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Kinetics of the zinc slag fuming process Richards, Gregory George 1983

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KINETICS OF THE ZINC SLAG FUMING PROCESS by GREGORY GEORGE RICHARDS B.A.Sc, The University of B r i t i s h Columbia, 1979 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE FACULTY OF GRADUATE STUDIES (Department of Meta l l u r g i c a l Engineering) We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n January 1983 Gregory George Richards, 1983 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of M e t a l l u r g i c a l Engineering The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date March. 9., 1983 DE-6 (3/81) ABSTRACT A study involving in-plant measurements, laboratory analysis and mathematical modelling was conducted to elucidate the k i n e t i c s of the zinc slag fuming process. The t r a d i t i o n a l assumption has been that the process operates at thermodynamic equilibrium. The res u l t s of i n d u s t r i a l measurements at f i v e d i f f e r e n t companies has demonstrated that t h i s approach i s not correct. Chemical assays of the slag show carbon lev e l s i n the range of 0.1 - 1.0% and char p a r t i c l e s have been extracted from slag samples. Tuyere back-pressure measurements revealed that the predominant mode of gas i n j e c t i o n behavior i s bubbling. This evidence indicates that a portion of the coal injected into the furnace i s entrained i n the slag. A model of the d i r e c t coal p a r t i c l e - s l a g reaction was developed and incorporated into an o v e r a l l model of the slag bath. This model included the behavior of the water-jacketed wall, a treatment of coal combustion i n the tuyere gas stream, and a model of the entrained coal residence time. F i t t i n g of the data to eleven i n d u s t r i a l fuming cycles showed that the f r a c t i o n of coal entering the bath was consis-tently about 35%. About 50% of the coal i s combusted i n the tuyere gas stream and 10% passes through the bath.unconsumed. Calculated oxygen u t i l i z a t i o n ranged from 70-95%, dependent on slag depth. The slag fuming process i s therefore k i n e t i c a l l y controlled. There are e s s e n t i a l l y two c r i t i c a l parameters: the f r a c t i o n of coal entrained i n the slag, and the rate of ferrous iron oxida-t i o n . The rate of f e r r i c reduction balances f e r r i c inputs to the bath by displacing previously reduced zinc from the entrained coal-slag reaction bubbles. Process e f f i c i e n c y can be increased therefore by increasing entrainment of coal i n the bath, perhaps by the use of high pressure i n j e c t i o n , and by reducing ferrous iron oxidation. The l a t t e r objective may be achieved by more complete combustion of tuyere coal or pre-combustion. A s i g n i f i c a n t control advan-tage might be gained by separating these two functions to d i f f e r e n t sets of tuyeres. In continuous fuming operations the model would suggest that improved e f f i c i e n c i e s could be obtained by using a more coarsely ground coal, higher fixed carbon coals, and operating at intermediate temperatures. i v TABLE OF CONTENTS Page ABSTRACT i i TABLE OF CONTENTS i v LIST OF TABLES v i i i LIST OF FIGURES x TABLE OF NOMENCLATURE xiv ACKNOWLEDGEMENTS x v i i i CHAPTER I INTRODUCTION: SLAGS AND SLAG PROCESSING 1 1.1 Slag Chemistry 3 1.2 Slag Cleaning 7 1.3 Zinc Slag Fuming 9 1.3.1 History 12 CHAPTER II LITERATURE REVIEW: STUDIES AND MODELLING 23 2.1 Thermodynamic Modelling 24 2.2 Empirical Modelling 32 2.3 Slag Fuming Investigations 38 2.3.1 Industrial Studies 39 2.3.2 P i l o t Plant Studies 44 2.3.3 Laboratory Studies 47 2.4 Indu s t r i a l Observations 52 2.5 Summary 53 CHAPTER III OBJECTIVES 56 CHAPTER IV EXPERIMENTAL TECHNIQUES 59 4.1 In d u s t r i a l Tests 59 4.1.1 Slag Sampling During the Fuming Cycle. 59 4.1.2 Tuyere Back-Pressure Measurements .... 63 4.1.3 -Tuyere Photography 64 4.1.4 Tuyere Accretion Sampling 66 V 4.2 Laboratory Methods 67 4.2.1 Chemical Analysis of Slag Samples .... 67 4.2.2 Slag Dissolution and P a r t i c l e Extraction 68 4.2.3 Slag Density and Porosity Measurements 69 4.2.4 X-ray D i f f r a c t i o n Analysis 72 4.2.5 Reflected Light Microscopy 72 4.3 Accuracy of Chemical Analysis 73 4.3.1 E f f e c t of Sulphide on the Ferrous Iron Assay 73 4.3.2 Uncertainty i n Assay Results 77 4.4 Remarks 80 CHAPTER V INDUSTRIAL RESULTS AND PRELIMINARY DISCUSSION: EQUILIBRIUM CONSIDERATIONS 81 5.1 Results 81 5.2 Equilibrium Analysis 93 5.2.1 Slag Carbon 94 5.2.2 Equilibrium Fuming Rate Calculations . 99 5.2.3 Slag Equilibrium 106 5.3 Summary 108 CHAPTER VI LABORATORY RESULTS AND KINETIC MODEL OF THE PROCESS .. 109 6.1 K i n e t i c Conception of the Process 10 9 6.1.1 Coal P a r t i c l e s i n the Slag 110 6.1.2 Slag Porosity 117 6.1.3 Tuyere Phenomena 122 6.1.4 Other I n d u s t r i a l Processes 133 6.2 A Kinetic Model of the Process 134 6.2.1 The Entrained Coal-Slag Reaction Regime 134 6.2.1.1 The Coal P a r t i c l e - S l a g Reaction 135 6.2.1.1.1 Zinc Balance 146 6.2.1.1.2 CO Balance 147 6.2.1.1.3 C0 2 Balance 147 6.2.1.1.4 H» Balance 148 6.2.1.1.5 HpO Balance 149 6.2.1.1.6 N 2 Balance 149 6.2.1.1.7 Bubble Radius 150 6.2.1.1.8 Char P a r t i c l e Radius 150 6.2.1.1.9 Char P a r t i c l e Weight 150 6.2.1.1.10 Gas Volume 151 6.2.1.1.11 Char P a r t i c l e Carbon 151 6.2.1.1.12 I n i t i a l Conditions 152 6.2.1.1.13 Thermodynamic Quantities 152 6.2.1.1.14 Mass-Transfer C o e f f i c i e n t s 159 v i 6.2.1.1.15 Boudouard Reaction Rate 162 6.2.1.1.16 Model Solution 163 6.2.1.2 Secondary Bubble Residence Time 163 6.2.2 Kinetics i n the Tuyere Gas Stream .... 168 6.2.3 Wall E f f e c t s 173 6.2.4 Other Considerations 179 6.2.5 Kinetic Model of the Process 180 6.2.5.1 Zinc Balance 181 6.2.5.2 F e r r i c Iron Balance 183 6.2.5.3 Ferrous Iron Balance 185 6.2.5.4 Lime Balance 18 5 6.2.5.5 S i l i c a Balance 186 6.2.5.6 Slag Wall Volume 18 6 6.2.5.7 Slag Wall Area 187 6.2.5.8 Slag Wall Thickness 187 6.2.5.9 Slag Bath Mass Balance 187 6.2.5.10 Bath Height 187 6.2.5.11 Bath Heat Balance 188 6.2.5.12 Solution of the Model 189 6.3 Discussion of Model F i t t i n g 190 CHAPTER VII SENSITIVITY ANALYSIS AND MODEL PREDICTIONS: KINETIC DESCRIPTION OF SLAG FUMING 207 7.1 S e n s i t i v i t y Analysis 207 7.2 Kinetic Description of the Process 221 7.3 Model Predictions 230 7.3.1 Batch Fuming 231 7.3.2 Consequences of the Model for Slag Fuming 238 7.3.3 Continuous Fuming 240 CHAPTER VIII SUMMARY AND CONCLUSIONS 244 8.1 Summary ' 244 8.2 Suggestions for Further Work 245 REFERENCES 247 APPENDIX I WET FERROUS IRON ASSAY TECHNIQUE 258 APPENDIX II FUMING CYCLE SAMPLING DATA 260 APPENDIX III EQUILIBRIUM FUMING RATE CALCULATION METHOD 272 APPENDIX IV RADIATION HEAT TRANSFER TO A COAL PARTICLE IN A TUYERE BUBBLE 288 v i i APPENDIX V FUMING FURNACE MASS BALANCE 292 APPENDIX VI FURNACE WALL HEAT TRANSFER MODEL 298 APPENDIX VII SLAG FUMING MODEL PROGRAM P301 v i i i LIST OF TABLES Table 1.1 Slag Fuming Operations 2 0 Table 2.1 E f f e c t s of Oxygen Enrichment On Slag Fuming 4 0 Table 2.2 E f f e c t of Coal Type on Slag Fuming 42 Table 4.1 The E f f e c t of Slag Sulphide on the Ferrous Iron Assay 75 Table 4.2 Free Energy of Formation of Various Sulphides from and the Metal Oxides at 1200°C 76 Table 4.3 Duplicate Assay Results 78 Table 4.4 Estimated Assay Uncertainty 79 Table 5.1 Free Energy of Formation of Various Carbonates from Carbon Dioxide and the Metal Oxide at 1200°C . . 97 Table 5.2 Free Energies and Equilibrium -'•' Constants for the Direct Reduction of Iron Oxides and Zinc Oxide 98 Table 6.1 Composition of Digested Slags 114 Table 6.2 Slag Porosity Through Three Fuming Cycles 121 Table 6.3 Thermodynamic Data for Reactions AG = AH-TAS 153 Table 6.4 Composition of Fuming Furnace Products, Cycle C41 170 Table 6.5 Mass Balance Calculation of Coal Carry Over 17 2 Table 6.6 Heat Transfer Parameters 17 5 Table 6.7 Frozen Wall Slags Assays 178 Table 6.8 F i t t e d Model Parameters 20 3 Table 6.9 Oxygen U t i l i z a t i o n and Bath Depth 205 ix Table 7.1 Standard Conditions for Slag Fuming Predictions 208 Table 7.2 Standard Slag Composition for Fuming E f f i c i e n c y Calculation 223 Table V . l Mass Balance Component Assays 295 Table V.2 Mass Balance Components 297 X LIST OF FIGURES Figure 1.1 Schematic of Fuming Furnace Cross Section 1 0 Figure 1.2 Oxide Ellingham Diagram (from reference (8)) I 4 Figure 4.1 Schematic of Charge Port Sampling 6 1 Figure 4.2 Schematic of Tuyere Back-Pressure Measurement Technique 65 Figure 5.1 Cycle A l , Fuming Cycle Sampling Data 82 Figure 5.2 Cycle A2A, Fuming Cycle Sampling Data 83 Figure 5.3 Cycle A2B, Fuming Cycle Sampling Data 84 Figure 5.4 Cycle BI, Fuming Cycle Sampling Data 85 Figure 5.5 Cycle B21, Fuming Cycle Sampling Data 86 Figure 5.6 "Cycle B22, Fuming Cycle Sampling Data 87 Figure 5.7 Cycle C l , Fuming Cycle Sampling Data ...... 88 Figure 5.8 Cycle C2, Fuming Cycle Sampling Data 8 9 Figure 5.9 Cycle Dl, Fuming Cycle Sampling Data (from reference (45)) 90 Figure 5.10 Cycle D2, Fuming Cycle Sampling Data (from reference (45) ) 91 Figure 5.11 Cycle E l , Fuming Cycle Sampling Data 92 Figure 5.12 Observed Fuming Rate versus Predicted Equilibrium Fuming Rate For Cycle Sample 4 3 Points (thermodynamic data from Kellogg ) 101 Figure 5.13 Observed Fuming Rate versus Predicted . Equilibrium Fuming Rate For Cycle Sample Points (thermodynamic data from Grant and Barnett. 4 4 ) 102 Figure 5.14 Observed Fuming Rate versus Predicted : Equilibrium Fuming Rate For Cycle Sample Points (thermodynamic data from Grant 4^) # m 103 x i Figure 5.15 Observed F e r r i c Iron Reduction Rate -versus Predicted Equilibrium Reduction Rate for Cycle Sample Points (thermodynamic data from Grant and Barnett 4 4 ) 1-05 Figure 5.16 Observed Fuming Rate versus (Fe 2 +) 2 ( Z n 2 + ) / ( F e 3 + ) 2 For Cycle Sample Points 108 Figure 6.1 Digested Slag (Cl,7) P a r t i c l e I l l (a) Photomicrograph (x2000), (b) X-ray Spectrum Figure 6.2 Digested Slag (C3,T) P a r t i c l e 112 (a) Photomicrograph (x4000), (b) X-ray Spectrum Figure 6.3 Digested Slag (C3,T) P a r t i c l e 113 (a) Photomicrograph (x4000), (b) X-ray Spectrum Figure 6.4 Digested Kaiser Coal P a r t i c l e 115 (a) Photomicrograph (x2000), (b) X-ray Spectrum Figure 6.5 Undigested Slag (Cl,7) P a r t i c l e s 116 (a) Photomicrograph (x800) (b) X-ray Spectrum Figure 6.6 Cross-Section of Quenched Slag Bar Sample (C2,3) (x50) 118 Figure 6.7 Cross-Section of Quenched Slag Bar Sample (C2,3) (x50) 119 Figure 6.8 Tuyere Back-Pressure Measurement Sequence (a) Empty Furnace, (b) 19T Charged, (c) 39T Charged, (d) 52T Charged Blast at 300 Standard m^/min 123 Figure 6.9 Tuyere Back-Pressure Measurement 5 Second Interval 12 6 Figure 6.10 Tuyere Back-Pressure Measurements 127 (a) with 70 kg/min coal, (b) no coal Figure.6.11 Schematic of Tuyere Phenomena 129 Figure 6.12 Entrained Slag Coal Reaction Sequence 136 Figure 6.13 Slag-Char P a r t i c l e Reaction System 13 9 x i i Figure 6.14 Radial Slag Concentration P r o f i l e s 141 From Slag Bubble Sample (Cl,5) (x600) (a) Zinc (b) Iron Figure 6.15 Radial Slag Concentration P r o f i l e s 142 From Slag Bubble Sample (Bl,l) (x600) (a) Zinc (b) Iron Figure 6.16 Secondary Bubble Residence Time Geometry .. 165 Figure 6.17 Schematic of Coal P a r t i t i o n i n Furnace .... 182 Figure 6.18 Cycle A l , I n d u s t r i a l Data and Model F i t ... 191 Figure 6.19 Cycle A2A, Ind u s t r i a l Data and Model F i t .. 192 Figure 6.20 Cycle A2B, Ind u s t r i a l Data and Model F i t .. 193 Figure 6.21 Cycle B l , Industrial Data and Model F i t ... 194 Figure 6.22 Cycle B21, Ind u s t r i a l Data and Model F i t .. 195 Figure 6.23 Cycle B22, Ind u s t r i a l Data and Model F i t .. 196 Figure 6.24 Cycle C l , Ind u s t r i a l Data and Model F i t ... 197 Figure 6.25 Cycle C2, I n d u s t r i a l Data and Model F i t ... 198 Figure 6.26 Cycle Dl, Industrial Data and Model F i t ... 199 Figure 6.27 Cycle D2, Ind u s t r i a l Data and Model F i t ... 200 Figure 6.28 Cycle E l , In d u s t r i a l Data and Model F i t ... 201 Figure 7.1 The E f f e c t of 'F* on Predicted Fuming Behavior 209 Figure 7.2 The E f f e c t of ' Y' on Predicted Fuming Behavior 212 Figure 7.3 The E f f e c t of 'F 0c' on Predicted Fuming Behavior 214 Figure 7.4 The E f f e c t of Slag Veloc i t y 'v ' on Predicted Fuming Behavior .? 216 Figure 7.5 The E f f e c t of Coal P a r t i c l e Size 'r ' on Predicted Fuming Behavior ? 218 Figure 7.6 The E f f e c t of the Non-stoichiometry Factor 'x' (FexO) on Predicted Fuming Behavior 219 x i i i Figure 7.7 Figure 7.8 Figure 7.9 Figure 7.10 Figure 7.11 Figure 7.12 Figure 7.13 Figure 7.14 Figure 7.15 Figure 7.16 Figure 7.17 Figure 7.18 Figure IV.1 Figure VI.1 The E f f e c t of the D i f f u s i v i t y Ratio 'D* ( D F e Q / D F e ) on Predicted Fuming Behavior 2 .3. 220 The E f f e c t of Slag Zn Concentration on Fuming E f f i c i e n c y and Furnace Heat Balance as a Function of P a r t i c l e Residence Time .. 222 The E f f e c t of Slag F e 3 + Concentration on Fuming E f f i c i e n c y and Furnace Heat Balance as a Function of P a r t i c l e Residence Time 226 The E f f e c t of Coal Reactivity on Fuming E f f i c i e n c y and Furnace Heat Balance as a Function of P a r t i c l e Residence Time 227 The E f f e c t of ZnO and F e ^ O ^ D i f f u s i v i t i e s on Fuming E f f i c i e n c y as ^a Function of P a r t i c l e Residence Time 228 The E f f e c t of Coal Reactivity on Predicted Fuming Behavior 232 The E f f e c t of Coal Composition on Predicted Fuming Behavior 233 The E f f e c t of Bath Weight on - -Predicted Fuming Behavior 23 5 The E f f e c t of Preheat and Oxygen Enrichment of Blast on Predicted Fuming Behavior 237 The E f f e c t of Bath Temperature on Fuming E f f i c i e n c y and Bath Heat Balance as a Function of P a r t i c l e Residence Time... 239 The E f f e c t of Coal Composition on Fuming E f f i c i e n c y and Bath Heat Balance as a Function of P a r t i c l e Residence Time . . 241 The E f f e c t of P a r t i c l e Size ' r p ' on Fuming E f f i c i e n c y and Bath Heat Balance as a Function of P a r t i c l e Residence Time .. 243 Coal Particle-Tuyere Bubble Geometry 290 Fuming Furnace Wall Structure 300 x i v TABLE OF NOMENCLATURE Surface area of x m2 Boudouard Reaction Rate kPa ^  s ^  pre-exponential constant A c t i v i t y of species j Boudouard Reaction rate s Furnace coal rate kg s ^  Concentration of species j i n phase p kg*mole m Wt. f r . of j i n coal where j i s : •fc: fixed carbon v o l : v o l a t i l e s ash: ash moist: moisture Ratio of ferrous to f e r r i c d i f f u s i v i t y 2 - 1 S e l f - d i f f u s i v i t y of species j m s 2 - 1 I n t e r - d i f f u s i v i t y of species j m m s phase p Diameter of x, thickness of x m where x i s : p b st s i p a r t i c l e bubble water-jacket steel frozen wall slag 3 - 1 Blast flow rate m s Boudouard Activation Energy kJ kg'mole Fraction of coal entrained i n slag Wt. f r . of species j i n phase p Tuyere bubble frequency s ^  Molar quantity of carbon i n char p a r t i c l e kg-mole Thermal conductivity of phase p J m ^ -2 Gravitational acceleration ms Equilibrium constant X V Slag bath height Heat transfer c o e f f i c i e n t slag-wall Equilibrium constant of reaction x Mass-transfer c o e f f i c i e n t of species j Furnace length Mass of slag bath Mass of phase p Mole f r a c t i o n of species j Molar quantity.1.of species j Molar mass-transfer rate of species j P a r t i a l pressure of species j Secondary bubble path length Heat transfer rate Gas constant Rate of reaction Radius of x Molar l i m e - t o - s i l i c a r a t i o (C+ash)/C wt r a t i o i n char p a r t i c l e Temperature Time Number of furnace tuyeres Volume of x, where x i s : m J m s K ms m kg -1 kg-mole kg-mole kPa m -1 J s 8.314Jlkg«mple~^K kg-mole m K s m~ bubble p a r t i c l e secondary bubble gas phase Velocit y of x Wt. f r . of coal v o l a t i l e s element j ; where j i s : C, 0, H, or N ms -1 Wt. f r . of j i n slag wall xv i W I w X Y Wt. of char p a r t i c l e Bath width Non-stoichiometric factor Fe 0 x Fraction of furnace coal consumed in tuyere gas stream Fraction of furnace coal unconsumed i n bath kg m Greek Symbols Y. P,m y x 'si A c t i v i t y c o e f f i c i e n t of species j Surface tension Wetting angle Density of phase p Molar density of phase p Density difference, - p ^ Vi s c o s i t y of slag X-ray wave length Tuyere gas column porosity Slag porosity Dimensionless d i f f u s i o n time Other Symbols AH w AH AH. Re Pe Sh Eo s, ZnO Heat of water (20°C- gas,100°C) Heat of solution of ZnO i n slag Heat of-reaction x (See Table 6 . 3 ) Reynolds Number Pecelt Number Sherwood Number Eotvos Number N m - 1 (degrees) kg/m3 kg-mole/m" kg m~3 i -1 -1 kg m s m J kg-mole J kg-mole -1 -1 J kg-mole -1 Phases (subscripts and superscripts) s i Slag tb Tuyere bubble b Bubble b l Blast i Interface w Water p Char p a r t i c l e st Steel g Gas f F i n a l Rate Phenomena (superscripts and subscripts) r Reduction cons Consumption m Melting gen Generation 0 Oxidation c Combustion 1 Input x v i i i ACKNOWLEDGEMENTS I would l i k e to extend my sincerest thanks to Dr. Keith Brimacombe for his un t i r i n g enthusiasm and guidance throughout t h i s project. Sincere thanks i s also extended to Dr. Gerry Toop for his invaluable assistance and continuous support, without which t h i s work would not have been possible. A personal note of thanks i s due to my wife for her p a r t i c u l a r patience and many e f f o r t s i n helping me to complete t h i s thesis. The invaluable co-operation of Cominco Ltd., through Dr. G. Toop, i s g r a t e f u l l y acknowledged. The assistance of Gordon Heney, i n the performance of various plant tests at Cominco Ltd., T r a i l , B.C., was greatly appreciated. The co-operation of the other companies which participated in t h i s study i s g r a t e f u l l y acknowledged. The f i n a n c i a l assistance of NSERC through an NSERC Post Graduate Scholarship has been sincerely appreciated. Thanks are also due to those members of the Department of Metal l u r g i c a l Engineering, past and present, who took the time to p a r t i c i p a t e i n whatever way i n t h i s endeavor. A special thanks to Ravi Kannan and Joanne Stenhouse. 1 CHAPTER I INTRODUCTION: SLAGS AND SLAG PROCESSING Slags are ubiquitious actors i n pyrometallurgical processes, where they often play v i t a l a l b e i t mysterious r o l e s . In general the slag i s involved i n both the physical and chemical processing of the metal by f u l f i l l i n g several functions. These may include: r e f i n i n g of the melt by the absorption of unwanted l i q u i d or s o l i d components, thermal in s u l a t i o n of the melt, protection of the melt from the surrounding atmosphere and control of the supply, of r e f i n i n g materials to the melt. To s a t i s f y these demands the slag must have a p a r t i c u l a r set of properties which are controlled by i t s composition and temperature. Of necessity the slag must have a lower melting point than the melt, i t must have a lower s p e c i f i c gravity and f i n a l l y must be immiscible with the melt. These requirements ensure that the slag forms a r e l a t i v e l y f l u i d and d i s t i n c t l y separate phase on the surface of the melt. In addition the slag must have a chemical composition such that i t can react with the melt i n the desired way to remove impurities. This requirement must be met within the l i m i t s imposed by the above constraints which usually means that some compromise be reached between the physical and chemical properties of the slag. For example, to dephosphorize and desulphurize s t e e l i t would be desirable to use a very high lime slag but such a material would be s o l i d at s t e e l making temperatures and consequently of l i t t l e p r a c t i c a l use. 2 F i n a l l y i t must be appreciated that within the context of i n d u s t r i a l processes, slags a r i s e from three sources. The f i r s t contribution to the slag i s gangue material introduced with the concentrate or ore. Second are fluxes deliberately added during the smelting operation, and t h i r d l y the slag may be b u i l t up i n part by oxidation of the melt, be i t metal or matte. If to these considerations are added questions of a v a i l a b i l i t y of materials, economics, and natural v a r i a t i o n i n the gangue composition the whole problem becomes quite complex. As a r e s u l t the e f f i c i e n c y with which slag performs any one of i t s functions i s l i m i t e d . Thus, for example, heat i s l o s t from the melt through the slag and the r e f i n i n g of the melt i s not as complete as i t possibly could be. These types of problems can be dealt within a p a r t i -cular process for example by increasing the thickness of the slag layer on the melt or increasing the mass of slag to compensate for the i n e f f i c i e n t r e f i n i n g . There exists however a series of problems associated with the presence of a slag that cannot be so e a s i l y resolved. One of the most important of these and that which forms the raison d'etre for t h i s thesis, i s the fact that metal values are unavoidably l o s t to the slag during processing. The losses can be of two forms. F i r s t are chemical or solution losses in which a metal dissolves i n the slag due to the p r e v a i l i n g chemical p o t e n t i a l . Second are physical losses such as the entrainment of copper droplets i n converter slag. Together or separately these losses can amount to a s i g n i f i c a n t f r a c t i o n of the metal input to a process and therefore j u s t i f y t h e i r removal. 3 This operation i s appropriately termed slag cleaning. Other problems of t h i s group include refractory attack and erosion, disposal of slag, and the thermal burden imposed on smelting processes by the presence of the slag. These w i l l not be d i s -cussed further as they are beyond the scope of t h i s t h e s i s . Before proceeding, and i n view of the above statements, i t i s worth mentioning the general philosophy that has guided the use of slags i n i n d u s t r i a l practice: t r a d i t i o n . For reasons that w i l l become apparent below, slags are very complex phases and are d i f f i c u l t to understand i n th e o r e t i c a l terms. (Part of t h i s problem i s the fact that they are solutions not dominated by any p a r t i c u l a r species.) Also due to the paucity of experi-mental data, l i t t l e i s known of t h e i r physical and chemical properties on a comprehensive scale. These two factors combine to ensure that slags are used i n a largely empirical and unima-ginative fashion based upon t r a d i t i o n a l practises. U n t i l a better understanding of slags i s achieved the analysis of slag-related problems and the development of slag processes i s destined to be slow. To summarize what i s known and thereby provide some background' for the discussions to follow, a short review of slag chemistry w i l l be made before slag cleaning and slag fuming are introduced. 1.1 Slag Chemistry 'Slag 1 , i s a generic term used to describe a mixture of molten oxides which may also contain sulphides and halides i n 4 smaller proportion. In practise slags are usually based on s i l i c a t e s and aluminates of metal oxides such as lime (CaO), magnesia (MgO), and ferrous oxide (FeO). Sulphides only appear as impurities and halides (most often CaF 2) are added only i n specialized applications. Because of the predominantly ion i c character of the a l k a l i and t r a n s i t i o n metal oxides and the more covalent type bonding of s i l i c a and alumina, molten mixtures of these compounds become quite complex. When ioni c compounds melt they simply form i o n i c melts as i n the case of CaO: CaO, \* t. Ca2+.-,s + 027n x (1.1) (s) (1) (1) When s i l i c a melts the process i s more complicated. Within the l a t t i c e of S i 0 2 each S i atom i s surrounded by four oxygen atoms each shared with a d i f f e r e n t S i atom. The structure can be envisaged as a three dimensional network of these tetrahedra. As s i l i c a i s heated the network starts to break down to form 6- 4 + large "ions" such as (Sig0 2^) and a small number of S i ions, Further heating acts to reduce the average size of these ions 8 — say to (Si-jOg) . Eventually at a very high temperature the 4-melt would consist of (SiO^) tetrahedra and an equal number of S i 4 + ions (1723°C). When a mixture of an ioni c oxide and s i l i c a i i s melted . together the di s s o c i a t i o n of the metal oxide generates 0 ions which act to break up the s i l i c a network: 5 =Si-0-Sl= + O 2 t =Si-0~ + 0-Si= ... (1.2) As r e s u l t a substantial reduction i n the melting point i s achieved (1436°C at 36% CaO; 74% S i 0 2 ) . The addition of other oxides can lead to further reductions i n the melting point and v i s c o s i t y . The most elementary understanding of slag systems i s based upon the simple chemistry of the acid-base model. Following the Bronstead's theory for aqueous solutions a basic oxide has been 2-defxned as one which contributes 0 ions to the melt, eg. CaO 2-ln Equation 1.1. An acid oxide i s one which accepts 0 ions, eg. S i 0 2 i n the presence of CaO: S i 0 2 + 20 2~ t ( S i 0 4 ) 4 - ... (1.3) F i n a l l y an oxide may behave as a base i n the presence of a stronger acid, eg.'Al^O^ i n the presence of S i 0 2 : A1 20 3 t 2A1 3 + + 30 2~ ... (1.4) or A1 20 3 + S i 0 2 t - ( S i 0 4 ) 4 ~ + 2A1 3 + + 02~... (1.5) and an acid i n the presence of a stronger base ( A l 2 0 3 i n CaO). A1 20 3 + 0 2" t- ( A 1 2 0 4 ) 2 ~ ... (1.6) In these terms a reasonable q u a l i t a t i v e understanding of the behavior of slags can be developed. For example v i s c o s i t y can often be related roughly to a r a t i o such as the Index of B a s i c i t y . T , c „ . . . wt% basic oxides Index of B a s i c i t y = — =-= =-= 2 wt% acid oxides 6 There have been several attempts to formulate t h e o r e t i c a l models from elementary thermodynamic and physical chemical p r i n c i p l e s as reviewed by Gaskell.^" 7 These have been only p a r t i a l l y success-f u l and generally deal with only binary systems (eg. MO - Si0 2) over a r e s t r i c t e d composition range. In addition, they usually make use of one or more empirical parameters which are not readily subject to measurement. It s u f f i c i e s to say that model-l i n g of slag systems i s only i n i t s early stages of development and i t w i l l be some time before a comprehensive understanding of slag chemistry i s arrived at. In the meantime, our analysis of slag systems : must, i n large part, be drawn from extrapola-tions or interpolations of experimental data. In summary, i n spite of our lack of knowledge, i t i s generally agreed that slags are i o n i c l i q u i d s consisting of metal cations 2 H" 2 "I- 2 H~ 2 2 _ (eg. Ca , Fe , Zn , Mg , etc.) oxygen anions (0 ) and 4- 6- 2-complex anions such as (SiO^) , ( S i 2 0 7 ) and (A1 20 4) . Due to t h i s structure, d i f f u s i v i t i e s i n polyanionic slags tend to be roughly an order of magnitude lower i n slags than i n l i q u i d metals. Thermal conductivity also tends to be quite low. In addition, melting points are usually not well defined because v i s c o s i t y i s a strong function of temperature. The io n i c nature of the melt also ensures that there are strong interactions be-tween' various species, r e s u l t i n g i n non-ideal thermodynamic behavior, i . e . large and variable a c t i v i t y c o e f f i c i e n t s . 7 1.2 Slag Cleaning The term 'slag cleaning' refers to a metallurgical process whereby metal values are recovered from the slag phase. There are b a s i c a l l y three d i f f e r e n t approaches to t h i s problem. The most predominant are pyrometallurgical reductive processes i n which molten slag i s treated with a reducing agent such as coal or pyrites to reduce dissolved metals to a metallic or sulphide form. For example, one process for the recovery of copper and nick e l from slags derived from the smelting of copper - nic k e l ores i s reduction by coke i n an e l e c t r i c furnace to produce a l i q u i d copper - n i c k e l a l l o y . The second cleaning process i s 'settling'' by which contained metals or metal sulphides r i s e or sink to form a d i s t i n c t layer from which the slag can be separated. S e t t l i n g may follow a reductive process or simply be used on i t s own. In general i f s e t t l i n g i s an important aspect of the slag cleaning process an e l e c t r i c arc furnace i s used to ensure that r e l a t i v e l y quiescent slag conditions are achieved. The t h i r d approach i s slag m i l l i n g and f l o t a t i o n . This involves grinding the cooled slag and separating metallic and sulphide p a r t i c l e s by a standard rougher-cleaner type c i r c u i t . This method has the advantage of more e f f i c i e n t recoveries (5-10% better than the e l e c t r i c furnace route for copper and nickel) and roughly half of the energy consumption. The d i s -advantages include a c a p i t a l cost of about twice the pyrometal-l u r g i c a l route and the i n a b i l i t y to recover less noble metals 2 such as lead, zinc, and t i n . 8 As the name implies, 'slag cleaning 1 i s usually a secondary operation which l i e s outside the main flow-of the smelting pro-cess. This s i t u a t i o n has arisen due to a lack of understanding of slag systems and has been perpetuated by the absence of the development of slag processing technology. Instead of attempting to use slag as active vehicles of metallurgical extraction, the attempt has been to minimize a l l 'losses' to the slag and correct for f a i l u r e s i n t h i s area by slag cleaning. This i s not necess-a r i l y the most e f f i c i e n t solution to the problem. For example, i t might be better to e f f e c t the separation of two metals by operating under conditions which promote the transfer of one to the slag phase from which i t w i l l be subsequently recovered. This discussion w i l l not be pursued here, except to note that i t has only been i n recent years that the problem df slag treatment of slag processing has been seriously addressed. Currentuunderstanding of slag systems and t h e i r treatment i s comprehensively reviewed by Floyd and Mackay . As t h e i r paper reveals, our knowledge i s sketchy and only beginning to provide a proper perspective from which slag processing can be viewed. See also the review by Snelgrove and Taylor . The whole question i s neatly i l l u s t r a t e d by the process of zinc slag fuming. The o r i g i n , the history and the development of t h i s process presents a v i v i d picture of the problems, p i t -f a l l s and philosophy of slag, processing. The k i n e t i c s of zinc slag fuming, the focus of t h i s thesis, w i l l be dealt with a f t e r t h i s background has been discussed. 9 1.3 Zinc Slag Fuming Zinc slag fuming i s the reductive treatment of molten slag to recover dissolved zinc. The process i s carried out i n a rectangular water-jacketed furnace on a batch basis. A schematic drawing of a cross section of the furnace i s shown i n F i g . 1.1. A charge consisting of approximately 50 tonnes of molten or molten and s o l i d slag i s charged to the furnace at the beginning of the cycle. A reducing mixture of a reductant, usually pul-verized coal, and a i r i s blown into the bath through sets of tuyeres which are set along the bottom of the long dimension on both sides of the furnace. The coal, normally of the bituminous or sub-bituminous cl a s s , i s ground to 80% -200 mesh (B.S.S.) and applied to the slag at a rate of 50-75 kg/min. I t i s carried by what i s termed the "primary a i r " which has a volume flow rate 3 of about 30 m /min. The main bla s t or "secondary a i r " enters the tuyere behind the coal stream with a volume flow rate of 300-400 m /min. In some operations t h i s blast i s preheated up to 700 C. Within the furnace the reducing mixture reduces the zinc from a dissolved oxide to metallic zinc, a gas at operating temperatures which l i e between 1150 and 1325°C. The o v e r a l l reactions are then: ZnO (slag) + C (coal) t Zn (g) + CO (g) ...(1.7) K 1200°C = 395, A H = 364000 J C,CO~—"C0 2 Tertiary air Slag fuming process Figure 1.1 Schematic of Fuming Furnace Cross-Section 11 and ZnO (slag) + CO (g) Zn (g) + CO 2(g) (1.8) K 120CTC o„ = 0.129 AH = 192500 J The zinc vapour and tuyere gases pass out of the bath into the 'freeboard space of the furnace where the zinc i s oxidized to a zinc oxide fume which i s subsequently captured i n a baghouse. Oxidation i s accomplished by the tuyere gas stream and a i r which leaks into the furnace above the bath, sometimes referred to as 'tertiary a i r ' . For t h i s reason the gas stream i s very hot and to recoup some of t h i s heat the gases are usually passed through a steam b o i l e r before entering the baghouse. Slag fuming i s normally applied to the recovery of zinc and lead from lead b l a s t furnace slag. At two operations however, i t i s used to treat copper reverberatory slag. In the former case the slag i n i t i a l l y contains 13-18% zinc, and i n the l a t t e r case about 8%. Fuming usually i s car r i e d out u n t i l the slag contains 1.5-2.5% zinc at which point the furnace i s tapped and the slag i s granulated and stockpiled. The o v e r a l l cycle takes about 3 hours including 3 0 minutes for charging and tapping. The re-maining time, about 150 minutes, i s termed the "fuming period" during which the majority of the zinc extraction takes place. The fuming period i s often subdivided into an i n i t i a l heating period followed by proper fuming. The heating period involves operating at a reduced coal rate i n order to ensure more complete combustion of the coal and thereby heat the bath to a desirable 12 operating temperature. This i s often necessary because many plants hold the bl a s t furnace slag i n ladles for up to several hours before charging to the slag-fuming furnace. In addition to lead and zinc, other v o l a t i l e elements present i n the slag are also fumed, usually as oxides or sulphides. These include t i n , cadmium, and indium. The fume also contains chlorides, f l u o r i d e s , some lime, s i l i c a and iron oxides, as well as carbon. The recovery of zinc from the slag i s normally 85-90% and requires 1-2 kg coal per kg zinc (3.3-6.5 kg moles C per kg mole Zn). Recovery of lead i s always near 100%. It i s immediately obvious that slag fuming represents a very complex inte r a c t i o n of physical and chemical processes: the dynamics of gas i n j e c t i o n into l i q u i d s , submerged combustion of coal, slag-gas reaction k i n e t i c s and slag thermodynamics. The complete description of the process i s the object of t h i s thesis and w i l l be developed i n due course. 1.3.1 History In the nineteenth century lead was usually smelted from s i l i c e o u s and carbonate ores due to the ease with which these could be treated,^'^ however, these sources of lead were rapidly exhausted and smelters were forced to use sulphide ores. Although the Scotch hearth smelting technique was available to treat these ores i t could only be used e f f e c t i v e l y on r e l a t i v e l y 13 pure galena (greater than 70% Pb, less than 4% iron pyrites and 7 sp h a l e r i t e ) . The majority of lead sulphide ores however contain a s i g n i f i c a n t quantity of zinc sulphide and i t therefore became necessary to develop a smelting practice that could be e f f e c t i v e l y used on them. This, of course, was the lead blast furnace which was developed i n the 1870*s by the smelting companies of the western United States. The lead blast furnace treatment of ores preceeded by s i n t e r i n g has become the mainstay of lead smelting i n the twentieth century.- The development of sele c t i v e f l o t a t i o n methods for the separation of zinc and lead sulphides from iron sulphide in c r y p t o c r y s t a l l i n e ores lead to even greater e f f i c i e n c i e s . However i t i s v i r t u a l l y impossible to remove a l l the zinc from lead concentrates and consequently there i s unavoidably zinc in the sinter charged to lead b l a s t furnaces. For several reasons zinc i s a c r i t i c a l factor i n the opera-ti o n of lead b l a s t furnace. Of p a r t i c u l a r importance i s the fact that m e t a l l i c zinc i s vapour at hearth temperatures. For t h i s reason i f me t a l l i c zinc i s produced i n the furnace i t i s ca r r i e d into the upper regions of the furnace where i t condenses or reacts with the charge which can cause severe problems of 'bridging' of the charge and may necessitate a shutdown. Examination of an oxide Ellingham diagram, F i g . 1.2, shows that at 1200°C l i q u i d lead can be produced from PbO at an _5 oxygen po t e n t i a l of approximately 1 Pa. (10 atm). At the same temperature the reduction of ZnO requires an oxygen XT Xo*„Jfs« Xcf> 1? k • <J Hr X»' X * W *r TEMPERATURE IN DEGREES CENTIGRADE 1 COC 000 WOO 1700 MOO WOO WOO M c e j i q o W » , ,0 This line is hypothetic*) and applies to •toichionte+nc compounds. Actual decomposition is to Fc3CU containing] F«jOi i.e. at lower activity >al I j \®r 0 . 200 400 -AESOtDTE ZERO 800 1000 1200 MOO 1600 1800 2000 2200 2400 9,'< TEMPERATURE IN DEGREES CENTIGRADE flO/R* RATIO N V H / S O I U T I O X \ . «* «<•* TT i i i "V \ _ i T •J \ Figure 1 . 