{"Affiliation":[{"label":"Affiliation","value":"Applied Science, Faculty of","attrs":{"lang":"en","ns":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","classmap":"vivo:EducationalProcess","property":"vivo:departmentOrSchool"},"iri":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","explain":"VIVO-ISF Ontology V1.6 Property; The department or school name within institution; Not intended to be an institution name."},{"label":"Affiliation","value":"Materials Engineering, Department of","attrs":{"lang":"en","ns":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","classmap":"vivo:EducationalProcess","property":"vivo:departmentOrSchool"},"iri":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","explain":"VIVO-ISF Ontology V1.6 Property; The department or school name within institution; Not intended to be an institution name."}],"AggregatedSourceRepository":[{"label":"Aggregated Source Repository","value":"DSpace","attrs":{"lang":"en","ns":"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider","classmap":"ore:Aggregation","property":"edm:dataProvider"},"iri":"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider","explain":"A Europeana Data Model Property; The name or identifier of the organization who contributes data indirectly to an aggregation service (e.g. Europeana)"}],"Campus":[{"label":"Campus","value":"UBCV","attrs":{"lang":"en","ns":"https:\/\/open.library.ubc.ca\/terms#degreeCampus","classmap":"oc:ThesisDescription","property":"oc:degreeCampus"},"iri":"https:\/\/open.library.ubc.ca\/terms#degreeCampus","explain":"UBC Open Collections Metadata Components; Local Field; Identifies the name of the campus from which the graduate completed their degree."}],"Creator":[{"label":"Creator","value":"Kyllo, Andrew Kevin","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/creator","classmap":"dpla:SourceResource","property":"dcterms:creator"},"iri":"http:\/\/purl.org\/dc\/terms\/creator","explain":"A Dublin Core Terms Property; An entity primarily responsible for making the resource.; Examples of a Contributor include a person, an organization, or a service."}],"DateAvailable":[{"label":"Date Available","value":"2009-06-04T23:39:49Z","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/issued","classmap":"edm:WebResource","property":"dcterms:issued"},"iri":"http:\/\/purl.org\/dc\/terms\/issued","explain":"A Dublin Core Terms Property; Date of formal issuance (e.g., publication) of the resource."}],"DateIssued":[{"label":"Date Issued","value":"1995","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/issued","classmap":"oc:SourceResource","property":"dcterms:issued"},"iri":"http:\/\/purl.org\/dc\/terms\/issued","explain":"A Dublin Core Terms Property; Date of formal issuance (e.g., publication) of the resource."}],"Degree":[{"label":"Degree (Theses)","value":"Doctor of Philosophy - PhD","attrs":{"lang":"en","ns":"http:\/\/vivoweb.org\/ontology\/core#relatedDegree","classmap":"vivo:ThesisDegree","property":"vivo:relatedDegree"},"iri":"http:\/\/vivoweb.org\/ontology\/core#relatedDegree","explain":"VIVO-ISF Ontology V1.6 Property; The thesis degree; Extended Property specified by UBC, as per https:\/\/wiki.duraspace.org\/display\/VIVO\/Ontology+Editor%27s+Guide"}],"DegreeGrantor":[{"label":"Degree Grantor","value":"University of British Columbia","attrs":{"lang":"en","ns":"https:\/\/open.library.ubc.ca\/terms#degreeGrantor","classmap":"oc:ThesisDescription","property":"oc:degreeGrantor"},"iri":"https:\/\/open.library.ubc.ca\/terms#degreeGrantor","explain":"UBC Open Collections Metadata Components; Local Field; Indicates the institution where thesis was granted."}],"Description":[{"label":"Description","value":"The Peirce-Smith converter, as used for copper and nickel converting, has changed\r\nlittle in the eighty years since its introduction. Over this time other metal production\r\ntechniques have been developed, including considerable improvements to non-ferrous\r\nsmelting. These improvements have had only a small effect on non-ferrous converting.\r\nThe tenacity of the Peirce-Smith converter can be attributed to its simplicity of operation,\r\nhowever, it is not an efficient process. While the converter itself is limited primarily by\r\nits overall heat balance, process improvement has been limited by the belief that it\r\noperated at thermodynamic equilibrium.\r\nA kinetic model has been developed to gain a better knowledge of the operation of\r\nthe Peirce-Smith converter. The model consists of two parts; a model of the gas flow in\r\nthe bath, and an overall model considering both the heat and mass flows around the\r\nconverter. The gas flow model calculates the bubble growth on the tuyere to detachment,\r\nand its subsequent rise through the bath. A combination of Kelvin-Helmolz and\r\nRayleigh-Taylor instability theories is used to determine the stability of the bubble, both\r\nduring growth and while rising through the bath. This allows the calculation of bubble\r\nbreakup, which can be used to determine the total gas\/liquid interfacial area.\r\nThe gas flow model calculates the amount of oxygen reacting within each phase, as\r\nwell as the heat lost to the gas and the total interfacial area. These values are applied to\r\nthe overall model which then calculates the heat and mass balances within the converter.\r\nMaterial flows are based on mass-transfer considerations, with each phase being\r\nconsidered separately. Both mass and heat-transfer occur between all phases present, and\r\neach phase is assumed to be in internal equilibrium. As well as calculating the behaviour of the more abundant elements within the converter, the behaviour of the more important\r\nminor elements is considered. The model is validated using published physical\r\nmodelling results, as well as measurements made on operating converters.\r\nThe model results indicate that the efficiency of the Peirce-Smith converter may be\r\nimproved by a number of methods, provided that some means of controlling the bath\r\ntemperature is available. Increasing the tuyere submergence and decreasing the tuyere\r\nsize are predicted to provide a substantial improvement in operation efficiency, without\r\nadversely affecting the minor element removal. The use of low levels of oxygen\r\nenrichment also improves efficiency, but tends to reduce the extent of minor element\r\nremoval. Higher levels of oxygen enrichment are predicted to alter the overall process\r\nchemistry, with the amount of iron reacting being controlled by liquid-phase\r\nmass-transfer. This improves both the overall process efficiency and the extent of minor\r\nelement removal.","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/description","classmap":"dpla:SourceResource","property":"dcterms:description"},"iri":"http:\/\/purl.org\/dc\/terms\/description","explain":"A Dublin Core Terms Property; An account of the resource.; Description may include but is not limited to: an abstract, a table of contents, a graphical representation, or a free-text account of the resource."}],"DigitalResourceOriginalRecord":[{"label":"Digital Resource Original Record","value":"https:\/\/circle.library.ubc.ca\/rest\/handle\/2429\/8802?expand=metadata","attrs":{"lang":"en","ns":"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO","classmap":"ore:Aggregation","property":"edm:aggregatedCHO"},"iri":"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO","explain":"A Europeana Data Model Property; The identifier of the source object, e.g. the Mona Lisa itself. This could be a full linked open date URI or an internal identifier"}],"Extent":[{"label":"Extent","value":"5475389 bytes","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/extent","classmap":"dpla:SourceResource","property":"dcterms:extent"},"iri":"http:\/\/purl.org\/dc\/terms\/extent","explain":"A Dublin Core Terms Property; The size or duration of the resource."}],"FileFormat":[{"label":"File Format","value":"application\/pdf","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/elements\/1.1\/format","classmap":"edm:WebResource","property":"dc:format"},"iri":"http:\/\/purl.org\/dc\/elements\/1.1\/format","explain":"A Dublin Core Elements Property; The file format, physical medium, or dimensions of the resource.; Examples of dimensions include size and duration. Recommended best practice is to use a controlled vocabulary such as the list of Internet Media Types [MIME]."}],"FullText":[{"label":"Full Text","value":"A KINETIC MODEL OF THEPEIRCE-SMITH CONVERTERByANDREW KEVIN KYLLOB.A.Sc., The University of British Columbia, 1986M.A.Sc., The University of British Columbia, 1989A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THEREQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE STUDIESMETALS AND MATERIALS ENG]NEERINGWe accept this thesis as conformingto the required standard.:.THE UMVERSITY OF BRITISH COLUMBIAAugust 1994\u00a9Andrew Kevin Kyllo, 1994In 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 NeIz2L ti,1J (\u20184tJev\u2019:alcThe University of British ColumbiaVancouver, CanadaDate_________DE-6 (2\/88)ABSTRACTThe Peirce-Smith converter, as used for copper and nickel converting, has changedlittle in the eighty years since its introduction. Over this time other metal productiontechniques have been developed, including considerable improvements to non-ferroussmelting. These improvements have had only a small effect on non-ferrous converting.The tenacity of the Peirce-Smith converter can be attributed to its simplicity of operation,however, it is not an efficient process. While the converter itself is limited primarily byits overall heat balance, process improvement has been limited by the belief that itoperated at thermodynamic equilibrium.A kinetic model has been developed to gain a better knowledge of the operation ofthe Peirce-Smith converter. The model consists of two parts; a model of the gas flow inthe bath, and an overall model considering both the heat and mass flows around theconverter. The gas flow model calculates the bubble growth on the tuyere to detachment,and its subsequent rise through the bath. A combination of Kelvin-Helmolz andRayleigh-Taylor instability theories is used to determine the stability of the bubble, bothduring growth and while rising through the bath. This allows the calculation of bubblebreakup, which can be used to determine the total gas\/liquid interfacial area.The gas flow model calculates the amount of oxygen reacting within each phase, aswell as the heat lost to the gas and the total interfacial area. These values are applied tothe overall model which then calculates the heat and mass balances within the converter.Material flows are based on mass-transfer considerations, with each phase beingconsidered separately. Both mass and heat-transfer occur between all phases present, andeach phase is assumed to be in internal equilibrium. As well as calculating the behaviour11of the more abundant elements within the converter, the behaviour