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Oxidation kinetics of molten copper sulphide Alyaser, Abdelmonem H. 1993

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Oxidation Kinetics of Molten Copper SulphideByAbdelmonem Hussein AlyaserB.Sc. (Metallurgical Engineering), Laurentian University, 1990A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinTHE FACULTY OF GRADUATE STUDIES(Department of Metals and Materials Engineering)We accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAJuly 1993© Abdelmonem Hussein Alyaser, 1993In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)Department of Metals and Materials EngineeringThe University of British ColumbiaVancouver, CanadaDate July 12 1993DE-6 (2/88)ABSTRACTThe oxidation kinetics of molten copper sulphide were investigated by quantitativemeasurements and qualitative observations. Off-gas analyses for SO2 and 02 wereconducted to determine the oxidation rates of approximately 200-gram samples, ofmolten 99.5% Cu2S. The molten sulphide was held in alumina crucibles (approximately44 mm diameter and 75 mm height), and top-lanced with Ar-02 gas mixtures in the hotzone of a vertical tube furnace. During the oxidation reaction, gravimetric measurementsof the copper sulphide baths were also conducted to further support the results of the gasanalysis measurements. A series of laboratory tests, involving reaction gas ranging incomposition from 20-78% 02, was conducted to determine the effect of oxygenconcentration on the kinetics of the oxidation reaction. To determine the influence ofvolumetric gas flow rate on the kinetics of the oxidation reaction and to study the gasphase mass transfer, a series of laboratory tests was carried out utilizing a gas flow raterange of 1-4 liters/min. The effects of other operating conditions, on the oxidation rates,such as bath mixing, and reaction temperature (1200-1300 °C), were also determined.The effect of surface-tension driven flow (the Marangoni effect) on the reaction kineticswas also investigated via surface observation and photography. The overall surfacebehavior was monitored for spontaneous motion, and the eruption of gas bubbles from themelt.The quantitative analysis of reaction rates was also aided by the micro-examination ofquenched bath samples via optical microscopy. Approximately 4-gram samples wereextracted at specific reaction times, using U-shaped quartz tubes. The samples wereexamined microscopically to determine the reaction progress based on the characteristicsof gas bubbles, copper droplets and the phases present.iiiiiThe oxidation reaction of molten copper sulphide was found to take place in two distinctkinetic stages. During the primary stage, simultaneous partial desulphurization andoxygen saturation of the melt, via liquid-gas reaction at the melt surface, takes place.Upon saturation of the melt with oxygen, the secondary stage immediately commences.Throughout the secondary stage, the sulphide phase remains at a constant composition(approximately 80.83 wt% Cu, 17.7 wt% S and 1.47 wt% 0 at 1200 °C and 1 atm), due tosimultaneous surface and melt reactions, until the overall reaction is complete. Threesimultaneous melt reactions occur within the sulphide phase which are responsible for theformation of the metal phase (approximately 98.89 wt% Cu, 0.95 wt% S and 0.16 wt% 0at 1200 °C and 1 atm). As a result of settling oxygen- and sulphur-saturated copperdroplets, the metal phase accumulates at the bottom of the bath.The experimental results revealed that the rate of reaction is controlled by the gas phasemass transfer of oxygen to the melt surface; the liquid phase mass transfer resistance andchemical reaction resistance are negligible. The bath was found to be vigorously mixed,primarily due to the effect of the Marangoni effect although the degree of mixing isslightly enhanced during the secondary stage as a result of rising SO2 gas bubbles andfalling copper droplets.Based on the electrochemical behavior of the sulphide melt and the experimentalrevelations, a mathematical model was constructed to carry out a fundamental study ofthe problem and provide an overall analysis extending beyond the experimentalconditions. The model predictions were found to be in good agreement with the observedresults.The practical implications of this work are: the copper-making reaction in copperconverting is limited by gas phase mass transfer; in the Peirce-Smith converter, one of thefactors for the high degree of mass transfer in the bath is the effect of surface-tensiondriven flows. It is also suggested that the ionic nature of the sulphide bath is anotherfactor for the low liquid phase mass transfer resistance.ivTable of ContentsABSTRACT^Table of ContentsList of Figures viiiList of Tables^ xvList of Symbols xixAcknowledgments xxiii1. Introduction^ 12. Literature Review 42.1. Copper Converting^ 42.1.1. History of the Copper Converter^ 42.1.2. Metallurgy of Copper Converting 52.1.2.1. The Slag-Forming Stage: 72.1.2.2. The Copper-Making Stage:^ 72.2. Thermodynamics of Copper Sulphide Oxidation 82.2.1. Cu-S System^ 92.2.2. Cu-S-0 System 102.3. Gas-Liquid Interactions 132.3.1. Superficial Gas-Liquid Contact^ 162.3.2. Convective Gas-Liquid Contact 172.3.2.1. Gas Jets Impinging on Liquid Surfaces^ 172.3.2.1.1. High Momentum Jetting Systems^ 192.3.2.1.2. Low Momentum Jetting Systems 212.4. Oxidation Kinetic Studies^ 232.5. Interfacial Phenomena 262.5.1. Generation of Spontaneous Interfacial Motion^272.5.1.1. Driving Force^ 272.5.1.2. Mechanism 293. Objectives and Scope^ 323.1. Experimental Objectives^ 343.2. Theoretical Objectives 354. Experimental^ 364.1. Experimental Apparatus^ 364.1.1. Reactor 364.1.2. Gas Drying And Control System^ 414.1.3. Gas Analysis System^ 414.1.3.1. SO2 Absorber 424.1.3.2. Final Off-Gas Flow Rate Measurement^484.1.4. Gravimetric Measurement System^ 494.1.5. Optical Photography System 524.2. Material^ 544.2.1. Copper Sulphide^ 544.2.1.1. Supplied Copper Sulphide^ 544.2.1.2. Prepared Copper Sulphide 54vi4.2.2. Gases^ 554.2.3. Hydrogen Peroxide Solution^ 564.2.4. Titration Reagents^ 574.3. Experimental Procedure 584.3.1. Oxidation Rate Measurement^ 584.3.1.1. Gas Analysis 604.3.1.2. Gravimetric Measurement 614.3.2. Microscopic-Examination of Frozen Melt Samples^ 614.3.3. Surface Observation^ 615. Experimental Results and Discussion 625.1. Oxidation Rate Results 625.1.1. Gas Analysis Data^ 625.1.1.1. Sulphur and Sulphur Dioxide Analyses^ 625.1.1.2. Oxygen Analysis 655.1.1.3. Overall Reaction Rate^ 685.1.2. Gravimetric Measurement Data 705.1.3. Summary Of The Oxidation Rate Results^ 715.1.3.1. Oxidation Rates^ 715.1.3.1.1. Effect of Admitted Gas Flow Rate^ 725.1.3.1.2. Effect of Gas Composition^ 755.1.3.1.3. Effect of Temperature 785.1.3.1.4. Effect of Bath Mixing 815.1.3.2. Reaction Transition Characteristics^ 825.2. Micro-Examination Of The Melt Samples^ 855.3. Observations of the Bath Surface^ 956. Gas Phase Mass Transfer^ 1036.1. Mathematical Analysis for Mass-Transfer Coefficient^ 1036.1.1. Material Balance^ 1036.1.2. Flux Equation: 1036.1.3. Equilibrium At Phase Boundaries: ^ 1036.1.4. Stoichiometry.^ 1046.1.5. Solution. 1046.2. Experimental Gas Phase Mass-Transfer Coefficient^ 1056.3. Gas Phase Mass-Transfer Correlation^ 1096.4. Sensitivity Analysis of the Effect of the Interfacial Area on GasPhase Mass-Transfer Coefficient^ 1136.5. Sensitivity Analysis of the Effect of Temperature on Gas PhaseMass-Transfer Coefficient 1167. Mathematical Modeling and Theoretical Predictions^ 1227.1. Mathematical Model^ 1227.1.1. Assumptions 1227.1.2. Reaction Mechanism and Flux Equations^ 1247.1.2.1. Primary Stage^ 1247.1.2.2. Secondary Stage 1257.1.3. Equilibrium at Phase boundaries^ 128vii7.1.4. Stoichiometry^ 1307.1.4.1. Primary Stage^ 1307.1.4.2. Secondary Stage 1317.1.5. Material Balance 1327.1.5.1. Primary Stage^ 1327.1.5.1.1. Sulphur Balance^ 1327.1.5.1.2. Oxygen Balance 1337.1.5.2. Secondary Stage^ 1337.1.5.2.1. Sulphide Phase 1337.1.5.2.1.1. Sulphur Ion Balance^ 1337.1.5.2.1.2. Oxygen Ion Balance 1347.1.5.2.1.3. Copper Ion Balance^ 1357.1.5.2.2. Metal Phase^ 1357.1.5.2.2.1. Sulphur Balance 1357.1.5.2.2.2. Oxygen Balance^ 1367.1.5.2.2.3. Copper Balance 1367.1.6. Mathematical Solution^ 1377.1.6.1. Primary Stage 1377.1.6.2. Secondary Stage 1407.2. Model Validation^ 1477.3. Model Sensitivity 1507.3.1. Temperature 1507.3.2. Pressure^ 1517.3.3. Reaction Gas Flow Rate^ 1537.3.4. Reaction Gas composition 1547.3.5. Reaction Interfacial Area 1557.4. Theoretical Predictions^ 1567.4.1. Oxidation Path 1567.4.2. Oxidation Rates 1607.4.2.1. Oxidation Rate as a Function of Gas Flow Rate^ 1607.4.2.2. Oxidation Rate as a Function of Gas Composition ^ 1647.4.2.3. Oxidation Rate as a Function of Temperature^ 1707.4.3. Oxygen Utilization^ 1738. Summary and Conclusions^ 175References^ 178Appendix A Experimental 1871. Reactor Insulating Materials^ 1872. Reactor Power Supply 1893. Load Cell Components 190Appendix B Gas Analysis Raw Data^ 191Appendix C Reaction gas Transport Properties^ 2101. Viscosity^ 2102. Diffusion Coefficient^ 2123. Density 214Appendix D Temperature Measurements^ 215List of FiguresFigure 2.1. (a) Cutaway of a horizontal side-blown Pierce-Smith converter, (b).Positions of the Pierce-Smith converter for charging, blowing, and skimming (slagor blister copper)^ 6Figure 2.2. The Cu-S system; high temperature portion only, not to scale (afterKellogg [15]). 10Figure 2.3. The 1300 °C isotherm of the Cu-O-S system, at 1 atm, (after Elliott[20])^ 11Figure 2.4. Schematic diagram of a hypothetical case of oxygen dissolution in aliquid metal bath, Rg and R1 are the gas phase resistance and the liquid phaseresistance respectively^ 14Figure 2.5. Comparative geometry of flow modes in top-blown systems^ 18Figure 2.6. Model of impinging gas jet used by Wakelin (after Themelis andSzekely [52])^ 19Figure 2.7. (a) Mass-transfer coefficient in gas phase at room temperature, (b)Mass-transfer coefficient in gas phase at elevated temperatures, (after Kikuchi etal [48])^ 22Figure 2.8. Type of adsorption at liquid-metal interfaces: (a), positive adsorption;(b) negative adsorption; (c), electrocapillary behaviour (after Brimacombe [83])^ 27Figure 2.9. Effect of oxygen on the surface tension of liquid copper, (after Monma[87])^ 28Figure 2.10. Effect of sulphur on the surface tension of liquid copper, (afterMonma [87])^ 29Figure 2.11. Interfacial motion generated on micro-scale due to eddy penetration(after Brimacombe [83])^ 30Figure 2.12 Interfacial motion generated on macro-scale by presence of partiallyimmersed piece of Cu2S in molten copper^ 30Figure 2.13. Mechanism of copper oxide patch spreading on the liquid coppersurface^ 31Figure 4.1. Cross-sectional view of the reactor^ 37Figure 4.2. Sectional view of the bottom of the reaction tube, including thecrucible supporting system^ 38Figure 4.3. Schematic diagram of the top of the reaction tube^40Figure 4.4. Schematic diagram of the gas train^ 41Figure 4.5. Schematic diagram of the off-gas analysis system, not including thesoap bubble-meter^ 42viiiixFigure 4.6. Schematic diagram of the absorber rubber stopper^43Figure 4.7. Plot of the amount of SO2 absorbed as a function of time for a test of 21/min of 13 % SO2 and 87% Ar at 23 °C^ 45Figure 4.8. Photograph of the SO2 absorber with a gas flow rate of 2 1/min, 13 %SO2 and 87 % Ar^ 46Figure 4.9. Photograph of the SO2 absorber with a gas flow rate of 260 ml/minpure SO2 47Figure 4.10. Schematic diagram of the soap bubble-meter^ 48Figure 4.11. Schematic diagram of the load cell^ 49Figure 4.12. Load cell calibration plot obtained with standard weights^ 51Figure 4.13. Schematic diagram of the optical system used in the photography ofthe melt surface^ 53Figure 5.1. Gas flows in the oxidation experiments^ 62Figure 5.2. The reaction gas and off-gas as function of time, for the experimentalconditions of: 200 grams of Cu2S, 2 1/min of 35% 02 and 65% Ar, at 1200 °C^ 63Figure 5.3. The final volumetric off-gas flow rate as a function of time for theexperimental conditions of : 200-grams of Cu2S, 21/min of 35% 02 and 65% Ar,at 1200 °C^ 64Figure 5.4. The molar sulphur and oxygen contents in the bath as a function oftime, for the experimental conditions of: 200-grams of Cu2S, 21/min of 35% 02and 65% Ar, at 1200 °C^ 68Figure 5.5. Change of bath weight with time for the experimental conditions of:200-grams of Cu2S, 2 1/min of 35% 02 and 65% Ar, at 1200°C^ 69Figure 5.6. A gravimetric plot for the experimental conditions of : 200-grams ofCu2S, 2 1/min of 22% 02 and 78% Ar, at 1200°C^ 71Figure 5.7. Oxygen reaction rate as a function of reaction gas volumetric flowrate; for the experimental conditions of 200-gram samples, 1200 °C, averagepressure of 1.08 atm and 23 % 02 72Figure 5.8. Sulphur removal rate as a function of reaction gas volumetric flowrate; for the experimental conditions of 200-gram samples, 1200 °C, averagepressure of 1.08 atm and 23 % 02 73Figure 5.9. Sulphur removal rate as a function of reaction gas volumetric flowrate; for the experimental conditions of 200-gram samples, 1200 °C, averagepressure of 1.08 atm and 23 % 02 74Figure 5.10. Oxygen reaction rate as a function of oxygen pressure for theexperimental conditions of: 1200 °C and 2000 ml/min^ 75Figure 5.11. Sulphur removal rate as a function of oxygen pressure for theexperimental conditions of: 1200 °C and 2000 ml/min^ 76Figure 5.12. Rate of weight loss as a function of oxygen pressure for theexperimental conditions of: 1200 °C and 2000 ml/min 77Figure 5.13. Oxygen reaction rate as a function of temperature for theexperimental conditions of: 2000 ml/min of 20-23% 02 and average pressure of1.08 atm^ 79Figure 5.14. Sulphur removal rate as a function of temperature for theexperimental conditions of: 2000 ml/min of 20-23% 02 and average pressure of1.08 atm^ 80Figure 5.15. Bath weight as a function of time for the experimental conditions of:1200 C, average pressure of 1.08 atm and 22 % 02^ 81Figure 5.17. Photomicrograph of polished section of frozen melt sample, at 7 minof reaction time (during the primary stage) 86Figure 5.17. Photomicrograph of polished section of frozen melt sample, at 7 minof reaction time (during the primary stage)^ 87Figure 5.18. Photomicrograph of polished section of frozen melt sample, at 15min of reaction time (1 min after the copper droplets and SO2 gas bubbles start toform in the melt)^ 87Figure 5.19. Photomicrograph of polished section of frozen melt sample, at 25min of reaction time 88Figure 5.20. Photomicrograph of polished section of frozen melt sample, at 25min of reaction time^ 89Figure 5.21. Photomicrograph of polished section of frozen melt sample, at 35min of reaction time 89Figure 5.22. Photomicrograph of polished section of frozen melt sample, at 40min of reaction time^ 90Figure 5.23. Photomicrograph of polished section of frozen melt sample, at 50min of reaction time 90Figure 5.24. Photomicrograph of polished section of frozen melt sample, at 60min reaction time (final reaction time is 70 min)^ 92Figure 5.25. Photomicrograph of polished section of frozen melt sample, at 60min reaction time (final reaction time is 70 min) 94Figure 5.26. Photomicrograph of polished section of a 99.99% Cu standardsample^ 94Figure 5.27. Bath surface, at 1200 °C with top-lancing at 2 1/min of Ar^ 95Figure 5.28. Photograph of the bath surface at the same time of the admittance ofthe reaction gas^ 96xxiFigure 5.29. Photograph of the surface of the bath at approximately 60 s, after theinitiation of the reaction^ 97Figure 5.30. Photograph of the surface at approximately 3.5 min^ 97Figure 5.31. Photograph of the surface of the bath at approximately 5 min^98Figure 5.32. Photograph of the surface of the melt at approximately 21 min^99Figure 5.33. Photograph of the surface of the melt at approximately 20 min for theexperimental conditions of 200 grams of Cu2S, at 1200 °C, and under the top-lancing of 21/min of 22% 02 and 78% Ar^ 99Figure 5.34. Photograph of the surface of the melt at approximately 10 min afterthe end of reaction^ 100Figure 5.35. Photograph of the surface of the melt at approximately 14.5 min,under the top-lancing of 2 1/min of 80% 02 and 20% Ar^ 101Figure 5.36. Photograph of the surface of the melt at approximately 14.5 min,under the top-lancing of 2 1/min of 80% 02 and 20% Ar 101Figure 6.1. The gas phase mass-transfer coefficient as a function of gas flow ratefor the experimental conditions of 200 grams of Cu2S at 1200 °C, 1.084 atm, 3mm inside diameter lance and 44 mm diameter of the interfacial reaction area^ 106Figure 6.2. The gas phase mass-transfer coefficient vs. the partial pressure ofoxygen^ 107Figure 6.3. The gas phase mass-transfer coefficient vs. the inverse of temperaturefor the experimental conditions of: 2000 ml/min of 20-23% 02 and averagepressure of 1.08^ 108Figure 6.4. The Sherwood number as a function of the Reynolds number for thetop-blown conditions of 200 grams of Cu2S at 1200 °C, 1.084 atm, 3 mm insidediameter lance and 44 mm diameter of the interfacial reaction area 110Figure 6.5. Sh(rs I dr SC° 5 plotted against the Reynolds number for top-blownconditions of 02-Ar/N2 onto molten Cu2S bath, at 1200-1300 °C, 1.084 atm, 0.5Sc 0.63, 7 rsld 11, 2-3 mm inside diameter lance and 44 mm diameter ofthe interfacial reaction^ 111Figure 6.6. Computed streamline patterns and concentration profiles at u = 200m/sec (laminar flow) (after Taniguchi et al [48])^ 114Figure 6.7. The sensitivity of the gas phase mass-transfer coefficient to thereaction interfacial area, for the experimental conditions of 200-grams of Cu2S at1200 °C, 3 mm inside diameter lance and 44 mm diameter of the interfacialreaction area^ 115Figure 6.8. The temperature change, due to the heat of reaction, as a function ofthe reaction gas flow rate^ 117xiiFigure 6.9. The temperature change, due to the heat of reaction, as a function ofthe reaction gas oxygen content^ 118Figure 6.10. The sensitivity of the gas phase mass-transfer coefficient totemperature, for the experimental conditions of 200-grams of Cu2S at 1200 °C,20-26% 02, 3 mm inside diameter lance and 44 mm diameter of the interfacialreaction area 120Figure 6.11. The effect of reaction gas composition on the gas phase mass-transfercoefficient, for the experimental conditions of 200 grams of Cu2S, average systempressure of 1.09 atm, 3 mm inside diameter lance and 44 mm diameter ofinterfacial reaction area^ 121Figure 7.1. Schematic diagram of the primary stage reaction system^ 125Figure 7.2. Schematic diagram of the secondary stage reaction system 127Figure 7.3. Secondary stage reaction rates^ 127Figure 7.4. Comparison of model predictions to measurements of the sulphur andoxygen contents in the bath as a function of time at a constant reaction gascomposition and for the range of reaction gas flow rate of 1480-4055 ml/min^ 148Figure 7.5. Comparison of model predictions to measurements of sulphur andoxygen contents in the bath as a function of time at a constant reaction gas flowrate and for the range of reaction gas composition of 22-78% 02^ 149Figure 7.6. Model-predicted sensitivity of transient bath weight to bathtemperature^ 151Figure 7.7. Model-predicted sensitivity of transient bath weight to total pressure ^ 152Figure 7.8. Model-predicted sensitivity of transient bath weight to flow rate ofadmitted gas^ 153Figure 7.9. Model-predicted sensitivity of transient bath weight to composition ofadmitted gas 154Figure 7.10. Model-predicted sensitivity of transient bath weight to bath surfacearea^ 155Figure 7.11. The sulphur content as a function of the oxygen content in the bath,showing the oxidation path of molten copper sulphide^ 157Figure 7.12. Selected portions of the Cu-S-0 isothermal section, showing theoxidation path of molten Cu2S at 1200 °C and 1 atm 158Figure 7.13. Oxygen reaction rate as a function of reaction gas volumetric flowrate for the experimental conditions of: 200-gram samples, 1200 °C, 23 % 02 andaverage pressure of 1.08 atm^ 161Figure 7.14. Sulphur removal rate as a function of reaction gas volumetric flowrate for the experimental conditions of: 200-gram samples, 1200 °C, 23 % 02 andaverage pressure of 1.08 atm^ 162Figure 7.15. Rate of weight loss as a function of reaction gas volumetric flow ratefor the experimental conditions of: 200-gram samples, 1200 °C, 23 % 02 andaverage pressure of 1.08 atm^ 163Figure 7.16. Oxygen reaction rate as a function of oxygen pressure for theexperimental conditions of: 1200 °C and 2000 ml/min^ 164Figure 7.17. Percent increase in gas phase mass transfer as a function of oxygenpressure for the experimental conditions of: 1200 °C and 2000 ml/min^ 165Figure 7.18. Sulphur removal rate as a function of oxygen pressure for theexperimental conditions of: 1200 °C and 2000 ml/min^ 167Figure 7.19. Oxygen reaction rate as a function of oxygen pressure for theexperimental conditions of: 1500 grams of Cu2S under the top-lancing of highvelocity jets of 02-N2 gas mixtures at 1250 °C, nozzle pressure of 5.4105 N/m2,nozzle diameter of 1 mm,^ 168Figure 7.20. Oxygen reaction rate as a function of temperature for theexperimental conditions of: 2000 ml/min of 20-23 % 02 and average pressure of1.08 atm^ 171Figure 7.21. Sulphur removal rate (dNsIdt) as a function of temperature for theexperimental conditions of: 2000 ml/min of 20-23 % 02 and average pressure of1.08 atm^ 172Figure 7.22. Oxygen utilization as a function of reaction gas volumetric flow rate;for the top-blown conditions of 200 grams of Cu2S at 1200 °C, 1.08 atm, 23%02, reaction interfacial diameter of 44 mm and lance nozzle diameter of 3 mm^ 173Figure A.1. Electrical circuit for the furnace power supply^ 189Figure A.2. Circuit design of the load cell^ 190Figure C.1. The viscosity of Ar-02 gas mixtures as a function of temperature, at 1atm^ 211Figure C.2. The diffusion coefficients of some selected binary gas mixtures as afunction of temperature, at 1 atm^ 213Figure C.3. The density of Ar-02 gas mixtures as a function of temperature^ 214Figure D.1. The manual temperature measurement of the center of the melt; 200-grams Cu2S, at 1200 °C^ 215Figure D.2. The manual temperature measurement of the gas at the same height ofthe lance nozzle; 200-grams Cu2S, at 1200 °C^ 216Figure D.3. The gas temperature measurement at the same height of the lancenozzle for Run No. 27, the experimental conditions of 200-grams Cu2S, at 1200°C, 1998 ml/min of 27% 02 and 73% Ar^ 217xivFigure D.4. The temperature measurement at the center of the melt for Run No.29, the experimental conditions of 200 grams Cu2S, at 1275 °C, 1994 ml/min of23% 02 and 77% Ar^ 217Figure D.5. The gas temperature measurement at the same height of the lancenozzle for Run No. 30, the experimental conditions of 200 grams Cu2S, at 1300°C, 2000 ml/min of 22% 02 and 78% Ar^ 218Figure D.6. The gas temperature measurement at the same height of the lancenozzle for Run No. 33, the experimental conditions of 200 grams Cu2S, at 1200°C, 3500 ml/min of 29% 02 and 71% Ar^ 218Figure D.7. The gas temperature measurement at the same height of the lancenozzle for Run No. 34, the experimental conditions of 200 grams Cu2S, at 1200°C, 2000 rnl/min of 79% 02 and 21% Ar^ 219Figure D.8. The gas temperature measurement at the same height of the lancenozzle for Run No. 37, for the experimental conditions of 200 grams of Cu2S at1200 °C, 2000 ml/min of 21% 02 and 79% N2^ 219Figure D.9. The gas temperature measurement at the same height of the lancenozzle for Run No. 41, for the experimental conditions of 200 grams of Cu2S at1200 °C, 3500 ml/min of 24% 02 and 76% Ar^ 220XVList of TablesTable 1.1. Copper and copper-nickel smelters in Canada, 1991 ^ 3Table 4.1. Trace analysis (wt%) of supplied copper sulphide 54Table 4.2. Impurity specification of gases in ppm^ 56Table 4.3. Maximum limits of impurities for the 29.0-32.0 % hydrogen peroxidesolution (supplied by BDH)^ 56Table 4.4. Maximum limits of impurities for the 98.0 % sodium hydroxide pellets(supplied by BDH)^ 57Table A.1. Physical properties of the insulating alumina brick^ 187Table A.2. Chemical analysis of the insulating alumina brick 187Table A.3. Thermal conductivity as a function of mean temperature for refractoryfibrous material^ 188Table A.4. Approximate chemical analysis ( wt %-binder removed) for refractoryfibrous material 188Table A.5. Strain gauges manufacturer (HBM ELEKRISCHES MESSENMECHANISCHER GROSSEN) specifications^ 190Table B.1. Run No. 4, the data for the experimental conditions of: 922 ml/min of26% 02 and 74% Ar, at 1200 °C, 1.05 atm pressure, ambient temperature of 23°C and average final gas temperature of 23 °C^ 191Table B.2. Run No. 5, the data for the experimental conditions of: 922 ml/min of26% 02 and 74% Ar, at 1200 °C, 1.05 atm pressure, ambient temperature of 23°C and average final gas temperature of 23 °C^ 191Table B.3. Run No. 6, the data for the experimental conditions of: 922 ml/min of26% 02 and 74% Ar, at 1200 °C, 1.05 atm pressure, ambient temperature of 23°C and average final gas temperature of 25 °C^ 192Table B.4. Run No. 7, the data for the experimental conditions of: 922 ml/min of26% 02 and 74% Ar, at 1200 °C, 1.05 atm pressure, ambient temperature of 23°C and average final gas temperature of 25 °C^ 192Table B.5. Run No. 8, the data for the experimental conditions of: 1010 ml/min of24% 02 and 76% Ar, at 1200 °C, 1.05 atm pressure, ambient temperature of 23°C and average final gas temperature of 24 °C^ 193Table B.6. Run No. 9, the data for the experimental conditions of: 1480 ml/min of22% 02 and 79% Ar, at 1200 °C, 1.07 atm pressure, ambient temperature of 23°C and average final gas temperature of 23 °C^ 193Table B.7. Run No. 10, the data for the experimental conditions of: 2078 ml/minof 20% 02 and 80% Ar, at 1200 °C, 1.07 atm pressure, ambient temperature of 23°C and average final gas temperature of 24 °C^ 194xviTable B.8. Run No. 11, the data for the experimental conditions of: 1987 ml/minof 20% 02 and 80% Ar, at 1200 °C, 1.05 atm pressure, ambient temperature of 23°C and average final gas temperature of 25 °C^ 194Table B.9. Run No 12, the data for the experimental conditions of: 1580 ml/minof 22% 02 and 78% Ar, at 1200 °C, 1.06 atm pressure, ambient temperature of 25°C and average final gas temperature of 25 °C 195Table B.10. Run No. 13, the data for the experimental conditions of: 1521 ml/minof 20% 02 and 80% Ar, at 1200 °C, 1.08 atm pressure, ambient temperature of 27°C and average final gas temperature of 26 °C 195Table B.11. Run No. 14, the data for the experimental conditions of: 1530 ml/minof 21% 02 and 79% Ar, at 1200 °C, 1.07 atm pressure, ambient temperature of 22°C and average final gas temperature of 22 °C 196Table B.12. Run No. 15, the data for the experimental conditions of: 2006 ml/minof 22% 02 and 78% Ar, at 1200 °C, 1.07 atm pressure, ambient temperature of 26°C and average final gas temperature of 27 °C 196Table B.13. Run No. 16, the data for the experimental conditions of: 2510 ml/minof 23% 02 and 77% Ar, at 1200 °C, 1.08 atm pressure, ambient temperature of 25°C and average final gas temperature of 25 °C 197Table B.14. Run No. 17, the data for the experimental conditions of: 1755 ml/minof 22% 02 and 78% Ar, at 1200 °C, 1.07 atm pressure, ambient temperature of 22°C and average final gas temperature of 24 °C 197Table B.15. Run No. 18, the data for the experimental conditions of: 2230 ml/minof 23% 02 and 77% Ar, at 1200 °C, 1.08 atm pressure, ambient temperature of 23°C and average final gas temperature of 23 °C 198Table B.16. Run No. 19, the data for the experimental conditions of: 3015 ml/minof 22% 02 and 78% Ar, at 1200 °C, 1.07 atm pressure, ambient temperature of 26°C and average final gas temperature of 27 °C 198Table B.17. Run No. 21, the data for the experimental conditions of: 4055 ml/minof 22% 02 and 78% Ar, at 1200 °C, 1.13 atm pressure, ambient temperature of 26°C and average final gas temperature of 26 °C 199Table B.18. Run No. 22, the data for the experimental conditions of: 2006 ml/minof 27% 02 and 73% Ar, at 1200 °C, 1.10 atm pressure, ambient temperature of 26°C and average final gas temperature of 26 °C 199Table B.19. Run No. 23, the data for the experimental conditions of: 2009 ml/minof 35% 02 and 65% Ar, at 1200 °C, 1.10 atm pressure, ambient temperature of 21°C and average final gas temperature of 21 °C 200Table B.20. Run No. 24, the data for the experimental conditions of: 1997 ml/minof 46% 02 and 54% Ar, at 1200 °C, 1.10 atm pressure, ambient temperature of 24°C and average final gas temperature of 24 °C 200xviiTable B.21. Run No. 25, the data for the experimental conditions of: 1997 ml/minof 64% 02 and 36% Ar, at 1200 °C, 1.10 atm pressure, ambient temperature of 22°C and average final gas temperature of 22 °C 201Table B.22. Run No. 27, the data for the experimental conditions of: 1998 ml/minof 23% 02 and 77% Ar, at 1250 °C, 1.13 atm pressure, ambient temperature of 23°C and average final gas temperature of 23 °C 201Table B.23. Run No. 28, the data for the experimental conditions of: 1999 ml/minof 23% 02 and 77% Ar, at 1300 °C, 1.08 atm pressure, ambient temperature of 22°C and average final gas temperature of 22 °C 202Table B.24. Run No. 29, the data for the experimental conditions of: 1994 ml/minof 21% 02 and 79% Ar, at 1275 °C, 1.08 atm pressure, ambient temperature of 24°C and average final gas temperature of 24 °C 202Table B.25. Run No. 30, the data for the experimental conditions of: 2006 ml/minof 22% 02 and 78% Ar, at 1325 °C, 1.08 atm pressure, ambient temperature of 25°C and average final gas temperature of 24 °C 203Table B.26. Run No. 31, the data for the experimental conditions of: 2006 ml/minof 22% 02 and 78% Ar, at 1275 °C, 1.08 atm pressure, ambient temperature of 23°C and average final gas temperature of 21 °C 203Table B.27. Run No. 33, the data for the experimental conditions of: 3490 ml/minof 27% 02 and 73% Ar, at 1200 °C, 1.11 atm pressure, ambient temperature of 24°C and average final gas temperature of 22 °C 204Table B.28. Run No. 34, the data for the experimental conditions of: 1996 ml/minof 78% 02 and 22% Ar, at 1200 °C, 1.11 atm pressure, ambient temperature of 23°C and average final gas temperature of 22 °C 204Table B.29. Run No. 36, the data for the experimental conditions of: 2032 ml/minof 22% 02 and 78% Ar, at 1200 °C, 1.08 atm pressure, ambient temperature of 23°C and average final gas temperature of 22 °C 205Table B.30. Run No. 37, the data for the experimental conditions of: 2000 ml/minof 21% 02 and 79% N2, at 1200 °C, 1.08 atm pressure, ambient temperature of21 °C and average final gas temperature of 22 °C 205Table B.31. Run No. 41, the data for the experimental conditions of: 3516 ml/minof 24% 02 and 76% Ar, at 1200 °C, 1.10 atm pressure, ambient temperature of 24°C and average final gas temperature of 24 °C 206Table B.32. The effect of volumetric flow rate of reaction gas on the reactionrates; sample weight of 200-grams of Cu2S; at 1200 °C and 1.08 atm; 22% 02and 78% Ar; lance inside diameter of 3 mm^ 207Table B.33. The effect of volumetric flow rate of reaction gas on the reactionrates; sample weight of 200-grams of Cu2S; at 1200 °C and 1.08 atm; 24% 02and 76% Ar; lance inside diameter of 3 mm^ 207xviiiTable B.34. The effect of reaction gas composition on the reaction rates; sampleweight of 200-grams of Cu2S; at 1200 °C and 1.10 atm, 2000 ml/min; lanceinside diameter of 3 mm^ 208Table B.35. The effect of temperature on the reaction rates; sample weight of 200-grams of Cu2S; at 1200°C and 1.09 atm, 2000 ml/min of 22% 02 and 78% Ar;lance inside diameter of 3 mm^ 208Table B.36. The effect of temperature on the reaction rates; sample weight of 200grams of Cu2S; at 1.09 atm, 2000 ml/min of 23% 02 and 77% Ar; lance insidediameter of 3 mm^ 209Table B.37. The effect of bath mixing on the reaction rates; sample weight of 200-grams of Cu2S; at 1200 °C and 1.09 atm, 2000 ml/min of 22% 02 and 78% Ar;lance inside diameter of 3 mm (approximately 77 ml/min Ar was used to invokeartificial mixing)^ 209Table B.38. The effect of carrier gas type on the reaction rates; sample weight of200-grams of Cu2S; at 1200 °C and 1.09 atm, 2000 ml/min of 21% 02 and 79%Ar 0Table C.1. The critical properties of some selected gases^ 212List of SymbolsA^cross-sectional area (m2)a^constantb^constantCs^concentration of reactants (moles/m3)DA-B^diffusion coefficient of species A in B (m2/s)d diameter (m)c/c.^diameter of cavity (m)do^diameter of orifice (m)ds^degree of desulphurization of the melt (%) (percent sulphur removed)Fr'^modified Froude numberG°^standard Gibbs free energy (kJ/mole)g^acceleration due to gravity (9.81 m/s2)H distance from the lance nozzle to the reaction interfacial area (m)Tic^depth of cavity (m)initial height of the sulphide melt (m)xixll'cu2sKj,u^jet constant for momentum transferK'^equilibrium constantk^mass transfer-coefficient (m/s)MA^molecular weight of species A (kg/kg mole)M.J^jet momentum (kg.m/s2), (1 g/cm.s2 = 1 dyne = 1 xl 0-5 kg.m/s2 (Newton))m constant in the gas phase mass transfer corelationNA^molar quantity of substance Amolar transfer rate of specie A (moles/s)°NAnRe^exponent of the Reynolds numbernsc^exponent of the Schmidt numberns^exponent of (dIrs)molar flux of species A (moles/m2.^)°n APA^pressure of species A (Pa), (1 atm = 101325 Pa)XXPs^system pressure (Pa)Pst^pressure due to static head (Pa)QA^volumetric flow rate of substance A (m3/s)Qoif^off-gas volumetric flow rate (m3/s)Qr^reaction gas volumetric flow rate (the same as Q) (m3 Is)R universal gas constant (8.3144 YK.mole), (82.06 cm3.attn/°K.mole)Re^Reynolds numberRg^gas phase mass transfer resistance (s/m)R1 liquid phase mass transfer resistance (s/m)Rs^load cell responser.J^radius of impacted surface (m)r radius of orifice (m)0rs^radius of reaction surface (m)Sc^Schmidt numberSh^Sherwood numberT^temperature (°K)Tg^final off-gas temperature (°K), measured at the entrance to the bubble meterTgas^gas temperature inside the reaction chamber (°K)Tmelt^melt temperature inside the reaction chamber (°K)t^time (s)u mean velocity inside nozzle of the lance (m/s)u jet velocity at axis (m/s)cu0^jet velocity at orifice (m/s)^ volume of the bath (m3)Va^volume of absorbing solution (m3)VNaOH^volume of NaOH titrated (m3)Vs^volume of the sample obtained from the absorber (m3)W^sample weight (kg)Wga^sample weight obtained from gas analysis (kg)Wt% A^weight percent of specie s AWw^sample weight obtained from gravimetric measurement (kg)rate of weight change (kg/s)XA^mole fraction of species Adistance from orifice (m)Greek Symbolsthe molar ratio of reacted oxygen to removed sulphursurface excess of solute s (mole/m2)FsYA^activity coefficient of species AAx^finite change in variable x8 x^variation in variable xpercent increase in mass transfer (likely due to the Marangoni effect)A^interaction parameter of A on BEBJig^gas viscosity (kg/m.^), (1 g/cm.s = 1 poise = 0.1 kg/m.