2 Oxide Ellingham Diagram (from reference (8)) 15 p o t e n t i a l of about 1 (10 ) Pa. (10 atm). I t i s therefore r e l a t i v e l y straightforward to produce lead and at the same time avoid most of the problems caused by zinc vapour. Since the zinc remains as an oxide i t reports to the slag and as a r e s u l t the lead smelting complexes of the world began to accumu-late large slag dumps that contained up to 20% zinc. World War I saw a sharp r i s e i n the demand for zinc which continued into the 1920's as the physical metallurgy of zinc and i t s i n d u s t r i a l p o t e n t i a l began to be seriously investigated. This ensured a growing market for the metal thus providing a strong incentive for the development of a process that could recover the zinc from such a r e a d i l y available source as a smelter slag p i l e . It was also r e a l i z e d that any technique that allowed for the recovery of substantial quantities of zinc from a lead smelting c i r c u i t could substantially reduce the degree of separation required i n f l o t a t i o n . F i n a l l y i t was appreciated that since the blast furnaces were constantly pro-ducing molten slag and that eventually t h i s would be the major source of slag for treatment a process that could treat the slag d i r e c t l y , and perhaps take advantage of the contained sensible heat, would be the most desirable. It must be appreciated that the metallurgists faced with th i s problem were only dimly aware what might be involved i n such a process. In addition only a limited range of technology existed that might be c a l l e d upon for the task. The handling of 16 slag had i n the past been largely r e s t r i c t e d to pouring i t into pots and hauling i t out to the slag dump. What was demanded was the controlled chemical and physical treatment of slag, a v i r t u a l l y unexplored area. However, two fundamental facts formed the germ of t h e i r approach to the problem. The f i r s t was that zinc metal was a vapour at molten slag temperatures. The second was not as well understood, the fact that slags were e s s e n t i a l l y molten oxides; but t h i s was s u f f i c i e n t to produce ideas. The e a r l i e s t report on slag treatment experiments was made by G. Courtney 9 i n 1920. In t h i s paper published i n the Proceedings of the Australasian In s t i t u t e of Mining and Metallurgy he describes a series of tests performed by the Sulphide Corporation of Cockle Creek, A u s t r a l i a . The e a r l i e s t work was done i n 1906 and simply involved blowing compressed a i r through the molten slag. Since zinc was gas at slag temperatures a 'gas purging 1 may have been thought to be an easy way to remove i t from the slag. Although the technique'did produce some fume the slag was rapidly cooled and frozen. In the second set of experiments a c o a l - a i r mixture was used instead of a i r . Whether or not the coal was simply viewed as a f u e l to make up the heat loss or whether i t was viewed as a reductant i s not c l e a r . Either way the experiments were successful to the extent that a patent was issued to F.H. Evans and P.A. McKay i n 1908. However i t seems no commercial develop-ment of the idea was made at that time. Courtney goes on to 17 describe several other methods that were tested at Cockle Creek. These included a reverberatory furnace treatment which involved f i r i n g the slag with coke and limestone to a temperature of 1600°C. This i s d i r e c t evidence that an analogy had been drawn between the reduction of s o l i d oxides and the reduction of slag. Agitation was found to be of some assistance and recoveries of 40% were achieved. Experiments were also conducted with an e l e c t r i c furnace which gave recoveries of 60% without any additions of coal, coke or fluxes. A valuable lesson was learned at t h i s point. During the f i r s t heat the slag completely dissolved the furnace l i n i n g and there aft e r i t was decided that the slag could only be e f f e c t i v e l y handled i n water-jacketed furnaces. Other tests were made with a bl a s t furnace type smelting furnace which would handle briquettes, nodules or lumps. It was only p a r t i a l l y successful. Despite a l l of t h i s work no commercial developments appear to have been made. North America was the s i t e of work which eventually lead to the construction of an operating furnace. In the early 1920's experiments were undertaken by the Consolidated Mining and Smelting Company at T r a i l , B.C. to f i n d a means of treating the slag i n an electrothermal way. 1 0 Due to the a v a i l a b i l i t y of hydroelectric power at T r a i l , i t was f e l t that t h i s would be the cheapest technique. Beginning i n 1925 experiments i n slag cleaning were independently begun by the Anaconda Copper Mining Co., i n Great F a l l s , Montana. 1 1 Their i n i t i a l investigations involved an e l e c t r i c furnace but they soon switched to studying the elimination of zinc from molten slag by the submerged 18 i n j e c t i o n of pulverized coal i n a copper converter. This work was done at the Tooele, Utah plant of the International Smelting Company. This was followed by the construction of experimental water-jacketed furnace and based on i t s success, a slag fuming plant was commissioned for the Anaconda smelter i n East Helena, Montana. This plant was b u i l t during 1927 and blown-in i n December 12 of that year. The furnace was 2.44 m (8 ft) by 3.66 m (12 ft) and used 22 - 10.2 cm (4 in) i . d . tuyeres. These tuyeres were borrowed from the design of burners for coal f i r e d reverberatory furnace. These were to be improved shortly by A. L a i s t who designed the double-inlet tuyeres described above. These were much safer devices because they e f f e c t i v e l y prevented the coal from entering the secondary a i r system. The East Helena furnace treated a batch charge of 23 tonnes (25 tons) with a d a i l y capacity of 300 tonnes. Recoveries of 85-90% were achieved i n 160 minute blowing times. Work continued at T r a i l with the construction of an experi-mental pulverized coal furnace i n 1927. Tests were also made with a combination of coal and electro-thermic reduction. In the end, i t was decided that the pulverized coal method was cheaper than the electro-thermic process for the treatment of molten slag. In addition i t was found that the coal-electrothermic process had problems due to the production of metallic iron. For these reasons i t was decided that the pulverized coal furnace would be 19 developed for commercial operation. A furnace was designed i n 1928, i n conjunction with further p i l o t plant work and the assistance of the Anaconda Co. The furnace was blown-in i n July, 1930. The T r a i l furnace was longer, 7.9 m (20 f t ) , and s l i g h t l y wider, 3.05 m (10 f t ) . In addition, i t incorporated the new double-inlet tuyeres and a b o i l e r unit to generate steam from the sensible heat of the o f f gases. Beyond that, i t was e s s e n t i a l l y the same as the East Helena furnace. Both furnaces were regularly used to treat a mixture of s o l i d and l i q u i d slag i n order to recover the zinc from slag dumps. Eventually, when these were consumed, the main source of slag became the blast furnaces. Although the process gradually spread to the lead smelters of the world, i t remained e s s e n t i a l l y unchanged except for par-t i c u l a r modifications made at a few locations. (See Table 1.1 for a survey of slag fuming operations reported i n the l i t e r a t u r e . ) In 1951, slag fuming was applied to the recovery of zinc from copper reverberatory slag at the F l i n Flon opera-13 tions of Hudson Bay Mining and Smelting. However, a furnace i d e n t i c a l to that used to treat lead blast furnace slag at Kellogg, Idaho was constructed. The second development was the introduction of a secondary bl a s t preheat on the slag fuming furnaces of Broken H i l l Associated Smelters of Port P i r i e i n 14 . . 1967. The t h i r d development which i s actually of major s i g n i -TABLE 1.1 Slag Fuming Operations PLJUIT HO. or OPERATING FURNACES ASARCO CHIHUAHUA 1 MEXICO ASARCO EAST HELENA 1 MONTANA ASARCO EL PASO 1 TEXAS ASARCO EELBT 1 CALIFORNIA BUNKER HILL KELLOGG IDAHO CCMINCO TRAIL 2 BRITISH COLUMBIA HUDSON BAT FLIN FLON 2 MANITOBA INTERNATIONAL SMELTINGtREFINING 1 TOOELE, UTAH BOLIDEN RCNNSXAR WORKS SWEDEN BROKEN HILL ASSOC. SMELTERS 2 PORT PtRIE, AUSTRALIA START LENGTH WIDTH UP In) In) 19S2 1964 7.9 4.57 1.0 4.57 .5 NO. OF TUYERE TUYERES I.D. (rn> 38.1 52 38.1 CHARGE MT %Zn (T.) 41 12» 52 141 45 13% 95 11-131 Sub-BituminoUB High Vol Bituminous 70% -200m High Vol BitutninouB High Vol Bituminous 80% -200m Sub-55 17.5% Bituminous B5% -200m 70 8% Bituminous 90% -200m 25 16% Bituminous 80% -100m 90% -200m Sub-Bituminous 80% -200m PRIMARY BLAST VOLUME PRESSURE Std m /min kPa, gauge Std m /min C 125 SECONDARY BLAST VOLUME TgMP. PRESSURE 185 79 48% of Total Air 235 60 21 130 50 245 245 160 325 kPa, gauge 59 100°C «9 79 52% of Total Air Ambient 70 Ambient 50 Primary + Secondary i 610 m /min 200-400 c 240 D.BLAGOEV BUI£ARIA 12-13% Maiut, Fuel O i l Total A l r i 1200-1300 m3/tonne slag TABLE 1.1 (continued) Slag Fuming Operations ASARCO CHIHUAHUA MEXICO ' ASARCO EAST HELENA MONTANA ASARCO EL PASO TEXAS ASARCO SELBY CALIFORNIA BUNKER HILL KELLOGG IDAHO COMINCO TRAIL BRITISH COLUMBIA HUDSON BAY FLIN FLON MANITOBA INTERNATIONAL SMELTINGtREPINING TOOELE, UTAH ROLIDEN RONNSKAR WORKS SWEDEN BROKEN HILL ASSOC. SMELTERS PORT PIRIE, AUSTRALIA D.BLAGOEV BULGARIA CYCLE TIME FUMING Heating Reducing COAL (mint Imln) RATE (kg/rain) 90 min 90-110 min 86 30 min 80 min 68 4 2 min 168 min 68 70 min 130 min 68 30 min 120 min 50 min 130 min 30 min 150 min 55 Continuous NOMINAL Un C o a l Wt R a t i o CAPACITY RECOVERY Zn (T/dayl 48-56 T ~ r day-m References 17 11,12,18 19,20 21,22 23,24,25 10,26,27,28,29 30,31,32 18 33 14,34,35,36,37 15,38 16 ficance i s the continuous fuming process developed i n Bulgaria, u t i l i z i n g f u e l o i l or 'mazut' instead of coa l . " ^ Unfortunately, l i t t l e i s known of t h i s process and the improvement i t represents over the t r a d i t i o n a l process i s therefore d i f f i c u l t to assess. F i n a l l y , i t has only recently been learned that the Russians 16 have developed a process for fuming by means of natural gas. Again, i n s u f f i c i e n t d e t a i l s are available to determine i f a s i g n i f i c a n t improvement i n the process has been achieved. Largely responsible for the neglect of the process has been the fact that slag fuming has been t r a d i t i o n a l l y viewed as f i t t i n g only into a corner of lead or copper pyrometallurgy. In t h i s r o l e , i t i s unl i k e l y that i t would be considered to j u s t i f y development by the non-ferrous industry. Development, where i t has taken place, (has been focused instead on the metal making operations. This, of course, r e f l e c t s the philosophy that the slag phase i s only a passive actor i n metallurgical processing. 23 CHAPTER II LITERATURE REVIEW: STUDIES AND MODELLING The chemistry and k i n e t i c s of slag fuming were only vaguely understood at the time the f i r s t furnaces were constructed. It was known that a substoichiometric mixture of coal and a i r gave the best fuming rates and that higher temperatures, i f they could be tolerated, gave higher fuming rates. From the e f f e c t of these and other operating variables such as slag depth, hot-to-cold charge r a t i o , and coal type, a simple picture of what was happening i n the process was developed. It was generally postulated that the coal entering the furnace burned immediately to a carbon monoxide-carbon dioxide mixture v i a the reactions: C + ho2 $ CO ... (2.1) C + 0 2 % C0 2 ... (2.2) As the gas stream then rose through the bath the carbon monoxide reacted at the gas-slag interface by the reaction: Z n 0 ( s l a g ) + CO t Z n ( g ) + C0 2 ... (2.3) 28 2 3 to produce zinc vapour. ' A second school of thought, that was seemingly i n the minority, considered that the reduction of the slag took place on s o l i d p a r t i c l e s of coal which were i n . 39 contact with i t , eg. Z n 0 ( s l a g ) + C * Z n ( g ) + C 0 ••• ( 2 ' 4 ) 24 For twenty-five years these ideas represented the general understanding of the process. There were no s c i e n t i f i c studies made u n t i l the c l a s s i c a l work of B e l l , Turner and Peters i n 1954. 4 0 2.1 Thermodynamic Modelling The f i r s t attempt to quantit a t i v e l y analyse the process i n terms of chemistry and k i n e t i c s .was' made-by B e l l , Turner and 40 Peters. They assumed that the chemistry of slag fuming was as given i n reactions 2.1-2.3, but i n addition included the V o l a t i l e components of the coal as active reductants. The v o l a t i l e carbon was considered to react as fixed carbon and the v o l a t i l e hydrogen reacted as follows: H 2 + h02 % H 20 ... (2.5) Z n 0 ( s l a g ) + H2 f z n ( g ) + H 20 ... (2.6) With regard to k i n e t i c s B e l l et a l . made the fundamental assump-tio n that the process ran at thermodynamic equilibrium and conse-quently, that Reations 2.1-2.3, 2.5 and 2.6 proceeded to e q u i l i -brium before the gas stream l e f t the surface of the slag. This i s the o r i g i n of what i s frequently termed the thermodynamic model of the process. B e l l et a l . developed a simple model based on mass balances on carbon, hydrogen, oxygen and nitrogen, and on the equilibrium of Equations (2.3) and (2.7): 25 i.e. H 20 + CO $ C0 2 + H 2 ... (2.7) P P K, Z n C°2 ... (2.8) 1 PCO*'ZnO and P P = C 0 2 H2 ... (2.9) "2 P P H 20 CO This i s a t o t a l of six equations that can be solved for the six unknowns: P C Q, P ^ , P^, P ^ , P ^ and P^. The only obstacle to solving t h i s system was that the a c t i v i t y of zinc oxide was not known as a function of slag composition. In order to over-come t h i s problem the authors monitored three controlled fuming runs and measured the fuming rate as a function of zinc concen-t r a t i o n . With the addition of a zinc balance to the above equations, a seventh unknown, the a c t i v i t y of zinc oxide, could be computed. Using t h i s data the authors analysed reqular furnace operation and found that t h e i r model accounted quite well for the furnace heat balance. They then proceeded to examine the consequences of various changes i n operating practise. The model showed that fuming rates could be s i g n i f i c a n t l y improved by increasing the hydrogen content of the f u e l . The use of natural gas was calculated to bring about a 37% increase i n fuming rates. They also determined that oxygen enrichment should improve fuming rates which was i n agreement with e a r l i e r t e s t 26 work."1"1" Preheating of the b l a s t was also shown to be of p o t e n t i a l l y s i g n i f i c a n t benefit. F i n a l l y and perhaps most inte r e s t i n g i s the suggestion that simply by separating the heating and reducing functions of a given f u e l - a i r mixture, fuming capacity could be increased by about 35%. This would involve heating the bath for a period at 95% of stoichiometric combustion and then switching to 55% combustion to fume. By alternating i n t h i s way or by running half the tuyeres at one l e v e l and the remainder at the other l e v e l increased e f f i c i e n c y could be expected. Unfortunately t h i s idea does not appear to have been tested i n d u s t r i a l l y . As mentioned, the model was successful i n predicting the e f f e c t of oxygen enrichment. I t was to be l a t e r demonstrated by .Broken H i l l Associated Smelters that b l a s t preheat could 14 bring about substantial improvements as suggested by the model. Their model, however, was found to be at variance with the r e s u l t s of tests using natural gas. It was suggested i n t h i s case that due to slow reaction k i n e t i c s equilibrium was not achieved. This 42 also appears to have been the problem with f u e l o i l . Although some discrepancies existed, the model on the whole seemed to agree r e l a t i v e l y well with r e a l i t y . This i n part i s to be expected since the model was i n i t i a l l y f i t t e d to i n d u s t r i a l data through the a c t i v i t y c o e f f i c i e n t of zinc oxide. There are a number of other weaknesses i n the model which include the lack of a complete heat balance and the omission of the role of 27 iron oxides i n the oxidation and reduction reactions. For example, magnetite and m e t a l l i c iron are sometimes observed i n the furnace under cert a i n conditions. Both of these facts indicate that the simple oxidation of carbon and reduction of zinc were not the only reactions taking place. F i n a l l y the evidence for the underlying assumption of equilibrium was only i n d i r e c t and there was no experimental data to support t h i s claim. During the summer of 1956, Kellogg conducted a 'no coal' 39 test on No. 2 slag fuming furnace at Cominco Ltd., T r a i l , B.C. This simply involved shutting o f f the coal to the furnace for a period of f i v e minutes and monitoring the changes which resulted. The test revealed that the ferrous iron declined and both f e r r i c iron and bath temperature rose. A mass balance on the change for f e r r i c iron and a heat balance based on the r i s e i n temper-ature both corresponded to a 100% u t i l i z a t i o n of the oxygen i n the b l a s t . Thus i t was concluded that the gas stream - slag interface was s u f f i c i e n t l y large to allow equilibrium to be achieved. Kellogg estimated that the i n t e r f a c a l area i s s u f f i c i e n t to allow fuming rates of roughly three times those normally observed. The author concluded then that the process very l i k e l y runs at equilibrium. 40 On the strength of the work of B e l l et a l . and t h i s experiment, Kellogg developed a comprehensive equilibrium model 43 of slag fuming i n 1967. The model took into account the 28 thermodynamics of the FeO-Fe"304 couple, PbO reduction as well as the behavior of dissolved sulphur. What i s c r i t i c a l about the f e r r o u s - f e r r i c couple i n the slag i s that i f equilibrium i s assumed then the reaction ZnO, , x + 3FeO, , , % Fe-,0. + Zn , x (2.10) (slag) (slag) ^ 3 4 (g) i s at equilibrium. The f e r r i c to ferrous r a t i o can then be said to control the fuming fate. A c t i v i t y c o e f f i c i e n t s , where possible, were taken from the l i t e r a t u r e . The heat balance included the sensible heat of the input slag, the bu i l d up of a frozen slag s h e l l on the water jackets and the reactions above the bath. As a r e s u l t , i n addition to zinc, Kellogg was able to predict the behavior of iron, sulphur, lead and temperature with time. The model worked very well and required l i t t l e f i t t i n g to actual operation data. The major parameters that were adjusted included values of the heat-transfer c o e f f i c i e n t s and a c t i v i t y c o e f f i c i e n t s . In a l l cases apparently, the f i t t e d values lay within the expected l i m i t s of error. Due to the d i f f i c u l t y i n obtaining good i n d u s t r i a l data, the model was v e r i f i e d against a one month average performance of ASARCO's E l Paso furnace. The model was able to predict the f i n a l zinc content of the slag and the value of the coal-to-zinc r a t i o f or the 'average' cycle to within 10%. Predicted temperatures and Fe^O^ behavior were reasonable i n terms of normal operating experience although these were not checked against i n d u s t r i a l measurements. 29 F i n a l l y the model was abl e to c o r r e c t l y - a c c o u n t f o r the behavior of a s l a g fuming furnace d u r i n g a 'no-coal' t e s t . The model was used to demonstrate the b e n e f i c i a l e f f e c t s of u s i n g a preheated b l a s t . Decreasing c o a l moisture and c o a l ash were a l s o shown t o r e s u l t i n b e t t e r fuming. K e l l o g g ' s model re p r e s e n t e d a s i g n i f i c a n t advance i n the a n a l y s i s of s l a g fuming and r e i n f o r c e d the id e a t h a t the process ran a t e q u i l i b r i u m . T h i s model c o n c l u s i v e l y e s t a b l i s h e d t h a t the assumption o f e q u i l i b r i u m i n the furance c o u l d q u a n t i t a t i v e l y account f o r z i n c e l i m i n a t i o n and a t l e a s t q u a l i t a t i v e l y f o r the bath temperature and i r o n b ehavior. The model was adopted and extended by a group a t Broken H i l l A s s o c i a t e d Smelters, P o r t P i r i e , A u s t r a l i a i n the e a r l y 1970's. 44 Grant and B a r n e t t improved c e r t a i n aspects o f the model which r e s u l t e d i n problems when the s l a g depth was low. In a d d i t i o n , the authors extended the heat balance to i n c l u d e the waste heat b o i l e r s and r e c u p e r a t o r s . Improvements were a l s o made to the f l e x i b i l i t y o f the model i n h a n d l i n g p r e d e f i n e d changes i n in p u t parameters such as number of weight of charges and c o a l r a t e s . Grant and Ba r n e t t a l s o c a r r i e d out two e x t e n s i v e p l a n t sampling campaigns i n order t o p i n p o i n t more a c c u r a t e l y the value o f o p e r a t i n g v a r i a b l e s . Again the agreement of the improved model wi t h p l a n t o p e r a t i o n i s good. Again the comparison has been made p r i m a r i l y to p l a n t 30 averages over a large number of runs although one s p e c i f i c run comparison i s detailed. In t h i s case bath temperature i s included and shows the model gives reasonable predictions. Unfortunately, no comparison i s made with regard to the l e v e l of ferrous and f e r r i c oxides i n the slag. I t i s important to mention that i n order to achieve t h e i r f i t , the a c t i v i t y c o e f f i c i e n t of zinc oxide had to be increased 43 2.6 times over the value used by Kellogg, an unl i k e l y difference considering the only weakly basic nature of ZnO. No j u s t i f i c a t i o n i s given. Considering the v i t a l r ole played by t h i s a c t i v i t y c o e f f i c i e n t , i t can therefore only be viewed as an adjustable parameter. This i n i t s e l f i s not p a r t i c u l a r l y disagreeable. The a b i l i t y to model an entire process with one adjustable parameter represents a considerable success. However, the whole weight of the equilibrium model now rests on t h i s point. S i g n i f i c a n t improvement of the process can only come through an increase i n t h i s a c t i v i t y c o e f f i c i e n t . The focus i s then on slag chemistry and temperature. If the process i s i n r e a l i t y k i n e t i c a l l y controlled, f i t t i n g i t with a thermodynamic parameter could be very misleading. 45 A further refinement of the model was made by Grant who reversed the equilibrium model to calculate the value of thermo-dynamic parameters required to account for observed fuming behavior. Based on the analysis of two c a r e f u l l y monitored fuming runs the author developed regression equations for the 31 a c t i v i t y c o e f f i c i e n t s of ZnO and PbO and for the a c t i v i t y co-e f f i c i e n t r a t i o s A F e 3 0 4 a n d YCaS / YCaO' ^ l a t i v e l y good correlations were obtained for ZnO: In y . = -335.18 N M - + 192.11 N_ _ - 36.07 N _/Nc.. 'ZnO MnO CaO CaO S i 0 2 -78.953 N c. n +28.417 ... (2.11) b i u 2 and the iron oxide a c t i v i t y c o e f f i c i e n t r a t i o . The average zinc oxide a c t i v i t y c o e f f i c i e n t obtained was 3.40 (S.D. 0.50) which 43 i s 1.8 times the value o r i g i n a l l y used by Kellogg. The average iron oxide a c t i v i t y c o e f f i c i e n t r a t i o reported i s 4.19 (S.D. 1.15), 3.7 times Kellogg's value. Despite the apparent success and implied vi n d i c a t i o n of the equilibrium model there are several problems with t h i s paper. The f i r s t i s that few fuming furnace slags contain manganese oxide to any appreciable degree immediately i n v a l i d a t i n g equa-tions such as 2.11 i n which MnO plays an obviously s i g n i f i c a n t r o l e . Second, the equation i s of dubious value i n any p r a c t i c a l application due to the s e n s i t i v i t y to N M n Q . (A 2% change in the mole f r a c t i o n MnO (e.g. 5.5 wt% Mn to 5.6 wt%) r e s u l t s i n roughly a 25% change i n Y Z nQ.) Considering the d i f f i c u l t y i n obtaining an MnO assay to within 2% and the d i f f i c u l t y of then ca l c u l a t i n g the mole f r a c t i o n , N M nQ/ i t becomes apparent that the equation i s not r e a d i l y applicable. Furthermore, given the very-large c o e f f i c i e n t for t h e ; N M n 0 ' t e r m , the equation has no fundamental•chemical si g n i f i c a n c e . 32 The reported average values of these parameters are perhaps more meaningful. However considerable scatter exists i n these res u l t s and they are very sensitive to the assumed l e v e l of a i r 4.1 at 0% leakage to 2.9 at 10% leakage.) Although 5% leakage was assumed no measurements were made to confirm t h i s . In spite of the l e v e l of sophistication that the equilibrium model of slag fuming has attained i t i s apparent that i t i n many ways has remained e s s e n t i a l l y empirical. As discussed above, there i s nothing wrong with t h i s i f i t s basic assumption i s correct. Considerable evidence exists however which suggests otherwise. 2.2 Empirical Modelling The f i r s t discussion of the idea that the zinc fuming process 46 does not run at equilibrium i s made by Quarm i n 1965. Quarm c i t e s the evidence of undocumented experiments i n which the coal and a i r rate to a furnace were adjusted to bring about a f i f t y percent reduction i n the calculated zinc p a r t i a l pressure. In spite of t h i s , no change i n the fuming rate was observed. Quarm developed a crude model based on the observed f i r s t - o r d e r nature of the c l a s s i c fuming curve, zinc i n slag versus time. Quarm suggests that t h i s f i r s t - o r d e r behavior i s a r e s u l t of the fuming reaction leakage from the tuyeres. (The calculated y ZnO declines from ZnO + 3FeO + Zn (g) (2.12) 33 i n which the concentration of ferrous oxide i s maintained at a constant l e v e l by the reduction reaction F e 3 0 4 + CO t 3FeO + C0 2 ...(2.13) The f i r s t - o r d e r nature of the fuming curve i s thus due to the decline i n the zinc oxide concentration. Quarm uses the empirical equation log (Zn 1/Zn 2) = v ( t ^ - t ^ / 2 . 303 ...(2.14) to model the process. Zn^ i s the zinc concentration at time t ^ and Zn 2, the zinc concentration at time t 2 - 1v' i s the v e l o c i t y c o e f f i c i e n t of reaction 2.12. A regression analysis of ..the--'same data, only one set of which i s reported, gave 'v' a value of 0.06 min 1 . This constant was then modified i n l i n e a r proportion to f r a c t i o n of iron i n the ferrous form, e.g. i f 60% of the iron 2+ was present as Fe then the v e l o c i t y c o e f f i c i e n t would be 0.60v. In order to perform a heat balance i t was assumed that reaction 2.13 was at equilibrium with both magnetite and ferrous oxide present at unit a c t i v i t y , which i s inconsistent with the basic approach to the problem. In spite of i t s r e l a t i v e l y rough assumptions the model was found to work "very well" when used to predict the behavior of the furnace from which i t s parameters were derived. Because the model i s t h i s s p e c i f i c l i t t l e s ignificance can be attributed to i t beyond suggesting that the role of the iron couple FeO-Fe^O^ i s important. The gross assumptions deprive the model of any information that might lead to an understanding of the process. 34 43 47 . In response to Kellogg's equilibrium model , Quarm i n t r o -duced a new argument to counter the model. The Kellogg model assumes that both v o l a t i l e and non-volatile portions of the coal burn and p a r t i c i p a t e i n the fuming reactions. In practise however Quarm states that coal supply i s adjusted on the basis of fixed carbon content. He c i t e s an example from the ASARCO E l Paso 2 6 plant operation. This i s l a t e r corroborated by Yurko. 48 In 1980 Quarm presented a modified reaction mechanism which included zinc f e r r i t e : 2ZnO + 2FeO X ZnOFe 20 3 + Z n ( g ) ... (2.15) 3ZnO-Fe 20 3 + CO X 3 Z n 0 + 2Fe 30 4 + C0 2 ... (2.16) F e 3 0 4 + CO 3FeO + C0 2 ... (2.17) He also gives several sets of* i n d u s t r i a l data (zinc concentration and temperature as a function of time) and the r e s u l t s of model predictions which are r e l a t i v e l y close to the measurements. In recognition of the new mechanism^velocity c o e f f i c i e n t s for both' zinc oxide reduction (Equation 2.15) v = 0.03 + 0.0001 (T-1000) ... (2.18) and zinc f e r r i t e reduction (Equation 2'.1-6) v = -0.23 + 0.0018 (T-1000) ... (2.19) are given. 'T' i s temperature i n degrees Celsius. The rate of zinc fuming i s then s t r i c t l y dependent on temperature; and there-fore by simply maintaining a c e r t a i n temperature profile,fuming 35 can be effected. This leads to inte r e s t i n g consequences for operating the process such as cutting the coal and a i r back s i g n i f i c a n t l y towards the end of the run when the fuming rate i s low. Unfortunately the author provides no i n d u s t r i a l v e r i f i c a t i o n of t h i s concept. In addition to the work done by Quarm, there have been two other empirical modelling exercises reported i n the l i t e r a t u r e . The f i r s t i s i n a paper by Sundstrom describing the slag fuming 33 plant at the Ronnskar Works of Boliden Aktiebolag i n Sweden. Operating data gathered from a large number of fuming runs and the r e s u l t s of special,tests were f i t t e d to the regression model: „ a 0 (k + z(k. X.))t ,„ o n N Zn t = a-^ZnQ 2 «e o l l . . . (2 .20) where; Zng = i n i t i a l Zn concentration Zn^ . = concentration of Zn at time t = independent variable t = elapsed time a^, a 2 , kg, k^, ... k n = regression c o e f f i c i e n t s Sundstrom states that 40 independent variables are used i n the equation. Unfortunately none of the variables or c o e f f i c i e n t s are given other than the following formula for 'normal' operation Zn t = 0 . 9-Zn 0 v e ( 0 ' 4 1 " °-<>154t) _ ( 2 > 2 1 ) for 40 < t •< 250 minutes 36 As a r e s u l t of applying the model they have concluded that zinc extraction i s primarily limited by the blast volume and that an even d i s t r i b u t i o n of coal down the furnace length i s necessary for maximum zinc extraction. The only other conclu-sion mentioned by the author i s that the degree of combustion should be reduced from 80-100% of stoichiometric at the beginning of the blow to less than 50% immediately p r i o r to tapping. No comments are advanced on the issue of k i n e t i c versus equilibrium control. In the second study, Ivanov et a l . developed a regression model using data taken from an operating 'furnace over 303 batch 47 runs. The following r e l a t i o n s h i p was determined for zinc extraction Y = -41.0 -1.3X-L -1.85X2 +83.0X3 +2'. 8X 4 + 0.47X5 .. (2.22) where: Y = extraction of zinc (%) X^ = amount of slag i n furnace, tonnes X 2 = ash content of coal (%) X^ = consumption of coal per tonne of slag, tonnes X^ = number of operating tuyeres X,- = length of blow, min The o v e r a l l c o r r e l a t i o n c o e f f i c i e n t obtained was r = 0.89. 37 It can be seen that increasing the amount of slag i n the furnace w i l l decrease the zinc extraction. The authors a t t r i -bute t h i s to the fact that as the weight of slag increases, the consumption of a i r and coal per unit of slag of course decreases. They reference however another study which concluded that higher zinc extractions could be obtained with increasing bath depth. In t h i s case, they suggest, care might have been taken to maintain a constant bl a s t i n t e n s i t y . The negative c o e f f i c i e n t s for the coal ash term i s to be expected because a higher ash content means a lower carbon content and a lower reducing power. Likewise, p o s i t i v e c o e f f i c i e n t s for the coal to slag r a t i o and blowing time are not surprising. The p o s i t i v e c o e f f i c i e n t for the number of operating tuyeres i s an i n t e r e s t i n g r e s u l t . I t implies that a f u l l set of tuyeres provides the optimum fuming conditions, perhaps i n terms of bath agit a t i o n . A reduction i n the number of tuyeres would then r e s u l t i n a departure from i d e a l k i n e t i c conditions. Perhaps i t leaves .quiescent zones' i n the slag and- leads to incomplete mixing. Although both of these models are empirical and do not d i r e c t l y address the question of process k i n e t i c s and thermo-dynamics some of the variables that have been i d e n t i f i e d as c r i t i c a l to the process could be interpreted as k i n e t i c e f f e c t s . The negative e f f e c t of bath weight could be explained by either a k i n e t i c or thermodynamic argument. The same applies to the 38 ash content of the coal. However the e f f e c t of slag depth and the number of opera'ting tuyeres are c l e a r l y k i n e t i c parameters. The importance of b l a s t volume or i n t e n s i t y , although not absolutely conclusive, i s strong evidence that the k i n e t i c factors of i n j e c t i o n are v i t a l aspects of the slag fuming process. This conclusion i s supported by Glinkov et al.~*° They present a graph of fuming furnace productivity (kg Zn/m /day) as a function of blast i n t e n s i t y (m /s/m ) which shows a d i r e c t r e l a t i o n s h i p between the two. In summary thermodynamic analysis has dominated t h e o r e t i c a l studies of slag fuming. Empirical modelling, i n which k i n e t i c factors are incorporated, has been undertaken i n the case of s p e c i f i c furnaces and suggests that k i n e t i c s are indeed im-portant. However, to date, there have been no attempts to model the process from the point of view of k i n e t i c mechanisms. Although t h i s section covers the l i t e r a t u r e d i r e c t l y relevant to the modelling of slag fuming there are several studies on s p e c i f i c aspects of the process which are valuable contributions to our knowledge. I t i s important that these be reviewed and assimilated into our f i n a l understanding of the process. 2.3 Slag Fuming Investigations Slag fuming studies have been conducted both i n the plant and i n the laboratory. 39 2.3.1 In d u s t r i a l Studies 41 51 McNaughton et a l . ' examined the e f f e c t of oxygen enrichment on normal fuming operation. The authors found that the addition of oxygen had b e n e f i c i a l r e s u l t s . These are summarized i n Table 2.1 which represents the average of 3 0 tes t s . In the oxygen enriched tests the coal rate was s l i g h t l y greater than that i n the a i r blows. The table shows that the concentra-tion at which the curve starts to l e v e l out i s s i g n i f i c a n t l y lower i n the oxygen enriched t e s t s . An important factor i n t h i s e f f e c t i s l i k e l y the bath temperature which i s much greater in the case of oxygen enrichment. The authors make no attempt to explain t h e i r r e s u l t s . They suggest, however, use of oxygen enrichment may permit the development of a continuous fuming process. It would not be productive to discuss these tests or any of the following i n d e t a i l at t h i s time. However i t should be noted that a study of the Ellingham Diagram, F i g . 1.2, shows the reduction of zinc oxide with carbon becomes more favorable with increasing temperature. Oxygen enrichment also reduces the amount of tramp nitrogen introduced into the furnace and thus lowers the heat demand. In terms of the thermodynamic model, reduction of the amount of nitrogen, which serves as a diluent for the product gas of Reaction 2.3 (Zn and CO,,) , would tend to reduce the rate of fuming. It i s d i f f i c u l t to say which would be the more s i g n i f i c a n t e f f e c t . 40 TABLE 2.1 E f f e c t s Of Oxygen Enrichment On S l a g Fuming 51 (Taken From McNaughton e t a l . ) OXYGEN AVG. CONTENT BLOWING INITIAL FINAL BATH OF BLAST TIME Zn Zn TEMP. (%) (min) (%) (%) (° O 20.9 160 16.8 2.9 1175 23.4 160 16.9 1.6 24.8 160 16.4 0.9 1260 41 The use of a preheated blast has been demonstrated to 14 produce a s i g n i f i c a n t improvement i n fuming rates by Blaskett at Broken H i l l Associated Smelters, (BHAS) SPort .P.irie, A u s t r a l i a . Blaskett presents equilibrium model calculations done when the fuming furnace at BHAS was being designed to confirm that blast preheat would be advantageous. Furnace operation has generally confirmed the predictions of the model. Coal to zinc r a t i o s at BHAS are 1.1 - 1.2 as compared to 1.5 - 1.6 at operations where cold b l a s t a i r i s used. The use of preheated blast reduces the amount of f u e l required to maintain the furnace heat balance. E s s e n t i a l l y t h i s allows operation at lower a i r - t o - c o a l r a t i o s and therefore more strongly reducing conditions. Improved furnace capacity and greater f u e l economy would follow. Blaskett also presents operating data which suggests that coal type has an influence on fuming e f f i c i e n c y . Over two periods of normal furnace operation, two d i f f e r e n t coal types were used. The re s u l t s are shown i n Table 2.2. Blaskett concludes that higher v o l a t i l e , lower fixed-carbon coals are not as e f f e c t i v e as ^ ;;> bituminous coals which have a higher fixed carbon content. 46 47 48 This i s i n agreement with the observations of Quarm. ' ' In a marked departure from t r a d i t i o n a l practise, engineers at the Non-Ferrous Metals Works 'D.Blagoev' i n Plovdiv, Bulgaria developed a continuous fuming furnace based on the use of f u e l 42 TABLE 2.2 Ef f e c t Of Coal Type On Slag Fuming (From Blaskett 1 4 ) Coal Type: Ash V o l a t i l e s Fixed Carbon PERK A 15 % 18-19 % 66-67 % DD B 14-18 % 21-32 % 52-60 % Zinc Elimination 86.1 % 83.9 % Coal/Zinc Wt Ratio 1.10 1.19 43 o i l or 'mazut'. The furnace which has a cross-sectional area 2 of 5.85 m receives slag from a shaft smelting furnace through an intermediate e l e c t r i c s e t t l i n g furnace. The mazut i s injected 3 at a rate of 5.4 m /hr (35 kg/min) at 4.0 MPa (40 atm.) with s u f f i c i e n t a i r to e f f e c t 70% of stoichiometric combustion. In his paper Abrashev emphatically states that according to t h e i r calculations the furnace operates at only 50% of the rate pre-dicted by an equilibrium analysis. The author states that the process i s li m i t e d by d i f f u s i o n k i n e t i c s . A reduction i n the 2 size of the furnace from 8.9 to 5.85 m cross-sectional area produced a two f o l d increase i n furnace capacity for unchanged a i r and mazut flow rates. Other test r e s u l t s are also presented which show increased fuming e f f i c i e n c y as a r e s u l t of increased blast i n t e n s i t y . F i n a l l y the author asserts that low sulphur fuels (0.5% S) give lower zinc slags than high sulphur fuels (3.5% S). That the use of f u e l o i l i s generally not e f f i c i e n t i s 47 confirmed by others. It i s possible that i n s u f f i c i e n t time i s available for the complete combustion of the mazut although t h i s does not appear to be considered by Abrashev. Grant and 44 Barnett contend that they have been able to predict the performance of t h i s furnace with t h e i r equilibrium model. Unfortunately they do not give any d e t a i l s of how t h i s was accomplished and do not address the evidence for the presence of k i n e t i c factors. 