UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

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

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-ubc_2004-901688.pdf [ 32.3MB ]
Metadata
JSON: 831-1.0058659.json
JSON-LD: 831-1.0058659-ld.json
RDF/XML (Pretty): 831-1.0058659-rdf.xml
RDF/JSON: 831-1.0058659-rdf.json
Turtle: 831-1.0058659-turtle.txt
N-Triples: 831-1.0058659-rdf-ntriples.txt
Original Record: 831-1.0058659-source.json
Full Text
831-1.0058659-fulltext.txt
Citation
831-1.0058659.ris

Full Text

FLUIDIZED BED ROASTING OF ZINC SULFIDE CONCENTRATE FACTORS AFFECTING THE PARTICLE SIZE DISTRIBUTION by JEAN PIERRE CONSTANTINEAU B . E n g . (Genie des M a t e r i a u x ) Ecole Polytechnique de M o n t r e a l , 1996 M A . S c . (Metals and M a t e r i a l s Engineering) U n i v e r s i t y of B r i t i s h C o l u m b i a , 1999 A THESIS S U B M I T T E D IN PARTIAL F U L F I L L M E N T O F THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in T H E FACULTY OF G R A D U A T E STUDIES D e p a r t m e n t of C h e m i c a l and B i o l o g i c a l E n g i n e e r i n g W e accept this thesis as conforming to the required s t a n d a r d  T H E UNIVERSITY OF BRITISH COLUMBIA M a r c h 2004 © Jean P i e r r e 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. Agglomeration 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 concentration 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 Chapter 1. 1.1  xx  Introduction  1  1.5 1.6 1.7  E l e c t r o l y t i c zinc p r o d u c t i o n 1.1.1 Objectives of roasting R o a s t i n g and its history 1.2.1 R o a s t i n g prior to the electrolytic zinc process 1.2.2 R o a s t i n g for the zinc electrolytic process 1.2.3 F l a s h or suspension roasting 1.2.4 I n t r o d u c t i o n of fluidized bed roasting 1.2.5 N e w roasters B r i e f i n t r o d u c t i o n to fluidized beds R e v i e w of operating knowledge 1.4.1 Feed: Z i n c concentrate 1.4.2 Feed: Gases 1.4.3 P r o d u c t : Z i n c calcine 1.4.4 C o n t r o l l i n g b e d particle size 1.4.5 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 bed roasters 1.4.6 Concentrate moisture content and concentrate agglomeration 1.4.7 L o w - m e l t i n g - p o i n t phases d u r i n g roasting Fundamentals of agglomeration i n fluidized beds A g g l o m e r a t i o n i n other fluidized bed systems Research objectives  2 4 5 6 6 8 9 14 14 15 16 17 17 19 20 22 23 24 25 28  1.8  Thesis outline  28  1.2  1.3 1.4  Chapter 2. 2.1  Thermodynamics and Kinetics of Roasting  30  Zinc 2.1.1 2.1.2  Thermodynamics K i n e t i c s of zinc sulfide o x i d a t i o n  30 30 35  2.1.3  F l u i d i z e d bed experimental studies  47  2.2  Iron  2.3 2.4  Lead Cadmium  .•  47 .'  iii  51 55  Table of  Contents  2.5 2.6 2.7  Copper Water Effect of roasting conditions on stable phases  57 59 60  2.8 2.9  Gas phase reactions L o w - m e l t i n g - p o i n t phases d u r i n g roasting 2.9.1 Phase diagrams - p r o d u c t t y p e 2.9.2 P h a s e diagrams - reactant t y p e  65 69 70 71  2.9.3  78  2.10  P h a s e diagrams - reacting type  Conclusions and recommendations  Chapter 3.  81  Experimental Methods  83  3.1  E x p e r i m e n t a l pilot plant  83  3.2  D e s c r i p t i o n of materials 3.2.1 Z i n c concentrates 3.2.2 B e d material: silica sand a n d a l u m i n a 3.2.3 Gases R o a s t i n g experiments: E x p e r i m e n t a l conditions 3.3.1 Experimental program 3.3.2 O p e r a t i n g procedure Sintering tests A n a l y s i s of solid products 3.5.1 C h e m i c a l analyses 3.5.2 S c a n n i n g electron microscopy and X - r a y diffraction  87 87 89 92 92 92 93 96 96 97 97  3.3  3.4 3.5  Chapter 4. 4.1 4.2 4.3  Experimental Results  99  E v o l u t i o n of bed particle size d i s t r i b u t i o n R a t e of bed mass increase Assays a n d mass balances 4.3.1 Conversion and sulfur balance  100 101 103 105  4.3.2 4.3.3  Base cases Effect of superficial gas velocity  107 120  4.3.4 4.3.5 4.3.6  Effect of temperature Effect of inlet oxygen concentration Effect of excess oxygen  125 134 134  4.3.7  Effect of bed m a t e r i a l and size  152  4.4 4.5 4.6  Gas and solid conversions Sintering test for zinc concentrate G r o w t h mechanism i n the l a b o r a t o r y roaster  161 164 166  4.7  A g g l o m e r a t i o n mechanism i n the l a b o r a t o r y roaster  168  Chapter 5. 5.1  Model Development  170  Steady-state fluidized bed reactor model: Gas reaction  171  5.1.1  P h a s e balances  171  5.1.2  G a s mole balances for H- and L-phases  173  5.1.3  Superficial gas velocities and phase volume fractions  175  5.1.4  E x p a n d e d bed height  176  iv  TabJe of  5.2  5.3  Contents  5.1.5  G a s conversion a n d average gas compositions  176  5.1.6 5.1.7  M i n i m u m fluidization velocity B u b b l i n g fluidized bed  177 178  5.1.8 Slugging fluidized bed 5.1.9 T r a n s i t i o n from b u b b l i n g to slugging Steady-state fluidized bed reactor m o d e l : R e a c t i o n of solids 5.2.1 M i x i n g of solids w i t h i n the fluidized bed 5.2.2 S o l i d residence times 5.2.3 Single-particle reaction m o d e l 5.2.4 C o n v e r s i o n of solids Solution method  Chapter 6. 6.1  Modelling Results  180 182 188 189 191 193 199 200  203  Unsteady-state single particle reaction  204  6.1.1 M o d e l parameters 6.1.2 T i m e for complete reaction 6.1.3 P a r t i c l e temperatures 6.1.4 G a s concentrations 6.1.5 Effectiveness factors Generalized slugging-bubbling m o d e l ( G S B M ) 6.2.1 C o m p a r i s o n w i t h previous models 6.2.2 Effect of effective gas reaction rate constant 6.2.3 Effect of reactor diameter  204 206 206 209 212 215 215 219 220  6.3  F l u i d i z e d bed roaster m o d e l 6.3.1 M o d e l parameters 6.3.2 F i t of l a b o r a t o r y experiments 6.3.3 Roaster sensitivity analysis 6.3.4 M o d e l - b a s e d predominance-like diagrams  225 225 227 231 255  6.4  Discussion of key coating and agglomeration results  258  6.5  Implications for the i n d u s t r i a l process 6.5.1 Effect of uneven spatial d i s t r i b u t i o n of feed m a t e r i a l  261 262  6.5.2 6.5.3 6.5.4  262 263 264  6.2  Chapter 7.  M e a n bed particle size too large M e a n bed particle size too s m a l l R e c o m m e n d a t i o n s w i t h respect to i n d u s t r i a l roasting  Conclusions and Recommendations  266  7.1 7.2  M a j o r contributions K e y conclusions  266 267  7.3 7.4  Secondary conclusions R e c o m m e n d e d future work  268 269  7.5  R e v i e w of objectives  273  Bibliography Appendix A . A.l  276 Instrument Calibration  293  Thermocouples  293  v  Table of  Contents  A.2  G a s flowmeters (rotameters) A . 2 . 1 Development of general rotameter equation A . 2.2 R o t a m e t e r c a l i b r a t i o n fit  A.3  Pressure transducers  295  A.4 A. 5  Solids feedrate Solids mass flowmeter  296 299  Appendix B. B. l  B.2 B. 3  Laboratory Roaster Procedures  C.8  300  Experimental run B. l . l Startup B . 1 . 2 Feeder startup  300 300 301  B.1.3 B.l.4 B.l.5  301 301 302  Feeder refill : Solid s a m p l i n g - B e d samples S o l i d s a m p l i n g - C a r r y o v e r samples  B . l . 6 Gas sampling B . l . 7 S c r u b b e r switchover (To be done every hour) B . l . 8 Shutdown B . l.9 Emergency shutdown Disassembly a n d cleaning Reassembly  Appendix C. Data Acquisition Software C l C. 2 C.3 C.4 C.5 C.6 C.7  293 294 295  302 303 303 303 303 306  307  D a t a acquisition Database Thermocouples Pressure transducers O x y g e n sensors G a s analyzer Controllers  307 307 308 308 308 308 308  C . 7.1 C.7.2  308 309  T e m p e r a t u r e Controllers Feeder C o n t r o l l e r  Solenoid Valves  Appendix D.  309  Experimental Apparatus Schematics  Appendix E . Sulfur Dioxide Scrubbers  310 320  E.l  O v e r a l l s c r u b b i n g reactions  320  E.2  S t r e n g t h of the caustic solution E.2.1 Solubilities of the various c o m p o u n d s E.2.2 Solubilities expressed as caustic concentration  321 321 321  E. 3  S c r u b b i n g efficiency  322  Appendix F. F. l  Detailed Experimental Results  A s s a y from independent l a b o r a t o r y  324 324  vi  List of Tables 1.1 1.2  T y p e s of fluidized bed roasters used i n the zinc i n d u s t r y P u b l i s h e d c o m p o s i t i o n of some zinc sulfide concentrates a n d pure zinc sulfide  11 16  2.1  T h e o r e t i c a l density a n d molar volume of zinc species  31  2.2  S u m m a r y of zinc sulfide o x i d a t i o n kinetic studies  38  2.3 2.4  Details of e x p e r i m e n t a l a n d pilot-scale roasters M e l t i n g temperature of various phases  48 80  3.1  Weight c o m p o s i t i o n of zinc concentrates  87  3.2  P a r t i c l e size d i s t r i b u t i o n of zinc concentrates  90  3.3 3.4 3.5 3.6 3.7 3.8  Weight c o m p o s i t i o n of i n i t i a l bed materials P a r t i c l e size d i s t r i b u t i o n of i n i t i a l bed materials C o m p o s i t i o n of gases Range of experimental variables S u m m a r y of experimental conditions for each experiment M e t h o d s used for chemical analysis of solid samples  90 91 92 94 94 97  4.1 4.2 4.3 4.4 4.5  Correspondence between r u n numbers and parameters studied S u m m a r y of total masses of samples used for overall mass balance Results of overall mass balance X - r a y spectroscopy analysis of particle coatings obtained after roasting at 9 7 5 ° C . . . . O v e r a l l p r o p o r t i o n of carryover as a function of excess oxygen, inlet oxygen concent r a t i o n a n d i n i t i a l bed particle size  100 105 106 130 136  5.1 5.2 5.3  V o l u m e a n d gas flow balances Correlations for bubble sizes Values of the surface integral (I) for various slug length to diameter r a t i o (L/D)  173 179 . . . . 182  5.4 5.5  S u m m a r y of equations describing the t r a n s i t i o n from b u b b l i n g to slugging fluidization 189 S u m m a r y of the b u b b l i n g , slugging and generalized m o d e l parameters 190  6.1 6.2  S u m m a r y of single particle m o d e l parameters a n d their values M o d e l parameters used to compare the generalized b u b b l i n g slugging m o d e l to the earlier slugging and b u b b l i n g models  205  6.3  S u m m a r y of the m o d e l parameters and their values  226  6.4 6.5  S u m m a r y of fitted m o d e l parameters and their values Parameter ranges for sensitivity analysis  229 232  6.6  C h a r a c t e r i s t i c solids m i x i n g times for l a b o r a t o r y a n d i n d u s t r i a l roasters  249  A.l  S t a n d a r d type K thermocouple p o l y n o m i a l coefficients  293  A.2  Rotameter description  A.3  Rotameter p o l y n o m i a l c a l i b r a t i o n  A.4  Pressure transducers - p o l y n o m i a l  297  F.l F.2  A s s a y of zinc concentrates I C P A s s a y of zinc concentrates, sands and some e x p e r i m e n t a l samples  324 325  216  296 fits  vii  297  List of Figures 1.1 1.2 1.3 1.4 1.5  Improved electrolytic zinc process Wedge roasting furnace F l a s h roasting furnace T y p i c a l fluidized bed roaster and associated streams Gas-solid flow regimes  4 7 8 12 15  2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19  Z n - 0 - S 0 P r e d o m i n a n c e diagram at 8 5 0 ° C Z n - 0 2-S O 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 Z n - 0 2-S O P r e d o m i n a n c e d i a g r a m at 1050°C Intrinsic reaction rate of various kinetic studies Representation of the grain m o d e l F e O - F e 0 phase d i a g r a m • F e - 0 - S 0 P r e d o m i n a n c e d i a g r a m at 8 5 0 ° C F e - 0 - S 0 P r e d o m i n a n c e diagram at 9 5 0 ° C F e - 0 2-S 0 P r e d o m i n a n c e diagram at 1050°C P b - 0 - S 0 P r e d o m i n a n c e diagram at 8 5 0 ° C P b - 0 - S 0 P r e d o m i n a n c e d i a g r a m at 9 5 0 ° C P b - 0 - S 0 P r e d o m i n a n c e d i a g r a m at 1050°C C d - 0 2-S O P r e d o m i n a n c e d i a g r a m at 8 5 0 ° C C d - 0 2-S O 2 P r e d o m i n a n c e diagram at 9 5 0 ° C C d - 0 2-S O P r e d o m i n a n c e d i a g r a m at 1050°C C u - 0 - S 0 P r e d o m i n a n c e d i a g r a m at 8 5 0 ° C C u - 0 2-S 0 P r e d o m i n a n c e diagram at 9 5 0 ° C C u - 0 2 - S O P r e d o m i n a n c e diagram at 1050°C Excess oxygen - Temperature predominance d i a g r a m for gaseous feed of air (21% O2)  34 34 35 42 45 49 49 50 50 52 53 54 55 56 56 57 58 58 62  2  2  2  2  3  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2.20 Gas concentrations for excess oxygen - temperature predominance d i a g r a m for gaseous feed of air (21% 0 ) Z i n c a n d c a d m i u m p a r t i a l pressures L e a d p a r t i a l pressures Z n O - S i O phase d i a g r a m P b O - P b S 0 phase d i a g r a m P b O - S i 0 phase d i a g r a m P b O - A l 0 phase d i a g r a m P b O - Z n O phase d i a g r a m P b O - F e 0 3 phase diagram F e S - Z n S phase d i a g r a m P b S - Z n S phase d i a g r a m C u 2 S - Z n S phase d i a g r a m F e S - P b S phase d i a g r a m C u S - P b S phase d i a g r a m Q u a t e r n a r y Z n S - F e S - P b S - C u 2 S phase d i a g r a m R e g i o n of the F e - S - 0 ternary phase diagram F e O - F e S - C u 2 S ternary phase d i a g r a m 2  2.21 2.22 2.23 2.24 2.25 2.26 2.27 2.28 2.29 2.30 2.31 2.32 2.33 2.34 2.35 2.36  2  4  2  2  3  2  2  viii  :  63 67 68 72 72 73 73 74 74 75 75 76 76 77 77 79 79  List  of Figures  3.1 3.2 3.3  Experimental apparatus Particle size distribution of zinc concentrates Particle size distribution of initial bed materials  4.1 4.2 4.3  Evolution of the average particle size for various experimental conditions 102 Rate of bed mass increase for various experimental conditions 104 Assays of bed and carryover samples, masses of feed, bed samples, carry-over and bed for run 10, base case 1 109 Variation in proportion of key elements based on mass balance for base cases 110 Assays of different bed particle size fractions for four base case runs Ill Distribution of mass of key elements with bed particle size fractions for four base case runs 112 Comparison of assays of carryover of base cases 113 SEM micrograph for product particles of run 10, +40 mesh 115 SEM micrograph for product particles of run 10, +70 mesh 115 SEM micrograph for product particles of run 10, +140 mesh 116 SEM micrograph for product particles of run 10, +230 mesh 116 SEM micrograph for product particles of run 10, -230 mesh (pan) 117 SEM micrograph for product particles of run 10, -230 mesh (pan), image of agglomerated particle : 117 SEM micrograph for product particles of run 10, +140 mesh, image of coated particle 118 SEM micrograph for product particles of run 10, carryover 118 SEM micrograph for product particles of run 10,. carryover, image of partially reacted particle 119 Variation in proportion of key elements based on mass balance for different superficial gas velocities 121 Effect of superficial gas velocity on assays for different bed particle size fractions. . . . 122 Effect of superficial gas velocity on distribution of mass of key elements with bed particle size fraction 123 Comparison of assays of carryover for different superficial gas velocities 124 Variation in proportion of key elements based on mass balance for different superficial temperatures 126 Effect of temperature on assays of different bed particle size fractions 127 Effect of temperature on distribution of mass of key elements with bed particle size fractions 128 Comparison of assays of carryover for different temperatures 129 SEM micrograph for product particles of run 16, +70 mesh 131 SEM micrograph for product particles of run 16, +70 mesh, image of particle coatingl31 SEM micrograph for product particles of run 16, +140 mesh 132 SEM micrograph for product particles of run 16, +230 mesh 132 SEM micrograph for product particles of run 16, -230 mesh (pan) 133 SEM micrograph for product particles of run 16, Carryover 133 Variation in proportion of key elements based on mass balance for different inlet oxygen concentrations 135 Effect of oxygen concentration on assays of different bed particle size fractions 136  4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.16 4.17 4.18 4.19 4.20 4.21 4.22 4.23 4.24 4.25 4.26 4.27 4.28 4.29 4.30 4.31 4.32  ix  84 89 91  List of  Figures  4.33 Effect of oxygen concentration on d i s t r i b u t i o n of mass of key elements w i t h b e d particle size fraction  137  4.34 C o m p a r i s o n of assays of carryover for different inlet oxygen concentrations  138  4.35 V a r i a t i o n i n p r o p o r t i o n of key elements based on mass balance for different excess oxygen a n d 50 mesh silica sand  140  4.36 Effect of excess oxygen on assays for different b e d particle size fractions w i t h 50 mesh silica sand 4.37 Effect of excess oxygen on d i s t r i b u t i o n of mass of key elements w i t h b e d particle size fraction for 50 mesh silica sand 4.38 C o m p a r i s o n of carryover assays for different excess oxygen for 50 mesh silica s a n d . . . 4.39 V a r i a t i o n i n p r o p o r t i o n of key elements based on mass balance for different excess oxygen a n d 125 mesh s i l i c a sand 4.40 Effect of excess oxygen on assays of different bed particle size fractions for 125 mesh silica sand 4.41 Effect of excess oxygen on d i s t r i b u t i o n of mass of key elements w i t h b e d p a r t i c l e size fraction for 125 mesh silica sand 4.42 C o m p a r i s o n of carryover assays for different excess oxygen for 125 mesh silica s a n d . . 4.43 Effect of excess oxygen and oxygen enrichment on assays of b e d particle of different size fractions w i t h 50 mesh silica sand 4.44 Effect of excess oxygen and oxygen enrichment on d i s t r i b u t i o n of mass of key elements w i t h b e d particle size for 50 mesh silica sand 4.45 Effect of excess oxygen and oxygen enrichment on assays of different b e d particle sizes for 125 mesh silica sand 4.46 Effect of excess oxygen and oxygen enrichment on d i s t r i b u t i o n of mass of key elements w i t h b e d particle size for 125 mesh silica sand 4.47 Effect of b e d m a t e r i a l on assays for different b e d particle size fractions 4.48 Effect of b e d m a t e r i a l on d i s t r i b u t i o n of mass of key elements w i t h b e d particle size fraction 4.49 S E M m i c r o g r a p h for p r o d u c t particles of r u n 8, +16 mesh 4.50 S E M m i c r o g r a p h for p r o d u c t particles of r u n 8, +40 mesh 4.51 S E M m i c r o g r a p h for p r o d u c t particles of r u n 8, +70 mesh 4.52 S E M m i c r o g r a p h for p r o d u c t particles of r u n 8, +140 mesh 4.53 S E M m i c r o g r a p h for p r o d u c t particles of r u n 8, +230 mesh 4.54 S E M m i c r o g r a p h for p r o d u c t particles of r u n 8, -230 mesh (pan) 4.55 S E M m i c r o g r a p h for p r o d u c t particles of r u n 24, +40 mesh 4.56 S E M m i c r o g r a p h for p r o d u c t particles of r u n 24, +70 mesh  141 142 143 144 145 146 147 148 149 150 151 153 154 155 155 156 156 157 157 158 158  4.57 S E M m i c r o g r a p h for p r o d u c t particles of r u n 24, +140 mesh  159  4.58 S E M m i c r o g r a p h for p r o d u c t particles of r u n 24, +230 mesh  159  4.59 S E M m i c r o g r a p h for p r o d u c t particles of r u n 24, -230 mesh (pan) 4.60 S E M m i c r o g r a p h for p r o d u c t particles of r u n 24, carryover 4.61 Freeboard oxygen concentration as a function of feedrate  160 160 162  4.62 Solids conversion as a function of feedrate 4.63 In-bed oxygen sensor mean o u t p u t as a function of feedrate 4.64 S E M m i c r o g r a p h for dried, unsintered, zinc concentrate 1(b), Secondary electrons image  162 163  x  165  L i s t of  Figures  4.65 S E M m i c r o g r a p h for dried, zinc concentrate 1(b) sintered for 1 hour at 9 5 0 ° C , Secondary electrons image  165  5.1  Schematic of two-phase fluidized bed m o d e l  172  5.2  B u b b l e rising velocity i n water  185  5.3 5.4  P r o b a b i l i t y of slugging C o n c e n t r a t i o n and temperature profiles of a single reacting particle  188 195  6.1  Unsteady-state particle model: T i m e to complete reaction i n seconds  206  6.2 6.3  Unsteady-state particle model: Dimensionless temperatures Unsteady-state particle model: Dimensionless gas concentrations. K i n e t i c s from F u k u n a k a et al Unsteady-state particle model: Dimensionless gas concentrations. F i t t e d K i n e t i c s . . . Unsteady-state particle model: Effectiveness factors Unsteady-state particle model: Heat enhancement factors C o m p a r i s o n of the G S B M m o d e l to the H o v m a n d slugging m o d e l a n d to the G r a c e 2-phase a n d O r c u t t b u b b l i n g models C o m p a r i s o n of the conversions calculated using G S B M m o d e l a n d its l i m i t i n g models as a function of gas reaction rate constant for different bed diameters C o m p a r i s o n of the conversions calculated using G S B M m o d e l a n d its l i m i t i n g cases as a function of bed diameter for different gas reaction rate constants C o m p a r i s o n of the variable m o d e l parameters and o u t p u t for the G S B M m o d e l a n d its l i m i t i n g models as a function of the vertical position i n the b e d for k = 0 . 1 s , D = 0.2 m C o m p a r i s o n of the variable m o d e l parameters a n d o u t p u t for the G S B M m o d e l a n d its l i m i t i n g models as a function of the vertical p o s i t i o n i n the bed for k = 1 0 s , D = 0.2 m , Gas-solid reactor m o d e l fit of the experimental conversion d a t a Gas-solid reactor m o d e l predictions of the freeboard oxygen concentration F i t t e d intrinsic reaction rate compared w i t h those of various k i n e t i c studies Effect of process parameters, varied one at a time, on the predicted particle-averaged oxygen concentrations i n the l a b o r a t o r y roaster for the fitted kinetics a n d a 150 pm average bed particle size Effect of process parameters, varied one at a time, on the predicted particle-averaged oxygen concentrations i n the laboratory roaster for the F u k u n a k a et al. kinetics a n d a 150 fim average bed particle size 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 a n d a 65 pm average bed particle size  207  6.4 6.5 6.6 6.7 6.8 6.9 6.10  210 211 212 214 217 218 221  - 1  r  6.11  223  - 1  r  6.12 6.13 6.14 6.15  6.16  6.17  224 229 230 230  233  234  235  6.18 Effect of process parameters, varied one at a time, on the predicted particle-averaged oxygen concentrations i n the laboratory roaster for the F u k u n a k a et al. kinetics and a 65 fim average bed particle size 6.19 Effect of process parameters, varied one at a time, on the predicted particle-averaged oxygen concentrations i n the i n d u s t r i a l roaster for the fitted kinetics a n d a 150 pm average bed particle size :  xi  236  238  L i s t of  Figures  6.20 Effect of process parameters, varied one at a time, on the predicted particle-averaged oxygen concentrations i n the i n d u s t r i a l roaster for the F u k u n a k a et al. kinetics and a 150 jj,m average b e d particle size 6.21 Effect of process parameters, varied one at a time, on the predicted particle-averaged oxygen concentrations i n the i n d u s t r i a l roaster for the fitted kinetics a n d a 65 / i m average bed particle size  239  240  6.22 Effect of process parameters, varied one at a time, on the predicted particle-averaged oxygen concentrations i n the i n d u s t r i a l roaster for the F u k u n a k a et al. kinetics a n d a 65 jLtm average b e d particle size 241 6.23 Effect of process parameters varied one at a time, on the p r e d i c t e d reaction t i m e of particles i n the H-phase of the l a b o r a t o r y 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 i m e of particles i n the H-phase of the l a b o r a t o r y roaster for the F u k u n a k a et al. kinetics a n d a 150 [im average bed particle size 246 6.25 Effect of process parameters varied one at a time, on the predicted reaction t i m e of particles i n the H-phase of the l a b o r a t o r y roaster for the fitted kinetics a n d 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 i m e of particles i n the H-phase of the l a b o r a t o r y roaster for the F u k u n a k a et al. kinetics and a 65 /zm average b e d particle size 248 6.27 Effect of process parameters varied one at a time, on the predicted reaction t i m e of particles i n the H-phase of the i n d u s t r i a l roaster for the fitted kinetics a n d a 150 fim average bed particle size 251 6.28 Effect of process parameters varied one at a time, on the p r e d i c t e d reaction t i m e of particles i n the H-phase of the i n d u s t r i a l roaster for the F u k u n a k a 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 i m e of particles i n the H-phase of the i n d u s t r i a l roaster for the fitted kinetics a n d a 65 /jm average bed particle size 253 6.30 Effect of process parameters varied one at a time, on the predicted reaction t i m e of particles i n the H-phase of the i n d u s t r i a l roaster for the F u k u n a k a 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 i a g r a m for the e x p e r i m e n t a l fluidized bed 256 6.32 G a s concentrations for excess oxygen - temperature G S B M model-based predominancelike d i a g r a m for the experimental fluidized bed 257 A.l  Z i n c concentrate automatic feedrate feedback control  D.l  E x p e r i m e n t a l apparatus - Reactor  311  D.2  E x p e r i m e n t a l apparatus - F l u i d connections  312  D.3 D.4 D.5  E x p e r i m e n t a l apparatus - Pressure connections E x p e r i m e n t a l apparatus - Power connections F a b r i c a t i o n d r a w i n g of preheater section  313 314 315  D.6  F a b r i c a t i o n d r a w i n g of roaster section  316  xii  298  List of  Figures  D.7  F a b r i c a t i o n d r a w i n g of solid samplers  317  D.8  L a y o u t of d i s t r i b u t o r plate holes  318  D. 9  C o p p e r gaskets  319  E. l  S o l u b i l i t y of compounds p r o d u c e d d u r i n g SO2 s c r u b b i n g using N a O H solutions  323  E.2  N a O H concentration to reach m a x i m u m solubility of the c o m p o u n d s p r o d u c e d during SO2 s c r u b b i n g  323  xiii  Nomenclature L e t t e r s  A  B e d cross-sectional area [m ]  Ad  D i s t r i b u t o r area per orifice [m ]  ai  Interphase mass transfer exchange area [ m ]  Ar  A r c h i m e d e s number ( A r = df  A  Dimensionless group (A  2  2  _ 1  sp  sp  CD i e  = -  = E^sZ^Si^.) [_] f c^f )(section  CAo  5.2.3) [-]  pc  A  P r o d u c t of the t o t a l gas concentration (sum of a l l gaseous species) times the gas diffusivity of i (section 5.2.3) [ m o l / ( m s)]  Cf/j  M o l a r concentration of species i i n H-phase [ m o l / m ]  d  Particle-averaged molar concentration for species i i n entire b e d [ m o l / m ]  3  3  Cij  Inlet molar concentration of species i [ m o l / m ]  Cji  C o n c e n t r a t i o n of gaseous species i , j = c : core, o: b u l k gas phase, s: surface (section  3  n  5.2.3) [mol / m ] 3  Cji  Particle-averaged molar concentration for species i i n phase j [ m o l / m ]  Cj_,i  M o l a r concentration of species i i n L-phase [ m o l / m ]  C  Heat capacity of unreacted core (section 5.2.3) [ J / ( k g K ) ]  C  V o l u m e t r i c heat capacity of p r o d u c t layer (section 5.2.3) [ J / ( m K ) ]  Cs  C o n c e n t r a t i o n of solid reactant (section 5.2.3) [mol / m ]  CT  T o t a l gaseous molar concentration (CT = 7 ^ ) [ m o l / m ]  D  R e a c t o r diameter [m]  DDQ  Lower b o u n d of bubbling-slugging t r a n s i t i o n interval [-]  DD\  U p p e r b o u n d of bubbling-slugging t r a n s i t i o n i n t e r v a l [-]  D  Effective bubble diameter [m]  pc  3  3  3  pe  e  3  3  D fi  I n i t i a l effective bubble diameter [m]  D ATo  Effective gas diffusivity at temperature To for gaseous reactant A [m /s]  D GTo  Effective gas diffusivity at t e m p e r a t u r e To for gaseous p r o d u c t G [m /s]  D ,oo  M a x i m u m bubble diameter due to coalescence a n d g r o w t h [m]  e  e  e  e  2  2  xiv  Nomenclature D max  M a x i m u m effective b u b b l e diameter [m]  D  G a s diffusivity  dp  P a r t i c l e surface to volume mean diameter [m]  dpi  Average diameter of each size fractions ( C h a p t e r 3) [m]  dp*  Dimensionless particle diameter (d ( ^ ^2 ^ ^j  Dradial  R a d i a l diffusion coefficient of solids i n a fluidized b e d [m /s]  d  P a r t i c l e volume mean diameter ( C h a p t e r 3) [m]  E  B e d expansion [m/m]  e>  g  v  [m /s] 2  p  p  Pv  P  9  (  2  E  A c t i v a t i o n energy [J/mol]  Emax  M a x i m u m slugging b e d expansion [m/m]  Excesso2  S t o i c h i o m e t r i c excess of oxygen [-]  /  Solids mean residence t i m e factor [-]  Fcarryover  Solids flowrate i n carryover [kg/s]  FFeed  Solids flowrate i n feed [kg/s]  FHI  M o l a r flowrate of species i i n H-phase [mol/s]  Ff{i,in  Inlet m o l a r flowrate of species  FHT  T o t a l molar flowrate i n H-phase [mol/s]  Fu  M o l a r flowrate of species i i n L-phase [mol/s]  Fhi,in  Inlet molar flowrate of species  FIT  T o t a l m o l a r flowrate i n L-phase [mol/s]  Foverflow  Solids flowrate i n overflow [kg/s]  Fr  F r o u d e number (Fr = ^ g )  f  S l u g shape factor  a  s  ^ ) [-]  i i n H-phase [mol/s]  i i n L-phase [mol/s]  [-]  [m /m ] 3  3  FT  T o t a l molar flowrate i n reactor [mol/s]  G  Dimensionless group (G = -  g  A c c e l e r a t i o n due to gravity (9.81) [m/s ]  H  E x p a n d e d b e d height [m]  ^ _ ^° p  i y  c  f / )  ) ( s e c t i o n 5.2.3) [-] 2  xv  Nomenclature  h  Convective heat transfer coefficient (section 5.2.3) [ J / ( m  c  Hf  B e d height at m i n i m u m  h  R a d i a t i o n a l heat transfer coefficient (section 5.2.3) [ J / ( m  /  S l u g surface integral (section 5.1.8) [-]  J  A x i a l solids flux due to bubbles [kg m  k  Effective t h e r m a l c o n d u c t i v i t y of p r o d u c t layer (section 5.2.3) [ J / ( m s K ) ]  kin  Interphase mass transfer coefficient  k  G a s - p a r t i c l e mass transfer coefficient  m  r  e  m  fluidization  K s)]  2  [m]  -  2  K  4  s)]  s ]  2  _ 1  [m/s] [m/s]  k  G a s reaction rate constant  k°  P r e - e x p o n e n t i a l constant for reaction rate constant (section 5.2.3) [m/s (depends  r  [s ] _1  on reaction orders)] k (Tc) s  R e a c t i o n rate constant at temperature T  c  (section 5.2.3) [m/s (depends on reac-  t i o n orders)] L  S l u g length (section 5.1.8) [m]  m  R e a c t i o n order w i t h respect to solid reactant S (section 5.2.3) [-]  Mbed  B e d mass [kg]  ^Concentrate  M a s s of concentrate equivalent to one mole of z i n c sulfide [g concentrate / m o l ZnS]  Mz s  M o l a r weight of zinc sulfide [g Z n S / m o l Z n S ]  n  R e a c t i o n order w i t h respect to gaseous reactant A (section 5.2.3) [-]  n  no  N u m b e r of moles of oxygen [moles]  2  Nu  c  M o d i f i e d Nusselt n u m b e r for convection ( N u = Rh /k )(section  Nu  r  M o d i f i e d Nusselt n u m b e r for r a d i a t i o n ( N u = Rh T^/k )(section  c  r  nz s  N u m b e r of moles of zinc sulfide [moles]  Pbubbiing  P r o b a b i l i t y of b u b b l i n g [-]  Pslugging  P r o b a b i l i t y of slugging [-]  Pstream  P a r t i c l e size d i s t r i b u t i o n function of stream [-]  PT  T o t a l reactor pressure [Pa]  R  G a s constant, 8.314 [ J / (mol K ) ]  n  xvi  c  r  e  e  5.2.3) [-] 5.2.3) [-]  Nomenclature  rA  R e a c t i o n rate of gas A (section 5.2.3) [ m o l / ( m  rc  R a d i u s of core (section 5.2.3) [m]  He f  R e y n o l d s n u m b e r at m i n i m u m f l u i d i z a t i o n  J  R a t e of reaction of oxygen [mol m ~  Hp  P a r t i c l e radius [m]  r$  R e a c t i o n rate of solid S (section 5.2.3) [ m o l / ( m  Sh  M o d i f i e d S h e r w o o d n u m b e r (Sh = $^r)  T  R e a c t o r t e m p e r a t u r e [K]  T  S l u g to slug distance (tail-to-nose)  Tc  C o r e t e m p e r a t u r e (section 5.2.3) [K]  t  T i m e for complete reaction of solid particle [s]  m  cr  (Re=^[£)  - 1  R a d i a l m i x i n g t i m e (lateral m i x i n g time) [s]  T$  Surface t e m p e r a t u r e (section 5.2.3) [K]  ^turnover  Turnover time (axial m i x i n g time) [s]  Tw  W a l l temperature (section 5.2.3) [K]  U  R e a c t o r superficial gas velocity [m/s]  Ui  B u b b l e rise velocity [m/s]  Uboo  Isolated bubble rise velocity [m/s]  U  Dimensionless core temperature (U  UH  H-phase superficial gas velocity [m/s]  UL  L-phase superficial gas velocity [m/s]  Uf  Superficial gas velocity at m i n i m u m  Ums  M i n i m u m slugging velocity [m/s]  U  Dimensionless surface temperature (U  c  s  = ^f)(section 5.2.3) [-]  fluidization  s  U  s)]  (section 5.1.8) [m]  tradial  m  2  [-]  I n i t i a l t e m p e r a t u r e (section 5.2.3) [K]  c  [-]  s ]  2  T  0  s)]  2  [m/s]  = | f ) ( s e c t i o n 5.2.3) [-]  S l u g velocity [m/s]  s  U  S l u g velocity of a single slug i n a b e d at m i n i m u m f l u i d i z a t i o n [ m /  U*  T e r m i n a l velocity calculated for spherical particles of 2.7d [m/s]  soo  p  xvii  Nomenclature  (  p  XJt*  Dimensionless t e r m i n a l velocity (Ut (  l  U  V o i d (bubble or slug) rise velocity [m/s]  v  \  2  1  /  3  ) )  p  g  )H  U  Free v o i d (bubble or slug) velocity [m/s]  U  Dimensionless w a l l temperature (U  X  C o n v e r s i o n of particle (1 - (%)  XAO  M o l a r fraction i n b u l k gas phase for gaseous reactant A [-]  X  Average conversion of mono-sized particles [-]  X  Average conversion of a wide size d i s t r i b u t i o n of particles [-]  XQO  M o l a r fraction i n b u l k gas phase for gaseous p r o d u c t G [-]  Xi  C o n v e r s i o n of component i [-]  Xi  G a s mole fraction (section 5.2.3) [-]  Xi  M a s s fraction of each size fractions ( C h a p t e r 3) [-]  Y  R a t i o of volumetric flowrate of bubbles to the excess gas flowrate [-]  z  V e r t i c a l p o s i t i o n i n bed [m]  voo  w  = ^ ) (section 5.2.3) [-]  w  = 1 - ^ ( s e c t i o n 5.2.3) [-]  3  Greek Letters P  C o n s t a n t to account for change i n mass due to reaction [-]  j3  Dimensionless group (p =  Pd  F r a c t i o n of solids carried up by a bubble w i t h i n its drift [-]  P  F r a c t i o n of solids carried u p by a bubble w i t h i n its wake [-]  AF02  N u m b e r of moles of oxygen reacted per unit time [moles/sec]  L\v  Difference i n gas stoichiometric coefficient due to reaction [-]  Az  F i n i t e height i n bed (control volume) [m]  ef  B e d voidage at incipient fluidization [ m / m ]  £fi  H-phase gas volume fraction [ m / m ]  €L  L-phase gas volume fraction [ m / m ]  Vs  Effectiveness factor (section 5.2.3) [-]  K  E l u t r i a t i o n velocity constant [ s ]  w  m  E~ )(section  CAoDcA T  5.2.3) [-]  AH)R  k e  3  3  3  _1  xviii  3  3  3  Nomenclature  [x  G a s viscosity [Pa s]  VA  S t o i c h i o m e t r i c 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  S t o i c h i o m e t r i c coefficient for c o m p o u n d i [moles i / moles reaction]  UJ  C  Dimensionless core molar fraction of component i (cu — ^ ) ( s e c t i o n 5.2.3) [-] c  LO  Dimensionless surface molar fraction of component i (UJ = ^f-)(section  <f>H  H-phase solids volume fraction  [m /m ]  4>r,  L - p h a s e solids v o l u m e fraction  [m /m ]  4>  T h i e l e m o d u l u s of solid particle (<f> = - ^ ^ g " ^ "  ipH  H-phase volume fraction  [m /m ]  tpL  L-phase v o l u m e fraction  [m /m ]  AH  Heat of reaction (section 5.2.3) [J/mol]  pc  C o r e density (section 5.2.3) [ k g / m ]  p  G a s density  S  s  g  S  3  3  3  3  a  3  3  1  ^ )  [-]  3  3  3  [kg/m ] 3  p  P a r t i c l e density  r  Average residence t i m e of solid particles i n fluidized b e d [s]  6  Dimensionless time {6 =  6  Dimensionless time for complete reaction of solid particle [-]  p  cr  £  c  [kg/m ] 3  fc C^C™" i/i? )(section 1  s(ro)  p  5.2.3) [-]  Dimensionless p o s i t i o n of core ( £ = ^ ) ( s e c t i o n 5.2.3) [-] c  xix  5.2.3) [-]  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 n a m e d the roast-leach-electrowin process, roasting of zinc sulfide concentrates is the most c o m m o n first step i n the manufacture of zinc. I n the last two decades, direct leaching of zinc concentrates i n autoclaves (pressure leaching) has been used successfully as an alternative to roasting. P r i o r to the development of the electrolytic process, most, if not a l l zinc was p r o d u c e d b y retort d i s t i l l a t i o n . Today, the e l e c t r o l y t i c process accounts for 80% of zinc p r o d u c t i o n w i t h the rest from p y r o m e t a l l u r g i c a l processes, such as the blast furnace, electrothermic a n d retort processes. P r i o r to the electrolytic zinc process, zinc was p r o d u c e d for centuries b y the d i s t i l l a t i o n of a m i x t u r e of zinc oxide ore a n d coal i n retorts of various designs [1]. A m i x t u r e of zinc oxide and coal was heated above 1000°C i n a coal-fired oven to produce zinc vapour, w h i c h was then condensed a n d collected. In 1738, W i l l i a m C h a m p i o n patented the process i n E n g l a n d , a n d by 1743, established a smelter i n B r i s t o l , U . K . [1]. B y c o m b i n i n g oriental knowledge a n d western large-scale technology, he brought c o m m e r c i a l zinc p r o d u c t i o n to E u r o p e . T o overcome the shortage of calamine (zinc carbonate), the original source of z i n c oxide, blende (zinc sulfide) was roasted to produce zinc oxide. I n 1758, J o h n 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 i n a coal-fired furnace. T h e C h a m pion d i s t i l l a t i o n process was used u n t i l about 1851. Because the C h a m p i o n process involved cooling a n d w i t h d r a w i n g the crucible a n d the retort after each cycle, the process was labourintensive a n d fuel-inefficient (24 tonnes of coal for each t o n of zinc p r o d u c e d ) . T h e reader is referred elsewhere [2] for a more complete description of the early i n d u s t r i a l p r o d u c t i o n of zinc.  1  Chapter  1.  Introduction  A r o u n d 1818, the development of the horizontal retort process i n B e l g i u m significantly i m proved the d i s t i l l a t i o n process. P l a c e d h o r i z o n t a l l y i n a furnace, retorts c o u l d be charged a n d discharged w i t h o u t cooling. T h e p o p u l a r i t y of the process grew rapidly, a n d by 1880, annual world p r o d u c t i o n was estimated to be more t h a n 200 000 metric tonnes of zinc, m o s t l y from G e r m a n y a n d B e l g i u m [3]. I n 1950, this process still p r o d u c e d as m u c h 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], i n favour of the electrolytic z i n c process. T h e use of retorts for the p r o d u c t i o n of z i n c has been the subject of several publications, and w i l l not be discussed further herein. D u r i n g the development of the electrolytic zinc process, roasting was already c o m m o n l y used to produce the feed m a t e r i a l required for retort d i s t i l l a t i o n . However, the electrolytic process imposes different requirements on roasting.  T o better u n d e r s t a n d the current  requirements  of the roasting process, the electrolytic zinc p r o d u c t i o n process is presented i n a somewhat chronological matter. T h e evolution of i n d u s t r i a l roasters a n d the current fluidized bed roasting technology are then discussed. A brief i n t r o d u c t i o n to fluidized beds a n d a review of the current operating knowledge follows.  