^)x x iP Cu ' P CU2S the density of the metal phase and the sulphide phase (kg/m3)Pg^gas density (mole/m3)P1^liquid density (mole/m3)6^interfacial tension (Newton/m), (1 dyne/cm = lx10-7 Newton/m)interfacial tension at the interfacecri^bulk interfacial tensioninterfacial tension at maximum of zero chargeOther Symbolsconcentration of species A (moles/m3)weight percent of species A in Bsolid substanceliquid substancegaseous substance[ 1^in liquid or ionic solutionSuperscriptsa^admitted (for the total admitted substance such as oxygen or argon)b bulk (property of the material in the bulk)f^final (designation for the variables at the end of the secondary stage)i^interfacial (property of the material at the interface) or initial (designationfor the variables at the beginning of reaction , t = 0)P^primary (primary stage variables)^ reacted (for the total reacted substance such as oxygen)s^secondary (secondary stage variables)u unreacted (for the total unreacted substance such as oxygen)* transition (designation for the variables at transition from the primary stageto the secondary stage)AcknowledgmentsFor his patience, understanding and guidance, I would like to express my utmost gratitudeto my supervisor, Professor J. Keith. Brimacombe.For their valuable discussions with me on the thermodynamics of copper sulphide melts, Iwould like to thank Professor E. Peters and Dr. G. G. Richards. My gratitude is alsoextended to Dr. S. Taniguchi, of Tohoku University, Sendai, Japan, for the helpfuldiscussions I have had with him in the area of gas phase mass transfer during the earlyperiod of this research project, and for the translations of some of the relevant issues ofhis Japanese written papers that were used in the literature review.I am indebted to Mr. P. R. Musil for his voluntary assistance in machining some parts ofthe experimental apparatus and with the setup of the optical system used in the surfacephotography. I would also like to thank Mr. S. Milaire, of the departmental electronicshop, for his assistance in the setup of the electrical systems of the experimentalapparatus. The assistance of Mr. R. McLeod, of the departmental machine shop, is alsoappreciated. I am also glad to acknowledge the assistance of Mrs. J. Kitchen, Mrs. M.Jansepar, Mr. R. Bennett, Mr. E. R. Armstrong and Mr. B. N. Walker, of the Metals andMaterials Engineering Department staff.I am greatly indebted to the Natural Sciences and Engineering Research Council ofCanada for financial support in the form of a research assistantship.1. IntroductionSince ancient times copper has been the back-bone of human civilization. The wordcopper originates from the Greek word "Kyprios" - the island of Cyprus, where much ofcopper of ancient Mediterranean was found. The Romans called copper aes Cvprium -"metal of Cyprus". Gradually the Roman name was changed to Cuprum. In the Englishlanguage, the word became "Copper". Today the chemical symbol for this valuable metalis Cu, the first two letters of the Roman word. Because it occurs in the native state, muchlike gold, copper was known to early man as far ago as 8000 B.C. It was about 4000 B.C.that man learned to produce copper and bronze by the smelting of copper and tin ores in acharcoal fire. History of the ancient civilizations indicates that copper played animportant role in shaping the past as well as the present of our world. Due to its nobility,the ancient Egyptians gave copper their symbol for everlasting life - a circle above a crossFor the modern world, copper is still as important as ever. It was the development ofthe electrical industry in the late nineteenth and early twentieth centuries that caused adramatic increase in the demand for copper.Although it is a classic of extractive metallurgy, the extraction of copper from its oresremains a subject that has to be further unravelled. Because approximately 90% of theworld's primary copper originates in sulphide ores, most of the copper today is producedby pyrometallurgical techniques. In general, the extraction of copper is carried out asfollows: concentration by froth flotation; roasting (an optional step); matte smelting (inblast, reverberatory, electric or flash furnaces); and converting to blister copper.  One ofthe relatively recent advances in the extractive metallurgy of copper is the continuousproduction of blister copper by combining the smelting, roasting and convertingoperations in a single unit process, such as in the Worcra, Noranda, Mitsubishi andIsasmelt processes. Most of the copper producing companies convert copper mattes, in1which blister copper is the ultimate product. In Canada, for example, there are a varietyof copper extraction processes employed by several companies, most of which involvethe copper converting process, as shown in Table 1.1.In copper converting, blister copper is produced by several cycles of matte oxidation inwhich the metallurgical phenomena are complex, such as heat transfer and accretiongrowth at the tuyeres. These have been studied in depth but many other important aspectsof copper converting are not fully comprehended. Perhaps some of the most importantfundamental aspects of copper converting to be further understood are thethermodynamics and kinetics of the copper-making reactions. In such fundamentalstudies, the methods of studying the problem, as well as the solution to the problem itself,are of relevance to the process of knowledge accumulation.Aiming to explain the kinetics of the oxidation of molten copper sulphide and to exploresome fundamental principles of gas-liquid reactions, this work was launched. Masstransfer and the effect of interfacial phenomena on the gas-liquid reactions are importantexamples of these fundamental principles.23Table 1.1. Copper and copper-nickel smelters in Canada, 1991 (rated annual capacity is intonnes of concentrates); Taken from the Canadian Minerals Yearbook.Company andLocationProduct RatedAnnualCapacityRemarksFalconbridgeLimited,Falconbridge,OntarioCopper-nickelmatte600,000 Fluid bed roasters and electric furnaces;1800 t/d sulphuric acid plant treats roastergases. Matte from the smelter is refined inNorway.Inco Limited,Sudbury, OntarioMolten "blister"copper, nickelsulphide and nickelsinter for thecompany'srefineries; nickeloxide sinter formarket, solublenickel oxide formarket500,000 Oxygen flash-smelting of copperconcentrate; converters for production ofblister copper. Roasters, reverberatoryfurnaces for smelting of nickel-copperconcentrate, converters for production ofnickel-copper Bessemer matte.Production of matte followed by mattetreatment, flotation, separation of copperand nickel sulphides, then by sintering tomake sintered nickel products for coppersulphide and conversion to blister copperFalconbridgeLimited, Timmins,OntarioMolten "blister"copper440,000 Mitsubishi-type smelting, separation andconverting furnaces, acid plant and oxygenplant to treat continuous copperconcentrate feed stream to yield molten99% pure copper.Noranda Inc. Hornesmelter, Noranda,QuebecCopper anodes 770,000a One continuous Noranda process reactorand five converters. Acid plant becameoperational at end of 1989. Treatsconcentrates from Noranda's miningoperations in Quebec and Ontario as wellas custom concentrates and scrap.Noranda Inc. Gaspesmelter,Murdochville,QuebecCopper anodes 221,500a Green charge reverberatory furnace, twoconverters, rotary anode furnace and onacid plant. Treats Gaspe and customconcentrates.Hudson BayMining andSmelting Co.,Limited (HBMS),Flin Flon, ManitobaCopper anodes 320,000 Five roasting furnaces, one reverberatoryfurnace and three converters. Companytreats its own copper concentrate as wellas custom copper concentrates: zinc plantresidues and stockpiled zinc-plant residuesfed to reverberatory furnace. Projectunder way to replace concentrate roastingand calcine smelting with Norandacontinuous converter technology.Source: Data provided by each company. a Concentrate and copper scrap.2. Literature Review2.1. Copper Converting2.1.1.^History of the Copper ConverterAs is the case with most metallurgical processes, implementation of new ideas for theproduction of copper initially produced disappointing results. Rittinger conducted thefirst experiments on the converting of copper matte in 1867, in Hungary, at theSchmollnitz works. Others such as Kupelweisse in 1868, and Jossa and Lalitin in 1871,used a Bessemer steel converter. The early experiments were halted as a result of tuyereblockage due to freezing of copper as it formed. It was the success of the Bessemerconverter in steel-making that kept the work on bessmerizing the copper matte going. In1880, Pierre Manhes and Paul David conducted their first experiments of copperconverting, in Vaucluse, France. They encountered their first success when they adoptedhorizontal tuyeres instead of bottom blown tuyeres that caused the copper to freezeamong other difficulties [1]. The cylindrical shape of the converter was adopted afterrealizing that in order to be able to treat different matte grades, the relative position of thetuyeres had to be varied with respect to the bottom of the bath. The need for tuyerepunching was soon realized to be a condition for the success of the operation, when thecopper converter was put to work at the Parrot Smelter (USA). The other major problemwas the refractory lining which was consumed by the slagging process that required silicaflux for the removal of iron from the matte phase. The use of neutral refractory liningwas implemented by Peirce and Smith in 1909, in Baltimore.The other significant developments in the Peirce-Smith converter, after 1909, were theincrease of its capacity, the improvement of its refractory lining life time and the additionof automatic tuyere punching. Further understanding of the metallurgy of copperconverting has been gained as a result of several fundamental studies [6,8,41,45,58-67].45Despite the many new developments in the production of copper, such as chalcocite flashconverting and the Isasmelt process, "the case of the Peirce-Smith converter isparticularly outstanding" [61].2.1.2.^Metallurgy of Copper ConvertingDue to its energy efficiency, the definition of copper converting is simply the autogenousprocess of iron and sulphur transfer from the matte to the slag and gas phasesrespectively.Depending on the matte grade, the feed to the copper converter might contain up to 40%Fe, 25% S and 3% dissolved 0 [2]. The matte also contains minor amounts of impuritymetals (e.g. As, Bi, Ni, Pb, Sb, Zn and precious metals). The whole purpose of theconverting process is the production of blister copper, that is about 98.5-99.5% Cu.The commonly used Peirce-Smith converter is shown in Figure 2.11. Iron is removedfrom matte as liquid fayalite (2FeO.Si02) slag as a result of silica fluxing during the slagformation stage. The slag and blister copper are formed at different stages of theconverting process and they are poured separately from the converter mouth by rotatingthe converter about its axis, as shown in Figure 2.1(b). The sulphur is removed as SO2which normally is recovered and processed to by-products such as H2SO4, liquid SO2and elemental sulphur.lAn industrial Peirce-Smith converter is typically 4 m in diameter and 9 m long (inside shell). Itis constructed of a steel shell 40-50 mm thick, lined with 250-750 cm of burned magnesite orchrome-magnesite brick. There are forty to fifty tuyeres, which consist of steel pipes imbeddedin the refractory and they are connected to a bustle pipe running along the vessel. The matte ischarged to the converter through a large opening (mouth), which is covered with a loose-fittinghood during the blow to collect the resulting off-gas [2-5].6Ott-gas(b)Charging^ Blowing^ SkimmingFigure 2.1. (a) Cutaway of a horizontal side-blown Peirce-Smith converter (Boldt andQueneau, 1967), (b). Positions of the Pierce-Smith converter for charging, blowing, andskimming (slag or blister copper) (Boldt and Queneau, 1967).7^2.1.2.1.^The Slag-Forming Stage:In the slag-forming stage, FeS is oxidized mainly to FeO and some Fe304 according toReaction (2.1).2((FeS))maue +3(02)Air + 2(Si02)Flux = 2((Fe0 .Si02 ))slag 2(S02 )0ff_Gas^(2.1)The silica flux is added by means of a flux gun to combine with the FeO and some of theFe304 as liquid slag (Figure 2.1 (a)). The slag forming-stage ends when the FeS mattecontent is reduced to about 1 wt%. Due to its relatively large volume, and for the purposeof matte addition, the slag is skimmed at various times during the slag - forming stage.2.1.2.2.^The Copper-Making Stage: The copper-making stage is characterized by the removal of sulfur and remaining iron,resulting in the formation of blister copper. The literature was found to be unclear inexplaining the metallurgy of this stage. Biswas and Davenport [2] presented different andinconsistent explanations of the metallurgical chemistry of the copper-making stage andfailed to support or reject either of the claims of King et al., 1973 [9] and Peretti, 1948[10]. King et al. suggested that the copper formation takes place by a combination ofReactions (2.2) and (2.3) according to the overall Reaction (2.4).((cu 2s ) ) +^( ID2) = (cu 20)1- (s02 ) (2.2)((Cu2S))+ 2(Cu20) = 6((Cu))+ (S02) (2.3)((Cu25))+ (02) = 2((Cu))+ (SO2) (2.4)However, Peretti indicated that the copper making-stage proceeds in two steps. The meltis partially desulphurized until the sulphur content is lowered to about 19.4%, accordingto Reaction (2.5).8((cu,^))+ x(02). ((cu,s,_x))+x(so,)^(2.5)During the second step, the sulphur deficient (white metal) phase is oxidized to form themetal phase (blister copper) according to Reaction (2.4).Rosenquist [11] indicated that the copper-making step proceeds in one distinct stageaccording to Reaction (2.4). Habashi [12] suggested that the copper-making stageproceeds according to Reactions (2.2) and (2.3) with the overall reaction being (2.4).In view of the disagreement in the literature about the actual chemistry of the copper-making stage, further investigation of this process is warranted.2.2. Thermodynamics of Copper Sulphide OxidationThermodynamic knowledge of the Cu-S-0 system is paramount to the understanding ofthe metallurgy of copper converting and of vital importance to any related kinetic studies.Since the birth of extractive metallurgy, the practical and fundamental aspects of the Cu-Fe-S-0 have always been of tremendous interest to the pyrometallurgist. The literature isapparently rich in thermodynamic studies of the Cu-Fe-S-0 system [13-26,116].However, most of the knowledge accumulated fails to deal with the ionic nature of such asystem. The paucity of knowledge in this field is attributed to the complexity of moltensalt thermodynamics and the lack of pure fundamental research in this area.As just stated, most thermodynamic studies on mattes, have failed to address mattes asionic substances and rather have dealt with them as neutral compounds that can only becharacterized as hypothetical species having no real physical existence. Very few studieshave attempted to tackle this problem in depth [24-25,116]. The literature survey on thistopic yielded no important data. For example, there has never been a high temperaturespectroscopic identification of the ionic species of molten Cu-S-0 mixtures ormeasurements of their ionic activities.92.2.1.^Cu-S SystemThe high temperature portion of the Cu-S binary, in which the composition limits arepurposely distorted to show the phase relations more clearly, is shown in Figure 2.2. Theliquid state region of this phase diagram clearly indicates the existence of only twodistinct phases with a wide miscibility gap. Liquid I (metal phase) has a finite but limitedsolubility for sulphur of 0.95-1.0 wt% at the monotectic temperature of 1105°C (1378°K).Liquid II (sulphide phase) is often called liquid Cu2S, but its composition can deviatefrom exact stoichiometry. Copper sulphide melts of 20-22.19 wt% S are within the rangeof single phase Cu2S. The gas phase over the Cu-S system contains (Cu), (S2) and (S).Species such as (CuS) and (Cu2S) are negligible. The partial pressure of (Cu) is verysmall over the sulphide phase and is maximum over the metal phase (1.2 x10-6 atm at1127°C). The partial pressures of (S2) and (S) are also very small for the Cu2S exactstoichiometry and slightly richer in copper. It is important to note that, based on thisdiscussion, the partial pressures of all of these species over the melt under study wereassumed to be negligible, for simplicity, in the kinetic analysis applied in the presentstudy.Lumsden [24] reported one of the very few studies on the electrochemicalthermodynamics of the Fe-Cu-S-0 system. He suggested that in melts on the sulphur-richside of Cu25, it can be assumed that Cut, Cu2+ and Cu° are present together with S2-anions. The calculated standard free energy of Reaction (2.6) is given by Equation (2.7).^[Cut] ^= [Cu2+1((cu,^)) + e _ (2.6)AG° =87.7+0.012T (2.7)Based on the Flood model [24], the free energy of the dissociation reaction of ((Cu2S)) toCu+ and S2- has been also calculated as given by Equation (2.8).Liq IILiq II + Cu S (y)CU 2S (y)Atom % S = 33.33AG° =1.8-0.0015T (2.8)Liq I + Liq IICu(c) + Cu2S (y)(1129 °C)Atom % SulphurFigure 2.2. The Cu-S system; high temperature portion only, not to scale (after Kellogg[15]).2.2.2.^Cu-S-0 SystemThe Cu-S-0 ternary system is of great importance to the current investigation of theoxidation kinetics of molten copper sulphide. An isothermal section at 1300°C, providedby Elliott [20], is shown in Figure 2.3. Another isothermal section at 1200°C, appearedin the literature [17], but it was found to be in disagreement with other equilibriummeasurements of this system [19,20]. It is very important to note that thermodynamically10(1105 °C)(1083.4 °C)Liq I + Cu 2S (y)(1067 °C)11the formation of the Cu20 phase is not possible under the conditions of copperconverting until all of the Cu2S phase is reacted completely. The other important point tonote is that the sulphide phase, as well as the metal phase, have finite solubilities ofoxygen.Figure 2.3. The 1300 °C isotherm of the Cu-O-S system, at 1 atm, (after Elliott [20]).12The Cu-S-0 system can be divided into two distinct sub-systems: the copper sulphidesystem (ionic melt) and the copper system (neutral metallic melt). Due to the complexityof the thermodynamics of ionic melts, the thermodynamic behaviour of the sulphidesystem has not yet been fundamentally described. For example, it is not yet possible tocarry out calculations of the equilibrium pressures of 02 and SO2 over the sulphide melt,based on the activities of Cut, 02- and S2-.The thermodynamic behaviour of the metallic phase has been described by Alcock [26].The S and 0 dissolution in copper is described by Reaction (2.9) and the free energy offormation of this reaction is given by Equation (2.10).(S02). [S]((co) + 2[0]((co)^ (2.9)AG° = 68367 —37T^ (2.10)In order to correct for the interaction of sulphur and oxygen in copper, the free energy ofmixing (given by Equation (2.11)) is subtracted from the free energy of formation ofReaction (2.9).SAG° = RT ln[yEsi((c)) •^ = 2RT(X0es°)= 4RT(XsEso)^(2.11)The oxygen and sulfur contents of the metal and sulphide phases, as functions of SO2pressure and system temperature, have been measured by Schmiedl [19]. Themeasurements have also been expressed in mathematical form, by Schmiedl, and are asfollows;Metal Phase: Wt 0 = 10(-1.38-(1278/T))^y,P so2 (2.12)Wt % Cu = 10(1098+(24IT))^(2.13)13Wt%S =100 — Wt%0 — Wt%Cu^ (2.14)Sulphide Phase: Wt 0 = 10(-I96+(1013,7)) x Py2 so2Wt %Cu = 79.61+0.26x1e2x T4WaS =100— Wt%0— Wt%Cu2.3. Gas -Liquid InteractionsA majority of the processes relevant to the extraction and refining of metals depend onmass transfer of the reacting species across an interface. Gas-liquid reactions can takeplace in many ways, e.g. superficial contact of a gas with a liquid surface via diffusionacross a stagnant gas film, gas jets impinging on a liquid surface and gas bubbles risingthrough a liquid. In order to determine the rate of reaction, the mass transfer of speciesacross the reaction interface must be considered. To illustrate some basic principles ofmass transfer encountered in the analysis of metallurgical systems, consider the followinghypothetical case in which an oxygen-inert gas mixture is in contact with a liquid metalMe (e.g. Fe, Cu, Mn,..) bath.As the gas mixture comes in contact with the liquid metal surface, the oxygen dissolves inMe according to Reaction (2.18).(02 ) = 2[0]ue^ (2.18)This process proceeds according to the following steps:1. The gas phase mass transfer of the oxygen species to the liquid metal surface.2. The chemical reaction at the interface which can be considered to be very fast,in most pyrometallurgical reactions.143. The mass transfer of oxygen in the liquid metal phase.Depending on the relative resistances to mass transfer in the gas and liquid phases, therate of oxygen dissolution in the metal is, therefore, controlled by either mass transfer inone of the phases or simultaneously in both phases.In order to determine the rate controlling step of the dissolution reaction, the followinganalysis can be carried out:Figure 2.4. Schematic diagram of a hypothetical case of oxygen dissolution in a liquidmetal bath , Rg and R1 are the gas phase resistance and the liquid phase resistancerespectively.Equilibrium at Phase Boundaries: Because the chemical reaction is very fast and does not offer any resistance to the overallreaction rate, equilibrium conditions must prevail at the gas-liquid interface. This impliesthat the interfacial concentrations can be considered to be dictated by the thermodynamicsof Reaction (2.18). Therefore, the relationship between the interfacial partial pressure ofoxygen in the gas phase and the interfacial concentration of oxygen in the liquid phasecan be derived from the equilibrium constant of the interface reaction, as follows:15(2.23)Stoichiometry: The interface reaction dictates that the relationship between no, and no is as follows:no = 2flo,^ (2.24)Flux Equations: The molar flux of 02 (n° 02) in the gas phase is given by Equation (2.19) and the molarflux of 0 (no)in the liquid phase is given by Equation (2.21).If the gas phase mass transfer resistance is negligible then the reaction rate is the molartransport rate of 0 in the liquid phase, as given by the following equation:= ko A [ rpt [^ (2.25)If the liquid phase mass transfer resistance is negligible, the reaction rate can be describedby the molar transport rate of 02 in the gas phase, as follows:No =2A--.k^[69b2]RT -2^K'(2.26)In most cases of gas phase mass transfer control, the interfacial partial pressure of 02 isnegligible with respect to the bulk partial pressure of 02, and can be ignored. Therefore,the rate expression can be described by Equation (2.27).k 0o = 2 A--2- PobRT 2To determine the general rate equation for mass transfer control in both phases, thestoichiometry of the reaction is invoked as follows:(2.27)[O] =4k0,—RTrIc0+.11[RTKIc0]2 +8k02[RTK'ko[O]" +2K'ko,Pcb)2]16k0 {[O] _ [O]" ] =2 191- [P(b) [o]2]RT 2 K'Equation (2.28) can be solved for [O]i:Material Balance: A molar balance on the bath yields the following:[rate of 0 input] [rate of 0 output = 0][rate of 0 generation =^[rate of 0 consumption = 0]= rate of 0 accumulationn°o• A = V d[Ordt(2.28)(2.29)(2.30)(2.31)Depending on the transport conditions, gas-liquid interactions can take place in differentregimes. Although the mass transfer analysis is generally similar in most processes, asoutlined above, it is the mass transfer coefficient2 that determines the transportcharacteristics of the regime.2.3.1.^Superficial Gas-Liquid ContactDiffusion of solutes in a gas mixture through a stagnant gas film to a liquid surface is themost obvious type of superficial gas-liquid contact. Thus the reacting species transfer tothe reaction interface driven by the concentration gradient, established by the interfacialreaction. Diffusion through a stagnant gas film in capillary tubes and around levitated2Depending on the transport conditions, the mass transfer coefficient can be determined from: thefilm model, the surface renewal model, from empirical mass transfer correlations and/or frommeasurements, (refer to J. Szekely and N. J. Themelis, Rate Phenomena in Process Metallurgy[52]).droplets, to study the kinetics of gas-liquid reactions has been adopted by severalinvestigators [27-33]. In cases of heterogeneous reactions involving interfacialphenomena, e.g. interfacial turbulence or interfacial blockage, due to surface activesolutes, however, diffusion tests are difficult to interpret. Furthermore, in systems withvery fast liquid phase mass transfer, diffusion methods may create conditions ofstarvation in the gas phase.2.3.2.^Convective Gas -Liquid ContactTop-blown and bottom-blown jets in bath smelting are the most common metallurgicalexamples of gas-liquid convective transport. A very high degree of bath mixing and highreaction gas utilization are some of the advantages gained by adopting bottom-blownjetting methods. On the other hand, top-blown jetting systems are advantageous withrespect to refractory wear and ease of maintenance. Due to its relevancy to theimprovement of the current bath smelting processes and to the development of new bathsmelting processes, several studies have been conducted to understand the fundamentaland practical aspects of gas injection including top-blown jets [62-67].2.3.2.1.^Gas Jets Impinging on Liquid Surfaces Owing to numerous advantages of top blown methods in metallurgical systems, theprinciple of lancing is employed in a variety of processes such as oxygen steel making,Worcra and Mitsubishi processes. Gas jet impingement techniques can be categorizedinto three main types [41], according to their flow behaviour, as follows:1. With low jet momentum, a classical wall jet pattern is formed including aslight surface depression (Figure 2.5a).2. With increased jet momentum, a shallow depression forms in the liquid(Figure 2.5b); a splashing pattern develops.173. With further increased jet momentum, much deeper penetration of the bathtakes place. Thus the penetration or re-entrant mode (Figure 2.5c) isestablished.18Figure 2.5. Comparative geometry of flow modes; (1) nozzle body; (2) entrainmentregion of the original jet; (3) entrainment region of the wall jet across the phase interface;(4) stagnation point of the original jet; (5) separation point of the wall jet; (6) two-phaseexit flow, (after Molloy [411).There have been numerous studies on the behaviour of impinging gas jets [35-43,45-48,51-53], as a result of their high degree of relevancy to metallurgical processes.Laboratory experiments that are carried out to study the kinetics of gas-liquid reactions,under top-blown conditions, often employ low momentum jets, which do not stir the bath19appreciably or penetrate the liquid surface. Due to its relevancy to the current work, thelow momentum type of gas jetting will be the main focus of this discussion. Owing to thedifficulties encountered in the kinetic measurements of metallurgical systems underactual operating conditions, room temperature models have been adopted by severalinvestigators [35-36,38,40-42,44-45,49-50,54].2.3.2.1.1.^High Momentum Jetting SystemsOne of the early models for the gas-liquid jetting systems is that of Wakelin and Lohe[38]. The geometry of the impingement area observed by Wakelin is shown in Figure2.5. Using air-water, CO2-water, air-mercury and CO2-mercury systems, Wakelininvestigated the effect of the jet characteristics on the size and shape of the depressionformed in the liquid, the bath circulation, and the rate of mass transfer.LanceOrifice-----",----,^ ..."-"^.----■ 1,-'z --'^, -,_..,_z---"-__----- \^ >^.„---, ------■r —---,.. ,..—..--.^ ..------,^,-----. ,---Figure 2.6. Model of impinging gas jet used by Wakelin (after Themelis and Szekely[52]).20Wakelin correlated the measured Sherwood number to the Reynolds number as follows:Sh= a[Re(1+ Fr')]n^ (2.32)where the gas phase mass coefficient can be calculated as follows:[^^2aDA_B d,Ki uudpg^p gu2^dckg = '^1+ 1d,^4Hp,g^gkpi —pg)d 21-1,(2.33)The ratio of the depth to the diameter of the cavity can be determined from the followingcorrelation:H, H + H2 = lquMid t d ) Ingp1d3where 1‘1,,, is the jet constant for momentum transfer, defined as:K = 14eYJ,. ur(2.34)(2.35)Experimental measurements using the above models yielded K1 ^15 [52] and 12.5 [35].Mass transfer correlations for an air jet impinging on water gave 6.57 and 0.43 for a and nrespectively3.This model provided a basis for experimentally obtaining empirical correlations that canbe used to estimate the gas phase mass-transfer coefficient for high momentum jettingsystems. The correlation obtained from the air-water system measurements which wereconducted using high momentum jets of 8000 dynes, cannot be used in the calculation ofthe gas phase mass transfer coefficients of the system under study. In the present work,low momentum jets of approximately 3-25 dynes were applied. The extrapolation of thiscorrelation, to calculate the gas phase mass-transfer coefficient for the conditions of jet3A plot of Sh Vs Re(1+ K Fr) was provided for the mass transfer correlation for an air jetimpinging on water [52]. The data were extracted from the graph and were used in thecalculation of a and n, via regression analysis.21momentum of one to two orders of magnitude below its range would result inconsiderable error.2.3.2.1.2.^Low Momentum Jetting SystemsIn order to obtain valid kinetic measurements of gas-liquid reactions, starvationconditions of both reactants must be avoided. In the case of crucible-type laboratorytests, for the investigation of process kinetics, a sufficient amount of reactant gas must bedelivered to the reaction interface, in order for the measurements to be valid. For acertain bath volume, the limiting gas flow rate of non-starvation conditions must bedetermined from preliminary tests4. In studying the kinetics of gas-liquid reactions, forexperimental simplicity and higher accuracy of measurement, the use of low momentumjetting in such experiments has been adopted by several investigators [45-49,55-57].Kikuchi et al. conducted several studies on top-blown lancing systems [45-48]. Theirstudies included room temperature and high temperature measurements of mass transferas well as numerical simulations of crucible-type top lancing systems. Room temperaturemeasurements of reaction rates of systems under conditions of gas phase mass transfercontrol yielded the formulation of several empirical correlations for the gas phase masstransfer coefficient. Room temperature experiments included: sublimation of naphthaleneinto a nitrogen stream; evaporation of pure liquid (toluene, water, and acetic acid wereused respectively) into a nitrogen stream; absorption of ammonia from an ammonia-nitrogen stream into water. For the latter system the gas phase mass transfer coefficient(kg) was evaluated by eliminating the liquid phase mass transfer resistance. Figure (2.7)shows a summary of the experimental results. The reaction rate measurements permittedthe correlation of the Sherwood number to the ratio of the radius of the reaction area and4The limiting gas flow rate of non-starvation conditions in the gas phase is the gas flow rate atwhich the reaction gas utilization is 100%.3 I40 ExperimentalcorrelationSh=m(rs/d)1 ReQ-66Scasm=0401-013Re=13-1500I-, = 1 -6- 5, H/d =0.4-30_,4(0-2^--c1,(0.47-1-26)xl m(a)1Key System• naphthalene -N2o toluene ---N 2• acetic acid -N2o water- N2ED water- N2' NH3- 0 Calculated valuesat Re= 133, rs/d =1-5I Hid =0155 100-5^1ScQ05 0150(b)510-5 -1 5 10010@ Graphite -0O2-00 system(•)Sh=(0-32±0_06)(.icrs'e-.Rrrs/d=1-4-3-1, 1-1/d =1-5-63Sc = 057-0-93, d =(0_6-1-3)x10-2rn500 10000 Liquid iron -0O2-00system0)Sh=(0-27-0.05)(1ci) -^Re°6rs/d =1-4-2-9 , Hid =0-8-1-5-Sc =057-0-9,c1,(0.66-1-3)x10-2mI 50Re22Figure 2.7. (a) Mass-transfer coefficient in gas phase at room temperature, (b) Mass-transfer coefficient in gas phase at elevated temperatures, (after Kikuchi et al. [481).23the inside diameter of the lance, the Reynolds number, and the Schmidt number, asfollows:Sh = (0.40 ± 0.1 3)(r /d)' Re"6 Scm^ (2.36)Elevated temperature experiments included: the oxidation of graphite by CO2-CO gasmixtures and the decarburization of liquid iron by a CO2-CO gas mixture. Themeasurements yielded the following correlations:Sh = (0.32 ± 0.06)(r; /d) 15 Re 0.66sc0.5^(2.37)Sh = (0.27 ± 0.05)(rs/d) 5 Re°36SC"^ (2.38)In determining the rate controlling mechanism of a gas-liquid reaction, the abovecorrelations can be used as a tool in the analysis of rate measurements. The abovecorrelations indicate that for a gas-liquid reaction rate to be controlled by gas phase masstransfer, the relationship between the reaction rate and the gas flow rate (or Re), mustyield an exponent of the gas flow rate (or Re) of approximately 0.66-0.76.2.4. Oxidation Kinetic StudiesIn the past twenty-five years, fundamental research involving experimental measurementsof the oxidation kinetics of metals and mattes has gained attention from metallurgicalinvestigators [7,27-32,34,51,53,56-57,69-77]. Because the understanding of theoxidation kinetics of copper sulphide is paramount to the overall comprehension of themetallurgy of copper converting, many studies have been conducted [7,27,30-31,57,68-77].In order to study the kinetics of copper converting, Ashman et al. [7] constructed amathematical model of the bubble formation at the tuyeres of a copper converter. Theirkinetic studies suggested that the copper converter operation is gas-phase mass transferlimited.24Toguri and Ajersch [27] measured the weight change of molten samples of coppersulphide, during oxidation by Ar-02 gas mixtures, in capillary tubes. Their resultsindicated that the oxidation reaction of copper sulphide proceeds in two stages. The firststage is an unsteady state period in which the loss of sulphur from the melt, in the form ofSO2, takes place. This loss of sulphur continues until the composition of the melt reachesthe miscibility gap after which the melt loses weight at a constant rate (according toReaction (2.4)) until the sulphide phase disappears. Their conclusion was that the rate ofreaction is limited by gas diffusion.Rottmann and Wuth [71] studied the kinetics of copper matte conversion, under top-blown conditions involving a subsonic N2-02 gas jet. Their experimental approachconsisted of the measurement of the bath weight as well as off-gas analysis. Their resultsconfirmed that the oxidation reaction of molten copper sulphide proceeds in two kineticstages. In the first stage, the bath is desulphurized and oxygen saturated (at about 0.6wt%); In the second stage, the bath is oxidized by both the dissolved oxygen andincoming oxygen, according to Reaction (2.4). Their conclusion was that the reaction isdriven by the gas diffusion through the gas boundary layer adjacent to the melt surface.However, according to the results of numerical analysis of the gas phase mass transfer oftop-blown systems [47], the existence of a boundary layer is highly questionable. Theanalysis of Rottmann and Wuth, however, did not explain the different reactions that takeplace in the two stages.The experiments of Jalkanen [57] consisted of the gravimetric measurement of 3- to 7-gram samples of copper sulphide under top-blown conditions of N2-02 gas mixtures.The experimental results confirm that the oxidation reaction of molten copper sulphidetakes place in two stages. Jalkanen claims that the first stage corresponds to thesaturation of the melt by oxygen and copper according to Reactions (2.39) and (2.40)respectively.25[s] + 3/2(02 ) = [0]+ (s02)^(2.39)[5]+ (02 ) = (s02 ) (2.40)When the copper sulphide melt is saturated by both oxygen and copper, the conversion ofcopper sulphide into metallic copper (the second stage) takes place according to Reaction(2.41).