcomposition_0(:,2))./...     (wtcomposition_0(:,2)+wtcomposition_0(:,1)); Fc_Fe = (specie_breakage_force(:,1).*wtcomposition_0(:,1)+...         specie_breakage_force(:,2).*wtcomposition_0(:,2))./...         (wtcomposition_0(:,1)+wtcomposition_0(:,2)); %calculate the bed volume using richardson zaki equation bin_volume=bin_volume_Fe+bin_volume_Ca; Density_avg = sum(sum(wtcomposition_0))/sum(bin_volume); D_debouckere = bin_meandiameter*bin_volume/sum(bin_volume)/1e6; %in m ddp = D_debouckere*(rho_g*9.8*(Density_avg-rho_g)/mu_g^2)^(1/3); uu_t=((18/ddp^2)^0.824+(0.321/ddp)^0.412)^(-1.214); U_t=uu_t/(rho_g^2/(mu_g*9.8*(Density_avg-rho_g)))^(1/3); Ar_avg = 9.8*D_debouckere^3*rho_g*(Density_avg-rho_g)/(mu_g^2); %use Richardson-Zaki equation to obtain bed voidage n_rz=(4.8+2.4*(0.043*Ar_avg^0.57))/((0.043*Ar_avg^0.57)+1); voidage = (U_superficial/U_t)^(1/n_rz); 231  V_bed = sum(bin_volume)/(1-voidage); %calculate bin wise number density bin_num_dens_Fe = bin_number_Fe/V_bed; bin_num_dens_Ca = bin_number_Ca/V_bed; %mass change in each bin each species in this iteration  mass_change = zeros(6,4); %the number of collisions experienced by each particle in each bin %(not species wise)  fatigue_collision_Fe = zeros(6,1); fatigue_collision_Ca = zeros(6,1); %% attrtion in this scenario 1: Fe-Fe collision % The probality of each case is associated with the volume fraction of each % phase: (Fe_frac+Ca_frac)^2=Fe_frac^2 + 2*Fe_frac*Ca_frac + Ca_frac^2 for i=1:6     for j=1:6         dpi = bin_meandiameter(i);         dpj = bin_meandiameter(j);         [u_pi,~] = impact_velocity(bin_density_Fe(i),rho_g,mu_g,dpi,u_orif);         [u_pj,~] = impact_velocity(bin_density_Fe(j),rho_g,mu_g,dpj,u_orif);         mi = (dpi*1e-6)^3*pi/6*bin_density_Fe(i);         mj = (dpj*1e-6)^3*pi/6*bin_density_Fe(j);         if j~=1             fc_i = 2*dpi*1e-6*(0.6*9.8*bin_num_dens_Fe(i)*pi)^0.5; 232              fc_j = 2*dpj*1e-6*(0.6*9.8*bin_num_dens_Fe(j)*pi)^0.5;             fatigue_collision_Fe(i) = fatigue_collision_Fe(i)+...                 sqrt(fc_i*fc_j)*collision_factor;         end         E_loss_total = mi*mj/(2*(mi+mj))*(1-COR^2)*(u_pi-u_pj)^2;         E_loss = E_loss_total/2;         % as long as one party of the two particles in a collision is         % from 0-63um this collision causes no attrition         if i==1 || j==1             collision_num = 0;         else             fc_i = 2*dpi*1e-6*(0.6*9.8*bin_num_dens_Fe(i)*pi)^0.5;             fc_j = 2*dpj*1e-6*(0.6*9.8*bin_num_dens_Fe(j)*pi)^0.5;             collision_num = sqrt(fc_i*fc_j)*dt*collision_factor;         end         %different impact velocity  collision         %typical attrition         if E_loss >= max(E_b_Fe(i),E_b_Fe(j))             %both fragmentation             if i~=1 && j~=1                 %no breakage for 0-63um, otherwise:                 V_frag_i = (dpi*1e-6)^3*pi/6*collision_num;                 mass_trans_i1 = vol_species(i,1)*compressionPSD.iron(:,i-1)/... 233                       100/sum(vol_species(i,1:2))*V_frag_i*solid_density(1);                 mass_trans_i2 = vol_species(i,2)*compressionPSD.ironoxide(:,i-1)/...                      100/sum(vol_species(i,1:2))*V_frag_i*solid_density(2);                 mass_change(i,:)=mass_change(i,:)-[sum(mass_trans_i1),...                      