T h e chemistry, t h e r m o d y n a m i c s , a n d kinetics of roasting are  reviewed i n the following chapters.  1.1  Electrolytic zinc production  T h e electrolytic p r o d u c t i o n of zinc first described more t h a n 100 years ago i n a 1883 patent by L e o n Letrange [5] is the basis of the m o d e r n electrolytic process ( F i g u r e 1.1). the zinc concentrate,  After roasting  the calcine is generally leached i n two stages: n e u t r a l leach a n d acid  leach. I n the n e u t r a l leach stage, calcine is added to neutralize the s o l u t i o n , while ferric iron is precipitated as ferric hydroxide, a gelatinous substance t h a t renders f i l t r a t i o n very difficult. P r e c i p i t a t i o n of iron i n the neutral stage is the first step i n p u r i f y i n g the zinc sulfate solution. Impurities such as arsenic, antimony, and g e r m a n i u m are co-precipitated w i t h i r o n . T h e solution from the n e u t r a l leach stage is sent to the purification c i r c u i t . S o l i d residue from the n e u t r a l stage passes to the acid leach stage to dissolve the r e m a i n i n g zinc oxide. T h e residue from the acid leach stage contains precipitated iron and any undissolved solids, i n c l u d i n g 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 , +  NH4  +  and K ) , goethite +  (FeOOH) or hematite (Fe203). These crystalline precipitates are easily filterable. These  3  Chapter  1.  Introduction  Zinc Concentrate Air + 0 S0  Roasting  2  2  Sulfuric Acid  Acid Plant  Zinc Calcine Neutral Leaching  Residue  Residue  Hot Acid Leaching  Iron Precipitation  Iron Residue  Cd, Cu, Ni, Co Residue  Purification  ZnS0 Solution 4  Electrolysis  H2SO4  Solution  Zinc Cathodes Melting and Casting  Zinc Dust  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 a n d 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 i n the calcine. • O p t i m i z e the amount of zinc sulfate i n the p r o d u c t .  Some sulfate is desirable i n the  calcine to compensate for sulfate losses d u r i n g leaching, purification, a n d electrowinning. • A t least m a t c h the calcine c o n s u m p t i o n rate of the leaching process.  I n order for the  roasting process to compensate for unscheduled shutdowns, the r o a s t i n g process s h o u l d be able to process zinc concentrate at a faster rate t h a n calcine is c o n s u m e d i n the leaching process. T h e second a n d t h i r d objectives are complementary. T h e i r i m p o r t a n c e depends o n the amount and type of iron i n the concentrate as well as the m e t h o d used to extract z i n c from zinc ferrite. For plants not recovering zinc contained i n zinc ferrite, fulfilling these two objectives is c r i t i c a l to m a x i m i z e 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. F o r more details o n these, the reader m a y consult reviews [9, 10]. T h e roasting of sulfide ores has been practised for centuries. In 1546, i n his b o o k "De R e M e t a l l i c a " Georgius A g r i c o l a presented different furnaces for roasting copper ores. Ores were roasted i n stalls of about 2 by 3 meters. T h e p r o d u c t i v i t y of stall roasting was l i m i t e d (20 tons i n 10 days) a n d the process was very l a b o u r intensive. Heap roasting replaced stall roasting i n large scale p r o d u c t i o n plants. Layers of ore were alternately stacked w i t h layers of w o o d to form a heap. T h e heap was t h e n i g n i t e d . A heap, 15 m wide and 30 m long, could produce 1700 tonnes of sinter i n about 100 days.  R o a s t i n g methods  next progressed from the p r i m i t i v e heap roasting to the h a n d - r a b b l e d reverberatory furnaces such as the Delplace, a n d later to the m e c h a n i c a l l y - r a b b l e d reverbatories such as the Hegeler k i l n a n d 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 z i n c process, roasting of z i n c sulfide p r o d u c e d the r a w m a t e r i a l required for the retort process. T h e 1906 b o o k of Ingalls [12] a n d the 1922 b o o k of H o f m a n [13], b o t h on the m e t a l l u r g y of zinc a n d c a d m i u m , describe several furnaces used for the roasting of blende. T h e first roasters were hand-raked a n d t y p i c a l l y consisted of a flat hearth heated b y a firebox at one end. T h e ore was charged at the flue end a n d moved slowly d o w n t o w a r d the where it was discharged t h r o u g h a d r o p hole i n the hearth.  firebox,  T h e r a k i n g a c t i o n exposed new  surfaces to the atmosphere a n d accelerated the reactions. A number of mechanical roasters were developed before the success of the circular multiplehearth 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 a n d Herreshoff roasters, w h i c h m a i n l y differed i n their mode of maintenance a n d the mechanical a c t i o n of the rabble arms. F i g u r e 1.2 presents a Wedge roasting furnace where ore is fed onto the u p p e r hearth, w h i c h , w a r m e d b y the heat generated i n the roasting operation, serves to d r y the concentrate.  The  rabbles are adjusted to g r a d u a l l y move the ore from the outer edge of the u p p e r h e a r t h toward the centre, a n d t h e n t h r o u g h a drop hole into hearth 1. T h e rakes move the ore across the hearth to a slot near the periphery, t h r o u g h w h i c h it drops into hearth 2. T h u s , i n a zig-zag fashion, the ore progresses t h r o u g h the furnace u n t i l it drops into a car or conveyor beneath the lowest hearth.  1.2.2  Roasting for the zinc electrolytic process  M e c h a n i c a l roasters were developed i n parallel to the electrolytic zinc process. T h e A n a c o n d a C o p p e r C o m p a n y a n d the C o n s o l i d a t e d M i n i n g a n d S m e l t i n g C o m p a n y adopted the Wedge mechanical roaster i n their new electrolytic zinc plants.  6  Chapter  1.  Introduction  OJ b 0 d e / g ft 1 j £ ( m 71 o P 4 r  Furnace shell Refractory lining Rabble arm Rabble blades Central shaft Air nutlet Air inlet Supply air duct Discharse air duct Motor Bevel gears Drying hearth Gas outlet Arm holder Calcine discharge Man-hole Inspection door (hinged) 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  Combustion chamber  b  Drying hearth  e  Collecting hearth  d  Air-cooled rotating shaft  e  Wet concentrate hopper  /  Dried concentrate discharge  g  Ball mill  h  Combustion air fan  & feeder  t  Burner  j  Calcine discharge  k  G a s outlet to acid plant  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 HobokenOverpelt [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 Lurgifluidizedbed roasters. Description of a typical fluidized bed roaster Figure 1.4 shows the principal features of a typical Lurgifluidizedbed 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: T y p e s of fluidized bed roasters used i n the z i n c i n d u s t r y Type 1  Feed S y s t e m Slurry (20-25 w t % H 0 )  Superficial Gas Velocity  Typical Roaster  0.3-0.8 m / s  Dorr-Oliver  0.3-0.8 m / s  Lurgi / Vieille-Montagne  1-3 m / s  BASF Metallurgie Hoboken-Overpelt  2  2  M o i s t concentrate (6-10 w t % H 0 ) 2  3  Pelletized and d r i e d concentrate  area, a new feeding system for the L u r g i roasters has recently been developed a n d is c u r r e n t l y under testing [31]. N o details of the new system have been p u b l i s h e d . T h e very large freeboard helps reduce e l u t r i a t i o n a n d increases the residence t i m e of entrained particles. T h e calcine is recovered i n the b e d overflow a n d by the gas treatment system, u s u a l l y consisting of a waste-heat boiler, cyclones a n d an electrostatic precipitator. T h e b e d overflow height is often adjustable [30, 32].  Some roasters use a bed underflow discharge p o r t to remove oversized,  settled particles [33]. D u r i n g startup, the roaster is preheated u s i n g o i l a n d / o r gas burners that can be inserted t h r o u g h burner ports located on the side of the roaster, just above the bed surface. T h e waste-heat boiler generates steam using heat liberated by the roasting reactions. Heat is recovered b y tubes located i n the fluidized bed, on the wall of the boiler a n d suspended in the boiler. S p r a y i n g water onto the bed or increasing the feed moisture content can be used to cool the bed. T o ensure the safety of the operators, the roaster is u s u a l l y operated under a slight v a c u u m [31]. C o n v e r s i o n of the zinc concentrate, based on residual sulfide sulfur, t y p i c a l l y ranges from 98 to 99.9% [34, 35]. U s i n g i n d u s t r i a l d a t a from a 32 m  2  L u r g i roaster, A v e d e s i a n  [33] calculated the residence time d i s t r i b u t i o n of various particle sizes. T h e m e a n residence time varied between 0.4 and 13.6 hours depending on the particle size. A radioactive tracer test provided e x p e r i m e n t a l verification of the results for the smallest particles [33]. T h e difference i n residence times is due to the fact that fine particles can leave the roaster b y two o u t p u t 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 o n l y a s m a l l volume of the roaster shown i n F i g u r e 1.4. It is, however, responsible for several very i m p o r t a n t phenomena: • D i s t r i b u t i o n of the concentrate feed (Efficient solids m i x i n g ) • H e a t i n g the concentrate particles u n t i l they reach i g n i t i o n ( H i g h heat transfer) • C o o l i n g the particles after they ignite ( H i g h heat transfer) • M a i n t a i n i n g a u n i f o r m bed temperature (Isothermal) • B r i n g i n g oxygen required for reaction to the particles (Efficient gas-solid contacting). Satisfactory control of these phenomena depends on the r e l i a b i l i t y of the fluidized bed to ensure r a p i d m i x i n g and heat transfer between the reacting particles a n d the calcine particles. W i t h o u t the bed to d i s t r i b u t e the concentrate a n d redistribute the heat, particles w o u l d sinter into an unmanageable heap. Therefore, the characteristics a n d the s t a b i l i t y of the b e d are c r i t i c a l to the operation of the roaster. Because the fluidized bed consists almost entirely of calcine particles, these define the behaviour of the bed. F l u i d i z e d b e d roasters have no internal m o v i n g parts.  T h i s reduces maintenance costs a n d  make t h e m mechanically more reliable t h a n m u l t i - h e a r t h or suspension roasters. T h e  fluidized  bed roaster has excellent heat recovery and produces a gas w i t h a h i g h sulfur dioxide content, suitable for acid p r o d u c t i o n while m a i n t a i n i n g good temperature u n i f o r m i t y a n d control. W h i l e there are m a n y advantages,  fluidized  bed roasters also suffer from disadvantages.  Successful  operation relies on the s t a b i l i t y of the fluidized bed, and on particle g r o w t h to reduce carry-over [37]. S m o o t h operation of fluidized bed roasters involves a delicate balance between sufficient growth of the calcine a n d complete reaction of the concentrate, w h i l e m i n i m i z i n g the risk of defluidization. E v e n after 50 years, there is very l i m i t e d knowledge of the mechanisms a n d rates of agglomeration, sintering a n d particle g r o w t h i n fluidized bed roasters. A large p o r t i o n of the literature on roasting focuses on zinc sulfide o x i d a t i o n , a n d the f o r m a t i o n of zinc sulfate a n d zinc ferrite because of their effects on downstream processes. A g g l o m e r a t i o n a n d defluidization 13  Chapter  1.  Introduction  influidizedbed 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. Circulatingfluidizedbed 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 coarsefluidizedparticles 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 lowflowrate,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 offluidization",the amount of gas entering the dense phase is equal to that required for minimumfluidization.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 OR DELAYED BUBBLING  BUBBLING I REGIME  S L U G FLOW  AGGREGATIVE  TURBULENT REGIME |  FAST FLUIDIZATION  PNEUMATIC CONVEYING  V 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 bubblingfluidizationregime.  1.4 Review of operating knowledge Before reviewing some of the issues related to the operation offluidizedbed 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 s u l f i d e c o n c e n t r a t e s a n d p u r e z i n c s u l f i d e ( w t % ) . B l a n k where amount not  specified. Zn  S  Fe  Pb  Cu  C o m i n c o C u s t o m s [44]  55  4.4  3.2  S u l l i v a n [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  K i d d c r e e k [43]  52.48  31.87  9.59  0.56  0.76  0.24  A m e r i c a n Z i n c [46]  54.55  30.65  5.64  0.68  0.58  0.4  G o r d o n s v i l l e [47]  65.7  32  0.53  Pure ZnS  67.1 •  32.9  0  0  0  0  1.4.1  Si0  Cd  2 2.13  0  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 rities.  2  T h e compositions  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 a r e s h o w n i n T a b l e 1.2.  impu-  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 s u l f i d e is a l s o 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 r e u s u a l l y c o m p o s e d o f z i n c s u l f i d e 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 s u l f i d e s , c o p p e r s u l f i d e s , 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 rea c t i o n of each sulfide requires different a m o u n t s of o x y g e n to p r o d u c e different c o m p o u n d s for c o m p l e t e  and  oxidation.  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 sulfide m a t r i x a n d c a n n o t be s e p a r a t e d b y g r i n d i n g and  flotation.  F o r example, z i n c sulfide often contains appreciable a m o u n t s of dissolved i r o n .  T h i s i r o n - r i c h z i n c s u l f i d e 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 present i n the c o n c e n t r a t e has also b e e n f o u n d to be dissolved i n sphalerite  [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 a r e u n l i k e l y t o affect a g g l o m e r a t i o n . lead, copper, arsenic a n d iron have been reported to contribute to agglomeration.  However,  T h e review  o f K r a u s s [48] p r e s e n t s i n d e t a i l t h e effect o f m a n y e l e m e n t s o n t h e e l e c t r o l y t i c z i n c p r o c e s s .  16  Chapter 1. Introduction  1.4.2  v .  "' '•  Feed: Gases  T h e fluidizing gas, air or oxygen-enriched air, enters the roaster t h r o u g h the d i s t r i b u t o r a n d reacts i n the b e d . I n the non-ferrous metallurgical industries, the t e r m oxygen enrichment is often used to indicate the oxygen concentration of the gas. F o r instance, 25% oxygen enrichment would mean that oxygen is added to air u n t i l the oxygen concentration reaches 25vol% rather t h a n the 2 1 % i n s t a n d a r d air. O x y g e n enrichment is used to increase the p r o d u c t i v i t y of fluidized b e d roasters [49]. O x y g e n enrichment has been found to significantly affect the particle size d i s t r i b u t i o n of several fluidized b e d roasters [35]. W i t h oxygen enrichment, an unstable fluidized b e d (low b e d pressure, significant amount of fine particles < 56 /j,m a n d few particles of size 100-400 z/m) became stable (high b e d pressure, few fine particles a n d significant 100-400 /j,m fraction) w i t h i n a few days [35]. T h e increase i n b e d pressure drop appears to have been caused b y increasing particle density a n d size. A dense oxidized layer coated the sulfide core of calcine particles [35]. O x y g e n enrichment has also been observed to affect the dust a n d sulfate formation i n process gas lines [35]. In a d d i t i o n to the metered fluidizing gas, air is believed to leak into the roaster freeboard, boiler and associated p i p i n g a n d equipment.  T h i s leakage, present because the roaster is operated  under a slight v a c u u m , c a n affect the reactions o c c u r r i n g i n the freeboard a n d the boiler. T h e r e is no p u b l i s h e d i n f o r m a t i o n o n the amount of leakage present. Gases leave the roaster to the waste-heat boiler, cyclones a n d electrostatic precipitator where calcine particles are separated. After cooling, the gases are treated for m e r c u r y i n a m e r c u r y removal plant before the p r o d u c t i o n of sulfuric acid.  1.4.3  Product: Zinc calcine  Zinc calcine is extracted from the roaster v i a the b e d overflow a n d t h r o u g h carry-over. T h e carryover m a t e r i a l m a y 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) a n d the electrostatic precipitator (99%<44/um) [33]. T h e calcine is formed of zinc oxide, zinc ferrite  (ZnOFe203)  a n d relatively s m a l l amounts of  lead sulfate and zinc silicate ( Z ^ S i C ^ ) [50]. O t h e r studies corroborate these findings [51, 43, 52, 53, 54]. T h e entrained m a t e r i a l contains a larger p r o p o r t i o n of zinc sulfate.  Z i n c sulfate  obtained i n the boiler, cyclones a n d electrostatic precipitator originates from the reaction of zinc oxide w i t h sulfur trioxide. T h e entrainment i n a fluidized b e d roaster is of two categories: entrainment of particles from the b e d and entrainment of feed m a t e r i a l prior to j o i n i n g the b e d . E n t r a i n m e n t from the bed is zinc calcine. T h e entrained feed, however, is m a i n l y zinc concentrate w h i c h m a y react i n 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 a n d unreacted zinc sulfide. It is therefore impossible to differentiate between the two types w h e n a n a l y z i n g samples of entrained m a t e r i a l . T h e effect of various variables on the entrained m a t e r i a l , freeboard and boiler must therefore be analyzed carefully. T h e d i s t i n c t i o n between the two streams is very i m p o r t a n t because the entrained feed cannot contribute to agglomeration i n the b e d while the feed w h i c h mixes into the b e d can. Some observations regarding each stream: F e e d e n t r a i n m e n t : A n increase i n feed entrainment is associated w i t h a decrease of the feed entering a n d m i x i n g into the bed. T h i s m a y be i n d i c a t e d b y a decrease i n b e d temperature [35] and an increase i n freeboard temperature [30, 35]. T h e moisture content of the concentrate and its size d i s t r i b u t i o n affect the p r o p o r t i o n of entrained feed. T h e feeding system geometry a n d velocity also influence feed entrainment.  B e d entrainment:  E n t r a i n m e n t has been studied i n m a n y  fluidized  b e d systems. Variables  that t y p i c a l l y affect entrainment include the superficial gas velocity, entrained particle size and density, and the entrainable particle concentration i n the b e d . T h e r e is large scatter a m o n g the numerous p u b l i s h e d e m p i r i c a l correlations. Because there is p r a c t i c a l l y no z i n c sulfide i n these particles, negligible heat is generated by c o m b u s t i o n i n the freeboard. Therefore, the freeboard temperature cannot increase above the b e d temperature because of increased b e d 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 thefluidizedbed. 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 tofluidizedbed 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 bubblingfluidizedbed (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 thefluidizationcharacteristics 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 muchfinerthan 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 i n d u s t r i a l zinc concentrates is usually o p t i m i z e d for the flotation process. Zinc concentrates where more t h a n 80% of the particles are smaller t h a n 20 to 40 /Ltm (dgo) are now c o m m o n . T h e bed calcine particle size (10 i i m to 30 m m [35]) is always m u c h larger t h a n the concentrate particle size. W h i l e as much as 25 w t % of the bed particles m a y be smaller t h a n 105 p,m, as m u c h as 35 w t % can be larger t h a n 1.1 m m [56]. E l u t r i a t i o n - the tendency for very fine particles to be preferentially entrained - and a t t r i t i o n the reduction of particle size due to the break-up of particles - also affect the b e d particle size d i s t r i b u t i o n . N o results on a t t r i t i o n i n fluidized bed roasters have been p u b l i s h e d .  However,  its importance must not be neglected.  1.4.5  Agglomeration in industrial fluidized bed roasters  A g g l o m e r a t i o n i n fluidized bed roasters was reported early i n the h i s t o r y of the process.  For  example, Fisher indicated i n a patent that agglomeration occurred d u r i n g the roasting of zinc concentrate containing significant levels of copper a n d lead [57]. A c c o r d i n g to i n d u s t r i a l experience [30], feed moisture, concentrate particle size and lead content, temperature, a n d bed agitation a l l influence agglomeration, bed particle size and accretion f o r m a t i o n . M o i s t u r e and agglomerated or pelletized feed have been said to be very i m p o r t a n t [37]. Several studies o n agglomeration [58, 59] concluded that low m e l t i n g point phases were present. H i g h e r temperatures and lower air velocity were also found to favour agglomeration.  I n d u s t r i a l experience indicates t h a t at 900 to 9 5 0 ° C some agglomeration occurs. T h e bed m a y sinter w i t h i n 30 minutes after sudden defluidization w i t h o u t c o o l i n g [60]. If the b e d were to defluidize before cooling, any residual sulfide could react w i t h the oxygen contained i n the interstitial gas space between particles (about 50 v o l % ) . A s a result of the poorer heat transfer i n a packed bed, the heat generated w o u l d locally increase the temperature, resulting i n b e d sintering. L i t t l e is k n o w n a b o u t agglomeration i n fluidized bed roasters.  T h e concentrate behaviour  depends on its mineralogy, composition, size d i s t r i b u t i o n , pre-treatment (filtration, 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 m i n i m i z e the risk of catastrophic defluidization. T h e amounts of copper a n d lead are l i m i t e d because they promote agglomeration. F o r example, C u is kept to less t h a n 0.8% a n d P b to less t h a n 2% [60]. Others m a i n t a i n 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 o n l y a p p l y to some concentrates b u t not to others[61]. Several papers a n d patents refer to various methods to control or alter the bed particle size distribution.  D e p e n d i n g on the methods, the goals are to promote larger bed particle sizes,  reduce the amount of carryover, decrease agglomeration or decrease the b u i l d - u p of settled particles. Measures reported are: • R e c y c l i n g p r o p e r l y sized calcine and c o n d i t i o n i n g the concentrate to o b t a i n particles of proper size (pelletizing) [62]. • C o m p a c t e d or agglomerated concentrate as a feed to a roaster such t h a t decrepitation leads to an appropriate bed particle size [63]. • B l e n d i n g to o b t a i n a feed w i t h a specified amount of agglomerating agent a n d p e l l e t i z a t i o n of the feed [56]. • C y c l i c temperature variation to cause p a r t i a l sintering [64]. • Increasing the  fluidizing  gas velocity if excessive agglomeration occurs due to fusion [57].  • P r o v i d e a l o c a l l y increased oxygen concentration b y a d d i t i o n a l localized i n t r o d u c t i o n of oxygen-containing gas into the bed to produce local p a r t i a l agglomeration [65]. • Pelletizing w i t h a binder, o p t i o n a l l y followed by d r y i n g [66, 67, 68], c o m p a c t i n g or b r i quetting the moist concentrate [69, 68] or creating s t r u c t u r e d pellets [70] • C o n t r o l l i n g the amount of feed, oxygen and water fed to the roaster such that fusion occurs d u r i n g 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 handling, 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 agglomeration. 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 (impurities). 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-SO 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. T h e i r experimental conditions differed from those i n a c o n t i n u o u s l y operating roaster. However, their test shows that basic lead sulfate can contribute to agglomeration of inert particles. I n a s t u d y on the effects of lead and copper concentrations i n the feed [59], several c o m p o u n d s were identified i n agglomerated calcines: lead sulfate, basic lead sulfate, lead silicate and copper sulfate. fluidized  L e a d oxide and silica have been linked to defluidization i n  bed roasters [36]. A n a l y s i s of defluidized bed m a t e r i a l has shown t h a t lead tends to  segregate to the coarse fractions of bed m a t e r i a l [36]. T w o types of particles were observed i n the defluidized m a t e r i a l : "globular" and "radiating g l o b u l a r " . T h e globular particle "is a more rounded particle that may have been formed by several spherical particles a t t a c h i n g themselves and joined by a binder phase. T h e r a d i a t i n g globular has clearer g r o w t h lines." [36] Z i n c oxide particles containing t h i n concentric layers of lead oxide and zinc silicate were found w i t h i n the coarse fraction of the roaster bed m a t e r i a l [36].  1.5  Fundamentals of agglomeration in fluidized beds  A g g l o m e r a t i o n and defluidization occur i n m a n y other fluidized bed systems such as granulation, chemical vapour deposition [84], coal combustion, biomass gasification a n d p y r o l y s i s . P r e v i o u s 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 b y Siegell [86] to observe the m e c h a n i s m 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 t e m p e r a t u r e increased, the average size of the agglomerates increased. Recent fundamental studies have looked at agglomeration of fine cohesive powders [87, 88], l i q u i d bridge forces [89, 90, 91], sintering [92, 93, 90] a n d V a n der waals forces [90]. L i q u i d bridges between particles are significant i n d r y i n g , g r a n u l a t i o n and three-phase  fluidization.  T h e strength of a l i q u i d bridge depends on the surface tension a n d  viscosity of the l i q u i d . I n one s t u d y [91], the a d d i t i o n of l i q u i d s modified the behaviour of a fluid bed from a G e l d a r 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 i n w h i c h m a t e r i a l migrates to the region of contact to form a neck.  Surface diffusion, volume diffusion, viscous flow and vaporization-condensation  contribute to sintering. T h e predominant mechanism depends on the m a t e r i a l i n question. T h e use of characteristic times [90] appears to be a p r o m i s i n g approach for m o d e l l i n g sintering i n fluidized  beds.  F u n d a m e n t a l approaches such as force balances and characteristic times have been used to predict agglomeration and defluidization. F u n d a m e n t a l models m a y provide useful insights, but are very difficult to a p p l y to i n d u s t r i a l roasters a n d other c o m m e r c i a l reactors. T h e c o m p o s i t i o n , quantity a n d properties of various phases present d u r i n g fluidized b e d r o a s t i n g are u n c e r t a i n and are likely to change over time and w i t h changes i n o p e r a t i n g conditions a n d / o r  charge  composition.  1.6  Agglomeration in other fluidized bed systems  Relevant i n f o r m a t i o n is available from fluidized bed reactors used to pyrolyse waste polymers particles. These reactors suffer from agglomeration a n d defluidization [94]. I n this process, the polymer particles are fed to a hot bed of sand (450-500°C) under inert or o x i d i z i n g conditions. T h e p o l y m e r then decomposes and volatilizes. U p o n entering the reactor, the p o l y m e r pellets quickly reach the p o l y m e r softening temperature and become very sticky. Layers of sand m a y attach to pellets, effectively f o r m i n g p o l y m e r - s a n d aggregates w h i c h m a y c r u m b l e if there is insufficient p o l y m e r to b i n d the sand particles and w i t h s t a n d the a g i t a t i o n of the bed. A g gregates grow quickly, leading to severe defluidization. T h e t i m e to achieve defluidization was found to depend on the bed temperature and on the ratio of i n i t i a l b e d weight to the p o l y m e r fed. T h i s indicates t h a t this is an unsteady-state process where the pyrolysis kinetics define the steady-state processing capacity. Feeding of p o l y m e r beyond t h a t capacity causes a c c u m u l a t i o n i n the reactor u n t i l the p o l y m e r concentration reaches a p o i n t where defluidization occurs. A similar defluidization process m a y occur i n a  fluidized  25  bed roaster if the agglomeration rate  Chapter  1.  Introduction  exceeds the rate of solids removal. Because particle growth is a main goal of the granulation process, published research on fluidized 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 agglomerated 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, agglomerate 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 influidizedbed 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 fine26  Chapter  1.  Introduction  grained l i q u i d minerals and t h r o u g h heterogeneous condensation of vapour-phase species such as N a , K a n d S. W h e n the particles have a t h i c k coating, e.g. w i t h a thickness of a p p r o x i m a t e l y 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 a n d sinter to the j o i n e d particles and a "raspberry"-shaped agglomerate is formed.  • "Egg" particles T h e egg-types agglomerates are hollow particles t h a t formed as a c o a t i n g on a b u r n i n g coal particle. T h e coating consists of coated bed particles that stick to the surface of the coal particle. A s h formed d u r i n g combustion of the particle interacts w i t h the particle a n d contributes to their sintering as a shell. W h e n the coal particle is completely b u r n e d out, a hollow shell remains. C o a t i n g of a coal particle depends on the type of coal (swellingindex, ash quantity, composition) and its size.  • Sintered fly ash These very fine dense particles consist m a i n l y of fly ash sintered w i t h sorbent m a t e r i a l . T h e y are found i n 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 m e l t i n g of alumina-silicate m a t e r i a l due to process upsets. O p e r a t i o n a l problems or oversized agglomerates m a y cause poor fuel-air m i x i n g leading to localized hot spots. I n these hot spots, m e l t i n g of an a l u m i n a silicate-based phase occurs, accelerating the formation and g r o w t h of agglomerates. These agglomerates appear as sintered l u m p s showing obvious signs of m e l t i n g [102]. T h e first two types of agglomerates are p r e d o m i n a n t l y found i n combustors. W i t h the exception of the fourth type of agglomerate, a l l are formed d u r i n g n o r m a l o p e r a t i o n of  fluidized  bed  combustors. T h e "egg"-type of agglomerates is d i r e c t l y related to coal c o m b u s t i o n . Therefore, "egg"-agglomerates are not expected i n fluidized bed roasters.  27  Chapter  1.7  1.  Introduction  Research objectives  T h e research reported i n this thesis seeks to provide a better u n d e r s t a n d i n g of particle g r o w t h processes i n zinc concentrate fluidized bed roasting. T h e objectives of the project were to: • Investigate particle g r o w t h i n a l a b o r a t o r y scale fluidized b e d roaster. • Identify particle growth mechanism(s) and quantify the rate(s) of different mechanisms for pure zinc sulfide a n d i n d u s t r i a l concentrates. • Identify the operating parameters influencing each m e c h a n i s m . • Develop a fundamental m o d e l , applicable to b o t h pure zinc sulfide a n d i n d u s t r i a l concentrates, describing the particle growth i n a fluidized b e d . • D e t e r m i n e the a p p l i c a b i l i t y of the results to an i n d u s t r i a l fluidized b e d roaster. T h e longterm objective of this research is to improve the u n d e r s t a n d i n g of i n d u s t r i a l  fluidized  bed roasters and to provide tools to predict their behaviour a n d i m p r o v e their o p e r a t i o n . U s i n g mechanistic models, the o p t i m i z a t i o n of the operation a n d m o d i f i c a t i o n to the roasters or their operation can be considered and evaluated.  1.8  Thesis outline  C h a p t e r 2 focusses on the chemical aspects of roasting zinc concentrates.  T h e chapter  first  looks at the t h e r m o d y n a m i c s of the Z n - S - 0 system, followed by the kinetics of zinc sulfide oxidation. N e x t , the t h e r m o d y n a m i c s of the F e - O - S , P b - O - S , C d - O - S a n d C u - O - S systems are briefly presented. T h e vapour pressures of the metallic species are presented. T h e chapter concludes w i t h an overview of phase diagrams w h i c h a p p l y for zinc concentrates, zinc calcine and any other transient phases w h i c h m a y occur d u r i n g roasting.  T h e first sections of C h a p t e r 3 describe t h o r o u g h l y the e x p e r i m e n t a l roaster set-up, accessories, and d a t a acquisition a n d control systems. A d d i t i o n a l technical specifications a n d drawings are assembled i n an a p p e n d i x . T h e next sections report the p h y s i c a l a n d c h e m i c a l 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 singleparticle reaction model, the chapter describes the conditions where the assumption of isothermality 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 sensitivity 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 recommendations 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: T h e o r e t i c a l density and molar volume of zinc species calculated from crystalline structures Structure  Density  M o l a r volume  P o w d e r diffraction  g/cm  cm /mol  file [108]  3  3  Z n S (sphalerite)  cubic  4.0966  23.789  5-566  Z n S (wurtzite)  hexagonal  4.0903  23.826  36-1450  ZnO  hexagonal  5.6752  14.341  36-1451  a-ZnS04  orthorhombic  3.884  41.57  8-491  /?-ZnS0  cubic  2.90  55.7  32-1477 ( 7 0 0 ° C )  4  ZnO-2ZnS0  4  monoclinic  3.8796  104.21  32-1475  ZnO-2ZnS0  4  orthorhombic  3.85  105  32-1476 ( 8 5 0 ° C )  particles. T h e phase transform may, however, affect the r e a c t i v i t y of the particles. Z i n c sulfate exists i n two crystalline forms. a - Z n S 0  4  transforms into / 3 - Z n S 0  4  above 7 3 4 ° C  [110]. T h e crystalline structure information for the high temperature c u b i c form of zinc sulfate was measured at 7 0 0 ° C [108].  Similarly, the crystallographic i n f o r m a t i o n for the h i g h  temperature form of the basic zinc sulfate was obtained at h i g h temperature. W h e n c o m p a r i n g the m o l a r volumes of the different compounds, a l l o n the basis of 1 mole of zinc, o n l y the reaction of zinc sulfide to zinc oxide w o u l d p o t e n t i a l l y create a porous structure i.e one mole of zinc sulfide is larger t h a n 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 p r o d u c t more v o l u m i n o u s t h a n the s t a r t i n g material. T h e b l o c k i n g of pores m a y therefore be caused by reactions to p r o d u c e sulfates.  T h e t h e r m o d y n a m i c s of the oxide, sulfate and basic sulfate were first s t u d i e d by measuring the S O 3 e q u i l i b r i u m pressures [110, 111] and later using high-temperature electrochemical cells [112, 113]. T h e t h e r m o d y n a m i c s of the system can be g r a p h i c a l l y represented as predominance diagrams. A predominance d i a g r a m is a graphical representation of w h i c h solid phase is the most stable w h e n i n e q u i l i b r i u m w i t h a given gas c o m p o s i t i o n . 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 and S 0 partial pressure, the required thermodynamic 2  2  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-2ZnS0 ) between FACTSage and HSC. The upper temperature limit for basic 4  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-2ZnS0  4  within HSC, the ZnO-2ZnS0 stability area at 850 °C virtually disappeared. Since basic zinc 4  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, i f a sulfation study were to be initiated, the t h e r m o d y n a m i c s of the zinc-oxygen-sulfur system should be clarified. T h e diagrams also present a family of lines representing different zinc p a r t i a l pressure i n equil i b r i u m w i t h the solid. T h e line where point A is located represents the gas c o m p o s i t i o n i n e q u i l i b r i u m w i t h a m i x t u r e of zinc sulfide a n d zinc oxide.  However, as discussed i n section  2.8, point A o n the predominance d i a g r a m represents the gas c o m p o s i t i o n i n e q u i l i b r i u m w i t h a m i x t u r e of zinc sulfide a n d zinc oxide also i n e q u i l i b r i u m w i t h their zinc vapour pressures, i.e. vaporization from b o t h zinc oxide a n d zinc sulfide. These a d d i t i o n a l lines a n d points are discussed i n section 2.8 below. A s the diagrams show, for a given temperature (see F i g u r e 2.2), the sulfate phases are stable at higher sulfur dioxide a n d oxygen concentrations  (upper right). However, w h e n c o m p a r i n g  different temperatures, the sulfates cannot be stable at atmospheric pressure, at h i g h temperature even at 1 atmosphere SO2  (log(Pso2) ~ 0). I n order for the sulfate t o be stable at 1050°C,  the required oxygen pressure is beyond one atmosphere. However, the sulfates are stable at lower temperature and h i g h sulfur dioxide concentration  (log(Pso2) ~ 0). T h e s e trends a p p l y  to many other systems. T h e sulfation of zinc oxide occurs significantly i n the gas h a n d l i n g equipment where the lower temperature and h i g h S O2 content of the gas enhance the s t a b i l i t y of zinc sulfate. T h e sulfation of zinc oxide proceeds very slowly when oxygen a n d sulfur dioxide are present. T h e reaction is much faster once the 0 - S 0 2 m i x t u r e contacts a V 2 O 5 catalyst to produce S O 3 [120]. T h e 2  catalyst c a n also be contained w i t h i n the zinc oxide sample. I n such a case, the sulfation rate of zinc oxide increased w i t h increasing amount of V 2 O 5 catalyst present [121]. I r o n oxide also catalyses the p r o d u c t i o n of SO3. Because i r o n oxide is omnipresent i n zinc calcine, its presence affects the sulfation of calcine o c c u r r i n g w i t h i n 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-S0 Predominance diagram at 950°C 2  34  Chapter  2.  