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Fluidized bed roasting of zinc sulfide concentrate : factors affecting the particle size distribution Constantineau, Jean Pierre 2004

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FLUIDIZED BED ROASTING OF ZINC SULFIDE CONCENTRATE FACTORS AFFECTING THE PARTICLE SIZE DISTRIBUTION by J E A N P I E R R E C O N S T A N T I N E A U B . E n g . (Genie des Mater iaux) Ecole Polytechnique de Mont rea l , 1996 M A . S c . (Metals and Mater ia ls Engineering) Univers i ty of B r i t i s h C o l u m b i a , 1999 A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F D O C T O R O F P H I L O S O P H Y in T H E F A C U L T Y O F G R A D U A T E S T U D I E S Department of Chemica l and Biological Engineer ing We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A M a r c h 2004 © Jean Pierre Constantineau, 2004 Abstract An experimental programme was established to study the effect of process parameters on the agglomeration behaviour of particles within a fluidized bed zinc concentrate roaster. A 102 mm internal diameter pilot scale roaster was designed, constructed and commissioned. Tests were then conducted with two industrial zinc concentrates at different temperatures (875-975C), superficial gas velocities (0.25-0.5 m/s), oxygen enrichments (inlet oxygen concentration: 21-30 vol%), stoichiometric excess oxygen (0-80%), initial inert bed materials (silica and alumina) and average bed particle sizes (81-223/im). With the exception of one experiment, all experiments were carried out with a zinc concentrate containing 53-54 wt% Zn, 30.5-31 wt% S, 4.5 wt% Fe, 3.5 wt% Pb, 0.34 wt% Cd, 0.145 wt% Cu, and 1.5 wt% S O 4 / S , with 80% of particles smaller than 24 pm. One experiment tested a different zinc concentrate, containing 51 wt% Zn, 30 wt% S, 8.1 wt% Fe, 4.7 wt% Pb, 0.14 wt% Cd, 0.05 wt% Cu, 1.5 wt% S O 4 / S , with 80% of particles smaller than 33 pm. The experimental results indicated that the temperature and excess oxygen had the greatest effect, followed by bed material, its size distribution and the superficial gas velocity. Agglom-eration increased when excess oxygen approached 0%. Lead, present in small proportion in the concentrate (3.5 wt%Pb), was observed to segregate to the larger bed particles. Lead sulfide volatilized from the zinc concentrate and deposited as a lead oxide/sulfate melt onto inert bed particles which caused fine particles to stick to the surface of larger particles. The lead concen-tration in the agglomerated particles suggested that the agglomeration mechanism, similar to the coating mechanism, relies on the transport of lead species from reacting particles to inert particles. The generalized slugging-bubbling fluidized bed reactor model (GSBM) handled seamlessly the transition from bubbling to slugging fluidization, using probabilistic averaging. The ratio of the bubble diameter to the column diameter was employed to correlate the probability of each of these fluidization flow regimes. The generalized fluidized bed reactor model was coupled to a solids reaction model and used to evaluate the effect of roasting parameters on the oxygen concentration in contact with the particles. Modelling of the fluidized bed under industrial (bubbling) and laboratory (slugging) conditions indicated that the effect of various parameters on the particle-averaged oxygen concentration depended greatly on the reactor in question (industrial vs laboratory). For the laboratory roaster, the effect of particle size was negligible, while the effect of excess oxygen was significant. For the industrial roaster, the effect of excess oxygen depended on the average particle size. For a relatively large average bed particle size (150 /um), the effect of excess oxygen was limited. For a small average bed particle size (65 ^m), the effect of excess oxygen was large, comparable to that in the laboratory roaster. 11 Table of Contents Abstract ii Table of Contents iii List of Tables vii List of Figures viii Nomenclature xiv Acknowledgements xx Chapter 1. Introduction 1 1.1 Elec t ro ly t ic zinc product ion 2 1.1.1 Objectives of roasting 4 1.2 Roast ing and its history 5 1.2.1 Roast ing prior to the electrolytic zinc process 6 1.2.2 Roas t ing for the zinc electrolytic process 6 1.2.3 F la sh or suspension roasting 8 1.2.4 Introduct ion of fluidized bed roasting 9 1.2.5 New roasters 14 1.3 Br ie f in t roduct ion to fluidized beds 14 1.4 Review of operating knowledge 15 1.4.1 Feed: Zinc concentrate 16 1.4.2 Feed: Gases 17 1.4.3 Produc t : Zinc calcine 17 1.4.4 Cont ro l l ing bed particle size 19 1.4.5 Agglomerat ion in industr ia l fluidized bed roasters 20 1.4.6 Concentrate moisture content and concentrate agglomeration 22 1.4.7 Low-melt ing-point phases dur ing roasting 23 1.5 Fundamentals of agglomeration in fluidized beds 24 1.6 Agglomerat ion in other fluidized bed systems 25 1.7 Research objectives 28 1.8 Thesis outline 28 Chapter 2. Thermodynamics and Kinetics of Roasting 30 2.1 Zinc 30 2.1.1 Thermodynamics 30 2.1.2 Kine t ics of zinc sulfide oxidat ion 35 2.1.3 F lu id i zed bed experimental studies 47 2.2 Iron .• 47 2.3 Lead .' 51 2.4 C a d m i u m 55 i i i Table of Contents 2.5 Copper 57 2.6 Water 59 2.7 Effect of roasting conditions on stable phases 60 2.8 Gas phase reactions 65 2.9 Low-melt ing-point phases dur ing roasting 69 2.9.1 Phase diagrams - product type 70 2.9.2 Phase diagrams - reactant type 71 2.9.3 Phase diagrams - reacting type 78 2.10 Conclusions and recommendations 81 Chapter 3. Experimental Methods 83 3.1 Exper imenta l pilot plant 83 3.2 Descr ipt ion of materials 87 3.2.1 Zinc concentrates 87 3.2.2 B e d material: s i l ica sand and a lumina 89 3.2.3 Gases 92 3.3 Roast ing experiments: Exper imenta l conditions 92 3.3.1 Exper imenta l program 92 3.3.2 Opera t ing procedure 93 3.4 Sintering tests 96 3.5 Analys is of solid products 96 3.5.1 Chemica l analyses 97 3.5.2 Scanning electron microscopy and X - r a y diffraction 97 Chapter 4. Experimental Results 99 4.1 Evo lu t ion of bed particle size d is t r ibut ion 100 4.2 Rate of bed mass increase 101 4.3 Assays and mass balances 103 4.3.1 Conversion and sulfur balance 105 4.3.2 Base cases 107 4.3.3 Effect of superficial gas velocity 120 4.3.4 Effect of temperature 125 4.3.5 Effect of inlet oxygen concentration 134 4.3.6 Effect of excess oxygen 134 4.3.7 Effect of bed material and size 152 4.4 Gas and solid conversions 161 4.5 Sintering test for zinc concentrate 164 4.6 G r o w t h mechanism i n the laboratory roaster 166 4.7 Agglomerat ion mechanism i n the laboratory roaster 168 Chapter 5. Model Development 170 5.1 Steady-state fluidized bed reactor model: Gas reaction 171 5.1.1 Phase balances 171 5.1.2 Gas mole balances for H- and L-phases 173 5.1.3 Superficial gas velocities and phase volume fractions 175 5.1.4 Expanded bed height 176 iv TabJe of Contents 5.1.5 Gas conversion and average gas compositions 176 5.1.6 M i n i m u m fluidization velocity 177 5.1.7 B u b b l i n g fluidized bed 178 5.1.8 Slugging fluidized bed 180 5.1.9 Trans i t ion from bubbl ing to slugging 182 5.2 Steady-state fluidized bed reactor model: React ion of solids 188 5.2.1 M i x i n g of solids wi th in the fluidized bed 189 5.2.2 Sol id residence times 191 5.2.3 Single-particle reaction model 193 5.2.4 Conversion of solids 199 5.3 Solut ion method 200 Chapter 6. Modelling Results 203 6.1 Unsteady-state single particle reaction 204 6.1.1 M o d e l parameters 204 6.1.2 T i m e for complete reaction 206 6.1.3 Par t ic le temperatures 206 6.1.4 Gas concentrations 209 6.1.5 Effectiveness factors 212 6.2 Generalized slugging-bubbling model ( G S B M ) 215 6.2.1 Compar ison w i t h previous models 215 6.2.2 Effect of effective gas reaction rate constant 219 6.2.3 Effect of reactor diameter 220 6.3 F lu id i zed bed roaster model 225 6.3.1 M o d e l parameters 225 6.3.2 F i t of laboratory experiments 227 6.3.3 Roaster sensitivity analysis 231 6.3.4 Model-based predominance-like diagrams 255 6.4 Discussion of key coating and agglomeration results 258 6.5 Implications for the industr ia l process 261 6.5.1 Effect of uneven spatial d is t r ibut ion of feed mater ial 262 6.5.2 M e a n bed particle size too large 262 6.5.3 M e a n bed particle size too smal l 263 6.5.4 Recommendations w i th respect to indust r ia l roasting 264 Chapter 7. Conclusions and Recommendations 266 7.1 Ma jo r contributions 266 7.2 K e y conclusions 267 7.3 Secondary conclusions 268 7.4 Recommended future work 269 7.5 Review of objectives 273 Bibliography 276 Appendix A . Instrument Calibration 293 A . l Thermocouples 293 v Table of Contents A . 2 Gas flowmeters (rotameters) 293 A.2 .1 Development of general rotameter equation 294 A . 2.2 Rotameter cal ibrat ion fit 295 A . 3 Pressure transducers 295 A . 4 Solids feedrate 296 A . 5 Solids mass flowmeter 299 Appendix B. Laboratory Roaster Procedures 300 B . l Exper imenta l run 300 B . l . l Star tup 300 B.1.2 Feeder startup 301 B.1.3 Feeder refill : 301 B . l . 4 Sol id sampling - B e d samples 301 B . l . 5 Sol id sampling - Carryover samples 302 B . l . 6 Gas sampling 302 B . l . 7 Scrubber switchover (To be done every hour) 303 B . l . 8 Shutdown 303 B . l .9 Emergency shutdown 303 B.2 Disassembly and cleaning 303 B . 3 Reassembly 306 Appendix C. Data Acquisition Software 307 C l D a t a acquisit ion 307 C . 2 Database 307 C.3 Thermocouples 308 C.4 Pressure transducers 308 C.5 Oxygen sensors 308 C.6 Gas analyzer 308 C.7 Controllers 308 C . 7.1 Temperature Controllers 308 C.7.2 Feeder Control ler 309 C.8 Solenoid Valves 309 Appendix D. Experimental Apparatus Schematics 310 Appendix E. Sulfur Dioxide Scrubbers 320 E . l Overa l l scrubbing reactions 320 E.2 Strength of the caustic solution 321 E.2.1 Solubili t ies of the various compounds 321 E.2.2 Solubili t ies expressed as caustic concentration 321 E . 3 Scrubbing efficiency 322 Appendix F. Detailed Experimental Results 324 F . l Assay from independent laboratory 324 v i List of Tables 1.1 Types of fluidized bed roasters used in the zinc industry 11 1.2 Publ ished composi t ion of some zinc sulfide concentrates and pure zinc sulfide 16 2.1 Theoret ical density and molar volume of zinc species 31 2.2 Summary of zinc sulfide oxidat ion kinetic studies 38 2.3 Details of experimental and pilot-scale roasters 48 2.4 M e l t i n g temperature of various phases 80 3.1 Weight composi t ion of zinc concentrates 87 3.2 Part ic le size d is t r ibut ion of zinc concentrates 90 3.3 Weight composi t ion of in i t i a l bed materials 90 3.4 Part ic le size d is t r ibut ion of in i t i a l bed materials 91 3.5 Compos i t ion of gases 92 3.6 Range of experimental variables 94 3.7 Summary of experimental conditions for each experiment 94 3.8 Methods used for chemical analysis of solid samples 97 4.1 Correspondence between run numbers and parameters studied 100 4.2 Summary of total masses of samples used for overall mass balance 105 4.3 Results of overall mass balance 106 4.4 X - r a y spectroscopy analysis of particle coatings obtained after roasting at 975°C . . . . 130 4.5 Overal l propor t ion of carryover as a function of excess oxygen, inlet oxygen concen-trat ion and in i t i a l bed particle size 136 5.1 Volume and gas flow balances 173 5.2 Correlations for bubble sizes 179 5.3 Values of the surface integral (I) for various slug length to diameter rat io (L/D) . . . . 182 5.4 Summary of equations describing the t ransi t ion from bubbl ing to slugging fluidization 189 5.5 Summary of the bubbl ing, slugging and generalized model parameters 190 6.1 Summary of single particle model parameters and their values 205 6.2 M o d e l parameters used to compare the generalized bubbl ing slugging model to the earlier slugging and bubbl ing models 216 6.3 Summary of the model parameters and their values 226 6.4 Summary of fitted model parameters and their values 229 6.5 Parameter ranges for sensitivity analysis 232 6.6 Characterist ic solids mix ing times for laboratory and indust r ia l roasters 249 A . l S tandard type K thermocouple po lynomia l coefficients 293 A . 2 Rotameter description 296 A . 3 Rotameter po lynomia l cal ibrat ion fits 297 A . 4 Pressure transducers - po lynomia l 297 F . l Assay of zinc concentrates 324 F .2 I C P Assay of zinc concentrates, sands and some experimental samples 325 v i i List of Figures 1.1 Improved electrolytic zinc process 4 1.2 Wedge roasting furnace 7 1.3 F lash roasting furnace 8 1.4 T y p i c a l fluidized bed roaster and associated streams 12 1.5 Gas-solid flow regimes 15 2.1 Z n - 0 2 - S 0 2 Predominance diagram at 850°C 34 2.2 Z n - 0 2-S O 2 Predominance diagram at 950°C 34 2.3 Z n - 0 2-S O 2 Predominance diagram at 1050°C 35 2.4 Intrinsic reaction rate of various kinetic studies 42 2.5 Representation of the grain model 45 2.6 F e O - F e 2 0 3 phase diagram • 49 2.7 F e - 0 2 - S 0 2 Predominance diagram at 850°C 49 2.8 F e - 0 2 - S 0 2 Predominance diagram at 950°C 50 2.9 F e - 0 2-S 0 2 Predominance diagram at 1050°C 50 2.10 P b - 0 2 - S 0 2 Predominance diagram at 850°C 52 2.11 P b - 0 2 - S 0 2 Predominance diagram at 950°C 53 2.12 P b - 0 2 - S 0 2 Predominance diagram at 1050°C 54 2.13 C d - 0 2-S O 2 Predominance diagram at 850°C 55 2.14 C d - 0 2-S O 2 Predominance diagram at 950°C 56 2.15 C d - 0 2-S O 2 Predominance diagram at 1050°C 56 2.16 C u - 0 2 - S 0 2 Predominance diagram at 850°C 57 2.17 C u - 0 2-S 0 2 Predominance diagram at 950°C 58 2.18 C u - 0 2 - S O 2 Predominance diagram at 1050°C 58 2.19 Excess oxygen - Temperature predominance diagram for gaseous feed of air (21% O2) 62 2.20 Gas concentrations for excess oxygen - temperature predominance d iagram for gaseous feed of air (21% 0 2 ) 63 2.21 Zinc and cadmium par t ia l pressures 67 2.22 Lead par t ia l pressures 68 2.23 Z n O - S i O 2 phase diagram 72 2.24 P b O - P b S 0 4 phase diagram 72 2.25 P b O - S i 0 2 phase diagram 73 2.26 P b O - A l 2 0 3 phase diagram 73 2.27 P b O - Z n O phase diagram 74 2.28 P b O - F e 2 0 3 phase diagram 74 2.29 F e S - Z n S phase diagram 75 2.30 P b S - Z n S phase diagram 75 2.31 Cu2S-ZnS phase diagram 76 2.32 F e S - P b S phase diagram 76 2.33 C u 2 S - P b S phase diagram : 77 2.34 Quaternary Z n S - F e S - P b S-Cu2S phase diagram 77 2.35 Region of the F e - S - 0 ternary phase diagram 79 2.36 FeO-FeS-Cu2S ternary phase diagram 79 v i i i L i s t of Figures 3.1 Experimental apparatus 84 3.2 Particle size distribution of zinc concentrates 89 3.3 Particle size distribution of initial bed materials 91 4.1 Evolution of the average particle size for various experimental conditions 102 4.2 Rate of bed mass increase for various experimental conditions 104 4.3 Assays of bed and carryover samples, masses of feed, bed samples, carry-over and bed for run 10, base case 1 109 4.4 Variation in proportion of key elements based on mass balance for base cases 110 4.5 Assays of different bed particle size fractions for four base case runs I l l 4.6 Distribution of mass of key elements with bed particle size fractions for four base case runs 112 4.7 Comparison of assays of carryover of base cases 113 4.8 SEM micrograph for product particles of run 10, +40 mesh 115 4.9 SEM micrograph for product particles of run 10, +70 mesh 115 4.10 SEM micrograph for product particles of run 10, +140 mesh 116 4.11 SEM micrograph for product particles of run 10, +230 mesh 116 4.12 SEM micrograph for product particles of run 10, -230 mesh (pan) 117 4.13 SEM micrograph for product particles of run 10, -230 mesh (pan), image of agglom-erated particle : 117 4.14 SEM micrograph for product particles of run 10, +140 mesh, image of coated particle 118 4.15 SEM micrograph for product particles of run 10, carryover 118 4.16 SEM micrograph for product particles of run 10,. carryover, image of partially reacted particle 119 4.17 Variation in proportion of key elements based on mass balance for different superficial gas velocities 121 4.18 Effect of superficial gas velocity on assays for different bed particle size fractions. . . . 122 4.19 Effect of superficial gas velocity on distribution of mass of key elements with bed particle size fraction 123 4.20 Comparison of assays of carryover for different superficial gas velocities 124 4.21 Variation in proportion of key elements based on mass balance for different superficial temperatures 126 4.22 Effect of temperature on assays of different bed particle size fractions 127 4.23 Effect of temperature on distribution of mass of key elements with bed particle size fractions 128 4.24 Comparison of assays of carryover for different temperatures 129 4.25 SEM micrograph for product particles of run 16, +70 mesh 131 4.26 SEM micrograph for product particles of run 16, +70 mesh, image of particle coatingl31 4.27 SEM micrograph for product particles of run 16, +140 mesh 132 4.28 SEM micrograph for product particles of run 16, +230 mesh 132 4.29 SEM micrograph for product particles of run 16, -230 mesh (pan) 133 4.30 SEM micrograph for product particles of run 16, Carryover 133 4.31 Variation in proportion of key elements based on mass balance for different inlet oxygen concentrations 135 4.32 Effect of oxygen concentration on assays of different bed particle size fractions 136 ix List of Figures 4.33 Effect of oxygen concentration on dis t r ibut ion of mass of key elements w i t h bed particle size fraction 137 4.34 Compar ison of assays of carryover for different inlet oxygen concentrations 138 4.35 Var ia t ion i n propor t ion of key elements based on mass balance for different excess oxygen and 50 mesh si l ica sand 140 4.36 Effect of excess oxygen on assays for different bed particle size fractions w i t h 50 mesh si l ica sand 141 4.37 Effect of excess oxygen on dis t r ibut ion of mass of key elements w i t h bed particle size fraction for 50 mesh si l ica sand 142 4.38 Compar ison of carryover assays for different excess oxygen for 50 mesh si l ica s a n d . . . 143 4.39 Var ia t ion in proport ion of key elements based on mass balance for different excess oxygen and 125 mesh s i l ica sand 144 4.40 Effect of excess oxygen on assays of different bed particle size fractions for 125 mesh si l ica sand 145 4.41 Effect of excess oxygen on dis t r ibut ion of mass of key elements w i th bed part icle size fraction for 125 mesh si l ica sand 146 4.42 Compar ison of carryover assays for different excess oxygen for 125 mesh si l ica s a n d . . 147 4.43 Effect of excess oxygen and oxygen enrichment on assays of bed particle of different size fractions wi th 50 mesh si l ica sand 148 4.44 Effect of excess oxygen and oxygen enrichment on d is t r ibut ion of mass of key ele-ments w i th bed particle size for 50 mesh si l ica sand 149 4.45 Effect of excess oxygen and oxygen enrichment on assays of different bed particle sizes for 125 mesh si l ica sand 150 4.46 Effect of excess oxygen and oxygen enrichment on d is t r ibut ion of mass of key ele-ments w i t h bed particle size for 125 mesh si l ica sand 151 4.47 Effect of bed material on assays for different bed particle size fractions 153 4.48 Effect of bed mater ial on dis t r ibut ion of mass of key elements w i t h bed particle size fraction 154 4.49 S E M micrograph for product particles of run 8, +16 mesh 155 4.50 S E M micrograph for product particles of run 8, +40 mesh 155 4.51 S E M micrograph for product particles of run 8, +70 mesh 156 4.52 S E M micrograph for product particles of run 8, +140 mesh 156 4.53 S E M micrograph for product particles of run 8, +230 mesh 157 4.54 S E M micrograph for product particles of run 8, -230 mesh (pan) 157 4.55 S E M micrograph for product particles of run 24, +40 mesh 158 4.56 S E M micrograph for product particles of run 24, +70 mesh 158 4.57 S E M micrograph for product particles of run 24, +140 mesh 159 4.58 S E M micrograph for product particles of run 24, +230 mesh 159 4.59 S E M micrograph for product particles of run 24, -230 mesh (pan) 160 4.60 S E M micrograph for product particles of run 24, carryover 160 4.61 Freeboard oxygen concentration as a function of feedrate 162 4.62 Solids conversion as a function of feedrate 162 4.63 In-bed oxygen sensor mean output as a function of feedrate 163 4.64 S E M micrograph for dried, unsintered, zinc concentrate 1(b), Secondary electrons image 165 x L i s t of Figures 4.65 S E M micrograph for dried, zinc concentrate 1(b) sintered for 1 hour at 950°C, Sec-ondary electrons image 165 5.1 Schematic of two-phase fluidized bed model 172 5.2 Bubble r ising velocity in water 185 5.3 Probab i l i ty of slugging 188 5.4 Concentrat ion and temperature profiles of a single reacting particle 195 6.1 Unsteady-state particle model: T i m e to complete reaction i n seconds 206 6.2 Unsteady-state particle model: Dimensionless temperatures 207 6.3 Unsteady-state particle model: Dimensionless gas concentrations. Kine t i c s from Fukunaka et al 210 6.4 Unsteady-state particle model: Dimensionless gas concentrations. F i t t e d Kine t i c s . . . 211 6.5 Unsteady-state particle model: Effectiveness factors 212 6.6 Unsteady-state particle model: Heat enhancement factors 214 6.7 Compar ison of the G S B M model to the Hovmand slugging model and to the Grace 2-phase and Orcu t t bubbl ing models 217 6.8 Compar ison of the conversions calculated using G S B M model and its l i m i t i n g models as a function of gas reaction rate constant for different bed diameters 218 6.9 Compar ison of the conversions calculated using G S B M model and its l im i t i ng cases as a function of bed diameter for different gas reaction rate constants 221 6.10 Compar ison of the variable model parameters and output for the G S B M model and its l imi t ing models as a function of the vertical posi t ion in the bed for kr = 0 . 1 s - 1 , D = 0.2 m 223 6.11 Compar ison of the variable model parameters and output for the G S B M model and its l imi t ing models as a function of the vert ical posi t ion i n the bed for kr = 1 0 s - 1 , D = 0.2 m , 224 6.12 Gas-solid reactor model fit of the experimental conversion data 229 6.13 Gas-solid reactor model predictions of the freeboard oxygen concentration 230 6.14 F i t t e d intr insic reaction rate compared w i t h those of various kinet ic studies 230 6.15 Effect of process parameters, varied one at a t ime, on the predicted particle-averaged oxygen concentrations in the laboratory roaster for the fitted kinetics and a 150 pm average bed particle size 233 6.16 Effect of process parameters, varied one at a time, on the predicted particle-averaged oxygen concentrations i n the laboratory roaster for the Fukunaka et al. kinetics and a 150 fim average bed particle size 234 6.17 Effect of process parameters, varied one at a time, on the predicted particle-averaged oxygen concentrations i n the laboratory roaster for the fitted kinetics and a 65 pm average bed particle size 235 6.18 Effect of process parameters, varied one at a time, on the predicted particle-averaged oxygen concentrations in the laboratory roaster for the Fukunaka et al. kinetics and a 65 fim average bed particle size 236 6.19 Effect of process parameters, varied one at a time, on the predicted particle-averaged oxygen concentrations i n the industr ia l roaster for the fitted kinetics and a 150 pm average bed particle size : 238 x i L i s t of Figures 6.20 Effect of process parameters, varied one at a time, on the predicted particle-averaged oxygen concentrations in the industr ia l roaster for the Fukunaka et al. kinetics and a 150 jj,m average bed particle size 239 6.21 Effect of process parameters, varied one at a time, on the predicted particle-averaged oxygen concentrations in the industr ia l roaster for the fitted kinetics and a 65 / im average bed particle size 240 6.22 Effect of process parameters, varied one at a t ime, on the predicted particle-averaged oxygen concentrations in the industr ia l roaster for the Fukunaka et al. kinetics and a 65 jLtm average bed particle size 241 6.23 Effect of process parameters varied one at a t ime, on the predicted reaction t ime of particles in the H-phase of the laboratory roaster for the fitted kinetics and a 150 /j,m average bed particle size 245 6.24 Effect of process parameters varied one at a time, on the predicted reaction t ime of particles in the H-phase of the laboratory roaster for the Fukunaka et al. kinetics and a 150 [im average bed particle size 246 6.25 Effect of process parameters varied one at a t ime, on the predicted reaction t ime of particles in the H-phase of the laboratory roaster for the fitted kinetics and a 65 / i m average bed particle size 247 6.26 Effect of process parameters varied one at a time, on the predicted reaction t ime of particles in the H-phase of the laboratory roaster for the Fukunaka et al. kinetics and a 65 /zm average bed particle size 248 6.27 Effect of process parameters varied one at a time, on the predicted reaction t ime of particles in the H-phase of the industr ia l roaster for the fitted kinetics and a 150 fim average bed particle size 251 6.28 Effect of process parameters varied one at a t ime, on the predicted reaction t ime of particles in the H-phase of the industr ia l roaster for the Fukunaka et al. kinetics and a 150 / i m average bed particle size 252 6.29 Effect of process parameters varied one at a time, on the predicted reaction t ime of particles i n the H-phase of the indust r ia l roaster for the fitted kinetics and a 65 /jm average bed particle size 253 6.30 Effect of process parameters varied one at a time, on the predicted reaction t ime of particles in the H-phase of the industr ia l roaster for the Fukunaka et al. kinetics and a 65 /j,m average bed particle size 254 6.31 Excess oxygen - Temperature G S B M model-based predominance-like d iagram for the experimental fluidized bed 256 6.32 Gas concentrations for excess oxygen - temperature G S B M model-based predominance-like diagram for the experimental fluidized bed 257 A . l Zinc concentrate automatic feedrate feedback control 298 D . l Exper imenta l apparatus - Reactor 311 D.2 Exper imenta l apparatus - F l u i d connections 312 D.3 Exper imenta l apparatus - Pressure connections 313 D.4 Exper imenta l apparatus - Power connections 314 D.5 Fabr icat ion drawing of preheater section 315 D.6 Fabricat ion drawing of roaster section 316 x i i List of Figures D.7 Fabricat ion drawing of solid samplers 317 D.8 Layout of dis tr ibutor plate holes 318 D . 9 Copper gaskets 319 E . l Solubi l i ty of compounds produced dur ing SO2 scrubbing using N a O H solutions 323 E .2 N a O H concentration to reach m a x i m u m solubil i ty of the compounds produced dur-ing SO2 scrubbing 323 x i i i Nomenclature L e t t e r s A B e d cross-sectional area [m 2] Ad Dis t r ibu tor area per orifice [m 2] ai Interphase mass transfer exchange area [ m _ 1 ] A r Archimedes number ( A r = df = E^sZ^Si^.) [_] Asp Dimensionless group (Asp = - CAofAc^fpc)(section 5.2.3) [-] CDei P roduc t of the total gas concentration (sum of al l gaseous species) times the gas diffusivity of i (section 5.2.3) [mol / (m s)] Cf / j M o l a r concentration of species i in H-phase [mol /m 3 ] d Particle-averaged molar concentration for species i i n entire bed [mol /m 3 ] Cijn Inlet molar concentration of species i [mol /m 3 ] Cji Concentrat ion of gaseous species i , j=c: core, o: bulk gas phase, s: surface (section 5.2.3) [mol / m 3 ] Cji Particle-averaged molar concentration for species i i n phase j [mol /m 3 ] Cj_,i M o l a r concentration of species i in L-phase [mol /m 3 ] Cpc Heat capacity of unreacted core (section 5.2.3) [ J / (kg K)] Cpe Volumetr ic heat capacity of product layer (section 5.2.3) [ J / ( m 3 K ) ] Cs Concentrat ion of solid reactant (section 5.2.3) [mol / m 3 ] CT To ta l gaseous molar concentration (CT = 7 ^ ) [mol /m 3 ] D Reactor diameter [m] DDQ Lower bound of bubbling-slugging transi t ion interval [-] DD\ Upper bound of bubbling-slugging transi t ion interval [-] De Effective bubble diameter [m] Defi In i t ia l effective bubble diameter [m] DeATo Effective gas diffusivity at temperature To for gaseous reactant A [m 2 /s] DeGTo Effective gas diffusivity at temperature To for gaseous product G [m 2 /s] De,oo M a x i m u m bubble diameter due to coalescence and growth [m] x iv Nomenclature De>max M a x i m u m effective bubble diameter [m] Dg Gas diffusivity [m 2 /s] dp Par t ic le surface to volume mean diameter [m] dpi Average diameter of each size fractions (Chapter 3) [m] dp* Dimensionless particle diameter (dp((p^Pv^2P^9^j ^ ) [-] Dradial R a d i a l diffusion coefficient of solids i n a fluidized bed [m 2 /s] dv Par t ic le volume mean diameter (Chapter 3) [m] E B e d expansion [m/m] Ea Ac t iva t ion energy [J/mol] Emax M a x i m u m slugging bed expansion [m/m] Excesso2 Stoichiometric excess of oxygen [-] / Solids mean residence t ime factor [-] Fcarryover Solids flowrate in carryover [kg/s] FFeed Solids flowrate in feed [kg/s] FHI M o l a r flowrate of species i in H-phase [mol/s] Ff{i,in Inlet molar flowrate of species i in H-phase [mol/s] FHT To ta l molar flowrate in H-phase [mol/s] Fu M o l a r flowrate of species i in L-phase [mol/s] Fhi,in Inlet molar flowrate of species i in L-phase [mol/s] FIT To ta l molar flowrate in L-phase [mol/s] Foverflow Solids flowrate in overflow [kg/s] Fr Froude number (Fr = ^ g ) [-] f s S lug shape factor [ m 3 / m 3 ] FT To ta l molar flowrate in reactor [mol/s] G Dimensionless group (G = - i y ^ p _ c ^ ° f / ) ) ( s e c t i o n 5.2.3) [-] g Accelerat ion due to gravity (9.81) [m/s 2 ] H Expanded bed height [m] x v Nomenclature hc Convective heat transfer coefficient (section 5.2.3) [ J / ( m 2 K s)] Hmf B e d height at m i n i m u m fluidization [m] hr Rad ia t iona l heat transfer coefficient (section 5.2.3) [ J / ( m 2 K 4 s)] / Slug surface integral (section 5.1.8) [-] J A x i a l solids flux due to bubbles [kg m - 2 s _ 1 ] ke Effective thermal conduct ivi ty of product layer (section 5.2.3) [ J / ( m s K)] kin Interphase mass transfer coefficient [m/s] km Gas-part icle mass transfer coefficient [m/s] kr Gas reaction rate constant [s _ 1 ] k° Pre-exponential constant for reaction rate constant (section 5.2.3) [m/s (depends on reaction orders)] ks(Tc) React ion rate constant at temperature Tc (section 5.2.3) [m/s (depends on reac-t ion orders)] L S lug length (section 5.1.8) [m] m React ion order w i t h respect to solid reactant S (section 5.2.3) [-] Mbed B e d mass [kg] ^Concentrate Mass of concentrate equivalent to one mole of zinc sulfide [g concentrate / mol ZnS] Mzns M o l a r weight of zinc sulfide [g Z n S / mol ZnS] n React ion order w i t h respect to gaseous reactant A (section 5.2.3) [-] n o 2 Number of moles of oxygen [moles] N u c Modi f ied Nusselt number for convection ( N u c = Rhc/ke)(section 5.2.3) [-] N u r Modi f ied Nusselt number for radiat ion ( N u r = RhrT^/ke)(section 5.2.3) [-] n z n s Number of moles of zinc sulfide [moles] Pbubbiing P robab i l i ty of bubbl ing [-] Pslugging P robab i l i ty of slugging [-] Pstream Par t ic le size d is t r ibut ion function of stream [-] PT To ta l reactor pressure [Pa] R Gas constant, 8.314 [ J / (mol K)] x v i Nomenclature rA React ion rate of gas A (section 5.2.3) [ m o l / ( m 2 s)] rc Radius of core (section 5.2.3) [m] Hemf Reynolds number at m i n i m u m fluidization (Re=^[£) [-] J Rate of reaction of oxygen [mol m ~ 2 s - 1 ] Hp Par t ic le radius [m] r$ React ion rate of solid S (section 5.2.3) [ m o l / ( m 2 s)] Sh Modi f i ed Sherwood number (Sh = $^r) [-] T Reactor temperature [K] T S lug to slug distance (tail-to-nose) (section 5.1.8) [m] Tc Core temperature (section 5.2.3) [K] tcr T i m e for complete reaction of solid particle [s] T0 In i t ia l temperature (section 5.2.3) [K] tradial R a d i a l m i x i n g t ime (lateral m i x i n g time) [s] T$ Surface temperature (section 5.2.3) [K] ^turnover Turnover t ime (axial mix ing time) [s] Tw W a l l temperature (section 5.2.3) [K] U Reactor superficial gas velocity [m/s] Ui Bubb le rise velocity [m/s] Uboo Isolated bubble rise velocity [m/s] Uc Dimensionless core temperature (Uc = ^f)(section 5.2.3) [-] UH H-phase superficial gas velocity [m/s] UL L-phase superficial gas velocity [m/s] Umf Superficial gas velocity at m i n i m u m fluidization [m/s] Ums M i n i m u m slugging velocity [m/s] Us Dimensionless surface temperature (Us = | f ) ( sec t ion 5.2.3) [-] Us Slug velocity [m/s] Usoo Slug velocity of a single slug in a bed at m i n i m u m fluidizat ion [m/ U* Te rmina l velocity calculated for spherical particles of 2.7dp [m/s] x v i i Nomenclature ( p 2 \ 1 / 3 XJt* Dimensionless terminal velocity (Ut ( lp )g ) )H Uv V o i d (bubble or slug) rise velocity [m/s] Uvoo Free void (bubble or slug) velocity [m/s] Uw Dimensionless wal l temperature (Uw = ^ ) (section 5.2.3) [-] X Conversion of particle (1 - (%)3 = 1 - ^ ( s e c t i o n 5.2.3) [-] XAO M o l a r fraction in bulk gas phase for gaseous reactant A [-] X Average conversion of mono-sized particles [-] X Average conversion of a wide size d is t r ibut ion of particles [-] XQO M o l a r fraction in bulk gas phase for gaseous product G [-] Xi Conversion of component i [-] Xi Gas mole fraction (section 5.2.3) [-] Xi Mass fraction of each size fractions (Chapter 3) [-] Y Ra t io of volumetric flowrate of bubbles to the excess gas flowrate [-] z Ver t ica l posi t ion in bed [m] Greek Letters P Constant to account for change i n mass due to reaction [-] j3 Dimensionless group (p = CAoDcAkTeE~AH)R)(section 5.2.3) [-] Pd Fract ion of solids carried up by a bubble w i th in its drift [-] Pw Fract ion of solids carried up by a bubble w i th in its wake [-] AF02 Number of moles of oxygen reacted per unit t ime [moles/sec] L\v Difference i n gas stoichiometric coefficient due to reaction [-] Az F in i t e height i n bed (control volume) [m] emf B e d voidage at incipient f luidization [ m 3 / m 3 ] £fi H-phase gas volume fraction [ m 3 / m 3 ] €L L-phase gas volume fraction [ m 3 / m 3 ] Vs Effectiveness factor (section 5.2.3) [-] K E lu t r i a t i on velocity constant [ s _ 1 ] x v i i i Nomenclature [x Gas viscosity [Pa s] VA Stoichiometric coefficient of gas A (section 5.2.3) [-] vs Stoichiometric coefficient of solid S (section 5.2.3) [-] VQ Stoichiometric coefficient of gas G (section 5.2.3) [-] vi Stoichiometric coefficient for compound i [moles i / moles reaction] UJC Dimensionless core molar fraction of component i (cuc — ^ ) ( s e c t i o n 5.2.3) [-] LOS Dimensionless surface molar fraction of component i (UJS = ^f-)(section 5.2.3) [-] <f>H H-phase solids volume fraction [ m 3 / m 3 ] 4>r, L-phase solids volume fraction [ m 3 / m 3 ] 4>s Thie le modulus of solid particle (<f>a = - ^ ^ g " ^ " 1 ^ ) [-] ipH H-phase volume fraction [ m 3 / m 3 ] tpL L-phase volume fraction [ m 3 / m 3 ] AH Heat of reaction (section 5.2.3) [J/mol] pc Core density (section 5.2.3) [kg/m 3 ] pg Gas density [kg/m 3 ] pp Par t ic le density [kg/m 3 ] r Average residence t ime of solid particles in fluidized bed [s] 6 Dimensionless t ime {6 = fcs(ro)C^C™"1i/i?p)(section 5.2.3) [-] 6cr Dimensionless t ime for complete reaction of solid part icle [-] £ c Dimensionless posi t ion of core (£ c = ^ ) ( sec t ion 5.2.3) [-] x i x Acknowledgement s This thesis would not have been possible without the initial enquiries of Murray Brown of Teck Cominco. The project spawned from talks with Bob Kerby and Greg Richards, first at the 1998 Conference of Metallurgists in Calgary, followed by a visit in Trail, B.C., in September of the same year. The project materialized before I graduated from my Master's in Metals and Materials Engineering in April 1999. I wish to thank Teck Cominco for providing the opportunity to work as a co-op student at the Roaster/Acid plant during the period of September to December 1999. This work term allowed me to familiarize myself with the practical aspects of industrial fluidized bed roasting. My stay at the plant has been beneficial to this project due to the help of Karla Dick, Gordon Masuch, Mike McDowell and the plant personnel. I also wish to thank Teck Cominco Metals Ltd. for their financial contribution, for providing samples and for the chemical analysis of laboratory roaster samples. I am grateful to the Science Council of British Columbia for their direct support through a GREAT Scholarship. The completion of this project would not have been possible without the help of the technical staff of the department: Peter Roberts, Robert Carrasco, Graham Lebelt, Geoff Corbett, Doug Yuen, Alex Thng, Horace Lam and Qi Chen. Their expertise and experience makes the process of planning, building and modifying an experimental setup an enjoyable learning experience. I am grateful to my co-supervisors, John Grace, Jim Lim and Greg Richards, for numerous discussions, reading preliminary drafts of this thesis and presenting much useful feedback. I would also like to thank my many colleagues from the Fluidization Group. The group seminars and the many informal discussions on various aspects of fluidization have enriched my knowledge and understanding of this diversified and complex field. Finally, I express my gratitude to Sylvie Bouffard, for her love, understanding, and support during the long months of this project. xx Chapter 1 Introduction In the electrolytic process, often named the roast-leach-electrowin process, roasting of zinc sulfide concentrates is the most common first step in the manufacture of zinc. In the last two decades, direct leaching of zinc concentrates in autoclaves (pressure leaching) has been used successfully as an alternative to roasting. P r io r to the development of the electrolytic process, most, if not al l zinc was produced by retort dis t i l la t ion. Today, the electrolytic process accounts for 80% of zinc product ion w i t h the rest from pyrometal lurgical processes, such as the blast furnace, electrothermic and retort processes. P r io r to the electrolytic zinc process, zinc was produced for centuries by the dis t i l la t ion of a mixture of zinc oxide ore and coal in retorts of various designs [1]. A mix ture of zinc oxide and coal was heated above 1000°C in a coal-fired oven to produce zinc vapour, which was then condensed and collected. In 1738, W i l l i a m C h a m p i o n patented the process in Eng land , and by 1743, established a smelter in Br i s to l , U . K . [1]. B y combining oriental knowledge and western large-scale technology, he brought commercial zinc product ion to Europe . To overcome the shortage of calamine (zinc carbonate), the original source of zinc oxide, blende (zinc sulfide) was roasted to produce zinc oxide. In 1758, John C h a m p i o n , W i l l i a m ' s brother, patented the conversion of blende to zinc oxide by roasting in a coal-fired furnace. T h e C h a m -pion dis t i l la t ion process was used unt i l about 1851. Because the C h a m p i o n process involved cooling and wi thdrawing the crucible and the retort after each cycle, the process was labour-intensive and fuel-inefficient (24 tonnes of coal for each ton of zinc produced). T h e reader is referred elsewhere [2] for a more complete description of the early indust r ia l product ion of zinc. 1 Chapter 1. Introduction A r o u n d 1818, the development of the horizontal retort process in B e l g i u m significantly i m -proved the dis t i l la t ion process. P laced horizontal ly i n a furnace, retorts could be charged and discharged without cooling. T h e popular i ty of the process grew rapidly, and by 1880, annual world product ion was estimated to be more than 200 000 metric tonnes of zinc, most ly from Germany and Be lg ium [3]. In 1950, this process s t i l l produced as much as 50% of the zinc. Nowadays, however, the horizontal retort process has disappeared from N o r t h A m e r i c a [4], in favour of the electrolytic z inc process. T h e use of retorts for the product ion of z inc has been the subject of several publications, and w i l l not be discussed further herein. Dur ing the development of the electrolytic zinc process, roasting was already commonly used to produce the feed mater ial required for retort dis t i l la t ion. However, the electrolytic process imposes different requirements on roasting. To better understand the current requirements of the roasting process, the electrolytic zinc product ion process is presented in a somewhat chronological matter. T h e evolution of industr ia l roasters and the current f luidized bed roasting technology are then discussed. A brief in t roduct ion to fluidized beds and a review of the current operating knowledge follows. T h e chemistry, thermodynamics, and kinetics of roasting are reviewed in the following chapters. 1.1 Electrolytic zinc production The electrolytic product ion of zinc first described more than 100 years ago i n a 1883 patent by Leon Letrange [5] is the basis of the modern electrolytic process (Figure 1.1). After roasting the zinc concentrate, the calcine is generally leached in two stages: neutral leach and acid leach. In the neutral leach stage, calcine is added to neutralize the solut ion, while ferric i ron is precipitated as ferric hydroxide, a gelatinous substance that renders f i l t rat ion very difficult. Precipi ta t ion of i ron in the neutral stage is the first step in pur i fying the zinc sulfate solution. Impurities such as arsenic, antimony, and germanium are co-precipitated w i t h i ron. T h e solution from the neutral leach stage is sent to the purification circuit . Sol id residue from the neutral stage passes to the acid leach stage to dissolve the remaining zinc oxide. T h e residue from the acid leach stage contains precipitated i ron and any undissolved solids, inc luding incompletely 2 Chapter 1. Introduction roasted zinc sulfide, zinc ferrite (ZnOFe2C>3, a zinc-iron spinel produced during roasting), lead sulfate, and silica. Losses of zinc to zinc ferrite are discussed later. The impure zinc sulfate solution leaving the neutral leach stage is then purified. During purification, zinc dust is added in various stages to the solution to remove copper, cadmium, nickel, and cobalt. Depending on the impurities to be removed and the removal efficiency, as much as 5 to 10 % of the cathode zinc produced may be diverted from sales to the purification process. The purified solution is then sent to the electrolytic cells where zinc is deposited onto aluminum cathodes, and sulfuric acid is regenerated at the lead anodes. The depleted electrolyte, rich in sulfuric acid, is returned to the leaching step to process additional calcine. Cathodes are periodically removed from the cells to recover zinc by stripping (or peeling) the deposit from the aluminum cathodes. Because the sulfate concentration within the electrolyte solution is usually controlled to remain within bounds, a sulfate balance must be performed on the entire electrolytic process. Any sulfate entering the system as zinc sulfate must be balanced by sulfate exiting the system into the residues and as a bleed from the spent electrolyte. Depending on their configuration and operation, some plants require soluble sulfates to offset losses. Close control of the zinc sulfate in the zinc calcine is an important roaster operating parameter. The leach zinc recovery depends greatly on the ore and on the roasting conditions. Zinc recovery is higher for concentrates with lower iron content because zinc ferrite (ZnOFe203), a zinc-iron spinel, does not dissolve under mild acid conditions. However, hot acid solutions ensure zinc ferrite dissolution while, unfortunately, dissolving iron as well. Precipitation of the dissolved iron as ferric hydroxide was not technically attractive because of the gelatinous nature of ferric hydroxide precipitates. During the 1960s, breakthroughs in the research of hydrometallurgical options to process zinc ferrite led to several patents of three types: jarosite process, goethite process, and hematite process. Depending on the process chosen, zinc ferrite is leached in hot' acid while iron is precipitated as jarosite, MFe3(S04)2(OH)6 (where M is typically N a + , N H 4 + and K + ) , goethite (FeOOH) or hematite (Fe203). These crystalline precipitates are easily filterable. These 3 Chapter 1. Introduction Zinc Concentrate Roasting Air + 0 2 S0 2 Acid Plant Zinc Calcine Neutral Leaching Residue Iron Precipitation Purification Cd, Cu, Ni, Co Residue ZnS0 4 Solution Electrolysis Zinc Dust Hot Acid Leaching Iron Residue Sulfuric Acid H 2 S O 4 Solution Zinc Cathodes Melting and Casting Residue Zinc Ingots Figure 1.1: Improved electrolytic zinc process processes either treat the residue to recover the ferritic zinc as a separate stream from the electrolytic process, or precipitate iron in an intermediate step between the hot acid and neutral leach stages, as shown in Figure 1.1. These processes are described in more detail in references [6, 7, 8]. 1.1.1 Objectives of roasting Based on the requirements of the unit processes of the electrolytic zinc process, roasting must: Maximize the conversion of zinc sulfide. In the traditional process, zinc sulfide is not 4 Chapter 1. Introduction leached and ends up i n the leach residue. Its presence i n zinc calcine is unwanted. • M a x i m i z e the amount of soluble zinc. • M i n i m i z e the amount of zinc ferrite in the calcine. • Opt imize the amount of zinc sulfate in the product . Some sulfate is desirable in the calcine to compensate for sulfate losses dur ing leaching, purif icat ion, and electrowinning. • A t least match the calcine consumption rate of the leaching process. In order for the roasting process to compensate for unscheduled shutdowns, the roast ing process should be able to process zinc concentrate at a faster rate than calcine is consumed i n the leaching process. The second and th i rd objectives are complementary. The i r importance depends on the amount and type of i ron in the concentrate as well as the method used to extract z inc from zinc ferrite. For plants not recovering zinc contained in zinc ferrite, fulfilling these two objectives is cr i t ical to maximize zinc recovery. 1.2 Roasting and its history Because this thesis focuses on the roasting of zinc concentrates, other types of roasting, such as chloridizing or segregating roasting, are not described here. For more details on these, the reader may consult reviews [9, 10]. T h e roasting of sulfide ores has been practised for centuries. In 1546, in his book "De R e Meta l l i ca" Georgius Agr ico la presented different furnaces for roasting copper ores. Ores were roasted in stalls of about 2 by 3 meters. T h e produc t iv i ty of stall roasting was l imi ted (20 tons i n 10 days) and the process was very labour intensive. Heap roasting replaced stall roasting in large scale product ion plants. Layers of ore were alternately stacked wi th layers of wood to form a heap. T h e heap was then ignited. A heap, 15 m wide and 30 m long, could produce 1700 tonnes of sinter in about 100 days. Roas t ing methods next progressed from the pr imi t ive heap roasting to the hand-rabbled reverberatory furnaces such as the Delplace, and later to the mechanically-rabbled reverbatories such as the Hegeler k i l n and the R o p p furnace. A significant advance began w i t h the development of the circular 5 Chapter 1. Introduction multiple-hearth roaster. T h e evolution of mechanical roasters was reviewed recently [11]. T h e present discussion focuses on the zinc industry. 1.2.1 Roasting prior to the electrolytic zinc process P r i o r to the electrolytic zinc process, roasting of zinc sulfide produced the raw mater ia l required for the retort process. T h e 1906 book of Ingalls [12] and the 1922 book of Hofman [13], bo th on the metallurgy of zinc and cadmium, describe several furnaces used for the roasting of blende. The first roasters were hand-raked and typical ly consisted of a flat hearth heated by a firebox at one end. T h e ore was charged at the flue end and moved slowly down toward the firebox, where it was discharged through a drop hole in the hearth. T h e raking act ion exposed new surfaces to the atmosphere and accelerated the reactions. A number of mechanical roasters were developed before the success of the circular mult iple-hearth roaster, the prototype being the M c D o u g a l l roaster. T h e M c D o u g a l l roaster evolved into numerous types, such as the Wedge, Skinner and Herreshoff roasters, which ma in ly differed in their mode of maintenance and the mechanical action of the rabble arms. Figure 1.2 presents a Wedge roasting furnace where ore is fed onto the upper hearth, which, warmed by the heat generated in the roasting operation, serves to dry the concentrate. T h e rabbles are adjusted to gradual ly move the ore from the outer edge of the upper hearth toward the centre, and then through a drop hole into hearth 1. T h e rakes move the ore across the hearth to a slot near the periphery, through which it drops into hearth 2. Thus , i n a zig-zag fashion, the ore progresses through the furnace unt i l it drops into a car or conveyor beneath the lowest hearth. 1.2.2 Roasting for the zinc electrolytic process Mechanical roasters were developed in parallel to the electrolytic zinc process. T h e Anaconda Copper Company and the Consol idated M i n i n g and Smelt ing Company adopted the Wedge mechanical roaster in their new electrolytic zinc plants. 6 Chapter 1. Introduction OJ Furnace shell b Refractory lining 0 Rabble arm d Rabble blades e Central shaft / Air nutlet g Air inlet ft Supply air duct 1 Discharse air duct j Motor £ Bevel gears ( Drying hearth m Gas outlet 71 Arm holder o Calcine discharge P Man-hole 4 Inspection door (hinged) r Main bearing Figure 1.2: Wedge roasting furnace [14] It was noted at an early stage during the development of the electrolytic zinc process that the formation of zinc ferrite during roasting detrimentally affects the recovery of zinc during leaching. It was recognized that higher temperatures and longer reaction times increased the conversion to zinc ferrite [15]. While roasting for the retort process could be performed at high temperature with excellent productivity and zinc extraction, roasting for the electrolytic zinc process required roasting at a lower temperature to avoid zinc ferrite production. Choosing the roasting temperature requires balancing the production of zinc sulfate and zinc ferrite with the conversion of zinc sulfide. More recent studies [16, 17], using pure zinc oxide and iron oxide have shown that increased contact between the oxides increases the ferrite production rate. This explains why marmatitic zinc concentrates produces large quantities of zinc ferrites. Marmatite is a zinc sulfide that contains a significant amount of iron dissolved within the zinc sulfide matrix. 7 Chapter 1. Introduction 1.2.3 Flash or suspension roasting During the 1920s and 1930s, a significant breakthrough in the roasting of sulfide ores occurred at the Consolidated Mining and Smelting Company of Canada. Engineers developed a plant to effectively recover and utilize sulfur dioxide off-gas in a contact acid plant. This plant requires a sulfur dioxide concentration higher than that can be obtained from the Wedge roaster. Inspired by pulverized coal combustion, they modified the existing Wedge roaster by removing all the hearths except for the top and bottom ones and installed a concentrate burner. The productivity improved so dramatically that sufficient roasting capacity was available after modifying 8 of the 25 Wedge roasters. The remaining 17 unmodified roasters were then permanently shut down. a C o m b u s t i o n c h a m b e r b D r y i n g h e a r t h e C o l l e c t i n g h e a r t h d A i r - c o o l e d r o t a t i n g s h a f t e W e t c o n c e n t r a t e h o p p e r & f e e d e r / D r i e d c o n c e n t r a t e d i s c h a r g e g B a l l m i l l h C o m b u s t i o n a i r f a n t B u r n e r j C a l c i n e d i s c h a r g e k G a s o u t l e t t o a c i d p l a n t Figure 1.3: Flash roasting furnace [14] Figure 1.3 presents the original flash roasting furnace of the Consolidated Mining and Smelting Company of Canada. Moist zinc concentrate entered the roaster on the top hearth where the concentrate dried. After drying, the concentrate left the roaster and entered a ball mill where the lumps were pulverized. After grinding, the dried concentrate was fed into the combustion chamber through the burner. The concentrate heated up rapidly and reacted to form calcine and sulfur dioxide. The calcine fell onto the bottom of the combustion chamber where it was pushed by a rabble into a chute. A significant portion of the calcine was carried with the gas 8 Chapter 1. Introduction to the boiler and the solids collection system. A portion of the calcine could be returned to the bottom hearth of the roaster for further reaction with sulfur dioxide to produce additional zinc sulfate. The new roaster was so energy efficient that a waste-heat boiler could be installed to recover the heat from the effluent gases. The suspension roaster was the first roaster equipped with a waste-heat boiler. In 1937, the roasting productivity was further increased by enriching the combustion air with oxygen [18]. The flash roaster was later redesigned to eliminate the central shaft within the combustion chamber by relocating the drying hearth beneath the roasting hearth [18]. In comparison to the Wedge roaster, the suspension roaster had a greater capacity, better heat utilization and recovery, produced a rich SO2 gas and less zinc ferrite (because of shorter particle residence times). In view of these advantages, most plants in the electrolytic zinc and copper industries adopted the flash roaster. 