[Cu2„5]-1-(02)= (2 + A)(Cu))+ (SA)Jalkanen suggested that Reaction (2.41) may take place in several steps:• oxygen adsorption into the melt surface according to following reaction:(02) = 2[0] ads• formation of an intermediate activated complex as follows:(2.41)(2.42)[S]+[0] = [50]^ (2.43)• formation and desorption of sulphur dioxide as follows:[0] +[so] = (so2) (2.44)Jalkanen concluded that both mass transfer in the gas phase and the kinetics of Reaction(2.44) control the overall rate of copper sulphide oxidation.Thus all of the above studies agree that the rate controlling mechanism of the oxidationreaction of molten copper sulphide is gas phase mass transfer but they did not underpintheir findings with a mathematical analysis. Nor did they explain the mechanism bywhich blister copper is made.In studying the kinetics of gas-liquid reactions, the effects of reaction gas flow rate andreaction gas composition on the reaction rates must be determined. In order for thereaction rate to be controlled by the gas phase mass transfer of oxygen to the melt surface,the following principal conditions must be satisfied:261. The rate of oxygen reaction must be proportional to the oxygen bulk partialpressure, as described by the following equation:.^ko AN o, = 2 PobRT 2(2.45)2. The gas phase mass transfer coefficient and the reaction gas flow rate musthave a relationship as follows:ko, = aQn^(2.46), where a and n are constants. For top-blown jetting systems, n should have avalue of approximately 0.6-0.8.3. The reaction rate must not have a strong dependence on the reactiontemperature4. The rate of oxygen reaction must be independent of the concentrations ofoxygen and any other reacting species in the bath.2.5. Interfacial PhenomenaIn describing the physical and chemical properties of a given phase, it must be recognizedthat the surface properties differ from those of the bulk. The interface between twointeracting phases is not to be regarded as a simple geometrical plane, upon either side ofwhich extend the interacting phases, but rather a complex part of the whole arrangement.In studying heterogeneous reaction systems, the consideration of interfacial effects isparamount to ensure the validity of the established results [55-56,80-104]. Depending onthe reaction system, interfacial phenomena can have negative or positive effects onreaction rates [99]. Non-reacting surface-active solutes may cause a decrease of reactionrates by preventing the reactant species from transferring to the interface [56,84,99-102].On the other hand, in some systems, surface tension-driven flows may enhance masstransfer by orders of magnitude [56].aCsbSolute Concentrationcs^CsbSolute Concentration272.5.1.^Generation of Spontaneous Interfacial Motion2.5.1.1.^Driving Force In some systems, it is known, that the surface tension is a strong function of surface-active solute concentration, electrical potential and/or temperature [83]. In liquid metalsystems, surface-active solutes can either lower or raise the interfacial tension, as shownin Figure 2.8.Em(-)Potential(+)PotentialSolute ConcentrationFigure 2.8. Type of adsorption at liquid-metal interfaces: (a), positive adsorption; (b)negative adsorption; (c), electrocapillary behaviour (after Brimacombe [83]).0_160.12 020 0.3fi 0.38 0.40[0] ( w 1 5)-0-- 1300•C1230°C115 0°C•^1^f^I   X0_04 0.0828The dependence of surface tension on the solute concentration is described by Equation(2.47), which is obtained from the Gibbs adsorption equation [83,86].(a:5^RT= —FsCsacs.lp(2.47)When two reacting phases are brought into contact, concentration gradients of surface-active solutes, along their interface, are established. Resulting interfacial tensiongradients may cause the interface to move toward the region of high interfacial tension.In the case of oxygen and sulphur in copper, it is clear that positive adsorption isexpected, as shown in Figures 2.9 and 2.10.1300-E 12001 1 0 00(I)z 1 0004-< 900(f)800Figure 2.9. Effect of oxygen on the surface tension of liquid copper, (after Monma [87]).1Z.'90 ^12004000 OA a2 0_3 0.4 05 0.6 02 0.8 OS 10S^(wt 94.)-1.3 17.61.21000900;)800700< 600500(i)A--- 1340°CA --- 1300°C^ 1200°C1114•C^ BASES AND KELLOGG,1120 C1•101.- FRACTIOt4 . OF C-u,S0 2 4^6 8 10 t2 14 16 18 20 22 24 26 x10Figure 2.10. Effect of sulphur on the surface tension of liquid copper, (after Monma[87]).It is very clear that the sulphur and oxygen have strong effects on the surface tension ofmolten copper. This is a strong indication that when investigating the oxidation kineticsof molten copper sulphide, the interfacial effects must not be ignored.2.5.1.2.^MechanismDue to non-uniform mass transfer, in real systems, gradients of a surface-active solutealong an interface are expected. In stirred systems these events can occur on a micro-scale by the essentially random penetration of eddies from the bulk of a fluid phase to aninterface. Spontaneous motion may develop as a result of the concentration differences ofthe penetrating eddy and its surroundings, as shown in Figure 2.11.2930Figure 2.11. Interfacial motion generated on micro-scale due to eddy penetration (afterBrimacombe [83]).Also macro-scale non-uniform mass transfer of surface-active solute can generateinterfacial turbulence at the mass transfer interface. A hypothetical example of macro-scale interfacial motion is the case of a solid Cu2S piece partially immersed in moltencopper, as shown in Figure 2.12. In this case, surface motion away from the solid Cu2Sis spontaneously generated. The experiments of Barton and Brimacombe indicated thatinterfacial turbulence is generated during the dissolution of solid Cu2S in molten copper[85].Figure 2.12. Interfacial motion generated on macro-scale by presence of partiallyimmersed piece of Cu2S in molten copper.31As show in Figure 2.13, the effect of oxygen is expected to be similar to that of sulphur.The experiments of Barton and Brimacombe also indicated that interfacial turbulence canenhance the liquid phase mass transfer coefficient by at least one order of magnitudeduring the absorption of oxygen by liquid copper [56]. In those experiments Ar-02 gasmixtures were top blown onto molten copper baths. Measurements of surface velocityand of oxygen concentration in the bath were conducted to determine the effect of surfacetension-driven flows on the kinetics of oxygen absorption by liquid copper. A copperoxide patch was observed beneath the oxygen lance, and the surface spreads rapidlyoutward as shown in Figure 2.13. Spreading of the copper surface in the presence ofcopper oxide can be described by the initial spreading coefficient, as follow:S^ Cu - (a oxide ± a oxidelCu)02VOxygen lance(2.48)Copper oxide patchOxide6 Cu^ 6^ CuOxide/CuLiquid CopperFigure 2.13. Mechanism of copper oxide patch spreading on the liquid copper surface,(surface spreads if act, cFOxide ± CulOxtcle)•Having reviewed the practical implications of the effects of oxygen and sulphur on thesurface tension of liquid copper, separately, it becomes very clear that their simultaneouseffect is of a very similar nature. Thus, when investigating the oxidation kinetics ofmolten copper sulphide, the effect of surface-tension driven flows must be considered.3. Objectives and ScopeThe understanding of the oxidation kinetics of molten copper sulphide is highly importantto the overall understanding of copper converting. The high oxygen utilization of thecopper converter and the findings of earlier studies indicate that the rate controllingmechanism of the oxidation reaction of molten copper sulphide is gas phase masstransfer. There are, however, fundamental discrepancies with respect to the chemistry ofthe copper-making stage. Earlier studies indicated that the oxidation of molten coppersulphide takes place in two stages. The measurements of Rottmann and Wuth [71]indicated that the ratio of the moles of reacted oxygen to the moles of evolved sulphurdioxide are greater than unity during the primary stage and less than unity (approximately0.9) during the secondary stage. Therefore, it is clear that neither Reaction (2.4) norReaction (2.5) can be the reactions during the primary stage. According to thestoichiometry of Reaction (2.2), the ratio of oxygen to sulphur dioxide is 3/2. This maysuggest that Reaction (2.2) is the primary reaction; however; the thermodynamics of thissystem indicates that the formation of Cu20 is not possible before the total oxidation ofCu2S. Furthermore, the formation of solid Cu20 results in surface blockage and likelycessation of the oxidation reaction. Therefore Reaction (2.2) is not the secondary copper-making reaction, as claimed by all of the investigators. It also is clear that treating thissystem as an aggregate of neutral compounds results in a fundamental dilemma incharacterizing the form of the dissolved oxygen5: it is well known that sulphide melts areionic in nature [24-25,115]. Therefore, in order to correctly deduce the chemicalreactions that take place during the copper-making stage, the electrochemical treatment ofthis system must be adopted rather than the conventional (neutral compounds) treatmentadopted by previous investigators.325Since the ratio of the moles of reacted 02 to the moles of evolved SO2 is greater than one, someof the oxygen must dissolve in the melt.33Although all of the previous investigators have concluded that the rate controllingmechanism of the oxidation reaction of molten copper sulphide is gas phase masstransfer, Jalkanen [57] has suggested that the rate of chemical reaction may be ratelimiting as well. None of the experimental studies provided any results of the reactiongas flow rate effect on the reaction rates. Perhaps this has not been possible inexperiments involving small bath size (3-7 grams [57]) and in the case of diffusion testes(0.1-0.15 grams [27]). As explained in Section 2.4, in studying the kinetics of gas-liquidreactions, it is vital that the effect of reaction gas flow rate be determined.Earlier studies revealed that the effect of interfacial phenomena in copper baths must beconsidered when investigating gas-liquid or solid-liquid reaction kinetics. It has beenestablished that surface tension-driven flows have a profound effect on the kinetics ofoxygen absorption by molten copper. The effect of interfacial phenomena on theoxidation kinetics of liquid mattes has not been investigated yet. In the light of thisdiscussion, the objectives of the present work can be outlined as follows:1. To elucidate further the rate controlling mechanism of the oxidation reactionof molten copper sulphide.2. To investigate the role of spontaneous interfacial motion in the oxidationreaction of molten copper sulphide.3. To formulate a mathematical model that can provide the fundamental evidencein support of the experimental findings.4. To extend the understanding of the oxidation kinetics of molten coppersulphide to the copper-making stage in the Peirce-Smith converter.343.1. Experimental ObjectivesIn order to determine the rate controlling mechanism of the oxidation reaction of moltencopper sulphide, the following experimental objectives were pursued:1. A series of laboratory tests was conducted to determine the rates of reactionsof molten copper sulphide baths.2. With the reaction gas composition, the melt volume, and the reactiontemperature fixed, a series of tests was carried out for a gas flow rate range of1-4 1/min.3. Fixing all other variables, a series of tests was conducted for a reaction gascomposition in the range of 20-80% 02.4. Similarly with respect to bath temperature, reaction rates at 1200-1300 °Cwere determined.5. To investigate the role of liquid phase mass transfer resistance in the oxidationkinetics, an artificially invoked mixing test was conducted in which thebubbling of argon gas in the bath during oxidation was adopted.6. In order to determine the effect of surface tension-driven flows on the reactionkinetics, photography and direct observations of the melt surface were carriedout.7. Microscopic examinations of frozen melt samples, at pre-defined reactionconditions, were undertaken to aid in the analysis of the reaction rate results.353.2. Theoretical ObjectivesIn order to confirm the findings of this work, a mathematical model was formulated andvalidated against the experimental results. Based exclusively on gas phase mass transferand the electrochemical behaviour of the melt, the model was constructed to achieve thefollowing objectives:1. To predict, within an acceptable degree of error, the measured bath sulphurand oxygen molar contents for the two stages and their time durations.2. To predict, within a reasonable margin of error, the molar reaction rates of thesulphur and oxygen as functions of reaction gas flow rate, reaction gascomposition and bath temperature.Based on the model predictions, the reason for the existence of two stages rather than onewas determined, and the rate controlling mechanism of the oxidation reaction of moltencopper sulphide was confirmed. The electrochemical reactions that take place during thetwo stages were inferred.4. Experimental 4.1. Experimental ApparatusIn order to achieve the experimental objectives, the experimental equipment was designedand built for use in all of the laboratory tests. The equipment consisted of: a reactor, gasdrying and control system, gas analysis system, gravimetric measurement systemequipped with a data acquisition system, and the melt surface photography system.4.1.1.^ReactorThe reactor, shown in Figure 4.1, consisted of a vertical tube resistance furnace, with areaction tube, heating elements and layers of insulation contained in a steel frame. In thecore of the reactor, an alumina 6 reaction tube, with dimensions of 57 mm inside diameter,64 mm outside diameter and 762 mm length, was located. Water-cooled brass couplingswere used for the support and mounting of the reaction tube to the steel frame. Vacuumgreased fluorocarbon 0-rings were used to seal the reaction tube to the brass couplings 7 .Insulating alumina bricks were used for the inner portion of the insulation, immediate tothe heating elements, and firebricks were used for the outer portion, between theinsulating alumina brick layer and the steel frame8 . Porcelain wool was used to fill thegaps between the bricks.Four 2-shank KANTHAL SUPER heating elements were carefully mounted around thereaction tube and connected in series. The heating elements were connected to a 5 kWpower-supply9 . Using this set-up, approximately 40 mm of ±0 °C hot zone was obtained.699.7% recrystallized alumina was used in all of the reactor components that are within andincluding the reaction tube.7To prevent the corrosion of the inside surface of the brass coupling, due to the long termexposure to SO2, the inside surface of the brass coupling was vacuum greased.8Reactor insulating materials properties are provided in Appendix A.9For more details about the electrical circuit of the power-supply, refer to Figure A.1 inAppendix A.3637Figure 4.1. Cross-sectional view of the reactor.38To maintain constant electrical conductivity of the electrical connectors of the heatingelements, two electric fans were used to cool the exposed portions of the heatingelements.Approximately 200-gram samples of molten copper sulphide were held in cylindrical, flatbottom, alumina crucibles of approximately 44 mm inside diameter, 50 mm outsidediameter and 75 mm height. The crucible supporting post, shown in Figure 4.2, consistedof a closed end alumina tube (6 mm I.D., 10 mm O.D. and 450 mm long) attached to analumina disc (40 mm in Dia and 3 mm thick), with high temperature ceramic cement.Figure 4.2. Sectional view of the bottom of the reaction tube, including the cruciblesupporting system. Note that the scale is offset to show the rubber diaphragm sealingarrangement.A thin sheet of porcelain wool was used as an insulator between the bottom of thecrucible and the alumina disci°.The bottom of the reaction tube consisted of a brass plate with a port for the cruciblesupporting post. For safety reasons and for the purpose of analyzing the off-gas, thesystem had to be very tightly sealed. A neoprene diaphragm arrangement was used toseal the bottom of the reactor, as shown in Figure 4.2.The top of the reaction tube, shown in Figure 4.3, consisted of ports for the lance, theauxiliary tube and the thermocouple sheet, the off-gas outlet pipe, and two viewing ports.The alumina tubes were fitted and sealed in the ports by 0-rings. Due to thecondensation of water vapor on the lower surface of the viewing port, the ability to cleanthe surface easily without allowing a large amount of gas to escape, required the viewingports to be equipped with shutters, as shown in Figure 4.3. The off-gas outlet pipe,permanently attached to the top of the reaction tube, consisted of a copper pipe of 6 mminside diameter, 8 mm outside diameter, and 400 mm length.3910Due to the release of the heat of fusion of the solidifying bath, during the withdrawal of thecrucible, the alumina disc was susceptible to cracking as a result of its low thermal shockresistance.I1^Socket-HeadSet ScrewViewing Port Shutter/ ,^Quartz Disc(^IFluorocarbon0-RingPlan ViewPolypropylene 0-RingI^I103 mm40Top ViewOff-Gas PipeViewing,Photographingand SamplingPortAuxiliary TubePortBrass PlateThermocouplePortLancePortFigure 4.3. Schematic diagram of the top of the reaction tube.SO 2 SupplyPlexiglas Columns60 mm ID, 70 mm OD,300 mm H--35\   To LanceTo AuxiliaryTubeOptionalRotameterCalibration andExhaust Gas LineOptionRotametersgi9 Pressure^ Gauge0r'MercuryManometerAr/O2Supply414.1.2.^Gas Drying And Control SystemTo control the gas flow rate and composition, and to reduce its moisture contentil, the gascontrol and drying system, shown in Figure 4.4, consisted of gas drying columns,rotameters, pressure gauge, mercury manometer and thermometer. Polyflow lines wereused to connect the components of the gas control and drying system.Silica Gel^02 Supply Calcium SulphateFigure 4.4. Schematic diagram of the gas train (not to scale).4.1.3.^Gas Analysis SystemManual measurements of the reaction rates were conducted by the use of an SO2 gasabsorber and a soap bubble meter. Due to its simplicity, the manual measurement systemwas found to be very reliable and more accurate than gravimetric measurement.However, gravimetric measurement was found to provide a general support to the manual11Water vapor, in the reaction gas, condenses on the inner surface of the quartz discs andprevents surface observations.42measurement. The gas analysis consisted of the determination of the amount of sulphurremoved from the bath by the use of the SO2 absorber and of the amount of unreactedoxygen using a soap bubble meter.4.1.3.1.^SO2 AbsorberThe SO2 gas absorber consisted of approximately 3 liters of 5 % H202 solutionvigorously mixed in a Plexiglas column, as shown in Figure 4.5.Figure 4.5. Schematic diagram of the off-gas analysis system, not including the soapbubble meter.43In order to reduce the temperature of the off-gas before introducing it to the absorber, itwas passed through a 300 mm long water-cooled copper jacket, as shown in Figure 4.5.To determine the amount of SO2 absorbed, a sampling port with a rubber stopper wasconstructed in the master rubber stopper of the absorber. Using a 5-ml pipet, sampleswere extracted through the sampling port, at specific intervals of reaction time. Duringthe time of the final gas flow rate measurement, using the soap bubble meter, thesampling port was sealed to prevent escape of the final off-gas. Due to the high aspectratio of the absorber, vigorous mixing of the solution had to be ensured for the extractionof representative samples. In order to achieve simultaneous mixing and sealing of theabsorber, the stirrer shaft had to be sealed to the rubber stopper port as shown in Figure4.6.Figure 4.6. Schematic diagram of the absorber rubber stopper (not to scale).Once the bubbles come in contact with the hydrogen peroxide solution, the SO2 isabsorbed from the bulk gas according to the following reaction:[H202] + (SO2) = [1-12SO41^ (4.1)44To ensure high SO2 absorption efficiency, vigorous mixing, a high aspect ratio of 6 and asufficient amount of the 5% H202 solution were adopted. It is well known that the rateof Reaction (4.1) is very fast [44]. Hence, in such a system, the rate must be bubblevolume limited i.e. the smaller the average bubble size, the higher is the absorptionefficiency. Vigorous mixing of the solution and the introduction of the gas at the wall ofthe absorber caused the gas bubbles to disintegrate to a small size and to be retained inthe region of the propeller, as shown in Figures 4.5 and 4.8, thereby increasing theirretention time and ensuring complete absorption of the SO2. The high aspect ratio wasalso important in achieving the high absorption efficiency.The total possible amount of SO2 that might be evolved from the oxidation of 200 gramsof Cu2S is approximately 1.257 moles. Therefore, according to Reaction (4.1), thecorresponding amount of H202 required is also 1.257 moles. However, to ensurecomplete SO2 absorption, 3 liters of 5% H202 solution system was utilized i.e.approximately 4.4 moles of H202.To determine the amount of SO2 absorbed, the samples were titrated with 0.1 N NaOHstandard solution, according to Reaction (4.2). Thus the moles of SO2 were calculated,accordingly, from Equation (4.3).[H2SO41+ 2[Na011]=[Na2SO4]+2((H20))ATS02 V=  NaOHN NaOH v'' 217,To test the absorber performance, an Ar-S02 gas mixture was admitted at a constant flowrate and composition for approximately 60 minutes. Samples were obtained at pre-defined intervals of time and the amount of SO2 absorbed was determined by acid-basetitration. The measured absorbed SO2 was found to be in agreement with the admittedamount as shown by Figure 4.7.(4.2)(4.3)45Figure 4.7. Plot of the amount of SO2 absorbed as a function of time for a test of 2 1/minof 13 % SO2 and 87% Ar at 23 °C.The absorber performance was also tested by admitting approximately 260 ml/min ofpure SO2 The gas flow rate from the absorber was found to be approximately 0 ml/min.The gas bubbles were observed to diminish in size as they traveled upward to the solutionsurface, as shown in Figure 4.9.11111111111114Figure 4.8. Photograph of the SO2 absorber with a gas flow rate of 21/min, 13 % SO2and 87 % Ar. Note the vigorous mixing attained by the design of the absorber.46Figure 4.9. Photograph of the SO2 absorber with a gas flow rate of 260 ml/min pure SO2.To determine the validity of the kinetic measurements, the following calibrationprocedure was performed both before and after each run:1. An Ar-S02 gas mixture with a gas flow rate and composition close to that ofthe expected off-gas (assuming 100 % oxygen utilization), was admitted for aperiod of 10 min.472. A sample was obtained and the amount of SO2 absorbed was determined bytitration and compared to the admitted amount.3. The final off-gas flow rate was measured by the soap bubble meter andcompared to the above results.4. The final off-gas was tested by smell to detect any residual SO2.5. If the above results were found to be consistent and the absorber efficiencywas found to be very close to 100 %, the results of the respective run wereaccepted12.4.1.3.2. Final Off-Gas Flow Rate MeasurementIn order to determine the final off-gas flow rate accurately, an appropriate size of the soapbubble meter was selected, for the given reaction conditions. Using a stop watch, thetime that a soap bubble takes to travel over a certain height of the graduated cylinder wasdetermined. To determine the gas flow rate, the volume was divided by the measuredtime.48Graduated Glass TubeDigital Piercing Thermometer ^Rubber Bulb ForInjecting Soap Bubble;—\Final Off-Gas From SulphurDioxide AbsorberCopper Pipe (heat exchanger)6 4 mm inside diameter,7.9 mm outside diameterand 1 m longRubber HoseRetort StandFigure 4.10. Schematic diagram of the soap bubble meter.12Due to the low percentage of rejection, approximately 3% for the entire program, the SO2absorber was considered to be very effective.Fixed EndUpper StrainGaugesTo Data AcquisitionSystem/1//Pre-MarkedFree EndDaytronic StrainGauge SignalConditionerModel 601BCrucible Supporting PostLower StrainGauges Fixed EndBracketSteel Bar49To ensure accurate measurements, graduated tubes that resulted in relatively low bubblevelocities, of approximately 20-50 mm/sec, were used. Depending on the expected finaloff-gas flow rate, the size of the soap bubble meter was selected. For final off-gas flowrates of 2 1/min, a 500-ml graduated tube was selected and for the measurement of finaloff-gas flow rates of < 2 1/min, a 250-ml graduated tube was used.4.1.4.^Gravimetric Measurement SystemIn order to obtain automatic measurement of the bath weight, a gravimetric measurementsystem, consisting of weighing and recording devices, was custom assembled from a loadcell and a data acquisition system.The load cell consisted of a cantilever beam that was made of a 3x19x120 mm steel bar,four temperature compensated strain gauges and strain gauge signal conditioner,assembled as shown below.Figure 4.11. Schematic diagram of the load cell".13For more details about the electric circuit and the components of the load cell, refer toAppendix A.The data acquisition system was comprised of a 286 IBM PC equipped with CIO-ADO8data acquisition board with a total of 32 channels, data acquisition program and aspreadsheet program.The crucible supporting post was placed on the pre-marked free end of the cantileverbeam, as shown in Figure 4.11. The fixed end of the cantilever beam was attached to thesupport frame by means of the fixed end brackets such that the beam could swing to theside to permit removal of the crucible at the end of a run.As mentioned earlier, the gravimetric measurement was found to be less reliable than themanual gas analysis to characterize the reaction rate. This is due to the fact that whenplacing the alumina post on the load cell, it was difficult to determine whether it wascompletely free 14 . It was only after 10 minutes of the reaction time that the visual displayof the gravimetric measurement on the PC screen, indicated if the measurement wassuccessful. The gravimetric measurement, therefore, was used only as a general check onthe validity of the results of the manual gas analysis. The rate of bath weight change wasexclusively used in comparing the gas analysis results to the gravimetric measurementresults. The overall rate of bath weight change was obtained by performing linearregression of the bath weight with time. Statistically, the validity of this regression wasdependent on the number of data collected over relatively long periods of time. This wasoften possible during the secondary stage only. In most of the runs, during the primarystage, it was not possible to obtain reliable results.14Success of the measurements was contingent upon the crucible being concentric with respect tothe reaction tube. On occasion, however this was difficult to accomplish because of the nature ofthe crucible supporting post. Due to manufacturing defects, the alumina tubes, used in makingthe crucible supporting posts were often warped at the bottom (in the vicinity of the bottom ofthe reaction tube). Because the gravimetric measurement system was added to the apparatus at alater stage of the experimental program, it was not possible to modify some key components ofthe apparatus to eliminate all of the problems associated with the gravimetric measurementsystem. For a newly designed apparatus, however, the elimination of these problems can beachieved.50Lineo InitialA FinalStandard weights were used in the calibration of the load cell before and after each run.An average equation for the relationship of the weight and the load cell reading wasobtained to convert the load cell response to weight measurement. As the relationshipbetween the weight and load cell reading is linear, as shown by Figure 4.12, a typicalequation for the best line can be calculated as follows:W= 87+82R,0^100^200^300^400^500Weight (grams)Figure 4.12. Load cell calibration plot obtained with standard weights.The load cell response, during the reaction time, was recorded by the data acquisitionsystem and stored in a spreadsheet. The millivolt readings were converted by thecalibration equation of the respective run.51(4.4)52Constant load cell reading for a period of time or permanently until the end of a run wasobserved to take place during some experiments. This indicated that due to somemechanical interference in the weighing system, the load cell was not measuring the fullweight. Then depending on how long this interference took place, the measurement waseither completely discarded or the straight line segments were used to calculate anaverage value for the rate of weight change. Due to the stabilization process that thesystem undergoes, as a result of the internal pressure change '5 at the beginning of thereaction, the measurements that were obtained during the first minute were discarded.For the secondary stage, reading for at least 10 minutes was taken as a validmeasurement. To determine the validity of the measurement and its time domain thesample weight was plotted against time and examined visually. Using the least squaresmethod [105], linear equations for weight as a function of time, were calculated for thelinear portions of the measurement. To determine the rate of weight change, theequations were differentiated with respect to time as follows:iil . dW d ,= La+ bt]= bdt dt4.1.5.^Optical Photography SystemIn optimizing the furnace parameters, the volume of the reaction tube was kept to aminimum in order to minimize the gas measurement time lag. This resulted in relativelysmall view ports, of approximately 20 mm in diameter. In order to photograph the meltsurface, of approximately 44 mm, the need to design a specific optical system wasinevitable. The variable focal length optical system consisted of a 450 mirror to reflectthe image horizontally, a focusing macro-lens and a magnifying eyepiece, as shown in15As a result of passing the off-gas through the SO2 absorber, the pressure head of the solution ofthe absorber increased the internal pressure of the reactor in a non-steady state manner at thebeginning of the reaction.(4.5)>^>^\TA,Figure 4.13. This system of lenses was installed on a 35 mm camera with the use of abellows.53250 mm170 mm 35 mm1^1# 35 mm Film45 ° MirrorFocal Pointirla (4111FocusingMacro-Lens1:2/50Magnifying LensPlan CorrectedEyepieceAlumina Reaction Tube400MMAlumina CrucibleMelt Surface# Variable dimensions•01d,^ 44 mm —IFigure 4.13. Schematic diagram of the optical system used in the photography of the meltsurface. The lenses were mounted and enclosed within a system of bellows.4.2. Material4.2.1.^Copper Sulphide4.2.1.1.^Supplied Copper SulphideApproximately 99.5% copper sulphide, monoclinic Cu2S (-200 mesh) supplied andcertified by Cerac Inc. was used for all of the runs except for the first 5 runs. Thechemical analysis given in Table 4.1 indicated that the impurities are negligible inquantity.Table 4.1. Trace analysis (wt%) of supplied copper sulphide.Ag <0.01Al <0.01Ca < 0.01Cr <0.01Fe <0.01Mg <0.01Mn <0.01Ni <0.01Pb <0.01Si <0.01Sn <0.01Ti <0.01Zr <0.014.2.1.2.^Prepared Copper SulphideFor the preliminary runs (the first 5 runs), prepared Cu2S was made of 99.9 % purecopper powder and laboratory reagent grade elemental sulphur. Approximately 1590grams of copper were well mixed with approximately 410 grams of sulphur16 in agraphite-clay crucible. The crucible was then placed in a larger graphite crucible, to161n order to compensate for the loss of sulphur during the Cu2S reaction, approximately 2 %excess sulphur was used.5455avoid damaging the furnace material in case of spillage. The crucible was then coveredwith a graphite lid and placed in a preheated muffle furnace, at approximately 400°C, forapproximately 3.5 hours. To minimize sulphur evaporation prior to its reaction withcopper, the reaction was allowed to take place at a temperature of 50 °C below the boilingpoint of elemental sulphur, according to Reaction (4.6). To prevent excessive reaction ofoxygen with the copper sulphide, argon gas at a flow rate of approximately 200 ml/minwas passed through the furnace.2(C0+ ((s)) = (Cu2S)^ (4.6)In order to homogenize the copper sulphide by melting according to Reaction (4.7), thecrucible was then placed in another preheated muffle furnace, at approximately 1200 °C,with argon atmosphere, for approximately thirty minutes. The crucible was then carefullyremoved from the furnace and placed on a steel plate, to slow cool. The copper sulphideingot then was removed from the crucible and crushed into small granules, for use.However, due to the difficulties in repreparing the same composition and the cost ofchemical analysis, the use of prepared copper sulphide was terminated.(Cu2S) = ((Cu2S))^ (4.7)4.2.2.^GasesAr-02 mixtures were used for most of the runs, except for a run to investigate the effectof reaction gas carrier type, where a N2-02 mixture was utilized. Ar-S02 gas mixtureswere employed for the calibration of the gas analysis system. The impurity specificationsof these gases are as given in Table 4.2. In order to reduce the moisture content of thegases, they were passed through silica gel and CaSO4 columns before being admitted intothe reaction tube, as shown in Figure 4.4.56Table 4.2. Imnuritv s ecifications of gases in porn.Gas MinimumPurityN2 02 H20 CO2 THC Kr Ar07 (U H P) 99.995% <40 <5 <1 <1 <15 <15N7 (U H P) 99.999% <5 <5 <1 <1 <25Ar (Pre-purified) 99.998% <3 <5SO2 (Anhydrous) 99.98%4.2.3.