sum(mass_trans_i2),0,0];                 mass_change(:,:)=mass_change(:,:)+[mass_trans_i1,...                      mass_trans_i2,zeros(6,1),zeros(6,1)];             end             if i~=1 && j~=1                 %no breakage for 0-63um, otherwise                 V_frag_j = (dpj*1e-6)^3*pi/6*collision_num;                 mass_trans_j1 = vol_species(j,1)*compressionPSD.iron(:,j-1)/...                      100/sum(vol_species(j,1:2))*V_frag_j*solid_density(1);                 mass_trans_j2 = vol_species(j,2)*compressionPSD.ironoxide(:,j-1)/...                      100/sum(vol_species(j,1:2))*V_frag_j*solid_density(2);                 mass_change(j,:)=mass_change(j,:)-[sum(mass_trans_j1),...                      sum(mass_trans_j2),0,0];                 mass_change(:,:)=mass_change(:,:)+[mass_trans_j1,...                      mass_trans_j2,zeros(6,1),zeros(6,1)];             end         elseif E_loss < min(E_b_Fe(i),E_b_Fe(j))             %both abrasion             if i~=1 && j~=1 234                  % no abrasion when 0-63um particles are involved                 Ei = 1/2*mi*u_pi^2;                 Ej = 1/2*mj*u_pj^2;                 abr__frac_i = K_abr_Fe(i)*Ei*bin_number_Fe(i)*dt/...                     (Fc_Fe(i)*time/bin_area(i));                 abr__frac_j = K_abr_Fe(j)*Ej*bin_number_Fe(j)*dt/...                     (Fc_Fe(j)*time/bin_area(j));                 mass_trans_i = wtcomposition_0(i,1:2)*abr__frac_i;                 mass_trans_j = wtcomposition_0(j,1:2)*abr__frac_j;                 mass_change(i,:) = mass_change(i,:)-[mass_trans_i,0,0];                 mass_change(j,:) = mass_change(j,:)-[mass_trans_j,0,0];                 mass_change(1,:) = mass_change(1,:)+[mass_trans_i+...                     mass_trans_j,0,0];             end         elseif (E_loss >= E_b_Fe(i)) && (E_loss < E_b_Fe(j))             %fragmentation in i and abrasion in j             % no abrasion when 0-63um particles are involved             if i~=1 && j~=1                 Ej = 1/2*mj*u_pj^2;                 abr__frac_j = K_abr_Fe(j)*Ej*bin_number_Fe(j)*dt/...                     (Fc_Fe(j)*time/bin_area(j));                 mass_trans_j = wtcomposition_0(j,1:2)*abr__frac_j;                 mass_change(j,1:2) = mass_change(j,1:2)-mass_trans_j; 235                  mass_change(1,1:2) = mass_change(1,1:2)+mass_trans_j;             end             if i~=1 && j~=1                 %no breakage for 0-63um                 V_frag_i = (dpi*1e-6)^3*pi/6*collision_num;                 mass_trans_i1 = vol_species(i,1)*compressionPSD.iron(:,i-1)/...                      100/sum(vol_species(i,1:2))*V_frag_i*solid_density(1);                 mass_trans_i2 = vol_species(i,2)*compressionPSD.ironoxide(:,i-1)/...                      100/sum(vol_species(i,1:2))*V_frag_i*solid_density(2);                 mass_change(i,:)=mass_change(i,:)-[sum(mass_trans_i1),...                      sum(mass_trans_i2),0,0];                 mass_change(:,:)=mass_change(:,:)+[mass_trans_i1,...                      mass_trans_i2,zeros(6,1),zeros(6,1)];             end         else              %fragmentation in j and abrasion in i             if i~=1 && j~=1                 %no abrasion if 0-63 particles are involved                 Ei = 1/2*mi*u_pi^2;                 abr__frac_i = K_abr_Fe(i)*Ei*bin_number_Fe(i)*dt/...                     (Fc_Fe(i)*time/bin_area(i));                 mass_trans_i = wtcomposition_0(i,1:2)*abr__frac_i;                 mass_change(i,1:2) = mass_change(i,1:2)-mass_trans_i; 236                  mass_change(1,1:2) = mass_change(1,1:2)+mass_trans_i;             end             if i~=1 && j~=1                 %no breakage for 0-63um, otherwise                 V_frag_j = (dpj*1e-6)^3*pi/6*collision_num;                 mass_trans_j1 = vol_species(j,1)*compressionPSD.iron(:,j-1)/...                      100/sum(vol_species(j,1:2))*V_frag_j*solid_density(1);                 mass_trans_j2 = vol_species(j,2)*compressionPSD.ironoxide(:,j-1)/...                      100/sum(vol_species(j,1:2))*V_frag_j*solid_density(2);                 mass_change(j,:)=mass_change(j,:)-[sum(mass_trans_j1),...                      sum(mass_trans_j2),0,0];                 mass_change(:,:)=mass_change(:,:)+[mass_trans_j1,...                      mass_trans_j2,zeros(6,1),zeros(6,1)];             end         end     end end %% attrtion in this scenario 1: Ca-Ca collision % The probality of each case is associated with the volume fraction of each % phase: (Fe_frac+Ca_frac)^2=Fe_frac^2 + 2*Fe_frac*Ca_frac + Ca_frac^2 for i=1:6     for j=1:6         dpi = bin_meandiameter(i); 237          dpj = bin_meandiameter(j);         [u_pi,~] = impact_velocity(bin_density_Ca(i),rho_g,mu_g,dpi,u_orif);         [u_pj,~] = impact_velocity(bin_density_Ca(j),rho_g,mu_g,dpj,u_orif);         mi = (dpi*1e-6)^3*pi/6*bin_density_Ca(i);         mj = (dpj*1e-6)^3*pi/6*bin_density_Ca(j);         if j~=1             fc_i = 2*dpi*1e-6*(0.6*9.8*bin_num_dens_Ca(i)*pi)^0.5;             fc_j = 2*dpj*1e-6*(0.6*9.8*bin_num_dens_Ca(j)*pi)^0.5;             fatigue_collision_Ca(i) = fatigue_collision_Ca(i)+...                 sqrt(fc_i*fc_j)*collision_factor;         end         E_loss_total = mi*mj/(2*(mi+mj))*(1-COR^2)*(u_pi-u_pj)^2;         E_loss = E_loss_total/2;         % as long as one party of the two particles in a collision is         % from 0-63um this collision causes no attrition         if i==1 || j==1             collision_num = 0;         else             fc_i = 2*dpi*1e-6*(0.6*9.8*bin_num_dens_Ca(i)*pi)^0.5;             fc_j = 2*dpj*1e-6*(0.6*9.8*bin_num_dens_Ca(j)*pi)^0.5;             collision_num = sqrt(fc_i*fc_j)*dt*collision_factor;         end         %different impact velocity  collision 238          %typical attrition         if E_loss >= max(E_b_Ca(i),E_b_Ca(j))             %both fragmentation             if i~=1 && j~=1 %i particle                 %no breakage for 0-63um, otherwise:                 V_frag_i = (dpi*1e-6)^3*pi/6*collision_num;                 mass_trans_i3 = vol_species(i,3)*compressionPSD.limestone(:,i-1)/...                      100/sum(vol_species(i,3:4))*V_frag_i*solid_density(3);                 mass_trans_i4 = vol_species(i,4)*compressionPSD.lime(:,i-1)/...                      100/sum(vol_species(i,3:4))*V_frag_i*solid_density(4);                 mass_change(i,:)=mass_change(i,:)-[0,0,...                     sum(mass_trans_i3),sum(mass_trans_i4)];                 mass_change(:,:)=mass_change(:,:)+[zeros(6,1),...                     