Thermodynamics  and Kinetics  of  Roasting  5  0  „  -5  o cn  OJ  CL cn o  -  -10  -15  -20 -20  -15  -10  -5  0  5  iog(P ) Q  2  Figure 2.3: Zn-02-S02 Predominance diagram at 1050°C 2.1.2  K i n e t i c s  o fz i n c  sulfide  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] w h o characterized the mineralogy of calcine samples from a n i n d u s t r i a l roaster. T h e y proposed that the m o r p h o l o g y of p r o d u c t calcine particles m a y indicate vapour-phase deposition or repeated c y c l i n g of the particles into a n d out of the fluidized bed. G r a y d o n a n d K i r k [82, 129] studied the o x i d a t i o n mechanism of zinc sulfide a n d the formation of zinc ferrite. T h e y concluded t h a t solid state i r o n diffusion, m e l t i n g of the F e - S - 0 eutectic and gaseous zinc species are i m p o r t a n t phenomena d u r i n g zinc concentrate roasting. Gaseous oxidation of zinc sulfide m a y deposit zinc oxide on the surface of the b e d particles, as i n chemical vapour deposition, thereby c o n t r i b u t i n g to the g r o w t h of calcine particles.  Modelling, rate expressions and activation energy N u m e r o u s studies have quantified the o x i d a t i o n kinetics of zinc sulfide a n d derived rate expressions from experiments. Table 2.2 summarizes the studies c o n t a i n i n g quantitative results applicable to a rate expression. T h e type of experiment and the m e t h o d used to follow the progress of the reactions a n d the sample m a t e r i a l are described i n the first c o l u m n s . experimental conditions varied from  fluidized  bed, suspended pellets to powders i n crucibles.  T h e measurement m e t h o d usually depends on the experimental conditions used. sis is performed either by SO2 n e u t r a l i z a t i o n a n d measurement or t i t r a t i o n or by infra-red measurement.  The  G a s analy-  of the s o l u t i o n c o n d u c t i v i t y  T h e extent of o x i d a t i o n of solid samples is m o n i -  tored using chemical analysis or by measuring the oxide layer thickness. F o r suspended pellets a n d suspended crucibles, the most c o m m o n m e t h o d of m o n i t o r i n g 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 i n i t i a l reaction rates (Denbigh and Beveridge (1962) [122], P r a b h u et al. (1984) [130], S a n d m a n et al. (1985) [125], K i m and T h e m e l i s (1987) [131] a n d Sofekun and D o r a i s w a m y (1996) [132]), the overall measured rates ( O n g et al. (1956) [133]), the overall modelled rates a n d the "settled" rates (rates once the m o d e l predicts the reaction rate) ( P i s k u n o v et al. (1981) [134]) have a l l been used to determine the activation energy. T h e models are briefly described below. T h e v a r i a b i l i t y a m o n g the analysis methods contribute to the v a r i a b i l i t y i n the measured a c t i v a t i o n energies.  36  For  Chapter  2.  Thermodynamics  and Kinetics  of  Roasting  instance, R a o et al. (1982) [135] considered b o t h the i n i t i a l rates a n d the m o d e l l e d rates a n d obtained very different activation energies for the same experiments (87 a n d 160 k J / m o l ) . It is i m p o r t a n t to note that the activation energy also depend on the analysis of the effect of oxygen concentration. F o r instance, the oxygen concentration ( m o l / m ) varies w i t h t e m p e r a t u r e for 3  a constant oxygen p a r t i a l pressure. T h i s effect is much smaller t h a n the scatter i n activation energies i n Table 2.2, b u t must be accounted for. T h e apparent activation energy and its applicable temperature range a n d the reaction order w i t h respect to the oxygen concentration are shown i n the table for each study. of m a x i m u m conversions (X)  T h e range  is indicated where available. I n most studies the 'kinetic rate  equation is of the form:  -r = kC^  (2.1)  2  where k is the reaction rate constant, Coi is the oxygen concentration ( m o l / m ) a n d n is the 3  reaction order w i t h respect to the oxygen concentration. T h e assumed or measured reaction orders are shown i n the table where given. Natesan a n d P h i l b r o o k (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. A g a r w a l and G u p t a (1976) [138], A g a r w a l and M o h a n t y (1976) [139], F u k u n a k a et al. (1976) [140] a n d R a o (1984) [141] have assumed t h a t the reaction order is 1. C a n n o n a n d D e n b i g h (1957) [124], D e n b i g h a n d Beveridge (1962) [122] a n d K i m u r a et al. (1983) [142] have measured the reaction order to be 1/2, and T a k a m u r a et al. (1974) [143] mentioned 1/2 but used first order for their modelling. A l l a y et al. [144, 145] observed a reaction order of 2 / 3 . P i s k u n o v et al. (1981) [134] measured different fractional reaction orders as a function of the controlling mechanism.  Some studies ( O n g et al. (1956) [133], C a n n o n and D e n b i g h  (1957) [124], reference 10 of [128] (1964) or G e r l a c h of [132], C o n r a d a n d W u t h (1970) [146] and Sofekun and D o r a i s w a m y (1996) [132]) have found that the L a n g m u i r - H i n s h e l w o o d - H o u g e n W a t s o n ( L H H W ) m o d e l for adsorption of reactant could be a p p l i e d to the o x i d a t i o n of zinc sulfide. T h e L H H W rate m o d e l is of the form:  kK C 2 A  1 + where KA is the adsorption e q u i l i b r i u m constant. 37  0  K C2 A  0  (2.2)  Chapter  2.  Thermodynamics  and Kinetics  of  Roasting  T3 O  J3  CO  ST*  o  lO CN CN  4  N  O  ai ^ °> O O CN  .-H ^  3 .  ,2 3  6 o  S A  co  V  cu" CO  c8  a  co 3  co  N  •a a  o  6?  cj •  CO  01 cs  O CB CJ  a S - coo. .5 'iCO CO 'w O.  Ol  CN CO  c si  £8  CD  M  CO  3 g? a,  6 6  "3  °  •O.S 01^r -°?™ £ CO CN m CM  oo  CO  cd  'to  13 c ce  cd C o cs 3 — T> ca o  "3 ct)  S3 O  f*  "2  _>> "3  s£  fao  o  32  CD  O &  0  CO  01  "3.  T3  -a  XI CD J3  O.  01 -O T3 01 N  T3 01 [S3  T3  '3  01 J2  01 -Q  •8  T) 01 SI  '3  '3  '3  E  T3  01  01 XI  KJ  *2  E  E  CM 3  E  -o , , CtS CN  a 01  bo C  O  §  ce  e  "  ?3  bo -Q bO  ^  01  CD  Ol  01 ^-^ CJ  to  o3 01  cri  38  -Q  6? 6?  I. ^  [fl  t,  CO CD Ol CD  Cri  do  r-i  cd ' —  01  cci Ol  to CD Ol  cri d  Chapter 2. Thermodynamics and Kinetics of Roasting CD  x fc. c  X  o S  O)  O  »S E  CO  t—  Ol  3 6 cq  O  bO — I c * ^  bO I fa  .S  X  .3,  O  2  »  •3  CJ  CS  1  d  3  CO ><  CO  X  o E  O  3  X  "oi  K  o  CO O  CD  o  r-  6  © H  n CN  o  o  o  o  o  O  IO  o  ci  CN  in ©  m  H N  N  fa fe?  H CO JO  CD  O) IO O.^ ^ CO i n CN  o  06  66 6  fa  "3 fe?fe?  J  ]  CO  ^co in  CO  O LO CD t O) CO OO CO in in  «S  CD  o ( N  CD fa  co a N  +j  ca  CJ  fe?  -a<  "a  o  eo  CD  CD  c  E 3  ca  fe?  3  s bO  s- s- J-  ci  c«  g  - - s-ai  c & N co  X  SWfe? ca e-. 00 CO CO  < O K co S  CO  CD CD  X  X  I  ^  a g "3fe?fe?co S^ JS 10 -cf  C  X is O  I  &  3  PH  a 10 co  CO CO CO  ca  cd  CO  >> " •J3  CO  _>>  Q  s  13 l-c  O  <  °-« H E  o  CO  M  oi H  •S  CO O i T-H  ci  iO tO  m H  a  O  fl  "3 C  ca  O  a  ca  O  13 E J3  "3  "3  cce ca  S  c  c3  <  O  O  O  O  CD  bO o3  Cu CO  O ">  CD  A S  S o  x a-  .s S X  '3 in p oi fa  CN  XI  a X  CD JO  X  x  CD -Q  CD J2  CD  X c  X>  X  X  X  CD  CD  [3 fa  3  CO  '3 fa  '3 fa  X  CD  " 3 a  '3 a  X  X  X aCD a Cfi  X a CD a cfi  CD  CD N  fa  3 CO  5 Q  CD  3 CO  "3 3  cd  o  X  c  C , ,  ce co  co  tin co CD  0  1  i3 3 Z, fa .  s Is  CD CD  JJ  t*-  39  O CO  c ? " in  is  ca r-l  Q >  bo  2 E ca ^  S i  G  d CU CD  TJ  CD  CD  +3  If  CU a  o O  CD  IS!  Si  d  x  CD  l—  a a  o CD  r-<  3 '—  22  o  O  O  Chapter 2. Thermodynamics and Kinetics of Roasting  T3  o 5 V " -a  o  •o  .S  C Co • S cj  CD  8o  «o  bO  I  6 0  s  d  p o  c S  •£  CD  lo O X  co O  o  o  Sf d  8  V  I  i  Sf - co  3 °  .2 cS 00 •x .2 d  T3  a  •c II  C6  •E  II  E  •5  S  tw  J5  CO  CJ *S  CN  o  go o  °  CN  c6  CO  CN  d i-H 1-1  1-1  CN  a  S  cd  O  CN CD GO CO  00  CN  T—t  1-1  a?  CO CD  m  O  b  O LO  S  CD  T3  3 "8 CD  ~3  fi CD  a  o  2  CO  o  co >-i  X X  C  [/] l O  £  r-! CN  O  o  >,  c ^  O c c co 0 N• fa O  o  ° 6?  5  CD  o  cu  E  G 2 -a 'C -a CD  O  a8  CO  '>  0)  S-i  a  o cu Pi  1  o  o  CO  CO  N  e  c  &  u  E  3  a  < O  CO  3 O  a  o  _>>  g  O -o & "o  CO  co  co  CS  C  C  co cn  o  s O  cn  8  o  o  ct  Q •  T3 TJ  ^1  '3  3 CO  3 CO  CO  y  6 I s T3 H '3 LO — CN fa  CO  a  s  ci  3  o  O 00 CO  CO c o  co  13 — •  ho 3  CQ  3  fi  fi , , co  c  a  i—^ CN  to  Co  LO £ CO cj>  1°  SP  CN CN  _ E  O CO  3.  co  CO CD  3 CO  CD  J j  a  o  £  ^  °> a a  <  co  CJ  a -K Cd E  bO cS  a  co cn Co  LQ IC  2  CJ  —  JCO C  3 .  CO  T3 C  '  CO Co CN  >  i—i  <D  "J = ?  O  00  — „  00^  2 o> Co  CO  40  w  2  fa  CO  CS  cd  CO  co  CO  O  T3 C . lO  O)  Q  o o  Ol  o b  a  "3 . 2  a  LO b b N H s CO CO N  O)  CD  'co  a  t - Cf)  a ^  co  •3 S  CD J 3  ~Ej cd  co-  CD  <  S  LSI m  T3 C  1»  o o o f- o  LO  CN fe?  CD  XI  2 u fi  co  Cu  E  CD  o  O  co ai  Sf  Q  co  H ^ H 00 CO H O ^ H CD r—I t—I 00 rH -H  o  o  00 CT> E  "1  cS  Chapter 2. Thermodynamics and Kinetics of Roasting •Srg S to  CP SH  cn  ° S d .5 -a -o  a  o u  tic I 5 s H •C  Ui  S-H  '2  ^  1  "  '2  HH HJ  i—i  H  c  HH  aj co bOXI  •Si  II  S  cS  o  o  CO CD  0  a  s  o  -g  'CO  SH  ct)  X X  at  -H  +1  CO rH LO CD CO rH  CO ^ . CO CO CN rH  IE II  5o  CO "cfj CO  c N  a  a a  CJ)  ai  S  CD T3  £ T3 O CD a 2  CO  c  cH  s  CD rH O,,  t, o  SI  _  CT)  +j  0>  to X5 H H^ CO « ,-  P  3  S Q  a 6 >, S co"?„ > o> X  rS «Q, I3-  cd \S  S <« S  tsl  o i .3, t--  CD  oi ff; 4 H  £  CD  -g S £ cd  3 CH  G  j>>  "3  CO  O ">  'SH CD  cH  S3 o  < *  <  O  O  < o  a  c§  X  cd  3  3  CO T3 CD  o tf  CC  a 8  S  3 CO  tt3  CD  3  3  CD  CD  Xl o  c  -  3  3.  u  a  <  § O H  S  3 CO  Q  TGA  cu , bD cS & 6  « *  c cd  "3  C cd cd c  co  CD  CP  SH  6 co  ft  OS  M  5 ^  J3  T3 c cd  CP  cd  fi O  O  3 , , P CN ^> H<  CD  J3  SH  c? oo  —  05  X• cd  o cd  oo  c cd co .  'c?. , bO CN cd co  CS  o CO  41  o ^ ' >  CD  Samp] cible  o  "cd  DTA  a •  C cd cd c  T3 X>  Samp] cible  "cd a cd  T3 X>  Chapter 2. Thermodynamics and Kinetics of Roasting 10-  „ 1 0 "  2  4  CO  M  E  ~Sio  -6  0> CO  o  |io-  8  c o  o CO  £  g 'co  1  10  1 0 ~  _1(  1  :  0.8  0.9  1  1.1  1.2  m-(K" ) 1  1.3  X10'  1.4 3  F i g u r e 2.4: Intrinsic reaction rate of various k i n e t i c studies. R a t e expressions from references [124, 143, 140, 135, 142, 130, 144, 145]. D a s h e d line corresponds to fitted kinetics (equation 2.3) discussed i n text.  T h e activation energy does not give a complete representation of the kinetics of the system. I n a d d i t i o n to the a c t i v a t i o n energy, the pre-exponential constant from the A r r h e n i u s equation, as well as the rate expression used to o b t a i n the rate constant, must a l l be considered when c o m p a r i n g kinetic i n f o r m a t i o n from various authors. F i g u r e 2.4 presents the rate i n f o r m a t i o n from several of the studies s u m m a r i z e d i n T a b l e 2.2 w h i c h offer a complete rate expression. N o t e that since the rate expressions differ (reaction order a n d use of concentration or p a r t i a l pressure for oxygen) from one s t u d y to another, c o m p a r i s o n must be m a d e o n a reaction basis. W i t h the exception of studies A a n d B , there is relatively l i t t l e scatter a m o n g the different studies.  T h e s t u d y of T a k a m u r a et al. [143] (line B ) clearly stands out as aberrant. T h a t of  F u k u n a k a et al. [140] (line A ) does not d i r e c t l y extend the clustered group of studies, b u t m a y represent an adequate upper b o u n d 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 T a k a m u r a et al. [143] a n d F u k u n a k a et al. [140]. N o t e that the slope of the line gives the negative value of the a c t i v a t i o n 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: (2.3) 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: (2.4) 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 oxidation 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 control. For the case where external mass transfer is rate-controlling, the conversion (X) increases 43  Chapter  2.  Thermodynamics  and Kinetics  of  Roasting  linearly w i t h t i m e (t):  X = Kt  (2.5)  W h e n mass transfer t h r o u g h the p r o d u c t 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  = Kt  3  (2.7)  U n d e r conditions of chemical control, the thickness of the p r o d u c t layer increases linearly w i t h time (proven b y replacing the conversion b y X — 1 — (r /R)  3  c  where r  c  is the core radius and  R is the particle radius). N o t e that these equations a p p l y to the reaction of spherical particles. T h e equations are different for geometries other t h a n spheres i.e. cylinders a n d flat plates. F o r flat plates under conditions of chemical kinetics or film diffusion control, b o t h the conversion and the p r o d u c t layer thickness increase linearly w i t h time. F o r a complete discussion of the model, the reader is referred elsewhere [156, 157]. T h e shrinking-core m o d e l is described further i n chapter 5.  Several studies have modelled the o x i d a t i o n of zinc sulfide w i t h the spherical shrinking-core model (equations 2.6 a n d 2.7).  These equations are often used w i t h e x p e r i m e n t a l d a t a to  identify the rate-controlling step. T o o b t a i n the activation energy of the process, the fitted rate constant (K) is plotted as a function of temperature i n an A r r h e n i u s plot. A m o n g the studies w h o have used the s h r i n k i n g core-model, o n l y N a t e s a n a n d P h i l b r o o k (1970) [149], T a k a m u r a et al. (1974) [143] and A g a r w a l and G u p t a (1976) [138] t r u l y considered cases where product layer diffusion affected the reaction rates.  T h e other studies o n l y considered  chemical kinetics control (equation 2.7).  Jander's equation has also been used to m o d e l the o x i d a t i o n kinetics ( P i s k u n o v et al. (1981) [134]). 3(1 - (1 - X )  44  1 / 3  )  2  = Kt  (2.8)  Chapter  2.  Thermodynamics  and Kinetics  (a) Homogenous  of  Roasting  (b) Intermediate  (c) Shrinking-core  F i g u r e 2.5: Representation of the grain m o d e l . A d a p t e d from [156]  Jander's equation is valid o n l y for slab-like particles or for the i n i t i a l stages for other geometries [156].  Therefore, J a n d e r ' s equation s h o u l d not be used i n place of the shrinking-core  m o d e l . Hence, the analysis of P i s k u n o v et al. (1981) [134], where o n l y the e x p e r i m e n t a l d a t a between 20% and 97% conversion were able to fit Jander's equation, is questionable.  The  C r a n k - G i n s t l i n g - B r o u n s h t e i n equation, proposed to m o d e l the reaction w h e n diffusion t h r o u g h the p r o d u c t layer of a spherical particle is c o n t r o l l i n g [128, 158] is equivalent to equation 2.6. Its use is therefore acceptable. T h e diffusion m o d e l of G o k a r n and D o r a i s w a m y [150, 159, 151] is another f o r m u l a t i o n of the shrinking-core m o d e l . B y neglecting chemical kinetics, they o b t a i n e d an equation similar to equations 2.5 a n d 2.6, i n c l u d i n g b o t h diffusive resistances (external a n d ash-layer). T h e grain m o d e l was also a p p l i e d to the o x i d a t i o n of zinc sulfide [135, 141, 142, 153, 160]. I n the grain model, the porous solid reactant consists of a large number of s m a l l non-porous grains, each treated as shrinking-core. O n e advantage of the grain m o d e l is t h a t it can effectively treat homogeneous reaction throughout a pellet as well as shrinking-core reaction. I n fact, these two opposite phenomena are extremes of the g r a i n m o d e l . F i g u r e 2.5 represents the g r a i n m o d e l and its extremes. W h e n the chemical kinetics are slow compared to the diffusion of species t h r o u g h 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 spherical 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. However, 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 shrinkingcore 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 b e h i n d . A s w i t h the g r a i n m o d e l described previously, the zone m o d e l combine the characteristics of the shrinking-core a n d models.  homogenous  P r a s a n n a n et al. [161] observed that the w i d t h of the reaction zone increases w i t h  pellet porosity. A m o d e l for the gaseous o x i d a t i o n of zinc sulfide was proposed b y D e n b i g h a n d Beveridge [122], who assumed that the process occurs as a double diffusion layer where gaseous zinc sulfide diffuses out a n d oxygen diffuses toward the particle. Gaseous o x i d a t i o n of zinc sulfide i n a fluidized bed was modelled b y H a t t o r i et al. [123] by c o m b i n i n g the 2-phase fluidized bed m o d e l of F u k u n a k a et al. [140] a n d the gaseous o x i d a t i o n model of D e n b i g h et al. [122].  2.1.3  Fluidized bed experimental studies  Table 2.3 summarizes the roasters used i n various experimental studies. M o s t l a b o r a t o r y roasters were used for batch experiments and h a d diameters between 35 a n d 100 m m . M o s t of these studies have looked at the o x i d a t i o n kinetics of zinc sulfide or of zinc concentrates.  T h e first  s t u d y on fluid b e d roasting of zinc sulfide, p u b l i s h e d b y Y a g 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], o n l y P a i k and P a r k [59] specifically studied agglomeration i n a fluid bed roaster. T h e gaseous o x i d a t i o n of zinc sulfide i n a  fluidized  bed has o n l y been considered i n the work of H a t t o r i et al. [123]  where the kinetics of zinc sulfide o x i d a t i o n were studied for low oxygen concentrations.  2.2  Iron  T h e iron-oxygen-sulfur system is very complex. O n l y a brief overview is presented here. D u e to the existence of two o x i d a t i o n states (ferric and ferrous), there are m a n y c o m p o u n d s i n the iron system. Several sulfides and oxides exist, b o t h w i t h significant non-stoichiometric c o m p o u n d s . A s F i g u r e 2.6 shows, a number of forms of iron oxide may exist. M a g n e t i t e  47  (Fe304)  is a spinel  Chapter  2.  Thermodynamics  and Kinetics  of  Roasting  u  ryo\>  CP  o  LO  rH  M—i  ' CP o  >>  r—I  CM  O  0.57  00  GIO  led.  CO  0.34  cci U  O  < m ,—i  CM  d  d  o  1  o  CM  CM  co  oo  d  CM  T-H  oo  T-H  co  f-  t  d  CO  CO  o  T-H  CM  CO  T-H  LO d LO CM  d  ft CO -rH  O  ...  v  o o  CD  +J cO CD S-i  dm  ere  cS  3  o  o  cn  O)  co  i  o  00  o  o  LO  1  o  O L 0O 5 1  O CO  o  T-H  CM CD  Ol  T—I  o  1  oo Ol  Ol  L O o>  i  o cn  CD  o  LO  r-H  f )  , ,  I )  o  Cn  o T-H  i  o  o oo  Cd  o  cn  o  o Ol  o  o  L O 00  o  o  LO  LO  oo  O l  CM  o  L cnO i  CO  LO  cn  cn  i  o  CM CO  i  t—  LO  oo  oo  o o  o  u  w  o tX  LO  o o  LO  LO  X  X  CO  LO  o  T  r-H  T-H  1  o  o  X o  LO  X o  X o  CO  CO  o  o  o 00  CM  X  X  o  LO  bo  X  r ^  :/hr  O  CD  H-  O  O  o o S  ntin  °  a  o  O  a  ^  H  CD  CO CJ  CO CJ  O 8 PQ S  d  O  +3 .2 « is g ft  CD CJ  o 1  o  8  ft  i* ZCD  ft CD  z  able  oT  a  co >*  '3 ft  P  &  03  cO  48  N  >-  CN rH  FH  CD CO  z  "a  o 3  co cn  CO  03  ft  co" CO T-H  ft  a,  "3 cn  o" ed, Canada  3 44 3  LO"  hide Cor  '3cO  <3  4=  huan et  — iH  H J  CO  •G- oo LO "a^3 G  O  i T H  G O  o  M  co  M  ( J ,  S  ft CD  Z  CD  N '  S  CD  G  43 rH  o E-i  ft s  O  CD "H  O  ^ ? += 4 3  cO  minco Resea ch [37]  CJ  wa et al.  44  ori et al.  '5b  "3  T-H  1>" o T-H  co" CM  CD  naka et  . H CD 3  CO  LO  T-H  lin et al.  et al. [ll  3  CO"  roz et al.  43  r—1  o" aT  and Par  CD  CN r—<  San huan e£  ft  ors or Com  To"  san and Ph  LO"  cci  rook  H >>  bO 4 4  CM  r-H  fH  ° 3  =£1 .3  TOC ess  CO CJ  ineti as pi cidat  "bb  <!  Z  CO CJ  ineti  g _o CD  ineti  CO CJ  - co 3 co cO o o _CH .y  o  3  co 3  anad  CD  HH  o  1-1  T-H  1  (H CO  'roc ess  F  03  PQ  .3  o  CM  i  r^  O  '-H=  ineti  ineti ew p  ineti'  CO o  „ cj co 0  rH  ntin  d .5  CO  CJ  v£  O co 3 CO  ntin  CM  3  3 CO  TOC ess  PQ  ^o  .„ °0  CO  3  ineti  CO  tch  -U  ntinuou 5 - 26.5 /min  CN  CO  X  o  o  o  nts  cO  LO PQ PQ CO  j - •* O O , O  bO  CO  ineti  ess  stu Type  o b0 O  LSI < b O fao  on  >>  PQ  N  3  O  inor ele  O  CO  co  ehaviou:  co  tch  o  T3  MH O  cn < a bo  3  tch  I  a CO LO PQ PQ d  CO  tch  Continuous /min 43 CJ 4H  CO  T-H  LO  T  oCN  ntin  m  00  tch  inuous tatch//Co:  d pilotex erii lent, 7  Det  X  X  LO  LO  i—i  o  fN-  no  CO  o  CO  CO  CO CO  o  no  o  o CO  o  o  o  no  ft  CO  c— X  no  co  H  co  X  o  LO LXO  o  p  •s  "cS  o  LO  X  CJ CO  o  study  "a  -4=  o  d Chemi cal  Das ers.  43  CO • H 43  Chapter 2. Thermodynamics and Kinetics of Roasting  Fe-liq*SUj Fe-bcc+SUg Fe-fcc^SIa*  F i g u r e 2.6:  Fe,0,  Weight * Fc,0,  FeO  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  -20 -20 1  of  ^ -15  Roasting  ' -10  ^ -5  • 0  1  5  iog(P ) n  Figure 2.8: Fe-02-S02 Predominance diagram at 950°C  -20' -20  •— -15  1  ' -10  •— -5 1  ' 0  1  5  iog(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_ S. Upon heating in air, pyrite decomposes into x  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 sulfate can form many intermediate compounds with lead oxide including the basic lead sulfates PbOPbS0 , 2PbO-PbS0 and 4PbOPbS0 . 3PbOPbS0 is a basic lead sulfate that can 4  4  4  4  only be synthesized by wet methods. It can be neglected in pyrometallurgical studies. The oxidation 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-PbS0 ), 1000K (2PbO-PbS0 ) and 1168K (4PbO-PbS0 ). These 4  4  51  4  Chapter  2.  Thermodynamics  and Kinetics  of  Roasting  (a) Predominance diagram  (b) P b Partial pressures  (c) PbS Partial pressures  (d) P b O Partial pressures  F i g u r e 2.10: P b - 0 - S 0 P r e d o m i n a n c e d i a g r a m at 8 5 0 ° C 2  2  52  Chapter  2.  Thermodynamics  and Kinetics  of  Roasting  950°C  950°C  PbS0  PbSO,  4  PbS  A  Pbs.  -~ - 5 o  CO  o  -10  -10 Pb  PbO  Pb  -15  -15  PbO T  •T: o ii£ &  o it  CL;  -20 -20  -15  -10 -5 iog(P )  -20 -20  0  -15  -10 -5 iog(P )  (b) P b P a r t i a l pressures  (a) P r e d o m i n a n c e d i a g r a m  -15  n. £  D.  0  0  -20  CL;  f: o  20  -10 -5 log(P )  -15  -10 iog(P ) 0  0  (d) P b O P a r t i a l pressures  (c) P b S 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  4  Chapter  2.  Thermodynamics  and Kinetics  of  Roasting  1050°C  1050°C ' PbSO, P b S ^ ^ / ^  —  ~~ o™  5  CO  a. -10 PbO  Pb -15  -20 -20  -15  -10  -10 -5 log(P )  | 0  0  -15  p o  -5 )  (b) P b P a r t i a l pressures  (a) P r e d o m i n a n c e d i a g r a m  -20  g(  -10 -5 log(P )  iog(P ) D  0  (d) P b O P a r t i a l pressures  (c) P b S P a r t i a l pressures  Figure 2.12: Pb-0 -S0 Predominance diagram at 1050°C 2  2  54  Chapter  2.  Thermodynamics  and Kinetics  of  Roasting  sulfates melt congruently or incongruently to form lead oxide - sulfate melts (see F i g u r e 2.24). T o allow some i n d i c a t i o n of the l i q u i d c o m p o s i t i o n , a l l three basic lead sulfates were kept i n the c a l c u l a t i o n of the predominance d i a g r a m .  A t 850°C, there are no l i q u i d phases formed unless the gas c o m p o s i t i o n is o n the P b O 4 P b O - P b S 0 4 e q u i l i b r i u m line where one m a y expect some l i q u i d since there is a eutectic between these two phases at  835°C. A t 950°C, lead oxide is m o l t e n , a n d 4 P b O - P b S C > 4 decom-  poses into 2 P b O - P b S 0 4 a n d a l i q u i d melt. B e y o n d  975°C, the basic lead sulfates are replaced  by an extensive lead oxide-sulfate l i q u i d 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  iog(P ) D  2  Figure 2.14:  CC1-O2-SO2  Predominance diagram at 950°C  log(P ) 0  2  Figure 2.15:  Cd-02-S02  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 (298717K). 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 iog(P )  0  5  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 m o l t e n phases were not clearly identified. was identified i n agglomerated  However, copper  sulfate  zinc calcines [59]. T h e probable presence of a t e r n a r y eutectic  between CU2S, CU2O a n d C u S 0 4 around 400 ° C was confirmed b y Rosenqvist [173]. A d d i t i o n a l studies are required to clearly identify the liquidus.  2.6  Water  T h e effect of water on concentrate lumps a n d pellets d u r i n g 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 a n d hydrogen sulfide [174]. T h i s reaction is not favoured t h e r m o d y n a m i c a l l y and can o n l y occur i f the hydrogen sulfide concentration is very s m a l l . In their system, c a l c i u m oxide was used to capture hydrogen sulfide, allowing the o x i d a t i o n 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 e q u i l i b r i u m be i n c l u d e d i n the analysis. S o h n and K i m [174] obtained a kinetic rate expression, applicable between 1023 a n d 1160K for steam concentrations between 3.94 a n d 9.84 m o l / m . 3  Because oxygen is omnipresent i n a roaster, hydrogen sulfide formation m a y be possible o n l y i n regions of very low oxygen concentration. H y d r o g e n sulfide w o u l d be very localized w i t h i n the roaster, r a p i d l y reacting w i t h oxygen to form steam a n d sulfur dioxide. Therefore H2S should not be detectable. T h e reaction of zinc oxide w i t h hydrogen sulfide to produce zinc sulfide was investigated for the desulfurization of gases from gasifiers [176]. U n d e r reducing conditions, hydrogen sulfide can react w i t h zinc oxide to form zinc sulfide and steam. However, at h i g h temperature, zinc oxide was reduced to gaseous zinc and then reacted to zinc sulfide. Z i n c oxide was stabilized by zinc titanates [177]. T h e regeneration of the desulfurization m e d i a was achieved b y r e o x i d i z i n g the zinc sulfide, releasing sulfur dioxide. Sasaoka et al. [178] have recently shown t h a t steam plays a role i n the o x i d a t i o n of zinc sulfide. U s i n g an oxygen isotope as a tag a n d a mass spectrometer,  59  Chapter  2.  Thermodynamics  and Kinetics  of  Roasting  they found that w i t h o u t oxygen, steam reacts w i t h zinc sulfide to p r o d u c e tagged sulfur dioxide and hydrogen, b u t w h e n oxygen was present, the tagged steam s t i l l reacted w i t h z i n c sulfide to produce tagged sulfur dioxide. W h e n no steam or s m a l l amounts of s t e a m were present, oxygen reacted d i r e c t l y 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 t o p r o d u c e zinc calcine.  T h e e q u i l i b r i u m c o m p o s i t i o n of the p r o d u c t s m a y b e calculated by m i n i m i z i n g the  G i b b s free energy of the system. T h e r m o d y n a m i c calculations c a n be performed for a n u m b e r of conditions of v a r y i n g temperature and c o m p o s i t i o n (amount of zinc concentrate a n d air). T h i s would give a n impressive list of c o m p o u n d s a n d concentrations. However, a s i m p l e r approach may be suitable, based o n predominance diagrams.  Because zinc sulfide is the major c o m p o u n d i n zinc concentrates, t h e reaction of oxygen to sulfur dioxide is governed b y t h e o x i d a t i o n of zinc sulfide.  A s s u m i n g t h a t reactions o f other  sulfides do n o t significantly affect the gas c o m p o s i t i o n , their end p r o d u c t m a y be predicted w i t h the help o f t h e final gaseous c o m p o s i t i o n o f t h e zinc o x i d a t i o n reaction:  Z n S + x0  2  + ?/N —> S 0 2  2  + solid p r o d u c t  + y~N  2  (2.10)  T h e solid p r o d u c t 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 c o m p o s i t i o n of the zinc o x i d a t i o n reaction depends o n the i n i t i a l amount of oxygen present. T h e resulting sulfur dioxide a n d any excess oxygen end u p i n the gaseous p r o d u c t . T o help predict t h e final gaseous composition, assuming the reaction of zinc sulfide to zinc oxide, we define the stoichiometric excess of oxygen b y : Excesso2 = ' l  Z n S  n  °  2  ~ 1  (2-H)  ^02"ZnS  where ni is the n u m b e r of moles of species i a n d vzn s a n d f o 2 are t h e 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  800  850 900 950 Temperature °C  1000  1050  1000  1050  (b) L e a d  (a) Z i n c  750  850 900 950 Temperature °C  1000  1050  750  (c) Iron  800  850 900 950 Temperature °C (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  -0.05-  0  and Kinetics  =01-  -0  -0.05-  AVJ-  of  Roasting  -0.1-  -0.01-0.001 — 0.0001 —  -0.0001  1e-005—| 1e-006 -1e-007— -1e-008 -1e-009-  -1e-009-10 750  -1e-010-  L  800  850 900 950 Temperature °C  1000  750  1050  850 900 950 Temperature °C  1000  1050  (b) Sulfur d i o x i d e c o n c e n t r a t i o n  (a) O x y g e n c o n c e n t r a t i o n  F i g u r e 2.20:  800  G a s c o n c e n t r a t i o n s for e x c e s s 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 f o r  g a s e o u s feed o f a i r (21% O2).  Calculated using thermodynamic data and equation  63  2.11  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  P502  - 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 concentration 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 operatingconditions (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 diagram. 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 b y a d o p t i n g the operating c o n d i t i o n (excess oxygen) instead of the gas p a r t i a l pressures (P02 a n d Psc.2) for a constant t o t a l p a r t i a l pressure. In section 6.3.4, the stoichiometric m o d e l w i l l be replaced by a complete fluidized bed roasting reactor model, a n d its o u t p u t w i l l be used to create a d i a g r a m s i m i l a r to F i g u r e 2 . 1 9 . A s kinetic m o d e l l i n g w i l l show, the use of t h e r m o d y n a m i c s for fluidized b e d roasters m a y result in erroneous conclusions. However, t h e r m o d y n a m i c s show very clearly t h a t excess oxygen m a y significantly affect the reaction products of the i m p u r i t i e s .  2.8  Gas phase reactions  Various elements a n d compounds are volatile d u r i n g the roasting of zinc concentrates.  For  example, due to their volatile nature, halides, m e r c u r y and arsenic species are separated from the calcine d u r i n g roasting. T h e m e r c u r y a n d arsenic species are gaseous at roasting temperatures and are not discussed here. C a d m i u m , lead a n d zinc species are not u s u a l l y gaseous at roasting temperatures. However, under some conditions, their p a r t i a l pressures are relatively h i g h a n d this may affect their volatilization.  F o r example, various researchers have s t u d i e d c a d m i u m  volatilization d u r i n g the roasting of zinc concentrates,  either to increase [180, 1 8 1 , 182] or  reduce [183, 184] its removal from the calcine.  V a p o r i z a t i o n chemistry has received very l i t t l e attention i n the roasting literature. However, an early review [185] has shown that it is more complex t h a n one w o u l d expect. D e p e n d i n g on the metal i n question, oxides and sulfides species have been found to e x h i b i t different features such as simple v a p o r i z a t i o n , dissociative v a p o r i z a t i o n a n d p o l y m e r i c gas species. Z i n c and c a d m i u m volatilize very similarly. T h e vapour pressures of zinc a n d c a d m i u m for the oxygen or sulfur systems are shown i n F i g u r e 2 . 2 1 . B o t h their oxide a n d sulfide dissociate to form Z n ( ) , Cd( ) and 0 ( ) , S ( ) . 5  fl  2  9  2  g  Because v a p o r i z a t i o n produces a n o n - m e t a l species, any  change i n its concentration affects the m e t a l vapour pressure.  T h i s has been e x p e r i m e n t a l l y  observed by measuring the vapour pressure of c a d m i u m over c a d m i u m oxide as a function of oxygen p a r t i a l pressure [185]. T h e analysis of the m e t a l vapour p a r t i a l pressure is very similar  65  Chapter  2.  Thermodynamics  and Kinetics  of  Roasting  to that of the s o l u b i l i t y of salts i n aqueous solutions where a s o l u b i l i t y p r o d u c t is used to establish the e q u i l i b r i u m ionic concentrations.  In the gaseous state, the p a r t i a l pressure of the  non-metal species is used w i t h the e q u i l i b r i u m constant to o b t a i n the e q u i l i b r i u m m e t a l vapour pressure. T h e v o l a t i l i t y of the oxide or sulfide i n v a c u u m or inert atmosphere is represented by points A i n F i g u r e 2.21. T h e v o l a t i l i t y of zinc i n retorting or slag fuming is enhanced b y using a reducing atmosphere i.e. m o v i n g to the left of point A . B e l o w a c r i t i c a l level, the condensed m e t a l is stable a n d its p a r t i a l pressure reaches a constant value. T h e zinc a n d c a d m i u m p a r t i a l pressures and the interaction of sulfur a n d oxygen i n the t e r n a r y systems are presented w i t h their respective predominance diagrams (see F i g u r e s 2.1 to 2.3 and 2.13 to 2.15). P o i n t A i n these diagrams represents the c o m p o s i t i o n of the gas i n e q u i l i b r i u m w i t h a m i x t u r e of sulfide and oxide. P o i n t A is a point because of the following e q u i l i b r i a :  MS + 2 M 0  = 3M(g)  + S0  (2.12)  2  (2.13) T h e m e t a l p a r t i a l pressure i n e q u i l i b r i u m w i t h the oxide-sulfide m i x t u r e is higher t h a n that i n e q u i l i b r i u m w i t h oxide or sulfide (Points A on F i g u r e 2.21). One of the zinc sulfide o x i d a t i o n mechanisms is its reaction i n the vapour phase. A s F i g u r e 2.21 suggests, under conditions of h i g h temperatures a n d / o r very low oxygen  concentrations,  the sulfide m a y sublimate and, once the oxygen concentration is sufficiently h i g h , react at a distance from the sulfide particle.  Such a mechanism has been observed i n various studies.  It has been shown that the o x i d a t i o n of zinc sulfide at very h i g h t e m p e r a t u r e (1800-2200K) proceeds by dissociative vaporization and reaction i n the gas phase [186].  However, t y p i c a l  roasters operate far from these temperatures. T h e same gas phase reaction has been observed at lower temperatures [122]. T h e vaporization chemistry of lead species is very different from t h a t of zinc a n d c a d m i u m species.  For instance,  lead species form p o l y m e r i c vapour c o m p o u n d s 66  (Pb2S2, Pb202, etc  Chapter  2.  Thermodynamics  and Kinetics  of  Roasting  log(P J  log(P_ ) 2  n  (a) Zinc-Oxygen  (b) Zinc-Sulfur  log(P )  log(P_ )  n?  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  [185]) a n d d o n o t d i s s o c i a t e .  of  Roasting  T h e exact c o m p o u n d s present i n the gaseous state d e p e n d o n  oxygen a n d sulfur p a r t i a l pressures. However, unlike the z i n c a n d c a d m i u m systems, the m e t a l v a p o u r p r e s s u r e d o e s n o t c h a n g e 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 r e s s u r e (see F i g u r e 2 . 2 2 ) .  log(P )  log(P )  n?  q2  (a) L e a d - O x y g e n  (b) L e a d - S u l f u r  log(P )  l 0  OP  9( s ) p  2  (c) L e a d - O x y g e n t o t a l pressure  (d) L e a d - S u l f u r 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 r e s s u r e s  68  the total  partial  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 concentrate, 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 concentrations. 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: ^Cd  > ^PbS >  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 a n d temperatures. U n l i k e the p r e d o m i n a n c e area diagram, their generation is very complex r e q u i r i n g difficult e x p e r i m e n t a l measurements. Several phase diagrams are presented i n this section, b o t h for the p r o d u c t s a n d the reactants. These diagrams give i n f o r m a t i o n on the possible m o l t e n phases present d u r i n g roasting. Because of the number of i m p u r i t i e s present i n a t y p i c a l concentrate, the m e l t i n g p o i n t of the calcine or concentrate m a y be well below that of its m a i n constituents. T h e phase diagrams m a y indicate w h i c h i m p u r i t y a n d phase contribute to agglomeration. L o w - m e l t i n g - p o i n t c o m p o u n d s can be classified i n three general types: reactant, p r o d u c t a n d reacting. T h e reactant low-melting-point c o m p o u n d s are those present i n the concentrate. T h e eutectics i n the  ZnS-FeS-PbS  system fall into this category.  Because the reactants react i n  the roaster, these c o m p o u n d s have a finite life. T h e p r o d u c t low-melting-point c o m p o u n d s are those present i n the zinc calcine p r o d u c t . T h e eutectics i n the P b O - P b S 0 4 and PbO-SiC"2 systems belong to this category. These are compounds stable i n the roaster gas and s h o u l d always be present d u r i n g roasting. A s u m m a r y of the m e l t i n g temperatures of various phases is shown below, i n T a b l e 2.4.  2.9.1  Phase diagrams - product type  T h e first phase d i a g r a m , shown i n F i g u r e 2.23, presents the zinc oxide silica phase d i a g r a m . D u e to its effect on d o w n s t r e a m processes, the p r o d u c t i o n of zinc silicate d u r i n g roasting has received some attention. Because the silica contained i n zinc silicate is acid soluble, the presence of zinc silicate does not affect zinc recovery, but does affect the amount of silica i n s o l u t i o n . Dissolved silica can polymerize, produce colloidal silica, gelify a n d cause severe filtering problems Z i n c silicate is o n l y found as Z i i 2 S i 0 4 .  [187].  F r o m the d i a g r a m , two eutectics are present,  b o t h are m u c h higher t h a n t y p i c a l roaster operating temperatures  (~950°C).  pure zinc silicate w o u l d likely be formed by a solid-state diffusion process.  but  Therefore, any L i u et al.  [188]  have studied the kinetics of formation of zinc silicate from h i g h s i l i c a - c o n t a i n i n g sphalerite concentrate.  T h e y have observed that the process could be m o d e l l e d b y the s h r i n k i n g core  70  Chapter  2.  Thermodynamics  and Kinetics  of  Roasting  model and that solid-state diffusion controls the process. T h e y o b t a i n e d a n a c t i v a t i o n energy of 406 k J / m o l . In the lead system, there is a significant s o l u b i l i t y amongst some of the species. For instance, Pb(;) and PbS(;) can be described as a single l i q u i d solution [195]. A s shown i n F i g u r e 2.24, the lead oxide-lead sulfate system has numerous phases a n d eutectics. F i g u r e 2.24 is the P b O - P b S 0 4 phase d i a g r a m refined b y B i l l h a r d t [190]. diagram, no solid solutions exist i n this system.  A s seen i n the  However, the lowest t e m p e r a t u r e at w h i c h  a l i q u i d phase can exist is 8 3 5 ° 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 w h i c h melts incongruently at 8 9 5 ° C . 2PbO-PbS0  4  is metastable below 6 4 0 ° C .  