^Hydrogen Peroxide SolutionTo prepare approximately 5% H202 solution for the absorption of SO2, approximately2500 ml of de-ionized water was added to 500 ml of 30% H202 solution, for which thechemical analysis is given in the Table 4.3. Due to their insignificant concentrations inthe supplied hydrogen peroxide solution, the impurities were ignored in the determinationof the amount of SO2 absorbed.Table 4.3. Maximum limits of impurities for the 29.0-32.0 % hydrogen peroxide solutionsuonlied by BDH .Impurity Maximum ConcentrationResidue after evaporation 0.002 %Titratable acid 0.006 meq/gChloride (Cl) 3 PpmNitrate (NO3) 2 ppmPhosphate (PO4) 2 ppmSulphate (SO4) 5 PpmAmmonium (NH4) 5 PPInHeavy metals (Pb) 1 ppmIron (Fe) 0.5 ppm574.2.4. Titration ReagentsApproximately 0.1 N NaOH standard solution was used in the acid-base titration of thesamples obtained from the gas absorber. The NaOH standard solution was prepared bydissolving pre-weighed amounts of reagent grade solid sodium hydroxide in de-ionizedwater and storing it in plastic bottles. The NaOH solution was then standardized bypotassium hydrogen phthalate (KHC811404) [106] and labeled for use. The chemicalanalysis given in Table 4.4 indicated that after standardizing the prepared solution, theeffect of impurities in the solid hydroxide can be ignored.Table 4.4. Maximum limits of impurities for the 98.0 % sodium hydroxide pellets(supplied by BDH).Impurity Maximum Concentration (%)Water insoluble matter 0.01Carbonate (Na7CO3) 1.0Chloride (Cl) 0.005Phosphate (PO4) 0.001Silicate (Si07) 0.01Sulphate (SO4) 0.005Aluminum (Al) 0.001Calcium (Ca) 0.002Copper (Cu) 0.0005Iron (Fe) 0.0005Lead (Pb) 0.0005Nickel (Ni) 0.0005Potassium (K) 0.05Nitrogen Compounds (N) 0.0005Approximately 0.1 % phenolphthalein was used as an indicator for the acid-base titration.The indicator was prepared by dissolving the solid in 80 % ethyl alcohol [106].58All glassware was cleaned with the use of laboratory glassware cleaning solution andsoap. The cleaning solution was prepared by mixing 10-15 grams of potassiumdichromate (K2Cr207) with about 15 ml water, in a 500 ml heat resistant conical flask.Enough concentrated sulphuric acid was added slowly, until all of the forming solid wasdissolved. The solution was discarded when it acquired a green color [108].4.3. Experimental Procedure4.3.1.^Oxidation Rate MeasurementTo measure the rate of oxidation of the molten copper sulphide bath, the following stepswere followed :1. Before each run, a complete leak test was performed on all of the couplings,polyflow fittings and valves. Leak tests were performed by pressurizing thesystem and testing for leaks by the use of bubbling soap. The gas supplieswere also checked to ensure sufficient supply for the run.2. Approximately 200 grams of the solid Cu2S were weighed in an aluminacrucible. The crucible was then carefully placed at the bottom of the reactiontube, on the alumina supporting post. The bottom of the post was placed on alaboratory jack, which was used to push up the post until the crucible waslocated at a pre-defined position, in the hot zone. To avoid thermal shock, thecrucible was pushed at a rate of approximately 10 mm/min. During thepreheating and melting of the sulphide sample, approximately 50 ml/min ofargon was introduced through the preheating tube.3. During the melting of the sulphide sample, the load cell and gas absorber werecalibrated, and the data acquisition system was activated.4. After the calibration of the load cell, the jack was removed and the aluminapost was carefully placed on the marked end of the load cell as shown inFigures 4.1 and 4.11.5. After ensuring that the sample was completely molten, by surface observationand from the temperature, the reaction gas flow rate and composition wereadjusted to the desired levels, and the thermocouple was lifted from the bathto the vicinity of the lance nozzle17. The reaction gas was then admitted to thereaction tube, through the lance, and the data collection proceededimmediately.6. The data collection was done via two independent sources: the gas analysis forSO2 and 02, and the gravimetric measurement of the bath weight.7. Due to the corrosive nature of copper oxide, the reaction was terminated justbefore Cu20 began to form. As the oxidation reaction of molten coppersulphide ended, the spontaneous motion of the surface was observed to cease.8. The final calibration of the gas absorber and the load cell were carried out.9. The temperature of the system was recorded throughout the run by the dataacquisition system and stored in a spread sheet. Using the mercurymanometer, the pressure of the system was monitored periodically throughoutthe run and an average value was recorded.10. The load cell was released and swung to the side for removal of the crucible.11.The crucible supporting post was then placed on the laboratory jack. The jackwas then lowered at the rate of approximately 10 mm/min. This was17Due to the intensity of the oxidation reaction, corrosion of the thermocouple sheath and theplatinum thermocouple was found to take place if the same thermocouple sheath was used inmore than one run, with its tip immersed in the melt.59important to avoid the rapid release of the heat of fusion, which started atapproximately mid-distance from the bottom of the reaction tube.12.The crucible was removed after it reached the bottom of the reaction tube.Once the temperature of the crucible reached room temperature, its weightwas determined and recorded.13. All of the glassware was washed and prepared for the next run.4.3.1.1.^Gas Analysis In order to determine the amount of sulphur removed from the bath as a function of time,samples were extracted from the gas absorber, at pre-defined time intervals, with a 5-mlpipet. The samples were stored in pre-labeled 250-rn1 conical flasks, until the end of therun. Due to the exothermic nature of the absorption reaction, the temperature of thesolution was observed to increase at a constant rate. This was used as another indicatorof the efficiency of the absorber in a particular run. For each sample obtained, thetemperature of the absorption solution was recorded. The amount of sulphur dioxideabsorbed was determined by the acid-base titration of the individual samples, using 0.1 NNaOH standard solution [107]. Since the molar ratio of sulphur to sulphur dioxide isunity, the number of moles of sulphur removed from the bath is the same as the moles ofsulphur dioxide absorbed.To determine the amount of unreacted oxygen in the off-gas, the soap bubble meter wasused to measure the off-gas flow rate. For each absorber sample obtained, at least fourvolumetric flow rate measurements were made. Due to the increase of the temperature ofthe absorption solution, the temperature of the gas was expected to deviate from roomtemperature, as it left the absorber. In order to avoid temperature effects, the temperatureof the gas inside the rubber hose, leading to the soap bubble meter, was recorded for eachset of measurements.60614.3.1.2.^Gravimetric MeasurementThis measurement was used to verify and support the gas analysis measurement. Thereaction system weight was performed automatically, using the data acquisition system.The numerical load cell response was converted to weight using the calibration equation.4.3.2.^Microscopic Examination of Frozen Melt SamplesFor further validation of the kinetic measurements, melt samples of known reaction wereobtained and microscopically examined. U-shaped quartz tubes with an approximateinside diameter of 5 mm were used to obtain approximately 4- 7-gram samples at specificintervals of reaction time. To minimize post sampling reaction, the samples wereimmediately quenched in an ice bath. The samples were sectioned, hot-mounted andpolished using 5 gm and 1 gm alumina polishing powder. The samples were thenexamined with an optical microscope to assess copper droplets, gas bubbles and thephases present.4.3.3.^Surface ObservationSurface observations were primarily undertaken to investigate the effect of surface-tension driven flows on the reaction kinetics. The observations included the qualitativemeasurement of surface movement, gas bubbles rising from the melt and surface velocity,under different reaction conditions. The surface observations also served as an indicationof the state of reaction and its termination. Using a 35-mm camera and the optical systempresented above, some runs were conducted to obtain photographic evidence of the visualobservations. Photographs were taken of the melt surface under specific reactionconditions.ReactionChamberI W(t), T(t)Figure 5.1. Gas flows in the oxidation experiments.A No2 (t)Bubble Meterv Tg (t) ^YN^ ,(t) T(t)SO2 4 (0Q7.^>Absorber5%H2 02Off-GasSoap625. Experimental Results and Discussion5.1. Oxidation Rate Results5.1.1.^Gas Analysis Data5.1.1.1.^Sulphur and Sulphur Dioxide Analyses The gas flows, which were characterized to determine the oxidation kinetics of moltenCu2S, are shown schematically in Figure 5.1. Typical results of the gas analysis, for eachrun, are plotted against time, in Figures 5.2-5.3. Because all of the SO2 is absorbed bythe 11202 solution, the moles of sulphur in the bath, N8 (t), can be calculated from themoles of SO2, N80 (t), absorbed as follows:N8(t)=N—N80(t)^ (5.1)Figure 5.2 reveals that there are two distinct stages, primary and secondary, for theformation of S02. In order to determine the rates of SO2 formation and the time domainsof the two stages, the following analysis was carried out:1. The time domains of the two stages were determined, as a first approximation,by visualization of the SO2 vs. time graphs.2. Since the time dependence of the two stages appears to be linear, a linearequation for each stage was calculated, via regression analysis; and thetransition time was calculated by equating the two equations. If the calculatedtransition time was found to be within the time domain of the adjacent two40^5010^20^3001.61.41.200.40.20.0o63measured points, the equations were accepted. If the calculated transition timewas found to be closer to another measured value, the linear equations wererecalculated, based on the new designated values. This procedure was iterateduntil the best agreement between the measured and calculated values wasachieved. Once the equations were accepted, the slopes of the equations wereregarded as the measured SO2 molar rates.Time (min)Figure 5.2. Moles of reaction gas and off-gas as a function of time, for the experimentalconditions of: 200 grams of Cu2S, 2 I/min of 35% 02 and 65% Ar, at 1200 °C; ^regression line for the absorbed SO2; 0 measured absorbed SO2; — — — regression linefor the dissolved 02; 0 dissolved oxygen by difference; — - - — reacted oxygen;^ admitted 02.1600641•111400,R 1200a 1000r:4^800  0600  o40020000^10^20^30^40^50Time (min)Figure 5.3. The final volumetric off-gas flow rate as a function of time for theexperimental conditions of : 200 grams of Cu2S, 21/min of 35% 02 and 65% Ar, at 1200°C; ^ measured final flow rate; - -^- reacted oxygen flow rate; — -A- unreactedoxygen flow rate.Assuming that the reaction takes place uniformly over the melt surface area, the SO2molar fluxes were calculated by dividing the SO2 molar rates by the crucible cross-sectional area, as follows:n so2A(5.2)655.1.1.2.^Oxygen Analysis The amount of oxygen dissolved in the bath as a function of time was determined fromthe measured SO2 and the final off-gas flow rate measurement by the followingprocedure.The admitted volumetric gas flow rate, Q , was composed of argon QA„ and oxygen,as follows:= 0)2 +^ (5.3)The volumetric off-gas flow rate, Qoiff (t), varies with time, with an unknown quantity ofSO2, Qs02(t), unreacted 02, Qou2(t), and Ar, as described by the following equation.aff (t) = QAr 0)2 (t) QS02(t)^(5.4)After the 502, the volumetric off-gas flow rate, Q.offf(t), also varies with time, with anunknown quantity of unreacted 02 and Ar, as described by the following equation.Q(t)=^(t)^ (5.5)Having defined the volumetric flow rate equations, the calculation of the volumetric flowrate of unreacted oxygen can be readily carried out. Since the gas temperature was notconstant, this calculation was based on molar flow rates rather than volumetric flow rates.Assuming that the gas mixture is ideal, the final volumetric gas flow rate can beconverted to molar flow rate as follows18:N off (t) =^of^Q(t)P^R1(t(5.6)Therefore the unreacted molar flow rate of oxygen can be determined from Equation(5.7).18Note that the molar flow rate of Ar, N Ar, is calculated from the rotameter reading (volumetricflow rate) which was calibrated at room temperature. There may be a difference between thetemperature of the measurement of the final off-gas flow rate and the rotameter calibrationtemperature.66. u^. f^.N 02(0 = N off (t)— NAr^ (5.7)The molar flow rate of unreacted oxygen is converted to volumetric flow rate as follows:. .N 0,(07;(t) Z2(t)=^P(5.8)A molar balance on the oxygen yields the following.QL,(t)= Z, - Q1(4), (t)^ (5.9)To determine the molar rate of reacted oxygen, the volumetric flow rate of oxygen isconverted to molar rate, according to the following equation.XTro,(t)= QL2 (t)13R7(t)(5.10)This molar flow rate of reacted oxygen is calculated from the measured final off-gas flowrate, for specific intervals of reaction time. The integrated measured molar flow rate ofreacted oxygen is described as follows:0 rNL2(t) = Ni(t1)+ 5 N 02(t1_2)dtt(5.11)To determine the molar flux of reacted oxygen, linear regression was applied to the dataobtained from Equation (5.11). The molar rate of reacted oxygen was found to beconstant throughout the reaction duration, as shown in Figures 5.2-5.3. Hence forsimplicity, the function of time notation, (t), is dropped. The oxygen molar flux wascalculated by dividing the calculated molar flow rate of reacted oxygen by the cross-sectional area of the crucible ( for notational simplicity, from this point on, the superscriptr is dropped), as follows:°^N 02n 02 =A(5.12)67Since the oxygen reacted must be removed in the form of SO2 or dissolved in the bath,the oxygen dissolved in the bath can be determined by a material balance on the oxygenas follows:N[0](0= 2[NL2 (t) NS02 (t)]^(5.13)Assuming plug flow conditions, the real time in the reaction was calculated bysubtracting the time needed for a given flow rate of gas to travel the distance from thereaction surface to the gas absorber ( the volume of the off-gas line was approximately 1liter and the employed range of volumetric flow rate was 1-4 1/min which resulted in atime lag of 15-60 s).In order to study the reaction kinetics, the measured sulphur and oxygen contents in thebath were plotted on graphs such as that of Figure 5.4. Comparing the closeness of themeasured values to the regression lines, the sulphur analysis exhibits less scatter than theoxygen analysis. From Figure 5.4, the sulphur and oxygen contents in the bath varylinearly with respect to time. Thus the rate at which the sulphur is removed from the bathis constant, but different in the two regimes. Similarly, the respective rate of oxygendissolution in the bath is also constant over the primary and secondary stages. In trying tounderstand the reaction mechanism, the oxygen behaviour is obviously the first clue. Asshown in Figure 5.4, the amount of dissolved oxygen increases linearly to a certain valueat the transition time, and then decreases to a minimum value, at the final reaction time.1.468' "^"10^20^30Time (mm)0.0 0^0 40^50Figure 5.4. The molar sulphur and oxygen contents of the bath as a function of time, forthe experimental conditions of: 200 grams of Cu2S, 2 I/min of 35% 02 and 65% Ar, at1200 °C; ^ regression line for the amount of sulphur in the bath; 0 measured amountof sulphur in the bath; - - - regression line for the amount of dissolved oxygen in thebath; 0 determined amount of dissolved oxygen.5.1.1.3.^Overall Reaction RateFurther analysis of the reaction kinetic data can be accomplished by examining the bathweight change with respect to time. The rate of weight change of the bath, W, can berelated to the rate of sulphur dioxide evolved from the bath, Nso2 , and the rate of oxygenreacted, NO2, as follows:69.^.W = N o2 MO2 — N so2 Ms02 (5.14)In order to study the oxygen and sulphur behaviour simultaneously, the bath weight wasplotted for each run in graphs typical of that shown in Figure 5.5.2051550195Ecl 185',..4td:i*1-5- 175crigq165, . 1 i i^I " "10^20^30^40^50Time (min)Figure 5.5. Change of bath weight with time for the experimental conditions of: 200grams of Cu2S, 2 I/min of 35% 02 and 65% Ar, at 1200 °C, ^ calculated fromEquations (5.15) and (5.16); 0 calculated from Equation (5.17).70The sample weight was calculated by integrating the rate of weight change with respect totime, as given by Equations (5.15) and (5.16) by using the determined amounts of oxygenand sulphur as given by Equation (5.17)19.. P^. P^ (5.15)147gPa (t)= Wga (0) + [No, Mo, —Nso, Mso, l•t,^0 s^0 sKa(t)= Wga(t* ) +[N 0, M0 — N so, M so,]•(t — t*)Wga(t)= W(0)+[NO2(t)M0, — N.,02(t)M502]5.1.2.^Gravimetric Measurement Data(5.16)(5.17)The sample weight measurement, determined gravimetrically with the load cellarrangement, was plotted against time for each successful experiment, an example ofwhich is shown in Figure 5.6. Applying the least squares method, the rate of weight lossin the two stages and the reaction transition time were determined. The reactiontransition time is the time at which the rate of sulphur dioxide formation changes. In thegravimetric measurement, the reaction transition time is the time at which the rate ofweight loss changes.19Note that Equations (5.15) and (5.16) describe the regression lines obtained from the measuredresults and Equation (5.17) represent the individual measured data points.220210200g 190 —0 GS^0^Q0 Q)bo74a° 180 ^'51ft 170 ^til16001500_0 g0 V 011445° t0 (O 00 . •of%r';',^00•(a 0...• ellesor90 90-140^IIIIIIII1fJI0IIIIIIIIII 1 I I ^I111111iiiiiIIIIIIIIIII1111^!Him1^1 III^1^II10^20^30^40^50^60^70oe0o0^Measured^ Best-fit71Time (min)Figure 5.6. Gravimetric plot of bath weight against time for the experimental conditionsof : 200 grams of Cu2S, 2 limin of 22% 02 and 78% Ar, at 1200 °C.5.1.3.^Summary of the Oxidation Rate Results5.1.3.1.^Oxidation Rates The raw data for each run consisted of: a complete description of the experimentalconditions and parameters, the gas absorber sampling time, the SO2 absorbed and thefinal off-gas volumetric flow rate. Tables containing the gas analysis data for all of theexperimental runs are provided in Appendix B. The experimental program included the0.10.010.0011000 1000072investigation of the influence of several variables-gas flow rate, gas composition, reactiontemperature and bath mixing- on the oxidation rate of the molten Cu2S bath. A summaryof the measured reaction rates is presented in Appendix B as well.5.1.3.1.1.^Effect of Admitted Gas Flow RateThe rate of oxygen reaction, NO2, was found to be a power function of the total reactiongas volumetric flow rate, as shown in Figure 5.7.Gas Flow Rate (ml/min)Figure 5.7. Oxygen reaction rate (No2) as a function of reaction gas volumetric flow rate,Q, (total admitted flow rate); for the experimental conditions of 200-gram samples, 1200°C, average pressure of 1.08 atm and 23 % 02;^ regression curve (=3.59x10-5Q°•79); D primary measured; 0 secondary measured.0.0011000 100000.1From a least squares fit, the average exponent on the admitted gas flow rate, obtainedfrom the results of both stages, is 0.79, which is similar to other systems in which gasphase mass transfer control prevails [48]. Interestingly the oxygen reaction rate is thesame in the primary and secondary stages.Figure 5.8 shows a log-log plot of rate of sulphur removal from the bath, Ns, againstadmitted gas flow rate. As already observed, the rate is faster in the secondary stage.Gas Flow Rate (ml/min)Figure 5.8. Sulphur removal rate (Ns) as a function of reaction gas volumetric flow rate;for the experimental conditions of 200 gram samples, 1200 °C, average pressure of 1.08atm and 23 % 02; primary regression curve (= 4.15x105Q0.72); 0 primary-measured; ^ secondary regression curve (= 2.39x10-5V.85); <> secondarymeasured.7374Exponents on the gas flow rate were calculated to be 0.72 and 0.85 for the primary andsecondary stages respectively, close to that obtained from the oxygen reaction rate, Figure5.7.10,-^0 ---^-....^--vi -----(5c)^-v) 0--to •.-., 0a) 0t4.° 0.1a.)r:40.01 ^1000• _-0- Ri • A0Gas Flow Rate (ml/min)10000Figure 5.9. Sulphur removal rate (Ns) as a function of reaction gas volumetric flow rate;for the experimental conditions of 200-gram samples, 1200 °C, average pressure of 1.08atm and 23 % 02; primary regression curve (= 1.2x10-3Q0.63); 0 primaryobtained from gas analysis; • primary obtained from gravimetric measurement,^secondary regression curve (= 0.71x1 0-3Q0.87); o secondary obtained from gas analysis;• secondary obtained from gravimetric measurement.In Figure 5.9, the combined behaviour of the oxygen reaction rate and the rate of sulphurremoval (overall reaction rate) with respect to gas flow rate are shown based on gas75analysis and gravimetric measurement. The exponents on the gas flow rate were found tobe 0.63 and 0.87 for the primary and secondary stages respectively.5.1 .3.1 .2.^Effect of Gas CompositionFigure 5.10 shows the influence of oxygen partial pressure in the admitted reaction gas onthe overall oxygen reaction rate. As expected in the case of gas phase mass transfercontrol, the reaction rate depends linearly on the partial pressure of oxygen in the reactiongas. From Figure 5.10, the slope of the rate of oxygen reacted with respect to the oxygenpressure is ko,AIRT.0.070.060.05VA 0.040.03r:(1)R) 0.0200.010.00^I^'^I^'^I^I^I^J^I^ '^I0.0^0.2^0.4^0.6^0.8Oxygen Partial Pressure (atm)Figure 5.10. Oxygen reaction rate as a function of oxygen partial pressure for theexperimental conditions of: 1200 °C and 2000 ml/min,  calculated fromregression line (=0.096P02); • primary measured; 0 secondary measured.1.00.000.0" I " ' ' I ' I^i0.4^0.6^0.8 1.00.20.080.07:-0-2 0.06E0.05rlei)7,4 0.04oEa)124 0.036-'v=Piv) 0.020.010',o,076Similarly, the rate of sulphur removal is plotted against the partial pressure of oxygen inFigure 5.11. It can be readily seen that the rate of sulphur removal is directly proportionalto the partial pressure of oxygen. This is an indication that the sulphur removal rate isdriven by the rate of oxygen transfer in the gas phase.Oxygen Partial Pressure (atm)Figure 5.11. Sulphur removal rate as a function of oxygen pressure for the experimentalconditions of: 1200 °C and 2000 ml/min, ^ primary calculated from regressionline (=0.052P02); 0 primary measured; ^ primary calculated from regression line(=0.07P02); 0 secondary measured.It can be seen that the slope of the sulphur removal rate with respect to the oxygenpressure is k02/aRT, where a is a stoichiometric factor. From linear regression, theslope of the secondary rate of sulphur removal was found to be approximately 1.3 timesthat in the primary stage.2.5•^2.0 ^^1.5 ^-to•,S 1.011czt0r:4 0.5 —77•9•0.0 "^ I^ "0.0^0.2^0.4^0.6^0.8^1.0Oxygen Partial Pressure (atm)Figure 5.12. Rate of weight loss (W) as a function of oxygen pressure for theexperimental conditions of: 1200 °C and 2000 ml/min, ^ primary calculated fromregression line (=1.08P02); 0 primary obtained from gas analysis measurements; •primary obtained from gravimetric measurements;^ primary calculated fromregression line (=2.29P02); Oseconda,ry obtained from gas analysis measurements; •secondary obtained from gravimetric measurements.78The rate of bath weight loss is plotted against the oxygen partial pressure in Figure 5.12.As expected, a linear relationship was found for both the primary and secondary stages.Due to its relatively short time duration, the primary stage yielded measurements withgreater experimental error than the secondary stage.5.1.3.1.3.^Effect of TemperatureProcesses in which the overall reaction kinetics are limited by the rate of chemicalreaction are strongly dependent on temperature [118]. When studying the effect oftemperature on reaction rates, it is customary to express them in the form of the Arrheniusrelationship. The logarithm of the oxygen reaction rate is plotted vs. 1/T in Figure 5.13,from which it is clear that the oxygen reaction rate is effectively independent oftemperature. This was also confirmed from the statistical F test, at the 5% level ofsignificance, which resulted in Fcalculated = 2.4x10-2 and Fsignificance = 0.88, thusindicating that the overall relationship is not significant at the 95% confidence limit[119]20.The dependence of the sulphur removal rate on the inverse of temperature is shown inFigure 5.14. In the primary stage, a small activation energy of approximately 37±17kJ/mole is calculated; this value is low compared to the activation energy range of 50 to500 kJ/mole more typical of chemical reaction control [118]. For the secondary sulphurremoval rate, however, as shown in Figure 5.14, the relationship appears to be statisticallyinsignificant which means that the secondary removal rate of sulphur is effectivelyindependent of temperature.20The significance of expressing the measured oxygen reaction rate in terms of this relationshipwas checked by the F test, where Fcalculated is obtained from the ratio of the sum of the squaresof the deviations accounted for by the regression to the error variance; and Fsi nificance isobtained from the probability distribution of variance ratio F at an acceptable level ofconfidence. For the applicability of the relationship to the measured data to be valid, thecalculated value of F must be greater than the value obtained from the probability distributioncurve.------0^8^0g o""1""1""1""II"III"'I''"1""I'"'790.016.10.106.2^6.3^6.4^6.5^6.6^6.7^6.8^6.9^7.0(1 / T) x 104 (1C1)Figure 5.13. Oxygen reaction rate as a function of temperature for the experimentalconditions of: 2000 ml/min of 20-23% 02 and average pressure of 1.08 atm,^primary calculated from regression curve (= 0.018exp -(1.9 kJ/mole)/0.0083144T, Feal =2.4x10-2 and F5%sig = 0.88); 0 primary measured; 0 secondary measured.8 a00.1800.001 'I""1""1""1""II"III"'1""I'"'6.1^6.2^6.3^6.4^6.5^6.6^6.7^6.8^6.9^7.0/ 7') x104 (°K-9Figure 5.14. Sulphur removal rate as a function of temperature for the experimentalconditions of: 2000 ml/min of 20-23% 02 and average pressure of 1.08 atm,^primary calculated from regression curve (= 0.2exp -(37 kJ/mole)/0.0083144T, Feal = 5and F5%sig = 0.06); ^ secondary calculated from regression curve(= 0.018 exp -(1.9 kJ/mole)/0.0083144T, Fcal = 1.8x10-2 and F5%sig = 0.89)0 primary measured; 0secondary measured.205200195175VIr2c1 170165160155815.1 .3.1 .4.^Effect of Bath MixingAlthough all of the experimental results indicated that the rate limiting step of theoxidation reaction is gas phase mass transfer, the liquid phase mass transfer resistancecontribution, if any, needed to be investigated. In order to examine the transportconditions of the liquid phase, a test during which the bath was mixed by injectingapproximately 77 ml/min of Ar was conducted. Figure 5.15 shows a comparison of thebath mixing run to a normal run. The bath weight change is seen to be almost identical;thus the liquid phase mass transfer resistance has a negligible contribution to the overallreaction rate. Interestingly the disruption of the bath surface by the gas bubbles appearsto have no significant effect on interfacial area.0^10^20^30^40^50^60^70^80Time (min)Figure 5.15. Bath weight as a function of time for the experimental conditions of: 1200C, average pressure of 1.08 atm and 22 % 02; 0 no mixing, 2006 ml/min; • mixing with77 ml/min of Ar, 2032 ml/min825.1.3.2.^Reaction Transition Characteristics The measured transition characteristics (sulphur and oxygen contents in the bath anddegree of desulphurization in wt% at the transition) and the molar ratios of reactedoxygen to sulphur removed in the primary and secondary stages are presented in Table5.1.Table 5.1. Reaction transition characteristics and the molar ratios of reacted oxygen toremoved sulphur.Run Q: %02 T [%s]*0]*d; aP ccs(ml/min) (°C) (%)4 922 26 1200 18.09 17.025 922 26 1200 16.95 20.376 922 26 1200 17.48 16.267 922 26 1200 16.63 1.62 19.76 1.5 0.978 1010 24 1200 16.75 1.67 18.97 1.5 0.939 1480 22 1200 17.27 1.04 16.57 1.3 0.9410 2078 20 1200 16.92 1.43 18.23 1.4 1.0811 1987 22 1200 16.90 1.74 18.01 1.5 0.9412 1579 24 1200 16.77 20.0013 1521 20 1200 17.75 1.73 13.04 1.7 0.9914 1532 21 1200 15.92 2.55 20.83 1.6 0.9715 2006 22 1200 17.56 1.54 14.35 1.8 0.9116 2510 23 1200 17.13 1.20 17.25 1.5 0.9217 1755 22 1200 16.52 1.37 20.60 1.4 0.9518 2234 23 1200 17.02 1.41 17.64 1.6 0.9119 3015 23 1200 18.35 0.40 11.00 1.3 1.0021 4055 22 1200 16.71 1.62 19.25 1.6 0.8622 2000 27 1200 17.06 1.40 17.47 1.6 0.9523 2000 35 1200 16.37 1.46 21.37 1.5 0.9124 2000 46 1200 16.46 0.82 21.50 1.2 1.0025 2000 64 1200 16.38 1.03 21.72 1.3 1.0027 2000 23 1250 17.17 1.25 16.97 1.4 0.9528 2000 23 1300 16.76 1.13 19.45 1.3 1.0129 1994 21 1275 16.21 1.36 22.43 1.4 0.9230 2000 22 1300 16.38 1.05 21.72 1.3 0.9931 2000 22 1250 17.00 1.16 18.06 1.4 0.9833 3493 27 1200 16.65 1.24 19.97 1.3 1.0634 2000 78 1200 16.08 1.30 23.19 1.3 1.0136 2032 22 1200 17.32 1.50 15.81 1.5 1.0037 2000 21 1200 17.60 1.50 14.18 1.8 0.9141 3516 24 1200 17.04 1.50 17.46 1.4 0.9883Thus the reaction transition characteristics seem to be independent of the reactionconditions. The average weight percents of sulphur and oxygen in the bath at transitionfrom the primary to the secondary stage were found to be 16.94±0.10% and 1.37±0.07%respectively. These values compare favorably with the equilibrium values of 17.7 and1.47% for sulphur and oxygen dissolved in Cu2S respectively, at 1200 °C and 1 atm [19].This is strong evidence that the melt, during the primary stage, is a single copper sulphidephase i.e. Cu2S becoming saturated with dissolved oxygen.The ratios of the rate of reacted oxygen to the rate of evolved sulphur dioxide, during theprimary, a", and secondary stages, as, are another important lead to the understanding ofthe reaction mechanism. The average measured ratio of the rate of reacted oxygen to therate of evolved sulphur dioxide was found to be 1.46±0.03 and 0.96±0.052, for theprimary and secondary stages respectively.In studying these results, the reaction mechanism is suggested to be as follows:Primary Stage: • Since aP > 1,(see Table 5.1) part of the reacted oxygen is dissolved in the meltand the rest is reacted with sulphur to form SO2.• Because aP > 1 while the melt consists of a single phase, the primaryoxidation reaction is likely to be:[S1+ 1.5(02) = (S02)-F[02-]^ (5.18)Secondary Stage: • Because a' <1, during the secondary stage, the amount of sulphur removedfrom the bath is greater than that of its reacted oxygen equivalent21. This inturn suggests that the sulphur removal, during the secondary stage, takes place21Assuming that the sulphur removed from the bath is only in the form of SO2.84at the melt surface, according to Reaction (5.18), and in the melt according toReaction (5.19).[S2-]+ 2[02-1+ 6{Cul = (S02)+ 6((Cu))^ (5.19)If ocs =1, then the rate of oxygen reaction is equal to the rate of sulphurremoval according to Reaction(5.20). This also implies that blister copperdoes not contain any sulphur or oxygen.[S2-]+ 2[Cu] + (02) = (S02)+ 2((Cu))^ (5.20)• It is apparent that the making of copper is accompanied by the simultaneousdissolution of sulphur and oxygen. Since the sulphide melt is ionic and thecopper phase is metallic, the process of oxygen and sulphur dissolution incopper must be accompanied by electron transfer by further copper making,according to Reactions (5.21-5.22). This is supported by the fact that theequilibrium metal phase composition is approximately 98.89% Cu, 0.95% Sand 0.16% 0.[S2- ]+ 2[Cul = [S]((co) + 2((Cu))^(5.21)[02--] + 2[Cul = [0]((C)) + 2((Cu)) (5.22)In summary, during the primary stage, the melt is partially desulphurized and becomesoxygen saturated according to Reaction (5.18). During the secondary stage, the makingof the metal phase takes place, according to Reactions (5.18), (5.19), (5.21) and (5.22).855.2. Micro Examination Of The Melt SamplesIn studying heterogeneous kinetics, it is important that a physical examination of thereaction system is carried out, however possible. The reaction rate results indicated that,during the primary stage, there is only one reaction site (at the melt surface according toReaction (5.18)), and during the secondary stage, there are two reaction sites (at the meltsurface according to Reaction (5.18) and in the melt according to Reactions (5.19), (5.21)and (5.22)). This implies that, during the primary stage, the melt consists only of thesulphide phase, and, during the secondary stage, the melt consists of the sulphide phase,the metal phase and the rising gas bubbles. In order to further investigate the validity ofthese results, melt samples were extracted at specific reaction conditions. These sampleswere sectioned, polished, examined via optical microscopy (magnification range of 80-400X), and photomicrographed. In order to correlate these observations to the reactionrate results, this examination included the investigation of the existence of copperdroplets, the traces of gas bubbles and phase constitutions.As mentioned above (see also Section 2.2), the melt initially consists of the single Cu2Sphase. As the reaction proceeds, during the primary stage, the melt is partiallydesulphurized and oxygen saturated until its composition reaches approximately (80.83%Cu, 17.7% S and 1.47% 0, at 1200°C and 1 atm [19].Figures 5.16 and 5.1722 show photomicrographs of polished bath samples at 7 min ofreaction time from the primary stage. Although metal (pink) precipitates are evidentaround the solidifying grains of the sulphide (green) and there are traces of gas bubbles(black), the morphology of the metal phase and the average size of the gas bubblessuggest that they result from the cooling process during the quenching of the sample. Asdiscussed in Section 4.3.2, quartz tubes were used in the sampling of the melt. Hence, it22A11 of the photomicrographs are for the experimental conditions of: 200 grams of Cu2S, at1200 °C and 1 atm, 2 I/min of 22% 02 and 78% Ar.86is impossible to completely prevent post reaction changes, during quenching23. In theabsence of vertical sections of the Cu-S-0 ternary system, it is not possible to account forthe gas bubbles. However, it is just as useful to consider the binary Cu-S system;ignoring the effect of oxygen, for compositions slightly below the exact stoichiometry ofCu2S, the melt cooled under equilibrium conditions, will decompose to Cu25 (7) andliquid copper, at the liquidus temperature of 1105 °C, and to Cu2S (7) and solid copper, atthe eutectic temperature of 1067 °C.iOOtnFigure 5.16. Photomicrograph of polished section of frozen melt sample, at 7 min ofreaction time (during the primary stage); green is sulphide; pink is metallic; black is gas.23Compared to other ceramics, quartz has a relatively high resistance to thermal shock. Itsrelatively low thermal conductivity, however, retards the quenching process.25g mFigure 5.17. Photomicrograph of polished section of frozen melt sample, at 7 min ofreaction time (during the primary stage).25[imFigure 5.18. Photomicrograph of polished section of frozen melt sample, at 15 min ofreaction time (1 min after the copper droplets and SO2 gas bubbles start to form in themelt).8788The reaction rate results indicated that the transition time for 2 1/min of 22% 02 and 78%Ar, at 1200 °C, is approximately 14 min (refer to Figure 5.6). This means that before 14min, there should be no copper and gas bubble formation in the melt. At 14 min thesecondary stage commences, for which Reactions (5.19), (5.21) and (5.22) proceed in themelt, thereby forming copper droplets and SO2 gas bubbles, as can be seen in Figures5.18-5.23.It is evident that the metal phase, at 15 min of elapsed reaction time, is in the form ofdroplets, of 11±14tm average diameter, as shown in Figure 5.18, rather than precipitatesaround the sulphide grain boundaries, as shown in Figure 5.17. This is an indication thatthe copper formed after 15 min is the result of the oxidation reaction, rather than theresult of the slow quenching process.wri -Nu-74_10011 mFigure 5.19. Photomicrograph of polished section of frozen melt sample, at 25 min ofreaction time.2511 mFigure 5.20. Photomicrograph of polished section of frozen melt sample, at 25 min ofreaction time.14 lit - Ifigh4„410111P 4*,Oh'10011 mFigure 5.21. Photomicrograph of polished section of frozen melt sample, at 35 min ofreaction time.891001.1m1^ IFigure 5.22. Photomicrograph of polished section of frozen melt sample, at 40 min ofreaction time.10011m1^IFigure 5.23. Photomicrograph of polished section of frozen melt sample, at 50 min ofreaction time.9091After 25 min of reaction time, the quantity of copper and gas bubbles increases, as shownin Figure 5.19. The average copper droplet diameter, of 26±31.tm appears to be larger asthe reaction time elapses. The other important point to note is that there are two types ofcopper formation: the large copper droplets, and small random copper droplets that areassociated with the gas bubbles. As suggested by Reactions (5.19), (5.21) and (5.22), thelatter are expected, since they share common reaction sites. The shape of the smallcopper droplets appear to be random, unlike the large copper droplets, which arespherical. Because the melt is spontaneously mixed as a result of surface-tension drivenflows and gas evolution, evidently the small copper droplets agglomerate to form thelarger droplets, as shown in Figures (5.19) and (5.20). From surface observations duringthe secondary stage, small numbers of gas bubbles were observed to rise randomly fromthe melt on a continuous basis and large quantities, in a boiling fashion, on a less frequentbasis. Due to the fluid dynamics of the system, the size and quantity of gas bubbles withrespect to time cannot be traced in a similar way to the copper droplets. However, whenthe sample was extracted just before an incident of intense boiling, in a coincidentalmanner, a large quantity of gas was found to be contained by the melt, as shown in Figure5.21.Due to the density difference between the metal phase (7.9 g/cm3) and the sulphide phase(5.5 g/cm3) [113], the copper droplets coalesce and settle to the bottom of the crucible.The gas bubbles coalesce and rise to the melt surface continuously as well. However, asmentioned previously, occasionally intense boiling was observed to occur at the meltsurface. During the secondary stage, the appearance of the sulphide phase remainedunchanged until its complete depletion, as shown in Figures 5.18-5.23. Once the sulphidephase was completely consumed, at the end of the secondary stage, the composition of themelt approaches that of the metal phase, viz. approximately 98% Cu, 0.95% S and 0.16%0, at 1200 °C and 1 atm [19]. As shown in Figures 5.24 and 5.25, towards the end of'p,; " NO%I%,- Jeffi C c.cc* t^°r-YA`o, • •^• d*31•.N't 114;11e:!