44 The primary focus of Russian work on the i n d u s t r i a l scale 16 has been to develop fuming by natural gas. I n i t i a l experiments in p i l o t plant f a c i l i t i e s demonstrated that i t was not feasi b l e to fume with natural gas - a i r mixtures due to the bui l d up of magnetite i n the slag. It was found that combustion had to be c a r r i e d out p r i o r to i n j e c t i o n . Oxygen enrichment apparently relieved the need to carry out pre-combustion but was only successful i f the blast i n t e n s i t y (measured i n blas t volume per unit volume of bath) was maintained. In t h i s work a s o l i d coal addition to the surface of 7 - 10% of bath weight was 52 necessary to give suitable fuming rates. Later plant studies demonstrated that although the lump coal addition could be d i s -pensed with, increased natural gas flow rates and oxygen enrich-ment to 28% were necessary to maintain furnace capacity. Attempts were also made to develop a continuous process 16 based on natural gas but these were only moderately successful. 2.3.2 P i l o t Plant Studies A number of p i l o t plant scale studies of various slag reduction techniques have been undertaken. Some of these do not deal d i r e c t l y with zinc slag fuming but the conclusions they draw provide valuable insights into the mechanisms by which slag cleaning takes place. 45 In the early 1960's a program was i n i t i a t e d at BHAS, Port P i r i e , A u s t r a l i a to study the treatment of granulated lead 53 blast furnace slag (17.5% Zn) i n a cyclone furnace. The f i n a l furnace design consisted of a 30.5 cm i . d . refractory l i n e d c y l i n d r i c a l vessel into which a granulated s l a g - a i r mixture was injected at the top and a c o a l - a i r mixture near the bottom. Each mixture was injected continuously through a water cooled tuyere which was aimed tahgentially to the inner wall and directed at 10° downward. A molten slag bath, approximately 12 cm i n depth was maintained i n the bottom. It was found that i n j e c t i o n of the c o a l - a i r mixture d i r e c t l y into the slag brought about the most e f f i c i e n t reduction. Recoveries of approximately 7 0% were obtained at coal to slag r a t i o s of about 0.3 and a i r preheat of 500°C. 54 This work was continued by Blanks- and Ward with a 83.8 cm i . d . furnace capable of treating 1 tonne of slag per hour. They found that maximum e f f i c i e n c y was achieved when in j e c t i n g the coal with 65% of the a i r required for s t o i c h i o -metric combustion. Recoveries of about 85% were obtained at coal to slag r a t i o s of 0.3 0 and slag depth of 30 cm. The authors 4 0 show that equilibrium of the form described by B e l l et a l . was not attained. Blanks and Ward observed unburnt coal p a r t i c l e s i n the slag during tapping of the furnace which would perhaps explain t h i s e f f e c t . Attempts to improve the s i t u a t i o n by increasing the slag depth by 40% were not successful. 46 The authors were able to achieve a recovery of 94% with batch operation which compares favourably with t r a d i t i o n a l slag fuming operations. Fuel o i l was t r i e d but recoveries of only 30% were attained, confirming e a r l i e r studies. 55 56 Floyd and Conochie ' studies the reduction of l i q u i d t i n smelting slags i n crucibles and 50 kg and 1 tonne p i l o t plant furnaces. Reduction was effected by the i n j e c t i o n of a fu e l ; natural gas, l i g h t o i l or powdered coal, and a i r through a top lance. The authors found that i n order to achieve acceptable fuming rates with natural gas i t was necessary to entrain pulverized coal i n the gas stream. During the reduction with coal i t was found that only the fin e coal burned i n the bath and that the coarse coal was trapped i n the slag. The intermediate f r a c t i o n tended to be carr i e d out of the furnace unconsumed. Experiments performed by Floyd and Conochie i n the labor-55 atory demonstrated that CO was a much poorer reductant than E^' Considering the fact that reduction by s o l i d coal was found to be roughly as fast as hydrogen i t was concluded that reduction by s o l i d coal must be by d i r e c t contact with the slag. F i n a l l y a b r i e f examination should be made of the same submerged combustion technology applied to cleaning copper slags 57 from the converter and anode furnace. Floyd et a l . found 47 that for s o l i d reductants added d i r e c t l y to the surface of the slag lump coal (+6mm to -25mm)'was the fastest reductant. With fine materials (-6mm) the rate of reduction decreased i n order from coal, carbonized coal, coke/coal mixture, coke to p a r t i a l l y burnt o i l (slowest). This suggests that i n t h i s size range there are s i g n i f i c a n t k i n e t i c e f f e c t s involved i n the rate of reduction. I t i s i n t e r e s t i n g to note that the authors found CO gas to be an e f f e c t i v e reductant for copper slags as compared to the t i n slag mentioned above. These papers demonstrate that k i n e t i c considerations such as slag depth, coal entrainment i n the slag and coal type appear in the study of other processes. This suggests that the claim for equilibrium, far from being the norm, i s a more unusual point of view. The remaining studies of slag fuming have been confined to laboratory experiments on the reduction of slags contained i n c r u c i b l e s . 2.3.3 Laboratory Studies With rare exceptions a l l laboratory studies of zinc slag fuming have been conducted i n the Soviet Union. The basic tenet of the Soviet approach to the process i s that k i n e t i c parameters are important. One aspect of t h e i r program, the study of i n j e c t i o n . k i n e t i c s , has been reviewed above. The majority of 48 t h e i r work has been conducted however, i n the area of slag reduction k i n e t i c s . The f i r s t series of studies examined the coal-slag reaction. Due to the d i f f i c u l t y of q u a n t i t a t i v e l y handling pulverized coal i n laboratory experiments, slag reduction by carbon was studied by in s e r t i n g graphite rods into crucibles of molten slag. ^ 8 6 3 The evidence presented i n these papers s a t i s f a c t o r i l y demon-strates that the reduction on graphite i s i n d i r e c t , that i s , i t takes place through an intermediate gas phase. A l l the studies agree that i n the i n i t i a l stages of reduction the rate of reduc-ti o n i s controlled by the Boudouard reaction on the carbon surface C + C0 2 2C0 ... (2.23) Several references 58,59,62 g U g g e s t t n a t c o n t r o l then s h i f t s 61 63 to oxide d i f f u s i o n i n the slag. The other papers ' conclude that control remains i n the gas phase. The o v e r a l l r e s u l t s are not conclusive but indicate under ordinary conditions the rate of reduction l i e s i n a region of t r a n s i t o r y control between oxide d i f f u s i o n and carbon g a s i f i c a t i o n . Several papers examining the carbon reduction of iron oxide containing slags ^ 4 6 6 support these conclusions. The Russian work has also concentrated on the role played by iron and iron oxides i n the reduction process. Several papers ^7,68 examine the reduction of molten slags on iron rods. 49 Unfortunately the papers are inconsistent, contradictory and 6 9 —7 6 incomplete. A series of papers attempt to unify the carbon and iron reduction of zinc slags i n a single model. The basic experiments performed i n these studies were graphite rod reductions of zinc and iron containing slags i n small c r u c i b l e s . Models were developed by performing a d i f f e r e n t i a l mass balance on each species, taking into account d i f f u s i o n and assuming f i r s t - o r d e r reaction k i n e t i c s . Experiments were then performed and the data f i t t e d into the model to determine the various reaction parameters. Correlations often showed that the rate constants f i t t e d at d i f f e r e n t temperatures obeyed an Arrhenius r e l a t i o n s h i p . One problem with the r e s u l t s i s that rate constants show enormous v a r i a t i o n from one experiment to another and appear to be strongly dependent on slag composition. Secondly, the models incorporate two active forms of metallic iron i n the slag, Fe* which l i e s at the gas-slag interface and i s accessible to the gas, and Fe° which i s 'dissolved' i n the melt. No experimental evidence i s presented for either of the species. In addition, t h e i r models use a parameter which i s the 'surface area' of the Fe* phase, a rather bold extrapolation of a hypo-t h e t i c a l concept. F i n a l l y , the d i f f u s i o n c o e f f i c i e n t s obtained from t h e i r work are s i g n i f i c a n t l y higher than would normally 77 be expected for slag systems. A l l of t h i s suggests that although the work i s i n t e r e s t i n g , i t i s far from conclusive. I t i s of l i t t l e help i n analysing the slag fuming process 50 as a-whole, because -no coherent attempt.is made to study the -e f f e c t of process parameters. 7 8 7 9 Two investigations ' studied the e f f e c t of surface-active agents on the rate of reduction of zinc from slag melts. 7 8 Vanyukov et a l . determined that the addition of a few percent of FeS or Na 20 to fuming slag greatly accelerated the reduction of slag drops on a graphite surface. These substances are also shown to bring about a s i g n i f i c a n t drop i n the surface tension of the slag which the authors suggest would improve the capture of coal p a r t i c l e s by the slag and hence increase the rate of reduction. 79 Mazurchuk et a l . examined the e f f e c t of P2°5' N a 2 0 ' CaF 2 and FeS on the gaseous reduction of iron containing slags and found that each additive except P2°5 i n c r e a s e 3 the rate of reduction. P2°5 reduced the rate. Experiments were also con-ducted on the e f f e c t of these additions on the pulverized coal reduction of zinc slags. Two types of t r i a l s were made. In the f i r s t the coal was impregnated with Ca(OH) 2 and Na 20. In the second dry FeS and Na 20 powder was added to the coal. Again the presence of the surface active agent was b e n e f i c i a l and found to bring up to a 350% increase i n reduction rate. The authors suggest that i n the case of a soda addition, the improvement was due to increased w e t t a b i l i t y of the coal, c a t a l y s i s of the Boudouard reaction, and increased oxide d i f f u s i v i t i e s i n the slag immediately surrounding the entrained coal p a r t i c l e . 51 Suzuki et a l . studied the gaseous reduction of copper converter and lead bl a s t furnace slags. Nitrogen gas as well as mixtures of CO, C0 2, H 2 and CH^ were blown through 300 gram batches of slag contained i n alumina c r u c i b l e s . The experiments with N 2 were p a r t i c u l a r l y i n t e r e s t i n g . The authors found that the copper converter slags showed v i r t u a l l y no v o l a t i l i z a t i o n of zinc when agitated by bubbling N 2 through them. Blast furnace slags of comparable zinc content showed s i g n i f i c a n t fuming rates when agitated i n t h i s manner. The s i g n i f i c a n t difference between the two slags i s t h e i r carbon content. The blas t furnace slag contained 0.2-0.3% carbon whereas the copper smelting slags contained none. The ag i t a t i o n by N 2 apparently s t i r s the carbon into reaction with the slag allowing zinc oxide reduction to take place. This interpretation i s supported by the fact that the fuming rate with N 2 was several orders of magnitude higher than that predicted by equilibrium. 43 46 The t r a d i t i o n a l explanation ' for t h i s e f f e c t has been that fuming occurs v i a the reaction ZnO + 3FeO $ Z n ( g ) + F e 3 ° 4 * " < 2- 2 4) Fuming with reducing gas mixtures (CO-C02) demonstrated that again carbon i n the slag was an important component i n the process, especially, at higher temperatures. Experiments with lime additions to the blas t furnace slag showed that at lower temperatures (I2 2 0°C),,the addition of lime had no s i g n i f i c a n t e f f e c t on the rate of fuming. At 1280°c, increasing the lime 52 reduced the rate of fuming, perhaps due to a resultant increase in slag v i s c o s i t y . 2:4 In d u s t r i a l Observations F i n a l l y there are a number of i n d u s t r i a l observations reported i n the l i t e r a t u r e which perhaps provide some additional clues to process operation. Murray indicates that the fuming rate increases with 18 temperature although i n another reference i t i s stated that i f too high a temperature i s reached fuming performance w i l l suffer. The fact that fuming rates improve with temperature was confirmed by operating personnel at Cominco Ltd., T r a i l , B.C. 2 8 McNaughton observed that the e f f i c i e n c y of bituminous and subbituminous coals were equal provided that the ash content was the same. V o l a t i l e matter was not found to p a r t i c i p a t e i n 40 the reduction reactions as suggested by B e l l et a l . 26 28 Yurko 'and McNaughton _.. state-that the presence of sulphur i n the slag has a deleterious e f f e c t on zinc elimination. This was observed when dry lead dross was added to the slag. No discussion of the importance of sulphur i n the coal or sulphur i n b l a s t furnace slag i s made. , 53 Feddersen et a l . , i n tests on the slag fuming furnace at Bunker H i l l , observed that slag depth was an important factor i n zinc elimination. Unfortunately no data i s presented except for the implication that increasing bath depths increased the fuming rate. 30 Mast and Kent note that for furnace operation at Hudson Bay Mining and Smelting, F l i n Flon, Manitoba, a minimum t o t a l 3 a i r flow of 270 m /min (9500 cfm), independent of coal rate, i s required otherwise zinc elimination suffers. 2.5 Summary It i s apparent that a review of the l i t e r a t u r e concerning slag fuming leads to no s a t i s f a c t o r y conclusion. On one hand there exists a complete model of the process which denies the influence of k i n e t i c factors. On the other,-za haphazard c o l l e c t i o n of experiments which suggest that k i n e t i c factors are important. In the middle are several empirical models of the process which incorporate k i n e t i c e f f e c t s . The two extremes cannot be reconciled and the empirical models are too weak to support either side. No clear picture emerges. The assumption that equilibrium i s achieved i n the furnace has been used to develop a model-of the complete process. The model can be successfully f i t t e d to i n d u s t r i a l data to give a sat i s f a c t o r y simulation of the process. This fact has • 54 e s s e n t i a l l y been used to j u s t i f y the i n i t i a l assumption. The only other attempts to model the entire process have been empirical. Unfortunately, these are poorly documented and although they tend to support a k i n e t i c interpretation of the process the evidence i s not conclusive. It i s d i f f i c u l t to attach a p a r t i c u l a r interpretation to a variable with certainty due to the p o s s i b i l i t y that i t may represent several factors. A s i g n i f i c a n t amount of evidence does e x i s t however which implies that slag fuming i s a k i n e t i c a l l y controlled process. In d u s t r i a l tests have shown that fuming with either f u e l o i l or natural gas does not take place at equilibrium. In these cases fuming can be enhanced i f steps are taken to improve k i n e t i c s , such as pre-combustion. Industrial evidence also exists which indicates fuming rates are dependent on blast i n t e n s i t y and slag depth. F a i r l y convincing data i s available which suggests that the process must be run to the fixed carbon content of the coal and that v o l a t i l e matter does not appear to play a s i g n i f i c a n t r o l e which i s d i r e c t l y contrary to the equilibrium model. P i l o t plant and laboratory experiments suggest that coal-slag i n t e r a c t i o n may be a major reaction system. Other experiments reveal that i n t h i s case oxide d i f f u s i o n control might be important. 55 The question of what ro l e equilibrium and k i n e t i c s play i n the process therefore remains. I t i s c r i t i c a l to the develop-ment of slag processing that t h i s issue be resolved. It may open up new v i s t a s or simply quiet nagging doubts. Either way, i t w i l l provide a firm foundation from which further explorations may be made. 5 6 CHAPTER III  OBJECTIVES It i s anticipated from an analysis of the l i t e r a t u r e that k i n e t i c factors are c r i t i c a l to the operation of zinc slag fuming. «The fa c t that k i n e t i c considerations have been treated empirically or ignored i n the past has s t i f l e d possible develop-ment of the process. Only a t h e o r e t i c a l understanding of k i n e t i c s w i l l allow a proper assessment of the pot e n t i a l of slag fuming. The objective of t h i s thesis then i s to determine and study the k i n e t i c s of zinc slag fuming and assess the implications of these r e s u l t s for process improvement. It should be noted that even i f i t i s demonstrated that equilibrium i s achieved, i t i s not necessarily the most desirable operating condition. It i s possible that maximum fuming e f f i c i e n c y i s achieved before equilibrium i s reached or under conditions that are d i f f e r e n t than those which are t r a d i t i o n a l l y considered to e x i s t . I t i s immediately obvious that an analysis of slag fuming ki n e t i c s i s a complex task. The number and variety of k i n e t i c processes taking place i s at least as great as any other pyrometallurgical process. The i n j e c t i o n of the a i r - c o a l mixture involves a two-phase flow through a pipe and the i n t e r a c t i o n of t h i s flow with the l i q u i d slag. The problem i s complicated by the fact that conditions are not isothermal and heat transfer from the slag to the injected mixture w i l l take place. Further-more not only w i l l the coal react with the slag but also with the gas stream. The combustion of coal i s i t s e l f only p a r t i a l l y understood for well defined systems. The evolution of the gas stream as i t r i s e s through the bath i s a matter of speculation. The reaction of coal with slag has never been studied i n d e t a i l . The f i e l d of gas-slag reactions has received l i t t l e attention. The physical and chemical properties of the slag, such as v i s c o s i t y , surface tension, and oxide a c t i v i t y c o e f f i c i e n t s and d i f f u s i v i t i e s , which are l i k e l y to be important to k i n e t i c processes, are poorly known. The melting and freezing behavior of slag on water-jacket surfaces has never been studied. And so on. These, however, are only general observations. Before an attempt can be made to apply what knowledge i s available and define those areas to explore further i t i s necessary to address a series of fundamental questions. The mode of i n j e c t i o n behavior be i t bubbling or j e t t i n g , must be determined before an i n t e l l i - " gent discussion of bath motion or the fate of the coal can be undertaken. The mechanism of slag reduction, whether i t be gas-slag reactions or coal-slag reactions must be elucidated. The behavior of the slag on the water jackets during heating and cooling of the furnace must be investigated. It i s d i f f i c u l t to develop more s p e c i f i c objectives than t h i s because so l i t t l e i s known of the process. Furthermore i n what directions the investigations w i l l lead w i l l l a r g e l y be determined as i t i s conducted. 5 8 One d e f i n i t e conclusion can be drawn however. The study must be primarily conducted on i n d u s t r i a l furnaces. It i s only on an i n d u s t r i a l scale that there would be any hope of i d e n t i -fying process dynamics. Laboratory studies would be premature because the system as a whole i s too imprecisely defined. The major thrust of t h i s thesis has therefore been the ac q u i s i t i o n and analysis of i n d u s t r i a l data. 59 CHAPTER IV EXPERIMENTAL TECHNIQUES As discussed, i t was of primary importance to obtain as much information as possible from operating slag fuming furnaces. . The following sections describe the experimental techniques applied to the ac q u i s i t i o n of i n d u s t r i a l data and the laboratory methods involved i n analysis of slag samples obtained from i n d u s t r i a l sampling. 4.1 Indu s t r i a l Tests As with most i n d u s t r i a l furnaces, observations of process operation must be i n d i r e c t . Because slag fuming i s a batch process, the most important data to obtain i s a record of the manner i n which the slag changes with time as a function of operating variables. Since the process i s concerned with the elimination of zinc from the slag, the basic information required i s the zinc content of the slag as a function of coal and a i r flow rates. 4.1.1 Slag Sampling During The Fuming Cycle The objective of t h i s procedure i s to obtain a comprehensive set of data on a slag fuming cycle. I t i s important therefore that the slag samples accurately r e f l e c t the state of the bath 60 at temperature, p a r t i c u l a r l y the zinc, ferrous and f e r r i c l e v e l s . To accomplish t h i s a water quench was incorporated into the sampling procedure. The following procedure was developed: 1) A sample and an estimate of the amount of slag l e f t i n the furnace from the previous run i s obtained. The sample may either be taken from the l a s t slag flowing out of the furnace at the end of the tap or from a bar sample afte r the tap hole has been closed. 2) A sample of each charge to the furnace, hot and cold, i s taken and an estimate of the weight of each addition made. If t h i s i s impossible a composite would s u f f i c e . 3) Once the run has started the task i s to obtain a series of quenched samples (of several hundred gram size) through the furnace charge port using an iron bar. A 5 m length of 6 mm (1/4 in) s t e e l pipe (the size and length used for lancing the bla s t furnace) serves t h i s purpose well. In addition a 3-4 m length of 100 mm (4 in) channel or angle iron placed to form a trough i s required to prevent contamination of the sample once i t i s taken from the furnace. Also available should be a hose or bucket of water. The procedure i s then to: a) run the length of pipe into the furnace through the charge port u n t i l i t touches the bottom of the furnace. (Because the pipe i s not very r i g i d i t bends i n an arc toward the bottom 1-2 m from the end of the furnace.) See F i g . 4.1. Gas Flue Sampling Bar \ Crane Aisle Tapping Spout Furnace Cross Section in Length Figure 4.1 Schematic of Charge Port Sampling 62 b) l e t i t s i t for roughly 5-10 seconds (or u n t i l ^ 3 mm of slag has frozen onto i t ) and then withdraw i t . c) place the length of pipe with slag into the trough and quench with water from the bucket or hose. d) then break the slag from the pipe and place i t i n a sample bag. Wash out the trough. 4) One sample i s taken immediately"after the l a s t hot pot has been charged, and then one every 10 minutes thereafter into the tapping period. 5) F i n a l l y , as at the beginning, a sample of the heel l e f t i n the furnace i s taken again, either by sampling the l a s t slag in the tap or by a bar sample following the above procedure. A record of operating parameters i s , of course, v i t a l to an analysis of a fuming cycle. The following time-dependent variables were monitored and recorded: a) temperature b) primary bl a s t volume and pressure c) secondary bl a s t volume and pressure d) coal rate e) coal type and composition. Within an i n d u s t r i a l i n s t a l l a t i o n i t i s not always possible to carry out a predefined procedure. It must be recognized that compromises may be necessary. In p a r t i c u l a r the following 63 modifications to the above procedure were made in s p e c i f i c cases: 1) In some operations slag sampling through the charge port i s not f e a s i b l e and quenched tuyere samples must be taken i n -stead. The procedure was b a s i c a l l y the same as for charge port samples except that a 2 m bar was used through a tuyere. 2) It i s not always possible to obtain charge samples and i n these cases at least information on the t o t a l charge weight and make up (hot slag and cold slag) should be obtained. 3) Third, temperature and bl a s t volume measurements are not necessarily made continuously. In these situations at least some 'average' value should be obtained. 4.1.2 Tuyere Back-Pressure Measurements The objective of t h i s procedure i s to measure and record the pressure fluctuations generated by the i n j e c t i o n of the coal-a i r mixture into the l i q u i d slag. It has been established by 81 Hoefele and Brimacombe that tuyere back-pressure d i r e c t l y r e f l e c t s tuyere t i p pressure. A study of the dynamics of i n j e c t i o n can therefore be ca r r i e d out by attaching a high frequency pressure transducer to the back of a tuyere. A low voltage s o l i d state pressure transducer (National - Semiconductor LX1704D) was obtained and calibrated. The transducer i s ^ referenced to the atmosphere and contains a pressure sensitive area on a s i l i c o n chip. A power supply and 6 4 amplifier'operating on 110 line.AC.voltage i s required to use the transducer. An oscilloscope with a screen storage f a c i l i t y (Tektronix Type 564, V e r t i c a l Type 3A3, Time Base Type 564) was used to observe and store the pressure traces. An o s c i l l o -scope camera mount and polaroid camera (Tektronix Camera C-12) were used to photograph stored pressure signals. In order to attach the pressure transducer to the tuyere, a 38.1 mm (1.5 in)-to-6.35 mm (0.25 in) pipe reducing f i t t i n g was attached to the back of the tuyere. A 6.35 mm (0.25 in) pipe-to-tubing adaptor was f i t t e d to the reducer and 6.35 mm (0.25 in) p l a s t i c tubing used to attach the transducer to the adaptor (See F i g . 4.2). 4.1.3 Tuyere Photography The objective of t h i s procedure i s to obtain a v i s u a l record of i n j e c t i o n phenomena. A ple x i g l a s window was placed across the end of a 10 cm length of 38.1 mm (1.5 in) pipe. This was f i t t e d to the back of the tuyere and the valve opened (See F i g . 4.2) permitting a view down the length of the tuyere into the furnace. In order to obtain a clear view i t was necessary to turn o f f the coal to the tuyere. Plastic Tubinq | \/\) Furnace Tranducer —( Secondary Primary Air w , Air And Coal \ Reducing Cable/ Fitting to Power Supply Tuyere Body Cross-Section F i g u r e 4.2 Schematic o f Tuyere Back-Pressure Measurement Technique 6 6 A 1 6 mm Bolex movie camera with a 1 6 to 1 0 0 Vario Switar lens was used at 6 4 frames per second to photograph i n j e c t i o n phenomena. Both colour and black and white f i l m were used and i t was determined that colour f i l m gave the f i n e s t d e t a i l . Grain e f f e c t s were c l e a r l y v i s i b l e with 4 0 0 ASA f i l m . 1 0 0 ASA f i l m at a lens setting of f = 4 , with a shutter speed of 1 / 6 4 second revealedathe most d e t a i l . Attempts to observe the slag surface were not successful. A 3 5 mm single lens r e f l e x camera with a 2 0 0 mm lens was used bn one occasion to take black and white s t i l l s of tuyere t i p accretions. In both cases a tripod was used to s t a b l i z e the camera. Exposure settings were determined i n repeated t r i a l s . 4 . 1 . 4 Tuyere Accretion Sampling The objective of t h i s procedure i s to obtain samples of accretions which b u i l d up at the tuyere t i p . A 9 . 5 3 mm ( 0 . 3 7 5 in) hole was d r i l l e d i n the tuyere window described above. A probe was assembled by placing a 1 . 3 m length of 6 . 3 5 mm ( 0 . 2 5 in) rod inside a i m length of 6 . 3 5 ( 0 . 2 5 in) pipe. 1 5 mm of the end of the rod was bent at a r i g h t angle to form a hook. 6 7 With the probe inserted through the hole i n the window i t was possible to observe the hook and manipulate i t to measure the size and shape of the accretion and take samples. 4.2 Laboratory Methods In order to extract the maximum amount of information from the slag samples obtained during fuming cycle sampling, a number of laboratory methods were used. It was assumed that the quenched bar samples were f a i t h f u l records of the state of the slag at bath temperature. By applying t h i s assumption the slag samples become valuable clues to the operation of the process. 4.2.1 Chemical Analysis of Slag Samples Chemical analysis of the slag samples was performed by the assay labs of Cominco Ltd., T r a i l , B.C. They routinely perform slag analysis for the metals and oxides of i n t e r e s t to t h i s study. Assays for a l l metals (Zn, Pb, Fe, Cu), oxides (CaO, Si02, MgO, A^O-j) and non-metal (S) were done by X-ray emission spectrography. Carbon assays were performed using a LECO analyser. Analysis for ferrous iron was car r i e d out by a wet chemical oxidative technique using potassium dichrpmate. The procedure i s summarized i n Appendix I. F e r r i c iron reported i n the thesis i s the difference between t o t a l iron determined by 68 X-ray analysis and ferrous iron obtained by wet chemistry. Un-certainty i n these re s u l t s w i l l be discussed i n Section 4.3. 4.2.2 Slag Dissolution and P a r t i c l e Extraction This procedure was developed to determine whether or not coal or coke p a r t i c l e s are present i n the slag. The following methods were f i n a l l y adopted: 1) Approximately one gram of f i n e l y ground slag (-100 mesh B.S.S.) i s accurately weighed and placed i n the bottom of a cleaned 125 ml polypropylene b o t t l e . 2) Several drops of water are added to the slag to wet i t . The bottle i s then clamped i n a stand and placed i n a water bath resting on a hot plate. The bottle i s submerged roughly one-quarter of i t s length and angled away from the experimenter at about 20°. The whole assembly i s set up at the back of a fume hood. 3) The water bath temperature i s brought to 80°C and 10 ml of concentrated hydrofluoric acid i s added slowly to the slag. 4) The digestion i s allowed to continue for 30 to 45 minutes over which time the water bath temperature i s increased to 100°C. The bottle should be gently rocked occasionally during t h i s period. This i s best accomplished by s l i g h t l y tipping the whole stand. 69 5) Following digestion i n HF 10 ml of a 2:1 mixture of HCl-HF i s added slowly to the slag. 6) This stage of the digestion i s carr i e d out for 90 minutes in a b o i l i n g water bath. Again occasional s t i r r i n g of the mixture i s undertaken by gentle rocking. 7) At the end of t h i s period 80 ml of 4% boric acid i s added to the b o t t l e . 8) The bott l e remains i n the bath for another 60 minutes, again with occasional s t i r r i n g . 9) After t h i s stage i s complete, the hot solution i s quickly f i l t e r e d through a m i l l i p o r e f i l t e r into a flask under vacuum. A M i l l i p o r e f i l t r a t i o n apparatus was used with a 0.50ym ; Schleicher and Schuell Teflon f i l t e r . The bottle i s rinsed as necessary with d i s t i l l e d water or ethanol. 10) F o l l o w i n g • f i l t r a t i o n , the f i l t e r with residue i s removed and stored i n a p e t r i glass. The above procedure was derived from a study of several - 82-85 references. 4.2.3 Slag Density and Porosity Measurements Measurement of the true density of the slag was undertaken by the procedure outlined i n the ASTM Standard Method of Test for True S p e c i f i c Gravity of Refractory Materials 70 (ASTM Designation: C135 -66) . The method e s s e n t i a l l y measures the amount of water displaced by a known weight of ground sample. The method used i n t h i s study followed the ASTM Standard except that 25 ml pycnometer bottles were used instead of 50 ml bot t l e s . The bottles containing sample and p a r t i a l l y f i l l e d with water were boiled under reduced pressure rather than at atmospheric pressure. The bulk density of bar-quenched slag samples was measured using a water displacement technique. Due to the r e l a t i v e l y high porosity of the slag (approximately 30%) and the fact that both open and closed pores occupied a s i g n i f i c a n t volume i t was necessary to develop a method of coating the surface. It was important to f i n d a way of e f f e c t i v e l y enclosing the open or surface pore volume. This problem was c r i t i c a l because the bubbles of a millimeter or so i n diameter lay broken open on the surface. The most s a t i s f a c t o r y technique found was to wrap the slag samples i n wax. Wax f i l m of a thickness of •0.127 mm (0...005 in),?was used. Often a thinner f i l m , obtained by stretching the standard f i l m , was used. The following procedure was developed: 1) A large piece of bar quenched slag was selected and accur-ately weighed (W1). Due to the f r i a b l e nature of the highly porous slag the largest pieces available were roughly 15 mm x 10 mm x 2.5 mm. ; These pieces weighed roughly 0.2 g. 2) The piece was then wrapped i n the thin layer of wax f i l m . 71 The minimum amount of wax was used, usually s u f f i c i e n t to cover the surface i n one layer only. Care was taken to stretch the wax t i g h t l y across surface pores. 3) The wrapped sample was weighed (V^). 4) The weight of the sample immersed i n water was then measured (W^). This was done by simply suspending a wire weighing basket i n a beaker of d i s t i l l e d water by a th i n wire from the balance arm. This sytem was calibrated with aluminum weights (0.1 and 0.2 gm) to correct for the displacement caused by the immersion of the extra length of suspension wire when a sample i s i n the basket. The correction was expressed as 'k', the displaced weight per unit of measured weight, (gm/gm). 5) The bulk density was then calculated with the formula: S l a g ' b u l k ' W 3(l'+ k) W 2 " W l ' ... (4.D p . p water wax where: W^ ,W2,W3, k are defined above P = density of x Due to the uncertainty i n the measurements and the l i k e l y inhomo-geneity of small slag pieces, at least four d i f f e r e n t pieces were measured i n each case. Slag porosity was then calculated from the above measurements. 7 2 4.2.4 X-Ray D i f f r a c t i o n Analysis In order to analyse the slag for c r y s t a l l i n e components X-ray d i f f r a c t i o n was used. X-ray d i f f r a c t i o n was ca r r i e d out with a P h i l i p s machine (diffractometer type PW 101220, power supply type PW 1011/80). An iron tube (P h i l i p s , type PW 2107/00) was used, normally at a setting of 36 kV and 26 mA. The time constant i n the counting c i r c u i t was set at 2 seconds. 4.2.5 Reflected Light Microscopy Reflected l i g h t microscopy was used to study the physical and c r y s t a l l i n e structure of the slag samples. The slag and contained c r y s t a l l i n e phases were too opaque to examine by thi n section. Slag pieces were mounted i n epoxy. A cycle alternating between vacuum and atmospheric pressure was applied to force epoxy into the open pores. The mounted slag was ground from 80 g r i t to 600 g r i t and then polished, f i r s t with 5 ym diamond paste and then with a 1 ym diamond paste on s i l k . The slags were polished for 2-5 minutes on each cl o t h making slow c i r c u i t s counter to the rotation of the wheel. The surface was then washed i n soap and water and dried with ethanol before viewing. No etching was done. 73 Photomicrographs were taken with a r e f l e c t e d l i g h t camera microscope (Zeiss ULTRAPHOT). 4.3 Accuracy of Chemical Analysis In order to properly assess the re s u l t s of any quantitative c a l c u l a t i o n i t i s necessary to know the uncertainty i n the data. In some cases t h i s i s r e l a t i v e l y straightforward, i n others, very d i f f i c u l t . 4.3.1 E f f e c t of Sulphide on the Ferrous Iron Assay It has been suggested that sulphur dissolved i n slags as sulphide w i l l i n t e r f e r e with the determination of ferrous iron 39 by reducing f e r r i c to ferrous iron during acid digestion. This would occur through the reaction: 2Fe3,+ . + S 2,~ . X 2 F e 2 + , + S° (4.2) (aq) (aq) (aq) 'E° = +1.278 v (reduction potential) Assuming that the oxygen p o t e n t i a l i n the slag i s very low -7 -12 (-.•v-10" Pa (^ 10 atm)) i t i s v i r t u a l l y c e r t a i n that the sulphur in fuming slag- (0 - 2.0%) i s present as the sulphide ion. 7 7 If sulphide ions are st o i c h i o m e t r i c a l l y reduced to elemental sulphur v i a Equation 4.2, the molar r a t i o of f e r r i c iron reduced to sulphur oxidized i s 2. This i s equivalent to a weight r a t i o of 3.5. The e f f e c t therefore can be s i g n i f i c a n t . 74 To assess the e f f e c t of slag sulphide on the ferrous iron assay, a laboratory test was performed. A base slag consisting of 35% S i 0 2 / 20% CaO and 45% m i l l scale was prepared, corres-ponding to the l i m e - t o - s i l i c a r a t i o and lime and s i l i c a l e v e l s found i n t y p i c a l fuming slags. To t h i s mixture was added various reducing agents and sulphides, as summarized i n Table 4.1. The mixtures were prepared and f i r e d simultaneously under s l i g h t l y reducing conditions i n a gas furnace at approximately 1150°C for 15 minutes. Water quenched samples were then taken and analysed for ferrous iron by the procedure outlined i n Appendix I. The res u l t s are given i n Table 4.1. The assay technique shows sa t i s f a c t o r y r e p r o d u c i b i l i t y . It i s evident that when sulphide i s added as pyrrhotite, sulphur has a d e f i n i t e e f f e c t on the ferrous assay, roughly equivalent to that expected from Equation 4.2 (Note that Slag 3 i s an exception.) However, when sulphide i s added as calcium sulphide, the ferrous assay declines s l i g h t l y , roughly equiva-lent to a simple d i l u t i o n e f f e c t . These somewhat ambiguous res u l t s suggest that when sulphur i s present i n a more stable form, CaS (see Table 4.2), i t has no e f f e c t on the ferrous iron assay. Apparently the residence time, at temperature, of the synthetic slag containing pyrrhotite was i n s u f f i c i e n t for the system to come to equilibrium. As observed i n coal p a r t i c l e extraction experiments, acid digestions of fuming furnace slag l e f t residues which contained a s i g n i f i -TABLE 4.1 The Eff e c t of Slag Sulphide on the Ferrous Iron Assay Base Slag: 35% S i 0 2 , 20% CaO, 45% M i l l Scale (Fe Q 8 _ Q gO) Temperature: 1150°C-(values i n percent) SLAG REMARKS CALCULATED SLAG S CALCULATED F e 2 + NO S 2~ WITH S 2~ EFFECT EFFECT * ASSAYED T , 2 + Fe 1 base slag - - - 20.2 20.2 2 + 'FeS1 1.3 21.8 26.4 24.8 24.6 3 + •FeS* 0.7 21.1 23.6 21.8 21.4 4 + CaS 1.0 19.8 23.2 19.1 19.0 5 Fe - 37.6** - 24.8 24.5 6 + Fe +'FeS' i 0.9 25.6 28.3 28.7 28.8 7 + Fe + CaS 0.9 24.5 27.5 20.3 23.4 8 + flour - - - 22.6 22.5 9 + flour +*FeS 1.0 23.7 27.1 26.5 26.8 3+ * 2Fe ** Fe + + s 2 -2 F e 3 + 2 F e 2 + + S° 3Fe 2 + during during acid fusion digestion 'FeS' : Pyrrhotite TABLE 4.2 Free Energy of Formation of Various Sulphides from J5S2 and the Metal Oxide at 1200°C Sulphide AG°, 1200°C kJ MgS 175 FeS 96 CaS 88 ZnS 83 (data from Rosenqvist ) 77 cant number of sulphide p a r t i c l e s . This suggests that under normal fuming conditions, sulphur may simply be t i e d up i n an insoluble form. It has been assumed that sulphur i n lead blast furnace slags has had s u f f i c i e n t time at temperature, to come to equilibrium and that i n the fuming furnace i t i s i n a stable form which does not a f f e c t the ferrous iron assay. The ferrous iron assays re-ported i n the thesis therefore do not have to be corrected for sulphide sulphur. 