1.2.4 I n t r o d u c t i o n o f fluidized b e d r o a s t i n g The fluidized bed technology was the next advance and is still the dominant roasting technology. Although Robinson patented the basis of a fluidized bed roaster in 1879 [19], it was not until the petrochemical industry mastered fluidized bed technology that it became attractive to the metallurgical industry. In 1944, Dorr-Oliver acquired the rights to Exxon's fluidization knowledge for applications outside the petroleum industry [20]. It developed the FluoSolids system for roasting of sulfide ores. In 1947, the first roaster was built in Ontario for roasting arsenopyrite to produce a calcine suitable for gold extraction by cyanidation. In 1952, a unit was installed in New Hampshire to produce SO2 from sulfide ores. Alcan (Arvida, Quebec) pioneered the Dorr-Oliver fluidized bed roaster for zinc concentrates [21, 22], roasting 150 tons of zinc concentrate per day to produce sulfuric acid for the aluminum industry. The zinc calcine was shipped to electrolytic zinc plants. In Japan, numerous electrolytic zinc plants adopted the FluoSolid roaster [23]. 9 Chapter 1. Introduction In 1945, the German company Badische Anilin und Soda-Fabrik (BASF) developed a fluidized bed roaster based on experience from the Winkler gas producer. Their first commercial roaster, with a capacity of 30 tons/day, went online in 1950, followed, two years later, by a 120 tons/day unit. The BASF roaster operates with a pelletized feed, a relatively shallow bed (0.6 m) and a high superficial gas velocity (1.3-2.3 m/s) [20]. Allied Chemical [24], St-Joseph Lead [25], New Jersey Zinc [25] and Metallurgie Hoboken-Overpelt [26, 27] have all developed different zinc fluidized bed roasters for their own use. The zinc industry uses primarily the Lurgi/Vielle-Montagne roaster. During the early 1960s, the Societe de la Vieille-Montagne in Balen, Belgium, built its own fluidized bed roasters [28], before Lurgi [29, 30] (now a division of Outokumpu Technology [31]) acquired the rights. The Lurgi/Vieille Montagne roaster was also called the turbulent layer roaster, not to be confused with the turbulent fluidization flow regime. The Lurgi roaster offers the advantages of minimal concentrate preparation prior to feeding and excellent heat recovery through steam production (mainly because the concentrate is not fed as a slurry). Types of fluidized bed roasters Zinc fluid bed roasters can be classified into three general types (Table 1.1), the second of which is most widely used. The first two types mainly differ by their concentrate feeding system. The first type comprises mostly Dorr-Oliver roasters where the concentrate is fed as a slurry. The Lurgi/Vieille-Montagne roaster is the most popular roaster of the second type. The moist concentrate is fed directly to the furnace. The third type generally uses a dried, pelletized feed, utilizes a higher superficial velocity, and can operate at higher temperatures than the other two. Several designs fall within the third type, but none is widely used. This work focuses on Lurgi fluidized bed roasters. Description of a typical fluidized bed roaster Figure 1.4 shows the principal features of a typical Lurgi fluidized bed roaster. Concentrate feed is introduced by side ports with the help of slinger belt feeders. The number of feeders varies depending on the bed area. To improve the distribution of the feed over the entire bed 10 Chapter 1. Introduction Table 1.1: Types of fluidized bed roasters used i n the zinc indus t ry T y p e Feed Sys tem Superf icial Gas Ve loc i ty T y p i c a l Roas ter 1 S l u r r y (20-25 w t % H 2 0 ) 0.3-0.8 m / s D o r r - O l i v e r 2 M o i s t concentrate (6-10 w t % H 2 0 ) 0.3-0.8 m / s L u r g i / V i e i l l e - M o n t a g n e 3 Pel le t ized and dr ied concentrate 1-3 m / s B A S F Meta l lu rg ie Hoboken-Overpe l t area, a new feeding system for the L u r g i roasters has recently been developed and is currently under testing [31]. N o details of the new system have been published. T h e very large freeboard helps reduce elutr iat ion and increases the residence t ime of entrained particles. T h e calcine is recovered in the bed overflow and by the gas treatment system, usual ly consisting of a waste-heat boiler, cyclones and an electrostatic precipitator. T h e bed overflow height is often adjustable [30, 32]. Some roasters use a bed underflow discharge port to remove oversized, settled particles [33]. D u r i n g startup, the roaster is preheated using o i l and /or gas burners that can be inserted through burner ports located on the side of the roaster, just above the bed surface. T h e waste-heat boiler generates steam using heat l iberated by the roasting reactions. Heat is recovered by tubes located in the fluidized bed, on the wal l of the boiler and suspended in the boiler. Spraying water onto the bed or increasing the feed moisture content can be used to cool the bed. To ensure the safety of the operators, the roaster is usual ly operated under a slight vacuum [31]. Conversion of the zinc concentrate, based on residual sulfide sulfur, typical ly ranges from 98 to 99.9% [34, 35]. Us ing industr ia l da ta from a 32 m 2 L u r g i roaster, Avedesian [33] calculated the residence t ime dis t r ibut ion of various particle sizes. T h e mean residence t ime varied between 0.4 and 13.6 hours depending on the particle size. A radioactive tracer test provided experimental verification of the results for the smallest particles [33]. T h e difference in residence times is due to the fact that fine particles can leave the roaster by two output streams (entrainment and overflow), whereas the larger particles only exit v i a the overflow stream. 11 Chapter 1. Introduction 12 Chapter 1. Introduction Advantages and disadvantages of fluidized bed roasters T h e fluidized bed occupies only a smal l volume of the roaster shown in F igure 1.4. It is, however, responsible for several very important phenomena: • Dis t r ibu t ion of the concentrate feed (Efficient solids mixing) • Heat ing the concentrate particles un t i l they reach igni t ion (High heat transfer) • Coo l ing the particles after they ignite (High heat transfer) • Ma in t a in ing a uniform bed temperature (Isothermal) • B r ing ing oxygen required for reaction to the particles (Efficient gas-solid contacting). Satisfactory control of these phenomena depends on the rel iabi l i ty of the fluidized bed to ensure rapid mix ing and heat transfer between the reacting particles and the calcine particles. W i t h o u t the bed to distr ibute the concentrate and redistribute the heat, particles would sinter into an unmanageable heap. Therefore, the characteristics and the stabil i ty of the bed are cr i t ical to the operation of the roaster. Because the fluidized bed consists almost entirely of calcine particles, these define the behaviour of the bed. F lu id ized bed roasters have no internal moving parts. T h i s reduces maintenance costs and make them mechanically more reliable than mult i-hearth or suspension roasters. T h e fluidized bed roaster has excellent heat recovery and produces a gas w i t h a high sulfur dioxide content, suitable for acid product ion while mainta ining good temperature uniformity and control . W h i l e there are many advantages, fluidized bed roasters also suffer from disadvantages. Successful operation relies on the stabil i ty of the fluidized bed, and on particle growth to reduce carry-over [37]. Smooth operation of fluidized bed roasters involves a delicate balance between sufficient growth of the calcine and complete reaction of the concentrate, while min imiz ing the risk of defluidization. Even after 50 years, there is very l imi ted knowledge of the mechanisms and rates of agglomeration, sintering and particle growth in fluidized bed roasters. A large por t ion of the literature on roasting focuses on zinc sulfide oxidation, and the formation of zinc sulfate and zinc ferrite because of their effects on downstream processes. Agglomerat ion and defluidization 13 Chapter 1. Introduction in fluidized bed roasters have received little attention. These problems have been left to be solved by plant operators. 1.2.5 New roasters In recent years, new types of roasters have been developed. Circulating fluidized bed technology developed by Lurgi for calcination of alumina and for coal combustion has been applied to the roasting of refractory gold ores (pyrite) [38, 39]. The Torbed reactor, invented during the early 1980s, has recently been used to roast zinc concentrates at the pilot scale [40]. The Torbed reactor has an unconventional geometry where a toroidal bed of coarse fluidized particles is used as a heat transfer medium into which the fine concentrate particles are injected [41]. Neither of these technologies has yet been applied industrially to the roasting of zinc sulfide concentrates. Due to the availability of proven technologies and to uncertainty associated with implementing a new unit process, it may be several years before these technologies are adopted by the zinc industry. 1.3 Brief introduction to fluidized beds When a gas flows upward through a bed of particles at a low flowrate, the gas simply percolates through the bed and no movement of the particles occurs. This describes a fixed bed (see Figure 1.5). If the upward flow of gas is increased, a point is reached where the pressure drop counterbalances the buoyed weight of the particles. The particles then become fluidized and the bed behaves like a liquid. When the gas flowrate is further increased, large instabilities are observed and bubbling occurs, as in a violently boiling liquid. The fluidized bed is then commonly described as being composed of two phases: bubbles (lean or low-density phase) and a particulate phase (also called dense phase, high-density phase or emulsion). The bubbles are gas voids containing few particles. The dense phase consists of closely-spaced particles supported by the relative motion of interstitial gas. Gas entering the bed through a gas distributor therefore divides into two phases: interstitial gas in the dense phase, and flow through and carried by the bubbles. As an approximation, called the "two-phase theory of fluidization", the amount of gas entering the dense phase is equal to that required for minimum fluidization. Bubbles . 14 Chapter 1. Introduction form at the gas distributor, rise, coalesce and finally burst at the surface of the bed. During their ascension, they entrain particles in their wakes and therefore engender solid mixing. If the bubbles reach a diameter similar to that of the reactor, the bed enters the slug flow regime. If the gas velocity is increased beyond the bubbling regime, the bed enters the turbulent regime where voids are unstable and transient in nature. In the fast fluidization regime, the solid particles now move in clusters surrounded by a relatively dilute suspension. FIXED BED BUBBLING SLUG FLOW TURBULENT FAST PNEUMATIC OR I REGIME REGIME | FLUIDIZATION CONVEYING DELAYED V BUBBLING AGGREGATIVE FLUIDIZATION INCREASING U. € Figure 1.5: Gas-solid flow regimes [42] Each flow regime has unique characteristics that differentiate it from other regimes. Unless special attention is taken, modelling of a reactor within one flow regime should not be extended to another regime. Fluidized bed roasters typically operate in the bubbling fluidization regime. 1.4 Review of operating knowledge Before reviewing some of the issues related to the operation of fluidized bed roasters, the materials present during roasting are described. 15 Chapter 1. Introduction T a b l e 1.2: P u b l i s h e d c o m p o s i t i o n o f s o m e z i n c su l f ide c o n c e n t r a t e s a n d p u r e z i n c su l f i de ( w t % ) . B l a n k w h e r e a m o u n t n o t spec i f i ed . Z n S F e P b C u C d S i 0 2 C o m i n c o Cus toms [44] 55 4.4 3.2 Su l l ivan [44] 51 9.5 5.2 R e d D o g [44] 52 8 3 C o m i n c o F B Feed [45] 54 32 7 4.2 0.3 2 K i d d c r e e k [43] 52.48 31 .87 9.59 0.56 0.76 0 .24 2.13 A m e r i c a n Z inc [46] 54.55 30.65 5.64 0.68 0.58 0.4 Gordonsv i l l e [47] 65.7 32 0.53 P u r e Z n S 67.1 • 32.9 0 0 0 0 0 1.4.1 Feed: Zinc concentrate Z i n c c o n c e n t r a t e s are f l o t a t i o n p r o d u c t s of m i l l e d ores c o n t a i n i n g v a r i o u s m i n e r a l s a n d i m p u -r i t i e s . T h e c o m p o s i t i o n s o f s e v e r a l z i n c c o n c e n t r a t e s are s h o w n i n T a b l e 1.2. F o r reference p u r p o s e s , t h e c o m p o s i t i o n o f p u r e z i n c su l f ide is a l so p r o v i d e d . T h e z i n c c o n c e n t r a t e s a re u s u -a l l y c o m p o s e d of z i n c su l f ide a s s o c i a t e d w i t h o t h e r s u l f i d i c a n d g a n g u e m i n e r a l s s u c h as g a l e n a ( P b S ) , i r o n su l f ides , c o p p e r su l f ides , s i l i c a ( S i O ^ ) , a l u m i n a ( A I 2 O 3 ) a n d l i m e ( C a O ) . T h e re-a c t i o n o f each su l f ide r equ i r e s di f ferent a m o u n t s o f o x y g e n t o p r o d u c e di f ferent c o m p o u n d s a n d for c o m p l e t e o x i d a t i o n . S o m e i m p u r i t i e s are d i s s o l v e d w i t h i n t h e z i n c su l f ide m a t r i x a n d c a n n o t b e s e p a r a t e d b y g r i n d i n g a n d flotation. F o r e x a m p l e , z i n c su l f ide o f ten c o n t a i n s a p p r e c i a b l e a m o u n t s o f d i s s o l v e d i r o n . T h i s i r o n - r i c h z i n c su l f ide m i n e r a l is c a l l e d m a r m a t i t e a n d is r e p r e s e n t e d as ( Z n , F e ) S . C a d m i u m presen t i n t h e c o n c e n t r a t e has a l so b e e n f o u n d t o b e d i s s o l v e d i n s p h a l e r i t e [43]. M o s t i m p u r i t i e s c o n t a i n e d i n z i n c c o n c e n t r a t e s are u n l i k e l y t o affect a g g l o m e r a t i o n . H o w e v e r , l e ad , c o p p e r , a r s en i c a n d i r o n have b e e n r e p o r t e d t o c o n t r i b u t e t o a g g l o m e r a t i o n . T h e r e v i e w of K r a u s s [48] p resen t s i n d e t a i l t h e effect o f m a n y e l emen t s o n t h e e l e c t r o l y t i c z i n c p roces s . 16 Chapter 1. Introduction v . "' '• 1.4.2 Feed: Gases The fluidizing gas, air or oxygen-enriched air, enters the roaster through the dis t r ibutor and reacts in the bed. In the non-ferrous metallurgical industries, the te rm oxygen enrichment is often used to indicate the oxygen concentration of the gas. For instance, 25% oxygen enrichment would mean that oxygen is added to air un t i l the oxygen concentration reaches 25vol% rather than the 21% in standard air. Oxygen enrichment is used to increase the product iv i ty of fluidized bed roasters [49]. Oxygen enrichment has been found to significantly affect the particle size d is t r ibut ion of several flu-idized bed roasters [35]. W i t h oxygen enrichment, an unstable fluidized bed (low bed pressure, significant amount of fine particles < 56 /j,m and few particles of size 100-400 z/m) became stable (high bed pressure, few fine particles and significant 100-400 /j,m fraction) w i t h i n a few days [35]. T h e increase in bed pressure drop appears to have been caused by increasing particle density and size. A dense oxidized layer coated the sulfide core of calcine particles [35]. Oxygen enrichment has also been observed to affect the dust and sulfate formation in process gas lines [35]. In addit ion to the metered fluidizing gas, air is believed to leak into the roaster freeboard, boiler and associated p ip ing and equipment. T h i s leakage, present because the roaster is operated under a slight vacuum, can affect the reactions occurr ing i n the freeboard and the boiler. There is no published information on the amount of leakage present. Gases leave the roaster to the waste-heat boiler, cyclones and electrostatic precipitator where calcine particles are separated. After cooling, the gases are treated for mercury i n a mercury removal plant before the product ion of sulfuric acid. 1.4.3 Product: Zinc calcine Zinc calcine is extracted from the roaster v i a the bed overflow and through carry-over. T h e carryover mater ial may constitute 70% of the calcine obtained from the process [33, 34]. It is a material of fine size (overall 70%<44/zm), collected from the waste-heat boiler (67%<44/im), 17 Chapter 1. Introduction the cyclones (83%<44/nm) and the electrostatic precipitator (99%<44/um) [33]. T h e calcine is formed of zinc oxide, zinc ferrite ( Z n O F e 2 0 3 ) and relatively smal l amounts of lead sulfate and zinc silicate ( Z ^ S i C ^ ) [50]. Other studies corroborate these findings [51, 43, 52, 53, 54]. T h e entrained mater ial contains a larger propor t ion of zinc sulfate. Z inc sulfate obtained in the boiler, cyclones and electrostatic precipitator originates from the reaction of zinc oxide w i t h sulfur tr ioxide. T h e entrainment in a fluidized bed roaster is of two categories: entrainment of particles from the bed and entrainment of feed material prior to jo in ing the bed. Ent ra inment from the bed is zinc calcine. T h e entrained feed, however, is main ly zinc concentrate which may react in the freeboard to form zinc calcine. B o t h type of entrained solids are collected i n the boiler, cyclone and electrostatic precipitator as zinc oxide, zinc ferrite, zinc sulfate and unreacted zinc sulfide. It is therefore impossible to differentiate between the two types when analyzing samples of entrained material . T h e effect of various variables on the entrained mater ial , freeboard and boiler must therefore be analyzed carefully. T h e dis t inct ion between the two streams is very important because the entrained feed cannot contribute to agglomeration i n the bed while the feed which mixes into the bed can. Some observations regarding each stream: F e e d e n t r a i n m e n t : A n increase in feed entrainment is associated w i t h a decrease of the feed entering and mix ing into the bed. T h i s may be indicated by a decrease i n bed temperature [35] and an increase i n freeboard temperature [30, 35]. T h e moisture content of the concentrate and its size d is t r ibut ion affect the proport ion of entrained feed. T h e feeding system geometry and velocity also influence feed entrainment. B e d e n t r a i n m e n t : Entra inment has been studied in many fluidized bed systems. Variables that typical ly affect entrainment include the superficial gas velocity, entrained particle size and density, and the entrainable particle concentration in the bed. There is large scatter among the numerous published empir ical correlations. Because there is pract ical ly no zinc sulfide i n these particles, negligible heat is generated by combustion in the freeboard. Therefore, the freeboard temperature cannot increase above the bed temperature because of increased bed entrainment. 18 Chapter 1. Introduction Any change in the entrainment rates may alter the residence time of particles in the bed, affecting the amount of unburned sulfide in the bed calcine (affecting the solids conversion). For example, in one study, increasing the amount of feed entering the bed reduced the amount of entrained material collected (increasing the bed calcine production), increased the mean particle size of the bed and increased the sulfide content of the bed calcine [35]. Because the mass of the fluidized bed is relatively constant (imposed by the weir height), an increase in the bed calcine production rate necessarily causes a decrease in particle residence time. The increase in the amount of sulfide in the bed calcine observed industrially [35], may have been compounded by increases in both bed particle size and bed calcine production. Accretions and cake wall as well as bed-set material build up in the roaster. Bed-set material is made of very large particles that settle within the fluidized bed. Entrained material forms accretions on the freeboard and the waste-heat boiler walls composed of zinc sulfates [30, 35] and zinc oxide, zinc ferrite, minor amounts of zinc silicate and lead zinc silicate (PbZnSiC^) [50]. 1.4.4 Controlling bed particle size Fluidized bed roasting is similar to fluidized bed coal combustion in that very few particles are in the process of reacting relative to the total number present. Typically only 0.1 to 1.0 % wt of particles in bubbling fluidized bed (BFB) coal combustion are reactive [55]. The particle size of the inert material (usually sand or partially sulfated limestone) governs the fluidization characteristics. In fluid bed roasting, the amount of unburned sulfide within the bed is small (<3 wt%). The size of the bed particles (mainly zinc oxide), not the feed material (zinc sulfide) governs the fluidization characteristics of the roaster. Unlike combustion where sand or limestone of the appropriate size is periodically added and removed to refresh the bed material and/or capture sulfur, the bed in the roaster is in continuous renewal through the reaction of zinc sulfide. The particle size of the zinc concentrate is generally much finer than that of the bed. Some degree of agglomeration is desirable to produce sustainable fluidization. It is also important to distinguish the concentrate, feed and calcine particle size distributions. 19 Chapter 1. Introduction T h e particle size of indust r ia l zinc concentrates is usually opt imized for the flotation process. Zinc concentrates where more than 80% of the particles are smaller than 20 to 40 /Ltm (dgo) are now common. T h e bed calcine particle size (10 i i m to 30 m m [35]) is always much larger than the concentrate particle size. W h i l e as much as 25 wt% of the bed particles may be smaller than 105 p,m, as much as 35 wt% can be larger than 1.1 m m [56]. E lu t r i a t ion - the tendency for very fine particles to be preferentially entrained - and a t t r i t ion -the reduction of particle size due to the break-up of particles - also affect the bed particle size dis t r ibut ion. N o results on at t r i t ion in fluidized bed roasters have been publ ished. However, its importance must not be neglected. 1.4.5 Agglomeration in industrial fluidized bed roasters Agglomerat ion in fluidized bed roasters was reported early in the history of the process. For example, Fisher indicated in a patent that agglomeration occurred dur ing the roasting of zinc concentrate containing significant levels of copper and lead [57]. Acco rd ing to indus t r ia l ex-perience [30], feed moisture, concentrate particle size and lead content, temperature, and bed agitation a l l influence agglomeration, bed particle size and accretion formation. Mois tu re and agglomerated or pelletized feed have been said to be very impor tant [37]. Several studies on ag-glomeration [58, 59] concluded that low melt ing point phases were present. Higher temperatures and lower air velocity were also found to favour agglomeration. Industr ial experience indicates that at 900 to 950°C some agglomeration occurs. T h e bed may sinter wi th in 30 minutes after sudden defluidization without cooling [60]. If the bed were to defluidize before cooling, any residual sulfide could react w i t h the oxygen contained i n the intersti t ial gas space between particles (about 50 vol%) . A s a result of the poorer heat transfer in a packed bed, the heat generated would local ly increase the temperature, resulting in bed sintering. L i t t l e is known about agglomeration in fluidized bed roasters. T h e concentrate behaviour depends on its mineralogy, composit ion, size dis t r ibut ion, pre-treatment (fil tration, micro-20 Chapter 1. Introduction agglomeration and handling) and moisture content [61]. E m p i r i c a l guidelines have been set to minimize the risk of catastrophic defluidization. T h e amounts of copper and lead are l imi ted because they promote agglomeration. For example, C u is kept to less than 0.8% and P b to less than 2% [60]. Others mainta in C u below 1.2%, especially i f arsenic is present [48]. P i l o t studies have shown that a generally accepted rule, i.e. P b + C u + S i 0 2 < 5% for no defluidization to occur may only apply to some concentrates but not to others[61]. Several papers and patents refer to various methods to control or alter the bed particle size dis t r ibut ion. Depending on the methods, the goals are to promote larger bed particle sizes, reduce the amount of carryover, decrease agglomeration or decrease the bu i ld-up of settled particles. Measures reported are: • Recycl ing properly sized calcine and condit ioning the concentrate to obta in particles of proper size (pelletizing) [62]. • Compacted or agglomerated concentrate as a feed to a roaster such that decrepitation leads to an appropriate bed particle size [63]. • B lend ing to obtain a feed wi th a specified amount of agglomerating agent and pellet izat ion of the feed [56]. • C y c l i c temperature variat ion to cause par t ia l sintering [64]. • Increasing the fluidizing gas velocity if excessive agglomeration occurs due to fusion [57]. • Provide a local ly increased oxygen concentration by addi t ional localized in t roduct ion of oxygen-containing gas into the bed to produce local par t ia l agglomeration [65]. • Pel let iz ing w i t h a binder, opt ional ly followed by d ry ing [66, 67, 68], compact ing or b r i -quett ing the moist concentrate [69, 68] or creating structured pellets [70] • Cont ro l l ing the amount of feed, oxygen and water fed to the roaster such that fusion occurs dur ing roasting, thereby forming agglomerated calcine particles of controlled size and shape [71]. 21 Chapter 1. Introduction • Adjusting the amount of oxygen fed to the furnace using continuous or occasional in-bed oxygen measurements [72]. • Increasing the oxygen content of the gas fed near the feed point using a feed gas distributor [73]. The feed gas distributor is above the main distributor and directs the gas horizontally, promoting horizontal mixing [74]. • An overflow gas distributor can be used to modulate the overflow calcine output rate and control the bed particle size distribution [75]. 1.4.6 C o n c e n t r a t e m o i s t u r e c o n t e n t a n d c o n c e n t r a t e a g g l o m e r a t i o n Moisture in the concentrate reduces dusting during shipping and handling [76]. During han-dling, moisture contributes to the natural formation of small pellets and lumps of up to 1 to 2 mm. Moisture in the concentrate is thought to be a binding agent, thereby assisting agglomer-ation of the concentrate [33, 30]. In another study, an increase in feed moisture content reduced the feed entrained, and increased the mean particle size of the bed [35]. In their study of the decrepitation of concentrate filter cakes, Carey and Hall [77] found that the moisture content influenced the size of decrepitated cakes. They reported that very little entrainable dust was generated during decrepitation. Aging of the filter cake also reduced decrepitation. They attributed this finding to the production of zinc sulfate, which promotes salt bridging. They also measured the strength of fresh, aged and dried filter cakes. Capillary forces were responsible for approximately 90% of the strength of a fresh compact. Aging increased the strength threefold. Heating tests on the cakes showed that as a result of sintering, the strength was more than 10 times higher following exposure to high temperatures (>800°C). However, it is unclear how much time was required to achieve this strength increase. Aging of zinc concentrates in a "last in, first out" storage facility has been said to contribute to defluidization due to the presence of large lumps [36]. During aging, oxidation of zinc sulfide produces higher proportions of zinc sulfate. Also during aging, large hard lumps are formed. These lumps may pass through the screening and crushing plant to enter the roaster [36]. 22 Chapter 1. Introduction The formation of lumps or pellets cannot explain entirely the fact that bed particles are much larger than zinc concentrate particles. There is evidence that when the concentrate is fed as a slurry (i.e., no pellets in the feed), the particle size of a roaster bed is also much larger than the concentrate particles [78]. Therefore, other mechanisms must also contribute to the enlargement of the particle size distribution. 1.4.7 Low-melting-point phases during roasting Zinc concentrates are generally impure zinc sulfides. Numerous reactions may therefore take place, generating various compounds, some of which may be molten and contribute to agglom-eration. The proportion of low-melting-point phases present in the roaster depends on the feed composition and operating temperature. Agglomeration depends on the adhesive properties, area of contact and particle momentum [79]. Agglomeration caused by low-melting-point phases therefore depends on the properties of the phase in question and on the operating conditions, such as temperature and superficial gas velocity. The presence of low-melting-point phases may be intentional (additives) or accidental (impu-rities). In one study, a sodium-iron sulfate eutectic mixture added to the feed reduced dust entrainment and increased the particle size [58]. The reaction of pyrite (FeS2) may contribute to agglomeration [80] by the formation of a Fe-S-O liquid phase during the reaction of zinc concentrate [81, 82, 53]. The Fe-S-0 liquid eutectic is present only during partial oxidation of the sulfide. With further reaction, the liquid would solidify and possibly act as a binder. Oxidation of lead sulfide can produce numerous low-melting-point compounds. Condina et al. [83] found that alumina, silica and calcine particles can be agglomerated by monobasic lead sulfate (PbO-PbS04) on the surface of the particles. The deposit originated from the gaseous oxidation of lead sulfide. In their experiments, a single, large pellet (1 pellet per experiment) of pure lead sulfide was suspended in a inert fluidized bed. Since the fluidizing medium was air, oxidation of the lead sulfide pellet occurred rapidly and the tests ended after 23 Chapter 1. Introduction only 2 minutes. The i r experimental conditions differed from those in a continuously operating roaster. However, their test shows that basic lead sulfate can contribute to agglomeration of inert particles. In a s tudy on the effects of lead and copper concentrations in the feed [59], several compounds were identified i n agglomerated calcines: lead sulfate, basic lead sulfate, lead silicate and copper sulfate. Lead oxide and si l ica have been l inked to defluidization in fluidized bed roasters [36]. Analys is of defluidized bed material has shown that lead tends to segregate to the coarse fractions of bed material [36]. T w o types of particles were observed in the defluidized material : "globular" and "radiating globular". T h e globular part icle "is a more rounded particle that may have been formed by several spherical particles at taching themselves and joined by a binder phase. The radiat ing globular has clearer growth lines." [36] Z inc oxide particles containing th in concentric layers of lead oxide and zinc silicate were found w i t h i n the coarse fraction of the roaster bed material [36]. 1.5 Fundamentals of agglomeration in fluidized beds Agglomerat ion and defluidization occur in many other fluidized bed systems such as granulation, chemical vapour deposit ion [84], coal combustion, biomass gasification and pyrolysis . Previous studies on defluidization have focused on the sintering temperature of various materials and the effect of agglomeration on defluidization [85]. H i g h speed photography was used by Siegell [86] to observe the mechanism of agglomeration and defluidization. T w o opposite phenomena influenced the agglomerate size: adhesion of single particles to each other, and break-up of particle agglomerates as they collide. If the fluidization velocity was increased, the break-up rate increased. If the temperature increased, the average size of the agglomerates increased. Recent fundamental studies have looked at agglomeration of fine cohesive powders [87, 88], l iqu id bridge forces [89, 90, 91], sintering [92, 93, 90] and V a n der waals forces [90]. L i q u i d bridges between particles are significant i n dry ing , granulat ion and three-phase fluidization. The strength of a l iqu id bridge depends on the surface tension and viscosity of the l iqu id . In one s tudy [91], the addi t ion of l iquids modified the behaviour of a fluid bed from a Geldar t group B (bubbling) to a group A (aeratable), an eventually to group 24 Chapter 1. Introduction C (cohesive). Sintering is a time-dependent process in which material migrates to the region of contact to form a neck. Surface diffusion, volume diffusion, viscous flow and vaporization-condensation contribute to sintering. The predominant mechanism depends on the mater ia l i n question. T h e use of characteristic times [90] appears to be a promising approach for model l ing sintering in fluidized beds. Fundamental approaches such as force balances and characteristic times have been used to predict agglomeration and defluidization. Fundamental models may provide useful insights, but are very difficult to apply to industr ia l roasters and other commercial reactors. T h e composit ion, quantity and properties of various phases present dur ing fluidized bed roasting are uncertain and are l ikely to change over t ime and w i t h changes in operating conditions and /o r charge composit ion. 1.6 Agglomeration in other fluidized bed systems Relevant information is available from fluidized bed reactors used to pyrolyse waste polymers particles. These reactors suffer from agglomeration and defluidization [94]. In this process, the polymer particles are fed to a hot bed of sand (450-500°C) under inert or oxid iz ing conditions. T h e polymer then decomposes and volatilizes. U p o n entering the reactor, the polymer pellets quickly reach the polymer softening temperature and become very sticky. Layers of sand may attach to pellets, effectively forming polymer-sand aggregates which may crumble if there is insufficient polymer to b ind the sand particles and wi ths tand the agitat ion of the bed. A g -gregates grow quickly, leading to severe defluidization. T h e t ime to achieve defluidization was found to depend on the bed temperature and on the ratio of in i t i a l bed weight to the polymer fed. Th i s indicates that this is an unsteady-state process where the pyrolysis kinetics define the steady-state processing capacity. Feeding of polymer beyond that capacity causes accumulat ion in the reactor un t i l the polymer concentration reaches a point where defluidization occurs. A similar defluidization process may occur in a fluidized bed roaster if the agglomeration rate 25 Chapter 1. Introduction exceeds the rate of solids removal. Because particle growth is a main goal of the granulation process, published research on flu-idized bed granulation is of relevance. Granulation is used to produce granules or dry powder (continuously or batchwise) from a liquid, which may be a melt, solution or slurry. Two types of granules have been observed: agglomerates formed from several bed particles "glued" together by feed material, and layered or "onion-ring" granules consisting of single particles coated with successive rings of deposited material [95, 96]. During granulation, a spray nozzle injects the liquid above or below the bed surface. If the liquid droplets solidify before reaching particles, they form fine particles, which may be elutriated or act as seeds for growth. If the droplet reaches a particle before solidifying, it may wet it (if the liquid wets the solid material) and, depending on the size of the droplet relative to the particles, engulf one or more particles or coat part of a particle. If a newly coated particle collides with another, a liquid bridge may form. On solidification, the liquid bridge forms a solid bridge. Depending on the strength of the bridges, two types of granules can be formed [97]. Growth models have been formulated for both the these "glued" and "onion-ring" particles [98]. Fluidized bed combustors are often used for power generation. In these combustors, coal or another fuel is distributed onto a bed of inert particles. Manzoori [99] observed that agglom-erated sand particles were coated with a sulfated ash layer transferred from coal particles by random collisions. Depending on the fuel, the ash may contain low melting point compounds and eutectics. The transfer of ash to the inert particles caused the particles to grow, agglom-erate and eventually defluidize. It was later verified that the deposition mechanisms proposed by Manzoori apply to various bed materials [100]. The growth of the sulfated layer can be modelled using a layered growth model (onion-ring model) [101]. Four types of agglomerates have been observed in fluidized bed coal combustors [102]: • "Glued" or "raspberries" particles The first stage of creating "glued" or "raspberries" particles is through the deposition of a sticky ash layer onto bed particles. The ash layer builds up by the deposition of fine-26 Chapter 1. Introduction grained l iqu id minerals and through heterogeneous condensation of vapour-phase species such as N a , K and S. W h e n the particles have a thick coating, e.g. w i th a thickness of approximately 10% of the particle diameter, the are able to stick to other coated particles. A s a result of continued deposition, sintering between particles occurs. A d d i t i o n a l particles stick and sinter to the joined particles and a "raspberry"-shaped agglomerate is formed. • "Egg" particles The egg-types agglomerates are hollow particles that formed as a coating on a burning coal particle. T h e coating consists of coated bed particles that stick to the surface of the coal particle. A s h formed dur ing combustion of the particle interacts w i t h the particle and contributes to their sintering as a shell. W h e n the coal particle is completely burned out, a hollow shell remains. Coa t ing of a coal particle depends on the type of coal (swelling-index, ash quantity, composition) and its size. • Sintered fly ash These very fine dense particles consist main ly of fly ash sintered w i t h sorbent material . T h e y are found in regions of low or stagnant flow. • High-temperature molten alumina-silicate agglomerates T h e fourth type of agglomerates is associated w i t h the mel t ing of alumina-sil icate material due to process upsets. Operat ional problems or oversized agglomerates may cause poor fuel-air mix ing leading to localized hot spots. In these hot spots, mel t ing of an a lumina-silicate-based phase occurs, accelerating the formation and growth of agglomerates. These agglomerates appear as sintered lumps showing obvious signs of mel t ing [102]. The first two types of agglomerates are predominantly found in combustors. W i t h the exception of the fourth type of agglomerate, a l l are formed dur ing normal operat ion of fluidized bed combustors. T h e "egg"-type of agglomerates is direct ly related to coal combust ion. Therefore, "egg"-agglomerates are not expected in fluidized bed roasters. 27 Chapter 1. Introduction 1.7 Research objectives T h e research reported in this thesis seeks to provide a better understanding of particle growth processes i n zinc concentrate fluidized bed roasting. T h e objectives of the project were to: • Investigate particle growth in a laboratory scale fluidized bed roaster. • Identify particle growth mechanism(s) and quantify the rate(s) of different mechanisms for pure zinc sulfide and industr ia l concentrates. • Identify the operating parameters influencing each mechanism. • Develop a fundamental model, applicable to both pure zinc sulfide and indus t r ia l concen-trates, describing the particle growth i n a fluidized bed. • Determine the appl icabi l i ty of the results to an industr ia l f luidized bed roaster. T h e longterm objective of this research is to improve the understanding of indus t r ia l fluidized bed roasters and to provide tools to predict their behaviour and improve their operation. Us ing mechanistic models, the opt imizat ion of the operation and modificat ion to the roasters or their operation can be considered and evaluated. 1.8 Thesis outline Chapter 2 focusses on the chemical aspects of roasting zinc concentrates. T h e chapter first looks at the thermodynamics of the Z n - S - 0 system, followed by the kinetics of zinc sulfide oxidation. Next , the thermodynamics of the F e - O - S , P b - O - S , C d - O - S and C u - O - S systems are briefly presented. T h e vapour pressures of the metall ic species are presented. T h e chapter concludes w i t h an overview of phase diagrams which apply for zinc concentrates, zinc calcine and any other transient phases which may occur dur ing roasting. T h e first sections of Chapter 3 describe thoroughly the experimental roaster set-up, accessories, and data acquisit ion and control systems. A d d i t i o n a l technical specifications and drawings are assembled i n an appendix. T h e next sections report the physical and chemical properties of 28 Chapter 1. Introduction the concentrates and bed material tested, the factors studied, the description of the operating, shutdown, and cleaning procedures, and, finally, chemical and microscopic assays performed on the bed and carry-over samples. The instrument calibrations and a description of the data acquisition software are attached in appendix. Chapter 4 presents the experimental results and their analysis. The various results are compared as a function of bed temperature, superficial gas velocity, base case, inlet oxygen concentration, excess oxygen and initial bed material and size. Results include the evolution of the particle distribution, rates of bed mass increase, overall mass balances, elemental balances, an analysis of the composition of bed samples as a function of the particle size, SEM images of coated and agglomerated bed particles as well as assays of carryover particles. The chapter concludes with a discussion of the mechanisms for the coating and agglomeration of particles in the laboratory roaster. A generalized slugging-bubbling fluidized bed reactor model (GSBM) is developed in Chapter 5 . This model can be used for both the bubbling and slugging flow regimes and transition between them. To model a fluidized bed roaster, the GSBM model is coupled to an isothermal single-particle reaction model. To help verify the validity of the assumption of perfect mixing, the times required for dispersing particles into the bed are briefly described. Results of the models are presented in Chapter 6. With the help of a non-isothermal single-particle reaction model, the chapter describes the conditions where the assumption of isother-mality is valid. Next, the generalized slugging-bubbling fluidized bed reactor model (GSBM) is compared to previous fluidized bed reactor models. Some of the experimental results presented in Chapter 4 are fitted with the complete gas-solid fluidized bed reactor model. A sensitiv-ity analysis finally compares the laboratory fluidized bed roaster to the industrial roaster for different conditions. The thesis concludes in Chapter 7 with a summary of the conclusions as well as recommenda-tions regarding laboratory and industrial roasters and future work. 29 Chapter 2 Thermodynamics and Kinetics of Roasting This chapter describes the chemistry of the roasting process from a thermodynamic and kinetics viewpoint. The thermodynamics and kinetics of the relevant zinc species are first reviewed, followed by the thermodynamics of iron and lead, copper and cadmium species. A number of studies have looked at the recovery or effect of minor elements such as magnesium [103, 104, 105], germanium [47], silver [106, 43] and other minor elements [107]. The focus of this thesis being agglomeration and related phenomena, only the major compounds and those shown to contribute to agglomeration are reviewed. 2.1 Zinc 2.1.1 Thermodynamics The zinc-sulfur-oxygen system is a relatively simple system where zinc sulfide is only found as ZnS, zinc oxide as ZnO, zinc sulfate as ZnSC"4 and only one basic zinc sulfate (ZnO-2ZnS04) exists. Table 2.1 presents the crystalline structures as well as the theoretical densities and molar volumes, all calculated from the crystallographic data contained within the powder diffraction files [108]. The number of significant digits for the densities and the molar volumes reflects the accuracy of the crystallographic data for the different compounds. At room temperature, the stable form of zinc sulfide is sphalerite. Upon heating, it transforms into wurtzite, the hexagonal form of zinc sulfide. The transformation temperature is 1019°C [109]. The difference between the sphalerite and wurtzite molar volumes is negligible. It is very unlikely that the phase transform would significantly affect the structure of zinc sulfide 30 Chapter 2. Thermodynamics and Kinetics of Roasting Table 2.1: Theoret ical density and molar volume of zinc species calculated from crystall ine structures Structure Densi ty M o l a r volume Powder diffraction g / c m 3 c m 3 / m o l file [108] Z n S (sphalerite) cubic 4.0966 23.789 5-566 Z n S (wurtzite) hexagonal 4.0903 23.826 36-1450 Z n O hexagonal 5.6752 14.341 36-1451 a - Z n S 0 4 orthorhombic 3.884 41.57 8-491 / ? - Z n S 0 4 cubic 2.90 55.7 32-1477 (700°C) Z n O - 2 Z n S 0 4 monoclinic 3.8796 104.21 32-1475 Z n O - 2 Z n S 0 4 orthorhombic 3.85 105 32-1476 (850°C) particles. T h e phase transform may, however, affect the reactivi ty of the particles. Zinc sulfate exists in two crystalline forms. a - Z n S 0 4 transforms into / 3 - Z n S 0 4 above 734°C [110]. T h e crystalline structure information for the high temperature cubic form of zinc sul-fate was measured at 700°C [108]. Similar ly, the crystallographic information for the high temperature form of the basic zinc sulfate was obtained at high temperature. W h e n comparing the molar volumes of the different compounds, a l l on the basis of 1 mole of zinc, only the reaction of zinc sulfide to zinc oxide would potential ly create a porous structure i.e one mole of zinc sulfide is larger than one of zinc oxide. T h e reaction to create any of the sulfates from the sulfide or the oxide w i l l create a product more voluminous than the start ing material . T h e blocking of pores may therefore be caused by reactions to produce sulfates. The thermodynamics of the oxide, sulfate and basic sulfate were first s tudied by measuring the S O 3 equi l ibr ium pressures [110, 111] and later using high-temperature electrochemical cells [112, 113]. T h e thermodynamics of the system can be graphical ly represented as predominance diagrams. A predominance diagram is a graphical representation of which solid phase is the most stable when in equi l ibr ium w i t h a given gas composit ion. Because predominance diagrams 31 Chapter 2. Thermodynamics and Kinetics of Roasting do not account for liquid and solid solutions, they represent a simplified system. They are, however, very useful to evaluate the effect of temperature and gas composition. The reader is referred to the articles of Bale [114, 115] for the theory of predominance diagrams and their calculation. Figures 2.1 to 2.3, as well as all other predominance diagrams presented in this thesis, were created using the thermodynamic data of HSC v4.0 [116]. FACTSage [117], a different thermodynamic package, could also have been used. The two software packages use similar sources for the thermodynamic data of pure inorganic compounds (JANAF [118], Barin [119], etc) and therefore give very similar predominance diagrams. However, FACTSage can generate higher order predominance diagrams (multi-metal or larger number of independent gaseous species) or take into account liquid and solid solutions. Since this thesis only considers simple predominance diagrams, FACTSage is not required here. HSC is therefore sufficient for the thermodynamic calculations of pure compounds in this thesis. To allow rapid and automatic thermodynamic calculation for any 0 2 and S0 2 partial pressure, the required thermodynamic information was exported, and the method of creating higher-order predominance diagrams, described by Bale[114, 115], was implemented using Matlab. The code was verified by means of numerous test cases. All predominance diagrams (standard and modified) shown in this thesis were created using this code. The upper temperature limit for the thermodynamic data for the basic zinc sulfate is 1200K. This temperature is not very far from the roasting temperature. If this phase was to be removed from the calculations, the ZnO - Z11SO4 equilibrium line would fall within the ZnO-2ZnS04 stability area. Note that there is a discrepancy in the thermodynamic data for basic zinc sulfate (ZnO-2ZnS04) between FACTSage and HSC. The upper temperature limit for basic zinc sulfate is approximately 800K within FACTSage. For HSC, the limit is 1200K. Since it is not clear which source is the more authoritative, the HSC data, which has a higher temperature limit, was assumed to be correct. Using the FACTSage thermodynamic data for ZnO-2ZnS04 within HSC, the ZnO-2ZnS04 stability area at 850 °C virtually disappeared. Since basic zinc sulfate is not produced under typical roasting conditions, except in the boiler and downstream equipment, this uncertainty with respect to the basic zinc sulfate stability is of little concern 32 Chapter 2. Thermodynamics and Kinetics of Roasting for this thesis . However, if a sulfation study were to be ini t iated, the thermodynamics of the zinc-oxygen-sulfur system should be clarified. T h e diagrams also present a family of lines representing different zinc par t ia l pressure i n equi-l i b r ium w i t h the solid. T h e line where point A is located represents the gas composi t ion i n equi l ibr ium w i t h a mixture of zinc sulfide and zinc oxide. However, as discussed i n section 2.8, point A on the predominance diagram represents the gas composi t ion in equi l ib r ium w i t h a mixture of zinc sulfide and zinc oxide also in equi l ibr ium w i t h their zinc vapour pressures, i.e. vaporizat ion from both zinc oxide and zinc sulfide. These addi t ional lines and points are discussed i n section 2.8 below. A s the diagrams show, for a given temperature (see Figure 2.2), the sulfate phases are stable at higher sulfur dioxide and oxygen concentrations (upper r ight) . However, when comparing different temperatures, the sulfates cannot be stable at atmospheric pressure, at h igh tempera-ture even at 1 atmosphere SO2 (log(Pso2) ~ 0). In order for the sulfate to be stable at 1050°C, the required oxygen pressure is beyond one atmosphere. However, the sulfates are stable at lower temperature and high sulfur dioxide concentration (log(Pso2) ~ 0). These trends apply to many other systems. The sulfation of zinc oxide occurs significantly in the gas handl ing equipment where the lower temperature and high S O2 content of the gas enhance the stabi l i ty of zinc sulfate. T h e sulfation of zinc oxide proceeds very slowly when oxygen and sulfur dioxide are present. T h e reaction is much faster once the 0 2 - S 0 2 mixture contacts a V 2 O 5 catalyst to produce SO3 [120]. The catalyst can also be contained wi th in the zinc oxide sample. In such a case, the sulfation rate of zinc oxide increased wi th increasing amount of V2O5 catalyst present [121]. I ron oxide also catalyses the product ion of SO3. Because i ron oxide is omnipresent i n zinc calcine, its presence affects the sulfation of calcine occurr ing wi th in the boiler. 