°^t• ,ivoilWert-^.4.-^•c $41T:-'•.:dAt" v •c--0 • .4^.446;K • al:,t:*^! ?:;ts WAt• co r."1"111• 7^• A °. I. C.4)11',2411 V^d Pt• 't^•'lit,'._JE^b•Z11,14,e 7 • 4,11.N4t.._-7 • a •^• ,61e^44‘4°Sre'°"IA^QA.• • 79gtANKA:k. • 3rtt^_Vc.^':;■•°^.41 •92secondary stage, the melt becomes predominately metallic (brown) containing theremaining sulphide phase (blue). Referring to the Cu-S binary, ignoring the effect ofoxygen, at 1200 °C, for compositions of less than 1.4% S, the melt consists of the liquidcopper phase such as that shown in Figure 5.26. In Figure 5.26, a polished section of99.99% pure copper is shown to illustrate the apparent microstructural differencesbetween pure copper and the copper produced at the end of the secondary stage. Forcompositions of greater than 1.4% S, the melt consists of the liquid copper and liquidcopper sulphide phases. Rapid quenching of the 1.4% S sample should result in thesuppression of any sulphide phase segregation, which takes place in the case ofequilibrium cooling. However, due to the use of quartz tubes in the sampling of the melt,the rate of cooling of the sample, during quenching, appears to have been relatively slow.As shown in Figure 5.24, the dendritic precipitate of the Cu2S phase (green/blue), in thematrix of the metal phase (light brown), is the result of equilibrium cooling.6 .:1251.1mFigure 5.24. Photomicrograph of polished section of frozen melt sample, at 60 minreaction time (final reaction time is 70 min).93This indicates that the sample was quenched at a relatively low rate of cooling. Thus it isapparent that the melt consists only of the metal phase, at the sampling time. At the finalreaction time, the composition of the melt is very close to blister copper, of 98.5-99.5%Cu. The compositional effect on the phase constitutions of the metal phase is shown inFigures 5.25-5.26.2511 mFigure 5.25. Photomicrograph of polished section of frozen melt sample, at 60 minreaction time (final reaction time is 70 min).25[tmFigure 5.26. Photomicrograph of polished section of a 99.99% Cu standard sample.94955.3. Observations of the Bath SurfaceSurface observations were useful, not only to investigate the Marangoni effect and gasbubbles eruptions, but also to gather more qualitative data about the reaction kinetics, andto aid in the termination of the reaction because surface-tension driven flows wereobserved to cease at the end of the secondary stage.When the copper sulphide bath completely melted under argon, a thin liquid opaque film,easily broken by movement, was observed to cover the stagnant melt surface evenly, withthe exception of some random shiny areas which appeared to be the sulphide melt, asshown in Figure 5.27.Figure 5.27. Bath surface, at 1200°C with top-lancing at 2 1/min of Ar; the blacktriangular area at the top is the tip of the lance appearing out of focus; the right and leftbottom segments of a ring are the inner rim of the crucible; the area within is the opaquefilm covering most of the melt except some random more shiny areas (the sulphide meltsurface). Note the absence of surface movement, due to the gas impingement on thesurface.Although its chemical composition is unknown, the opaque film appeared to beimmiscible with respect to the sulphide melt. Due to the apparent difference between its96emissivity and the emissivity of the copper sulphide melt, this film was used as anadditional indicator of the surface motion. Upon admittance of the reaction gas, thesurface of the sulphide melt (shiny area) was immediately uncovered in the area beneaththe lance, as shown in Figure 5.28, after which the film moved outwardly from the areabeneath the lance towards the crucible wall, as shown in Figure 5.29. As the reactionproceeded, the outline of the exposed and covered sulphide surface was observed toincrease in diameter, in a vibrating fashion, as shown in Figure 5.29. The spontaneousmotion of the melt surface from the center of the crucible to the wall was observed toincrease, as shown in Figures 5.28-5.32.Figure 5.28. Photograph of the bath surface at the same time of the admittance of thereaction gas; the sulphide melt surface is starting to be exposed in the area beneath thelance (slightly above the center of the crucible); for the experimental conditions of 200grams of Cu2S, at 1200 °C, and under the top-lancing of 2 11min of 80% 02 and 20% Ar.Figure 5.29. Photograph of the surface of the bath at approximately 60 s, after theinitiation of the reaction. The film is pushed away from the center of the crucible to thewall, as seen by the further exposure of the sulphide shiny surface.Figure 5.30. Photograph of the surface at approximately 3.5 min; spontaneous wavymotion of the melt surface is fully developed and the film is entirely pushed towards thecrucible wall, as seen by the full exposure of the sulphide surface. The difference in thecolor of the surface is due to its wavy motion.9798Once the spontaneous surface motion was fully developed, it continued throughout theduration of the reaction time, as shown in Figures 5.30-5.32. The speed at which thesurface moved, due to the effect of surface tension, was observed to be apparently highenough to cause the stirring of the whole bath. Due to the motion of the melt surface, thethermocouple sheath, when immersed in the melt, was observed to continuously vibrateabout its vertical axis, in a pendulum-like motion, creating a clinking noise. Because theeruption of gas bubbles from the melt surface occurred only during the secondary stage,the high degree of turbulence is attributed mainly to surface tension-driven flows. Instudying the effects of reaction gas flow rate, reaction gas composition, and reactiontemperature, the general behaviour of the melt surface was observed to be the same.However, the speed at which the surface moved was observed to be faster with higherreaction flow rate and composition, as shown in Figures 5.31 and 5.32. On the otherhand, the effect of temperature was not detectable.Figure 5.31. Photograph of the surface of the bath at approximately 5 min; the oxidationrate results indicated that the transition time for these experimental conditions was 5 min.Note that the film is entirely pushed away from the center of the crucible to the wall.Figure 5.32. Photograph of the surface of the melt at approximately 21 min; spontaneouswavy motion of the melt surface continues throughout the duration of the reaction time.The oxidation rate results indicated that the final reaction time for these experimentalconditions was 22 min.Figure 5.33. Photograph of the surface of the melt at approximately 20 min for theexperimental conditions of 200 grams of Cu2S, at 1200 °C, and under the top-lancing of21/min of 22% 02 and 78% Ar. The transition and the final reaction times for theseexperimental conditions are 14 and 70 min respectively.99100At the end of the oxidation reaction, the surface movement was observed to completelycease, and the film was observed to be pushed to the crucible wall (no surface spreadingis occurring which may be the result of surface tension effects), as shown in Figure 5.34.Figure 5.34. Photograph of the surface of the melt at approximately 10 min after the endof reaction. At the end of the secondary stage, the surface movement completely ceases.Note the difference in emissivity between the copper surface (shiny reflecting the lancenozzle at slightly above the center of the melt) and the emissivity of the film, at thecrucible wall.During the secondary stage, bubbles were observed to erupt from the melt surface in acontinuous fashion. Occasional intense boiling was observed to occur at the melt surfaceas shown in Figure 5.35. The intensity and the frequency of boiling were observed toincrease with increasing reaction gas flow rate and oxygen content, as shown in Figures5.35 and 5.36.101Figure 5.35. Photograph of the surface of the melt at approximately 14.5 min, under thetop-lancing of 2 1/min of 80% 02 and 20% Ar. Intense boiling at the melt surface, causedby the eruption of SO2 gas bubbles, as a result of the melt reactions.Figure 5.36. Photograph of the surface of the melt at approximately 14.5 min, under thetop-lancing of 2 1/min of 80% 02 and 20% Ar. Intense boiling at the melt surface, causedby the eruption of SO2 gas bubbles, as a result of the melt reactions.102The frequent intense boiling indicates that as the number of gas bubbles increases, thebubbles coalesce and rise to the melt surface, causing the interruption of surface-tensiondriven flow. As discussed in Chapter 6, the effect of this phenomenon, on the transportconditions, was relatively strong. The break-up of the melt surface causes an increase inthe interfacial area, while the increased surface turbulence causes the enhancement of thetransport conditions.6. Gas Phase Mass Transfer6.1. Mathematical Analysis for Mass-Transfer CoefficientTo obtain mass-transfer coefficients from the experimental data, the followingmathematical analysis was undertaken.^6.1.1.^Material BalanceAs the reaction takes place, sulphur is removed from the bath in the form of SO2, therebychanging the bath sulphur content. The sulphur molar balance on the bath yields thefollowing.[rate of S input = 0] – [rate of S output]–[rate of S consumption = 0] + [rate of S generation = 0]= rate of S accumulationdN^–flso2. A = -^dt^6.1.2.^Flux Equation:As shown in Figures 5.10, 5.11 and 5.12, the response of the reaction rates to oxygencontent in the gas is characteristic of gas phase mass transfer control. The results shownin Figure 5.16 also reveal that the liquid phase mass transfer resistance is negligible.Thus the rate of reaction can be described by the oxygen molar flux, as follows:k02^b^nino2 =—RT [Po, – r-o21^6.1.3.^Equilibrium At Phase Boundaries:If the chemical reaction rate is fast, the interfacial partial pressure of oxygen must be thatof the equilibrium oxygen pressure, dictated by Reaction (5.18). There are no availableequilibrium data for this reaction; however, since the intercepts of the regression lines in103(6.1)(6.2)(6.3)104Figures 5.10, 5.11 and 5.12 are approximately zero, the partial pressure of oxygen mustbe negligible in magnitude, compared to the bulk partial pressure of oxygen.6.1.4.^Stoichiometry:The molar ratio of reacted oxygen to evolved sulphur dioxide, a , is calculated asfollows:(6.4)During the primary stage, the sulphur removal takes place only as a result of Reaction(5.18). Since aP is very close to 1.5, thusoP^2k02nso, = ---L PLif;3 RT 2(6.5)During the secondary stage, the experimental results indicate that the ratio of the 02molar flux to the secondary SO2 molar flux, is approximately 0.96. The correspondingequation for the molar flux of SO2 in the secondary stage is, therefore, described asfollows:it' :02 = 0.196 R1(07, p,02 ^2 6.1.5.^Solution:In order to develop an expression for the sulphur content of the bath, the first orderdifferential equation ( Equation (6.2)) is solved by substituting for the respective fluxequations, and integrating between the following limits:t = 0, N=s A Ps.t = t* , Ns = N;For the primary stage the resulting integration is:(6.6)Ns 2 kodN s =^A 13(b) dtIs4^3 RT^02 koNs = N's^APob .t3 RTSimilarly, the secondary stage expression is derived as follows:1 ko APG: [t —Ns = N*s ^0.96 RTwhere t* is the transition time. Thus with gas phase mass transfer control, the bathsulphur content varies linearly with time. In general terms,Ns=a+bt^ (6.10)When compared to Figure 5.4 which exhibits a linear relationship between the measuredmoles of sulphur in the bath and time, clearly the oxidation of molten Cu2S is controlledby gas phase mass transfer of oxygen to the melt surface.6.2. Experimental Gas Phase Mass-Transfer CoefficientThe gas phase mass-transfer coefficient is calculated from the slope of the plot of sulphurmolar content in the bath vs. time, as follows:aP RT ANgAP0b2 At—as RT AN ;);k-2^AP,'2 AtFigure 6.1 shows the effect of admitted gas flow rate on the gas phase mass-transfercoefficient.(6.11)(6.12)105(6.7)(6.8)(6.9)11000 10000100106Gas Flow Rate (ml/min)Figure 6.1. The gas phase mass-transfer coefficient as a function of gas flow rate for theexperimental conditions of 200 grams of Cu2S at 1200 °C, 1.084 atm, 3 mm insidediameter lance, 44 mm diameter of the interfacial reaction area and 10 mm distance fromthe nozzle to the reaction surface; 0 primary measured; A secondary measured,^primary calculated from regression curve (= 0.03 Q0.73),^  secondary calculatedfrom regression curve (= 0.01 Q0.88).Although the measured oxygen fluxes for the two stages appear to be identical, theircorresponding gas phase mass-transfer coefficients seem to be slightly different. It can beseen that this is similar behaviour to the reaction rates, which exhibited greater exponentsfor the secondary stage (see Section 5.1.3). The exponents indicate that the relationshipbetween the gas phase mass-transfer coefficient and the gas flow rate, is stronger in the107secondary stage than in the primary stage likely because during the former, gas bubbleserupt from the melt surface (see Figure 5.35 and 5.36), thereby increasing the gas/liquidinterfacial area. Due to the difficulty of estimating the changes in the reaction interfacialarea, it is not possible to account for this effect. Surface observations of the meltindicated that the frequency of gas bubbling and the interfacial turbulence were enhancedby an increase in the gas flow rate and the oxygen concentration in the gas.In Figure 6.2, the gas phase mass-transfer coefficient is plotted against the partial pressureof oxygen, from which it appears that there is a slight dependence on the oxygen content.0^P^I I 11111 11110.0^0.2^0.4^0.6 0.8^1.0Oxygen Partial Pressure (atm)Figure 6.2. The gas phase mass-transfer coefficient vs. the partial pressure of oxygen forthe experimental conditions of 200 grams of Cu25, average system pressure of 1.09 atm,3 mm inside diameter lance, 44 mm diameter of the interfacial reaction area and 10 mmdistance from the nozzle to the reaction surface; • primary measured; 0 secondarymeasured, ^ regression line( Equation (5.15)),^ average.108Under normal conditions, the gas phase mass-transfer coefficient is effectivelyindependent of the oxygen concentration in the gas phase; however, owing to theMarangoni effect, the gas phase mass transfer coefficient slightly increases withincreasing oxygen content in the reaction gas.k02 = (8.2 ±0.2) + (1.5 ±0.3)13, (6.13)The average gas phase mass-transfer coefficient, from the primary and secondary stages,is plotted against the inverse of temperature in Figure 6.3, from which it is clear that thegas phase mass-transfer coefficient has a slight positive dependence on temperature.6.2^6.3^6.4^6.5^6.6^6.7^6.8^6.9^7.0(1 / T) x104 (°K-')Figure 6.3. The gas phase mass-transfer coefficient vs. the inverse of temperature for theexperimental conditions of: 2000 ml/min of 20-23% 02 and average pressure of 1.08; 0^mean of the measured primary and secondary, ^ regression curve (Equation(6.14)).109From least squares, the Arrhenius relationship, described by Equation (6.14), yielded anactivation energy of 14±12 kJ/mole, which is a characteristic of mass transfer.[  14 ±12kJ/ mole  iiln^= ln(3. 3 ± O. 9)O. 0083144 kJ/°K. mole] T (6.14)6.3. Gas Phase Mass -Transfer CorrelationThe gas phase mass-transfer coefficient is empirically24 related to the transport conditionsof the system via the Sherwood number, Sh. As discussed in Section 2.3.2.1.2, forlaminar top-blown systems, Sh is related to the Schmidt number, Sc, and the Reynoldsnumber, Re, as follows [48125:Sh = m(rd dr RenR' Ses'^ (6.15)Figure 6.4 shows a logarithmic plot of Sh against Re based on the results of this study.For constant Sc and (rsId), the exponents of Re are 0.73 and 0.88 for the primary stageand secondary stage respectively, as described by Equations (6.16) and (6.17), whichindicate that the empirical relationships of the Sh-Re are identical to the empiricalrelationships of the k02 — Q.ShP = 0.03Re°^(6.16)Shs = 0.02 Ream^(6.17)24The transport properties of the gas are considered to be those of the reaction gas mixture, forwhich the calculation procedures are presented in Appendix C.25The Sherwood number, Sh, is the ratio of the total mass transfer to the mass transfer bymolecular diffusion; the Schmidt number, Sc, is the ratio of the momentum diffusivity to themolecular diffusivity and the Reynolds number, Re, is the ratio of the inertia force of a fluid tothe viscous force.100.111010^1 00^1000ReFigure 6.4. The Sherwood number as a function of the Reynolds number for the topblown conditions of 200 grams of Cu2S at 1200 °C, 1.084 atm, 3 mm inside diameterlance, 44 mm diameter of the interfacial reaction area and 10 mm distance from thenozzle to the reaction surface and Sc = 0.57; 0 primary measured; A secondary measured;^ primary calculated from regression curve (— 0.03 Re0-73); ^ secondarycalculated from regression curve (= 0.02 Re0.88).From boundary-layer theory [120], and in most mass transfer correlations, the exponentof the Schmidt number, nsc, is of the order of 1/5-1/3. Since the Schmidt number is afunction of the physical properties of the fluid involved in mass transfer, at roomtemperature, the range of Sc is high enough (0.05-5) to allow the determination of itsexponent more accurately from measurements. However, in high temperature systems,the Schmidt number is only of the order of 0.57-0.9 [48] (in the case of 02-Ar/N2 gas111mixtures at 1200-1300 °C, it is 0.57-0.61). In their evaluation of the Sherwood number athigh temperature, Taniguchi et al. [48] assumed that n ^0.5. Similarly, their resultsgave the best fit when the exponent of (rid), ns, was -1 for room temperature systemsand -1.5 for the high temperature systems. Figure 6.5 shows a plot of Sh(r.141.5Sc-°-5against Re from the experimental results obtained in this study.100101 10^100^1000ReFigure 6.5. Sh(rs 141)1.5 SC° 5 plotted against the Reynolds number for top-blownconditions of 02-Ar/N2 onto molten Cu2S bath, at 1200-1300°C, 1.084 atm, 0.56 Sc0.63, 7 rid _C.11, 2-3 mm inside diameter lance, 44 mm diameter of the interfacialreaction area and 10 nun distance from the nozzle to the reaction surface; 0 primarymeasured; • secondary measured; ^ calculated from regression curve (Sh = (0.64±0.07)(d/rs) 1 -5 sc0.6Re(0.79±0.06)); ^ secondary calculated from regression curve (Sh=(m= 0.74) ((d/rs)1-5Sc"Re036, from decarburization of liquid iron, after Taniguchi et al.[48])).112The resulting correlation is as follows:Sh = (0.64 ± 0.07)(r, 1 d) 5 Sc° 5 Re(°79±°°6)^(6.18)By comparison Taniguchi et al. [48] found the exponent of Re to be 0.66 for roomtemperature systems and 0.76 obtained from the rate of decarburization of liquid iron, (ofgreater than 0.2 wt% carbon). The results presented in Figure 6.5 clearly agree with theexperimental measurements of Taniguchi et al. for Re = 13-1500, r s/d = 1.6-5 and Hid =0.4-30, for which (Sh = m (r s/d)-1-5Sc0.5Re°3 6). In the system under study these valuesare Re = 33-147, r s/d = 11-7.3 and Hid = 3.33-5, and the value for m that gives the bestagreement is 0.74. As shown in Figure 2.7 (a), m appears to vary slightly with the type ofsystem. For the water-N2-NH3 system, it is 0.27 and it is 0.53 for the toluene-N2 system.Although the exponents of the correlation obtained from the decarburization of liquidiron are closer to those of the current system, m appears to differ greatly. For thedecarburization of liquid iron, m = 0.27 ± 0.05, while it was found to be 0.74 ± 0.01 forthe current system.For the purpose of analyzing the oxidation kinetics of molten Cu2S, Equation (6.18) wasused in the prediction of the gas phase mass-transfer coefficient. Since all of theapparently relevant parameters are in agreement with those obtained from systems of gasmass transfer control [45-48], this correlation was accepted in the prediction of the gasphase mass-transfer coefficient.Table 6.1 shows the effect of lance diameter on the gas phase mass-transfer coefficient.The lance nozzle-diameter appears to be an important parameter in the gas phase mass-transfer. Where a 33% decrease in the diameter results in an approximately 20% increasein the gas phase mass-transfer coefficient, the correlation provides a better predictionwhen nsc is -1.5 than when it is -1, as shown in Table 6.1.113Table 6.1. The effect of the lance diameter on the gas phase mass transfer coefficient.These runs were conducted at 1200 °C and average oxygen content of 21%.Q/a- d rdd Hidk02m= 0.64,n, = -1.5and nRe = 0.79_k02m = 0. 25, ns = –1and nRe = 0.78Icf)2measuredkns•-.2measured(ml/min) (mm) (cm/s) (cm/s) (cm/s) (cm/s)1480 3 7 3 6.57 6.49 5.95 6.451520 2 11 5 7.57 23.12 7.42 7.406.4. Sensitivity Analysis of the Effect of the Interfacial Area on Gas PhaseMass-Transfer CoefficientIn top-blown systems, the reaction interfacial area is a function of the flow characteristicsof the jet and the diameter of the crucible. For highly turbulent systems, the reactioninterfacial area may be considered to be the area of the paraboloid, outlined by the jetimpingement area, as follows:A = —Tc [D. + 4Hc13/2 —116(6.19)In laminar flow systems in a certain crucible diameter range, the reaction interfacial areais assumed to be the cross-sectional area of the crucible. The experimental measurementsand the numerical computations of Taniguchi et al. [47-48] revealed that for laminar flowconditions, the reaction interfacial area can be assumed to be the cross-sectional area ofthe crucible, as shown in Figure 6.6. From a numerical solution of the gas phase flowequations, and from visualizing the flow pattern of the gas phase by a tracer (TiC14) [47],it was deduced that this assumption was acceptable.114Figure 6.6. Computed streamline patterns and concentration profiles at u = 200 ink(laminar flow) (after Taniguchi et al. [48]); (a) streamline patterns iv, (b) concentrationprofiles Y.From Equation (6.18), the variation in the predicted gas phase mass-transfer coefficient isrelated to the variation in the reaction interfacial area as follows:Sko, = --3 (0.64)7t3/4D^crISC Re° 794^02 -ArSA(6.20)The variation in the experimentally determined gas phase mass-transfer coefficient isrelated to the variation in the interfacial reaction area as follows:= N 02 RT SA (6.21)Pbo2 A2Due to the rising gas bubbles frequently erupting from the melt during the secondarystage, the reaction interfacial area may vary to an uncertain extent. In order to investigatethe effect of this possible variation on the gas phase mass-transfer coefficient, a100101115sensitivity analysis was carried out using Equations (6.20) and (6.21). The results areshown in Figure 6.7 and indicate that a 20% variation in the area, results in approximately15% and up to 21% uncertainties in the estimation of the measured and predicted gasphase mass-transfer coefficients respectively.1000^ 10000Gas Flow Rate (ml/min)Figure 6.7. The sensitivity of the gas phase mass-transfer coefficient to the reactioninterfacial area, for the experimental conditions of 200 grams of Cu2S at 1200 °C, 3 mminside diameter lance, 44 mm diameter of the interfacial reaction area and 10 mm distanceform the nozzle to the reaction surface; 0 mean, determined from measurement (A =15.14 cm2); .. uncertainty bars (OA = 3.028 cm2 equivalent to 20 % variation), ^predicted (A = 15.14 cm2);^ predicted uncertainty limits (SA = 3.028 cm2equivalent to 20 % variation).1166.5. Sensitivity Analysis of the Effect of Temperature on Gas Phase Mass-Transfer CoefficientIn the calculation of transport coefficients, such as the gas phase mass-transfer coefficientor the heat-transfer coefficient, the temperature at which the thermophysical propertiesare computed, is often considered to be the mean film temperature. In systems of highgas velocity and a very steep thermal gradient between the reaction region and the gasdelivery regions (such as the lance nozzle), it is feasible to consider the temperature of thegas to be at a mean temperature between the hot zone and the gas. However, in thesystem under investigation, the lance extends over a distance of approximately 400 mm inwhich the thermal gradient inside the reaction tube26 is relatively gradual. This allows thegas to reach a temperature close to that of the hot zone. Due to the exothermic heat ofreaction, depending on the gas flow rate and oxygen content in the gas, the temperaturesof the bath and the gas were observed to increase by up to 60 °C, relative to the start ofreaction. Due to the expected small effect of temperature on the reaction rate, and to theshort life of the alumina thermocouple sheaths in the vicinity of the reaction, it was notpossible to obtain a continuous temperature measurement for some of the runs. However,reasonably sufficient data, on the thermal behaviour of the reaction system, have beengathered27 to reveal that the temperature rise is proportional to the increase in the oxygencontent and gas flow rate of the reaction gas, as given by Equations (6.22)-(6.24) andshown in Figures 6.8 and 6.9.26Refer to Section 4.1.1 (Figure 4.1).27Melt and gas temperature measurements are provided in Appendix D.70 1176050400E 3000 2010-1 0 I I II""1""1""1""I""1""1""0^^500 1000 1500 2000 2500 3000 3500 4000Gas Flow Rate (ml/min)Figure 6.8. The temperature change, due to the heat of reaction, as a function of thereaction gas flow rate; LI melt temperature change (the tip of the thermocouple sheath waslocated at the center of the melt), ^ regression line (Equation (6.22)); 0 gastemperature change (the tip of the thermocouple sheath was located at the same height asthat of the lance nozzle28); ^ regression line (Equation (6.23)).28Due to the poor heat transfer conditions between the thermocouple and the gas, the gastemperature measurements are expected to be lower than the actual temperature (for moreaccurate measurements to be conducted, a suction thermocouple should be used).706050a)czi 40a)EE-4g 30CI)c‘C9U2010118'^I^''0^20^40^60^80^100Oxygen Content (%)Figure 6.9. The temperature change, due to the heat of reaction, as a function of thereaction gas oxygen content; o gas temperature change (the tip of thermocouple sheath^was located at the same height as that of the lance^nozzle), ^ regression line(Equation (6.24)).^ATmelt = —8 +0.018Q:^(6.22)= —15+0.014Q: (6.23)t‘Tgas = —7.3 + 0. 8002)^ (6.24)119Using the estimated correlations for AT, a temperature sensitivity analysis was carriedout to investigate the effect of temperature uncertainty on the calculated values of the gasphase mass-transfer coefficients. The mean temperature of the melt and the gas wascalculated from the estimated correlations, and it was used to compute the gas phasemass-transfer coefficients, as shown in Figures 5.11-5.12. The gas phase mass-transfer-temperature sensitivity analysis indicated that a ±50°C uncertainty in temperature canresult in approximately ±4% uncertainty in the calculation of the gas phase mass-transfercoefficients, which is within the tolerance limit, as shown in Figures 6.10 and 6.11.According to the gas phase mass-transfer corelation, the gas phase mass-transfercoefficient is expected to be slightly dependent on the gas composition mainly throughthe Schmidt number. However, at high temperatures, the contribution of Sc is smallcompared to Re. When increasing the oxygen content in the reaction gas, the temperaturechange and surface-tension driven flows are higher. From the above discussion, itappears that the effect of temperature on the gas phase mass transfer coefficient isnegligible. The experimental results suggest that the dependence of the gas phase mass-transfer coefficient on the oxygen content in the gas is slightly higher than predicted bythe correlation, as shown in Figure 6.11. It seems that there is only a small dependence,for compositions of approximately 50% 02 and higher. Since the temperature effect isinsignificant, this dependence is attributed to the effect of surface-tension driven flowsand the eruption of gas bubbles. Surface observations indicated that the spontaneousmotion is increased with increasing oxygen content of the reaction gas (see Section 5.3). 1001011201000^ 10000Gas Flow Rate (ml/min)Figure 6.10. The sensitivity of the gas phase mass-transfer coefficient to temperature, forthe experimental conditions of 200 grams of Cu2S at 1200 °C, 20-26% 02, 3 mm insidediameter lance, 44 mm diameter of the interfacial reaction area and 10 mm distance fromthe nozzle to the reaction surface; 0 primary measured (T = 1200 °C); CI secondarymeasured (T = 1200 °C); ^ predicted (T = 1200 °C); 111 primary measured (mean);0 secondary measured (mean);^ predicted (mean).0^8ao90a^I .^1^I^i .^.^1^I12112100.0^0.2^0.4^0.6^0.8 1.0^1.2Oxygen Partial Pressure (atm)Figure 6.11. The effect of reaction gas composition on the gas phase mass-transfercoefficient, for the experimental conditions of 200 grams of Cu2S, average systempressure of 1.09 atm, 3 mm inside diameter lance, 44 mm diameter of the interfacialreaction area and 10 mm distance from the nozzle to the reaction surface; 0 primarymeasured (T = 1200 °C); 0 secondary measured (T = 1200 °C),  predicted (T =1200 °C); ^ predicted (mean temperature form Equation (6.26)).7. Mathematical Modeling and Theoretical PredictionsHaving presented and discussed the experimental findings of this work, it is conducive toexamine these findings theoretically via mathematical modeling of the oxidation reaction.A theoretical description of the oxidation of molten Cu2S bath is essential for furtherunderstanding of this process and for the support and validation of the experimentalmeasurements. In this chapter, a detailed formulation of the mathematical model ispresented. Using the experimental results, validation and sensitivity analyses of thismodel are also examined. To provide a theoretical description of the oxidation of moltencopper sulphide, the oxidation path and the oxidation rates of molten copper sulphidebaths are discussed in terms of the model predictions.7.1. Mathematical Model7.1.1.^Assumptions1. The melt is vigorously mixed and consists of a homogeneous solution ofS2-, 02- and Cu+ ions (sulphide phase), during the primary stage. Theformation of the copper-rich phase (metal phase) takes place during thesecondary stage, as a product of the melt reactions only29. The metalphase remains in equilibrium with the sulphide phase until the completedepletion of the sulphide phase at the end of the secondary stage (end ofthe oxidation reaction).2. The oxidation reaction is controlled by the gas phase mass transfer ofoxygen to the melt surface.12229Note that Reaction (5.18) is referred to as the surface reaction and Reactions (5.19), (5.21) and(5.22) are referred to as the melt reactions.1233. The melt at the end of the primary stage is assumed to be the equilibriumcomposition of the sulphide phase saturated with oxygen at the giventemperature and pressure.4. The melt at the end of the secondary stage is assumed to be coppercontaining equilibrium amounts of oxygen and sulphur.5. Equilibrium conditions are assumed to prevail at the gas-liquid interface.The surface reaction apparently has a large negative Gibbs free energywith a large equilibrium constant. Thus under gas phase mass transfercontrol, the interfacial partial pressure of oxygen is very small comparedwith the bulk partial pressure of oxygen. Due to the absence ofthermodynamic data for the activities of [S2-] and [021 in the melt, it isnot possible to calculate the equilibrium partial pressure of oxygendictated by the surface reaction. The molar flux of oxygen can bedescribed as follow:ko r bno2 =--IPRT 26. The transport properties of the gas are assumed to be those of the reactiongas mixture i.e. Ar+02.7. The transition period from the primary stage to the secondary stage is verysmall and was assumed to be negligible.8. Due to the effect of bubbles rising from the melt during the secondarystage, the reaction interfacial area is increased causing the overall rate toincrease by a minor amount. This was apparent from the gas phase mass-transfer coefficient determined in the secondary stage which was found to124be slightly higher than that of the primary stage". However, since themeasured gas phase mass-transfer coefficient was found to increase onlyby about 4% in the secondary stage, it is assumed that the gas phase mass-transfer coefficient remains constant throughout the reaction duration.9. The reaction interfacial area is assumed to be the cross-sectional area ofthe crucible.10. Isothermal conditions prevail throughout the duration of the reaction time.In spite of the fact that the temperature of the system was observed toincrease at the beginning of the reaction time and to remain constantthroughout the duration of the experiments (as a result of the exothermicreaction), this assumption was adopted because of the small effect that thetemperature has on the overall reaction rate.11. The gas phase is assumed to be at the same temperature as the liquidphase. Due to the low value of the specific heat capacity of gases and tothe nature of this reaction system31, it is safe to assume that the heattransfer to the reacting gas, in the hot zone, is instantaneous.7.1.2.