F i g u r e 2.25 presents the lead oxide silica phase d i a g r a m . T h e r e are three lead silicates a n d three eutectics, a l l m o l t e n above 7 6 0 ° C . T h e lead oxide zinc oxide phase d i a g r a m , shown i n F i g u r e 2.27, has one eutectic m e l t i n g at 8 6 1 ° C . T h e P b O - Z n O - S i 0 2 system was recently o p t i m i z e d [196] such t h a t a complete t h e r m o d y n a m i c representation of the system is available i n the F A C T t h e r m o d y n a m i c database c o m p u t i n g system. T h e alumina-lead oxide phase d i a g r a m is shown i n F i g u r e 2.26. S i m i l a r l y to the zinc oxide - lead oxide system, the a l u m i n a system o n l y has one eutectic.  2.9.2  Phase diagrams - reactant type  Impurities i n the zinc concentrate m a y contribute to the presence of low-melting-point phases. T h e phase diagrams presented i n Figures 2.29 to 2.31 are needed w h e n considering the effect of impurities on the m e l t i n g temperature of zinc concentrates. N o t e that these diagrams neglect solid solutions a n d were created to represent the liquidus and solidus lines.  T h e m i n i m u m m e l t i n g temperatures for the three b i n a r y systems are 1 1 6 0 ° C ( F e S - Z n S , F i g u r e 2.29), 1041°C ( P b S - Z n S , F i g u r e 2.30) and 1130°C ( C u S - Z n S , F i g u r e 2.31). 2  However, the  a d d i t i o n of F e S to the P b S - Z n S system produces a t e r n a r y eutectic w h i c h melts as low as 7 1 7 ° C [81]. Figures 2.32 a n d 2.33 present the F e S - P b S and C u S - P b S phase diagrams. B o t h 2  71  Chapter  2.  Thermodynamics  and Kinetics  of  Roasting  F i g u r e 2.23: Z n O - S i 0 2 phase d i a g r a m . [189], T e m p e r a t u r e i n ° C  < -Mol % PbO F i g u r e 2.24: P b O - P b S 0  72  4  phase d i a g r a m [190]  Chapter  2.  Thermodynamics  and Kinetics  of  Roasting  F i g u r e 2.25: P b O - S i 0 2 phase d i a g r a m [191]. C o m p o s i t i o n i n wt%,  F i g u r e 2.26: P b O - A l 0 2  3  Temperature in °C  phase d i a g r a m [192] T e m p e r a t u r e i n ° C  73  Chapter  2.  Thermodynamics  and Kinetics  of  y 9 7 5  Roasting  8  1  1  -  1  1000  1  Z n 0 + L i q.  Liquid j  900 888  —  861:2° / / /  PbOss+ZnO t  800  i  PbO  l  l  40  20  60 Mol.  80  ZnO  %  F i g u r e 2.27: P b O - Z n O phase d i a g r a m [193] T e m p e r a t u r e i n ° C  1400  T  r  T  J  1300  Fe 0* 9  r 1315  + Liquid  1200 I  1100 i i I I  1000 >  B + Liquid  i i  jB+FejjOjl —  945' r » Liquid 910 V  -  900 800  8+r  PbO \  760° \  750' 1:2  700 600  PbO+ 8  S + Fe O 2  10  20  30  F i g u r e 2.28: P b O - F e 0 2  3  40  50 Mol %  i:6 650°  s  2:i 0 PbO  r»Fa,O.J  -X—  60  _1_ 70  80  90 F e  100 z°3  phase d i a g r a m [194] T e m p e r a t u r e 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  1190  1200  1100  v  Bmtt.34,87 -  0  -Kerby-fa '  p4  381  139  O  Kopvtav-76 *"  •  Eric-94 >, Solid + Liquid  o  Eric-94 >. Liquid  1  1120.5]  f37  p7  Calculated  1000  H  900  i • o o • ..• c a  800  o.o  FeS  Q2  0.4  0.6  0B  Mole fraction of PbS  Figure 2.32: FeS-PbS phase diagram [197]  76  1.0 PbS  Chapter 2. Thermodynamics and Kinetics of Roasting  Figure 2.33: Cu S-PbS phase diagram [197] 2  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) a n d 5 1 7 ° C ( F i g u r e 2.33), respectively. It is clear that it is the interaction of impurities that m a y lead to low-melting-point phases w i t h i n zinc concentrates. A complete ternary or quaternary phase d i a g r a m is therefore helpful i n e v a l u a t i n g the effect of the m a i n i m p u r i t i e s on the m e l t i n g temperatures of zinc concentrates. F i g u r e 2.34 presents the liquidus surface of the Z n S - F e S - C u 2 S - P b S quaternary system (shown as 4 t e r n a r y systems). N o t e that the liquidus surface represents the composition and temperature of complete melting. Since roasting involves p r e d o m i n a n t l y solid phases and agglomeration m a y be p r o m o t e d by very s m a l l amounts of liquids, the solidus surface (surface of the conditions where a l i q u i d phase first appears) offers the most useful information. However, a quaternary (or ternary) section (phases at a given temperature) or solidus surface phase d i a g r a m is not available. A n a l y s i s is therefore l i m i t e d to the quaternary phase d i a g r a m a n d to the b i n a r y diagrams presented previously. Z i n c concentrates may, depending on their m i n e r a l o g y a n d their extended exposure to high temperatures w i t h i n the roaster, form l i q u i d phases w i t h compositions near the F e S - P b S a n d Cu2S-PbS eutectics.  N o t e that amongst these phases, P b S is the most  volatile under roasting conditions. Its presence w i t h i n l i q u i d phases w o u l d likely be influenced by vaporization.  2.9.3  Phase diagrams - reacting type  T h e last type of phase d i a g r a m represents the reacting low-melting-point l i q u i d formed from reactant and products. T h e ternary eutectic i n the F e - S - 0 system, s h o w n i n F i g u r e 2.35, is a good example. T h e ternary eutectic i n the F e S - F e O - Z n S system at 9 2 0 ° C [201] also falls w i t h i n this category. A l i q u i d phase would only be present for a short t i m e d u r i n g the reaction. T h e i n i t i a l reactant a n d final p r o d u c t m a y be solid, b u t the intermediate m a y pass near the eutectic composition a n d become l i q u i d u n t i l it resolidifies as the reaction proceeds. S u c h a low-melting-point phase w o u l d be transient a n d w o u l d depend on the reaction p a t h and the kinetic conditions. Such a reactive solidification has been observed i n the copper system [173]. A CU2S-CUSO4 m i x t u r e was m o l t e n at 4 5 0 ° C under an atmosphere of SO2, b u t 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 temperature 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  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]  Cu S-PbS  Binary Eutectic  517°C from Figure 2.33  [197]  FeS-ZnS-PbS  Ternary Eutectic  717°C  [81]  Pure  880°C  Binary Eutectics  835°C from Figure 2.24  [190]  Binary Eutectics  720°C from Figure 2.25  [191]  Binary Eutectic  861°C from Figure 2.27  [193]  Binary Eutectic  730°C from Figure 2.28  [194]  Fe-S-0  Ternary Eutectic  915°C from Figure 2.35  [199]  FeS-FeO-ZnS  Ternary Eutectic  920°C  [201]  Ternary Eutectic  <450°C  [173]  Ternary Eutectic  850°C from Figure 2.36  [200]  Reactant type  2  Product type PbO . PbO-PbS0 PbO-Si0  4  2  PbO-ZnO PbO-Fe 0 2  3  Reacting type  Cu S-Cu 0-CuS0 2  2  Cu S-FeS-FeO 2  4  The low-melting-point phases discussed and shown in the various phase diagrams are summarized in Table 2.4. Zinc sulfide, zinc oxide or zinc silicates are not molten at typical roaster operating 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-meltingpoint 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-meltingpoint 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 reactions. 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 w h e n F e S was involved. E q u i l i b r i u m calculations of m a t t e against solid sulfides is currently l i m i t e d to zinc and copper sulfide solid solutions. E q u i l i b r i u m calculations of the m a t t e w i t h other solid sulfide phases is c u r r e n t l y not recommended.  It is  likely that the database w i l l allow calculations w i t h i n a relatively near future. T h e most c o m m o n c o m p o u n d c o n t r i b u t i n g to low-melting-point phases is lead oxide ( P b O ) . P u r e lead oxide is a l i q u i d at t y p i c a l roaster operating temperatures ( ~ 9 5 0 ° C ) . Several c o m pounds are soluble i n lead oxide, and some create eutectics that melt at even lower temperatures.  8 2  Chapter 3 Experimental Methods  In the light of the complex features of i n d u s t r i a l fluidized bed roasters, the process must be simplified i n an experimental setup capable of evaluating agglomeration phenomena.  For i n -  stance, unlike the feed, to the i n d u s t r i a l roaster, the feed to the e x p e r i m e n t a l roaster consists of dried concentrate particles where no l u m p s are present. A l s o , since entrainment of concentrate particles prior to their entry into the i n d u s t r i a l fluidized bed cannot be clearly separated from entrainment  from the bed, the feed is d i r e c t l y injected into the e x p e r i m e n t a l fluidized bed.  Hence moisture, l u m p s and concentrate entrainment are absent i n the experiments so that we can determine how the chemical phenomena influence the particle size d i s t r i b u t i o n . M o s t experiments used the same i n i t i a l bed m a t e r i a l and same i n d u s t r i a l concentrate.  Since  the concentrate was the same and o n l y the operating conditions varied from one experiment to another, the experiments focussed on how the operating variables affect the bed particle size distribution.  3.1  Experimental pilot plant  T h e pilot scale roaster used i n the present s t u d y is similar to t h a t of Y a z a w a et al. [107], requiring continuous feeding for experimental runs lasting several hours.  However, because  they studied the behaviour of m i n o r elements d u r i n g fluidized bed zinc roasting, Y a z a w a et al. [107] required a gas cleanup system s i m i l a r to the i n d u s t r i a l process. I n this work, the focus is on the processes o c c u r r i n g i n the fluidized bed. Therefore, a simplified gas treatment system was used. F i g u r e 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 b e d d i d not fail prematurely. T h e outputs of these sensors are p r o p o r t i o n a l to the l o g a r i t h m of the ratio of the oxygen pressures inside a n d outside the sensing element. Therefore, the o u t p u t is sensitive to b o t h the overall pressure of the system a n d the oxygen p a r t i a l pressure. T h e elutriated m a t e r i a l is collected by a hot gas filter u n i t at the exit of the roaster. T h i s is a chamber w h i c h functions like a high-temperature baghouse e q u i p p e d w i t h three porous ceramic candles [202]. T o enhance particle capture a n d to m i n i m i z e the l o a d i n g of the candles, the particle-laden gas enters the filter "tangentially". T h e candles are cleaned b y a pulse system involving solenoid valves, w i t h the t i m i n g a n d d u r a t i o n of the pulses controlled b y the d a t a acquisition computer. A chemical scrubber removes sulfur dioxide from the outlet gas stream. The  scrubber consists of two 57 litre stainless tanks (beer kegs) filled w i t h 16 w t % N a O H  solution. T h e choice of the s o l u t i o n strength is discussed i n a p p e n d i x E . T h e draft t h r o u g h the entire system is created by an eductor-type v a c u u m p u m p (Vaccon C D F - 2 0 0 ) . T h e feeding system (not shown i n F i g u r e 3.1) allows the roaster to be fed continuously. Solid additions to the fluidized b e d are metered using a scale a n d a speed-controlled r o t a r y valve. The  concentrate is conveyed p n e u m a t i c a l l y a n d enters the b e d t h r o u g h couplings near the  d i s t r i b u t o r plate. A K a l m a n filter w i t h integral control a u t o m a t i c a l l y controls the feeder motor speed to o b t a i n the desired feedrate. A p p e n d i x A presents more details o n the feeder. A pressure switch a n d a safety manometer are connected to the b o t t o m of the preheater to allow for overpressure a n d underpressure protection. If plugging occurs anywhere i n the system, the system w i l l pressurize u p to the pressure switch l i m i t . O n c e this l i m i t has been reached, the system a u t o m a t i c a l l y stops the power to the furnaces a n d interrupts the flow of gases to the system. If the pressure still increases b e y o n d the pressure switch l i m i t , a second l i m i t m a y be reached, set by the safety manometer. T h e safety manometer w i l l d r a i n a n d vent the gases to the b u i l d i n g exhaust system. Underpressure protection is set b y the safety manometer water height. If excessive underpressure occurs, the water w i l l d r a i n a n d air w i l l enter the system. Once the safety manometer seal has been broken, an experiment cannot be continued u n t i l the  .86  Chapter  3.  Experimental  Methods  manometer is refilled w i t h coloured water.  3.2 3.2.1  Description of materials Zinc concentrates  T h e zinc concentrates used i n this study were chosen because of the large experience of this project's sponsor using w i t h these concentrates.  T h e i r compositions are t y p i c a l of most zinc  concentrates. A p p r o x i m a t e l y 200 k g of zinc concentrate were s h i p p e d to U B C by T e c k C o m i n c o i n 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 u n t i l required.  Samples  were gathered from a n u m b e r of pails for assay of m u l t i p l e elements ( i n c l u d i n g t o t a l sulfur and silica) a n d sulfate sulfur.  A second batch of 140 k g of zinc concentrate ( C o n c e n t r a t e 1(b)),  shipped i n September 2002, was also assayed. Table 3.1 presents the concentrates chemical compositions. These results were o b t a i n e d from an independent l a b o r a t o r y (International P l a s m a L a b o r a t o r y L t d , V a n c o u v e r ) . O n l y the major elements are shown i n the table; the complete assays are presented i n A p p e n d i x F . T h e zinc, and sulfur assays were obtained by t i t r a t i o n and gravimetric methods, while the other elements were obtained by m u l t i - a c i d digestion followed by i n d u c t i v e l y coupled p l a s m a ( I C P ) analysis. T a b l e 3.1: Weight c o m p o s i t i o n of zinc concentrates (wt%) Element  Concentrate 1(a)  Concentrate 1(b)  Concentrate 2  Zn  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  Pb  3.5  3.5  4.7  Cd  0.34  0.34  0.14  Cu  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  S i l i c a a n d lead sulfide m a y have accounted for some of the very s m a l l peaks detected, but their presence is inconclusive. E l e c t r o n microscopy and X - R a y spectroscopy c o u l d not detect any sulfide phases other t h a n sphalerite. Some gangue m i n e r a l inclusions, m a i n l y composed of silica, were observed. T h e solid density are 4170 k g / m a n d 4040 k g / m for concentrates 1 and 2, respectively, based 3  3  on the wet picnometer m e t h o d . E l e c t r o n microscopy indicated that there is l i t t l e or no porosity present w i t h i n the concentrate particles. T h e particle size distributions were obtained using a M a l v e r n Mastersizer 2000 e q u i p p e d w i t h a Scirroco 2000 d r y feeder.  T h i s instrument  distributions ranging from 0.02 to 2000 pm. pressure of 2.5 bar.  uses laser diffraction to measure particle size T h e d r y feeder was operated w i t h a dispersion  P a r t i c l e size d i s t r i b u t i o n analyses of concentrate 1 a n d of concentrate 2  are shown i n F i g u r e 3.2 and Table 3.2. T h e two batches of concentrate 1 have, for a l l p r a c t i c a l purposes, the same particle size d i s t r i b u t i o n . T h e particle size d i s t r i b u t i o n of a pure zinc sulfide is also shown i n F i g u r e 3.2. Since pure zinc sulfide has a m u c h finer particle size d i s t r i b u t i o n t h a n that of the concentrates, no fluidized bed roasting experiment was a t t e m p t e d w i t h pure ZnS.  Note that d  v  is the area averaged particle size a n d d  v  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 = — ~x£ l  ^  (3.1)  d  upi  dy — ^ ] %idpi  A p p r o x i m a t e l y one week before an experiment, the contents of one p a i l were transferred  (3-2)  into  stainless steel a n d glass containers that were then placed i n an 5 0 ° C oven u n t i l they reached a constant weight (after a p p r o x i m a t e l y 6 days). T h e d r i e d concentrate was then sieved t h r o u g h a 63 pm screen a n d the oversize fraction was rejected. T h e screened concentrate was also assayed for the same elements as listed i n Table 3.1. 88  Chapter  3.  Experimental  Methods  Particle Size (um) F i g u r e 3.2: P a r t i c l e size d i s t r i b u t i o n of zinc concentrates.  L i n e for C o n c e n t r a t e 1 is for b o t h  Concentrate 1 (a) and 1 (b).  3.2.2  Bed material: silica sand and alumina  T o determine whether agglomeration occurred on the surfaces of the particles i n i t i a l l y present i n the bed, or alternatively from newly-formed zinc calcine seeds, the t y p i c a l zinc calcine bed material was replaced w i t h silica sand or a l u m i n a particles, because of their relative inertness at high temperatures. Furthermore, the large difference between the molecular weights of silica and zinc oxide enhanced the v i s u a l differentiation between these phases i n backscattered electron microscopy. 50 k g each of 50 mesh and 125 mesh L a n e M o u n t a i n silica sand, (> 99 w t % S i 0 2 ) , were obtained in 25 k g bags from Target P r o d u c t s (Burnaby, B . C . ) . U p o n reception, the silica sand was stored i n pails and sampled for chemical analysis. Similarly, a 25 k g bag of 100 mesh b r o w n a l u m i n a was purchased from M a n u s A b r a s i v e s .  89  Chapter  3.  Experimental  Methods  Table 3.2: P a r t i c l e size d i s t r i b u t i o n of z i n c concentrates Concentrate  Pure  1(a)  1(b)  2  ZnS  3.67  3.71  6.48  0.51  V o l u m e average: d„ (/xm)  14.6  14.8  21.5  0.59  d m (/-*m)  1.49  1.49  2.90  0.32  do  (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  S u r f a c e / V o l u m e average: d  p  5  (/xm)  Table 3.3 presents the sand chemical c o m p o s i t i o n . T h e metals are s h o w n i n their oxide form. T h e reader is referred to a p p e n d i x F for the complete assay i n m e t a l form. T h e particle size distributions are shown i n F i g u r e 3.3 a n d the Sauter mean size of the various sands are reported i n Table 3.4. T h e measured solids densities of silica a n d a l u m i n a are 2650 k g / m a n d 3960 k g / m 3  3  respectively. E l e c t r o n microscopy of cross-sections have shown that b o t h s i l i c a a n d a l u m i n a are non-porous.  Table 3.3: Weight c o m p o s i t i o n of i n i t i a l b e d materials (wt%). S i l i c a sand assays performed by m u l t i - a c i d digestion and I C P . A l u m i n a assay performed by fusion a n d T C P . Element  Si0  2  50 mesh  Si0  125 mesh  2  2  3  100 mesh  A1 0  3  0.21  0.30  92.34  Fe 0  3  0.033  0.048  0.23  K 0  0.056  0.077  0.14*  Na 0  0.019  0.021  0.043*  Si0  balance  balance  1.1+  TiC-2  <0.016  <0.016  2.94  ZnO  0.029  0.010  0.103*  2  2  2  2  2  * : M u l t i - a c i d digestion m a y be incomplete +  A1 0  : F u s i o n and I C P l a b o r a t o r y 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 (jum)  80.9  223  173  Volume average: d„ (/im)  126  307  191  dio (Mm)  47.7  122  111  dso (Mm)  94.0  266  173  d o (Mm)  147  411  230  dgo (M )  186  500  263  p  8  m  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%, A1 0 : average=88wt%, cr=2.2wt%) 2  3  91  Chapter  3.  Experimental  3.2.3  Gases  Methods  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: R a n g e of experimental  variables  Min  Max  Temperature  875°C  975°C  Feed gas oxygen concentration  21%  30%  Superficial gas velocity  0.25  Inert bed mass  m/s  0.5 m / s  3 kg  Inert bed material  Si0  5 kg A1 0  2  2  223  3  pm  B e d material size  81 /um  Concentrate  Concentrate 1  Concentrate 2  D r y concentrate feed rate  10 g / m i n  36 g / m i n  Excess O x y g e n  0 %  80 %  Table 3.7: S u m m a r y of experimental conditions for each e x p e r i m e n t Run  Feed rate  Temperature  Sup. gas velocity  10 g/min  940 °C  0.25 m/s  21%  0  2  Cone. 1  10 g/min  940 °C  0.25 m/s  21%  0  2  2  Cone. 1  10 g/min  940 "C  0.25 m/s  21%  0  2  2  Cone. 1  10 g/min  940 "C  0.25 m/s  21%  0  2  Cone. 1  10 g/min  940 "C  0.22 m/s  25%  0  2  Cone. 1  10 g/min  940 °C  0.22 m/s  25%  0  2  Cone. 1  17.5 g/min  940 °C  0.25 m/s  21%  0  2  Cone. 1  17.5 g/min  940 °C  0.25 m/s  21%  0  2  Cone. 1  16.25 g/min  940 °C  0.25 m/s  21%  0  2  Bed Material  1  50  Si0  2  50  Si0  3  125 S i 0  4  125 S i 0  5  50  6  125  7  50  Si0  2  2  2  Si0 Si0  2  2  8  125  Si0  9  125  Si0  10  50 S i 0  11  125  12  50  Si0  13  50  Si0  14  50 S i 0  15  50  Si0  16  50  Si0  17  50 S i 0  Concentrate C. 1 + 125  2  2  Si0  2  Gas composition  Cone. 1  16.25 g/min  940 °C  0.25 m/s  21%  0  2  Cone. 1  17.5 g/min  940 °C  0.22 m/s  25%  0  2  2  Colic. 1  17.5 g/min  940 °C  0.22 m/s  25%  0  2  2  Cone. 1  15 g/min  940 °C  0.25 m/s  21%  0  2  2  Cone. 1  15 g/min  940 °C  0.25 m/s  21%  0  2  2  Cone. 1  16.25 g/min  875 °C  0.25 m/s  21%  0  2  2  Cone. 1  16.25 g/min  975 °C  0.25 m/s  21%  0  2  2  Cone. 1  16.25 g/min  905 °C  0.25 m/s  21%,  0  2  2  Cone. 2  14.85 g/min  940 °C  0.25 m/s  21%  0  2  2  Cone. 1  36 g/min  940 °C  0.5 m/s  21%  0  2  2  Cone. 1  23.25 g/min  940 °C  0.25 m/s  30%  0  2  26.25 g/min  940 "C  0.375 m/s  21%  0  2  2  Si0  2  18  50  Si0  19  50  Si0  20  50  Si0  21  50 S i 0  2  Cone. 1  22  50  Si0  2  Cone. 1  19.8 g/min  940 °C  0.25 m/s  25%  0  2  23  50  Si0  2  Cone. 1  16.25 g/min  940 °C  0.25 m/s  21%  0  2  Cone. 1  16.25 g/min  975 °C  0.25 m/s  21%  0  2  Cone. 1  Varies  940 °C  0.25 m/s  21 and 25%  Cone. 1  Varies  940 "C  0.25 m/s  21%  0  2  Cone. 1  16.25 g/min  940 "C  6.25 m/s  21%  0  2  24  100 A 1 0 2  25  50  26  125  27  50  Si0  2  Si0 Si0  2  2  3  94  Excess Oxygen 80 % 80 % 80 % 80 % 80 % 80 % 0 % 0 % 10 % 10 % 0 % 0 % 20 % 20 % 10 % 10 % 10 % 10 % 10 % 10 % 10 % 10 % 10 % 10 %  0  2  varies varies 10 % + 10 %  Chapter  3.  Experimental  Methods  a 150 m m long, 25.4 m m (1 inch) wide strainless steel 316 t u b e (cup) u s i n g a Swagelok fitting, hand-tightened w i t h R o c k and R o l l ceramic anti-seize (for details, see a p p e n d i x D ) . T h e fitting was screwed into a p l u g welded at one end of the wider tube. T h e other end was also sealed w i t h a p l u g . F o u r 9.5 m m (3/8") wide, 12.5 m m (1/2") long slots were m a c h i n e d into this t u b e as openings for c a p t u r i n g particles. A longer version of this sampler is capable of c a p t u r i n g about twice as m u c h solids. T h e s a m p l i n g valve was opened to lower the s a m p l i n g device into the bed, u n t i l it reached the level of the d i s t r i b u t o r , p l a t e . T h e sampler was continuously purged w i t h n i t r o g e n gas, injected through the t u b e to "quench" reactions of particles w h i c h h a d 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 m e t a l cup s t a n d i n g i n a water b a t h . A f t e r cooling, the samples  were bagged a n d labelled. T h e carry-over particles accumulated at the b o t t o m of the filter were collected according to the following m e t h o d . After o p e n i n g the filter outlet valve, the b o t t o m of the filter was h a m m e r e d to dislodge adhering particles into the hopper. T h e filter outlet valve was closed before unscrewing the cap below the hopper a n d discharging the solids (60-600 g, average 100 g) into a P y r e x d i s h . These solids were at ambient temperature a n d d i d not require further cooling. T h e solids were bagged and labelled. D u r i n g some e x p e r i m e n t a l runs, the gas was analyzed for oxygen. T h e analysis t r a i n consisted of an inline cooler, a solids collection tube, an inline gas filter (Swagelok SS-2F-0.5/xm), a s m a l l sulfur dioxide scrubber (two 1 litre E r l e n m e y e r containing 500 m l 16wt% N a O H solution) a n d a gas dryer. T h e s a m p l i n g t r a i n effectively removed particles a n d SO2 from the sampled gas prior to analysis. A H o r i b a E S - 5 1 0 s a m p l i n g u n i t a n d a H o r i b a P G - 2 5 0 A p o r t a b l e gas analyzer terminated the s a m p l i n g t r a i n . T h e s a m p l i n g u n i t p u m p e d the necessary gas volume required for analysis t h r o u g h the s a m p l i n g t r a i n . T h e feeder was t u r n e d off after s u p p l y i n g the available concentrate ( t y p i c a l l y 8 to 10 h ) . Samples were collected d u r i n g the next hour, after w h i c h the electrical heaters, as well as the nitrogen  95  Chapter  3.  Experimental  Methods  a n d oxygen gas supplies, were shut off, leaving o n l y a flow of air. S a m p l i n g c o n t i n u e d d u r i n g the next hour. T h e fluidizing gas delivery was discontinued w h e n the temperatures d r o p p e d to between 700 a n d 8 0 0 ° C . D u r i n g cooling, the scrubber by-pass valve was opened, while the eductor m a i n t a i n e d a slight v a c u u m w i t h i n the roaster.  W h e n the temperatures i n the three zones were near ambient ( a p p r o x i m a t e l y 36 hours later), a t u b e was inserted t h r o u g h the s a m p l i n g valve to extract the b e d particles b y v a c u u m cleaning. T h e solids were t h e n weighed. T h e roaster was disassembled a n d cleaned. A m e t a l wire b r u s h was used to scrub the inside walls for particulates a n d accretions w h i c h were collected a n d weighed. T h e particles i n the pre-heater, outlet pipe, a n d filter were also collected.  T h e scrubber tanks, c o n t a i n i n g a spent s o l u t i o n of s o d i u m h y d r o x i d e , a m i x t u r e of s o d i u m sulfite a n d s o d i u m bisulfite, were e m p t i e d . T h e solutions were disposed i n waste d r u m s . Some samples of the solutions were assayed. W i t h the exception of sulfur, w h i c h exceeded the I C P detection range, a l l assayed elements were i n negligible amounts.  For further details of the e x p e r i m e n t a l procedures, see A p p e n d i x B .  3.4 Sintering tests T o determine the sintering tendency of the materials d u r i n g roasting, static s i n t e r i n g tests were performed i n V i c o r tubes (96% SiC-2 glass). A n u m b e r of tubes were p r e p a r e d b y sealing one end of the t u b e a n d filling w i t h zinc concentrate. a n d sealed.  T h e filled tubes were d r i e d i n air at 1 0 5 ° C  T h e sealed tubes were placed i n a cold muffle furnace, heated to the sintering  temperature ( 9 5 0 ° C ) , a n d held at that temperature for 1 hour. T h e muffle furnace was then t u r n e d off a n d the sample was furnace cooled. After cooling, the t u b e was b r o k e n to access the sample a n d prepare it for electron microscopy.  3.5 Analysis of solid products E i t h e r the solids collected d u r i n g the last b e d s a m p l i n g or the leftover b e d solids were split a n d then sieved o n 16 (1.18 m m ) , 40 (425 pm),  96  70 (210 nm),  140 (105 pm),  a n d 230 (63 pm)  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 Inductively Coupled P l a s m a A t o m i c Emission Spectroscopy (ICP-AES) S0 /S 4  (Gravimetric) Fe++/Fe+  Fuse samples in NaOH/Na2C>2 over flame. Button dissolved in HCI. Dilute to 10% HCI. Simultaneous multi-element analysis by ICP-AES. Digest samples to dryness with HCI. Dissolve residue in Na2C03 and filter. Neutralize and add BaCbFilter off BaSC>4 precipitate and ash in muffle furnace.  (Redox Titration)  Digest samples in HCI. Redox Titration with Na2Cr2C>7.  Loss on ignition ( 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 conductive 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 Experimental Results  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 conditions 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  1  2  3  4  Cone. 1(a)  Cone. 1(b)  Cone. 1(b)*  Cone. 2  10  23  27  18  Base Run Experiment number *: A n a d d i t i o n a l  10% excess o x y g e n (pure o x y g e n ) was a d d e d i n t o t h e  freeboard.  Inlet oxygen concentration  21 vol%  25 vol%  30 vol%  Experiment number  10 and 23  22  20  Excess oxygen  0%  10 %  20 %  80 %  7  10 and 23  14  2  8  9  4  12  22  5  Experiment number (large particles, 21% inlet oxygen) Experiment number (small particles, 21% inlet oxygen) Experiment number (large particles, 25% inlet oxygen) Experiment number (small particles, 25% inlet oxygen)  Bed material  Silica  Silica  Large particles  Small particles  see above  Experiment number  4.1  6  11 Alumina  24  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 i n i t i a l l y present, the presence of very fine calcine particles (new particles) shifts the average to smaller sizes. F o r the experiments w i t h small i n i t i a l average particle size at low excess oxygen (0 a n d 10%) ( F i g u r e 4.1(f)), the bed particle size was larger t h a n that of the i n i t i a l b e d m a t e r i a l . However, for large excess oxygen, there was little change i n the average bed particle size. N o t e t h a t the average b e d particle size does not give any i n f o r m a t i o n on whether agglomeration occurs, or to w h a t extent.  4.2  Rate of bed mass increase  T h e l a b o r a t o r y roaster does not have an overflow or underflow exit stream, a n d m a t e r i a l entrained is not returned to the bed. M a t e r i a l a c c u m u l a t i n g i n the b e d leads to an increase i n bed mass. I n the i n d u s t r i a l roaster, there is a weir whose height is constant.  Therefore, any  material a c c u m u l a t i n g i n the i n d u s t r i a l roaster b e d is balanced by m a t e r i a l overflowing from the bed. Since there is no exit stream i n the l a b o r a t o r y roaster other t h a n the entrained material, material not entrained stays i n the b e d . T h e b e d mass increase rate i n the l a b o r a t o r y roaster should therefore be related to the overflow rate i n the i n d u s t r i a l roaster. T h e rate of bed mass increase is calculated from the b e d pressure d r o p recorded d u r i n g the experimental r u n . S a m p l i n g caused a s m a l l reduction i n b e d pressure d r o p , therefore, the b e d pressure drop d a t a between bed samples is used for the c a l c u l a t i o n of the rate of b e d mass increase.  T h e b e d s a m p l i n g frequency was adjusted to keep the average b e d pressure d r o p  relatively constant.  F i g u r e 4.2 presents rates of bed mass increase.  T h e c a l c u l a t i o n of each  d a t a point is done by fitting one slope a n d m u l t i p l e origins to the logged b e d pressure drops. T h e error bars correspond to ± one s t a n d a r d d e v i a t i o n of the rate of b e d mass increase for consecutive 15-30 minutes intervals d u r i n g a given r u n . It is not k n o w n w h y the v a r i a b i l i t y (error bar range) of some runs is very small, while the v a r i a b i l i t y of others is v e r y large.  T h e rate of b e d mass increase increases w i t h temperature a n d 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  900 950 (a) Temperature (°C)  1000  0.3 0.4 0.5 (b) Superficial gas velocity (m/s) 300 r  300  20 22 24 26 28 30 32 (d) Inlet oxygen concentration (vol%)  2 3 (c) Base run 150  300  ^250 E X v 200 v E  ro  '"° 150 u t S.100 c ru 2  o S 9  X  X  X  I o  o o  e  8  50  20 40 60 (e) Excess oxygen (%)  20 40 60 (f) Excess oxygen (%)  80  Figure 4.1: Evolution of the sur face/volume average particle size for various experimental conditions, x: initial conditions, o: during experiment at different times, *:finalconditions, (a) Temperature, (b): superficial gas velocity, (c): Base run number, (d): Inlet oxygen concentration, (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 i n f o r m a t i o n on whether agglomeration occurred, nor to what extent, i.e. there is no i n f o r m a t i o n on whether the new particles are s m a l l or large non-elutriable particles. Therefore, a more detailed analysis is required.  4.3  Assays and mass balances  T h e v a l i d i t y of the assay and mass i n f o r m a t i o n collected d u r i n g the e x p e r i m e n t a l runs is evaluated by means of an overall mass balance. Table 4.2 summarizes the overall mass i n f o r m a t i o n gathered for a l l the experiments.  T h e five last columns of the table give masses of the sam-  ples collected d u r i n g cleaning of the l a b o r a t o r y roaster after an experiment.  T h e preheater  contained some solids that fell t h r o u g h the d i s t r i b u t o r plate holes. After r e m o v i n g the bed of particulate m a t e r i a l at the end of a r u n , the d i s t r i b u t o r plate (grid) was s t i l l covered w i t h some solids. A c c r e t i o n s were scraped from the walls of the roaster. T h e pipe connecting the roaster to the filter contained some entrained solids. N o t e that the first two experiments lack the  final  bed mass i n f o r m a t i o n . T h e amount of calcine produced is calculated using the t o t a l mass of samples collected (collected from carryover ( C O . ) , bed, preheater, g r i d , walls, pipe), the i n i t i a l and final bed mass :  C a l c i n e P r o d u c e d = Samples collected + F i n a l B e d — I n i t i a l B e d  (4-1)  T h i s calculation subtracts the mass of the i n i t i a l bed, consisting of a different m a t e r i a l , from the t o t a l mass of collected material. Table 4.3 presents the overall mass balance results. A l l the final samples, i n a d d i t i o n to those collected d u r i n g each experiment, are used to calculate the amount of calcine p r o d u c e d .  The  p r o p o r t i o n of calcine collected as carryover is shown. T h e mass conversion ratio (/?), i.e. ratio of mass of zinc calcine p r o d u c e d to mass of zinc concentrate fed, is shown i n the last c o l u m n . For complete conversion of pure zinc sulfide to pure zinc oxide, (5 w o u l d 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 T a b l e 4.3 agree well w i t h the theoretical value. T h e calculated value of (3 is influenced by the extent of conversion as well any i n a c c u r a c y i n  103  Chapter  4.  Experimental  Results  900 950 (a) Temperature (°C)  1000  2 3 (c) Base run  -5 0.2  0.3 0.4 0.5 (b) Superficial gas velocity (m/s)  20 22 24 26 28 30 32 (d) Inlet oxygen concentration (vol%)  20 40 60 (f) Excess oxygen (%)  20 40 60 (e) Excess oxygen (%)  Figure 4.2: Rate of bed mass increase (g/min). Calculated from bed pressure drop measurements 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 Run  Feed  bed  Bed  Carryover  Final  samples  samples  bed (g)  Preheater  Grid  Walls  Pipe  (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  2942.4  422.8  0  199.9  0  126.8  360.7  9.4  103.8  6  3501  6458.1  474.5  3151.2  7  3303  8972.5  1492.1  4513.2  3869.9  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  142.6  45.6  70.5  144.4  12  3304.3  9972.9  1735.3  4660.9  4384  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  3999.1  4328.9  44.4  56.3  57.2  120.4  20  3311.3  8815.5  1847.6  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 r o p o r t i o n of calcine as carryover a n d calcine to concentrate mass ratio (f3) 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  Run  leach i n downstream processes, this m e t h o d of c a l c u l a t i n g the conversion is u s u a l l y preferred. Because the s c r u b b i n g efficiency is not k n o w n a n d no sulfur analysis was performed o n the scrubbing solutions, a complete sulfur mass balance cannot be calculated. However, the p r o p o r t i o n of sulfur leaving i n the gas m a y be estimated from the solid sample masses a n d compositions. T h e converted sulfur is therefore taken as the ratio of unaccounted sulfur i n the solid at the end of the r u n to the amount of sulfur fed to the roaster. I n general, 90-95% of the sulfur was not accounted for i n the solid product. Therefore 90-95% of the sulfur fed to the roaster was assumed to be converted to sulfur dioxide, w i t h the remainder collected i n t h e carryover a n d bed m a t e r i a l .  106  Chapter  4.  Experimental  4.3.2  Base cases  Results  T h e base cases can be used to estimate the variation from one experiment to another when no experimental conditions changed. T h e base case runs are runs 10, 23, 27 a n d 18 (labelled base cases 1, 2, 3 and 4 respectively, below a n d i n Figures 4.1 (c) a n d 4.2 (c)). A l l base cases were operated at 9 4 0 ° C , at a superficial gas velocity of 0.25 m / s , at 10% excess oxygen. T h e y differ o n l y i n the concentrate used (base case 4) and, for base case 3, by a d d i t i o n a l injection of oxygen into the freeboard (equivalent to an a d d i t i o n a l 10% excess oxygen, for a t o t a l of 20% excess oxygen). A l l four base cases had an overall p r o p o r t i o n of carryover between 61 and 65% (see Table 4.3). F i g u r e 4.3 presents the time-variation of some parameters used i n the mass balance for experimental r u n 10. T h e instantaneous mass of the bed is estimated from the instantaneous bed pressure drop. T h e sharp variations i n apparent bed mass m a y be due to adjustments i n purge gas flowrate, port b l o c k i n g or other related factors affecting pressure d r o p measurement. Some experiments showed significant variations while others d i d not. T h e assays of the bed samples clearly show an a c c u m u l a t i o n of zinc and other elements, w h i l e the assays for the carryover material suggest t h a t the c o m p o s i t i o n d i d not vary significantly w i t h time. F i g u r e 4.4 presents the elemental mass balance results for the four base cases runs. I n general, a p p r o x i m a t e l y 50 % of the iron and zinc stayed w i t h i n the bed w h i l e the remainder left w i t h the carryover. T h e p r o p o r t i o n staying w i t h i n the bed was slightly higher (60-70%) for copper and c a d m i u m .  F o r lead, the p r o p o r t i o n staying i n the bed was 75 to 80%.  T h e differences  between the overall a n d elemental p r o p o r t i o n i n carryover comes from the a s s u m p t i o n of the same calcine c o m p o s i t i o n for the overall mass balance. A closer analysis of bed samples reveals that the compositions of the different sizes of bed particles (see F i g u r e 4.5) differed very little. T h e o n l y exception is that the p r o p o r t i o n of lead i n the fine particles (+230 mesh) of the experimental r u n w i t h concentrate 2 (base case 4) was much larger t h a n for the other sizes a n d base cases. T h e assays do not a d d u p to 100% since oxygen is not determined i n the analyses. T h e large v a r i a b i l i t y of the silica assays is likely the  107  Chapter  4.  Experimental  Results  cause of some s u m m a t i o n s exceeding 100% (Figure 4.5 (a), +70 mesh) A n a l y s i s of the assays of the carryover samples and the mass balance reveals t h a t there was a p p r o x i m a t e l y 3 to 4% sulfur left i n the carryover calcine, 20 to 40% of w h i c h was i n the form of sulfate.  T h e carryover conversion, based on the r e m a i n i n g sulfide sulfur, ranged from 90  to 95%. T h i s conversion is much smaller t h a n observed i n d u s t r i a l l y . However, i n i n d u s t r i a l roasters, the very large freeboard leads to a m u c h longer residence t i m e t h a n c o u l d be achieved i n the present equipment. A p p r o x i m a t e l y 94 to 95% of the sulfur could not be accounted for in the solid p r o d u c t . 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 s m a l l . i n the freeboard d i d not have any significant effect.  