of the more importantminor elements is considered. The model is validated using published physicalmodelling results, as well as measurements made on operating converters.The model results indicate that the efficiency of the Peirce-Smith converter may beimproved by a number of methods, provided that some means of controlling the bathtemperature is available. Increasing the tuyere submergence and decreasing the tuyeresize are predicted to provide a substantial improvement in operation efficiency, withoutadversely affecting the minor element removal. The use of low levels of oxygenenrichment also improves efficiency, but tends to reduce the extent of minor elementremoval. Higher levels of oxygen enrichment are predicted to alter the overall processchemistry, with the amount of iron reacting being controlled by liquid-phasemass-transfer. This improves both the overall process efficiency and the extent of minorelement removal.111TABLE OF CONTENTSAbstract iiTable of Contents ivTable of Tables viiiTable of Figures xiiAcknowledgments xx1 INTRODUCTION 11.1 Development of the Copper Converter 11.2 Development of Ferrous Converting 41.3 Comparison of Ferrous and Non-Ferrous Converting 52 LITERATURE REVIEW 82.1 Introduction 82.2 Converter Modelling 82.2.1 Converter Operation 82.2.2 Impurity Distribution 102.3 Process Kinetics 122.3.1 Copper Converting Kinetics 132.3.2 Kinetics of Gas\/Liquid Reactions 142.3.3 Kinetics of Liquid\/Liquid Reactions 152.4 Process Thermodynamics 162.4.1 Matte Thermodynamics 162.4.2 Slag Thermodynamics 182.4.3 Internal Phase Equilibrium 183 OBJECTIVES AND SCOPE 194 INDUSTRIAL DATA 214.1 Copper Converter Trials 214.2 Nickel Converter Trials 264.3 Analysis 334.3.1 Oxygen Efficiency 334.3.2 Material Deportment 364.3.2.1 Major components 364.3.2.2 Minor elements 40iv4.3.3 Converter Dusts.444.3.3.1 Flue dust 454.3.3.2 Cottrell dust 524.3.3.3 Baghouse dust 575 GASFLOWINTHEBATH 595.1 Basic Bubble Growth 595.2 Bubble Detachment Criterion 675.3 Bubble Break-up During Growth 715.4 Bubble Rise 775.5 Bubble Recombination 796 MODEL DEVELOPMENT 816.1 Introduction 816.2 Preliminary Considerations 816.2.1 Bath Velocity and Gas Holdup 816.2.2 Converter Geometry 846.3 Mass Balance 906.3.1 Equilibrium Within Phases 906.3.1.1 Blister copper 906.3.1.2 Matte 906.3.1.3 White metal 916.3.1.4 Slag 916.3.1.5 Gas 916.3.1.6 Calculation technique 926.3.2 Gas-Liquid Mass-transfer 926.3.2.1 Gas flow 926.3.2.2 Mass transfer from liquid to gas bubbles 956.3.3 Mass Transfer Between Liquid Phases 986.4 Energy Balance 1006.4.1 Energy Loss 1006.4.2 Energy Consumption 1026.4.3 Energy Generation 1046.4.4 Interphase Heat-transfer 105v6.5Data.1056.5.1 Physical and Thermal Properties 1056.5.2 Thermodynamic Data 1076.5.2.1 Free energy 1076.5.2.2 Enthalpy of reaction 1116.5.2.3 Activity coefficients 1126.5.2.4 Equilibrium vapour pressures 1186.5.3 KineticData 1196.5.3.1 Diffusivities 1196.5.3.2 Mass-Transfer coefficients 1216.5.3.3 Heat-Transfer coefficients 1227 MODEL VALIDATION 1237.1 Bubble Model Validation 1237.1.1 Bubble Growth 1237.1.2 Bubble Rise 1247.2 Copper Converter Validation 1287.2.1 Bath Temperature 1287.2.2 Slag Composition 1307.2.3 Matte Composition 1337.3 Nickel Converter Validation 1367.3.1 Bath Temperature 1377.3.2 Slag Composition 1407.3.3 Matte Composition 1437.4 Discussion 1467.4.1 Phase Compositions 1467.4.1.1 Error in assays 1467.4.1.2 Sulphur in slag 1477.4.1.3 Oxygen in matte 1487.4.1.4 Minor element distribution 1497.4.2 Copper Blow 1538 MODEL PREDICTIONS AND DISCUSSION 1578.1 Gas Flow Model 157vi8.2 ConverterModel. 1668.2.1 Introduction 1668.2.2 Copper Converter Charge 1678.2.3 Sensitivity Analysis 1718.2.4 Converter Operation 1868.2.4.1 Gasflowrate 1868.2.4.2 Oxygen enrichment 1888.2.4.3 Tuyere submergence and diameter 1978.2.4.4 Slag skimming procedure 2028.2.5 Minor Element Removal 2048.2.5.1 Introduction 2048.2.5.2 Minor element behaviour in the base charge 2058.2.5.3 Model predictions 2138.2.5.3.1 Gasflowrate 2138.2.5.3.2 Oxygen enrichment 2148.2.5.3.3 Tuyere submergence and diameter 2298.2.5.4 Summary 2338.2.6 Comparison with Previous Work 2348.2.6.1 Overall model 2348.2.6.2 Minor element distribution 2359 MODEL APPLICATION 2389.1 Introduction 2389.2 Converter Optimization 2389.3 New Process Development 24210 CONCLUSIONS AND FURTHER WORK 24711 NOMENCLATURE 25012 REFERENCES 25513 APPENDIX 266vi\u2019TABLE OF TABLESTable IV-I Details of copper charges followed 22Table IV-ll Material assays, copper converter charge 586, Feb. 1, 1994.Nunbers in parentheses refer to the blow number in Table TV-I 23Table TV-HI Material assays, copper converter charge 588, Feb. 2, 1994.Nunbers in parentheses refer to the blow number in Table TV-I 24Table TV-TV Material assays, copper converter charge 595, Feb. 4, 1994.Nunbers in parentheses refer to the blow number in Table TV-I 25Table TV-V Flux assay, copper converter plant trials, Feb., 1994 25Table TV-VT Methods of detennination for each assay 26Table IV-Vll Details of nickel converter charges 29Table IV-VllI Material assays, nickel converter charge 105, May 2, 1988. Slagsamples numbers correspond to the blow they were skimmed after. Nunbers inparentheses refer to the blow number in Table TV-VU 31Table IV-IX Material assays, nickel converter charge 106, May 24, 1988. Slagsamples numbers correspond to the blow they were skimmed after. Nunbers inparentheses refer to the blow number in Table TV-VU 31Table IV-X Material assays, nickel converter charge 107, May 25, 1988. Slagsamples numbers correspond to the blow they were skimmed after. Nunbers inparentheses refer to the blow number in Table IV-Vll 32Table IV-XT Material assays, nickel converter charge 108, May 26, 1988. Slagsamples numbers correspond to the blow they were skimmed after. Nunbers inparentheses refer to the blow number in Table TV-VU 32Table IV-Xll Overall oxygen efficiencies for copper converter chargesfollowed in plant trials 34Table IV-XllI Oxygen efficiencies calculated from matte samples 34Table IV-XTV Calculated nickel converter oxygen efficiencies 35Table TV-XV Distribution of major components between output streams of thecopper converter 37Table IV-XVT Distribution of major components in nickel converting 38Table IV-XVTI Compositions of converter dust samples 44viiiTable V-I Tpical copper converting conditions used for bubble sizecalculations 60Table V-TI Bubble size at detachment calculated from different models 61Table VT-I. Reacting components of the matte 90Table VT-fl Reactions required to calculate the equilibrium composition of thematte 91Table VT-HI Integrated values of C. for use in equation 6.73.\u2019 103Table VT-TV Enthalpies of reaction required for energy generationcalculation.\u201936 104Table VT-V Physical and thermal properties of the gas and condensed phases. .. 106Table VT-VT Coefficients for gas viscosity equation (air).\u201942 107Table VI-VIl Free energy of formation of matte compounds.142 107Table VT-VIIT Free energy of reaction for matte-slag reactions.\u201935 108Table VT-TX Free energy of reaction for slag and gas reactions.135 108Table VI-X Activity coefficients of the major constituents of the matte andslag 112Table VT-XT Minor element activity coefficients used in the model 117Table VI-Xll Equilibrium vapour pressures of the minor elements 119Table VT-XIIT Atomic\/ionic\/molecular radii of matte, slag and bullionconstituents.\u201936 121Table VTT-T Comparison of measured\u201d and predicted gas penetration inmercury 123Table VTT-IT Comparison of measured and predicted gas fraction, bath velocity,and spout height in vertical injection systems 126Table VTT-TTT Comparison of model predicted slag compositions with assays,(weight percent), #1 converter charge 586, Feb., 1994 131Table VH-TV Comparison of model predicted slag compositions with assays,(weight percent), #1 converter charge 588, Feb., 1994 131Table VTI-V Comparison of model predicted slag compositions with assays,(weight percent), #1 converter charge 595, Feb., 1994 132xTable Vu-VT Comparison of model predicted matte and blister coppercompositions with assays, (weight percent), #1 converter charge 586, Feb.,1994 134Table Vu-Vu Comparison of model predicted matte and blister coppercompositions with assays, (weight percent), #1 converter charge 588, Feb.,1994. Asterisk indicates combined matte and slag to bring the matte silicacontent up to assayed value 134Table VIT-VITI Comparison of model predicted matte compositions withassays, (weight percent), #1 converter charge 595, Feb., 1994. Asteriskindicates combined matte and slag to bring the matte silica content up to assayedvalue 135Table Vu-TX Comparison of model predicted slag compositions with assaystaken at the end of the blow, (weight percent), #3 converter charge 105, May1988 141Table VuT-X Comparison of model predicted slag compositions with assaystaken at the end of the blow, (weight percent), #3 converter charge 106, May1988 141Table VIT-XI Comparison of model predicted slag compositions with assaystaken at the end of the blow, (weight percent), #3 converter charge 107, May1988 142Table VII-XII Comparison of model predicted slag compositions with assaystaken at the end of the blow, (weight percent), #3 converter charge 108, May1988 142Table VIT-XITI Comparison of model predicted matte compositions withassays, (weight percent), #3 converter charge 105, May 1988 144Table VII-XTV Comparison of model predicted matte compositions withassays, (weight percent), #3 converter charge 106, May 1988 144Table VTT-XV Comparison of model predicted matte compositions with assays,(weight percent), #3 converter charge 107, May 1988 144Table VuT-XVT Comparison of model predicted matte compositions withassays, (weight percent), #3 converter charge 108, May 1988 145Table VII-XVII Comparison of slag assays obtained using TCP and \u2018wet\u2019 assaytechniques 147Table VuuT-T Parameters tested in the sensitivity analysis 172Table Vu-TI Predicted distribution of minor elements to the blister copper anddust after 400 minutes of charge 586 (72 tonnes of blister copper produced) 205xTable VIJI-ifi Comparison of equilibrium and kinetic model predicted minorelement distributions with commercially observed ranges 237Table IX-I Conditions used in the \u2018improved\u2019 charge 240Table IX-il Conditions used in the \u2018new process\u2019 244Table TX-HI Composition of matte added in the \u2018new process\u2019 244xiTABLE OF FIGURESFigure 1.1 Schematic of the Peirce-Smith converter 4Figure 2.1 Comparison of reported values of FeS activity coefficient in coppermattes.