33 Chapter 2. Thermodynamics and Kinetics of Roasting Figure 2.1: Z11-O2-SO2 Predominance diagram at 850°C Figure 2.2: Zn-02-S02 Predominance diagram at 950°C 34 Chapter 2. Thermodynamics and Kinetics of Roasting 5 0 „ -5 OJ o cn CL cn o - -10 -15 -20 -20 -15 -10 -5 0 5 iog(PQ) 2 Figure 2.3: Zn-02-S02 Predominance diagram at 1050°C 2.1.2 K i n e t i c s o f z i n c s u l f i d e o x i d a t i o n The oxidation of zinc sulfide has been studied using relatively pure natural sphalerite crystals, synthetic powders and zinc concentrates. While the goal of most studies was to understand the oxidation of zinc sulfide for metallurgical processes, more recent studies have been concerned with the regeneration of zinc oxide for gas desulfurization processes. Gaseous zinc sulfide oxidation can significantly influence the reaction rates [122, 123]. The oxidation of gaseous zinc sulfide, observed in several studies [124, 122, 123, 125, 126, 127] was not discussed in the review on the oxidation of zinc sulfide by Dimitrov [128]. In most cases, the evaporation of zinc sulfide, followed by oxidation to produce zinc oxide, depended on the temperature and on the oxygen concentration in the gas. Oxidation in the gas phase has been observed at temperatures as low as 900°C and in environments containing very little oxygen. This indicates that zinc sulfide vaporization and gaseous oxidation could occur if the oxygen concentration is low. The gaseous oxidation of zinc sulfide may deposit zinc oxide on the surface of the bed particles, as in chemical vapour deposition. This is partly supported by Chen et 35 Chapter 2. Thermodynamics and Kinetics of Roasting al. [52] who characterized the mineralogy of calcine samples from an indus t r ia l roaster. T h e y proposed that the morphology of product calcine particles may indicate vapour-phase deposit ion or repeated cycl ing of the particles into and out of the fluidized bed. Graydon and K i r k [82, 129] studied the oxidation mechanism of zinc sulfide and the formation of zinc ferrite. T h e y concluded that solid state i ron diffusion, mel t ing of the F e - S - 0 eutectic and gaseous zinc species are important phenomena dur ing zinc concentrate roasting. Gaseous oxidation of zinc sulfide may deposit zinc oxide on the surface of the bed particles, as i n chemical vapour deposition, thereby contr ibut ing to the growth of calcine particles. Modelling, rate expressions and activation energy Numerous studies have quantified the oxidat ion kinetics of zinc sulfide and derived rate ex-pressions from experiments. Table 2.2 summarizes the studies containing quanti tat ive results applicable to a rate expression. T h e type of experiment and the method used to follow the progress of the reactions and the sample mater ial are described i n the first columns. T h e experimental conditions varied from fluidized bed, suspended pellets to powders in crucibles. T h e measurement method usually depends on the experimental conditions used. Gas analy-sis is performed either by SO2 neutral izat ion and measurement of the solution conduct ivi ty or t i t ra t ion or by infra-red measurement. T h e extent of oxidat ion of solid samples is moni-tored using chemical analysis or by measuring the oxide layer thickness. For suspended pellets and suspended crucibles, the most common method of moni tor ing the extent of reaction is by thermo-gravimetric analysis ( T G A ) i.e. continuously weighing the reacting sample. Various methods have been used to analyze the reaction rates. T h e in i t i a l reaction rates (Den-bigh and Beveridge (1962) [122], P r abhu et al. (1984) [130], S a n d m a n et al. (1985) [125], K i m and Themelis (1987) [131] and Sofekun and Doraiswamy (1996) [132]), the overall measured rates (Ong et al. (1956) [133]), the overall modelled rates and the "settled" rates (rates once the model predicts the reaction rate) (Piskunov et al. (1981) [134]) have a l l been used to de-termine the activation energy. T h e models are briefly described below. T h e var iabi l i ty among the analysis methods contribute to the var iabi l i ty i n the measured act ivat ion energies. For 36 Chapter 2. Thermodynamics and Kinetics of Roasting instance, Rao et al. (1982) [135] considered both the in i t i a l rates and the modelled rates and obtained very different activation energies for the same experiments (87 and 160 k J / m o l ) . It is important to note that the activation energy also depend on the analysis of the effect of oxygen concentration. For instance, the oxygen concentration ( m o l / m 3 ) varies w i t h temperature for a constant oxygen par t ia l pressure. T h i s effect is much smaller than the scatter i n activation energies in Table 2.2, but must be accounted for. The apparent activation energy and its applicable temperature range and the reaction order wi th respect to the oxygen concentration are shown i n the table for each study. T h e range of m a x i m u m conversions (X) is indicated where available. In most studies the 'kinetic rate equation is of the form: -r = kC^2 (2.1) where k is the reaction rate constant, Coi is the oxygen concentration ( m o l / m 3 ) and n is the reaction order w i t h respect to the oxygen concentration. T h e assumed or measured reaction orders are shown in the table where given. Natesan and Ph i lb rook (1969) [136], Sachdev and M a n n (1980) [137], P r a b h u et al. (1984) [130] and Sanchuan et al. (1985) [125] determined the reaction order to be 1. Agarwa l and G u p t a (1976) [138], Aga rwa l and M o h a n t y (1976) [139], Fukunaka et al. (1976) [140] and Rao (1984) [141] have assumed that the reaction order is 1. Cannon and Denbigh (1957) [124], Denbigh and Beveridge (1962) [122] and K i m u r a et al. (1983) [142] have measured the reaction order to be 1/2, and Takamura et al. (1974) [143] mentioned 1/2 but used first order for their modell ing. A l l a y et al. [144, 145] observed a reaction order of 2 /3 . P iskunov et al. (1981) [134] measured different fractional reaction orders as a function of the controll ing mechanism. Some studies (Ong et al. (1956) [133], C a n n o n and Denbigh (1957) [124], reference 10 of [128] (1964) or Gerlach of [132], C o n r a d and W u t h (1970) [146] and Sofekun and Doraiswamy (1996) [132]) have found that the Langmuir-Hinshelwood-Hougen-Watson ( L H H W ) model for adsorption of reactant could be applied to the oxidat ion of zinc sulfide. T h e L H H W rate model is of the form: kKAC02 1 + KAC02 where KA is the adsorption equi l ibr ium constant. 37 (2.2) Chapter 2. Thermodynamics and Kinetics of Roasting T3 O S T * o 3 . ,2 3 c8 a co CD a S -CO 'w O. 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O XI CD JO [3 fa T J C , , ce co x o S CO O CO O iO tO M m o i o © n H H ( N H C N o o o o o O O LO CD t -• S O) CO OO CO i n i n 6 6 6 o C N m H i n © N N eo c ci c« g - - s-ai < O K co S E 3 Q s x CD J 2 X> CD X '3 fa S i i3 3 s I s Q > fa fe? SWfe? ca e-. 00 CO CO C O "3 C ca O CD CD CD X O » S E t— O l 3 6 cq bO I fa .S » CS •3 d 1 CO >< PH 3 CO _>> fl O 13 E J 3 O X CD - Q X CD IS! X '3 fa I f IO CO fe? o CD X c & N co "3 fe? fe? JS 10 -cf a 10 co CO CO CO ce c ca O x CD X CD N fa JJ t*-3 CO ] J o CO 06 ca " a s- s- J-CD CD CD X X I ^ a g & co S ^  CO cd "3 c c3 CD CD "3 '3 a a X X CD CD X X a a CD CD a a Cfi cfi 3 3 CO CO c 2 co c ? " E i n ca ^  i s ca r-l 3 "oi X is O I < O CO l— r-< 3 '— 2 2 X o E a o 3 s bO C ca •J >> "3 a ca "3 S 5 Q "3 3 cd bo O o CD d CU +3 X C D a a o CD O O 39 Chapter 2. 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LSI m CN CN ~Ej cd a ^ CD CJ 3 CO 2 c & u E 3 < O SP to a CO CD o CD J 3 a -K Cd E 1 » 5 C D < a •3 S C J co E £ ^ CO < o a co 3 O T3 C co-co 'co "3 .2 a a co g cn co Co cn O -o & "o cn o _>> CO C co s O co C CS 8 o a Co o c ct Q • cu bO cS a C O O '> 0) S-i a o cu Pi 1 o o G 2 'C -a a 8 °> a J j a -a e CD O N CO 1° 3. o CO CD a _ E LO £ CO cj> 1^ i—^  CN 3 CO '3 3 CO T3 y TJ 6 I s T 3 H '3 LO — CN fa CO a 3 O fi , , co 00 CO 13 — • ho 3 ci o CO c o co — J CO C 3 . O CO Co CN fi C O ' C O > — <D „ " ? ^ J= 00 2 o> Co CO w 2 CO fa CO s 3 T3 lO C CO co i—i O 00 CS O) CQ T3 C . cd Q cS 40 Chapter 2. Thermodynamics and Kinetics of Roasting -o o •Srg .5 -a CP S to SH ° S d a o 0 tic u I 5 s H • C S II cS ^ cn CO CD Ui S-H '2 '2 1" H i—i • S i s ct) HH HJ SH aj co bOXI a o 'CO -g o c HH at X X -H +1 CO rH LO CD CO rH CO ^ . CO CO CN rH I E 5o II CO "cfj a CO c a N a CJ) ai 0> CD T 3 £ T3 O CD a 2 cH CO t, c o SI _ CT) +j S s CD rH O , , S Q a 6 >, S c o " ? „ > o> X to X5 H3 H ^ CO « ,-rS « I tsl Q, 3-oi .3, t--oi ff; 4 G H P cd \S S <« S CD £ CD 3 cd -g CH S £ a • "cd a cd o T3 X> C cd cd c « * cH O < "cd T3 X> C cd cd c < * O c§ "3 j>> "3 c cd S3 o a < o Q cu , bD cS & CO O "> CP SH ft CP fi O O 6 o 'SH t f CD CC a 8 3 S 3 CO 3 CO X 3 tt3 S cd CD CO X l T3 - o CD 3 3. u a < § O co H 3 3 CD CD DTA TGA c CD CD Samp] cible Samp] cible cd SH 3 , , P CN >^ H< 5 ^ J3 6 co M OS T3 c cd c? oo — 05 J 3 X • cd o cd c cd co . oo CD 'c?. , bO CN cd co o CO CS o ^ ' > 41 Chapter 2. Thermodynamics and Kinetics of Roasting 1 0 - 2 „ 1 0 " 4 CO M E ~Sio - 6 CO 0> o | i o - 8 c o o CO _1( £ 1 0 g 'co 1 1 0 ~ 1 : 0.8 0.9 1 1.1 1.2 1.3 1.4 m-(K"1) X 1 0 ' 3 Figure 2.4: Intrinsic reaction rate of various kinetic studies. Rate expressions from references [124, 143, 140, 135, 142, 130, 144, 145]. Dashed line corresponds to fitted kinetics (equation 2.3) discussed i n text. The activation energy does not give a complete representation of the kinetics of the system. In addi t ion to the activation energy, the pre-exponential constant from the Ar rhen ius equation, as well as the rate expression used to obtain the rate constant, must a l l be considered when comparing kinetic information from various authors. F igure 2.4 presents the rate information from several of the studies summarized in Table 2.2 which offer a complete rate expression. Note that since the rate expressions differ (reaction order and use of concentration or par t ia l pressure for oxygen) from one s tudy to another, comparison must be made on a reaction basis. W i t h the exception of studies A and B , there is relatively l i t t le scatter among the different studies. T h e s tudy of Takamura et al. [143] (line B ) clearly stands out as aberrant. T h a t of Fukunaka et al. [140] (line A ) does not direct ly extend the clustered group of studies, but may represent an adequate upper bound to the kinetics. T h e dashed line represents the least-squares fit of the end-points of a l l the studies except those of Takamura et al. [143] and Fukunaka et al. [140]. Note that the slope of the line gives the negative value of the act ivation energy. 42 Chapter 2. Thermodynamics and Kinetics of Roasting Since the Fukunaka et al. [140] kinetic study is the only study with a complete rate expression at high temperature and since the data are from a fluidized bed, this study it is not dismissed as aberrant, but used to provide a probable upper-limit for the kinetics. Fukunaka et al. [140] obtained their kinetics by fitting their fluidized bed model to their experimental data, while the other kinetic studies obtained their rate information directly from kinetic experiments. The dashed line shown in Figure 2.4 and given by the kinetic rate expression: provides a reasonable fit to most of the kinetic studies and may be considered as a reasonable lower limit to the kinetic rates. The Fukunaka et al. [140] rate expression: provides an upper limit. Until a better kinetic rate expression is available to calculate the reaction rate at high temperature, it is recommended that both of these kinetic rate expression be considered in sensitivity analyses. These two rate expressions are used in the remainder of this thesis. Numerous approaches have been used to model the oxidation of zinc sulfide. The early works did not use models to predict the conversion with time. They often measured the reaction rates with the measured oxide thicknesses and assumed that the chemical reaction was rate-limiting. The shrinking-core model was the first comprehensive model applied successfully to the oxida-tion of zinc sulfide. In the shrinking-core model, the solid reactant is assumed to be impervious to the gas, while the solid product is porous. The solid reactant is present as a core, which shrinks as the reaction proceeds. The core is surrounded by a porous ash layer. In the complete model, the effect of the chemical kinetics, the mass transport through the product layer and the effects of transport from the bulk gas phase to the surface of the particles are taken into account. Very simple equations are obtained from the shrinking-core model for the cases of chemical kinetics control, product layer mass transfer control and external mass transfer con-trol. For the case where external mass transfer is rate-controlling, the conversion (X) increases (2.3) (2.4) 43 Chapter 2. Thermodynamics and Kinetics of Roasting l inearly w i th t ime (t): X = Kt (2.5) W h e n mass transfer through the product layer is rate-controlling: l - 3 ( l - X ) 1 / 3 + 2 ( l - X ) = Kt (2.6) W h e n the chemical reaction is rate-controlling: 1 - (1 - X ) 1 / 3 = Kt (2.7) Under conditions of chemical control, the thickness of the product layer increases l inearly w i t h t ime (proven by replacing the conversion by X — 1 — (rc/R)3 where r c is the core radius and R is the particle radius). Note that these equations apply to the reaction of spherical particles. T h e equations are different for geometries other than spheres i.e. cylinders and flat plates. For flat plates under conditions of chemical kinetics or film diffusion control, bo th the conversion and the product layer thickness increase l inearly w i t h time. For a complete discussion of the model, the reader is referred elsewhere [156, 157]. T h e shrinking-core model is described further in chapter 5. Several studies have modelled the oxidat ion of zinc sulfide w i t h the spherical shrinking-core model (equations 2.6 and 2.7). These equations are often used w i t h experimental da ta to identify the rate-controlling step. To obtain the activation energy of the process, the fitted rate constant (K) is plotted as a function of temperature in an Arrhenius plot. A m o n g the studies who have used the shr inking core-model, only Natesan and Ph i lb rook (1970) [149], Takamura et al. (1974) [143] and Agarwal and G u p t a (1976) [138] t ru ly considered cases where product layer diffusion affected the reaction rates. T h e other studies only considered chemical kinetics control (equation 2.7). Jander's equation has also been used to model the oxidat ion kinetics (Piskunov et al. (1981) [134]). 3(1 - (1 - X ) 1 / 3 ) 2 = Kt (2.8) 44 Chapter 2. Thermodynamics and Kinetics of Roasting (a) Homogenous (b) Intermediate (c) Shrinking-core Figure 2.5: Representation of the grain model . A d a p t e d from [156] Jander's equation is val id only for slab-like particles or for the in i t i a l stages for other geome-tries [156]. Therefore, Jander 's equation should not be used i n place of the shrinking-core model . Hence, the analysis of P iskunov et al. (1981) [134], where only the experimental data between 20% and 97% conversion were able to fit Jander's equation, is questionable. T h e Crank-Gins t l ing-Brounshte in equation, proposed to model the reaction when diffusion through the product layer of a spherical particle is controll ing [128, 158] is equivalent to equation 2.6. Its use is therefore acceptable. T h e diffusion model of Gokarn and Doraiswamy [150, 159, 151] is another formulation of the shrinking-core model . B y neglecting chemical kinetics, they obtained an equation similar to equations 2.5 and 2.6, inc luding both diffusive resistances (external and ash-layer). The grain model was also applied to the oxidat ion of zinc sulfide [135, 141, 142, 153, 160]. In the grain model, the porous solid reactant consists of a large number of smal l non-porous grains, each treated as shrinking-core. One advantage of the grain model is that it can effectively treat homogeneous reaction throughout a pellet as well as shrinking-core reaction. In fact, these two opposite phenomena are extremes of the grain model . Figure 2.5 represents the grain model and its extremes. W h e n the chemical kinetics are slow compared to the diffusion of species through the pores, (Figure 2.5, left), the gas concentration 45 Chapter 2. Thermodynamics and Kinetics of Roasting throughout the pellet is constant. Each grain of the pellet is surrounded by fluid of the same composition. At a given time, the conversion of every grain is the same and equal to the overall conversion. This is described as homogeneous reaction. This type of homogeneity must not be confused with the typical l-phase homogenous reaction i.e. reactions of two species within the same fluid. For conditions where the resistance due to chemical kinetics is comparable to diffusional resistance through the pores (Figure 2.5, center), there is a concentration gradient through the pellet. For a given overall conversion (or time), the gas composition around each grain varies as a function of its position within the pellet. The reaction interface of the pellet is very diffuse. The grains located closer to the periphery of the pellet are more converted than those near the center. For conditions where the chemical kinetic resistance is much less than diffusion resistance through the pores (Figure 2.5, right), the reaction occurs within a very narrow reaction zone separating an unreacted core from a reacted shell. The entire pellet then reacts as a shrinking-core. Takamura et al. (1974) [143] observed that the oxidation in air of 10 mm zinc sulfide spher-ical pellets occurred homogenously below 600 °C. Above 690 °C, the reaction proceeded in a topochemical matter (shrinking-core). Between these temperatures (600-690 °C), the reaction did not occur homogenously, but as a widespread reaction zone. Instead of using the grain model, Takamura et al. [143] used the simpler shrinking-core and homogenous models. How-ever, they only used the extrapolated initial rate for the calculation of their activation energy. The final equation of the homogenous model is: X = 1 - e'Kt (2.9) Two studies (Dimitrov and Vanyukov(1970) [148] and Rayakar and Dixit(1975) [152]) used the homogenous model to analyze their experimental results. Prasannan et al. [161] verified the applicability of the zone model of Mantri et al. [162] for the oxidation of sintered zinc sulfide pellets at 600°C. The zone model is similar to the shrinking-core model except that the reaction interface is replaced by a reaction zone. In this model, the reaction zone first expands into the pellet. Once a critical thickness is reached, the reaction 46 Chapter 2. Thermodynamics and Kinetics of Roasting zone moves into the pellet, leaving a product layer behind. A s wi th the grain model described previously, the zone model combine the characteristics of the shrinking-core and homogenous models. Prasannan et al. [161] observed that the w id th of the reaction zone increases w i th pellet porosity. A model for the gaseous oxidat ion of zinc sulfide was proposed by Denbigh and Beveridge [122], who assumed that the process occurs as a double diffusion layer where gaseous zinc sulfide diffuses out and oxygen diffuses toward the particle. Gaseous oxidat ion of zinc sulfide in a fluidized bed was modelled by Ha t to r i et al. [123] by combining the 2-phase fluidized bed model of Fukunaka et al. [140] and the gaseous oxidat ion model of Denbigh et al. [122]. 2.1.3 Fluidized bed experimental studies Table 2.3 summarizes the roasters used in various experimental studies. M o s t laboratory roast-ers were used for batch experiments and had diameters between 35 and 100 m m . Mos t of these studies have looked at the oxidat ion kinetics of zinc sulfide or of zinc concentrates. T h e first s tudy on fluid bed roasting of zinc sulfide, published by Yag i et al. [163], presented valuable information (bed expansion, conversions, feed rates, residence times) for the design of fluid bed roasters. A l t h o u g h agglomeration has been observed i n some studies [164, 59, 37], only Pa ik and Park [59] specifically studied agglomeration in a fluid bed roaster. T h e gaseous oxidat ion of zinc sulfide in a fluidized bed has only been considered i n the work of Ha t to r i et al. [123] where the kinetics of zinc sulfide oxidat ion were studied for low oxygen concentrations. 2.2 Iron The iron-oxygen-sulfur system is very complex. O n l y a brief overview is presented here. Due to the existence of two oxidation states (ferric and ferrous), there are many compounds i n the i ron system. Several sulfides and oxides exist, bo th w i th significant non-stoichiometric compounds. A s Figure 2.6 shows, a number of forms of i ron oxide may exist. Magnet i te ( F e 3 0 4 ) is a spinel 47 Chapter 2. Thermodynamics and Kinetics of Roasting u CP ryo\> o o C O C O T-H 1 oo rH cci LO o C M U C M oo co CO 00 0.34 r—I 0.57 C M f- co T-H C M LO d led. >> C M O <m , — i O d t T-H C M d d C O T-H LO C M M—i 'o GIO o d d CP ft CO -rH ... v O o o o o O o C M o O o o LO I ) o , , o C O LO CD co o LO T-H C O LO f ) LO 3 cn O ) o 05 C D T—I O l o o cn o> T-H r - H cn cn cn cS +J i 1 LO 1 1 o oo i i i i i cO S-i o o o o Ol Ol o o LO C M oo LO o t— LO CD 00 o LO C d Ol o Cn o C M ere dm 00 oo C D cn O l C O oo oo 4 3 ers. o ers. 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[ll huan e£ and Par lin et al. naka et ori et al. wa et al. san and huan et minco Re hide Cor ed, Canada d Chemi study 4 3 . H '5b CJ '3 3 03 CD o minco Re a, 4 3 CD CO CD San 4 4 N 3 CO r H " H • H 3 3 co San '3 cO 3 cO CO co 03 "3 o 4 3 a >* San ft P & >- z cn ft cn E-i 48 Chapter 2. Thermodynamics and Kinetics of Roasting Fe-liq*SUj Fe-bcc+SUg Fe-fcc^SIa* FeO Weight * Fc,0, Fe,0, F i g u r e 2.6: FeO-Fe203 phase d i a g r a m [167] Figure 2.7: Fe-02-S02 Predominance diagram at 850°C 49 Chapter 2. Thermodynamics and Kinetics of Roasting -20 1 ^ ' ^ • 1 -20 -15 -10 - 5 0 5 i o g ( P n ) Figure 2.8: Fe-02-S02 Predominance diagram at 950°C -20' •— 1 ' •—1 ' 1 -20 -15 -10 - 5 0 5 i o g ( P n ) Figure 2.9: Fe-02-S02 Predominance diagram at 1050°C 50 Chapter 2. Thermodynamics and Kinetics of Roasting formed of hematite (F32O3) and iron oxide (FeO). Wustite, often designated FeO, is clearly a distinct high-temperature oxide phase. Non-stoichiometric iron oxide also exists as Fei-^O. It is important to note that magnetite (FeO^203) and zinc ferrite (ZnO-Fe203) are two spinels that form extensive solid solutions [168]. A number of iron sulfides exists: marcasite and pyrite, two crystalline forms of FeS2, FeS and pyrrhotite a non-stoichiometric sulfide Fei_xS. Upon heating in air, pyrite decomposes into porous pyrrhotite and elemental sulfur. Iron sulfide may also be present dissolved within zinc sulfide. The predominance diagrams in figures 2.7 to 2.9 assume pure stoichiometric compounds (no non-stoichiometric compounds and no solid solutions). 2.3 Lead The lead-sulfur-oxygen system is a complex system where many compounds exist. Lead sul-fate can form many intermediate compounds with lead oxide including the basic lead sulfates PbOPbS0 4 , 2PbO-PbS04 and 4PbOPbS0 4. 3PbOPbS0 4 is a basic lead sulfate that can only be synthesized by wet methods. It can be neglected in pyrometallurgical studies. The oxi-dation kinetics of lead sulfide have recently been reviewed by the author [169]. Therefore, only the thermodynamics are reviewed here. Predominance diagrams are presented in Figures 2.10 to 2.12. As mentioned above, predominance area diagrams do not account for solid or liquid solutions. Each of these figures contain the predominance diagram and the partial pressures of the different gaseous lead'species. The gaseous species are discussed in section 2.8. When comparing the zinc and lead systems, one can see that, for the same temperatures, the stability areas of lead sulfates are at lower sulfur partial pressures than those of zinc sulfates. Also, unlike the zinc system, lead sulfide and lead oxide cannot co-exist in equilibrium with the gas. Instead they react to form lead and sulfur dioxide in a reaction called the roast reaction [170]. Note that the valid temperature range for the thermodynamic data for the basic lead sulfates is limited to 1200K (PbO-PbS04), 1000K (2PbO-PbS04) and 1168K (4PbO-PbS04). These 51 Chapter 2. Thermodynamics and Kinetics of Roasting (a) Predominance diagram (b) Pb Partial pressures (c) PbS Partial pressures (d) PbO Partial pressures Figure 2.10: P b - 0 2 - S 0 2 Predominance diagram at 850°C 52 Chapter 2. Thermodynamics and Kinetics of Roasting -~ -5 o CO -10 -15 -20 950°C PbSO, 4 PbS A Pb PbO -20 -15 -10 -5 0 iog(P 0 ) o -10 -15 -20 950°C PbS0 4 Pbs. Pb PbO T o •T: f : o o it ii- n. £ & £ CL; CL; D . -20 -15 -10 -5 iog(P 0 ) (a) P redominance d i ag ram (b) P b P a r t i a l pressures -20 -15 -10 -5 log(P 0 ) 20 -15 -10 iog(P 0 ) (c) P b S P a r t i a l pressures (d) P b O P a r t i a l pressures F i g u r e 2 .11 : P b - 0 2 - S 0 2 P r e d o m i n a n c e d i a g r a m at 9 5 0 ° C 53 Chapter 2. Thermodynamics and Kinetics of Roasting — ~~ 5 o™ CO a. -10 -15 1050°C ' PbSO, P b S ^ ^ / ^ Pb PbO -20 -20 -15 -10 -5 log(P 0 ) 1050°C -10 -5 | 0 g ( p o ) (a) P redominance d iag ram (b) P b P a r t i a l pressures -20 -15 -10 -5 log(P 0 ) iog(P D ) (c) P b S P a r t i a l pressures (d) P b O P a r t i a l pressures Figure 2.12: Pb-0 2-S0 2 Predominance diagram at 1050°C 54 Chapter 2. Thermodynamics and Kinetics of Roasting sulfates melt congruently or incongruently to form lead oxide - sulfate melts (see F igure 2.24). To allow some indicat ion of the l iqu id composit ion, al l three basic lead sulfates were kept in the calculation of the predominance diagram. A t 850°C, there are no l iqu id phases formed unless the gas composi t ion is on the P b O -4 P b O - P b S 0 4 equi l ibr ium line where one may expect some l iqu id since there is a eutectic between these two phases at 835°C. A t 950°C, lead oxide is molten, and 4 P b O - P b S C > 4 decom-poses into 2 P b O - P b S 0 4 and a l iqu id melt. Beyond 975°C, the basic lead sulfates are replaced by an extensive lead oxide-sulfate l iqu id phase. 2.4 Cadmium 2 Figure 2.13: Cd-02-S02 Predominance diagram at 850°C Cadmium is usually found as an impurity within zinc ores. Cadmium has been observed to be dissolved in the zinc concentrate (i.e. no distinct cadmium rich phases were found) and in the product within zinc ferrites and zinc and lead silicates [43]. Cadmium species have not been implicated in agglomeration problems within the fluidized roaster. However, they may have a significant effect on the leaching process [171]. Figures 2.13 to 2.15 presents predominance 55 Chapter 2. Thermodynamics and Kinetics of Roasting i o g ( P D ) 2 Figure 2.14: C C 1 - O 2 - S O 2 Predominance diagram at 950°C l o g ( P 0 ) 2 Figure 2.15: C d - 0 2 - S 0 2 Predominance diagram at 1050°C 56 Chapter 2. Thermodynamics and Kinetics of Roasting diagrams for the Cd-O-S system. Since the partial pressure of cadmium reaches 1 for conditions beyond the metallic stability area, liquid metallic Cd cannot exist at atmospheric pressure for the temperatures shown here. Point A- and the cadmium partial pressures lines are discussed in section 2.8. Note that the basic cadmium sulfate ((CdO^CdSO^ is well beyond its validity range (298-717K). Since there is no other information available, it was retained. 2.5 Copper 5 0 „ -5 CM o cn CL cn o - -10 -15 -20 -20 -15 -10 -5 0 5 i o g ( P 0 ) 2 Figure 2.16: CU-O2-SO2 Predominance diagram at 850°C The Cu-O-S system is very complex, and only a brief overview is presented here. Figures 2.16 to 2.18 present predominance diagrams for the Cu-O-S system. The copper system is more complicated than indicated in these diagrams. For instance, in the presence of iron, copper and iron form 2-metal phases such as chalcopyrite and copper ferrite. Therefore a 2-metal predominance diagram is more appropriate [115]. Copper has been found to contribute to agglomeration in zinc fluidized bed roasters [59, 172]. 57 Chapter 2. . Thermodynamics and Kinetics of Roasting Figure 2.18: CU-O2-SO2 Predominance diagram at 1050°C 58 Chapter 2. Thermodynamics and Kinetics of Roasting T h e exact mechanism or molten phases were not clearly identified. However, copper sulfate was identified in agglomerated zinc calcines [59]. T h e probable presence of a ternary eutectic between CU2S, CU2O a n d C u S 0 4 around 400 °C was confirmed by Rosenqvist [173]. A d d i t i o n a l studies are required to clearly identify the l iquidus. 2.6 Water The effect of water on concentrate lumps and pellets dur ing roasting has been discussed i n section 1.4.6. Here, we focus on its chemical aspects. Sohn and K i m observed that zinc sulfide can react w i t h water to form zinc oxide and hydrogen sulfide [174]. T h i s reaction is not favoured thermodynamical ly and can only occur i f the hy-drogen sulfide concentration is very small . In their system, ca lc ium oxide was used to capture hydrogen sulfide, al lowing the oxidat ion reaction to proceed [175]. T h e reaction kinetics are first order w i t h respect to the steam concentration. T h e effect of hydrogen sulfide was not studied, but the authors suggest that the H2O /H2S equi l ibr ium be included in the analysis. Sohn and K i m [174] obtained a kinetic rate expression, applicable between 1023 and 1160K for steam concentrations between 3.94 and 9.84 m o l / m 3 . Because oxygen is omnipresent in a roaster, hydrogen sulfide formation may be possible only in regions of very low oxygen concentration. Hydrogen sulfide would be very localized w i t h i n the roaster, rapidly reacting wi th oxygen to form steam and sulfur dioxide. Therefore H2S should not be detectable. The reaction of zinc oxide w i t h hydrogen sulfide to produce zinc sulfide was investigated for the desulfurization of gases from gasifiers [176]. Under reducing conditions, hydrogen sulfide can react w i th zinc oxide to form zinc sulfide and steam. However, at h igh temperature, zinc oxide was reduced to gaseous zinc and then reacted to zinc sulfide. Zinc oxide was stabil ized by zinc titanates [177]. T h e regeneration of the desulfurization media was achieved by reoxidizing the zinc sulfide, releasing sulfur dioxide. Sasaoka et al. [178] have recently shown that steam plays a role in the oxidat ion of zinc sulfide. Us ing an oxygen isotope as a tag and a mass spectrometer, 59 Chapter 2. Thermodynamics and Kinetics of Roasting they found that wi thout oxygen, steam reacts w i t h zinc sulfide to produce tagged sulfur dioxide and hydrogen, but when oxygen was present, the tagged steam st i l l reacted w i t h zinc sulfide to produce tagged sulfur dioxide. W h e n no steam or smal l amounts of steam were present, oxygen reacted direct ly w i t h the sulfide. 2.7 Effect of roasting conditions on stable phases D u r i n g roasting, zinc concentrate is contacted w i t h air or oxygen-enriched air to produce zinc calcine. T h e equi l ibr ium composi t ion of the products may be calculated by min imiz ing the Gibbs free energy of the system. Thermodynamic calculations can be performed for a number of conditions of varying temperature and composit ion (amount of zinc concentrate and air) . T h i s would give an impressive list of compounds and concentrations. However, a simpler approach may be suitable, based on predominance diagrams. Because zinc sulfide is the major compound i n zinc concentrates, the reaction of oxygen to sulfur dioxide is governed by the oxidat ion of zinc sulfide. Assuming that reactions of other sulfides do not significantly affect the gas composit ion, their end product may be predicted w i t h the help of the final gaseous composi t ion of the zinc oxidat ion reaction: Z n S + x02 + ? / N 2 — > S 0 2 + solid product + y~N2 (2.10) The solid product may be Z n 0 , Z n S O 4 or Z n O - 2 Z n S O 4 . T h e final gaseous composi t ion of the zinc oxidat ion reaction depends on the in i t i a l amount of oxygen present. T h e result ing sulfur dioxide and any excess oxygen end up in the gaseous product . To help predict the final gaseous composit ion, assuming the reaction of zinc sulfide to zinc oxide, we define the stoichiometric excess of oxygen by: Excesso2 = l ' Z n S n ° 2 ~ 1 (2 -H) ^ 0 2 " Z n S where ni is the number of moles of species i and vzn s and f o 2 are the stoichiometric coefficients for the reaction of zinc sulfide to zinc oxide. A n excess oxygen value of 0 (log(Excess02) = —00) 60 Chapter 2. Thermodynamics and Kinetics of Roasting indicates that there is exactly a sufficient amount of oxygen for complete oxidation of zinc sulfide to zinc oxide (1.5 moles of oxygen for each mole of zinc sulfide). An excess oxygen value of 1 (log(Excesso2) = 0) indicates that there is twice the sufficient amount of oxygen required for complete oxidation of zinc sulfide to zinc oxide (3 moles of oxygen for each mole of zinc sulfide). With this definition, a negative excess oxygen may exist for conditions where there is less oxygen than the stoichiometric requirement. Equation 2.11 may be considered a stoichiometric model where the resulting gas composition after reaction depends on the input gas composition, the excess oxygen and the stoichiometry of the reaction. As for a standard predominance area diagram, the most stable compound in equilibrium with the resulting gas composition can be determined by calculating the A G for each compound considered and selecting the one with the lowest A G . The most stable compound is then shown on the predominance diagram. However, instead of using the gas concentrations for the axes, as in the standard predominance diagram, we can create a new type of diagram by using excess oxygen to dictate the gas composition (using the stoichiometric model), with temperature as the other axis. Equation 2.11 must be used carefully. Assuming a given reaction is acceptable, if the most stable compound is the same as the product of the reaction. However, the reaction must be changed if the assumption proves to be invalid. To calculate the equilibrium gas composition, one mole of zinc sulfide is completely reacted with the stoichiometric number of moles of oxygen and any excess as given by Excesso2- If the calculated gas composition is in equilibrium with zinc oxide, the gas composition is valid. If it is not, zinc sulfide reacts to produce a mixture of zinc oxide and basic zinc sulfate, pure basic zinc sulfate or a mixture of basic zinc sulfate and zinc sulfate. (Note that pure zinc sulfate cannot be produced since it requires that a given amount of sulfur dioxide be present to be stable.) Once the equilibrium gas composition is calculated, the reaction products of the other compounds are those which are in equilibrium with the gaseous products. Figure 2.19 presents the predominant phases for various elements assuming the reaction of 61 Chapter 2. Thermodynamics and Kinetics of Roasting ZnO/ZnO 2ZnS0, ZnO ZnO/ZnO 2ZnSO, 750 800 850 900 950 Temperature °C 1000 1050 750 800 850 900 950 Temperature °C 1000 1050 (a) Z inc (b) L e a d 750 800 850 900 950 Temperature °C 1000 1050 750 800 850 900 950 Temperature °C 1000 1050 (c) Iron (d) C o p p e r Figure 2.19: Excess oxygen - Temperature Predominance diagram for gaseous feed of air (21% O2). Calculated from thermodynamic data and equation 2.11 62 Chapter 2. Thermodynamics and Kinetics of Roasting _ 0 - 0 . 0 5 - = 0 1 --0 A V J --0.0001 -1e-009--10 L -0.01--0.05--0.1--0.001 — 0.0001 — 1e-005—| 1e-006 - 1 e - 0 0 7 — -1e-008 -1e-009--1e-010-750 800 850 900 950 Temperature °C 1000 1050 750 800 850 900 950 Temperature °C 1000 1050 (a) O x y g e n concentra t ion (b) Sulfur d ioxide concent ra t ion F i g u r e 2.20: G a s c o n c e n t r a t i o n s for excess o x y g e n - t e m p e r a t u r e p r e d o m i n a n c e d i a g r a m for gaseous feed o f a i r (21% O2). C a l c u l a t e d u s i n g t h e r m o d y n a m i c d a t a a n d e q u a t i o n 2.11 63 Chapter 2. Thermodynamics and Kinetics of Roasting air with zinc sulfide. The shape of these diagrams can be understood when considering the trajectory of the resulting gas composition on a typical log(Pso2) — log(Pc-2) predominance diagram as the amount of excess oxygen is increased. When the amount of excess oxygen is very small, the resulting sulfur dioxide concentration is large and the oxygen concentration is very small. Any change in the amount of excess oxygen dramatically changes the resulting oxygen concentration, but not the sulfur dioxide, i.e. the gas composition moves horizontally on the log(Pso2) — log(Po2) predominance diagram. When the amount of excess oxygen is very large, the resulting oxygen concentration is still very large and effectively dilutes the resulting sulfur dioxide i.e. the gas composition moves vertically on the P 5 0 2 - P02 predominance diagram. This analysis is complicated by the fact that under some conditions, the predominant zinc compound after reaction to zinc oxide is not zinc oxide. In such cases, the gas composition moves along the ZnO-ZnO-2ZnSC>4 equilibrium lines and enters the ZnO-2ZnSC>4 stability area once there is sufficient oxygen for sulfation. Figure 2.20 presents the gas composition related to Figure 2.19. The oxygen concentration is very small for small excess oxygen and increases with excess oxygen. The sulfur dioxide concen-tration is 15% for low excess oxygen, and slowly decreases with increasing excess oxygen. When the excess oxygen passes 100% (0 on Figures 2.19 and 2.20) the sulfur dioxide concentration rapidly decreases due to the dilution effect of additional gas. The system is very sensitive to excess oxygen between an exact stoichiometric amount of oxygen and twice that amount (—00 < log(Excesso2) < 0). Any major departure from the operating-conditions (typically 10-20 % excess oxygen) has dramatic effects. Major departures from the operating conditions may arise from inefficient feed distribution and mixing. This is best shown by the lead species. These diagrams are similar to the constant total pressure predominance diagrams presented by Kusano et al. [179]. Their diagrams were three-dimensional surfaces at a constant total partial pressure representing a cross-section of the three-dimensional (Po2,Psc>2>T) predominance di-agram. The main difference from the diagrams presented here is that the graph is transposed 64 Chapter 2. Thermodynamics and Kinetics of Roasting to 2 dimensions by adopting the operating condi t ion (excess oxygen) instead of the gas par t ia l pressures (P02 and Psc.2) for a constant total par t ia l pressure. In section 6.3.4, the stoichiometric model w i l l be replaced by a complete f luidized bed roasting reactor model, and its output w i l l be used to create a diagram similar to F igure 2 .19. A s kinetic model l ing w i l l show, the use of thermodynamics for fluidized bed roasters may result in erroneous conclusions. However, thermodynamics show very clearly that excess oxygen may significantly affect the reaction products of the impuri t ies . 2.8 Gas phase reactions Various elements and compounds are volatile dur ing the roasting of zinc concentrates. For example, due to their volatile nature, halides, mercury and arsenic species are separated from the calcine dur ing roasting. T h e mercury and arsenic species are gaseous at roasting temperatures and are not discussed here. C a d m i u m , lead and zinc species are not usually gaseous at roasting temperatures. However, under some conditions, their par t ia l pressures are relatively high and this may affect their volat i l izat ion. For example, various researchers have studied cadmium volat i l izat ion dur ing the roasting of zinc concentrates, either to increase [180, 181 , 182] or reduce [183, 184] its removal from the calcine. Vapor iza t ion chemistry has received very l i t t le attention in the roasting l i terature. However, an early review [185] has shown that it is more complex than one would expect. Depending on the metal i n question, oxides and sulfides species have been found to exhibi t different features such as simple vaporizat ion, dissociative vaporizat ion and polymeric gas species. Zinc and cadmium volati l ize very similarly. T h e vapour pressures of zinc and cadmium for the oxygen or sulfur systems are shown in Figure 2 .21 . B o t h their oxide and sulfide dissociate to form Zn( 5 ) , Cd( f l) and 0 2 ( 9 ) , S 2 ( g ) . Because vaporizat ion produces a non-metal species, any change i n its concentration affects the metal vapour pressure. T h i s has been experimental ly observed by measuring the vapour pressure of cadmium over cadmium oxide as a function of oxygen par t ia l pressure [185]. T h e analysis of the metal vapour par t ia l pressure is very similar 65 Chapter 2. Thermodynamics and Kinetics of Roasting to that of the solubil i ty of salts in aqueous solutions where a solubi l i ty product is used to establish the equi l ibr ium ionic concentrations. In the gaseous state, the par t ia l pressure of the non-metal species is used w i t h the equi l ibr ium constant to obtain the equ i l ib r ium metal vapour pressure. The volat i l i ty of the oxide or sulfide in vacuum or inert atmosphere is represented by points A in Figure 2.21. T h e volat i l i ty of zinc i n retorting or slag fuming is enhanced by using a reducing atmosphere i.e. moving to the left of point A . Below a cr i t ica l level, the condensed metal is stable and its par t ia l pressure reaches a constant value. The zinc and cadmium par t ia l pressures and the interaction of sulfur and oxygen i n the ternary systems are presented w i t h their respective predominance diagrams (see Figures 2.1 to 2.3 and 2.13 to 2.15). Point A in these diagrams represents the composi t ion of the gas i n equi l ib r ium wi th a mixture of sulfide and oxide. Point A is a point because of the following equil ibr ia: T h e metal par t ia l pressure in equi l ibr ium wi th the oxide-sulfide mix ture is higher than that in equi l ibr ium w i t h oxide or sulfide (Points A on Figure 2.21). One of the zinc sulfide oxidat ion mechanisms is its reaction in the vapour phase. A s Figure 2.21 suggests, under conditions of high temperatures and /or very low oxygen concentrations, the sulfide may sublimate and, once the oxygen concentration is sufficiently high, react at a distance from the sulfide particle. Such a mechanism has been observed in various studies. It has been shown that the oxidat ion of zinc sulfide at very high temperature (1800-2200K) proceeds by dissociative vaporizat ion and reaction in the gas phase [186]. However, typica l roasters operate far from these temperatures. T h e same gas phase reaction has been observed at lower temperatures [122]. T h e vaporizat ion chemistry of lead species is very different from that of zinc and cadmium species. For instance, lead species form polymeric vapour compounds (Pb2S2, Pb202, etc M S + 2 M 0 = 3M(g) + S 0 2 (2.12) (2.13) 66 Chapter 2. Thermodynamics and Kinetics of Roasting l o g ( P n J log(P_2) (a) Zinc-Oxygen (b) Zinc-Sulfur log(P n ? ) log(P_2) (c) Cadmium-Oxygen (d) Cadmium-Sulfur Figure 2.21: Zinc and cadmium partial pressures. Points A represents the partial pressure in equilibrium with pure oxide or sulfide. 67 Chapter 2. Thermodynamics and Kinetics of Roasting [185]) a n d d o n o t d i s s o c i a t e . T h e e x a c t c o m p o u n d s p resen t i n t h e gaseous s t a t e d e p e n d o n t h e o x y g e n a n d su l fu r p a r t i a l p ressures . H o w e v e r , u n l i k e t h e z i n c a n d c a d m i u m s y s t e m s , the t o t a l m e t a l v a p o u r p r e s su re does n o t change as s i g n i f i c a n t l y w i t h c h a n g i n g o x y g e n o r s u l f u r p a r t i a l p re s su re (see F i g u r e 2 .22) . log(P n ? ) log(P q 2) (a) L e a d - O x y g e n (b) Lead-Sul fur log(PO P) l 0 9 ( p s 2 ) (c) L e a d - O x y g e n to ta l pressure (d) Lead-Sul fur t o t a l pressure F i g u r e 2.22: L e a d p a r t i a l p ressures 68 Chapter 2. Thermodynamics and Kinetics of Roasting Similar to the zinc and cadmium systems, the partial pressures of the lead species are presented on the predominance diagram of the lead system (see Figures 2.10 to 2.12). However, to simplify the representation of more than one predominant gaseous species, the partial pressures of the oxide, sulfide and metal are shown as different sub-figures. The vapour pressures in equilibrium with zinc concentrates will mainly be governed by the predominant sulfide phase i.e. zinc sulfide. Therefore, under equilibrium conditions, the con-centrate, a mixture of zinc, iron, lead and cadmium sulfides, generates a gaseous mixture close to point A on the zinc diagram. The gas composition at point A on the zinc diagram (Figures 2.1 to 2.3) falls within the cadmium sulfide stability area (Figures 2.13 to 2.15). The cadmium partial pressures in this area are relatively high compared to those at higher oxygen concentra-tions. The gas composition at point A on the zinc diagram is located within the lead stability area, close to the lead-lead sulfide equilibrium line (Figures 2.10 to 2.12). The region near this equilibrium line is where the total lead partial pressure is a maximum, Because it is near the equilibrium line, the most important lead gaseous species is lead sulfide, even within the metallic lead area. In summary, all three systems discussed here (Zn, Cd and Pb) have their highest partial pressures at low oxygen partial pressures. For conditions near point A on the zinc system (Figure 2.2), the metal partial pressures rank as follows: ^ C d > ^ P b S > Pzn Therefore, significant transport of cadmium and lead would occur prior to the gaseous mass transport of zinc. Very low oxygen concentrations are required for the gaseous transport of metal species. If the oxygen partial pressure increases, "precipitation" from the gas phase would occur. 2.9 Low-melting-point phases during roasting In addition to predominance area diagrams, phase diagrams are graphical representations of the thermodynamics of the system. They represent the solids, liquids and solutions present 69 Chapter 2. Thermodynamics and Kinetics of Roasting i n a given system, for different compositions and temperatures. Un l i ke the predominance area diagram, their generation is very complex requiring difficult experimental measurements. Several phase diagrams are presented in this section, bo th for the products and the reactants. These diagrams give information on the possible molten phases present dur ing roasting. Because of the number of impuri t ies present in a typica l concentrate, the mel t ing point of the calcine or concentrate may be well below that of its main constituents. T h e phase diagrams may indicate which impur i ty and phase contribute to agglomeration. Low-melt ing-point compounds can be classified i n three general types: reactant, product and reacting. T h e reactant low-melting-point compounds are those present i n the concentrate. T h e eutectics in the ZnS-FeS-PbS system fall into this category. Because the reactants react in the roaster, these compounds have a finite life. T h e product low-melting-point compounds are those present in the zinc calcine product . T h e eutectics in the P b O - P b S 0 4 and PbO-SiC"2 systems belong to this category. These are com-pounds stable in the roaster gas and should always be present dur ing roasting. A summary of the mel t ing temperatures of various phases is shown below, in Table 2.4. 2.9.1 Phase diagrams - product type The first phase diagram, shown i n Figure 2.23, presents the zinc oxide s i l ica phase diagram. Due to its effect on downstream processes, the product ion of zinc silicate dur ing roasting has received some attention. Because the si l ica contained i n zinc silicate is acid soluble, the presence of zinc silicate does not affect zinc recovery, but does affect the amount of s i l ica i n solution. Dissolved sil ica can polymerize, produce colloidal sil ica, gelify and cause severe fil tering problems [187]. Zinc silicate is only found as Z i i 2 S i 0 4 . F r o m the diagram, two eutectics are present, but both are much higher than typical roaster operating temperatures (~950°C). Therefore, any pure zinc silicate would l ikely be formed by a solid-state diffusion process. L i u et al. [188] have studied the kinetics of formation of zinc silicate from high si l ica-containing sphalerite concentrate. T h e y have observed that the process could be modelled by the shr inking core 70 Chapter 2. Thermodynamics and Kinetics of Roasting model and that solid-state diffusion controls the process. T h e y obtained an act ivat ion energy of 406 k J / m o l . In the lead system, there is a significant solubil i ty amongst some of the species. For instance, Pb(;) and PbS(;) can be described as a single l iqu id solution [195]. A s shown i n F igure 2.24, the lead oxide-lead sulfate system has numerous phases and eutectics. Figure 2.24 is the P b O - P b S 0 4 phase diagram refined by B i l l ha rd t [190]. A s seen in the diagram, no solid solutions exist i n this system. However, the lowest temperature at which a l iqu id phase can exist is 835°C corresponding to the P b O - 4 P b O - P b S C ^ eutectic. A l l the phases melt congruently except tetrabasic lead sulfate which melts incongruently at 895°C. 2 P b O - P b S 0 4 is metastable below 640°C. Figure 2.25 presents the lead oxide si l ica phase diagram. There are three lead silicates and three eutectics, a l l molten above 760°C. T h e lead oxide zinc oxide phase diagram, shown in Figure 2.27, has one eutectic mel t ing at 861°C. T h e P b O - Z n O - S i 0 2 system was recently opt imized [196] such that a complete thermodynamic representation of the system is available in the F A C T thermodynamic database comput ing system. T h e alumina-lead oxide phase diagram is shown in Figure 2.26. S imi la r ly to the zinc oxide - lead oxide system, the a lumina system only has one eutectic. 2.9.2 Phase diagrams - reactant type Impurities in the zinc concentrate may contribute to the presence of low-melt ing-point phases. The phase diagrams presented in Figures 2.29 to 2.31 are needed when considering the effect of impurit ies on the mel t ing temperature of zinc concentrates. Note that these diagrams neglect solid solutions and were created to represent the l iquidus and solidus lines. T h e m i n i m u m melt ing temperatures for the three binary systems are 1160°C ( F e S - Z n S , Figure 2.29), 1041°C ( P b S - Z n S , Figure 2.30) and 1130°C ( C u 2 S - Z n S , F igure 2.31). However, the addit ion of FeS to the P b S - Z n S system produces a ternary eutectic which melts as low as 717°C [81]. Figures 2.32 and 2.33 present the F e S - P b S and C u 2 S - P b S phase diagrams. B o t h 71 Chapter 2. Thermodynamics and Kinetics of Roasting Figure 2.23: Z n O - S i 0 2 phase diagram. [189], Temperature i n °C < -Mol % PbO Figure 2.24: P b O - P b S 0 4 phase diagram [190] 72 Chapter 2. Thermodynamics and Kinetics of Roasting Figure 2.25: P b O - S i 0 2 phase diagram [191]. Compos i t ion i n wt%, Temperature in °C Figure 2.26: P b O - A l 2 0 3 phase diagram [192] Temperature i n °C 73 Chapter 2. Thermodynamics and Kinetics of Roasting 1000 9 0 0 8 8 8 8 0 0 y 9 7 5 8 1 1 1 -1 Z n 0 + L i q. L iqu id j 8 6 1 : 2 ° — / / P b O s s + Z n O / t i l l PbO 2 0 4 0 6 0 Mol. % 8 0 Z n O Figure 2.27: P b O - Z n O phase diagram [193] Temperature i n °C 1400 1300 1200 1100 1000 900 800 700 600 T r T r J Fe90* + Liquid 1315 I i i i i I I > — -B + Liquid 945' PbO \ PbO+ 8 r » Liquid 910 V 8 + r 750' 760° \ jB+FejjOjl r » F a , O . J - X — S + Fe2O s 1:2 i:6 6 5 0 ° 2:i _1_ 0 10 20 30 40 50 60 70 80 90 100 PbO Mol % F e z ° 3 Figure 2.28: P b O - F e 2 0 3 phase diagram [194] Temperature i n °C 74 Chapter 2. Thermodynamics and Kinetics of Roasting Figure 2.30: PbS-ZnS phase diagram [109] 75 Chapter 2. Thermodynamics and Kinetics of Roasting 1300 1200 1100 1000 H 900 i 1190 v Bmtt.34,87p4-381 0 -Kerby-fa139' O Kopvtav-761*" • Eric-94f37>, Solid + Liquid o Eric-94p7>. Liquid Calculated 1120.5] 800 • o o • ..• c a o.o FeS Q2 0.4 0.6 Mole fraction of PbS 0B 1.0 PbS Figure 2.32: FeS-PbS phase diagram [197] 76 Chapter 2. Thermodynamics and Kinetics of Roasting Figure 2.33: Cu2S-PbS phase diagram [197] Figure 2.34: Quaternary ZnS-FeS-PbS-Cu2S phase diagram [198] Temperature in °C 77 Chapter 2. Thermodynamics and Kinetics of Roasting are relatively simple phase diagrams w i t h eutectics at 863 (Figure 2.32) and 517°C (Figure 2.33), respectively. It is clear that it is the interaction of impuri t ies that may lead to low-melting-point phases w i th in zinc concentrates. A complete ternary or quaternary phase diagram is therefore helpful i n evaluating the effect of the main impuri t ies on the mel t ing temperatures of zinc concentrates. F igure 2.34 presents the liquidus surface of the ZnS-FeS -Cu2S -PbS quaternary system (shown as 4 ternary systems). Note that the l iquidus surface represents the composit ion and temperature of complete melt ing. Since roasting involves predominantly solid phases and agglomeration may be promoted by very smal l amounts of l iquids, the solidus surface (surface of the conditions where a l i qu id phase first appears) offers the most useful information. However, a quaternary (or ternary) section (phases at a given temperature) or solidus surface phase diagram is not available. Analys is is therefore l imi ted to the quaternary phase diagram and to the b inary diagrams presented previously. Zinc concentrates may, depending on their mineralogy and their extended exposure to high temperatures w i th in the roaster, form l iqu id phases w i t h composit ions near the F e S - P b S and Cu2S-PbS eutectics. Note that amongst these phases, P b S is the most volatile under roasting conditions. Its presence wi th in l iqu id phases would l ikely be influenced by vaporizat ion. 2.9.3 Phase diagrams - reacting type The last type of phase diagram represents the reacting low-melting-point l i qu id formed from reactant and products. T h e ternary eutectic i n the F e - S - 0 system, shown i n F igure 2.35, is a good example. T h e ternary eutectic in the F e S - F e O - Z n S system at 920°C [201] also falls wi th in this category. A l iqu id phase would only be present for a short t ime dur ing the reaction. T h e in i t ia l reactant and final product may be solid, but the intermediate may pass near the eutectic composit ion and become l iqu id unt i l it resolidifies as the reaction proceeds. Such a low-melting-point phase would be transient and would depend on the reaction pa th and the kinetic conditions. Such a reactive solidification has been observed i n the copper system [173]. A CU2S-CUSO4 mixture was molten at 450°C under an atmosphere of SO2, but solidified at 78 Chapter 2. Thermodynamics and Kinetics of Roasting 20 %0 20 %S Weight per cent Iron Figure 2.35: Region of the Fe-S-0 ternary phase diagram [199] Temperature in FeS 1170* Figure 2.36: FeO-FeS-Cu2S ternary phase diagram [200] Temperature in °C 79 Chapter 2. Thermodynamics and Kinetics of Roasting 550°C after loss of S0 2 . A eutectic melting at temperatures below typical roasting temperatures is also present in the Cu2S-FeS-FeO system (Figure 2.36). This phase diagram clearly shows that the melting tem-perature may be lowered by adding a third component to where a ternary eutectic is present. Table 2.4: Melting temperature of various phases Type Melting Temperature Reference Reactant type PbS-ZnS Binary Eutectic 1041°C from Figure 2.30 [197] PbS-FeS Binary Eutectic 842°C from Figure 2.32 [197] FeS-ZnS Binary Eutectic 1160°C from Figure 2.29 [109] Cu2S-PbS Binary Eutectic 517°C from Figure 2.33 [197] FeS-ZnS-PbS Ternary Eutectic 717°C [81] Product type PbO Pure 880°C . PbO-PbS0 4 Binary Eutectics 835°C from Figure 2.24 [190] PbO-Si0 2 Binary Eutectics 720°C from Figure 2.25 [191] PbO-ZnO Binary Eutectic 861°C from Figure 2.27 [193] PbO-Fe 20 3 Binary Eutectic 730°C from Figure 2.28 [194] Reacting type Fe-S-0 Ternary Eutectic 915°C from Figure 2.35 [199] FeS-FeO-ZnS Ternary Eutectic 920°C [201] Cu 2S-Cu 20-CuS0 4 Ternary Eutectic <450°C [173] Cu2S-FeS-FeO Ternary Eutectic 850°C from Figure 2.36 [200] The low-melting-point phases discussed and shown in the various phase diagrams are summa-rized in Table 2.4. Zinc sulfide, zinc oxide or zinc silicates are not molten at typical roaster op-erating temperatures (~950°C). Therefore, any roasting of pure zinc sulfide would not produce 80 Chapter 2. Thermodynamics and Kinetics of Roasting any low-melting-point phases, even if silica was present. Agglomeration caused by low-melting-point phases would therefore be impossible in a pure ZnS roasting system. However, once impurities are present, as it is the case for zinc concentrates, a large number of low-melting-point phases can be produced. Depending on the temperature, liquid lead oxide can dissolve various amounts of lead sulfate (Figure 2.24), zinc oxide (Figure 2.25), iron oxide (Figure 2.28) and silica (Figure 2.25), all of which are present during roasting of zinc concentrates. 