T h e injection of a d d i t i o n a l oxygen  T h i s may be due to the relatively s m a l l  freeboard of the equipment. T h e origin of the large difference i n the fraction of iron as ferric iron (Figure 4.7(d)) between base case 1 a n d the other base case runs is u n k n o w n . E v e n if the amount of zinc a n d iron staying w i t h i n the bed was slightly higher for concentrate 2 (Figure 4.4), the p r o p o r t i o n of calcine (zinc, iron and lead) r e p o r t i n g to the very s m a l l particles was much larger for concentrate 2 t h a n concentrate 1 (Figure 4.6).  A s m u c h as 50% of the  calcine staying w i t h i n the bed was present w i t h i n the very fine particles (-230 mesh or pan). T h 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 o c c u r r e d a n d more zinc reported to the very s m a l l particles.  108  Chapter  4.  Experimental  Results  100 i  100  < 40  4  6  Time (h) (a) B e d samples assays. » : Z n , o:Si02, x : P b , +:Fe (b) C a r r y o v e r samples assays. » : Z n , o:Si02, x : P b , + :Fe  3600 r  (d) B e d mass  (c) I n p u t a n d o u t p u t masses  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  1  Results  2 3 (a) C d Base run  2 3 (b) C u Base run  4  0.8  0.6  O O  t  §.0.4 o  o  o  0.2  1  2 3 (c) Fe Base run  4  2 3 (d) Pb Base run  ! 0.98  0.8  0.6 o  o o  §.0.4 o  o  o  3 M0.96  |  'to  0.94  O  o  o  o  Q.  o £ 0.92  0.2  2 3 (e) Z n Base run  0.9  4  1  2 3 (f) S Base run  4  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  F i g u r e 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 , Z n , F e , P b . 2  Ill  Chapter 4. Experimental Results  Init.  Final  Zn  Pb  Fe  Si02  Init.  Final  (a) Base run 1  Init.  Final  Zn  Pb  Zn  Pb  Fe  Si02  Fe  Si02  (b) Base run 2  Fe  Si02  Init.  (c) Base run 3  Final  Zn  Pb  (d) Base run 4  F i g u r e 4.6: D i s t r i b u t i o n of mass of key elements w i t h b e d particle size fractions for four base case runs. 1: C o n c e n t r a t e 1(a), 2: Concentrate 1(b), 3: C o n c e n t r a t e 1(b), oxygen injection i n freeboard, 4: C o n c e n t r a t e 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 b e d particles for base case 1 (experimental r u n 10). T h e larger b e d particles clearly consist of a silica core w i t h a coating. T w o other type of particles are present w i t h i n the smaller + 230 mesh a n d -230 mesh particles: u n agglomerated and agglomerated calcine particles. T h e unagglomerated particles m a i n l y appear i n the carryover a n d the -230 mesh fraction (pan). A few agglomerated particles appear i n the upper right p o r t i o n of F i g u r e 4.11. F i g u r e 4.13 presents such an agglomerated particle. X - r a y spectroscopy on several locations w i t h i n this type of particle shows t h a t such agglomerated particles are very rich i n lead. Since X - r a y spectroscopy does not give accurate results for oxygen, the oxygen peak was not used to quantify the c o m p o s i t i o n of the particle, even w h e n an oxygen peak was present. T h e core of the particle contains a p p r o x i m a t e l y 73 w t % P b , 17 w t % Z n , 8 w t % S a n d s m a l l amounts of Fe and C a (approximately 1 w t % each). A t the periphery, higher concentrations of zinc (25-46 w t % Z n ) and iron (2-3.5 wt%Fe) were found. T h i s m a y indicate that calcine particles adhere to the surface of these agglomerated particles.  F i g u r e 4.14 shows an intermediate size (+140 mesh) particle. P a r t i c l e s of this type u s u a l l y present a silica 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 a n d 16 w t % S i ) i n some locations a n d a detached coating r i c h i n zinc, i r o n a n d silica (up to 81 w t % Z n , 2-10 w t % F e , 9-15 w t % S i ) . T h e coherent coating is very t h i n a n d d i r e c t l y on the surface of the silica particle.  F i g u r e 4.15 portrays carryover particles. F i g u r e 4.16 shows an i n c o m p l e t e l y reacted particle found i n the entrained calcine. T h i s particle, like other similar particles, has a core of zinc concentrate (66 w t % Z n , 26 w t % S , 7.5 w t % F e , 0.5 w t % P b ) and a p r o d u c t layer of zinc calcine (89 w t % Z n , 8 w t % Fe, 1.3 w t % S , 0.6 w t % P b a n d 0.4 w t % S i ) . T h e particles m a y not be spherical or have a u n i f o r m p r o d u c t layer. However, it is reasonable to assume t h a t they react according i n a shrinking-core m a n n e r .  X - r a y diffraction on the b e d particles detected silica and zinc silicate. T h e carryover is composed of zinc oxide, zinc ferrite, and zinc silicate. A few peaks were unidentified for b o t h the carryover and bed samples. O n e of the peaks found on b o t h samples is p r o b a b l y zinc sulfide.  114  Chapter  4.  Experimental  Results  F i g u r e 4.8: S E M m i c r o g r a p h for p r o d u c t particles of r u n 10, +40 mesh, Secondary electrons image  F i g u r e 4.9: S E M m i c r o g r a p h for p r o d u c t particles of r u n 10, +70 mesh, Secondary electrons image  115  Chapter 4. Experimental Results  F i g u r e 4.10: S E M m i c r o g r a p h for p r o d u c t particles of r u n 10, +140 mesh, S e c o n d a r y electrons image  F i g u r e 4.11: S E M m i c r o g r a p h for p r o d u c t particles of r u n 10, +230 mesh, Secondary electrons image  116  Chapter 4. Experimental Results  F i g u r e 4.12: S E M m i c r o g r a p h for product particles of r u n 10, -230 mesh (pan), Secondary electrons image  ''  1  >  />>*« :  **,:  .  % 1  • ' , *  ».  * • *4  •  xl.Qk 1  <  . .-^ C ^  . -  V  \  ? #  . ft *  4  .<  0880  20kV  5@.urn  -2  F i g u r e 4.13: S E M m i c r o g r a p h for p r o d u c t particles of r u n 10, -230 mesh (pan), Secondary electrons image of agglomerated particle  117  Chapter  4.  Experimental  Results  K60@  0808  20kV  58ym  F i g u r e 4 . 1 4 : S E M m i c r o g r a p h for p r o d u c t particles of r u n 10, + 1 4 0 mesh, S e c o n d a r y electrons image of coated p a r t i c l e  F i g u r e 4 . 1 5 : S E M m i c r o g r a p h for product particles of r u n 10, carryover, Secondary electrons image  118  Chapter  4.  Experimental  Results  X i  @k  0000  F i g u r e 4 . 1 6 : S E M m i c r o g r a p h for p r o d u c t particles of r u n 10, carryover, S e c o n d a r y electrons image of p a r t i a l l y 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 significantly for different superficial gas velocities. However, as the superficial gas velocity increased, the proportion of veryfineparticles (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 afluidizedbed increases strongly with increasing superficial gas velocity. Not surprisingly, increasing the superficial gas velocity led to a smaller proportion offinesin 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) C d Superficial gas velocity (m/s)  0.2  0.3 0.4 0.5 (b) C u 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) Z n 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 superficial gas velocities, (a) Cadmium, (b) Copper, (c) Iron, (d) Lead, (e) Zinc, (f) Sulfur.  121  C h a p t e 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 , Zn, Fe, Pb 2  122  Chapter 4. Experimental Results  100  2  80  +  60  +  40  2o\\  20  _ _  •  I  mm I  I  Init. Final Zn Pb Fe Si02 (b) Superficial gas velocity: 0.25 m/s  Init. Final Zn Pb Fe Si02 (a) Superficial gas velocity: 0.25 m/s 100 r  100  o  + o  + O  Init. Final Zn Pb Fe Si02 (d) Superficial gas velocity: 0.5 m/s  Init. Final Zn Pb Fe Si02 (c) Superficial gas velocity: 0.375 m/s  F i g u r e 4.19: Effect of superficial gas velocity o n d i s t r i b u t i o n of mass of key elements w i t h b e d particle size fraction. B o t t o m to top: pan,+230,+140,+70,+40  123  4.  Experimental  0.2  .2 0.95 s  0.9  Results  0.3 0.4 0.5 (a) Superficial gas velocity (m/s)  0.2  0.3 0.4 0.5 (b) Superficial gas velocity (m/s)  0.2  0.3 0.4 0.5 (d) Superficial gas velocity (m/s)  o OOOG  Chapter  O  O £1  ^  3  °  •» 0.85  0.8 0.2  0.3 0.4 0.5 (c) Superficial gas velocity (m/s)  F i g u r e 4.20: C o m p a r i s o n of assays of carryover for different superficial gas velocities, (a) T o t a l sulfur, (b) F r a c t i o n of sulfur as sulfate, (c) Conversion based on r e m a i n i n g sulfide sulfur, F r a c t i o n of i r o n as ferric iron.  124  (d)  Chapter  4.  Experimental  4.3.4  E f f e c t  Results  o f t e m p e r a t u r e  E x p e r i m e n t a l runs 10, 23 ( 9 4 0 ° C ) , 15 ( 8 7 5 ° C ) , 17 ( 9 0 5 ° C ) and 16 ( 9 7 5 ° C ) allow the effect of the roasting temperature to be examined. R u n 24 was also performed at 9 7 5 ° C , b u t used b r o w n a l u m i n a particles instead of silica sand as the i n i t i a l bed m a t e r i a l . T h e overall carryover (Table 4.3) varied from 84% at 875 ° C to 56% at 975 ° C for the s i l i c a sand. F o r the a l u m i n a , however, the p r o p o r t i o n leaving the roaster as carryover was 38%, a further decrease from the silica. W h e n c o m p a r i n g the p r o p o r t i o n of key elements r e p o r t i n g to the b e d for the e x p e r i m e n t a l runs w i t h silica sand, see F i g u r e 4.21, there is a clear u p w a r d trend of the m a t e r i a l s t a y i n g w i t h i n the bed w i t h increasing temperature.  F o r example, the p r o p o r t i o n of lead s t a y i n g w i t h i n the  fluidized bed increased from a p p r o x i m a t e l y 40% at 8 7 5 ° C to more t h a n 80% at 9 7 5 ° C . For iron and zinc, the increase was not as d r a m a t i c as for lead. However, it nevertheless increased from a p p r o x i m a t e l y 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 c o n s t i t u t i o n of the bed samples is shown i n Figures 4.22 and 4.23.  A s the bed temperature increased, the p r o p o r t i o n of fine particles i n the bed decreased,  while the p r o p o r t i o n of zinc r e p o r t i n g to the s m a l l particles was also m u c h lower. T h e assays also indicate that as the temperature increased, the particles contained a m u c h larger p r o p o r t i o n of zinc. T h i s suggests that agglomeration increases w i t h  temperature.  F i g u r e 4.24 presents the assays of the carryover. W i t h the experiment w i t h a l u m i n a excluded, the p r o p o r t i o n of sulfur as sulfate w i t h i n the carryover calcine decreased w i t h  temperature.  However, if the r u n w i t h a l u m i n a particles is i n c l u d e d , this trend m a y disappear.  T h e microstructures of sieved particles collected d u r i n g the e x p e r i m e n t a l r u n at 9 7 5 ° C are shown i n Figures 4.25 to 4.30. These particles appear to be denser a n d have a m u c h coarser microstructure t h a n for particles formed at lower temperature (Figures 4.8 to 4.12). F i g u r e 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, a k i n to a lead-zinc silicate eutectic.  125  T a b l e 4.4  Chapter 4. Experimental Results 1,  1  •  0.8  0.8  O  o  : 0.6  + O  : 0.6  o o ct  o ct  0.2  0.2  850  950 900 (a) C d Temperature (°C)  1000  850  0.8 \  0.8  .£ °- r  c 0.6  6  c  c  t  '€  950 900 (b) C u Temperature (°C)  1000  900 950 (d) Pb Temperature (°C)  1000  o  o  <LOA\  8.0.4  0.2  0.2  850  900 950 (c) Fe Temperature (°C)  850  1000  0.8 [  IS 0.98 bO  : 0.6  g.0.4 o  +  5 bo0.96  0.94  r  o £ 0.92  0.2  850  O  900 950 (e) Zn Temperature (°C)  1000  "'850  900 950 (f) S Temperature (°C)  1000  Figure 4.21: Variation in proportion of key elements based on mass balance for different temperatures, 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  F i g u r e 4.22: Effect of t e m p e r a t u r e on assays of different b e d particle size fractions. B o t t o m to top: SiC-2, Z n , F e , P b  127  Chapter  4.  Experimental  Results  (c) Temperature: 940 °C  (d) Temperature: 975 °C  F i g u r e 4.23: Effect of 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 size fractions.  B o t t o m to top:  of mass of key elements w i t h b e d  pan,+230,+140,+70,+40  128  particle  Chapter 4. Experimental Results  O  0.8  O  3 0.6  O O  + + |o.4 "3 CO  o o  1/1  0.2  o  900 950 (a) Temperature (°C)  e i/i  o o  850  900 950 (b) Temperature (°C)  1000  900 950 (d) Temperature (°C)  1000  o 8 OOO  0.9  1000  + +  8  10.95  |  o— 1  850  "3  • o  i/ico  "3 10.85  0.8 — 850 1  900 950 (c) Temperature (°C)  1000  F i g u r e 4.24: C o m p a r i s o n of assays of carryover for different temperatures, o: S i l i c a sand bed, +: A l u m i n a bed.  (a) T o t a l sulfur, (b) F r a c t i o n of sulfur as sulfate, (c) C o n v e r s i o n based on  r e m a i n i n g sulfide sulfur, (d) F r a c t i o n of i r o n as ferric iron.  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 w i t h i n the coating are rich i n lead, a n d the dark phases are r i c h i n zinc. B o t h contain a significant p r o p o r t i o n of silica. T h e coherent coating on the surface of the s i l i c a particles is much more omnipresent for particles roasted at 9 7 5 ° C t h a n for those s h o w n p r e v i o u s l y (roaster at 9 4 0 ° C ) . C a d m i u m was detected i n non-negligible amounts i n the coherent c o a t i n g and the white phase. Iron appears to be i n relatively s m a l l amounts i n the coherent coatings a n d dark phases (compared to the i n i t i a l iron concentration w i t h i n the concentrate).  Table 4.4: X - r a y spectroscopy analysis of particle coatings o b t a i n e d after r o a s t i n g at 9 7 5 ° C . B l a n k w h e n not detected. D e t e c t i o n l i m i t is t y p i c a l l y 0.5 w t % or less a n d v a r y w i t h elements detected Pb  Zn  Fe  Si  Cd  Cu  wt%  wt%  wt%  wt%  wt%  wt%  Coherent  73  20  Coherent  62  14  Coherent  43  12  W h i t e phase  65  20  W h i t e phase  49  W h i t e phase  65  D a r k phase D a r k phase  0.43  4.4 0.34  1.8  21  1.8  43  1.3  2  11  1.8  35  1.7  11  1.8  22  2.5  8  0.9  86  0.68  13  88  1.0  11  T h e +230 mesh particles are p r e d o m i n a n t l y of agglomerated type. W h e n c o m p a r e d w i t h the +140 mesh particles, one can clearly see that the silica cores are smaller a n d the coatings are thicker for particles formed at higher temperature.  T h i s indicates t h a t these particles have  grown. T h e microstructures of particles (not shown) formed at lower temperatures (875, 9 0 5 ° C ) have a m u c h thinner coating on the silica particles, i n d i c a t i n g negligible agglomeration. T h e c o m p o u n d s w i t h i n the b e d and carryover particles p r o d u c e d at 9 7 5 ° C were identified using  130  Chapter  4.  Experimental  Results  F i g u r e 4.25: S E M m i c r o g r a p h for p r o d u c t particles of r u n 16, +70 mesh, Secondary electrons image  F i g u r e 4.26: S E M m i c r o g r a p h for p r o d u c t particles of r u n 16, +70 mesh, B a c k s c a t t e r e d electrons image of particle c o a t i n g  131  Chapter  4.  Experimental  Results  F i g u r e 4.27: S E M m i c r o g r a p h for p r o d u c t particles of r u n 16, +140 mesh, Secondary electrons image  F i g u r e 4.28: S E M m i c r o g r a p h for p r o d u c t particles of r u n 16, +230 mesh, S e c o n d a r y electrons image  132  Chapter  4.  Experimental  Results  F i g u r e 4.29: S E M m i c r o g r a p h for p r o d u c t particles of r u n 16, -230 mesh (pan), Secondary electrons image  F i g u r e 4.30: S E M m i c r o g r a p h for p r o d u c t particles of r u n 16, C a r r y o v e r , 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 enrichment 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 thefluidizinggas. Experimental runs 12 (0%) and 5 (80%) also used 50 mesh silica sand, but the fluidizing gas was oxygen-enriched air (25 vol% 0 ). Experimental runs 8 2  (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% 0 ). 2  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  20  22  Results  24  26  28  30  32  20  (a) Cd Inlet oxygen concentration (vol%)  22  24  26  28  30  32  (b) Cu Inlet oxygen concentration (vol%)  0.8  c 0.6 c o 't  o  o o  §.0.4  o  0.2  20  22  24  26  28  30  32  20  (c) Fe Inlet oxygen concentration (vol%)  22  24  26  28  30  32  (d) Pb Inlet oxygen concentration (vol%)  0.98 5  MO.96  t o  o 00  o  0.94  o  ct 0.92  20  22  24  26  28  30  32  (e) Z n Inlet oxygen concentration (vol%)  0.9  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 (b) Inlet oxygen concentration: 21 vol%  pan +230 +140 +70 +40 (a) Inlet oxygen concentration: 21 vol% 100  a N  0  pan +230 +140 +70 +40 (d) Inlet oxygen concentration: 30 vol%  pan +230 +140 +70 +40 (c) Inlet oxygen concentration: 25 vol%  F i g u r e 4.32: Effect of oxygen concentration o n assays of different b e d p a r t i c l e size fractions. B o t t o m to top: S i 0 , Z n , F e , P b 2  Table 4.5: O v e r a l l p r o p o r t i o n of carryover as a function of excess oxygen, inlet oxygen concent r a t i o n a n d i n i t i a l b e d particle size. B l a n k when no experiment, N . A . w h e n i n f o r m a t i o n is not available. I n i t i a l b e d material: 125 mesh: s m a l l particles, 50 mesh: large particles. Excess  125 mesh  50 mesh  Oxygen  21 %  25 %  21 %  25 %  0  78  65  63  59  10  73  62, 66  60  79  20 80  N.A.  85  136  N.A.  78  Chapter 4. Experimental Results  Init. Final Zn Pb Fe Si02 (a) Inlet oxygen concentration: 21 vol%  Init. Final Zn Pb Fe Si02 (b) Inlet oxygen concentration: 21 vol%  Init. Final Zn Pb Fe Si02 (c) Inlet oxygen concentration: 25 vol%  Init. Final Zn Pb Fe Si02 (d) Inlet oxygen concentration: 30 vol%  F i g u r e 4.33: Effect of oxygen concentration o n d i s t r i b u t i o n of mass of key elements w i t h b e d particle size fraction. B o t t o m to top: pan,+230,+140,+70,+40  137  Chapter  4.  Experimental  Results  10  0.8  |  0.6  6f  o o £  4  1/1  o  i0.4  o  O  0.2 [  20 22 24 26 28 30 32 (b) Inlet oxygen concentration (vol%)  20 22 24 26 28 30 32 (a) Inlet oxygen concentration (vol%)  0.8  .2 0.95 \ O  0.9 \  O  50.6  8 O  0.4  10.85 \  0.2  20 22 24 26 28 30 32 (c) Inlet oxygen concentration (vol%)  ~  20 22 24 26 28 30 32 (d) Inlet oxygen concentration (vol%)  F i g u r e 4.34: C o m p a r i s o n of assays of carryover for different inlet oxygen concentrations,  (a)  T o t a l sulfur, (b) F r a c t i o n of sulfur as sulfate, (c) Conversion based on r e m a i n i n g sulfide sulfur, (d) F r a c t i o n of i r o n as ferric i r o n .  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 different r e s u 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 size.  F o r a larger m e a n p a r t i c l e size, the large p a r t i c l e s h a d n e g l i g i b l e calcine  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 fine s i l i c a s a n d (125 m e s h ) ,  t h e effect  of excess o x y g e n was s i m i l a r , e x c e p t  where large calcine particles were created.  for t h e 0 % e x c e s s o x y g e n c a s e  T h e calcine particles adhered excessively to very  large particles, c a u s i n g d e f l u i d i z a t i o n to o c c u r due to segregation.  Lead again  preferentially  segregated to larger particles.  F o r b o t h p a r t i c l e s i z e s (see F i g u r e s 4 . 3 8 a n d 4 . 4 2 ) , i n c r e a s i n g t h e e x c e s s 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 o f s u l f u r as s u l f a t e , 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 f e 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 w a s less i m p o r t a n t  than  t h e effect o f e x c e s s o x y g e n ( F i g u r e s 4 . 4 3 t o 4 . 4 6 ) .  show  any clear t r e n d ( F i g u r e s 4.44 a n d 4.46).  139  T h e elemental mass balances do not  Chapter 4. Experimental Results  0.8  0.8  •  o  c o  o  o.4  0.6  c  o  c o  o  t  •  V  JD  o  0.6  a  "O  •  •  o  c  1  Proporti  "O CU -O  1  O  o  O  0.2  0.2  Q  O 0  20  0  40  60  0  80  20  0  (a) C d Excess oxygen (%)  60  80  1  1  • 0.8 o  0.8 <u c  40  (b) C u Excess oxygen (%)  8  <0  0.6  •  0.6  c  c  c  t §.0.4  o Q.  o  O O  t  •  a  O  0-  o  0.2  o o.4  O  0.2  O 0  20  0  40  60  0  80  20  0  (c) Fe Excess oxygen (%)  60  80  1  1  0.8  Ul  ra bO  | 0.95 - •  T3 OJ c  40  (d) Pb Excess oxygen (%)  0.6  b0 C  c  @  O  ">  O  0  t  §.0.4 . o  G  •-  c  o  1  O  0.9  o  O  ci  0.2  0  ro  O 0  20  40  60  O 0.85  80  0  20  40  60  80  (f) S Excess oxygen (%)  (e) Zn Excess oxygen (%)  F i g u r e 4.35: V a r i a t i o n i n p r o p o r t i o n of key elements based o n mass balance for different excess oxygen a n d 50 mesh silica sand, o: S i l i c a sand, • : S i l i c a sand w i t h 2 5 % O2 i n the gas. (a) C a d m i u m , (b) C o p p e r , (c) Iron, (d) L e a d , (e) Z i n c , (f) Sulfur.  140  fluidizing  Chapter  4.  Experimental  Results  F i g u r e 4.36: Effect of excess oxygen on assays for different b e d particle size fractions w i t h 50 mesh silica sand. B o t t o m to top: SiC-2, Z n , F e , P b  141  Chapter 4. Experimental Results  Init.  Final  Zn  Pb  Fe  (c) Excess oxygen: 20 %  Si02  Init.  Final  Zn  Pb  Fe  (d) Excess oxygen: 80 %  Si02  F i g u r e 4.37: Effect 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 mass o f key elements w i t h b e d particle size 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 :  L42  pan,+230,+140,+70,+40  Chapter  4.  Experimental  Results  20 40 60 (a) Excess oxygen (%)  20 40 60 (c) Excess oxygen (%)  20 40 60 (b) Excess oxygen (%)  20 40 60 (d) Excess oxygen (%)  80  F i g u r e 4.38: C o m p a r i s o n of carryover assays for different excess oxygen for 50 mesh silica sand, o: Silica sand, • : S i l i c a sand w i t h 25% O2 i n the fluidizing gas. (a) T o t a l sulfur, (b) F r a c t i o n of sulfur as sulfate, (c) Conversion based o n remaining sulfide sulfur, (d) F r a c t i o n of i r o n as ferric iron.  143  Chapter  4.  Experimental  Results  0.8  0.8  O  -o  O  c 0.6 c  o  ti  •  •  (U J2  0.6  •  o  •  o  .0.4  o  o  o  0-  §.0.4  0.2 0.2  20  0  40  60  20  0  80  40  60  80  (b) Cu Excess oxygen (%)  (a) Cd Excess oxygen (%)  0.8  •  0.6  • o  O  O  o  0.2  0  20  40  60  (c) Fe Excess oxygen (%)  20  0  80  40  60  80  (d) Pb Excess oxygen (%)  • o • .  0  20  40  60  (e) Zn Excess oxygen (%)  o  o •  20  80  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  C h a p t e r 4.  Experimental Results  (c) Excess oxygen: 80 %  F i g u r e 4.40: Effect of excess oxygen o n assays of different b e d p a r t i c l e size fractions for 125 mesh silica sand. B o t t o m to top: S i 0 , Z n , F e , P b 2  145  Chapter  4.  Experimental  Results  (c) Excess oxygen: 80 %  F i g u r e 4.41: Effect of excess oxygen on d i s t r i b u t i o n of mass of key elements w i t h b e d particle size fraction for 125 mesh silica sand. B o t t o m to top: p a n , + 2 3 0 , + 1 4 0 , + 7 0 , + 4 0  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 (%)  20 40 60 (d) Excess oxygen (%)  80  F i g u r e 4.42: C o m p a r i s o n of carryover assays for different excess oxygen for 125 mesh silica sand, o: S i l i c a sand, • : S i l i c a sand w i t h 25% O2 i n the fluidizing gas. (a) T o t a l sulfur, (b) F r a c t i o n of sulfur as sulfate, (c) Conversion based on remaining sulfide sulfur, (d) F r a c t i o n of i r o n as ferric iron.  147  Chapter  4.  Experimental  Results  100  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  pan +230 +140 +70 +40 (d) 25% Inlet oxygen, 80% Excess Oxygen  Figure 4.43: Effect of excess oxygen a n d oxygen enrichment o n assays of b e d particle of different size fractions w i t h 50 mesh silica sand. B o t t o m to top: S i 0 2 , Z n , F e , P b  148  Chapter  4.  Experimental  Results  Init. Final Zn Pb Fe Si02 (a) 21% Inlet oxygen, 0% Excess Oxygen  Init. Final Zn Pb Fe Si02 (b) 25% Inlet oxygen, 0% Excess Oxygen  Init. Final Zn Pb Fe Si02 (c) 21% Inlet oxygen, 80% Excess Oxygen  Init. Final Zn Pb Fe Si02 (d) 25% Inlet oxygen, 80% Excess Oxygen  F i g u r e 4.44: Effect o f excess o x y g e n a n d oxygen 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 elements w i t h b e d p a r t i c l e size 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  F i g u r e 4.45: Effect of excess oxygen and oxygen enrichment on assays of different b e d particle sizes for 125 mesh silica sand. B o t t o m to top: SiC>2, Z n , F e , P b  150  Chapter  4.  Experimental  Results  Init. Final Zn Pb Fe Si02 (a) 2 1 % Inlet oxygen, 0 % Excess Oxygen  Init. Final Zn Pb Fe Si02 (b) 2 5 % Inlet oxygen, 0 % Excess Oxygen  Init. Final Zn Pb Fe Si02 (c) 2 1 % Inlet oxygen, 8 0 % Excess Oxygen  Init. Final Zn Pb Fe Si02 (d) 2 5 % Inlet oxygen, 8 0 % Excess Oxygen  F i g u r e 4 . 4 6 : E f f e c t o f e x c e s s 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 elem e n t s w i t h b e d p a r t i c l e s i z e f o r 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 :  151  pan,+230,+140,+70,+40  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 a n d defluidized. Some silica particles are embedded w i t h i n the agglomerates. T h e r e is essentially no coating on the silica particles. It is i m p o r t a n t 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 t h i n the particles were caused by p o l i s h i n g . A s previously shown i n Table 4.5, the p r o p o r t i o n of calcine as carryover is larger for the fine bed m a t e r i a l t h a n for the coarser m a t e r i a l . O n e experiment was performed w i t h b r o w n a l u m i n a at 9 7 5 ° C . A s F i g u r e s 4.55 to 4.60 portray, no significant coating was present on the a l u m i n a particles after the experiment.  T h e larger  particles were created by agglomeration of smaller particles w i t h a lead-rich phase t h a t contained some t i t a n i u m (checked by X - r a y spectroscopy).  T h e P b O - T i 0 2 phase d i a g r a m , calculated  from the F A C T t h e r m o d y n a m i c database, indicates that some t i t a n i u m dioxide m a y dissolve w i t h i n l i q u i d lead oxide. Since the a l u m i n a particles contained a s m a l l p o r t i o n of t i t a n i u m , it is possible t h a t the t i t a n i u m w i t h i n the lead-rich phase originated from the bed particles. T h e morphology of the a l u m i n a particles differs from t h a t of the silica particles, possibly due to their different reactivities w i t h P b O . T h e lead-rich phase m a y wet the s i l i c a particles more readily t h a n the a l u m i n a particles. X - r a y diffraction of the bed and carryover samples indicate t h a t b o t h consist m a i n l y of zinc oxide.  T h e carryover sample also contained detectable quantities of zinc ferrite.  T h e same  peaks as for the two other set of silica samples could not be identified. N o t e t h a t there were fewer unidentified peaks for the a l u m i n a samples. T h i s suggests t h a t the c o m p o u n d ( s ) related to some of the unidentified peaks i s / a r e silica-based.  152  Chapter  4.  Experimental  pan  Results  +230 +140 +70 +40 (c) Large S i Q sand, 975 °C  pan  2  F i g u r e 4.47:  +230 +140 +70 (d) A I 2 O 3 , 975 °C  +40  E f f e c t o f b e d m a t e r i a l o n a s s a y s for d i f f e r e n t b e d p a r t i c l e s i z e f r a c t i o n s .  t o t o p : Si0 o r A1 0 , Z n , F e , P b 2  2  3  153  Bottom  C h a p t e r 4.  Experimental  Results  (c) Large S i 0  2  sand, 975 °C  (d) A I 2 O 3 , 975 °C  F i g u r e 4.48: Effect of bed m a t e r i a l on d i s t r i b u t i o n of mass of key elements w i t h b e d 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  F i g u r e 4.53: S E M m i c r o g r a p h for p r o d u c t particles of r u n 8 , +230 mesh, S e c o n d a r y electrons image  F i g u r e 4.54:  S E M m i c r o g r a p h for p r o d u c t particles of r u n 8 , -230 mesh (pan), Secondary  electrons image  157  Chapter  4.  Experimental  Results  F i g u r e 4.55: S E M m i c r o g r a p h for p r o d u c t particles of r u n 24, +40 mesh, Secondary electrons image  F i g u r e 4.56: S E M m i c r o g r a p h for product particles of r u n 24, +70 mesh, Secondary electrons image  158  Chapter  4.  Experimental  Results  F i g u r e 4.58: S E M m i c r o g r a p h for p r o d u c t particles of r u n 24, +230 mesh, S e c o n d a r y electrons image  159  Chapter  4.  Experimental  Results  F i g u r e 4.59: S E M m i c r o g r a p h for p r o d u c t particles of r u n 24, -230 mesh (pan), Secondary electrons image  F i g u r e 4.60: S E M m i c r o g r a p h for p r o d u c t particles of r u n 24, carryover, Secondary electrons image  160  Chapter  4.4  4.  Experimental  Results  Gas and solid conversions  E x p e r i m e n t a l runs 25 and 26 differed from the other experiments. I n these experiments, the concentrate feedrate was varied a n d the freeboard gas was sampled, s c r u b b e d to remove sulfur dioxide, d r i e d a n d sent to a portable gas analyzer. T h e solids collected i n the s a m p l i n g t r a i n were collected a n d sent for assay. F i g u r e 4.61 presents the freeboard oxygen concentration as a function of the concentrate feedrate and i n i t i a l b e d particle size. T h e oxygen concentration clearly decreased w i t h increasing feedrate.  T h e oxygen concentration was slightly higher for  the 125 mesh silica sand for a similar concentrate feedrate, bypassing caused by the bubbles.  p r o b a b l y due to increased gas  A s expected, for a given concentrate feedrate, the outlet  oxygen concentration was higher w h e n oxygen enrichment was used.  T h e solid conversion corresponding to the d a t a i n F i g u r e 4.61 is shown i n F i g u r e 4.62. O x y g e n 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 i m p l y increased the excess oxygen. T h e b e d particle size does not seem to have h a d a significant effect.  The  d a t a i n Figures 4.61 a n d 4.62 are used i n chapter 6 to fit the fluidized b e d reactor m o d e l . F i g u r e 4.63 presents the averaged o u t p u t of the oxygen sensor w i t h i n the fluidized bed. T h e output of the sensor is p r o p o r t i o n a l to the log of the ratio of outside to inside oxygen p a r t i a l pressures.  A s m a l l o u t p u t signal indicates a high in-bed oxygen concentration, while a large  output value indicates a s m a l l in-bed oxygen concentration. A n interesting feature observed i n F i g u r e 4.63 is t h a t the oxygen concentration w i t h i n the b e d was not significantly affected by the oxygen enrichment, but was significantly influenced by the average b e d 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 a p p r o x i m a t e l y 15 to 30 p p m . N o N O was present w h e n no concentrate was fed to the roaster. combustion of the concentrate.  T h i s indicates that the N O m a y originate from the  However, it is not clear whether the N O p r o d u c t i o n rate  depends u p o n the excess oxygen, in-bed oxygen concentration or just the concentrate  161  feedrate.  Chapter 4. Experimental Results  CD  10 u  12  14  16  18  Concentrate feedrate (g/min)  F i g u r e 4.61: Freeboard oxygen concentration (SO2 scrubbed,dry) as a function of feedrate. o: 50 mesh silica sand, 21%C>2, + : 50 mesh silica sand, 25%C>2, x : 125 mesh silica sand, 21%C>2.  0  X  + 0  0.98  +  X  0  0  c  •3, cu > c  +  0  0  0.96  X  +  X  o  0  " 0.94  X  o  0  CO  0.92  0.9  10  12  .  14  16  •  18  Concentrate feedrate (g/min)  20  F i g u r e 4.62: Solids conversion as a function of feedrate. o: 50 mesh silica sand, 21%C>2, + : 50 mesh silica sand, 25%C>2, x : 125 mesh silica sand, 21%C>2.  162  Chapter  4.  Experimental  Results  60 x x  >  +  x  X  x  O  £ 50  o ° °  3  +  X  ^ 40 o  o  +  °  o  £30  9  cu ^ 2 0  S  oo  210  10  12 14 16 18 Concentrate feedrate (g/min)  20  F i g u r e 4 . 6 3 : I n - b e d o x y g e n s e n s o r m e a n o u t p u t as a f u n c t i o n o f f e e d r a t e . s a n d , 21%C>2, + :  o: 5 0 m e s h s i l i c a  5 0 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  measured output, lower oxygen concentration  163  Chapter  4.5  4.  Experimental  Results  Sintering test for zinc concentrate  T h e raw unsintered concentrate is shown i n F i g u r e 4.64.  A careful search u s i n g the electron  microscope d i d not reveal any significant phases other t h a n zinc sulfide.  Sealed ampoules of d r i e d zinc concentrate (concentrate 1(b), a p p r o x i m a t e l y l g ) were s u b m i t t e d to a r a m p - u p to 9 5 0 ° C , a n d held for an hour at that temperature, a n d t h e n cooled slowly to r o o m temperature. Since the ampoules c o u l d not be sealed under v a c u u m or a nitrogen atmosphere, a s m a l l amount of air was i n i t i a l l y present w i t h i n the ampoules. T h e n u m b e r of moles of oxygen contained w i t h i n the the air i n the ampoules was smaller t h a n 1% of the Z n S i n the concentrate. After the sintering cycle, the concentrate h a d formed a porous elongated r o d of diameter slightly smaller t h a n the tube diameter. T h e r o d showed some signs of o x i d a t i o n near the end where the b u l k of the air was present. A sample of the r o d was taken from the opposite end a n d prepared for electron microscopy. A n image of the sintered concentrate is presented i n F i g u r e 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". N o t e t h a t the cube is m u c h larger t h a n any of the original concentrate particles.  T h e lead sulfide cubes p r o b a b l y originate from deposition of lead sulfide from the gaseous phase d u r i n g cooling. T h e gaseous composition of a m i x t u r e of zinc sulfide a n d zinc oxide is located at point A on F i g u r e 2.2. T h i s location is valid because the concentrate is m a i n l y composed of zinc sulfide, but, as the assays show, a s m a l l fraction of the sulfur is present as sulfate. the ampoule c o u l d not be vacuum-sealed nor nitrogen-purged.  Also,  Therefore, the s m a l l amount  of oxygen r e m a i n i n g w h e n the ampoule was sealed w o u l d react to form zinc oxide a n d sulfur dioxide. T h e e q u i l i b r i u m gas composition of a m i x t u r e of zinc sulfide a n d z i n c oxide, represented by point A on F i g u r e 2.2, is adequate to represent the gas c o m p o s i t i o n of the sealed ampoule. W h e n transposing point A of F i g u r e 2.2 onto F i g u r e 2.11, the gas c o m p o s i t i o n falls w i t h i n the lead stability area, very close to the lead sulfide area. W h e n considering the gaseous lead species, lead sulfide is still the most predominant  164  gaseous lead species, even t h o u g h it falls  Chapter 4. Experimental Results  F i g u r e 4.64: S E M m i c r o g r a p h for dried, unsintered, zinc concentrate 1(b), Secondary electrons image.  F i g u r e 4.65: S E M m i c r o g r a p h for dried, zinc concentrate 1(b) sintered for 1 hour at 9 5 0 ° C , Secondary electrons image. C u b e is pure lead sulfide.  165  Chapter  4.  Experimental  Results  w i t h i n the lead s t a b i l i t y area. N o t e i n F i g u r e 2.11 t h a t if the oxygen concentration is increased, the lead sulfide p a r t i a l pressure decreases. E v e n though the lead oxide p a r t i a l pressure increases w i t h oxygen p a r t i a l pressure, it remains m u c h lower t h a n that of lead sulfide at lower oxygen p a r t i a l pressures. D u r i n g cooling, lead sulfide "precipitated" from the gaseous phase to form lead sulfide cubes. F r o m this simple experiment, it is clear that lead sulfide can evaporate from zinc concentrate. However, this experiment does not offer any information on the v a p o r i z a t i o n kinetics.  4.6  Growth mechanism in the laboratory roaster  A probable growth mechanism m a y now be suggested from the e x p e r i m e n t a l observations. P r i o r to formulating a growth mechanism, let us summarize the most relevant  observations:  • F r o m the sample mass balances, we have observed t h a t larger particles contain a larger p r o p o r t i o n of lead t h a n smaller particles. • T e m p e r a t u r e has a significant effect on the thickness a n d m o r p h o l o g y of the coating. T e m p e r a t u r e also affects the p r o p o r t i o n of calcine leaving the roaster as carryover. • Excess oxygen also affects the coating and the p r o p o r t i o n of calcine leaving the roaster as carryover. • F r o m the electron microscope observations, the silica particles were observed to be coated w i t h a two-phase coating, one rich i n lead, the other zinc-rich, w h i l e the inner silica was coated w i t h a t h i n "coherent" layer of lead-rich c o m p o u n d . A l l have silicon (silica) present. A l u m i n a particles were not coated w i t h any zinc. However, some of the a l u m i n a particles were agglomerated w i t h a lead-rich phase. • L e a d sulfide sublimates from zinc concentrate when exposed to roasting temperatures and oxygen-deficient atmospheres. T h e mechanism m a y now be postulated as follows:  166  Chapter  4.  Experimental  Results  • W h e n process conditions are such that low oxygen concentrations a n d h i g h sulfur dioxide concentrations are favoured, excess oxygen is one of the most i m p o r t a n t factors.  Under  such conditions, the lead p a r t i a l pressure is m a x i m i z e d , w i t h lead p r e d o m i n a n t l y present as lead sulfide. • L e a d sulfide vaporizes from the zinc concentrate. • Gaseous lead sulfide is t r a n s p o r t e d to regions of the bed where higher oxygen concentrations are present. It then reacts w i t h oxygen to produce lead oxide. • Since the lead oxide p a r t i a l pressure is lower t h a n for the lead sulfide, lead oxide precipitates out. • L e a d deposits onto the bed particles to form a very t h i n lead-oxide-based coating.  The  reactivity of the particles w i t h lead oxide affects whether or not a significant coating appears on the surface of the particles. • L e a d oxide is l i q u i d at roasting temperatures. It can dissolve an increasing amount of various compounds w i t h increasing temperature. Since it is l i q u i d , it is sticky. • T h e sticky particle surface can t r a p other very s m a l l particles. T h e m o m e n t u m of these particles is insufficient to break up the viscous l i q u i d lead oxide bridges u p o n  contact.  Larger particles, however, have sufficient m o m e n t u m to r e m a i n separate. C o n d i t i o n s that may influence the m o m e n t u m of particles such as the gas d i s t r i b u t i o n a n d the vigour of fluidization (superficial gas velocity) affect coating a n d agglomeration. • R a p i d sintering of the coated particles is favoured by l i q u i d lead oxide. T h 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 a l u m i n a , silica and calcine agglomerates.  Condina  et al. [83] observed agglomerates,  but d i d not observe g r o w t h of single particles.  I n their  they used a "caged" lead sulfide source, immersed i n a b e d of inert  particles.  experiments,  After a few minutes the particles started to agglomerate outside the cage, due to gaseous lead species. Since their experiments lasted o n l y a few minutes, no lead silicates were observed i n 167  Chapter  4.  Experimental  the agglomerates.  Results  It is i m p o r t a n t to note that the experimental conditions of C o n d i n a et al.  [83] differed from those expected i n a continuously operating fluidized bed roaster.  