\u20199\u201959 17Figure 4.1 Variation in measured bath temperature and air rate in a nickelconverter, (#3 converter, charge 105, May 23, 1988) 28Figure 4.2 Variation of total copper, nickel, and cobalt in slag with nickelconverter matte grade 39Figure 4.3 Variation of total copper, nickel, and cobalt in slag with slag oxygenpotential 40Figure 4.4 Minor element distribution in Hudson\u2019s Bay Mining and Smeltingcopper converters, charges 586, 588, and 595, February 1994 41Figure 4.5 Antimony and bismuth distribution in Hudson\u2019s Bay Mining andSmelting copper converter charge 595, February 1994 42Figure 4.6 Minor element distribution in Inco nickel converter (#3 converter,charges 105, 107, and 108, May 1988) 43Figure 4.7 Schematic of the dust collection system at Hudson\u2019s Bay Miningand Smelting\u2019s Fun Flon smelter. Numbers indicate approximate position fromwhich Cottrell dust samples were taken 45Figure 4.8 Copper converter flue dust, x25 47Figure 4.9 Copper converter flue dust, a. coated particle, x150, b. particle withpore, x300 48Figure 4.10 Copper converter flue dust, mounted and sectioned, x25 49Figure 4.11 Copper converter flue dust, mounted and sectioned, a. particlecontaining entrained slag and copper droplets, xl 25, b. particle containingcopper droplets, xlOO, c. fractured particle containing copper, x125, d. slagparticle containing copper droplet, x80 51Figure 4.12 Copper converter Cottrell dust, a. sample 1, xl 00, b. sample 2,xlOO, c. sample 4, x160. Numbers refer to sample positions shown inFigure 4.7 54Figure 4.13 Copper converter Cottrell dust with \u2018matrix\u2019 removed, a. sample 1,xlOO, b. sample 2, x160, c. sample 3, x160. Numbers refer to sample positionsshown in Figure 4.7 55xiiFigure 4.14 Copper converter Cottrell dust, a. sample 2, x300, b. sample 1,agglomerated fume, x2000. Numbers refer to sample positions shown inFigure 4.7 56Figure 4.15 Smelter baghouse dust, x1500 58Figure 5.1 Schematic of high Froude number injection of air into water.11\u2019 62Figure 5.2 Ellipsoidal bubble growth 64Figure 5.3 Comparison of horizontal and vertical injection conditions 65Figure 5.4 Bubble detachment process 68Figure 5.5 Bubble detachment geometry 69Figure 5.6 Variation of the height of the bubble centre above the tuyerecentreline (h) and the distance of the bubble centre from the tuyere centre (s)with bubble radius at detachment 70Figure 5.7 Variation of bubble position at detachment with bubble diameter 71Figure 5.8 Schematic illustration of flow around a bubble.\u201918 73Figure 5.9 Variation of maximum bubble diameter and wavenumber with bathvelocity 77Figure 6.1 Schematic cross-section of an idle converter 85Figure 6.2 Schematic cross-sections of an operating converter: a. no gas flowthrough the slag, b. gas flow through matte and slag, c. gas flow through slagonly 87Figure 6.3 Schematic of emulsion formation during submerged injection\u201927 89Figure 6.4 Comparison of reported values of free energy of reaction 109Figure 6.5 Comparison of reported values of free energy of formation of SbSand SbO 110Figure 6.6 Comparison of reported values of free energy of formation of AsSandAsO 111Figure 7.1. Comparison of measured37and predicted spout height 125Figure 7.2 Variation of fraction sulphur dioxide reacted with gas flow rateincluding the fitted effect of surface reaction 127Figure 7.3 Variation of fraction sulphur dioxide reacted with tuyeresubmergence including the fitted effect of surface reaction 128xiiiFigure 7.4 Comparison of measured and predicted copper convertertemperatures charge 586, February, 1994 129Figure 7.5 Comparison of measured and predicted copper convertertemperatures charge 588, February, 1994 129Figure 7.6 Comparison of measured and predicted copper convertertemperatures charge 595, February, 1994 130Figure 7.7 Comparison of measured and predicted iron and silica contents incopper converter slags, charges 586, 588, and 595, Feb. 1994 132Figure 7.8 Comparison of measured and predicted a. iron and b. coppercontents in copper converter mattes, charges 586, 588, and 595, Feb. 1994 136Figure 7.9 Comparison of model predicted matte and slag temperatures withplant data, #3 converter charge 105, May 1988 138Figure 7.10 Comparison of model predicted matte and slag temperatures withplant data, #3 converter charge 106, May 1988 138Figure 7.11 Comparison of model predicted matte and slag temperatures withplant data, #3 converter charge 107, May 1988 139Figure 7.12 Comparison of model predicted matte and slag temperatures withplant data, #3 converter charge 108, May 1988 139Figure 7.13 Comparison of measured and predicted iron and silica contents innickel converter slags, #3 converter, charges 105, 106, 107, and 108, May 1988.143Figure 7.14 Comparison of measured and predicted iron, nickel, and coppercontents in nickel converter mattes, #3 converter, charges 105, 106, 107, and108, May 1988 145Figure 7.15 Calculated variation of mole fractions ofFe304and FeO in matte. ... 149Figure 7.16 Comparison of model predicted lead, zinc and arsenic distributionswith measured values, copper converter charges 586, 588, and 595 Flin Flon,February 1994. Solid lines indicate commercially observed range. 1 151Figure 7.17 Comparison of model predicted antimony and bismuthdistributions with measured values, copper converter charge 595, Flin Flon,February 1994 152Figure 7.18 Comparison of model predicted lead, zinc and arsenic distributionswith measured values, nickel converter charges 105, 107, and 108, Copper Cliff,May 1988 153xivFigure 7.19 Predominance area diagrams for the iron-copper-sulphur-oxygensystem; a. 1300 K, b. 1500 K. Dashed lines indicate partial pressure of sulphurdioxide 155Figure 8.1 Variation of primary bubble temperature with time for injectionconditions given in Table V-I 158Figure 8.2 Effect of ellipse eccentricity on surface area at constant volume,shaded area indicates eccentricity range predicted by the model 160Figure 8.3 Variation of primary bubble volume with time for injectionconditions given in Table V-I 160Figure 8.4 Variation of average oxygen partial pressure with tuyeresubmergence for injection conditions given in Table V-I 161Figure 8.5 Variation of average oxygen partial pressure with tuyere diameter,all other conditions given in Table V-I 161Figure 8.6 Variation of primary bubble volume with tuyere diameter, all otherconditions given in Table V-I 162Figure 8.7 Variation of total oxygen reacted with inlet gas oxygen content, allother conditions given in Table V-I 164Figure 8.8 Variation of primary bubble temperature with bath material, all otherconditions given in Table V-I 164Figure 8.9 Variation of number of bubbles formed with bath material, all otherconditions given in Table V-I 165Figure 8.10 Effect of tuyere interaction on average oxygen partial pressure , allother conditions given in Table V-I 165Figure 8.11 Effect of tuyere interaction on primary bubble volume, all otherconditions given in Table V-I 166Figure 8.12 Predicted matte temperature, charge 586. F-flux addition, M-matteaddition, I-idle period start, I*idle period end, S-slag skimmed, Sc-scrap added,C-copper blow start 168Figure 8.13 Predicted variation of oxygen use with time 170Figure 8.14 Predicted variation of tuyere submergence (including spout) withtime 170Figure 8.15 Predicted variation of oxygen use with tuyere submergence(including spout), charge 586, Feb. 1994 171Figure 8.16 Effect of model time step on the predicted variation of mattetemperature and iron content (weight percent) with time 173xvFigure 8.17 Effect of gas flow calculation frequency on the predicted variationof matte temperature and iron content (weight percent) with time 174Figure 8.18 Effect of initial bath temperature on the predicted variation ofmatte temperature and iron content (weight percent) with time 175Figure 8.19 Effect of initial bath temperature on the predicted variation ofmatte oxygen content (weight percent) with time 176Figure 8.20 Effect of slag emissivity on the predicted variation of slagtemperature with time 177Figure 8.21 Effect of liquid-phase diffusivity on the predicted variation ofmatte temperature and iron content (weight percent) with time 178Figure 8.22 Effect of liquid-phase diffusivity on the predicted variation ofmatte zinc content (weight percent) with time 179Figure 8.23 Effect of liquid-phase diffusivity on the predicted variation of slagoxygen content (weight percent) with time 180Figure 8.24 Effect of liquid-phase diffusivity on the predicted variation ofoxygen use with time 180Figure 8.25 Effect of gas-phase mass-transfer coefficient on the predictedvariation of matte temperature and iron content (weight percent) with time 182Figure 8.26 Effect of gas-phase mass-transfer coefficient on the predictedvariation of slag oxygen content (weight percent) with time 183Figure 8.27 Effect of weight of matte in a ladle on the predicted variation ofmatte temperature and iron content (weight percent) with time 185Figure 8.28 Effect of gas flow rate on the predicted variation of mattetemperature and iron content (weight percent) with time 187Figure 8.29 Effect of gas oxygen content, with total oxygen input constant, onthe predicted variation of matte temperature and iron content (weight percent)with time 190Figure 8.30 Effect of gas oxygen content, with total oxygen input constant, onthe predicted variation of matte iron content with iron as magnetite removed(weight percent) with time 191Figure 8.31 Effect of gas oxygen content, with increased oxygen input, on thepredicted variation of matte temperature and iron content (weight percent) withtime 192Figure 8.32 Effect of gas oxygen content on the predicted variation of matteiron content (weight percent) with time at 1400 K 195xviFigure 8.33 Effect of gas oxygen content on the predicted variation of oxygenuse with time at 1400 K 195Figure 8.34 Variation of the predicted amount of iron and copper suiphidesreacting, as a percentage of the total reaction in the matte, with time at 1400 Kand 84% oxygen in the injected gas 196Figure 8.35 Effect of gas oxygen content on the predicted variation of copperproduced with time at 1400 K 196Figure 8.36 Effect of gas oxygen content on the predicted variation of sulphurpotential with time at 1400 K 197Figure 8.37 Effect of tuyere submergence on the predicted variation of mattetemperature and iron content (weight percent) with time 199Figure 8.38 Effect of tuyere diameter on the predicted variation of mattetemperature and iron content (weight percent) with time 200Figure 8.39 Effect of a combined reduction in tuyere diameter and increase intuyere submergence on the predicted variation of matte temperature and ironcontent (weight percent) with time 201Figure 8.40 Effect of skimming procedure on the predicted variation of mattetemperature and iron content (weight percent) with time 203Figure 8.41 Effect of skimming procedure on the predicted variation of oxygenuse with time 204Figure 8.42 Predicted variation of minor element concentrations in blistercopper with time, a. lead and zinc, b. arsenic, antimony, and bismuth 207Figure 8.43 Variation of surface area-to-volume ratio of blister copper withdepth 208Figure 8.44 Predicted variation of minor element concentrations in matte withtime, a. lead and zinc, b. arsenic, antimony, and bismuth 210Figure 8.45 Predicted variation of minor element concentrations in slag