zeros(6,1),mass_trans_i3,mass_trans_i4];             end             if i~=1 && j~=1 %j particle                 %no breakage for 0-63um, otherwise                 V_frag_j = (dpj*1e-6)^3*pi/6*collision_num;                                 mass_trans_j3 = vol_species(j,3)*compressionPSD.limestone(:,j-1)/...                      100/sum(vol_species(j,3:4))*V_frag_j*solid_density(3);                 mass_trans_j4 = vol_species(j,4)*compressionPSD.lime(:,j-1)/...                      100/sum(vol_species(j,3:4))*V_frag_j*solid_density(4);                 mass_change(j,:)=mass_change(j,:)-[0,0,sum(mass_trans_j3),... 239                       sum(mass_trans_j4)];                 mass_change(:,:)=mass_change(:,:)+[zeros(6,1),zeros(6,1),...                      mass_trans_j3,mass_trans_j4];             end         elseif E_loss < min(E_b_Ca(i),E_b_Ca(j))             %both abrasion             if i~=1 && j~=1                 % no abrasion when 0-63um particles are involved                 Ei = 1/2*mi*u_pi^2;                 Ej = 1/2*mj*u_pj^2;                 abr__frac_i = K_abr_Ca(i)*Ei*bin_number_Ca(i)*dt/...                     (Fc_Ca(i)*time/bin_area(i));                 abr__frac_j = K_abr_Ca(j)*Ej*bin_number_Ca(j)*dt/...                     (Fc_Ca(j)*time/bin_area(j));                 mass_trans_i = wtcomposition_0(i,3:4)*abr__frac_i;                 mass_trans_j = wtcomposition_0(j,3:4)*abr__frac_j;                 mass_change(i,:) = mass_change(i,:)-[0,0,mass_trans_i];                 mass_change(j,:) = mass_change(j,:)-[0,0,mass_trans_j];                 mass_change(1,:) = mass_change(1,:)+[0,0,mass_trans_i+...                     mass_trans_j];             end         elseif (E_loss >= E_b_Ca(i)) && (E_loss < E_b_Ca(j))             %fragmentation in i and abrasion in j 240              if i~=1 && j~=1 % j particles                 % no abrasion when 0-63um particles are involved                 Ej = 1/2*mj*u_pj^2;                 abr__frac_j = K_abr_Ca(j)*Ej*bin_number_Ca(j)*dt/...                     (Fc_Ca(j)*time/bin_area(j));                 mass_trans_j = wtcomposition_0(j,3:4)*abr__frac_j;                 mass_change(j,3:4) = mass_change(j,3:4)-mass_trans_j;                 mass_change(1,3:4) = mass_change(1,3:4)+mass_trans_j;             end             if i~=1 && j~=1 %i patticles                 %no breakage for 0-63um                 V_frag_i = (dpi*1e-6)^3*pi/6*collision_num;                 mass_trans_i3 = vol_species(i,3)*compressionPSD.limestone(:,i-1)/...                      100/sum(vol_species(i,3:4))*V_frag_i*solid_density(3);                 mass_trans_i4 = vol_species(i,4)*compressionPSD.lime(:,i-1)/...                      100/sum(vol_species(i,3:4))*V_frag_i*solid_density(4);                 mass_change(i,:)=mass_change(i,:)-[0,0,...                     sum(mass_trans_i3),sum(mass_trans_i4)];                 mass_change(:,:)=mass_change(:,:)+[zeros(6,1),...                     zeros(6,1),mass_trans_i3,mass_trans_i4];             end         else              %fragmentation in j and abrasion in i 241              if i~=1 && j~=1 % i particles                 %no abrasion if 0-63 particles are involved                 Ei = 1/2*mi*u_pi^2;                 abr__frac_i = K_abr_Ca(i)*Ei*bin_number_Ca(i)*dt/...                     (Fc_Ca(i)*time/bin_area(i));                 mass_trans_i = wtcomposition_0(i,3:4)*abr__frac_i;                 mass_change(i,3:4) = mass_change(i,3:4)-mass_trans_i;                 mass_change(1,3:4) = mass_change(1,3:4)+mass_trans_i;             end             if i~=1 && j~=1 % j particles                 %no breakage for 0-63um, otherwise                 V_frag_j = (dpj*1e-6)^3*pi/6*collision_num;                 mass_trans_j3 = vol_species(j,3)*compressionPSD.limestone(:,j-1)/...                      100/sum(vol_species(j,3:4))*V_frag_j*solid_density(3);                 mass_trans_j4 = vol_species(j,4)*compressionPSD.lime(:,j-1)/...                      100/sum(vol_species(j,3:4))*V_frag_j*solid_density(4);                 mass_change(j,:)=mass_change(j,:)-[0,0,sum(mass_trans_j3),...                      sum(mass_trans_j4)];                 mass_change(:,:)=mass_change(:,:)+[zeros(6,1),zeros(6,1),...                      mass_trans_j3,mass_trans_j4];             end         end     end 242  end %% attrtion in this scenario 1: Fe-Ca collision % The probality of each case is associated with the volume fraction of each % phase: (Fe_frac+Ca_frac)^2=Fe_frac^2 + 2*Fe_frac*Ca_frac + Ca_frac^2 % Fe: i         Ca: j % Attrition rate will be multiply by 2 because i-j collision and j-i % collision are symmettrical (counting for Fe as j and Ca as i) for i=1:6     for j=1:6         dpi = bin_meandiameter(i);         dpj = bin_meandiameter(j);         [u_pi,~] = impact_velocity(bin_density_Fe(i),rho_g,mu_g,dpi,u_orif);         [u_pj,~] = impact_velocity(bin_density_Ca(j),rho_g,mu_g,dpj,u_orif);         mi = (dpi*1e-6)^3*pi/6*bin_density_Fe(i);         mj = (dpj*1e-6)^3*pi/6*bin_density_Ca(j);         if j~=1             fc_i = 2*dpi*1e-6*(0.6*9.8*bin_num_dens_Fe(i)*pi)^0.5;             fc_j = 2*dpj*1e-6*(0.6*9.8*bin_num_dens_Ca(j)*pi)^0.5;             Fc_ij = sqrt(fc_i*fc_j)*collision_factor;             fatigue_collision_Fe(i) = fatigue_collision_Fe(i)+Fc_ij;             fatigue_collision_Ca(i) = fatigue_collision_Ca(i)+Fc_ij;         end         E_loss_total = mi*mj/(2*(mi+mj))*(1-COR^2)*(u_pi-u_pj)^2; 243          E_loss = E_loss_total/2;         % as long as one party of the two particles in a collision is         % from 0-63um this collision causes no attrition         if i==1 || j==1             collision_num = 0;         else             fc_i = 2*dpi*1e-6*(0.6*9.8*bin_num_dens_Fe(i)*pi)^0.5;             fc_j = 2*dpj*1e-6*(0.6*9.8*bin_num_dens_Ca(j)*pi)^0.5;             collision_num = sqrt(fc_i*fc_j)*dt*collision_factor;         end         %different impact velocity  collision         %typical attrition         if E_loss >= max(E_b_Fe(i),E_b_Ca(j))             %both fragmentation             if i~=1 && j~=1 %i particle (Fe)                 %no breakage for 0-63um, otherwise:                 V_frag_i = (dpi*1e-6)^3*pi/6*collision_num;                 mass_trans_i1 = vol_species(i,1)*compressionPSD.iron(:,i-1)/...                      100/sum(vol_species(i,1:2))*V_frag_i*solid_density(1);                 mass_trans_i2 = vol_species(i,2)*compressionPSD.ironoxide(:,i-1)/...                      100/sum(vol_species(i,1:2))*V_frag_i*solid_density(2);                 mass_change(i,:)=mass_change(i,:)-[sum(mass_trans_i1),...                      sum(mass_trans_i2),0,0]*2; 244                  mass_change(:,:)=mass_change(:,:)+[mass_trans_i1,...                      