2.10 Conclusions and recommendations Predominance diagrams are readily available for most metals. However, they usually assume pure solid compounds. Current thermodynamic data are relatively limited when considering sulfates, especially with respect to the thermodynamics of molten sulfates. The decomposition temperatures of sulfates may be estimated using current data. However, most of their melting temperatures are unknown. Except for the PbO-PbS04 system (Figure 2.24), no binary or ternary sulfate, oxide-sulfate or sulfide-sulfate phase diagrams were found in the literature. Research on these systems may uncover new avenues for industrial extraction processes. Little is known on how to treat solid-liquid phase transforms during isothermal gas-solid re-actions. Liquid products behave very differently from solid products. The diffusion of species between the solid and the gas-liquid interface becomes important. There is also the possibility of ionic and electrochemical reactions and frothing of the melt if there are gaseous reaction products. Since it is the interaction of various impurities that lead to various low-melting-point phases, a complete ZnS-FeS-PbS-Cu2S quaternary phase diagram would be helpful in determining the melting temperatures of various concentrates. Zinc was recently included into the matte, slag and blister copper databases of the FACT thermodynamic database computing system [109]. The FeS-ZnS, PbS-ZnS and Cu2S-ZnS phase diagrams were calculated from the database. It is not clear whether the database for copper matte would apply and if there are sufficient data in the database to create this ternary diagram. Attempts to recreate the binary diagrams using 81 Chapter 2. Thermodynamics and Kinetics of Roasting FactSage 5.1 [117] were not successful when F e S was involved. E q u i l i b r i u m calculations of matte against solid sulfides is currently l imi ted to zinc and copper sulfide solid solutions. E q u i l i b r i u m calculations of the matte w i t h other solid sulfide phases is currently not recommended. It is l ikely that the database w i l l allow calculations w i th in a relatively near future. T h e most common compound contr ibut ing to low-melting-point phases is lead oxide ( P b O ) . Pure lead oxide is a l iqu id at typical roaster operating temperatures ( ~ 9 5 0 ° C ) . Several com-pounds are soluble in lead oxide, and some create eutectics that melt at even lower temperatures. 8 2 Chapter 3 Exper imenta l M e t h o d s In the light of the complex features of industr ia l fluidized bed roasters, the process must be simplified i n an experimental setup capable of evaluating agglomeration phenomena. For in -stance, unlike the feed, to the industr ia l roaster, the feed to the experimental roaster consists of dried concentrate particles where no lumps are present. Also , since entrainment of concentrate particles prior to their entry into the industr ia l fluidized bed cannot be clearly separated from entrainment from the bed, the feed is direct ly injected into the experimental fluidized bed. Hence moisture, lumps and concentrate entrainment are absent in the experiments so that we can determine how the chemical phenomena influence the particle size d is t r ibu t ion . Mos t experiments used the same in i t i a l bed material and same indus t r ia l concentrate. Since the concentrate was the same and only the operating conditions varied from one experiment to another, the experiments focussed on how the operating variables affect the bed particle size dis t r ibut ion. 3.1 Experimental pilot plant The pilot scale roaster used in the present study is similar to that of Yazawa et al. [107], requiring continuous feeding for experimental runs lasting several hours. However, because they studied the behaviour of minor elements dur ing fluidized bed zinc roasting, Yazawa et al. [107] required a gas cleanup system similar to the industr ia l process. In this work, the focus is on the processes occurr ing i n the fluidized bed. Therefore, a simplified gas treatment system was used. Figure 3.1 presents the experimental set-up. 83 Chapter 3. Experimental Methods Chapter 3. Experimental Methods The gases fed are compressed air.and nitrogen. Oxygen is also available for oxygen enrichment. The gases are metered using rotameters, mixed and sent to the gas preheater, built from 316 stainless steel pipe, 102 mm ID, 114 mm OD (4" pipe, schedule 40), 710 mm long with standard flanges at its ends. Pipe couplings for thermocouples and pressure transducers, gas inlet and oxygen sensors are located 90 mm from each end. The preheater is filled with alumina packing and preheats the gas before entering the roaster. The preheater can be bypassed if no preheating is required. The roaster consists of a fluid bed at the bottom and freeboard above, enlarged to reduce elutriation. The fluid bed zone consists of a 316 stainless steel pipe, 102 mm ID, (4" pipe, schedule 40), 660 mm long. The freeboard zone was built with a 316 stainless pipe, 154 mm ID, (6" pipe, schedule 40), 365 mm long. A standard 4" x 6" (100 x 150 mm) reducer joins the two zones. Standard flanges are located at the bottom and top of the roaster. Temperature and pressure ports are located 90, 281, 435, 626, 799 and 1080 mm above the distributor, while the top cover is 1165 mm above the distributor. Larger couplings for the gas outlet, feed inlet and oxygen sensor are installed 90 mm from the ends. A removable gas distributor, made of a 6.3 mm (1/4") thick 316 stainless steel plate and drilled with thirty-seven 1.2 mm (3/64") holes evenly distributed on a hexagonal grid, is located between the preheater and the roaster. The entire reactor assembly is suspended from the top flange. To compensate for thermal expansion and help compress the copper gaskets at high temperature, the lower support is held using compression springs. To minimize axial temperature gradients and to simplify modelling, the temperature of each zone is controlled independently using three furnaces (see Figure D in appendix D). The controllers are connected to a computer, which can remotely change their setpoints. The top furnace is suspended from the top of the reactor. The middle furnace is supported by the flange of the distributor plate. The lower furnace is held by the lower support. Insulation is added or removed between the fluidized bed and freeboard furnaces during heat-up and cool-down of the reactor. Zirconia-based automotive oxygen sensors (shown as component A in Figure 3.1) are located at three locations in the reactor. The lifetime of these sensors is mainly limited by the 85 Chapter 3. Experimental Methods electrical connections at the back of the sensor. O n l y the sensor located w i t h i n the bed d id not fail prematurely. T h e outputs of these sensors are propor t ional to the logar i thm of the ratio of the oxygen pressures inside and outside the sensing element. Therefore, the output is sensitive to both the overall pressure of the system and the oxygen par t ia l pressure. The elutriated mater ial is collected by a hot gas filter unit at the exit of the roaster. T h i s is a chamber which functions like a high-temperature baghouse equipped w i t h three porous ceramic candles [202]. To enhance particle capture and to minimize the loading of the candles, the particle-laden gas enters the filter "tangentially". T h e candles are cleaned by a pulse system involving solenoid valves, w i t h the t iming and durat ion of the pulses controlled by the data acquisition computer. A chemical scrubber removes sulfur dioxide from the outlet gas stream. The scrubber consists of two 57 li tre stainless tanks (beer kegs) filled w i t h 16 wt% N a O H solution. T h e choice of the solution strength is discussed in appendix E . T h e draft through the entire system is created by an eductor-type vacuum pump (Vaccon C D F - 2 0 0 ) . T h e feeding system (not shown in Figure 3.1) allows the roaster to be fed continuously. Sol id additions to the fluidized bed are metered using a scale and a speed-controlled rotary valve. T h e concentrate is conveyed pneumatical ly and enters the bed through couplings near the distr ibutor plate. A K a l m a n filter w i t h integral control automatical ly controls the feeder motor speed to obtain the desired feedrate. A p p e n d i x A presents more details on the feeder. A pressure switch and a safety manometer are connected to the bo t tom of the preheater to allow for overpressure and underpressure protection. If plugging occurs anywhere i n the system, the system w i l l pressurize up to the pressure switch l imi t . Once this l imi t has been reached, the system automatical ly stops the power to the furnaces and interrupts the flow of gases to the system. If the pressure s t i l l increases beyond the pressure switch l imi t , a second l imi t may be reached, set by the safety manometer. T h e safety manometer w i l l dra in and vent the gases to the bui ld ing exhaust system. Underpressure protection is set by the safety manometer water height. If excessive underpressure occurs, the water w i l l d ra in and air w i l l enter the system. Once the safety manometer seal has been broken, an experiment cannot be continued un t i l the .86 Chapter 3. Experimental Methods manometer is refilled w i t h coloured water. 3.2 Description of materials 3.2.1 Zinc concentrates T h e zinc concentrates used in this study were chosen because of the large experience of this project's sponsor using w i t h these concentrates. The i r compositions are typ ica l of most zinc concentrates. Approx ima te ly 200 kg of zinc concentrate were shipped to U B C by TeckCominco in June 2001 i n 16 sealed 11 litres pails (concentrate 1(a) and concentrate 2). T h e pails were weighed, labelled, and stored outside i n a covered, locked enclosure un t i l required. Samples were gathered from a number of pails for assay of mult iple elements ( including total sulfur and silica) and sulfate sulfur. A second batch of 140 kg of zinc concentrate (Concentrate 1(b)), shipped in September 2002, was also assayed. Table 3.1 presents the concentrates chemical compositions. These results were obtained from an independent laboratory (International P l a s m a Labora tory L t d , Vancouver) . O n l y the major elements are shown in the table; the complete assays are presented in A p p e n d i x F . T h e zinc, and sulfur assays were obtained by t i t ra t ion and gravimetric methods, while the other elements were obtained by mul t i -ac id digestion followed by induct ively coupled p lasma ( I C P ) analysis. Table 3.1: Weight composit ion of zinc concentrates (wt%) Element Concentrate 1(a) Concentrate 1(b) Concentrate 2 Z n 53.22 54.28 51.12 30.51 31.19 29.83 1.76 1.38 1.48 Fe 4.47 4.57 8.1 P b 3.5 3.5 4.7 C d 0.34 0.34 0.14 C u 0.15 0.14 0.05 X - R a y diffraction of one of the concentrate 1(a) samples confirmed the presence of sphalerite. 87 Chapter 3. Experimental Methods Si l ica and lead sulfide may have accounted for some of the very smal l peaks detected, but their presence is inconclusive. Elec t ron microscopy and X - R a y spectroscopy could not detect any sulfide phases other than sphalerite. Some gangue mineral inclusions, ma in ly composed of silica, were observed. T h e solid density are 4170 k g / m 3 and 4040 k g / m 3 for concentrates 1 and 2, respectively, based on the wet picnometer method. Elec t ron microscopy indicated that there is l i t t le or no porosity present wi th in the concentrate particles. The particle size distr ibutions were obtained using a M a l v e r n Mastersizer 2000 equipped wi th a Scirroco 2000 dry feeder. T h i s instrument uses laser diffraction to measure particle size distr ibutions ranging from 0.02 to 2000 pm. T h e dry feeder was operated w i t h a dispersion pressure of 2.5 bar. Par t ic le size dis t r ibut ion analyses of concentrate 1 and of concentrate 2 are shown in Figure 3.2 and Table 3.2. T h e two batches of concentrate 1 have, for a l l pract ical purposes, the same particle size d is t r ibut ion. T h e particle size d is t r ibut ion of a pure zinc sulfide is also shown i n Figure 3.2. Since pure zinc sulfide has a much finer particle size d is t r ibut ion than that of the concentrates, no fluidized bed roasting experiment was at tempted w i t h pure Z n S . Note that dv is the area averaged particle size and dv is the volume averaged particle size. T h e y are calculated from the average size (dpi) and the mass fractions ( X J ) of each size fractions, using the following equations: dp = —l~x£ (3.1) ^ d upi dy — ^ ] %idpi (3-2) Approx imate ly one week before an experiment, the contents of one pa i l were transferred into stainless steel and glass containers that were then placed i n an 50°C oven un t i l they reached a constant weight (after approximately 6 days). T h e dried concentrate was then sieved through a 63 pm screen and the oversize fraction was rejected. T h e screened concentrate was also assayed for the same elements as listed in Table 3.1. 88 Chapter 3. Experimental Methods Particle Size (um) Figure 3.2: Part ic le size d is t r ibut ion of zinc concentrates. L ine for Concentrate 1 is for both Concentrate 1 (a) and 1 (b). 3.2.2 Bed material: silica sand and alumina To determine whether agglomeration occurred on the surfaces of the particles in i t i a l ly present in the bed, or alternatively from newly-formed zinc calcine seeds, the typ ica l zinc calcine bed material was replaced w i t h si l ica sand or a lumina particles, because of their relative inertness at high temperatures. Furthermore, the large difference between the molecular weights of si l ica and zinc oxide enhanced the visual differentiation between these phases i n backscattered electron microscopy. 50 kg each of 50 mesh and 125 mesh Lane M o u n t a i n si l ica sand, (> 99 wt% S i 0 2 ) , were obtained in 25 kg bags from Target Products (Burnaby, B . C . ) . U p o n reception, the s i l ica sand was stored in pails and sampled for chemical analysis. Similar ly, a 25 kg bag of 100 mesh brown a lumina was purchased from Manus Abrasives. 89 Chapter 3. Experimental Methods Table 3.2: Part ic le size dis t r ibut ion of zinc concentrates Concentrate Pure 1(a) 1(b) 2 Z n S Surface/Volume average: dp (/xm) 3.67 3.71 6.48 0.51 Volume average: d„ (/xm) 14.6 14.8 21.5 0.59 dm (/-*m) 1.49 1.49 2.90 0.32 d 5o (pro) 9.53 9.58 16.30 0.51 d 8 0 (/xm) 23.4 24.1 33.2 0.72 d 9 0 (/xm) 32.9 33.6 44.2 0.86 Table 3.3 presents the sand chemical composit ion. T h e metals are shown i n their oxide form. T h e reader is referred to appendix F for the complete assay i n metal form. T h e particle size distributions are shown in Figure 3.3 and the Sauter mean size of the various sands are reported in Table 3.4. T h e measured solids densities of s i l ica and a lumina are 2650 k g / m 3 and 3960 k g / m 3 respectively. E lec t ron microscopy of cross-sections have shown that bo th s i l ica and a lumina are non-porous. Table 3.3: Weight composi t ion of in i t ia l bed materials (wt%). S i l ica sand assays performed by mult i -acid digestion and I C P . A l u m i n a assay performed by fusion and TCP. Element S i 0 2 50 mesh S i 0 2 125 mesh A 1 2 0 3 100 mesh A 1 2 0 3 0.21 0.30 92.34 F e 2 0 3 0.033 0.048 0.23 K 2 0 0.056 0.077 0.14* N a 2 0 0.019 0.021 0.043* S i 0 2 balance balance 1.1+ TiC -2 <0.016 <0.016 2.94 Z n O 0.029 0.010 0.103* * :Mul t i -ac id digestion may be incomplete + : Fusion and I C P laboratory 2 90 Chapter 3. Experimental Methods Particle Size (urn) Figure 3.3: Particle size distribution of initial bed materials Table 3.4: Particle size distribution of initial bed materials Silica Sand 125 Silica Sand 50 Alumina Sur face/Volume average: d p (jum) 80.9 223 173 Volume average: d„ (/im) 126 307 191 dio (Mm) 47.7 122 111 dso (Mm) 94.0 266 173 d8o (Mm) 147 411 230 dgo (Mm) 186 500 263 Between 3 and 3.5 kg of silica (5 kg for alumina) were taken from any pail before an experiment. A sample was assayed for the same elements as listed for the concentrates. The silica and alumina compositions differed slightly, during the course of the experimental program (SiC>2: average=95.5wt%, a=3.9wt%, A1203: average=88wt%, cr=2.2wt%) 91 Chapter 3. Experimental Methods 3.2.3 Gases The gases used were air, nitrogen and oxygen. Nitrogen was used as a purge gas for the various pressure transducers and as the carrier gas for the pneumatic concentrate feeder. Air and oxygen were the main reaction gases. Nitrogen and oxygen were supplied in compressed gas cylinders by Praxair. Table 3.5 presents the purities guaranteed by the supplier. The relative humidity of the air supplied by the building compressor was measured on June 10, 2003 to be 8.6% at a temperature of 23.6°C. At this relative humidity, air contains approximately 0.25 vol% water. Similar humidity readings were measured in December 2003. Table 3.5: Composition of gases Gas Supplier Purity Industrial Nitrogen Praxair 99.995 vol% Medical Oxygen Praxair 99.0 vol% 3.3 Roasting experiments: Experimental conditions 3.3.1 Experimental program The experimental runs tested the effects of temperature, superficial gas velocity, stoichiometric excess oxygen, inlet oxygen concentration, bed material and size distribution. Table 3.6 presents the range of conditions of each factor. The superficial gas velocity is the velocity of the fluidizing gas at the roasting temperature and one atmosphere pressure. The maximum temperature is the maximum safe temperature which can be sustained by the reactor material without excessive oxidation.The experimental conditions were chosen by setting the bed temperature, gas velocity, inlet oxygen concentration and, knowing the concentrate composition, calculating the required feedrate for a chosen stoichiometric excess oxygen. Table 3.7 lists the experiments performed during the experimental program. In experiments 5, 6, 11 and 12, where oxygen enrichment (higher oxygen concentration) was used, the gas velocity was chosen so that the same feedrate as without oxygen enrichment could be used for a given 92 Chapter 3. Experimental Methods stoichiometric excess oxygen. For experiments 25 and 26. the freeboard oxygen concentration was measured for different feedrates and inlet oxygen concentrations. Experiment 27 is identical to experiment 23 except that additional oxygen was inserted into the freeboard to provide an additional 10% excess oxygen (total: 20% excess oxygen). This experiment was performed to evaluate whether the freeboard affects the bed particle behaviour. 3.3.2 Operating procedure The day prior to an experiment, the zinc concentrate was sieved, 24 kg of 16 wt% sodium hydroxide (NaOH) solution were prepared, transferred to the scrubber tanks, and allowed to cool before use, and the bed sand was pre-weighed. On the day of an experiment after the three zones of the roaster had been preheated to roughly 600 to 700°C, the pre-weighed sand was loaded into a hopper and discharged through the sampling port at the top of the roaster. Dry air supplied by the building compressor was simultaneously blown at a rate of 20 to 25 l/min (STP) to prevent particles from falling through the distributor plate. The temperature in the three zones was then allowed to reach the roasting temperature before the oxygen, nitrogen, and air flow rates were adjusted to their set levels. Preheating and bed material loading typically required 3 hours. The feeder hopper was filled with 2 kg of concentrate, enough to last for 1 to 2 h. Grab samples for chemical analysis were occasionally taken from the prepared feed prior to refilling the hopper. The feeder was activated by first specifying the desired feed rate on the display screen of the data acquisition and control software, and then pressing the start key. Together with the furnace controllers, the data acquisition system monitored and logged periodically (1 s intervals) temperatures, pressures, oxygen concentrations, at several locations throughout the set-up, including the preheater, bed, freeboard, filter, cooler, and outlet. The concentrate feed rate and feeder weight were also recorded. The hopper was refilled periodically over the course of an experiment. Bed and carry-over samples were typically collected every 30 min. The bed sampling device consisted of a 3 m long, 6.3 mm (1/4 inch) wide stainless steel 316 tube connected at one end to 93 Chapter 3. Experimental Methods Table 3.6: Range of experimental variables M i n M a x Temperature 875°C 975°C Feed gas oxygen concentration 21% 30% Superficial gas velocity 0.25 m / s 0.5 m / s Inert bed mass 3 kg 5 kg Inert bed material S i 0 2 A 1 2 0 3 B e d material size 81 /um 223 pm Concentrate Concentrate 1 Concentrate 2 D r y concentrate feed rate 10 g / m i n 36 g / m i n Excess Oxygen 0 % 80 % Table 3.7: Summary of experimental conditions for each experiment Run Bed Material Concentrate Feed rate Temperature Sup. gas velocity Gas composition Excess Oxygen 1 50 S i 0 2 C. 1 + 125 S i 0 2 10 g/min 940 °C 0.25 m/s 21% 0 2 80 % 2 50 S i 0 2 Cone. 1 10 g/min 940 °C 0.25 m/s 21% 0 2 80 % 3 125 Si0 2 Cone. 1 10 g/min 940 "C 0.25 m/s 21% 0 2 80 % 4 125 Si0 2 Cone. 1 10 g/min 940 "C 0.25 m/s 21% 0 2 80 % 5 50 S i 0 2 Cone. 1 10 g/min 940 "C 0.22 m/s 25% 0 2 80 % 6 125 S i 0 2 Cone. 1 10 g/min 940 °C 0.22 m/s 25% 0 2 80 % 7 50 S i 0 2 Cone. 1 17.5 g/min 940 °C 0.25 m/s 21% 0 2 0 % 8 125 S i 0 2 Cone. 1 17.5 g/min 940 °C 0.25 m/s 21% 0 2 0 % 9 125 S i 0 2 Cone. 1 16.25 g/min 940 °C 0.25 m/s 21% 0 2 10 % 10 50 Si0 2 Cone. 1 16.25 g/min 940 °C 0.25 m/s 21% 0 2 10 % 11 125 S i 0 2 Cone. 1 17.5 g/min 940 °C 0.22 m/s 25% 0 2 0 % 12 50 S i 0 2 Colic. 1 17.5 g/min 940 °C 0.22 m/s 25% 0 2 0 % 13 50 S i 0 2 Cone. 1 15 g/min 940 °C 0.25 m/s 21% 0 2 20 % 14 50 Si0 2 Cone. 1 15 g/min 940 °C 0.25 m/s 21% 0 2 20 % 15 50 S i 0 2 Cone. 1 16.25 g/min 875 °C 0.25 m/s 21% 0 2 10 % 16 50 S i 0 2 Cone. 1 16.25 g/min 975 °C 0.25 m/s 21% 0 2 10 % 17 50 Si0 2 Cone. 1 16.25 g/min 905 °C 0.25 m/s 21%, 0 2 10 % 18 50 S i 0 2 Cone. 2 14.85 g/min 940 °C 0.25 m/s 21% 0 2 10 % 19 50 S i 0 2 Cone. 1 36 g/min 940 °C 0.5 m/s 21% 0 2 10 % 20 50 S i 0 2 Cone. 1 23.25 g/min 940 °C 0.25 m/s 30% 0 2 10 % 21 50 Si0 2 Cone. 1 26.25 g/min 940 "C 0.375 m/s 21% 0 2 10 % 22 50 S i 0 2 Cone. 1 19.8 g/min 940 °C 0.25 m/s 25% 0 2 10 % 23 50 S i 0 2 Cone. 1 16.25 g/min 940 °C 0.25 m/s 21% 0 2 10 % 24 100 A1 2 0 3 Cone. 1 16.25 g/min 975 °C 0.25 m/s 21% 0 2 10 % 25 50 S i 0 2 Cone. 1 Varies 940 °C 0.25 m/s 21 and 25% 0 2 varies 26 125 S i 0 2 Cone. 1 Varies 940 "C 0.25 m/s 21% 0 2 varies 27 50 S i 0 2 Cone. 1 16.25 g/min 940 "C 6.25 m/s 21% 0 2 10 % + 10 % 94 Chapter 3. Experimental Methods a 150 m m long, 25.4 m m (1 inch) wide strainless steel 316 tube (cup) using a Swagelok fitt ing, hand-tightened w i t h Rock and R o l l ceramic anti-seize (for details, see appendix D ) . T h e fi t t ing was screwed into a p lug welded at one end of the wider tube. T h e other end was also sealed w i t h a plug. Four 9.5 m m (3/8") wide, 12.5 m m (1/2") long slots were machined into this tube as openings for captur ing particles. A longer version of this sampler is capable of captur ing about twice as much solids. The sampling valve was opened to lower the sampling device into the bed, un t i l it reached the level of the distr ibutor,plate. T h e sampler was continuously purged w i t h nitrogen gas, injected through the tube to "quench" reactions of particles which had been collected. T h e device was quickly retracted and removed 5 s later and allowed to cool before discharging the solids (60-140 g, sampler-dependent) into a metal cup standing i n a water bath. After cooling, the samples were bagged and labelled. The carry-over particles accumulated at the bo t tom of the filter were collected according to the following method. After opening the filter outlet valve, the bo t tom of the filter was hammered to dislodge adhering particles into the hopper. T h e filter outlet valve was closed before unscrewing the cap below the hopper and discharging the solids (60-600 g, average 100 g) into a P y r e x dish. These solids were at ambient temperature and d id not require further cooling. T h e solids were bagged and labelled. D u r i n g some experimental runs, the gas was analyzed for oxygen. T h e analysis t ra in consisted of an inline cooler, a solids collection tube, an inline gas filter (Swagelok SS-2F-0.5/xm), a smal l sulfur dioxide scrubber (two 1 litre Erlenmeyer containing 500 m l 16wt% N a O H solution) and a gas dryer. T h e sampling t ra in effectively removed particles and SO2 from the sampled gas prior to analysis. A H o r i b a ES-510 sampling unit and a H o r i b a P G - 2 5 0 A portable gas analyzer terminated the sampling t ra in . T h e sampling unit pumped the necessary gas volume required for analysis through the sampling t ra in . T h e feeder was turned off after supplying the available concentrate ( typical ly 8 to 10 h) . Samples were collected dur ing the next hour, after which the electrical heaters, as wel l as the nitrogen 95 Chapter 3. Experimental Methods and oxygen gas supplies, were shut off, leaving only a flow of air. Sampl ing continued dur ing the next hour. T h e fluidizing gas delivery was discontinued when the temperatures dropped to between 700 and 800°C. D u r i n g cooling, the scrubber by-pass valve was opened, while the eductor maintained a slight vacuum wi th in the roaster. W h e n the temperatures in the three zones were near ambient (approximately 36 hours later), a tube was inserted through the sampling valve to extract the bed particles by vacuum cleaning. The solids were then weighed. T h e roaster was disassembled and cleaned. A metal wire brush was used to scrub the inside walls for particulates and accretions which were collected and weighed. T h e particles in the pre-heater, outlet pipe, and filter were also collected. The scrubber tanks, containing a spent solution of sodium hydroxide, a mix tu re of sodium sulfite and sodium bisulfite, were emptied. T h e solutions were disposed in waste drums. Some samples of the solutions were assayed. W i t h the exception of sulfur, which exceeded the I C P detection range, a l l assayed elements were in negligible amounts. For further details of the experimental procedures, see A p p e n d i x B . 3.4 Sintering tests To determine the sintering tendency of the materials dur ing roasting, static sintering tests were performed in V i c o r tubes (96% SiC-2 glass). A number of tubes were prepared by sealing one end of the tube and filling w i t h zinc concentrate. T h e filled tubes were dr ied in air at 105°C and sealed. T h e sealed tubes were placed in a cold muffle furnace, heated to the sintering temperature (950°C) , and held at that temperature for 1 hour. T h e muffle furnace was then turned off and the sample was furnace cooled. After cooling, the tube was broken to access the sample and prepare it for electron microscopy. 3.5 Analysis of solid products Ei ther the solids collected dur ing the last bed sampling or the leftover bed solids were split and then sieved on 16 (1.18 mm) , 40 (425 pm), 70 (210 nm), 140 (105 pm), and 230 (63 pm) 96 Chapter 3. Experimental Methods mesh screens. Except where the weight of the solids collected on a given screen was negligible, the solids of each size fraction were packaged and assayed. Similarly, some of these solids were prepared for electron microscopy. 3.5.1 Chemical analyses The bed samples required for analysis were riffled three times and split. This procedure was repeated, if needed, until the halves weighed about 30 g. Grab samples of about 60 g were taken from the required carry-over samples. The 3-4.5 kg of solids left in the roaster were also riffled, split, and sampled. These samples were packaged in plastic bags, labelled, and shipped to the analytical laboratory for chemical analysis. Typical analyses, performed by the TeckCominco Analytical Laboratory according to the methods described in Table 3.8, comprised: ICP scan (including sulfur and silicon reported as silica), sulfate sulfur, ferric iron, chlorides, and fluorides. Table 3.8: Methods used for chemical analysis of solid samples Induct ive ly C o u p l e d P l a s m a -A t o m i c E m i s s i o n Spectroscopy ( I C P - A E S ) Fuse samples in NaOH/Na2C>2 over flame. Button dissolved in HCI. Dilute to 10% HCI. Simultaneous multi-element analysis by ICP-AES. S 0 4 / S (Grav imet r i c ) Digest samples to dryness with HCI. Dissolve residue in Na2C03 and filter. Neutralize and add BaCb-Filter off BaSC>4 precipitate and ash in muffle furnace. F e + + / F e + + + (Redox T i t r a t i o n ) Digest samples in HCI. Redox Titration with Na2Cr2C>7. Loss on ign i t ion ( L O I ) Weigh samples before and after ashing at 800°C for one hour. 3.5.2 Scanning electron microscopy and X-ray diffraction Less than 0.5 g of sieved solids was placed into a silicone rubber crucible over which was poured a viscous epoxy solution, comprised of 2 parts of epoxy resin and 1 part of hardener (Cold Cure resin and Jet Cure Hardener from Industrial Formulators Burnaby, B.C.), previously stirred thoroughly for approximately 3 min. The solution was gently mixed to disperse the particles and to ensure good contact between particles and epoxy. The epoxy mount was allowed to harden at room temperature, then ground with silicon carbide paper, and finally polished using alumina slurries from 6 down to 1 pm. After rinsing with water and ethanol, and allowing the samples 97 Chapter 3. Experimental Methods to dry, the mount was carbon-coated. Qualitative analysis and imaging were performed using a Hitachi S-2300 scanning electron microscope (SEM) equipped with an X-ray energy dispersion spectrometer (EDS), operated with an accelerating voltage of 20 kV, and a working distance of 23 mm. Backscattered and secondary electron images were simultaneously acquired and stored on a PC computer for later analysis. For the samples observed without epoxy mounting, the samples were laid on an electrically con-ductive double-sided adhesive pad. The samples were than carbon-coated prior to observation. X-ray diffraction was performed on a few samples. The samples were ground to a fine powder using a mortar and pestle prior to mounting in the sample holder. The diffractograms were obtained from a Philips PW1830 X-Ray generator equipped with a copper source (operated at 35 kV and 20 mA) and a diffractometer. The scanning angle, 26, usually ranged from 20 to 90°. 98 Chapter 4 Exper imenta l Resul ts In this chapter, the experimental results are presented for different operating conditions. Table 4.1 summarizes the comparisons to be made for the different experimental conditions. The evolution of the bed particle size distribution and the rate of bed mass increase are first described. These two variables are similar to monitoring the bed size distribution and the amount of bed overflow over time in industrial fluidized bed roasters. This laboratory study has the advantage that many other variables are monitored and a complete mass balance can be performed on the metallic species. For instance, an overall mass balance is done to evaluate the overall proportion of carryover calcine. Elemental balances are used to determine if and which elements stay preferentially in the bed. Bed samples were assayed by particle size fraction. Elemental mass balances over the samples were performed to determine if coating and agglomeration with the initial inert bed particles occurred and to evaluate if some elements preferentially segregated to some size fractions. The microstructure of bed and carryover particles are presented in scanning electron images for the key conditions. These images show coatings and agglomerates produced in the laboratory roaster. Assays of carryover samples for various experimental conditions are summarized as conversions, sulfate to sulfur ratios and ferric to total iron ratios. 99 Chapter 4. Experimental Results Table 4.1: Correspondence between run numbers and parameters studied. For operating con-ditions of each experiment, see Table 3.7 Temperature 875°C 905°C 940°C 975°C Experiment number 15 17 10 and 23 16 Superficial gas velocity 0.25 m/s 0.375 m/s 0.5 m/s Experiment number 10 and 23 21 19 Base Run 1 Cone. 1(a) 2 Cone. 1(b) 3 Cone. 1(b)* 4 Cone. 2 Experiment number 10 23 27 18 *: A n add i t iona l 10% excess oxygen (pure oxygen) was added into the freeboard. Inlet oxygen concentration 21 vol% 25 vol% 30 vol% Experiment number 10 and 23 22 20 Excess oxygen 0 % 10 % 20 % 80 % Experiment number (large particles, 21% inlet oxygen) 7 10 and 23 14 2 Experiment number (small particles, 21% inlet oxygen) 8 9 4 Experiment number (large particles, 25% inlet oxygen) 12 22 5 Experiment number (small particles, 25% inlet oxygen) 11 6 Bed material Silica Large particles Silica Small particles Alumina Experiment number see above 24 4.1 Evolution of bed particle size distribution The initial bed material for each experiment differs from any of the materials produced during the experiments. The initial bed size distribution is that of the initial bed material. Any changes in the size distribution and bed average particle size are attributed to agglomeration, elutriation and reaction of zinc concentrate. Figure 4.1 presents the average bed particle sizes for the samples taken during each experiment. The initial and final particle sizes are highlighted. Except for experiments at higher superficial gas velocity (Figure 4.1(b)), or with very fine initial bed material (Figure 4.1(f)) all experiments produced a smaller average bed particle size than the initial size. The decrease in size for most experiments is simply due to the presence of very 100 Chapter 4. Experimental Results fine calcine particles. Since few fine particles were in i t ia l ly present, the presence of very fine calcine particles (new particles) shifts the average to smaller sizes. For the experiments w i th small in i t ia l average particle size at low excess oxygen (0 and 10%) (Figure 4.1(f)), the bed particle size was larger than that of the in i t i a l bed material . However, for large excess oxygen, there was l i t t le change i n the average bed particle size. Note that the average bed particle size does not give any information on whether agglomeration occurs, or to what extent. 4.2 Rate of bed mass increase T h e laboratory roaster does not have an overflow or underflow exit stream, and mater ial en-trained is not returned to the bed. Mate r i a l accumulating in the bed leads to an increase in bed mass. In the industr ia l roaster, there is a weir whose height is constant. Therefore, any material accumulat ing in the industr ia l roaster bed is balanced by mater ial overflowing from the bed. Since there is no exit stream in the laboratory roaster other than the entrained material , material not entrained stays in the bed. T h e bed mass increase rate i n the laboratory roaster should therefore be related to the overflow rate in the industr ia l roaster. T h e rate of bed mass increase is calculated from the bed pressure drop recorded dur ing the experimental run. Sampl ing caused a smal l reduction in bed pressure drop, therefore, the bed pressure drop data between bed samples is used for the calculat ion of the rate of bed mass increase. T h e bed sampling frequency was adjusted to keep the average bed pressure drop relatively constant. F igure 4.2 presents rates of bed mass increase. T h e calculat ion of each data point is done by fitting one slope and mult iple origins to the logged bed pressure drops. The error bars correspond to ± one standard deviat ion of the rate of bed mass increase for consecutive 15-30 minutes intervals dur ing a given run. It is not known why the var iabi l i ty (error bar range) of some runs is very small , while the var iabi l i ty of others is very large. T h e rate of bed mass increase increases w i t h temperature and decreases w i t h excess oxygen. It also increases w i t h superficial gas velocity because of the increasing concentrate feed rate (constant excess oxygen). 101 Chapter 4. Experimental Results 300 300 300 300 ^250 E v 200 v E ro '"° 150 u t S.100 c ru 2 50 900 950 (a) Temperature (°C) 1000 0.3 0.4 0.5 (b) Superficial gas velocity (m/s) 300 r 2 3 (c) Base run 20 22 24 26 28 30 32 (d) Inlet oxygen concentration (vol%) X X X X o I o S o 9 o e 8 150 20 40 60 (e) Excess oxygen (%) 80 20 40 60 (f) Excess oxygen (%) Figure 4.1: Evolution of the sur face/volume average particle size for various experimental con-ditions, x: initial conditions, o: during experiment at different times, *: final conditions, (a) Temperature, (b): superficial gas velocity, (c): Base run number, (d): Inlet oxygen concentra-tion, (e): Excess oxygen for large inert particles, (f): Excess oxygen for small inert particles. 102 Chapter 4. Experimental Results T h e rate of bed mass increase does not offer information on whether agglomeration occurred, nor to what extent, i.e. there is no information on whether the new particles are smal l or large non-elutriable particles. Therefore, a more detailed analysis is required. 4.3 Assays and mass balances T h e val idi ty of the assay and mass information collected dur ing the experimental runs is eval-uated by means of an overall mass balance. Table 4.2 summarizes the overall mass information gathered for a l l the experiments. T h e five last columns of the table give masses of the sam-ples collected dur ing cleaning of the laboratory roaster after an experiment. T h e preheater contained some solids that fell through the distr ibutor plate holes. After removing the bed of particulate material at the end of a run, the distr ibutor plate (grid) was s t i l l covered w i t h some solids. Accret ions were scraped from the walls of the roaster. T h e pipe connecting the roaster to the filter contained some entrained solids. Note that the first two experiments lack the final bed mass information. T h e amount of calcine produced is calculated using the total mass of samples collected (collected from carryover ( C O . ) , bed, preheater, gr id , walls, pipe), the in i t i a l and final bed mass : Calcine Produced = Samples collected + F i n a l B e d — In i t ia l B e d (4-1) Th i s calculation subtracts the mass of the in i t i a l bed, consisting of a different material , from the total mass of collected material . Table 4.3 presents the overall mass balance results. A l l the final samples, i n addi t ion to those collected dur ing each experiment, are used to calculate the amount of calcine produced. T h e proport ion of calcine collected as carryover is shown. T h e mass conversion ratio (/?), i.e. ratio of mass of zinc calcine produced to mass of zinc concentrate fed, is shown in the last column. For complete conversion of pure zinc sulfide to pure zinc oxide, (5 would have a value of 0.835. T h e theoretical value of (3 for zinc concentrate 1, calculated from the concentrate assays, is 0.801. W i t h some exceptions, the values of (3 i n Table 4.3 agree well w i th the theoretical value. The calculated value of (3 is influenced by the extent of conversion as well any inaccuracy in 103 Chapter 4. Experimental Results 900 950 (a) Temperature (°C) 1000 - 5 0.2 0.3 0.4 0.5 (b) Superficial gas velocity (m/s) 2 3 (c) Base run 20 22 24 26 28 30 32 (d) Inlet oxygen concentration (vol%) 20 40 60 (e) Excess oxygen (%) 20 40 60 (f) Excess oxygen (%) Figure 4.2: Rate of bed mass increase (g/min). Calculated from bed pressure drop measure-ments for various experimental conditions, o 21 vol% inlet oxygen concentration, • 25 vol% inlet oxygen concentration, Lines correspond to ± standard deviation from experimental data over durations of 15-30 minutes, (a): Temperature, (b): superficial gas velocity, (c): Base run, (d): Inlet oxygen concentration, (e): Excess oxygen for large inert particles, (f): Excess oxygen for small inert particles. 104 Chapter 4. Experimental Results Table 4.2: Summary of total masses of samples used for the overall mass balance. Blank when unavailable. Initial Feed Bed Carryover Final Preheater Grid Walls Pipe Run bed samples samples bed (g) (g) (g) (g) (g) (g) (g) (g) (g) 2 3000 6000 1728.8 5295.8 4 3502.8 6221.6 772.4 4405.7 5 3300.1 6484.4 811.4 3912.2 2854.4 242.7 0 198.3 285.5 6 3501 6458.1 474.5 3151.2 2942.4 422.8 0 199.9 0 7 3303 8972.5 1492.1 4513.2 3869.9 126.8 360.7 9.4 103.8 8 3307 6357.7 1023.8 3560.1 3300.7 9 3306.6 9456.6 1261 5471.9 3689.4 198.6 53.5 54.4 90.2 10 3300.3 7598.3 1669 3543.6 3059.3 216.6 47.7 37.2 119.4 11 3301.1 9631 1639.5 5178.8 3835.4 138.8 169.5 109.7 138.8 12 3304.3 9972.9 1735.3 4660.9 4384 142.6 45.6 70.5 144.4 14 3302 9097.8 1306.7 5812 2947.8 265 143.3 34.1 132.7 15 2917.8 8637.6 620.6 5789.3 2977.9 131.9 124.3 12.3 137.5 16 3303.1 9553.3 2994 4287.5 3386.2 54.3 44.5 74.6 152 17 3300.9 7893.5 795.2 4545.3 3310.4 182.1 0 70.6 191 18 3300.9 6592.6 1298.2 3217.8 3542 52.9 11.3 23.9 238.3 19 3301.1 9207.9 948.5 6409 3447.7 18.4 41.4 16.6 56.5 20 3311.3 8815.5 1847.6 3999.1 4328.9 44.4 56.3 57.2 120.4 21 3300.3 8604.5 1903.1 4629.8 3573.5 14.7 29.3 29.9 9.1 22 3297.7 7767.3 1426.7 3650 4019.7 151.9 72.4 49.2 21.3 23 3304.4 8605.5 1786.2 4459.7 3926.3 58.3 121.4 74.7 115.2 24 5000 7453.2 2180.7 2328.1 4699 34.7 88.3 1668.2 156.7 27 3300.5 8224.7 1679.6 4450.7 3023.6 588.7 196.9 40.9 139.1 the mass of concentrate fed. Inaccuracies are mainly caused by the loss of some concentrate during feeder upsets. The proportion of calcine collected as carryover varied between 37 and 84 %. The experimental conditions which influenced these proportions are discussed below. 4.3.1 Conversion and sulfur balance The method used to calculate the conversion uses the residual sulfur left as sulfide. Both sulfate and sulfide sulfur are unwanted in the calcine. However, because sulfide sulfur does not typically 105 Chapter 4. Experimental Results Table 4.3: Results of overall mass balance: P ropor t ion of calcine as carryover and calcine to concentrate mass ratio (f3) Run Total Calcine Carryover 0 (g) (%) (-) 5 5004.4 78.1 0.771 6 3689.8 85.4 0.571 7 7172.9 62.9 0.799 8 4577.6 77.7 0.720 9 7512.4 72.8 0.794 10 5392.5 65.7 0.709 11 7909.4 65.4 0.821 12 7879 59.1 0.790 14 7339.6 79.1 0.806 15 6876 84.1 0.796 16 7690 55.7 0.804 17 5793.7 78.4 0.733 18 5083.5 63.2 0.771 19 7637 83.9 0.829 20 7142.6 55.9 0.810 21 6889.1 67.2 0.800 22 6093.5 59.9 0.784 23 7237.4 61.6 0.841 24 6155.7 37.8 0.825 27 6819 65.2 0.829 leach in downstream processes, this method of calculat ing the conversion is usual ly preferred. Because the scrubbing efficiency is not known and no sulfur analysis was performed on the scrub-bing solutions, a complete sulfur mass balance cannot be calculated. However, the proport ion of sulfur leaving i n the gas may be estimated from the solid sample masses and compositions. T h e converted sulfur is therefore taken as the ratio of unaccounted sulfur in the solid at the end of the run to the amount of sulfur fed to the roaster. In general, 90-95% of the sulfur was not accounted for in the solid product. Therefore 90-95% of the sulfur fed to the roaster was assumed to be converted to sulfur dioxide, w i th the remainder collected in the carryover and bed material . 106 Chapter 4. Experimental Results 4.3.2 Base cases T h e base cases can be used to estimate the variat ion from one experiment to another when no experimental conditions changed. T h e base case runs are runs 10, 23, 27 and 18 (labelled base cases 1, 2, 3 and 4 respectively, below and i n Figures 4.1 (c) and 4.2 (c)). A l l base cases were operated at 940°C, at a superficial gas velocity of 0.25 m/s , at 10% excess oxygen. T h e y differ only i n the concentrate used (base case 4) and, for base case 3, by addi t ional injection of oxygen into the freeboard (equivalent to an addi t ional 10% excess oxygen, for a total of 20% excess oxygen). A l l four base cases had an overall proport ion of carryover between 61 and 65% (see Table 4.3). Figure 4.3 presents the t ime-variat ion of some parameters used in the mass balance for exper-imental run 10. T h e instantaneous mass of the bed is estimated from the instantaneous bed pressure drop. T h e sharp variations in apparent bed mass may be due to adjustments in purge gas flowrate, port b locking or other related factors affecting pressure drop measurement. Some experiments showed significant variations while others d id not. T h e assays of the bed samples clearly show an accumulat ion of zinc and other elements, while the assays for the carryover material suggest that the composi t ion d id not vary significantly w i t h t ime. Figure 4.4 presents the elemental mass balance results for the four base cases runs. In general, approximately 50 % of the i ron and zinc stayed wi th in the bed while the remainder left w i t h the carryover. T h e proport ion staying wi th in the bed was sl ightly higher (60-70%) for copper and cadmium. For lead, the proport ion staying in the bed was 75 to 80%. T h e differences between the overall and elemental proport ion in carryover comes from the assumption of the same calcine composi t ion for the overall mass balance. A closer analysis of bed samples reveals that the compositions of the different sizes of bed particles (see Figure 4.5) differed very l i t t le . T h e only exception is that the propor t ion of lead i n the fine particles (+230 mesh) of the experimental run w i t h concentrate 2 (base case 4) was much larger than for the other sizes and base cases. The assays do not add up to 100% since oxygen is not determined in the analyses. T h e large var iabi l i ty of the s i l ica assays is l ikely the 107 Chapter 4. Experimental Results cause of some summations exceeding 100% (Figure 4.5 (a), +70 mesh) Analys is of the assays of the carryover samples and the mass balance reveals that there was approximately 3 to 4% sulfur left in the carryover calcine, 20 to 40% of which was i n the form of sulfate. T h e carryover conversion, based on the remaining sulfide sulfur, ranged from 90 to 95%. T h i s conversion is much smaller than observed industr ial ly. However, i n industr ia l roasters, the very large freeboard leads to a much longer residence t ime than could be achieved i n the present equipment. Approx imate ly 94 to 95% of the sulfur could not be accounted for in the solid product . T h i s sulfur is expected to have reacted to sulfur dioxide and escaped to the scrubbers. In general, differences between the base cases are small . T h e injection of addi t ional oxygen in the freeboard d id not have any significant effect. T h i s may be due to the relatively smal l freeboard of the equipment. T h e origin of the large difference i n the fraction of i ron as ferric i ron (Figure 4.7(d)) between base case 1 and the other base case runs is unknown. Even if the amount of zinc and iron staying wi th in the bed was sl ightly higher for concentrate 2 (Figure 4.4), the propor t ion of calcine (zinc, i ron and lead) report ing to the very smal l particles was much larger for concentrate 2 than concentrate 1 (Figure 4.6). A s much as 50% of the calcine staying wi th in the bed was present w i th in the very fine particles (-230 mesh or pan). Th i s indicates that concentrate 2 appears to have a lower agglomeration tendency. In summary, by changing to concentrate 2 (base case 4), less agglomeration occurred and more zinc reported to the very smal l particles. 108 Chapter 4. Experimental Results 100 100 i < 40 4 6 Time (h) (a) B e d samples assays. » :Zn , o:Si02, x : P b , +:Fe (b) Car ryover samples assays. » : Z n , o:Si02, x : P b , + :Fe 3600 r (c) Input and output masses (d) B e d mass Figure 4.3: Assays of bed and carryover samples, masses of feed, bed samples, carry-over and bed for run 10, base case 1 109 Chapter 4. Experimental Results 0.8 0.6 t §.0.4 o 0.2 1 2 3 (a) Cd Base run 4 O O o o 1 2 3 (c) Fe Base run 4 0.8 0.6 o §.0.4 o 0.2 2 3 (b) Cu Base run o o o o ! 0.98 3 M0.96 | 0.94 't o Q . o £ 0.92 2 3 4 (e) Z n Base run 0.9 2 3 (d) Pb Base run O o o o 1 2 3 4 (f) S Base run Figure 4 .4: Variation in proportion of key elements based on mass balance for base cases. Concentrate 1(a), 2: Concentrate 1(b), 3: Concentrate 1(b), freeboard oxygen injection, Concentrate 2. (a) Cadmium, (b) Copper, (c) Iron, (d) Lead, (e) Zinc, (f) Sulfur. 110 Chapter 4. Experimental Results Figure 4.5: Assays of different bed particle size fractions for four base case runs. 1: Concentrate 1(a), 2: Concentrate 1(b), 3: Concentrate 1(b), freeboard oxygen injection, 4: Concentrate 2. B o t t o m to top: S i 0 2 , Z n , Fe , P b . I l l Chapter 4. Experimental Results Init. Final Zn Pb Fe Si02 Init. Final Zn Pb Fe Si02 (a) Base run 1 (b) Base run 2 Init. Final Zn Pb Fe Si02 Init. Final Zn Pb Fe Si02 (c) Base run 3 (d) Base run 4 Figure 4.6: D i s t r ibu t ion of mass of key elements w i th bed particle size fractions for four base case runs. 1: Concentrate 1(a), 2: Concentrate 1(b), 3: Concentrate 1(b), oxygen injection in freeboard, 4: Concentrate 2. B o t t o m to top: pan,+230,+140,+70,+40 112 Chapter 4. Experimental Results 2 3 (a) Base run 2 3 (b) Base run 2 3 (c) Base run 2 3 (d) Base run Figure 4.7: Comparison of assays of carryover of base cases. 1: Concentrate 1(a), 2: Concentrate 1(b), 3: Concentrate 1(b), freeboard oxygen injection, 4: Concentrate 2. (a) Total sulfur, (b) Fraction of sulfur as sulfate, (c) Conversion based on remaining sulfide sulfur, (d) Fraction of iron as ferric iron. 113 Chapter 4. Experimental Results Figures 4.8 to 4.12 present the microstructures of sieved bed particles for base case 1 (exper-imental run 10). T h e larger bed particles clearly consist of a si l ica core w i t h a coating. T w o other type of particles are present w i th in the smaller + 230 mesh and -230 mesh particles: un-agglomerated and agglomerated calcine particles. T h e unagglomerated particles ma in ly appear in the carryover and the -230 mesh fraction (pan). A few agglomerated particles appear i n the upper right por t ion of Figure 4.11. Figure 4.13 presents such an agglomerated particle. X - r a y spectroscopy on several locations w i th in this type of particle shows that such agglomerated par-ticles are very rich in lead. Since X - r a y spectroscopy does not give accurate results for oxygen, the oxygen peak was not used to quantify the composit ion of the particle, even when an oxygen peak was present. T h e core of the particle contains approximately 73 wt% P b , 17 wt% Z n , 8 wt% S and smal l amounts of Fe and C a (approximately 1 wt% each). A t the periphery, higher concentrations of zinc (25-46 wt%Zn) and iron (2-3.5 wt%Fe) were found. T h i s may indicate that calcine particles adhere to the surface of these agglomerated particles. Figure 4.14 shows an intermediate size (+140 mesh) particle. Part icles of this type usually present a si l ica core, w i t h a "coherent" lead-rich coating (up to 65 w t % P b , 7.5 w t % C d , 10.5 w t % Z n and 16 wt%Si) in some locations and a detached coating r ich i n zinc, i ron and si l ica (up to 81 w t % Z n , 2-10 wt%Fe, 9-15 wt%Si ) . T h e coherent coating is very t h in and direct ly on the surface of the si l ica particle. Figure 4.15 portrays carryover particles. F igure 4.16 shows an incompletely reacted particle found in the entrained calcine. T h i s particle, like other s imilar particles, has a core of zinc concentrate (66 wt% Z n , 26 wt%S, 7.5 wt%Fe, 0.5 w t % P b ) and a product layer of zinc calcine (89 wt% Z n , 8 wt% Fe, 1.3 w t%S, 0.6 wt% P b and 0.4 wt% Si) . T h e particles may not be spherical or have a uniform product layer. However, it is reasonable to assume that they react according i n a shrinking-core manner. X - r a y diffraction on the bed particles detected si l ica and zinc silicate. T h e carryover is composed of zinc oxide, zinc ferrite, and zinc silicate. A few peaks were unidentified for bo th the carryover and bed samples. One of the peaks found on both samples is probably zinc sulfide. 