withtime, a. lead and zinc, b. arsenic, antimony, and bismuth 211Figure 8.46 Predicted variation of minor element partial pressures in gas withtime, a. lead and zinc, b. arsenic, antimony, and bismuth 212Figure 8.47 Predicted variation of minor element distribution to the dust withgas flow rate, a. lead b. zinc, c. arsenic, d. antimony, and e. bismuth 214Figure 8.48 Predicted variation of minor element distribution to the dust withgas oxygen content with constant total oxygen input, a. lead b. zinc, c. arsenic,d. antimony, and e. bismuth 216xviiFigure 8.49 Predicted variation of minor element distribution to the blistercopper with gas oxygen content with constant total oxygen input, a. lead b. zinc,c. arsenic, d. antimony, and e. bismuth 217Figure 8.50 Predicted variation of minor element distribution to the dust withgas oxygen content, with increased total oxygen input, a. lead b. zinc, c. arsenic,d. antimony, and e. bismuth 218Figure 8.51 Effect of gas oxygen content, with increased total oxygen input, onthe predicted variation of arsenic partial pressure in the off gas with time 219Figure 8.52 Predicted variation of minor element distribution to the blistercopper with gas oxygen content, with increased total oxygen input, a. leadb. zinc, c. arsenic, d. antimony, and e. bismuth 220Figure 8.53 Effect of gas oxygen content, with increased total oxygen input, onthe predicted variation of arsenic content in blister copper with time 221Figure 8.54 Effect of gas oxygen content, with increased total oxygen input, onthe predicted variation of antimony content in blister copper with time 222Figure 8.55 Predicted variation of minor element distribution to the blistercopper with gas oxygen content, with constant total oxygen input andtemperature, a. lead b. zinc, c. arsenic, d. antimony, and e. bismuth 225Figure 8.56 Effect of gas oxygen content, with constant total oxygen input, onthe predicted variation of arsenic content in blister copper with time at 1400 K.226Figure 8.57 Predicted variation of minor element distribution to the dust withgas oxygen content, with constant total oxygen input and temperature, a. leadb. zinc, c. arsenic, d. antimony, and e. bismuth 227Figure 8.58 Effect of gas oxygen content, with constant total oxygen input, onthe predicted variation of arsenic partial pressure in the off gas with time at1400 K 228Figure 8.59 Effect of gas oxygen content, with constant total oxygen input, onthe predicted variation of moles of arsenic and mole fraction of copper sulphidein matte with time at 1400 K 228Figure 8.60 Predicted variation of minor element distribution to the blistercopper with tuyere submergence, a. lead b. zinc, c. arsenic, d. antimony, ande. bismuth 231Figure 8.61 Predicted variation of minor element distribution to the dust withtuyere submergence, a. lead b. zinc, c. arsenic, d. antimony, and e. bismuth 232Figure 8.62 Effect of tuyere submergence on the predicted variation of arseniccontent in blister copper with time 233xviiiFigure 9.1 Effect of modifications given in Table DC-I on the predictedvariation of matte temperature and iron content (weight percent) with time 241Figure 9.2 Effect of modifications given in Table DC-I on the predictedvariation of oxygen use with time 242Figure 9.3 Predicted variation of matte temperature and iron content (weightpercent) with time for the \u2018new process\u2019 245Figure 9.4 Predicted variation of oxygen use with time for the \u2018new process\u2019. ... 246Figure 9.5 Predicted variation of weight of blister copper produced with timefor the \u2018new process\u2019 246Figure 13.1 Simplified flow chart of the overall model 267Figure 13.2 Flow chart of the gas flow calculation 268Figure 13.3 Flow chart of the mass balance calculation 269Figure 13.4 Flow chart of the heat balance calculation 270xixACKNOWLEDGMENTSI would like to acknowledge the financial support for this project from The NationalScience and Engineering Council and Hudson Bay Mining and Smelting Ltd. I wouldalso like to thank Kevin Scott and Dominic Verheist for their assistance during the planttrials, and my supervisor, Dr. Greg Richards. Finally, I should thank my wife for hercontinued patience and assistance and my children for allowing me to work.xx1.1 Development of the Copper Converter1 INTRODUCTIONThe pyrometallurgical production of copper from sulphide concentrates is acomplex procedure which at present requires a number of steps before the refining stage.Although some modernization of the process has been carried out, most smelters usetechniques which have changed little in eighty years. In the last forty years importantinnovations have been made in copper smelting technology, but only a small amount ofresearch has been carried out on copper converting. Thus the Peirce-Smith converter haschanged little in this period,\u2019 and has not taken advantage of many innovations whichhave benefitted other industries. In order to demonstrate the extent of the problem thedevelopment of the copper converter can be compared with that of the ferrous converter.1.1 Development of the Copper ConverterCopper converting originated at the same time as steel converting with Bessemer\u2019sintroduction of the pneumatic converter. However, there are problems associated withcopper mattes which do not arise in the converting of pig iron. The most important ofthese are the relative densities of three phases involved, (slag, matte and blister copper)and the volume of slag produced.The blister copper is the most dense of the phases produced, and so forms thebottom layer in the converter. This leads to two operating difficulties for theBessemer-type converter: the heat generated by the reaction of air with copper isinsufficient to prevent tuyere blockage and the air oxidizes the copper rather than thematte. Although both of these difficulties are experienced only after the formation ofblister copper, they proved to be a serious impediment to the development of the copperconverter. The corrosive nature of the matte and slag on the acidic refractories also posed11.1 Development of the Copper Convertera problem. The large volume of slag produced required intermediate slag skimming andmatte charging before the finishing blow. This was not a serious problem, but it didrequire extra cranes, longer overall charge times, and frequent relining.The problems relating to bottom blowing were overcome in 1880 by Pierre Manh\u00e8s.His solution was to move the tuyeres to the side of the converter and place them a fewinches above the base to give a quiescent zone for the copper to collect in. This form ofconverter was introduced into the United States four years later, where it was developedfurther, first as the Parrot converter, and then as the Great Falls converter. It is no longerin use.Manh\u00e8s had also worked with the idea of using a horizontal converter, although hegave this up in favour of the Bessemer style upright converter. However, others in theindustry preferred the use of the barrel converter, apparently due to the lower injectionpressures which could be used with it.2 Both types of converters used a sacrificial liningof siicious material, which had to be replaced after only a few charges. It was not until1909 that this problem was solved by Peirce and Smith who developed the basicmagnesite lining which allowed, with a change in fluxing, a much longer refractory life.3The horizontal, basic lined converter then became known as the Peirce-Smith converter.Over the last 80 years the size of the Peirce-Smith converter has increased, thequality of the refractory has improved and automatic tuyere punching has been added.Some smelters have introduced oxygen enrichment of up to 30% in the injected air.Otherwise there has been little change.The present form of the Peirce-Smith converter is shown in Figure 1.1. It is ahorizontal cylinder with lengths from seven to eleven metres. Chrome-magnesiterefractory is used in most operations, but the proportions of the components varies. A21.1 Development of the Copper Convertercopper converter charge consists of a number of slag blows followed by the copper orfinish blow. Before each slag blow molten matte is charged to the converter. Air is thenblown through the matte causing the iron to be removed by the reaction3 ...[l.1]FeS +O2 = FeO+ SO2The iron oxide is removed to the slag, where it reacts with the silica in the flux to formfayalite,2FeO-i-Si0=FeSiO4Blowing then continues until almost all of the iron has been removed. The slag is thenskimmed, more matte is added, and blowing continues. After the last slag blow, slag isskimmed, but no more matte is added. During the copper blow the oxygen in the injectedgas reacts with the copper sulphide to produce copper,Cu2S+0=2Cu+S0Nickel converting is similar to copper converting, except that the copper blow isreplaced with \u2018miss\u2019 and \u2018dry-up\u2019 blows. The procedure for these is the same as for thecopper blow, in that no matte is added, but the purpose is to ensure that the iron levels inthe matte are sufficiently low for further processing. The slag formed in the \u2018dry-up\u2019blow is very viscous, and contains a large amount of nickel. It is generally termed\u2018mush\u2019, and remains in the converter to be cleaned and to provide the flux for the firstslag blow of the following charge.Recently new methods for the pyrometallurgical processing of copper suiphideshave been developed. Although the majority of these are new smelting techniques, therehas been some advance in converting technology. Flash smelting has been found to beable to produce a high grade matte or blister copper, but the slag losses under the31.2 Development of Ferrous ConvertingBUSTLEPIPEFigure 1.1 Schematic of the Peirce-Smith converter.conditions required for direct blister production are quite high.4 The Noranda Process, aside blown bath smelting technology can also be used to produce copper directly, but thismode of operation is avoided due to impurity and refractory problems.5 The Mitsubishicontinuous converter uses a top lancing system in which oxygen enriched air is generallyemployed.6 Most recently Inco has developed a modified Peirce-Smith converter whichallows oxygen top lancing.71.2 Development of Ferrous ConvertingShortly after the introduction of the Bessemer converter a basic lining for ferrousconverting was developed by Gilchrist and Thomas in 1877, primarily to allow theremoval of phosphorous from the steel. The use of tonnage oxygen was first introducedin Austria in 1948. This was in a top blown Bessemer converter, and has become knownas the L-D process.41.3 Comparison of Ferrous and Non-Ferrous ConvertingSince then further innovations include the combined-blowing converter, which usesoxygen lancing with inert gas stirring, and the introduction of the shrouded tuyere whichallows oxygen to be introduced either through the bottom or the side of the converter.These recent improvements all make use of high pressure