A i r was  used to fluidize the inert bed m a t e r i a l , and no m a t e r i a l other t h a n the pure lead sulfide pellet could react w i t h the fluidizing gas. A l s o , i n their experiments no zinc sulfide was present to form zinc oxide. C o n d i n a et al. [83] d i d not consider the effect of different particles sizes on agglomeration, growth or a t t r i t i o n nor d i d they indicate the effect of the oxygen concentration. It is not k n o w n whether this coating mechanism w o u l d a p p l y to calcine particles since their reactivity w i t h lead oxide is u n k n o w n . However, considering the s o l u b i l i t y of the particles i n 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 0 2  3  phase diagrams (Figures 2.25 to 2.27), it  is likely that the r e a c t i v i t y of calcine particles lies between that of silica a n d a l u m i n a . Since vaporization a n d deposition kinetics are not k n o w n , it is premature to m o d e l the coating of particles. However, since the p a r t i a l pressures are strongly dependent on the oxygen concentrations, it w o u l d be beneficial to evaluate the effect of various process parameters on the oxygen concentration experienced by the particles i n the fluidized bed. A s s u m i n g t h a t coating depends on the relationship between the oxygen concentration and the t r a n s p o r t of metallic species through the gas phase, m o d e l l i n g the oxygen concentration w i t h i n the fluidized bed w o u l d give i m p o r t a n t insights on the coating of particles.  4.7  Agglomeration mechanism in the laboratory roaster  Since o n l y one experiment generated catastrophic agglomerates  (defluidization due to segre-  gated agglomerates), there are insufficient d a t a to clearly formulate an agglomeration mechanism. However, since lead strongly segregated to these agglomerates, it is probable t h a t lead species play a strong role i n the agglomeration mechanism.  Some s m a l l agglomerates  were  found i n the fine particles of other experiments (see Figures 4.13). These agglomerates were also rich i n lead. It is possible that these agglomerates are formed i n a s i m i l a r manner to the catastrophic agglomerates p r o d u c e d d u r i n g r u n 8 (see F i g u r e 4.49 to 4.54). O t h e r agglomerates were formed d u r i n g the experiment w i t h a l u m i n a as the inert bed m a t e r i a l (see F i g u r e s 4.57  168  Chapter  4.  Experimental  Results  and 4.58). T h e following agglomeration mechanism may be suggested:  • T r a n s p o r t of lead from the concentrate particles to the b u l k of the bed occurs i n a manner similar to the g r o w t h mechanism described previously. • However, for the conditions of catastrophic agglomeration, the roaster operated w i t h no excess oxygen. U n d e r these conditions, very low oxygen concentrations are present a r o u n d the concentrate particles. T h i s lower oxygen concentration enhances the transfer of lead to other particles. T h i s m a y produce a larger amount of l i q u i d s w i t h i n the bed. • A larger amount of l i q u i d m a y contribute to the formation of agglomerates t h r o u g h l i q u i d bridging. • A t t r i t i o n l i m i t s the agglomeration rate and possibly the m a x i m u m agglomerate size. Since catastrophic agglomeration o n l y occurred for the experiment w i t h a fine b e d particle size, it is possible that a t t r i t i o n of the agglomerates depends on the b e d particle size. L a r g e bed particles w o u l d l i m i t the size of agglomerates w h i l e fine b e d particles w o u l d not have sufficient m o m e n t u m 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 mentioned above, C o n d i n a et al. [83] neither varied the particle size nor the oxygen concentration. S i m i l a r l y to the coating of particles, there is still too m u c h i n f o r m a t i o n m i s s i n g for the m o d e l l i n g of agglomeration w i t h the mechanism described here. Therefore, assuming t h a t agglomeration is related to the coating mechanism, any i m p o r t a n t insights on the c o a t i n g of particles may be useful to predict agglomeration. T h e next chapter describes a fluidized bed reactor m o d e l applicable to the l a b o r a t o r y and i n d u s t r i a l roasters. T h e results of this m o d e l w i l l be used to evaluate the conditions w h e n the coating and agglomeration mechanisms can be extended to the i n d u s t r i a l roaster.  169  Chapter 5  Model Development  A gas-solid fluidized bed reactor m o d e l is formulated i n this chapter i n order to evaluate the "effect of excess oxygen, oxygen enrichment, temperature and other o p e r a t i n g parameters on the oxygen concentration close to reacting particles. T h e i m p o r t a n t issue of scale-up of the results from a slugging fluidized bed to a b u b b l i n g fluidized bed must be addressed to a p p l y the results from the l a b o r a t o r y roaster to i n d u s t r i a l fluidized bed roasters. A n y fluidized bed gas-solid reactor m o d e l requires that the gas reaction m o d e l be coupled to the solids reaction m o d e l . T h e gas reaction m o d e l accounts for the h y d r o d y n a m i c s of the fluidized bed reactor. T h e solids reaction m o d e l requires that a single-particle reaction m o d e l be selected and used i n conjunction w i t h a m o d e l for the m i x i n g of the solids w i t h i n the  fluidized  bed.  T h i s chapter proposes a new generalized slugging-bubbling fluidized b e d reactor m o d e l . T h e reaction a n d m i x i n g of solids w i t h i n a fluidized bed is presented next. F i n a l l y , a n unsteady-state m o d e l for the reaction of single particles is described. T h e m o d e l assumes t h a t the entire fluidized bed, as well as the reacting particles, are isothermal. T h e m o d e l also assumes that the particles are well-mixed, a x i a l l y a n d r a d i a l l y w i t h i n the fluidized  bed. E l u t r i a t i o n , a t t r i t i o n and agglomeration are not considered.  Reactions i n the  freeboard of the roaster are neglected. T h e time for complete reaction, the m i x i n g times and the single particle unsteady-state m o d e l are used i n the next chapter to verify some of these assumptions.  170  Chapter  5.1  5.  Model  Development  Steady-state fluidized bed reactor model: Gas reaction  T h e steady-state fluidized bed reactor m o d e l accounts for the fluidized b e d h y d r o d y n a m i c s , gas reactions, and solids reactions. and fast  fluidization  T h e m o d e l extends the generalized b u b b l i n g , turbulent  reactor m o d e l of A b b a et al. [203, 204, 205], w h i c h accounts for variable  gas density a n d b u l k flow i n the interphase mass transfer.  T h i s m o d e l , consisting of a single  set of steady-state differential equations, can be applied across several flow regimes from the b u b b l i n g regime to the fast fluidization regime by using a p r o b a b i l i s t i c approach to specify the parameters. C o n t r a r y to the generalized b u b b l i n g , turbulent, fast  fluidization  m o d e l , the  model developed i n this chapter ignores the turbulent a n d fast f l u i d i z a t i o n flow regimes. Instead, the m o d e l is extended from b u b b l i n g into the slugging flow regime. A l s o , the approach used to m o d e l changes i n t o t a l gas molar flow differs from the generalized m o d e l of A b b a et ai [203, 204, 205].  F i g u r e 5.1 represents the two phases of the model, named the L - and H-phases for low-density and high-density phases respectively.  I n the b u b b l i n g 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 b o t t o m of the fluidized bed where it is d i s t r i b u t e d between the L - a n d H-phases. T h e gas then rises i n each phase a n d reacts w i t h the solids present. E x c h a n g e occurs between the two phases. A x i a l and r a d i a l dispersion c o u l d be i n c l u d e d w i t h i n each phase, a n d the former w o u l d need to be incorporated to extend the m o d e l to the turbulent flow regime.  5.1.1  Phase balances  T h e fluidized bed is d i v i d e d into the L - and H-phases (Figure 5.1). T h e b e d v o l u m e fractions of these phases(ipr, and tpn)  add up to  one:  </>L + < M = l  (5.1)  E a c h phase volume is composed of particles a n d v o i d space occupied by the gas. T h e particle volume fraction (<f>) and gas volume fraction (e) w i t h i n each phase also a d d u p to one.  The  t o t a l gas molar flowrate (FT) t h r o u g h the reactor equals the s u m of the m o l a r flowrates t h r o u g h  171  Chapter  5.  Model  Development  Freeboard  A  Az H-phase  u F i g u r e 5.1: Schematic of two-phase  fluidized  bed model  each phases (Fr, and FH), i.e.: FT  +  — FLT  FHT  A c c o r d i n g to the ideal gas law, for a given t o t a l pressure (P) a n d t e m p e r a t u r e (T),  (5.2) the t o t a l  concentration (CT) (sum of a l l gaseous species) is constant (CT — T^JO- Therefore, for a given reactor area (A), the gaseous m o l a r flowrates are related to the superficial gas velocities (U, UL and  UH)  by: (5.3)  F  =  FHT  =  .IPHAUHCT  (5.4)  FT  =  IPLAULCT  (5.5)  T  L  AC U T  Similarly, the m o l a r flowrate of gaseous species i i n the H - a n d L-phases are:  F  m  =  ip AU Cm H  172  H  (5.6)  Chapter  5.  Model  Development  F  Li  =  ifj AU C L  L  (5.7)  Li  After replacing the m o l a r flowrates into equation 5.2 a n d simplifying, we o b t a i n :  U = I/J U L  L  +  (5.8)  i> U H  H  These volume a n d gas flow balances are s u m m a r i z e d i n T a b l e 5.1. T a b l e 5.1: V o l u m e a n d gas flow balances B e d volume  G a s  m o l e  = 1  +  L-phase volume  4>L  H-phase volume  <f>H + (-H = 1  b a l a n c e s  for  + £L = 1  U = ip U +  G a s flow  5.1.2  4>L  L  H- a n d  L  IPHUH  L - p h a s e s  Referring to F i g u r e 5.1, the gas mole balance over the control v o l u m e for a n increment of time is, i n general terms: number of moles entering 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  _l_  'number of moles flowing into the control volume due to bulk inter. phase mass transfer  ' number of moles trans^ ferred to the control I volume by interphase [ ^mass transfer / 'number of moles a c - i cumulating within the > ^control volume J  (5-9)  A s s u m i n g steady-state conditions a n d neglecting axial a n d r a d i a l dispersion, i.e. assuming t h a t the a c c u m u l a t i o n a n d dispersion terms are zero, the mass balance over the low-density phase (L) leads to (terms are explained below):  Fu  -  (FLi  +  ^ff  A, J  + {0} +  ^AAzi/j k Haj L  L  F  F  Ll  m  Aip U H  A^Azkrd,^-^-)  +  I A*l> Azk (j)HAv H  r  FHO2  \ (  A^ U )\F T H  173  AX/JLUL  H  H  L  Fi L  + = (0X5.10)  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 a n d reaction terms i n equations 5.10 a n d 5.11 require some clarification.  T h e interphase mass transfer coefficient (km)  is defined as the v o l u m e t r i c rate of  transfer per u n i t bubble surface area. T h e interphase mass transfer exchange area (a/) is the interfacial bubble area per u n i t bubble volume. M u l t i p l y i n g the two (k^n • « r ) gives the volumetric rate of transfer per u n i t bubble volume. T o o b t a i n the n u m b e r of moles transferred, we need to m u l t i p l y b y the bubble volume w i t h i n the control v o l u m e  (AAzipL.)  a n d b y the  concentration difference between the L - a n d H-phase. T h e concentration of each species w i t h i n each phase is given b y equations 5.6 a n d 5.7. N o t e that the interphase mass transfer terms are identical i n equation 5.10 a n d 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 k is based o n the particle volume. T o o b t a i n the number of moles reacted w i t h i n the L-phase r  of the control volume per u n i t time, the reaction rate constant k is m u l t i p l i e d b y the particle r  volume w i t h i n the phase  (AtpiAzcpi,),  the stoichiometric constant for species i (z/j), a n d the  oxygen concentration ( A^V ) • Similarly, for the H-phase, the reaction rate constant L  m u l t i p l i e d b y the particle volume w i t h i n the phase  (AtpffAzcpff),  for species i (i/j), a n d the oxygen concentration ( A^U  H  k is r  the stoichiometric constant  )'  B u l k interphase mass transfer is required w h e n a change i n gas v o l u m e occurs w i t h i n the H phase. A c c o r d i n g to the two-phase for  fluidization  bubbles.  fluidization  theory, a given flow of gas, UmfA  is required  of the high-density phase. A n y excess gas enters the low-density phase to create  I n a reacting system, the requirement for the high-density phase is s t i l l present.  However, i f there is a v o l u m e change, i t must be balanced b y b u l k interphase transfer. T h e b u l k interphase mass transfer terms i n equations 5.10 a n d 5.11 are very s i m i l a r t o the reaction t e r m of the H-phase (equation 5.11). However, the required stoichiometric coefficient is now the change i n the t o t a l number of gaseous moles (Ai/) m u l t i p l i e d b y the gas m o l a r 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 l o w 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 t h e s i g n o f Au.  I n t h i s c a s e , i t is n e g a t i v e s i n c e , i n t h e r e a c t i o n o f z i n c s u l f i d e 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 s u l f u 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 i d e o f t h e 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 g a s e o u s p r o d u c t o n t h e r i g h t - h a n d s i d e . I f Au  roasting  were positive,  a n y e x c e s s gas p r o d u c e d i n t h e d e n s e p h a s e w o u l d g o t o t h e b u b b l e p h a s e . T h e r e f o r e , t h e molar fraction w o u l d become  gas  F o r z i n c s u l f i d e r o a s t i n g , t h e b u l k f l o w 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 . 1 1 .  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 dF  ,ipL,Fm  Li  F  L i  - j — + k aj{-—r— dz VHUH U dF (F ip F i\ 3 — + k aA— -—— dz \UL WHU  \  , r  1  L  Li  L  F 2 L0  + k 4> Ui—— U , , , F 2 + k <p Vi— U  LH  m  , L  L  H  H0  LH  r  J  H  H  H  , ,  ,  A  F 2  F  H0  Li  + k cf> Au———— U i ± A F 2 k (p Au—-—-— U r  are:  = 0  H  H  H0  r  L  = 0 FT  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 value solver a n d the b o u n d a r y Fi L  Fm  = F in= Lly  = F  H i t i n  . . (5.13)  Li  H  H  (5.12)  bT F L  conditions:  ipLAU C  at  2 = 0  (5.14)  = ipHAU C  at  z = 0  (5.15)  L  H  itin  l}in  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 o w is d i s t r i b u t e d a m o n g H - and  L-phases.  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)  and the phase volume fractions  the  ('ipL a n d ipn)  c a l c u l a t e d at' a s e r i e s 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  are  surface.  s u p e r f i c i a l gas v e l o c i t y (U) is first c a l c u l a t e d f r o m t h e g a s e o u s m o l a r f l o w r a t e s (FHT  and  The FLT)-  T h e l o w - d e n s i t y p h a s e 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 = U ). v  T h i s c a l c u l a t i o n requires the b u b b l e size correlations 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 p h a s e 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 - Uf V*L = — y j - - ^ m  . (- ) 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 p h a s e 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 r e t h e n c a l c u l a t e d b y m e a n s o f 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 d i s t r i b u t o r (z = 0) to the surface of the expanded b e d (z = H), the expanded b e d height (H) must be k n o w n , 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 e x p a n d e d b e d height (H), the b e d height at m i n i m u m fluidization velocity (H f)  a n d the L-phase v o l u m e fraction  m  is relatively simple:  H — H f = f"ip dz Jo io  (5.17)  L  m  Similarly, i f the H-phase fraction is integrated over the expanded b e d height, we o b t a i n  H f= T h e b e d height at m i n i m u m  fluidization  H  sectional area (A), particle density p  p  Jo  (H f)  depends on the b e d mass (M^),  m  m  (5.18)  f ^Hdz  m  H f.  b e d cross-  a n d v o i d space ( e / ) . m  Hmf =  M  b  £  (5.19)  d  n  Pp(l - tmf)A For i n d u s t r i a l zinc roasters, the expanded b e d height is l i m i t e d by the weir overflow height. Therefore, H is k n o w n a n d constant while H f  m a y vary. For the l a b o r a t o r y roaster, on the  m  other h a n d , the expanded bed height is u n k n o w n . However, the b e d mass can be be used to calculate H f. m  I n this case, the calculation of the expanded b e d height proceeds iteratively  (since we need to integrate from 0 to H a n d H is not k n o w n at  5.1.5  first).  Gas conversion and average gas compositions  T h e overall gas conversion, i.e. the oxygen conversion (X02), is calculated as follows: Fi02,out  v  1  " ° X  2  =  + F~H02 ,OUt  C^-AU  / ( 5  r  -  o r  ,N  2 0 )  Similarly, the number of moles of oxygen reacted per u n i t t i m e is given by: AF  0  2  = C , m ^ c 7 - {F 2,out 0 2  L0  + F 2,out) H0  (5.21)  T h e number of moles of oxygen reacted per u n i t time must be coupled to the solids reaction. W i t h the freeboard neglected, F  i ) 0 U t  is equal to 176  Fi ntZ=  Chapter  5.  Model  Development  T h e solids reaction m o d e l assumes that the particle reaction times are l o n g c o m p a r e d to their vertical m i x i n g times. Therefore, the solids c o m p o s i t i o n is assumed to be independent of the vertical p o s i t i o n i n the b e d . T h e solids m o d e l therefore uses the average gas c o m p o s i t i o n seen by the solid particles to calculate their conversion.  T h e gas reaction m o d e l calculates  the  particle-averaged gas concentrations as: rH  / ^  Ci=  rH  <f>HipHCm dz+ / H fj / Jo  (PL^LCU dz :  (jiHipH dz+ I 4> ip Jo rH / tpjCjidz L  L  ^777  Cji=  (5-22)  dz  (j = LovH)  (5.23)  ipj dz  A s s u m i n g that the solid volume fractions (</>/, a n d 4>H) do not change w i t h height a n d using the volume balances (equations i n T a b l e 5.1) a n d the b e d expansion c a l c u l a t i o n (equations 5.17 a n d 5.18), these equations reduce to: 7f _ C  I  4>L (H - H )  Cg  mf  ~  </>L(H-H )  +  <PH (H f) m  + (f>H(H )  mf  mf  f /  -  Cm  (<  l b  -  2 4 j  H  ipr,Cudz  mf  11  1 1  H ipHCm  C  Hl  dz.  — J J —  =  (5.26)  rnf  n  T h e solid reaction m o d e l uses the particle-averaged oxygen concentration to calculate the solids reaction rates. Since the gas concentrations a n d the solids v o l u m e fractions differ between the L - a n d H-phases, averaging the oxygen concentration over the particles w i t h i n each of the two phases allows a simple c o u p l i n g between the fluidized bed a n d the solids reaction m o d e l while accounting for the effect of particles w i t h i n the L-phase.  5.1.6  Minimum fluidization velocity  M o s t m i n i m u m fluidization velocities correlations are of the form: Re  m /  -  ^JCl + C A r - d 2  177  (5.27)  9  ^  Chapter  5.  Model  where C\ a n d C  Development  2  are constants. T h e A r c h i m e d e s number ( A r ) is given by: A r = df  =  PgiPp ~ Pg)9dp  (5.28)  T h e dimensionless particle size (d*) is the cubic root of the A r c h i m e d e s n u m b e r . 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 b y G r a c e [207] are Ci = 27.2 and C  2  = 0.0408.  T h e choice of the average particle size (d ) p  is i m p o r t a n t .  F o r fluidization calculations, the  Sauter mean size (mean surf a c e / v o l u m e size) is c o m m o n l y used, w i t h : 1  (5.29)  where xi is the weight fraction of particles i n each size range a n d d i is the average of adjacent p  sieve apertures.  N o t e t h a t this definition gives more weight to smaller particles t h a n larger  ones.  5.1.7  Bubbling fluidized bed  T h e i n d u s t r i a l roaster is operating i n the b u b b l i n g fluidized bed regime. Since b u b b l e velocities depend on their size, the effective bubble size (D ) e  must be calculated as a function of the  vertical p o s i t i o n i n the bed. I n this work, the bubble size is calculated u s i n g the correlations i n Table 5.2. M o s t bubble size correlations require the bed diameter D, a n d the d i s t r i b u t o r surface area per orifice (Ad)size (D o) e<  T h e M o r i and W e n [208] correlation also gives an i n i t i a l bubble  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 i n t r o d u c e d by H a r r i s o n et al. [210], is of critical i m p o r t a n c e i n evaluating bubble diameters i n fluidized beds of fine ( G e l d a r t G r o u p A ) particles. T h e m a x i m u m bubble size is obtained by using the t e r m i n a l velocity (U°) of spherical particles  of 2.7d [207, 211]: p  •2 D,  = 2.0  e.max  178  9  (5.32)  Chapter  5.  Model  Development  Table 5.2: Correlations for bubble sizes  D a r t o n et al. [209]  D  =  e  M o r i and W e n [208]  0.54( 7-t/ L  D  e  =  D  6 i C O  =  1.49  e f i  =  1.38g-  Z? D  e  t  0  0  )°- (2 4  m /  -(D  e  !  0  0  4v^)°V  +  -D  e  !  o)e-°'  3  z  (p \U - U ))° 2  A  /  a 2  (5.30)  D  (5.31)  mf  (A (U - U ))  0A  02  d  mf  T h e factor 2.7 was o b t a i n e d e m p i r i c a l l y to better predict the m a x i m u m stable b u b b l e diameter observed experimentally. T h e dimensionless t e r m i n a l 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 c o m m o n to use the bubble size correlation at 40% of the b e d height, i.e. at z = 0AH. (U )  can be obtained by:  0OO  U  = 0.71^/g~L\  boo  The  T h e isolated b u b b l e rise velocity  (5.34)  isolated b u b b l e rise velocity (Uboo) is the rise velocity of a single b u b b l e injected i n a  fluidized bed operated at the m i n i m u m fluidization velocity. For freely b u b b l i n g beds, the bubble rise velocity (£/(,) is given by:  U = U b  The  boo  + (U-  (5.35)  U ) mf  bubble rise velocity cannot be used to calculate the superficial gas velocity i n the L -  phase.  A c c o r d i n g to the two-phase theory of  minimum  fluidization  fluidization,  velocity. However, at m i n i m u m  the superficial gas velocity is [ 7  6oo  a l l the gas enters the H-phase at  fluidization,  equation 5.35 predicts that  and not 0. T h e expression for the b u b b l e rise velocity is  179  Chapter  5.  Model  Development  t h e r e f o r e m o d i f i e d s o t h a t Ut, —> 0 as U —> U f  [212]:  m  U = (U-U )(l b  T h e b e d e x p a n s i o n (E)  + ^^VgD~e)  mf  (5.36)  can be estimated from:  E =  g  ~  g  E q u a t i o n 5.37 r e s u l t s f r o m t h e  two-phase  e x p a n s i o n is c a u s e d b y a n y g a s  flow  " / =  (5.37)  t h e o r y of fluidization  b e y o n d U f,  i.e. b y (U — Umf).  m  a s s u m e s a n a v e r a g e b u b b l e s i z e for t h e e n t i r e  a n d assumes that the  fluidized  bed  T h i s c a l c u l a t i o n also  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 s e d . I n t h e p r e s e n t m o d e l , t h e b u b b l e s i z e is n o t set a t a n a v e r a g e v a l u e , 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 v a l u e s o f 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 l s o c h a n g e as t h e b u b b l e s i z e v a r i e s 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 a n s f e r c o e f f i c i e n t [213] a n d a r e a a r e o b tained from: 1/2  fcL// = %  £  + 2f  D g € m  ^°° )  (5.38)  N  ai = J -  (5.39)  T h e s e t w o p a r a m e t e r s w e r e 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 c o e f f i c i e n t is c o m p o s e d o f 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 T h e diffusion c o m p o n e n t diameter  5.1.8  A  varies w i t h gas d i f f u s i v i t y  mass  a n d a diffusion  ( D ) , b u b b l e v e l o c i t y (U^o) f l  transfer  component. and  bubble  (D ). e  S l u g g i n g  fluidized  b e d  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 t o a b u b b l i n g  fluidized  bed.  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 l u g s ( e l o n g a t e d shaped bubbles constrained by the walls). s u p e r f i c i a l v e l o c i t y (U)  bullet-  T h r e e c o n d i t i o n s are necessary for s l u g g i n g .  must be higher t h a n the m i n i m u m slugging velocity ( < 7  180  m s  );  the  The bed  Chapter  5.  Model  Development  height (H) must be greater t h a n 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 c o l u m n diameter (D). velocity (U ) ms  T h e m i n i m u m slugging  is calculated using [214]:  Ums = U  mf  Us m  + 0.07V^/J  = Umf + 0.07  if H  mf  + 0.16(1.3£>°-  > 1.3D  175  0  ( 5.40)  1 7 5  - H )  (5.41)  2  mf  E q u a t i o n 5.40 and 5.41 a p p l y for shallow beds and deep beds respectively. T h e m a x i m u m bed height  (H ) max  d u r i n g slugging can be estimated from [215, 216]:  H  Hf  max  U—Uf U oo  m  m  Hf m  T h e velocity of a single slug  (5.42)  S  (U ) is given by: soo  U  = 0.35^/gD  soo  For a continuously slugging bed, the slug velocity (U ) s  U =U s  soo  (5.43)  is':  + (U- U )  (5.44)  mf  W i t h the exception of the single slug velocity, the last three equations are s i m i l a r to those for b u b b l i n g fluidized beds, but w i t h s (slug) i n place of b (bubble). C o m p a r i n g the H o v m a n d slugging m o d e l [217] to the O r c u t t "piston-flow" [218, 219] shows that the derivations are identical. (km)  fluidized  bed m o d e l  T h e interphase mass transfer  coefficient  and area (aj) can be expressed i n a form similar to that of the b u b b l i n g case:  a, .  (5.46)  T h e surface integral (I) (shown i n Table 5.3) and the slug shape factor (f ) s  are functions of the  slug length-to-diameter ratio (-g) :  ^ = ^ = (§)r°- (s) 495  181  1/2 + 0 0 6 1  (547)  Chapter  5.  Model  Development  Table 5.3: Values of the surface integral (I) for various slug length to diameter ratio L/D  I  0.3  0.5  1.0  2.0  3.0  4.0  5.0  0.13  0.21  0.39  0.71  0.98  1.24  1.48  (L/D)  T h e slug length to diameter ratio ( ^ ) can be obtained by solving the q u a d r a t i c equation [217]:  !- - o W * V  i  (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 m a y be considered as a special case of b u b b l i n g fluidization where the b u b b l e size is physically restricted b y the walls of the reactor. I n a b u b b l i n g fluidized b e d , bubbles coalesce as they rise t h r o u g h the bed causing their average diameter to increase w i t h increasing height vertical p o s i t i o n . 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 a n d one expects a s m o o t h t r a n s i t i o n from b u b b l i n g to slugging fluidization.  M o d e l l i n g the t r a n s i t i o n to slug flow may be attempted i n various ways: • O n e could use two separate models, one for b u b b l i n g and one for slugging, a p p l y i n g a b u b b l i n g m o d e l below a given criteria, then switch to the slug flow m o d e l . T h e p r o b l e m w i t h this approach is that there w o u l d be a discontinuity at the point where the switch is made, while i n practice the t r a n s i t i o n occurs gradually. Moreover, there is uncertainty i n characterizing the regime t r a n s i t i o n . • O n e could use the results from the two models and interpolate or average their results. A p r o b a b i l i s t i c average could be used and w o u l d better characterize the uncertainty of the regime t r a n s i t i o n . T h e p r o b a b i l i s t i c average w o u l d be the weighted s u m of the results where the weights are based on the p r o b a b i l i t y of b e i n g i n a given regime.  182  A problem  Chapter  5.  Model  Development  w i t h this approach is that the interpolated results are not necessarily consistent w i t h the physics of the system, especially where there are non-linearities. • A better m e t h o d is to combine the two models into a single m o d e l w h i c h predicts results similar to the two l i m i t i n g models outside the t r a n s i t i o n range. I n the t r a n s i t i o n region between two flow regimes, the m o d e l uses the p r o b a b i l i s t i c average of the parameters (not the final predictions) for each regime. T h i s approach has been used p r e v i o u s l y to m o d e l the t r a n s i t i o n from the b u b b l i n g to the turbulent fluidization regime a n d from turbulent to fast fluidization [212, 220, 203, 205]. I n that case, relatively s i m p l e R e vs A r correlations describe the transitions from b u b b l i n g to the t u r b u l e n t and from turbulent to fast  fluidization  fluidization  regime  [205]. T h e probabilities were related to the root-  mean-square deviations from these correlations [205]. Currently, the t r a n s i t i o n from b u b b l i n g to the slugging the m i n i m u m slugging velocity  fluidization  regime is o n l y described by  (U ), the necessary conditions for slugging (see section 5.1.8) ms  and the criterion [216]: = 0.2  (5.49)  T h i s criterion does not quantify the p r o b a b i l i t y of slugging and b u b b l i n g , nor does it allow for a transition w i t h i n the fluidized bed, i.e. b u b b l i n g near the d i s t r i b u t o r a n d slugging above. T h e bubble rise velocity as a function of the bubble-to-column-diameter ratio is used i n the next section to characterize the t r a n s i t i o n from b u b b l i n g to the slugging T h e regime probabilities are then obtained.  fluidization  flow  regime.  These probabilities are then used to calculate  probabilistic averages of the parameters required by the m o d e l .  Void velocity In order to bridge the b u b b l i n g and slugging velocities  fluidization  regimes, the v o i d (bubble or slug) rise  (U oo) are described as a function of the Froude number: v  Fr =  voo  V = b or s  183  (5.50)  Chapter  5.  Model  Development  U s i n g the Froude number, equations 5.34 and 5.43 m a y be converted to: Bubbling  Fr  =  0.71^D /D  (5.51)  Slugging  Fr  =  0.35  (5.52)  e  T h e modified bubble rise velocity (from equation 5.36) can be w r i t t e n :  U = (U -U )(l V  mf  + ^VgD)  (5-53)  A s for several other aspects of the h y d r o d y n a m i c s of fluidized bed systems, the t r a n s i t i o n to slug flow i n fluidized bed systems is analogous to that i n gas-liquid systems. T h e e x p e r i m e n t a l d a t a from  fluidized  bed systems presents a similar t r e n d as i n the water system.  However,  the scatter is m u c h larger [216]. F i g u r e 5.2 shows that the velocities at the two extremes are described b y equations 5.51 a n d 5.52. T h e t r a n s i t i o n between the two extremes is s m o o t h and occurs for y/D /D e  between about 0.38 and 0.7 [216].  T h e behaviour at each end of the t r a n s i t i o n interval clearly approaches the two l i m i t i n g cases. In other words, the slopes at each end of the interval are equal to each of the l i m i t i n g cases. T h e fit of the e x p e r i m e n t a l d a t a must also approach the l i m i t i n g cases s i m i l a r l y w i t h a s i g m o i d a l fit in-between to express the p r o b a b i l i t y of slugging passing from 0 to 1 as  y/D /D e  goes from  small values to values approaching unity. T o simplify the fitting for the t r a n s i t i o n region, a transformation is used such that the bubbling-to-slugging t r a n s i t i o n i n t e r v a l (X)  goes from 0  to 1 a n d the corresponding Froude numbers (Y) also passes from 0 to 1. Here:  X  where DDQ and  _ ~  ^DjD-DDo DD\ - DD '  ( 5  0  DD\ are the lowest and highest values of yjD /D e  -  M )  i n the t r a n s i t i o n interval,  i.e. the endpoints of the t r a n s i t i o n interval. Similarly, Y is taken as: Fr-0.7LPA) 0.35 - 0 . 7 L D A )  '  so that it represents a fraction departure from the wall-effect free b u b b l e velocity. B y i m p o s i n g the values a n d the slopes at the end points, the following t h i r d order p o l y n o m i a 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)X  2  + (K-  2)X  (5.56)  3  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(DD -DDQ) 1  0.35 - 0.71DA. Note that once this initial slope is set, there are no degrees of freedom to set any other parameters in the transformed coordinates. Therefore, the only fitting parameters are the endpoints of the interval, i.e. the values of  ^/D /D E  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' < DD  0  Fr = 0.71^fD /D e  185  (5.51)  Chapter  •  5.  Model  F o r DD  Development  < y/D /D  0  <  e  DD  1  Y = KX + (3 - 2K)X + (K 2  • F o r jDjD  2)X  3  (5.56)  > DDi Fr =  (5.52)  0.35  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 s q u a r e s o f t h e d i f f e r e n c e b e t w e e n the fitted function a n d the experimental  data.  (^D /D)  obtained by using a transition interval  e  A n e x c e l l e n t fit o f t h e e x p e r i m e n t a l  d a t a is  b e t w e e n 0.319 a n d 0 . 7 1 4 . 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 r g e r t h a n s u g g e s t e d 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.  With  t h e s e v a l u e s , 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 e p r e s e n 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 of b u b b l i n g .  probability  F o r instance, the probability of slugging should not increase p r o p o r t i o n a l l y  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  then more slowly.  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  ^/D /D e  Outside the transition  < DDQ a n d 1 for  yjD /D e  interval,  > DD\.  In  to the the  transition interval, the p r o b a b i l i t y of slugging increases f r o m 0 to 1 i n an a p p r o p r i a t e m a n n e r .  A r e a s o n a b l e 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 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  corresponding  w a l l - e f f e c t i n d e p e n d e n t b u b b l e r i s e v e l o c i t y ( e q u a t i o n 5.51) i n t h e l o w e r p a r t o f t h e interval, a n d t h e n considering the  s h r i n k i n g difference  between the  obtained  void velocity  transition (equation  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 . condition  (^D /D e  =  0 . 3 5 / 0 . 7 1 = 0.493) w h e n the velocities are e q u a l ( e q u a l F r f r o m  The  equation  5.51 a n d 5.52) d e f i n e s 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 r e e q u a l , i.e.  Pslugging = Pbubbiing i n t e r v a l b e i n g DDQ  • F o r ^JL\|D  = 0.5. H e n c e t h e p r o b a b i l i t i e s a r e a s s i g n e d as f o l l o w s , w i t h t h e  < ^D /D E  <  transition  DD : X  < DDQ (5.58)  186  Chapter  5.  Model  Development  Pbubbling — T  F o r DD  < sjD /D  0  < 0.493  e  KX - (KX  = s  J  u  M  m  f  2 [value of  f  2K) X + (K - 2) X ) n u m e r a t o r a t JL\]~D = 0.493] -  Pbubbling  F o r 0.493 <  (5.59)  yHjjD  2  (3 -  1  =  3  1  Pslugging  —  '  '  (5.61)  < DD  X  _ f bubbling  l-(KX-(3-2K)X  +  2  —  ,  (K-2)X ) 3  ,.  c  ^O.DZJ  v.  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 Pslugging — 1  F o r y/De/D  >  Pbubbling  (5.63)  DDi Pslugging  =  1  (5.64)  Pbubbling = 0  (5.65)  F i g u r e 5.3 p r e s e n 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 yjD /D. e  T h e proba-  b i l i t y o f s l u g g i n g first i n c r e a s e s 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 . 5 1 , r e a c h e s 5 0 % , t h e n i n c r e a s e s a t 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 d e c r e a s e s . 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 a r e s u m m a r i z e d i n T a b l e 5.4.  Note that  t h e s u g g e s t e d 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 (P i gging s U  = 1)  a  s  y/De/D  i n c r e a s e s 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 -  ally similar to the probabilistic transitions introduced i n the generalized  fluidized  bed  reactor  m o d e l [212, 2 2 0 , 2 0 3 , 205], o n e 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 a k e s p l a c e o v e r h e i g h t as  \/D /D e  grows due to coalescence, whereas i n the b u b b l i n g / t u r b u l e n t / f a s t  transitions of the generalized  fluidized  b e d r e a c t o r m o d e l [212, 2 2 0 , 2 0 3 , 2 0 5 ] , t h e  fluidization transitions  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 generalized b u b b l i n g - s l u g g i n g interphase mass transfer coefficient a n d a r e a are 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 o f 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  s u f f i c i e n t for c a t a l y t i c  fluidized  the  fluidized  bed dynamics and the  bed reactors.  gas r e a c t i o n .  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 ,  the  T h i s is fluidized  bed reactor m o d e l must be coupled to a solid reaction m o d e l such that the n u m b e r of moles consumed  and produced  i n the  gas  are b a l a n c e d  produced i n the solid. T h e m o d e l assumes the  w i t h the  number  of moles consumed  reaction:  3 l S ( ( u Q + 2°2(gas) = l O ( H d ) + l S 0 ( a s ) Zn  and  Z n  s0  s o  2  S  (5.66)  T o o b t a i n an overall solids conversion, the solids reaction m o d e l must include assumptions  on  the m i x i n g of the solids w i t h i n the  the  fluidized  residence times of the solids w i t h i n the  bed, the single particle reaction m o d e l a n d  fluidized  188  bed.  Chapter 5. Model Development  T a b l e 5.4: S u m m a r y of equations describing the t r a n s i t i o n from b u b b l i n g to slugging  fluidization  Transformation ^/D /D to X  X  e  Fr to  Y  Y  = ^Boi-OBo  0  =  V ^ e / i ) = DDQ + X (DD\  OT  O^S'-VTIDDo  o  r  F  r  =  F  (°-  3 5  - 0.71DDo) +  -  DDQ)  0.71DD  0  Bubble velocity Fr = 0.7ly/D /D  y/D /D < DDQ  e  e  DDQ < y/D /D < DD\  Y = 2.27X - 1 . 5 4 X + 0 . 2 7 X 2  e  ^D /D > DDi  3  F r = 0.35  e  Probability y/D /D e  DD  Q  <  DDQ  < jD /D e  0.493 < y/D /D e  •^slugging — 0  Pslugging = 2 - 7 9 X  < 0.493 <  - 0.490X  Pslugging = " 0 . 8 1 3 + 4 . 1 2 X - 2 . 7 9 X  DDi  VD /D > DDx  2  3  + 0.490X  3  Pslugging — 1  e  Interval: DDQ = 0.319, DD  X  5.2.1  2  = 0.714  Mixing of solids within the fluidized bed  I n this m o d e l , the solids are assumed to be well m i x e d a x i a l l y a n d radially, as i m p l i e d i n the gas m o d e l . If m i x i n g were not perfect, some regions of the  fluidized  b e d w o u l d contain higher  concentrations of reacting solids t h a n others. T h e gas reaction is formulated i n terms of solids volume fraction w i t h i n each phase w h i c h are constant ((f)H = l — e f m  a n d (pr, = constant) for the  entire reactor a n d does not differentiate the t y p e of solids (reacting or inert). Therefore, any difference i n the concentration of reacting solids (i.e. insufficient m i x i n g ) affects the r e a c t i v i t y of the solids m i x t u r e .  T o account for variations i n the concentration of reacting particles, a solids m i x i n g a n d flow m o d e l s h o u l d be coupled to the gas reaction m o d e l . T h i s approach has been used to m o d e l shallow fluidized beds [221, 222, 223, 224, 225] where r a d i a l m i x i n g is accounted for, w h i l e a x i a l m i x i n g is assumed t o ' b e perfect.  189  Chapter  5.  