114 Chapter 4. Experimental Results Figure 4.8: S E M micrograph for product particles of run 10, +40 mesh, Secondary electrons image Figure 4.9: S E M micrograph for product particles of run 10, +70 mesh, Secondary electrons image 115 Chapter 4. Experimental Results Figure 4.10: S E M micrograph for product particles of run 10, +140 mesh, Secondary electrons image Figure 4.11: S E M micrograph for product particles of run 10, +230 mesh, Secondary electrons image 116 Chapter 4. Experimental Results Figure 4.12: S E M micrograph for product particles of run 10, -230 mesh (pan), Secondary electrons image ''' > < . . - ^ C ^ 1 />>*« : . % 1 . - V ? **, : • ' , * \ # . ft * 4 ». * • * 4 • . < x l . Q k 0880 2 0 k V 1 -2 5@.urn Figure 4.13: S E M micrograph for product particles of run 10, -230 mesh (pan), Secondary electrons image of agglomerated particle 117 Chapter 4. Experimental Results K 6 0 @ 0 8 0 8 2 0 k V 5 8 y m Figure 4.14: S E M micrograph for product particles of run 10, + 1 4 0 mesh, Secondary electrons image of coated particle Figure 4 .15 : S E M micrograph for product particles of run 10, carryover, Secondary electrons image 118 Chapter 4. Experimental Results X i @k 0 0 0 0 Figure 4 .16: S E M micrograph for product particles of run 10, carryover, Secondary electrons image of par t ia l ly reacted particle 119 Chapter 4. Experimental Results 4.3.3 Effect of superficial gas velocity The effect of superficial gas velocity is explored in experimental runs 10, 23 (U= 0.25 m/s), 21 (TJ=0.375 m/s) and 19 (U=0.5 m/s). It is important to note that as the superficial gas velocity increased, the concentrate feed rate also increased to keep the excess oxygen constant. However, the proportion of calcine leaving as carryover increased to 83.9% at the highest superficial gas velocity. The intermediate velocity did not see a significant increase in carryover over the lower velocities. Figure 4.17 presents the mass balance results. As for the base cases, cadmium and copper stayed within the bed in slightly larger proportion (50-60%) than zinc and iron (25-50%). Lead remained within the bed in similar proportions as for the base cases. Increasing the superficial gas velocity decreased the proportion of zinc and iron staying within the bed. This trend is less clear for cadmium, copper and lead. The superficial gas velocity had a similar effect on the sulfur leaving with the gas. The compositions of the different sizes of bed particles (see Figure 4.18) did not differ signifi-cantly for different superficial gas velocities. However, as the superficial gas velocity increased, the proportion of very fine particles (pan or -230 mesh) decreased (See Figure 4.19). The effect of superficial velocity on the bed particle size distribution can also be observed in Figure 4.1. It is well known that elutriation from a fluidized bed increases strongly with increasing superficial gas velocity. Not surprisingly, increasing the superficial gas velocity led to a smaller proportion of fines in the bed and a larger proportion of calcine leaving in the carryover. The superficial gas velocity did not have significant effects on the quantity of sulfur, the form of sulfur (sulfate to total sulfur ratio), the conversion or the proportion of ferric iron in the carryover (See Figure 4.20). 120 Chapter 4. Experimental Results 0.2 0.3 0.4 0.5 (a) Cd Superficial gas velocity (m/s) 0.2 0.3 0.4 0.5 (b) Cu Superficial gas velocity (m/s) 0.2 0.3 0.4 0.5 (c) Fe Superficial gas velocity (m/s) 0.2 0.3 0.4 0.5 (d) Pb Superficial gas velocity (m/s) 0.2 0.3 0.4 0.5 (e) Zn Superficial gas velocity (m/s) 0.2 0.3 0.4 0.5 (f) S Superficial gas velocity (m/s) Figure 4.17: Variation in proportion of key elements based on mass balance for different super-ficial gas velocities, (a) Cadmium, (b) Copper, (c) Iron, (d) Lead, (e) Zinc, (f) Sulfur. 121 Chapte r 4. Experimental Results pan +230 +140 +70 +40 (a) Superficial gas velocity. 0.25 m/s pan +230 +140 +70 +40 (b) Superficial gas velocity: 0.25 m/s pan +230 +140 +70 +40 (c) Superficial gas velocity: 0.375 m/s pan +230 +140 +70 +40 (d) Superficial gas velocity: 0.5 m/s Figure 4.18: Effect of superficial gas velocity on assays for different bed particle size fractions. Bottom to top: S i 0 2 , Zn, Fe, Pb 122 Chapter 4. Experimental Results 2o\\ Init. Final Zn Pb Fe S i 0 2 (a) Superficial gas velocity: 0.25 m/s 100 2 80 + + 60 40 20 _ _ • I mm I I Init. Final Zn Pb Fe S i 0 2 (b) Superficial gas velocity: 0.25 m/s 100 100 r o + o + O Init. Final Zn Pb Fe S i 0 2 (c) Superficial gas velocity: 0.375 m/s Init. Final Zn Pb Fe S i 0 2 (d) Superficial gas velocity: 0.5 m/s Figure 4.19: Effect of superficial gas velocity on dis t r ibut ion of mass of key elements w i t h bed particle size fraction. B o t t o m to top: pan,+230,+140,+70,+40 123 Chapter 4. Experimental Results 0.2 0.3 0.4 0.5 (a) Superficial gas velocity (m/s) .2 0.95 s 0.9 •» 0.85 0.8 0.2 0.3 0.4 0.5 (b) Superficial gas velocity (m/s) o OOOG O O £ 1 ^ 3 ° 0.2 0.3 0.4 0.5 (c) Superficial gas velocity (m/s) 0.2 0.3 0.4 0.5 (d) Superficial gas velocity (m/s) Figure 4.20: Compar ison of assays of carryover for different superficial gas velocities, (a) To ta l sulfur, (b) Fract ion of sulfur as sulfate, (c) Conversion based on remaining sulfide sulfur, (d) Fract ion of i ron as ferric i ron. 124 Chapter 4. Experimental Results 4.3.4 E f f e c t o f t e m p e r a t u r e Exper imenta l runs 10, 23 (940°C) , 15 (875°C) , 17 (905°C) and 16 (975°C) allow the effect of the roasting temperature to be examined. R u n 24 was also performed at 975°C, but used brown a lumina particles instead of si l ica sand as the in i t ia l bed material . T h e overall carryover (Table 4.3) varied from 84% at 875 °C to 56% at 975 °C for the s i l ica sand. For the a lumina, however, the proport ion leaving the roaster as carryover was 38%, a further decrease from the sil ica. W h e n comparing the propor t ion of key elements report ing to the bed for the experimental runs wi th si l ica sand, see Figure 4.21, there is a clear upward trend of the mater ia l s taying wi th in the bed wi th increasing temperature. For example, the propor t ion of lead staying wi th in the fluidized bed increased from approximately 40% at 875°C to more than 80% at 975°C. For i ron and zinc, the increase was not as dramatic as for lead. However, it nevertheless increased from approximately 20 to 40-50%. T h e mass balance on sulfur, however, does not show any clear trend. T h e effect of temperature on the const i tut ion of the bed samples is shown in Figures 4.22 and 4.23. A s the bed temperature increased, the proport ion of fine particles i n the bed decreased, while the propor t ion of zinc report ing to the smal l particles was also much lower. T h e assays also indicate that as the temperature increased, the particles contained a much larger proport ion of zinc. T h i s suggests that agglomeration increases wi th temperature. Figure 4.24 presents the assays of the carryover. W i t h the experiment w i t h a lumina excluded, the proport ion of sulfur as sulfate wi th in the carryover calcine decreased w i t h temperature. However, if the run wi th a lumina particles is included, this trend may disappear. T h e microstructures of sieved particles collected dur ing the experimental run at 975°C are shown in Figures 4.25 to 4.30. These particles appear to be denser and have a much coarser microstructure than for particles formed at lower temperature (Figures 4.8 to 4.12). Figure 4.26 portrays the microstructure of the coating of a 70 mesh particle. T h i s figure clearly shows that the coating consists of two-phases, akin to a lead-zinc silicate eutectic. Table 4.4 125 Chapter 4. Experimental Results 1, • 1 0.8 : 0.6 o o ct 0.2 O o 0.8 : 0.6 o ct 0.2 + O 850 900 950 1000 850 900 950 1000 (a) Cd Temperature (°C) (b) Cu Temperature (°C) 0.8 \ .£ °-6r c o t <LOA\ 0.2 0.8 c 0.6 c o '€ 8.0.4 0.2 850 900 950 1000 (c) Fe Temperature (°C) 850 900 950 1000 (d) Pb Temperature (°C) 0.8 [ : 0.6 g.0.4r o 0.2 IS 0.98 bO 5 bo0.96 0.94 o £ 0.92 + O 850 900 950 1000 "'850 900 950 1000 (e) Zn Temperature (°C) (f) S Temperature (°C) Figure 4.21: Variation in proportion of key elements based on mass balance for different tem-peratures, o: Silica sand, +: Alumina, (a) Cadmium, (b) Copper, (c) Iron, (d) Lead, (e) Zinc, (f) Sulfur. 126 Chapter 4. Experimental Results pan +230 +140 +70 +40 (a) Temperature: 875 °C pan +230 +140 +70 +40 (b) Temperature: 905 °C pan +230 +140 +70 +40 (c) Temperature: 940 °C pan +230 +140 +70 +40 (d) Temperature: 975 °C Figure 4.22: Effect of temperature on assays of different bed particle size fractions. B o t t o m to top: SiC-2, Z n , Fe , P b 127 Chapter 4. Experimental Results (c) Temperature: 940 °C (d) Temperature: 975 °C F i g u r e 4 .23 : Ef fec t o f t e m p e r a t u r e o n d i s t r i b u t i o n o f m a s s of k e y e l e m e n t s w i t h b e d p a r t i c l e s ize f r ac t i ons . B o t t o m t o t o p : p a n , + 2 3 0 , + 1 4 0 , + 7 0 , + 4 0 128 Chapter 4. Experimental Results o 850 0 . 8 1 — 850 900 950 (a) Temperature (°C) 10.95 8 e i/i o o o 8 | 0.9 OOO "3 co • o i/i "3 10.85 900 950 (c) Temperature (°C) + + 1000 0.2 O 0.8 O O 3 0.6 O |o.4 "3 CO 1/1 o1— 850 1000 o o 900 950 (b) Temperature (°C) + + 900 950 (d) Temperature (°C) 1000 1000 Figure 4.24: Compar i son of assays of carryover for different temperatures, o: S i l i ca sand bed, +: A l u m i n a bed. (a) Tota l sulfur, (b) Fract ion of sulfur as sulfate, (c) Conversion based on remaining sulfide sulfur, (d) Fract ion of i ron as ferric i ron. 129 Chapter 4. Experimental Results presents the results of X - r a y spectroscopy at different locations on 140 mesh particles. T h e white phases wi th in the coating are r ich in lead, and the dark phases are r ich i n zinc. B o t h contain a significant proport ion of si l ica. T h e coherent coating on the surface of the s i l ica particles is much more omnipresent for particles roasted at 975°C than for those shown previously (roaster at 940°C) . C a d m i u m was detected in non-negligible amounts in the coherent coating and the white phase. Iron appears to be i n relatively smal l amounts in the coherent coatings and dark phases (compared to the in i t i a l i ron concentration wi th in the concentrate). Table 4.4: X - r a y spectroscopy analysis of particle coatings obtained after roast ing at 975°C. B l a n k when not detected. Detect ion l imi t is typical ly 0.5 wt% or less and vary w i t h elements detected P b Z n Fe Si C d C u wt% wt% wt% wt% wt% wt% Coherent 73 20 4.4 1.8 Coherent 62 14 0.34 21 1.8 Coherent 43 12 43 1.3 W h i t e phase 65 20 2 11 1.8 W h i t e phase 49 35 1.7 11 1.8 W h i t e phase 65 22 2.5 8 0.9 D a r k phase 86 0.68 13 D a r k phase 0.43 88 1.0 11 The +230 mesh particles are predominantly of agglomerated type. W h e n compared wi th the +140 mesh particles, one can clearly see that the si l ica cores are smaller and the coatings are thicker for particles formed at higher temperature. T h i s indicates that these particles have grown. T h e microstructures of particles (not shown) formed at lower temperatures (875, 905°C) have a much thinner coating on the si l ica particles, indicat ing negligible agglomeration. T h e compounds wi th in the bed and carryover particles produced at 975°C were identified using 130 Chapter 4. Experimental Results Figure 4.25: S E M micrograph for product particles of run 16, +70 mesh, Secondary electrons image Figure 4.26: S E M micrograph for product particles of run 16, +70 mesh, Backscat tered electrons image of particle coating 131 Chapter 4. Experimental Results Figure 4.27: S E M micrograph for product particles of run 16, +140 mesh, Secondary electrons image Figure 4.28: S E M micrograph for product particles of run 16, +230 mesh, Secondary electrons image 132 Chapter 4. Experimental Results Figure 4.29: S E M micrograph for product particles of run 16, -230 mesh (pan), Secondary electrons image Figure 4.30: S E M micrograph for product particles of run 16, Carryover , Secondary electrons image 133 Chapter 4. Experimental Results X-ray diffraction. The bed particles consisted of zinc silicate and silica. The carryover samples were composed of zinc oxide, zinc ferrite and some zinc silicate. Again, some peaks could not be identified. The unidentified peak locations were at the same positions as those for the samples produced at lower temperature. One of these peaks may be due to zinc sulfide. 4.3.5 Effect of inlet oxygen concentration Experimental runs 10, 23 (21%), 22 (25%) and 20 (30%) allow the effect of oxygen enrichment or inlet oxygen concentration to be investigated. The overall proportion of calcine as carryover decreased marginally as the inlet oxygen concentration increased: from 66 and 62 % to 60% at 25 vol% to 56% at 30 vol% oxygen (Table 4.3). As shown by Figures 4.31 to 4.34, there is no significant difference for most variables among the different inlet oxygen concentrations. However, as indicated by Figure 4.33, the proportion of lead in the very fine particles (-230 mesh or pan) of the runs with oxygen enrichment was smaller than that of iron or zinc, indicating that lead may segregate to larger particles. 4.3.6 Effect of excess oxygen The effect of excess oxygen was studied in combination with two other factors: oxygen enrich-ment and bed particle size. Two bed particle sizes and two inlet oxygen concentrations were considered. Experimental runs 7 (0%), 10, 23 (10%), 14 (20%) and 2 (80%) used 50 mesh silica sand, with air as the fluidizing gas. Experimental runs 12 (0%) and 5 (80%) also used 50 mesh silica sand, but the fluidizing gas was oxygen-enriched air (25 vol% 02). Experimental runs 8 (0% excess oxygen), 9 (10%) and 4 (80%) used 125 mesh silica sand and air. Experimental runs 11 (0%) and 6 (80%) employed 125 mesh silica sand and oxygen-enriched air.(25 vol% 02). Table 4.5 summarizes the overall proportion of carryover from the various experimental runs for different excess oxygen and oxygen inlet concentrations. In general, increasing excess oxygen increased the proportion of calcine leaving the roaster as carryover. Higher excess oxygen led to a smaller coating than for the base case, a decrease in the amount of zinc on the large particles, and a decreased rate of bed mass increase. 134 Chapter 4. Experimental Results 20 22 24 26 28 30 32 (a) Cd Inlet oxygen concentration (vol%) 20 22 24 26 28 30 32 (b) Cu Inlet oxygen concentration (vol%) 0.8 c 0.6 c o ' t §.0.4 0.2 o o o o 20 22 24 26 28 30 32 (c) Fe Inlet oxygen concentration (vol%) 20 22 24 26 28 30 32 (d) Pb Inlet oxygen concentration (vol%) 0.98 5 M O . 9 6 0.94 t o o ct 0.92 20 22 24 26 28 30 32 (e) Zn Inlet oxygen concentration (vol%) 0.9 o o 00 20 22 24 26 28 30 32 (f) S Inlet oxygen concentration (vol%) Figure 4.31: Variation in proportion of key elements based on mass balance for different in oxygen concentrations, (a) Cadmium, (b) Copper, (c) Iron, (d) Lead, (e) Zinc, (f) Sulfur. 135 Chapter 4. Experimental Results pan +230 +140 +70 +40 (a) Inlet oxygen concentration: 21 vol% pan +230 +140 +70 +40 (b) Inlet oxygen concentration: 21 vol% 100 a N 0 pan +230 +140 +70 +40 (c) Inlet oxygen concentration: 25 vol% pan +230 +140 +70 +40 (d) Inlet oxygen concentration: 30 vol% Figure 4.32: Effect of oxygen concentration on assays of different bed part icle size fractions. B o t t o m to top: S i 0 2 , Z n , Fe , P b Table 4.5: Overa l l propor t ion of carryover as a function of excess oxygen, inlet oxygen concen-trat ion and in i t ia l bed particle size. B lank when no experiment, N . A . when information is not available. In i t ia l bed material : 125 mesh: small particles, 50 mesh: large particles. Excess Oxygen 125 mesh 50 mesh 21 % 25 % 21 % 25 % 0 78 65 63 59 10 73 62, 66 60 20 79 80 N . A . 85 N . A . 78 136 Chapter 4. Experimental Results Init. Final Zn Pb Fe Si02 Init. Final Zn Pb Fe Si02 (a) Inlet oxygen concentration: 21 vol% (b) Inlet oxygen concentration: 21 vol% Init. Final Zn Pb Fe Si02 Init. Final Zn Pb Fe Si02 (c) Inlet oxygen concentration: 25 vol% (d) Inlet oxygen concentration: 30 vol% Figure 4.33: Effect of oxygen concentration on dis t r ibut ion of mass of key elements w i t h bed particle size fraction. B o t t o m to top: pan,+230,+140,+70,+40 137 Chapter 4. Experimental Results 10 0.8 | 6f £ 4 o o o o 0.6 1/1 i 0 . 4 0.2 [ O O 20 22 24 26 28 30 32 (a) Inlet oxygen concentration (vol%) 20 22 24 26 28 30 32 (b) Inlet oxygen concentration (vol%) .2 0.95 \ 0.9 \ O 8 O 0.8 50.6 0.4 10.85 \ 0.2 20 22 24 26 28 30 32 ~ 20 22 24 26 28 30 32 (c) Inlet oxygen concentration (vol%) (d) Inlet oxygen concentration (vol%) Figure 4.34: Compar i son of assays of carryover for different inlet oxygen concentrations, (a) Tota l sulfur, (b) Fract ion of sulfur as sulfate, (c) Conversion based on remaining sulfide sulfur, (d) Fract ion of i ron as ferric i ron. 138 Chapter 4. Experimental Results T h e e x p e r i m e n t s at 0 % excess o x y g e n gave di f ferent r e su l t s d e p e n d i n g o n t h e o r i g i n a l average b e d p a r t i c l e s ize . F o r a l a rge r m e a n p a r t i c l e s ize , t h e l a rge p a r t i c l e s h a d n e g l i g i b l e c a l c i n e c o a t i n g . F o r t h e coarse i n i t i a l b e d , v e r y l i t t l e a g g l o m e r a t i o n o c c u r r e d . F o r t h e f ine s i l i c a s a n d (125 m e s h ) , t h e effect o f excess o x y g e n was s i m i l a r , e x c e p t for t h e 0 % excess o x y g e n case w h e r e l a rge c a l c i n e p a r t i c l e s were c r e a t e d . T h e c a l c i n e p a r t i c l e s a d h e r e d e x c e s s i v e l y t o v e r y la rge p a r t i c l e s , c a u s i n g d e f l u i d i z a t i o n t o o c c u r d u e t o s e g r e g a t i o n . L e a d a g a i n p r e f e r e n t i a l l y segrega ted t o l a rge r p a r t i c l e s . F o r b o t h p a r t i c l e s izes (see F i g u r e s 4.38 a n d 4 .42) , i n c r e a s i n g t h e excess o x y g e n l e d t o i n c r e a s e d c o n v e r s i o n o f c a r r y o v e r c a l c i n e , a h i g h e r p r o p o r t i o n of su l fu r as su l fa te , a n d a n i n c r e a s e d p r o -p o r t i o n o f i r o n as fe r r i c i r o n . O v e r a l l , t h e effect o f o x y g e n e n r i c h m e n t was less i m p o r t a n t t h a n t h e effect o f excess o x y g e n ( F i g u r e s 4.43 t o 4 .46) . T h e e l e m e n t a l m a s s b a l a n c e s d o n o t s h o w a n y c l ea r t r e n d ( F i g u r e s 4 .44 a n d 4 .46) . 139 Chapter 4. Experimental Results 1 1 0.8 0.8 "O CU -O c 0.6 • o o "O V JD c 0.6 • o c o c o • t a o.4 o O o • Proporti o O o 0.2 0.2 Q O 0 0 0 20 40 60 (a) Cd Excess oxygen (%) 80 0 20 40 60 (b) Cu Excess oxygen (%) 80 1 1 • 0.8 0.8 o 8 <u <0 c 0.6 c 0.6 • c c t §.0.4 o o O O • t a o.4 o o Q. O 0- O 0.2 O 0.2 0 0 0 20 40 60 (c) Fe Excess oxygen (%) 80 0 20 40 60 (d) Pb Excess oxygen (%) 80 1 1 0.8 Ul ra bO T3 OJ | 0.95 - • c 0.6 b0 C @ O c 0 O "> ro t §.0.4 . o G • - c o O 1 0.9 O o 0.2 O ci O 0 0.85 0 20 40 60 (e) Zn Excess oxygen (%) 80 0 20 40 60 (f) S Excess oxygen (%) 80 Figure 4.35: Var ia t ion in proport ion of key elements based on mass balance for different excess oxygen and 50 mesh si l ica sand, o: S i l ica sand, • : S i l ica sand w i t h 25% O2 i n the fluidizing gas. (a) C a d m i u m , (b) Copper , (c) Iron, (d) Lead , (e) Zinc , (f) Sulfur. 140 Chapter 4. Experimental Results Figure 4.36: Effect of excess oxygen on assays for different bed particle size fractions w i t h 50 mesh si l ica sand. B o t t o m to top: SiC-2, Z n , Fe , P b 141 Chapter 4. Experimental Results Init. Final Zn Pb Fe Si02 Init. Final Zn Pb Fe Si02 (c) Excess oxygen: 20 % (d) Excess oxygen: 80 % F i g u r e 4 .37: Ef fec t o f excess o x y g e n o n d i s t r i b u t i o n o f m a s s o f k e y e l e m e n t s w i t h b e d p a r t i c l e s ize f r a c t i o n for 50 m e s h s i l i c a s a n d . B o t t o m t o t o p : p a n , + 2 3 0 , + 1 4 0 , + 7 0 , + 4 0 L42 Chapter 4. Experimental Results 20 40 60 (a) Excess oxygen (%) 20 40 60 (b) Excess oxygen (%) 20 40 60 (c) Excess oxygen (%) 80 20 40 60 (d) Excess oxygen (%) Figure 4.38: Compar ison of carryover assays for different excess oxygen for 50 mesh si l ica sand, o: Si l ica sand, • : S i l ica sand wi th 25% O2 in the fluidizing gas. (a) To ta l sulfur, (b) Fract ion of sulfur as sulfate, (c) Conversion based on remaining sulfide sulfur, (d) Frac t ion of i ron as ferric i ron. 143 Chapter 4. Experimental Results 0.8 -o (U J2 c 0.6 c o t i §.0.4 0.2 O O • o • 0.8 0.6 o 0.2 0 20 40 60 (c) Fe Excess oxygen (%) 0.8 0.6 o 0-.0.4 0.2 • o • o o 0 20 40 60 80 (a) Cd Excess oxygen (%) • • O O o 80 0 20 40 60 80 (e) Zn Excess oxygen (%) 0 20 40 60 80 (b) Cu Excess oxygen (%) 0 20 40 60 80 (d) Pb Excess oxygen (%) • o • . o o • 20 40 60 80 (f) S Excess oxygen (%) Figure 4.39: Variation in proportion of key elements based on mass balance for different excess oxygen and 125 mesh silica sand, o: Silica sand, •: Silica sand with 25% O2 in the fluidizing gas. (a) Cadmium, (b) Copper, (c) Iron, (d) Lead, (e) Zinc, (f) Sulfur. 144 Chapte r 4. E x p e r i m e n t a l Resu l t s (c) Excess oxygen: 80 % Figure 4.40: Effect of excess oxygen on assays of different bed part icle size fractions for 125 mesh sil ica sand. B o t t o m to top: S i 0 2 , Z n , Fe , P b 145 Chapter 4. Experimental Results (c) Excess oxygen: 80 % Figure 4.41: Effect of excess oxygen on dis t r ibut ion of mass of key elements w i t h bed particle size fraction for 125 mesh si l ica sand. B o t t o m to top: pan,+230,+140,+70,+40 146 Chapter 4. Experimental Results 20 40 60 (a) Excess oxygen (%) 20 40 60 (b) Excess oxygen (%) S0.95 s i/i 0.9 J0.85 0.8 20 40 60 (c) Excess oxygen (%) 80 20 40 60 (d) Excess oxygen (%) Figure 4.42: Compar i son of carryover assays for different excess oxygen for 125 mesh si l ica sand, o: Si l ica sand, • : S i l ica sand wi th 25% O2 i n the f luidizing gas. (a) To ta l sulfur, (b) Fract ion of sulfur as sulfate, (c) Conversion based on remaining sulfide sulfur, (d) Fract ion of i ron as ferric i ron. 147 Chapter 4. Experimental Results 100 pan +230 +140 +70 +40 (a) 21% Inlet oxygen, 0% Excess Oxygen pan +230 +140 +70 +40 (c) 21% Inlet oxygen, 80% Excess Oxygen 100 pan +230 +140 +70 +40 (d) 25% Inlet oxygen, 80% Excess Oxygen Figure 4.43: Effect of excess oxygen and oxygen enrichment on assays of bed particle of different size fractions wi th 50 mesh sil ica sand. B o t t o m to top: S i 0 2 , Z n , Fe , P b 148 Chapter 4. Experimental Results Init. Final Zn Pb Fe Si02 Init. Final Zn Pb Fe Si02 (a) 21% Inlet oxygen, 0% Excess Oxygen (b) 25% Inlet oxygen, 0% Excess Oxygen Init. Final Zn Pb Fe Si02 Init. Final Zn Pb Fe Si02 (c) 21% Inlet oxygen, 80% Excess Oxygen (d) 25% Inlet oxygen, 80% Excess Oxygen F i g u r e 4 .44: Ef fec t o f excess o x y g e n a n d o x y g e n e n r i c h m e n t o n d i s t r i b u t i o n o f m a s s o f k e y e lements w i t h b e d p a r t i c l e s ize for 50 m e s h s i l i c a s a n d . B o t t o m t o t o p : p a n , + 2 3 0 , + 1 4 0 , + 7 0 , + 4 0 149 Chapter 4. Experimental Results Figure 4.45: Effect of excess oxygen and oxygen enrichment on assays of different bed particle sizes for 125 mesh si l ica sand. B o t t o m to top: SiC>2, Z n , Fe , P b 150 Chapter 4. Experimental Results Init. Final Zn Pb Fe S i 0 2 Init. Final Zn Pb Fe S i 0 2 (a) 2 1 % Inlet oxygen, 0 % Excess Oxygen (b) 2 5 % Inlet oxygen, 0 % Excess Oxygen Init. Final Zn Pb Fe S i 0 2 Init. Final Zn Pb Fe S i 0 2 (c) 2 1 % Inlet oxygen, 8 0 % Excess Oxygen (d) 2 5 % Inlet oxygen, 8 0 % Excess Oxygen F i g u r e 4.46: Ef fec t o f excess o x y g e n a n d o x y g e n e n r i c h m e n t o n d i s t r i b u t i o n o f m a s s o f k e y ele-m e n t s w i t h b e d p a r t i c l e s ize for 125 m e s h s i l i c a s a n d . B o t t o m t o t o p : p a n , + 2 3 0 , + 1 4 0 , + 7 0 , + 4 0 151 Chapter 4. Experimental Results 4.3.7 Effect of bed material and size Figures 4.49 to 4.54 show the microstructures of the sieved bed (product) particles for the experiment w i t h fine bed particles and 0% excess oxygen (run 8). A s mentioned previously, excessive agglomeration led to very large particles that segregated and defluidized. Some si l ica particles are embedded wi th in the agglomerates. There is essentially no coating on the si l ica particles. It is important to note that the particles are relatively porous and that, because of their relatively large size, some particles were not able to be adequately truncated. Therefore, the apparent cavities w i th in the particles were caused by pol ishing. A s previously shown i n Table 4.5, the proport ion of calcine as carryover is larger for the fine bed material than for the coarser material . One experiment was performed wi th brown a lumina at 975°C. A s Figures 4.55 to 4.60 portray, no significant coating was present on the a lumina particles after the experiment. T h e larger particles were created by agglomeration of smaller particles w i t h a lead-rich phase that contained some t i t an ium (checked by X - r a y spectroscopy). T h e P b O - T i 0 2 phase diagram, calculated from the F A C T thermodynamic database, indicates that some t i t an ium dioxide may dissolve wi th in l iqu id lead oxide. Since the a lumina particles contained a smal l por t ion of t i t an ium, it is possible that the t i t an ium wi th in the lead-rich phase originated from the bed particles. T h e morphology of the a lumina particles differs from that of the s i l ica particles, possibly due to their different reactivities w i th P b O . The lead-rich phase may wet the s i l ica particles more readily than the a lumina particles. X - r a y diffraction of the bed and carryover samples indicate that bo th consist ma in ly of zinc oxide. The carryover sample also contained detectable quantities of zinc ferrite. T h e same peaks as for the two other set of si l ica samples could not be identified. Note that there were fewer unidentified peaks for the a lumina samples. T h i s suggests that the compound(s) related to some of the unidentified peaks is/are silica-based. 152 Chapter 4. Experimental Results pan +230 +140 +70 +40 pan +230 +140 +70 +40 (c) Large S i Q 2 sand, 975 °C (d) A I 2 O 3 , 975 °C F i g u r e 4.47: E f fec t o f b e d m a t e r i a l o n assays for d i f ferent b e d p a r t i c l e s i ze f r a c t i o n s . B o t t o m t o t o p : Si0 2 o r A1203, Z n , F e , P b 153 Chapte r 4. E x p e r i m e n t a l Results (c) Large Si0 2 sand, 975 °C (d) A I 2 O 3 , 975 °C Figure 4.48: Effect of bed material on dis t r ibut ion of mass of key elements w i t h bed particle size fraction. B o t t o m to top: pan,+230,+140,+70,+40 154 Chapter 4. Experimental Results Figure 4.49: SEM micrograph for product particles of run 8, +16 mesh, Secondary electrons image Figure 4.50: SEM micrograph for product particles of run 8, +40 mesh, Secondary electrons image 155 Chapter 4. Experimental Results Figure 4.52: SEM micrograph for product particles of run 8, +140 mesh, Secondary electrons image 156 Chapter 4. Experimental Results Figure 4.53: S E M micrograph for product particles of run 8 , +230 mesh, Secondary electrons image Figure 4.54: S E M micrograph for product particles of run 8 , -230 mesh (pan), Secondary electrons image 157 Chapter 4. Experimental Results Figure 4.55: S E M micrograph for product particles of run 24, +40 mesh, Secondary electrons image Figure 4.56: S E M micrograph for product particles of run 24, +70 mesh, Secondary electrons image 158 Chapter 4. Experimental Results Figure 4.58: S E M micrograph for product particles of run 24, +230 mesh, Secondary electrons image 159 Chapter 4. Experimental Results Figure 4.59: S E M micrograph for product particles of run 24, -230 mesh (pan), Secondary electrons image Figure 4.60: S E M micrograph for product particles of run 24, carryover, Secondary electrons image 160 Chapter 4. Experimental Results 4.4 Gas and solid conversions Exper imenta l runs 25 and 26 differed from the other experiments. In these experiments, the concentrate feedrate was varied and the freeboard gas was sampled, scrubbed to remove sulfur dioxide, dried and sent to a portable gas analyzer. T h e solids collected in the sampl ing t ra in were collected and sent for assay. Figure 4.61 presents the freeboard oxygen concentration as a function of the concentrate feedrate and in i t ia l bed particle size. T h e oxygen concentration clearly decreased w i t h increasing feedrate. T h e oxygen concentration was sl ight ly higher for the 125 mesh si l ica sand for a similar concentrate feedrate, probably due to increased gas bypassing caused by the bubbles. A s expected, for a given concentrate feedrate, the outlet oxygen concentration was higher when oxygen enrichment was used. T h e solid conversion corresponding to the data in Figure 4.61 is shown in F igure 4.62. Oxygen enrichment increased the solids conversion for a given feedrate. A g a i n , this is expected because for a given concentrate feedrate, an increase i n the inlet oxygen concentration s imply increased the excess oxygen. T h e bed particle size does not seem to have had a significant effect. T h e data in Figures 4.61 and 4.62 are used i n chapter 6 to fit the fluidized bed reactor model . Figure 4.63 presents the averaged output of the oxygen sensor w i t h i n the fluidized bed. T h e output of the sensor is proport ional to the log of the ratio of outside to inside oxygen par t ia l pressures. A smal l output signal indicates a high in-bed oxygen concentration, while a large output value indicates a smal l in-bed oxygen concentration. A n interesting feature observed in Figure 4.63 is that the oxygen concentration wi th in the bed was not significantly affected by the oxygen enrichment, but was significantly influenced by the average bed particle size. B y increasing the concentrate feedrate from 10 to 20 g / m i n , the N O concentration i n the sampled freeboard gas increased from approximately 15 to 30 p p m . N o N O was present when no concentrate was fed to the roaster. T h i s indicates that the N O may originate from the combustion of the concentrate. However, it is not clear whether the N O product ion rate depends upon the excess oxygen, in-bed oxygen concentration or just the concentrate feedrate. 161 Chapter 4. Experimental Results CD u 10 12 14 16 18 Concentrate feedrate (g/min) Figure 4.61: Freeboard oxygen concentration (SO2 scrubbed,dry) as a function of feedrate. o: 50 mesh si l ica sand, 21%C>2, +: 50 mesh sil ica sand, 25%C>2, x : 125 mesh si l ica sand, 21%C>2. 0.98 c •3, 0.96 cu > c o " 0.94 o C O 0.92 0.9 0 X + 0 + 0 + X 0 0 0 X + X 0 X 0 • 10 12 . 14 16 18 20 Concentrate feedrate (g/min) Figure 4.62: Solids conversion as a function of feedrate. o: 50 mesh si l ica sand, 21%C>2, +: 50 mesh sil ica sand, 25%C>2, x : 125 mesh si l ica sand, 21%C>2. 162 Chapter 4. Experimental Results 60 > £ 50 3 ^ 40 o £ 3 0 cu ^ 2 0 S 2 1 0 x x x X x O + X o ° ° + + o ° o 9 o o 10 12 14 16 18 20 C o n c e n t r a t e feedrate (g/min ) F i g u r e 4 .63: I n - b e d o x y g e n sensor m e a n o u t p u t as a f u n c t i o n o f feedra te . o: 50 m e s h s i l i c a s a n d , 21%C>2, + : 50 m e s h s i l i c a s a n d , 25%C>2, x : 125 m e s h s i l i c a s a n d , 2 1 % 0 2 - N o t e : H i g h e r m e a s u r e d o u t p u t , l ower o x y g e n c o n c e n t r a t i o n 163 Chapter 4. Experimental Results 4.5 Sintering test for zinc concentrate The raw unsintered concentrate is shown in Figure 4.64. A careful search using the electron microscope d id not reveal any significant phases other than zinc sulfide. Sealed ampoules of dr ied zinc concentrate (concentrate 1(b), approximately lg ) were submit ted to a ramp-up to 950°C, and held for an hour at that temperature, and then cooled slowly to room temperature. Since the ampoules could not be sealed under vacuum or a nitrogen atmosphere, a smal l amount of air was in i t ia l ly present w i th in the ampoules. T h e number of moles of oxygen contained w i t h i n the the air i n the ampoules was smaller than 1% of the Z n S in the concentrate. After the sintering cycle, the concentrate had formed a porous elongated rod of diameter sl ightly smaller than the tube diameter. T h e rod showed some signs of oxidat ion near the end where the bulk of the air was present. A sample of the rod was taken from the opposite end and prepared for electron microscopy. A n image of the sintered concentrate is presented i n F igure 4.65. T h e lighter-coloured cube is composed of pure lead sulfide. Several of these cubes appeared on the periphery of the sintered "cylinder". Note that the cube is much larger than any of the original concentrate particles. The lead sulfide cubes probably originate from deposition of lead sulfide from the gaseous phase dur ing cooling. T h e gaseous composit ion of a mixture of zinc sulfide and zinc oxide is located at point A on Figure 2.2. T h i s location is val id because the concentrate is ma in ly composed of zinc sulfide, but, as the assays show, a smal l fraction of the sulfur is present as sulfate. Also , the ampoule could not be vacuum-sealed nor nitrogen-purged. Therefore, the smal l amount of oxygen remaining when the ampoule was sealed would react to form zinc oxide and sulfur dioxide. T h e equi l ibr ium gas composit ion of a mixture of zinc sulfide and zinc oxide, represented by point A on Figure 2.2, is adequate to represent the gas composi t ion of the sealed ampoule. W h e n transposing point A of Figure 2.2 onto Figure 2.11, the gas composi t ion falls w i th in the lead stabil i ty area, very close to the lead sulfide area. W h e n considering the gaseous lead species, lead sulfide is s t i l l the most predominant gaseous lead species, even though it falls 164 Chapter 4. Experimental Results Figure 4.64: S E M micrograph for dried, unsintered, zinc concentrate 1(b), Secondary electrons image. Figure 4.65: S E M micrograph for dried, zinc concentrate 1(b) sintered for 1 hour at 950°C, Secondary electrons image. Cube is pure lead sulfide. 165 Chapter 4. Experimental Results wi th in the lead s tabi l i ty area. Note in Figure 2.11 that if the oxygen concentration is increased, the lead sulfide par t ia l pressure decreases. Even though the lead oxide par t ia l pressure increases wi th oxygen par t ia l pressure, it remains much lower than that of lead sulfide at lower oxygen part ia l pressures. D u r i n g cooling, lead sulfide "precipitated" from the gaseous phase to form lead sulfide cubes. F rom this simple experiment, it is clear that lead sulfide can evaporate from zinc concentrate. However, this experiment does not offer any information on the vaporizat ion kinetics. 4.6 Growth mechanism in the laboratory roaster A probable growth mechanism may now be suggested from the experimental observations. P r io r to formulating a growth mechanism, let us summarize the most relevant observations: • F rom the sample mass balances, we have observed that larger particles contain a larger proport ion of lead than smaller particles. • Temperature has a significant effect on the thickness and morphology of the coating. Temperature also affects the proport ion of calcine leaving the roaster as carryover. • Excess oxygen also affects the coating and the proport ion of calcine leaving the roaster as carryover. • F rom the electron microscope observations, the si l ica particles were observed to be coated wi th a two-phase coating, one r ich in lead, the other zinc-r ich, while the inner si l ica was coated wi th a th in "coherent" layer of lead-rich compound. A l l have si l icon (silica) present. A l u m i n a particles were not coated w i t h any zinc. However, some of the a lumina particles were agglomerated wi th a lead-rich phase. • Lead sulfide sublimates from zinc concentrate when exposed to roasting temperatures and oxygen-deficient atmospheres. T h e mechanism may now be postulated as follows: 166 Chapter 4. Experimental Results • W h e n process conditions are such that low oxygen concentrations and high sulfur dioxide concentrations are favoured, excess oxygen is one of the most impor tant factors. Under such conditions, the lead par t ia l pressure is maximized , w i t h lead predominant ly present as lead sulfide. • Lead sulfide vaporizes from the zinc concentrate. • Gaseous lead sulfide is transported to regions of the bed where higher oxygen concentra-tions are present. It then reacts w i t h oxygen to produce lead oxide. • Since the lead oxide par t ia l pressure is lower than for the lead sulfide, lead oxide precipi-tates out. • Lead deposits onto the bed particles to form a very th in lead-oxide-based coating. T h e reactivity of the particles w i t h lead oxide affects whether or not a significant coating appears on the surface of the particles. • Lead oxide is l iqu id at roasting temperatures. It can dissolve an increasing amount of various compounds w i t h increasing temperature. Since it is l iqu id , it is sticky. • T h e st icky particle surface can trap other very smal l particles. T h e momentum of these particles is insufficient to break up the viscous l iqu id lead oxide bridges upon contact. Larger particles, however, have sufficient momentum to remain separate. Condi t ions that may influence the momentum of particles such as the gas d is t r ibut ion and the vigour of fluidization (superficial gas velocity) affect coating and agglomeration. • R a p i d sintering of the coated particles is favoured by l iqu id lead oxide. Th i s mechanism is consistent w i t h the observations of C o n d i n a et al. [83] (see section 1.4.7) where monobasic lead sulfate was observed i n alumina, s i l ica and calcine agglomerates. C o n d i n a et al. [83] observed agglomerates, but d id not observe growth of single particles. In their experiments, they used a "caged" lead sulfide source, immersed i n a bed of inert particles. After a few minutes the particles started to agglomerate outside the cage, due to gaseous lead species. Since their experiments lasted only a few minutes, no lead silicates were observed in 167 Chapter 4. Experimental Results the agglomerates. It is important to note that the experimental conditions of C o n d i n a et al. [83] differed from those expected in a continuously operating fluidized bed roaster. A i r was used to fluidize the inert bed material , and no material other than the pure lead sulfide pellet could react w i t h the f luidizing gas. Also , in their experiments no zinc sulfide was present to form zinc oxide. C o n d i n a et al. [83] d id not consider the effect of different particles sizes on agglomeration, growth or a t t r i t ion nor d id they indicate the effect of the oxygen concentration. It is not known whether this coating mechanism would apply to calcine particles since their reactivity w i th lead oxide is unknown. However, considering the solubi l i ty of the particles in P b O i n the P b O - Z n O , P b O - S i 0 2 and P b O - A l 2 0 3 phase diagrams (Figures 2.25 to 2.27), it is l ikely that the reactivi ty of calcine particles lies between that of s i l ica and a lumina . Since vaporization and deposition kinetics are not known, it is premature to model the coating of particles. However, since the par t ia l pressures are strongly dependent on the oxygen con-centrations, it would be beneficial to evaluate the effect of various process parameters on the oxygen concentration experienced by the particles in the fluidized bed. A s s u m i n g that coating depends on the relationship between the oxygen concentration and the transport of metall ic species through the gas phase, model l ing the oxygen concentration w i t h i n the fluidized bed would give important insights on the coating of particles. 4.7 Agglomeration mechanism in the laboratory roaster Since only one experiment generated catastrophic agglomerates (defluidization due to segre-gated agglomerates), there are insufficient data to clearly formulate an agglomeration mecha-nism. However, since lead strongly segregated to these agglomerates, i t is probable that lead species play a strong role i n the agglomeration mechanism. Some smal l agglomerates were found in the fine particles of other experiments (see Figures 4.13). These agglomerates were also rich in lead. It is possible that these agglomerates are formed i n a s imilar manner to the catastrophic agglomerates produced dur ing run 8 (see Figure 4.49 to 4.54). Other agglomerates were formed dur ing the experiment w i t h a lumina as the inert bed mater ia l (see Figures 4.57 168 Chapter 4. Experimental Results and 4.58). The following agglomeration mechanism may be suggested: • Transport of lead from the concentrate particles to the bulk of the bed occurs i n a manner similar to the growth mechanism described previously. • However, for the conditions of catastrophic agglomeration, the roaster operated wi th no excess oxygen. Under these conditions, very low oxygen concentrations are present around the concentrate particles. T h i s lower oxygen concentration enhances the transfer of lead to other particles. T h i s may produce a larger amount of l iquids w i t h i n the bed. • A larger amount of l iqu id may contribute to the formation of agglomerates through l iqu id bridging. • A t t r i t i o n l imits the agglomeration rate and possibly the m a x i m u m agglomerate size. Since catastrophic agglomeration only occurred for the experiment w i t h a fine bed particle size, it is possible that a t t r i t ion of the agglomerates depends on the bed particle size. Large bed particles would l imi t the size of agglomerates while fine bed particles would not have sufficient momentum to break up the agglomerates into smaller ones. T h i s agglomeration mechanism is very similar to that observed by C o n d i n a et al. [83]. A s men-tioned above, C o n d i n a et al. [83] neither varied the particle size nor the oxygen concentration. S imi lar ly to the coating of particles, there is s t i l l too much information missing for the model l ing of agglomeration w i t h the mechanism described here. Therefore, assuming that agglomeration is related to the coating mechanism, any important insights on the coating of particles may be useful to predict agglomeration. The next chapter describes a fluidized bed reactor model applicable to the laboratory and industr ia l roasters. T h e results of this model w i l l be used to evaluate the conditions when the coating and agglomeration mechanisms can be extended to the indust r ia l roaster. 169 Chapter 5 Model Development A gas-solid fluidized bed reactor model is formulated in this chapter i n order to evaluate the "effect of excess oxygen, oxygen enrichment, temperature and other operat ing parameters on the oxygen concentration close to reacting particles. T h e important issue of scale-up of the results from a slugging fluidized bed to a bubbl ing fluidized bed must be addressed to apply the results from the laboratory roaster to industr ia l fluidized bed roasters. A n y fluidized bed gas-solid reactor model requires that the gas reaction model be coupled to the solids reaction model . T h e gas reaction model accounts for the hydrodynamics of the fluidized bed reactor. T h e solids reaction model requires that a single-particle reaction model be selected and used i n conjunction w i t h a model for the mix ing of the solids w i t h i n the fluidized bed. Th i s chapter proposes a new generalized slugging-bubbling fluidized bed reactor model . T h e reaction and m i x i n g of solids wi th in a fluidized bed is presented next. F ina l ly , an unsteady-state model for the reaction of single particles is described. T h e model assumes that the entire fluidized bed, as well as the reacting particles, are isothermal. T h e model also assumes that the particles are well-mixed, axial ly and radia l ly w i t h i n the fluidized bed. E lu t r i a t ion , a t t r i t ion and agglomeration are not considered. Reactions in the freeboard of the roaster are neglected. T h e t ime for complete reaction, the m i x i n g times and the single particle unsteady-state model are used in the next chapter to verify some of these assumptions. 170 Chapter 5. Model Development 5.1 Steady-state fluidized bed reactor model: Gas reaction T h e steady-state fluidized bed reactor model accounts for the fluidized bed hydrodynamics , gas reactions, and solids reactions. T h e model extends the generalized bubbl ing , turbulent and fast fluidization reactor model of A b b a et al. [203, 204, 205], which accounts for variable gas density and bulk flow in the interphase mass transfer. T h i s model , consist ing of a single set of steady-state differential equations, can be applied across several flow regimes from the bubbl ing regime to the fast f luidization regime by using a probabil is t ic approach to specify the parameters. Cont ra ry to the generalized bubbl ing, turbulent, fast fluidization model , the model developed in this chapter ignores the turbulent and fast f luidizat ion flow regimes. Instead, the model is extended from bubbl ing into the slugging flow regime. A l so , the approach used to model changes in total gas molar flow differs from the generalized model of A b b a et ai [203, 204, 205]. Figure 5.1 represents the two phases of the model, named the L - and H-phases for low-density and high-density phases respectively. In the bubbl ing fluidized bed, the L-phase represents the bubbles, while the H-phase represents the dense phase or emulsion. T h e gas enters at the bot tom of the fluidized bed where it is dis t r ibuted between the L - and H-phases. T h e gas then rises in each phase and reacts w i th the solids present. Exchange occurs between the two phases. A x i a l and radial dispersion could be included wi th in each phase, and the former would need to be incorporated to extend the model to the turbulent flow regime. 5.1.1 Phase balances T h e fluidized bed is d ivided into the L - and H-phases (Figure 5.1). T h e bed volume fractions of these phases(ipr, and tpn) add up to one: </>L + < M = l (5.1) Each phase volume is composed of particles and void space occupied by the gas. T h e particle volume fraction (<f>) and gas volume fraction (e) w i th in each phase also add up to one. T h e total gas molar flowrate (FT) through the reactor equals the sum of the molar flowrates through 171 Chapter 5. Model Development Freeboard A Az H-phase u Figure 5.1: Schematic of two-phase fluidized bed model each phases (Fr, and FH), i.e.: FT — FLT + FHT (5.2) Accord ing to the ideal gas law, for a given total pressure (P) and temperature (T), the total concentration (CT) (sum of a l l gaseous species) is constant (CT — T J^O- Therefore, for a given reactor area (A), the gaseous molar flowrates are related to the superficial gas velocities (U, UL and UH) by: FT = ACTU FHT = .IPHAUHCT FLT = IPLAULCT (5.3) (5.4) (5.5) Similarly, the molar flowrate of gaseous species i in the H - and L-phases are: Fm = ipHAUHCm 172 (5.6) Chapter 5. Model Development FLi = ifjLAULCLi (5.7) After replacing the molar flowrates into equation 5.2 and simplifying, we obtain: U = I/JLUL + i>HUH These volume and gas flow balances are summarized i n Table 5.1. Table 5.1: Volume and gas flow balances B e d volume 4>L + = 1 L-phase volume 4>L + £L = 1 H-phase volume <f>H + (-H = 1 Gas flow U = ipLUL + IPHUH (5.8) 5.1.2 G a s m o l e b a l a n c e s f o r H - a n d L - p h a s e s Referring to Figure 5.1, the gas mole balance over the control volume for an increment of t ime is, in general terms: number of moles enter-ing minus those exiting the control volume by I flow number of moles produced minus those consumed by reaction within the control ^ volume + > + ' number of moles enter- ^ ing minus those exiting the control volume by . dispersion 'number of moles flow-ing into the control vol-ume due to bulk inter-. phase mass transfer ' number of moles trans-_l_ ^ ferred to the control I volume by interphase [ ^mass transfer / 'number of moles ac- i cumulating within the > (5-9) ^control volume J Assuming steady-state conditions and neglecting axial and radial dispersion, i.e. assuming that the accumulation and dispersion terms are zero, the mass balance over the low-density phase (L) leads to (terms are explained below): F m FLl Fu - (FLi + ^ff A , A^Azkrd,^-^-) J + {0} + ^AAzi/jLkLHaj + I A*l>HAzkr(j)HAv AipHUH AX/JLUL FHO2 \ ( FLi A^HUH)\FLT + = (0X5.10) 173 Chapter 5. Model Development For the high-density phase (H), the same development leads to: { F „ , _ ( F „ , + ^ ) } + { 0 } + { ^ A * W , ( ^ - ^ ) } + T h e interphase mass transfer and reaction terms in equations 5.10 and 5.11 require some clar-ification. T h e interphase mass transfer coefficient (km) is defined as the volumetr ic rate of transfer per unit bubble surface area. T h e interphase mass transfer exchange area (a/) is the interfacial bubble area per unit bubble volume. M u l t i p l y i n g the two (k^n • « r ) gives the vol-umetric rate of transfer per unit bubble volume. To obtain the number of moles transferred, we need to mul t ip ly by the bubble volume wi th in the control volume (AAzipL.) and by the concentration difference between the L - and H-phase. T h e concentration of each species w i th in each phase is given by equations 5.6 and 5.7. Note that the interphase mass transfer terms are identical in equation 5.10 and 5.11, except for their signs. T h e reaction is first order w i t h respect to the oxygen concentration. T h e reaction rate constant kr is based on the particle volume. To obtain the number of moles reacted w i t h i n the L-phase of the control volume per unit t ime, the reaction rate constant kr is mul t ip l i ed by the particle volume wi th in the phase (AtpiAzcpi,), the stoichiometric constant for species i (z/j), and the oxygen concentration ( A^VL ) • Similar ly, for the H-phase, the reaction rate constant kr is mult ipl ied by the particle volume wi th in the phase (AtpffAzcpff), the stoichiometric constant for species i (i/j), and the oxygen concentration ( A^UH )' B u l k interphase mass transfer is required when a change in gas volume occurs w i th in the H -phase. Accord ing to the two-phase fluidization theory, a given flow of gas, UmfA is required for fluidization of the high-density phase. A n y excess gas enters the low-density phase to create bubbles. In a reacting system, the requirement for the high-density phase is s t i l l present. However, if there is a volume change, it must be balanced by bulk interphase transfer. T h e bulk interphase mass transfer terms in equations 5.10 and 5.11 are very s imilar to the reaction term of the H-phase (equation 5.11). However, the required stoichiometric coefficient is now the change i n the total number of gaseous moles (Ai/) mul t ip l ied by the gas molar fraction of 174 Chapter 5. Model Development t h e L - p h a s e (jj^)- T h e d i r e c t i o n o f t h e b u l k f low a n d t h e r e q u i r e d gas m o l a r f r a c t i o n d e p e n d s o n the s i g n of Au. I n t h i s case, i t is n e g a t i v e s ince , i n t h e r e a c t i o n o f z i n c su l f i de w i t h o x y g e n t o p r o d u c e z i n c o x i d e a n d su l fu r d i o x i d e , 1.5 m o l e s o f gas o n t h e l e f t - h a n d s ide o f t h e r o a s t i n g r e a c t i o n p r o d u c e o n l y 1 m o l e . o f gaseous p r o d u c t o n t h e r i g h t - h a n d s ide . I f Au we re p o s i t i v e , a n y excess gas p r o d u c e d i n t h e dense phase w o u l d go t o t h e b u b b l e phase . T h e r e f o r e , t h e gas m o l a r f r a c t i o n w o u l d b e c o m e F o r z i n c su l f ide r o a s t i n g , t h e b u l k f low t e r m is d e s c r i b e d b y e q u a t i o n s 5.10 a n d 5.11. A f t e r s i m p l i f i c a t i o n , t h e m o l e b a l a n c e e q u a t i o n s for t h e L - a n d H - p h a s e s are : dFLi ,ipL,Fm F L i \ , , FL02 , , , A FH02 FLi - j — + kLHaj{-—r- — + kr4>LUi—— + krcf>HAu———— = 0 (5.12) dz VHUH UL 1 UL UH bLT dFm (FLi ipLFHi\ , , , FH02 i ± A FH02 FLi . . 3 — + kLHaA— -—— + kr<pHVi— kr(pHAu—-—-— = 0 (5.13) dz \UL WHUHJ UH UH FLT T h e s e e q u a t i o n s are s o l v e d u s i n g a n i n i t i a l v a l u e so lve r a n d t h e b o u n d a r y c o n d i t i o n s : FLi = FLlyin= ipLAULCitin a t 2 = 0 (5.14) Fm = F H i t i n = ipHAUHCl}in a t z = 0 (5.15) T h e s e b o u n d a r y c o n d i t i o n s o r i g i n a t e f r o m t h e fact t h a t t h e i n l e t f l ow is d i s t r i b u t e d a m o n g t h e H - a n d L - p h a s e s . 5.1.3 Superficial gas velocities and phase volume fractions T h e s u p e r f i c i a l gas v e l o c i t i e s (UL a n d UH) a n d t h e phase v o l u m e f r a c t i o n s ('ipL a n d ipn) are c a l c u l a t e d at ' a series o f v e r t i c a l p o s i t i o n s i n t h e b e d i n c l u d i n g t h e b o u n d a r y sur face . T h e s u p e r f i c i a l gas v e l o c i t y (U) is f irst c a l c u l a t e d f r o m t h e gaseous m o l a r f lowra te s (FHT a n d FLT)-T h e l o w - d e n s i t y phase s u p e r f i c i a l gas v e l o c i t y (UL) is c a l c u l a t e d u s i n g e q u a t i o n 5.53 (i .e. UL = Uv). T h i s c a l c u l a t i o n r equ i r e s t h e b u b b l e s ize c o r r e l a t i o n s d e s c r i b e d i n s e c t i o n 5.1.7. T h e l o w - d e n s i t y phase v o l u m e f r a c t i o n (ipL) is c a l c u l a t e d u s i n g [206]: U - Umf . V*L = — y j - - ^ (5-16) T h e s u p e r f i c i a l gas v e l o c i t y a n d phase v o l u m e f r a c t i o n o f t h e h i g h - d e n s i t y p h a s e a re t h e n c a l -c u l a t e d b y m e a n s of e q u a t i o n s 5.1 a n d 5.8. 