injection, either in the lance orthrough the tuyeres.1.3 Comparison of Ferrous and Non-Ferrous ConvertingFrom the outlines of converter development given above it is evident thattechnologically the non-ferrous industries are considerably behind the ferrous. While theuse of high pressure gas has been tested,8 it is not yet used in any installation. The mainconcern which is preventing its use is that the increased energy input to the bath will bemore likely to cause bath slopping and increased splashing. Physical modelling studiesof slopping in the Peirce-Smith converter have shown that it is directly related to thebouyant power per unit mass of the bath.9 These studies also indicate that increasingtuyere submergence allows a greater gas flow rate to be used,9 and that for anintermediate range of tuyere submergences there is a range of gas flow rates, in somecases quite high, at which no waves are formed.1\u00b0 This suggests that higher flow ratescould be used. In the steel converter, the vessel shape and tuyere arrangement allows aconsiderably higher flow rate to be used. The vessel shape also allows an increasedtuyere submergence.The batch nature of the copper converter can lead to it being idle for over 50% ofthe total charge time.1\u2019 The steel converter is also a batch process, but the differencesbetween the processes allow the steel converter to operate more efficiently. The maindifference between the two processes is the final form of the material being removedfrom the bath. In steel converting carbon is removed as a mixture of CO and CO2gas,51.3 Comparison of Ferrous and Non-Ferrous Convertingwhile in the slag blows of a copper converter iron must be removed as an oxide containedin a liquid slag. This results in a large volume of slag which must be removed from thecopper converter. It is interesting to note that there is a considerable amount of researchbeing carried out to develop a continuous steel making process.1\u20194It is possible that thedevelopment of a continuous copper converting process would be preferable to alteringthe present process.Oxygen lancing has recently been introduced in a modified converter,7and oxygenenrichment of the blast air is a fairly common practice.1\u2019 The use of oxygen gives ahigher converting rate and gives an off gas high in SO2,which is more economical toclean than the low concentrations presently obtained. However, the use of tonnageoxygen, as in steel converting has not been used. There are three main reasons forlimiting the oxygen content of the blast air. The first of these is that at high oxygencontents the tuyere life is reduced dramatically. The solution to this problem is alreadyavailable, in the form of shrouded tuyeres, as used in bottom blown steel converters. Thesecond problem relates to the heat balance. It has been determined that the off gasaccounts for the majority of heat removal from the converter.\u20195 Reducing the nitrogencontent and, therefore, total gas throughput will cause a large increase in bathtemperature and a related decrease in refractory life. However, improved refractory andchanges in slagging practices may allow higher temperatures to be used. Also, the highermatte grades available from the new smelting furnaces produce considerably less heatdue to their lower iron contents, and any increase in available heat could be used toincrease scrap recycling. The other potential problem relating to the use of tonnageoxygen in the copper converter is the removal of minor elements. It has been determinedthat a large proportion of lead, arsenic and bismuth are removed from the converter by61.3 Comparison of Ferrous and Non-Ferrous Convertingvolatilization, and it has been suggested that the use of oxygen will result in a muchlower removal of these elements.16 This problem, along with obtaining a better overallunderstanding of the Peirce-Smith converter through the use of a kinetic model, will bethe focus of this study.72.2.1 Converter Operation2 LITERATURE REVIEW2.1 IntroductionThe development of a kinetic model of the Peirce-Smith converter requires a widerange of background information. This chapter will cover previous models of theconverter and related technology, as well as the general kinetics and overallthermodynamics required. The literature relating to other aspects of the modelling willbe introduced where appropriate.2.2 Converter ModellingThe majority of models relating to the copper converter deal with the distribution ofimpurities between matte, metal, and slag. Three models attempt to reproduce the overallmaterial balances and of these only one attempts to reproduce the heat balance as well. Arecent model of the nickel converter reproduces both the material and heat balances. Allof these rely on the assumption that the converter is in thermodynamic equilibrium.2.2.1 Converter OperationA model of the copper converter, developed by Goto, has been gradually improvedover the last fifteen years, most recently being applied to the copper flash smelter.\u201972\u2019The first part of the model to be developed considered only the mass balance.\u20197Assuming that the converter is in thermodynamic equilibrium, a set of simultaneousequations was formed and solved using a modified form of the Newton-Raphsontechnique formulated by Brinkley.22 The activity coefficients required in these equationswere derived from published data and experimental work by the authors. The modelconsidered nine elements and nineteen compounds, to give a representation of thedistribution of most of the important elements present in copper concentrates in Japanesesmelters. Of the minor elements of interest here only lead was considered.82.2.1 Converter OperationThe second development was the addition of a heat balance to complete therepresentation of the entire converter.\u20198 The model applied a heat balance to theconverter, using the mass balance calculations to derive a heat generation term. Aniterative technique was used to calculate the temperature change caused by any net heatproduction during a given interval. Calculations were carried out over a two minute timestep throughout the converting cycle, allowing for charging and skimming. It wasclaimed that the model was able to predict temperature variations fairly well,18 but nodirect comparison with plant data was published, and no comparison of matte or slagcomposition was given. More recent developments of the model have included itsextension to cover the copper flash furnace,\u20199and the addition of a calculation of oxygenconsumption using kinetic considerations.2\u2019Amodel of the heat and mass balances in the nickel converter has recently beenproduced.14\u2019It is based on the work of Goto et al., and has been found to be able topredict both the bath temperature and composition fairly accurately.A model of the Noranda continuous converting process has been developed whichconcentrates primarily on the minor element distribution.\u2019 This model calculates theequilibrium phase compositions at a given temperature, partial pressure of sulphurdioxide, magnetite activity, and, in the case of matte-making, matte grade. It does notattempt to model the entire process. The most important findings of these papers withrespect to the present project relate to impurity removal, particularly removal to the gasphase. The majority of volatilization occurs during matte-making and the removal ratesof arsenic and antimony are very slow during copper-making. Increasing temperaturewas found to have only a slight effect on the removal rates, but calculations were notdone above 1250\u00b0C. Oxygen enrichment was found to be detrimental to impurity92.2.2 Impurity Distributionvolatilization due to the reduction in gas throughput. The slag composition was found tohave no significant effect. More recently the model has been extended to the flashfurnace and converting with high oxygen enrichment and calcium ferrite slags by Sohn etal. 16,29-3 1 The results of these calculations will be discussed below. The modellingtechnique used in these papers appears to have some problems. In particular, theprediction that oxygen partial pressure is independent of the 0\/Fe ratio in the slag issuspect.The other model which assumes a constant temperature appears to be more ademonstration of a possible use for the Solgasmix program than a bone fide model.32 Amore recent extension of this model using a modification of Solgasmix has been writtento simulate a concentrate injection smelting technique.32 It does not include a heatbalance as the process is assumed to be isothermal and the important minor elementswere not considered.2.2.2 Impurity DistributionThe more recent papers on modelling of the Noranda Process and other newprocesses are primarily concerned with the distribution and volatilization of impurities,which are of particular importance in direct smelting systems.16\u2019263 The distribution ofminor elements between copper, matte and slag is calculated assuming that there is onlymonatomic dissolution of arsenic, antimony and bismuth in the slag, and that the oxidesand sulphides are unstable.25 However, the model significantly underpredicts the amountof each of these elements reporting to the slag. Although the value ofL (% As incopper\/% As in slag) is brought close to the industrially reported value using mechanical102.2.2 Impurity Distributionsuspension indices, the calculated values of 14 and 14 remain very high.25 This indicatesthat the oxide form of these minor elements may be an important factor in theirdissolution in slags.A technique to calculate the relative amount of impurities lost to the off-gas is alsoformulated.26 The technique calculates the partial pressure of the minor elements andtheir compounds from various thermodynamic variables, and in particular the partialpressures of oxygen and sulphur. It should be reiterated that this is an equilibrium modelcalculating steady-state volatilization. The overall minor element removal is directlyrelated to the volume of gas passing through the bath and the final equilibriumcomposition of the constituent phases. As such it is not valid for a batch process with acontinuously changing composition. In fact its validity can be questioned for anysubmerged injection process, including the Noranda process for which it was written, asit is not likely that the gas leaving the bath close to the charging end of the reactor will bein equilibrium with the final products. The equilibrium calculations do give an indicationof which compounds are likely to be the most important with respect to minor elementremoval to the gas. However, when this model is compared to industrial observationsfrom the Noranda process it significantly under predicts the amounts of arsenic andantimony reporting to the off-gas during copper-making, although it is closer forslag-making.27 The under prediction during copper-making is the result of theequilibrium assumption. Both arsenic and antimony have very low activity coefficientsin copper. Under equilibrium this causes the activities of these elements to dropsignificantly in all phases when copper is present in the system. This lower activitycauses a reduction in the volatilization rate and, hence, an under prediction of theamounts of these elements reporting to the off gas.112.3 Process KineticsThe same model has been applied to copper converting by considering the processas a series of \u201cmicrosteps\u201d Overall it is a simplistic model which does not allow forchanging temperatures or charging to and skimming from the bath. The results of themodel agree with industrial data to a certain extent, but the amount of data available isvery limited. The effects of increasing the oxygen enrichment were also studied,3\u00b0 andfound to have a very detrimental effect on minor element removal. This result isexpected due to the reduced gas throughput. The effects of oxygen enrichment and theuse of a calcium ferrite slag on the overall minor element distribution have also beenpredicted with this model.