Model  Development  0)  +  =3  a  CD CSJ  CD -a 3  CD  £  O  fl Q  CD  o  ba  a  -a  1  s  I  § o  o 03  O  a o '•+3  a  3 cr CD  M  cu  el I  3 O  O  L6  O '43  LO  ro  bD  a  O  LO CO  'So  +  LO  bD cn  oo  I  bD  co  3  a .2  fc o  rH  a  PQ  +  T-H  o  +  I _ce co  I «3  § o  3 o + 3  s  .2  CJ  CB (D  o  Ph  ffl  .2  a  CD  ^ s  .8  a  3  o  3 a ft  'co  X  O. CO  CO bJO  CD  03  a  CD  3 'o cfi CD  CD  CD  PQ  190  CD  03  O  o  CD  3 d ,3 o bJO  X  Chapter  5.  Model  Development  T o verify if the assumption of perfect m i x i n g is valid, m i x i n g times w i l l be c o m p a r e d to the reaction and residence times of the reacting particles. Solids m i x i n g i n a fluidized bed must be considered separately i n the two i m p o r t a n t dimensions. A x i a l m i x i n g m a y be characterized b y the turnover time, the time required for the bubbles to displace the entire mass of the bed. T h e solids turnover t i m e is calculated using the axial solids flux ( J ) , bed mass (M^ed) and cross-sectional area (A) [226]:  ^>  J = PP(1-  tmf) (U - U )  Y  MF  ^turnover  ((3  W  0.38&)  +  (5.67)  ~AJ~  (5.68)  T o calculate the solids flux, the values suggested by Baeyens a n d G e l d a r t [226] for rounded sand are used: j3  w  — 0.32, (3d = 0.7, Y = 0.82. C o m p l e t e a x i a l m i x i n g can be achieved i n 2 to  3 turnover times. For a complete discussion on axial m i x i n g and turnover t i m e , see [226]. T h e solids are also assumed to be well m i x e d radially. R a d i a l m i x i n g is u s u a l l y quantified using a dispersion m o d e l [227, 228, 229, 230]. T h e r a d i a l diffusion coefficient of solids  (D n i) ra(  in a  a  b u b b l i n g fluidized bed may be expressed [227] as: Dradiai = 3.66 • I O "  4U  ~ ^  f  .  (5.69)  mf  U  B y considering r a d i a l diffusion i n a cylinder, a characteristic t i m e m a y be obtained [231].  Uadial — .  D  K  *  „  Q n  (5.70)  T h e constant 5.78 is the square of the root of the Bessel function of zero order. T h e most i m p o r t a n t difference between i n d u s t r i a l a n d l a b o r a t o r y roasters is the r a d i a l m i x i n g time. T h e assumption of a perfectly m i x e d bed is verified by c o m p a r i n g the particle residence time and reaction times to the two m i x i n g times described above.  5.2.2  Solid residence times  T h e solids mean residence t i m e characterizes the average t i m e spent b y particles i n the  fluidized  bed. T h e solids mean residence time is required i n section 5.2.4 to calculate the average solids 191  Chapter  5. Model  conversion.  Development  F o r n o n - r e a c t i n g m o n o - s i z e d particles, t h e m e a n residence t i m e is related to t h e  space-time: r=^L  (5.  7 1 )  Fpeed However, since a is n o t v a l i d .  fluidized  b e d roaster has r e a c t i n g p a r t i c l e s o f different sizes, t h i s c a l c u l a t i o n  T o evaluate t h e m e a n residence t i m e o f different p a r t i c l e sizes w e f o r m u l a t e a n  overall mass balance a n d a mass balance by-size over t h e reactor:  Fover flow  (3Fp d ee  PFpeedPFeed  Fcarryover  ~ Fover flowPOver flow  —0  FcarryoverPCarryover  (5.72) —0  (5.73)  w h e r e PFeed, POverflow a n d pcarryover a r e t h e p a r t i c l e s i z e 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, overflow a n d carryover respectively. T h e s e mass balances assume steady-state, complete conv e r s i o n a n d n o c h a n g e s i n p a r t i c l e s i z e s . 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 f o r t h e 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 s u 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 i s u s e d t o convert the concentrate  feedrate i n t o a calcine feedrate.  F o r p u r e z i n c s u l f i d e a n d o x i d e , (3 is  — ^ug/mol  s i m p l y t h e r a t i o o f t h e m o l a r m a s s e s i . e . (3 =  ~ 0-835.  T h e m e a n residence t i m e for a g i v e n size is c a l c u l a t e d f r o m t h e carryover a n d overflow mass flowrates,  i n a d d i t i o n t o t h e size d i s t r i b u t i o n s a n d b e d mass: _  Mb d POverflow e  (5.74)  Fo ver flow POverflow ~\~ Fcarryover PCa rryover B e c a u s e of e l u t r i a t i o n , t h e residence t i m e of a g i v e n size of particles d e p e n d s o n t h e p a r t i c l e size i n q u e s t i o n . V e r y s m a l l particles have a short m e a n residence t i m e i n t h e b e d , w h i l e larger p a r t i c l e s s p e n d m u c h l o n g e r i n t h e r o a s t e r . T h i s i s b e c a u s e fine p a r t i c l e s c a n l e a v e t h e r o a s t e r by two output  streams,  whereas larger ones o n l y exit v i a t h e overflow s t r e a m .  It has been  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 residence t i m e of carryover a n d overflow particles o f t h e s a m e d i a m e t e r i s t h e s a m e [232].  T h e e l u t r i a t i o n constant is related t o t h e carryover mass  flowrate  Fcarryover PCarryover K —  —  a n d size d i s t r i b u t i o n , b y : /r  r,r\  [p.10)  Mbed POverflow 192  Chapter  5.  Model  Development  w h i c h can be used to obtain: r =  p r  (5.76)  1  over flow  M  i  +  BED  K  U s e o f e q u a t i o n 5.76 r e q 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 .  Elutriation  i n c o m m e r c i a l fluidized b e d roasters has not been characterized, a n d p r e d i c t i o n s f r o m available 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 o f t h e p a r t i c l e r e s i d e n c e t i m e is not possible w i t h o u t direct  measurements.  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 o f 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 i z e 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  _  M pd bed  ^  Be  77  -j  (3F~FeedPFeed T h e effective s i z e 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 i n c e c o n centrate particles f o r m l u m p s due to the presence of water.  H o w e v e r , t h e feed p a r t i c l e size  d i s t r i b u t i o n of the l a b o r a t o r y , roaster c a n be m e a s u r e d u s i n g p a r t i c l e size 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 s u l t s i n m e a n r e s i d e n c e t i m e s e q u a l t o 0. F o r t h e s e 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 i d e n c e 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 t o  be  e q u a l t o t h e m e a n r e s i d e n c e 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 :  _ H A(l mf  'minimum —  - <t> ) + (H- H )A(l H  mf  - <f> ) _ H (l L  mf  - <j> ) + (H - H )(l  JJ A  H  mf  U (5.78)  5.2.3  Single-particle reaction model  T h i s section briefly describes a transient  n o n - i s o t h e r m a l solid reaction m o d e l a n d its s i m p l i -  fied 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  bed.  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 o f 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 reactor  m o d e l assumes t h a t the p a r t i c l e s are i s o t h e r m a l , at the 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 s o 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  - cj> ) L  Chapter  5.  Model  Development  T h e single particle reaction m o d e l is a transient m o d e l aimed at p r e d i c t i n g the gas concentrations at the reaction site, the particle temperature and the evolution of conversion w i t h time. A s s u m m a r i z e d b y W e n and W a n g [234] the m o d e l accounts for t h e r m a l a n d diffusional effects i n 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 diffusion and heat generation. T h e resulting m o d e l can predict various p h e n o m e n a such as ignition, extinction, geometric i n s t a b i l i t y and a b r u p t changes i n the c o n t r o l l i n g m e c h a n i s m . T h e nomenclature of the equations is the same as i n W e n and W a n g [234] w i t h m i n o r changes to allow for the calculation of gaseous p r o d u c t concentrations. T h e m o d e l applies to the following general reaction: aA(gas) + S(solid) = #G(gas) + c C ( s o l i d ) For the roasting of zinc sulfide, A is O2, S is Z n S , G is SO2 and C is Z n O .  (5.79) A s for the  fluidized bed m o d e l , the stoichiometric coefficients, z/j, are positive for p r o d u c t s a n d negative for reactants. T h e rate of reaction can be represented as:  TA = "ATS = VAhCfCX  (5.80)  where m and n are the orders of the reaction w i t h respect to the solid a n d the gaseous reactants concentrations, respectively. T h e reaction rate constant, k  s  is per u n i t reacting surface area.  T h e temperature dependency of the reaction rate constant is assumed to be of A r r h e n i u s type, i.e.: (5.81) where k° is the pre-exponential constant a n d E  a  is the activation energy. F i g u r e 5.4 presents  the geometry of the m o d e l as well as t y p i c a l concentration a n d t e m p e r a t u r e profiles.  194  Chapter  5.  Model  Development  Reaction ^Surface ^ * \ ^ A s h Layer  Gas  Film  F i g u r e 5.4: C o n c e n t r a t i o n a n d temperature profiles of a single reacting p a r t i c l e [234]  Mole balances In terms of gas mole fractions (xj), the steady-state gas mole balance over the reacted layer (r  c  < r < R) of a spherical reacting particle can be described as: d?x; dr  2  H  2 dxi r  dr  =  0  (5.82)  where i can either be the gaseous reactant ( A ) or p r o d u c t ( G ) . A l t h o u g h equimolar counterdiffusion is assumed, the following treatment can be applied to the z i n c roasting system w h e n the reactant a n d resulting p r o d u c t gas concentration is s m a l l , w h i c h is assumed to be the case. T h e b o u n d a r y c o n d i t i o n at the surface (r = R) is:  dxi.  — (k iC)To{Xio ~ %is)  [CD i)To~^\r=R  m  e  (5.83)  T h e p r o d u c t of the t o t a l gas concentration (sum of a l l gaseous species) times the diffusivity  (CD i) e  (r = r ) c  is assumed to be temperature-independent.  T h e b o u n d a r y c o n d i t i o n at the core surface  is  — —ViK(Tc)C™CAc  (CD i)To—T^\r=r e  c  (5.84)  where V{ is the stoichiometric coefficient for component i. T h e e v o l u t i o n of the core radius w i t h time is described by:  (CD ) — ei To  dxj  dr  r  =vC A  195  s  d t  (5.85)  Chapter  5.  Model  Development  w i t h the i n i t i a l c o n d i t i o n , r = R w h e n t = 0. T h e subscripts T a n d T i n d i c a t e t h a t the quanc  0  c  tities are evaluated at the b u l k conditions or at t h e reaction interface c o n d i t i o n s , respectively.  Heat balance T h e energy balance i n t h e ash layer is given b y :  8T k (d T m=cVe{-dr^ 2  e  where k  e  and C  pe  +  2dT\ rfr)  ( 5  -  8 6 )  are the effective t h e r m a l c o n d u c t i v i t y a n d v o l u m e t r i c heat c a p a c i t y of t h e  ash layer respectively. T h e b o u n d a r y c o n d i t i o n at the surface (r = R) is:  dT - f c e ^ T = h (T - T ) + h (T* - T )  (5.87)  4  c  s  0  R  N o t e that r a d i a t i o n is i n c l u d e d using a radiative heat transfer coefficient. T h e radiative heat transfer coefficient  (hfi),  includes the emissivity of the particle (e rtide),  constant (a = 5.67 x I O  the Stefan-Boltzmann  pa  - 8  W m  2  K " ) a n d view factors, i f applicable. T h e first r i g h t - h a n d 4  t e r m is the heat transfer b y convection, w h i l e t h e second t e r m allows for t h e r a d i a t i o n from the particle surface t o a w a l l surface. F o r a particle i n a fluidized b e d , t h e w a l l surface consists of other b e d particles. T h e b o u n d a r y c o n d i t i o n at the unreacted core surface (r = r ) , assuming c  that the core is at a u n i f o r m temperature ( T ) , is: c  ^ r l k ^ - ^rlv k CfC {-AH)  =lrrr  n  A  sTc  Ac  3 c  p C <3 c  p  (5.88)  Solution T h e reader is referred t o W e n a n d W a n g [234] for more details o n the s o l u t i o n of the mass a n d heat balances. T h e equations can be r e w r i t t e n i n dimensionless f o r m . T h e s o l u t i o n of the mass balance for the gaseous reactant ( A ) is given b y :  w  cA  = uA 8  +  Sh (l-u )^\-^ A  sA  196  (5.89)  Chapter  5. Model  Development  T h e solution of the mass balance for t h e gaseous p r o d u c t (G) is given b y :  WcG = w G + S h S  ~{U )  (l-o; G)^l-^  G  {RT  \  eXP  C  (5.91)  S  0  U ))\v  l  c  D  A  eGTo  X )  [  b  m  )  Go  T h e p o s i t i o n of the reaction front ( £ ) can be calculated b y integration: c  Sh (l  - UJ )  A  _  sA  d£  _  c  (5.93)  T h e solution of the heat balance is given by:  U = U +(l8  d  U  c  6/3(^)^  8  ( N u ( ( 7 , - 1) + N u ( C /  c  c  R  - (U - ^ c ) ( ^ X ) + ^ - ( 1 + ^ a  +  4 s  -  U-  (5.94)  e (l4cT(Nfc H^u^) +  0+  (5.95)  where  C D (-AH)R kE  p=  Ao  eATo  e  A  ( 5 9 6 )  a  DeAToC =- C ^ e ^ e Ao  sp  ^  pe  A  P  V Ck A  s  (5  97)  e  T h e last two dimensionless numbers originate from the transient analysis of t h e heat balance. Several parameters are grouped into dimensionless numbers such as t h e T h i e l e m o d u l u s  DeATo  and the modified S h e r w o o d number (Sh): Sh =  (5.100)  T h e T h i e l e m o d u l u s accounts for mass transfer resistance w i t h i n t h e p r o d u c t layer, while the modified S h e r w o o d number accounts for the external mass transfer resistance.  197  Chapter  5.  Model  Development  E q u a t i o n s 5.89 to 5.95 must be solved simultaneously by integrating over dimensionless time (9). If steady-state is assumed, there is no energy a c c u m u l a t i o n i n the ash layer (A = 0) or the unreacted core (G = 0). T h e equations thus simplify to the results of I s h i d a a n d W e n [235]. T o o b t a i n the solids conversion from the reaction interface p o s i t i o n , the following relationship is used: x = i~e  (5.101)  c  Isothermal solid reaction model T h e isothermal solid reaction m o d e l assumes that the particle has no i n t e r n a l t e m p e r a t u r e gradient a n d reacts at a constant temperature, equal to the environment (or b u l k ) t e m p e r a t u r e . For such an i s o t h e r m a l system, there are no heat effects. T h e effectiveness factor (r/ ) a n d the s  reaction interface p o s i t i o n ( £ ) are given by: c  Vs =  j, 1 + ^  (  1  -  ^  (5.102)  + ^ 2  where 9 is the dimensionless time. T h e dimensionless time required for complete reaction  (9 ) cr  is obtained by setting £ to 0 i n equation 5.103. c  T h e t i m e for complete reaction of the solid particles is required for c a l c u l a t i n g the overall conversion of the solids i n the fluidized bed.  T o o b t a i n the (dimensional) t i m e for complete  reaction, we note that: tcr =  ^ °  r m  ksToC^Cl  71  1  (5.104)  A dimensionless t i m e of 1 ( # = l ) signifies that the reaction is controlled b y c h e m i c a l kinetics c r  only.  T h e reciprocal of the dimensionless time for complete reaction m a y be viewed as the  overall effectiveness factor. F o r an isothermal system, the effectiveness factor varies between 0 a n d 1. W h e n heat effects are accounted for a n d the reaction is exothermic, the factor can exceed 1.  198  effectiveness  Chapter  5. Model  Development  E q u a t i o n s 5.102, 5.103 a n d 5.104 are used i n the gas-solid fluidized b e d reactor m o d e l to calculate the overall solids conversion, as discussed i n the next section.  5.2.4  Conversion of solids  A s s u m i n g that the b e d solids are perfectly m i x e d , the solids reactions are m o d e l l e d i n similar fashion to the reaction of a macro-fluid where the solid conversion is integrated over the age d i s t r i b u t i o n . F o r mono-sized particles reacting as s h r i n k i n g cores under c h e m i c a l control, the solids conversion i n a w e l l - m i x e d fluidized b e d is a function of the mean solids residence t i m e ( t ) , a n d the t i m e required for complete conversion of a single particle (t ) [232, 157] is given cr  by: ftcv  1-X=  + \ 3  /  1  f - -  2(f)  2  D u e to n u m e r i c a l i n s t a b i l i t y at h i g h  T  dt  JO V After integration, the overall solid conversion is:  X =3f  ~ / t  e  tcr J  (5.105)  T  + 2(f]\l  - e^)\  (5.106)  the exponential is expanded using the T a y l o r series.  If a wide size d i s t r i b u t i o n is modelled, the overall solids conversion of a given stream (carryover, overflow) m a y be calculated as the size-distribution-weighed s u m of the conversions of the different sizes [232]:  X= where  pstream  rdp,rn.ax  I  Jo  X(d )p p  dd  stream  (5.107)  p  is the particle size d i s t r i b u t i o n function of the stream, the s u m of w h i c h equals 1.  T h e calculation of the conversion for a given particle size is the same as i n equation 5.106, b u t uses the average residence time for this given particle size. E a c h particle size w i l l therefore have different average conversions to complete conversion  (X(d )) due p  (t (d )). cr  p  to different residence t i m e ( t ( c ? ) ) a n d different times p  U n l i k e 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.  5.3  Model  Development  Solution method  P r i o r to solving the model, the reactor geometry, the operating conditions, particle properties and other m o d e l parameters must be set. T h e m o d e l is implemented assuming pure zinc sulfide as solid i n p u t . T h e z i n c sulfide feedrate is calculated by setting the superficial gas velocity (17), inlet oxygen concentration (Co ,m) a n d 2  excess oxygen (Excess02) and using the equation:  Similarly, the zinc concentrate feedrate is calculated by replacing the zinc sulfide molar mass ( M z s ) by its concentrate equivalent (M n  )  i.e.:  concentrate  j-,  A ^ZnS  F ,concentrate Feed  ^concentrate  ~ A ^  (  ^  1  ^^—^——J  T h e excess oxygen is calculated for a given experiment  \ r~<  TT  Co , U  using equation  2 ln  (K m n \  (5.109)  5.109 (by isolating  Excessoi)T w o a d d i t i o n a l parameters are required prior to fitting the experimental d a t a shown i n section 4.4. M  t te)  is the mass of zinc concentrate equivalent to a mole of zinc sulfide for the  concen ra  reaction:  , ZnS + ^ 0  A value of M entrate conC  2  = ZnO+S0  2  larger t h a n the molar mass of zinc sulfide (97.456 g / m o l z n s )  (5.110) indicates  that more concentrate is required t h a n pure zinc sulfide to react w i t h 1.5 moles of oxygen. M trate concen  can be calculated by adding the oxygen requirement for each element i n the con-  centrate assuming complete conversion to Z n O , SO2, F e 2 0 3 , P b S 0 4 a n d accounting for the presence of oxygen i n sulfates i n the concentrate. T h e p r o p o r t i o n of each element i n the concentrate is obtained from the zinc concentrate assays. For the same operating conditions, i.e. inlet oxygen concentration, superficial gas velocity a n d excess oxygen, equations 5.108 a n d 5.109 can be combined to relate the concentrate a n d Z n S molar masses a n d feedrates: ^concentrate Mzn S  M ncentrate CO  200  (5.111)  Chapter  5.  Model  M centrate  Development  is o n l y used w h e n a concentrate feedrate must be converted to a n equivalent pure  con  zinc sulfide feedrate. T h e second parameter, the particle mean residence time factor ( / ) is used to adjust the residence time of the reacting particles to account for the change i n particle mass (ft) a n d for the fact that the mass of zinc concentrate fed differs from the pure zinc sulfide assumed i n the m o d e l :  H  concentrate  lvl  T h e particle residence time is therefore: fM p T = — FFeed PFeed b e d  B e d  (5.113)  T h e e x p e r i m e n t a l d a t a shown i n section 4.4 are fitted by adjusting the solids reaction rate constant  (k ). s  Once the parameters are set, the m o d e l is solved following these steps: • Guess i n i t i a l values for k , a n d H or H f. r  m  N o t e that once either H or H f m  is k n o w n , the  other one can estimated. • Integrate the fluidized b e d mole balance equations (equations 5.12 a n d 5.13) over the height. • If the calculated b e d expansion (equation 5.17) does not agree w i t h the i n i t i a l values of H or H f, m  step.  adjust their values using the calculated b e d expansion a n d repeat the previous Convergence is obtained w h e n the difference between the b e d expansions is less  than 5 x l 0 ~  4  (0.5 m m ) .  • C a l c u l a t e the gas conversion using equation 5.20. • C a l c u l a t e the average gas concentrations seen by the solids (equation 5.23). • U s i n g the gas concentrations from the previous step, calculate the t i m e for complete reaction (equations 5.102, 5.103 and 5.104) a n d the average solids conversions (equations 5.106 or 5.107 ). 201  Chapter  5.  Model  Development  • C o m p a r e the gas to the overall solids conversions.  If the number of moles reacted do  not balance, adjust the effective gas reaction rate constant (k ) r  a n d r e t u r n to the second  step. If they balance, the m o d e l has converged to the desired s o l u t i o n . T h e effective gas reaction rate constant (k ) r  i n the fluidized bed m o d e l is an adjustable parameter chosen  so that the moles of reactant balance according to the stoichiometry:  residual,  T h e m o d e l finds the value of k  r  —  F  F  e  e  d  —  AF  J W 1 0 0 0  02  (5.114]  for w h i c h the residual (equation 5.114) is zero.  The  iterative procedure searches for the zero by n a r r o w i n g the interval where the sign of the residual changes. T o constrain the solver, the log of k  r  is used to ensure t h a t k  r  is never  negative. T h e i n i t i a l k interval is 1 0 ~ to 1 0 . Convergence is o b t a i n e d w h e n the interval, 8  8  r  on a log scale, is smaller t h a n 2 x l 0 ~ . T h e effective gas reaction rate constant is adjusted 4  such that the fluidized bed reactor m o d e l consumes the correct amount of oxygen.  202  C h a p t e r  6  M o d e l l i n g 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 s u m e s t h a t l e a d s p e c i e s a s s i s t a g g l o m e r a t i o n t h r o u g h lead sulfide 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 onto b e d particles.  Since the p a r t i a l pressure of lead  sulfide d e p e n d s s t r o n g l y o n the o x y g e n p a r t i a l pressure, it seems t h a t increased a g g l o m e r a t i o n t h r o u g h this m e c h a n i s m w o u l d o c c u r w h e n the b e d particles experience a l o w average o x y g e n partial pressure.  Therefore, m o d e l l i n g l o o k s at the average o x y g e n c o n c e n t r a t i o n  surrounding  the particles t h r o u g h the s i m p l e reaction of pure z i n c sulfide to p u r e z i n c oxide.  No  other  c o m p o n e n t s a r e 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 i n g 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 the particle temperature can exceed the environment temperature.  T h i s m o d e l is u s e d  to evaluate the assumptions  inside the  of 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 gradients  a n d constant particle temperature equal to the fluidized b e d temperature).  particles  N e x t , the general-  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 and bubbling  fluidized  bed models.  T h e scale-up of  fluidized  b e d s is b r i e f l y d i s c u s s e d .  c o m p l e t e g a s - s o l i d s 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 o a s t e r d a t a . aid of the e s t i m a t e d parameters,  With  The the  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 the average o x y g e n p a r t i a l pressure a r o u n d particles.  203  the  Chapter  6.1  6.  Modelling  Results  Unsteady-state single particle reaction  T h e unsteady-state single particle reaction m o d e l is used to evaluate the conditions under w h i c h the particle temperature exceeds the temperature of its surroundings. Since the fluidized bed m o d e l assumes that the particles are isothermal and at the same t e m p e r a t u r e as the fluidized  bed, the conditions where the unsteady-state m o d e l predicts excessive temperatures  w i l l therefore be conditions w h i c h require more complex m o d e l l i n g to replace the i s o t h e r m a l i t y assumptions.  6.1.1  Model parameters  T h e m o d e l requires a number of kinetic, heat and mass transfer parameters as i n p u t s . T h e values used here are also employed for the solids reaction of the  fluidized  b e d m o d e l . B o t h kinetic  expressions suggested i n chapter 2 are used for the m o d e l . 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  modelling. T h e sulfur dioxide concentration does not influence the reaction kinetics i n any way. B o t h the b u l k oxygen concentration a n d the particle size are varied. T h e effective diffusivity i n the ash layer is based on the gas diffusivity of oxygen i n sulfur dioxide (obtained using C h a p m a n - E n s k o g theory [231, 236]), a porosity of 0.4 a n d a tortuosity factor of 3. These values are similar to those obtained by G o k a r n a n d D o r a i s w a m y [150, 159] where they measured the diffusivity w i t h i n an ash layer of reacted zinc sulfide pellets. G o k a r n and D o r a i s w a m y [150, 159] obtained gas diffusivities w h i c h are 38-47% of the b u l k diffusivity. A smaller value is chosen here because the pellets of G o k a r n a n d D o r a i s w a m y were i n i t i a l l y porous, w h i l e the single particles m o d e l l e d here were i n i t i a l l y non-porous. T h e effective t h e r m a l c o n d u c t i v i t y was estimated from those of ceramic materials w i t h similar porosities [231]. T h e heat capacities a n d 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 r a d i a t i o n . R a d i a t i o n is therefore neglected. However, once a temperature difference occurs, r a d i a t i o n s h o u l d be taken into account. For an exothermic reaction, such as zinc sulfide roasting, r a d i a t i o n w o u l d s i m p l y reduce the overheating.  204  Chapter  6.  Modelling  Results  T a b l e 6.1: S u m m a r y of single 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 values Value  Parameter  Chemical kinetics F i t t e d kinetics 6.28-10  P r e - e x p o n e n t i a l constant k° ( c m / s )  12  288  A c t i v a t i o n energy E ( k J / m o l ) F u k u n a k a et al. [140] k i n e t i c s  2.96-10  P r e - e x p o n e n t i a l constant k° ( c m / s )  15  314  A c t i v a t i o n energy E ( k J / m o l ) R e a c t i o n orders O x y g e n n (-)  1  Solids m (-)  0  Particle properties R e a c t a n t (core) density p  4100  (kg/m ) 3  c  R e a c t a n t (core) m o l a r weight M  97.4  (g/mol)  c  P r o d u c t (ash layer) d e n s i t y p ( k g / m )  5600  P r o d u c t (ash layer) m o l a r weight M  81.4  3  (g/mol)  Mass transfer Effective gas diffusivity i n ash layer D ( \ eA  Modified Sherwood number  (m /s) 2  To  D02-SO2 x 0 . 4 / 3 1  Sh  Heat generation and transfer Effective t h e r m a l c o n d u c t i v i t y of ash layer k  e  H e a t c a p a c i t y of ash layer C  pe  H e a t c a p a c i t y of u n r e a c t e d core C  pc  H e a t o f r e a c t i o n AH  (W/(m K))  0.3 54  (J/(mol K)) (J/(mol K))  56.8 -448  (kJ/mol)  M o d i f i e d N u s s e l t n u m b e r for c o n v e c t i o n Nuc M o d i f i e d N u s s e l t n u m b e r for r a d i a t i o n NUR  (-) (-)  1 0 1  I n i t i a l dimensionless t e m p e r a t u r e UQ  Environment conditions 940  Temperature T (°C)  l e - 3 to 0.5  B u l k O2 c o n c e n t r a t i o n XQV (-)  0.17  B u l k SO2 c o n c e n t r a t i o n xso2 (-)  1 to 10 000  P a r t i c l e d i a m e t e r d (tim)  205  Chapter  6.  Modelling  Results  6.1.2  Time for complete reaction  T h e time for complete reaction is the most i m p o r t a n t o u t p u t for the fluidized bed m o d e l . It is used i n conjunction w i t h the residence time d i s t r i b u t i o n to evaluate the average conversion.  F i g u r e 6.1 presents the time required for complete conversion as a function of particle size and b u l k oxygen concentration for b o t h kinetic rate expressions.  A s expected from the pre-  exponential constants, the fitted kinetics are slower by a factor of a p p r o x i m a t e l y 50 to 100 compared to values from the expression of F u k u n a k a et al. [140]. A s expected, the t i m e for complete conversion is reduced as the particle size is reduced and the b u l k 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 Particle diameter  m  m  10 mm  (b) F i t t e d k i n e t i c s (dashed line i n F i g u r e 2.4)  (a) K i n e t i c s f r o m F u k u n a k a et al. [140]  F i g u r e 6.1: Unsteady-state particle m o d e l : T i m e to complete reaction i n seconds.  6.1.3  Particle temperatures  T h e average particle temperatures (averaged over time) are shown i n F i g u r e 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 t e m p e r a t u r e of 1.01 is equivalent to a 1 2 ° C increase from the surroundings. 206  Chapter  0.1 1 pm  6.  Modelling  10 /jm  Results  100 pm 1 mm Particle diameter  (a) A v e r a g e core dimensionless  t e m p e r a t u r e (U ) c  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  F i t t e d kinetics  10 pm  100 pm 1 mm Particle diameter  10 mm  (b) A v e r a g e surface dimensionless t e m p e r a t u r e (U  s  F u k u n a k a et al. [140] K i n e t i c s  100 pm 1 mm Particle diameter  (c) A v e r a g e core dimensionless  0.1 1 pm  10 mm  0.1 1 pm  10 mm  t e m p e r a t u r e (U ) c  10 pm  100 pm 1 mm Particle diameter  10 mm  (d) A v e r a g e surface dimensionless t e m p e r a t u r e F i t t e d kinetics  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  (U ) s  Chapter  6.  Modelling  Results  For particles smaller t h a n about 100 ^ m , the core and surface dimensionless temperatures are identical for most conditions. T h i s indicates that t h e r m a l gradients are negligible. F o r larger particles, t h e r m a l gradients may be significant, especially for oxygen concentrations larger t h a n 10 v o l % . T h e assumption that the particles have no internal t e m p e r a t u r e gradients is acceptable for the concentrate particles i n this study. T h e kinetic results of F u k u n a k a et al. [140] suggest much higher temperatures t h a n the fitted kinetics (equation 2.3). For instance, large particles (larger t h a n 3 m m ) m a y experience very large temperature excursions w h e n the oxygen concentration exceeds 10% if the F u k u n a k a et al. kinetics apply. However, for the fitted kinetics, particle overheating is m u c h smaller. Regardless of the kinetics, any b u l k oxygen concentration less t h a n 5 v o l % does not promote overheating. If the particles are w i t h i n a b u l k atmosphere containing 10% oxygen, the overheating w o u l d be l i m i t e d to about 1 2 ° C for the largest particles. Since the e x p e r i m e n t a l l a b o r a t o r y roaster d i d not have any feed particles larger t h a n 100 pm, the a s s u m p t i o n t h a t the particle temperature is equal to that of the bed is reasonable. If the F u k u n a k a et al. kinetics apply, these particles may experience a s m a l l temperature increase of less t h a n 1 0 ° C i f they also encounter oxygen concentrations larger t h a n about 10 v o l % . For the assumption to be valid for the i n d u s t r i a l roaster, the large particles must not experience oxygen concentrations larger t h a n about 5 to 10 v o l % . However, calculations for the very large particles should be made w i t h the grain m o d e l since the current m o d e l assumes t h a t the i n i t i a l solid is non-porous a n d that these large particles are likely to be l u m p s of smaller concentrate particles.  Since l u m p s are created w i t h smaller grains, the diffusion resistance t h r o u g h the  the b u l k of the l u m p w o u l d be smaller t h a n that for a similarly-sized particle. L u m p s m a y therefore react faster t h a n particles of the same size. Heat transfer l i m i t a t i o n s from a l u m p to the surroundings are likely to be similar to their particle counterpart.  Therefore, l u m p  overheating m a y be greater a n d occur for smaller l u m p s t h a n for particles.  Temperature excursions for large particles have been documented p r e v i o u s l y [160, 237]. P a t i s s o n et al. [160] used 10 m m porous pellets i n a thermogravimetric balance w i t h an atmosphere of  208  Chapter  6.  Modelling  Results  pure oxygen a n d pellet temperatures up to 1100°C while the s u r r o u n d i n g atmosphere was o n l y at  550 to 650°C. M u c h less overheating was observed w h e n air was used (740°C for a 600°C  atmosphere).  Natesan a n d P h i l b r o o k [237]  obtained more modest overheating (+50  °C) i n  an 27 v o l % oxygen atmosphere at 960 °C. T h e i r smaller overheating m a y 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 a n d at the surface of the particle are shown i n d i m e n sionless form i n Figures 6.3 a n d 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 b u l k . A dimensionless concentration lower t h a n one indicates that the mole fraction is o n l y a fraction of the b u l k concentration w h i l e a dimensionless concentration higher t h a n one, the mole fraction is larger t h a n that of the b u l k . T h e dimensionless oxygen concentration at the unreacted s h r i n k i n g core of a particle is lower t h a n t h a t of the b u l k . T h i s is not unexpected since mass transfer  limi-  tations from the b u l k to the surface of the unreacted core are present. However, the particle size for w h i c h the oxygen concentration at the core start to be smaller t h a n 90% of the b u l k (^c02  < 0.9)  depends on the kinetics used. For instance, if the F u k u n a k a et al. [140]  kinetics  are used, particles larger t h a n about 3 pm have less t h a n 90% of the b u l k oxygen concentration at their core. However, if the fitted kinetics are used instead, any particles smaller t h a n 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 because o n l y the b u l k oxygen concentration is varied. T h e sulfur dioxide concentrations is governed by the d y n a m i c e q u i l i b r i u m between the p r o d u c t i o n of S 0  2  a n d its t r a n s p o r t to the b u l k  gas. T h i s process is similar to the generation and transport of heat, a n d therefore, the SO2 profiles are similar 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 a n d at the core surface depend greatly on the kinetics used.  However, to calculate the p r e d o m i n a n t phase, a s m a l l  209  Chapter  6.  Modelling  Results  OOP p o0 > GO ~J cn *. <*>  $0.5  o  o b  0.2 0.1 1  um  10  um  100 (im  1  10 mm  1  Particle diameter  um  10  fj,m  100 /im  1 mn  10 mm  Particle diameter  (a) A v e r a g e core dimensionless o x y g e n concentra- (b) A v e r a g e core dimensionless sulfur d i o x i d e c o n centration  t i o n (W ,02) c  Ci  50 r  50  1  (u> so2)  10  um  um  100  um  1 mm  10 mm  1  Particle diameter  um  10  um  (c) A v e r a g e surface dimensionless o x y g e n concen- (d) A v e r a g e surface t r a t i o n (td 02) S)  100  um  1 mm  10 mm  Particle diameter  dimensionless sulfur d i o x i d e  concentration (w so2) S)  Figure 6.3: Unsteady-state particle model: Dimensionless gas concentrations. Kinetics from Fukunaka et al. [140]  210  Chapter  6.  Modelling  Results  50 o co 21 s? 10  0.5 o  0.2  CO  0.1 ' — 1 pm  10 pm  o p  O ^ CO  100 pm 1 mm Particle diameter  1 pm  10 mm  10 pm  100 pm 1 mm Particle diameter  10 mm  (a) A v e r a g e core dimensionless o x y g e n c o n c e n t r a - (b) A v e r a g e core d i m e n s i o n l e s s sulfur d i o x i d e c o n -  tion (w 2)  centration  C|0  50  50  (t0 SO2) Ct  r  o  CO  21 10 5  0.5 0.2 0.1 1 pm 1  10 pm  100 pm 1 mm Particle diameter  10 mm  10 pm  (c) A v e r a g e surface dimensionless o x y g e n concen- (d) A v e r a g e surface t r a t i o n (w o2) Sj  100 pm 1 mm Particle diameter dimensionless  sulfur  10 mm  dioxide  c o n c e n t r a t i o n (LU ,SC>2) S  Figure 6.4: Unsteady-state particle model: Dimensionless gas concentrations. Fitted Kinetics  211  Chapter  6.  Modelling  Results  deviation from the b u l k concentration (dimensionless concentrations between 0.75 a n d 1.25) would not represent a significant shift (-0.12 to +0.09 on the log scale) o n the predominance diagram (Figure 2.2). Since the concentrate particles are m u c h smaller t h a n 100 pm  (80% of  the concentrate particles are smaller t h a n 23 pm, see Table 3.2), the concentrations i n the b u l k and the concentrations at the particle core do not differ significantly. T h i s argument does not hold for large particles such as l u m p s present w i t h i n the feed to the i n d u s t r i a l roaster.  6.1.5  Effectiveness factors  W e n a n d co-workers u t i l i z e d 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 b u l k c o m p o s i t i o n and temperature.  In isothermal  systems, effectiveness factors are equal to or less t h a n one, d e p e n d i n g on the mass transfer limitations.  F o r non-isothermal exothermic systems, the effectiveness factor can exceed one,  due to self-heating of the reacting particles.  o d  0.2 0.1 ^ 1 um  10  100 um 1 mm Particle diameter  um  0.2 0.1 — L  10 mm  1  um  10  100 um 1 mm Particle diameter  um  10 mm  (b) F i t t e d k i n e t i c s  (a) K i n e t i c s f r o m F u k u n a k a et al. [140]  F i g u r e 6.5: Unsteady-state particle m o d e l : Effectiveness factors.  F i g u r e 6.5 shows effectiveness factors as a function of the b u l k oxygen concentration and particle  212  Chapter  size.  6.  Modelling  It is i m p o r t a n t  Results  t o n o t e t h a t t h e c o n d i t i o n s for factors  >  1 are n o t i d e n t i c a l to the  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 effectiveness f a c t o r is s m a l l for large particles ( > l m m ) , even i f they reach v e r y h i g h t e m p e r a t u r e s . mass transfer 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 effectiveness  particles i n oxygen-rich atmospheres. particles, a s m a l l overheat  T h i s is d u e t o t h e large factor > 1 is for s m a l l  B e c a u s e t h e m a s s transfer resistance is s m a l l for s m a l l  increases d r a m a t i c a l l y t h e effectiveness  factor leading to a higher  r e a c t i o n r a t e . T h i s i s 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 n e s 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 e f f e c t i v e n e s s f a c t o r is l a r g e r t h a n 1. I n g e n e r a l , t h e e f f e c t i v e n e s s  f a c t o 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 effectiveness  factor  ( s h o w n i n F i g u r e 6.5) d o e s n o t p o r t r a y  t h e e x t e n t o f h e a t effects o n t h e r e a c t i o n r a t e .  adequately  T o better visualize the conditions where heat  g e n e r a t i o n affects t h e r e a c t i o n r a t e , a n e w f a c t o r i s i n t r o d u c e d . T h e h e a t e n h a n c e m e n t  factor  (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 e f f e c t i v e n e s s f a c t o r ( e q u a t i o n 5 . 9 3 ) t o t h e i s o t h e r m a l effectiveness f a c t o r ( e q u a t i o n 5.102) i . e . ^  Vs,non—iso  ^  Vs,iso r e p r e s e n t s 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 o v e r t h e i s o t h e r m a l m o d e l . I f h e a t effects a r e i m p o r t a n t , t h e h e a t e n h a n c e m e n t l i m i t i n g steps.  