^Reaction Mechanism and Flux Equations7.1.2.1.^Primary StageThe formation of copper does not take place until the sulphide phase is saturated withoxygen. This is due to the relatively high oxygen solubility in molten copper sulphide, ofapproximately 1.47 wt% at 1200°C and 1 atm pressure. During the primary stage, thesulphide melt is partially desulphurized and oxygen saturated until its composition hasreached approximately 80.83 wt% Cu, 17.7 wt% S and 1.47 wt% 0 at 1200 °C and 1 atm30For details about the calculation of the measured gas phase mass transfer coefficient, refer toSection 5.1.5.1.31The basis for this assumption has been discussed in detail in Section 5.1.5.2.[s 21VDistanceAGas PhasebPO2\Concentration>^Liquid Phase13`02SO2 02/125[19]. This process is controlled by the gas phase mass transfer of oxygen to the meltsurface, where it reacts with sulphide melt, in the absence of any other reactions as shownin Figure (7.1), according to Reaction (5.18).Due to the Marangoni effect at the bath surface, the sulphur and oxygen concentrations inthe melt are assumed to be constant throughout the liquid phase i.e. the liquid phase masstransfer resistance is virtually non-existent. Therefore, as mentioned above, theexpression describing the reaction rate is Equation (7.1).44 mmFigure 7.1. Schematic diagram of the primary stage reaction system; (1) alumina lance;(2) , vigorously mixed molten sulphide as the result of surface tension driven flows(Marangoni effect); (3) schematic diagram of the reaction gas flow pattern; (4) aluminacrucible.7.1.2.2.^Secondary Stage Immediately upon the melt composition reaching the transition composition of 80.83 wt%Cu, 17.7 wt% S and 1.47 wt% 0 at 1200 °C and 1 atm, the secondary stage commences.126During the secondary stage, the copper formation reactions (Reactions (5.19), (5.21) and(5.22)) take place beneath the surface throughout the melt. Simultaneously with theformation of copper, oxygen and sulphur dissolve in the metal, according to Reactions(5.21) and (5.22), to yield about 98.89% Cu, 0.95% S and 0.16% 0. Reaction (5.19) istriggered when the oxygen concentration at a nucleating site has slightly exceeded theequilibrium concentration of the sulphide phase. Once this reaction initiates, theformation of copper droplets and SO2 gas bubbles provides more reaction sites to keepthe sulphide phase in equilibrium with the metal and gas phases. Because the reactionsare electrochemical, ionic mobility and electron transport tremendously retard the liquidphase mass transfer resistance (on the microscopic scale). Growth and coalescence of thegas bubbles are followed by their rise to the melt surface. These phenomena provide anenhancement of the stirring action caused by the surface-tension driven flow. Due to thesurface eruptions caused by the rising gas bubbles, the gas-liquid interfacial reaction areaincreases and enhances the overall reaction rate by up to 6%. The frequency of rising gasbubbles has been observed to increase with increasing flow rate oxygen partial pressure inthe reaction gas. Spontaneous mixing of the melt is further enhanced by the coalescenceand settlement of the copper droplets. However, because the copper droplets and the gasbubbles exist only during the secondary stage, the melt is believed to be mainly mixed bythe effect of surface-tension driven flow phenomena.The metal phase at the bottom of the bath grows at the expense of the sulphide phase untilthe secondary stage is ended, at which time all of the sulphide phase is consumed. Thesecondary stage reaction system is shown schematically in Figures 7.2 and 7.3, fromwhich, it is apparent that the reaction conditions of the secondary stage are slightlydifferent from those of the primary stage. However, the rate limiting step remains themass transfer of oxygen in the gas phase above the bath.Suiphide PhaseMetal Phase127DistanceGas Phase02ConcentrationSuiphide PhaseIMetal Phase(1)  44mm  Figure 7.2. Schematic diagram of the secondary stage reaction system; (1) alumina lance;(2) alumina crucible; (3) schematic diagram of the reaction gas flow pattern; (4) sulphidephase; (5) metal phase; 0 sulphur dioxide gas bubbles; copper droplets.Figure 7.3. Secondary stage; (1) surface reaction interface for Reaction (5.18); (2)reacting sulphide phase (according to Reactions (5.19), (5.21) and (5.22)); (3) sulphide-metal interface (showing the net metal phase formation rates); Suiphide phase; 0sulphur dioxide gas bubbles; copper droplets.1287.1.3.^Equilibrium at Phase boundariesIt is safe to suggest that equilibrium conditions prevail at the melt surface i.e. at the gas-liquid interface. Therefore the interfacial partial pressure of oxygen is assumed to be theequilibrium partial pressure of oxygen, as dictated by the thermodynamics of Reaction(5.18) and at least one order of magnitude smaller than the bulk partial pressure ofoxygen. Then Equation (7.1) is transformed as follows:.^k02no2 ..==^2 PoRT 2Due to the spontaneous mixing of the melt, there is no concentration gradient in either ofthe liquid phases. The oxygen- and sulphur-saturated metal phase is in equilibrium withboth the gas and sulphide phases.Since the amount of copper formed, due to Reactions (5.19), (5.21) and (5.22), issaturated with oxygen and sulphur, the moles of oxygen and sulphur dissolved in coppercan be related to the moles of copper formed via their equilibrium relationships, asfollows:N0 =m 0[{100 —[% Si^100 1c. i[[% CuN =^N cu M cal00s M s[[100 —{100 700]cut[% s]cu 1]—[% O]cdN cisM 0,100(7.2)(7.3)(7.4)129By differentiating Equations (7.3) and (7.4) with respect to time and noting that[% s] and [%0], are constants, relationships between the rate of copper formationand the rates of oxygen and sulphur dissolution in copper are obtained,N cu A 1 0,100No =as follows:(7.5)m^100u0[[100—[%s]ctmc.100=Let^On,100 (7.6)m0[[100—[%Si cu][ [%picaN = Ocu NCu^ (7.7)N cu M100Ns = (7.8)100A^ -]_[%0]cu]s[[100—[%O]cui[ [%s]cw^1Ain, 100let^So, = (7.9)100Ais^6] [%0L[[100^[%^c 1[u^[%S]cuN s = ScuNcu^ (7.10)The oxygen and sulphur concentrations in the metal phase are calculated from theequilibrium measurements of J. Schmiedl [19], as given by the following equations32:32Note that Ps02 (in Equations (7.11)) is in mmHg.130[%oicu = 10 (-1.4-(1278/T))^y.p 2SO2[%cu] =10(2+(2""[ % S] ^100 —[% Cu] --[%O]cuwhere the SO2 partial pressure, in the melt, is equal to the system pressure, Ps, and theaverage sulphide phase static head on an SO2 gas bubble located at a mid-distance fromthe surface, Pst, as follows:PS02 = P Pst^ (7.14)As seen in Figures 5.18-5.23, the sulphide phase contains the freshly formed copperdroplets throughout the secondary stage. Thus, as the metal phase is formed within thesulphide phase, the sulphide melt density is assumed to be the average value for thesulphide phase and metal phase densities, as given by the following equation:(Hicu2s)(Pcu,s+Pcu Pt = 2^2(7.15)7.1.4.^Stoichiometry7.1.4.1.^Primary Stage Reaction (5.18) is the surface reaction that takes place when a copper sulphide melt,having a stoichiometric Cu2S composition33, is brought in contact with oxygen gas. Meltsurface observations and micro-examination of quenched bath samples, obtained duringthe primary stage, indicated very clearly that there is no bubble formation during thisperiod. The stoichiometric relationship between the molar flux of oxygen and theprimary molar flux of sulphur dioxide can be obtained from Reaction (5.18) as given by33The Cu-S binary, at 1200 °C and 1 atm, indicates that liquid copper sulphide can range incomposition from 20 to 22.19 wt % sulphur (refer to Section 2.2).Equation (7.16). By substituting for n 02 from Equation (7.2) in Equation (7.16), anPexpression for nso, is obtained as follows:0 P^1nS02 = —12—no23P^2 k02nso23 RT 2131(7.16)(7.17)7.1.4.2.^Secondary Stage During the secondary stage, Reaction (5.18) is no longer the only reaction that isresponsible for the sulphur removal from the sulphide phase. Reactions (5.19) and (5.21)take place in the melt, contributing further to sulphur ion removal. By maintaining thesulphide phase composition below the transition composition, the melt reactions sustainthe chemical potential for reaction (5.18). Due to the dissolution of oxygen and sulphurin copper, the proportions of Reactions (5.18) and (5.19) are not known. Therefore it isnot possible to formulate theoretically a direct stoichiometry between the no2 and ns02.The overall reaction for the copper formation can be represented by Reaction (7.18).Therefore the rate of copper ion consumption from the sulphide phase can be directlyrelated to the rate of copper generation, as given by Equation (7.19).{Cul+ = ((Cu))0N cu* = N(7.18)(7.19)From the stoichiometry of Reactions (5.21) and (5.22), the relationships between the ratesof oxygen and sulphur ions consumption from the sulphide phase are related to the ratesof oxygen and sulphur dissolution in the metal phase, as follows:o2- = o^ (7.20)N s2- = Ns^ (7.21)1327.1.5.^Material BalanceFor simplicity, this mathematical model will be constructed to describe each of the twostages in a distinct manner. For the primary stage, a material balance on the sulphidephase yields the formulation of a model that predicts the sulphur and oxygen contents ofthe bath. For the secondary stage, a material balance on the sulphide phase shall beperformed to develop expressions for the rates of copper, oxygen and sulphurconsumption from the sulphide phase. The description of the metal phase generation canbe obtained by performing a material balance on the metal phase. By combining theresults of the material balances on the sulphide phase and the metal phase an overalldescription of the bath, during the secondary stage, can be formulated.7.1.5.1.^Primary Stage 7.1.5.1.1.^Sulphur BalanceAssuming that there is no concentration gradient of sulphur in the bath, a molar balancefor sulphur in the bath yields the following:[rate of S2- input = O]-[rate of S2- output]+[rate of S2- generation = OF [rate of S2- consumption = 01=^(7.22)rate of S2- accumulationSince the sulphur removed from the bath is in the form of SO2, the rate of S2- outputfrom the bath is directly related to the SO2 molar flux as follows:. Prate of S2- output = ns02. A^ (7.23)Substituting for Equation (7.23) in Equation (7.22);. P^dN ,2_— n SO2 . A = '^dt(7.24)1337.1.5.1.2.^Oxygen BalanceSimilarly for oxygen;[rate of 02- input ] - [rate of 02- output ] +[rate of 02- generation = OF [rate of 02- consumption = 0] =^(7.25)rate of 02- accumulationOxygen is dissolved in the bath as 02- and is removed from the bath in the form of S02•Therefore the rate of 02 input is the product of the molar flux of 02 and the cross-sectional area of the crucible, as given by Equation (7.26). The rate of 02 output can beexpressed in terms of the molar flux of SO2, as given by Equation (7.27).rate of 02- input = 2 I; 02. A^ (7.26). Prate of 02- output = 2nso2• A (7.27)Substituting Equations (7.26) and (7.27) in Equation (7.25), the following expression isobtained:.^. 13^dN 2_2 no2. A —2 ns,92. A = ^°dt (7.28)7.1.5.2.^Secondary Stage 7.1.5.2.1.^Sulphide Phase7.1.5.2.1.1. Sulphur Ion Balance As shown in Figure 7.3, some of the sulphur reacts to form SO2, according to Reactions(5.18), (5.19), and some dissolves in the metal phase according to Reaction (5.21). Amaterial balance for the sulphur yields the following:dN 2_. s^A^. r.,— fl s02 • A — IV s2 = S^dt(7.32)134[rate of S2- input = O]- [rate of S2- output] +[rate of S2- generation = 0]— [rate of S2- consumption ] =rate of S2- accumulationThe rate of sulphur output is related to the secondary SO2 molar flux as follows:rate of S2- output = ns02. A(7.29)(7.30)rate of S2- consumption = Ns2-^ (7.31)Substituting Equations (7.30) and (7.31) in Equation (7.29), we obtain the followingexpression:7.1.5.2.1.2. Oxygen Ion Balance The oxygen input to the sulphide phase is a known quantity, given by the transportconditions of the reaction system. As outlined in Figure 7.3, some of the oxygen reactswith the sulphur at the melt surface, according to Reaction (5.18); some of it is removedfrom the bath in the form of SO2, according to Reaction (5.19), and some of it dissolvesin the metal phase, according to Reaction (5.21). Hence, the oxygen balance yields thefollowing:[rate of 02- input ] - [rate of 02- output] +[rate of 02- generation = 0] — [ rate of 02- consumption i =^(7.33)rate of 02- accumulationThe rate of oxygen input is related to the 02 molar flux, as follows:rate of 02- input = 2 n 02 • A^ (7.34)The rate of oxygen output is related to the secondary SO2 molar flux, as follows:135„ srate of 02- output = 2 ns02. A^ (7.35)The rate of oxygen consumption is described as follows:rate of 02- consumption = No2-^ (7.36)Substituting Equations (7.34), (7.35) and (7.36) into Equation (7.33), an expression forthe oxygen balance is obtained, as follows:^. ^,s^0^dN ,^2,(n02- ^nso,)• A — N o2 =^dt7.1.5.2.1.3. Copper Ion BalanceSimilarly for copper;[rate of Cu+ input = 0 ]-[rate of Cu+ output = 0] +[rate of Cu+ generation = 0 ] — [rate of Cu+ consumption ] =rate of Cu+ accumulation(7.37)(7.38)rate of Cu+ consumption = N cw.^ (7.39).^dNCI4+— N Cu+ =dt(7.40)7.1.5.2.2.^Metal Phase7.1.5.2.2.1. Sulphur Balance As shown in Figure 7.3, the sulphur dissolves in the metal phase in the form of neutralsulphur atoms, according to Reaction (5.21). A material balance for the sulphur yieldsthe following:[rate of S input = 0 ] - [rate of S output = 0]+[rate of S dissolution]— [rate of S consumption = 0 ] =^(7.41)rate of S accumulation136rate of S dissolution = Nsk s . dNsdt7.1 .5.2.2.2. Oxygen BalanceSimilarly for oxygen;[rate of 0 input = 0 ]- [rate of 0 output = 0]+[rate of 0 dissolution] — [rate of 0 consumption = 0 ] =rate of 0 accumulationrate of 0 dissolution = Nok 0 . dNodt7.1.5.2.2.3. Copper Balance The copper material balance is described as follows:[rate of Cu input = 0 ] - [rate of Cu output = 0]+[rate of Cu generation ]— [rate of Cu consumption = 0 ] =rate of Cu accumulation(7.42)(7.43)(7.44)(7.45)(7.46)(7.47)rate of Cu generation = Ncu^ (7.48).^dNNcu = c^udt(7.49)1377.1.6.^Mathematical Solution7.1.6.1.^Primary Stage For 0 t t , where t* is the transition time, expressions for the moles of sulphur andoxygen in the bath are developed by integrating Equations (7.24) and (7.28) subject to thefollowing initial condition:at t =0, N52 = N's„ and NO2 = 0Arca-PdN 2 = nS02 • Ai dts0(7.50)PBecause nso2 # f (Ns2_ ), the expression for the moles of sulphur in the bath is given bythe following equation:N = —(n sP +s2-^2 • _ _Equation (7.28) is integrated subject to the initial condition, as follows:No2-.dN 02_ = 2(no2—nso2)• AS dt(7.51)(7.52)PBecause nso, # f(NO2) and no, # f(NO2_), the expression for the moles of oxygen inthe bath is given by the following equation:0 PN0 = 2(no2— nso2}4 • t- (7.53)PSubstituting for nso2 and no2 in Equations (7.51) and (7.53), the final formulations forthe sulphur and oxygen in the bath are developed.02 k^ bN2 = Ns12_ —(—3 RT2 A P°2 *t(7.54)138NO2_ =(3-RkC)7,2 A Pob2)• t^ (7 .55)The primary rates of sulphur removal and oxygen dissolution, as functions of the oxygenpartial pressure, are derived as follows:dNsp,_ = (2 ko2A)pbdt^3 RT ) 02dNop,_ =12 ko,A)pbdt^3 RT ) 02(7.56)(7.57)Substituting for the gas phase mass-transfer coefficient expression (Equation (6.18)) inEquations (7.56) and (7.57), the primary rates of sulphur removal and oxygen dissolutioncan be expressed in terms of the reaction gas flow rate, as follows:,^0.79 ]dNsP2_ = ( 2 P/12 AI  O. 64 Do, _Ar ( d r \I 1-1, g  [M.- P g  j^Q0.79dt^3 RT^d^rs^p gD02_Ar 4g0.79]dNop2_ =r 2 Pict A O. 64 Do2 _Ar " dl  .11  11g ^(7cd-, P g)^Q0.79dt^3 RT )^d^rs^p gD02-Ar 411.g(7.58)(7.59)At the transition time, the sulphide bath composition is dictated by the equilibriumconditions of the system, as given by the following equations:N* u* m cul00N s* 2_ =^1 100 ^1—[% GI] cu2s]m s[[100 —[% 0] cu2s .1[{% S]cu2s(7.60)No* 2- =^[% clmo[[100— [% S ] cu2s100 ^11_{% s]1cu2s cu2sN* M 100ca(7.65)*^Nis2_ N*s2_t =r2k02^b)3 RT A P°2 )139(7.61)The oxygen and sulphur concentrations in the sulphide phase at the transition time arecalculated from the equilibrium measurements of J. Schmiedl [19], as given by thefollowing equations:[%°1CU2S = 10(-2+0013/T)) pY2 (7.62)so2[%Cutu2s = 79.605 + 0.26 x 10-12 T4^ (7.63)[%Slcu2s = 100 —[% Cu] [% O]Cu2s (7.64)Substituting for the conditions at the transition time in Equation (7.54) or Equation(7.55), an expression for the transition reaction time can be developed as given by thefollowing equation:During the primary stage, the moles of copper ions in the bath are constant; therefore themoles of copper ions (N.+ ) at transition are the initial moles of copper in the bath.Using Equations (7.54) and (7.55), an expression for the bath weight as a function oftime, during the primary stage, can be expressed as follows:WP (t) = w(o) +[M0 — Ms .1[—=-2 A 13,;',]• t3 RT^2(7.66)140An expression for the rate of weight change in the primary stage as a function of theoxygen pressure can be derived by differentiating Equation (7.66) with respect to time, asfollows:0 P^2 ko AW =[111° —Ms] 3 R2 T PCb'2The rate of weight change can be expressed in terms of the reaction gas flow rate asfollows:° P 2^0.641002-ArPob2 ^ incrpg )0.79 0.79W {Mo Ms]^QRT P gD02-Ar 41147.1.6.2.^Secondary Stage Unlike the primary stage, the secondary stage does not offer a direct stoichiometricosrelationship between the nso2 and n02. The following equations are to be solvedsimultaneously for the unknown reaction rates and the final reaction time34.Sulphide phase sulphur balance: dN 2_n SO2 • A — N S2 = S^dtSulphide phase oxygen balance: 2(no2—nso2)• A _NO2 = dA 1 n2dtSulphide phase copper balance: dN— N0 =  Cu dt(7.67)(7.68)(7.32)(7.37)(7.40)34The unknown reaction rates and the final reaction time are constants in a determined system ofequations that can be solved simultaneously.141Sulphur solubility in the metal phase: = S^(7.69)Oxygen solubility in the metal phase: NO2- = Ocu Ncu.^ (7.70)Experimental results indicated that all reaction rates are constants, i.e. they are neitherfunctions of composition nor functions of time. Integrating Equations (7.32), (7.37) and(7.40) for the following initial conditions:at^,^Ns, = Pts2_NO2 = N*o2_ and N+ = N*cu^cu+N2 ^0 sdN s,_ = +s02. A+ N s2-jf dtN s2-^ t.(7.71)*N2 = NS , —S s^ r^*1nso2. A+ N S2-)• Lt^t (7.72)No2- o s ]tf dNo,_ 42 (n o2— so2)• A— N 02-^dt (7.73)N.02-^ t*0 sNO2 = N*^+ [2(n02— nso2)A— No2- • [t — (7.74)NdN^= —^cu+^dtcu+ (7.75)N*Ncu+ = N., — jvc.. [ t (7.76)At the end of the reaction time, the sulphide phase is completely depleted, i.e.142at t=tfN =0'^s2-^'No 2 = 0 and NCu+ = 0-Substituting for these final conditions in Equations (7.72), (7.74) and (7.76), permits thesolution for the unknown reaction rates35, as follows:. S^0^,N;2_ — (nS02 ' A + Ns2- )•[tf — ] = 0 (7.77).^. sNo*2_ +[2(no, —nso, )44 — k02- ] • [tf —t*1= 0^ (7.78)N*— N° cu+[tf — ]= 0cu+(7.79)Solving for {tf — t*] form Equation (7.79) and substituting in Equations (7.77) and (7.78),the following is obtained:o s,,^,, ro^N,_ NCn so, . I-1 ± IV S2" = - *Ncu+0^0 s *^02(no2— n SO2 )A — No2- = N o2_ AT cu+N*Cu+(7.80)(7.81)Using Equation (7.69) to solve for Nce and substituting in Equations (7.70), (7.80) and(7.81), the following is obtained:0.^ Or. Ns2-No2 .  ,Ii (7.82) SCu35Note that the unknowns are the constants in a system of equations, in which all of thedependent variables are known.143*. s^.^NN s2-nso2. A+ N s 2_ (7.83)s2^=^*NCu+SCu.^. s^.^N*^N s2-2(no2— ns02)A—2N02 = (7.84)N* +Scu^cuSubstituting for Equation (7.82) in Equation (7.84), and solving for iVs2-, as follows:o s.N S2 =N* +Scu nso2. ACu (7.85)[N* 2 — N* S ]s -^cu+^cuo^o s2N*^S,-, (no —nso),4cu+^,,,,^2^2iVs2 (7.86)=[6°CUNC*U+ _N]]Equating Equations (7.85) and (7.86), the following expression is obtained:0 sn so2 =^1 (7.87)no21 1+[ [OcuN c* u+ — N 0* 2_]]r2[AT;2_ —Nc*.+ScuiSubstituting for no2 in Equation (7.87), an expression for the molar flux of SO2 isobtained as given by the following equation:° s^ 1^k02^pb(7.88)=n so,1+r[OcuArc*a+ — N*02_ 1 RT^°2r21 N*s2_ — Nc*u„ Scu ]Expressions for the consumption rates of sulphur, oxygen and copper ions from thesulphide phase are derived as follows:144Ar°^2/Vc% Scu A^k, pbiv s2 = r r^ -21.21.N;2_ — NC* u*Scul+[OcuNc* u+ — No* ,]]RT2NC* u*OcuA^ko2NO2- = r r^ pb[21.N; — A Icsu*Scu]±[OcuNc* u, No* ]] RT '92^2N* + A^k 02 pbCu ^02N cu+ = r r1.2[N*s2- NL,Scu [()CuN*cu*^2_]] RTThe expression for the final reaction time is derived as follows:RT^tf =[3N` 2_ — N* — N* 2_ + Nu* ^— 2S Icu L^0 b^S^S^0^cu^2Ak 2 • Po2By integrating Equations (7.43), (7.46) and (7.49) for the following initial condition,expressions for the metal phase growth can be derived:at t =0, Ns =0,No = 0 and Nc. = 0(7.89)(7.90)(7.91)(7.92)NsdNs = Ns dtNs= Ns•[t —No^tidNo= No dt0No= No•[t—t1Arc„^tdku = NCu dt0(7.93)(7.94)(7.95)(7.96)(7.97)145Ncu = Ncu•Lt —^ (7.98)By adding the respective equations of the sulphide and metal phases, and utilizing therelationships of Equations (7.19), (7.20) and (7.21), expressions for the secondary molesof copper, sulphur and oxygen in the bath can be derived as follows:Os=N2 —nso,• A -[t — (7.99)0^SAIL = N*o2_ 2(no2—nso,),4•{t — t*I^ (7.100)Ns = N*cu^cu+ (7.101)Substituting for no„ nso2 and t* in Equations (7.99)-(7.101), the expressions for thesecondary moles of sulphur and oxygen (total) are given by the following equations:2[Ns*,_ — Nc*u„Scu]= N*,_ + r^s^1.2N;2_ — N 0* 2_ + Nc* u,.[Ocu— 2Sc.a]]2[N*,52_ — Nc* u+Scui ATL N*02_^r[2N*,_ — No*,_ + Arc*a+ [On, — 2Scu]]3 rN,,^N*, (7.102)[21-^s^s(k0,APcb,2)RT_^_1^3[Arls, — N*s22k, AP b,t (7.103)-2RTBy differentiating Equations (7.102) and (7.103) with respect to time, expressions for therate of sulphur and oxygen removal from the bath in the secondary stage as a functions ofthe oxygen partial pressure are derived as follows:^dN^F^2[N*s2_ — Arc* u,Scu]^k02A)pb^dt^[2N*s2_ — N*02_ + Nc* u,[0cu —2Scu]] RT )(7.104)^d„,^2[N*s2_ — Nc*.„,] ^lir  21CO2A)pt:t^{2N*s2_ — N2 + c*u+[Ocu —2S0u]]^RT^02(7.105)146Expressions for the secondary rates of sulphur and oxygen removal in terms of thereaction gas flow rate are derived as follows:0.79O. 64700,_„^[tgdr,dN's'^2[N;2 — I c*u.Sculdt^[PN*52_ —^+ NTcd-P g (7.106)dN0...,[0cu-2ScujQ0. 9RT^p gD02 _Ar— N cs a+ scu]41. gdt1][2 Ns,_ — N os 2_ + N cs u+{Ocu —2s]](7.107)gdrs g)x [1.287CD02_ArP73,^(1Cd3pRT^p gD02_Ar^411g^]Q0.79An expression for the bath weight as a function of time in the secondary stage is derivedas follows:_^c*Ws (t) = W(e) — [2M0 —{2M0—Mstr^2[N*e — Nu+Scu*^* .0^(7.108)X1.2 N s2_ No2_ Nc*u+ [Ocu 2Scujj[-3 [Ni — Ns^11(02AP(b)2 t]2 s2-^s2- RTThe rate of weight change as a function of the oxygen partial pressure in the secondarystage is derived by differentiating Equation (7.108) with respect to time as follows:IV *1;2_ — A Iu+Scul= 2M0—{2M0—Mst[^cs ^ko A-2 ^pb[2 N:s2_ — N*02_ ± N*cu+ [Oct, — 2S cu]]]( RT) 02(7.109)Similarly, the rate of weight change in the secondary stage is expressed in terms of thereaction gas flow rate as follows:1472[N*s,_ — A TW = [2M0 — [2M0AI]—^s r— N + [Ocu — 2Scu ]](7.110)_ArPob2 179gdr,X[0.64700,RT(Tcd3pg iQ0.79pgD02-Ar^411 g7.2. Model ValidationThe general criteria for the model validity are comparison of its prediction of the sulphurand oxygen contents for the two stages and their time domains to measurements from thelaboratory experiments. From Equations (7.54) and (7.55), the primary sulphur andoxygen molar contents were calculated; the reaction transition time was calculated fromEquation (7.65); and the secondary sulphur and oxygen molar contents were calculatedfrom Equations (7.102) and (7.103). These predicted results were plotted along with thecorresponding measured values for typical runs, as shown in Figures 7.4-7.5.The apparent curvature of the measured oxygen content is due to experimental scatter. Itis important to note that the accuracy of the sulphur content measurement is higher thanthat of the oxygen content measurement36. The relative disagreement between thepredicted and the measured results is attributed to the errors associated with the inputparameters to the model (reaction gas flow rate, reaction gas composition and themeasured pressure of the system) and the estimation of the gas phase mass transfercoefficient. The model predictions, however, appear to be in very good agreement withthe measured results, for the employed range of the reaction gas flow rate, as shown inFigure 7.4.36The sulphur content was determined by the acid-base titration method, which is a moreconventionally accurate method than the gas flow rate measurement technique, which was usedin the determination of the oxygen content. As explained in Section 4.1.5.5, in general, the errorin the measurement of the reaction gas flow rate is proportional to the flow rate.12080^1000^20^40^601.41.21.00.40.20.0148Time (min)Figure 7.4. Comparison of model predictions to measurements of the sulphur and oxygencontents in the bath as a function of time at a constant reaction gas composition and forthe range of reaction gas flow rate of 1480-4055 ml/min; for the experimental conditionsof: 200 grams of Cu2S of: 22% 02 and 78% Ar, at 1200 °C,^ predicted for 1480ml/min; Emeasured sulphur content for 1480 ml/min; 0 measured oxygen content for1480 ml/min; ^ predicted for 2006 ml/min; 0 measured sulphur content for 2006ml/min; A measured oxygen content for 2006 ml/min; — — — predicted for 4055ml/min; + measured sulphur content for 4055 ml/min; • measured oxygen content for4055 ml/min.Similarly for the reaction gas composition range, the predicted and measured results areas shown in Figure 7.5.10^20^30^40^50^60^70^80149Time (min)Figure 7.5. Comparison of model predictions to measurements of sulphur and oxygencontents in the bath as a function of time at a constant reaction gas flow rate and for therange of reaction gas composition of 22-78% 02; for the experimental conditions of: 200grams of Cu2S of: 2000 ml/min, at 1200 °C,^ predicted for 22% 02; 0 measuredsulphur content for 22% 02; 0 measured oxygen content for 22% 02; — — — predictedfor 35% 02; o measured sulphur content for 35% 02; • measured oxygen content for35% 02;^ predicted for 78% 02; A measured sulphur content for 78% 02; +measured oxygen content for 78% 02.150The relative deviation from the measured results, at the highest reaction gas compositionconditions, is mainly attributed to the effect of surface-tension driven flows 37 . It isevident, however, that the model provides an acceptable predictability for theexperimental range of reaction gas composition.Considering the error involved in the measured results, the model predictions appear to bewell within the experimental uncertainty of the measured values. It is thereforereasonable to state that the model predictions are in good agreement with the overallrange of the measured results.7.3. Model SensitivitySince all of the reaction parameters are set or read with some degree of uncertainty, it isinevitable that the input variables to the mathematical model carry some degree of error.In order to examine the effect of these uncertainties on the model predictions, and toisolate as much as possible the experimental error from the model deviations, thisanalysis is carried out using the results of a run that appears to contain the least relativeerrors.7.3.1.^TemperatureAs shown in Figure 7.6, the uncertainty in the temperature evidently has a very minoreffect on the oveall model predictions. An error of ±50 °C (2.5%) results in less than 1%error in the sample weight prediction and less than 6% error in the prediction of thetransition time.37The effect of surface-tension driven flows was found to be higher with oxygen content in thereaction gas; as a result, the transport conditions are enhanced beyond the accountability of themodel (see Figure 6.2).205200195^190 ^EE5, 185 ^toi 180 —*81 175 ^gcl170 ^165160155 ' '0^10" I '20^30^40^50^60Time (mm)151Figure 7.6. Model-predicted sensitivity of transient bath weight to bath temperature38 forthe experimental conditions of; ^ predicted for 1200 °C; 0 measured at 1200 °C;— - — - predicted for 1150 °C;^ predicted for 1250 °C.7.3.2.^PressureDue to the pressure head created by the SO2 absorber, the measurements were conductedunder pressures of slightly higher than that of the atmospheric pressure viz., 1.05-1.112atm. For systems such as that under study, however, it is well known that the pressure38The experimental conditions of this run, used in all of the sensitivity analyses, are: 200 gramsof Cu2S, 2000 ml/min of 35% 02 and 65% Ar152has a minor effect on most thermodynamic properties [114]. As shown in Figure 7.7, theresults of this sensitivity analysis indicated that a 5% uncertainty in the pressure of thesystem results in less than 3% error in the prediction of the reaction transition time and aless than 2% error in the prediction of the sample weight.^205 ^200195 —^190 ^R., 185....,Zto 1801 175 ^(4170 ^165 ^160 ^155 ^0 " I "10^20^30^40^50Time (mm)60Figure 7.7. Model-predicted sensitivity of transient bath weight to total pressure,predicted for 1.09 atm; 0 measured at 1.09 atm; — - - — predicted for 1 atm; predicted for 1.15 atm.205200195190I ::c9 i85.4 iso.8.= 175'c'Elal1701651601550 20" I I30 40 50 601537.3.3.^Reaction Gas Flow RateAs shown in Figure 7.8, the results of the model-reaction gas flow rate sensitivity analysisindicated that a 5% error in the reaction gas flow rate results in less than 4% error in theprediction of the reaction transition time and less than 0.8% error in the prediction of thesample weight.Time (min)Figure 7.8. Model-predicted sensitivity of transient bath weight to flow rate of admittedgas; ^ predicted for 2000 ml/min; 0 measured for 2000 ml/min; — - - —predicted for 1900 ml/min; ^ predicted for 2100 ml/min." I '' I ",205200195..^175'401gq1701651601550^10^20^30^40^50^601547.3.4. Reaction Gas compositionIn this analysis, a 5% uncertainty in the reaction gas composition was found to result inless than 6% error in the prediction of the reaction transition time and less than 2% errorin the prediction of the sample weight, as shown in Figure 7.9.Time (min)Figure 7.9. Model-predicted sensitivity of transient bath weight to composition ofadmitted gas;^ predicted for 35% 02; 0 measured for 35% 02; — - - —predicted for 33% 02;^ predicted for 37% 02.In the experiments, the reaction gas mixture was obtained by metering each gas streamusing a separate rotameter. Thus the error in the reaction gas composition isapproximately the sum of the errors of the two readings. Since the reaction rate is195190g 185to-:a.0 180*Ei175121170165160155155directly proportional to the reaction gas composition, its error contribution is expected tobe higher than that of the reaction gas flow rate.7.3.5.^Reaction Interfacial AreaIf the error associated with the reaction interfacial area was 5%, then the correspondingerrors were 5% and 1% in the predictions of the reaction transition time and the sampleweight respectively, as shown in Figure 7.10.2052000" I '' '10^20 30^40^50 60Time (min)Figure 7.10. Model-predicted sensitivity of transient bath weight to bath surface area;^ predicted for 15.14 cm2; c.), measured for 15.14 cm2; — - - — predicted for14.38 cm2;^ predicted for 15.90 cm2.1567.4. Theoretical Predictions7.4.1.