\u20196\u201931 In general it was predicted that increasing oxygenenrichment reduced the amount of volatilization due to the reduced volume of off gasproduced. However, the amount of minor elements reporting to the slag was increased.The overall result was an increased minor element content in the copper.3\u2019 The use of acalcium ferrite slag was predicted to have little effect on the elimination of lead andbismuth, but to be extremely detrimental in the removal of arsenic and antimony due to alarge reduction in the extent of volatilization.\u20196An attempt to theoretically model the distribution of impurities between matte andblister copper in the copper converter using the Temkin model has been carried out.34The model gives good results for some of the impurity elements, but is quite poor forpredicting arsenic and antimony distributions.2.3 Process KineticsThe kinetics of some of the processes involved are important, particularly withrespect to the minor element removal. Therefore, a review of a variety of aspects relatingto the process kinetics is required.122.3.1 Copper Converting Kinetics2.3.1 Copper Converting KineticsThe kinetics of copper converting have undergone little study. This is due to theapparently high oxygen efficiency which suggests that it operates close to equilibrium.Calculations by Ashman et al.35 have shown that the reactions in both the slag and copperblows are under gas-phase mass-transfer control. The high oxygen efficienciessuggest,therefore, that the gas residence time in the bath is sufficient to allow thereactions to come close to or attain equilibrium.A more recent study of the oxidation of molten iron sulphide assumed that the ratewas under mixed control through the gas and liquid boundary layers around a bubble.36A physical model of mass transfer in the copper converter has shown that kineticcalculations cannot be limited to the bubbles after detachment from the tuyere, as asignificant portion of the reaction occurs during bubble growth.37 Unfortunately, thisstudy neglected the effect of mass-transfer at the bath surface, which can be considerable,especially at low tuyere submergences.38Other kinetic studies related to copper converting are of limited practical use. Theyeither demonstrate that the process is controlled by gas-phase mass-transfer,39\u20194\u00b0orconcern the controlling stage of the chemical reaction,41\u20192which is not relevant, since thereaction is considerably faster than the mass-transfer in the system.Although it does not concern the converter directly, a study of the removal ofbismuth and lead from copper during vacuum induction melting does highlight a factorwhich could be of considerable importance in converting.43 It was determined that theremoval rates of these elements were controlled by liquid-phase mass-transfer andevaporation. This suggests that the removal of the minor elements during converting will132.3.2 Kinetics of Gas\/Liquid Reactionsalso be controlled by liquid-phase mass-transfer and evaporation and will not be wellrepresented by equilibrium calculations. This conclusion is supported by a study ofimpurity removal from copper mattes.2.3.2 Kinetics of Gas\/Liquid ReactionsThere have been some studies relating to the mass-transfer around submerged gasjets.37\u20198455\u00b0These were primarily low temperature physical models, a majority dealingwith the reaction of CO2with an NaOH solution.4648 Two studies have considered thekinetics of the deoxidation of copper by carbon monoxide.49\u20195\u00b0The first determined thatthe deoxidation rate was controlled by gas-phase mass-transfer down to an oxygenconcentration of 0.1%, below which it was under liquid-film control.48 The second studyfound that liquid-phase control remained in effect down to 0.005% oxygen, below whichthe reaction rate became significant.A model of mass-transfer between a horizontal jet and a liquid was combined with aphysical model injecting a mixture of air and SO2 into a bath containingH20.45 Theexperimental work was designed to ensure that the process was limited by gas-phasemass transfer. For this work it was assumed that the gas flow could be represented by anexpanding jet, so the results are given as k\u2019, where x\u2019 is the interfacial area per unitlength of the jet. Unfortunately, the lowest modified Froude number used in this studywas 88, which is considerably higher than that found in the copper converter.Another study combining mathematical and physical modelling used the absorptionof CO2 in water during vertical injection. In this case the rate of absorption wascontrolled by liquid-phase mass transfer, which was represented in the model usingHigbie\u2019 s penetration theory. One of the more interesting results of this study was the142.3.3 Kinetics of Liquid\/Liquid Reactionsdetermination of the effect of surface reactions. In particular, it was found that at lowflow rates and low tuyere submergences surface reactions could account for well over50% of the total CO2absorbed.382.3.3 Kinetics of Liquid\/Liquid ReactionsA number of studies have been carried out to determine the rates of mass transferbetween two immiscible phases under gas stirred conditions, and those prior to 1989 arereviewed by Mon.51 All of these are studies related to bottom injection, particularly ladlerefining, and have determined that the rate of mass-transfer is dependent upon the gasflow rate. There are three mass-transfer regimes, depending upon the gas flow rate:I. at low flow rates there is a slow increase in the mass-transfer coefficient withincreasing gas flow, probably related to the increase in bath mixing velocity,II. above a critical gas flow rate there is a rapid increase in mass-transfer rates, dueto the formation of droplets of \u2018slag\u2019 in the \u2018metal\u2019, andIll, with further increases in gas flow the increase in mass-transfer rate is reduced,since the entire slag has been emulsified.5254The values of the critical flow rates are dependent upon the slag depth, reactordimensions, and tuyere position, as well as the physical properties of the phasesinvolved.54 As such, the values obtained in physical modelling studies are nottransferable directly to the copper converter, however the three mass-transfer regimes arelikely to be found in the converter. Also, the observation that off-centre tuyeres have aconsiderably greater critical velocity for emulsion formation than central tuyeres,suggests that the conditions in a Peirce-Smith converter are far from ideal for matte-slag152.4.1 Matte Thermodynamicsmass-transfer. A large stagnant region of \u2018slag\u2019 was also observed in a two-phasephysical model with an off-centre tuyere,55 again suggesting that the mass-transferconditions in the Peirce-Smith converter are far from ideal.2.4 Process Thermodynamics2.4.1 Matte ThermodynamicsIndustrial mattes are usually a complex mixture of a number of differentcomponents. However, most of these are only present in small amounts, so mattes aregenerally considered as ternary Cu-Fe-S systems. The use of a Cu-Fe-S-O quaternarysystem appears to be an unnecessary complication, since the oxygen appears to be presentas dissolved iron oxides. The first reported thermodynamic measurements on this systemwere carried out by Krivsky and Schuhmann in 1957.56 They determined that theCu2S-FeS pseudobinary deviated negatively from ideality. Later researchers determinedthat the Temkin57or Flood58models could be used to calculate activities within thepsuedobinary system, but that the addition of oxygen invalidated their use.58 Workcarried out by Sinha and Nagamori determined the activity coefficients of cobalt, iron,and their suiphides in copper-saturated mattes.59 The authors also determined that theresults of Krivsky and Schuhmann were a factor of 1.32 too high, due to uncertainties inthe free energy data when the original experiments were made.In developing a mathematical model of the converter, Goto et al. 17-20 derived a set ofequations for the activity coefficients of FeS, FeO, and Fe304in the matte. These werederived from the data of Korakas,6\u00b0Rosenqvist and Hartvig,6\u2019and Kuxmann and Bor,62and relate to mattes saturated with magnetite)7 The relationship obtained for the activitycoefficient of FeS16= exp((1\u20198 J ln(O.54 +1 \u20224XFeS logX + 0.52XFeS)J2.4.1 Matte Thermodynamicsis plotted in Figure 2.1. The same figure shows the experimental points of Sinha andNagamori59in copper saturated matte. It is evident that the agreement is very poor,demonstrating the extreme difficulty which exists in characterizing the solutionthermodynamics of mattes.U)cjU1.10.90.80.70.60.50.40.30Figure 2.1 Comparison of reported values of FeS activity coefficient in coppermattes.