4.3.2 Uncertainty i n Assay Results In order to determine the uncertainty i n the chemical assays performed, as outlined i n Section 4.2.1, a series of 16 duplicate samples were submitted for analysis. The res u l t s are presented in Table 4.3. The absolute difference of each duplicate and the r e l a t i v e ,difference (absolute difference divided by the mean of the d u p l i -cate) were calculated. The average values for each species are summarized i n Table 4.4 The approximate uncertainty i n each assay is-then plus or minus one half the average r e l a t i v e difference. 2+ The r e s u l t s are acceptable for Zn, S i 0 2 , CaO, Fe and Fe 3+ The uncertainty i n the Fe value i s to be expected because i t i s obtained by the difference of two numbers which are close i n 3+ value. Attempts to assay Fe independently by a reductive TABLE 4.3  DUPLICATE ASSAY RESULTS (Values i n Percent) Al,3 Al,4 Al,5 Al,6 Al,7 A2A,1 A2B,3 A2B,6 Bl,5 Cl,4 Cl,7 C2,3 C2,5 C2,10 C2,14 C2,16 Zn 9.9 9.1 9.5 (?) 9.4(?) 9.2(?) 4.5 2.5 0.8 5.1 5.4 3.4 10.9 9.9 5.7 2.9 2.2 9.6 9.1 8.2 7.2 6.4 4.9 2.4 1.0 5.1 6.1 3.6 10.9 9.7 5.6 2.8 3.3 Pb 0.12 0.08 0.07 0.04 0.04 0.3 0.14 0.05 0.07 0.12 0.13 0.46 0.5 0.07 0.11 0.07 0.1 0.09 0.06 0.05 0.04 0.2 0.1 0.1 0.1 0.1 0.2 0.40 0.3 0.06 0.06 0.3 S _ _ 1.2 1.2 1.2 1.0 1.4 1.4 0.3 0.1 0.03 0.09 0.03 0.6 0.7 0.7 0.7 0.7 1.1 1.3 1.3 1.2 1.3 1.4 0.2 0.2 0.1 0.10 0.1 Fe 24.5 24.5 24.8 25.2 25.1 26.4 24.9 25.2 28.9 33 .0 34.2 27.8 28.4 29.8 30.8 31.1 24.6 23.9 24.5 24.7 24.9 25.5 25.9 26.0 27.3 31.8 32.5 27.7 28.9 29.4 30.1 30.7 F e 2 + 22.0 22.4 22.5 22.9 22.5 24.5 24.8 25.2 25.1 31.5 32.5 21.5 20.5 26.5 27.3 26.4 22.6 22.5 23 .0 23.5 23.5 24.6 25.4 25.3 24.5 3.1.5 32.1 21.2 22.4(?) 26.3 27 .5 25.8 F e 3 + 2.5 2.1 2.3 2.3 2.6 1.9 0.1 0.0 3.8 1.5(?) 1.7 (?) 6.3 7.9 3.3 3.5 4.7 2.0 1.4 1.5 1.2 1.4 0.9 0.5 (?) 0.7 ( ?) 2.8 0.3 0.4 6.5 6.5(?) 3.1 2.6 4.9 SiOj 26.5 26.8 27.1 27.7 28.2 27.8 34.7 36.2 28.3 26.9 27.7 26.1 26.2 29 .2 31.0 31.2 29.6 31.9 31.7 32.3 33.2 29.5 31.0 32.0 31.6 28.2 29.4 28.3 27.4 32.1 34.5 31.1 CaO 18.0 18.4 18.4 18.6 19.0 23.0 23.3 23.9 15.5 13.6 13.7 14.4 14.4 15.4 15.7 15.9 18.8 19.3 19.4 19.7 19.9 22.0 23.0 23.0 16.1 13.6 14.2 15.3 14.8 16.5 17.0 16.0 Al-O, _ _ _ 5.5 6.3 6.4 5.6 5.3 5.6 4.6 4.7 5.4 5.9 5.9 2 3 5.0 5.2 5.1 5.3 5.5 5.4 6.0 6.2 6.3 5.4 5.8 5.1 5.0 6.1 6.6 5.8 C 0.44 0.44 0.33 0.65 0.49 0.65 0.44 0.65 0.38 0.82 0.76 0.16 0.16 0.09 0.16 o.i: 0.21 0.33 0.44 0.44 - - - - - - 0.76 - 0.03 0.03 -(?) Assay Ignored (value i n c o n s i s t e n t w i t h time p r o f i l e ) 0 0 79 TABLE 4.4 Estimated Assay Uncertainty Average Absolute Difference Average:;: Estimated Relative Uncertainty Difference Zn SiO, CaO Fe Fe 2+ 3 Fe + 0.25% 3.0 % 0.74% 0.74% 0.39% 0.71% 7.8% 10.0% 4.1% 2.6% 1.9% 34 % ± 4% ± 5% ± 2% ± 1.3% ± 1% ± 17% 80 assay technique did not give consistent r e s u l t s . Because the f e r r i c l e v e l i n the slag i s low (normally 0-4%) the high l e v e l of r e l a t i v e uncertainty represents only a moderate absolute 3+ uncertainty, e.g. at 2% Fe the uncertainty i s 2% ± 0.35% 3+ (absolute), 1.65% to 2.35% Fe . Admittedly however, the uncertainty i s s i g n i f i c a n t and cannot be ignored i n subsequent discussions. Carbon assays were not found to be very reproducible (See Table 4.3) and thus serve only .as .a q u a l i t a t i v e i n d i c a t i o n of the presence of carbon i n the slag. 4.4 Remarks The a c q u i s i t i o n of i n d u s t r i a l data i s always a d i f f i c u l t task. The problem i s e s p e c i a l l y acute when measurements and sampling are conducted on a comprehensive scale during normal process operation. Often the ideals of research must be compromised and the best job done under conditions well beyond the control of the researcher. As a r e s u l t the data cannot always be complete and may r e f l e c t l i m i t a t i o n s imposed by operating schedules or the plant environment. F i n a l l y i t must be acknowledged that the value of operating parameters, e.g. coal rate, can often only be r e a l i s t i c a l l y obtained by r e l y i n g on normal plant measuring devices. I t i s a question of t r u s t i n g that the indicated lev e l s are correct. This assumption can only be v e r i f i e d by self-consistent r e s u l t s obtained over several runs. 81 'CHAPTER V INDUSTRIAL RESULTS AND PRELIMINARY- DISCUSSION:  EQUILIBRIUM CONSIDERATIONS In order to make a proper assessment of process k i n e t i c s i t i s imperative, as previously discussed, to study i n d u s t r i a l furnaces. I t i s only l o g i c a l that the greater the number of d i f f e r e n t furnaces and operations investigated the more com-prehensive, complete and conclusive w i l l be the r e s u l t s . 5.1 Results Slag samples and operating conditions for 11 fuming cycles at f i v e d i f f e r e n t companies were obtained. The data are pre-sented i n Figures 5.1 to 5.11 and tabulated i n Appendix I I . To avoid the complications introduced by using names, c a p i t a l l e t t e r s A through E are used to designate the d i f f e r e n t companies. The author participated d i r e c t l y i n the sampling of the cycles reported for Company C. In the other cases, with one exception, the sampling was carr i e d out by plant personnel at t h e i r respec-t i v e locations according to the procedure outlined i n Section 4.1.1. The slag samples and data were sent to the author for analysis. As mentioned e a r l i e r , chemical assays of the slags were done by Cominco Ltd., T r a i l , B.C. In the case of Company D 45 the reported data was taken from the l i t e r a t u r e . F i g u r e 5.2 C y c l e A2A, Fuming C y c l e Sampling Data CO 2 5 h 3 7 h 24 23 0.9 0.7 0.5 0.3 CM H i 35 h 33 8 io 6 a> c N >S 4 l 1 1 1 1 r A 2 B SiO, CaO H 1 1 — I \ O / Fe 2 + • A A -- A . / , o — o -Coal rate Zn F e 3 * <f>-r-<fc> <t> <l> <t>-. > 10 20 30 40 Elapsed time (min) XT 50 60 Figure 5.3 Cycle A2B, Fuming Cycle Sampling Data % Fe H-iQ C H (D Ui Ul n <^ o CD w ro <Q O o t—1 (D cn l H -!3 a ft p o p CM o V o c p Ul o o o ro ro ro ro ro ro oi ^ cn cn I I I I I p o % C a O % Z n , F e 3 * * Ul CD 00 I I I I | % S i 0 2 CM CM CM CM OJ m • a •o : co 3 <B U 9) m o> O Si C o a l r a t e ( k g / m i n ) 98 Figure 5 . 6 Cycle B22, Fuming Cycle Sampling Data 00 to OI Oi to — Of W CT) ->J O O O Coal rate (kg/min) J I I _ — ro cn oo o o O o Temperature (°C) 8 8 -rrj C CD CO ro o ro ro % C % F e ro 2 * ro ro CD O p OJ p cn O % C a O * cn cn ro V o Z n . F e 3 * cn a> % S i 0 2 ro n <^ o CD O ro m 3 : a -o iQ <n a O a. •< O — !-• 3 CD <B to 3 OJ 3 ' — M H-3 vQ D fu rt fu 1 ro O o CD O O O ro o o T ro cn — 3 I O < ± _L _L ro GO O J o O J ro T • o J 2 o o \ ~ o . b 1 o 1 a I • 6 a ro V • \ x • • • —I i i • i • o oo jo 5 o o § C o a l rate ( k g / m i n ) 1 I L_ ro O ro o o ro ro ro ro cn oj ro CD oo o K o o o o o ° Tempera ture ( * C ) 68 % Fe 2 * ro 10 M> I—1 n ro o 3 O h-1 1-1 -ro r-h ^ ro e n 3 ro H-3 3 O <Q ro o <^ *» a tn M w (r, cn 0) I i—1 O O r t % C a O q> a> i—i—r % S i 0 2 ro ro CO + DO _L D O T O w CO • O o o o I \ • o \ \ • o \ \ o H C o a l ra te ( k g / m i n ) _ J I I _L (0 o ro ro ro o i o i o o T e m p e r a t u r e (°C) 06 1 *4 H-iQ C H (0 tn r - 1 O o <^ — o M i M H 0) o 3 O to H -(D r+i *1 (D g H 3 ro H-O iQ ft) O —»*< *» o tn i-1 — (D CO CU 3 TJ H H-3 a tu r t o — m o TJ U> CO a. 3 «> 3 3 ro O o o o CD o -si o 1 1 1 1 Ul tn CD CD O tn O tn Coal rate (kg/min) 1 — — ro CD CD O O O O Temperature (°C) T6 93 It should be noted that at Companies B and E i t was not possible to take charge port samples. In these cases quenched bar samples were taken through the tuyeres. A study of the results w i l l show that i n several cases the data i s incomplete. For example, slag bath temperature i s only monitored at operations C and D. The d i f f i c u l t i e s introduced by t h i s problem can i n large part be surmounted by making reasonable assumptions and extrapolating from other operations or the l i t e r a t u r e . F i n a l l y , i t should be noted that i n general the re s u l t s of the slag assays from point to point through each run are s e l f -consistent. This would tend to indicate that both the sampling and assay procedures were not subject to s i g n i f i c a n t random error. Furthermore t h i s i s evidence that the re s u l t s were not unduly sensitive to variations i n quenching times that ' undoubtedly occurred. 5.2 Equilibrium Analysis The precedent set i n the l i t e r a t u r e dictates that any analysis of the data must s t a r t with an examination of the question of equilibrium. If the data supports the assumption of equilibrium, then our task w i l l be b r i e f . There are two areas to be addressed. F i r s t i s the question of whether the slag i t s e l f i s i n i n t e r n a l equilibrium. Second i s whether or not equilibrium fuming rates calculated from the data (operating parameters and slag composition) agree with observed rates. 94 5.2.1 Slag Carbon A survey of the slag assays c l e a r l y reveals that carbon i s found i n every sample. In general, carbon i s present i n fuming slag i n the range 0.1 to 1.0%. The presence of carbon i s a non-equilibrium phenomenon. In order to properly discuss t h i s proposition i t i s necessary to b r i e f l y assess the form which carbon w i l l take i n the slag. At high temperatures, under strongly reducing 2-conditions carbon i s known to dissolve i n slag as C 2 and CN 88 89 ions up to 1.3 wt%. ' It also has been suggested that carbon 2-w i l l dissolve as a carbonate ion (CO ^) under more oxidizing conditions. 89,90,91 F i n a l l v , c a r b o n m a y b e p r e s e n t a s a s o l i d either at saturation or under non-equilibrium conditions. The studies on carbon s o l u b i l i t y as carbide or cyanide ions were performed with CaO-Al 20 3, CaO-Si0 2, and CaO-SiO-A^O-j slags i n the temperature range 1550 - 1725 C. At 1600 C the s o l u b i l i t y of carbon i s s i g n i f i c a n t (>0.1% C) for oxygen p a r t i a l pressures less than 5(10 ^) Pa (5(10 ^ ) atm). Carbon s o l u b i l i t y i s inversely proportional to the square root of oxygen p a r t i a l pressure and also declines with temperature. Fuming furnace slag which contains a s i g n i f i c a n t amount of iron i s i n a s i g n i f i c a n t l y more oxidized state. The minimum oxygen poten t i a l i n t h i s system can be calculated by assuming the slag to be saturated with metallic i r o n . Normally t h i s condition i s 95 not achieved i n practice. However i n t h i s unusual case the _g —13 oxygen po t e n t i a l would drop to 2.2(10 ) Pa (2.2(10 ) atm) assuming N F e Q =0.4 and Y F e Q = 1 and ca l c u l a t i n g v i a the reaction: Fe + h 0 2 t FeO ... (5.1) K i 2 0 0 ° e = 8 - 6 ( 1 ° 5 ) (from F i g . 1.2) This i s an oxygen poten t i a l approximately three orders of magnitude greater than that of the above iron-free slags. Carbon s o l u b i l i t y on t h i s basis would drop to 0.03 wt%. Furthermore fuming furnaces are operated at considerably lower temperatures (1200°C) which--would"also tend to reduce carbon s o l u b i l i t y (by six orders of magnitude based on an extrapolation 89 of the given data) . Both of these arguments imply that carbon s o l u b i l i t y as carbide or cyanide w i l l be n e g l i g i b l e i n fuming furnace slag. As previously mentioned, at higher oxygen potentials carbon may enter the slag as a carbonate ion. Ponomarenko and Kozlov ^ conclude that i n non-ferrous slags at 1550°C i n the — 6 —11 range of oxygen potentials from 2.8(10 ) Pa (2.8(10 ) atm) to — 3 —8 5.1(10 ) Pa (5(10 ) atm) carbon s o l u b i l i t y i s approximately 0.02 wt%. Further the authors state that s o l u b i l i t y i s indepen-91 dent of temperature under these conditions. Pearse studied the s o l u b i l i t y of carbon dioxide i n sodium s i l i c a t e melts at temperatures from 1000°C to,1200 GC. A maximum s o l u b i l i t y of 3% CO 2 at 1O0O"C was found for • the&m"elt composition (Na2©) S i 0 2 96 at 101 kPa (1 atm) C0 2. The s o l u b i l i t y at 1200°C was roughly one-tenth that at 1000°C. Using the free energy of formation of carbonates as a guide (Table 5.1), i t could be estimated that the s o l u b i l i t y of C0 2 i n calcium-iron s i l i c a t e melts should be less than i n sodium s i l i c a t e melts. S o l u b i l i t i e s s u b s t a n t i a l l y less than 0.3% C0 2 are to be expected at 1200°C from t h i s data. Furthermore, considering the low oxygen pote n t i a l of the slag r e l a t i v e to 101 kPa (1 atm) C0 2, a s i g n i f i c a n t reduction i n the dissolved C0 2 i s to be expected as well. The above discussion suggests that for the assayed lev e l s of carbon, the carbon present i n fuming furnace slag must be at unit a c t i v i t y . Based on t h i s fact, a c a l c u l a t i o n can be made of the equilibrium concentration of ZnO, FeO and F e ^ O ^ expected in the slag, using the following reactions: Z n 0 ( s l a g ) + C ( s ) * Z n ( g ) + C 0 ( g ) -..(5.2) F e 0 ( s l a g ) + C ( s ) " F e ( s ) + C 0 ( g ) ...(5.3) Fe,0. + C, . t 3FeO + CO, . ...(5.4) J 4 (slag) ( < 3 ) Free energy data and equilibrium constants taken from F i g . 1.2 are given i n Table 5.2. The maximum a c t i v i t y of ZnO i n the slag w i l l be about -4 6.3(10 ), assuming that gas bubbles of equal p a r t i a l pressures of zinc vapour and carbon monoxide (50 kPa (0.5 atm)) are associated with the carbon. Using a zinc oxide a c t i v i t y 97 TABLE 5.1 Free Energy of Formation of Various Carbonates from Carbon Dioxide and the Metal Oxide at 1200 C A G 1200° C CJ/kg.mole) Na 2C0 3 - 123600 CaC0 3 + 40800 FeC0 3 + 54000 92 (Data from Rosenqvist ) TABLE 5.2 Free Energies and Equilibrium Constants for the Direct Reduction of Iron Oxides and Zinc Oxide Reaction A G1200° C (J) K1200° C ZnO + C t Zn, ,+ CO * (g) -73200 395 FeO + C % Fe + CO -73200 395 F e 3 0 4 + C % 3FeO + CO -115100 12030 (Data from F i g . 1.2) 99 c o e f f i c i e n t of 2> from Kellogg t h i s a c t i v i t y corresponds to about 0.03 wt% Zn. Repeating the c a l c u l a t i o n for Reaction 5.3, assuming the p a r t i a l pressure of carbon monoxide associated with the carbon to be 101 kPa (1 atm) and the a c t i v i t y of iron metal formed to be unity, the equilibrium a c t i v i t y for FeO w i l l be _3 about 2.5(10 ). For an a c t i v i t y c o e f f i c i e n t of FeO of 2 43 2+ (from Kellogg ) t h i s represents approximately 0.1 wt% Fe in slag. F i n a l l y for Reaction 5.4 making similar assumptions and using a F e 0 = 0.5, the equilibrium a c t i v i t y of magnetite w i l l -5 43 be 1(10 ). For an a c t i v i t y c o e f f i c i e n t of 20 (from Kellogg ) t h i s represents 0.00009 wt% F e 3 + . In each of the above cases the equilibrium l e v e l of d i s -solved species i n the:presence of carbon' at unit a c t i v i t y i s at- least two orders of magnitude.; lower than that observed i n • practice. The slag i t s e l f i s obviously not at i n t e r n a l e q u i l i -brium. T h i s . i s , of course, a d i r e c t contradiction of the basic assumption of the equilibrium model. 5.2.2 Equilibrium Fuming Rate Calculations A second test of the thermodynamic model i s to compare the equilibrium fuming rates calculated from the slag composition at each data point with the observed fuming rate at that point. A program was written, as outlined i n Appendix I I I , to calculate the equilibrium gas composition of a c o a l - a i r mixture injected into a fuming furnace slag containing dissolved zinc oxide and 100 ferrous and f e r r i c i r o n . From the gas composition (CO, C0 2, H 2, H20, Zn, N 2, 0 2) the zinc fuming rate and iron oxidation on reduction can be determined. The actual fuming rate at each point was estimated by taking the slope across the point using the points on either side, correcting for changes i n bath weight and i n t r i n s i c fuming rate. Owing to the fact that the assayed points are s e l f consistent and i n a majority of cases, form a smooth, almost l i n e a r curve, the slopes estimated by t h i s method are the same as would be determined from a smoothed curve analy-s i s . At ±4% r e l a t i v e uncertainty, the gross error would range from about ±50% at high zinc concentrations to about ±12% at low zinc concentrations. However the uncertainty i n a smoothed curve tangent estimate w i l l be smaller due to the information provided by other points i n the smoothing process. See Appendix III . In Figure 5.12 the observed fuming rate i s graphed against 43 the equilibrium fuming rate predicted by Kellogg data. The l i n e bn the graph has a slope of one corresponding to exact agreement. I t i s apparent that i n most cases the model under predicts the actual fuming rate. Furthermore there i s no apparent c o r r e l a t i o n at a l l between the two variables. Similar calculations have been performed for the data of Grant and 44 45 Barnett, and Grant, shown i n Figures 5.13 and 5.14 res-44 pectively. The data of Grant and Barnett i n general tends to over predict the fuming rate, even accounting for possible error. Considerable scatter exists i n t h i s c o r r e l a t i o n as well. F i g u r e 5.12 Observed Fuming Rate v e r s u s P r e d i c t e d E q u i l i b r i u m Fuming Rate For C y c l e Sample P o i n t s 4 , (thermodynamic d a t a from K e l l o g g ) Observed fuming rate (kg mole Zn/s) C H (D OJ O fl) H cr rt fD to (D Oi (D n-3* a> n 3 o & K: 3 &> 3 o O O r t M (D o K td a £> I—1 c fD < CD c 3 H - 3 O i CO H -rt 3 tu 13 rt. fD fl) rt (D O 3 O i-i fl> r t P> 3 o> W fl) H 3 fD f t r t H - 3 3 H" rt 3 (0 vQ (D n CO c CO m c 3 c 3 Q CD <n 3 g_ CD N 8 tn » 8 0> 8 D • • C • O CD 00 CD > > > — ro ro — ro ro — c ro ~ to > g o < < > > *» m o o o o - ro - ro - 5 o ZOT *1 C H CD tn » O rt cr (D H 3 0 a-3 ft) tu n cr rt (D in (D DJ (D H- H »fl O < 0 rr ' H fD Cb O •< M C 3 O A 3 o ro H- 3 H-cr » H tu H- rt e ro cu co Cu cu rt 3 fu »rj I—1 rti ro O 3 O Cu 3 rt < rfj rrj ([) O C H - 3 3 H-rt 3 01 cn C 01 tn Observed fuming rate (kg mole Zn/s) m c c 3 Q CD 3 ro N 3 O o ro p o p o cn •8 CD C D • a c • o CD CO CD > > > c ro ro — ro ro — 3 ro — CD > 3 <£> o « < • > m o o o o O «< _ ro - ro - o GOT 104 The r e s u l t s of the Grant model, given i n Figure 5.14 are not any better. This model over predicts almost a l l of the points with considerable scatter, again accounting for error. If these models are b a s i c a l l y correct on average, the scatter should be evenly d i s t r i b u t e d around the drawn l i n e . The 44 re s u l t s of the Grant and Barnett model come closest to approx-imating t h i s . (Fig. 5.13) However, even here, there are a s i g n i f i c a n t number of points spread out across the diagram to the r i g h t of which should be associated with much higher fuming rates. In a l l cases these points would tend to give any regres-sion an almost horizontal slope. In Figure 5.15 the predicted net f e r r i c iron reduction rates of the Grant and Barnett model are graphed against the observed rates. The net reduction rate i s the difference between f e r r i c iron reduction and ferrous iron oxidation. Negative values represent net ferrous iron oxidation. Observed values are the average calculated from instantaneous changes i n measured ferrous and f e r r i c l e v e l s . It i s apparent that more scatter i s evident in these r e s u l t s than i n those for the zinc fuming rate. A considerable number of points l i e o f f t h i s diagram, even farther away from the drawn l i n e which indicates exact prediction. The r e s u l t s of the Kellogg data and the Grant data show no better c o r r e l a t i o n s . 0.0075 0.0050 0.0025 0.0025 0.0050 F u m i n g c y c l e O A l A C I • A 2 A A C 2 © A 2 B V D l • B I T D 2 • B 2 I O E I 8 B 2 2 o B H y T T -0.075 -0.050 -0.025 0J025 0.050 0.075 F i g u r e 5.15 Equilibrium reduction rate (kg moles/s) Observed F e r r i c i r o n R eduction Rate versus P r e d i c t e d E q u i l i b r i u m R eduction Rate Fo r C y c l e Sample P o i n t s 44 (thermodynamic d a t a from Grant and B a r n e t t ) 106 It should be borne i n mind that these models can be f i t t e d to the data as claimed i n the l i t e r a t u r e . This fact i s not i n dispute. What these r e s u l t s imply however^ i s that the f i t t i n g must be done on an i n d i v i d u a l basis, cycle by cycle. As such, the concept of an equilibrium model i s not i n t e r e s t i n g because i t cannot be extrapolated with confidence from operation to operation and perhaps not from cycle to cycle. This suggests that the equilibrium model i s not an accurate representation of the zinc slag fuming process. One i s forced to conclude that either thermodynamic conditions vary s i g n i f i -cantly from one operation to another, or k i n e t i c factors are important. Returning to Figures 5.12 to 5.14, i t i s apparent that there i s a maximum fuming rate which i s independent of the predicted equilibrium rate. Something other than a i r - c o a l - s l a g equilibrium i s c o n t r o l l i n g the process. 5.2.3 Slag Equilibrium It might be argued that i n s p i t e of the evidence for non-equilibrium within the slag, given i n Section 5.2.1, the zinc and iron species i n the slag are i n equilibrium v i a the reaction: 2 F e 2 + + Z n 2 + t 2 F e 3 + + Zn, . ...(5.5) (g) Zinc fuming would r e s u l t from the escape of zinc vapour into any gas phases i n contact with the slag. These might include the tuyere gas stream, the atmosphere above the bath surface and 107 bubbles nucleated within the slag i t s e l f . If Equation 5.5 governs the fuming rate, the following relationships hold: ...(5.6) ...(5.7) and the observed fuming rates should, i n general, be proportional to the weight percent r a t i o term i n Equation 5.7. A graph of the observed fuming rate against t h i s term i s shown i n Figure 5.16. There i s no cle a r r e l a t i o n s h i p between the two variables. Again the fuming rate i s independent of equilibrium. 5.3 Summary The re s u l t s of i n d u s t r i a l sampling i n f i v e operations have demonstrated that the equilibrium model does not re a d i l y en-compass a l l the data. The existence of a maximum fuming rate independent of equilibrium considerations suggests that k i n e t i c factors are c r i t i c a l to the process. 0.020 h 0.015 0.010 0.005 v7 • A A A | _ A O ^ o o ob-»-1000 F u m i n g c y c l e O A l A C I • A 2 A A C 2 © A 2 B V D I • B I T D 2 • B 2 I O E I B B 2 2 a B 2000 12 3000 1 4000 2H~ 2 3~K 2 Figure 5.16 Observed Fuming Rate versus [Fe ] [Zn]/[Fe ] For Cycle Sample Points 109 CHAPTER VI LABORATORY RESULTS AND KINETIC MODEL OF THE PROCESS It i s the tenet of t h i s thesis that the zinc slag fuming process does not run at equilibrium and consequently that a knowledge of k i n e t i c s i s v i t a l to a complete understanding of the process. To remove the assumption of equilibrium, however, i s to pose many questions. The object of t h i s chapter i s to address a l l of these and thereby construct a complete k i n e t i c model. 6.1 Kinetic Conception of the Process The fundamental basis of a correct conception of the slag fuming process i s the observation that carbon i s present i n the slag. This implies that some f r a c t i o n of the coal injected into the furnace ends up i n the slag. This fact has several important consequences. The f i r s t i s that reduction of the slag takes place within the slag bath on s o l i d coal p a r t i c l e s i n the absence of a i r . Second, i f a portion of the coal i s removed from the tuyere gas stream and enters the slag the oxygen to carbon r a t i o i n the tuyere gas stream i s increased. If a s i g n i f i c a n t f r a c t i o n of the coal i s entrained i n the slag, conditions i n the tuyere gas stream w i l l be too oxidizing to e f f e c t any slag reduction and the only reactions taking place w i l l be the combustion of coal and oxidation of ferrous iron 110 in the slag to f e r r i c i r o n . I t i s v i t a l then that the presence of coal i n the slag be confirmed i n a d i r e c t way. Based on the procedure outlined in Section 4.2.2, an e f f o r t was made to extract coal p a r t i c l e s from quenched slag samples. 6.1.1 Coal P a r t i c l e s i n the Slag In F i g . 6.1, 6.2 and 6.3, t y p i c a l p a r t i c l e s from two d i f f e r e n t fuming slags are shown along with t h e i r X-ray spectra. The slag samples were taken at Company C. The slag p a r t i c l e s i n F i g . 6.1 are from sample Cl,7 (Company C, Run 2, Slag Sample #7), and those i n F i g . 6.2 and 6.3 from a d i r e c t l y water-quenched t a i l slag samples (C2,16). Compositions for these slags are given i n Table 6.1. For purposes of comparison, a coal p a r t i c l e and X-ray spectrum are given i n F i g . 6.4. Undigested slag from sample Cl,7 i s presented i n F i g . 6.5. The p a r t i c l e s i n F i g . 6.1, 6.2 and 6.3 are roughly 15 ym i n diameter which i s well within the size range of the coal injected into the furnace (80% -200 mesh BSS, ^ 75 ym). Of more significance however i s the X-ray spectra of these p a r t i c l e s which show an almost complete absence of any element with a greater molecular weight than sodium. Considering the slag assay and the elements l i g h t e r than sodium i t i s d i f f i c u l t to I l l Figure 6.1 Digested Slag (Cl,7) P a r t i c l e (a) Photomicrograph (x2000), (b) X-ray Spectrum 112 Figure 6.2 Digested Slag (C2,16) P a r t i c l e (a) Photomicrograph (x4000) t (b) X-ray Spectrum 113 X (b) Figure 6.3 Digested Slag (c2,16) P a r t i c l e (a) Photomicrograph (x4000) , (b) X-ray Spectrum TABLE 6.1 SLAG COMPOSITIONS fValues In Percent) Cl,7 C2,16 ; Zn 3.4 2.2 Pb 0.13 0.07 S 1.4 0.03 C 0.79 0.11 F e 2 + 32.5 26.4 F e 3 + 0.4 4.7 CaO 13.7 15.9 s i o 2 27.7 31.2 A1 20 3 5.6 5.9 115 Figure 6.4 Digested Kaiser Coal P a r t i c l e (a) Photomicrograph (x2000), (b) X-ray Spectrum 116 F i g u r e 6.5 Undigested S l a g (Cl,7) P a r t i c l e s (a) Photomicrograph (x800), (b) X-ray Spectrum 117 conclude that these p a r t i c l e s are any thing other than carbon. This conclusion i s supported by the analysis of the coal p a r t i -c l e , F i g . 6.4. Further evidence i s the fact that many of the p a r t i c l e s with no s i g n i f i c a n t elemental analysis have surface 'blow holes' and the general appearance of coal p a r t i c l e s which 93 94 have been d e v o l a t i l i z e d . ' See F i g . 6.2. These r e s u l t s , along with the carbon assays v i r t u a l l y comfirm the fact that coal i s penetrating into the slag. I t i s i n t e r e s t i n g to note that the slag carbon p a r t i c l e s show the presence of some sulphur. This r e s u l t was observed to a greater degree i n p a r t i c l e s not shown here and suggests that sulphur i n the slag i s present i n a form which escapes acid digestion. This supports the conclusion drawn i n Section 4.3.1 that the slag sulphur has no e f f e c t on the ferrous iron assay. 6.1.2 Slag Porosity In F i g . 6.6 and 6.7, t y p i c a l cross-sections of quenched slag bar samples are shown. The l i g h t grey area i s slag and the dark grey areas at the edge of the pictures the epoxy matrix. The most rapidl y quenched region i n the samples, that next to the s t e e l bar, i s free of the small white exsolved c r y s t a l s evident over most of the slag cross-section. The black shapes are pores. The pore size ranges from 20 - 500 ym with an average size of about 200 ym. Pores up to 2000 ym are regularly 118 Figure 6 . 6 Cross-Section of Quenched Slag Bar Sample (C2,3) (x50) 119 F i g u r e 6.7 C r o s s - S e c t i o n of Quenched S l a g Bar Sample (C2,3) (x50) 120 observed i n the slag samples. The presence of pores i n the rapidly quenched region c l e a r l y indicates that small bubbles exis t i n the l i q u i d slag. If a coal p a r t i c l e 40 ym i n diameter, consisting of pure carbon, i s converted to CO gas at 1200°C, a bubble 1000 ym i n diameter w i l l be formed.- Thus the bubble size found i n the slag i s approximately that which would be expected to r e s u l t from the reaction of a coal p a r t i c l e with the slag. The fa c t that i n general, only smaller bubbles are seen i n F i g . 6.6 and 6.7 may simply be a function of the greater tendency larger bubbles have to r i s e - out -.of the bath-. In Table 6.2 the porosity of the slag over three d i f f e r e n t fuming cycles i s presented. In each operation i t i s evident that the slag i s r e l a t i v e l y porous i n agreement with the large -f r a c t i o n of the cross-section i n F i g . 6.6.and 6.7 occupied by bubbles. The average bubble size expected from the break up of the tuyere gas stream can be calculated by several methods. Using 95 the formula derived by Turkdogan from water modelling studies. -1/3 j, d b «>-0i053p^ a 2 • ... (6.1) the expected bubble size should be 6000 ym. (A value for surface -1 8 0 tension of 0.33 Nm was used, taken from Suzuki et a l .) It TABLE 6.2 SLAG POROSITY THROUGH THREE FUMING CYCLES (values i n %) Cycle Cycle Sample A l BI C l No. 1 16.0 44.7 31.8 2 16.7 •41.9 30.2 3 21.1 49.6 30.2 4 27.4 48.7 32.5 5 29.1 47.1 33.0 6 34.2 34.8 7 28.9 34.9 8 28.2 26.7 9 26.3 122 i s obvious that t h i s i s i n excess of the size observed i n the slag. The presence of coal or 'char' p a r t i c l e s i n the slag and the porosity of the slag i t s e l f both confirm that coal i s pene-tr a t i n g into the slag. In order to gain an understanding of how t h i s may be taking place, tuyere back-pressure measurements were made on the fuming furnace at Company C. 6.1.3 Tuyere Phenomena In F i g . 6.8 a pressure trace sequence during the charging of a fuming furnace i s shown. In each photograph the v e r t i c a l scale i s gauge pressure from zero at the bottom horizontal to about 83 kPa (12 psi) at the top. The time i n t e r v a l i n each case i s 2 seconds. In the empty furnace, F i g . 6.8a, the pressure trace i s constant at about 8 kPa (1.2 psi) indicating that the flow i s i n a j e t t i n g regime. ^1/96 j ^ f t e r 19 T of l i q u i d slag have been charged c e r t a i n i n s t a b i l i t i e s are found i n the flow, F i g . 6.8b. This indicates a predominantly j e t t i n g regime with only a minor amount of bubbling. At 39 T charged, the flow i s pre-97—100 dominantly bubbling, F i g . 6.8c. By the time the furnace i s f u l l y charged, F i g . 6.8d, the average back-pressure i s about 33 kPa (4.2 psi) and the bubbling regime i s well developed. The bubbling frequency i s r e l a t i v e l y constant at 5 bubbles per second. 83 (b) w K H D fS O CQ Oi D CO « < W PH Figure 6.8 Tuyere Back-Pressure Measurement Sequence, (a) Empty Furnace/ (b) 19T Charged, (c) 39T Charged, (d) 352T Charged. Blast at 300 Standard m /min 124 •«= 2 s > Figure 6.8 Tuyere Back-Pressure Measurement Sequence, (a) Empty Furnace, (b) 19T Charged, (c) 39T Charged, (d) 352T Charged. Blast at 300 Standard m /min 125 A pressure trace over a f i v e second period i s shown i n Fig. 6.9. Over t h i s more representative time the bubbling f r e -quency i s 6 bubbles per second and quite regular. In F i g . 6.10 t y p i c a l pressure traces with coal to the tuyere and without coal to the tuyere are compared. In both cases the bubbling frequency i s the same. However, i n the case with the coal flow, the average pressure i s about 4 kPa (0.6 psi) greater than i n the absence of coal i n j e c t i o n . This may simply r e f l e c t the additional pressure required to carry the two-phase mixture the length of the tuyere. Bubbling behaviour and bubbling frequencies measured, using the pressure transducer, were confirmed by tuyere photo-graphy. Several papers i n the l i t e r a t u r e report on model studies of gas-solid i n j e c t i o n into l i q u i d baths. The major emphasis of these papers i s the quantitative e f f e c t of the presence of p a r t i c l e s on i n j e c t i o n behaviour. In each case, however, penetration of the p a r t i c l e s into the l i q u i d was observed and i s evident i n the photographs presented. Un-fortunately no quantitative assessment of the extent of p a r t i c l e entrainment was made. In general however, i t was found that greater entrainment of p a r t i c l e s occurred i n those cases where the p a r t i c l e was wetted by the l i q u i d . - ^ l - 1 0 - * I n tests made 102 by Farxas and Robertson using horizontal i n j e c t i o n , ' i t was found that i n a bubbling regime p a r t i c l e s tended to just hrj H-iQ C fD cn VD C C n K (D (D O H O fD 3 Ch W PJ H O 3 ^ (+ I (D t) H H < (D P> Ul M tn K fD s fl) (II tn 11 fD ft GAUGE PRESSURE KPa co Ui ui cn 127 128 penetrate the interface and then r i s e up i n a column p a r a l l e l to the r i s i n g bubbles. In addition, non-wetted p a r t i c l e s tended to c l u s t e r and clump together a f t e r entering the l i q u i d . Thus the conclusion reached e a r l i e r that coal penetrates into the slag of the fuming furnace i s consistent with the res u l t s of physical modelling. In f a c t , the idea that none of the coal would enter the slag i s rather unreasonable. A schematic representation of the expected tuyere phenomena i s shown i n F i g . 6.11. If entrained coal i s to be a s i g n i f i c a n t reaction s i t e i n the slag fuming process a s i g n i f i c a n t f r a c t i o n must penetrate the gas-slag interface. The work of O'Malley et a l 1 0 5 and 106 Apelian et a l allow an assessment to be made of t h i s phenomenon. 105 O'Malley et a l give the following formula, based on an energy balance for the c r i t i c a l diameter of a p a r t i c l e s that can penetrate through a gas - l i q u i d interface at a 90° impact angle. 8a cos 8 d P 2 v p • P P-... (6.2) In order to perform the c a l c u l a t i o n , values must be found for each of the variables. The surface tension, a, i s about — 1 8 0 0.33 Nm as reported by Suzuki et a l . According to the available information coal p a r t i c l e s , d e v o l a t i l i z e d coal 1 2 9 Bubble schematic Figure 6.11 Schematic of Tuyere Phenomena 130 107 108 p a r t i c l e s and graphite are not wetted by slag. ' The wetting angle, 6/ i s e s s e n t i a l l y 180°. The density of a _3 bituminous coal i s approximately 1500 kg m although a cert a i n v a r i a t i o n can be expected between p a r t i c l e s i n a pulverized 109 sample. The v e l o c i t y of the coal p a r t i c l e s i n the coal-a i r stream injected into the furnace i s d i f f i c u l t to estimate. Measurements made by Ghosh and Lange and Engh et a l ~*"^ 3 i n physical models have shown s o l i d v e l o c i t i e s to be about half of the gas v e l o c i t y . Although loadings (mass r a t i o of s o l i d flow to gas flow) were of the order of that encountered i n the fuming furnace, 0.1-1.0, the size of the piping i s s i g n i f i c a n t l y smaller. In studies performed on the pneumatic transport of coal i n 2.54 cm (1 in.) l i n e s 111 p a r t i c l e v e l o c i t i e s were found to l i e within 8 0% of the gas v e l o c i t y . Using the information i n Table 1.1, the gas v e l o c i t y i n a fuming furnace tuyere should be 100-200 ms 1 . Assuming that the v e l o c i t y of coal p a r t i c l e s that emerge from the tuyere i s equal to the gas v e l o c i t y and constant as the p a r t i c l e crosses the diameter of the tuyere bubble, the minimum p a r t i c l e size to penetrate the slag at v p = 100 ms - 1 i s d p = 0.2 um. If a p a r t i c l e v e l o c i t y of 50 ms 1 i s used, d p = 0.7 ym. Since i n a 80% -200 mesh (B.S.S.) v i r t u a l l y a l l of the p a r t i c l e s w i l l be larger than 109 1 ym , t h i s c a l c u l a t i o n would predict that a large f r a c t i o n of the injected coal could penetrate the slag. Once i n the slag, due to the high wetting angle, c l u s t e r i n g should occur. I t w i l l be assumed that p a r t i c l e s c l u s t e r together to form the equivalent of 80 ym p a r t i c l e s . 131 This c a l c u l a t i o n assumes two things. F i r s t , that the coal p a r t i c l e s survive t h e i r passage across the bubble without burning. Second, that t h e i r v e l o c i t y i s unchanged i n t h e i r passage across the bubble. The f i r s t assumption i s of obvious importance. The time required for the i g n i t i o n of pulverized c o a l - a i r mixture injected 112 xnto a small heated enclosure was measured by Ghosh and Orning. They measured i g n i t i o n time for bituminous coals as a function of furnace temperature, coal to a i r r a t i o , p a r t i c l e size, and coal composition. For conditions which most nearly match those i n the fuming furnace tuyere bubble, an i g n i t i o n time of about 30 ms was obtained. The i g n i t i o n temperature of several bitum-113 mous coals was measured by Finney and Spicer as a function of p a r t i c l e size and coal composition. In most cases a minimum i g n i t i o n temperature of 6 00°C was found. Assuming that a single 80 ym coal p a r t i c l e - s i t s i n the centre of a spherical tuyere bubble, heated exclusively by radiation, the time required to reach the i g n i t i o n temperature i s about 350 ms. For d e t a i l s see Appendix IV. The order of magnitude difference between these two figures may be due to more rapid heating of the coal p a r t i c l e s i n the actual furnace. This might r e s u l t from the entrainment of hot gases into the injected c o a l - a i r stream. Since t h i s condition i s probably a more accurate representation of conditions i n the fuming furnace, the lower figure w i l l be used. 132 If approximately 30 ms are to pass before i g n i t i o n , a coal p a r t i c l e moving at 50 ms ^ w i l l t r a v e l 1.5 m. The maximum spherical bubble diameter at a fuming furnace tuyere w i l l t y p i c a l l y be ^ 0.6 m (bubbling frequency of 6 per second). Considering the tendency for bubbles to r i s e and extend v e r t i -c a l l y during formation 81,97,100 ^ e a c t u a ^ distance across a tuyere bubble may be s i g n i f i c a n t l y less than 0.6 m. Since the distance the p a r t i c l e w i l l t r a v e l before i g n i t i o n i s larger than the bubble diameter, there i s a reasonable p r o b a b i l i t y that the coal p a r t i c l e w i l l survive i t s passage across the bubble. With regard to the second assumption, i t can only be suggested that the j e t of coal and a i r entering the tuyere bubble i s not s i g n i f i c a n t l y disrupted by the entrainment of gases from the bubble and maintains i t s momentum rig h t across the bubble. This assumption i s q u a l i t a t i v e l y supported by the pictures taken by Farias and Robertson and Engh et a l . In these cases the incoming tuyere j e t , within the bubble, c l e a r l y pene-trates across the tuyere bubble. An energy balance on coal p a r t i c l e s which penetrate the interface indicate that t h e i r depth of penetration i s less than the p a r t i c l e radius. P a r t i c l e s would therefore be subject to almost cert a i n r e j e c t i o n back into the tuyere gas stream. However i t must be noted that the coal p a r t i c l e s impinging on the slag interface do not arrive d i s c r e t e l y , but i n a constant stream. As a r e s u l t the p a r t i c l e s at the interface may be pushed further 133 i n t o , t h e s l a g . In a d d i t i o n , as observed by F a r i a s and Robertson and o t h e r s , the s o l i d s stream may f o r c e a bubble cone to extend i n t o the s l a g d i r e c t l y a c r o s s from the tuyere (see F i g . 