factor w i l l differ f r o m one, regardless o f t h e  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 heat e n h a n c e m e n t  factor is s i g n i f i c a n t l y greater  t h a n one signifies 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 adequately represent t h e a c t u a l reaction rates. F i g u r e 6.6 p r e s e n t s t h e h e a t e n h a n c e m e n t A heat enhancement  factors 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  considered.  f a c t o r o f 1.1 r e p r e s e n t a n i n c r e a s e 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 rate. U n l i k e t h e effectiveness factor w h e r e n o clear 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 h e a t o n t h e r e a c t i o n r a t e c a n b e d r a w n for l a r g e p a r t i c l e s i n a n o x y g e n - r i c h environment, the heat enhancement  factor clearly shows t h a t even i f t e m p e r a t u r e deviations  a r e l a r g e f o r t h e l a r g e s 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  i um  Results  10 um 100 /j,m 1 mm Particle diameter  1 um  10 mm  (a) K i n e t i c s f r o m F u k u n a k a et al. [140]  10 um 100 um 1 mm Particle diameter (b) F i t t e d k i n e t i c s  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  factors.  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 well represented  10 mm  reasonably  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 e f f e c t i v e n e s s  factor  caused b y large mass transfer 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 e a r t h a t h e a 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 h e a t )  a n d temperature deviation (particle temperature m u c h higher t h a n that of the are t w o different p h e n o m e n a . For  environment)  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 .  the reaction of z i n c concentrate,  heat enhancement  w i l l affect  the overall reaction  rate,  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 p h a s e s , p r o d u c t l a y e 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 where the heat enhancement factor exceeds 1 d e p e n d o n the k i n e t i c s a n d particle size.  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 o 1, r e g a r d l e s s o f t h e k i n e t i c s o r p a r t i c l e s i z e . enhancement  f a c t o r is <  1.1.  the heat enhancement  f a c t o r is v e r y c l o s e  For oxygen concentrations  <  10%, the  I f a d e v i a t i o n ( o r e r r o r ) i n r e a c t i o n r a t e o f 1 0 % is  acceptable  (Ti < 1.1), t h e i s o t h e r m a l m o d e l m a y b e 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  heat  Chapter  6.  Modelling  Results  In summary, the unsteady-state single particle reaction m o d e l has shown t h a t particle overheating occurs o n l y for large particles and h i g h b u l k oxygen concentrations.  Effectiveness factors  greater t h a n one o n l y occur for h i g h b u l k oxygen concentrations. T h e t i m e for complete reaction depends greatly on the kinetics used. T h e gas compositions are not significantly different from the b u l k w h e n very s m a l l particles, similar to the concentrates used i n this study, are reacting. It is u n k n o w n at this point w h i c h kinetic rate expression s h o u l d be used. T h e a s s u m p t i o n of isothermal particles w i t h i n the fluidized bed is therefore reasonable if the particles do not experience oxygen concentrations larger t h a n a few percent. T h e relatively s i m p l e i s o t h e r m a l single particle reaction m o d e l is used for the gas-solid fluidized b e d reactor m o d e l l i n g t h a t follows i n this chapter.  6.2  Generalized slugging-bubbling model (GSBM)  T h i s section. presents some results of the generalized s l u g g i n g - b u b b l i n g fluidized bed reactor m o d e l for gas c a t a l y t i c reactions. Since no solid reaction occurs, the m o d e l is not coupled w i t h a solid reaction m o d e l nor any solids m i x i n g m o d e l .  6.2.1  Comparison with previous models  P r i o r to using the generalized slugging-bubbling fluidized bed m o d e l , it must be compared w i t h the currently available fluidized bed models. F i g u r e 6.7 presents conversions calculated from the H o v m a n d slugging bed m o d e l [216, 217], the O r c u t t mixed-flow a n d plug-flow models [218, 219], the G r a c e two-phase b u b b l i n g bed reactor m o d e l [239] and the generalized sluggingb u b b l i n g m o d e l ( G S B M ) , developed i n C h a p t e r 5 for pure slugging a n d pure b u b b l i n g w i t h constant average bubble size a n d variable bubble size. T h e constant average b u b b l e size case is considered because the O r c u t t and G r a c e models use an average b u b b l e size. Since previous models do not consider gas volume changes, the stoichiometry adopted for the generalized model is equimolar (1 to 1).  F o r a l l models, the reaction is first order w i t h respect to the  oxygen concentration.  In general, the predictions for the b u b b l i n g  fluidized  215  b e d models are higher t h a n those of  Chapter  6.  Modelling  Results  Table 6.2: M o d e l parameters used to compare the generalized b u b b l i n g slugging m o d e l to the earlier slugging and b u b b l i n g models 0.5 m / s  u  0.02 m / s 1 m  H  calculated 0.45 Gas diffusivity:  D  10 - 1 0 -  g a s  m /s 2  M o r i a n d W e n [208]  B u b b l e correlation I n i t i a l bubble size: D  5  e o  0.01 m -1  ^0 2  +1 Ai/  0  the slugging models. N o t e that the fluidized bed models are applied w i t h o u t any allowance for slugging, even w h e n the bubble size exceed the reactor diameter. For this reason, the predictions for s m a l l c o l u m n diameters must be considered w i t h caution. T h e r e is very little difference between the results of the H o v m a n d slugging m o d e l a n d the G S B M m o d e l when the p r o b a b i l i t y 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 m o d e l i n the l i m i t . W h e n considering pure b u b b l i n g behaviour (Pbu6Ming l)) the G S B M compares favorably w i t h all the other models. =  However, there is a  much larger scatter between the different models.  Since the generalized m o d e l compares well w i t h the previous slugging a n d b u b b l i n g 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  0.1  0.08  0.08  . 0.06  . 0.06  o GSBM, P ..,. =1, Constant De _ ' Bubbhng + Orcutt, Plug Flow •ft Orcutt, Mixed . GSBM, P„ . =1, Variable De x Grace 2-phase' 0  0.02  0.02  . GSBM, P . =1 Slugging x Hovmand C I  10  K K I  (a) S l u g g i n g m o d e l s ,  10  10  Bed diameter (m) fc =0.1  (b) B u b b l i n g m o d e l s , k =0.1  s"  1  r  0.5 r  0.4  0.4  . 0.3  . 0.3  D  10  Bed diameter (m)  (c) S l u g g i n g m o d e l s , k = l r  s  -  10  0.8  0.8  . 0.6  . 0.6  c 0.4 o O 0.2  . GSBM, P„. . Slugging x Hovmand  Bed diameter (m)  (e) S l u g g i n g m o d e l s , k = 10 s  •  fc =l r  _ 1  •—  10  Bed diameter (m)  (f) B u b b l i n g m o d e l s , k =10  _ 1  r  r  s  . GSBM, P„ .... =1, Variable De BubbJ ng + Orcutt, Plug Flow AOrcutt, Mixed x Grace 2-phase o GSBM, P„ Bubbling=1, Constant De 10  10  10  Bed diameter (m)  (d) B u b b l i n g m o d e l s ,  1  11  10  _ 1  + Orcutt, Plug Flow * Orcutt. Mixed o GSBM, P ..,. =1, Constant De „ Bubbling x Grace 2-phase . GSBM, P„ =1, Variable De Bubbling  . GSBM, P., . =1 Slugging x Hovmand  0.2  s  r  0.5  10  10  Bed diameter (m)  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 d i a m e t e r : 0.1 m , (pr,: 0  (b) B e d d i a m e t e r : 0.1 m , (p^: 0.005  (c) B e d d i a m e t e r : 0.5 m , (pr,: 0  (d) B e d d i a m e t e r : 0.5 m , (pr,: 0.005  (e) B e d d i a m e t e r : 1 m , (pr,: 0  (f) B e d d i a m e t e r : 1 m , (pi: 0.005  F i g u r e 6.8: C o m p a r i s o n of the conversions calculated using G S B M m o d e l a n d its l i m i t i n g models as a function of gas reaction rate constant for different b e d diameters. F o r conditions, see T a b l e 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 (k ) r  on the gas conversion (X) is presented  i n F i g u r e 6.8 for different reactor diameters a n d w i t h </)£, = 0.005 a n d neglecting the solids present w i t h i n the bubbles (i.e. (fir, = 0). T h e figure presents the results of the complete generalized s l u g g i n g - b u b b l i n g m o d e l , as well as the predictions w h e n the probabilities of b u b b l i n g and slugging are set equal to one (entirely slugging or b u b b l i n g ) .  W h e n the p r o b a b i l i t y of  slugging equals one, no b u b b l i n g region is considered prior to slugging. W h e n the p r o b a b i l i t y of b u b b l i n g is one, the m o d e l either calculates a given bubble size for each v e r t i c a l p o s i t i o n or uses a constant average b u b b l e size calculated at 40% of the expanded b e d height (x =  0AH).  T h e m o d e l parameters a n d conditions appear i n Table 6.2.  For slugging beds (Figure 6.8,(a) a n d (b)), using a b u b b l i n g fluidized b e d m o d e l clearly overpredicts the conversions.  For small k , r  the generalized s l u g g i n g - b u b b l i n g  predicts conversions s i m i l a r to that w h e n i m p o s i n g pure slugging higher k , r  the generalized slugging-bubbling  fluidized  (P i gi  fluidized  s  ug  ng  —  l).  bed model  However, for  b e d m o d e l predictions diverge from the  pure slugging predictions due to the increasing i m p o r t a n c e of mass transfer from the  bubbles  to the dense phase. For such conditions, the b u b b l i n g region at the base of the b e d before the onset of slugging is of c r i t i c a l i m p o r t a n c e to the conversion. T h e presence of particles w i t h i n the bubbles ((pL) significantly augments the predicted gas conversions for large  k. r  For large beds where slugging does not occur (Figure 6.8,(e) and (f)), the G S B M m o d e l predicts the same conversions as for pure b u b b l i n g (Pbubbling ^) • U s i n g pure slugging to m o d e l =  a b u b b l i n g fluidized b e d clearly underestimates the conversion. T h e use of an average bubble size also underestimates the gas conversion for large reaction rate constants. F o r large k , r  mass  transfer from the bubbles to the dense phase is rate-controlling. T h e r e is a significant beneficial effect on interphase mass transfer from the s m a l l bubbles near the d i s t r i b u t o r .  T h i s effect is  neglected w h e n using an average bubble size. A s for slugging beds, a c c o u n t i n g for the presence of particles w i t h i n the bubbles (cpi) is significant for large  For  fluidized  k. r  beds of intermediate sizes (Figure 6.8,(c) a n d (d)), the p r e d i c t i o n of the  219  GSBM  Chapter  6.  Modelling  Results  m o d e l diverge slightly from the predictions for pure b u b b l i n g due to the effect of walls on the larger bubbles causing a decrease i n interphase mass transfer. In summary, if ones chooses to use a regime-specific m o d e l , choosing the appropriate m o d e l (pure b u b b l i n g or pure slugging) is critical to o b t a i n i n g adequate results. F o r reactions where large values of the effective reaction rate constant (k ) r  are expected, the m o d e l s h o u l d not use  an average b u b b l e size to characterize the entire reactor and must include the effect of the solids w i t h i n the bubbles. T h e generalized slugging-bubbling fluidized bed m o d e l allows the modelling of fluidized systems where a t r a n s i t i o n from b u b b l i n g to slugging occurs w i t h i n the bed, or where there are appreciable wall effects.  6.2.3  Effect of reactor diameter  T h e effect of scale-up of a reactor may be evaluated from the gas conversions for different reactor diameters a n d different reaction rate constants. F i g u r e 6.9 g r a p h i c a l l y presents the conversion for various rate constants. For the c o n d i t i o n considered, the G S B M m o d e l predictions depart from pure slugging for large reaction rate constants and for reactor diameters larger t h a n about 0.1 m . T h e departure from pure slugging at h i g h reaction rate constants results from the significance of the b u b b l i n g region near the d i s t r i b u t o r . For the conditions studied, the predictions of the G S B M m o d e l converge to pure b u b b l i n g 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 m o d e l l e d as pure b u b b l i n g . T h i s implies t h a t results from s m a l l and large i n d u s t r i a l fluidized beds must be compared w i t h care.  N o t e that this diameter applies o n l y for reactors o p e r a t i n g at the  conditions i n T a b l e 6.2.  T h e bubble sizes were calculated u s i n g the M o r i a n d W e n bubble  correlation [208]. Since this correlation is l i m i t e d to reactor diameters smaller t h a n 1.22 m , predictions for larger reactors must be treated w i t h some c a u t i o n .  In the t r a n s i t i o n region, the generalized m o d e l predicts conversions less t h a n for pure b u b b l i n g and more t h a n for pure slugging (See F i g u r e 6.9).  220  T o u n d e r s t a n d how this can occur, one  Chapter  6. Modelling  Results  Bed diameter (m)  (a)  fc =0.1.s-\  Bed diameter (m)  4> - 0  r  (b) fc =0.1 s " , 4> : 0.005 1  r  L  Bed diameter (m)  Bed diameter (m)  (c) k =l s " , <p - 0  (d) k =l s  1  r  L  _ 1  r  Bed diameter (m)  , (/> : 0.005 L  Bed diameter (m)  (e) i k = 1 0 s - \ 4> - 0 r  L  (f) fc =10 s - , 0 : 1  r  L  L  0.005  F i g u r e 6.9: C o m p a r i s o n of the conversions calculated using G S B M m o d e l a n d its l i m i t i n g 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  the  b u b b l i n g a n d s l u g g i n g f l o w r e g i m e s . F i g u r e 6.10 p r e s e n t s i n m o r e d e t a i l t h e v a l u e s o f t h e v a r i o u s variables w h i c h lead to such conversions.  W e first 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 transfer t e r m of e q u a t i o n  {Interphase mass transfer t e r m } =  5.12:  km l( a  (6.2)  )  T h e f i r s t p a r t o f t h e t e r m is t h e m a s s t r a n s f e r c o e f f i c i e n t a n d i n t e r f a c i a l a r e a . T h e s e a r e d i r e c t l y related to bubbles and slug properties. gas c o n c e n t r a t i o n 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 f o r c e i.e. t h e d i f f e r e n c e i n  T h i s d r i v i n g f o r c e 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  bubbles  (or s l u g s ) a n d t h e d e n s e p h a s e . U n l i k e t h e m a s s t r a n s f e r c o e f f i c i e n t a n d a r e a , i t d o e s n o t  have  any direct relationship w i t h any of the b u b b l e or s l u g properties.  W e next consider the transition from b u b b l i n g to slugging by observing that the p r o b a b i l i t y of s l u g g i n g goes f r o m 0 t o 1 i n t h e height i n t e r v a l b e t w e e n the conditions studied.  T h e mass transfer  a p p r o x i m a t e l y 0.1 a n d 0.3 m  c o e f f i c i e n t a n d i n t e r f a c i a l a r e a (kLH  a n d aj)  for  both  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 a n s f e r c o e f f i c i e n t ( F i g u r e 6.10 ( b ) ) v a r i e s 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 s c a l e . T h e d r i v i n g f o r c e for t h e  interphase  m a s s t r a n s f e r ( F i g u r e 6.10 (c)) d o e s n o t i n c r e a s e 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 o v e r a m u c h l o n g e 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 n e t effect is a r a p i d d e c r e a s e followed b y a slow increase i n interphase mass transfer d r i v i n g force).  flow.  T h e b u b b l i n g region ensures g o o d  interphase  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 the b u b b l e s a n d dense p h a s e ( s m a l l However, once the  bubbles have g r o w n a n d coalesced into slugs, the  small  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 transfer 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 d e n s e p h a s e increases t h e d r i v i n g f o r c e t o v a l u e s c l o s e r 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 e v e n for s m a l l reaction rate constants,  i n t e r p h a s e m a s s t r a n s f e r m a y h a v e s i g n i f i c a n t effects.  T h i s effect  may  not be o b s e r v e d e x p e r i m e n t a l l y due to the s m a l l difference i n o v e r a l l conversions.  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 r g e 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 % o f 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 a n s f e 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  222  slowly  Chapter  6,  Modelling  Results  MAAA A A A—ft—ft—ft—ft ft ft ft 0  0.2  0.4  0.6  0.8  Position in bed (m)  0.2  0.4  (b) Interphase  (a) P r o b a b i l i t i e s  0.6  0.8  Position in bed (m)  1  mass transfer  coeffi-  cient  x 10"  x 10 '  0.2  0.4  0.6  Position in bed (m)  0.8  (c) Interphase d r i v i n g force  0.2  0.4  0.6  Position in bed (m)  o.  (e) G a s conversion i n b u b b l e phase  3  0.2  0.4  0.6  Position in bed (m)  O.i  (d) Interphase m o l a r flow  0.2  0.4  0.6  Position in bed (m)  O.i  (f) G a s conversion i n dense phase  F i g u r e 6.10: C o m p a r i s o n of the variable m o d e l parameters a n d o u t p u t for the G S B M m o d e l and its l i m i t i n g models as a function of height the vertical p o s i t i o n i n the b e d for k = 0 . 1 s , - 1  r  D = 0.2 m , *: B u b b l i n g , o: Slugging, •: G S B M . For conditions, see T a b l e 6.2 223  Chapter  6.  Modelling  Results  (c) Interphase d r i v i n g force  0  0.2 0.4 0.6 o Position in bed (m)  (e) G a s conversion i n b u b b l e phase  (d) Interphase m o l a r flow  0.2  0.4 0.6 0.8 Position in bed (m)  1  (f) G a s c o n v e r s i o n i n dense phase  F i g u r e 6.11: C o m p a r i s o n of the variable m o d e l parameters a n d o u t p u t for the G S B M m o d e l and its l i m i t i n g models as a function of the vertical position i n the b e d for k = 1 0 s " , D = 0.2 1  r  m , *: B u b b l i n g , o: Slugging, •: G S B M . F o r conditions, see T a b l e 6.2 224  Chapter  6.  Modelling  Results  once the slugging flow regime is reached. T h e overall effect of i n c l u d i n g the b u b b l i n g region at the b o t t o m is to increase the conversion. In summary, w h e n the generalized slugging-bubbling fluidized b e d m o d e l is used for one of the l i m i t i n g cases (pure b u b b l i n g or slugging), it closely matches the results of the earlier regimespecific models.  F o r the t r a n s i t i o n between the slugging and b u b b l i n g regimes, the  GSBM  m o d e l adequately represents the system. I n the transition, the m o d e l predicts conversions and evolution between the two l i m i t i n g cases.  6.3 6.3.1  Fluidized bed roaster model Model parameters  T h e fluidized bed reactor m o d e l requires the  fluidized  bed reactor geometry, o p e r a t i n g c o n d i -  tions, kinetics of the reaction, as well as some parameters related to the  fluidized  bed. Table  6.3 summarizes the various parameters a n d their values used for the m o d e l l i n g of the i n d u s t r i a l and l a b o r a t o r y fluidized bed roasters. T h e i n d u s t r i a l roaster geometry and conditions are taken from p u b l i s h e d i n f o r m a t i o n [33, 34]. T h e l a b o r a t o r y roaster c o l u m n geometry is that of this study. T h e e x p a n d e d bed height a n d the height at m i n i m u m  fluidization  are related to each other using the calculated bed expansion.  Since the i n d u s t r i a l bed height is l i m i t e d to the weir overflow height, H f m  is calculated while  solving the m o d e l . Since there is no overflow weir for the l a b o r a t o r y roaster, H is calculated from a k n o w n H f m  w h i c h is related to the bed mass.  T h e v o i d space at m i n i m u m fluidization was measured from the particle density a n d b u l k density of the experimental m a t e r i a l . 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 e x p e r i m e n t a l evidence. T h e solids reaction kinetics are as proposed i n C h a p t e r 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 Parameter  values  Industrial  Laboratory  84  0.00785  Reactor geometry Area A (m ) 2  D i a m e t e r D (m) E x p a n d e d b e d height H (m) B e d height at m i n i m u m  fluidization  Hf  (m)  m  D i s t r i b u t o r a r e a per orifice Ad ( m ) 2  10.34  0.1  1.2  variable  variable  0.27  .01  0.00021  Fluidized bed model 0.005  B u b b l e solids v o l u m e f r a c t i o n <j>i (-) V o i d space at m i n i m u m f l u i d i z a t i o n e f  0.45  (-)  m  Solids reaction kinetics F i t t e d kinetics P r e - e x p o n e n t i a l c o n s t a n t k° ( c m / s )  6.28-10  A c t i v a t i o n energy E ( k J / m o l )  12  287.5  F u k u n a k a et al. [140] k i n e t i c s P r e - e x p o n e n t i a l c o n s t a n t k° ( c m / s ) A c t i v a t i o n energy E  a  2.96-10  (kJ/mol)  15  313.8  R e a c t i o n orders O x y g e n n (-)  1  Solids m (-)  0  Effective gas diffusion coefficient i n ash layer  H A(To) e  (  m  V ) s  Base operating conditions  D02-S02 x 0.4/3 1  M o d i f i e d S h e r w o o d n u m b e r S h (-) (Sensitivity analysis)  950  Temperature T (°C)  101.3  Pressure P (kPa) 0.66  Superficial gas v e l o c i t y U ( m / s ) E x c e s s O x y g e n Excessoi  (%)  21  Inlet O x y g e n C o n c e n t r a t i o n (vol%)  Bed and concentrate properties  (Sensitivity analysis)  A v e r a g e b e d p a r t i c l e diameter d (/um)  65 o r 150  p  Inert solids p a r t i c l e d e n s i t y p  A v e r a g e c o n c e n t r a t e p a r t i c l e diameter C o n c e n t r a t e p a r t i c l e density  2650  (kg/m ) 3  p  0.25 10  d  V  pconcentrate  t  C  o  n  c  e  n  t  r  a  (kg/m ) 3  te  (/mi)  14 4000 1  P a r t i c l e m e a n residence t i m e factor / (-)  226  Chapter  6.  Modelling  Results  6.3.2  Fit of laboratory experiments  T w o parameters of the m o d e l are still u n k n o w n . 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 i m e factor.  P r e l i m i n a r y fitting of the experimental d a t a showed that the choice of the k i n e t i c rate expression ( F u k u n a k a et al. or fitted kinetics) has more influence on the predictions t h a n either the residence time factor ( / ) or the equivalent m o l a r mass of concentrate (M  ate)-  concentr  the values of / a n d M  ate  concentr  Therefore,  were chosen as 1 a n d 110. A value of 1 was chosen for the mean  solids residence t i m e factor since 1/(3 (which increases the residence time) is compensated by using concentrate as a feed, requiring a d d i t i o n a l feed mass for the same oxygen c o n s u m p t i o n (which decreases the residence time).  M  ate  concentr  was calculated from the z i n c concentrate  assays assuming complete conversion to Z n O , SO2, F e 2 0 3 , P b S 0 4 a n d accounting for the presence of sulfates i n the concentrate.  Since there is i n f o r m a t i o n for o n l y one  only a single value of the rate constant is  temperature,  fitted.  F i t t i n g a m o d e l to experimental d a t a i n v o l v i n g two or more o u t p u t s requires m u l t i p l e response non-linear regression [240]. Such a p r o b l e m must be addressed using weighted least squares regression.  T h e choice of weights is c r i t i c a l to o b t a i n 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:  (6.3)  T h e variance of the experimental points was either obtained from the logged d a t a (oxygen concentration) or estimated from the detection l i m i t s of the assays (solids conversions). P r e l i m i n a r y fitting of the experimental d a t a was not able to adequately fit any of the outlet oxygen concentrations using reasonable M  ate  concentr  oxygen concentrations, values of M  t te  concen ra  values. T o allow closer predictions of the  a r o u n d 90 were required.  T h i s is unacceptable  since it is impossible t h a t i m p u r e zinc sulfide (containing less sulfur a n d zinc t h a n pure Z n S )  227  Chapter  6,  Modelling  Results  w o u l d require more oxygen t h a n pure zinc sulfide. It was noticed long after the experimental phase t h a t the oxygen sensor i n the gas analyser used for the measurement of the freeboard oxygen concentrations h a d failed. T h e failure was noticed a p p r o x i m a t e l y one year after the experiments.  Since the analyzer was not used d u r i n g this  period, there is uncertainty i n the measurement provided here. In a d d i t i o n , simple calculations show that oxygen concentrations should be higher t h a n measured: A s s u m i n g complete solids conversion, 10% excess oxygen should give a p p r o x i m a t e l y 2 v o l % oxygen. T h i s value is measured for feedrates of a p p r o x i m a t e l y 14 g / m i n . Concentrate assays show t h a t this value should be observed at a feedrate of a p p r o x i m a t e l y 16 g / m i n . F u r t h e r fitting w i l l not consider the freeboard oxygen concentrations.  However, the d a t a adequately represent the t r e n d t h a t outlet oxygen  decreases w i t h increasing feedrate and that a d d i t i o n a l feed can be used w h e n oxygen enrichment is employed. F i g u r e 6.12 presents the experimental d a t a and the m o d e l predictions for the parameters presented i n Table 6.4. Since o n l y one temperature was available from the e x p e r i m e n t a l data, the reaction rate constant, shown i n T a b l e 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 m o d e l  parameters are the same as those shown i n T a b l e 6.3. T h e operating conditions (temperatures, inlet gas concentrations and superficial gas velocities) used for fitting the e x p e r i m e n t a l d a t a are those used experimentally. T h e particle parameters are those described i n chapter 3. Figures 6.12 and 6.13 present the m o d e l 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 ( C o m p a r e Figures 6.13 a n d 4.61). D u e to the incertitude i n 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 literature.  The  fitted rate is between the fitted kinetics (dashed line) a n d the F u k u n a k a et al. kinetics, close to F u k u n a k a et al. kinetics. T h e temperature of the experiments clearly exceeds the temperature range of a l l rate expressions shown. Since o n l y one point was o b t a i n e d from the fit of experiments, there is s t i l l some incertitude regarding the appropriate k i n e t i c rate expression.  228  Chapter  6.  Modelling  Results  Table 6.4: S u m m a r y of fitted m o d e l 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. Value  Parameter /  (-)  Mconcentrate ( g / m o l )  not  fitted  1  not  fitted  110  fitted  R e a c t i o n rate constant (cm/s)  37.3  1  0.91  r  0.9  1  1  10  ' 12  1  '  1  14  16  ' 18  20  Concentrate feedrate (g/min) F i g u r e 6.12: G a s - s o l i d reactor m o d e l fit of the e x p e r i m e n t a l conversion d a t a . • : 50 mesh silica sand, 2 1 % 0 2 , m o d e l , +: 50 mesh silica sand, 2 5 % 0 2 , m o d e l , x : 125 mesh silica sand, 2 1 % 0 2 , m o d e l . M o d e l predictions are joined by lines. 0: 50 mesh silica sand, 2 1 % 0 , experiments, ©: 2  50 mesh silica sand, 2 5 % 0 2 , experiments, <g>: 125 mesh silica sand, 2 1 % 0 2 , experiments  229  Chapter  6.  Modelling  F i g u r e 6.13: (scrubbed),  Results  Gas-solid reactor  m o d e l predictions of the freeboard  o: 50 mesh silica sand, 2 1 % 0 2 , +:  oxygen concentration  50 mesh silica sand, 2 5 % 0 2 , x : 125 mesh  silica sand, 21%02-  F i g u r e 6.14: F i t t e d i n t r i n s i c reaction rate compared w i t h those of various k i n e t i c studies. R a t e expressions from references [124, 143, 140, 135, 142, 130, 144, 145]. D a s h e d line corresponds to fitted kinetics discussed i n C h a p t e r 2. o: F i t t e d i n t r i n s i c kinetics  230  Chapter  6.  Modelling  Results  However, the fitted reaction rate is bracketed by the fitted and the F u k u n a k a et al. [140] kinetics. Sensitivity analysis w i l l consider b o t h kinetics as appropriate bounds.  6.3.3  Roaster sensitivity analysis  A sensitivity analysis provides useful information on w h i c h process a n d m o d e l parameters are most i m p o r t a n t . T h e m o d e l calculates the gas compositions for the reaction of pure zinc sulfide. Differences between concentrates and pure zinc sulfide are taken into account b y converting the oxygen d e m a n d of each concentrate to its equivalent for zinc sulfide (see section 5.3). Therefore the equivalent m o l a r mass of zinc concentrate (Mconcentrate) is not required for the sensitivity analysis. T h e sensitivity analysis uses mono-sized particles for the concentrate a n d the inert b e d m a t e r i a l (not size d i s t r i b u t i o n s ) . T h e actual mean residence t i m e of particles depends o n the concent r a t i o n of particles of the same size i n the bed (see equation 5.77).  Since the two types of  particles are of different sizes, equation 5.77 no longer holds m a t h e m a t i c a l l y . I n a real system, the bed w o u l d be composed of m a i n l y inert bed m a t e r i a l c o n t a i n i n g an e q u i l i b r i u m amount of concentrate-sized particles.  Since i n this sensitivity analysis, the e q u i l i b r i u m amount of  concentrate-sized particles is u n k n o w n , the residence times of the reacting concentrate particles are assumed to be equal to: fM  bed  r = —  (6.4)  FFeed  w i t h / as i n T a b l e 6.3. T h e volume-based average particle size (d ) v  of the concentrates is used  i n the sensitivity analysis. T h e m o d e l parameters a n d o p e r a t i n g conditions are s u m m a r i z e d i n Table 6.3. For this analysis, each parameter i n Table 6.5 is varied one at a time. Since there is incertitude i n the choice of kinetic rate expression for the reaction of solids, b o t h the fitted kinetics and the F u k u n a k a et al. [140] are used i n the sensitivity analysis. These two rate expressions are considered as the two possible extremes i n the reaction rates.  231  Chapter  6.  Modelling  Results  T a b l e 6.5: Parameter ranges for sensitivity analysis Range  Parameter  0 - 100 %  Excess O x y g e n Inlet O x y g e n C o n c e n t r a t i o n  21 - 100 v o l % 50 - 250  Average particle size  pm  0.25 - 0.75 m / s  Superficial gas velocity Temperature  800 - 1000 ° C  Height at m i n i m u m fluidization ( L a b o r a t o r y )  0.25 - 1.25 m  E x p a n d e d bed height (Industrial)  0.5 - 2 m  Oxygen available to the particles Since oxygen governs the vapour pressure of lead species, any significant v a r i a t i o n i n its concent r a t i o n 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 laboratory roaster for the fitted a n d F u k u n a k a et al. [140] kinetics for s m a l l (65 p,m) a n d large (150 pm) particles. E x c e p t for the effect of temperature, there is very l i t t l e 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 s m a l 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.  O v e r a l l , for the l a b o r a t o r y roaster, the particle-  averaged oxygen concentration (which affects agglomeration) is m o s t l y affected b y the excess oxygen, followed by the inlet oxygen concentration. These observations are p a r t l y s u p p o r t e d by the in-bed oxygen sensor measurements (See F i g u r e 4.63) where the oxygen concentration was m o s t l y influenced by excess oxygen, followed by bed particle size.  O x y g e n enrichment  had a negligible effect. T h e discrepancy may originate from the fact t h a t the sensor measures a localized oxygen measurement,  close to the gas d i s t r i b u t o r as opposed to the m o d e l w h i c h  calculates an average oxygen concentration. B e d height is the next most i m p o r t a n t factor. T h e trends of particle-averaged oxygen concentration w i t h bed height are e x p l a i n e d later.  232  Chapter  6.  Modelling  Results CD  Pi CO  O  b£)  CM  a  co  a  Cu  CD  CQ  -a a> CQ  T3  fcuO co o3 CD  4) r-J  § .2 o  03 OH  CJ J—H  -a CD  CP CS3  Tcp3—  o  SH  a  CP  O Cl O o CD  CP  "J3  a3  a -o  cu  a  OH  b>> fl <D  3  O  CD XI CD  bfl !-I  CD  S3  S  CD  £ a. cS  > >1  o3  S-i CD  o  >  cbu O a  o 3 bO CO  O  CD  o3 d o3 PU ^  co  cu o X  cp  a  3  CO O CD  f-H  CD CP  CJj  a CP  CD to  i_ CD  sepiued'jo" CD  3  o3 o  bO ,£3 233  Chapter  6. Modelling  Results  3 O  g CO SH CD CJ  CD -3  73  73  -a  d  J2 03  § ^CD CJ C D 3  co  CD  bO co 3  O  a -a  CP  03  3  CD bp 03  o CJ  CD  S-i  fe r° 03 pL| i CD  73  CD  -s '» a3  3  CD  cp o 3 o o  C  3  a  CP  CP b O > > X O  a  a  CD bciO SH CD  £  3  += o 03  CD 3 O  03  ^,  CO  cj  T3  cu SH  CD  3  03  > •£  — •  <*>  o o 73 >  C C Pi b C > > X O  CO 03 bjO  CP  X  a 3  CD  C  so  53 $ 03  Cu  co CO  2H 3  "2  8 £ r v ^3  °c2 O SH M3 co CD 03 CD O SH  d 03 3 3 S >HO bO , Q  U  234  Chapter  6. Modelling  Results CD nfl  fl .2 o3 f—i +^ fl CD CD fl  CD  .3  o  'to  -fl  bO  _CD  '55 -fl -a  SH  Q,  CD  PQ  -a CD  PQ  CD  fl « CD  CO  £js  X  O  X!  o3  bp $ CD  CD  o3  co  SH  co"  S> ?  o  CD  fl £  o  a »  f-H  a o  £ 2 » 03  CH  a  CD  CD O  fl o  CD O 03  CD  CH  CD  a.  b O. > CD  a  3  8  CD  fl ^  faO CD o3 SH  CD  CD fl O LO CD  C O  03  CO SH  CD CD  >  b O > > X  b0 .  CD  cfl  o  CD  CD CD  SH  X  CD  O, 3  03 CO CD CD  CD  fl  fl  o3  M  CO CO  CD -g  8  cS  CL r f l l-H  ^  CJ CD  CD  '  -SJ  '  SH  CO 03 O  C O  o>  o3  ojO  X>  flfl  ^ o  E JS 235  Chapter  6.  Modelling  Results  CO  Xi  _o  xi  M '53  Cu T3  xi -a  CD  CD  PQ  C CD  cp -±!  CJ  X !  CJ  L  3  CD  CD  CO CO  bO 3  X <D  brj  o  "d 3  o  03  CJ  S-i . « 4^  CD CS]  o3 '» CD +3 CJ  a o  +3  S-i  03  a  CD CJ  -  a  o  CD ft  s  cj el  b>O >  o f  5  CD  a a  CD  a.  x o  CD  te * CD sepiyed'go  CD  'SH a >  CO -V CJ  El  CD  co"  S-i  of  Q CD >  CD  > X>  b£>  bO  o  CD 4^ CD  g 03  Q,  CD 03 J4  3  EG ^  y=l u CD ft P  X  CM +4  CJ CD  w S3|0!ired'jo saioiijed'20  oo rH CO CD  3 bJO fa  236  CD 4^ CO 03  o" >^  o 03 o  x>  Chapter  6.  Modelling  Results  Figures 6.19 to 6.22 present the predicted particle-averaged oxygen concentrations for the i n d u s t r i a l roaster for the fitted and F u k u n a k a et al. [140] kinetics for s m a l l (65pm) bed particles (150pm).  a n d large  T h e effect of temperature again differs from one k i n e t i c rate expression  to the other. C o n t r a r y to the l a b o r a t o r y roaster, the average b e d particle size is predicted to significantly affect the particle-averaged oxygen concentration. T h e sharp increase i n predicted oxygen concentration for s m a l l particles (<70pm)  is due to the m a x i m u m effective bubble size  l i m i t (equation 5.32) being reached. For 150 p,m particles, there is o n l y a s m a l l effect of any of the operating variables on the oxygen concentration. However, for 65 / i m particles, excess oxygen and inlet oxygen concentration are predicted to have significant effects. Since the oxygen concentration affects the v o l a t i l i z a t i o n of lead sulfide, the mean particle diameter w i l l affect the agglomeration behaviour of the i n d u s t r i a l fluidized bed.  A s Figures 6.15 to 6.22 show, the particle-averaged oxygen concentration increases w i t h b e d height i n the l a b o r a t o r y roaster a n d for the i n d u s t r i a l roaster w i t h a m e a n particle size of 65 pm.  W h e n the particle size is large ( 1 5 0 / i m ) i n the i n d u s t r i a l roaster, the oxygen concentration  decreases slightly.  Since these trends are counter-intuitive, a more detailed e x p l a n a t i o n is  required. It is c o m m o n l y accepted that i n fluidized bed reactors, as the expanded b e d height is increased, for the same o p e r a t i n g conditions (superficial gas velocity), a d d i t i o n a l gas conversion occurs w h i c h leads to a decreased particle-averaged oxygen concentration. T h i s m a y be s u m m a r i z e d as: " W i t h deeper beds, the gas can reach higher conversions." T h i s reasoning originates from catalytic reactors where o n l y the gas reacts a n d as such, a d d i t i o n a l particles s i m p l y increase gas conversion. I n c a t a l y t i c fluidized beds, the gas reaction rate constant k does not change. T h e r  gas conversion at a given v e r t i c a l p o s i t i o n i n 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 a d d i t i o n a l conversion p r o v i d e d by increasing the expanded bed height (through increased solids inventory) lowers the overall gas concentration. For gas-solid fluidized beds reactors, the assumption t h a t the effective gas reaction rate constant  237  Chapter  6. Modelling  Results CD -fl  cn  fl .2 o3  SH  4^  fl CD CD fl  -fl .bp '5  -fl  -o  CL)  pa  o  CD  fl ^ CD  § ^ X O  o3 H  CD hO o3  CD CD cn  -d  - Q  SH CD  CO  fe  S  o  o3  -2 "S 7D  X)  03  CD  ° < CD  SH  fl fe  CD T3  CD  CD  -2  HA  SH 03  OH  cu  r  OH  -a CD  a  CD bO o3  SH  CD CD  a 3.  fl o  -a o CD  LO  £  «3 -  T3  fl  CO SH  03  CD CD  CD  3  2  CD  ±5  o o  ^ ®  ^  -fl  3 CCi ho CD  cu  CC  i-< OH  fl  HH O  o  U  O  SH  ,CD fcM  CD  H  CO  CTS  SH  o3  I-H  CO  .2  CD  43  SH  CO  OJO  -O  fl fl  fe .s  238  Chapter  6. Modelling  Results  CD  3 O  ll «  CO 3 C D O 3 O D C CD C CD O c o" 3 3 O C D faC SH  -3 bp '53  n3 CD  >>  ^oX i§  C D TJ b aiO O3 CD CD SH  5 fto r£ 13 CD SH  >  r  I  _ '£J3 ' »N CD 03 3j a  CD T3 3D cdbO C O -3 03 CD SH  PH  CD a S  SH  •b a.  °^3 °LO  °3 03 C D^ 31 3 o 3 TJ ^  H  CD 0 >33CD  o JToD  >  cbO ci CO  C D CH 3 jd  "3  g 03 b r^! el  co 3 CH  JH  8 ^  CD Mb o  CN  co .2  +3 33 bO TJ cu SH  239  CO  E .3  Chapter  6.  Modelling  Results CD  -fl  fl O  S  CD CJ  E  fl -fl bp  o in tcc  'CD  -fl  cc!  T3  OH  CQ  CD  T3  o CJ  fl  CM  CD  bO <co JD  >v X  O J e5 bO  T3  CD  CL)  03  PQ  CD  CD CO  i  -2 "CD *4J T3 SH  saiojedg'o ,  fl o  03  a  cj  CD  R  +=> _cj  -3  O  CD N  CD  CH  fl CL) O fl O  ?  fe  " CD  B  CD  -fl .= 2 += + SH  CJ  CD OH  fl CD  a  bO O  fl  03  O  CH  fl '-3  CD  X>  03  0 3  S3 -o  2  fe ™  CD  §  s  CD  L O 03  co" fl  S3 -8 8 S '-^ 03  fl CD  cbi)c)  o  CD  CD CD  CC  bi) >> X  CO  X H  SH  CD OH fl  CJ  O  r+f  a  CD  *  -G  MH  +=  O  SH  CD CD  SH  CD  "fl  * H  ••  sepiuedjo '  i-H  ^  ,2 t? CO  O  SH  CQ CO CD  SH  .5 £ CO  fl fl  bO T3  fa .5 240  Chapter  6.  Modelling  Results  JD  03  CM  Cu  CO  II  °E  co 7o33 co CP  -a  JD  bp  '53 -a -a  Cu  CP  -a  PQ  CP  PQ  CD  jCl  1 2  «  -3 O 03  U  r?  « CD  PH CD  .2  c'o  3  CD CD . . fcuO J D  g 3 *d  &  -d  CD  I  2  C P o 3 a  C  3  Cu " CD  CP  fe  OH  o  4J  o  a  03  °  CP  bO >>  SH fD  3.  <D'~ L O  o  s  ^  _ ' T_3  03  03 T3  CD 15 § 3 O X3 CD  S30| !pedg' o  03  >  43 CD  a  CP  bO >> X  03  CL) 03  CD  03  03 SH  3  £  CD  CD CD  ii S  ho  o  o cn  CP  o X  SH CP CM  3  2  S9D | !MBdg'o  « -s co  CD  3  bp PH  241  3  -d  3 '~ CD  4^  Chapter  6.  Modelling  Results  does not vary is flawed. C o n t r a r i l y to c a t a l y t i c reactors where the reaction proceeds as long as the gas is not completely converted a n d tha