mass_trans_i2,zeros(6,1),zeros(6,1)]*2;             end             if i~=1 && j~=1 %j particle (Ca)                 %no breakage for 0-63um, otherwise                 V_frag_j = (dpj*1e-6)^3*pi/6*collision_num;                                 mass_trans_j3 = vol_species(j,3)*compressionPSD.limestone(:,j-1)/...                      100/sum(vol_species(j,3:4))*V_frag_j*solid_density(3);                 mass_trans_j4 = vol_species(j,4)*compressionPSD.lime(:,j-1)/...                      100/sum(vol_species(j,3:4))*V_frag_j*solid_density(4);                 mass_change(j,:)=mass_change(j,:)-[0,0,sum(mass_trans_j3),...                      sum(mass_trans_j4)]*2;                 mass_change(:,:)=mass_change(:,:)+[zeros(6,1),zeros(6,1),...                      mass_trans_j3,mass_trans_j4]*2;             end         elseif E_loss < min(E_b_Fe(i),E_b_Ca(j))             %both abrasion             if i~=1 && j~=1                 % no abrasion when 0-63um particles are involved                 Ei = 1/2*mi*u_pi^2;                 Ej = 1/2*mj*u_pj^2;                 abr__frac_i = K_abr_Fe(i)*Ei*bin_number_Fe(i)*dt/...                     (Fc_Fe(i)*time/bin_area(i))*2; 245                  abr__frac_j = K_abr_Ca(j)*Ej*bin_number_Ca(j)*dt/...                     (Fc_Ca(j)*time/bin_area(j))*2;                 mass_trans_i = wtcomposition_0(i,1:2)*abr__frac_i;                 mass_trans_j = wtcomposition_0(j,3:4)*abr__frac_j;                 mass_change(i,:) = mass_change(i,:)-[mass_trans_i,0,0];                 mass_change(j,:) = mass_change(j,:)-[0,0,mass_trans_j];                 mass_change(1,:) = mass_change(1,:)+[mass_trans_i,...                     mass_trans_j];             end         elseif (E_loss >= E_b_Fe(i)) && (E_loss < E_b_Ca(j))             %fragmentation in i and abrasion in j             % no abrasion when 0-63um particles are involved             if i~=1 && j~=1 % j particles abrasion (Ca)                 Ej = 1/2*mj*u_pj^2;                 abr__frac_j = K_abr_Ca(j)*Ej*bin_number_Ca(j)*dt/...                     (Fc_Ca(j)*time/bin_area(j))*2;                 mass_trans_j = wtcomposition_0(j,3:4)*abr__frac_j;                 mass_change(j,3:4) = mass_change(j,3:4)-mass_trans_j;                 mass_change(1,3:4) = mass_change(1,3:4)+mass_trans_j;             end             if i~=1 && j~=1 % i patticles fragmentation (Fe)                 %no breakage for 0-63um                 V_frag_i = (dpi*1e-6)^3*pi/6*collision_num; 246                  mass_trans_i1 = vol_species(i,1)*compressionPSD.iron(:,i-1)/...                      100/sum(vol_species(i,1:2))*V_frag_i*solid_density(1);                 mass_trans_i2 = vol_species(i,2)*compressionPSD.ironoxide(:,i-1)/...                      100/sum(vol_species(i,1:2))*V_frag_i*solid_density(2);                 mass_change(i,:)=mass_change(i,:)-[sum(mass_trans_i1),...                      sum(mass_trans_i2),0,0]*2;                 mass_change(:,:)=mass_change(:,:)+[mass_trans_i1,...                      mass_trans_i2,zeros(6,1),zeros(6,1)]*2;             end         else              %fragmentation in j and abrasion in i             if i~=1 && j~=1 % i patticles abrasion (Fe)                 %no abrasion if 0-63 particles are involved                 Ei = 1/2*mi*u_pi^2;                 abr__frac_i = K_abr_Fe(i)*Ei*bin_number_Fe(i)*dt/...                     (Fc_Fe(i)*time/bin_area(i))*2;                 mass_trans_i = wtcomposition_0(i,1:2)*abr__frac_i;                 mass_change(i,1:2) = mass_change(i,1:2)-mass_trans_i;                 mass_change(1,1:2) = mass_change(1,1:2)+mass_trans_i;             end             if i~=1 && j~=1 % j particles fragmentation (Ca)                 %no breakage for 0-63um, otherwise                 V_frag_j = (dpj*1e-6)^3*pi/6*collision_num; 247                  mass_trans_j3 = vol_species(j,3)*compressionPSD.limestone(:,j-1)/...                      100/sum(vol_species(j,3:4))*V_frag_j*solid_density(3);                 mass_trans_j4 = vol_species(j,4)*compressionPSD.lime(:,j-1)/...                      100/sum(vol_species(j,3:4))*V_frag_j*solid_density(4);                 mass_change(j,:)=mass_change(j,:)-[0,0,sum(mass_trans_j3),...                      sum(mass_trans_j4)]*2;                 mass_change(:,:)=mass_change(:,:)+[zeros(6,1),zeros(6,1),...                      mass_trans_j3,mass_trans_j4]*2;             end         end     end end %% sum up wtcomposition_1 = wtcomposition_0+mass_change; %reduce specie_breakage_energy due to fatigue  %E_b=E_b0*fatigue^(-3*collision_frequency*dt) %Fc=Fc0*fatigue^(-1.5*collision_frequency*dt) specie_breakage_energy_Fe = specie_breakage_energy(:,1:2).*(fatigue_Fe.^...     (-3*fatigue_collision_Fe*dt)); specie_breakage_energy_Ca = specie_breakage_energy(:,3:4).*(fatigue_Ca.^...     (-3*fatigue_collision_Ca*dt)); specie_breakage_energy = [specie_breakage_energy_Fe,...     specie_breakage_energy_Ca]; 248  % specie_breakage_energy(2:end,:) specie_breakage_force_Fe = specie_breakage_force(:,1:2).*(fatigue_Fe.^...     (-1.5*fatigue_collision_Fe*dt)); specie_breakage_force_Ca = specie_breakage_force(:,3:4).*(fatigue_Ca.^...     (-1.5*fatigue_collision_Ca*dt)); specie_breakage_force = [specie_breakage_force_Fe,...     specie_breakage_force_Ca]; % specie_breakage_force(2:end,:) error_flag = 0; end end     249  Appendix I  Engineering drawings of proposed impinging jet unit: to be constructed and tested in future work The building air with up to 200 LPM flow through two acceleration flow pipes, respectively. Particles up to 50 g will be loaded to each particle feeder. Those particle feeders and acceleration pipes are designed to be heated up to 800°C. When those parts are heated up, the valves connected to particle feeders will be opened and particles will flow through the pipe by gravitational force. Particles flowing through the pipe will collide each other in the middle of particle collision column. After the collision, particles will be gathered in the dust collector. The dust collector will be cleaned-up after each test. Each test will be done in few seconds, ideally. Details of engineering drawings for the construction of impinging jet unit are provided in this appendix. All the units are in millimeters.    250  Particle collision column60°Bag filterAcceleration pipe 230°Particle velocity probeParticle feederThermocoupleParticle velocity probeBuildingairFlowmeterFlowmeterAcceleration pipe 1Cyclone and dust collectorTo ventilation systemHeaterHeated and insulated to maintain gas stream above 700°C 251   252   253   254   255   256   257   258   259   260   

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