6.11). T h i s r e g i o n , c o n t a i n i n g a h i g h f r a c t i o n of c o a l , may be broken o f f from the bulk of the bubble a t detachment and the c o a l en-t r a i n e d i n the s l a g . The c o a l would then r i s e v e r t i c a l l y i n a column p a r a l l e l t o the tuyere gas stream. 6.1.4 Other I n d u s t r i a l Processes F i n a l l y t h e r e i s evidence of c o a l entrainment i n l i q u i d 114 baths i n two d i f f e r e n t i n d u s t r i a l t e s t s . Wijk and M e l l b e r g s t u d i e d (a) the c a r b u r i z a t i o n of molten i r o n by the i n j e c t i o n of c o a l i n argon and, (b) the d e c a r b u r i z a t i o n of molten i r o n by the i n j e c t i o n of magnetite i n argon, and (c) c o a l g a s i f i c a t i o n by i n j e c t i o n o f c o a l and oxygen i n t o molten i r o n . In cases (a) and (b), the s o l i d p a r t i c l e s were found to e n t r a i n i n the molten metal and r e a c t d i r e c t l y w i t h the l i q u i d . Wijk and M e l l b e r g conclude t h a t i n a r e a c t o r , two zones are formed: the bulk of the bath and a ' j e t ' r e g i o n c o n s i s t i n g of a r i s i n g column of gas and accompanying l i q u i d . The p a r t i c l e s i n j e c t e d with the gas r e s i d e i n t h i s r i s i n g l i q u i d zone and r e a c t w i t h the bath as they r i s e , the r a t e of r e a c t i o n being c o n t r o l l e d by d i f f u s i o n i n the l i q u i d phase. Rummell d e s c r i b e s the development and o p e r a t i o n of a molten s l a g - c o a l g a s i f i e r . In t h i s p r o c e s s , p u l v e r i z e d c o a l i s 134 ga s i f i e d by i n j e c t i n g i t into a molten slag bath. The gasifying medium, steam or carbon dioxide, i s injected into the slag through a separate tuyere. The fac t that g a s i f i c a t i o n proceeds indicates that the coal i s entrained i n the slag and i s carr i e d into the reaction d i r e c t l y or i n d i r e c t l y with the gasifying medium. Carbon was also observed i n slag assays. The inescapable conclusion of t h i s analysis i s that a s i g n i f i c a n t portion of the coal injected into the furnace i s entrained i n the slag. Having established t h i s fundamental concept i t simply remains to construct the detailed quantitative model. In fact, the whole k i n e t i c model follows d i r e c t l y from t h i s point. 6.2 A Kinetic Model of the Process The basic k i n e t i c e f f e c t i n the zinc slag fuming process i s the :partitioning i-of the^coal -.between the. slag bath"and the tuyere gas stream. This separation establishes two d i s t i n c t reaction zones: (a) a region of d i r e c t reaction between entrained coal and the slag, and (b) the tuyere gas stream. 6.2.1 The Entrained Coal - Slag Reaction Regime Coal which penetrates into the slag bath w i l l enter a r i s i n g column of l i q u i d slag. This fact i s evident from e a r l i e r 135 discussions, as well as several references i n the 116—118 l i t e r a t u r e . The hydrodynamics of i n j e c t i o n i n the slag fuming furnace should e s t a b l i s h two bath c i r c u l a t i o n c e l l s . Slag should be drawn up by the r i s i n g bubbles against the furnace wall, move across the bath surface to the centre and then descend and move out to the walls along the bottom. Coal p a r t i c l e s which enter the slag at the tuyere l e v e l w i l l be carried to the surface i n t h i s flow during which period they w i l l react with the slag, enclosing themselves i n a gas envelope. As these secondary, coal-formed bubbles move along the surface layer they w i l l r i s e and break the surface, emptying t h e i r contents into the atmosphere above the bath. This scenario i s i l l u s t r a t e d i n F i g . 6.12. The analysis of the fate of the entrained coal then involves modelling (a) the reaction of the coal with the slag, and (b) the residence time of coal i n the bath. 6.2.1.1 The Coal P a r t i c l e - Slag Reaction Given that coal p a r t i c l e s injected into the furnace impact the gas-slag interface at half t h e i r i g n i t i o n time or le s s , i t w i l l be assumed that they undergo no reaction before t h i s point. In most operations the pulverized coal i s injected without drying. I t w i l l be assumed that the coal powder dries as i t crosses the bubble and that t h i s moisture becomes part of the tuyere gas stream. 136 Fig. 6.12 Entrained Slag Coal Reaction Sequence 137 At the instant the coal p a r t i c l e penetrates the gas-slag interface i t i s subject to very rapid heating due to the d i r e c t contact.with the slag. This w i l l r e s u l t i n v i r t u a l l y instantaneous p y r o l y s i s . The behaviour of coal p a r t i c l e s during pyrolysis i s very complex. The products of pyroly s i s vary from H 2 to organic tars, depending on coal composition, heating rate, f i n a l temperature, pressure and the residence time of v o l a t i l e s 93 94 around the p a r t i c l e . ' The reaction i s poorly understood. 94 Wen and Dutta suggest that for rapid heating to high temper-ature (1200°C i n 1 to 10 ms) the products of pyroly s i s are almost e n t i r e l y gaseous with l i t t l e tar production. The gas tends to contain a s i g n i f i c a n t percentage of unsaturated hydro-carbons such as ^2^2 ( a k ° u t 20%), i n addition to R^, CO, CH^ and C 2H g. It would be impossible to properly account for pyroly s i s in the context of the slag fuming process. I t w i l l be assumed that i n p y r o l y s i s , (a) a l l proximate v o l a t i l e hydrogen i s released as H 2, (b) a l l proximate v o l a t i l e nitrogen i s released as N 2, (c) a l l proximate v o l a t i l e oxygen reacts with v o l a t i l e carbon to form CO, and (d) the remaining proximate v o l a t i l e carbon p r e c i p i t a t e s on the char p a r t i c l e . Following p y r o l y s i s then a d e v o l a t i l i z e d coal p a r t i c l e or char p a r t i c l e surrounded by an atmosphere of H 2, CO, and N 2 resides i n the slag. This char p a r t i c l e - gas envelope system or secondary bubble then starts: to react with the slag. 138 The reaction system which develops i n schematically i l l u s t r a t e d i n F i g . 6.13. Because conditions are very reducing at the bubble interface both zinc oxide and f e r r i c oxide w i l l d i f f u s e to the bubble where they w i l l be reduced by H 2 or CO. The CO2 generated by the reduction reactions ZnO, + CO t Zn, . + C0 o ...(6.3) (si) (g) 2 F e2°3(sl) + C 0 * 2 F e 0 ( s l ) + C 0 2 ...(6.4) w i l l d i f f u s e through the gas phase to the surface of the char p a r t i c l e where i t w i l l react v i a the Boudouard Reaction to produce CO: C0 2 + C t 2C0 ... (6.5) The p a r t i a l pressure of Zn and C0 2 and H 20 w i l l therefore gradually b u i l d up i n the bubble and the char p a r t i c l e w i l l shrink as the bubble i s swept upward by the bath. Equation 4.6 was d e l i b e r a t e l y written i n terms of Fe-^O^ rather than Fe^O^. I t i s considered that f e r r i c ions tend to 2- 4- 119 form complexes such as F e 2 0 4 or F e ^ 0 ^ i n slag. 3+ 2+ Because Fe i s a smaller xon than Fe and also has a higher charge, i t has a strong tendency to surround i t s e l f with oxygen ions. Thus, on a mechanistic basis the d i f f u s i o n of f e r r i c ions i s not l i k e l y to be accompanied by the co-diffusion of ferrous ions. Particle reaction model F i g . 6.13 Slag-Char P a r t i c l e R e a c t i o n System £ I 140 The fact that a secondary bubble reaction system exists i s supported by the evidence of electron microprobe analysis. Radial zinc and iron concentration p r o f i l e s around quenched slag bubbles are shown in F i g . 6.14 and 6.15. In both cases, d e f i n i t e d i f f u s i o n gradients are present for both species, i n -dicating the bubbles are not at equilibrium with the slag, but are a c t i v e l y reacting. I t w i l l be assumed that electron transfer through the slag v i a the F e 3 + / F e ^ + couple plays no role i n the reduction of F e 3 + i r o n . Measurements of the e l e c t r i c a l conductivity of FeO-CaO-S i 0 2 melts under reducing conditions (certainly present i n the v i c i n i t y of the secondary bubble) suggest that about 90% of the A 4- • . . . 120,95 _ . 121 • 4 . U l t , conduction i s i o n i c . Grievson reviews the r e s u l t s of several studies of the reduction and oxidation of Fe 0-Feo0-. x 2 3 containing melts which conclude that the rate c o n t r o l l i n g process i s the d i f f u s i o n of iron oxide. F i n a l l y , even i f electron transfer i s s i g n i f i c a n t , reduction must s t i l l be accom-panied by the d i f f u s i o n of oxygen which may then be the rate c o n t r o l l i n g step. As discussed i n the coal p a r t i c l e - s l a g reaction system des-cribed, there i s also mass transfer of species within the bubble gas phase. It i s important to assess whether or.not t h i s i s an important rate c o n t r o l l i n g step i n the reaction. In order to address t h i s question, the structure of the secondary bubble must be established. If a rather large coal p a r t i c l e (d^=74 ym, a b F i g . 6.14 R a d i a l S l a g C o n c e n t r a t i o n P r o f i l e s F r o m S l a g B u b b l e S a m p l e ( C l , 5 ) (x 600 ) (a) Z i n c (b) I r o n 143 200 mesh B.S.S.) reacts to form a bubble consisting of H 2 and equal amounts of Zn and CO consuming a l l the carbon, the bubble diameter w i l l be about 2.5 mm at 1200°C. Using a slag density -3 -1 of 3900 kg m and a slag surface tension of 0.33 Nm gives the bubble an Eotvos Number of 0.7. 2 Eo = 4gApr b / a ...(6.6) The terminal r i s e v e l o c i t y of the bubble w i l l be about 2.8 cm/s, according to Stoke's Law: t e r m i n a l = ^ 4 A p / 1 8 v ...(6.7) -1 -1 122 This i s assuming an average slag v i s c o s i t y of 0.5 kg m s The bubble Reynolds Number w i l l therefore be 0.5 Re = 2prfc)Vj_)/y ...(6.8) 123 According to C l i f t et a l under these conditions, the secondary bubbles w i l l behave as r i g i d spheres. Considering that the bubble diameter and v e l o c i t y w i l l , on average be less than the extreme values chosen above, t h i s conclusion i s sound. For r i g i d spheres i n creeping flow, according to C l i f t et , 123 _ a l , for species j : Shj = 1 + (1 + Pe..) 1 / 3 ... (6.9) where Pe i s the Peclet Number; Pe. = 2r,v,/D. ...(6.10) 3 b b' j and Sh i s the Sherwood Number; Sh. = 2k .r,/D . ... (6.11) 3 3 b' j 144 Equations 6.9, 6.10 and 6.11 can be solved for the mass-transfer c o e f f i c i e n t , using a bubble v e l o c i t y obtained from Equation 6.7. The Sherwood number changes from an i n i t i a l value of 2 to about 50. According to C l i f t et a l for r i g i d spheres i n creeping flow the following c r i t e r i a apply for mass transfer control for species j : (a) i f H (Dj / D^ 1)^ >> 1 ...(6.12) there i s external (slag phase) resistance control for short times, (b) i f H (Dj / D? 1) >> Shj ...(6.13) there i s external (slag phase) resistance control for long times, where b s i H = C. / C. at equilibrium ...(6.14) 3 3 and time i s dimensionless time, defined by the equation: •T = D1? t/r. 2 ... (6.15) 3 b These c r i t e r i a are not immediately applicable to the complex reaction system under analysis here. However, i t i s only i n th i s simple form that any attempt at a l l can be made to answer t h i s question. Thus, to simplify the problem, i t w i l l be assumed that Equation 6.16 defines the equilibrium ZnO, + C % Zn, , + CO ...(6.16) (si) ^ (g) and that the 'equilibrium' gas composition at any moment i s 50% zinc vapour and 50% CO, throughout the bubble. At 1200°C, a system pressure of 101.4 kPa (1 atm) and. 8 wt% zinc i n the 145 slag, H- w i l l be 8.5(10 4 ) . The d i f f u s i v i t y of zinc vapour i n CO can be evaluated by 95 Chapman - Enskog theory. Using data from Turkdogan t h i s -4 2 i s 3(10 )m /s. As w i l l be discussed l a t e r , the d i f f u s i v i t y -10 2 of zinc i n the slag phase w i l l be about 2(10 )m /s. For short times (T<1) H ' Ezn / DE> H ' 1-° t < 2,ys For long times (T>1) H D k / D s l _ 1 275 Zn ' Zn t > 2ys Thus for short times which are t r i v i a l there probably w i l l be some form of consecutive control. For long times which com-prise the entire l i f e of the bubble, i t appears that since Equation 6.13 i s marginally s a t i s f i e d , the reaction system w i l l be under slag phase d i f f u s i o n control. In addition to these considerations i t should be remembered that the bubble w i l l contain several s o l i d char p a r t i c l e s which i n a l l • probabibilty w i l l riot s i t stationary..; at the centre: of the bubble. The motion of these" p a r t i c l e s i n the bubble w i l l serve to enhance i n t e r n a l mass transport. 146 A simple model of t h i s system can now be developed. In addition to the assumptions discussed above, i t w i l l be assumed that: a) the char p a r t i c l e i s spherical, b) the char p a r t i c l e reacts only with CG^, and c) the system i s isothermal at bath temperature. 3D ID There are eight unknown, time dependent quantities, , C-,^ , ID ID ID ID C/-^ . i c u i c u of C„ , r and r, . In order to simplify the 2 2 2 2 ^ mathematics, three additional variables w i l l be introduced. These are Wp, the weight of the char p a r t i c l e , Vg, the volume of the bubble gas; and G, the molar amount of carbon i n the char p a r t i c l e . Eleven equations can be developed. 6.2.1.1.1 Zinc Balance The mass transfer of zinc oxide to the bubble can be empirically characterized by the equation: AZnO = A b kZnO ( CZnO " CZnO } ...(6.17) Since zinc vapour i s not consumed or generated i n the bubble, t h i s i s simply equal to the rate of zinc accumulation i n the bubble gas phase: 3D ID * 7 n n = d ( ° Z n V = Vff d C Z n + C d V ...(6.18) Z n 0 dt g - d f - Z n dt 147 thus ; dC Zn dt V r, b dV nZnO " CZn — 3 -dt ... (6.19) 6.2.1.1.2 CO Balance No CO enters or leaves the bubble. CO i s consumed by reactions 6.3 and 6.4 and generated by the"Boudouard Reaction, reaction 6.5. Thus rCO,cons nZnO + n F e 2 0 3 "CO,gen = 2 BG ... (6.20) ...(6.21) where B i s the Boudouard Reaction rate i n kg mole/kg mole^s. Equating t h i s to the CO accumulation term gives dC dt CO = _1 V 2 B G - »ZnO " * F e , 0 , " CCO ^ g • 1 6 dt ...(6.22) 6.2.1.1.3 C0 2 Balance S i m i l a r l y to the CO balance: rC0 2,cons B G ... (6.23) rC0 2,gen nZnO + n F e 2 0 3 ... (6.24) and dC CO 2 = — V dt AZnO + A F e 2 0 3 " B G " C C 0 2 ^ 2 dt (6.25) 148 6.2.1.1.4 H2 Balance Since instantaneous i n t e r n a l mass transfer and in t e r n a l gaseous equilibrium are assumed, the concentration of H,, and H 20 respond i n s t a n t l y to changes i n the concentration of CO and C0 2 by the reaction CO + H 20 H 2 + C0 2 K. P P H2 C Q 2 P P CO H 20 r b _b H2 C 0 2 c b c b UCO^H20 ... (6.26) ... (6.27) If H i s the t o t a l molar quantity of H 2 released as v o l a t i l e s , then and V C„ + V C„ rt = H g H 2 g H 20 C = H - C UH„0 V„ 2. g 2 ... (6.28) ...(6.29) Substituting Equation 6.29 .into 6.27 gives H - C H. CC0 K3 'CO, D i f f e r e n t i a t i n g and solving for d C„ gives: H2 ... (6.30) dt 149 dC H. dt r b „ b _ b U C 0 2 CC0 2 CCO 3 r b K C 0 2 3 l V g dt b 3 - K3 CC0 ^ g ' dt CC0 o CC0 K 3 H dV 2 c v _ 2 d t . (6.31) 6.2.1.1.5 H 20 Balance As discussed above, a balance on H 2 can be performed, Equation 6.28. D i f f e r e n t i a t i n g • t h i s equation-and solving for dC H Q gives dt dt dt c»2 + c " 2 ° J ^ ! a V dt ... (6.32) 6.2.1.1.6 N 2 Balance Since nitrogen does not p a r t i c i p a t e i n any reactions and dC b dt dt -C N 0 dV dt (6.33) ... (6.34) 150 6.2.1.1.7 Bubble Radius Based on the assumption of spherical geometry, the gas volume can be written as: V g = 4/3 i r r b 3 - 4/3 T t r p 3 ... (6.35) dr D i f f e r e n t i a t i n g and solving for b gives dt dr b = dt 4ir dt dt ...(6.36) 6.2.1.1.8 Char P a r t i c l e Radius The radius of the char p a r t i c l e i s d i r e c t l y related to the weight of the p a r t i c l e 4/3 ir.r W ...(6.37) It w i l l be assumed that the char p a r t i c l e density i s the same as the coal density. D i f f e r e n t i a t i n g y i e l d s dr 1 = dt 4Trr 1 dW .. (6.38) o - dt c 6.2.1.1.9 Char P a r t i c l e Weight Assuming that the char p a r t i c l e loses weight at a rate 151 proportional to the rate of the Boudouard Reaction dW E dt -BG ;s 1- (12.01) . (6.39) where s-^  i s the- char'particle weight (carbon+ash) to 7weight of-contained carbon a f t e r p y r o l y s i s , and (12.01) i s the molecular weight of carbon. 6.2.1.1.10 Gas Volume The gas volume i s changing as a function of the reduction reactions and the Boudouard Reaction r = 2n„ _ + 2BG g,gen ZnO r = n„ ^ + BG g,cons ZnO ... (6.40) ... (6.41) Therefore 2"znO + 2 B G " ( AZnO + B G ) = dt and dV = dt pg nZnO + B G ...(6.42) ... (6.43) where p .^ i s the gas molar density at temperature. 6.2.1.1.11 Char P a r t i c l e Carbon The carbon of the char p a r t i c l e i s consumed by the Boudouard Reaction, thus 152 g | = -BG ....(6.44) 6.2.1.1.12 I n i t i a l Conditions In order to solve the above system of equations i t i s necessary to e s t a b l i s h the i n i t i a l conditions. The i n i t i a l gas composition and volume of the bubble i s calculated, assuming equilibrium i n Equations 6.26 and 6.5, _ and performing a mass balance on the v o l a t i l e oxygen, hydrogen and nitrogen. This gives f i v e equations i n f i v e unknowns, C C k , C „ b , C „ b , cj3. The i n i t i a l zinc vapour concen-2 2 2 2 t r a t i o n i s assumed to be zero. Once the gas composition i s known the i n i t i a l gas volume, V , can be calculated. The i n i t i a l char p a r t i c l e weight and i n i t i a l carbon content of the char p a r t i c l e then follow from a carbon balance. The i n i t i a l values of r and r, can then be found, p b 6.2.1.1.13 Thermodynamic Quantities Thermodynamic data i s required to evaluate the equilibrium constants for the various reactions involved as well as the a c t i v i t y c o e f f i c i e n t s of relevant slag species. The reactions and free energy data used i n the thesis are given.in Table 6.3. To calculate n Z n Q , i t i s necessary to determine the i n t e r -f a c i a l concentration, C^nQ. I t i s assumed that Q i s the TABLE 6.3 Thermodynamic Data for Reactions, AG=AH-TAS Reaction AH AS , Reference (J) JK" 1 1 ZnO + CO t Zn + c 0 2 179300 ^113.1 95 2 Fe 20 3+(3-2/x)CO t (2/x)Fe xO+(3-2/x)C0 2 8870 _36.0 95,124 3 H20 + CO t H 2 + C0 2 -33470 -29.4 95 4 C0 2 + C ? 2CO 166570 171 95 5 (2/x)Fe xO + (1.5-l/x)0 2 t F^2°3 -291300 -130 124 6 (3/x)Fe xO + (2-1.5/x)0 2 t F e 3 0 4 -312200 ; -125 124 7 c + o 2 t c o 2 -395350 0.544 95 8 C + Js02 t CO -114390 85.75 95 9 H 2 + 3202 t H20 -247500 -55.9 95 10 Zn + Js02 t ZnO -460240 -198.3 95 154 s l a g c o n c e n t r a t i o n i n e q u i l i b r i u m w i t h the bubble gas composi-t i o n v i a " E q u a t i o n 6.3. : T h i s • e s s e n t i a l l y - a ssumes•that'reaction k i n e t i c s a t the i n t e r f a c e are instantaneous. Thus P P K± = Z n C 0 2 ... (6.45) and then PCO aZnO VznO NZnO - F Z n P C ° 2 ...(6.46) s i n c e N. = C. / p , ...(6.47) P P Zn CO- p .,. , n v c i _ 2 . ^ s l f m ...(6.48) To c a l c u l a t e C ^ n 0 the e q u i l i b r i u m constant K^, as w e l l as p s l m a n d YZnO m u s t ^ e f ° u n c ^ ' T n e e q u i l i b r i u m c o n s t a n t , , can be o b t a i n e d from Table 6.3. The s l a g molar d e n s i t y , p , , ^ 1 ' sl,m' can be c a l c u l a t e d from the s l a g d e n s i t y and the s l a g composition. The v a l u e o f the a c t i v i t y c o e f f i c i e n t , Y Z n 0 * i s more d i f f i c u l t to o b t a i n . 45 Grant has reviewed the l i t e r a t u r e on the a c t i v i t y co-e f f i c i e n t o f z i n c o x i d e . He r e p o r t s v a l u e s o f 0.1 to 5.6 wit h a m a j o r i t y o f the s t u d i e s showing the va l u e t o l i e i n the range 0.8 to 3.0. A study o f the l i t e r a t u r e has r e v e a l e d o n l y s e v e r a l 155 125—127 125 papers to be useful. The data of Azuma et a l was 126 in good agreement with Richards and Thorne and s l i g h t l y 127 higher than that of Fi l i p o v s k a and B e l l . . This may be due to the use of lower oxygen potentials i n the work of Fil i p o v s k a and B e l l . Because the more oxidizing conditions i n the work of Azuma et a l most cl o s e l y simulate the conditions i n the fuming furnace, t h i s data was selected. A regression analysis of t h e i r data gave the following equation for the a c t i v i t y of zinc oxide as a function of the molar l i m e - t o - s i l i c a r a t i o (S) in the slag at 1200°C: YZnO = 1 , 0 6 ( S ) + 1 , 8 8 ...(6.49) In order to incorporate the temperature dependence of the a c t i v i t y c o e f f i c i e n t i t was assumed that the temperature dependence i s the same as that of FeO below an a c t i v i t y of 0.6, 119 as derived from Bodsworth for the CaO-FeO-Si0 2 system. Then; l n v _ 16400 (S)-12000 In Y Z n 0 - rji - 10.7(S) + 8.8 ...(6.50) This equation gives the a c t i v i t y c o e f f i c i e n t a value of 2.4 at 1200°C at a molar l i m e - t o - s i l i c a r a t i o of 0.5. The thermodynamics of the f e r r i c - f e r r o u s system i n the slag i s s i g n i f i c a n t l y more complex. F i r s t , the composition of iro n oxide, l i q u i d or s o l i d , i n equilibrium with m e t a l l i c iron 77 119 i s non-stoichiometric, i . e . Fe 0. ' The equilibrium oxide composition contains a c e r t a i n f r a c t i o n of f e r r i c ions. For 156 example, i n a slag containing 2 0 wt% CaO, 4 0 wt% S i 0 2 , and 40% 'iron oxide', i n equilibrium with m e t a l l i c iron , the 'iron oxide' portion w i l l be 1.4 wt% F e 2 0 3 , 38.6 wt% FeO or 119 F e 0 984°* Since the l e v e l of f e r r i c iron found i n the fuming slag i s 0-4 wt% (See F i g . 5.1-5.11) i t i s apparent that the l e v e l of f e r r i c iron as non-stoichiometric iron oxide may therefore be s i g n i f i c a n t . The reduction Equation 6.5 must therefore be rewritten -as: Fe.,0,. + (3-2/x)CO t (2/x)Fe 0 + (3-2/x)CO- ...(6.51) z J ( s l ) x z If x = 1 then t h i s s i m p l i f i e s to Equation 6>,.5. The reduction of f e r r i c iron involves the transfer of f e r r i c iron ions to the secondary bubble surface and the trans-fer of the ferrous ions produced back into the bulk of the slag: n F e 2 0 3 = - A b k F e 2 0 3 s i i C F e 2 0 3 - C F e 2 0 3 . (6.52) and nFe O '~ " Ab kFe O x x s i i c - c Fe 0 Fe 0 x x . ... (6.53) As discussed e a r l i e r , what Equation 6.53 suggests i s : not' . s t r i c t l y v a l i d , i . e . that there i s a co-diffusion of f e r r i c and ferrous ions i n a single compound. This however, i s the best solution to a d i f f i c u l t problem because i t accounts for 15 7 the equilibrium bath f e r r i c - f e r r o u s l e v e l automatically. To attempt to work with stoichiometric FeO creates problems because the standard state for thermodynamic data i s defined as the non-stoichiometric compound. Furthermore the error involved in t h i s approach i s not large because the value of x i s close to 1. According to Bodsworth x should be i n the range of 0.96 to 0.99. Fuming slags generally contain ^5 wt% A l 2 0 3 which w i l l tend to associate with CaO and ' a c i d i f y ' the melt. This w i l l increase x because the presence of F e 3 + ions i s s t a b i l i z e d by CaO which forms stable calcium f e r r i t e s . It w i l l be assumed that x i s 0.99. In order to account for the coupled d i f f u s i o n of f e r r i c and ferrous ions, Equations 6.52 and 6.53 must be combined to derive the value of n -. required for the model. From F e 2 ° 3 Equation 6.51 n F e 0 = ( 2 / x ) n F e 9 0 , x 2 3 ...(6.54) and 2/x p(3-2/x) FeO C0 2 (3-2/x) aFe 20 3 PCO ... (6.55) In terms of concentrations and slag molar density K 2 Y F e 2 ° 3 2/x (2/x-l) 'si ,111 'FeO p (3-2x) . 2/x 'CO. CO 'Fe 0 x ' F e2°3 .. . (6.56) 158 Substituting Equations 6.53, 6.54 and 6.56 into 6.52 gives n. F e 2 ° 3 A b k F e 2 0 3 , s i ' F e2°3 V C 0 2 PC0-1 (3-2/x) (2/x) n 0.. s i 2 3 C UFeO kFeO A b 2/x -| . . (6.57) This equation was solved i t e r a t i v e l y using an i n i t i a l estimate at x = 1. To calculate K 0' values are required for Y„ _ and Yr, ^-2 ^ 'Fe203 'FeO The a c t i v i t y c o e f f i c i e n t of Fe 0 was developed from Bodsworth 127 X 2 6 Richards and Thorne and Fili p o v s k a and B e l l . From these sources the a c t i v i t y c o e f f i c i e n t should have a value of 1.95 at 1200°C at S = 0.5. 1]-9,127 T n e l i m e - t o - s i l i c a r a t i o 119 127 dependence of the a c t i v i t y c o e f f i c i e n t i s 0.71. ' Thus at 1200°C 119 Y P E 0 = 0 . 7 K S ) + 1.59 ...(6.58) The temperature dependence of Y F e Q was derived from the data of Bodsworth for a F e Q>0.6. This y i e l d s In Y F e Q = 3300(S) + 1660 - 1.89(S) - 0.64 ..(6.59) referenced to the pure non-stoichiometric s o l i d . 159 The only discussion of the a c t i v i t y of f e r r i c iron i n these 43 slags i s provided by Kellogg. equation for Y „ _ N * e3 U4 Kellogg gives the following l n y F e 3 ° 4 8495 - 2653 This can be converted to a value of l n y F e 2 ° 3 ...(6.60) , assuming that either of the t h e o r e t i c a l iron couples, i n the slag F e x O ~ ^e2^3 or Fe O - Fe-.0. would exert the same oxygen p o t e n t i a l . From (2/x) Fe xO + (1.5-l/x)0 2 t F e 2 ° 3 (3/x) Fe O + (2-1.5/x)0 2 F e 3 ° 4 ... (6.61) ... (6.62) equating oxygen potentials gives: 2/x 2/x v v N K rFe 90, = YFeO,l FeO,l 5 N F e 2 ° 3 r Y F e 3 ° 4 N. F e 3 ° 4 3/x 3/x FeO ,2 NFeO,2 K, (1.5 - 1/x) -] (2 - 1.5/x) (6.63) where K,- i s the equilibrium constant of Equation 6.61 and Kg the equilibrium constant of Equation 6.62. N p e o l ^ e mole fr a c t i o n Fe 0 that would be associated with the f e r r i c compound F e 2 0 3 i n the slag. N p e o 2 "*'s *"ne mo-'-e f r a c t i o n of Fe xO that would be present i f the other f e r r i c species was Fe^O^. 6.2.1.1.14 Mass-Transfer C o e f f i c i e n t s To calculate n„ ^, and n„ _ , i t i s necessary to calculate ZnO F e ^ ^ the mass-transfer c o e f f i c i e n t s k Z n Q ^p eo a n c ^ -^pe O ' As 160 discussed above the bubble reaction system w i l l behave as a r i g i d sphere and therefore the mass-transfer c o e f f i c i e n t s can be obtained from Equations 6.7 and 6.9-6.11. A l l terms i n these equations can be evaluated as a function of model variables and values of physio-chemical properties used above. It remains then to f i n d appropriate d i f f u s i v i t i e s . Unfortunately there i s l i t t l e information on the values of d i f f u s i v i t y i n slags i n general and even less on i n t e r r d i f f u s i -v i t i e s . No studies have been conducted on lead b l a s t furnace slags. There are several studies on the d i f f u s i v i t y of iron 77128—132 in slags, ' but none on zinc. The behaviour of zinc can then only be estimated by suggesting that since i t has an 2+ • • 133 i o n i c radius equal to Fe (r 2+ ~ 0.75 A, r 2+ = 0.75 A) Fe Zn i t w i l l have s i m i l a r d i f f u s i o n properties. This i s of l i t t l e assistance because measurements of iron d i f f u s i v i t i e s vary over three orders of magnitude. 128 Mori and Suzuki found values of iron i n t e r - d i f f u s i v i t y of 5(10~ 9) <m2s_1 to 4(10~ 8) m 2s _ 1 i n iron oxide melts at 1500°C. They suggest that i n s i l i c a t e melts with large anions such as 4-SiO^ , the i n t e r - d i f f u s i v i t y should be s i g n i f i c a n t l y lower. 129 Borom and Pask measured the i n t e r - d i f f u s i v i t y of iron i n sodium d i s i l i c a t e glass over the range 900°C to 1100°C. They found values of about 2(10 - 1 1) m 2s - 1 for FeO at 1100°C i n t h i s system. In general i n t e r - d i f f u s i v i t i e s for cations such as 2+ 2+ Ca and Fe are believed to l i e i n the range 161 -11 — 9 2 — 1 77 5(10 ) to 5(10 )-Tin^s . According to Richardson , as a f i r s t approximation i n complex systems, i n t e r - d i f f u s i v i t y may be equated to the s e l f - d i f f u s i v i t y of the more rapidly 2+ 2+ difussing species. Assuming that Fe and Zn are e s s e n t i a l l y similar and the most rapidl y d i f f u s i n g species i n the slag then 2+ the s e l f - d i f f u s i v i t y of Fe i n iron calcium s i l i c a t e slags w i l l be the best estimate of the i n t e r - d i f f u s i v i t y that can be made. Agarwal and Gaskell ^~3® have measured the s e l f - d i f f u s i v i t y of iron i n a CaFeSi0 4 melt over the range of 1250°C to 1540°C. This system i s the closest to the lead b l a s t furnace slag which has been investigated. T.hey obtained the following equation * 2-1 for D p e (in m s ) log Dp* = 5450±620 - 1.93 ±0.37 - 4 ...(6.64) The s e l f - d i f f u s i v i t y at 1200°C i s 2.3(10 1 0 ) m 2s - 1. This value l i e s i n the middle of the expected range of i n t e r -d i f f u s i v i t i e s . Furthermore, the ac t i v a t i o n energy i n t h i s equation i s 105 kJ which i s i n reasonable agreement with the activ a t i o n energy determined for i n t e r - d i f f u s i v i t y by Borom and Pask: 125 kJ. F i n a l l y , t h i s value i s within the range of 132 quasibmary i n t e r - d i f f u s i v i t i e s measured by Ukyo et a l . For these reasons i t w i l l be assumed that Equation 6.64 gives the i n t e r - d i f f u s i v i t y of FeO and ZnO i n fuming furnace slag. 1 6 2 The reaction of f e r r i c i r o n i n the.slag has been written i n terms of F e 2 0 ^ . T ^ e on^-Y reference to the i n t e r - d i f f u s i v i t y of Fe20^ i s given by Borom and Pask. In t h e i r study they found the i n t e r - d i f f u s i v i t y of Fe20^ to be almost exactly one-tenth the i n t e r - d i f f u s i v i t y of FeO. Having nothing else to go on, t h i s r e l a t i o n s h i p was assumed to apply i n the fuming furnace slag. A value one-tenth that calculated by Equation 6.64 was used. 6.2.1.1.15 Boudouard Reaction Rate The f i n a l term i n the model to evaluate i s the Boudouard Reaction rate, B. Reviews of the l i t e r a t u r e have been done by 94 134 Wen and Dutta and Skxnner and Smoot . Both of these papers emphasize the almost completely empirical nature of measurements of Boudouard Reaction rates. Measured rates are sensitive to measurement techniques, p a r t i c l e size, system temperature and pressure, residence times and a host of other variables. Thus, although there i s a wealth of information available, very l i t t l e of i t i s d i r e c t l y applicable to the p a r t i c l e reaction model. 134 The most useful data i s given by Skinner and Smoot for bituminous coal char of a 'pulverized' size (70% through 200 mesh). The rate equation i s f i r s t order i n the quantity of carbon l e f t unreacted and C0 2 p a r t i a l pressure B = AQexp(-E.a/RT) ( P C Q ) ...(6.65) 16 3 where A q = 3.13(10 ) kg*mole kg'mole kPa s E a = 196200 kJ kg-mole - 1 for the case defined above. Unfortunately there i s l i t t l e to compare t h i s to. The value of the a c t i v a t i o n energy and pre-exponential constant are reasonable i n terms of other data for coals of t h i s r e a c t i v i t y . Because of the paucity of information these values w i l l be used for a l l bituminous and sub-bituminous coals. 6.2.1.1.16 Model Solution The model described above i s an i n i t i a l value problem i n a system of ordinary d i f f e r e n t i a l equations. This was solved using a fourth order Runga-Kutta technique with error control developed by the University of B r i t i s h Columbia (U.B.C.) Computing Centre. A double p r e c i s i o n form of the routine was used. 6.2.1.2 Secondary Bubble Residence Time The char particle-bubble system continues to react with the slag according to the model developed i n Section 6.2.1.1 u n t i l i t reaches the surface of the slag. By t h i s time i t s v e l o c i t y r e l a t i v e to the slag should be s u f f i c i e n t to carry i t to the surface where i t s contents w i l l be released into the atmosphere above the bath, as i l l u s t r a t e d i n F i g . 6.12. The residence time of the secondary bubble obviously w i l l be an 164 important factor i n determining the extent to which the char p a r t i c l e i s consumed and the amount of zinc oxide reduced. To make an estimate of the residence time, a slag bath geometry shown i n F i g . 6.16 was considered. The tuyere gas stream i s assumed to r i s e up the furnace wall i n a column the width of which i s defined by the diameter of the tuyere bubbles. The tuyere bubbles are assumed to heat to bath temperature rapidly and reach t h e i r maximum diameter at the tuyere. The volume of the tuyere bubble i s therefore V., = ET , tb s i .. . (6.66) U T b l f where E i s the blas t flow rate and U i s the number of furnace tuyeres. And ltb 6V t b 1/3 ... (6.67) If the porosity of the tuyere gas column, e^ ., and the porosity of the bath, e , , are known, then a volume balance on the slag i n the furnace w i l l give the expected bath height, h: M ( 1 - £ s l ^ s l =' L(W-2d t b)h + 2 (l - e t ) d t bhL Thus h = M ( l - e s l ) p s l L (W-2.fet d t b ) ...(6.68) 165 L T u y e r e g a s c o l u m n S l a g (a) Top view w ——H (b) Cross section F i g u r e 6.16 Secondary Bubble Residence Time Geometry 166 Assuming that on average, the secondary bubbles leave the slag half-way through t h e i r passage across the slag bath surface (See F i g . 6.16), the secondary bubble path length, p, i s ... (6.69) If the v e l o c i t y of the slag bath i s , v then the secondary bubble residence time i s S r e s = p / v s l ••• ( 6-P., = h + W. - 2d t b To calculate t , i t i s necessary to evaluate f, e. , e ^ res' •* ' t ' s i and v ,. The bubbling frequency, f, has been measured and as S X discussed i n Section 6.1.3 i s roughly 6 bubbles per second. The porosity of the slag i t s e l f , e ,, has been measured and the r e s u l t s reported i n Table 6.2. An average value of the porosity i s roughly 0.30. The porosity of the tuyere gas column i s not as r e a d i l y available. I t probably w i l l be greater than 0.30. The expected radius of tuyere bubbles at slag temperature i s roughly equal to the spacing between tuyeres. The tuyere bubbles therefore can be expected to overlap. In addition the bubble diameter i s roughly half of the calculated bath height. This suggests that i f the bubbles r i s e very rapidly a f t e r detachment from the tuyere, the tuyere column porosity should be be about 0.5. Since the r i s e following detachment i s not instantaneous, the porosity i s perhaps greater since the bubble i s resident i n the zone longer. A two-dimensional array of close packed bubbles w i l l have a porosity of 0.60. This value 167 f a l l s into the expected range but i s not high, and w i l l be used i n the c a l c u l a t i o n s . F i n a l l y , the bath v e l o c i t y must be known. As with the porosity of the gas column, no measurements of t h i s parameter have ever been made. From the calculations of Ashman et a l 117 118 and others ' i t can be safely concluded that v . i s of J s i the order of 1 m/s. The probable range of bath c i r c u l a t i o n v e l o c i t y i s 0.5 to 2 m/s. I t w i l l be assumed that v , i s J s i 1 m/s as an average of t h i s range. For a furnace 4.5m long by 2.5 m wide, containing 45 T of slag at 1200°C with a bl a s t of 300 standard m3/min blowing through 3 0 tuyeres, t h i s c a l c u l a t i o n gives a residence time of 2.4 seconds. This appears to be an e n t i r e l y reasonable estimate. The model of the coal-slag reaction regime i s now complete. It has been assumed that a l l of the coal entrained i n the slag at the tuyere l e v e l leaves the bath when i t reaches the surface. The fact that the charge port sampling reported i n the thesis reveals coal p a r t i c l e s and secondary bubbles with slag d i f f u s i o n gradients c l e a r l y indicates that a cert a i n amount of the coal c i r c u l a t e s through at least one complete cycle of the furnace c e l l . To account for t h i s phenomenon would introduce a degree of complexity that may not be warranted and cannot be immediately j u s t i f i e d . As stated above, i t w i l l , be assumed that t h i s 16 8 f r a c t i o n of the coal i s negligible-.---6.2.2 Kinetics i n the Tuyere Gas Stream Coal which i s not entrained i n the slag but remains i n the tuyere gas stream w i l l be subject to combustion. The f a c t that some coal penetrates into the slag means that the oxygen to f u e l r a t i o i n the tuyere gas stream i s increased. If the f r a c t i o n of entrained coal i s s i g n i f i c a n t then there may be an excess of oxygen present. However, even i f t h i s i s not the case the oxygen p o t e n t i a l w i l l be high. Under these conditions i t i s u n l i k e l y that reduction of the slag w i l l take place. Instead there probably w i l l be oxidation of the ferrous iron according to Equation 6.61. In addition, of course, there w i l l also be the combustion of coal. The combustion of coal i s a very complex phenomenon and a thorough analysis of submerged combustion i s well beyond the scope of t h i s t h e s i s . As discussed e a r l i e r the i g n i t i o n time of coal i n the tuyere bubbles might be expected to be of the 113 order of 30 ms. At a bubbling frequency of 7 per second, the bubble i s resident at the tuyere for about 14 0 ms. Combustion therefore should be well under way before the bubble detaches. Following detachment the bubble r i s e s rapidly to the surface and during the process, breaks up into smaller bubbles. The maximum residence time for the c o a l - a i r mixture under t y p i c a l conditions might be 280 ms (calculated from the analysis 169 in Section 6.2.1.2). 