\u2019Attempts to represent copper and nickel mattes using the associated solution modelhave been carried out.6377 These models appear to have a good predictive capability inbinary and ternary systems, but require a large number of fitted parameters, and have notbeen extended sufficiently to allow their use for industrial mattes.Kemori et al. [20]1400 K- 1500 KSinha and Nagamori [59]\u2022 1400Kx 1500K*xx0.2 0.4 0.6 0.8X FeS172.4.2 Slag Thermodynamics2.4.2 Slag ThermodynamicsThere has been a considerable amount written regarding slag thermodynamics, andan extensive review was produced by Mackey in 1980.78 More recent studies appear tohave concentrated on ferrite slags, as are used in the Mitsubishi process.7983 The activitycoefficients for the major constituents in fayalite slags have been calculated by Goto17from the data ofMuan,84Michal and Schuhmann,85and Korakas.6\u00b0An associatedsolution model of the Fe-O-Si02-CaOsystem has also been produced.85\u201962.4.3 Internal Phase EquilibriumThe distribution of various elements between the matte and the slag at equilibriumis an important topic, since it relates both to the extent of valuable metal losses and ofslagging of unwanted components of the matte. The importance of copper losses to theslag is evidenced by the large body of papers written about the subject.8895The form of the copper in the slag appears to depend primarily upon the mattegrade.88 At low matte grades dissolution as a sulphide predominates, while oxidicdissolution becomes important as the matte grade increases. It would probably be morecorrect to consider the form of dissolution as a function of oxygen potential, with oxidicdissolution being favoured by the high oxygen potentials which exist with high mattegrades.96 In fact, measurements made in ferrite slags show a large variation in withoxygen partial pressure.82 In order to deal with this the Temkin or Herasymeriko modelshave been applied to the slag.95 The Herasymenko model has been shown to representcopper slags well, including the transition between sulphidic and oxidic dissolution ofcopper.183 OBJECTIVES AND SCOPE3 OBJECTIVES AND SCOPEThe persistence of the copper converter indicates that it fulfils its functionsatisfactorily. However, it has a number of drawbacks. All the elements required todevelop a new, efficient process are in existence, yet little has been done. One of themost important problems which has to be overcome before oxygen can be effectivelyutilized in a coppermaking process is that of minor element removal. In the Peirce-Smithconverter most of the arsenic, antimony, bismuth and lead are removed under presentpractices, however it has been found that under direct coppermaldng conditions there isinsufficient removal of these elements. Also, previous models of minor element removalindicate that using oxygen injection will exacerbate the problem.The main objective of this work is to develop an improved understanding of theoperation of copper and nickel converters. In particular, a better understanding of themechanism by which minor elements are removed from the converter is to be obtained,and so aid in the development of an improved overall process. The emphasis is to beplaced on the behaviour of the more important minor elements: arsenic, antimony,bismuth, lead, and zinc. To aid in attaining this goal a kinetic model of Peirce-Smithconverter operation will be developed and validated. The model may then be used topredict the effects of altering process variables on overall converter operation, as well asminor element behaviour.Equilibrium models of both the copper and nickel converters have been previouslydeveloped, and appear to successfully represent converter operation. However, oxygenpotential measurements carried out in an operating converter indicated that the threecondensed phases were not in equilibrium.96 It has been determined that the rates of theprimary converting reactions are controlled by gas-phase mass-transfer. This is dealt193 OBJECTWES AND SCOPEwith in the thermodynamic models by assuming that a certain proportion of the oxygenreacts with the bath. However, the actual amount of oxygen reacting may varyconsiderably within the course of a charge, and possibly even within a blow, so assuminga single value may lead to incorrect conclusions. Finally, when considering thebehaviour of the minor elements, the kinetics are likely to become more important due tothe relatively low concentrations in the liquid phases.Validation of the model will be carried out using data obtained from operatingconverters. Validation will cover nickel converting operation, using data obtained duringplant trials at Inco\u2019s Copper Cliff smelter, and copper converting using data obtainedfrom plant trials at Hudson\u2019s Bay Mining and Smelting\u2019s Fun Flon smelter. Followingvalidation, the model will be applied to determining the effects of process variables onconverter operation. These will concentrate primarily upon factors which can be changeddirectely in converting practice, as well as simulating conditions which are not normallyobtainable in a standard converter, but may result in a significant improvements in overalloperation. The effects of these variables on the distribution of the minor elements willalso be considered. A comparison with a previous equilibrium model of the nickelconverter will also be made.204.1 Copper Converter Trials4 INDUSTRIAL DATA4.1 Copper Converter TrialsTo obtain further information regarding converter operation, and data for use inmodel verification, in-plant sampling was carried out at Hudson\u2019s Bay Mining andSmelting\u2019s Fun Flon smelter between January 31 and February 5, 1994. Two completecharges and the slag blows of a third charge were followed in detail, taking samples ofmost materials added to and removed from the converters. Occasional tuyere sampleswere also taken throughout each charge. The times of all sampling, as well as blowingand idle periods were recorded, along with the amount of air blown. Since this particularinstallation does not routinely monitor the bath temperature, temperature measurementswere also carried out, using disposable thermocouples inserted into a tuyere. Off gascompositions were not measured, as facilities for this were not present, and the prescenceof leakage air makes accurate interpretation of such measurements difficult.Details of the charges followed are given in Table IV-I, and the assays of thesamples obtained are given in Tables IV-II to IV-V. The assay techniques used to obtainthese values are given in Table IV-VI. Approximate magnetite contents of all sampleswere measured using an Inspiration Consolidated Copper Company Magnetite Meter,which is based on magnetic inductance.The magnetite meter was calibrated usingstandard samples. None of the charges followed can be considered \u2018normal\u2019. This isbecause the other operating converter was in its final charges before relining, so the\u2018white metal\u2019 was transferred to the test converter before the copper blow. This providedan unusual input stream for the two full charges followed, leading to shorter overallcharge lengths. The final charge followed, charge 595, was the second charge in a newlyrelined converter. While no material was transferred to the converter during this charge,214.1 Copper Converter Trialscharge 586 588 595nitial Contents Matte 132+80(1) vlatte 48 Vlatte 148tonnes) Slag 12 Slag 8 Slag 8Scrap 4 Scrap 4 Scrap 4ilow 1 2 C 1 2 C 1 2 3 4 5otal Time 113 100 241 118 128 254 126 92 64 164 84(mm)Eime Idle (mm) 50 34 28 44 66 22 78 60 46 56 14fldle Periods 7 5 3 5 5 5 4 4 1 9 3vlatte Added 16 32 - 16 32 - 16 48 32 32 32tonnes) 72(1)1ux Added 5.5 7.7 - 6.6 9.9 - 6.6 4.4 - 9.9 8.25tonnes)Scrap Added - - 15 - - 15 12 25(2) - - -tonnes)Slag Skimmed 31.25 37.5 25 31.25 43.75 18.75 0 18.75 12.5 62.5 25tonnes)(1) Transferred matte(2) Copper slagTable TV-I Details of copper charges followed.the amount of flux added in the first blows was insufficient, as can be seen from the firsttwo slag assays in Table TV-TV. The low silica and corresponding high magnetite contentof the slag caused it to become very viscous. This can also be seen in the high copperand sulphur contents of the slag samples, indicating a large amount of matte entrainment.The fluxing problems are also the main cause of the large amount of \u2018slag\u2019 in thefirst \u2018matte\u2019 samples and their correspondingly high magnetite contents. While the mattesamples taken in the first blow of the other charges followed do contain a higher silicacontent than the other mattes, they are still considerably lower than the values fromcharge 595, and are caused by the lower volume of material in the bath, which drops theslag level close to the tuyereline. It should be noted that the average converter slag224.1 Copper Converter Trialscomposition at the Fun Ron smelter is 26% silica and 38% iron, with magnetite rangingbetween 20 and 30%. Only one of the slag samples taken during the trials is close to this(charge 595, slag 3), but even this slag had a high magnetite content.Sample Cu Fe Zn Pb S Si02 Fe304 As(Blow)Initial Matte 42.8 25.2 2.78 1.08 24.5 .21 9.0 0.05Matte 1 (1) 70.9 4.1 0.83 2.89 20.2 2.33 2.5 0.03Matte 2 (2) 71.0 3.09 0.59 2.63 21.6 0.28 1.5 0.02Matte 3 (2) 74.7 1.1 0.3 0.65 19.8 0.5 1.2 0.01Transfer Matte 65.6 7.3 1.01 1.13 17.9 2.25 11.0 0.03\u201cMetal\u201d (C) 90.1 0.49 0.13 0.23 5.55 0.22 0.0 0.04Blister Copper 99.04 0.08 0.002 1 0.0072 - - - 0.0073Slag 1 (1) 7.13 41.6 3.97 0.7 2.2 17.6 66.0 0.04Slag 2 (2) 6.46 39.2 3.89 0.73 2.07 22.0 53.0 0.04Slag 3 (2) 6.13 37.4 4.00 1.28 1.66 22.8 52.0 0.04Copper Slag 38.2 21.8 2.16 2.84 0.6 12.1 21.5 0.04Table TV-il Material assays, copper converter charge 586, Feb. 1, 1994. Numbersin parentheses refer to the blow number in Table IV-I.234.1 Copper Converter TrialsSample Cu Fe Zn Pb S Si02 Fe304 As(Blow)Initial Matte 42.2 23.7 2.81 0.91 25.1 0.29 8.0 0.05Matte 1 (1) 23.2 38.6 4.82 0.47 7.7 14.3 24.2 0.03Matte 2 (2) 70.3 2.87 0.66 0.51 20.8 0.19 1.4 0.03Matte 3 (2) 74.0 1.43 0.28 0.4 19.7 0.25 1.5 0.02Transfer Matte 71.2 2.88 0.54 0.67 20.0 0.31 1.9 0.03Blister Copper 97.89 0.67 0.0044 0.0072 - - - 0.0096Slag 1 (1) 5.35 45.1 4.51 0.67 1.54 21.8 44.0 0.05Slag 2 (2) 7.04 36.5 3.82 0.95 2.39 23.2 37.0 0.05Copper Slag 1 31.4 22.3 2.48 3.21 0.64 18.3 44.5 0.05Copper Slag 2 41.5 20.1 2.16 2.55 0.33 14.0 47.0 0.04Table IV-ffl Material assays, copper converter charge 588, Feb. 2, 1994. Numbersin parentheses refer to the blow number in Table TV-I.244.1 Copper Converter TrialsSample Cu Fe Zn Pb S SiC)2 Fe304 As Sb Bi(Blow)Initial Matte 42.2 20.8 2.59 1.35 22.5 0.53 7.5 0.034 .0045 .0032Matte 1 (1) 37.7 23.3 2.75 1.00 15.1 7.43 23.2 0.022Matte 2 (1) 31.2 25.6 2.95 0.8 11.1 9.62 28.5 0.019Matte 3 (1) 57.1 11.8 1.6 1.17 17.9 4.33 10.0 0.014 .0028 .0013Matte 4 (2) 49.8 14.5 1.83 1.01 17.1 4.24 12.0 0.02Matte 5 (2) 58.4 9.01 1.31 1.13 18.4 2.96 6.0 0.014Matte 6 (3) 63.2 7.43 1.33 1.21 20.1 0.83 3.8 0.018 .0022 .0014Matte 7 (4) 58.5 8.89 1.48 1.18 20.0 0.72 3.0 0.016Matte 8 (4) 59.0 8.45 1.45 1.32 21.2 0.45 4.0 0.017Matte 9 (4) 62.7 7.87 1.3 1.15 20.3 1.03 3.2 0.015 .0019 .0002Matte 10 (5) 65.7 4.15 0.75 0.89 19.9 1.06 2.2 0.012Matte 11 (5) 62.8 4.39 0.82 0.73 17.3 2.55 3.6 0.01Slag 1 (2) 8.1 39.8 3.93 0.8 2.54 18.8 47.0 0.015Slag 2 (3) 12.4 38.3 3.8 0.7 4.71 17.8 41.5 0.022 .0058 .0007Slag 3 (4) 4.16 38.2 4.38 1.45 1.19 25.5 34 0.012Slag 4 (5) 3.52 40.6 4.44 2.06 0.67 24.3 48.5 0.016 .0057 .0002Table IV-IV Material assays, copper converter charge 595, Feb. 4, 1994. Numbersin parentheses refer to the blow number in Table IV-I.Si02 Fe CaO A1203 H20Flux I 75.6 2.2 1.4 8.2 I 7.0Table TV-V Flux assay, copper converter plant trials, Feb., 1994.254.2 Nickel Converter TrialsSample Element Assay MethodMatte, White Metal, Cu, Zn, Fe, Na20-NaCO3fusion with LC.P. finishSlag, Dusts S, Si02As HC1O4digestion with AAS finishSb, Bi High: Distillation and I.C.P.Low: Digestion with graphite furnaceanalysisBlister Copper Cu Digestion, interference removal andelectroplating finishZn Acid digestion with AAS finishPb, As, Fe, Digestion, hydroxide precipitation,Bi, Sb