175 Chapter 5. Model Development 5.1.4 Expanded bed height Since the set of differential equations is solved from the dis tr ibutor (z = 0) to the surface of the expanded bed (z = H), the expanded bed height (H) must be known, or first estimated and then calculated iteratively. Since it is only the volume occupied by the bubbles (L-phase) that contributes to the expansion of the bed, the relationship between the expanded bed height (H), the bed height at m i n i m u m fluidization velocity (Hmf) and the L-phase volume fraction is relatively simple: H — Hmf io = f"ipLdz (5.17) Jo Similarly, i f the H-phase fraction is integrated over the expanded bed height, we obtain Hmf. Hmf= fH^Hdz (5.18) Jo T h e bed height at m i n i m u m fluidization (Hmf) depends on the bed mass (M^), bed cross-sectional area (A), particle density pp and void space ( e m / ) . Hmf = n M b £ d (5.19) Pp(l - tmf)A For industr ia l zinc roasters, the expanded bed height is l imi ted by the weir overflow height. Therefore, H is known and constant while Hmf may vary. For the laboratory roaster, on the other hand, the expanded bed height is unknown. However, the bed mass can be be used to calculate Hmf. In this case, the calculation of the expanded bed height proceeds iteratively (since we need to integrate from 0 to H and H is not known at first). 5.1.5 Gas conversion and average gas compositions The overall gas conversion, i.e. the oxygen conversion (X02), is calculated as follows: v Fi02,out + F~H02 ,OUt / r o r , N 1 " X ° 2 = C^-AU ( 5 - 2 0 ) Similarly, the number of moles of oxygen reacted per unit t ime is given by: A F 0 2 = C 0 2 , m ^ c 7 - {FL02,out + FH02,out) (5.21) The number of moles of oxygen reacted per unit t ime must be coupled to the solids reaction. W i t h the freeboard neglected, F i ) 0 U t is equal to FitZ=n-176 Chapter 5. Model Development The solids reaction model assumes that the particle reaction times are long compared to their vertical mix ing times. Therefore, the solids composit ion is assumed to be independent of the vertical posi t ion in the bed. T h e solids model therefore uses the average gas composi t ion seen by the solid particles to calculate their conversion. The gas reaction model calculates the particle-averaged gas concentrations as: rH rH / <f>HipHCm dz+ / (PL^LCU dz Ci= ^ H fj : (5-22) / (jiHipH dz+ I 4>LipL dz Jo Jo rH / tpjCjidz Cji= ^ 7 7 7 (j = LovH) (5.23) ipj dz Assuming that the solid volume fractions (</>/, and 4>H) do not change w i t h height and using the volume balances (equations in Table 5.1) and the bed expansion calculat ion (equations 5.17 and 5.18), these equations reduce to: 7 f _ 4>L (H - Hmf) Cg + <PH (Hmf) Cm (<- 9 ^ C I ~ </>L(H-Hmf) + (f>H(Hmf) l b - 2 4 j fH / ipr,Cudz 1 1 11mf H ipHCm dz. CHl = — J J — (5.26) nrnf T h e solid reaction model uses the particle-averaged oxygen concentration to calculate the solids reaction rates. Since the gas concentrations and the solids volume fractions differ between the L - and H-phases, averaging the oxygen concentration over the particles w i t h i n each of the two phases allows a simple coupling between the fluidized bed and the solids reaction model while accounting for the effect of particles w i th in the L-phase. 5.1.6 Minimum fluidization velocity Most m i n i m u m fluidization velocities correlations are of the form: R e m / - ^JCl + C 2 A r - d (5.27) 177 Chapter 5. Model Development where C\ and C 2 are constants. T h e Archimedes number (Ar) is given by: A r = df = PgiPp ~ Pg)9dp (5.28) The dimensionless particle size (d*) is the cubic root of the Archimedes number. T h e form of the correlation was developed by equating the pressure drop calculated from the E r g u n equation to the buoyed weight of the bed per unit area. T h e values recommended by Grace [207] are Ci = 27.2 and C 2 = 0.0408. The choice of the average particle size (dp) is important . For f luidizat ion calculations, the Sauter mean size (mean surf ace/volume size) is commonly used, w i th : where xi is the weight fraction of particles in each size range and dpi is the average of adjacent sieve apertures. Note that this definition gives more weight to smaller particles than larger ones. 5.1.7 Bubbling fluidized bed The industr ia l roaster is operating i n the bubbl ing fluidized bed regime. Since bubble velocities depend on their size, the effective bubble size (De) must be calculated as a function of the vertical posi t ion in the bed. In this work, the bubble size is calculated using the correlations in Table 5.2. Mos t bubble size correlations require the bed diameter D, and the dis tr ibutor surface area per orifice (Ad)- T h e M o r i and W e n [208] correlation also gives an in i t i a l bubble size (De<o) and a m a x i m u m bubble size due to bubble coalescence ( D e o o ) . T h e concept of m a x i m u m bubble size, first introduced by Harr i son et al. [210], is of cr i t ical importance in evaluating bubble diameters i n fluidized beds of fine (Geldart G r o u p A ) particles. The m a x i m u m bubble size is obtained by using the terminal velocity (U°) of spherical particles 1 (5.29) of 2.7dp [207, 211]: • 2 D, e.max = 2.0 (5.32) 9 178 Chapter 5. Model Development Table 5.2: Correlations for bubble sizes Dar ton et al. [209] De = 0 . 5 4 ( L 7 - t / m / ) ° - 4 ( 2 + 4 v ^ ) ° V a 2 (5.30) M o r i and Wen [208] De = D e t 0 0 - ( D e ! 0 0 - D e ! o ) e - ° ' 3 z / D Z ? 6 i C O = 1.49 (p2\U - Umf))°A (5.31) D e f i = 1.38g-02 (Ad(U - Umf))0A T h e factor 2.7 was obtained empir ical ly to better predict the m a x i m u m stable bubble diameter observed experimentally. T h e dimensionless terminal velocity (U£) of spherical particles can be estimated from the dimensionless particle diameter (d*) [20]: (5.33) To estimate parameters that depend on the effective bubble size, it is common to use the bubble size correlation at 40% of the bed height, i.e. at z = 0AH. T h e isolated bubble rise velocity (U0OO) can be obtained by: Uboo = 0.71^/g~L\ (5.34) T h e isolated bubble rise velocity (Uboo) is the rise velocity of a single bubble injected i n a fluidized bed operated at the m i n i m u m fluidization velocity. For freely bubbl ing beds, the bubble rise velocity (£/(,) is given by: Ub = Uboo + (U- Umf) (5.35) T h e bubble rise velocity cannot be used to calculate the superficial gas velocity in the L -phase. Accord ing to the two-phase theory of fluidization, a l l the gas enters the H-phase at m i n i m u m fluidization velocity. However, at m i n i m u m fluidization, equation 5.35 predicts that the superficial gas velocity is [7 6 o o and not 0. T h e expression for the bubble rise velocity is 179 Chapter 5. Model Development therefore m o d i f i e d so t h a t Ut, —> 0 as U —> Umf [212]: Ub = (U-Umf)(l + ^^VgD~e) (5.36) T h e b e d e x p a n s i o n (E) c a n b e e s t i m a t e d f r o m : E = g ~ g " / = (5.37) E q u a t i o n 5.37 r e su l t s f r o m t h e t w o - p h a s e t h e o r y of f l u i d i z a t i o n a n d a s s u m e s t h a t t h e b e d e x p a n s i o n is c a u s e d b y a n y gas flow b e y o n d Umf, i .e. b y (U — Umf). T h i s c a l c u l a t i o n a l so a s sumes a n average b u b b l e s ize for t h e en t i r e fluidized b e d . B e c a u s e H is u s u a l l y u n k n o w n , a n i t e r a t i v e p r o c e d u r e is u sed . I n t h e p resen t m o d e l , t h e b u b b l e s ize is n o t set at a n average va lue , b u t is v a r i e d a l o n g t h e v e r t i c a l p o s i t i o n i n t h e b e d . T h e va lues of o t h e r d e p e n d a n t p a r a m e t e r s a lso change as t h e b u b b l e s ize var ies w i t h i n t h e b e d . F o r t h r e e - d i m e n s i o n a l b u b b l e s , t h e i n t e r p h a s e m a s s t r ans fe r coeff ic ient [213] a n d a r e a are ob -t a i n e d f r o m : 1/2 fcL// = % £ + 2 f D g € m ^ ° ° N ) (5.38) ai = J - (5.39) T h e s e t w o p a r a m e t e r s were b r i e f l y d i s c u s s e d i n s e c t i o n 5.1.2. T h e i n t e r p h a s e m a s s t r ans fe r coeff icient is c o m p o s e d of a t h r o u g h f l o w ( c o n v e c t i o n ) c o m p o n e n t a n d a d i f f u s i o n c o m p o n e n t . T h e d i f f u s i o n c o m p o n e n t var ies w i t h gas d i f f u s i v i t y ( D f l ) , b u b b l e v e l o c i t y (U^o) a n d b u b b l e d i a m e t e r (De). 5.1.8 S l u g g i n g fluidized b e d A s l u g g i n g f l u i d i z e d b e d is s i m i l a r to a b u b b l i n g fluidized b e d . H o w e v e r , b u b b l e g r o w t h is r e s t r i c t e d b y t h e r e a c t o r w a l l s a n d b u b b l e s t r a v e l t h r o u g h t h e b e d as s lugs ( e l o n g a t e d b u l l e t -s h a p e d b u b b l e s c o n s t r a i n e d b y t h e w a l l s ) . T h r e e c o n d i t i o n s a re n e c e s s a r y for s l u g g i n g . T h e s u p e r f i c i a l v e l o c i t y (U) m u s t b e h i g h e r t h a n t h e m i n i m u m s l u g g i n g v e l o c i t y ( < 7 m s ) ; t h e b e d 180 Chapter 5. Model Development height (H) must be greater than the m i n i m u m slugging height; and the m a x i m u m bubble size (De,max) must be at least of the order of the column diameter (D). T h e m i n i m u m slugging velocity (Ums) is calculated using [214]: Ums = Umf + 0 .07V^/J if Hmf > 1 .3D 0 1 7 5 ( 5.40) Ums = Umf + 0.07 + 0 .16(1 .3£>°- 1 7 5 - Hmf)2 (5.41) Equat ion 5.40 and 5.41 apply for shallow beds and deep beds respectively. T h e m a x i m u m bed height (Hmax) dur ing slugging can be estimated from [215, 216]: Hmax Hmf U — Umf Hmf USoo T h e velocity of a single slug (Usoo) is given by: (5.42) Usoo = 0.35^/gD (5.43) For a continuously slugging bed, the slug velocity (Us) i s ' : Us = Usoo + (U- Umf) (5.44) W i t h the exception of the single slug velocity, the last three equations are s imilar to those for bubbl ing fluidized beds, but w i t h s (slug) in place of b (bubble). Compar ing the H o v m a n d slugging model [217] to the Orcu t t "piston-flow" fluidized bed model [218, 219] shows that the derivations are identical . T h e interphase mass transfer coefficient (km) and area (aj) can be expressed in a form similar to that of the bubb l ing case: a, . (5.46) The surface integral (I) (shown in Table 5.3) and the slug shape factor (fs) are functions of the slug length-to-diameter ratio (-g) : ^ = ^  = (§)r°-495 (s)1/2 + 0 0 6 1 ( 5 4 7 ) 181 Chapter 5. Model Development Table 5.3: Values of the surface integral (I) for various slug length to diameter ratio (L/D) L/D 0.3 0.5 1.0 2.0 3.0 4.0 5.0 I 0.13 0.21 0.39 0.71 0.98 1.24 1.48 The slug length to diameter ratio ( ^ ) can be obtained by solving the quadrat ic equation [217]: i !- - o W * V (l + " - ' f e U 0.061 _ (T/D-omi)(u-uml) _ where T is the slug-to-slug spacing (tail-to-nose spacing). 5.1.9 Transition from bubbling to slugging Slugging may be considered as a special case of bubbl ing f luidizat ion where the bubble size is physically restricted by the walls of the reactor. In a bubbl ing fluidized bed, bubbles coalesce as they rise through the bed causing their average diameter to increase w i t h increasing height vertical posi t ion. A s the bubble diameter approaches the reactor diameter, slugging takes over. A s the mean bubble size increases, the effect of the walls becomes greater and one expects a smooth t ransi t ion from bubbl ing to slugging fluidization. Mode l l ing the transi t ion to slug flow may be attempted in various ways: • One could use two separate models, one for bubbl ing and one for slugging, applying a bubbl ing model below a given criteria, then switch to the slug flow model . T h e problem wi th this approach is that there would be a discontinuity at the point where the switch is made, while in practice the transi t ion occurs gradually. Moreover, there is uncertainty in characterizing the regime transi t ion. • One could use the results from the two models and interpolate or average their results. A probabil is t ic average could be used and would better characterize the uncertainty of the regime transi t ion. T h e probabil is t ic average would be the weighted sum of the results where the weights are based on the probabi l i ty of being i n a given regime. A problem 182 Chapter 5. Model Development wi th this approach is that the interpolated results are not necessarily consistent w i th the physics of the system, especially where there are non-linearities. • A better method is to combine the two models into a single model which predicts results similar to the two l imi t ing models outside the t ransi t ion range. In the t ransi t ion region between two flow regimes, the model uses the probabil is t ic average of the parameters (not the final predictions) for each regime. T h i s approach has been used previously to model the t ransi t ion from the bubbl ing to the turbulent f luidizat ion regime and from turbulent to fast f luidization [212, 220, 203, 205]. In that case, relatively simple R e vs A r correlations describe the transitions from bubbl ing to the turbulent fluidization regime and from turbulent to fast fluidization [205]. T h e probabili t ies were related to the root-mean-square deviations from these correlations [205]. Currently, the t ransi t ion from bubbl ing to the slugging fluidization regime is only described by the m i n i m u m slugging velocity (Ums), the necessary conditions for slugging (see section 5.1.8) and the cri terion [216]: Th i s criterion does not quantify the probabi l i ty of slugging and bubbl ing , nor does it allow for a transit ion wi th in the fluidized bed, i.e. bubbl ing near the dis t r ibutor and slugging above. T h e bubble rise velocity as a function of the bubble-to-column-diameter ratio is used in the next section to characterize the transi t ion from bubbl ing to the slugging fluidization flow regime. The regime probabili t ies are then obtained. These probabili t ies are then used to calculate probabil ist ic averages of the parameters required by the model . Void velocity In order to bridge the bubbl ing and slugging fluidization regimes, the void (bubble or slug) rise velocities (Uvoo) are described as a function of the Froude number: = 0.2 (5.49) Fr = voo (5.50) V = b or s 183 Chapter 5. Model Development Using the Froude number, equations 5.34 and 5.43 may be converted to: B u b b l i n g Fr = 0.71^De/D (5.51) Slugging Fr = 0.35 (5.52) T h e modified bubble rise velocity (from equation 5.36) can be wri t ten: UV = (U -Umf)(l + ^VgD) (5-53) A s for several other aspects of the hydrodynamics of fluidized bed systems, the t ransi t ion to slug flow in fluidized bed systems is analogous to that in gas-liquid systems. T h e experimental data from fluidized bed systems presents a s imilar t rend as in the water system. However, the scatter is much larger [216]. F igure 5.2 shows that the velocities at the two extremes are described by equations 5.51 and 5.52. T h e transi t ion between the two extremes is smooth and occurs for y/De/D between about 0.38 and 0.7 [216]. The behaviour at each end of the transi t ion interval clearly approaches the two l imi t i ng cases. In other words, the slopes at each end of the interval are equal to each of the l imi t i ng cases. T h e fit of the experimental data must also approach the l imi t ing cases s imi la r ly w i t h a sigmoidal fit in-between to express the probabi l i ty of slugging passing from 0 to 1 as y/De/D goes from small values to values approaching unity. To simplify the fitting for the t ransi t ion region, a transformation is used such that the bubbling-to-slugging t ransi t ion interval (X) goes from 0 to 1 and the corresponding Froude numbers (Y) also passes from 0 to 1. Here: _ ^DjD-DDo X ~ DD\ - DD0 ' ( 5 - M ) where DDQ and DD\ are the lowest and highest values of yjDe/D i n the t ransi t ion interval, i.e. the endpoints of the t ransi t ion interval. Similar ly, Y is taken as: F r - 0 . 7 L P A ) 0.35 - 0 . 7 L D A ) ' so that it represents a fraction departure from the wall-effect free bubble velocity. B y imposing the values and the slopes at the end points, the following th i rd order po lynomia l is obtained: 184 Chapter 5. Model Development Figure 5.2: Bubble rising velocity in water. Experimental points obtained from Hovmand and Davidson [216] Y = KX + (3 - 2K)X2 + (K- 2)X3 (5.56) where K is the required slope at X = 0. The slope, obtained from equation 5.51 and transformed into X,Y coordinates is: 0.71(DD1-DDQ) 0.35 - 0.71DA. Note that once this initial slope is set, there are no degrees of freedom to set any other param-eters in the transformed coordinates. Therefore, the only fitting parameters are the endpoints of the interval, i.e. the values of ^/DE/D at which one sets X — 0 and X = 1 (DDQ and DD\). The Froude number is described for the three ranges as follows: For y/De/D' < DD0 Fr = 0.71^fDe/D (5.51) 185 Chapter 5. Model Development • F o r DD0 < y/De/D < DD1 Y = KX + (3 - 2K)X2 + (K - 2)X3 (5.56) • F o r jDjD > DDi F r = 0.35 (5.52) T h e o p t i m u m t r a n s i t i o n i n t e r v a l is o b t a i n e d b y m i n i m i z i n g t h e squa res o f t h e d i f fe rence b e t w e e n t h e f i t t ed f u n c t i o n a n d t h e e x p e r i m e n t a l d a t a . A n exce l l en t fit o f t h e e x p e r i m e n t a l d a t a is o b t a i n e d b y u s i n g a t r a n s i t i o n i n t e r v a l (^De/D) b e t w e e n 0.319 a n d 0 .714. T h i s i n t e r v a l is o n l y s l i g h t l y l a rge r t h a n sugges t ed b y H o v m a n d a n d D a v i d s o n [216] w h o e m p l o y e d 0.38 t o 0.7. W i t h these va lues , K is e q u a l t o 2.27. Probability of slugging T h e fit i n F i g u r e 5.2 c a n n o t d i r e c t l y r epresen t t h e p r o b a b i l i t y o f s l u g g i n g o r t h e p r o b a b i l i t y of b u b b l i n g . F o r i n s t a n c e , t h e p r o b a b i l i t y o f s l u g g i n g s h o u l d n o t i n c r e a s e p r o p o r t i o n a l l y t o t h e v o i d v e l o c i t y , i .e. r a p i d l y at first t h e n m o r e s l o w l y . O u t s i d e t h e t r a n s i t i o n i n t e r v a l , t h e p r o b a b i l i t y o f s l u g g i n g is t a k e n as 0 for ^/De/D < DDQ a n d 1 for yjDe/D > DD\. I n t h e t r a n s i t i o n i n t e r v a l , t h e p r o b a b i l i t y o f s l u g g i n g increases f r o m 0 t o 1 i n a n a p p r o p r i a t e m a n n e r . A r ea sonab le w a y o f e s t i m a t i n g t h e p r o b a b i l i t y f r o m t h e fit o f t h e F r o u d e n u m b e r s w a s o b t a i n e d b y c o n s i d e r i n g t h e g r o w i n g d e v i a t i o n o f t h e v o i d v e l o c i t y ( e q u a t i o n 5.56) f r o m t h e c o r r e s p o n d i n g wal l -effect i n d e p e n d e n t b u b b l e r i se v e l o c i t y ( e q u a t i o n 5.51) i n t h e l ower p a r t o f t h e t r a n s i t i o n i n t e r v a l , a n d t h e n c o n s i d e r i n g t h e s h r i n k i n g di f ference b e t w e e n t h e v o i d v e l o c i t y ( e q u a t i o n 5.56) a n d t h e s l u g flow ( e q u a t i o n 5.52) l i m i t i n t h e u p p e r s e c t i o n o f t h e t r a n s i t i o n i n t e r v a l . T h e c o n d i t i o n (^De/D = 0 . 35 /0 .71 = 0.493) w h e n t h e v e l o c i t i e s a re e q u a l ( e q u a l F r f r o m e q u a t i o n 5.51 a n d 5.52) def ines t h e p o i n t w h e r e t h e p r o b a b i l i t i e s o f s l u g g i n g a n d b u b b l i n g a re e q u a l , i .e. Pslugging = Pbubbiing = 0.5. H e n c e t h e p r o b a b i l i t i e s are a s s igned as f o l l o w s , w i t h t h e t r a n s i t i o n i n t e r v a l b e i n g DDQ < ^DE/D < DDX: • F o r ^JL\|D < DDQ (5.58) 186 Chapter 5. Model Development Pbubbling — T (5.59) F o r DD0 < sjDe/D < 0.493 = KX - (KX - (3 - 2K) X2 + (K - 2) X 3 ) s J u M m f f 2 [value of n u m e r a t o r at JL\]~D = 0.493] 1 ' ' Pbubbling = 1 — Pslugging (5.61) F o r 0.493 < yHjjD < DDX _ l-(KX-(3-2K)X2 + (K-2)X3) f bubbling — , , . c v. O^.DZJ s a m e n u m e r a t o r as m e q u a t i o n 5.60 a b o v e F o r y/De/D > DDi Pslugging — 1 Pbubbling (5.63) Pslugging = 1 (5.64) Pbubbling = 0 (5.65) F i g u r e 5.3 p resen t s t h e r e s u l t i n g p r o b a b i l i t y o f s l u g g i n g as a f u n c t i o n o f yjDe/D. T h e p r o b a -b i l i t y o f s l u g g i n g first increases p r o p o r t i o n a l l y t o t h e d e v i a t i o n o f e q u a t i o n 5.56 f r o m e q u a t i o n 5.51, reaches 5 0 % , t h e n increases at a d e c r e a s i n g r a t e as t h e d e v i a t i o n o f e q u a t i o n 5.56 f r o m e q u a t i o n 5.52 decreases . T h e e q u a t i o n s d e s c r i b i n g t h e p r o b a b i l i t y o f s l u g g i n g as w e l l as o t h e r e q u a t i o n s r e q u i r e d t o d e s c r i b e t h e t r a n s i t i o n r e g i m e are s u m m a r i z e d i n T a b l e 5.4. N o t e t h a t the sugges t ed p r o c e d u r e a l l o w s a s m o o t h t r a n s i t i o n b e t w e e n p u r e b u b b l i n g (Pbubbling = 1) a n d p u r e s l u g g i n g (PsiUgging = 1) a s y/De/D increases f r o m DDo t o DD\. W h i l e t h i s is c o n c e p t u -a l l y s i m i l a r t o t h e p r o b a b i l i s t i c t r a n s i t i o n s i n t r o d u c e d i n t h e g e n e r a l i z e d fluidized b e d r e a c t o r m o d e l [212, 220, 203 , 205], one m u s t n o t e t h a t i n t h e c u r r e n t case, t h e t r a n s i t i o n t akes p l a c e over he igh t as \/De/D g r o w s d u e t o coa lescence , w h e r e a s i n t h e b u b b l i n g / t u r b u l e n t / f a s t fluidization t r a n s i t i o n s of t h e g e n e r a l i z e d fluidized b e d r e a c t o r m o d e l [212, 220 , 203 , 205], t h e t r a n s i t i o n s are o n l y f u n c t i o n s o f t h e s u p e r f i c i a l v e l o c i t y . T h e g e n e r a l i z e d b u b b l i n g - s l u g g i n g i n t e r p h a s e m a s s t r ans fe r coeff ic ient a n d a r e a a re c a l c u l a t e d u s i n g t h e e q u a t i o n s i n T a b l e 5.5. 187 Chapter 5. Model Development F i g u r e 5.3: P r o b a b i l i t y of s l u g g i n g 5.2 Steady-state fluidized bed reactor model: Reaction of solids S o far , t h e m o d e l has d e s c r i b e d t h e fluidized b e d d y n a m i c s a n d t h e gas r e a c t i o n . T h i s is suff ic ient for c a t a l y t i c fluidized b e d r eac to r s . H o w e v e r , for g a s - s o l i d r e a c t i o n s , t h e fluidized b e d r eac t o r m o d e l m u s t b e c o u p l e d t o a s o l i d r e a c t i o n m o d e l s u c h t h a t t h e n u m b e r o f m o l e s c o n s u m e d a n d p r o d u c e d i n t h e gas are b a l a n c e d w i t h t h e n u m b e r o f m o l e s c o n s u m e d a n d p r o d u c e d i n t h e s o l i d . T h e m o d e l a s sumes t h e r e a c t i o n : 3 l Z n S ( s 0 ( u Q + 2°2(gas) = l Z n O ( s o H d ) + lS0 2 ( S as) (5.66) T o o b t a i n a n o v e r a l l s o l i d s c o n v e r s i o n , t h e so l i d s r e a c t i o n m o d e l m u s t i n c l u d e a s s u m p t i o n s o n t h e m i x i n g o f t h e s o l i d s w i t h i n t h e fluidized b e d , t h e s ing l e p a r t i c l e r e a c t i o n m o d e l a n d t h e r e s idence t i m e s o f t h e so l i d s w i t h i n t h e fluidized b e d . 188 Chapter 5. Model Development Table 5.4: Summary of equations describing the t ransi t ion from bubbl ing to slugging fluidization Transformation ^/De/D to X X = ^Boi-OBo0 OT V ^ e / i ) = DDQ + X (DD\ - DDQ) Fr to Y Y = O^S'-VTIDDo o r F r = F ( ° - 3 5 - 0 .71DDo) + 0.71DD0 Bubble velocity y/De/D < DDQ Fr = 0.7ly/De/D DDQ < y/De/D < DD\ Y = 2.27X - 1 . 5 4 X 2 + 0 . 2 7 X 3 ^De/D > DDi Fr = 0.35 Probability y/De/D < DDQ •^slugging — 0 DDQ < jDe/D < 0.493 Pslugging = 2 - 7 9 X 2 - 0 . 4 9 0 X 3 0.493 < y/De/D < DDi Pslugging = "0 .813 + 4 . 1 2 X - 2 . 7 9 X 2 + 0 . 4 9 0 X 3 VDe/D > DDx Pslugging — 1 Interval: DDQ = 0.319, DDX = 0.714 5.2.1 Mixing of solids within the fluidized bed In this model , the solids are assumed to be well mixed axia l ly and radially, as impl ied i n the gas model . If mix ing were not perfect, some regions of the fluidized bed would contain higher concentrations of reacting solids than others. T h e gas reaction is formulated i n terms of solids volume fraction wi th in each phase which are constant ((f)H = l — emf and (pr, = constant) for the entire reactor and does not differentiate the type of solids (reacting or inert) . Therefore, any difference in the concentration of reacting solids (i.e. insufficient mixing) affects the reactivity of the solids mixture . To account for variations in the concentration of reacting particles, a solids m i x i n g and flow model should be coupled to the gas reaction model . T h i s approach has been used to model shallow fluidized beds [221, 222, 223, 224, 225] where radial m i x i n g is accounted for, while axia l mix ing is assumed to 'be perfect. 189 Chapter 5. Model Development CD CSJ CD CD o bD a 'So bD cn bD a 3 PQ Ph ffl fl Q 1 s I § 03 O O '43 co rH a . 2 _ce co I § «3 o 0) =3 a CD -a 3 O £ ba a -a o o L O oo T-H o o a o '•+3 a 3 cr CD M el 3 O O L6 L O C O (D CD ^ s .8 3 L O ro O + I o I o CB 3 o +3 CJ a . 2 a O . CO C O bJO I fc s . 2 'co 3 a ft X CD CD PQ CD 03 a + cu + + 3 CD 'o cfi CD O o 03 CD CD bJO 3 d ,3 o X 190 Chapter 5. Model Development To verify if the assumption of perfect mix ing is valid, m ix ing times w i l l be compared to the reaction and residence times of the reacting particles. Solids m i x i n g in a f luidized bed must be considered separately in the two important dimensions. A x i a l m i x i n g may be characterized by the turnover t ime, the t ime required for the bubbles to displace the entire mass of the bed. The solids turnover t ime is calculated using the axial solids flux ( J ) , bed mass (M^ed) and cross-sectional area (A) [226]: >^ J = PP(1- tmf) (U - UMF) Y ((3W + 0.38&) (5.67) ^turnover ~AJ~ (5.68) To calculate the solids flux, the values suggested by Baeyens and Geldar t [226] for rounded sand are used: j3w — 0.32, (3d = 0.7, Y = 0.82. Complete axia l m i x i n g can be achieved in 2 to 3 turnover times. For a complete discussion on axial mix ing and turnover t ime, see [226]. T h e solids are also assumed to be well mixed radially. R a d i a l m i x i n g is usual ly quantified using a dispersion model [227, 228, 229, 230]. T h e radial diffusion coefficient of solids (Dra(nai) in a bubbl ing fluidized bed may be expressed [227] as: Dradiai = 3.66 • I O " 4 U ~ ^ f . (5.69) Umf B y considering radial diffusion in a cylinder, a characteristic t ime may be obtained [231]. - D * Uadial — . K „ Q n (5.70) T h e constant 5.78 is the square of the root of the Bessel function of zero order. The most important difference between industr ia l and laboratory roasters is the radia l mix ing time. The assumption of a perfectly mixed bed is verified by comparing the particle residence t ime and reaction times to the two mix ing times described above. 5.2.2 Solid residence times T h e solids mean residence t ime characterizes the average t ime spent by particles i n the fluidized bed. The solids mean residence t ime is required in section 5.2.4 to calculate the average solids 191 Chapter 5. Model Development c o n v e r s i o n . F o r n o n - r e a c t i n g m o n o - s i z e d p a r t i c l e s , t h e m e a n r e s idence t i m e is r e l a t e d to t h e s p a c e - t i m e : r=^L ( 5 . 7 1 ) Fpeed H o w e v e r , s ince a fluidized b e d roas t e r has r e a c t i n g p a r t i c l e s o f d i f ferent s izes , t h i s c a l c u l a t i o n is n o t v a l i d . T o e v a l u a t e t h e m e a n r e s idence t i m e o f di f ferent p a r t i c l e s izes we f o r m u l a t e a n o v e r a l l m a s s b a l a n c e a n d a m a s s b a l a n c e b y - s i z e over t h e r eac to r : (3Fpeed Fover flow Fcarryover — 0 (5.72) PFpeedPFeed ~ Fover flowPOver flow FcarryoverPCarryover — 0 (5.73) w h e r e PFeed, POverflow a n d pcarryover are t h e p a r t i c l e s ize d i s t r i b u t i o n f u n c t i o n s o f t h e feed, ove r f low a n d c a r r y o v e r r e spec t i ve ly . T h e s e m a s s b a l a n c e s a s s u m e s t e a d y - s t a t e , c o m p l e t e c o n -v e r s i o n a n d n o changes i n p a r t i c l e s izes . T h e m a s s c o n v e r s i o n r a t i o , (3, w a s b r i e f l y d i s c u s s e d for the o v e r a l l m a s s b a l a n c e o f t h e e x p e r i m e n t a l r e su l t s i n s e c t i o n 4 .3 . T h e c o n s t a n t (3 is u s e d t o conve r t t h e c o n c e n t r a t e feedra te i n t o a c a l c i n e feedrate . F o r p u r e z i n c su l f i de a n d o x i d e , (3 is s i m p l y t h e r a t i o o f t h e m o l a r masses i .e. (3 = — ^ug/mol ~ 0-835. T h e m e a n r e s idence t i m e for a g i v e n s ize is c a l c u l a t e d f r o m t h e c a r r y o v e r a n d ove r f low m a s s flowrates, i n a d d i t i o n t o t h e s ize d i s t r i b u t i o n s a n d b e d mass : _ Mbed POverflow Fo ver flow POverflow ~\~ Fcarryover PCa (5.74) rryover B e c a u s e o f e l u t r i a t i o n , t h e r e s idence t i m e of a g i v e n s ize o f p a r t i c l e s d e p e n d s o n t h e p a r t i c l e s ize i n q u e s t i o n . V e r y s m a l l p a r t i c l e s have a s h o r t m e a n r e s idence t i m e i n t h e b e d , w h i l e l a rge r p a r t i c l e s s p e n d m u c h l onge r i n the roas te r . T h i s is because fine p a r t i c l e s c a n leave t h e roas te r b y t w o o u t p u t s t r e a m s , w h e r e a s l a rge r ones o n l y e x i t v i a t h e ove r f low s t r e a m . I t has b e e n s h o w n t h e o r e t i c a l l y t h a t t h e average r e s idence t i m e of c a r r y o v e r a n d o v e r f l o w p a r t i c l e s o f t h e s ame d i a m e t e r is t h e s a m e [232]. T h e e l u t r i a t i o n c o n s t a n t is r e l a t e d t o t h e c a r r y o v e r m a s s flowrate a n d s ize d i s t r i b u t i o n , b y : Fcarryover PCarryover /r r,r\ K — — [p.10) Mbed POverflow 192 Chapter 5. Model Development w h i c h c a n b e u s e d t o o b t a i n : r = p 1 (5.76) r over flow i MBED + K U s e of e q u a t i o n 5.76 r eq u i r e s a p p r o p r i a t e i n f o r m a t i o n o n t h e e l u t r i a t i o n c o n s t a n t . E l u t r i a t i o n i n c o m m e r c i a l f l u i d i z e d b e d roas te r s has n o t b e e n c h a r a c t e r i z e d , a n d p r e d i c t i o n s f r o m a v a i l a b l e c o r r e l a t i o n s v a r y w i d e l y [233]. T h e r e f o r e , a c c u r a t e p r e d i c t i o n of t h e p a r t i c l e r e s idence t i m e is n o t p o s s i b l e w i t h o u t d i r e c t m e a s u r e m e n t s . A m o r e a d e q u a t e r e p r e s e n t a t i o n of e q u a t i o n 5.71 w h e n c o n s i d e r i n g r e a c t i n g p a r t i c l e s a n d a w i d e s ize d i s t r i b u t i o n m a y b e o b t a i n e d f r o m e q u a t i o n s 5.73 a n d 5.74: t _ MbedpBed ^ 7 7 - j (3F~FeedPFeed T h e effective s ize d i s t r i b u t i o n o f t h e i n d u s t r i a l feed is v e r y d i f f i c u l t t o c h a r a c t e r i z e s ince c o n -cen t r a t e p a r t i c l e s f o r m l u m p s d u e t o t h e p resence of w a t e r . H o w e v e r , t h e feed p a r t i c l e s ize d i s t r i b u t i o n of t h e l a b o r a t o r y , roas te r c a n b e m e a s u r e d u s i n g p a r t i c l e s ize a n a l y z e r s . S o m e p a r t i c l e s o f t h e feed m a y b e s m a l l e r t h a n t h e s m a l l e s t p a r t i c l e i n t h e b e d . I n s u c h cases, e q u a t i o n 5.77 r e su l t s i n m e a n re s idence t i m e s e q u a l t o 0. F o r these p a r t i c l e s , a m i n i m u m m e a n p a r t i c l e r e s idence t i m e is r e q u i r e d . T h i s m i n i m u m m e a n p a r t i c l e r e s i d e n c e t i m e is set to b e e q u a l to t h e m e a n re s idence t i m e o f t h e gas i n t h e f l u i d i z e d b e d : _ HmfA(l - <t>H) + (H- Hmf)A(l - <f>L) _ Hmf(l - <j>H) + (H - Hmf)(l - cj>L) (5.78) 'minimum — JJ A U 5.2.3 Single-particle reaction model T h i s s e c t i o n b r i e f l y de sc r ibe s a t r a n s i e n t n o n - i s o t h e r m a l s o l i d r e a c t i o n m o d e l a n d i t s s i m p l i -f ied p s e u d o - s t e a d y - s t a t e i s o t h e r m a l v e r s i o n for t h e r e a c t i o n s o f s o l i d s w i t h i n t h e fluidized b e d . T h e t r a n s i e n t n o n - i s o t h e r m a l p a r t i c l e r e a c t i o n m o d e l is u s e d t o v e r i f y t h a t t h e a s s u m p t i o n of i s o t h e r m a l i t y is v a l i d a n d t o e s t i m a t e u n d e r w h i c h c o n d i t i o n s i t is n o t . T h e fluidized b e d r e a c t o r m o d e l a s s u m e s t h a t t h e p a r t i c l e s a re i s o t h e r m a l , a t t h e s a m e t e m p e r a t u r e as t h e f l u i d i z e d b e d a n d uses t h e s i m p l i f i e d so l i d s r e a c t i o n m o d e l d e s c r i b e d at t h e e n d o f t h i s s e c t i o n . 193 Chapter 5. Model Development The single particle reaction model is a transient model aimed at predict ing the gas concentra-tions at the reaction site, the particle temperature and the evolution of conversion w i t h t ime. A s summarized by Wen and Wang [234] the model accounts for thermal and diffusional effects in noncatalytic solid gas reactions. T h e model, based on the unreacted-shrinking-core model, includes temperature predictions and uses effectiveness factors to describe the effects of diffu-sion and heat generation. T h e resulting model can predict various phenomena such as igni t ion, extinction, geometric instabi l i ty and abrupt changes i n the controll ing mechanism. T h e nomenclature of the equations is the same as in W e n and W a n g [234] w i t h minor changes to allow for the calculation of gaseous product concentrations. T h e model applies to the following general reaction: For the roasting of zinc sulfide, A is O2, S is Z n S , G is SO2 and C is Z n O . A s for the fluidized bed model , the stoichiometric coefficients, z/j, are positive for products and negative for reactants. T h e rate of reaction can be represented as: where m and n are the orders of the reaction w i t h respect to the solid and the gaseous reactants concentrations, respectively. T h e reaction rate constant, ks is per uni t reacting surface area. The temperature dependency of the reaction rate constant is assumed to be of Arrhen ius type, i.e.: where k° is the pre-exponential constant and Ea is the activation energy. F igure 5.4 presents the geometry of the model as well as typica l concentration and temperature profiles. aA(gas) + S(solid) = #G(gas) + cC(solid) (5.79) TA = "ATS = VAhCfCX (5.80) (5.81) 194 Chapter 5. Model Development Reaction ^ S u r f a c e ^ * \ ^ Ash Layer Gas Film Figure 5.4: Concentrat ion and temperature profiles of a single reacting part icle [234] Mole balances In terms of gas mole fractions (xj), the steady-state gas mole balance over the reacted layer (rc < r < R) of a spherical reacting particle can be described as: d?x; 2 dxi H = 0 dr2 r dr (5.82) where i can either be the gaseous reactant (A) or product (G) . A l t h o u g h equimolar counter-diffusion is assumed, the following treatment can be applied to the zinc roasting system when the reactant and resulting product gas concentration is small , which is assumed to be the case. T h e boundary condi t ion at the surface (r = R) is: dxi. [CDei)To~^\r=R — (kmiC)To{Xio ~ %is) (5.83) T h e product of the total gas concentration (sum of a l l gaseous species) times the diffusivity (CDei) is assumed to be temperature-independent. T h e boundary condi t ion at the core surface (r = rc) is (CDei)To—T^\r=rc — —ViK(Tc)C™CAc (5.84) where V{ is the stoichiometric coefficient for component i. T h e evolution of the core radius wi th t ime is described by: dxj drr (CDei)To— = vACs d t (5.85) 195 Chapter 5. Model Development wi th the in i t i a l condit ion, rc = R when t = 0. T h e subscripts T 0 and T c indicate that the quan-tities are evaluated at the bulk conditions or at the reaction interface conditions, respectively. Heat balance The energy balance in the ash layer is given by: 8T ke (d2T 2dT\ m=cVe{-dr^ + rfr) ( 5 - 8 6 ) where ke and Cpe are the effective thermal conduct ivi ty and volumetr ic heat capacity of the ash layer respectively. T h e boundary condit ion at the surface (r = R) is: dT - f c e ^ T = hc(Ts - T0) + hR(T* - T 4 ) (5.87) Note that radiat ion is included using a radiative heat transfer coefficient. T h e radiative heat transfer coefficient (hfi), includes the emissivity of the particle (epartide), the Stefan-Boltzmann constant (a = 5.67 x I O - 8 W m 2 K " 4 ) and view factors, if applicable. T h e first r ight-hand term is the heat transfer by convection, while the second term allows for the radiat ion from the particle surface to a wal l surface. For a particle in a fluidized bed, the wal l surface consists of other bed particles. T h e boundary condit ion at the unreacted core surface (r = r c ) , assuming that the core is at a uniform temperature (T c ) , is: ^ r l k ^ - ^rlvAksTcCfCnAc{-AH) = l r r r c 3 p c C p < 3 (5.88) Solution T h e reader is referred to Wen and Wang [234] for more details on the solution of the mass and heat balances. T h e equations can be rewrit ten i n dimensionless form. T h e solut ion of the mass balance for the gaseous reactant (A) is given by: wcA = u8A + ShA(l-usA)^\-^ (5.89) 196 Chapter 5. Model Development The solution of the mass balance for the gaseous product (G) is given by: WcG = w SG + S h G ( l - o ; S G ) ^ l - ^ (5.91) ~{UC) eXP{RT0 \ l Uc))\vA DeGTo XGo) [ b m ) T h e posit ion of the reaction front (£ c ) can be calculated by integration: ShA(l - UJsA) _ d£c _ T h e solution of the heat balance is given by: U8 = Uc+(l- ( N u c ( ( 7 , - 1) + N u R ( C / s 4 - U-d U c 6 / 3 ( ^ ) ^ 8 - (Ua - ^ c ) ( ^ X ) + ^ - ( 1 + ^ + e 0 + ( l 4 c T ( N f c + H ^ u ^ ) (5.93) where (5.94) (5.95) p=CAoDeATo(-AH)R ( 5 9 6 ) keEa Asp = - ^ e A ^ P e (5^97) CAoDeAToCpe VACske The last two dimensionless numbers originate from the transient analysis of the heat balance. Several parameters are grouped into dimensionless numbers such as the Thie le modulus DeATo and the modified Sherwood number (Sh): Sh = (5.100) The Thiele modulus accounts for mass transfer resistance wi th in the product layer, while the modified Sherwood number accounts for the external mass transfer resistance. 197 Chapter 5. Model Development Equations 5.89 to 5.95 must be solved simultaneously by integrating over dimensionless t ime (9). If steady-state is assumed, there is no energy accumulat ion i n the ash layer (A = 0) or the unreacted core (G = 0). T h e equations thus simplify to the results of Ishida and W e n [235]. To obtain the solids conversion from the reaction interface posi t ion, the following relationship is used: x = i~ec (5 .101) Isothermal solid reaction model T h e isothermal solid reaction model assumes that the particle has no internal temperature gradient and reacts at a constant temperature, equal to the environment (or bulk) temperature. For such an isothermal system, there are no heat effects. T h e effectiveness factor (r/ s) and the reaction interface posit ion (£ c ) are given by: Vs = j, (5.102) 1 + ^ ( 1 - ^ + ^ 2 where 9 is the dimensionless t ime. T h e dimensionless t ime required for complete reaction (9cr) is obtained by setting £ c to 0 in equation 5.103. T h e t ime for complete reaction of the solid particles is required for calculat ing the overall conversion of the solids in the fluidized bed. To obtain the (dimensional) t ime for complete reaction, we note that: ksToC^Cl71 tcr = ^ °rm 1 (5.104) A dimensionless t ime of 1 (# c r =l ) signifies that the reaction is controlled by chemical kinetics only. T h e reciprocal of the dimensionless t ime for complete reaction may be viewed as the overall effectiveness factor. For an isothermal system, the effectiveness factor varies between 0 and 1. W h e n heat effects are accounted for and the reaction is exothermic, the effectiveness factor can exceed 1. 198 Chapter 5. Model Development Equations 5.102, 5.103 and 5.104 are used in the gas-solid fluidized bed reactor model to cal-culate the overall solids conversion, as discussed i n the next section. 5.2.4 Conversion of solids Assuming that the bed solids are perfectly mixed, the solids reactions are model led i n similar fashion to the reaction of a macro-fluid where the solid conversion is integrated over the age dis t r ibut ion. For mono-sized particles reacting as shr inking cores under chemical control, the solids conversion in a well-mixed fluidized bed is a function of the mean solids residence t ime ( t ) , and the t ime required for complete conversion of a single particle (tcr) [232, 157] is given by: ftcv / + \ 3 e ~ t / T 1-X= 1 dt (5.105) JO V tcr J T After integration, the overall solid conversion is: X = 3 f f - - 2(f)2 + 2(f]\l - e^)\ (5.106) Due to numerical instabi l i ty at high the exponential is expanded using the Taylor series. If a wide size d is t r ibut ion is modelled, the overall solids conversion of a given stream (carryover, overflow) may be calculated as the size-distribution-weighed sum of the conversions of the different sizes [232]: rdp,rn.ax X= I X(dp)pstreamddp (5.107) Jo where pstream is the particle size d is t r ibut ion function of the stream, the sum of which equals 1. T h e calculation of the conversion for a given particle size is the same as in equation 5.106, but uses the average residence t ime for this given particle size. E a c h particle size w i l l therefore have different average conversions (X(dp)) due to different residence t ime ( t ( c ? p ) ) and different times to complete conversion (tcr(dp)). Unl ike the calculation of the average particle size (equation 5.29), the calculated average conversion weighs the larger unconverted particles equally to the smaller particles. 199 Chapter 5. Model Development 5.3 Solution method Pr io r to solving the model , the reactor geometry, the operating conditions, part icle properties and other model parameters must be set. T h e model is implemented assuming pure zinc sulfide as solid input . T h e zinc sulfide feedrate is calculated by setting the superficial gas velocity (17), inlet oxygen concentration (Co2,m) and excess oxygen (Excess02) and using the equation: Similarly, the zinc concentrate feedrate is calculated by replacing the zinc sulfide molar mass ( M z n s ) by its concentrate equivalent (Mconcentrate) i.e.: j-, A ^ZnS ^concentrate ( 1 \ r~< TT (K m n \ FFeed,concentrate ~ A ^ ^ ^^—^——J Co2,lnU (5.109) T h e excess oxygen is calculated for a given experiment using equation 5.109 (by isolating Excessoi)-T w o addit ional parameters are required prior to fitting the experimental da ta shown i n section 4.4. Mconcentrate) is the mass of zinc concentrate equivalent to a mole of zinc sulfide for the reaction: , Z n S + ^ 0 2 = Z n O + S 0 2 (5.110) A value of MconCentrate larger than the molar mass of zinc sulfide (97.456 g / m o l z n s ) indicates that more concentrate is required than pure zinc sulfide to react w i t h 1.5 moles of oxygen. Mconcentrate can be calculated by adding the oxygen requirement for each element i n the con-centrate assuming complete conversion to Z n O , SO2, Fe203, P b S 0 4 and accounting for the presence of oxygen in sulfates in the concentrate. T h e propor t ion of each element in the concen-trate is obtained from the zinc concentrate assays. For the same operating conditions, i.e. inlet oxygen concentration, superficial gas velocity and excess oxygen, equations 5.108 and 5.109 can be combined to relate the concentrate and Z n S molar masses and feedrates: ^concentrate Mzn S MCOncentrate 200 (5.111) Chapter 5. Model Development Mconcentrate is only used when a concentrate feedrate must be converted to an equivalent pure zinc sulfide feedrate. T h e second parameter, the particle mean residence t ime factor ( / ) is used to adjust the residence t ime of the reacting particles to account for the change in particle mass (ft) and for the fact that the mass of zinc concentrate fed differs from the pure zinc sulfide assumed in the model: Hlvl concentrate The particle residence t ime is therefore: f M b e d p B e d T = — FFeed PFeed (5.113) The experimental data shown in section 4.4 are fitted by adjusting the solids reaction rate constant (ks). Once the parameters are set, the model is solved following these steps: • Guess in i t i a l values for kr, and H or Hmf. Note that once either H or Hmf is known, the other one can estimated. • Integrate the fluidized bed mole balance equations (equations 5.12 and 5.13) over the height. • If the calculated bed expansion (equation 5.17) does not agree w i t h the in i t i a l values of H or Hmf, adjust their values using the calculated bed expansion and repeat the previous step. Convergence is obtained when the difference between the bed expansions is less than 5 x l 0 ~ 4 (0.5 mm) . • Calculate the gas conversion using equation 5.20. • Calculate the average gas concentrations seen by the solids (equation 5.23). • Us ing the gas concentrations from the previous step, calculate the t ime for complete reaction (equations 5.102, 5.103 and 5.104) and the average solids conversions (equations 5.106 or 5.107 ). 201 Chapter 5. Model Development • Compare the gas to the overall solids conversions. If the number of moles reacted do not balance, adjust the effective gas reaction rate constant (kr) and re turn to the second step. If they balance, the model has converged to the desired solution. T h e effective gas reaction rate constant (kr) in the fluidized bed model is an adjustable parameter chosen so that the moles of reactant balance according to the stoichiometry: F F e e d J W 1 0 0 0 AF02 residual, — — (5 .114] T h e model finds the value of kr for which the residual (equation 5.114) is zero. T h e iterative procedure searches for the zero by narrowing the interval where the sign of the residual changes. To constrain the solver, the log of kr is used to ensure that kr is never negative. T h e in i t i a l kr interval is 1 0 ~ 8 to 1 0 8 . Convergence is obtained when the interval, on a log scale, is smaller than 2 x l 0 ~ 4 . T h e effective gas reaction rate constant is adjusted such that the fluidized bed reactor model consumes the correct amount of oxygen. 202 C h a p t e r 6 Model l ing Results T h e m e c h a n i s m , p r o p o s e d i n c h a p t e r 4, a s sumes t h a t l e a d spec ies ass is t a g g l o m e r a t i o n t h r o u g h l e a d su l f ide v a p o r i z a t i o n a n d d e p o s i t i o n o n t o b e d p a r t i c l e s . S i n c e t h e p a r t i a l p r e s s u r e of l e a d su l f ide d e p e n d s s t r o n g l y o n t h e o x y g e n p a r t i a l p ressu re , i t seems t h a t i n c r e a s e d a g g l o m e r a t i o n t h r o u g h t h i s m e c h a n i s m w o u l d o c c u r w h e n t h e b e d p a r t i c l e s e x p e r i e n c e a l o w average o x y g e n p a r t i a l p re s su re . T h e r e f o r e , m o d e l l i n g l o o k s a t t h e average o x y g e n c o n c e n t r a t i o n s u r r o u n d i n g t h e p a r t i c l e s t h r o u g h t h e s i m p l e r e a c t i o n of p u r e z i n c su l f ide t o p u r e z i n c o x i d e . N o o t h e r c o m p o n e n t s are m o d e l l e d , e.g. l e a d , s i l i c a , i r o n , c o p p e r a n d c a d m i u m . T h e u n s t e a d y - s t a t e s ing l e p a r t i c l e r e a c t i o n m o d e l is first u s e d t o e v a l u a t e t h e c o n d i t i o n s u n d e r w h i c h t h e p a r t i c l e t e m p e r a t u r e c a n e x c e e d t h e e n v i r o n m e n t t e m p e r a t u r e . T h i s m o d e l is u s e d to e v a l u a t e t h e a s s u m p t i o n s o f i s o t h e r m a l i t y (no t e m p e r a t u r e g r a d i e n t s i n s i d e t h e p a r t i c l e s a n d c o n s t a n t p a r t i c l e t e m p e r a t u r e e q u a l t o t h e f l u i d i z e d b e d t e m p e r a t u r e ) . N e x t , t h e gene ra l -i z e d s l u g g i n g - b u b b l i n g f l u i d i z e d b e d m o d e l (gas o n l y ) is c o m p a r e d w i t h t h e p r e v i o u s s l u g g i n g a n d b u b b l i n g fluidized b e d m o d e l s . T h e s ca l e -up o f fluidized b e d s is b r i e f l y d i s c u s s e d . T h e c o m p l e t e gas - so l ids m o d e l is t h e n u s e d t o fit e x p e r i m e n t a l l a b o r a t o r y r oa s t e r d a t a . W i t h t h e a i d o f t h e e s t i m a t e d p a r a m e t e r s , t h e m o d e l is t h e n e m p l o y e d t o e v a l u a t e t h e effect o f v a r i o u s m o d e l p a r a m e t e r s a n d o p e r a t i n g c o n d i t i o n s o n t h e average o x y g e n p a r t i a l p r e s s u r e a r o u n d t h e p a r t i c l e s . 203 Chapter 6. Modelling Results 6.1 Unsteady-state single particle reaction The unsteady-state single particle reaction model is used to evaluate the conditions under which the particle temperature exceeds the temperature of its surroundings. Since the fluidized bed model assumes that the particles are isothermal and at the same temperature as the fluidized bed, the conditions where the unsteady-state model predicts excessive temperatures w i l l therefore be conditions which require more complex model l ing to replace the isothermali ty assumptions. 6.1.1 Model parameters The model requires a number of kinetic, heat and mass transfer parameters as inputs . T h e values used here are also employed for the solids reaction of the fluidized bed model . B o t h kinetic expressions suggested i n chapter 2 are used for the model . T h e sulfur dioxide concentration is taken to be constant at 17 v o l % , a value similar to that obtained below for the fluidized bed modell ing. T h e sulfur dioxide concentration does not influence the reaction kinetics i n any way. B o t h the bulk oxygen concentration and the particle size are varied. The effective diffusivity in the ash layer is based on the gas diffusivity of oxygen i n sulfur dioxide (obtained using Chapman-Enskog theory [231, 236]), a porosity of 0.4 and a tortuosity factor of 3. These values are similar to those obtained by Goka rn and Dora iswamy [150, 159] where they measured the diffusivity w i th in an ash layer of reacted zinc sulfide pellets. Gokarn and Doraiswamy [150, 159] obtained gas diffusivities which are 38-47% of the bulk diffusivity. A smaller value is chosen here because the pellets of Gokarn and Doraiswamy were in i t ia l ly porous, while the single particles modelled here were in i t ia l ly non-porous. T h e effective thermal conduct ivi ty was estimated from those of ceramic materials w i t h s imilar porosities [231]. T h e heat capacities and the heats of reaction were obtained from H S C [116]. Since the particle temperature is assumed to be the same as the temperature of the surroundings, there is no net heat transfer by radiat ion. Rad ia t ion is therefore neglected. However, once a temperature difference occurs, radiat ion should be taken into account. For an exothermic reaction, such as zinc sulfide roasting, radiat ion would s imply reduce the overheating. 204 Chapter 6. Modelling Results T a b l e 6 .1: S u m m a r y of s ing le p a r t i c l e m o d e l p a r a m e t e r s a n d t h e i r v a l u e s Parameter Va lue Chemical kinetics F i t t e d kinet ics Pre-exponent ia l constant k° (cm/s) 6 .28-10 1 2 A c t i v a t i o n energy E ( k J / m o l ) 288 F u k u n a k a et al. [140] kinetics Pre-exponent ia l constant k° (cm/s) 2 .96-10 1 5 A c t i v a t i o n energy E ( k J / m o l ) 314 Reac t ion orders O x y g e n n (-) 1 Solids m (-) 0 Particle properties Reactan t (core) density pc ( k g / m 3 ) 4100 Reac tan t (core) molar weight Mc (g /mol ) 97.4 P r o d u c t (ash layer) densi ty p ( k g / m 3 ) 5600 P r o d u c t (ash layer) molar weight M (g /mol ) 81.4 Mass transfer Effective gas diffusivity in ash layer DeA(To\ ( m 2 / s ) D02-SO2 x 0 .4 /3 M o d i f i e d Sherwood number Sh 1 Heat generation and transfer Effective t he rma l conduc t iv i ty of ash layer ke ( W / ( m K ) ) 0.3 Heat capaci ty of ash layer Cpe ( J / ( m o l K ) ) 54 Heat capaci ty of unreacted core Cpc ( J / ( m o l K ) ) 56.8 Hea t of react ion AH ( k J / m o l ) -448 M o d i f i e d Nussel t number for convect ion Nuc (-) 1 M o d i f i e d Nussel t number for rad ia t ion NUR (-) 0 In i t i a l dimensionless temperature UQ 1 Environment conditions Tempera ture T ( °C) 940 B u l k O2 concentra t ion XQV (-) l e -3 to 0.5 B u l k SO2 concentra t ion xso2 (-) 0.17 Pa r t i c l e diameter d (tim) 1 to 10 000 205 Chapter 6. Modelling Results 6.1.2 Time for complete reaction The time for complete reaction is the most important output for the fluidized bed model . It is used in conjunction w i t h the residence t ime dis t r ibut ion to evaluate the average conversion. Figure 6.1 presents the t ime required for complete conversion as a function of particle size and bulk oxygen concentration for both kinetic rate expressions. A s expected from the pre-exponential constants, the fitted kinetics are slower by a factor of approximately 50 to 100 compared to values from the expression of Fukunaka et al. [140]. A s expected, the t ime for complete conversion is reduced as the particle size is reduced and the bulk oxygen concentration is increased. dl 0- 5 0.1 1 um 10 um 100 1 mm Particle diameter 10 mm 0.1 1 um 10 um 100 um 1 m m Particle diameter 10 mm (a) K i n e t i c s from F u k u n a k a et al. [140] (b) F i t t e d kinet ics (dashed l ine i n F igu re 2.4) Figure 6.1: Unsteady-state particle model: T i m e to complete reaction i n seconds. 6.1.3 Particle temperatures The average particle temperatures (averaged over time) are shown in F igure 6.2. B o t h the core and surfaces temperatures are equal to the temperature of the surroundings (dimensionless temperature =1) for conditions of low oxygen concentrations. A dimensionless temperature of 1.01 is equivalent to a 12°C increase from the surroundings. 206 Chapter 6. Modelling Results 0.1 1 pm 10 /jm 100 pm 1 mm Particle diameter 10 mm 0.1 1 pm 10 pm 100 pm 1 mm Particle diameter 10 mm (a) Average core dimensionless temperature (Uc) (b) Average surface dimensionless temperature (Us F u k u n a k a et al. [140] K i n e t i c s F u k u n a k a et al. [140] K i n e t i c s 0.1 1 p, 10 pm 100 pm 1 mm Particle diameter 10 mm 0.1 1 pm 10 pm 100 pm 1 mm Particle diameter 10 mm (c) Average core dimensionless temperature (Uc) (d) Average surface dimensionless temperature (Us) F i t t e d kinet ics F i t t e d kinet ics F i g u r e 6.2: U n s t e a d y - s t a t e p a r t i c l e m o d e l : D i m e n s i o n l e s s t e m p e r a t u r e s . 