^Oxidation PathAs presented and discussed in Chapter 5, gas analysis measurements and gravimetricmeasurements revealed that the oxidation reaction of molten copper sulphide proceedsaccording to two distinct stages, during which the rates are constant, as shown in Figures5.5 and 5.6. The fact that these two independent measurements are in general agreementis evidence of their validity. The melt composition at transition and the molar ratio ofreacted oxygen to removed sulphur (a) are independent of reaction conditions (see Table5.1).By eliminating time from the expressions for the molar sulphur and oxygen contents(Equations (7.51), (7.53), (7.99) and (7.100)), the relationship between the sulphur andoxygen contents are found to be independent of the oxidation kinetics as given by thefollowing equations:= Nis — Arf,[N* 2_ — Sc N* rM = N;+ s^u cu+ IN — N*02_1Al*, — OcuN*cu_0 -(7.112)Although the experimental scatter is considerable, experimental measurements are inagreement with the predictions of Equations (7.111) and (7.112) as shown in Figure 7.11.The experimental results indicate very clearly that the oxidation path is controlledprimarily by the thermodynamics of the Cu-S-0 system. From Figure 7.11, the predictedresults indicate that the effect of temperature on the oxidation path is minimal, where a100 °C increase in temperature causes a slight shift in point b and appears to have noeffect on point c.Transition Pointa>1)0^- <>A - X X +O 0 •^fii>^X^0 •^'X,Primary Stage^0^• 4+• X°0 + A0A°''• 0••A• AAA •X0+•0Secondary StageII" Il""1""I'"Il""1"0A><157252000.0^0.2^0.4^0.6^0.8^1.0^1.2^1.4^1.6^1.8Cuwt% OxygenFigure 7.11. The sulphur content as a function of the oxygen content in the bath, showingthe oxidation path of molten copper sulphide, ^ predicted at 1200 °C and 1 atm;^ predicted at 1300 °C and 1 atm; measured at 1200 °C and 24 % 02, 0 1480ml/min, A 1755 ml/min, + 1987 ml/min, 0 2006 ml/min, x 4055 ml/min; measured at1200 °C and 2510 ml/min of 23 % 02; measured at 1200 °C and 2000 ml/min, • 27 %02, • 35 % 02, El 46 % 02, • 64 % 02•Based on the findings of the current work and on earlier thermodynamic studies of theternary system, the oxidation path of Cu2S is constructed as shown in Figure 7.12.Primary StageOxidation Path19.6% S17.7 % S and 1.47 % 0Liquid Metal Phase((Cu))1.33 % S   gf^1.97 % 0Wt % S^ Wt % 0Secondary StageOxidation Path20 d Liquid Sulphide Phase((Cu2S))21.72 % S/158CuFigure 7.12. Selected portions of the Cu-S-0 isothermal section, showing the oxidationpath of molten Cu2S at 1200 °C and 1 atm (points b and c are after Schmiedl [19]; pointsd, e, f and g are after Elliott [201). Note that the dashed lines outlining the metal andsulphide phases are assumed.As stated in Section 5.1.3.2, gas analysis measurements yielded 16.94 ± 0.10% and 1.37 ±0.07% for the sulphur and oxygen transition concentrations respectively. Rottmann andWuth [71] found that the melt oxygen content at the end of the primary stage is 0.6%.Peretti [10] suggested that, based on the Cu-S binary phase diagram, in the Peirce-Smith159converter, the second step of the copper-making reaction starts when the meltcomposition is about 19.4% sulphur. Peretti, however, ignored the effect of oxygen byconsidering the melt to be a binary system. According to the present work, the binaryassumption can be misleading in studying the reaction mechanism of the oxidation ofcopper sulphide. The 1300 °C isothermal section, shown in Figure 2.3, indicates that thesulphur and oxygen concentrations at saturation in Cu2S are approximately 18.59% and1.38% respectively. At 1200 °C and 1 atm, the equilibrium measurements of Schmiedl[19] yielded 17.7% and 1.47% for the sulphur and oxygen solubilities in Cu2Srespectively. From comparing the measured transition composition to the equilibriumcomposition of sulphur and oxygen in the melt, clearly the melt composition at transitionis that of the equilibrium composition of oxygen and sulphur. Therefore, during theprimary stage, the melt is partially desulphurized and oxygen saturated without anyformation of copper according to path a-b in Figure 7.12. Once the melt reaches point b,the chemical potential for the formation of the metal phase is attained. An increaseddegree of desulphurization accompanies the metal phase formation which takes placeaccording to path b-c, as shown in Figures 7.11 and 7.12.As discussed in Section 5.1.3.2, the average value for aP = 1.46 permitted the postulationof Reaction (5.18) as the principal reaction in the primary stage. In the formulation of themathematical model, this postulate was implemented in deriving the relationshipsbetween the reaction rates of the primary stage. As shown in Figures 7.4 and 7.5, themodel predictions of the primary stage are in good agreement with the measured results.This can best be seen by concentrating on the prediction of the transition point. It is clear,therefore, that Reaction (5.18) is the only reaction that takes place during the primarystage. It is very important to note that obtaining a large number of relatively accuratemeasurements permitted the calculation of a statistically valid mean for a", from which itwas possible to postulate Reaction (5.18). Although the time duration of the primary160stage is only about 20-25 % of the total time of the oxidation reaction, the understandingof the chemical reactions of the primary stage is very crucial to the comprehension of thesecondary stage.During the secondary stage, the molar ratio of reacted oxygen to removed sulphur wasfound to be as = 0.96 ± 0.052. At first glance this might seem to be an indication thatthe actual ratio is unity. However, this can be a very misleading judgment. As discussedabove, because of the reactions are electrochemical in which the dissolution of oxygenand sulphur in copper, according to Reactions 5.21 and 5.22, is accompanied by electrontransfer, the degree of desulphurization during the secondary stage is further enhanced. Itis important to note that, as explained in Sections 5.1.3.2 and 7.1.2.2, without consideringthe electrochemical nature of the system it would not have been possible to account forthe oxygen and sulphur in the metal phase.7.4.2.^Oxidation Rates7.4.2.1.^Oxidation Rate as a Function of Gas Flow Rate From the mathematical model, the oxygen gas phase mass transfer rate is related to thereaction gas volumetric flow rate as follows:^0 . 6470,92_ ArPob2^I1gd1ç [7cc13p g)° 79^0 70N0, = ^RT P gD02-Ar^41.14 g(7.113)For the oxidation reaction to be gas phase mass transfer limited, the oxygen reaction ratemust be equal to the oxygen gas phase mass transfer rate, predicted by Equation (7.113).In Figure 7.13, the predicted oxygen reaction rate is compared to the measured oxygenreaction rate, from which the theoretical prediction appears to be in good agreement withmeasured rates.0.0011000 100000.100161Gas Flow Rate (mlhnin)Figure 7.13. Oxygen reaction rate (No, ) as a function of reaction gas volumetric flow ratefor the experimental conditions of: 200 gram samples, 1200 °C, 23 % 02 and averagepressure of 1.08 atm,^ predicted ; 0 primary measured; • secondary measured.0.10.0011000 10000162In Figure 7.14, the measured and predicted sulphur removal rates (Equations (7.56) and(7.58)) are plotted against the gas flow rate. As expected, since the sulphur removal ratesare limited by gas phase mass transfer, the predicted and measured rates appear to be ingood agreement.Gas Flow Rate (ml/min)Figure 7.14. Sulphur removal rate (Ns) as a function of reaction gas volumetric flow ratefor the experimental conditions of: 200 gram samples, 1200 °C, 23 % 02 and averagepressure of 1.08 atm;^ primary predicted; 0 primary measured;^secondary predicted; 0 secondary measured.-163The predictions of Equations (7.68) and (7.110) and the measured rates of weight losswere predicted and plotted against the admitted gas flow rate in Figure 7.15. Consideringthe experimental scatter, the predicted measured results appear to be in generalagreement.100.01 ^1000 10000Gas Flow Rate (mUmin)Figure 7.15. Rate of weight loss (W) as a function of reaction gas volumetric flow ratefor the experimental conditions of: 200 gram samples, 1200 °C, 23 % 02 and averagepressure of 1.08 atm; primary predicted; El primary obtained from gas analysis;• primary obtained from gravimetric measurement; ^ secondary predicted; 0secondary obtained from gas analysis; • secondary obtained from gravimetricmeasurement.0.070.06oo3E 0.05 ^a)CEcit) 0.04 ^P4o2ki 0.03 ^a)19td)00.010.000.0' I "0.2^0.4^0.6^0.8Oxygen Partial Pressure (atm)01.01647.4.2.2.^Oxidation Rate as a Function of Gas CompositionAs shown in Figure 7.16, the predicted and experimentally determined oxygen reactionrates are plotted against the partial pressure of oxygen.Figure 7.16. Oxygen reaction rate (No, ) as a function of oxygen partial pressure for theexperimental conditions of: 1200 °C and 2000 ml/min; predicted; 0 measuredprimary; <> measured secondary.In a linear fashion, as shown in Figure 7.17, the measured oxygen reaction rate appears todeviate from the predicted rate of oxygen gas phase mass transfer for oxygen partialpressures of greater than 0.11.o0165201816140.0^0.2^0.4^0.6^0.8^1.0Oxygen Partial Pressure (atm)Figure 7.17. Percent increase in gas phase mass transfer as a function of oxygen partialpressure for the experimental conditions of: 1200 °C and 2000 ml/min,^regression line; 0 determined from measurement.This deviation is attributed to the increase in the gas phase mass-transfer coefficient, dueto surface tension-driven flows (the Marangoni effect), which were observed to increasewith the partial pressure of oxygen. In mathematical terms, the percent increase in gasphase mass transfer, C, likely due to the Marangoni effect, was found to correlate to thepartial pressure of oxygen as follows:C = (22.7±3.6)P0', —(2.7±1.9)^ (7.114)166Because, the gas phase mass-transfer coefficient was calculated from a correlation whichdoes not account for the increase in the transport conditions due to surface-tension drivenflows, the predicted reaction rates are less than the measured reaction rates.As discussed in Chapter 5, if the reaction is to be controlled by gas phase mass transferthe sulphur and oxygen molar contents in the bath must be linear with time.Experimental results presented in Chapter 5 and the mathematical validation in Chapter 7established that the rate controlling mechanism of the oxidation reaction of molten Cu2Sis gas phase mass transfer (see Figures 5.4, 7.4 and 7.5).The rates of sulphur removal are directly proportional to the partial pressure of oxygen, asdescribed by Equations (7.56) and (7.104). In Figure 7.18, the measured rates of sulphurremoval were plotted against the partial pressure of oxygen along with the theoreticalpredictions of Equations (7.56) and (7.104). In a similar behaviour to the oxygen reactionrates, the rates of sulphur removal appear to be influenced by the increased degree of gasphase mass transfer. In general, however, there is a reasonable agreement between thepredicted and measured rates of sulphur removal, which is an additional evidence that therates of sulphur removal are limited by the rates of oxygen gas phase mass transfer.0.0716700.06E 0.05ooE2,1 0.0474oE 0.030r4,..',2r4= 0.02c40.0100.2^0.4^0.6^0.8^1.0Oxygen Partial Pressure (atm)0.000.0Figure 7.18. Sulphur removal rate (dNsIdt) as a function of oxygen pressure for theexperimental conditions of: 1200 °C and 2000 ml/min,^ primary predicted; 0primary measured; ^ secondary predicted; 0 secondary measured.0.8 1.00.0^0.2^0.4^0.6002.01.81.60cal 0.8r:400.40.20.0 "I"^IIII"I"Increase in the reaction rate with oxygen concentration in the reaction gas, in theoxidation of molten Cu2S, was also exhibited by the experimental results of Rottmannand Wuth [71], as shown in Figure 7.19.Oxygen Partial Pressure (atm)Figure 7.19. Oxygen reaction rate (N o,) as a function of oxygen pressure for theexperimental conditions of: 1500 grams of Cu2S under the top-lancing of high velocityjets of 02-N2 gas mixtures at 1250 °C, nozzle pressure of 5.4x105 N/m2, nozzle diameterof 1 mm, nozzle to bath distance of 65 mm and crucible inner diameter of 100 mm;^ predicted (after Rottmann and Wuth [71] (based on gas phase mass transfer ofoxygen through a viscous sub-layer)); 0 measured (after Rottmann and Wuth).1688vis, = U0.9g,max2 9 v 0 .9 x 0.1RTD02-N2 AP02no, = (7.116)169As discussed in Section 2.4, Rottmann and Wuth measured the reaction rates of theoxidation of molten Cu2S for different oxygen concentrations in the bulk gas at 1250 °C.In their prediction of the reaction rates, Rottmann and Wuth assumed that the reaction islimited by the oxygen diffusion in a viscous sub-layer of thickness 8. Using acorrelation for the thickness of the boundary layer at a plate exposed parallel to aturbulent stream, they calculated 8 as follows:(7.115)from which the rate of oxygen reaction was calculated as follows:Because they did not measure the reaction rates for a range of gas flow rates, it is notpossible to validate the assumption of diffusion through a viscous layer and in turndetermine the validity of Equation (7.116). It is likely, however, that the predictedreaction rates are linear with the oxygen pressure in the gas phase. Assuming that theactual reaction rates are very close to those predicted by Rottmann and Wuth, it issuggested that the deviation exhibited by the measured results is due to increased surface-tension driven flows with oxygen concentration in the admitted gas. The percent increasein the gas phase mass transfer was similarly correlated to the partial pressure of oxygen asfollows:= (29 ±4)137,2 + (12 ± 2)^ (7.117)in which, the slope is slightly higher than that in Equation (7.114). It is therefore,suggested that, due to the Marangoni effect, the gas phase mass transfer conditions areenhanced with increasing oxygen concentration in the reaction gas phase. As discussed inSection 2.5, increases in mass transfer, due to the Marangoni effect, have been observed170to occur in many systems [56,82,84,99,101,121]. In the oxidation of molten Cu2S, asshown in Section 5.3, there is an overwhelming evidence that surface-tension drivenflows play an important role in the overall reaction rate kinetics. By stiffing the bath,surface-tension driven flows virtually eliminate any liquid phase mass transfer resistance,as shown in Figure 5.15. As the radial movement of the surface is increased with higherconcentrations of oxygen in the gas phase, the mass transfer conditions are likely toincrease as the moving liquid causes further drag of the gas, thereby, enhancing thereaction rate beyond the values accounted for by ordinary transport conditions.7.4.2.3.^Oxidation Rate as a Function of TemperatureFrom Equation (7.2), the rate of oxygen reaction is inversely proportional to temperature.The predicted and measured oxygen reaction rates are plotted against temperature inFigure 7.20. Although the gas phase mass-transfer coefficient is positively dependent ontemperature, the predicted oxygen reaction rate appears to have a slight negativedependence on temperature, as shown in Figure 7.20. In general, however, it can bestated that both the measured and predicted oxygen reaction rates are effectivelyindependent of temperature.In comparing Equations (7.56) and (7.104) theoretically, the temperature dependence ofthe rate of sulphur removal during the secondary stage is greater than that during theprimary stage. In Equation (7.104), the secondary molar ratio of reacted oxygen toremoved sulphur, as, is a function of the equilibrium concentrations of the melt, asdescribed by the following equation:as . 1+ RocuNc*., —which yields 0.9169 and 0.9250 fora' at 1200 and 1300 °C respectively. Conversely, theprimary molar ratio of reacted oxygen to removed sulphur dioxide, a'', is 1.5(independent of temperature).N*02_ ]/2[N*5,2_ — SGUNL,]] (7.118)171(1 / T) x104 (70Figure 7.20. Oxygen reaction rate (No2) as a function of temperature for the experimentalconditions of: 2000 ml/min of 20-23 % 02 and average pressure of 1.08 atm,^primary predicted 22 % 02; 0 primary measured; • secondary measured.In Figure 7.21, the predicted and measured rates of sulphur removal are plotted againsttemperature, from which it appears that measured and predicted results are in agreement.The primary rate of sulphur removal seems to have a similar behaviour to that of theoxygen reaction rate, but the secondary rate of sulphur removal appears to be virtuallyindependent of temperature.0.1001728-8•••000••0.001 ^ '^' I ' '6.0^6.2^6.4^6.6 6.8^7.0^7.2(1 / 7') x104 (°K-1)Figure 7.21. Sulphur removal rate (dNsIdt) as a function of temperature for theexperimental conditions of: 2000 ml/min of 20-23 % 02 and average pressure of 1.08atm,^ primary predicted 22 % 02,^ secondary predicted 22 % 02; 0primary measured; • secondary measured.100101737.4.3.^Oxygen UtilizationThe oxygen utilization as a function of gas flow rate is shown in Figure 7.22, from whichit appears that very high reaction efficiencies are attained in the oxygen-Cu2S system.This is consistent with the observed oxygen utilization in the Peirce-Smith converter.100^ 1000^ 10000Gas Flow Rate (ml/min)Figure 7.22. Oxygen utilization as a function of reaction gas volumetric flow rate for thetop-blown conditions of: 200 grams of Cu2S at 1200 °C, 1.08 atm, 23% 02, reactioninterfacial diameter of 44 mm, lance nozzle diameter of 3 mm and lance nozzle to initialinterfacial area of approximately 10 mm;^ predicted; 0 measured.To obtain valid kinetic measurements of heterogeneous reaction systems in laboratorytests, reactants must be supplied at rates beyond their rates of consumption by the reaction174at the given experimental conditions. From Figure 7.22, the predicted oxygen curveindicates that the limit for obtaining useful kinetic measurements is 750 ml/min i.e. belowthis value the oxidation reaction rate is higher than that of the rate of oxygen supply.Industrial processes in which gas-liquid reactions are involved, the utilization of thereaction gas is of high economic importance. It is important that the reaction gasefficiency be as high as possible. Since however, the high efficiency is accompanied bylower reaction rates, the optimization of a given process may dictate that the gasutilization be much lower than can be attained.1758. Summary and ConclusionsThe primary objective of this work was to investigate the oxidation kinetics of moltencopper sulphide under top-blown conditions. The major findings of this work can besummarized as follows:1. The oxidation reaction of molten copper sulphide takes place according to twodistinct stages.2. During the primary stage, the melt is a single phase, being partially desulphurized andbecoming oxygen saturated, according to the surface reaction as follows:[s2 ]+ % (o2 ) = (so2) +[o2- ]3. Upon saturation of the melt with oxygen, the secondary stage commences, duringwhich the following reactions in the sulphide phase produce metallic copper:[52]+ 2[01+ 6[Cu] = (S02)+6((Cu))[S1 +2[Cul = [S]((co) +2((Cu))[01 + 2[Cul = [0]((c)) + 2((Cu))(5.18)while the surface reaction involving gaseous oxygen continues to take place until theend of the secondary stage.4. The rate of sulphur removal and oxygen dissolution during the primary stage werefound to be independent of sulphur and oxygen contents in the melt. Similarly, therates of sulphur and oxygen removal during the secondary stage are independent ofsulphur and oxygen contents in the melt.5. The rate controlling mechanism in the oxidation of molten Cu2S is gas phase masstransfer of oxygen to the melt surface; the oxidation rate was found to be directly176proportional to the partial pressure of oxygen in the reaction gas. From theexperimental data obtained in this work, the gas phase-mass transfer coefficient wascorrelated to experimental variables via the Sherwood number, Sh, the Schmidtnumber, Sc (0.56 5. Sc 0.63), the Reynolds number, Re (33 5 Re 300), the radiusof the crucible, rs, and the diameter of the lance nozzle, d (7 rid 11), as follows:Sh = (0.64 ± 0.07)(rs/d) Sca5 Re (0.79±0.06)^(6.18)6. Surface-tension driven flows (Marangoni effect) were observed to take place duringthe oxidation reaction. As a result transport conditions at the gas-liquid interfacewere slightly enhanced. The degree of surface-turbulence was observed to be arelatively strong function of the oxygen content in the reaction gas, while the gas flowrate was observed to cause only a slight increase. The effect of temperature onsurface-tension driven flows was undetectable.7. In a continuous fashion, the eruption of small numbers of gas bubbles from the meltsurface was observed to take place during the secondary stage, while at random timeintervals, occasional intense boiling was observed to occur as well. The intensity andfrequency of boiling were observed to increase with increasing gas flow rate andoxygen partial pressure.8. The liquid phase mass transfer resistance was found to be negligible, likely due to theionic nature of the sulphide melt and the Marangoni effect. Because of theelectrochemical nature of the sulphide melt, the local transport of electrons is veryrapid (the specific conductance of Cu25 is 150 C2-1cm-1 at 1500 °C [115]), and owingto surface-tension driven flows, the bath is vigorously mixed. During the secondarystage, the degree of mixing in the bath is enhanced by rising SO2 bubbles and settlingcopper droplets. Due to the eruption of gas bubbles at the melt surface, the177dependence of the reaction rate on the gas flow rate was found to be slightly higher asa result of increasing gas-liquid interfacial area.8. The effect of temperature on the overall reaction rate was found to be negligible.9. Based on the experimental results and the likely electrochemical reactions, amathematical model was formulated and was found to provide a reliable descriptionof the oxidation reaction.The practical implications of these findings are as follows:1. The high oxygen utilization in the Peirce-Smith converter is due to the ionic nature ofthe sulphide melt and the effect of surface-tension driven flows which give rise to gasphase mass transfer control.2. In systems similar to copper sulphide (negligible liquid phase mass transfer resistanceand very fast chemical reaction), high reaction gas utilization can be attained undertop-lancing conditions. Thus by adopting top-lancing as in the Mitsubishi Process,high oxygen efficiencies are achievable while the problems of refractory wear intuyere region are eliminated.References1. T. M. Morris, "History of Copper Converting", Journal of Metals, July 1968, pp 73-75.2. A. K. Biswas and W. G. Davenport, "Extractive Metallurgy of Copper", 2ndEdition, Pergamon Press, Beccles and London, 1980.3. C. L. . Milliken and F. F. Hofinger, "An Analysis of Copper Converter Size andCapacity", Journal of Metals, April 1968, pp 39-45.4. R. E. Johnson, N. J. Themelis and G. A. Eltringham, "A Survey of Worldwide CopperConverter Practices", Copper and Nickel Converters, Conference Proceedings, TheMetallurgical Society of AIME, 1979, pp 1-32.5. F. E. Lathe and L. Hodentt, "Data on Copper Converter Practice in VariousCountries",  Transactions of The Metallurgical Society of AIME, October 1958, pp603-615.6. A. A. Bustos, J. K. Brimacombe and G. G. Richards, "Heat Flow in CopperConverters", Metallurgical Transactions, Volume 17B, No 4, Process Metallurgy,December 1986, pp 677-685.7. D. W. Ashman, J. W. McKelliget and J. K. Brimacombe, "Mathematical Model ofBubble Formation at the Tuyeres of a Copper Converter", Canadian Metallurgical Quarterly, Volume 20, No 4, 1981, pp 387-395.8. A. A. Bustos, J. K. Brimacombe and G. G. Richards, "Accretion Growth at theTuyeres of a Peirce-Smith Copper Converter", Canadian Metallurgical Quarterly,Volume 27, No 1, pp 7-21, 1988.9. King, A. D. Mah and L. B. Pankratz, "Thermodynamic Properties of Copper and itsInorganic Compounds", INCRA Monograph II, The Metallurgy of Copper,International Copper Research Association, Inc., New York, 1973.10. E. A. Peretti, "An Analysis of the Converting of Copper Matte", Discuss. FaradaySociety 4, 1948, pp 179-184.11. T. Rosenquist, "Principles of Extractive Metallurgy",  2nd Edition, McGraw-Hill,New York, 1983.12. F. Habashi, "Principles of Extractive Metallurgy, Volume 3, Pyrometallurgy",Gordon and Breach, New York, 1986.13. W. Oelsen in Clausthal, "Die Desoxydation von Kupferschmelzen mit Eisen, mitPhosphor und mit Schwefel", Giesserei Techn.-Wissensch. Beihefte, Heft 6/8, Marz,1952, pp 383-387.14. U. Kuxmann and T. Benecke, "Untersuchungen zur LOslichkeit von Sauerstoff inKupfersulfid-Schmelzen", Erzmetall, Mai 1966, pp 215-274.15. H. H. Kellogg, "Thermochemical Properties of the System Cu-S at ElevatedTemperature", Canadian Metallurgical Quarterly, Volume 8, No 1, 1969, pp 3-23.17817916. A. Yazawa and T. Azakami, "Thermodynamics of Removing Impurities DuringCopper Smelting", Canadian Metallurgical Quarterly, volume 8, No 3, 1969, pp 257-261.17. J. Schmiedl, M. tofko and V. Repcak, "Gleichgewichtsuntersuchungen im SystemCu-Fe-0", Neue Hiitte, 16 jg, Heft 7, Juli 1971, pp 390-395.18. F. Y. Bor and P. Tarassoff, "Solubility of Oxygen in Copper Mattes", CanadianMetallurgical Quarterly, Volume 10, No 4, 1971, pp 267-271.19. J. Schmiedl, "Physical Chemistry of Continuous Copper Smelting", Physical Chemistry of Process Metallurgy: The Richardson Conference, The Institution ofMining and Metallurgy, 1974, pp 127-134.20. J. F. Elliott, "Phase Relationships in the Pyrometallurgy of Copper", MetallurgicalTransactions, Volume 7B, March 1976, pp 17-33.21. R. C. Sharma and Y. A. Chang, "A Thermodynamic Analysis of Copper-SulphurSystem", Metallurgical Transactions, Volume 11B, December 1980, pp 575-583.22. R. Schmid, "A Thermodynamic Analysis of the Cu-0 System with an AssociatedSolution Model", Metallurgical Transactions, Volume 14B, September 1983, pp 473-481.23. S. Otsuka and Y. A. Chang, "Activity Coefficient of Oxygen in Copper-SulphurMelts", Metallurgical Transactions, Volume 15B, June 1984, pp 337-343.24. J. Lumsden, "Thermodynamics of Iron-Copper-Sulphur-Oxygen Melts", Metal-Slag-Gas Reactions and Processes, The Electrochemical Society, Inc., Princeton, NewJersey, 1975, pp 155-168.25. T. Rosenquist. "Thermodynamics of Copper Smelting", Advances in SulphideSmelting, Volume 1, TMS-AIME, 1983, pp 239-255.26. C. B. Alcock, "Principles of Pyrometallurgy",  Academic Press, 1976, pp 170-175.27. F. Ajersch and J. M. Toguri, "Oxidation Rates of Liquid Copper and Liquid CopperSulphide", Metallurgical Transactions, Volume 3, August 1972, pp 2187-2193.28. Z. Asaki, F. Ajersch, and J. M. Toguri, "Oxidation of Molten Ferrous Sulphide",Metallurgical Transactions, Volume 5, August 1974, pp 1753-1759.29. Y. Fukunaka and J. M. Toguri, "The Oxidation of Liquid Ni3S2", Metallurgical Transactions, Volume 10B, June 1979, pp 191-201.30. Z. Asaki, S. Ando, and Y. Kondo, "Oxidation of Molten Copper Matte",Metallurgical Transactions, Volume 19B, February 1988, pp 47-52.31. F. Ajersch and M. Benlyamani, "Thermogravimetric Identification and Analysis ofReaction Products During Oxidation of Solid or Liquid Sulphides", ThermochimicaActa, 143, 1989, pp 221-237.32. T. Tanabe, K. Kanzaki, M. Kobayashi and Z. Asaki, "Kinetics of Desulphurizationand Oxidation of Molten Nickel-Cobalt Sulphide in the Temperature Range between1801473 and 1673 °K", Materials Transactions, JIM, Volume 31, No. 3, 1990, pp 207-212.33. Y. Fukunaka, K. Tamura, N. Taguchi and Z. Asaki, "Deoxidation Rate of CopperDroplet Levitated in Ar-H2 Gas Stream", Metallurgical Transactions, Volume 22B,October 1991, pp 631-637.34. K. Li, D. A. Dukelow, and G.C. Smith, " Decarburization in Iron-Carbon System byOxygen Top Blowing", Transactions of The Metallurgical Society of AIME, Volume230, February 1964, 71-76.35. R. B. Banks and D. V. Chandrasekhara, "Experimental Investigation of thePenetration of a High-Velocity Gas Jet Through a Liquid Surface", Journal of FluidMechanics, Volume 15, Part 1, June 1962, pp 13-34.36. Gasstrahlen auf Fltissigkeitsoberflkhen, "Zum Warme- und Stoffaustausch beimSenkrechten Aufblasen", Chemie-Ing-Techn 38, Heft 3, Jahrg 1966, pp 309-314.37. G. C. Smith, "Multiple Jet Oxygen Lances-Theoretical Analysis and Correlation withPractice", Journal of Metals, July 1966, pp 846-851.38. W. G. Davenport, D. H. Wakelin and A. V. Bradshaw, "Interaction of Both Bubblesand Gas Jets With Liquids",  Heat and Mass Transfer in Process Metallurgy,Proceedings of a Symposium held by the John Percy Research Group in ProcessMetallurgy, Imperial College, London, 19 and 20 April, 1966, Edited by A. W. D.Hills, The Institution of Mining and Metallurgy, 1967, pp 207-237.39. N. J. Themelis and P. R. Schmidt, "Deoxidation of Liquid Copper by a SubmergedGas Jet", Transactions of The Metallurgical Society of AIME, Volume 239,September 1967, pp 1313-1318.40. N. J. Themelis, P. Tarassoff and J. Szekely, "Gas-Liquid Momentum Transfer in aCopper Converter", Transactions of The Metallurgical Society of AIME, Volume 245,1969, pp 2425-2433.41. N. A. Molloy, "Impinging Jet Flow in a Two-Phase System: The Basic Flow Pattern",Journal of Iron and Steel Institute, October 1970, pp 943-950.42. A. Chatterjee and A. V. Bradshaw, "Break-Up of a Liquid Surface by an ImpingingGas Jet", Journal of The Iron and Steel Institute, March 1972, pp 179-187.43. J. Szekely and S. Asai, "Turbulent Fluid Flow Phenomena in Metals ProcessingOperations: Mathematical Description of the Fluid Flow Field in a Bath Caused by anImpinging Gas Jet", Metallurgical Transactions, Volume 5, February 1974, pp 463-467.44. J. K. Brimacombe, E. S. Stratigakos and P. Tarassoff, "Mass Transfer Between aHorizontal, Submerged Gas Jet and a Liquid", Metallurgical Transactions, Volume 5,March 1974, pp 763-771.45. S. Taniguchi, A. Kikuchi and S. Maeda, "Model Experiments on Mass Transfer inGas Phase Between an Impinging Jet of Gas and Liquid Iron", Tetsu-to-Hagane, 1976,62(2), pp 191-200.18146. S. Taniguchi, A. Kikuchi and S. Maeda, "Kinetics of the Oxidation of Graphite by theImpinging Jet of Gas", Tetsu-to-Hagane, 1977, 63(7), pp 1071-1080.47. S. Taniguchi, A. Kikuchi, T. Tadaki and S. Maeda, "Numerical Analysis on the Gas-Phase Mass Transfer Between an Impinging Jet of Gas and Liquid Iron", Tetsu-to-Hagane, 1979, 65(13), pp 1830-1873.48. A. Kikuchi, S. Taniguchi, T. Tadaki and S. Maeda, "Fluid Flow and Mass Transfer inthe Gas-Liquid Iron System with a Laboratory-Scale Induction Furnace",Metallurgical Applications of Magnetohydrodynamics, Proceedings of a Symposiumof the International Union of Theoretical and Applied Mechanics held at TrinityCollege, Cambridge, UK, 6-10 September 1982, Edited by H. K. Moffatt and M. R. E.Proctor, The Metals Society Institute.49. J. Zong, H. Park and J. Yoon, "The Cold Model Study on the Decarburization Rate inOxygen Steelmaking Processes by CO2/KOH System", ISIJ International, Volume30,No 9, 1990, pp 748-755.50. S. Chung, J. Zong, H. Park and J. Yoon, "The Effect of the Gas Jet on the Gas/LiquidReactivity in the Metallurgical Vessel", ISIJ International, Volume 31, No 1, 1991, pp69-75.51. A. Chatterjee, D. H. Wkelin and A. V. Bradshaw, "Mass Transfer from an Oxygen Jetto Liquid Silver", Metallurgical Transactions, Volume 3, December 1972, pp 3167-3172.52. J. Szekely and N. J. Themelis, "Rate Phenomena In Process Metallurgy",  JohnWiley & Sons, Inc., 1971.53. A. Chatterjee and A. V. Bradshwaw, "The Influence of Gas Phase Resistance on MassTransfer to a Liquid Metal", Metallurgical Transactions, Volume 4, May 1973, pp1359-1364.54. S. Taniguchi, A. Kikuchi, H. Matsuzaki and N. Bessho, "Dispersion of Bubbles andGas-Liquid Mass Transfer in a Gas-Stirred System", Transactions ISM Volume 28,1988, pp 262-270.55. J. K. Brimacombe and F. Weinberg, "Observations of Surface Movements of LiquidCopper and Tin", Metallurgical Transactions, Volume 3, August 1972, pp 2298-2299.56. R. G. Barton and J. K. Brimacombe, "Influence of Surface Tension-Driven Flow onthe Kinetics of Oxygen Absorption in Molten Copper", Metallurgical Transactions,Volume 8B, September 1977, pp 417-427.57. H. Jalkanen, "Phenomenology of the Oxidation Kinetics of Molten Cuprous Sulphideand Copper", Scandinavian Journal of Metallurgy 10, 1981, pp 257-262.58. J. K. Brimacombe, A. A. Bustos, D. Jorgenson and G. G. Richards, "Toward a BasicUnderstanding of Injection Phenomena in the Copper Converter", Physical Chemistryof Extractive Metallurgy, Edited by V. Kudryk and Y. K. Rao, Warrendale, PA: TheMetallurgical Society, 1985, pp 327-351.18259. G.G. Richards, K. J. Legeard, A. A. Bustos, J. K. Brimacombe and D. Jorgenson,"Bath Slopping and Splashing in the Copper Converter", The Reinhardt Schuhmann International Symposium., Warrendale, PA: The Metallurgical Society, 1987, pp 385-402.60. J. Liow and N. B. Gray, "Slopping Resulting from Gas Injection in a Peirce-SmithConverter, Metallurgical Transactions, Volume 21B, 1990, pp 657-664 and 987-996.61. H. H. Kellogg and C. Diaz, "Bath Smelting Processes in Non-Ferrous Pyrometallurgy:An Overview", Proceedings of the Savard/Lee International Symposium on BathSmelting, Edited by J. K. Brimacombe, P. J Mackey, G. J. W. Kor, C. Bickert and M.G. Ranade, The Minerals, Metals & Materials Society, 1992, pp 39-65.62. Y. Kishimoto, T. Sakuraya and T. Fujii, "Recent Advances in Top and BottomBlowing Converters Based on a Mathematical model", Proceedings of the Savard/LeeInternational Symposium on Bath Smelting, Edited by J. K. Brimacombe, P. JMackey, G. J. W. Kor, C. Bickert and M. G. Ranade, The Minerals, Metals &Materials Society, 1992, pp 293-323.63. M. Sano and k. Mori, "Fundamentals of Gas Injection in Refining Processes",Proceedings of the Savard/Lee International Symposium on Bath Smelting, Edited byJ. K. Brimacombe, P. J Mackey, G. J. W. Kor, C. Bickert and M. G. Ranade, TheMinerals, Metals & Materials Society, 1992, pp 465-492.64. N. B. Gray and M. Nilmani, "Injection in Matte Converting and Metal Refining",Proceedings of the Savard/Lee International Symposium on Bath Smelting, Edited byJ. K. Brimacombe, P. J Mackey, G. J. W. Kor, C. Bickert and M. G. Ranade, TheMinerals, Metals & Materials Society, 1992, pp 523-551.65. G. G. Richards, "Submerged Injection in Non-Ferrous Processes", Proceedings of the Savard/Lee International Symposium on Bath Smelting, Edited by J. K. Brimacombe,P. J Mackey, G. J. W. Kor, C. Bickert and M. G. Ranade, The Minerals, Metals &Materials Society, 1992, PP 553-563.66. G. J. Hadie, I. F. Taylor, J. M. Ganser, J. K. Wright, M. P. Davis and C. W. Boon,"Adoption of Injection Technology for the HIsmeltTM Process", Proceedings of theSavard/Lee International Symposium on Bath Smelting, Edited by J. K. Brimacombe,P. J Mackey, G. J. W. Kor, C. Bickert and M. G. Ranade, The Minerals, Metals &Materials Society, 1992, pp 623-644.67. G. Savard and R. G. H. Lee, "Submerged Oxygen Injection for Pyrometallurgy",Proceedings of the Savard/Lee International Symposium on Bath Smelting, Edited byJ. K. Brimacombe, P. J Mackey, G. J. W. Kor, C. Bickert and M. G. Ranade, TheMinerals, Metals & Materials Society, 1992, pp 645-660.68. T. Emi, W. Boorstein and R. D. Pehlke, "Absorption of Gaseous Oxygen by LiquidIron", Metallurgical Transactions, Volume 5, September 1974, pp 1959-1966.69. J. J. Byerley, G. L. Rempel and N. Takebe, "Interaction of Copper Sulphide withCopper Oxides in the Molten State", Metallurgical Transactions, Volume 5,December 1974, pp 2501-2506.18370. H. H. Kellogg vs. J. Byerley, G. L. Rempel and N. Takebe, "Discussion of Interactionof Copper Sulphide with Copper Oxides in the Molten State", MetallurgicalTransactions, Volume 6B, January 13 1975, pp 350-351.71. G. Rottmann and W. Wuth, "Conversion of Copper Matte by Use of the Top-BlowingTechnique", Copper Metallurgy: Practice and theory, Edited by M. J. Jones, TheInstitution of Mining and Metallurgy, 1975, pp 49-52.72. C. F. Acton and G. R. Belton, "On the Kinetics of Oxidation of Liquid Copper andCopper-Sulphur Alloys by Carbon Dioxide", Metallurgical Transactions, Volume 7B,December 1976, pp 693-697.73. V. A. Bryukvin, 0. I. Tsybin, L. I. Blokhina and G. N. Zviadadze, "An Investigationof the Oxidation Kinetics of a Copper Sulphide Melt with Oxygen", UDC 669: 546.221, (Moscow), 1976, pp 24-27.74. V. A. Bryukvin, 0. I. Tsybin, L. I. Blokhina and G. N. Zviadadze, "PhaseComposition of Oxidation Products of Molten Copper Sulphide", UDC 669.332,(Moscow), 1977, pp 51-53.75. R. H. Radzilowski and R. D. Pehlke, "Absorption of Gaseous Oxygen by LiquidCobalt, Copper , Iron and Nickel", Metallurgical Transactions, Volume 9B, March1978, pp 129-137.76. Y. Fukunaka, K. Nishikawa, H. S. Sohn and Z. Asaki, "Desulphurization Kinetics ofMolten Copper by Gas Bubbling", Metallurgical Transactions, Volume 22B, February1991, pp 5-11.77. Z. Asaki, Y. Chiba, T. Oishi and Y. Kondo, "Kinetic Study on the Reaction of SolidSilica with Molten Matte", Metallurgical Transactions, Volume 21B, February 1990,pp 19-25.78. R. Ohno, "Desulphurization and Deoxidation of Cu-S-0 Alloy in Induction Meltingand Solidification under Argon and their Rates of Elimination in Vacuum InductionMelting", Metallurgical Transactions, Volume 22B, August 1991, pp 405-416.79. R. B. Bird, W. E. Stewart and E. N. Lightfoot, "Transport Phenomena",  John Wiley& Sons, Inc. New York, 1960, pp 570.80. J. T. Davies and E. K. Rideal, "Interfacial Phenomena", Academic Press, NewYork, 1961.81. J. K. Brimacombe, A. D. Graves and D. Inman, "Origins of Spontaneous Movementsat Interfaces Between Amalgams and Aqueous Electrolyte", Chemical EngineeringScience, 25, 1970, pp 1917-2008.82. J. K. Brimacombe and F. D. Richardson, "Mass Transfer and Interfacial Phenomenain Bubble-Agitated Systems", Transactions of The Institution of Mining andMetallurgy, Section C: Mineral Process and Extractive Metallurgy, 80, 1971, pp 140-151.18483. J. K. Brimacombe, "Interfacial Turbulence in Liquid-Metal Systems", Physical Chemistry of Process Metallurgy: The Richardson Conference, The Institution ofMining and Metallurgy, 1974, pp 175-185.84. F. D. Richardson, "Interfacial Phenomena in Metallurgical Reactions", Special Lecture, Transactions ISIJ, Volume 14, 1974, pp 1-8.85. R. G. Barton and J. K. Brimacombe, "Interfacial Turbulence during Dissolution ofSolid Cu2S in Molten Copper", Metallurgical Transactions, Volume 7B, March 1976,pp 144-145.86. P. L. T. Brian, "Effect of Gibbs Adsorption on Marangoni Instability", AICHEJournal, Volume 17, No. 4, July 1971, pp 765-672.87. K. Monma and H. Suto, "Effect of Dissolved Sulphur, Oxygen, Selenium andTellurium on the Surface Tension of Liquid Copper", Transactions of JIM, Volume 2,1961, pp 148-153.88. J. C. Berg and A. Acrivos, "The Effect of Surface Active Agents on Convection CellsInduced Surface Tension", Chemical Engineering Science, Volume 20, 1965, pp 737-745.89. R. E. Davis and A. Acrivos, "The Influence of Surfactants on the Creeping Motion ofBubbles", Chemical Engineering Science, Volume 21, 1966, pp 681-685.90. J. C. Berg and C. R. Morig, "Density Effects in Interfacial Convection", Chemical Engineering Science, Volume 24, 1969, pp 937-946.91. 