13 6 According to Essenhigh p a r t i c l e s i n the size range of pulverized coal have a combustion time of the order of 1 second. 137 Hottel and Stewart present data showing,pulverized coal combustion to complete i n 500 ms. They also indicate that under c e r t a i n conditions combustion may be only 90% complete 138 in 300 msv Other work tends to support these figures. Although no d e f i n i t e conclusions can be drawn from t h i s analysis i t does suggest that the assumption that combustion of coal i n the tuyere gas stream i s complete by the time the mixture leaves the surface of the bath, i s probably not correct. This has been v e r i f i e d by plant sampling at Company C. In addition to oxide fume, the slag fuming process produces two minor products: b o i l e r ash and flue " c l i n k e r 1 . Together ash and c l i n k e r make up about 5 to 10% of the t o t a l output. As shown i n Table 6.4, i n a t y p i c a l cycle a l l three products contain carbon. A c e r t a i n amount of coal passes through the bath and a c e r t a i n f r a c t i o n of t h i s escapes combustion to end up i n the fume, ash and c l i n k e r . As confirmation of t h i s , the presence of burning coal i n the fl u e from the furnace has been observed by the author. TABLE 6.4 Composition of Fuming Furnace Products, Cycle C41 (values i n %) Fume Ash Clinker Zn 46 38 48 Pb 29 29 21 s i o 2 0.6 2.3 4.4 Fe 0.1 1.3 4.6 Cd 0.7 1.2 0.2 As 0.5 0.5 0.2 C 1.3 1.48 0.21 171 Slag fuming furnace product samples were taken for seven d i f f e r e n t runs. Measurements of i n i t i a l and f i n a l bath compo-s i t i o n and coal rate for each of these runs allowed a mass balance to be performed around the furnace. The col l e c t e d data and d e t a i l s of the mass balance are presented i n Appendix V. Due to uncertainties i n the assays and a lack of knowledge of the r e l a t i v e amounts of the products, the balance could not be closed p r e c i s e l y . However the mass balance could be solved for the range of coal carry over into the products. The r e s u l t s of t h i s analysis are presented i n Table 6.5. The column t i t l e d "% Coal Carry Over as Coal" represents the coal carry over required to account for the carbon balance. The "% Coal Carry Over as Coal and Coal Ash" i s the coal carry over required to account for the s i l i c a - t o - i r o n r a t i o i n the fume r e l a t i v e to the slag, as well as the carbon balance. The r e s u l t s suggest that about 3% of the coal passes unconsumed through the furnace d i r e c t l y into the products. About 10% of the coal as coal and coal ash passes through the bath to be combusted i n the f l u e s . The alternative assumption that coal ash from coal-slag reaction or submerged combustion could escape the scrubbing action of the bath i s unreasonable, due to the a b i l i t y of the slag to wet the ash. As the coal p a r t i c l e - s l a g reaction model (Section 6.2.1.1) can be used to show^nder normal circumstances the coal entrained i n the bath i s completely consumed before i t leaves the bath surface. Therefore, the coal which passes through the bath must be TABLE 6.5 Mass Balance Calculation of Coal Carry Over Cycle % Coal Carry Over As Coal % Coal Carry Over As Coal & Coal Ash Min. Max. Min. Max. C41 1.9 2.7 10.4 18.5 C42 4.3 5.1 20.4 31.1 C43 2.9 3.3 12.3 18.3 C44 2.6 2.9 13.5 26.9 C51 2.8 3.8 6.7 10.7 C52 3.8 4.6 4.2 8.1 C53 3.3 3.8 5.6 8.1 173 associated with the tuyere gas stream. Given that a portion of the coal i s entrained i n the slag and a portion of remaining tuyere stream coal passes unreacted out of the bath, a considerable excess of oxygen w i l l be present i n the tuyere gas stream. For t h i s reason i t w i l l be assumed that the coal which does burn i n t h i s zone burns completely to CC>2 and E^O. As mentioned e a r l i e r , the oxidation of ferrous to f e r r i c iron w i l l be the other major reaction taking place i n the tuyere stream. 6.2.3 Wall E f f e c t s The t h i r d dynamic zone of the furnace i s the water-jacketed wall. Because temperature changes i n the bath r e s u l t in melting and freezing of the slag from the wall, the wall plays a role i n the composition-time p r o f i l e s observed during furnace operation. Furthermore the water-jacketed walls represent a s i g n i f i c a n t thermal burden on the process and therefore an important consideration i n the bath heat balance. Unfortunately l i t t l e i s known of the behaviour of a water-jacketed wall i n a slag bath. I t i s not known whether the melting-freezing of slag i s e n t i r e l y a thermal phenomenon or i f i t involves chemical reactions and equilibrium phase pre-c i p i t a t i o n . Only a few experimental studies have been 139 140 performed. ' These have been done simply to measure 174 heat transfer c o e f f i c i e n t s and no microscopic examination of the frozen slag was made. To avoid a l l of these problems i t w i l l be assumed that temperature changes i n the bath are s u f f i c i e n t l y slow that the wall responds i n a quasi-steady state manner. In addition i t w i l l be assumed that the wall melts and freezes a constant slag composition. This avoids the problem of modelling a continuously varying slag layer composition. This refinement could be made when the phenomenon i s better under-stood. The heat transfer from the slag bath to the frozen slag layer has been characterized by the empirical equation q = h.A (T ,-T ) ^ t s l mp ... (6.71) where T i s the slag melting point 3,43,44,139 By performing a steady state heat balance on the furnace wall, the following equation can be developed for^the thickness of the slag layer l s l g s l t C - T mp w s l mp d s t g s l (6.72) g st where g i s thermal conductivity and T^ i s the temperature of the water i n the water jacket. See Appendix VI. To solve t h i s equation several parameters must be evaluated of which g -, , h. and T are c r i t i c a l . Values of g , and h. 3 s l t mp ^ s l t reported i n the l i t e r a t u r e are given i n Table 6.6. Because the frozen slag-bath interface i s highly s t i r r e d , heat transfer should be i n the high end of the range quoted for h . A value TABLE 6.6 Heat Transfer Parameters 1 Reference g s l w/m-K h t  w /m2-K 3 1.67 615 43 1.26 404 139 1.24 325 141 — 335-500 176 of 600 w/m^ -K was assumed. An intermediate value of slag thermal conductivity, 1.5 w/m-K was assumed. In order to avoid p o t e n t i a l problems i t w i l l be assumed that s u f f i c i e n t slag i s present on the wall i n i t i a l l y , to supply whatever melting takes place. The conductivity of the 142 steel i s about 50 w/m-K. A ste e l thickness, d s t r of 1 cm w i l l be assumed. The term 1 d g t ^ s l ^ s t ' ^ s n o t l i n P O r t a n t because i t i s about two orders of magnitude smaller than the other term i n Equation 6.72. The question of the slag melting point i s d i f f i c u l t to resolve. I t would be legitimate to hold that the single-valued property T i s not a v a l i d concept. As a f i r s t approximation however, i t i s j u s t i f i e d because the empirical heat transfer, Equation 6.71, was i n i t i a l l y used to derive h^ from measured data. The '.melting point' of the slag has been established to be i n the range 1100°C to 1150°C. 43 o Kellogg uses a value of 1125 C. This value i s consistent with the CaO-FeO-Si0 2 ternary and other data and therefore, w i l l be used. The temperature of the cooling water w i l l be assumed to be 50°C. This i s not a c r i t i c a l parameter. 177 It remains to determine what the composition of the wall slag normally i s . A sample of wall material taken during an accidental shutdown of a fuming furnace at Company C was s p l i t v e r t i c a l l y and the inner and outer sections assayed separately. The t o t a l frozen wall thickness was about 2.3 cm. This i s consistent with Equation 6.72 which gives a thickness of 2.7 cm for a bath temperature of 1225°C. The assay r e s u l t s are given i n Table 6.7. In t h i s sample there appears to be no s i g n i f i c a n t v a r i a t i o n through the thickness. This supports the idea that the frozen slag layer has a homogeneous composition. The most s t r i k i n g feature of the assays i s the very high f e r r i c iron content which i s about ten times the normal bath l e v e l . This observation confirms that the tuyere gas stream i s highly ox i d i z i n g . The zinc content of the wall i s approximately midway between the l e v e l i n slag charged and slag tapped. The lime and s i l i c a l e v e l s are reduced somewhat from t h e i r l e v e l s i n the bath. This and the high l e v e l of f e r r i c iron i n the slag suggest that freezing involves a certain degree of equilibrium p r e c i p i t a t i o n . In the absence of other data i t 2+ w i l l be assumed that the wall composition i s 10% Zn, 17% Fe , 3+ 15% Fe , 10% CaO and 20% S i 0 2 . In addition since the wall slag i s s l i g h t l y porous, i t w i l l be assumed that i t has a density equal to the l i q u i d . TABLE 6.7 Frozen Wall Slag Assays (values i n %) Inner Outer Half Half Zn 10.9 12.7 Pb 0.8 0.6 F e 2 + 17.5 15.5 F e 3 + : 15.4 19.6 S 0.1 0.1 c 0.11 0.52 CaO 9.5 6.9 s i o 2 22.5 18.0 A1 20 3 5.9 6.8 179 To melt the slag and heat i t to bath temperature absorbs • 44 a cer t a i n quantity of heat. Grant and Barnett give the heat of fusion, A H ^ u s , as 3412000 J/kg and the slag heat capacity, C ^, as 873.2 J/kg-K. Since t h i s data i s i n ' 43 agreement with Kellogg and other sources, i t w i l l be used. F i n a l l y since'the bottom of the furnace i s water cooled as well, i t w i l l be assumed to behave as the wall and be included i n the wall area: A = 2h(L+W) + LW ...(6.73) w 6.2.4 Other Considerations The three major dynamic aspects of the process have been characterized. Before proceeding to the process model, two points must be considered. F i r s t , i t w i l l be assumed that the surface of the bath i s not a reaction s i t e . I t i s anticipated that the furnace atmosphere i s very turbulent and well mixed. Gases emerging from the tuyere gas stream w i l l be rapidly mixed with gases emerging from the bath, as well as the unregulated t e r t i a r y a i r that leaks through the charge port and other places. The net e f f e c t w i l l be to create an oxidizing atmosphere. Any oxidation i n t h i s region w i l l be accounted for i n the tuyere gas stream. 180 Second, the dynamics of furnace charging and tapping w i l l not be addressed. During charging the behaviour of the process i s strongly influenced by the following variables, (a) the r a t i o of s o l i d to l i q u i d slag charged, (b) the temperature of each charge, and (c) the time between charges to the furnace. During charging and tapping, (d) furnace mixing c h a r a c t e r i s t i c s , and (e) the changes i n i n j e c t i o n dynamics with changes i n bath depth are important variables. These are s i g n i f i c a n t factors in furnace operations and are d e f i n i t e k i n e t i c processes. A proper analysis of these questions would involve a study at least as long as the present one. Furthermore, the general objectives and the techniques of investigation would be quite d i f f e r e n t . 6.2.5 Kinetic Model of the Process The three dynamic zones i n the furnace are t i e d together by a k i n e t i c process which has not yet been quantified: the p a r t i t i o n i n g of coal -between: the slag,.-the tuyere gas stream and the carry over. In addition there i s a t h i r d parameter, the amount of oxygen i n the tuyere stream that oxidizes ferrous to f e r r i c i r o n . These factors cannot be estimated a p r i o r i and therefore must be derived from i n d u s t r i a l data. The model must be f i t t e d with these parameters. If F i s the f r a c t i o n of coal which i s entrained i n the slag and reacts to produce secondary bubbles, Y i s the f r a c t i o n 181 of coal consumed i n the tuyere of coal that passes unconsumed F + Y + Y =1 o F i n a l l y , F w i l l be defined as 2 ' oc tuyere gas stream unconsumed by iron. gas stream and Y i s the f r a c t i o n 3 o through the bath (see F i g . 6.17): ...(6.74) the f r a c t i o n of oxygen i n the coal which reacts with ferrous A k i n e t i c model of the process can now be assembled by performing balances on the slag bath, incorporating the ideas discussed above. A l l rates are expressed i n kg-mole/s. 6.2.5.1 Zinc Balance Zinc i s reduced from the bath i n the secondary bubbles which leave the bath at residence time, t . If C.' ' res j represents the f i n a l concentration of species j i n the secondary bubble, the rate of zinc reduction i s r b , f r j = Zn . F C c r v D ... (6.75) Zn . f r—p vol H [/H2 H 2 ° i 2.016 where C i s the coal rate (kg/s); c -jy the weight f r a c t i o n v o l a t i l e s i n the coal; and v„, the weight f r a c t i o n of hydrogen in the v o l a t i l e s . 182 F i g . 6.17 Schematic o f C o a l P a r t i t i o n i n Furnace 183 Zinc enters the slag as a r e s u l t of wall melting: :Zn Zn 65.37 dV s l , s w ...(6.76) dt where W„ i s the weight f r a c t i o n zinc i n the wall slag layer, and V i s the wall volume, w The o v e r a l l balance i s then • TCI • TC (r™ - r j ) 65.37 = Zn Zn d< FZn M ) dt (6.77) thus dF s l Zn = dt 6.5. 37 (r„ -r.„ ) Zn Zn M 7Sl Zn dM M dt (6.78) s l where F^ i s the weight f r a c t i o n of species j i n the slag, 6.2.5.2 F e r r i c Iron Balance F e r r i c iron i s reduced at a rate equivalent to the rate of oxygen pickup of the secondary bubbles minus the oxygen present, due to v o l a t i l e oxygen and zinc oxide reduction. • r 3+ Fe = 2 F C c , v T T  vol H 2.016 184 The factor 2 appears i n the equation because two f e r r i c ions are reduced for every oxygen oxidized. F e r r i c i r o n enters the bath due to wall melting: •m Fe 3+ 3+ - Fe 55.85 dV s i , s w dt .. (6.80) F e r r i c iron i s also produced by ferrous oxidation at the tuyere, This requires that tuyere stream combustion be dealt with. It i s assumed that the coal which burns i n the tuyere (fraction Y) burns completely to CC^ and H^O. Therefore; r = Y o u2 C ( c f c + C v o l V C ) + C c v o l V H 12.01 - C c , vol O 32.0 2 (2.016) ..(6.81) If r i s the oxygen input to the furnace, then u2 r ' ° , . = 4 F ( r i - r ° )" F e 2 + O C °2 °2 ..(6.82) The o v e r a l l f e r r i c balance i s then • O ' , • m r 2+ + r 3 + F e Z Fe J + + r Fe 3+ 55.85 = d ( F s \ M) Fe dt and dF s i Fe 3+ 55.85 M dt • o , • m • r r 2+ + r 3+ " r Fe Fe Fe 2+ s i -F ^ , dM Fe dt M (6.83) .. (6.84) 185 6.2.5.3 Ferrous Iron Balance The ferrous iron balance r e f l e c t s the f e r r i c balance, except for the melting/freezing term •m W„ 2+ dV. r 2+ = F e p s l s ^-S Fe 55.85 s ± , s dt ... (6.85) The ferrous balance gives dF s l Fe 2+ = 55.85 — M dt •r «.m *o r 3+ 2+ ~ r 2+ Fe J Fe Fe - F s l Fe M 2+ dM dt (6.86) 6.2.5.4 Lime Balance Lime enters or leaves the slag by melting or freezing on the wall. •m :CaO W~ ~ dV - CaO p ^ , w s l , s (6.87) 56.0 dt Therefore dF s l CaO = 56.0 r' dt M m CaO ?8l CaO dM M dt (6.88) 186 6.2.5.5 S i l i c a Balance S i l i c a p a r t i c i p a t e s i n the wall melting and freezing • m rSi(X SiO~ p , w 2 K s l , s ... (6.89) 60.0 dt In addition, i t i s the major constituent of coal ash. Assuming that the coal ash i s a l l s i l i c a : r n = F C c , 1 ash 60.0 1 -' c , +.C , \ ' v „ - C , V ' fc .vol C v o l O 12.01 16.00 _ 4 3 c 3 p .. (6.90) where r ^ i s the rate of ash addition to the slag from the entrained coal. Performing a balance y i e l d s : dt 1 • TT1 • =: (60.0r"._ + YC c . + 60. Or,) M S l 0 2 a + F„ . n SiO M 2 dM dt ... (6.91) 6.2.5.6 Slag Wall Volume The equation for the wall volume i s : V = d ,A w s l w (6.92) D i f f e r e n t i a t i n g y i e l d s dV dt w = A d ( d . ) + d ., dA w s l s l w dt dt ... (6.93) 187 6.2.5.7 Slag Wall Area D i f f e r e n t i a t i n g Equation 6.73 gives dA w = dt 2(L + W) H .. (6.94) 6.2.5.8 Slag Wall Thickness D i f f e r e n t i a t i n g Equation 6.72 gives d ( d s l ) = dt 'si h t (T - T \ \ mp w/ \ s l mpj dT s l dt (6.95) 6.2.5.9 Slag Bath Mass Balance The mass of the bath changes as a r e s u l t of these reactions: dM _ - £X„ (81.37) - r r - (8.00) + r° , (8.00) dt " Z n F e 3 + F e Z + + Y C cash + * l ( 6 0 - ° ) + p s l , s 2k dt (6.96) 6.2.5.10 Bath Height D i f f e r e n t i a t i n g Equation 6.69 gives dh _ 1 'cM dt ( l - £ s l ) P s l L ( W - 2 £ l d t b ) dt (6.97) 188 6.2.5.11 Bath Heat Balance The heat balance i n c l u d e s the f o l l o w i n g terms q = h. A (T , - T ) w^ t w s l mp ... (6.71) Assuming the tuy e r e gas stream l e a v e s a t bath temperature: •x = r„ c l t g " ^ 2 ~p,0 2 ( T s l " T b l ) + r N 2 C p , N 2 ^ s l ^ b l 0 + C (1 - c . . ) c. moxst p , c o a l + C c m o i s t < A H W + c H (T -373.16)) 18.01 w P' H2 U s i + YC C f C + C v o l V c AH + C v o l V H AH 1 12.01 2.016 . ... (6.98) and q° 2+ = 2+ AH_/4(1.5-1/x) Fe Fe .'. . (6.99) In the secondary bubbles; • r «.r q = - r (AH 1 A+AH_ _ ) - r r AHI,/4(1.5-1/x) Fe 3 Zn v""10 s,ZnO + H H ( C ^ J - AHg + AH 7 + AH 9) . (6.100) where RH = FC c , V T T v o l H 2.016(c£'f + C^'b H 2 ° . (6.101) A Hs,ZnO i s t h e h e a t o f s o l u t i o n o f ZnO i n the s l a g ( 19 6 80 j/kg-mole) 142 189 and q = - P , a w (AH. +c , (T ,-T ) ) ...(6.102) m s l , s ^  rus p , s l s l mp F i n a l l y , i t i s assumed that due to the presence of oxide fume in the atmosphere, the water cooling of the upper furnace walls and the i n flow of t e r t i a r y a i r , there i s no net heat exchange between the bath and the free board gases. Combining gives qw + q t g + q p e 2 + + q + q " - c p f 8 l d f c s l ...(6.103) and dT s l = dt 1 M • o ,*r,*m> ( q w + q t g + q . 2+ + q + q > 'p,sl Fe - T ' dM S l dt (6.104) 6.2.5.12 Solution of the Model This system of eleven equations was solved using a f i r s t order Euler method with a time step of 2 minutes. The use of a second order improved Euler method showed no s i g n i f i c a n t improvement over the f i r s t order method. The program written to solve the system i s reproduced i n Appendix VII. 190 6.4 Discussion of Model F i t t i n g The complete model, consisting of the co a l p p a r t i c l e - s l a g reaction model, residence time c a l c u l a t i o n , and bath model, was used to analyse the i n d u s t r i a l fuming cycles presented i n Chapter 5, F i g . 5.1 to 5.11. The objective was to determine those values of F, Y and F which gave the best f i t to the oc measured data for each i n d i v i d u a l cycle. The r e s u l t s of the f i t t i n g are presented i n F i g . 6.18 to 6.28. In these figures, the symbols are the measured data points and the s o l i d l i n e s , 3+ the model predictions. The important species, Zn, Fe and 2+ Fe are presented together with the temperature p r o f i l e . The predicted l e v e l of CaO i s given i n each to show the behaviour of an i n e r t compound. The model i s seen to r e p l i c a t e the i n d u s t r i a l data reason-ably well. Two cycles however are only s a t i s f a c t o r y . In cycle BI the model was unable to account for furnace behaviour during the f i r s t 20 minutes. The slow fuming rate during t h i s period i s inconsistent with the remainder of the cycle. A l i k e l y explanation for t h i s i s that i n the f i r s t part of the cycle, s o l i d charge material, high i n zinc, was melting into the bath. The model appears to be able to account for the rest of the cycle. However, note that 'x' must be lowered to 0.96 i n order to achieve the required fuming rates i n the presence of the f e r r i c l e v e l . This may i n part be due to the r e l a t i v e l y higher leve l s of i r o n i n the slag. %Fe 2* ro ro ro ro * m cn s I 1 1 1 % C o O ro ro ro ro oi w * * 'O cn O cn ro o o • ° o 2 o o o del : CO «< 3 cr o. CO • • • H • H — ro ro ro ro to O — ro OJ o o ° o ° Temperature C O ro ro ro ro ro J> cn 00 1 1 1 1 1 1 1 1 o / o p e 3 * % C a O Temperature (°C) 96T 0 10 20 30 40 50 60 70 Elapsed time (min) Fig. 6.24 Cycle CI, Industrial Data and Model F i t i 1 1 1 1 1 r J i i i i i i i i 1 0 20 40 60 80 100 120 140 Elapsed time (min) F i g . 6.25 C y c l e C2, I n d u s t r i a l Data and Model F i t F i g . 6.27 C y c l e D2, I n d u s t r i a l Data and Model F i t O O J I I -4 00 CO Temperature (°C) i j i TOZ j 202 In cycle C2, F i g . 6.25, there i s a serious deviation between the model and the data. A possible explanation for t h i s run i s that due to the enormous changes i n the coal rate (see F i g . 5.8) the parameters F, Y and F q c are not constant through the cycle. At high loadings there may be a s i g n i f i c a n t drop i n the coal p a r t i c l e v e l o c i t y r e s u l t i n g i n a drop i n F. Y may change s i g n i f i c a n t l y under these conditions as well. In addition the i n a b i l i t y to follow the f e r r i c iron peak may r e f l e c t the existence of k i n e t i c or thermodynamic saturation of the bath i n magnetite. The large and rapid changes i n temperature observed i n t h i s cycle may have resulted i n wall e f f e c t s that were not e f f e c t i v e l y handled by the model. Although there are obviously improvements that could -be made, the model i s able to account for fuming operation under normal conditions. The model can be adjusted to match the behaviour i n each of f i v e d i f f e r e n t operations reasonably well. Predictions of zinc elimination and ferrous iron p r o f i l e s are good. Predictions of f e r r i c i r o n , temperature and i n e r t behaviour are s a t i s f a c t o r y . What i s most s i g n i f i c a n t however i s the consistency of the f i t t i n g parameters over the f i v e operations. As shown i n Table 6 . 8 the v a r i a t i o n i n F and Y i s well within an expected range of uncertainty. The values of Y , the f r a c t i o n of coal un-consumed, are consistent with the mass balance calculations made i n Section 6.2.2. The value of F l i e s i n the range 0.28 TABLE 6.8 Model Parameters CYCLE F Y Y o F oc X % o 2 U t i l i z a t i o n A l 0.33 0.55 0.12 0.16 0.99 73 A2A 0.28 0.52 0.20 0.12 0.99 71 A2B 0.30 0.57 0.13 0.13 1.00 80 Bl 0.37 0.57 0.06 0.34 0.96 87 B21 0.37 0.60 0.03 0.45 1.00 92 B22 0.32 0.54 0.14 0.24 0.99 85 Cl 0.29 0.54 0.17 0.04 1.00 67 C2 0.26 0.45 0.29 0.44 0.975 Dl 0.37 0.49 0.14 0.53 0.99 92 D2 0.39 0.41 0.20 0.42 0.99 83 E l 0.33 0.62 0.05 0.29 1.00 94 204 to 0.39 (excluding C2). On average then, about 33% of the coal injected into a fuming furnace i s entrained i n the slag. About 55% of the coal burns i n the tuyere gas stream and the balance, about 12%, passes through the bath unconsumed. The values of F Q C / the f r a c t i o n of oxygen remaining aft e r the combustion of the tuyere coal (fraction Y) which reacts with ferrous iron , show a wide v a r i a t i o n . Because there i s no evident pattern to these values, i t i s probably not the correct way to quantify the oxidation of i r o n . The oxygen u t i l i z a t i o n however, calculated from Y and F , shows more consistent ' oc' behaviour. However, there i s s t i l l a s i g n i f i c a n t v a r i a t i o n between operations. If the oxygen u t i l i z a t i o n i s compared to the calculated slag bath depth, a reasonable c o r r e l a t i o n can be seen. (Table 6.9.)The operation with the lowest slag depth, Company C, has the lowest oxygen u t i l i z a t i o n . Bath depth increases from C to A, then B, D and f i n a l l y Company E. Average oxygen u t i l i z a t i o n also increases i n t h i s order. This suggests that the observed range of values i s a r e f l e c t i o n of a r e a l difference due i n fact to slag depth. It should be noted that i n t h i s thesis i t has been assumed that there i s no leakage of a i r from the tuyeres. I t has been suggested that a leakage of 43 44 45 *5% of the a i r occurs through the tuyere b a l l valves. ' ' I f t h i s indeed i s the case, the oxygen u t i l i z a t i o n s i n Tables 6.7 and 6.8 would be increased by about 5%. This would give operations B, D and E u t i l i z a t i o n s i n excess of 90%; Company A would have a u t i l i z a t i o n of 80% and Company C, 70%. Values TABLE 6.9 Oxygen U t i l i z a t i o n and Bath Depth Calculated Quiescent % Oxygen Bath Depth Bath Depth Cycle U t i l i z a t i o n h (m) (m) Al 73 1.7 0.82 A2A 71 1.7 0.82 A2B 80 1.8 0.86 Bl 87 2.0 0.94 B21 92 1.9 0.90 B22 85 1.95 0.92 Cl 67 1.0 0.56 C2 — 1.0 0.55 Dl 92 2.1 1.03 D2 83 2.1 1.04 E l 94 2.3 1.15 206 above 80% are consistent with measurements i n copper 117 converters. The general agreement of f i t t e d parameters within the context of a model that contains so many estimated values i s strong evidence that the model i s an important step i n defining the k i n e t i c s of the process. Considering a l l of the differences in variables between operations such as slag depth, coal type, blast preheat, coal rate, furnace dimensions, slag composition and blast flow rate, the a b i l i t y of the model to extract such constant parameters i s confirmation of a correct conception. It remains to assess the s e n s i t i v i t y of the model to important parameters and check the model against i n d u s t r i a l observations. And f i n a l l y , by an analysis of model predictions, determine the c o n t r o l l i n g k i n e t i c processes. 207 CHAPTER VII SENSITIVITY ANALYSIS AND MODEL PREDICTIONS:  KINETIC DESCRIPTION OF SLAG FUMING In order to come to an understanding of the dynamics of the zinc slag fuming process, i t i s necessary to move from detailed k i n e t i c considerations to the integrated e f f e c t of these phenomena over time. I t i s only from t h i s perspective that the c r i t i c a l factors i n furnace operation can be i d e n t i f i e d . It i s therefore important that t h i s study begin with an analysis of the s e n s i t i v i t y of the model to f i t t e d parameters and parameters such as bath v e l o c i t y which represent only best guesses. For purposes of t h i s analysis, a standard case was selected which represented an 'average' of the d i f f e r e n t opera-tions studied i n t h i s thesis. These process parameters are l i s t e d i n Table 7.1 7.1 S e n s i t i v i t y Analysis The central focus of the k i n e t i c model i s the f r a c t i o n of coal which i s entrained i n the slag, F. The s e n s i t i v i t y of the process to F i s i l l u s t r a t e d i n F i g . 7.1. The standard case, F = 0.35, i s shown as l i n e 2. An increase i n F to 0.40 brings about an increase i n the fuming rate r e s u l t i n g i n a decrease i n the Zn concentration i n the slag of 0.75% i n 100 minutes. The increased fuming rate increases the heat load on the process and therefore brings about a greater decline i n temperature. 3+ The freezing of slag r e s u l t i n g from t h i s gives the Zn-and Fe TABLE 7.1 Standard Conditions for Slag Fuming Predictions Operating Parameters F = 0.35 Y = 0.55 Y = 0.10 o F = 0.35 oc Furnace Dimensions L = 4.5 m W = 2.5 m Injection Dynamics -1 Bath Velocity = 1 ms No. of Tuyeres = 30 ^  Bubble Freq. = 7 s~ Tuyere Column Void Fr = 0.60 Boudouard Reaction A = 3.16 (10 1 0) kPa" 1 s - 1 o E = 196200 kJ kg-mole a 3 -1 Slag Data: I n i t i a l Composition 14* 25* Zn Fe 2+ 3+ 2% Fe 15% CaO 25% S i 0 2 5% A l 2 0 3 I n i t i a l T = 1473 K I n i t i a l Wt = 45 T Porosity = 30% Density = 3900 kgm~3 V i s c o s i t y = 0.50 kg m~ 1s~ 1 DFeO / D F e 2 0 3 Fe xO = 10 x = 0.99 Coal Data: Assay (wt. fr) 0.50 F.C. 0.25 Vol 0.15 Ash 0.10 Moist. V o l a t i l e 0.50 C Comp. 0.2 0 H (wt. fr) 0.20 0 0.05 N Rate = 65 kg min 1 Density = 1500 kg m -3 Blast A i r 3 . -1 Primary : 30 m mm ,STP 2 0°C Secondary : 322 m3min 1 STP 20°C 209 0 20 40 60 80 100 Elapsed time (min) F i g . 7.1 The E f f e c t of 'F' on Predicted Flaming Behavior 210 curves a steeper slope than i s seen for F = 0.35. Later i n the cycle as the rate of zinc reduction slows, the thermal burden decreases and the temperature starts to r i s e . Melting of wall slag r e s u l t s , which feeds additional zinc and f e r r i c iron into the bath giving an increased f e r r i c l e v e l and a d e f i n i t e re-duction i n the slope of the zinc elimination curve. The l e v e l -l i n g out of the zinc curve i s also due i n part to the higher f e r r i c iron l e v e l which competes with zinc for carbon. A decrease i n F to 0.30, the lower l i m i t of values obtained during f i t t i n g , gives slower fuming rates and an increase i n the f i n a l zinc concentration of 1.5% i n 100 minutes. Due to a lack of a s i g n i f i c a n t change i n temperature during the f i r s t half of the cycle the fuming rate i s r e l a t i v e l y constant. Toward the end however, as the thermal burden declines, the temperature starts to r i s e , melting of wall slag occurs which produces a s l i g h t decrease i n the slope of the zinc curve. It i s apparent that the model i s moderately sensitive to the value of F. Since F e s s e n t i a l l y represents the amount of reductant which i s available to the slag t h i s e f f e c t i s not surprising. If the values of F at each operation are examined, see Table 6.7, i t can be seen that with the exception of cycle B22, the values are reasonably consistent at each operation. The v a r i a t i o n i n F may then r e f l e c t to some extent, variations i n i n j e c t i o n conditions. It i s inte r e s t i n g to note that the operations with the higher values of F, i . e . B and D, are also 211 those with the higher bl a s t i n t e n s i t i e s expressed as bl a s t volume flow rate at bath temperature per unit area of furnace cross-section. Some differences i n F are therefore to be expected and the observed variations are probably legitimate. The e f f e c t of the f r a c t i o n of coal combusted, Y, on the process, a l l other variables constant, i s shown i n F i g . 7.2. Over the range 0.45 to 0.65 Y has a s i g n i f i c a n t influence on fuming. Increasing Y to 0.65 increases fuming rates, r e s u l t i n g i n a decrease of 1.7% i n the f i n a l zinc concentration i n 100 minutes. Decreasing Y to 0.45 re s u l t s i n a 2% increase i n zinc concentration i n 100 minutes of fuming. Y also has a s i g n i f i c a n t influence on bath temperature, but most important i s the e f f e c t on f e r r i c iron l e v e l s . Owing to the manner i n which the model i s formulated a constant f r a c t i o n of the oxygen remaining aft e r coal combustion, F , reacts with ferrous iron i n the slag. o c Increasing Y therefore has the e f f e c t of consuming more oxygen i n the tuyere stream and reducing the amount available for ferrous oxidation. Thus increasing Y reduces the f e r r i c l e v e l i n the bath and therefore the amount of f e r r i c iron competing with zinc for reduction. Zinc reduction i s thereby increased. Reducing Y has the opposite e f f e c t . A majority of the f i t t e d Y values ended up i n the range 0.5-0.6 (see Table 6.7) so i n most cases, the variations are not as dramatic as i l l u s t r a t e d i n F i g . 7.2. Furthermore, as discussed i n Section 6.4, the model has indicated that a better 212 213 way of handling the oxygen u t i l i z a t i o n i n the tuyere gas stream may be to express i t as a function of bath depth. This would then require a p a r t i t i o n to be made between coal combustion and ferrous iron oxidation. If a r e l a t i v e l y constant f r a c t i o n of the coal i s combusted (Y = 0.55) then the difference between the oxygen used for combustion and the o v e r a l l u t i l i z a t i o n would oxidize ferrous iron . The same questions are raised by an analysis of the e f f e c t of F . The e f f e c t of F i s si m i l a r . Increasing F from oc oc . oc the standard condition, F = 0.30, to 0.45 increases the oc temperature and l e v e l of f e r r i c iron i n the bath. See Fig.,. 7,3. The fuming rate i s consequently slowed. Decreasing F q c to 0.15 decreases the f e r r i c iron, allowing more rapid reduction of zinc, r e s u l t i n g i n s i g n i f i c a n t cooling of the bath. In the l a t t e r part of the run when zinc reduction rate decreases, the temperature s t a r t s to r i s e , melting of wall slag begins and material high i n zinc enters the bath, producing a noticeable decrease i n the slope of the zinc elimination curve. The e f f e c t of F i s e s s e n t i a l l y the same as that of Y, oc J ' and the same considerations apply. As discussed i n Section 6.4 'F ' i s probably not the best way of representing ferrous iron oxidation. Instead, t o t a l oxygen u t i l i z a t i o n as a function of slag depth seems to be a more r e a l i s t i c parameter. To quantify t h i s e f f e c t however, would require a special set of i n d u s t r i a l experiments. 214 0 20 40 60 80 100 Elapsed time (min) F i g . 7.3 The E f f e c t of 'F 1 on Predicted oc Fuming Behavior 215 In addition to the f i t t e d parameters F, Y and F , there oc are several model parameters which could at best only be good guesses. These include the slag bath c i r c u l a t i o n v e l o c i t y , v s l ' t^ i e coa-'- P a r t i c l e radius or coal p a r t i c l e c l u s t e r i n g e f f e c t , r ; the non-stoichiometry of ferrous oxide, x; and P the r e l a t i v e d i f f u s i v i t y of ferrous and f e r r i c iron which was set to 10, ferrous to f e r r i c . I t i s important to examine the e f f e c t of these variables. The r e s u l t s of changing bath c i r c u l a t i o n v e l o c i t y , which i s e s s e n t i a l l y to change the secondary bubble residence time, are i l l u s t r a t e d i n F i g . 7.4. The standard case, v g ^ = 1.0 m/s, i s shown as l i n e 2. Increasing bath v e l o c i t y by 50% (decreasing residence time by a third) has only a s l i g h t negative e f f e c t on zinc elimination. Decreasing bath v e l o c i t y by 50% (increasing residence time by a factor of two) again has only a small e f f e c t on zinc elimination, t h i s time a s l i g h t p o s i t i v e e f f e c t . A s i g n i f i c a n t difference i s found however, i n the f e r r i c iron l e v e l s . In the case of a higher bath v e l o c i t y , shorter r e s i d -ence time, the f e r r i c iron l e v e l i s higher. It was suggested i n the development of the model that due to the fact that the coal p a r t i c l e s are not wetted by the slag, they w i l l tend to c l u s t e r together. A c l u s t e r i n g , the equivalent of a p a r t i c l e with a radius of 8 0 ym was assumed. This represents a c l u s t e r i n g of eight p a r t i c l e s of 40 ym radius or about 32 p a r t i c l e s of 25 ym radius (approximately the weight 216 217 mean size of pulverized coal) . J'u"/ The e f f e c t of t h i s clustering on the zinc elimination curve i s n e g l i g i b l e . See F i g . 7.5. Again there i s a s i g n i f i c a n t e f f e c t on the f e r r i c iron l e v e l . The larger the coal p a r t i c l e s or the greater the cl u s t e r i n g , the higher w i l l be the re s u l t i n g f e r r i c iron l e v e l . The e f f e c t of the non-stoichiometry factor;, x in. Fe-O, i s shown i n F i g . 7.6. Again over a s i g n i f i c a n t range the e f f e c t on zinc fuming rates and recovery i s small. The temperature of the slag i s e s s e n t i a l l y the same over the course of the cycle. Again however, the f e r r i c iron l e v e l responds. The larger the value of x, the lower i s the f e r r i c iron l e v e l . This i s i n accord with the e a r l i e r discussion on the ef f e c t of x. Increasing x moves the slag towards a lower f e r r i c iron l e v e l at equilibrium. Turning to the influence of the r a t i o of ferrous to f e r r i c iron d i f f u s i v i t y , D, the e f f e c t i s again small, as seen i n Fi g . 7.7. The f e r r i c iron l e v e l i s the only variable influenced by t h i s change. It can now be appreciated why the value of F i s r e l a t i v e l y constant and consistent from operation to operation. This i s due to the fact that few of these variables have any s i g n i f i c a n t influence on the zinc elimination curve or zinc reduction curve. Thus variations i n slag v e l o c i t y , b l a s t i n t e n s i t y or coal p a r t i c l e c l u stering which might vary from one operation to another w i l l not a f f e c t zinc elimination unless they have some 2 1 8 i— i— i— i— i— i— i— i i—i r » » i i 1 i i i i i L_ 0 20 4 0 60 80 100 Elapsed time (min ) F i g . 7 . 5 The E f f e c t of Coal P a r t i c l e Size 'r ' on Predicted Fuming Behavior p 2 1 9 0> l I I I L_ I I I I I U 0 20 40 60 80 100 Elapsed time (min) F i g . 7.6 The E f f e c t of the Non-Stoichiometry Factor 'x' (Fe v0) on Predicted Fuming Behavior 220 l 1 1 1 1 r \ 1 1 1 1 1 1 h i 1 r • l I I I I I I I 1 L_ 0 20 4 0 60 80 100 Elapsed time (min) F i g . 7.7 The E f f e c t of the D i f f u s i v i t y R a t i o 'D' (D n/D_ n ) on P r e d i c t e d Fuming Behavior 2 3 221 e f f e c t on F. On the other hand, t h e " f i t t e d values of Y and F q c (or oxygen u t i l i z a t i o n ) which therefore e s s e n t i a l l y f i t the f e r r i c iron l e v e l i n the bath to F are more scattered because they are f a i r l y sensitive to estimates of v g^, r , x and D. I t therefore i s a v i n d i c a t i o n of the model and the estimates made of these parameters that the scatter i n Y and F o c (or oxygen u t i l i z a t i o n ) are as small as they are. To explain the s e n s i t i v i t y of the f e r r i c iron l e v e l to these variables and the r e l a t i v e i n s e n s i t i v i t y of the zinc fuming rate i s to understand the process. 7.2 Kinetic Description of the Process - The coal p a r t i c l e - s l a g reaction i s the-basis.of,the description-of process k i n e t i c s . ' This reaction i s i l l u s t r a t e d by F i g . 7.8. In the lower part of t h i s figure the fuming e f f i c i e n c y , expressed as the r a t i o of zinc to t o t a l furnace coal, i s graphed against the residence time of the entrained coal i n the bath. The upper part of the figure, the bath heat balance, expressed as the rate of bath temperature change, i s graphed against the entrained coal residence time. These curves are drawn for a p a r t i c u l a r bath composition which i s assumed to be fixed over the indicated residence time. The standard slag composition i s given i n Table 7.2. The standard values of other parameters are given i n Table 7.1. 