207 Chapter 6. Modelling Results For particles smaller than about 100 ^ m , the core and surface dimensionless temperatures are identical for most conditions. T h i s indicates that thermal gradients are negligible. For larger particles, thermal gradients may be significant, especially for oxygen concentrations larger than 10 v o l % . T h e assumption that the particles have no internal temperature gradients is acceptable for the concentrate particles in this study. The kinetic results of Fukunaka et al. [140] suggest much higher temperatures than the fitted kinetics (equation 2.3). For instance, large particles (larger than 3 mm) may experience very large temperature excursions when the oxygen concentration exceeds 10% if the Fukunaka et al. kinetics apply. However, for the fitted kinetics, particle overheating is much smaller. Regardless of the kinetics, any bulk oxygen concentration less than 5 v o l % does not promote overheating. If the particles are w i th in a bulk atmosphere containing 10% oxygen, the overheat-ing would be l imi ted to about 12°C for the largest particles. Since the experimental laboratory roaster d id not have any feed particles larger than 100 pm, the assumption that the particle temperature is equal to that of the bed is reasonable. If the Fukunaka et al. kinetics apply, these particles may experience a smal l temperature increase of less than 10°C i f they also encounter oxygen concentrations larger than about 10 v o l % . For the assumption to be val id for the industr ia l roaster, the large particles must not experience oxygen concentrations larger than about 5 to 10 v o l % . However, calculations for the very large particles should be made w i t h the grain model since the current model assumes that the in i t i a l solid is non-porous and that these large particles are l ikely to be lumps of smaller concentrate particles. Since lumps are created w i t h smaller grains, the diffusion resistance through the the bulk of the lump would be smaller than that for a s imilarly-sized particle. L u m p s may therefore react faster than particles of the same size. Heat transfer l imita t ions from a lump to the surroundings are l ikely to be similar to their particle counterpart. Therefore, lump overheating may be greater and occur for smaller lumps than for particles. Temperature excursions for large particles have been documented previously [160, 237]. Patisson et al. [160] used 10 m m porous pellets in a thermogravimetric balance w i t h an atmosphere of 208 Chapter 6. Modelling Results pure oxygen and pellet temperatures up to 1100°C while the surrounding atmosphere was only at 550 to 650°C. M u c h less overheating was observed when air was used (740°C for a 600°C atmosphere). Natesan and Ph i lb rook [237] obtained more modest overheating (+50 °C) in an 27 v o l % oxygen atmosphere at 960 °C. The i r smaller overheating may have been due to pre-sintering prior to exposing the pellet to the reactive gas. 6.1.4 Gas concentrations T h e average concentrations at the core and at the surface of the particle are shown in dimen-sionless form in Figures 6.3 and 6.4. A core dimensionless concentration of 1 indicates that the mole fraction at the surface of the unreacted core is equal to that of the bulk . A dimensionless concentration lower than one indicates that the mole fraction is only a fraction of the bulk concentration while a dimensionless concentration higher than one, the mole fraction is larger than that of the bulk. T h e dimensionless oxygen concentration at the unreacted shr inking core of a particle is lower than that of the bulk. T h i s is not unexpected since mass transfer l i m i -tations from the bulk to the surface of the unreacted core are present. However, the particle size for which the oxygen concentration at the core start to be smaller than 90% of the bulk (^c02 < 0.9) depends on the kinetics used. For instance, if the Fukunaka et al. [140] kinetics are used, particles larger than about 3 pm have less than 90% of the bu lk oxygen concentration at their core. However, if the fitted kinetics are used instead, any particles smaller than about 125 /im w i l l not have any significant oxygen concentration difference. T h e sulfur dioxide concentrations follow a profile different from the oxygen concentration be-cause only the bulk oxygen concentration is varied. T h e sulfur dioxide concentrations is gov-erned by the dynamic equi l ibr ium between the product ion of S 0 2 and its t ransport to the bulk gas. T h i s process is s imilar to the generation and transport of heat, and therefore, the SO2 profiles are s imilar to the temperature profiles. A s mentioned previously, the sulfur dioxide concentration does not affect the reaction rate. In summary, the dimensionless gas concentrations at the outer surface and at the core surface depend greatly on the kinetics used. However, to calculate the predominant phase, a smal l 209 Chapter 6. Modelling Results $0.5 0.2 o p o > GO ~J 0 O O P cn *. <*> 0.1 1 um o b 10 um 100 (im 1 Particle diameter 10 mm 1 um 10 fj,m 100 /im 1 mn Particle diameter 10 mm (a) Average core dimensionless oxygen concentra-t i on (W c,02) 50 (b) Average core dimensionless sulfur dioxide con-centra t ion (u>Ciso2) 50 r 1 um 10 um 100 um 1 mm Particle diameter 10 mm 1 um 10 um 100 um 1 mm 10 mm Particle diameter (c) Average surface dimensionless oxygen concen-t r a t ion (tdS)02) (d) Average surface dimensionless sulfur dioxide concentra t ion (wS )so2) Figure 6.3: Unsteady-state particle model: Dimensionless gas concentrations. Kinetics from Fukunaka et al. [140] 210 Chapter 6. Modelling Results 50 21 s? 10 0.5 0.2 o co 0.1 ' — 1 pm (a) Average t ion (w C | 0 2) 50 o CO o p O ^ CO 10 pm 100 pm 1 mm Particle diameter 10 mm 1 pm 10 pm 100 pm 1 mm 10 mm Particle diameter 21 10 5 0.5 0.2 core dimensionless oxygen concentra- (b) Average core dimensionless sulfur dioxide con-centra t ion (t0CtSO2) 50 r o CO 0.1 1 1 pm 10 pm 100 pm 1 mm Particle diameter 10 mm 10 pm 100 pm 1 mm Particle diameter 10 mm (c) Average surface dimensionless oxygen concen- (d) Average surface dimensionless sulfur dioxide t ra t ion (wS jo2) concentra t ion (LUS,SC>2) Figure 6.4: Unsteady-state particle model: Dimensionless gas concentrations. Fitted Kinetics 211 Chapter 6. Modelling Results deviation from the bulk concentration (dimensionless concentrations between 0.75 and 1.25) would not represent a significant shift (-0.12 to +0.09 on the log scale) on the predominance diagram (Figure 2.2). Since the concentrate particles are much smaller than 100 pm (80% of the concentrate particles are smaller than 23 pm, see Table 3.2), the concentrations in the bulk and the concentrations at the particle core do not differ significantly. T h i s argument does not hold for large particles such as lumps present wi th in the feed to the indus t r ia l roaster. 6.1.5 Effectiveness factors Wen and co-workers ut i l ized the concept of effectiveness factors for gas-solid reactions [238, 235, 234]. T h e effectiveness factor is the ratio of the predicted rate of reaction over the rate of reaction if the reaction sites were at the bulk composi t ion and temperature. In isothermal systems, effectiveness factors are equal to or less than one, depending on the mass transfer l imitat ions. For non-isothermal exothermic systems, the effectiveness factor can exceed one, due to self-heating of the reacting particles. o d 0.2 0.2 0.1 ^ 1 um 10 um 100 um Particle diameter 1 mm 10 mm 0.1 L — 1 um 10 um 100 um Particle diameter 1 mm 10 mm (a) K i n e t i c s from F u k u n a k a et al. [140] (b) F i t t e d kinet ics Figure 6.5: Unsteady-state particle model: Effectiveness factors. Figure 6.5 shows effectiveness factors as a function of the bu lk oxygen concentration and particle 212 Chapter 6. Modelling Results s ize . I t is i m p o r t a n t t o n o t e t h a t t h e c o n d i t i o n s for fac tors > 1 are n o t i d e n t i c a l t o t h e c o n d i t i o n s t h a t p r o m o t e v e r y h i g h p a r t i c l e t e m p e r a t u r e s . T h e effect iveness f a c t o r is s m a l l for la rge p a r t i c l e s ( > l m m ) , even i f t h e y r e a c h v e r y h i g h t e m p e r a t u r e s . T h i s is d u e t o t h e l a rge m a s s t r ans fe r l i m i t a t i o n . T h e o n l y c o n d i t i o n s w h e r e t h e effect iveness f ac to r > 1 is for s m a l l p a r t i c l e s i n o x y g e n - r i c h a t m o s p h e r e s . B e c a u s e t h e m a s s t r ans fe r r e s i s t a n c e is s m a l l for s m a l l p a r t i c l e s , a s m a l l ove rhea t increases d r a m a t i c a l l y t h e effect iveness f ac to r l e a d i n g t o a h i g h e r r e a c t i o n ra te . T h i s is o b s e r v e d o n F i g u r e 6.1 w h e r e t h e c o n t o u r l i nes b e n d s l i g h t l y a r o u n d t h e l o c a t i o n w h e r e t h e effect iveness fac to r is l a rge r t h a n 1. I n g e n e r a l , t h e effect iveness f ac to r is < 1 for a n y p a r t i c l e w i t h o x y g e n b u l k c o n c e n t r a t i o n s less t h a n 10 v o l % . T h e n o n - i s o t h e r m a l effect iveness fac to r ( s h o w n i n F i g u r e 6.5) does n o t p o r t r a y a d e q u a t e l y t h e e x t e n t o f hea t effects o n t h e r e a c t i o n ra te . T o b e t t e r v i s u a l i z e t h e c o n d i t i o n s w h e r e hea t g e n e r a t i o n affects t h e r e a c t i o n ra te , a n e w fac to r is i n t r o d u c e d . T h e hea t e n h a n c e m e n t f ac to r (Ti) t a k e n as t h e r a t i o o f t h e n o n - i s o t h e r m a l effectiveness f ac to r ( e q u a t i o n 5.93) t o t h e i s o t h e r m a l effectiveness f ac to r ( e q u a t i o n 5.102) i .e. ^ Vs,non—iso ^ Vs,iso represents t h e d e v i a t i o n (as a r a t i o ) o f t h e n o n - i s o t h e r m a l m o d e l over t h e i s o t h e r m a l m o d e l . I f hea t effects are i m p o r t a n t , t h e hea t e n h a n c e m e n t fac to r w i l l differ f r o m one , r ega rd le s s o f t h e l i m i t i n g s teps . F o r e x o t h e r m i c s y s t e m s , Ti > 1. F o r e n d o t h e r m i c s y s t e m s , Ti < 1. S i n c e o u r s y s t e m is e x o t h e r m i c , a n y c o n d i t i o n s w h e r e t h e hea t e n h a n c e m e n t f ac to r is s i g n i f i c a n t l y g rea te r t h a n one s igni f ies t h a t t h e i s o t h e r m a l m o d e l does n o t a d e q u a t e l y r ep resen t t h e a c t u a l r e a c t i o n ra tes . F i g u r e 6.6 p resen t s t h e hea t e n h a n c e m e n t fac tors for t h e t w o k i n e t i c e x p r e s s i o n s c o n s i d e r e d . A hea t e n h a n c e m e n t fac to r o f 1.1 represen t a n inc rease o f t h e n o n - i s o t h e r m a l r e a c t i o n r a t e o f 10% over t h e i s o t h e r m a l r e a c t i o n ra te . U n l i k e t h e effect iveness f ac to r w h e r e n o c lea r c o n c l u s i o n r e g a r d i n g t h e effect o f hea t o n t h e r e a c t i o n r a t e c a n be d r a w n for l a rge p a r t i c l e s i n a n o x y g e n - r i c h e n v i r o n m e n t , t h e hea t e n h a n c e m e n t fac to r c l e a r l y shows t h a t e v e n i f t e m p e r a t u r e d e v i a t i o n s are l a rge for t h e l a rges t p a r t i c l e s i n a n o x y g e n r i c h e n v i r o n m e n t (see F i g u r e 6.2, F u k u n a k a et 213 Chapter 6. Modelling Results i um 10 um 100 /j,m 1 mm 10 mm 1 um 10 um 100 um 1 mm 10 mm Particle diameter Particle diameter (a) K i n e t i c s from F u k u n a k a et al. [140] (b) F i t t e d kinet ics F i g u r e 6.6: U n s t e a d y - s t a t e p a r t i c l e m o d e l : H e a t e n h a n c e m e n t f ac to r s . al. k i n e t i c s , 10 m m d i a m e t e r p a r t i c l e s , 2 1 - 5 0 % o x y g e n ) , t h e r e a c t i o n r a t e c a n b e r e a s o n a b l y w e l l r ep r e sen t ed b y t h e i s o t h e r m a l m o d e l (Ti. = 1) . T h i s is d u e t o t h e l o w effect iveness fac to r c a u s e d b y l a rge m a s s t r ans fe r l i m i t a t i o n s . F r o m t h i s a n a l y s i s , i t is c l ea r t h a t hea t e n h a n c e m e n t (faster r e a c t i o n s d u e t o t h e effect o f hea t ) a n d t e m p e r a t u r e d e v i a t i o n ( p a r t i c l e t e m p e r a t u r e m u c h h i g h e r t h a n t h a t o f t h e e n v i r o n m e n t ) are t w o dif ferent p h e n o m e n a . B o t h r e q u i r e use o f a n o n - i s o t h e r m a l m o d e l for t h e i r d e t e c t i o n . F o r t h e r e a c t i o n of z i n c c o n c e n t r a t e , hea t e n h a n c e m e n t w i l l affect t h e o v e r a l l r e a c t i o n ra te , w h i l e t e m p e r a t u r e d e v i a t i o n w i l l affect l o w - m e l t i n g - p o i n t phases , p r o d u c t l aye r s i n t e r i n g a n d v a p o u r phases . T h e c o n d i t i o n s w h e r e t h e hea t e n h a n c e m e n t fac to r exceeds 1 d e p e n d o n t h e k i n e t i c s a n d p a r t i c l e s ize . H o w e v e r , for o x y g e n c o n c e n t r a t i o n s < 1%, t h e hea t e n h a n c e m e n t f ac to r is v e r y c lose t o 1, r egard less o f t h e k i n e t i c s o r p a r t i c l e s ize . F o r o x y g e n c o n c e n t r a t i o n s < 1 0 % , t h e hea t e n h a n c e m e n t f ac to r is < 1.1. I f a d e v i a t i o n (or e r ro r ) i n r e a c t i o n r a t e o f 1 0 % is a c c e p t a b l e (Ti < 1.1), t h e i s o t h e r m a l m o d e l m a y be u s e d for a n y o x y g e n c o n c e n t r a t i o n b e l o w 1 0 % . 214 Chapter 6. Modelling Results In summary, the unsteady-state single particle reaction model has shown that particle overheat-ing occurs only for large particles and high bulk oxygen concentrations. Effectiveness factors greater than one only occur for high bulk oxygen concentrations. T h e t ime for complete reaction depends greatly on the kinetics used. T h e gas compositions are not significantly different from the bulk when very smal l particles, s imilar to the concentrates used i n this study, are reacting. It is unknown at this point which kinetic rate expression should be used. T h e assumption of isothermal particles w i t h i n the fluidized bed is therefore reasonable if the particles do not expe-rience oxygen concentrations larger than a few percent. T h e relatively simple isothermal single particle reaction model is used for the gas-solid fluidized bed reactor model l ing that follows in this chapter. 6.2 Generalized slugging-bubbling model (GSBM) This section. presents some results of the generalized slugging-bubbling fluidized bed reactor model for gas catalytic reactions. Since no solid reaction occurs, the model is not coupled w i t h a solid reaction model nor any solids mix ing model . 6.2.1 Comparison with previous models Pr io r to using the generalized slugging-bubbling fluidized bed model , it must be compared wi th the currently available fluidized bed models. F igure 6.7 presents conversions calculated from the Hovmand slugging bed model [216, 217], the Orcu t t mixed-flow and plug-flow models [218, 219], the Grace two-phase bubbl ing bed reactor model [239] and the generalized slugging-bubbl ing model ( G S B M ) , developed i n Chapter 5 for pure slugging and pure bubb l ing wi th constant average bubble size and variable bubble size. T h e constant average bubble size case is considered because the Orcut t and Grace models use an average bubble size. Since previous models do not consider gas volume changes, the stoichiometry adopted for the generalized model is equimolar (1 to 1). For a l l models, the reaction is first order w i t h respect to the oxygen concentration. In general, the predictions for the bubbl ing fluidized bed models are higher than those of 215 Chapter 6. Modelling Results Table 6.2: M o d e l parameters used to compare the generalized bubb l ing slugging model to the earlier slugging and bubbl ing models u 0.5 m / s 0.02 m / s H 1 m calculated 0.45 Gas diffusivity: D g a s 10 - 1 0 - 5 m 2 / s Bubb le correlation M o r i and Wen [208] In i t ia l bubble size: D e o 0.01 m ^ 0 2 -1 +1 A i / 0 the slugging models. Note that the fluidized bed models are applied wi thout any allowance for slugging, even when the bubble size exceed the reactor diameter. For this reason, the predictions for smal l column diameters must be considered w i t h caution. There is very l i t t le difference between the results of the Hovmand slugging model and the G S B M model when the probabi l i ty of slugging is imposed at 1. T h e G S B M can therefore adequately represent the H o v m a n d slugging model in the l imi t . W h e n considering pure bubb l ing behaviour (Pbu6Ming =l)) the G S B M compares favorably wi th al l the other models. However, there is a much larger scatter between the different models. Since the generalized model compares well w i t h the previous slugging and bubb l ing models for the conditions studied here, the G S B M is used below to evaluate the effects of the gas reaction rate constant and bed diameter on the predicted gas conversion. 216 Chapter 6. Modelling Results 0.1 0.08 . 0.06 0.02 . GSBM, P C I . =1 Slugging x Hovmand 0.1 0.08 . 0.06 10 10 Bed diameter (m) (a) Slugging models, fcr=0.1 s"1 0.5 0.4 . 0.3 . GSBM, P., . =1 Slugging x Hovmand 10 10 Bed diameter (m) (c) S lugging models, kr = l s - 1 0.8 . 0.6 0.2 . GSBM, P„. . -Slugging x Hovmand 0.02 o GSBM, P 0 ..,. =1, Constant De _ ' Bubbhng + Orcutt, Plug Flow •ft Orcutt, Mixed . GSBM, P„ K K I . =1, Variable De x Grace 2-phase' 10 10 Bed diameter (m) (b) B u b b l i n g models, kr=0.1 s _ 1 0.5 r 0.4 . 0.3 + Orcutt, Plug Flow * Orcutt. Mixed o GSBM, P D ..,. =1, Constant De „ Bubbling x Grace 2-phase . GSBM, P„ =1, Variable De Bubbling 10 10 Bed diameter (m) (d) B u b b l i n g models, fcr=l s _ 1 11 • • — 0.8 . 0.6 c 0.4 o O 0.2 . GSBM, P„ .... =1, Variable De BubbJ ng + Orcutt, Plug Flow AOrcutt, Mixed x Grace 2-phase o GSBM, P„ =1, Constant De Bubbling 10 10 10 10 Bed diameter (m) (e) Slugging models, kr = 10 s _ 1 Bed diameter (m) (f) B u b b l i n g models, kr=10 s _ 1 Figure 6.7: Comparison of the GSBM model to the Hovmand slugging model and to the Grace 2-phase and Orcutt bubbling models. For conditions, see Table 6.2 217 Chapter 6. Modelling Results (a) B e d diameter: 0.1 m , (pr,: 0 (b) B e d diameter: 0.1 m , (p^: 0.005 (c) B e d diameter: 0.5 m , (pr,: 0 (d) B e d diameter: 0.5 m , (pr,: 0.005 (e) B e d diameter: 1 m , (pr,: 0 (f) B e d diameter: 1 m , (pi: 0.005 Figure 6.8: Compar ison of the conversions calculated using G S B M model and its l im i t i ng models as a function of gas reaction rate constant for different bed diameters. For conditions, see Table 6.2 218 Chapter 6. Modelling Results 6.2.2 Effect of effective gas reaction rate constant T h e effect of the effective gas reaction rate constant (kr) on the gas conversion (X) is presented in Figure 6.8 for different reactor diameters and wi th </)£, = 0.005 and neglecting the solids present w i th in the bubbles (i.e. (fir, = 0). T h e figure presents the results of the complete gen-eralized slugging-bubbling model, as well as the predictions when the probabil i t ies of bubbl ing and slugging are set equal to one (entirely slugging or bubbl ing) . W h e n the probabi l i ty of slugging equals one, no bubbl ing region is considered prior to slugging. W h e n the probabi l i ty of bubbl ing is one, the model either calculates a given bubble size for each vert ical posi t ion or uses a constant average bubble size calculated at 40% of the expanded bed height (x = 0AH). T h e model parameters and conditions appear in Table 6.2. For slugging beds (Figure 6.8,(a) and (b)), using a bubbl ing fluidized bed mode l clearly over-predicts the conversions. For smal l kr, the generalized slugging-bubbling fluidized bed model predicts conversions s imilar to that when imposing pure slugging (Psiugging — l). However, for higher kr, the generalized slugging-bubbling fluidized bed model predictions diverge from the pure slugging predictions due to the increasing importance of mass transfer from the bubbles to the dense phase. For such conditions, the bubbl ing region at the base of the bed before the onset of slugging is of cr i t ical importance to the conversion. T h e presence of particles w i th in the bubbles ((pL) significantly augments the predicted gas conversions for large kr. For large beds where slugging does not occur (Figure 6.8,(e) and (f)), the G S B M model pre-dicts the same conversions as for pure bubbl ing (Pbubbling=^) • Us ing pure slugging to model a bubbl ing fluidized bed clearly underestimates the conversion. T h e use of an average bubble size also underestimates the gas conversion for large reaction rate constants. For large kr, mass transfer from the bubbles to the dense phase is rate-controlling. There is a significant beneficial effect on interphase mass transfer from the smal l bubbles near the dis t r ibutor . T h i s effect is neglected when using an average bubble size. A s for slugging beds, accounting for the presence of particles w i th in the bubbles (cpi) is significant for large kr. For fluidized beds of intermediate sizes (Figure 6.8,(c) and (d)), the predict ion of the G S B M 219 Chapter 6. Modelling Results model diverge sl ightly from the predictions for pure bubbl ing due to the effect of walls on the larger bubbles causing a decrease in interphase mass transfer. In summary, if ones chooses to use a regime-specific model , choosing the appropriate model (pure bubbl ing or pure slugging) is cr i t ical to obtaining adequate results. For reactions where large values of the effective reaction rate constant (kr) are expected, the model should not use an average bubble size to characterize the entire reactor and must include the effect of the solids w i th in the bubbles. T h e generalized slugging-bubbling fluidized bed model allows the modell ing of fluidized systems where a t ransi t ion from bubbl ing to slugging occurs w i th in the bed, or where there are appreciable wal l effects. 6.2.3 Effect of reactor diameter The effect of scale-up of a reactor may be evaluated from the gas conversions for different reactor diameters and different reaction rate constants. Figure 6.9 graphical ly presents the conversion for various rate constants. For the condit ion considered, the G S B M model predictions depart from pure slugging for large reaction rate constants and for reactor diameters larger than about 0.1 m . T h e departure from pure slugging at high reaction rate constants results from the significance of the bubb l ing region near the dis tr ibutor . For the conditions studied, the predictions of the G S B M model converge to pure bubbl ing at diameters close to 1 m . T h i s is the m i n i m u m reactor diameter for the system to be modelled as pure bubbl ing. T h i s implies that results from small and large indust r ia l fluidized beds must be compared w i t h care. Note that this diameter applies only for reactors operat ing at the conditions i n Table 6.2. T h e bubble sizes were calculated using the M o r i and Wen bubble correlation [208]. Since this correlation is l imi ted to reactor diameters smaller than 1.22 m, predictions for larger reactors must be treated wi th some caution. In the t ransi t ion region, the generalized model predicts conversions less than for pure bubbl ing and more than for pure slugging (See Figure 6.9). To understand how this can occur, one 220 Chapter 6. Modelling Results Bed diameter (m) Bed diameter (m) (a) fcr=0.1.s-\ 4>L- 0 (b) fcr=0.1 s " 1 , 4>L: 0.005 Bed diameter (m) Bed diameter (m) (c) kr=l s " 1 , <pL- 0 (d) kr=l s _ 1 , (/>L: 0.005 Bed diameter (m) Bed diameter (m) (e) ik r =10 s - \ 4>L- 0 (f) fcr=10 s - 1 , 0L: 0.005 Figure 6.9: Compar i son of the conversions calculated using G S B M model and its l imi t i ng cases as a function of bed diameter for different gas reaction rate constants. For conditions, see Table 6.2 221 Chapter 6. Modelling Results m u s t c o n s i d e r t h e b a s i c e q u a t i o n o f t h e m o d e l ( e q u a t i o n 5.12) a n d t h e i n t e r a c t i o n b e t w e e n t h e b u b b l i n g a n d s l u g g i n g f low r eg imes . F i g u r e 6.10 p resen ts i n m o r e d e t a i l t h e va lues o f t h e v a r i o u s v a r i a b l e s w h i c h l e a d t o s u c h c o n v e r s i o n s . W e f i rs t c o n s i d e r t h e i n t e r p h a s e m a s s t r ans fe r t e r m of e q u a t i o n 5.12: T h e f irst p a r t o f t h e t e r m is t h e m a s s t r ans fe r coeff ic ient a n d i n t e r f a c i a l a rea . T h e s e are d i r e c t l y r e l a t e d t o b u b b l e s a n d s l u g p r o p e r t i e s . T h e s e c o n d p a r t is t h e d r i v i n g force i .e. t h e d i f ference i n gas c o n c e n t r a t i o n s . T h i s d r i v i n g force is a f u n c t i o n o f t h e gas c o n c e n t r a t i o n s w i t h i n t h e b u b b l e s (or s lugs) a n d t h e dense phase . U n l i k e t h e m a s s t r ans fe r coeff ic ient a n d a rea , i t does n o t have a n y d i r e c t r e l a t i o n s h i p w i t h a n y o f t h e b u b b l e o r s l u g p r o p e r t i e s . W e n e x t c o n s i d e r t h e t r a n s i t i o n f r o m b u b b l i n g t o s l u g g i n g b y o b s e r v i n g t h a t t h e p r o b a b i l i t y o f s l u g g i n g goes f r o m 0 t o 1 i n t h e he igh t i n t e r v a l b e t w e e n a p p r o x i m a t e l y 0.1 a n d 0.3 m for t h e c o n d i t i o n s s t u d i e d . T h e m a s s t r ans fe r coeff icient a n d i n t e r f a c i a l a r e a (kLH a n d aj) b o t h v a r y i n t h i s i n t e r v a l . T h e r e f o r e , t h e i n t e r p h a s e m a s s t r ans fe r coeff ic ient ( F i g u r e 6.10 (b)) var ies s t r o n g l y w i t h i n t h i s i n t e r v a l . N o t e t h e l o g a r i t h m i c scale . T h e d r i v i n g force for t h e i n t e r p h a s e mass t r ans fe r ( F i g u r e 6.10 (c)) does n o t inc rease w i t h i n t h i s t r a n s i t i o n i n t e r v a l b u t over a m u c h longe r i n t e r v a l t h a n t h e b u b b l i n g - s l u g g i n g t r a n s i t i o n i n t e r v a l . T h e ne t effect is a r a p i d decrease f o l l o w e d b y a s l o w inc rease i n i n t e r p h a s e f low. T h e b u b b l i n g r e g i o n ensures g o o d i n t e r p h a s e mass t r ans fe r a n d l o w c o n c e n t r a t i o n differences b e t w e e n t h e b u b b l e s a n d dense p h a s e ( s m a l l d r i v i n g force) . H o w e v e r , once t h e b u b b l e s have g r o w n a n d coa l e sced i n t o s lugs , t h e s m a l l d r i v i n g force l i m i t s i n t e r p h a s e m a s s t r ans fe r u n t i l t h e r e a c t i o n w i t h i n t h e dense phase inc reases t h e d r i v i n g force t o va lues c loser t o t h e p u r e s l u g g i n g m o d e l . T h i s s h o w s t h a t even for s m a l l r e a c t i o n r a t e c o n s t a n t s , i n t e r p h a s e m a s s t r ans fe r m a y have s i g n i f i c a n t effects. T h i s effect m a y n o t be o b s e r v e d e x p e r i m e n t a l l y d u e t o t h e s m a l l d i f ference i n o v e r a l l c o n v e r s i o n s . T h e s a m e t r a n s i t i o n i n t e r v a l a p p l i e s for a s y s t e m w i t h a l a rge r e a c t i o n r a t e c o n s t a n t (see F i g u r e 6.11 (a)) . M o r e t h a n 5 0 % of t h e c o n v e r s i o n is d u e t o r e a c t i o n w i t h i n t h e b u b b l i n g r e g i m e . S i n c e i n t e r p h a s e m a s s t r ans fe r is v e r y s m a l l w i t h i n t h e s l u g g i n g r e g i m e , t h e r e a c t i o n p r o c e e d s s l o w l y {Interphase mass transfer t e r m } = kmal( ) (6.2) 222 Chapter 6, Modelling Results MAAA A A A—ft—ft—ft—ft ft ft ft 0 0.2 0.4 0.6 0.8 1 Position in bed (m) 0.2 0.4 0.6 0.8 Position in bed (m) (a) Probabi l i t i e s x 10 ' (b) Interphase mass transfer coeffi-cient x 10" 3 0.2 0.4 0.6 0.8 Position in bed (m) 0.2 0.4 0.6 O.i Position in bed (m) (c) Interphase d r i v i n g force (d) Interphase molar flow 0.2 0.4 0.6 o. Position in bed (m) 0.2 0.4 0.6 O.i Position in bed (m) (e) G a s conversion i n bubble phase (f) Gas conversion i n dense phase Figure 6.10: Compar ison of the variable model parameters and output for the G S B M model and its l imi t ing models as a function of height the vert ical posi t ion i n the bed for kr = 0 . 1 s - 1 , D = 0.2 m, *: Bubb l ing , o: Slugging, •: G S B M . For conditions, see Table 6.2 223 Chapter 6. Modelling Results (c) Interphase d r i v i n g force (d) Interphase molar flow 0 0.2 0.4 0.6 o Position in bed (m) 0.2 0.4 0.6 0.8 1 Position in bed (m) (e) G a s conversion i n bubble phase (f) Gas conversion i n dense phase Figure 6.11: Compar i son of the variable model parameters and output for the G S B M model and its l imi t ing models as a function of the vert ical posi t ion in the bed for kr = 1 0 s " 1 , D = 0.2 m, *: Bubb l ing , o: Slugging, •: G S B M . For conditions, see Table 6.2 224 Chapter 6. Modelling Results once the slugging flow regime is reached. T h e overall effect of inc luding the bubb l ing region at the bot tom is to increase the conversion. In summary, when the generalized slugging-bubbling fluidized bed model is used for one of the l imi t ing cases (pure bubbl ing or slugging), it closely matches the results of the earlier regime-specific models. For the t ransi t ion between the slugging and bubb l ing regimes, the G S B M model adequately represents the system. In the transit ion, the model predicts conversions and evolution between the two l imi t ing cases. 6.3 Fluidized bed roaster model 6.3.1 Model parameters T h e fluidized bed reactor model requires the fluidized bed reactor geometry, operat ing condi-tions, kinetics of the reaction, as well as some parameters related to the fluidized bed. Table 6.3 summarizes the various parameters and their values used for the model l ing of the industr ia l and laboratory fluidized bed roasters. T h e industr ia l roaster geometry and conditions are taken from published information [33, 34]. T h e laboratory roaster co lumn geometry is that of this study. T h e expanded bed height and the height at m i n i m u m fluidization are related to each other using the calculated bed expansion. Since the industr ia l bed height is l imi ted to the weir overflow height, Hmf is calculated while solving the model . Since there is no overflow weir for the laboratory roaster, H is calculated from a known Hmf which is related to the bed mass. The void space at m i n i m u m fluidization was measured from the particle density and bulk density of the experimental material . T h e solids volume fraction i n the L-phase (<PL) is taken as 0.005 as suggested by K u n i i and Levenspiel [20] based on some experimental evidence. T h e solids reaction kinetics are as proposed in Chapter 2. 225 Chapter 6. Modelling Results T a b l e 6.3: S u m m a r y o f t h e m o d e l p a r a m e t e r s a n d t h e i r v a l u e s Parameter Indus t r i a l L a b o r a t o r y Reactor geometry A r e a A ( m 2 ) 84 0.00785 Diameter D (m) 10.34 0.1 E x p a n d e d bed height H (m) 1.2 var iable B e d height at m i n i m u m fluidization Hmf (m) var iable 0.27 Di s t r i bu to r area per orifice Ad ( m 2 ) .01 0.00021 Fluidized bed model B u b b l e solids volume fract ion <j>i (-) 0.005 V o i d space at m i n i m u m f lu id iza t ion emf (-) 0.45 Solids reaction kinetics F i t t e d kinetics Pre-exponent ia l constant k° (cm/s) 6 .28-10 1 2 A c t i v a t i o n energy E ( k J / m o l ) 287.5 F u k u n a k a et al. [140] kinet ics Pre-exponent ia l constant k° (cm/s) 2 .96-10 1 5 A c t i v a t i o n energy Ea ( k J / m o l ) 313.8 Reac t ion orders O x y g e n n (-) 1 Solids m (-) 0 Effective gas diffusion coefficient i n ash layer HeA(To) ( m V s ) D02-S02 x 0.4/3 M o d i f i e d Sherwood number Sh (-) 1 Base operating conditions ( S e n s i t i v i t y a n a l y s i s ) Tempera ture T ( °C) 950 Pressure P (kPa) 101.3 Superficial gas veloc i ty U (m/s ) 0.66 0.25 Excess O x y g e n Excessoi (%) 10 Inlet O x y g e n Concen t ra t ion (vol%) 21 Bed and concentrate properties ( S e n s i t i v i t y a n a l y s i s ) Average bed part ic le diameter dp (/um) 65 or 150 Inert solids par t ic le densi ty pp ( k g / m 3 ) 2650 Average concentrate par t ic le diameter d V t C o n c e n t r a t e (/mi) 14 Concent ra te par t ic le density pconcentrate ( k g / m 3 ) 4000 Par t i c l e mean residence t ime factor / (-) 1 226 Chapter 6. Modelling Results 6.3.2 Fit of laboratory experiments T w o parameters of the model are s t i l l unknown. T h e first is the mass of concentrate equivalent to a mole of pure zinc sulfide (Mconcentrate) while the second, / is the residence t ime factor. P re l iminary fitting of the experimental data showed that the choice of the kinet ic rate expres-sion (Fukunaka et al. or fitted kinetics) has more influence on the predictions than either the residence t ime factor ( / ) or the equivalent molar mass of concentrate (Mconcentrate)- Therefore, the values of / and Mconcentrate were chosen as 1 and 110. A value of 1 was chosen for the mean solids residence t ime factor since 1/(3 (which increases the residence time) is compensated by using concentrate as a feed, requiring addi t ional feed mass for the same oxygen consumption (which decreases the residence t ime). Mconcentrate was calculated from the zinc concentrate assays assuming complete conversion to Z n O , SO2, Fe203, P b S 0 4 and accounting for the presence of sulfates in the concentrate. Since there is information for only one temperature, only a single value of the rate constant is fitted. F i t t i n g a model to experimental data involving two or more outputs requires mul t ip le response non-linear regression [240]. Such a problem must be addressed using weighted least squares regression. T h e choice of weights is cr i t ical to obtain an adequate fit. T h e weights used for each observation is the reciprocal of its variance. T h e objective function for the weighted least squares is then: The variance of the experimental points was either obtained from the logged da ta (oxygen concentration) or estimated from the detection l imits of the assays (solids conversions). P re l iminary fitting of the experimental data was not able to adequately fit any of the outlet oxygen concentrations using reasonable Mconcentrate values. To allow closer predictions of the oxygen concentrations, values of Mconcentrate around 90 were required. T h i s is unacceptable since it is impossible that impure zinc sulfide (containing less sulfur and zinc than pure ZnS) (6.3) 227 Chapter 6, Modelling Results would require more oxygen than pure zinc sulfide. It was noticed long after the experimental phase that the oxygen sensor i n the gas analyser used for the measurement of the freeboard oxygen concentrations had failed. T h e failure was noticed approximately one year after the experiments. Since the analyzer was not used dur ing this period, there is uncertainty i n the measurement provided here. In addi t ion, simple calculations show that oxygen concentrations should be higher than measured: A s s u m i n g complete solids conversion, 10% excess oxygen should give approximately 2 v o l % oxygen. T h i s value is measured for feedrates of approximately 14 g / m i n . Concentrate assays show that this value should be observed at a feedrate of approximately 16 g / m i n . Further fitting w i l l not consider the freeboard oxygen concentrations. However, the data adequately represent the t rend that outlet oxygen decreases w i t h increasing feedrate and that addi t ional feed can be used when oxygen enrichment is employed. Figure 6.12 presents the experimental da ta and the model predictions for the parameters pre-sented in Table 6.4. Since only one temperature was available from the experimental data, the reaction rate constant, shown in Table 6.4, does not allow the pre-exponential constant and the activation energy of the reaction rate equation to be separated . T h e fluidized bed model parameters are the same as those shown in Table 6.3. T h e operating conditions (temperatures, inlet gas concentrations and superficial gas velocities) used for fitting the experimental da ta are those used experimentally. T h e particle parameters are those described in chapter 3. Figures 6.12 and 6.13 present the model fit results. T h e predicted solids conversion predict relatively well the experimental conversions. T h e predicted scrubbed oxygen concentrations are different from the observed values (Compare Figures 6.13 and 4.61). Due to the incert i tude in oxygen measurements (sensor failure, as discussed previously), these measurements are not fitted. F i g -ure 6.14 compares the fitted kinetics w i t h the kinetic rates obtained from the li terature. T h e fitted rate is between the fitted kinetics (dashed line) and the Fukunaka et al. kinetics, close to Fukunaka et al. kinetics. T h e temperature of the experiments clearly exceeds the temper-ature range of a l l rate expressions shown. Since only one point was obtained from the fit of experiments, there is s t i l l some incerti tude regarding the appropriate kinet ic rate expression. 228 Chapter 6. Modelling Results Table 6.4: Summary of fitted model parameters and their values. T h e chosen values are the best estimates from theory, literature, measurements or calculations. O n l y the reaction rate constant was fitted, see text. Parameter Value / (-) not fitted 1 Mconcentrate (g/mol) not fitted 110 React ion rate constant (cm/s) fitted 37.3 1 0.91 r 0.91 1 ' 1 1 ' ' 10 12 14 16 18 20 Concentrate feedrate (g/min) Figure 6.12: Gas-sol id reactor model fit of the experimental conversion data. • : 50 mesh si l ica sand, 21%02, model , +: 50 mesh si l ica sand, 25%02, model , x : 125 mesh si l ica sand, 21%02, model . M o d e l predictions are joined by lines. 0: 50 mesh si l ica sand, 2 1 % 0 2 , experiments, ©: 50 mesh si l ica sand, 25%02, experiments, <g>: 125 mesh si l ica sand, 21%02, experiments 229 Chapter 6. Modelling Results Figure 6.13: Gas-sol id reactor model predictions of the freeboard oxygen concentration (scrubbed), o: 50 mesh si l ica sand, 21%02, +: 50 mesh si l ica sand, 25%02, x : 125 mesh si l ica sand, 21%02-Figure 6.14: F i t t e d intr insic reaction rate compared wi th those of various kinet ic studies. Rate expressions from references [124, 143, 140, 135, 142, 130, 144, 145]. Dashed line corresponds to fitted kinetics discussed in Chapter 2. o: F i t t ed intr insic kinetics 230 Chapter 6. Modelling Results However, the fitted reaction rate is bracketed by the fitted and the Fukunaka et al. [140] kinetics. Sensit ivity analysis w i l l consider both kinetics as appropriate bounds. 6.3.3 Roaster sensitivity analysis A sensitivity analysis provides useful information on which process and model parameters are most important . T h e model calculates the gas compositions for the reaction of pure zinc sulfide. Differences between concentrates and pure zinc sulfide are taken into account by converting the oxygen demand of each concentrate to its equivalent for zinc sulfide (see section 5.3). Therefore the equivalent molar mass of zinc concentrate (Mconcentrate) is not required for the sensit ivity analysis. The sensitivity analysis uses mono-sized particles for the concentrate and the inert bed material (not size distr ibutions) . T h e actual mean residence t ime of particles depends on the concen-trat ion of particles of the same size in the bed (see equation 5.77). Since the two types of particles are of different sizes, equation 5.77 no longer holds mathematical ly. In a real system, the bed would be composed of main ly inert bed mater ial containing an equi l ib r ium amount of concentrate-sized particles. Since in this sensitivity analysis, the equ i l ib r ium amount of concentrate-sized particles is unknown, the residence times of the reacting concentrate particles are assumed to be equal to: fMbed r = — (6.4) FFeed with / as in Table 6.3. T h e volume-based average particle size (dv) of the concentrates is used in the sensitivity analysis. The model parameters and operating conditions are summarized i n Table 6.3. For this analysis, each parameter in Table 6.5 is varied one at a t ime. Since there is incerti tude i n the choice of kinetic rate expression for the reaction of solids, bo th the fitted kinetics and the Fukunaka et al. [140] are used in the sensit ivity analysis. These two rate expressions are considered as the two possible extremes in the reaction rates. 231 Chapter 6. Modelling Results Table 6.5: Parameter ranges for sensitivity analysis Parameter Range Excess Oxygen 0 - 100 % Inlet Oxygen Concentrat ion 21 - 100 v o l % Average particle size 50 - 250 pm Superficial gas velocity 0.25 - 0.75 m / s Temperature 800 - 1000 °C Height at m i n i m u m fluidization (Laboratory) 0.25 - 1.25 m Expanded bed height (Industrial) 0.5 - 2 m Oxygen available to the particles Since oxygen governs the vapour pressure of lead species, any significant var ia t ion i n its concen-trat ion affects the transport of lead species to other particles where agglomeration can occur. Figures 6.15 to 6.18 present the predicted particle-averaged oxygen concentrations for the labo-ratory roaster for the fitted and Fukunaka et al. [140] kinetics for smal l (65 p,m) and large (150 pm) particles. Except for the effect of temperature, there is very l i t t le effect of the kinetics or the average particle size on the oxygen available to the particles. T h e choice of kinetics changes the effect of temperature. However, its influence is smal l compared to the effect of excess oxy-gen or inlet oxygen concentration. T h e average bed particle size does not significantly affect the particle-averaged oxygen concentration. Overa l l , for the laboratory roaster, the particle-averaged oxygen concentration (which affects agglomeration) is most ly affected by the excess oxygen, followed by the inlet oxygen concentration. These observations are par t ly supported by the in-bed oxygen sensor measurements (See Figure 4.63) where the oxygen concentration was mostly influenced by excess oxygen, followed by bed particle size. Oxygen enrichment had a negligible effect. T h e discrepancy may originate from the fact that the sensor measures a localized oxygen measurement, close to the gas dis tr ibutor as opposed to the model which calculates an average oxygen concentration. B e d height is the next most impor tant factor. T h e trends of particle-averaged oxygen concentration w i t h bed height are explained later. 232 Chapter 6. Modelling Results CD a Cu -a a> CQ o a CD O Cl O o a <D bfl >  O a cu bO O cu o X b£) CD CQ cu OH 3 > 1 o > CO o3 bO cp a 3 CO Pi O a co C M T3 CD fcuO co o3 4) r-J § .2 03 OH -a CD o CJ J—H CP CS3 T3 cp — SH CP CP "J3 a3 a -o CD X I CD bfl !-I CD S3 CD S £ a. cS > S-i CD CD o3 o3 d o3 PU ^ co CD CO CD CJ j O f-H a CP CP i_ CD CD to sepiued'jo" CD o3 3 o bO ,£3 233 Chapter 6. Modelling Results CD 73 d a -a CP 03 3 cp o 3 o o a CP bO >> X O Ci CP bC >> X O X d - 3 73 -a C 3 CP a a o o 73 > CO 03 bjO CP a 3 3 O g CO SH CD J 2 CJ 03 § ^ CJ CD CD 3 co CD bO co 3 O CD 3 b p o 03 CJ CD S-i fe r ° 03 pL| i CD 73 CD -s '» a3 CD CD b O ci SH CD £ 3 += o 03 03 CD 3 O ^ , CO T3 cj cu SH CD 03 3 > •£ <*> — • CD C so 53 $ 03 2 Cu H 3 co CO "2 8 £ r v ^3 ° c 2 O SH CD CD M3 co 03 O SH U 03 3 >H 3S O bO , Q 234 Chapter 6. Modelling Results CD n f l C D .3 ' to _ C D S H Q, -a CD PQ a o a CD O fl o CD C D bO >. 8 fl C D bO >  X o C D C D X - f l bO '55 -fl -a CD PQ CD a. a 3 C D > b.0 C D cfl S H CD O , 3 fl .2 o3 f—i +^ fl CD CD fl o CD fl « CD C O £ j s X X! O o3 CD CD bp $ o3 co S H S> co" ? o CD fl £ o a » f-H £ 0 3 2 » CH CD CD O 03 CH CD fl ^ CD faO o3 S H CD CD fl O CD CO S H CD CD L O C O 03 fl 03 CO CD CD o3 M CO CD CO - g 8 cS CL r f l l - H ^ CJ S H CD CD ' ' - S J CO 03 O C O o> o3 fl ^ fl o ojO X> E JS 235 Chapter 6. Modelling Results CO Xi saioiijed'20 Cu T3 CD a o a CD CJ a o cj el CD bO >> x o CD CD b£> >  X o X xi M '53 xi -a CD PQ s e p i y e d ' g o S3|0!ired'jo CD ft s of Q CD > bO y=l u CD ft P _o C cp CD - ± ! CJ X ! CJ L 3 CD CD CO bO X CO 3 o <D " d brj 3 03 o CJ S-i . « CD 4 ^ CS] o3 '» CD + 3 +3 S-i CJ 03 - o f 5 CD a a a. te * CD -V CD 'SH a > co" S-i CD 4 ^ CD g 03 CO CJ CD El CD 03 J4 Q, 3 EG ^ CM +4 CJ CD CD 4 ^ CO 03 o w oo " r H >^ C O o CD 03 3 o bJO x> fa 236 Chapter 6. Modelling Results Figures 6.19 to 6.22 present the predicted particle-averaged oxygen concentrations for the in -dustr ial roaster for the fitted and Fukunaka et al. [140] kinetics for smal l (65pm) and large bed particles (150pm). T h e effect of temperature again differs from one kinet ic rate expression to the other. Cont ra ry to the laboratory roaster, the average bed particle size is predicted to significantly affect the particle-averaged oxygen concentration. T h e sharp increase i n predicted oxygen concentration for smal l particles (<70pm) is due to the m a x i m u m effective bubble size l imi t (equation 5.32) being reached. For 150 p,m particles, there is only a smal l effect of any of the operating variables on the oxygen concentration. However, for 65 / i m particles, excess oxy-gen and inlet oxygen concentration are predicted to have significant effects. Since the oxygen concentration affects the volat i l izat ion of lead sulfide, the mean particle diameter w i l l affect the agglomeration behaviour of the industr ia l fluidized bed. A s Figures 6.15 to 6.22 show, the particle-averaged oxygen concentration increases w i t h bed height in the laboratory roaster and for the industr ia l roaster w i t h a mean particle size of 65 pm. W h e n the particle size is large ( 1 5 0 / i m ) in the indust r ia l roaster, the oxygen concentration decreases slightly. Since these trends are counter-intuitive, a more detailed explanat ion is required. It is commonly accepted that i n fluidized bed reactors, as the expanded bed height is increased, for the same operating conditions (superficial gas velocity), addi t ional gas conversion occurs which leads to a decreased particle-averaged oxygen concentration. T h i s may be summarized as: " W i t h deeper beds, the gas can reach higher conversions." T h i s reasoning originates from catalytic reactors where only the gas reacts and as such, addi t ional particles s imply increase gas conversion. In catalytic fluidized beds, the gas reaction rate constant kr does not change. T h e gas conversion at a given vert ical posi t ion in the bed is the same regardless of the expanded bed height. A d d i t i o n a l height leads to higher gas conversions. W h e n averaged, the addi t ional conversion provided by increasing the expanded bed height (through increased solids inventory) lowers the overall gas concentration. For gas-solid fluidized beds reactors, the assumption that the effective gas reaction rate constant 237 Chapter 6. Modelling Results CD - f l -fl .bp '5 - f l -o CL) pa cu O H a CCi ho CD C C i-< cu O H fl cn fl .2 o3 SH 4^ fl CD CD fl o CD fl ^ CD § ^ X - Q O o3 - d H CD CD h O CD o3 cn SH CD CO fe S o3 o -2 "S 7D X ) fl 0 3 CD ° < SH CD fe T 3 CD CD HA CD -2 SH 03 OH -a r CD CD fl o CD b O o3 SH CD a 3. -a o CD L O £ «3 - T 3 CO fl SH 03 CD CD CD 3 3 2 CD ±5 o ^ o ® ^ -fl H H O U O o ,CD SH fcM CD H CO o3 CTS SH I - H CO . 2 CD 43 SH CO fl fl OJO -O fe .s 238 Chapter 6. Modelling Results CD -3 bp '53 n3 CD CD a S o JD To > CO cci bO CD CH 3 jd "3 3 O l l « SH 3 CD O 3 O CD 3 CD faC >> X o CO CD CD CO co" 3 O ^ i§ CD TJ bO 3 ai O SH CD CD > SH 5 r o I ft r£ 13 CD '_J3 N £ ' » CD 03 3j a CD T3 SH P H CD cd -3 bO 03 SH CD 3O •b a. ^ ° °3 LO ^ H °3 03 CD ^ 31 3 o 3 TJ CD 03 CD > 3 g 03 b r^ ! el C H J H co 3 8 ^ CD Mb o CN co .2 cu +3 SH CO 3 3 bO TJ E .3 239 Chapter 6. Modelling Results CD -fl S E o t in cc saiojed'go , cc! OH T3 CL) PQ O fl CL) O fl O C J fl CD bO O -o 2 fl CD bi) >> X o CD CD X H sepiued'jo -fl bp 'CD -fl T3 CD CQ CD OH a cc) bi) CD CC SH CD OH fl CD "fl fl O CD C J fl o C J C M fl CD bO <co >v X J D e5 T3 OJ bO CD 0 3 CD i -2 "CD *4J SH 03 a CD CO T3 fl o cj CD R ? +=> fe _cj - 3 CD CD N CH " B CD CD -fl .2 += += SH fl 0 3 O C H fl X> '-3 CD 0 3 03 S3 fe CD ™ § s CD L O 0 3 co" fl S3 0 3 -8 8 S '-^  CO CD C J r+f O * a -G M H + = O SH CD ^ CD SH * ,2 H t? CO •• O i-H SH CQ C O .5 CD £ SH CO fl fl bO T3 fa .5 240 Chapter 6. Modelling Results J D ° E J D Cu -a CP PQ a CP o 3 o o a CP bO >> o a CP bO >> X o CP o X -a bp '53 -a -a CP PQ C 3 CP OH S3|0!ped'go S9|D!MBd'go 03 ho o cn SH CP C M 3 03 CM Cu C O I I CP CD jCl co o3 73 co 1 2 « -3 O 0 3 U « r? CD PH CD .2 'co CD 3 CD . . fcuO J D g 3 *d & CD -d 2 I Cu " SH CD fD fe 4J 03 ° 3 . <D'~ L O s ^ '_T_3 03 03 T3 15 § CD 3 O X 3 CD 03 > CD 43 CD CL) 03 03 3 03 SH £ CD CD ii CD S 2 « -s co 3 -d 3 3 ' ~ bp CD PH 4^  CD 241 Chapter 6. Modelling Results does not vary is flawed. Cont ra r i ly to catalytic reactors where the reaction proceeds as long as the gas is not completely converted and that it contacts active catalyst, the gas i n gas-solid reactors only reacts to the same extent as the solids. Increasing the bed height does not necessarily increase the gas conversion. In fact, for a l l other parameters being constant, the effective gas reaction rate constant in gas-solid reactors decreases w i t h increasing expanded bed height. T h i s decrease in effective gas reaction rate constant is reasonable. Increasing the expanded bed height increases the number of inert particles while the number of reactive particles stays relatively the same (same solids feedrate, same superficial gas velocity) . T h i s dilutes the concentration of reactive particles in the bed and effectively lowers the effective gas reaction rate constant. T h i s may be summarized as: " W i t h deeper beds, the gas has more height to react w i t h the reactive particles." The gas conversion at a given ver t ical posi t ion w i l l depend on the expanded bed height. A d d i t i o n a l height does not direct ly lead to higher gas conversions since the gas conversion is t ied to the solids conversions. T h e effect of increasing the expanded bed height (through increased solids inventory) on the overall gas concentration w i l l be different in gas-solid fluidized bed reactors than in catalytic fluidized bed reactors. Fi rs t , we consider the effect of height on the average oxygen concentration for the laboratory roaster (Figures 6.15 to 6.18). A s previously discussed, to reach a s imilar solids conversion, the reaction rate constant decreases when the bed height is increased (here, H m j ) . T h i s leads to a decreased reaction of the gas per unit volume of reactor. A l so , the interphase mass transfer coefficient and area, governed by slugs, does not vary when the bed height is varied. Therefore, interphase mass transfer per unit volume of reactor is approximately the same (similar d r iv ing force). T h e combinat ion of a decreased gas reaction and similar interphase mass transfer leads to an increased average oxygen concentration wi th increasing expanded bed height (increasing H m / ) . Next , we consider the effect of expanded bed height on the average oxygen concentration for the industr ia l roaster w i t h a bed of 65 pm (small) particles (Figures 6.21 and 6.22). S imi la r ly to the laboratory roaster, the reaction of gas per unit volume decreases as expanded bed height increases (due to decreasing reaction rate constant). The interphase mass transfer coefficient 242 Chapter 6. Modelling Results and area is governed by the effective bubble size. Since the effective bubble diameter reached its m a x i m u m value somewhere i n the bed, interphase mass transfer coefficient and area for the addi t ional height are s imilar to most of the bed. Therefore, the net effect of decreasing the reaction of gas per uni t volume and a similar interphase mass transfer is to increase the average oxygen concentration. Final ly , we consider the effect of expanded bed height on the average oxygen concentration for the industr ia l roaster for a bed of large particles (Figures 6.19 and 6.20). fn this case, the m a x i m u m bubble size (which is very large) is never reached, significantly affecting the interphase mass transfer coefficient and area. A n y addi t ional bed height has smaller interphase mass transfer than any other upstream port ion of the bed. T h e combinat ion of decreased reaction rate (everywhere) and smaller interphase mass transfer (in addi t ional height) leads to a smal l decrease i n average oxygen concentration w i t h increasing expended bed height. Th i s decrease applies for the conditions modelled here. For other conditions, the decrease may be of a different magnitude or even be an increase. In summary, changing the expanded bed height can affect the overall oxygen concentration by changing the relative importance of the gas reaction rate and interphase mass transfer. It is interesting to note that for conditions where the bubble size is l imi ted (i.e. laboratory reactor and industr ia l reactor w i t h smal l bed particles (particle diameter < 70 pm)) increasing the bed height increases the overall oxygen concentration. Such an increase reduces the t ime for complete conversion of concentrate particles. A reduced time for complete conversion combined wi th an increased residence t ime i n the bed (larger bed mass) signifies that the average solids conversion is increased further than what would be expected by just increasing the residence time. For industr ia l fluidized beds w i t h beds of large particles, only the increase i n residence t ime posit ively affects the solids conversion. In summary, for an industr ia l roaster w i th 150 pm particles, the particle-averaged oxygen concentration is low, regardless of the operating conditions. For the same roaster w i t h 65 pm particles, excess oxygen significantly affects the oxygen concentration, thereby affecting the 243 Chapter 6. Modelling Results agglomeration behaviour. T h i s is due to the enhanced interphase mass transfer caused by the much smaller bubbles (with the m a x i m u m bubble size being reached). Oxygen enrichment (inlet oxygen concentration) also affects the particle-averaged oxygen concentration. However, since the pract ical range of oxygen enrichment is l imi ted , changing the particle-averaged oxygen concentration using oxygen enrichment has l i t t le influence. For the laboratory roaster, excess oxygen and oxygen enrichment bo th significantly affect the particle-averaged oxygen concentration, regardless of the particle size. T h i s is explained by significant wal l effects in the laboratory roaster. T h e interphase mass transfer for the laboratory roaster reaches a m i n i m u m , constant value once slugging is established. However, for the industr ia l roaster w i t h 150 /zm particles, the bubble diameter does not reach a l imi t i ng value (maximum bubble size or reactor diameter). Since interphase mass transfer decreases as bubbles grow larger, there is no lower l imi t on interphase mass transfer i n the indus t r ia l roaster. For the laboratory roaster, the lower l imi t on interphase mass transfer is governed by the reactor diameter. Since particle size does not affect the slug diameter (diameter of the laboratory roaster), particle size has l i t t le influence on the particle-averaged oxygen concentration. For the industr ia l roaster, however, particle size significantly affects the particle-averaged oxygen concentration once the bubble size l imi t (equation 5.32) is reached. Mixing in the laboratory and industrial roasters In the previous chapter, we have seen that mix ing i n a fluidized bed must be characterized in its two main dimensions (axial and radial) independently. T h e fluidized bed roaster model assumes that perfect mix ing applies to both the laboratory and the indus t r ia l roasters. To verify this assumption, the characteristic mix ing times of the roasters are compared w i t h the particle reaction times. Table 6.6 summarizes the m i x i n g times for both the industr ia l and laboratory roasters. T h e turnover t ime (calculated using equation 5.68) for both the laboratory and the indust r ia l is of order 1 to 10 s. R a d i a l mix ing (equation 5.70), however, differs greatly between the laboratory and industr ia l roasters. For the laboratory roaster, the radial m i x i n g t ime is approximately 1 244 Chapter 6. Modelling Results o CP (-)H (-)H T - O) 00 03 Ct, -d CP m s cu CJ C o cj fl cu bO >> X o fl cu bo >, X o X (-)H '53 -fl -a cu m s_. fl cu cu 03 bo CJ cfl Sh cu PH fl J H " f l TJ -fl Ph 1 CP -fl CP S H 03 CH C O - 2 CP CP c l . 