0. Smigelschi, D. G. Suciu and E. Ruckenstein, "Absorption under the Action ofArtificially Provoked Marangoni Effect", Chemical Engineering Science, Volume 24,1969, pp 1227-1234.92. P. P. Pugachevich and V. B. Lazarev, "Surface Phenomena in Ternary MetalSolutions", The Role of Surface Phenomena in Metallurgy, Edited by V. N.Eremenko, Consultants Bureau New York, 1963, pp 24-30.93. Y. V. Naidich, V. N. Eremenko, V. V. Fesenko, M. I. Vasiliu and L. F. Kirichenko,"Variation of the Surface Tension of Pure Copper with Temperature", The role ofSurface Phenomena in Metallurgy, Edited by V. N. Eremenko, Consultants BureauNew York, 1963, pp 41-45.94. P. P. Pugachevich and V. I. Yashkichev, "Measurement of Surface Tension of LiquidMetals at High Temperatures", The Role of Surface Phenomena in Metallurgy, Editedby V. N. Eremenko, Consultants Bureau New York, 1963, pp 46-53.95. V. N. Eremenko, Y. V. Naidich, "Surface Activity of Oxygen in the Silver-OxygenSystem", The Role of Surface Phenomena in Metallurgy, Edited by V. N. Eremenko,Consultants Bureau New York, 1963, pp 65-67.96. V. V. Fesenko, "Determination of the Surface Tension by the Method of theMaximum Pressure in a Bubble for Nonwetting Systems", The Role of SurfacePhenomena in Metallurgy, Edited by V. N. Eremenko, Consultants Bureau New York,1963, pp 80-84.18597. Bernard and C. H. P. Lupis, "The Surface Tension of Liquid Silver Alloys: Part II.Ag-O Alloys", Metallurgical Transactions, Volume 2, November 1971, pp 2991-2998.98. Rubin and C. J. Radke, "Dynamic Interfacial Tension Minima in Finite Systems",Chemical Engineering Science, Volume 35, 1980, pp 1129-1138.99. F. D. Richardson, "Interfacial Phenomena and Metallurgical Processes", CanadianMetallurgical Quarterly, Volume 21, No. 2, 1982, pp 111-119.100.J. C. Berg, "Interfacial Hydrodynamics: An Overview", Canadian Metallurgical Quarterly, Volume 21, No. 2, 1982, pp 121-136.101.G. R. Belton, "The Interplay Between Strong Adsorption of Solutes and InterfacialKinetics at the Liquid Metal Surface", Canadian Metallurgical Quarterly, Volume 21,No. 2, 1982, pp 137-143.102.K. W. Lange and M. Wilken, "Marangoni Type Interfacial Phenomena In High andLow temperature Systems", Canadian Metallurgical Quarterly, Volume 22, No. 3,1983, pp 321-326103.J. C. Slattery, "Interfacial Transport Phenomena", Springer-Verlag, New York,1990.104.C. Choo, K. Mukai and J. M. Toguri, "Marangoni Interaction of a Liquid DropletFalling onto a Liquid Pool", Welding Research Supplement, April 1992, pp 139-146.105.J. B. Kennedy and A. M. Neville, "Basic Statistical Methods For Engineers andScientists", 2nd Edition, New York, 1976, pp 255-276.106.D. A. Skoog and D. M. West, "Fundamentals of Analytical Chemistry",  FourthEdition, CBS College Publishing, 1982, pp 740-743.107.D. A. Skoog and D. M. West, "Fundamentals of Analytical Chemistry",  FourthEdition, CBS College Publishing, 1982, pp 195-216.108.D. A. Skoog and D. M. West, "Fundamentals of Analytical Chemistry",  FourthEdition, CBS College Publishing, 1982, pp 696.109.J. 0. Hirschelder, C. F. Curtiss, R. B. Bird, "Molecular Theory of Gases and Liquids", John Wiley & Sons, Inc., New York, 1954, pp (528, 604-605).110.J. 0. Hirschelder, C. F. Curtiss, R. B. Bird, "Molecular Theory of Gases andLiquids", John Wiley & Sons, Inc., New York, 1954, pp (530).111.N. H. Chen and D. F. Othmer, "New Generalized Equation for Gas DiffusionCoefficient", Journal of Chemical Engineering Data, Volume 7, No. 1, January 1962,pp (37-41).112.R. B. Bird, W. E. Stewart and E. N. Lightfoot, "Transport Phenomena", John Wiley& Sons, Inc. New York, 1960, pp 744.113.J. J. Byerley and N. Takebe, "Densities of Molten Nickel Mattes", MetallurgicalTransactions, Volume 2, April 1971, pp 1107-1111.186114.D. R. Gaskell, "Introduction To Metallurgical Thermodynamics", Second Edition,McGraw-Hill Book Company, New York, 1981, pp 164-167.115.F. D. Richardson, "Physical Chemistry of Melts in Metallurgy", Volume 1,Academic Press Inc., New York, 1974, pp 61-62.116.F. D. Richardson, "Physical Chemistry of Melts in Metallurgy", Volume 2,Academic Press Inc., New York, 1974, pp 318-325.117.L. Coudurier, D. W. Hopkins, I. Wilkomirsky, "Fundamentals of MetallurgicalProcesses", 2nd Edition, Pergamon Press, 1985, pp 225-227.118.T. Rosenquist, "Principles of Extractive Metallurgy", 2nd Edition, McGraw-Hill,New York, 1983, pp 105-106.119.J. B. Kennedy and A. M. Neville, "Basic Statistical Methods For Engineers andScientists", 2nd Edition, New York, 1976, pp 232,460-461.120.R. B. Bird, W. E. Stewart and E. N. Lightfoot, "Transport Phenomena",  John Wiley& Sons, Inc. New York, 1960, pp 601-619.121.G. H. Geiger and D. R. Poirier, "Transport Phenomena In Metallurgy", Addison-Wesley, 1973, pp 527.Appendix A Experimental 1. Reactor Insulating MaterialsInsulating alumina refractories (Alundum L) were supplied by NORTONREFRACTORIES. The supplied properties of this insulating material are as follows:Table A.1. Physical properties of the insulating alumina brick.Bulk Density 1.36 (g/cm3)Total Porosity 65-70%Maximum Operating Temperature 1850 °CCompressive Deformation at 1500 °C 0 % to 10 p.s.i.Thermal Conductivity at 860 °C 0.89 (watt/m.°K)Thermal Expansion from 21-1510 °C 1.02x10-5 (°C-1)Table A.2. Chemical analysis (approximate).Alumina (Al203) 99.01%Silica (SiO2) 0.58%Other 0.41%187188Porcelain wool (refractory fibrous material) was supplied by THE CARBORUNDUMCOMPANY. REFRACTORY DIVISION. The manufacturer supplied properties of thisinsulating material are as follows:Table A.3. Thermal conductivity as a function of mean temperature (0.08 /cm3).Temperature (°C) 200 427 760 980Thermal Conductivity (watt/m.°K) 0.66 1.12 2.08 3.11Table A.4. Approximate chemical analysis wt % - binder removed).Silica (SiO2) 46.8Alumina (Al203) 50.9B2O3 1.2Na2O 0.8Trace Inorganic 0.3-0.5MI )234To HeatingElementsC?2. Reactor Power Supply189KAB 25 ON-OFF i^RelayPRD-7AY0-120^S.S. RelaySSR240D4525:5 CT220 VACKAB 25i^—h^315AO.OB.OWall•Ia.Vb.Pt-Pt 10% RhThermocoupleL6 10 9C. N.O.51120 1VAC2N220 V/120 VAutotransformer-CN 9121Omega MicroprocessorTemperature ControllerFigure A.1. Electrical circuit for the furnace power supply.Compression StrainGaugeTension StrainGaugeCompression StrainGaugeTension StrainGauge+ Exc- Sig OutTo Daytronic Strain GaugeSignal Conditioner- Exc- Sig Out3. Load Cell ComponentsTable A.5. Strain gauges manufacturer (HBM ELEKRISCHES MESSENMECHANISCHER GRÔSSEN) specifications.Gauge factor 2.05 ± 1 %Temperature coefficient of gauge factor 95 ppm/°KResistance 120 S2 ± 0.02 %Figure A.2. Circuit design of the load cell.190Appendix B Gas Analysis Raw Data191Table B.1. Run No. 4, the data for theexperimental conditions of: 922 ml/min of26% 02 and 74% Ar, at 1200 °C, 1.05 atmpressure, ambient temperature of 23 °C,average final gas temperature of 23 °C #.Time Nso, (t) efff (t) 84 (t)(min) (mole) (ml/min) (ml/min)0 0.0005 0.00010 0.03215 0.07520 0.08430 0.10840 0.16350 0.22460 0.28470 0.36780 0.45190 0.526100 0.605110 0.694120 0.769Table B.2. Run No. 5, the data for theexperimental conditions of: 922 ml/min of26% 02 and 74% Ar, at 1200 °C, 1.05 atmpressure, ambient temperature of 23 °C,average final as temperature of 23 °C 4.Time Ns02 (t) aofff (t) 84 (t)(mm) (mole) (ml/min) (ml/min)0 0.0005 0.03810 0.06715 0.08620 0.11730 0.16340 0.19750 0.26660 0.35270 0.42680 0.49790 0.584100 0.669110 0.751120 0.835It This run was carried out using prepared Cu2S (20.30% sulphur and 79.05% copper).192Table B.3. Run No. 6, the data for theexperimental conditions of: 922 ml/min of26% 02 and 74% Ar, at 1200 °C, 1.05 atmpressure, ambient temperature of 23 °C,average final gas temperature of 25 °C.Time N0(t) aoff. (t) 84 (t)(min) (mole) (ml/min) (ml/min)0 0.0005 0.01910 0.04915 0.07820 0.10830 0.13140 0.17150 0.20360 0.25570 0.34080 0.43990 0.528100 0.611110 0.716120 0.804Table B.4. Run No. 7, the data for theexperimental conditions of: 922 ml/min of26% 02 and 74% Ar, at 1200 °C, 1.05 atmpressure, ambient temperature of 23 °C,average final gas temperature of 25 °C.Time Nso, (t) 4(0 Saf,ff (t)(min) (mole) (ml/min) (ml/min)0 0.000 0 05 0.019 756 910 0.044 749 815 0.07220 0.10425 0.131 744 730 0.166 747 1435 0.203 748 1840 0.246 760 1445 0.286 745 450 0.329 746 1155 0.374 744 160 0.416 751 1080 0.603 754 11100 0.778 746 8120 0.963 758 10140 1.142 744 1160 1.137193Table B.5. Run No. 8, the data for theexperimental conditions of: 1010 ml/min of24% 02 and 76% Ar, at 1200 °C, 1.05 atmpressure, ambient temperature of 23 °C,average final gas temperature of 24 °C.Time Ns02 (t) V:17. (t) 84 (t)(min) (mole) (ml/min) (ml/min)0 0.000 0 05 0.031 798 710 0.061 783 1215 0.089 789 1620 0.117 776 1025 0.145 789 1230 0.174 803 1435 0.213 799 1940 0.251 788 1745 0.295 797 2150 0.333 796 955 0.372 801 860 0.415 792 980 0.588 814 3100 0.757 823 15120 0.971 816 19140 1.120 817 20160 1.156 814 7180 1.165 822 15Table B.6. Run No. 9, the data for theexperimental conditions of: 1480 ml/min of22% 02 and 79% Ar, at 1200 °C, 1.07 atmpressure, ambient temperature of 23 °C,average final gas temperature of 23 °C.Time Ns02 (t) a° ff. (t) 84 (t)(min) (mole) (ml/min) (ml/min)0 0.000 0 05 0.037 1213 1410 0.077 1235 1115 0.120 1222 220 0.153 1220 825 0.203 1221 430 0.263 1198 435 0.319 1194 2140 0.373 1213 1045 0.432 1192 1250 0.498 1179 2355 0.556 1178 1560 0.627 1218 2880 0.889 1209 13100 1.107 1195 10120 1.123 1243 17140 1.118 1287 16160 1.150 1326 11194Table B.7. Run No. 10, the data for theexperimental conditions of: 2078 ml/min of20% 02 and 80% Ar, at 1200 °C, 1.07 atmpressure, ambient temperature of 23 °C,average final gas tem erature of 24 °C.Time Ns02 (t) go ff. (t) 84 (t)(min) (mole) (ml/min) (ml/min)0 0.000 0 05 0.050 1620 1010 0.105 1665 1915 0.152 1677 4120 0.207 1688 1225 0.271 1712 1730 0.345 1663 1635 0.416 1665 1940 0.483 1639 1545 0.555 1677 4150 0.627 1639 1555 0.697 1665 1960 0.750 1677 4165 0.826 1665 1970 0.89675 0.976 1639 1580 1.055 1677 4185 1.106 1665 19Table B.8. Run No. 11, the data for theexperimental conditions of: 1987 ml/min of20% 02 and 80% Ar, at 1200 °C, 1.05 atmpressure, ambient temperature of 23 °C,average final gas tem erature of 25 °C.Time Ns02 (t) Q.01ff. (t),84 (t)(min) (mole) (ml/min) (ml/min)0 0.000 0 05 0.036 1607 610 0.088 1604 515 0.136 1673 1120 0.194 1691 1425 0.256 1703 1230 0.32635 0.387 1695 440 0.461 1690 1145 0.534 1680 1250 0.592 1690 1055 0.657 1685 1460 0.726 1689 465 0.802 1640 770 0.872 1670 2275 0.956 1676 680 1.014 1675 1485 1.016 1972 1190 1.018 1578 3195Table B.9. Run No 12, the data for theexperimental conditions of: 1580 ml/min of22% 02 and 78% Ar, at 1200 °C, 1.06 atmpressure, ambient temperature of 25 °C,average final as tem erature of 25 °C.Time N0(t) af:ff (t) 84 (t)(mm) (mole) (ml/min) (ml/min)0 0.0001 0.0052 0.0123 0.0114 0.02310 0.07915 0.12020 0.16925 0.23130 0.29535 0.36740 0.43545 0.51250 0.58855 0.665Table B.10. Run No. 13, the data for theexperimental conditions of: 1521 ml/min of20% 02 and 80% Ar, at 1200 °C, 1.08 atmpressure, ambient temperature of 27 °C,average final gas temperature of 26 °O. .Time Ns02 (t) aoff. (t) 8Q,f,ff (t)(mm) (mole) (ml/min) (ml/min)0 0.000 0 01 0.002 1234 22 0.0063 0.0134 0.0175 0.02510 0.060 1238 615 0.100 1236 620 0.140 1233 725 0.191 1231 1730 0.250 1218 035 0.312 1224 440 0.366 1218 650 0.484 1253 460 0.611 1259 1270 0.734 1244 1380 0.869 1217 1290 0.987 1232 1399 1.076 1240 23of . Approximately 2 mm inside diameter alumina lance was used in this run.196Table B.11. Run No. 14, the data for theexperimental conditions of: 1530 ml/min of21% 02 and 79% Ar, at 1200 °C, 1.07 atmpressure, ambient temperature of 22 °C,average final as temperature of 22 °C#.. .Time N0(t) af,ff (t) 8Q/0; (t)(min) (mole) (ml/min) (ml/min)0 0.000 0 05 0.027 1236 710 0.063 1250 1415 0.104 1247 1020 0.130 1247 925 0.180 1250 630 0.215 1262 840 0.317 1267 850 0.433 1260 860 0.555 1252 1870 0.652 1245 1480 0.810 1220 4690 0.947 1245 1495 1.010 1236 9Table B.12. Run No. 15, the data for theexperimental conditions of: 2006 mUmin of22% 02 and 78% Ar, at 1200 °C, 1.07 atmpressure, ambient temperature of 26 °C,average final gas temperature of 27 °C.Time Ns02 (t) Q.0 ff. (t) 8Q.offf (t)(min) (mole) (ml/min) (ml/min)0 0.000 0 05 0.047 1614 1510 0.099 1598 1615 0.131 1635 1420 0.213 1664 1325 0.306 1617 830 0.416 1653 1335 0.464 1645 1240 0.553 1636 1245 0.611 1647 750 0.707 1668 3155 0.793 1672 2260 0.876 1631 1665 0.952 1635 570 1.040 1639 875 1.087 1668 13.ff.. Approximately 2 mm inside diameter alumina lance was used in this run. Prepared Cu2S, ofapproximately 19% sulphur and 77.05% copper, was used in this run.197Table B.13. Run No. 16, the data for theexperimental conditions of: 2510 ml/min of23% 02 and 77% Ar, at 1200 °C, 1.08 atmpressure, ambient temperature of 25 °C,average final as tem erature of 25 °C.Time Nso, (t) 4(0 84 (t)(mm) (mole) (mllmin) (ml/min)0 0.000 0 05 0.039 2196 1310 0.095 2124 615 0.156 2111 3520 0.253 2089 4325 0.342 2077 4030 0.444 2059 6235 0.542 2066 8540 0.641 2067 10445 0.747 2064 9350 0.847 2058 7055 0.939 2045 3060 1.031 2194 21165 1.072 2270 241Table B.14. Run No. 17, the data for theexperimental conditions of: 1755 ml/min of22% 02 and 78% Ar, at 1200 °C, 1.07 atmpressure, ambient temperature of 22 °C,average final gas tem erature of 24 °C.Time Ns02 (t) Q(t) 84 (t)(mm) (mole) (ml/min) (ml/min)0 0.000 0 05 0.030 1425 1310 0.078 1445 715 0.120 1455 1420 0.171 1442 6425 0.234 1439 9230 0.300 1410 2135 0.370 1384 5740 0.430 1508 5945 0.500 1467 2650 0.564 1557 1755 0.637 1414 1860 0.703 1399 765 0.763 1440 1870 0.835 1422 1075 0.908 1436 7198Table B.15. Run No. 18, the data for theexperimental conditions of: 2230 ml/min of23% 02 and 77% Ar, at 1200 °C, 1.08 atmpressure, ambient temperature of 23 °C,average final gas tem erature of 23 °C.Time Nso, (t) Qf,ff (t) SQL. (t)(min) (mole) (ml/min) (ml/min)0 0.000 0 05 0.033 1863 2910 0.086 1894 615 0.145 1881 1720 0.239 1839 9625 0.327 1865 6430 0.420 1831 4835 0.516 1868 6340 0.606 1860 4645 0.698 1962 4550 0.782 1956 12055 0.876 1812 1760 0.959 1849 365 1.043 1862 2269 1.071 1899 7Table B.16. Run No. 19, the data for theexperimental conditions of: 3015 ml/min of22% 02 and 78% Ar, at 1200 °C, 1.07 atmpressure, ambient temperature of 26 °C,average final gas temperature of 27 °C" .Time Nso, (t) Q-0 fff (t) Saofff (t)(min) (mole) (ml/min) (ml/min)0 0.000 0 02 0.020 2435 54 0.0665 0.0896 0.1108 0.17310 0.214 2377 241520 0.492 2375 4725 0.637 2454 1730 0.762 2526 1035 0.877 2476 2940 0.979 2470 2744 1.051 2556 19It° The lance nozzle was located at the melt surface in this run. In all of the other runs the initial lance tomelt surface was fixed at approximately 1 cm.199Table B.17. Run No. 21, the data for theexperimental conditions of: 4055 ml/min of22% 02 and 78% Ar, at 1200 °C, 1.13 atmpressure, ambient temperature of 26 °C,average final gas tem erature of 26 °C.Time Nso, (t) aofff (t) 84 (t)(mm) (mole) (ml/min) (ml/min)0 0.000 0 02 0.023 3448 634 0.0495 0.0556 0.0748 0.109 3514 3310 0.145 3507 2715 0.262 3429 3220 0.371 3480 1925 0.497 3507 3630 0.630 3518 17635 0.775 3526 6540 0.938 3429 25Table B.18. Run No. 22, the data for theexperimental conditions of: 2006 ml/min of27% 02 and 73% Ar, at 1200 °C, 1.10 atmpressure, ambient temperature of 26 °C,average final gas tem erature of 26 °C.Time Nso, (t) afo:ft. (t) 84 (t)(mm) (mole) (ml/min) (ml/min)0 0.000 0 02 0.016 1528 344 0.0375 0.0476 0.0618 0.09110 0.11415 0.207 1525 1020 0.304 1523 1725 0.408 1526 1330 0.515 1516 1035 0.629 1487 2440 0.735 1513 345 0.855 1499 950 0.968 1502 755 1.044 1534 27200Table B.19. Run No. 23, the data for theexperimental conditions of: 2009 ml/min of35% 02 and 65% Ar, at 1200 °C, 1.10 atmpressure, ambient temperature of 21 °C,average final gas temperature of 21 °C.Time Ns02 (t) 4(0 84 (t)(min) (mole) (ml/min) (ml/min)0 0.000 0 02 0.018 1503 224 0.050 1415 55 0.069 1457 86 0.083 1463 128 0.120 1452 2410 0.154 1457 2015 0.268 1459 2320 0.393 1441 2125 0.532 1459 830 0.664 1446 4635 0.822 1432 1240 0.945 1416 1745 1.045 1419 6649 1.038 1377 35Table B.20. Run No. 24, the data for theexperimental conditions of: 1997 ml/min of46% 02 and 54% Ar, at 1200 °C, 1.10 atmpressure, ambient temperature of 24 °C,average final gas temperature of 24 °C.Time Nso, (t) 4(0 84 (t)(min) (mole) (mil/min) (ml/min)0 0.000 0 02 0.029 1339 904 0.086 1208 245 0.108 1270 546 0.140 1185 258 0.202 1196 7510 0.265 1177 1715 0.447 1176 820 0.623 1176 925 0.804 1180 1430 0.982 1202 1235 1.071 1204 5439 1.081 1179 6201Table B.21. Run No. 25, the data for theexperimental conditions of: 1997 ml/min of64% 02 and 36% Ar, at 1200 °C, 1.10 atmpressure, ambient temperature of 22 °C,average final gas temperature of 22 °C.Time Ns02 (t) 4(0 84 (t)(min) (mole) (ml/min) (ml/min)0 0.000 0 02 0.046 1005 2524 0.128 809 225 0.156 777 26 0.2028 0.302 765 1410 0.39815 0.644 810 1520 0.911 796 625 1.066 789 4629 1.066 807 10Table B.22. Run No. 27, the data for theexperimental conditions of: 1998 ml/min of23% 02 and 77% Ar, at 1250 °C, 1.13 atmpressure, ambient temperature of 23 °C,average final gas temperature of 23 °C.Time Ns02 (t) efff (t).,8Q-offf (t)(min) (mole) (ml/min) (ml/min)0 0.000 0 02 0.014 1570 134 0.028 1684 95 0.045 1624 126 0.051 1648 368 0.068 1619 610 0.094 1709 4215 0.151 1657 920 0.220 1670 1725 0.301 1650 1029 0.372 1639 1835 0.447 1624 1240 0.538 1639 1845 0.617 1679 2850 0.708 1677 2755 0.804 1672 3260 0.848202Table B.23. Run No. 28, the data for theexperimental conditions of: 1999 ml/min of23% 02 and 77% Ar, at 1300 °C, 1.08 atmpressure, ambient temperature of 22 °C,average final gas temperature of 22 °C.Time Ns02 (t) aof.ff. (t) SQ-ofli. (t)(min) (mole) (ml/min) (ml/min)0 0.000 0 02 0.013 1675 574 0.024 1660 415 0.0276 0.0708 0.07610 0.096 1617 315 0.156 1627 1320 0.22825 0.315 1632 1529 0.372 1652 3035 0.463 1627 1940 0.543 1631 1645 0.619 1623 1250 0.719 1589 2255 0.797 1601 1960 0.873 1648 3165 0.931 1687 6370 0.992 1673 8Table B.24. Run No. 29, the data for theexperimental conditions of: 1994 ml/min of21% 02 and 79% Ar, at 1275 °C, 1.08 atmpressure, ambient temperature of 24 °C,average final gas temperature of 24 °C.Time Ns02 (t) Q(t) 8a0fif (t)(min) (mole) (ml/min) (ml/min)0 0.000 0 02 0.014 1674 654 0.0296 0.0378 0.06910 0.083 1687 4115 0.125 1686 3320 0.17825 0.24530 0.30135 0.37040 0.43245 0.49850 0.57355 0.63060 0.729 1662 1665 0.805 1680 1970 0.888 1665 14203Table B.25. Run No. 30, the data for theexperimental conditions of: 2006 ml/min of22% 02 and 78% Ar, at 1325 °C, 1.08 atmpressure, ambient temperature of 25 °C,average final gas temi,erature of 24 °C.Time Nso, (t) Q(t) 6Q47(t)(min) (mole) (ml/min) (ml/min)0 0.000 0 02 0.009 1632 134 0.029 1629 135 0.043 1625 56 0.057 1634 18 0.083 1637 510 0.103 1635 415 0.166 1633 920 0.243 1634 1525 0.327 1637 1230 0.403 1632 1035 0.481 1633 1040 0.570 1617 545 0.654 1600 1350 0.738 1605 2855 0.828 1602 1660 0.907 1640 2565 0.975 1654 670 1.043 1684 974 1.045 1652 8Table B.26. Run No. 31, the data for theexperimental conditions of: 2006 ml/min of22% 02 and 78% Ar, at 1275 °C, 1.08 atmpressure, ambient temperature of 23 °C,average final gas tem erature of 21 °C.Time Ns02 (t) Q(t) 84 (t)(min) (mole) (ml/min) (ml/min)0 0.000 0 02 0.008 1626 14 0.029 1597 45 0.044 1611 36 0.057 1626 138 0.071 1626 1310 0.105 1627 1315 0.166 1625 720 0.245 1614 525 0.331 1609 1030 0.418 1597 2335 0.538 1596 1340 0.606 1595 345 0.687 1596 1950 0.784 1603 1155 0.881 1599 1360 0.975 1605 865 1.028 1607 1768 1.053 1624 31204Table B.27. Run No. 33, the data for theexperimental conditions of: 3490 ml/min of27% 02 and 73% Ar, at 1200 °C, 1.11 atmpressure, ambient temperature of 24 °C,average final gas temperature of 22 °C.Time Ns02 (t) Q.0 fff. (t) 84 (t)(min) (mole) (ml/min) (ml/min)0 0.000 0 02 0.012 3039 214 0.051 3119 185 0.062 3073 06 0.086 3196 328 0.110 3145 4110 0.163 3289 2815 0.295 3271 3720 0.438 2883 6425 0.581 2827 3930 0.765 2787 5035 0.924 2806 2438 1.042 2798 37Table B.28. Run No. 34, the data for theexperimental conditions of: 1996 ml/min of78% 02 and 22% Ar, at 1200 °C, 1.11 atmpressure, ambient temperature of 23 °C,average final as temperature of 22 °C.Time N0(t) Qcf,ff (t) 84 (t)(min) (mole) (ml/min) (ml/min)0 0.000 0 02 0.066 447 204 0.157 426 135 0.217 436 36 0.264 471 88 0.390 476 1110 0.498 479 1712 0.629 489 1714 0.74115 0.836 486 216 0.882 428 218 0.999 481 3620 1.033 384 1822 1.049 406 18205Table B.29. Run No. 36, the data for theexperimental conditions of: 2032 rnl/min of22% 02 and 78% Ar, at 1200 °C, 1.08 atmpressure, ambient temperature of 23 °C,average final gas temperature of 22 °C** .Time Nso, (t) Q(t) 84 (t)(min) (mole) (ml/min) (ml/min)0 0.000 0 02 0.012 1735 64 0.027 1768 295 0.032 1757 126 0.041 1724 238 0.065 1713 1110 0.082 1724 3215 0.148 1717 1920 0.219 1708 1025 0.302 1691 2130 0.391 1711 1035 0.462 1691 1540 0.544 1691 745 0.629 1696 650 0.711 1677 955 0.795 1692 760 0.882 1688 1865 0.969 1693 12Table B.30. Run No. 37, the data for theexperimental conditions of: 2000 ml/min of21% 02 and 79% N2, at 1200 °C, 1.08 atmpressure, ambient temperature of 21 °C,average final gas temperature of 22 °C.Time Ns02 (t) aoff. (t) 84 (t)(min) (mole) (ml/min) (ml/min)0 0.000 0 02 0.012 1590 324 0.024 1616 165 0.042 1603 96 0.048 1645 08 0.060 1639 710 0.077 1651 815 0.117 1631 2320 0.198 1635 725 0.271 1598 1630 0.361 1584 2335 0.451 1608 4740 0.540 1599 1245 0.636 1587 1250 0.713 1582 655 0.801 1594 1360 0.896 1583 1765 0.990 1597 1270 1.018 1559 4** Approximately 77 ml/min argon was used for invoking bath mixing. in this run.Table B.31. Run No. 41, the data for theexperimental conditions of: 3516 ml/min of24% 02 and 76% Ar, at 1200 °C, 1.10 atmpressure, ambient temperature of 24 °C,average final gas temperature of 24 °C.Time Nso, (t) 4(0 84 (t)(mm) (mole) (ml/min) (ml/min)0 0.000 0 02 0.024 3029 644 0.049 3053 135 0.067 2971 826 0.103 3017 408 0.130 2830 1010 0.167 2933 5315 0.261 2889 5020 0.388 2902 11025 0.545 2938 2730 0.690 2888 3635 0.827 2883 4340 1.001 2839 17206Table B.32. The effect of volumetric flow rate of reaction gas on the reaction rates; sample weight of 200 grams of Cu2S; at 1200 °C and 1.08atm; 22% 0 and 78% Ar; lance inside diameter of 3 mm.Run Q° o PN so2 0sN so, 0 PN 02 OsN 02 t * OpW ga OsW ga 0 PW w o^sW w(ml/min) (mol/min) (mol/min) (mol/min) (mol/min) (mm) (g/min) (g/min) (g/min) (g/min)9 1480 0.008 0.012 0.011 0.012 25 -0.18 -0.4212 1579 0.009 0.015 2417 1755 0.009 0.013 0.013 0.013 19 -0.16 -0.45 -0.11 -0.2115 2006 0.009 0.016 0.016 0.015 14 -0.07 -0.5736 2032 0.010 0.016 0.015 0.016 14 -0.17 -0.53 -0.14 -0.6621 4055 0.015 0.026 0.023 0.002 11 -0.21 -0.95Table B.33. The effect of volumetric flow rate of reaction gas on the reaction rates; sample weight of 200 grams of Cu2S; at 1200 °C and 1.08atm; 24% 0 and 76% Ar; lance inside diameter of 3 mm.Run alOpNso2OsNs02OpN 02o sN 02 t*0pW ga0 sW ga0 PW w0 sWi,_ (ml/min) (mol/min) (mol/min) (mol/min) (mol/min) (min) (g/min) (g/min) (g/min) (g/min)8 1010 0.006 0.009 0.009 0.008 36 -0.10 -0.3041 3516 0.018 0.028 0.025 0.028 13 -0.34 -0.92207Table B.34. The effect of reaction gas composition on the reaction rates; sample weight of 200 grams of Cu2S; at 1200 °C and 1.10 atm, 2000ml/min, lance inside diameter of 3 mm.Run %02OpNso2o sN502OpN o2o sN 02 t* OpW gaOsW gaOPWw0 sWw(mol/min) (mol/min) (mol/min) (mol/min) (min) (g/min) (g/min) (g/min) (g/min)15 22 0.009 0.016 0.016 0.015 14 -0.07 -0.5722 27 0.012 0.021 0.020 0.020 11 -0.15 -0.71 -0.1423 35 0.017 0.027 0.024 0.024 11 -0.28 -0.9424 46 0.027 0.036 0.033 0.036 7 -0.67 -1.15 -1.4225 64 0.037 0.050 0.048 0.050 5 -0.81 -1.6334 78 0.048 0.061 0.063 0.061 5 -1.03 -1.95 -0.85 -2.18Table B.35. The effect of temperature on the reaction rates; sample weight of 200 grams of Cu2S; at 1200 °C and 1.09 atm, 2000 ml/min of 22%0 and 78% Ar, lance inside diameter of 3 mm.Run TOpNs020 sN5020pN o2o^sN o2 tOpW gaOsW ga0PWW0 sWW(°C) (mol/min) (mol/min) (mol/min) (mol/min) (min) (g/rnin) (g/min) (g/min) (g/min)15 1200 0.009 0.016 0.016 0.015 14 -0.07 -0.5731 1250 0.012 0.017 0.016 0.017 13 -0.23 -0.57 -0.16 -0.9830 1300 0.013 0.016 0.016 0.016 17 -0.30 -0.53 -0.29 -0.87208Table B.36. The effect of temperature on the reaction rates; sample weight of 200 grams of Cu2S; at 1.09 atm, 2000 ml/min of 23% 02 and 77%Ar, lance inside diameter of 3 mm.Run T. PN so,o^sN so,. PNO2OsNO2 tOpW gao sW gaOPW w0 sW(°C) (mol/min) (mol/min) (mol/min) (mol/min) (min) (g/min) (g/min) (g/min) (g/min)27 1250 0.010 0.016 0.015 0.015 15 -0.19 -0.54 -0.3128 1300 0.012 0.016 0.016 0.016 16 -0.25 -0.49 -0.16 -0.34Table B.37. The effect of bath mixing on the reaction rates; sample weight of 200 grams of Cu2S; at 1200 °C and 1.09 atm, 2000 ml/min of 22%02 and 78% Ar, lance inside diameter of 3 mm (t appoximate1y 77 ml/min Ar was used to invoke artificial mixing).Run Q:. PN so,o^sN so,o PN 02OsN 02OPW gao sW ga0PW wo sWw(nil/min) (mol/min) (mol/min) (mol/min) (mol/min) (min) (g/min) (g/min) (g/min) (g/min)15 2006 0.009 0.016 0.016 0.015 14 -0.07 -0.5736t 2032 0.010 0.016 0.015 0.016 14 -0.17 -0.53 -0.14 -0.66Table B.38. The effect of carrier gas type on the reaction rates; sample weight of 200 grams of Cu2S; at 1200 °C and 1.09 atm, 2000 ml/min of21% 0 and 79% Ar, lance inside diameter of 3 mmRun GasOPNso20 sN so2opN 0,0 sN 0, to PW ga0 sW gaOPW iv0 sW,„Type (mol/min) (mol/rnin) (mol/min) (mol/min) (min) (g/min) (g/min) (g/min)_ (g/min)37 Nitrogen 0.008 0.018 0.015 0.016 16 -0.05 -0.61 -0.04 -0.4529 Argon 0.009 0.014 0.013 0.023 22 -0.18 -0.49 -0.08 -0.51209Appendix C Reaction Gas Transport Properties1. ViscosityThe kth approximation of the coefficient of viscosity is given by Equation (C.1), wherethe function of 4,(k) is a very slowly varying function of T* and differs only slightly fromunity [109].266.93 x10-7 1722(21,2)*(T f12(k)L- Example C.1. This example is to illustrate the procedure for the calculation of theviscosity of a pure gas. The viscosity of pure argon gas at 1200 °C is calculated asfollows: The molecular weight of argon is MAr = 39.948 g/g.mole. The force constantsfor argon are qic= 124°K and a = 3.418A. The reduced temperature is thenT* = KT le = 11.935. The data for the integral S2(2'2)*,for the Lennard-Jones potential(taken from Hirschfelder et al. [109]) was fitted to a function of the reduced temperature,as given by Equation (B.2). The value for argon is 0.819. The higher approximationcoefficient, for the viscosity, is fp(k) =1.0073. Substituting for these values in Equation(C.1), yields gm. = 6.83 x10-4 g/cm.sec.S2(2'2)* =1.208474/T415703The viscosity of binary gas mixtures was calculated as follows [110]:^]]2Example C.2. The viscosity of a gas mixture of 20% 02 and 80% Ar, at 1200 °C, iscalculated, Using Equation (C.3), as given by Equation (B.4). The parameters for 02 gasare the molecular weight of oxygen is M = 31.9988 g/g.mole. The force constants for210(C.1)(C.2)(C.3)775750725.i14 7000.t,".? 675• ^mer■ ^ MINAMMINE6500°625600575211oxygen are Eix= 113°K and a = 3.433A. The reduced temperature is thenT* = KT le = 13.035. The higher approximation coefficient is filk) =1.008. Substitutingfor these values in Equation (C.1), the viscosity of pure 02, at 1200 °C, is calculated tobe 6.16x10-4 g/cm.sec.[  6.84 x10^6.16 x10-40.8 0.21-t A r 02 =[/ 1^ +  ^= 6.67 x 10-4(g / cm. sec)1/-4^1/ The viscosity of Ar-02 gas mixtures for the temperature range of 1000-1500 °C and at 1atm is presented below.5501000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500Temperature (°C)Figure C.1. The viscosity of Ar-02 gas mixtures as a function of temperature, at 1 atm;^ pure Ar;^20% 02,^ 40% 02; — - — - 60% 02; — - - — 80%02,^ pure 02.(C.4)2122. Diffusion CoefficientThe diffusion coefficients of some selected binary gas mixtures are calculated usingEquation (C.5), as given by equations (C.6-C.10) [1111 The critical properties for thesegases are provided in Table B.1. The results of these calculations were found to comparevery favorably with the measured and calculated results of Hirschfelder et al [109], asshown in Figure C.2.DA_B030.43(  T  )1 81(  1  +100^1  )M A MB( 7' 7' )01405 (KA) rPlOCA,00CB0)^[100)0.4^117c0B0)" 2Table C.1. The critical properties of some selected gases (taken from Bird et al. [112]).Gas Tc (°K) Pc (atm) Vc (cm3/mole)Argon 151 48.0 75.2Nitrogen 126.2 33.5 90.1Oxygen 154.4 49.7 74.4Sulphur Dioxide 430.7 77.8 122.00.028565r T 1"DO —Ar =2^P^L1000.0272107 [ TD02-N2=^P^Llooi(C.5)1.81(C.6)(C.7)D ^0.020118r T 11 . 81S02-02 —^P^L1000.020103 7' -11 81DS02-Ar = P^Lim.]0.019287 I TDs02-N2^p^Lloo(C . 1 0)213(C.8)(C.9)1 001 0oE8')C.)t,r.4^1a)CI■1C•110•1z^0.01100 1000^1 0000Temperature (°K)Figure C.2. The diffusion coefficients of some selected binary gas mixtures as a functionof temperature, at 1 atm;^ 02-Ar; 0 02-As (after Hirschfelder, calculated); 0 02-Ar (after Hirschfelder, measured); X 02-N2 (after Hirschfelder, calculated); 0 02-N2(after Hirschfelder, measured); — — — 02-S02;^ N2-S02.PMmix P mix = RT (C.12)(C.13)Mmix = XAM A+ XBMB•••+XzMz2143. DensityAssuming that the gases involved and their mixtures are ideal, the calculation of the gasdensity of a pure gas was done via the following equation:PMAPA =RT (C. 1 1 )The density of a gas mixture was calculated from Equation (C.12), where the molecularweight of the gas mixture was calculated using Equation (C.13). The results of thesecalculations are shown in Figure C.3.0.400.380.360.340.32to0.30'TA 0.28a 0.260.240.220.205.0^ I _^1(4/ SI I MIRIMINIMIIIMMIliali•ErmINIO,■■^ IMIN■Ml■AMIIIMMMIMIE%/11111111MINNINE■INIMMii•••■Mi•■■••11% IiM1llMPNiill1MIE••O•P'■-Ml!?.'dlMlIP"'%IMPCf/I•lM1••lil'■''IMMil-I1•Il_•."d•lIMIMIIr,-...IMMiI•MiMP!r4llMRr/" MCI= MaINIIIMINIMISUMM■^ ...1•1■111■121■-■1•MaIMIPROMPLAMPERNIP"%■12% MIPTMENIPMWMINPIMINIIP."-_./•■■•••alIMMIIIMMEOMINNEIMIMMIMIMI•10,--.M.IIIMPISA■1•MaNINIMIIMIMMMIMP/11111=-.■-aNIP%WaINIENNIIMil■MMOMWW■1/1.1111•M-../..■■■■•••%111/%11•110.3%1M/MMIIMINI■•=1=EMMINOW/M%-■-■•■■■••18■■■■■■1'11•1111"-^111■1•1•M■■allEil■-■11%111•MINI./"/"--a■-■MIMPIMAMIP■IMMPras ..... ■11=MNII,A1•1•%V"-■•■MIN/aMPE21•1%.■ IIIIVAIMPW•ONEall•MMINP/MINN= ..... NMI=MINOMNP!..a1M10--■■■•••■.%•/51•1•2MIIIP///%11■■■■•■• MINII-MIMONN ^IMP/■••■■•■•%..MIEMM1,•/- I ■"--dMIP/_■""■■■■.1.171.1P.:711:1117111111111111111111111111111=I=111 1111671T 1;;IIMMIIIIIIF^IU 5.5 6.0 6.5 7.0 7.5 8.0(1/T) x10-4 ( °K-')Figure C.3. The density of Ar-02 gas mixtures as a function of temperature; for each 10%increments.Appendix D Temperature Measurements21512401235 71230 —- X x XX XXXXXxXXXX1225^ X■-■(1) 1220 —0 0 0 o 0 0 0 0 0^ 0^0^0 0 0tEls,ra,") 121501^AAAAA9210 A^AAAEli)A^A^A^A1205 - 000U 0 aoao X o o1200 -/)-DO^ X^0011950 50 100Time (min)150 200Figure D.1. The manual temperature measurement of the center of the melt; 200 gramsCu2S, at 1200 °C, E Run No. 5. (922 ml/min of 26%02 and 74% Ar); 0 Run No.7 (922ml/min of 26%02 and 74% Ar); A Run No. 8 (1010 ml/min of 24%02 and 76% Ar); 0Run No. 9. (1546 of 24%02 and 76% Ar); x Run No. 15. (2006 mllmin of 22%02 and78% Ar); + Run No. 16. (2510 ml/min of 23%02 and 77% Ar).AAt +f +0I I^'^'11 ,Ill!L I ILI,_, , p I1200 -D-a1195---000000^0^0^000^ 00^00^00^0_-_.0^000^0^0^0--0-__00^0^0^00 0^0^0^0^00^0124012351230;7.(`).-112250 1220——-0-1205 --:00^10^20^30^40^50^60^70^80Time (min)Figure D.2. The manual temperature measurement of the gas at the same height of thelance nozzle; 200 grams Cu2S, at 1200 °C, III Run No. 18. (2234 ml/min of 23%02 and77% Ar); 0. Run No. 22. (1998 mllmin of 27%02 and 73% Ar); 0 Run No. 19. (3015 of23%02 and 77% Ar).216217^1210 ^1208 -P'--' 1206 -2=ci 1204 -t,s=10 1202 ^41200 -1198 ^0 10^20^30^40^50^60^70Time (min)Figure D.3. The gas temperature measurement at the same height of the lance nozzle forRun No. 27, the experimental conditions of 200 grams Cu2S, at 1200 °C, 1998 ml/min of27% 02 and 73% Ar.1288 - ^1286 -a 1284 -c`---' 1282§ 1280t 12781.1 1276E-4 1274 -1272 -1270  0 10^20^30^40^50^60^70^80Time (min)P^,i^ 1i ) 6Figure D.4. The temperature measurement at the center of the melt for Run No. 29, theexperimental conditions of 200 grams Cu2S, at 1275 °C, 1994 ml/min of 23% 02 and77% Ar.1330218//1325P\'..-- 13200.)6-'vd 1315 _atsa.0 1310E-41305f13000.^1^.10^20^30^40^50^60^70^80Time (min)I1i, /Figure D.5. The gas temperature measurement at the same height of the lance nozzle forRun No. 30, the experimental conditions of 200 grams Cu2S, at 1300 °C, 2000 ml/min of22% 02 and 78% Ar.12351230P 1225.....,a) 1220+6:16-41-, 1215P.°1) 1210E-112051200 0^5^10^15^20^25^30^35^40Time (min)Figure D.6. The gas temperature measurement at the same height of the lance nozzle forRun No. 33, the experimental conditions of 200 grams Cu2S, at 1200 °C, 3500 ml/min of29% 02 and 71% Ar.2191270 ^1260 7E6.3 1250 72). 1240 -=9.,(1) 1230 7E-1 1220 71210 -1200 ^0Time (min)Figure D.7. The gas temperature measurement at the same height of the lance nozzle forRun No. 34, the experimental conditions of 200 grams Cu2S, at 1200 °C, 2000 ml/min of79% 02 and 21% Ar.5^10^15 20 251218121612141212.)AR' 121012081206120412020^10^20^30^40^50^60^70Time (min)Figure D.8. The gas temperature measurement at the same height of the lance nozzle forRun No. 37, for the experimental conditions of 200 grams of Cu2S at 1200 °C, 2000ml/min of 21% 02 and 79% N2.220Figure D.9. The gas temperature measurement at the same height of the lance nozzle forRun No. 41, for the experimental conditions of 200 grams of Cu2S at 1200 °C, 3500ml/min of 24% 02 and 76% Ar.

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