222 r —i 1 1 r Residence time (s) F i g . 7 . 8 The E f f e c t of Slag Zn Concentration on Fuming E f f i c i e n c y and Furnace Heat Balance as a Function of P a r t i c l e Residence Time TABLE 7.2 STANDARD SLAG COMPOSITION FOR FUMING EFFICIENCY CALCULATION Species wt % Zn 8.0 F e 2 + 25.0 F e 3 + 2.0 CaO 15.0 s i o 2 25.0 A1 20 3 5.0 224 The most s t r i k i n g feature of the fuming e f f i c i e n c y curve i s that there i s a maximum. For the standard curve, 8% Zn, 2% F e 3 + at 1200°C, .a"peak e f f i c i e n c y of.0.95 Zn/coal occurs at a residence time of 1.3'seconds. Up to t h i s point zinc i s d i f f u s i n g into the secondary bubble and being reduced. Its concentration i n the secondary bubble gas phase i s increasing. At the same time, f e r r i c iron i s also d i f f u s i n g to the bubble and undergoing reduction. Since zinc oxide d i f f u s i o n i s faster than f e r r i c d i f f u s i o n , zinc reduction proceeds more rapidly and zinc builds up i n the bubble. The zinc and carbon dioxide p a r t i a l pressures increase u n t i l the equilibrium i n t e r f a c i a l concentration of zinc oxide i s equal to the bulk concentration, see Equation 6.45. At t h i s point zinc reduction ceases. F e r r i c reduction however, continues to higher oxygen p a r t i a l pressures in the bubble because f e r r i c reduction i s thermodynamically favoured over zinc reduction (see F i g . 1.2). As f e r r i c reduction proceeds, the carbon monoxide concentration decreases and the carbon dioxide concentration increases. As the CC^/CO r a t i o increases the i n t e r f a c i a l zinc concen-t r a t i o n becomes greater than the bath concentration. Zinc therefore i s .oxidized''from the -gas phase onto the .interface and diffuses away from the bubble. The zinc content of the secondary bubble declines and hence the decline i n fuming e f f i c i e n c y . This process w i l l continue u n t i l the bubble i s i n equilibrium with the slag, which occurs af t e r a period of 10 seconds or more. 225 The bath heat balance mirrors t h i s curve. The bath heat balance declines from the s t a r t to a maximum,heat loss at the peak of the zinc fuming e f f i c i e n c y curve. Following t h i s point, the heat balance gradually becomes more favourable because the heat of f e r r i c reduction i s less than the heat of zinc • oxidation. In F i g . 7.8, the e f f e c t of a declining zinc concentration at a constant f e r r i c iron l e v e l i s examined. Increasing the zinc concentration s h i f t s the peak to a shorter residence time and higher e f f i c i e n c i e s , and decreasing the zinc concentration reduces the e f f i c i e n c y with a peak at a longer residence time. In Fig.. 7.9, the e f f e c t of the f e r r i c iron l e v e l i s shown and i s t s e e n to be dramatic. At 3% f e r r i c iron the e f f i c i e n c y peak i s - r e l a t i v e l y steep.on both sides. At 1%,-a very high e f f i c i e n c y i s achieved over a longer residence time. The rate c o n t r o l l i n g processes i n the coal p a r t i c l e - s l a g reaction can best be i d e n t i f i e d by studying Figs. 7.10 and 7.11. In F i g . 7.10 the e f f e c t of the Boudouard Reaction pre-exponen-t i a l constant, A q , on the reaction i s seen. In F i g . 7.11, the eff e c t of the i n t e r - d i f f u s i v i t i e s of zinc oxide and f e r r i c oxide are shown. In the period up to the maximum zinc e f f i c i e n c y the Boudouard Reaction i s rate'Controlling as evidenced by the strong influence of t h i s factor on the e f f i c i e n c y curve. The zinc i n t e r - d i f f u s i v i t y has a small e f f e c t and f e r r i c d i f f u s i v i t y 226 1 1 1 r J • I I I I I I I I L 0 1 2 3 4 5 Residence time (s) F i g . 7.9 The E f f e c t of Slag Fe Concentration on Fuming E f f i c i e n c y and Furnace Heat Balance as a Function of P a r t i c l e Residence Time 227 Residence time (s) F i g . 7.10 The E f f e c t of Coal R e a c t i v i t y on Fuming E f f i c i e n c y and Furnace Heat Balance as a Function of P a r t i c l e Residence Time 2 2 8 1 1 1 1 1 1 [ I 2 0 0 ° C 8%Zn,2%Fe Residence time (s) F i g . 7.11 The E f f e c t o f ZnO and F e 2 0 3 D i f f u s i v i t i e s on Fuming E f f i c i e n c y as a F u n c t i o n of P a r t i c l e Residence Time 229 o n l y begins t o become important i n the r e g i o n of the maximum. Fo l l o w i n g the maximum however, f e r r i c d i f f u s i o n i s c l e a r l y the r a t e c o n t r o l l i n g process a t the higher Boudouard Re a c t i o n r a t e s . The consequences of t h i s r e a c t i o n scheme i s the explana-t i o n of the process dynamics. The process n a t u r a l l y seeks a l e v e l of dynamic e q u i l i b r i u m i n which the r a t e processes such as heat t r a n s f e r , are balanced. The c r i t i c a l balance i n z i n c s l a g fuming i s the f e r r i c i r o n e q u i l i b r i u m . Due t o the s e n s i t i v i t y of the r e d u c t i o n r e a c t i o n a t any f i x e d r e s i d e n c e time to the f e r r i c i r o n l e v e l (see F i g . 7.9), the process r a p i d l y responds t o any change i n the f e r r i c i r o n l e v e l . I t responds t o ensure t h a t the r a t e o f f e r r i c r e d u c t i o n e x a c t l y balances f e r r i c i n p u t t o the bath by f e r r o u s o x i d a t i o n and net w a l l m e l t i n g . V a r i a b l e s such as Y and F which r oc c o n t r o l the r a t e o f f e r r i c i r o n g e n e r a t i o n have a d i r e c t i n -f l u e n c e on the p r o c e s s . I f the f e r r i c i n p u t r a t e t o the process i s i n c r e a s e d , the z i n c r e d u c t i o n s u f f e r s . V a r i a b l e s such as v ,, r , x and D a f f e c t the r a t e a t S -L p which f e r r i c i r o n can be reduced. For example, c o n s i d e r the s l a g bath v e l o c i t y , v ,. Assume t h a t the process i s a t steady 3+ s t a t e a t 8% Zn and 2% Fe . I f v., i s i n c r e a s e d , the r e s i d e n c e s l time decreases and the process moves up towards the peak along l i n e 2 i n F i g . 7.9. T h i s immediately means t h a t there i s l e s s f e r r i c i r o n r e d u c t i o n . The f e r r i c i n p u t t h e r e f o r e gets ahead 2 3 0 of the f e r r i c reduction and the f e r r i c content of the bath i n -creases. The fuming e f f i c i e n c y curve therefore s h i f t s downward 3+ towards the 3% Fe l i n e m the figure. It w i l l s h i f t to compensate exactly for the decrease i n residence time. At t h i s point the fuming rate w i l l return to i t s o r i g i n a l value. The reason for t h i s i s very i n t e r e s t i n g . As implied above, the i n i t i a l period of secondary bubble residence time i s involved almost exclusively with reducing zinc. Following t h i s period, reduction of f e r r i c iron takes place e s s e n t i a l l y by displacing zinc from the bubble. The char carbon has been almost e n t i r e l y consumed during the period of zinc dominated reduction. There-fore, to reduce a given amount of f e r r i c iron, a fixed amount of zinc must be displaced whether the residence time i s short or long, or the f e r r i c d i f f u s i v i t y i s large or small. The f e r r i c i r o n l e v e l simply adjusts to the point where reduction equals net input. The zinc fuming rate therefore depends on the rate of ferrous oxidation. Hence decreasing F or increasing Y should ^ oc ' be b e n e f i c i a l to the process, as i l l u s t r a t e d i n F i g . 7.2 and 7.3 . 7.3 Model Predictions The model w i l l be used to analyse the consequences of changes i n d i f f e r e n t variables for batch fuming and the 231 i m p l i c a t i o n s - i t -holds f o r continuous fuming. 7.3.1 Batch Fuming As shown i n F i g . 7.12 and i m p l i e d by F i g . 7.10, an i n c r e a s e i n c o a l r e a c t i v i t y above a c e r t a i n l e v e l i s somewhat b e n e f i c i a l to the p r o c e s s . By i n c r e a s i n g the r e a c t i v i t y of the c o a l , the r a t i o of z i n c to i r o n reduced, when z i n c r e d u c t i o n stops, i s i n c r e a s e d , see F i g . 7.10. Given then t h a t a f i x e d amount of z i n c must be d i s p l a c e d by f e r r i c i r o n , the amount of z i n c w i l l be h i g h e r i n the case of the more r e a c t i v e c o a l . I t i s important to a p p r e c i a t e t h a t when d e a l i n g with c o a l i t i s u n r e a l i s t i c to expect to be able to change one v a r i a b l e independent of.-another. Ah i n c r e a s e " i n r e a c t i v i t y i s l i k e l y to be accompanied by an i n c r e a s e i n v o l a t i l e and perhaps ash content. However, i n the absence of good data, i t would be unwise to e x t r a p o l a t e by making unwarranted assumptions. The p r e d i c t e d e f f e c t of c o a l composition i s shown i n F i g . 7.13. L i n e 2 r e p r e s e n t s the standard case. L i n e 1 r e p r e s e n t s the replacement of 10% v o l a t i l e s with f i x e d carbon, and l i n e 3 r e p r e s e n t s 10% replacement of f i x e d carbon with v o l a t i l e s . The ash content and r e a c t i v i t y were h e l d constant. Although a t i n t e r m e d i a t e times the higher f i x e d carbon c o a l g i v e s a b e t t e r performance, o v e r a l l the c o a l s t u r n out to be e q u a l . T h i s i s 232 F i g . 7.12 The E f f e c t of Coal R e a c t i v i t y on Predicted Fuming Behavior 233 F i g . 7.13 The E f f e c t of Coal Composition on Predicted Fuming Behavior 234 in agreement with the observations of Yurko-. and McNaughton who found that the e f f i c i e n c y of bituminous and sub-bituminous coal i s equal, provided the ash content i s constant. The higher fixed carbon curve intersects the others at low zinc l e v e l s due to melting and the introduction of additional f e r r i c iron into the bath. I n i t i a l l y due to the lower f u e l value the bath cools off more rapidly, removing f e r r i c from the bath and allowing somewhat greater fuming rates. The e f f e c t of reducing the ash content of the standard coal and replacing i t with fixed carbon i s quite s i g n i f i c a n t . In the f i r s t place, i t increases the amount of combustion i n the tuyere gas stream, decreasing the rate of ferrous oxidation. Second, i t increases the rate of carbon inputito the bath, some-what equivalent to increasing F. As a function of both e f f e c t s , the fuming rate increases. These r e s u l t s are i n agreement with 28 26 the statements of McNaughton and Yurko . The data 14 coll e c t e d by Blaskett tends to support t h i s r e s u l t , although he explained i t i n terms of v o l a t i l e content. The e f f e c t of bath weight i s shown i n F i g . 7.14. Assuming that bath depth has no e f f e c t on oxygen u t i l i z a t i o n , lower bath weights, not unexpectedly, show better fuming rates. This i s simply a function of the smaller bath mass. Any e f f e c t on the residence time, through changes i n bath depth, i s compensated for by changes i n the f e r r i c iron l e v e l . 235 j — i — i — i — i — i — i i r i n Elapsed time (min) F i g . 7.14 The E f f e c t of Bath Weight on Predicted Fuming Behavior 236 In F i g . 7.15 the influence of two blast parameters, preheat and oxygen enrichment are explored. In both cases the o v e r a l l oxygen to carbon r a t i o into the furnace was held constant. The resu l t s of the model are i n reasonable agreement with McNaughton although the blowing times are d i f f e r e n t . This would be i n part due to the higher i n i t i a l zinc l e v e l and perhaps a lower value of F. The important fact however, i s that the difference i n the zinc between the standard case and 25% oxygen enrichment i n model i s 1.3% at about the same zinc l e v e l s that McNaughton observed a difference of 2.0%. The model predicts a temperature difference of 75°C between the two cases, while McNaughton observed a difference of 8 5°C. Thus the model appears to be consistent with i n d u s t r i a l observation.: The model also predicts that blast preheat w i l l be benefi-14 c i a l , i n agreement with Blaskett. The model does not predict as great an improvement as Blaskett notes, but ..no data i s . presented and-it i s impossible to make a quantitative comparison. Since the ferrous oxidation rate i s the same i n each case, the important e f f e c t i s wall melting and absolute temperature. A unit r i s e i n temperature at a lower temperature re s u l t s i n a greater increment i n melting than at a higher temperature. (See Equation 6.95). Thus i n the standard case at a r e l a t i v e l y low temperature, the temperature r i s e at the end of the cycle puts s i g n i f i c a n t l y more f e r r i c iron into the bath. Fuming rate F i g . 7.15 The E f f e c t of Preheat and Oxygen Enrichment of B l a s t on Predicted Fuming Behavior 238 drops more s i g n i f i c a n t l y as a consequence. Furthermore, as shown i n F i g . 7.16, increased temperatures at a given residence 3+ time and f e r r i c content (2% Fe ) tend to increase fuming e f f i c i e n c y . 7.3.2 Consequences of the Model for Slag Fuming The model suggests that to improve the process, attention should be paid primarily to F and Y and F o c « To increase fuming rates the f r a c t i o n of coal entrained i n the slag should be increased. As shown in F i g . 7.1 a s i g n i f i c a n t improvement in fuming e f f i c i e n c y can be achieved i n t h i s manner. Probably the easiest way to e f f e c t t h i s improvement would be to use higher bl a s t pressures and coarser coal. Of equal importance i s control of ferrous iron oxidation. If t h i s i s high, then fuming rates are going to be slow. The best way to reduce ferrous iron oxidation would be to achieve more.complete combustion of - the tuyere coal. This might i n -volve using a f i n e r ^ c o a l grind-for tuyere coal, _although coarse coal w o u l d . s t i l l be p r e f e r r e d . f o r entrainment. Care must be taken to balance F against Y so that the heat balance i s s a t i s f i e d . A l t e r n a t i v e l y , a temperature p r o f i l e which does not drop too close to the melting point i s important. Oxygen enrichment could be an important factor i n maintaining a heat balance that did not allow the temperature to drop during 239 0 1 2 3 4 Residence lime (s) F i g . 7.16 The E f f e c t of Bath Temperature on Fuming E f f i c i e n c y and Bath Heat Balance as a Function of P a r t i c l e Residence Time 240 the i n i t i a l stages of reduction. See F i g . 7.15. An inter e s t i n g idea i n t h i s regard i s pre-combustion of the c o a l - a i r mixture. As mentioned e a r l i e r , t h i s technique has been used i n the U.S.S.R. to e f f e c t fuming with natural gas. Pre-combustion of the coal would reduce the carry over of coal, and reduce the oxidation of ferrous iron. The operating scheme discussed above b a s i c a l l y implies that the reduction and heat balance requirements of the furnace be f u l f i l l e d separately. One set of high pressure tuyeres, using high loading r a t i o s and i n e r t gas, would be used to in j e c t the coal for slag reduction. A second set of tuyeres, operating at low pressure, would burn natural gas or pulverized coal to make up the heat balance. Pre-combustion or pre-i g n i t i o n of the mixture would be used to ensure e f f i c i e n t use of the f u e l and to prevent free oxygen from entering the furnace and reacting with the slag. 7.3.3 Continuous Fuming The curves of residence time versus fuming e f f i c i e n c y are d i r e c t l y applicable to continuous fuming. These diagrams could be used to define operating points where the heat balance i s just s a t i s f i e d (dT g l/dt = 0). For example, i n F i g . 7.17, the ef f e c t of substituting fixed carbon for v o l a t i l e s on continuous fuming can be assessed. Thus, although higher fixed carbon 241 F i g . 7.17 The E f f e c t of Coal Composition on Fuming E f f i c i e n c y and Bath Heat Balance as a Function of P a r t i c l e Residence Time 242 coals y i e l d more e f f i c i e n t fuming, the heat balance i s not s a t i s f i e d . In t h i s case, the highest e f f i c i e n c y i s 0.94 for 50% fixed carbon coal at a residence time of 1.1 seconds. A technique of c o n t r o l l i n g residence time such as varying bath depth would have to be available. In F i g . 7.18, the e f f e c t of p a r t i c l e size or cl u s t e r i n g i s examined. From t h i s figure i t i s apparent that increasing p a r t i c l e size i s of s i g n i f i c a n t benefit at the zero heat balance point. Although there are zero points at longer residence times, the highest zinc e f f i c i e n c y i s found at the shorter residence times. From an analysis of F i g . 7.16, i t i s apparent that i n t e r -mediate temperatures, say 1200°C, represent the most e f f i c i e n t fuming point. At higher temperatures the zero heat balance point occurs at a much lower residence time where the fuming e f f i c i e n c y i s s i g n i f i c a n t l y lower. At lower temperatures, the e f f i c i e n c y never r i s e s very high. F i n a l l y from F i g . 7.10, coal r e a c t i v i t y does not seem to be an important variable, as long as the r e a c t i v i t y i s the assumed value or greater. 243 Residence time (s) F i g . 7.18 The E f f e c t of P a r t i c l e Size ' r ^ ' on Fuming E f f i c i e n c y and Bath Heat Balance as a Function of P a r t i c l e Residence Time CHAPTER VIII SUMMARY AND CONCLUSIONS 8.1 Summary The r e s u l t s of i n d u s t r i a l measurements at f i v e d i f f e r e n t operations has demonstrated that the equilibrium model of slag fuming i s not generally applicable. Tuyere back-pressure measurements revealed that the predominant mode of gas behaviour was bubbling. Analysis of slag samples has shown that, as expected from.injection dynamics, a portion of the coal injected into the furnace enters the slag. A model of the d i r e c t coal p a r t i c l e - s l a g reaction was developed assuming mass transfer control i n the slag phase and a f i n i t e Boudouard Reaction rate on the i n t e r n a l char p a r t i c l e . This model was incorporated into a model of the slag bath, 2+ 3+ mvolving balances on the species Zn, Fe , Fe , CaO, Si02 and including the behaviour of the water-jacketed wall. F i t t i n g of the process model to i n d u s t r i a l data showed that the f r a c t i o n of coal entering the bath was consistently about 35%. Roughly 55% of the coal i s combusted i n the tuyere gas stream and 10% passes through the bath unconsumed. Oxygen u t i l i z a t i o n i n the tuyere gas stream ranged from 70-95%, dependent on slag depth. 245 The s l a g fuming process i s k i n e t i c a l l y c o n t r o l l e d , e s s e n t i a l l y by two parameters: the f r a c t i o n of c o a l which i s e n t r a i n e d i n the s l a g , and the r a t e of f e r r o u s i r o n o x i d a t i o n . The r a t e of f e r r i c r e d u c t i o n balances f e r r i c i r o n i n p u t s to the bath by d i s p l a c i n g p r e v i o u s l y reduced z i n c . f r o m the e n t r a i n e d secondary bubbles. An i n c r e a s e i n process e f f i c i e n c y can t h e r e -f o r e o n l y r e s u l t from i n c r e a s i n g the entrainment of c o a l i n the bath or r e d u c i n g t h e - o x i d a t i o n "of f e r r o u s i r o n . The former o b j e c t i v e may be achieved by h i g h e r i n j e c t i o n p r e s s u r e s . The l a t t e r may be achieved by more complete combustion of t u y e r e c o a l by u s i n g f i n e r c o a l g r i n d s or pre-combustion. The i m p l i c a t i o n s f o r continuous fuming are important. Improved e f f i c i e n c i e s c o u l d r e s u l t from u s i n g c o a r s e r ground and h i g h e r f i x e d carbon c o a l s , and by o p e r a t i n g at i n t e r m e d i a t e temperatures, about 1200°C. 8.2 Suggestions f o r F u r t h e r Work T h i s t h e s i s has served as an attempt to d e f i n e a v e r y complex system wi t h an enormous number of i n t e r - r e l a t e d p r o c e s s e s . The i n f o r m a t i o n a v a i l a b l e on each of these i s very poor. In order to b e t t e r c h a r a c t e r i z e the s l a g fuming process, i t would be important to study: (a) fehe whole f i e l d of .submerged c o a l combustion; > 2 4 6 (b) the coal p a r t i c l e - s l a g reaction as a function of parameters such as temperature, surface tension, coal and slag composition; (c) the physio-chemical properties of these slag systems, and; (d) the physical entrainment of pulverized coal i n slag; In addition, further i n d u s t r i a l tests could be performed, including: (e) experimental studies on the e f f i c i e n c y of high pressure i n j e c t i o n for coal entrainment; (f) experimental studies on continuous fuming to v e r i f y the predictions of the model; (g) further sampling i n fuming furnaces to study the slag-coal reaction zone; (h) the measurement of slag c i r c u l a t i o n v e l o c i t i e s i n fuming furnaces, and; (i) further sampling and analysis of water-jacketed wall e f f e c t s . 247 REFERENCES 1) D.R. 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Chem., 32, 1940, pp. 719-730 138) R.H. Essenhigh, "Fundamentals of Coal Combustion", i n Chemistry of Coal U t i l i z a t i o n , 2nd Supp. Vol., M.A. E l l i o t t , ed., Wiley-Interscience, New York, 1981, pp. 1153-1312 139) A.V. Tonkonogi, B.P. Ustimenko, V.N. Zmeikov, B.N. Gutsalyuk, K.A. Zhurgembaev, and V.N. Glushko, "Heat Transfer From Matte and Slag to Jacketed Surfaces", Tsvetnye Metally, 9, (11), 1968, pp. 37-41 140) V.I. Donets, Yu.A. Bykhovski, and L.M. Bochkarev, "An Examination of Heat Exchange Between Melts and A Jacketed Surface", Tsvetnye Metally, 13(9 ), 1972, pp. 9-10 141) J.F. E l l i o t t and J.D. Nauman, "Liquid S i l i c a t e s as Media for Heat Transfer" i n Metal-Slag-Gas Reactions and Processes, Z.A. Zoroulis and W.W. Smeltzer, eds., The Electrochemical S o c , 1975, pp. 238-250 142) G.W. Toop, Cominco Ltd., T r a i l , B.C., private communication 143) F. Kreith, P r i n c i p l e s of Heat Transfer, IEP, New York, 1973 258 APPENDIX I WET FERROUS IRON ASSAY TECHNIQUE 259 Weigh a suitable weight of sample into a clean, dry 250 ml erlenmeyer f l a s k . Add 2 gm calcium carbonate, 100 ml d i s t i l l e d water and 25 ml HCl. Cover, and digest on a bare plate u n t i l the sample i s decomposed. Remove from the hot plate, one at a time. Add a pinch of calcium carbonate and stopper t i g h t l y with a rubber stopper. Cool to room temperature i n a water bath. Add 5 ml phosphoric acid, and t i t r a t e with standard dichromate solution (0.005 gm fe/ml I^C^O^) using sodium diphenylamine sulphonate as indicator. NOTE: In complex materials containing other oxidizing or reducing agents, the exact determination of F e + + i s one fraught with uncertainties. 2 6 0 APPENDIX II FUMING CYCLE SAMPLING DATA COMPANY A CYCLE NO.1 BATH WEIGHT: 49668.0 KG COAL COMPOSITION: WEIGHT FRACTION COAL VOLATILES: WEIGHT FRACTION* FIXED CARBON: 0.429 VOLATILES: 0.330 ASH: 0.096 MOISTURE: 0.145 TIME MIN O.O 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 TEMP* ' C 1 175 .0 1 175 .O 1175.0 1175.0 1 175 .0 1 175 .0 1175 .O 1 175 .0 1175 .O Zn % 11.0 10. 3 9.9 9 . 1 8 . 3 7 . 5 6 . 5 5 . 7 5.0 Fe 2 + % 20.0 2 1.5 22 .0 22.4 22 . 5 22 .9 22 . 8 22 . 9 23 . 4 CARBON: 0.400 HYDROGEN: 0.168 OXYGEN: 0.177 NITROGEN: 0.050 PRIMARY SECOND BLAST BLAST F e 3 + CARBON SULFUR LEAD CaO SiO* A1*03 MgO STP STP 7= % % % % % % % M'/S MVS 4.5 0.49 0.47 17.1 25.5 5.0 0.3 5.2 2.9 0.33 0.25 17.6 25.9 5.0 ' 0.3 5.2 2.5 0.44 0.12 18.0 26.5 5.0 0.3 5.2 2.1 0.44 0.7 0.08 18.4 26.8 5.0 1.9 0.3 5.2 2.3 0.33 0.7 0.07 18.4 27.1 5.0 1.9 0.3 5.2 2.3 0.55 0.7 0.03 18.6 27.7 5.0 2.0 0.3 5.2 2.6 0.49 0.7 0.04 19.0 28.2 5.0 1.9 0.3 5.2 2.6 0.49 0.04 19.1 28.3 5.0 0.3 5.2 2.3 0.49 0.03 19.2 28.4 5.0 0.3 5.2 SECOND COAL BLAST RATE TEMP ' C 104.4 104.4 104.4 104 . 4 104.4 104.4 104.4 104.4 104 .4 KG/S 1 .06 1 .06 \ .06 1 .06 1 .06 1 .06 1 .06 1 .06 1 .06 * Estimated to COMPANY A C Y C L E N O . 2 A B A T H W E I G H T : 4 9 6 3 2 . 0 KG C O A L C O M P O S I T I O N : WEIGHT F R A C T I O N C O A L VOLAT I L E S : WEIGHT F R A C T I O N * F I X E D C A R B O N : 0 . 4 2 8 V O L A T I L E S : 0 . 3 6 5 A S H : 0 . 0 9 7 M O I S T U R E : 0 . 1 1 0 T I M E M I N 0 . 0 1 0 . 0 2 0 . 0 3 0 . 0 4 0 . 0 5 0 . 0 6 0 . 0 7 0 . 0 8 0 . 0 T E M P * ' C 1 2 0 0 . 0 1 2 0 0 . 0 1 2 0 0 . 0 1 2 0 0 . 0 1 2 0 0 . 0 1 2 0 0 . O I 2 0 0 . 0 1 2 0 0 . O 1 2 0 0 . 0 Zn % 4 . 5 3 . 6 3 . 0 2 . 3 1 . 7 1 . 2 O . 8 0 . 8 0 . 8 F e 2 + % 24 . 5 25 . 3 25 . O 25 . 2 2 5 . 3 26 . 0 26 . 1 25 . 6 22 . 8 C A R B O N : 0 . 4 0 0 HYDROGEN: 0 . 1 6 8 O X Y G E N : 0 . 1 7 7 F e 3 + % 1 . 9 1 . 3 1 . 9 1 . 7 1 . 7 1 . 2 1 . 2 1 . 8 4 . 0 CARBON SULFUR % 0 . 6 5 0 . 6 5 0 . 5 4 0 . 4 4 0 . 5 4 0 . 5 4 0 . 54 0 . 54 0 . 54 % 1 . 2 1 . 2 1 . 3 1 . 2 1 . 2 1 . 3 1 . 3 1 . 5 1 . 3 LEAD /o 0 . 3 0 0 . 19 0 . 1 3 0 . 10 0 . 10 0 . 1 2 0 . 0 9 0 . 1 7 0 . 10 CaO % 23 . 0 23 . 3 2 3 . 5 2 4 . 1 2 4 . 3 2 4 . 3 2 4 . 4 24 . 0 24 . 3 S i O * % 2 7 . 8 2 8 . 6 2 8 . 6 2 9 . 9 3 0 . 3 3 0 . 4 3 0 . 7 3 0 . 7 3 2 . 1 N I T R O G E N : 0 . 0 5 0 P R I M A R Y SECOND B L A S T B L A S T A l 2O1 % 5 . 5 5 . 7 5 . 7 5 . 7 5 . 9 6 . 0 6 . 1 6 . 1 6 . 0 MgO % 2 . 3 2 . 4 2 . 4 2 . 6 2 . 5 2 . 4 2 . 6 2 . 5 2 . 5 STP M 3 / S 0 . 3 0 . 3 0 . 3 0 . 3 0 . 3 0 . 3 0 . 3 0 . 3 0 . 3 STP M ] / S 5 . 7 5 . 7 5 . 7 5 . 7 5 . 7 5 . 7 5 . 7 5 . 7 5 . 7 SECOND COAL B L A S T RATE TEMP. * C 1 0 0 . 0 1 0 0 . 0 1 0 0 . 0 1 0 0 . 0 1 0 0 . 0 1 0 0 . 0 1 0 0 . 0 1 0 0 . 0 1 0 0 . 0 K G / S 1 . 2 0 1 . 2 0 1 . 2 0 1 . 2 0 1 . 2 0 1 . 2 0 1 . 2 0 1 . 2 0 1 . 2 0 * E s t i m a t e d to to COMPANY A CYCLE NO.2B BATH WEIGHT: 52344.(5 KG COAL COMPOSITION: WEIGHT FRACTION COAL VOLATILES: WEIGHT FRACTION* FIXED CARBON:' 0.428 VOLATILES: 0.365 ASH: 0.097 MOISTURE: 0.110 TIME MIN 0.0 10.0 20.0 30.0 40.0 50.0 60.0 TEMP* * C 1200.0 1200.0 I 200.0 1200.0 1200.0 1200.0 1200.O Zn % 4 . 3 3.4 2 . 5 1 . 9 1 . 3 0.8 0.9 Fe ! * 24 .6 24 . 3 24 . 8 24 .9 24 .9 25 . 2 23.6 CARBON: 0.400 HYDROGEN: 0.168 OXYGEN: 0.177 Fe 3 * % 0.3 0. 1 0. 1 0.2 0. 1 0.0 1 . 1 CARBON SULFUR % 0.44 0.33 0.44 0.44 0.54 0.65 0.88 % 1 . 1 1 . 1 1 .2 1 .2 1 .2 1 . 2 1 . 3 LEAD % O. 1 0.08 O. 14 0.09 0.06 0.05 0.18 CaO % 22 .9 23.5 23 . 2 23 . 5 23.8 23.9 23 . 5 SiO; % 33.3 34.9 34 . 7 35 . 2 36. 1 36 . 2 37 . 3 NITROGEN: 0.050 PRIMARY SECOND SECOND COAL' BLAST BLAST BLAST RATE A1*03 MgO STP STP TEMP % % M3/S M3/S 'C KG/S 5.9 2.3 0.3 5.2 104.4 1.16 6.0 2.4 0.3 5.2 104.4 1.16 6.3 2.2 0.3 5.2 104.4 1 . 16 6.2 2.3 0.3 5.2 104.4 1.16 6.4 2.3 0.3 5.2 104.4 1 . 16 6.4 2.2 0.3 5.2 104.4 1 . 16 6.4 2.3 0.3 5.2 104.4 1.16 * Estimated to (Ti LO COMPANY E CYCLE NO.1 BATH WEIGHT: 40823.0 KG COAL COMPOSITION: WEIGHT FRACTION COAL VOLATILES: WEIGHT FRACTION* TIME MIN 0.0 20.0 40.0 60.0 80.0 100.0 TEMP* ' C 1150.0 1150.0 1150.0 1150.0 1150.0 1 150.0 Zn % 14.5 13.1 10.2 7 . 4 5 . 1 2.6 Fe' + % 21.9 21:5 23 . 1 23.5 25 . 1 26 .0 FIXED CARBON: 0.499 VOLATILES: 0.335 ASH: 0.067 MOISTURE: 0.010 CARBON: 0.400 HYDROGEN: 0.168 OXYGEN: 0.177 NITROGEN: 0.050 PRIMARY SECOND SECOND Fe 3 4 % 3 . 2 4.8 3.8 4 . 5 3.8 3.9 CARBON SULFUR % 0.44 0.44 0. 44 0.54 0.38 0.54 % 0.9 0.8 0.9 0.9 1 .0 0.9 LEAD % O. 45 0. 24 0. 10 0.09 0.07 0.07 CaO % 14.2 14.0 14.9 15.2 15.5 15.8 S i O z % 24.6 23 . 2 26 .0 27 . 1 28 . 3 26 . 7 A b O . % 4 . 5 4 . 3 4.9 5 . 2 5.6 5.9 MgO** BLAST STP MJ/S 2 . 5 2 . 5 2 . 5 2 . 5 2.5 2.5 BLAST STP M3/S 2.4 2.4 2.4 2.4 2.5 2.6 BLAST TEMP ' C 20.0 20.0 20.0 20.0 20.0 20.0 COAL RATE K G / S 0.99 1 .01 1 .01 1 .02 1 .00 1 .00 * Estimated ** Not Assayed CTi COMPANY B CYCLE NO.21 BATH WEIGHT: 39190.4 KG COAL COMPOSITION: WEIGHT FRACTION* COAL VOLATILES: WEIGHT FRACTION FIXED CARBON: 0.499 VOLATILES: 0.335 ASH: 0.067 MOISTURE: 0.099 TIME MIN O.O 15.0 25 .0 35 .0 45 .0 55 .0 65 .0 75 .0 95 .0 TEMP* ' C 1 175 .0 1175 .0 1175 .0 1175 .0 1 175 .0 1175.0 1 175.0 1175 .0 1175.0 Zn % 13.4 11.1 9 . 7 8 . 3 6.9 5 . 6 4 . 4 3 . 3 1 .4 Fe ! + % 22 .4 23. 1 23 .6 24 . 2 25 .0 25 . 3 25 . 7 26 . 2 26.4 CARBON: 0.400 HYDROGEN: 0.168 OXYGEN: 0.177 Fe 3 + % 1 .8 1 . 7 1 .6 1 .4 1 . 1 1 .0 0.9 0.4 0.5 CARBON SULFUR % O. 54 0.54 0.54 0.54 0.57 0.65 0. 76 0. 54 0.65 % 1 . 2 1 . 3 1 .2 1 . 3 1 . 3 1 . 3 1 . 3 1 . 3 1 . 3 LEAD % 1 . 2 0. 38 0.18 0.14 0.13 0. 10 0. 10 0.06 0.02 CaO % 14.7 15.3 15.7 15.9 16. 1 16.4 16.5 16.9 17.4 S i O z % 28.4 30.3 31.6 32.5 33.2 34 . 4 35.2 36.6 38 . 7 NITROGEN: 0.050 PRIMARY SECOND BLAST BLAST Al Z 0 3 % 5.4 5.8 6.0 6.2 6.4 6.7 6.9 7. 1 7.3 MgO % 2.7 2.8 2.9 2.9 2.9 3.0 2.9 3.0 3.0 STP M3/S 2.5 2.6 2.6 2.6 2.6 2.6 2.5 2.5 2.5 STP M3/S 2 . 5 2 . 3 2 . 2 2 . 2 2 . 3 2 . 3 2.4 2.4 2.6 SECOND COAL BLAST RATE TEMP ' C 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 KG/S 1 .00 1 .00 1 .00 1 .00 1 .00 1 .00 1 .00 1 .00 1 .00 * Estimated t o CTi U l COMPANY B CYCLE NO . 22 BATH WEIGHT: 40097.6 KG COAL COMPOSITION: WEIGHT FRACTION* COAL VOLATILES: WEIGHT FRACTION FIXED CARBON: 0.499 VOLATILES: 0.335 ASH: 0.067 MOISTURE: 0.099 CARBON: 0.400 HYDROGEN: 0.168 OXYGEN: 0.177 NITROGEN: 0.050 PRIMARY SECOND SECOND COAL BLAST BLAST BLAST RATE TIME MIN 0.0 10.0 20.0 30.0 40. O 50.0 60.0 70.0 80.0 90.0 TEMP* * C 1 175 .0 1 175 .0 1 175.0 1175 .0 1 175 .0 1175 .0 1 175 .O 1 175 .0 1175 .0 1175 .0 Zn % 12.5 10.9 9 . 8 8 . 3 7 . 1 5 . 9 4 . 7 3 . 7 2 . 7 1 . 8 Fe* + % 22 .6 23.4 23.9 24.5 25.2 25 . 4 25 .9 26 . 2 26.4 26.9 Fe 3 + % 1 .6 1 . 5 1 .4 1 .4 1 .0 1 . 2 1 .0 0.9 1 . 3 1 .8 CARBON SULFUR % 0.65 0.54 0.65 0.65 0.60 0.76 0.60 0.71 0.71 0.65 % 1 .3 1 .2 1 .3 1 . 3 1 .3 1 .3 1 . 4 1 .4 1 .3 LEAD % 1 .00 0. 38 0.21 0.12 0.09 0.08 0.07 0.05 0.04 CaO % 15.3 15.9 16. 1 16.3 16.5 16.8 17.0 17.1 17.1 17.0 SiO* % 29 . 3 30.0 30.6 31.6 32 . 3 33 . 2 34 . 1 34.9 34 . 5 33 . 7 Al *03 % 5 . 3 5 . 5 5 . 7 5.9 6 . 1 6 . 3 6 . 5 6.8 6 . 7 6.6 MgO % 2.4 2.4 2 . 5 2 . 5 2.6 2.5 2.7 2.7 2.6 STP MVS 2 . 5 2.6 2.6 2.6 2.6 2.5 2.5 2 . 5 2.5 2.5 STP MVS 2.2 2. 1 2.0 2 . 1 2. 1 2. 1 2.2 2 . 2 2.3 2 . 3 TEMP ' C 20.0 KG/S 1 .00 20.O 1.00 20.O 1.00 20.0 1.00 20.0 1.00 20.O 1.00 20.0 1.00 20.0 1.00 20.0 1.00 20.0 1 .00 * Estimated COMPANY C CYCLE NO.1 BATH WEIGHT: 52617.0 KG COAL COMPOSITION: WEIGHT FRACTION COAL VOLAT I LES : WEIGHT FRACTION FIXED CARBON: 0.600 VOLATILES: 0.235 ASH: 0.165 MOISTURE: 0.0 TIME MIN 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 TEMP ' C 1210.0 1200.0 1200.0 1190.0 1 170.0 1170.0 1180.0 1180.0 Zn % 8 . 5 7 . 1 6 . 5 5.4 4.6 3 . 7 3 . 4 3 . 7 Fe 2 4 % 29 . 3 30.5 32 . 5 31.5 33.5 33.5 32.5 33 . 8 CARBON: 0.526 HYDROGEN: 0.171 OXYGEN: 0.245 Fe 3 4 % 2.7 2.2 0.6 0.3 0.2 0.5 0.4 0.2 CARBON SULFUR % 0.76 0.65 0. 76 0.82 0. 76 0.60 0.79 0.92 % 1 .3 1 .3 1 . 3 1 . 4 1 .4 1 .4 1 .4 1 .6 LEAD % 0.21 0.11 0.13 0.12 0.07 0.06 0. 13 0.38 CaO % 13.0 13.2 13.1 13.6 13.5 13.7 13.7 13.4 S i O z % 24.6 25 . 5 25.4 26 . 9 26.9 27 . 5 27 . 7 27.4 NITROGEN: 0.045 PRIMARY SECOND SECOND COAL BLAST BLAST BLAST RATE AliOs MgO** STP STP TEMP % % M3/S M3/S 'C KG/S 4.6 0.5 5.7 20.0 0.98 5.0 0.5 5.7 20.0 0.98 5.1 0.5 5.8 20.0 0.98 5.3 0.5 6.0 20.0 0.98 5.5 0.5 6.0 20.0 1.12 5.6 0.5 5.9 20.0 1.12 5.6 0.5 6.0 20.0 0.98 5.7 0.5 6.0 20.0 0.84 ** Not Assayed to COMPANY C CYCLE NO.3 BATH WEIGHT: 52072.4 KG COAL COMPOSITION: WEIGHT FRACTION COAL VOLAT ILES: WEIGHT FRACTION FIXED CARBON: 0.GOO VOLATILES : 0.235 ASH: 0.165 MOISTURE: 0.0 TIME MIN 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 95 .0 100.0 110.0 120.0 130.0 150.0 TEMP " C . 1230.0 1250.0 1275 .0 1305.O 1315.0 1305.0 1290.0 1275.0 1260.0 1245 .0 1232 . 5 1220.0 1232.5 1245 .0 1255 .0 1260.0 Zn % 12.1 11.6 10.9 10. 5 10.0 9 . 5 9.0 8 .O 6 . 8 5 . 7 5.0 4 . 4 3 . 5 2.9 2 . 5 2 . 2 Fe ! + % 24 . 9 22 . 8 21.5 20.6 20.5 2 1 .O 22 . 8 24 . 4 25 . 7 26 . 5 27.9 28 . 2 28 . 1 27 . 3 27.0 26.4 CARBON: 0.526 HYDROGEN: 0.171 OXYGEN: 0.245 NITROGEN: 0. Fe 3 + % 1 . 9 4.8 6.3 7.6 7.9 7.8 6.0 4.9 3.9 3 . 3 2.5 2.3 2.8 3.4 4.0 4.7 CARBON % 0.49 0.33 0. 16 0. 16 0. 16 0.11 0.11 0. 16 0.11 0.09 0.16 0.06 0.06 0. 16 0.11 0.11 SULFUR % 0. 89 0.64 0. 28 O. 19 0. 10 0.07 0.07 0.06 0.11 0.03 0.03 0.01 0.02 0.09 i 0.11 0.03 LEAD % 1 .8 0.88 0.46 0.48 0. 50 0. 35 0.31 0.17 0.12 0.07 0.08 0.06 0.07 0.11 0.11 0.07 CaO % 13.9 14.0 14.4 14.4 14.4 14.3 14.6 14.7 15.0 15.4 15.2 15.4 15.5 15.7 15.7 15.9 SiO; % 25 . 1 25 . 1 26 . 1 26 .0 26 .2 26 . 3 27 . 1 27 . 3 28 . 1 29 . 2 29 . 3 29 . 7 30. 1 31.0 30.9 31.2 Al : 0 i % 4 . 5 4.6 4.6 4.6 4 . 7 4 . 8 4 . 9 5. 1 5.3 5.4 5 . 7 5.6 5.7 5.9 5.9 5.9 MgO % 0.94 0.95 0.97 .0 . 1 . 1 . 1 . 1 . 1 .0 . 1 .0 . 2 . 1 . 1 . 1 045 PRIMARY BLAST STP M3/S 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 SECOND BLAST STP M3/S 7.9 7.8 7.6 7.4 7 . 3 7 . 3 7.2 7.2 7.2 7.3 7 . 2 7 . 2 7.2 7.3 7.7 8 . 1 SECOND BLAST TEMP * C 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 • 20.0 20.0 20.0 20.0 20.0 COAL RATE KG/S 1 . 40 1.12 1.12 1.12 1 .40 1 . 39 1 .68 1 . 68 1 .68 1 .96 1 . 96 1 . 96 1 .96' 1 .68 1 .68 1 .68 cn 00 COMPANY D CYCLE NO.1 BATH WEIGHT: 44964.0 KG COAL COMPOSITION: WEIGHT FRACTION COAL VOLATILES: WEIGHT FRACTION FIXED CARBON: 0.597 VOLATILES: 0.195 ASH: 0.181 MOISTURE: 0.027 CARBON: 0.545 HYDROGEN: 0.201 OXYGEN: 0.193 •TIME TEMP Zn Fe ; + F e 3 + CARBON SULFUR LEAD CaO SiO* MIN *C % % % % % % % % 0.0 1195.0 11.7 19.7 1.4 0.60 0.09 15.2 25.6 9.0 1190.0 10.8 19.3 2.0 0.64 0.04 15.6 25.8 19:0 1200.0 9.2 19.9 2.4 0.64 0.02 16.0 26.8 29.0 1200.0 8.0 20.5 1.7 0.45 0.01 16.2 27.0 38.0 1210.0 6.3 20.7 2.1 0.64 0.01 16.7 28.1 48.0 1215.0 5.0 2 1.3 2.1 0.68 0.01 16.9 28.4 58.0 1230.0 3.9 22.2 1.6 0.64 0.02 17.5 29.2 68.0 1240.0 2.5 21.8 2.2 0.70 0.01 17.7 29.6 79.0 1250.0 1.9 21.7 2.4 0.66 0.01 17.7 30.0 NITROGEN: 0.0 . PRIMARY SECOND SECOND COAL BLAST BLAST BLAST RATE A l * 0 3 MgO STP STP TEMP % % MVS MVS 'C KG/S 7.6 0.0 4.0 460.0 0.96 7.6 0.0 4.0 500.0 0.96 6.6 0.0 4.0 515.0 0.96 7.6 0.0 4.0 520.0 0.96 7.9 0.0 4.0 520.0 0.96 7.6 0.0 4.0 520.0 0.96 7.5 0.0 4.0 520.0 0.96 7.7 0.0 4.0 510.0 0.96 7.7 0.0 4.0 505.0 0.96 Data taken from reference 45 COMPANY D CYCLE NO.2 BATH WEIGHT: 45320.0 KG COAL COMPOSITION: WEIGHT FRACTION COAL VOLATILES: WEIGHT FRACTION FIXED CARBON: 0.597 VOLATILES: 0.195 ASH: 0.181 MOISTURE: 0.027 CARBON: 0.545 HYDROGEN: 0.201 OXYGEN: 0.193 TIME TEMP Zn Fe ! + F e 3 + CARBON SULFUR LEAD CaO S i O z MIN "C % % % % % % % % 0.0 1 165.0 10.1 17.4 2.7 0.63 0.61 15.7 24.0 10.0 1183.0 9.4 18.1 2.4 0.63 0.28 16.3 24.0 20.0 1190.0 8.5 18.8 2.2 0.65 0.15 16.4 24.4 30.0 1190.0 7.2 19.6 2.0 0.67 0.08 16.8 24.6 40.0 1186.0 6.3 19.9 1.8 0.69 0.05 16.8 25.3 50.0 1180.0 5.0 20.1 1.7 0.69 0.03 17.5 25.4 60.0 1188.0 4.1 20.7 2.1 0.72 0.03 17.7 26.0 70.0 1194.0 3.1 21.3 1.8 0.69 0.01 17.7 26.6 NITROGEN: 0.050 PRIMARY SECOND SECOND COAL BLAST BLAST BLAST RATE A l z 0 3 MgO STP STP TEMP % % M'/S M3/S 'C KG/S 7.6 0.0 4.1 428.0 0.94 7.8 0.0 4.0 497.0 0.96 8.0 0.0 4.0 562.0 0.98 8.2 0.0 4.0 580.0 0.98 8.0 0.0 4.0 581.0 0.99 8.1 0.0 4.0 613.0 1.02 8.1 0.0 4.0 621.0 1.02 8.5 0.0 4.0 598.0 1.02 Data taken from reference 45 to o COMPANY E C Y C L E NO.1 BATH WEIGHT: 7 0 0 0 0 . 0 KG COAL COMPOSITION: WEIGHT FRACTION COAL V O L A T I L E S : WEIGHT FRACTION* F I X E D CARBON: 0.540 V O L A T I L E S : 0.23G ASH: 0 . 1 8 0 MOISTURE: 0.072 TIME MIN 0.0 15.0 3 0 . 0 45 .0 6 0 . 0 75 .0 9 0 . 0 105 .0 TEMP* ' C 1 175 .0 1 175.0 1175 .0 1 175.0 1 175.0 1 175 .O 1 175 .O 1 175 .O Zn % 7 . 8 6 . 2 6.0 5.4 4 . 4 3 . 7 2.6 2 . 3 F e * * % 33 .6 32 . 4 32 . 5 3 3 . 6 33 . 7 33 . 7 34 . 1 33 . 2 CARBON: 0.400 HYDROGEN: 0.168 OXYGEN: 0.177 F e 3 + % 1 .0 1 .0 0.9 0.5 0.8 1 . 3 1 .5 1 . 5 CARBON SULFUR % 0.81 0.61 0.41 0 45 0.47 0.54 0.49 0.48 % 1 .2 0.8 0.7 0.7 0.7 0.6 0.6 0.6 LEAD % O. 1 0. 1 0. 1 0. 1 0. 1 0. 1 O. 1 0. 1 CaO % 4.7 4.8 4.8 4.9 4.9 4.9 5.0 5.0 S i O z % 29 .0 34 .0 34 .0 35 .0 37 .0 33 .0 37 .0 38 .0 NITROGEN: 0.050 PRIMARY SECOND SECOND COAL B L A S T B L A S T B L A S T RATE A l i O s MgO STP STP TEMP % % M 3/S M 3/S 'C KG/S 4.4 1.8 2.4 2.4 0.0 0.91 . 5.2 1.6 2.4 2.4 0.0 0.91 5.2 1.7 2.4 2.4 0.0 0.91 5.3 1.7 2.4 2.4 0.0 0.91 5.4 1.6 2.4 2.4 0.0 0.91 5.3 1.7 2.4 2.4 0.0 0.91 5.4 1.7 2.4 2.4 0.0 0.91 5.6 1.7 2.4 2.4 O.O 0.91 * E s t i m a t e d M —1 APPENDIX III EQUILIBRIUM FUMING RATE CALCULATION METHOD 273 The equilibrium fuming rate i s calculated assuming that the c o a l - a i r mixture injected into the furance comes to chemical and thermal equilibrium with the slag. The slag bath i s assumed to be an i n f i n i t e resevior. with a fixed temperature and fixed a c t i v i t i e s of ZnO, FeO, and Fe^C^. The fuming rate can then be calculated as outlined below: The reaction: 3FeO + h02 % F e 3 0 4 . . . ( I I I . l ) = a F e3 ° 4 ...(III.2) Fe 0 2 at equilibrium immediately dictates the oxygen po t e n t i a l i n the gas leaving the slag surface. From the slag composition the mole fractions of Fe^O^ and FeO, N p e 0 respectively, can be calculated. Using the given a c t i v i t y c o e f f i c i e n t s then; P = Y N °2 F e 3 ° 4 F e 3 ° 4 ^ ...(III.2) Kr Y N 6 YFeO FeO 'Kg 1 i s calculated from free energy data for slag temperature. Then the zinc p a r t i a l pressure i n the gas can be determined from the equation: ZnO % Z n ( g ) + **°2 ...(III.3) 274 K 1 = P Zn 0, ZnO ... (III.4) Again c a l c u l a t i n g the mole f r a c t i o n ZnO, N Z n 0 / from the slag composition and taking the a c t i v i t y c o e f f i c i e n t from the given data: P = Y N K ^ Zn YZnO ZnO 2 ...(III.5) P H °2 Having established the oxygen poten t i a l a c a l c u l a t i o n can be performed to check whether or not s o l i d carbon w i l l be present at equilibrium. Using the equation: 2C + 0 2 X 2C0 ...(III.6) 2 2 K = P 8 CO ...(III.7) F o 2 V l e t C^ = :the amount of CO formed (kgrmoles) = t o t a l kg-moles of gas P m = t o t a l pressure then ; 2 2 2 p c o = ^ o / c 2 C 2 2 2 P T 2 = K.8P a c 2 nm 2 C 1 - n m a c ( K 2 p } % ...(III.8) "V 2 275 Likewise for the equation: C + 0 2 t C0 2 ...(III.9) p c o 9 K = - _ _ f _ ...(III.10) °2 C l e t C 2 = the amount of C0 2 formed (kg-moles) h m = t o t a l kg-moles of gas P m = t o t a l pressure then; P C 0 2 = K 7 P 0 2 a C — P T = K 7 P 0 / C n m 2. c 2 = V c K 7 p o 2 ...(III.11) P T I n i t i a l l y rim i s assumed to be the t o t a l amount df nitrogen i n the gas stream i n a cert a i n unit time (e.g. 1 second). The a c t i v i t y of carbon i s assumed to be unity. If the sum of 'C and 'C2' exceeds the carbon input to the furnace as coal i n that unit time then no s o l i d carbon exists at equilibrium. This i s the s i t u a t i o n under conditions normally encountered i n a fuming furnace. If a l l of the carbon i s consumed, assuming i t i n i t i a l l y appears as CO, then the quantities of CO and C0 2 per unit time can be calculated.