2 I  - 8 fl S H • 2 r ° •43 fe CJ CD ^ P M o3 jo T 3 S H CP 03 CP -fl T3 CP -Q cp bO CD CP CP a % 03 I cd O O o3 T3 T3 CP fl * S H ^ 5 CO . 2 C O 4 ^ S H CP CD fl .fl cp a ^ 3 "g CO CH Cfl CP CJ o S H CD -t^  CO CO O CJ ct! fe •• O CO +s> 03 CD S H o co fl bC cp fe -5 245 Chapter 6. Modelling Results 246 Chapter 6. Modelling Results o CD (-)h ( - ) H CL -o cu PQ s o 3 cu CJ 3 o o s CP bO >> x o a CP bO >> X o cu cj X a (-)H - 3 _bp '53 -a -a CP PQ cu CL a o3 bD CC S H CP O H 3 H3 a I CP H3 c o 3 ~ D 03 a3 O H U CD , — K CO CO H M .S a —- _o CP ' "*H S TJ .3 ci O 3 ° O S H '•£ r° O M H a3 <U ni 3 o 03 TJ coa> += CP .y 13 -d '43 CP TH 3 03 CL CL ^ -g CP bO 03 SH CP g 0 03 -d "d cu 3 'C «3 g co > CP CO '-+3 SH CP CD J H CD 1 * I -CO O H C43 CO CD CO r j CD •is CD ^ SH O O ,<*> H 3 H L O C N SH CD 03 O SH > > SH o CD O o3 3 bD CD S H9 247 Chapter 6. Modelling Results ( - ) H C D • 03 OH T3 C D m el o ci C D C D Ci O C D Ci C D bO >> X o C D 13 ci C D bfl o C D C J (-)H -ci bp '53 -C T3 C D PQ su c C D OH > CO o3 bo CD cC SH C D OH 3 T3 CU CO 03 -0 C M PH OJ H H 73 oi H OJ cu S H SH o3 O o l ^ o co o fa OJ S CD ' £ o ^ CD CD CD S H 03 OH T3 - O CD CD •8 -° - d CD S H O H CD 01 o CD fcuO o3 S H 1 g a. „ L O CD C O S o3 Tj" 03 01 ^ 0 3 § g T3 '0 . 2 ol "e CD g CD o3 i i o3 fl OH fa CD CD O CO o3 O S H C J ,<° ctt fa C O C M C O C D S H O " b O CD fa -5 CD S H O - O CD 248 Chapter 6. Modelling Results s or less. For the indust r ia l roaster, on the other hand, the radia l m i x i n g t ime is much longer, ranging from 2000 to 11000 s, main ly depending on the particle size and gas velocity. Figures 6.23 to 6.26 present contour plots of the solids reaction t ime w i t h dimensionless vert ical posit ion i n the bed and varying parameters, calculated using the local concentration i n the H -phase for the laboratory roaster. T h e reaction times i n these figures are calculated differently from those i n the model: T h e model calculates a single particle-averaged oxygen concentration from which it calculates the t ime for complete reaction. T h e figures, however, are calculated for each vertical posi t ion i n the bed. T h e Subfigures (f) i n Figures 6.23 to 6.26 present the reaction t ime wi th dimensionless vert ical posi t ion in the bed for a varying bed height at m i n i m u m fluidization. T h e expanded bed height increases as the bed height at m i n i m u m fluidization (Hmf) increases. Therefore, a dimensionless vertical posi t ion of 1 (bed surface) represents an increasing bed height as Hmf is increased. Table 6.6: Character is t ic solids mix ing times for laboratory and indust r ia l roasters. For condi-tions, see Table 6.2. A l l times are given in seconds. Effect of f on —> L a b o r a t o r y Indus t r i a l R a d i a l t ime Turnover t ime R a d i a l t ime Turnover t ime Par t i c l e size (50 - 250 pm) 0.5-1.6 2.35-2.6 2000-6000 1.8-2.6 Ve loc i ty 65 pm part icles 0.6-0.2 2.4-0.8 6000-2000 8-2 150 pm part icles 1.1-0.35 2.4-0.8 11000-3500 8.5-2 B e d height 65 pm part icles 0.6 2-11 2400 1-3.6 150 pm part icles 1.1 2-11 4200 1-4.5 A s for figures 6.15 to 6.18, the t ime for complete reaction wi th in the H-phase does not differ greatly for the smal l (65 / i m ) and large (150 / i m ) particles. However, large differences appear when comparing the two reaction rate expressions from Chapter 2 (fitted and Fukunaka et al. [140]). Since the Fukunaka et al. rate expression gives much faster rates, the times for complete reaction are much smaller. Compar ison of these times w i t h the turnover and rad ia l times for the laboratory roaster reveals that radial mix ing is extensive. A x i a l mix ing , however, may be incomplete i f the Fukunaka et al. kinetics apply. T h i s can be seen for conditions of high excess 249 Chapter 6. Modelling R.esults oxygen on Figure 6.24 (a). In this figure, a large por t ion of the contour plot gives reaction times of less than 10 s. Since the turnover t ime is of the order of 2.5 s, operat ion at excess oxygen larger than approximately 60% may not achieve perfect mix ing . For other conditions, however, the region where the reaction t ime is less than the turnover t ime is relatively l imi ted, generally to very close to the distr ibutor . Since only a smal l area near the dis t r ibutor has reaction times smaller than the turnover time, assuming that particles in the bed are perfectly mixed is reasonable. If the fitted kinetics apply, the assumption of radia l and axia l m i x i n g is val id since the t ime for complete reaction is larger than any of the m i x i n g times. Figures 6.27 to 6.30 present contour plots of the solids reaction times calculated using the local concentration i n the H-phase for the industr ia l roaster. A s for the laboratory roaster, axia l mix ing may only be a concern if the Fukunaka et al. kinetics apply to the system. T h e turnover t ime is larger than the reaction t ime only when the inert particles are smal l and the excess oxygen is large. < In contrast to the laboratory roaster, radial solids mix ing times in the indus t r ia l roaster are often larger than the corresponding reaction times. T h i s may be of concern if the feed is unevenly dis t r ibuted. T h e importance of radial mix ing depends on the efficiency of the feeding system to distr ibute the zinc concentrate over the entire cross-section of the fluidized bed. If the feed is evenly dis t r ibuted over the entire area, the importance of radial m i x i n g may not be cr i t ical . However, if the feed is not dis tr ibuted evenly, local differences i n excess oxygen may occur and effective radial dispersion of the unreacted concentrate may be cr i t ica l to the success of the process. Note that the most favourable radial mix ing conditions i n the indust r ia l roaster corresponds to large particles and low excess oxygen (see Figure 6.27 (a)). For indus t r ia l roasters containing very smal l average particle sizes (left of Figure 6.29 (c), <70/im), the reaction t ime decreases more quickly than the m i x i n g time, due to the m a x i m u m effective bubble size (equation 5.32). For fluidized beds of fine particles, the bubble size is relatively smal l leading to enhanced interphase mass transfer. W i t h faster interphase mass transfer, the oxygen concentration wi th in 250 Chapter 6. Modelling Results ( - ) H On % \ < \ < X \ c _ - ^ \ 1 ( - ) H J 5 73 03 D. T3 CD CQ fl o c C D O fl o C J fl C D bO >> X O JD " f l G C D bO >> X O CD X a ( - ) H ( - ) H - f l bO 'CD -fl T J CD pa C D SH fl +^ 03 SH C D OH C D > o3 buO CD a C D " f l C U C O 03 H G P H cu - G C O ^ CU c o C D C D P H H C U O OD C O G cu ."S G T j • G G O G U ° fe "tl £ CD . C U C U s 'co T J C U SH SH 03 a a H H C U += C U fcuO C D SH C U G O cu" s o3 £ 0 3 o C U L O T J G C D T J .2 ' S H * C D > C O C O .2 SH += C U C U G cu . G G ^ T J C U C D a -•-= C G C O C O C D 8 a <2 u C U tj JS cu 55 to 2 « -s C O G SH G G fcuO C U 251 Chapter 6. Modelling Results ( - ) H ( - ) H 03 C H -d CD m 3 o : 43 a CD o a o o 3 CD bfl X O a CD bO >> X o CD o X ( - ) H ( - ) H -3 '53 H3 TJ CD m s- 3 CD OH 3 CD 03 b.0 C J c3 SH CD OH 3 CD H3 OH CN m < ° CD ^ HG HO 3 H CD CO CD s 2 OH .4-5 H H T J O 3 O CO CJ 3 ' i fa CD 3 CD .3 N 3 .2 4 3 o 0 3 CD S H T J CD T J CD CD n3 4 3 3 O CD" 0 3 a T J CD JO CD bO 03 S H CD ;§ g 3 . o LO o3 T ? 03 CD 3 O T J .2 'G o3 > CO S H CD 03 03 CD g CO ^ ii T1 CO CO CD CD rn ° i CD CD S fa ^ 2 00 ' S H ^ -s c o 3 CD "2 S H 3 3 ' ~ bO CD fa 4 ^ 252 Chapter 6. Modelling Results Chapter 6. Modelling Results ( - ) H \ c X X. X ( - ) H o ^ d S ( - ) H a CD PQ c o a CD O A o CJ CD bO >> X o JO "fl fl CD bO >> X o CD o X a ( - ) H ( - ) H hp 'CD .fl T D * CD PQ CD SH fl -4^ 03 SH CD OH a CD > CO oi bO cfl SH CD OH fl CD CD CO CD H A a t d ^ " CO CD HA ^ . 3 H _CD CD T j CO CD « OH .2 H H ."fl O T j s fl co O . 3 ^ o CD CH 3 • • fl CD - u N fl O CD CJ CD CD SH T J CD T J CD .CD H A fl o CD OH T J CD r O CD bC ctS SH CD CD CD LO fl « 3 T J fl 03 CO CJ CD fl ,_ O CD T j . 3 CD J4 03 > CO SH CD •H= CD CD CO r-j CQ co a) •H fl OH , P SH CD 4^ CO CD o SH °SH H J CO fl T J CJ cfci W o CO CO CD SH SH fl ' r t faO CD CH "5 2 5 4 Chapter 6. Modelling Results the H-phase increases rapidly, causing a significant reduction in the t ime for complete reaction. T h i s increase is seen on the particle-averaged oxygen concentration presented in F igure 6.21. 6.3.4 Model-based predominance-like diagrams The figures presented in section 2.7 show that temperature and excess oxygen have a significant effect on the stable phases after complete reaction. Since the fluidized bed reactor model can more adequately predict the gas composi t ion experienced by the particles, the results from the reactor model may be used to predict the most stable phases. T h e stoichiometry of the reaction is adjusted so that the reaction and the gas composi t ion are consistent w i t h the stable phase. Since the main reaction products for the oxidat ion of zinc sulfide are zinc oxide, basic zinc sulfate and zinc sulfate, the stoichiometric coefficients [yo2 and ^ 5 0 2 ) for each reaction (oxidation and sulfation) are mul t ip l ied by the ratio of zinc oxide or zinc sulfate to converted zinc i.e. t^znsi o r — n z " s ° 4 and added to obtain the overall stoichiometric coefficient. " Z n S 0 4 + n Z n O " Z n S O 4 + ™ Z n O This allows for a variable stoichiometry from pure oxide to pure sulfate. F igure 6.31 presents the stable phases predicted from the gas composit ion from the fluidized bed reactor model using the model parameters for the laboratory fluidized bed. T h i s F igure is calculated s imi lar ly as Figure 2.19 in section 2.7 w i t h the exception that the gas composi t ion is calculated using the G S B M model , coupled to a solids reaction model instead of a simple stoichiometric model (equation 2.11). In other words, the gas composit ion is first calculated using the reactor model . T h e most stable compound is then determined using this calculated gas composi t ion. Since the conversion is incomplete at low temperature, sufficient oxygen is available to produce basic zinc sulfate, even if it requires more oxygen. For the diagram calculated using the stoi-chiometric model , F igure 2.19, a mixture of zinc oxide and basic zinc sulfate is produced due to the complete conversion and to the insufficient amount of oxygen present to completely convert the zinc oxide to basic zinc sulfate. W h e n comparing Figures 2.19 and 6.31, it is clear that considering thermodynamics without considering reactor hydrodynamics and kinetics may yie ld erroneous results. T h e thermody-namics show that the lead system is highly sensitive to excess oxygen, especially near stoichio-255 Chapter 6. Modelling Results 0 -1 -2 -3 O -4 w w u | -6 -7 -8 -9 -10 L 750 o w c ' N ZnO CM 6 ' c N 800 850 900 950 Temperature °C 1000 1050 0 -1 -2 -3 o -4 0) o X LU -10 750 „ o PbSO, 4 CO Q. PbO-(PbO 800 850 900 950 Temperature °C 1000 1050 (a) Z inc (b) L e a d 850 900 950 Temperature °C 1050 850 900 950 Temperature °C 1000 1050 (c) I ron (d) C o p p e r Figure 6.31: Excess oxygen - Temperature GSBM model-based predominance-like diagram for the experimental fluidized bed conditions shown in Table 6.3 256 Chapter 6. Modelling Results 750 800 850 900 950 Temperature °C 1000 1050 -10 750 800 850 900 950 Temperature °C 1000 1050 (a) O x y g e n concentra t ion (b) Sulfur d ioxide concent ra t ion Figure 6.32: Gas concentrations for excess oxygen - temperature G S B M model-based predominance-like diagram for the experimental fluidized bed conditions shown i n Table 6.3 257 Chapter 6. Modelling Results metric operation. However, model l ing clearly shows that the lead species are not sensitive to excess oxygen. Note that since the oxygen par t ia l pressure is sensitive to excess oxygen, so w i l l be the lead par t ia l pressures. Figure 6.32 presents the particle-averaged gas concentration related to F igure 6.31. T h e particle-averaged oxygen gas concentration increases w i th increasing excess oxygen. T h i s is mostly observed between 1 and 100% excess oxygen (between -2 and 0 on Figure 6.32). T h e gas con-centrations do not change appreciably below approximately 1% excess oxygen. T h e directions of the iso-concentration lines differ greatly from those presented in F igure 6.32. T h i s is due to greater reactivity of the solids w i t h increasing temperature. The particle-aver aged oxygen concentration is smaller than 1% for most conditions. It is larger than 1% only at lower temperatures were Z n O - 2 Z n S 0 4 is produced. In this region, the kinetics and the model applied to the system probably no longer apply since the solid product is no longer Z n O and pore-blocking may occur (see Table 2.1). Note that these calculations assume that the activities of a given species when it is stable is 1 and that the gas concentrations used averages for al l particles w i t h i n the fluidized bed. Since the act ivi ty of lead oxide w i th in a lead oxide solution is less than 1, a l iqu id mix ture of lead oxide wi th sil ica, zinc oxide or basic lead sulfate could exist, even for gas composit ions where lead sulfate or basic lead sulfate is predicted. To correctly predict the appropriate stable phases for such conditions, the overall G ibbs free energy should be min imized , inc luding gaseous phases and l iqu id solutions. T h i s figure nevertheless demonstrates that thermodynamics alone and thermodynamics coupled to reactor model l ing give very different results. 6.4 Discussion of key coating and agglomeration results • Effect of excess oxygen Excess oxygen had a significant effect on coating and agglomeration i n the laboratory roaster. In addit ion, model l ing of the laboratory roaster showed that the oxygen concen-trat ion surrounding the particles varies significantly w i t h excess oxygen. Since the par t ia l 258 Chapter 6. Modelling Results pressure of lead sulfide varies w i th oxygen par t ia l pressure (see F igure 2.11), these results are consistent w i th the mechanism proposed for coating and agglomeration. For the industr ia l roaster, the model predicts that the effect of excess oxygen greatly depends on the mean bed particle size. For large average bed particle sizes, the effect of excess oxygen is small . However, for smal l average bed particle sizes (<70pm), excess oxygen has a significant effect on the average oxygen concentration surrounding the par-ticles. T h i s may imp ly that when the industr ia l roaster has a smal l average bed particle size, agglomeration and coating in the roaster may significantly vary w i t h excess oxygen. W h e n the average bed particle size is large, agglomeration and coating i n the industr ia l roaster should not be significantly affected by the excess oxygen. • Effect of inlet oxygen concentration T h e experimental results do not show any significant effect of inlet oxygen concentration on the coating and agglomeration behaviour. Similar ly , model l ing predicts that the inlet oxygen concentration has a l imi ted effect on the oxygen surrounding the particles, main ly because of the l imi ted pract ical range of inlet oxygen concentrations. M o d e l predictions for the industr ia l roaster indicate that the average oxygen surrounding the particles does not vary significantly i n the pract ical range of oxygen enrichment. T h i s implies that coating and agglomeration should not be significantly affected by oxygen enrichment. It was observed by operators of industr ia l fluidized bed roasters that changes i n inlet oxygen concentration can affect the bed particle size d is t r ibut ion of the roasters [35]. Unfortunately, this s tudy cannot explain the effect of changes i n oxygen enrichment on the bed particle size dis t r ibut ion. One possibi l i ty may be that excess oxygen may have also been modified at the same time. • Effect of roasting temperature Temperature had a significant effect on coating and agglomeration' i n the laboratory roaster. Consider ing the proposed mechanisms, this observation is consistent' w i t h the increased lead par t ia l pressures at higher temperatures (Figures 2.10 to 2.12 and 2.22) 259 Chapter 6. Modelling Results a n d t h e m o r e p r e d o m i n a n t l i q u i d l e a d phases i n t h e di f ferent p h a s e d i a g r a m s ( F i g u r e s 2.24 t o 2 .28) . T h e m e t a l spec ies p a r t i a l p ressures a n d t h e p r o p o r t i o n o f l i q u i d s w i t h i n p h a s e d i a g r a m s a l l i nc rease w i t h t e m p e r a t u r e . C o n s i d e r i n g t h a t t e m p e r a t u r e has a s i m i l a r effect o n t h e pa r -t i c les r ega rd less o f t h e r e a c t o r geome t ry , i t is r e a s o n a b l e t h a t t e m p e r a t u r e affect c o a t i n g a n d a g g l o m e r a t i o n i n a s i m i l a r m a n n e r i n t h e i n d u s t r i a l a n d l a b o r a t o r y roas t e r s . • Effect of superficial gas velocity T h e s u p e r f i c i a l gas v e l o c i t y d i d n o t have a s i g n i f i c a n t effect o n c o a t i n g a n d a g g l o m e r a t i o n . T h i s is c o n s i s t e n t w i t h m o d e l p r e d i c t i o n o f t h e o x y g e n c o n c e n t r a t i o n s u r r o u n d i n g p a r t i c l e s . F o r b o t h t h e l a b o r a t o r y a n d i n d u s t r i a l roas te r s , s u p e r f i c i a l gas v e l o c i t y u s u a l l y h a d l i t t l e effect o n t h e o x y g e n c o n c e n t r a t i o n . I t d i d , howeve r , have a n effect o n t h e p r o p o r t i o n o f f ine p a r t i c l e s i n t h e l a b o r a t o r y f l u i d i z e d b e d . T h i s is c o n s i s t e n t w i t h t h e a c c e p t e d k n o w l e d g e o f e l u t r i a t i o n . O n e c a n a l so a s s u m e t h a t a t t r i t i o n w o u l d b e i n c r e a s e d w h e n t h e gas v e l o c i t y is i n c r e a s e d . • Effect of bed material T h e e x p e r i m e n t s have s h o w n t h a t t h e b e d m a t e r i a l has a s i g n i f i c a n t effect o n t h e c o a t i n g a n d a g g l o m e r a t i o n b e h a v i o u r . T h i s c a n be e x p l a i n e d b y c o n s i d e r i n g t h e p h a s e d i a g r a m s of t h e m a i n c o n s t i t u e n t s o f t h e p a r t i c l e s , i n p a r t i c u l a r w i t h l e a d o x i d e . F o r s i l i c a p a r t i c l e s , t h e p resence o f e x t e n s i v e l i q u i d phases i n t h e p h a s e d i a g r a m ( F i g u r e 2.25) i n d i c a t e s a s i gn i f i can t r e a c t i v i t y o f l e a d o x i d e w i t h s i l i c a . S u c h a r e a c t i v i t y w o u l d m a n i f e s t i t s e l f b y s i g n i f i c a n t " w e t t i n g " of t h e p a r t i c l e s b y a l i q u i d l aye r w h i c h w o u l d c o n t r i b u t e t o t h e c o a t i n g o f s u c h p a r t i c l e s . F o r a l u m i n a p a r t i c l e s , t h e p hase d i a g r a m ( F i g u r e 2.26) a l so p resen t s a e u t e c t i c c o m p o s i -t i o n , l i q u i d at t y p i c a l r o a s t i n g t e m p e r a t u r e s . H o w e v e r , t h e p r o p o r t i o n o f l i q u i d is m u c h s m a l l e r t h a n for s i l i c a . T h e r e a c t i v i t y o f l e a d o x i d e w i t h a l u m i n a c a n the re fo re b e a s s u m e d t o be s m a l l e r , ye t s t i l l ex i s t en t . T h i s s m a l l e r r e a c t i v i t y w o u l d b e m a n i f e s t e d b y a di f ferent " w e t t i n g " b e h a v i o u r . T h i s was o b s e r v e d e x p e r i m e n t a l l y . 260 Chapter 6. Modelling Results For the calcine particles, one can assume from the phase diagrams (Figures 2.27 and 2.28) that the reactivity of calcine w i t h lead oxide may be larger than for a lumina yet smaller than sil ica. Th i s implies that the coating and agglomeration behaviour of calcine particles would l ikely rank between the si l ica and a lumina particle. Mode l l ing characterizes the effect of bed material only i n terms of its density and size. It cannot predict the chemical effects of the bed mater ial on the agglomeration and coating processes. • Effect of average bed particle size Differences i n the behaviour of industr ia l fluidized bed roasters have been observed wi th changes i n average bed particle size [35]. Mode l l i ng has shown that the average bed particle size significantly affects the behaviour of the industr ia l fluidized bed roaster. T h e span of particle-aver aged oxygen concentra-tions for changes in excess oxygen strongly depends on the average particle size. For fine (Geldart Group A ) particles, the bubble diameter is l imi ted and the range of particle-averaged oxygen concentrations is greater than for larger (Geldart G r o u p B ) particles where bubble diameter is not l imi ted . For the laboratory roaster, no significant changes were found. Experimental ly , the bed particle size affected the agglomeration behaviour in the lab-oratory roaster. W h e n the laboratory roaster was operated w i t h smal l particles under conditions of no excess oxygen, agglomeration was excessive and lead to defluidization. Under the same operating conditions for a bed of larger particles, agglomeration occurred but not excessively. Therefore, it is reasonable to assume that the average bed particle size affects the later steps of the agglomeration and coating mechanisms. 6.5 Implications for the industrial process Excess oxygen and temperature were found to influence the agglomeration behaviour i n the ex-perimental fluidized bed. Since model l ing has shown differences i n behaviour between the lab-oratory and indust r ia l roasters, and since there were significant difference in scale and moisture 261 Chapter 6. Modelling Results content of the feed, direct extrapolat ion of the results from the experimental to the industr ia l fluidized bed must be done cautiously. The model l ing results imp ly that the coating and agglomeration behaviour i n the industr ia l roaster depend on the mean bed particle size. The strategy on how to affect and control the bed particle size w i l l therefore depend on the mean bed particle size. 6.5.1 Effect of uneven spatial distribution of feed material It is l ikely that the industr ia l fluidized bed roaster experience "feed-rich" and "feed-lean" regions due to the way slinger belts distr ibute feed onto the bed surface. For this discussion, assume that the feed-rich and feed-lean areas are equal (i.e. 50% of the bed area each). For a properly functioning gas distr ibutor , the gas would be evenly dis t r ibuted among the two areas (50/50%). Assume that the overall excess oxygen is 20%. If the feed is dis t r ibuted among the feed-rich and feed-lean areas in a 60/40% proport ion, the local excess oxygen of the two areas, neglecting lateral mix ing of the solids, would be 0 and 50%. Note that agglomeration could therefore proceed in the sector w i t h no excess oxygen even though the overall proport ion of oxygen is well above stoichiometric. Overa l l , agglomeration in the industr ia l fluidized bed roaster involves a balance between local agglomeration, which depends on local process conditions, lateral mix ing of the feed and agglomerates, e lutr iat ion and at t r i t ion. Therefore, overall agglomeration would depend on the extent of the feed-rich and feed-lean areas and the proport ion of feed delivered to each areas, as well as m i x i n g and reaction kinetics. Uneven feed dis t r ibut ion is clearly an issue which requires further attention, bo th from theo-retical and indust r ia l points of view. 6.5.2 Mean bed particle size too large T h e model results presented i n section 6.3.3 suggests that for a large mean part icle size i n the industr ia l roaster, the average oxygen concentration surrounding the particles is not signifi-cantly affected by most operating variables. Smal l changes in the operat ing conditions should 262 Chapter 6. Modelling Results not therefore greatly affect agglomeration and coating. However, since the coating and agglom-eration mechanisms require a source of lead sulfide, uniform dis t r ibut ion of z inc concentrate over the entire bed cross-section is beneficial to promoting uniform coating and agglomeration behaviour. Since the reaction t ime of the particles in beds of large mean particle size is much larger than for smal l mean particle size, lateral m i x i n g is more l ikely to be sufficient to provide sufficient lead sulfide to areas not direct ly fed. If there is too much agglomeration in the industr ia l fluidized bed roaster, the mean particle size of the bed would become very large. Since few parameters affect the oxygen i n the bed (and therefore agglomeration) when the mean particle size is large (e.g. >100/xm), temperature may be the main parameter affecting agglomeration due to the dependence of the lead par t ia l pressure on temperature. T h e bed temperature is a consequence of the heat balance between the heat supplied by the reaction, the heat removed by the boiler tubes in the bed, the heat carried out by nitrogen and the heat used to generate steam from feed moisture. Therefore, a reduction in bed temperature through a decrease in concentrate feedrate may be appropriate. Increasing excess oxygen may also help to decrease agglomeration since the oxygen concentration leads to a smaller lead sulfide par t ia l pressure and a shorter reaction t ime (decreased per iod where lead sulfide can volati l ize). If the feed is dis t r ibuted unevenly over a bed of large particles, agglomeration would occur i n the feed-rich areas and l i t t le or no agglomeration would occur i n the feed-lean areas. There are no experimental results corresponding to the conditions in a fluidized bed containing large particles where bubble size is not l imi ted by the reactor diameter. However, i f the laboratory results apply, agglomeration i n the feed-rich area may produce particles of an adequate size (for a bed of large particles). 6.5.3 Mean bed particle size too small If conditions i n the industr ia l roaster are such that the average part icle size is smal l (<70pm), significant variations i n average oxygen concentrations occur for changes i n excess oxygen (see Figures 6.19 to 6.22). T h i s is due to l imi ted bubble diameter which increases interphase mass 263 Chapter 6. Modelling Results transfer (compared to an unl imi ted bubble size system). Since the coating and agglomeration mechanisms rely on vapour-phase transport of lead, variations i n average oxygen concentrations affect coating and agglomeration. Therefore, extreme care must be taken to ensure adequate excess oxygen and proper feed dis t r ibut ion over the entire bed cross-section. Improper feed dis t r ibut ion may lead to areas w i t h very small , even negative excess oxygen (see equation 2.11), while other areas of the fluidized bed may experience excessive oxygen. T h e extent of variat ion i n excess oxygen wi th in the bed w i l l depend on the degree of feed mald is t r ibu t ion and on lateral mixing . Note that the reaction t ime of concentrate particles in a bed of smal l mean particle size is much less than for large particles. T h i s makes uniform excess oxygen and efficient lateral mix ing more difficult to achieve. Therefore, it is even more important to ensure a uniform feed dis t r ibut ion. If there is too l i t t le agglomeration i n the industr ia l fluidized bed roaster, the mean particle size of the bed becomes smal l . Excess oxygen has a significant effect on the oxygen i n the bed when the mean particle size is smal l (<70 / im) . Decreasing the overall excess oxygen is expected to increase agglomeration. However, feed-rich areas may experience excessive agglomeration (production of very large particles) while feed-lean areas have negligible agglomeration. Th i s may lead to a bed where only smal l and very large particles exist (i.e. no intermediate sized particles). Such a bed may be susceptible to defluidization by segregation of sizes. Increasing temperature may also cause increased agglomeration. However, wi thout even feed d is t r ibut ion it is possible that increasing temperature w i l l exacerbate excessive agglomeration i n the feed-rich areas. Un i fo rm feed dis t r ibut ion is especially cr i t ical to achieve adequate agglomeration i n beds of smal l mean particle size. 6 . 5 . 4 Recommendations with respect to industrial roasting Overal l excess oxygen should be s t r ic t ly monitored to find the appropriate level for adequate agglomeration. Once the op t imum excess oxygen level is found, excess oxygen must be carefully controlled, keeping in m i n d the significant difference in the average oxygen concentration for small and large mean particle sizes and the variations in feed composi t ion. 264 Chapter 6. Modelling Results It is currently not known how uniformly the feed is dis t r ibuted. M o n i t o r i n g and improving the uniformity of feed dis t r ibut ion may allow better control of the bed behaviour. Feed dis t r ibut ion in an industr ia l fluidized bed roaster is possibly the most difficult variable to quantify and monitor. Changes in bed behaviour may be caused by even smal l changes in the feeding system. A n y changes to the feeding system, due to maintenance or other reasons, should be recorded. Increasing the number of feed points and/or changing the method of feeding should be considered seriously to improve the uniformity of the bed, especially if the mean bed particle size is small . If even feed d is t r ibut ion cannot be achieved economically, one should consider non-uniform gas dis t r ibut ion. T h i s method has recently been proposed to control agglomeration in a fluidized bed roaster [73]. Appropr ia te gas dis t r ibut ion may allow better control of the excess oxygen wi th in the feed-rich and feed-lean areas of the bed. 265 Chapter 7 Conclusions and Recommendations 7.1 Major contributions • C o a t i n g a n d a g g l o m e r a t i o n m e c h a n i s m s have b e e n f o r m u l a t e d . T h e m a i n c o n t r i b u t i o n is t h e c o a t i n g m e c h a n i s m . T h e s e c o n d c o n t r i b u t i o n is t h a t t h e o x y g e n c o n c e n t r a t i o n o f t h e s u r r o u n d i n g gas i s , for t h e f i rs t t i m e , s h o w n t o p l a y a s i g n i f i c a n t r o l e i n t h e c o a t i n g a n d a g g l o m e r a t i o n processes . E x c e s s o x y g e n affects a g g l o m e r a t i o n , e s p e c i a l l y n e a r s t o i c h i o -m e t r i c (0% excess o x y g e n ) . E x p e r i m e n t a l l y , a g g l o m e r a t i o n i n c r e a s e d w h e n excess o x y g e n a p p r o a c h e d 0%. T h i s is a n i m p o r t a n t c o n t r i b u t i o n . T h i s b e h a v i o u r w a s e x p l a i n e d u s i n g t h e m e c h a n i s m s , t h e i r d e p e n d e n c e o n t h e o x y g e n c o n c e n t r a t i o n a n d t h e f l u i d i z e d b e d re-a c t o r m o d e l . I n a d d i t i o n is has b e e n ve r i f i ed t h a t t h e z i n c c o n c e n t r a t e does n o t r e q u i r e t h a t a l e a d su l f ide p h ase b e p resen t i n t h e c o n c e n t r a t e for v o l a t i l i z a t i o n o f l e a d su l f i de t o o c c u r . • A p r o b a b i l i s t i c f l u i d i z e d b e d r eac to r m o d e l has b e e n f o r m u l a t e d w h i c h c a n b e u s e d for b o t h t h e b u b b l i n g a n d s l u g g i n g f l u i d i z a t i o n f low r eg imes . T h e k e y c o n t r i b u t i o n is t h e m a n n e r i n w h i c h t h e b u b b l i n g - t o - s l u g g i n g t r a n s i t i o n has b e e n h a n d l e d . • T h e l as t i m p o r t a n t c o n t r i b u t i o n is t h e m o d e l c o n f i r m a t i o n t h a t t h e m e a n b e d p a r t i c l e s ize o f a n i n d u s t r i a l f l u i d i z e d b e d roas t e r c a n s t r o n g l y affect h o w t h e i n d u s t r i a l roas te r r e s p o n d s t o changes i n o p e r a t i n g c o n d i t i o n s . I n p a r t i c u l a r , t h e m o d e l has s h o w n t h a t a change i n excess o x y g e n affects t h e f l u i d i z e d b e d roas t e r d i f f e r e n t l y d e p e n d i n g o n t h e average b e d p a r t i c l e s ize . 266 Chapter 7. Conclusions and Recommendations 7.2 Key conclusions • T h e experimental results show that temperature and excess oxygen significantly affect agglomeration wi th in the laboratory roaster. Excess oxygen was not previously thought to be a significant variable. M o d e l l i n g indicates that excess oxygen can also be significant for the indust r ia l roaster. • Oxygen enrichment d id not have a significant effect on coating and agglomeration i n the laboratory roaster for the restricted range investigated. T h i s is opposite to what is suggested i n the li terature [35]. Mode l l i ng suggests that oxygen enrichment is also of l imi ted importance in the industr ia l roaster. • A coating mechanism has been formulated, relying on the vaporizat ion of lead sulfide from the zinc concentrate followed by deposition of lead oxide/sulfate onto bed particles. Lead oxide is a l iqu id at typica l roasting temperatures. T h e l iqu id lead oxide/sulfate film can trap smaller particles onto the surface of larger particles. • A n agglomeration mechanism has been formulated. S imi lar to the coating mechanism, the agglomeration mechanism relies on vaporizat ion of lead sulfide from the zinc concentrate, followed by deposition of l iqu id lead oxide/sulfate onto particles. T h e coated particles can then agglomerate to form larger particles. • T h e first step of both mechanism, the vaporizat ion of lead sulfide, is strongly affected by the oxygen par t ia l pressure. • Lead sulfide was observed to volatil ize from zinc concentrate. • T h e coating and agglomeration mechanisms formulated i n this work are consistent w i t h the observations of C o n d i n a et al. [83] and extend their work to both coating and agglom-eration in fluidized bed roasting conditions. • A sensitivity analysis indicates that there are significant differences between laboratory and industr ia l fluidized beds, the most significant being the effects of excess oxygen and bed particle size. 267 Chapter 7. Conclusions and Recommendations • T h e behaviour of the industr ia l roaster depends greatly on the average inert particle size. For a large average bed particle size (150 pm), the operating conditions have only minor effects on the oxygen concentration experienced by the reacting particles. However, for a smal l average particle size (65 pm), excess oxygen has a significant effect on the average oxygen concentration seen by the reacting particles. Inlet oxygen concentration also has an effect. However, the inlet oxygen concentration is usually varied over only a narrow range (e.g. 21 to 25-30 vol%), thereby l imi t ing its influence. 7.3 Secondary conclusions • Reactor model l ing has shown that scale-up from laboratory to indus t r ia l scale reactors must be carried-out very carefully, accounting for the differences i n interphase mass trans-fer and radial mix ing . Exper imenta l results are more scalable once the reactor diameter is sufficiently large such that wal l effects are negligible on the bubbles. T o reach such conditions, the m i n i m u m diameter must exceed approximately 1 meter i n practice. • The oxygen present wi th in the fluidized bed, determined using an in-bed oxygen sensor, is a function of excess oxygen and bed particle size. Oxygen enrichment, however, does not have a significant effect for the l imi ted range investigated. P r io r to this study, there was no information on the effect of process parameters on the oxygen present w i th in the fluidized bed. T h e measurements are consistent w i t h the model predictions. • Low-melt ing-point phases wi th in zinc concentrates originate from the interaction of i m -purities. T h e ma in impurit ies are P b S , CU2S and F e S . • A single compound, lead oxide, accounts for numerous low-melting-point phases. If lead oxide or any of the basic lead sulfates is produced, the l ikel ihood of producing low-melting-point phases is high, especially for particles that spend long times w i t h i n the roaster. • T h e stable phases calculated using the fluidized bed reactor model differ considerably from those based on stoichiometry and thermodynamics. T h e identi ty of the stable phase varies much less for the reactor model than when predicted from pure thermodynamics . 268 Chapter 7. Conclusions and Recommendations 7.4 Recommended future work In light of the implicat ions of the current work on the indust r ia l process, more detailed model l ing of industr ia l fluidized bed roasters is recommended: • Distribution, mixing and reaction of zinc concentrates in industrial fluidized beds In this study, it was assumed that concentrates were introduced uniformly over the entire cross-section of the fluidized bed. For large industr ia l roasters, this is unl ikely to be the case. T h e effect of non-uniform solids d is t r ibut ion in large indus t r ia l f luidized bed roasters should be evaluated. A non-uniform feed dis t r ibut ion could cause regions of the fluidized bed to experience very low or even negative local excess oxygen conditions (e.g. where the concentrate enters the bed), while other regions would experience high excess oxygen. Since it is the goal of fluidized bed roasting to efficiently react the concentrate w i t h oxygen in the gas, maldis t r ibut ion of the feed may affect the m a x i m u m achievable produc t iv i ty from a given roaster. Since the effect of excess oxygen is greatest for roasters w i t h smal l bed particles, any non-uniform feed dis t r ibut ion, beyond that which can be dissipated by radial dispersion, would significantly affect bed agglomeration. Mode l l i ng the dis t r ibut ion, mix ing and reaction of zinc concentrates in indust r ia l fluidized beds would allow evaluation of the effectiveness of increasing the oxygen content of the gas fed near the feed point using a feed gas dis tr ibutor as proposed by Taskinen et al. [73]. T h e current model should be extended by accounting for lateral m i x i n g using an approach used for shallow fluidized beds [221, 222, 223, 224, 225]. However, the model would not need to account for slugging since industr ia l fluidized bed roasters are too large to encounter slugging. In addi t ion to the d is t r ibut ion of feed, the mix ing of zinc concentrates w i t h i n the fluidized bed roaster should be clarified. In this study, it was assumed that the m i x i n g of the concentrates is rap id and that each concentrate particle can be treated individual ly . If 269 Chapter 7. Conclusions and Recommendations the concentrate particles tend to move i n groups or clusters, macro-mix ing would also need to be considered. • Particle size distribution modelling T h e particle size d is t r ibut ion was only accounted for when fi t t ing the model to exper-imental results. T h e experimental particle size distr ibutions were used to calculate the residence times of the reacting particles. However, since the result ing bed particle size distr ibutions are not predicted in this study, the sensit ivity analysis d id not consider the size distr ibutions of the concentrate and inert bed particles. To include the effect of the particle size distr ibutions (concentrate and inert bed particles) a populat ion balance should be coupled w i t h the solids reaction model . U s i n g a popula t ion balance, agglomeration, coating, a t t r i t ion, elutr iat ion can a l l be accounted for and the resulting bed particle size d is t r ibut ion can be predicted. T h e result ing bed d is t r ibut ion is then coupled to the solids mean residence t ime (see equation 5.113). • Reaction of concentrate lumps in industrial fluidized beds Concentrate lumps were not studied in this research project. Such lumps should react s imi lar ly to the grain model . Us ing the shrinking-core model , we have seen that very large particles have the possibil i ty of reaching temperatures greater than their environ-ment. Since the two models are fundamentally different, concentrate lumps may behave differently from single particles. Th i s work has shed light on some gaps i n current pyrometal lurgical knowledge. A p p l i e d research could be ini t ia ted in the following areas: • Kinetics of zinc concentrate oxidation The oxidat ion kinetics of zinc sulfide and zinc concentrates were reviewed. A number of studies have suggested rate expressions. Mos t of these expressions give similar rates. F i t t i n g of the model to the experimental data obtained in this s tudy indicated rates of reaction which are higher than predicted by most kinetic rate expressions, but sl ightly lower than those of Fukunaka et al. [140]. Since the rates obtained from the Fukunaka 270 Chapter 7. Conclusions and Recommendations et al. [140] kinetic rate expression were larger than almost a l l other rate expressions, further kinet ic results are needed. In part icular, most kinetic rate da ta were obtained at temperatures below those employed i n industr ia l fluidized bed roasters. T h e intr insic kinetics should be evaluated for typica l roasting temperatures. Since the reaction rates can be enhanced by vaporizat ion and oxidat ion of zinc sulfide in the gas phase [122, 123], bo th the vaporizat ion and reaction kinetics must be included in the higher temperature reaction rate analysis. • Vaporization kinetics from zinc concentrates N o model l ing of coating and agglomeration can be rel iably performed un t i l the lead vapor-izat ion kinetics from zinc concentrates are studied. Vapor iza t ion is l ikely to be influenced by the process conditions (temperature, oxygen and sulfur dioxide concentrations) and is probably influenced by the concentrate composi t ion and mineralogy. • Coating and agglomeration in the fluidized bed roaster Since different behaviour was observed for si l ica and a lumina inert particles, it would be advantageous to evaluate whether the proposed coating and agglomeration mechanisms would apply to a bed of calcine particles. Further s tudy on the agglomeration mechanism is required. Since catastrophic agglomer-ation occurred only dur ing one of the experiments carried out in this work, l imi ted insight was gained. • Melting point of zinc concentrates T h e melt ing of zinc concentrates is discussed briefly in Chapter 2 on the basis of phase diagrams for various sulfides. Various low-melting-point phases were found. However, a complete Z n S - F e S - P b S ternary phase diagram would prove useful to determine the m i n i m u m temperature and composit ion of the l iqu id phases. Since copper also affects agglomeration, the complete quaternary diagram would also be useful. Cont ra ry to what is proposed i n the literature, agglomeration d id not occur i n this s tudy by the mel t ing of zinc concentrates [73, 72] (see section 2.9.2) or by the mel t ing of a reactive 271 Chapter 7. Conclusions and Recommendations l o w m e l t i n g p o i n t p h ase [80, 81 , 82, 53] (see s e c t i o n 2 .9 .3) . E v a l u a t i n g t h e c o n d i t i o n s w h e r e c o n c e n t r a t e m e l t i n g a n d r e a c t i v e m e l t i n g c a n o c c u r w o u l d b e b e n e f i c i a l t o t h e i n d u s t r y . T h e s e l o w - m e l t i n g - p o i n t phases m a y b e c o n c e n t r a t e - d e p e n d e n t . I t is l i k e l y t h a t t h e t h r ee m a j o r i m p u r i t i e s ( l ead , c o p p e r a n d i r o n ) c o n t r i b u t e t o a g g l o m e r a t i o n i n i n d u s t r i a l fluidized b e d roas te r s a c c o r d i n g to di f ferent m e c h a n i s m s . T h e r e f o r e c o n c l u s i o n s f r o m one c o n c e n t r a t e m a y n o t a p p l y to a n o t h e r . I n a d d i t i o n t o t h e a p p l i e d p y r o m e t a l l u r g i c a l r esea rch , f u n d a m e n t a l . f l u i d i z e d b e d r e sea rch w o u l d be b e n e f i c i a l t o t h e b e t t e r u n d e r s t a n d i n g of t h e c o a t i n g a n d a g g l o m e r a t i o n p rocesses : • Generalized slugging bubbling fluidized bed reactor model T h e g e n e r a l i z e d s l u g g i n g b u b b l i n g fluidized b e d r e a c t o r m o d e l s h o u l d b e t e s t e d aga in s t e x p e r i m e n t a l d a t a for c a t a l y t i c r e a c t i o n s . I f p o s s i b l e , these d a t a s h o u l d s p a n b o t h flu-i d i z a t i o n r e g i m e s a n d cover a w i d e r a n g e o f r e a c t i o n r a t e c o n s t a n t s . T h e m o d e l s h o u l d a l so b e i n t e g r a t e d i n t o t h e c u r r e n t g e n e r a l i z e d fluidized b e d r e a c t o r m o d e l [205]. H o w e v e r , t h e t r a n s i t i o n f r o m s l u g g i n g t o t u r b u l e n t m u s t first b e c l a r i f i e d a n d c h a r a c t e r i z e d . • Agglomeration behaviour of binary fluidized beds in the presence of liquids F u r t h e r s t u d y is r e q u i r e d t o e l u c i d a t e t h e c o a t i n g a n d a g g l o m e r a t i o n b e h a v i o u r of fluidized b e d s c o n t a i n i n g dif ferent t y p e s a n d sizes o f p a r t i c l e s i n t h e p re sence o f l i q u i d s . T h e fluidized b e d roas t e r o f t h i s s t u d y h a d v e r y s m a l l c o n c e n t r a t e a n d c a l c i n e p a r t i c l e s i n a b e d o f l a rge r s i l i c a s a n d p a r t i c l e s . T h e r e a c t i v i t y o f l e a d o x i d e / s u l f a t e m e l t s m a y v a r y w i t h t h e t y p e o f p a r t i c l e s ( concen t r a t e , c a l c i n e , o r i n e r t s a n d ) . T h i s d i f fe rence i n r e a c t i v i t y w o u l d cause di f ferent d y n a m i c - w e t t i n g b e h a v i o u r . T h e a t t r i t i o n b e h a v i o u r m a y d e p e n d o n t h e a m o u n t a n d c o m p o s i t i o n o f l i q u i d p resen t a n d t h e s ize o f t h e i n i t i a l b e d m a t e r i a l . A f u n d a m e n t a l s t u d y o n t h e a g g l o m e r a t i o n o f v e r y f ine p a r t i c l e s w i t h i n a fluidized b e d o f coarse r p a r t i c l e s , i n t h e p resence of a l i q u i d phase , m a y s h e d s o m e l i g h t o n t h e m e c h a n i s m of a g g l o m e r a t i o n w i t h i n t h e fluidized b e d roas te r . T h e effect o f t h e q u a n t i t y of l i q u i d p resen t w i t h i n t h e b e d a n d t h e a t t r i t i o n of a g g l o m e r a t e s b y l a rge r p a r t i c l e s m a y b e s t u d i e d 272 Chapter 7. Conclusions and Recommendations in a controlled experiment. Such a s tudy may also reveal information on the growth of particles. T h e study may reveal the conditions under which the fine particles are glued onto larger particles by a l iqu id f i lm and the conditions to create agglomerates of fine particles held together by a l iquid . T h e important variables to account for in such a study would include the amount of l iqu id , the size of the fine and large particles, their surface properties and the superficial gas velocity. • Effect of particle stickiness on minimum fluidization velocities and average bubble diameters T h e fluidized bed roaster relies strongly on interphase mass transfer for the transport of oxygen from the bubbles to the reacting particles. T h e most impor tant parameter for interphase mass transfer is the average bubble diameter. Eva lua t ing how the bubble diameter varies as a function of particle stickiness would give insight whether or not particle stickiness improves interphase mass transfer. 7.5 Review of objectives T h e research reported in this thesis has sought to provide a better understanding of particle growth processes in zinc concentrate fluidized bed roasting. We now conclude by relating the thesis results to the project objectives set forth in section 1.7. • Investigate particle growth in a laboratory scale fluidized bed roaster. Part ic le growth and agglomeration were studied in a laboratory fluidized bed roaster (see Chapters 3 and 4). T h e temperature and excess oxygen were found to significantly affect entrainment and agglomeration wi th in the laboratory roaster. • Identify particle growth mechanism(s) and quantify the rate(s) of different mechanisms for pure zinc sulfide and industrial concentrates. Mechanisms for the growth and agglomeration of particles have been identified (see sec-tions 4.6 and 4.7). B o t h mechanism rely on the transport of lead species to the inert bed particles. T h e rates for each mechanism have not been quantified. However, it is 273 Chapter 7. Conclusions and Recommendations clear that the rates would depend greatly on the lead species par t ia l pressure, their va-porizat ion and deposition kinetics and the interaction of the deposited lead phase w i t h the bed particles. Agglomerat ion in a pure zinc sulfide system also has not been studied because, as explained in Chapter 3, pure Z n S particles of the right size could not be found. In light of the proposed mechanisms, it is doubtful that significant coating and agglomeration would have been observed if such runs had been carried out. • Identify the operating parameters influencing each mechanism. A number of operating parameters were varied experimental ly to evaluate their influence on particle growth and agglomeration (see Chapters 3 and 4). Since catastrophic agglom-eration occurred only dur ing one experiment carried out i n this work, l imi ted insight on agglomeration was gained. T h experiments showed that the temperature and excess oxy-gen have the greatest effects on particle growth, w i t h bed material , its size d is t r ibut ion and superficial gas velocity also playing significant roles. • Develop a fundamental model, applicable to both pure zinc sulfide and indus-trial concentrates, describing the particle growth in a fluidized bed. To model growth and agglomeration in a fluidized bed roaster, a popula t ion balance on the solids must be coupled to a fluidized bed reactor model incorporat ing a vaporizat ion and deposition model . T h e fundamental model developed in this s tudy predicted the ef-fects of various parameters on the oxygen concentration i n the bed. T h e model developed in this thesis provides the first step of a comprehensive model describing particle growth i n a fluidized bed roaster. The relationship between the oxygen concentration in the bed, the vaporizat ion and deposition kinetics and the growth and agglomeration of particles must first be quantified to complete the fundamental growth and agglomeration model . • Determine the applicability of the results to an industrial fluidized bed roaster. Sensit ivi ty analysis has allowed the laboratory results to be extended to the industr ia l scale. However, the appl icabi l i ty of the results to an industr ia l fluidized bed roaster s t i l l remains to be verified. 274 Chapter 7. 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