- Using the equation: 276 2C0 + 0 2 X 2 C 0 2 . . . ( I I I . 1 2 ) P 2 K e = C0 2 P 2P CO o 2 l e t n C Q = the amount of CO i n i t i a l l y present (kg-moles) Ax = the amount of CO consumed (kg'moles) then; (the amount of C0 2 formed) P = P 2 °2 C 0 2 PC0 K e Ax 2 P0„ = nT '2 n C 0 _ A X 2 K e 2 thus P Q = Ax 2 ( n C 0 ~ A x ) 2 K e Solving for Ax gives h A x = ( P q K e + (P Q Ke)..•) ...(III.13) ( 1 - P Q K^) u2 In a sim i l a r manner the d i s t r i b u t i o n of hydrogen between H 2 and H 20 can be determined. Using the equation 2H 2 + 0 2 % 2H20 ...(III.14) 2 P 2 Kg = H 20 p 2 p H2 °2 277 l e t n„ = the amount of H. from coal v o l a t i l e s (kg-moles) H2 2 n R _ = the amount of moisture associated with coal 2 (kg*moles) Ay = the amount of, H 2 consumed (kg-moles) Therefore; (n + Ay) 2 P n _ H 2 °  ( n ^ - A y ) K g . and where; Ay = 9 -b + (b 2 - 4ac)^ ...(III.15) Z 2a a = 4(P 0 2K 2 - 1) b = " 4 ( nH 20 + nH 2 P0 2 K9 2> «  2T> V2 r,2 n H 2 P 0 2 K 9 . - nH 20 F i n a l l y the amount of zinc vapour i n the equilibrium gas stream i s calculated. If n Z n = the amount of zinc vapour (kg-moles) present i n the gas per unit time then; p z n = ^ £ - P T nT nZn = n T P Z n ...(III.16) P T An oxygen balance i s also performed but under normal circum-stances the oxygen p a r t i a l pressure i s so low that the quantity of oxygen present at equilibrium i s n e g l i g i b l e . 278 Using the quantities n C C ) / AX, n H , n R Q , A Y , nin' a n d nN 2' t h e quantity of nitrogen present per unit time, a new t o t a l molar quantity, n m, can be calculated. With t h i s value the c a l c u l a t i o n can be repeated from Equation I I I . 6. Iterations are performed i n t h i s manner u n t i l the change i n n m i s n e g l i g i b l e . The zinc fuming rate can then be calculated from the f i n a l t o t a l molar flow rate n m per unit time and . The net rate of T * Zn f e r r i c reduction can be determined from an oxygen balance on the gas stream taking into account the oxygen derived from the a i r , coal and zinc oxide. The observed fuming rate can be calculated i n the following manner. If 'Z' represents the weight of zinc i n the slag bath and 'W' i s the weight of the bath at a p a r t i c u l a r point, then; Z (%Zn) 100 W . . .(III.17) Therefore; dz dt 1 W d(%Zn) dt ...(III.18) 100 where dz dt actual fuming rate (kg/s) d(%Zn) dt = (%Zn) change with time-(kg/s) (measured from zinc elimination curve) Assuming that the main mass change i n the bath weight i s due to the removal of zinc oxide, then 279 dW • 81.37 dz ...(III.19) dt 65;37 dt Substituting Equation III.19 into III.18 gives the actual fuming rate as a function of bath weight, zinc content of the bath (%Zn) and percent fuming rate: w » d < % Z n > dz ..(III.20) 1 0 0 " < % Z N > § 5 7 3 7 The actual molar fuming rate i s then -dz.y'gj. 2^ (kg-mole Zn/s) This quantity i s termed 'observed fuming rate' i n F i g . 5.12 through 5.14. The net f e r r i c reduction rate can be calculated i n a simil a r way. If f^ i s the mass of f e r r i c iron i n the bath, i . e . 3+ f3 = ( % i o o } • w ...(III.21) then df, _L_ d(%Fe 3 +) + (%Fe 3 +) . 81.37 dz ...(III.22) 100 dt 65.37 dt For ferrous iron; df _ _JL_ d(%Fe 2 +) + (%Fe 2 +) . 81.37 dz ...(III.23) dt 100 dt - 65.37 dt where f 2 = mass of ferrous iron i n the bath (kg). 280 These quantities should be related by the iron balance d £ 2 = - d £ 3 ...(III.24) dt dt These quantities were converted to molar rates and the average graphed as 'net observed f e r r i c reduction rate' i n F i g . 15.15. A l i s t i n g of the computer program written to perform t h i s c a l c u l a t i o n i s given on the following pages. 281 C C C C C C C C c c IMPLICIT REAL*8 (A-Z) INTEGER WFL,I,INT,JT,JT 1 ,1X,J,N REAL*4 STAR,BLNK,WARN(20),NAME(2),R1,R2,GB1,GB2,KEL1,KEL2 1,HATCH DIMENSION TEST(4),H(12),COAL(20),PAIR(20),PP(20),SAIR(20) 1,SP(20),BATHT(20),Z(20),C(20),FE2(20),FE3(20),CAO(20), 2SIO2(20),AL2O3(20),DELTAT(20),OXY(20),OXYP(20),COMET(9), 3CHR(4),WR(4),FUMRT(20,7),INPTT(20),FERED(20,7) DATA R/8.31300006/,AC/1.0000000/,PT/1.0000000000/, 1BLNK/' ,/,Rl/'RICH'/,R2/'ARDS'/,GBl/,G & '/,GB2/'B 2KEL1/'KELL'/,KEL2/'OGG '/,HATCH/" ##'/,STAR/'*'/ READ (7,43) IX,OX,BX,CX READ (7,45) INT READ (7,47) OBJ READ (7,53) BTHWTI READ (7,48) (COMET(l), 1=1,9) READ (7,49) TEST(1),TEST(2),TEST(3),TEST(4) READ (7,51) N,JT N = 1 RICHARDS DATA • 2 GRANT AND BARNETT DATA 3 KELLOGG DATA C1,C2,C3,C4,V1,V2,V3,V4 WX,FE3ST (COAL(J), J=1,JT) (PAIR(J), J=1,JT) (PP(J), J=1,JT) (SAIR(J), J=1,JT) (SP(J), J=1,JT) (INPTT(J), J=1,JT) (OXY(J), J=1,JT) (OXYP(J), J=1,JT) (BATHT(J), J=1,JT) (Z(J ) , J=1,JT) (C(J), J=1,JT) (FE2(J), J=l,JT) (FE3(J), J=1,JT) (CAO(J), J=1,JT) (SI02(J), J=1,JT) (AL203(J), J=1,JT) (DELTAT(J), J=1,JT) FURLEN,FURWID SLMPT BMM READ (7,54 READ (7,50 JT1=JT-1 READ (7,55 READ (7,57 READ (7,59 READ (7,57 READ (7,59 READ (7,65 READ (7,57 READ (7,59 READ (7 , 65 READ (7,69 READ (7,69 READ (7,69 READ (7,69 READ (7,69 READ (7,69 READ (7,69 READ (7,71 READ (7,73 READ (7,75 READ (7,75 43 FORMAT (I 2,1X,A4,F8.1,1X,A4) 45 FORMAT (12) 47 FORMAT (A4) 48 FORMAT (9A4) 49 FORMAT (20A4) 50 FORMAT (F5.3, 1X,F4.2) 51 FORMAT (212) 54 FORMAT (20F6. 4) 53 FORMAT (20F8. 1 ) 55 FORMAT (20F7. 3) 57 FORMAT (20F7. 3) 59 FORMAT (20F8. 3) 65 FORMAT (20F8. 3) 69 FORMAT (20F7. 4) 71 FORMAT (20F6. 3) 73 FORMAT (2F6.2) 75 FORMAT (F6.1) IF (N .EQ. 2 .OR. N .EQ. 3) WX=1.0 NAME(1)=R1 NAME(2)=R2 IF (N .EQ. 2) NAME(1)=GB1 IF (N .EQ. 2) NAME(2)=GB2 IF (N .EQ. 3) NAME(1)=KEL1 IF (N .EQ. 3) NAME(2)=KEL2 DO 1000 INT=1,JT WFL=0 ZN0=Z(INT)*81.37/65.37 CA=CA0(INT) SI=SI02(INT) AL=AL203(INT) WX1=3.0*WX-2.0 WX2=2.0*(1.0-WX) IF (WX .LT. 1.0) GOTO 77 FE304=FE3(INT)*231.54/(2.0*55.85) FE0=FE2(INT)*71.85/55.85"FE304*71.85/231.54 MF2=FEO/71.85 MF3=FE304/231.54 GOTO 79 77 MF3=(1.0/55.85)*(FE2(lNT)-WXl/WX2*FE3(lNT))/ 1(1.0-2.0*WX1/WX2) MF2=(FE3(INT)/55.85-2.0*MF3)/WX2 IF (MF3 .LE. 0.0) WFL=1 IF (MF3 .GT. 0.0) GOTO 78 MF2=(FE3(INT)+FE2(INT))/(WX*5 5.85) 78 FEO=MF2*(WX*55.85+16.00) FE304=MF3*231.54 79 MZ=ZN0/81.37 MS=Sl/60.09 MC=CA/56.06 MA=AL/101.96 UNK=100.0-(ZNO+SI+CA+AL+FEO+FE304) MUNK=UNR/60.0 MT=MZ +MS +MC+MA+MF 2 +MF 3 +MUNK MFZ=MZ/MT 283 MFS=MS/MT MFC=MC/MT MFA=MA/MT MFF2=MF2/MT MFF3=MF3/MT CSS=MC/MS C MF3G=FE3(lNT)/(2.0*55.85) MF2G=(FE2(INT)-55.85*MF3G)/(0.945*55. 85) FEOG=MF2G*68.78 FE304G=MF3G*231.54 UNKG=100.0-(ZNO+SI+CA+AL+FEOG+FE304G) MUNKG=UNKG/60.0 MTG=MZ+MS+MC+MA+MF2G+MF3G+MUNKG MFZG=MZ/MTG MFF2G=MF2G/MTG MFF3G=MF3G/MTG c BTK=BATHT(INT)+273. 1 6 LNZ=(16390.0*CSS-12031.0)/BTK-10.694*CSS+8.8317 IF (N . EQ. 2) LNZ = 2331 .0/B.TK IF (N .EQ. 3) LNZ=920.0/BTK ACZNO=DEXP(LNZ) C LNFE2=(3310.0*CSS+1656.5)/BTK-1.887*CSS-0.6394 IF (N .EQ. 2) LNFE2=1501.0/BTK IF (N .EQ. 3) LNFE2=1501.0/BTK ACFEO=DEXP(LNFE2) LNFE3=84 95.O/BTK-2.653 IF (N .EQ. 2 .OR. N. .EQ. 3 ) LNFE3=8495.O/BTK-2.653 ACFE30=DEXP(LNFE3) AFE=1.0 C c PAIRA=PAIR(INT) PPA=PP(INT) SAIRA=SAIR(INT) SPA=SP(INT) INPTTA=INPTT(INT) GP=PAIRA*PPA/101.325*(273.16/(INPTTA+273.16)) GS=SAIRA*SPA/101.325*(273.16/(INPTTA+273.16)) G=GP+GS OXYA=OXY(INT) OXYPA=OXYP(INT) O I N = 0 . 2 0 9 * G / ( 0 . 0 8 2 0 5 * 2 7 3 . 1 6 ) + (0XYA*0XYPA/101.325)/ 1 ( 0 . 0 8 2 0 5 * 2 7 3 . 0 ) C c COALA=COAL(lNT) CARB=COALA*C1/12.01 VOLTH=COALA*C2*V2/l.008 V0LT0=C0ALA*C2*V3/16.0 V0LTC=C0ALA*C2*V1/12.01 V0LTN=C0ALA*C2*V4/14.007 HSC=VOLTH/(CARB+VOLTC) NSC=VOLTN/(CARB+VOLTC) 284 OSC=VOLTO/(CARB+VOLTC) C c c E=R*BTK G0=-228781.1-171.5*BTK K0=DEXP(-1.0*G0/E) G1=-395346.2-0.5439*BTK K1=DEXP(-1.0*G1/E) GA=-561911.3+l70.4*BTK KA=DEXP(-1.0*GA/E) G2=-494967.2+111.7*BTK K2=DEXP(-1.0*G2/E) G5=-624420.0+250.2*BTK IF (N .EQ. 2 .OR. N .EQ. 3) G5=-600026.0+213.84*BTK C2 G5=-582580.0+260.0*BTK K5=DEXP(-1.0*G5/E) G6=-920480.0+396.6*BTK IF (N .EQ. 2 .OR. N .EQ. 3) G6=-925736.0+398.8*BTK K6=DEXP(-1.0*G6/E) XI=ACFEO**3/ACFE30 GK=-264890.0+65.3 5*BTK KK=DEXP(-1.0*GK/E) 80 NH20=COALA*C4/18.016 NCO2=0.0 NCO=0.0 NN2=VOLTN/2.0 ANN2=NN2+0.791*G/(0.08205*273.16) NC=CARB+VOLTC NO2=VOLTO/2.0 AN02=N02+OIN NH2=(VOLTH)/2.0 C IF (FE3(INT) .GT. 0.0) GOTO 81 FUMRT(INT,6)=999999.9 FUMRT(INT,7)=9999.9 GOTO 82 81 FUMRT(INT,6)=FE2(INT)**2*Z(INT)/FE3(INT)**2 FUMRT(INT,7)=MFF2**3*MFZ/MFF3 C 82 MFF20=MFF2 C1 X1=ACFEO**3.168/ACFE30 CI P02=MFF3**2/(X1**2*MFF2**6.3 358*K5) P02D=(ACFEO*MFF2/(AFE*KK))**2.0 IF (WFL .NE. 1) GOTO 83 PO2C=0.0 GOTO 84 83 P02C=((ACFE3O*MFF3)**2.0/((ACFEO*MFF2)**(6.0/WX)*K5)) 1.0/(4.0-3.0/WX)) 84 IF (P02C .GT. P02D) P02=P02C IF (P02D .GE. P02C) P02=P02D C 85 DO 900 1=2,5 IF (I .EQ. 3) NN2=ANN2 IF (I .EQ. 3) N02=AN02 IF (I .LT. 4) GOTO 97 285 KA=DEXP(67451.O/BTK-20.484) K2=DEXP(60201.O/BTK-13.768) K5=DEXP(31118.5/BTK-11.884) K6=DEXP(111952.0/BTK-48.322) ACZNO=3.401 P02A=(ACFE0*MFF2/(AFE*KK))**2.0 IF (MFF3G .LE. 0.0) P02=P02A IF (MFF3G .LE. 0.0) GOTO 95 X1=4.187 P02B=(MFF3G/(X1*MFF2G**3.1746*K5))**2.42307 IF (P02B .GT. P02A) P02=P02B IF (P02A .GT. P02B) P02=P02A 95 NH20=COALA*C4/18.016 NCO2=0.0 NCO=0.0 NN2=VOLTN/2.0 NC=CARB+VOLTC NO2=VOLTO/2.0 NH2=(VOLTH)/2.0 MFZ=MFZG MFF2=MFF2G MFF3=MFF3G IF (I .EQ. 5) NN2=ANN2 IF (I .EQ. 5) N02=AN02 C 97 NT=NCO+NC02+NH2+NH20+N02+NN2 NTOLD=NT N T I = N T D F = 0 . 0 PZN=ACZNO*MFZ / (P02*K6)**0 . 5 C 100 NCOP=0.0 DXA=0.0 DX0=0.0 DX1=0.0 IF (NC .LE. 0.0) GOTO 190 DX0=2.0*NT*AC*(K0*PO2)**0.5/PT C WRITE (6,98) I,P02,NT,AC,K1,PT 98 FORMAT ( 3X,I 2,5(5X,D12.5) ) DX1=NT*AC*K1*P02/PT I F (NC . G T . 2.0*DX0+DX1) G O T O 290 D X 0 = 0 . 0 DX 1 = 0 . 0 N C O P = N C G O T O 2 0 0 190 N C O P = 0 . 0 200 NCOT=NCOP+NCO DXA=NCOT*( -1,0*PO2*KA+(PO2*KA)**0.5)/(2.0*(1 ,0 -PO2*KA)) G O T O 3 0 0 2 90 N C O P - 0 . 0 N C O T = N C O 300 DXP=DX0+DX1+DXA+NCOP/2.0 C W R I T E (6,301) NT,DF,DX0,DX1,DXA 301 FORMAT (2(E13.5,5X),/,'DX ',3(E13.5)) A11=4.0*(PO2*K2-1.0) 286 B11=-4.0*(NH2O+NH2*PO2*K2) C11=NH2**2*P02*K2-NH20**2 B12=(B11**2-4.0*A11*C11 ) IF (B12 .LT. 0.0) B12=0.0 DY=(-1.0*B11-(B12)**0.5)/(2.0*A11) DM=-1.0*NT*PZN/(2.0*PT) 400 NT=NTI+DX0-DXA+NCOP/2.0-3.0*DM~DF-DY DFP=-1.0*NT*PO2/PT+(N02-DXP-DY-DM) CHK=DABS((DFP-DF)/DFP) IF (CHR .LE. 0.000001) GOTO 500 DF=DFP -GOTO 400 500 NTNEW=NT IF (DABS((NTNEW-NTOLD)/NTOLD) .LT. 0.000001) GOTO 600 NTOLD=NT GOTO 100 600 FZN=PZN FH2=(NH2-2.0*DY)/NTNEW FH20=(NH20+2.0*DY)/NTNEW FN2=NN2/NTNEW F02=P02/PT*NTNEW FCO=(NCOT-2.0*DXA+2.0*DXO)/NTNEW FCO2=(NCO2+2.0*DXA+DX1)/NTNEW WRITE (8,630) INT,I 630 FORMAT (5X,' (' ,12,' ,12,' )' ,/) 840 WRITE (8,650) FZN,FCO,FC02,FH2,FH20,F02,FN2 650 FORMAT (3X,'FZN=',F8.5,/,'FCO=',F8.5,5X,'FC02=',F8.5,/, 1'FH2=',F8.5,5X,'FH20=',F8.5,/,'F02=',F8.5,5X,'FN2=', 2F8.5) WRITE (8,655) NTNEW 655 FORMAT ('NTNEW=',E13.6) WRITE (8,660) K0,K1,KA,K2,K5,K6 660 FORMAT (3X,1K0=',E13.5,3X,'K1=',E13.5,3X,'KA=',E13.5,/, 1'K2=',E13.5,/,'K5=',E13.5,3X,'K6=',E13.5) WRITE (8,670) P02,ACZNO,X1 670 FORMAT (3X,'P02=',E13.5,/,'ACZNO=',E13.5,5X, 1'ACFEO**3/ACFE304=',E13.5) WRITE (8,680) MFZ,MFF2,MFF3 680 FORMAT ('MFZ=',F7.5,3X,'MFF2=',F7.5,3X,'MFF3=',F7.5) WRITE (8,690) NC,N02,NH2,NN2,NCO 690 FORMAT ('NC=1 ,E13.6,3X,'N02=' ,E13.6,3X,'NH2=' ,El 3.6,/, 1'NN2=',E13.6,3X,'NCO=',E13.6,/) 7 00 FUMRT(INT,I ) = (F ZN*NTNEW) OFER=(FCO+2.0*FCO2+FH2O+2.0*FO2-FZN)*NTNEW-2.0*NO2~NH2O FERED(INT,I)=2.0*OFER 900 CONTINUE IF (INT .EQ. 1) GOTO 930 IF (INT .EQ. JT) GOTO 940 Z1=Z(INT-1) Z2=Z(INT+1) F22=FE2(INT+1) F21=FE2(INT-1) F31=FE3(INT-1) F32=FE3(INT+1) ' DT=DELTAT(INT)+DELTAT(INT-1) 287 GOTO 950 930 Z1=Z(INT) Z2=Z(INT+1) F21=FE2(INT) F22=FE2(INT+1) F31=FE3(INT) F32=FE3(INT+1) DT=DELTAT(INT) GOTO 950 940 Z1=Z(INT-1) Z2=Z(INT) F21=FE2(INT-1) F22=FE2(INT) F31=FE3(INT-1) F32=FE3(INT) DT=DELTAT(INT-1) C 950 BTHWT=BTHWTI*(CAO(1)/CAO(INT)+SI02(1)/SI02(INT))/2.0 DZDT=(Z2-Z1)/DT*BTHWT/(l00.0-Z(lNT)*1.2 448) FUMRT(INT,1)=-1.0*DZDT/65.37 FERED(INT,1)=(1.0/100.0)*((F22-F21)/DT*BTHWT+FE2(INT)* 1DZDT*1.2448)/55.85 FERED(lNT,6)=-(1.0/100.0)*((F32-F31)/DT*BTHWT+FE3(INT)* 1DZDT*1.2448)/55.85 FERED(INT,7)=(FERED(INT,1)+FERED(INT,6))/2.0 C IF (WFL .EQ. 1) WARN(INT)=STAR IF (WFL .EQ. 0) WARN(INT)= BLNK C 1 0 0 0 CONTINUE WRITE (6,1001) (TEST(I), 1=1,4) 1001 FORMAT ( ' 1 ' ,1 OX,4A4,/) WRITE (6,1002) WX 1002 FORMAT (/,12X,'FEXO X=',F5.3,//, 112X,'REDUCTION RATES (KGMOLES/MIN)',//) WRITE (6,1003) NAME(1),NAME(2) 1 003 FORMAT (3X,'PT' ,4X,'ACTUAL 1 ,6X,2A4,1X,1 DATA' ,6X, 1'GRANT DATA',7X,'(FE2+)2(ZN2+)/',4X,'(FEO)3(ZNO)/1,/, 219X,1 COAL 1 ,4X,'COAL+AIR' ,5X,'COAL' ,4X,'COAL+AIR' ,7X, 3'(FE3+)2',12X,'(FE304)',//) DO 1100 INT=1,JT WRITE ( 6 , 1 0 0 5 ) INT, (FUMRT(INT,J), J =1 ,3),WARN(INT), 1 (FUMRT(IN T,J), J = 4,7) 1 0 0 5 FORMAT (3X,I 2,3X,F7.4,3X,F7.4,2X,F7.4,1X,A1 ,2X,F7.4, 12X,F7.4,5X,F9.2,8X,F9.4,/) WRITE ( 6 , 1 0 1 0 ) HATCH,FERED(I NT, 1 ) , (FERED(I NT,J), J = 2 , 5 ) , 1FERED(I NT,7),FERED(INT,6) 1010 FORMAT (3X,A2,2X,F8.4,3X,F8.4,2X,F8.4,4X,F8.4,2X,F8.4, 130X,F8.4,/,7X,F'8.4,/) 1100 CONTINUE WRITE ( 6 , 1 1 1 0 ) 1110 FORMAT ( / / , 3 0 X , ' * : METALLIC IRON SHOULD BE PRESENT',//, 130X,'## : FE3+ REDUCTION',///) STOP END APPENDIX IV RADIATION HEAT TRANSFER TO A COAL PARTICLE IN A TUYERE BUBBLE 289 As the coal p a r t i c l e traverses the tuyere bubble, i t i s heated by radia t i o n . The s i t u t a t i o n i s schematically i l l u s t r a t e d i n F i g . IV.1. To simplify the problem i t w i l l be assumed that both the coal p a r t i c l e and the tuyere bubble are spherical, and that the p a r t i c l e i s stationary i n the centre of the bubble. Performing a heat balance on the p a r t i c l e : *p = a F 2 - l ( T s l - Tp> A s l ...(IV.l) The rate of heat accumulation i s then CTF 0 1 ( T 4 , - T 4 ) A = 4TT r 3 p C dTp ...(IV.2) 2-1 s l p s l — p c p,c where c i s the s p e c i f i c heat of coal. This assumes that p,c * there i s n e g l i g i b l e resistance to heat flow (maximum heating ra t e ) . This equation becomes dT _ oF0 ,A , -T-2? ~ 3 dt ...(IV.3) T ,-T 4TT r p c s l p — p c p,c Let . aF„ , A , = 2-1 s l ...(IV.4) 4TT , 3 — o - r p c 3 p c p,c The time required to heat the p a r t i c l e from T^ to T f i s dV - / W T . . . ( I V . 5 , 4 4 T ,-T s l p 290 F i g . IV.1 Coal Particle-Tuyere Bubble Geometry 291 giving In 4T s l T ,+T Sl £ T ,-T s l p T + 1 arctan _£ 2T s l s l ..(IV.6) From Kreith 142 F „ , = A 2-1 _p_ e-A s l (IV.7) Substituting t h i s into Equation IV.4 gives 3 = 3 a e. 4r p c P c p,c (IV.8) Evaluating parameters: (a) ei t - 0.7, from Kreith 143 for graphite at room temperature, source temperature 12 00 C -8 2 4 (b) a = Stefan Boltzman constant = 5.671(10 ) J/s-m -K (c) p c ~ 1500 kg/m (d) c p,c reference (109) 1340 J/kg-K, reference (109) (e) r = 40 ym P Therefore 3 * 3.70(10 1 0 ) K~ 3s~ 1 Assuming an i n i t i a l temperature of 20 C and f i n a l temper-ature of 600°C, evaluation of Equation IV.6 gives t = 350 ms APPENDIX V FUMING FURNACE MASS BALANCE 293 There are nine d i f f e r e n t components to the fuming furnace mass balance at Company C: 1 : i n i t i a l slag 2 : f i n a l slag 3 : lead blast furnace dust 4 : coal ash carry over 5 : slag carry over 6 : coal carry over 7 : fl u e c l i n k e r 8 : b o i l e r ash 9 : fume Lead bl a s t furnace dust (component 3) i s blown into the slag fuming system and therefore must be included i n the balance. If W . i s the weight f r a c t i o n of j i n component x and M i s x, 3 x the mass of component x, a mass balance over the furnace gives: W l , j M l + W 3 , j M 3 + W 4 , j M 4 + W 5 , j M 5 + W 6 , j M 6 = W 2 , j M 2 + W 7 , j M 7 + W 8 , j M 8 + W 9 , j M 9 ...<V.1> Due to uncertainties i n chemical assays, only balances on p a r t i c u l a r species have any v a l i d i t y . The following species were selected for the balance: Zn, S i 0 2 , Fe and C. Several other equations are available r e l a t i n g various quantities i n Equation V . l . The i n i t i a l bath weight (M,) and 294 the amount of bla s t furnace dust (M^) are numbers which are r e l a t i v e l y easy to obtain. F i n a l l y , from h i s t o r i c a l data, the following relationships were obtained 0.75 Mx < M2 < 0.96 Mx ...(V.2) and 0.02 Mg < M ? + Mg < 0.20 Mg ...(V.3) Equation V.2 relates the f i n a l bath weight to the i n i t i a l wieght. Equation V.3 i s a r e l a t i o n between the fume, ash and c l i n k e r . Since t h i s system of equations contains i n e q u a l i t i e s i t cannot be solved for a s p e c i f i c solution. Instead only the range i n which a p a r t i c u l a r variable l i e s can be determined. A l i n e a r programming routine developed by the U.B.C. Computing Centre was used. The assays on each component are presented i n Table V . l . Note that the slag bath was not assumed to be a source of Fe, SiC^ or C, except through component 5, slag carry over. Thus any discrepancy between the charge and t a i l mass of non-fumed components was ignored. The slag carry over assay was estimated as the average of the charge and t a i l assays. In order to determine the coal carry over as coal ash, the s i l i c a content of the coal ash was set to the s i l i c a content of the coal. F i n a l l y the carbon content of the coal was assumed to be fixed carbon content because d e v o l a t i l i z a t i o n i s l i k e l y TABLE V . l Mass Balance Component Assays (values i n %) Cycle Components 1 2 3 4 5 6 7 8 9 Zn 14.1 4.5 14.8 — 9.3 — 49 39 48 C41 S i 0 o - - 0.9 4.3 27.8 4.3 4.6 2.7 0.7 Fe 2 — — 0.3 - 29 - 4.3 1.6 0.1 C - - - - 0.1 62 0.3 1.3 1.0 Zn 14.0 2.5 14.8 — 8.3 — 48 38 46 C42 SiO„ - - 0.9 4.3 25.5 4.3 4.4 2.3 0.6 Fe - - 0.3 - 31 - 4.6 1.3 0.1 C - - - - 0.1 62 0.2 1.5 1.3 Zn 13.0 2.8 14.8 — 7.9 — 36.5 39 42 C43 SiO~ - - 0.9 4.3 25.9 4.3 5.5 2.7 0.6 Fe 2 — - 0.3 - 31.1 - 5.9 2.0 0.1 C - - - - 0.1 62 0.25 1.4 1.2 Zn 14.4 4.2 14.8 — 9.3 - 40.5 40 41.5 C44 S i 0 2 - - 0.9 4.3 25.5 4.3 4.5 3.6 0.7 Fe — - 0.3 - 30.1 - 4.4 1.5 0.1 C - - - - 0.1 62 0.3 0.9 1.2 Zn 13.6 4.3 14.8 — 9.0 — 49.8 39 46.8 C51 SiO„ - - 0.9 9.6 28.0 9.6 5.1 2.0 0.75 Fe 2 — - 0.3 - 29.0 - 4.7 1.0 0.1 C - - - - 0.1 61 0.25 1.5 1.2 Zn 13.8 6.4 14.8 — 10.1 - 38 39 43 C52 S i 0 o - - 0.9 9.6 23.9 9.6 4.0 2.0 0.7 Fe 2 - - 0.3 - 30.1 - 3.9 1.0 0.2 C - - - - 0.1 61 0.3 1.5 1.7 Zn 13.4 5.4 14.8 — 9.4 — 38 39.5 40 C53 S i 0 o - - 0.9 9.6 25 9.6 4.0 1.9 0.7 Fe 2 - - 0.3 - 29.5 - 3.9 1.2 0.1 C - - — - 0.1 61 0.3 1.2 1.5 296 to have occurred by the time the coal reaches the fume. Bath weight, bl a s t furnace dust weight and coal weight to the furnace over the mass balance period are reported i n Table V.2. TABLE V.2 Mass Balance Components C y c l e t (min) M l (kg) M U 3 (kg) T o t a l C o a l (kg) C41 140 52000 3730 8590 C42 75 52000 2000 6350 C43 125 52000 3330 9560 C44 150 52000 4000 10400 C51 120 52000 4130 7140 C52 125 52000 3860 7510 C53 140 52000 3730 8850 APPENDIX VI FURNACE WALL HEAT TRANSFER MODEL 299 The transfer of heat through the wall of the slag fuming furnace can be simply modelled i f we assume the wall structure shown i n F i g . VI.1 and neglect any contact resistance at the interface between the slag and the s t e e l . The following equations express the heat transfer i n t h i s system: *bath = h t A ( Tsl -V ...(VI.l) * s l = ^ s l ^ s l * A ( Tmp- TI ) ...(VI.2) *st = ( 9 s t / d s t ) A(W ...(VI. 3) At steady state ^bath = %1 = *st -..(VI. 4) Solving the above system of four equations to eliminate T j , and the heat flow terms gives d g l = ^ s l mp w - s t ^ s l ...(VI.5) h. (T . —T ) g . t s l mp y s t - T, w r Water ^ Steel _^i_...4J_Mf:._." *t 'A - - -Solid /, - - -s / slag / Liquid slag F i g . VI.1 Fuming Furnace Wall Structure 301 APPENDIX VII SLAG FUMING MODEL PROGRAM 302 IMPLICIT REAL*8 (A~Z) C REAL*4 OX,CX C INTEGER JFLAG,JCOUNT,JC,STEP,STEP2,LFLAG,STEPC,STEP3,IFL, 1JCNT2,JCNT3,MST,INT,J,JT,JT1,I,IX,IN,INTS,PH,CTR,N,KFL C DIMENSION TEST(4),HM(12),COALM(20),PAIR(20),PP(20), 1SP(20),BATHT(20),ZM(20),C(20),FE2M(20),FE3M(20),CAOM(20), 2AL2O3M(20),DELTAT(20),OXY(20),OXYP(20),COMET(9),CHR(4), 3INPTT(20),SIO2M(20),FZNM(20),FCOM(20),FCO2M(20),FH2M(20), 4FH2OM(20),FCM(20),SM(20),Y(11),F(11),T(11),S(11),G(11), 5SAIR(20),WR(4) C EXTERNAL FUNC C COMMON C1S,C2,C3,C4,V1,V2,V3,V4,ZN,FE2,FE3X,CAO,SI02, 1AL203,TEMP,INTR,PT,TRES,ACZNO,ACIR1,DR,DELT1,DELT2,DELTI, 2A0,EA,RO,DZNOF,DFEOF,DFE3F, 3WX,PYRRT,INT,JCOUNT,JCNT2,JCNT3,MST,STEPC,PH,CTR C DATA HZNOS/19680.0000/,HZNO/46024 0.000/rHCO/-114390.55/, 1HCO2/-395346.20/,HH2O/-247 483.60/,HFE2O/329615.50/, 2HVOL/-430.000000/,RC/0.0820500000/,RHOC/1500.000/, 3RHOSL/3900.0000/,VIS/0.5000000/,KSL/1.5000/,HC/600.0/, 4STT/373.0/,GE/'>'/,LE/,<,/,EQ/'='/,HFUS/341200.0/, 5CP/13 57.0000/,CPV/1l92.4/,Pl/3.141592654/ C READ (7,43) READ (7,45) READ (7,47) READ (7,53) READ (7,48) READ (7,49) READ (7,51) C C IN : 1 = NO DATA PRINTED C 2 = ALL DATA PRINTED C C CTR : 1 = WALL EFFECT C 2 = NO WALL EFFECTS C 3 = ZN/COAL, HEAT BALANCE PROFILES C ('TEND' BECOMES TRES(MAX) SEC) C 4 = 2ND ORDER BATH MODEL C C READ (7,54) READ (7,50) JT1=JT-1 READ (7,55) READ (7,57) READ (7,59) READ (7,57) READ (7,59) READ (7,65) READ (7,57) IX,OX,BX,CX I NTS OBJ BTHWT1 (COMET(I), 1=1,5) TEST(1),TEST(2) IN,JT,CTR C1,C2,C3,C4,V1,V2,V3,V4 WX,FE3ST (COALM(J), J=1,JT1) (PAIR(J), J=1,JT) (PP(J), J=1,JT) (SAIR(J), J=1,JT) (SP(.J), J=1,JT) (INPTT(J), J=1,JT) (OXY(J), J=1,JT) 303 READ (7 59) (OXYP(J), J=1,JT) (BATHT(J), J=1,JT) READ (7 65) READ (7 69) (ZM(J), J=1,JT) READ (7 69) (C(J), J=1,JT) READ (7 69) (FE2M(J), J=1,JT) READ (7 69) (FE3M(J), J=1,JT) READ (7 69) (CAOM(J), J=1,JT) READ (7 69) (SI02M(J), J=1,JT) READ (7 ,69) (AL203M(J), J=1,JT) READ (7 ,71 ) (DELTAT(J), J=1,JT1) READ (7 r73) FURLEN,FURWID,NTUY READ (7 ,75) SLMPT,PORO,TCP READ (7 ,76) VBATH,BFREQ READ (7 ,69) CHCAO,CHSI0,CHFEO,CHFEM,CHZNO READ (7 ,69) WCAO,WSI02,WFEO,WFEM,WZNO 43 45 47 48 49 50 51 54 53 55 57 59 65 69 71 73 75 76 77 79 83 FORMAT FORMAT FORMAT FORMAT FORMAT FORMAT FORMAT FORMAT FORMAT FORMAT FORMAT FORMAT FORMAT FORMAT FORMAT FORMAT FORMAT FORMAT FORMAT FORMAT FORMAT READ (7 READ (7 READ (7 READ (7 READ (7 READ (7 READ (7 READ (7 READ (7 12,1X,A4,F8.1,1X,A4) 12) • A8) 6A8) 1 0A8) F5.3,1X,F4.2) 212,1X,I1) 20F6.4) 20F8. 1 ) 20F7.3) 20F7.3) 20F8.3) 20F8.3) 20F7.4) 20F6.3) 2(F5.2,1X),F3.0) F6.1,1X,F4.1,1X,F5.3) F5.2,1X,F5.1) 20(F7.5,IX)) 3 (F5.3,1X)) 3(F7.3,1X)) 77) (FZNM(J), J=1,JT1) 77) (FCOM(J), J=1,JT1) 77) (FC02M(J), J=1,JT1) 77) (FH2M(J), J=1,JT1) 77) (FH20M(J), • J=1 ,JT1 ) 77) (FCM(J), J=1,JT1) 79) FF,YY 79) FOC 83) TSR,TEND,TP THIRD=1.0/3.0 KFL=0 RHOSLF = RHOSL*( 1 . O-PORO/1-00 . 0 ) INT=INTS-1 C1S=C1 YO=1.0-FF-YY TS2=0.0 304 TT=0.0 90 INT=INT+1 TN=TT+DELTAT(INT) IF (TS2 .EQ. 0.0) TS=TSR IF (TS2 .NE. 0.0) TS=TS2 IF (TS2 .NE. 0.0) TS2=0.0 C BAREA=FURLEN*FURWID PAIRA=(PAIR(INT)+PAIR(INT+1))/2.0 PPA=(PP(INT)+PP(INT+1) ) /2.0 SAIRA=(SAIR(INT)+SAIR(INT+1))/2.0 SPA=(SP(INT)+SP(INT+1))/2.0 INPT=(INPTT(INT)+INPTT(INT))/2.0+27 3.16 GP=PAIRA*PPA/101.325*(273.16/(INPT)) GS=SAIRA*SPA/101.325*(273.16/(INPT)) GG=GP+GS 0XYA=(0XY(INT)+0XY(INT))/2.0 OXYPA=(OXYP(INT)+OXYP(INT+1))/2.0 OIN=0.209*GG/(0.08205*273.16) + (0XYA*0XYPA/101.325)/ 1(0.08205*273.0) COAL=COALM(lNT) HCOALC=(C1+C2*V1)/12.01*HC02+(C2*V2)/2.016*HH20-HVOL C c 02=(C1+C2*V1)/l2.0l+0.5*(C2*V2)/2.0l6-(C2*V3)/32.00 C 02C=02*YY*COAL IF (02C . G E . OIN) YY=OIN/(02*COAL) KTOX=HCOALC*YY*COAL C IF (TT .GT. 0.0) GOTO 430 C SLMPT=SLMPT+273.16 ZN2=ZM(INT) FE22=FE2M(lNT)-3.484*SM(INT) FE3 2=FE3M(lNT)+3.484*SM(INT) CA02=CA0M(INT) SI022=SI02M(INT) AL2032=AL203M(INT) BTHWT2=BTHWT1 C B T H T 2 = BATHT(INT)+27 3 . 1 6 C C C c ******** R EAD INPUT DATA FOR PARTICLE CONSUMPTION MODEL C READ (8,101) INTR,TEMP,PT 101 FORMAT (D9.3,1X,F6.1,1X,F6.3,1X,F7.4) READ (8,105) ACZNO,ACIR1 105 FORMAT (F6.3,1X,F6.3) READ (8,111) DZNOF,DFEOF,DFE3F,DR 111 FORMAT (F9.5,1X,F9.5,1X,F9.5,1X,F7.3) C C IF STEPC = 1 NO BOUDOUARD REACTION 305 READ (8,115) DELT1,DELT2,E 115 FORMAT (//,D9.3,1X,D9.3,1X,D9.3) READ (8,121) A0,EA,RO 121 FORMAT (D9.3,1X,D9.3,1X,F4.1) READ (8,125) JCOUNT,JCNT2,JCNT3,MST 125 FORMAT (I 5,1X,I 5,1X,I 5,1X,I 5) READ (8,131) PYRRT 131 FORMAT (D9.3) C C IF (IN .EQ. 1) GOTO 400 C WRITE (6,199) 199 FORMAT (' 1' ,20X,'FUMING CYCLE PREDICTION*,1 OX, 1'VERSION 7',///) C WRITE (6,201) TEST(1),TEST(2) 201 FORMAT (3OXCOMPANY:',2X,2A8,//) C IF (CTR .EQ. 2) WRITE (6,202) 202 FORMAT (35X,'### NO WALL EFFECT ###',//) C IF (CTR .EQ. 3) WRITE (6,203) 203 FORMAT (35X,'#### ZN/COAL & DT/DT VS TRES PROFILES 1 ####',//) C WRITE (6,205) 205 FORMAT (20X,'COAL',40X,'AlR',//) C WRITE (6,207) COAL,PAIRA,PPA 207 FORMAT (25X,'COAL RATE:',2X,F5.2,2X,'KG/MIN',16X,'PRIMARY 1 AIR' ,4X,F7.2,2X, 'M<3>/MIN' ,/,90X,F6.1 ,2X,'KPASCALS' ) C WRITE (6,209) C1,C2,SAIRA,C3,SPA,C4 209 FORMAT (24X,'COAL ASSAY:',2X,F5.3,2X,'FlXED CARBON',/, 137X,F5.3,2X,'VOLATILES',12X,'SECONDARY AIR',3X,F7.2,2X, 2'M<3>/MIN',/,37X,F5.3,2X,'ASH',35X,F6.1,2X,'KPASCALS',/, 337X,F5.3,2X,'MOISTURE',/) C WRITE (6,211) V1,INPT,V2,V3 211 FORMAT (2OX,'VOLATILE ASSAY:',2X,F5.3,2X,'C',28X,'TEMP:', 14X,F6.1,2X,'DEG K',/,37X,F5.3,2X,'H',/,37X,F5.3,2X,'O', 2//) C ZNOI=ZM(lNT)*8l.37/65.37 WRITE (6,213) ZM(INT),BTHT2,ZNOI,CAOM(INT),BTHWT1, 1SI02M(INT),AL203M(INT),SLMPT 213 FORMAT (20X,'SLAG ASSAY (PER CENT) ',20X, 1 'BATH DATA (INITIAL)',//,36X f 1 INITIAL5X, .2/,30X,'ZN' ,5X,F5,2,2OX, 'TEMP 1 ,9X,F6.1 ,2X, 'DEG K' ,/,29X, 3'ZNO' , 1 (5X,F5.2),/,29X,'CAO' ,5X,F5.2,2OX,'BATH WT' ,5X, 4F8. 1 , 1X, 'KG' ,/,28X, ' SI02'., 1 (5X,F5.2) ,/, 52 7X,'AL203',5X,F5.2,20X,'SLAG MPT',5X,F6.1,2X,'DEG K',/) C WRITE (6,215) FE22,FE32,FE3ST,WX 3 0 6 215 FORMAT (29X,'FE2+',4X,F5.2, 1/,29X,'FE3+',4X,F5.2,//,20X,'FE3+ SATURATION AT ', 2F5.2, '%' ,/,30X,'FEXO X=' ,F5.3,/) C WRITE (6,220) FURLEN,NTUY,FURWID 220 FORMAT (/,2OX,'FURNACE LENGTH = ',F6.2,1X,'M',20X, 1'NUMBER OF TUYERES = ',F3.0,/,20XFURNACE WIDTH = * , 2F6.2,1X,'M',/) C WRITE (6,225) BFREQ,VBATH,TCP 225 FORMAT (20X,'BUBBLE FREQUENCY = ',F5.1,1X,'SEC-1',15X, 1'BATH VELOCITY = ',F5.2,1X,'M/SEC',/,20X,'TUYERE', 2'COLUMN VOID FRACTION = ',F5.3,/) C WRITE (6,230) FF,YY,YO,FOC 230 FORMAT (//,20X,'F = ' ,F5.3,/,20X,'Y = ' ,F5.3,1 OX,'YO = ', 1F5.3,//,20X,'FOC = ',F5.3,2X(FRACTION .02 CONSUMED)',//) C WRITE (6,240) TS 240 FORMAT (20X,'TIME STEP = ',F7.3,' (MIN)',///) C C ******** RECORD OF RUN PARTAMETERS PRINTED C C IF (STEPC .NE. 1) GOTO 312 WRITE (6,310) 310 FORMAT (//,30X,' PARTICLE REACTION ANALYSIS (INCLUDING', 1' PYROLYSIS)',///) GOTO 317 312 WRITE (6,314) 314 FORMAT (//,30X,'PARTI CLE REACTION ANALYSIS (INCLUDING' , 1' BOUDOUARD REACTION AND PYROLYSIS)',///) RHOSLM=0.0 317 WRITE ( 6 , 3 2 0 ) INTR,RHOSL,TEMP,RHOC,PT,PORO,VIS 320 FORMAT (20X,'PARTI CLE RADIUS = ',F9.7,1X,'(M)',20X, 1'SLAG DENSITY = ' ,F6.1 ,1X,' (KG/M3)' ,/,20X, 2'BATH TEMP = ',F6.1,1X,'(K)',29X,'COAL DENSITY = ',F6.1, 31X,'(KG/M3)',/,20X,'SYSTEM PRESSURE = ',F5.1,1X,'(ATM)', 422X,'SLAG POROSITY = ',F5.2,1X,'%',/,71X, 5'SLAG VISCOSITY = ',F7.4,1X,'(KG/M-SEC)*,/) W R I T E ( 6 , 3 3 3 ) D R , D Z N O F , D F E O F,DFE3F 3 3 3 FORMAT ( 2 0 X , 'RATIO DFEO/DFE304 = ' ,F4 . 1 ,/,20X, 1'DZ.NO FACTOR = ' , F 9 . 5 , 1 O X , ' D F E O FACTOR = ' , F9 .5,10X, 2 ' D F E 2 0 3 FACTOR = ',F9.5,//) W R I T E ( 6 , 3 3 5 ) P Y R R T 335 FORMAT ( / ,20X,'PYROLYSIS RATE = ',D11.4,1X, 1'(DEG K/SEC)',/) IF (STEPC . E Q . 1) GOTO 345 WRITE ( 6 , 3 4 0 ) AO,EA,RO 3 4 0 F O R M A T ( 2 O X , ' B O U D O U A R D REACTION CONSTANTS:1,5X,'AO = ', 1 D 9 . 3 , ' ( S E C - 1 - A T M - 1 ) ' , / , 5 4 X , 2'EA = ',F9.1,' (RJ/KG-MOLE)',/,55X,'N = ',F4.1,//) 3 4 5 W R I T E ( 6 , 3 4 6 ) D E L T 1 346 FORMAT (30X,'TIME STEP = ',F12.10,1X,'(SEC)',/) C 307 400 WRITE (6,410) 410 FORMAT (//,7X,'T' ,1 OX,'ZN' ,1 OX,'FE3+' ,7X,'FE2+1 ,7X, 1'TEMP',12X,'BATH WT',7X,'CAO',8X,'ZN FR',7X,'FE3 R', 27X,'FE2 0',/) C IF (CTR .EQ. 3) GOTO 416' WRITE (6,415) 415 FORMAT (15X,'RHOSLM' ,1 OX,'ACZNO' ,5X,'ACIR1 ' ,8X,'TRES' ) C 416 WRITE (6,417) 417 FORMAT (9X,'FZN' ,1 OX,'FCO' ,1 OX,'FC02' ,9X,'FH2' ,1 OX, 1'FH20',9X,'FN2',10X,'FC',1IX,'PH') C IF (CTR .EQ. 3) WRITE (6,418) 418 FORMAT (5X,'T',9X,'ZFR',8X,'ZNP',7X,'ZN/COAL',5X, 1'DT/DT',/) WRITE (6,610) TT,ZN2,FE32,FE22,BTHT2,BTHWT2,CA02 420 CONTINUE IF (TS2 .EQ. 0.0) TS=TSR 430 CONTINUE ZN1=ZN2 FE21=FE22 FE31=FE32 CA01=CA02 SI021=SI022 AL2031=AL2032 BTHT1=BTHT2 BTHWT1=BTHWT2 C FE2=FE21 ZN=ZN1 FE3=FE31 CAO=CA01 SI02=SI021 AL203=AL2031 C C FE3X=FE3 IF (FE3 .GT. FE3ST) FE3X=FE3ST C TEMP=BTHT1 C VBUBB=(GG/60.0)*(1.0/NTUY)*(TEMP/27 3.16)*(1.0/BFREQ) D3UBB=(6.0*VBUBB/PI)* * THIRD SLGH = BTHWT 1 /.(RHOSLF*FURLEN* (FURWID-2 . 0*TCP*DBUBB) ) XPATH=SLGH+(FURWID-2.0*DBUBB)/4.0 TRES=XPATH/VBATH C WRITE (6,435) 435 FORMAT (/,3X, ' ' , , . ) C X=0.0 PH=0 N=1 1 308 PARTOI=4.0*Pl/3.0*INTR**3*RHOC C CALL FUNC (X,Y,F) YT=Y(1)+Y(2)+Y(3)+Y(4)+Y(5)+Y(6) FZN=Y(1)/YT FCO=Y(2)/YT FC02=Y(3)/YT FH2=Y(4)/YT FH20=Y(5)/YT FN2=Y(6)/YT FC=Y(11)*12.01/PARTOI C IF (CTR .EQ. 3) WRITE (6,440) FZN,FCO,FC02,FH2,FH20, 1FN2,FC C IF (CTR .EQ. 3) TRES=0.0 432 IF (CTR .EQ. 3) TRES=TRES+DELT2 C Z=TRES H=DELT1 HMIN=1.0D-04*H C 438 CALL DRKC(N,X,Z,Y,F,H,HMIN,E,FUNC,G,S,T) C C1=C1S YT=Y(1)+Y(2)+Y(3)+Y(4)+Y(5)+Y(6) FZN=Y(1)/YT FCO=Y(2)/YT FC02=Y(3)/YT FH2=Y(4)/YT FH20=Y(5)/YT FN2=Y(6)/YT FC=Y(11)*12.01/PARTOI C WRITE (6,440) FZN,FCO,FC02,FH2,FH20,FN2,FC,PH 440 FORMAT (1 OX,7(F7.5,5X),I 1) C WALLA 1=SLGH*2.0*(FURLEN+FURWID)+BAREA WALLA=WALLA1 IF (CTR .EQ. 2) WALLA=0.0 C ZFR=FZN/(FCO+FC02)*FF*COAL*(C1+C2*V1-FC)/12.01 ZNP=ZFR*TS*65.37 ZNTCL=ZNP/(COAL*TS) FE3R=2.0*((FCO+2.0*FCO2+FH2O)/(FCO+FC02)*FF*COAL* 1(C1+C2*V1-FC)/12.01-ZFR-FF*COAL*C2*V3/16.00) FEOO=4.0*FOC*(OIN-02C) IF (FEOO .LT. 0.0) WRITE (6,451) 451 FORMAT (' FEOO < 0.0',//) IF (FEOO .LT. 0.0) FEOO=0.0 COP=FCO/(FCO+FC02)*FF*COAL*(C1+C2*V1-FC)/1 2. 01 C02P=COP*FC02/FCO H20P=COP*FH20/FCO C HRED=ZFR*(-1.0*HZNOS+HZNO)+COP*HCO+C02P*HC02+H20P*HH20 1+FE3R/2.0*HFE2O 309 HFEOO=FEOO*(-1.0*HFE2O)/2.0 C 480 QH1=- 1 .0*(GP*(BTHT1-293.0)*CP+GS*(BTHT1-INPT) 1 *CP+C4*COAL/18.0*(45200000.0 + 41840.0*(BTHT1-373.16)) + 2COAL *2050200.0 +HC * 6 0.0 *WALLA 1 *(BTHT1 -SLMPT) + 3(HRED+HTOX+HFEOO)* 10 0 0.0) QA=QH1*TS/(CPV*BTHWT1) QB=1.0*KSL*WALLA*RHOSL*(SLMPT-STT)/(HC*CPV*BTHWT1) A11=1.0+QB*CPV/(BTHT1-SLMPT) B11=-2.0*QB*SLMPT*CPV/(BTHT1-SLMPT)-SLMPT-BTHT1-QA 1-QB*CPV+QB*HFUS/(BTHT1-SLMPT) C11=SLMPT**2*QB*CPV/(BTHT1-SLMPT)+SLMPT*(BTHT1+QA 1+QB*CPV-QB*HFUS/(BTHT1-SLMPT))-QB*HFUS C BTHT2=(-1.0*B11+(B11**2-4.0*A11*C11)**0.5)/(2.0*A11) C DTPDT=(BTHT2-BTHT1)/TS IF (CTR .EQ. 3) WRITE (6,435) IF (CTR .EQ. 3) WRITE (6,500) X,ZFR,ZNP,ZNTCL,DTPDT 500 FORMAT (3X,F6.3,5X,F6.3,5X,F6.2,5X,F6.3,5X,F8.3,/) IF (CTR .EQ. 3) WRITE (6,435) IF (CTR .EQ. 3 .AND. X .GT. TEND) GOTO 700 IF (CTR .EQ. 3) GOTO 432 C C C WALLC=-1.0*(KSL/HC)*(SLMPT-STT)*(1.0/(BTHT2-SLMPT) 1 -1 .0/(BTHT1-SLMPT))*WALLA*RHOSL C 510 WRITE (6,515) WALLC 515 FORMAT (1 OX, 'WALLC = ',F7.2) C WRITE (6,435) C BTHWT2=BTHWT1-ZFR*TS*81.37-FE3R/2.0*TS*16.00+FEOO/2.0* 1TS*16.00+WALLC+COAL*TS*C3 ZN2=(ZN1/100.0*BTHWT1-ZFR*TS*6 5.3 7+WZNO*WALLC*0.8034/ 1100.0)/BTHWT2*100.0 FE32=(FE31/100.0*BTHWT1+FEOO*TS* 55.85-FE3R*TS* 55.85 + 1WFEM*WALLC*0.4824/100.0)/BTHWT2*100.0 FE22=(FE21/100.0*BTHWT1+FE3R*TS*55.85~FEOO*TS*55.85+ 1(WFEO*0.7773+WFEM*0.2412)*WALLC/100.0)/BTHWT2*100.0 C CA02=(CA01*BTHWT1+WCAO*WALLC)/BTHWT2 SIO 2 2 =(SIO 21 *BTHWT1+WS102 *WALLC)/BTHWT 2 AL2032=(AL2031 *BTHWT1+5.0*WALLC)/BTHWT2 C IF (CTR .NE. 4) GOTO 580 IF (KFL .EQ. 1) GOTO 540 IF•(KFL .EQ. 2) GOTO 580 ZNS=ZN1 FE2S=FE21 FE3S=FE31 CAOS=CA01 SI02S=SI021 AL203S=AL2031 310 ZFR1=ZFR FE3R1=FE3R FE001=FEOO HRED1=HRED HFEOO1=HFEOO BTHTS=BTHT1 BTHWTS=BTHWT1 KFL= 1 GOTO 430 C 540 ZN1=ZNS FE21=FE2S FE31=FE3S CA01=CAOS SI021=SI02S AL2031=AL203S BTHWT1=BTHWTS ZFR=(ZFR+ZFR1)/2.0 FE3R=(FE3R+FE3R1)/2.0 FEOO=(FEOO+FEOO1)/2.0 HRED=(HRED+HRED1)/2.0 HFEOO=(HFEOO+HFEOO1)/2.0 BTHT1=BTHTS KFL=2 GOTO 480 C 580 KFL=0 TT=TT+TS • TTT=TT+TS IF (TT+TS .GT. TN) TS2=TTT~TN IF (TT+TS .GT. TN) TS=TN-TT IF (TT .GE. TN) GOTO 630 IF (TT .GE. TP) GOTO 600 GOTO 650 C 600 WRITE (6,610) TT,ZN2,FE32,FE22,BTHT2,BTHWT2,CA02,ZFR, 1FE3R,FEOO 610 FORMAT (/,3X,5(F7.2,5X),5X,F7.1,5X,4(F7.2,5X),/) C TPS=TP TP=TT+1.0 IF (TP .LT. TPS+TS) TP=TPS+TS GOTO 650 630 WRITE (6,631) TT,ZN2,FE32,FE22,BTHT2,BTHWT2,CA02,ZFR, 1FE3R,FEOO 631 FORMAT (//,3X,5(F7.2,5X),5X,F7.1,5X,4(F7.2,5X),//) IF (TT .LT. TEND) GOTO 90 C 650 IF (TT .LT. TEND) GOTO 420 WRITE (6,610) TT,ZN2,FE32,FE22,BTHT2,BTHWT2,CA02,ZFR, 1FE3R,FEOO C 7 00 CONTINUE STOP END 311 C SUBROUTINE FUNC(X,Y,F) C C C C Q ***************************************** c * * C * COAL PARTICLE - SLAG REACTION ANALYSIS * C * * C * ZNO AND FE203 REDUCTION ON COAL PARTICLE BUBBLE * C * WITH MASS TRANSFER OF THESE SPECIES (AND FEO) * C * AND BOUDOUARD REACTION AS THE RATE CONTROLLING * C * STEPS * C * INCLUDING PYROLYSIS * C * * Q ****************************************************** C C IMPLICIT REAL*8 (A"Z) C INTEGER JFLAG,JCOUNT,JC,STEP,STEP2,LFLAG,STEPC,STEP3,IFL, 1JCNT2,JCNT3,MST,I NT,RFL,PH,CTR,11 C DIMENSION Y(11),F(11) C COMMON C1S,C2,C3,C4,V1,V2,V3,V4,ZN,FE2,FE3X,CAO,SI02, 1AL203,TEMP,INTR,PT,TRES,ACZNO,ACIR1,DR,DELT1,DELT2,DELTI, 2A0,EA,RO,DZNOF,DFEOF,DFE3F, . 3WX,PYRRT,INT,JCOUNT,JCNT2,JCNT3,MST,STEPC,PH,CTR C DATA PI/3.141592654/,RHOC/1500.000000/,RHOSL/3900.00 100000/,G/9.81000000/,VIS/0.500000000/,AC/1.000000000/, 2RC/0.08205000000/,RJ/8.314400000000/ c c c c c C ******** CALCULATION OF SLAG MOLAR DENSITY FOR CONVERSION C OF ACTIVITY LEVELS TO MOLAL CONCENTRATIONS C C UNKNOWN SPECIES (UNK) MOLECULAR WT = 60.0 C C M-X = KG-MOLES X (PER 100 WT UNITS) C X = % X C C-X-B = BULK CONCENTRATION X (KG-MOLES/M3) C RHOSL = SLAG DENSITY (KG/M3) C C PCO2I=0.0 IF (X .GT. 0 . 0 .OR. PH .EQ. 2) GOTO 90 WX1=3.0*WX-2.0 WX2=2.0*(1.0-WX) • 25 FE3=FE3X MZNO=ZN/65.37 312 MFEO=FE2/(WX1*55.85) MFE203=1.0/55.85*(FE3-WX2/WX1*FE2)/2.0 MFE304=(1.0/55.85)*(WX2*FE2-WX1*FE3)/(WX2-2.0*wX1) MFE02=(FE2/55.85-MFE304)/WX1 C MCAO=CAO/56,08 MSIO2=SIO2/60.09 MAL203=AL203/101.96 WTT=MZN0*81.37+MFEO*(WX*55.85+16.00)+MFE203*159.7+CAO+ 1SI02+AL203 UNK=100.0-WTT MUNK=UNK/60.0 ZN0=MZN0*81.37 FE0=MFE0*71 .85 FE203=MFE203*159.7 CZN0B=RH0SL*MZN0/100.0 CFE0B=RH0SL*MFE0/100.0 CFE20B=RHOSL*MFE203/100.0 CFE304=RH0SL*MFE304/100.0 CFE02=RH0SL*MFE02/100.0 CCAOB=RHOSL*MCAO/i00.0 CSI02B=RH0SL*MSI02/100.0 CAL20B=RH0SL*MAL203/100.0 CUNKB=RH0SL*MUNK/100.0 RHOSLM=CZNOB+CFEOB+CFE20B+CCAOB+CSI02B+CAL20B+CUNKB C CS=MCAO/MSI02 LNACF=(3310.0*CS+1656.5)/TEMP-1.887*CS-0.6394 LNACZ=(16390.0*CS-12030.0)/TEMP-l0.894*CS+8.8317 ACZNO=DEXP(LNACZ) ACFEO=DEXP(LNACF) ACFE3O=DEXP(8495.0/TEMP-2.653) ACIR1=ACFE30/ACFEO**(3.0/WX) C MFFEO=CFEOB/RHOSLM MFFE20=CFE20B/RHOSLM MFFE02=CFE02/RHOSLM MFFE30=CFE304/RHOSLM C E=RJ*TEMP G5=-62442 0.0+250.2*TEMP K5=DEXP(-1.0*G5/E) G7=-582580.0+260.6*TEMP K7=DEXP(-1.0*G7/E) C C2 ACIR2=(K7/K5)**0.5*ACIR1*(MFFEO**2)/(MFFEO-MFFE20)**3 AC 1=MFFEO* *(4.0/WX)*K7/MFFE20**2 AC2=(ACIR1**2*MFFE3O**2/K5/MFFEO2**(6.0/WX)) AC3=AC2**( (3.0-2. 0'/WX)/( 4. 0-3. 0/WX) ) ACIR2=(AC1*AC3)**0.5 C DBASE=10.0**("5450.0/TEMP-1.93-4.0) DZNO=DZNOF*DBASE DFEO=DFEOF*DBASE DFE203=DFE3F*DFEO/DR W=A0*DEXP(-1.0*EA/(RJ*TEMP)) 313 C C C C C C *********** REDUCTION PHASE I: REDUCTION IN THE PRESENCE OF C COAL PARTICLE C C C C C ********** TITLES PRINTED C C c ********** FREE ENERGY DATA AND EQUILIBRIUM CONSTANTS C E=RJ*TEMP G0=-228781.1-171.5*TEMP K0=DEXP(-1.0*G0/E) G6=~920480.0+396.6*TEMP K6=DEXP(-1.0*G6/E) C C H20 + CO = C02 + H2 GF=-3 347 2.05+29.3 5*TEMP KF=DEXP(-1.0*GF/E) GD=212756.4-142.45*TEMP KD=DEXP(-1.0*GD/E) GG=17 9284.3 5-113.1*TEMP KG=DEXP(-1.0*GG/E) C2 GH=18179.0-52.7*TEMP GH=8870.1-35.95*TEMP KH=DEXP(-1.0*GH/E) C C C + C02 = 2CO GJ=166565.1-170.96*TEMP KJ=DEXP(- 1 .0*GJ/E) C C EXP23=2.0/3.0 EXP13=1.0/3.0 C C c ********** INITIAL VALUE CALCULATIONS C C RHOB = BUBBLE DENSITY C PARTOI = INITIAL PARTICLE WT C CC = CONTAINED C (WT) C T = ELAPSED TIME C P-X = PARTIAL PRESSURE X C G-X = KG-MOLES X IN GAS PHASE C IF (PH .EO. 2 .OR. X .GT. 0.0) GOTO 90 C Q ************* PYROLYSIS C PARTOI=4.0*Pl/3.0*INTR**3*RHOC 314 GC0=PART0I*C2*V3/16.00 GH2=PARTOI*C2*V2/2.016 GN2=PARTOI*C2*V4/28.014 GTN=GCO+GH2+GN2 VCO2=0.0 VK2G=0.0 VH2=GH2 VCO=GCO 61 VT=VH2+VCO+VH20+VC02+GN2 VC02P=VCO**2*PT/(VT*AC*KJ) VH20P=VH2*VC02P/(VCO*KF) IF (DABS((VH20P-VH20)/VH20P) .LT. 0.000000001) GOTO 65 VH20=VH20P VC02=VC02P VH2=GH2-VH20 VCO=GCO-2.0*VCO2-VH2O GOTO 61 65 RHOG=PT/(RC*TEMP) GASV=VT/RHOG PCO=GCO/GTN*PT CU=GCO*12.01 PARTN=PARTOI-PARTOI*(C2*V3*28.01/16.00+C2*V2+C2*V4) CI =C1 S C1=(PARTOI*C1+PARTOI*C2*V1~CU)/PARTN COALV=PARTN/RHOC Y(1)=0.0 Y(2)=VCO/VT*RHOG Y(3)=VC02P/VT*PT*RHOG Y(4)=VH2/VT*RHOG*PT Y(5)=VH20/VT*PT*RHOG Y(6)=GN2/VT*RHOG Y(7)=(3.0*(GASV+COALV)/(4.0*PI))**EXP13 Y(8) = (3.0 *COALV/(4.0 * PI))* *EXP13 Y(9)=PARTN Y(10)=GASV Y(11)=PARTN*C1/12.01 COCR=1.0/C1 T=(TEMP-2 98.0)/PYRRT WRITE (6 r85) RHOSLM,ACZNO,ACIR1,TRES 8 5 FORMAT (15X,F7.3,8X,F5.2,5X,F5.2,8X,F5.2) PH=2 GOTO 900 90 YT=Y(1)+Y(2)+Y(3)+Y(4)+Y(5)+Y(6) PZN=Y(1)/YT*PT PC02=Y(3)/YT*PT PH20=Y(5)/YT*PT PCO=Y(2)/YT*PT PH2=Y(4)/YT*PT PN2=Y(6)/YT*PT RHOG=PT/(RC*TEMP) GASWT=Y{10)*(Y(1)*65.37+Y(2)*28.01+Y(3)*44.01+Y(4)* 12.016+Y(5)*18.016+Y(6)*28.014) RHOB=(GASWT+Y(9))/(4.0/3.0*PI*Y(7)**3) 315 C LFLAG=0 C C c C ************* PARTICLE CONSUMPTION STEPS 101 - 310 C C AR = BUBBLE SURFACE AREA C UTS = BUBBLE RISE VELOCITY C PE-X = PECLET NO. OF SPECIES X C SH-X = SHERWOOD NO. OF X C K-X = MASS TRANSFER COEFFICIENT OF X C N-X = MOLAR TRANSFRE RATE OF X C C CZNOI = INTERFCIAL ZNO CONCENTRATION C 101 AR=4.0*PI*Y(7)**2 PO2=PCO**2/(AC**2*K0) UTS=G*(2.0*Y(7) )**.2*(RHOSL-RHOB)/( 18.0*VIS) IF (UTS .LT. 0.0) WRITE (6,103) GASWT,RHOB,Y(9),RHOSL, 1G,UTS C PEZNO=2.0*Y(7)*UTS/DZNO PEFEO=2.0*Y(7)*UTS/DFEO PEFE20=2.0*Y(7)*UTS/DFE203 C IF (PEZNO .LT. 0.0 .OR. PEFE20 .LT. 0.0 .OR. PEFEO .LT. 1 0.0) WRITE (6,103) PEZNO,PEFEO,PEFE20,UTS,Y(7) 103 FORMAT (5X,6(D12.5,5X)) SHZNO=1.0+(1.0+PEZNO)**EXP13 SHFEO=1.0+0.0+PEFEO)**EXP13 SHFE20=1.0+0.0+PEFE2O)**EXP13 C KZNO=SHZNO*DZNO/(2.0*Y(7)) KFEO=SHFEO*DFEO/(2.0*Y(7)) KFE2O3=SHFE2O*DFE2O3/(2.0*Y(7)) C 110 CZNOI=(PZN*PC02/(KG*ACZNO/RHOSLM*PCO)) C NZNO=KZNO*AR*(CZNOB-CZNOI) C IF (PC02 .GT. 0 . 0 ) GOTO 115 NFE20A=KFE203*AR*CFE20B NFE203=NFE20A IF (PC02 .EQ. 0 . 0 ) GOTO 120 C KHP=KH*ACIR2*RHOSLM 115 KHP=KH*ACIR2*RHOSLM**(2.0/WX-1.0) C A=PC02 B1=(KFEO*AR/4.0) B2=(KHP*PCO*KFEO+4.0*KFE2O3*CFEOB*PC02)/KFE203 B=B1*B2 CA=(KFEO**2*AR**2)/(4.0) CB=CFEOB**2*PC02-KHP*PCO*CFE20B C=CA*CB 316 NFE20B=(-1.0*B+(B**2-4.0*A*C)**0.5)/(2.0*A) NFE8=NFE20B BOT=NFE8/2.0 TOP=NFE8*2.0 116 N1=(1.0/KHP)*(PCO2/PCO)**(3.0-2.0/WX) N2=2.0/WX*NFE8/KFEO/AR+CFEOB IF (N2 .LE. 0.0) WRITE (6,111) ( Y ( l l ) , 11 = 1,11) 111 FORMAT (5X,5(D12.5,3X)) N3=N2**(2.0/WX) NFE9=AR*KFE203*(CFE20B-N1*N3) CK=(NFE8-NFE9)/NFE8 IF (DABS(CK) .LT. 0.00001) GOTO 118 NFE8=NFE9 GOTO 116 112 IF (CK .GT. 0.0) GOTO 117 BOT=NFE8 NFE8=(BOT+TOP)/2.0 • GOTO 116 117 TOP=NFE8 NFE8=(BOT+TOP)/2.0 GOTO 116 118 NFE20B=NFE8 119 NFE203=NFE20B 120 IF (RO .NE. 0.0) GOTO 200 BOURD=A0*DEXP(-1.0*EA/(RJ*TEMP)) GOTO 2 50 200 BOURD=A0*DEXP(-1.0*EA/(RJ*TEMP))*(PC02-PC02I)**RO 2 50 F(1)=1.0/Y(10)*(NZNO-Y(1)*F(10)) F(2)=1.0/Y(10)*(2.0*BOURD*Y(11)-NZNO-NFE203-Y(2)*F(10)) F(3)=1.0/Y(10)*(NZNO+NFE203-BOURD*Y(11)-Y(3)*F(10)) F(4)=1.0/(Y(3)**2+Y(3)*Y(2)*KF)*(Y(3)*(GH2/Y(l0)-Y(4))* 1KF*F(2)-(GH2/Y(10)-Y(4))*Y(2)*KF*F(3)-Y(3)*Y(2)*KF* 2GH2/Y(10)**2*F( 10)) F(5)=-1.0*GH2/Y(10)**2*F(10)-F(4) F(6)=-1.0*Y(6)/Y(10)*F(10) F(7)=1.0/Y(7)**2*(F(10)/(4.0*PI)+Y(8)**2*F(8)) F(8)=F(9)/(4.0*PI*Y(8)**2*RHOC) F ( 9 ).= - 1 . 0*BOURD* 1 2 . 0 1 * Y ( 1 1 ) *COCR F(10)=1.0/RHOG*(NZNO+BOURD*Y(11)) F( 1 1 )=-1 .0*BOURD*Y(11 ) 900 CONTINUE RETURN END 

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