separation, redigestion with AAS finishFlux Si02 NaOH-Na20fusion with Si02 dehydrationFe NaOH-Na fusion, Fe3precipitation andconcentratedNH4SOtitrationCaO, A1203 HF, HC1O4and HC1 digestion with AASTable IV-VI Methods of determination for each assay.4.2 Nickel Converter TrialsData similar to that obtained from the copper converters is also available for a totalof four complete charges of a nickel converter. These data were obtained during aprevious study at the Copper Cliff smelter of Inco Ltd.97 In this case both the air rate andbath surface temperature were measured constantly, and recorded on the smeltercomputer at one minute intervals. These two variables are plotted for one charge inFigure 4.1. This figure shows that there is considerable variation of both temperature andair rate throughout a charge. Through a single blow there is usually an initial temperaturedrop corresponding to flux addition, followed by a relatively continuous rise up to theend of the blow. Interruptions to the steady temperature increase may be due to matte or264.2 Nickel Converter Trialsscrap additions, or enforced idle times required by environmental considerations. The airrate usually follows a similar pattern through a blow, with a rapid initial drop related toflux addition, followed by a steady increase.Details of the charges followed are given in Table IV-Vll, and assays of the primarycomponents are given in Tables IV-VIll to IV-XI. It can be seen from a comparison ofthese tables with Tables TV-IT to IV-IV that there is more composition data available fromthe copper converter, while the continuous temperature measurements in the nickelconverter gives considerably more information regarding the heat balance.Table TV-VU shows that there is considerable variation between charges, with anumber of different sources of converter inputs. The relatively large number of operatingconverters at Copper Cliff increases the potential for inter-converter transfers of bothmatte and slag, as well as transfers of material with a high copper content from thecopper converters which are situated in the same converter aisle. It is also evident thatconsiderably more scrap is used in nickel converting than in copper converting. This isdue to the larger amount of iron present in the nickel reverberatory furnace matte, whichcauses an increased amount of heat generation.2715501500wD1450UiI\u20141400700600zUi50004.2 Nickel Converter TrialsFigure 4.1 Variation in measured bath temperature and air rate in a nickelconverter, (#3 converter, charge 105, May 23, 1988).400200 400 600 800TIME (mm)28IH -\u2014\u2014.-D c.\u2014!\u2018.-.-C\u2019)\u2018aCDCDCCD0CDI-i)0\u00b0\u2018E1uIIIIIiHCDcC\u2019,aC,)\u2018\u2014s\u2018_-C,,\u2018-\u2018CD\u2018\u2014\u2018CD 0\u2014\u2014\u2014CD\u2018C\u2018i\u2022z-\u2014-\u2014-\u2014CD ,,\u2014 00CIIIIII\u2014I-\u2019%__\u2014\u2014-\u20181:\u20193\u2014\u2014II00iJiCC\u2022c\u2022c)\u2014\u2014 %\u20144.2 Nickel Converter TrialsCharge 105 106 107 1085 total time (mm) 126 74time idle (mm) 30 30# of idle periods 3 2matte added (tonnes) 20+40(1) 36(2)flux added (tonnes) 18.2 18.2scrap added (tonnes) 10 4.5slag skimmed (tonnes) 36 366 total time (mm) 64 48time idle (mm) 22 18# of idle periods 1 1matte added (tonnes) - -flux added (tonnes) 18.2 7.3scrap added (tonnes) - -slag skimmed (tonnes) 36 187 total time (mm) 18 26time idle (mm) - -# of idle periods - -matte added (tonnes) - -flux added (tonnes) 20 20scrap added (tonnes) 15 10slag skimmed (tonnes) - -(1) Transferred Matte(2) Copper converter \u2018washout\u2019Table IV-Vll Details of nickel converter charges (continued).304.2 Nickel Converter TrialsSample Cu Ni Co Fe S Si02 Pb Zn As(Blow)F. Matte 1 8.32 25.6 1.16 33.9 28.0 0.0894 0.104 0.0272 0.0202F. Matte 2 8.47 21.8 0.85 37.5 27.9 0.0638 0.11 0.0414 0.0139C. Matte 1 (1) 13.8 38.8 1.6 16.9 25.2 0.181 0.080 0.0116 0.0202C. Matte 2 (4) 15.4 42.5 1.45 11.4 24.9 0.0618 0.071 0.0043 0.0218Bess. Matte 23.5 48.3 0.949 0.792 22.4 <.0079 0.0625 0.003 0.0252Slag 1 0.568 0.972 0.591 51.1 1.95 24.4 0.0419 0.0555 <.0115Slag 2 0.487 0.77 0.536 51.7 1.75 24.1 0.0352 0.0574 <.0113Slag 3 0.496 1.02 0.605 50.6 1.39 26.7 0.0414 0.0552 <.0116Slag 4 0.444 0.90 0.675 49.7 1.01 29.5 0.0497 0.052 <.0114Slag 5 1.43 3.39 1.14 48.6 1.39 26.0 0.0585 0.0467 <.0115Slag 6 1.07 3.35 1.55 44.6 0.619 30.0 0.07770.0401 <.0119Table TV-Vu Material assays, nickel converter charge 105, May 2, 1988. Slagsamples numbers correspond to the blow they were skimmed after. Numbers inparentheses refer to the blow number in Table IV-Vll.Sample Cu Ni Co Fe S Si02 Pb Zn AsF. Matte 1 8.52 27.7 1.19 33.8 28.4 0.0519 0.0957 0.0242 0.0133F. Matte 2 7.25 27.5 1.04 33.2 27.4 0.0918 0.114 0.0224 0.0181C. Matte 1 (2) 18.4 42.5 1.27 9.83 24.1 0.165 0.0693 <.0024 0.0165C. Matte 2 (3) 21.7 46.8 1.03 5.79 22.5 0.0591 0.0853 <.0025 0.0206Bess. Matte 24.1 51.4 0.789 0.956 21.8 0.0247 0.058 <.0023 0.0225Slag 1 1.1 2.28 0.788 49.8 1.56 24.2 0.0494 0.054 <.0118Slag 2 0.863 2.6 1.37 51.1 .55 26.9 0.0607 0.0442 <.0118Slag 3 0.712 1.17 0.515 55.6 2.15 20.4 0.0363 0.0792 <.012Slag 4 1.23 3.95 1.56 46.0 0.581 26.8 0.0833 0.0418 <.0111Table IV-IX Material assays, nickel converter charge 106, May 24, 1988. Slagsamples numbers correspond to the blow they were skimmed after. Numbers inparentheses refer to the blow number in Table IV-Vll.314.2 Nickel Converter TrialsSample Cu Ni Co Fe S Si02 Pb Zn AsF. Matte 1 6.6 25.9 1.06 34.6 27.6 0.0994 0.0976 0.0246 0.0168F. Matte 2 8.34 24.1 0.943 34.5 27.4 0.136 0.0922 0.0337 0.0154C. Matte (2) 14.7 42.8 1.53 14.6 25.5 0.0726 0.085 0.0040 0.02Bess. Matte 21.9 51.7 1.1 1.17 23.0 0.13 0.0634 <.0024 0.0352Slag 1 0.759 1.39 0.545 55.2 2.62 21.1 0.0334 0.0611 <.0105Slag 2 0.54 0.99 0.602 52.6 1.57 24.8 0.0346 0.0505 <.0113Slag 3 1.72 4.37 0.754 48.6 3.02 23.9 0.0375 0.0442 <.012Slag 4 1.32 3.46 0.787 48.0 1.97 26.2 0.042 0.047 <.012Slag 5 1.85 4.79 1.09 42.7 2.23 29.9 0.0637 0.0362 <.012Slag 6 2.22 6.00 1.36 39.3 1.96 31.9 0.0671 0.0328 <.0116Table IV-X Material assays, nickel converter charge 107, May 25, 1988. Slagsamples numbers correspond to the blow they were skimmed after. Numbers inparentheses refer to the blow number in Table IV-Vfl.Sample Cu Ni Co Fe S Si02 Pb Zn AsF. Matte 1 6.62 27.4 1.27 32.8 27.8 0.108 0.101 0.0176 0.0176F. Matte 2 9.48 24.2 0.833 34.1 27.8 0.08 14 0.138 0.0435 0.0148C. Matte 1 (1) 14.8 45.5 1.53 12.5 25.5 0.083 0.0916 0.005 0.0263C. Matte 2 (3) 14.9 44.9 1.39 12.4 25.2 0.253 0.0813 0.0074 0.0243Bess. Matte 19.5 55.6 1.05 1.1 23.0 0.0606 0.0613 <.0025 0.0326Slag 1 0.952 2.27 0.663 50.4 1.72 24.1 0.0464 0.0501 <.0119Slag 2 0.637 1.54 0.778 49.2 1.07 28.1 0.0543 0.0469 <.0119Slag 3 0.862 2.82 1.31 46.8 0.716 28.8 0.064 0.0426 <.0118Table IV-XI Material assays, nickel converter charge 108, May 26, 1988. Slagsamples numbers correspond to the blow they were skimmed after.324.3.1 Oxygen Efficiency4.3 Analysis4.3.1 Oxygen EfficiencyThe oxygen efficiency of non-ferrous converters is usually thought to be very high,but reported values show a wide variation.\u201d In fact, it has been found that there is aconsiderable variation within a single operation.98 Also, there is no way to calculate anaccurate value of oxygen efficiency. Johnson et al. give the equation\u201dTheoretical 02 Required to Convert Matte to Blister .. .[4. 1]% 0 efficiency = 100 x02 Blown into Converterwhich appears straightforward, but is far from accurate. There are a number ofcomplicating factors, including an imprecise knowledge of the amount of matte and othermaterials which are added to the converter.Values of oxygen efficiency can be derived from the data collected in the planttrials by calculating the total amounts of iron removed between matte samples andcomparing it with the amount of air blown during that period. While this procedure maystill suffer from the same problems, especially for cases where the matte samples wereseparated by material charging, better values should be obtained where the samples weretaken close together.Overall oxygen efficiencies calculated from the assays for the copper convertercharges followed are given in Table IV-Xll. Separate values are also given for thecombined slag blows and the copper blow. It is evident that oxygen efficiencies areconsiderably lower than generally thought, and that efficiencies are higher in the copperblow. This has been reported previously,98but no explanation has been given.The oxygen efficiencies calculated from the matte assays are shown inTable IV-XllI. Not all of the matte assays could be used, due to the high silica contents,334.3.1 Oxygen EfficiencyCharge Oxygen Efficiency (%)Overall Slag Blows Copper Blow586 76 55 82588 69 63 72595 - 68 -Table IV-Xll Overall oxygen efficiencies for copper converter charges followed inplant trials.indicating a large slag content in the samples. The first oxygen efficiency reported foreach charge in the table is for the period between charge up and the given matte sample.In all cases the first matte sample taken contained too much slag to allow it to be used.Charge Matte Oxygen Efficiency (%)586 2 943 48588 2 753 59595 6 707 508 679 6510 78Table IV-XllI Oxygen efficiencies calculated from matte samples.It can be seen in charges 586 and 588, that there is considerable variationthroughout the charges, with a generally lower efficiency when the iron contents are low.The lower oxygen efficiencies at low iron contents suggest that the iron removal rate maycome under liquid phase mass-transfer control, with the oxygen beginning to react withcopper sulphide. This does not reduce the overall efficiency, and may cause the344.3.1 Oxygen Efficiencycalculated efficiency in the copper blow to be too high. This is not apparent in charge595; however, the iron content in these mattes did not drop below 4%, so the reduction inefficiency is not likely to be seen.As mentioned above, the values calculated for oxygen efficiency in the nickelconverter can only be approximate, since weights of the mattes at the time of samplingare not known. Also, both the weights and compositions of other materials addedbetween sampling were not measured accurately. To determine approximate weights forthe sampled mattes, copper and nickel balances can be carried out using the requiredweights as unknowns. The balances provide two equations which can be solvedsimultaneously to give the required weights. An iron balance can then give the amount ofiron reacted. Table IV-X1V gives the values of oxygen efficiency calculated in thismanner as well as the overall efficiencies for the charges where inter-sample values couldnot be determined.Charge Matte Oxygen Efficiency (%)105 - 93106 1 662 98107 - 90108 1 882 55Table IV-XIV Calculated nickel converter oxygen efficiencies.Generally, the calculated oxygen efficiency is higher than in the copper converter.The most likely explanation for this is the greater tuyere submergence in this nickelconverter, due to its larger size. However, the amount of magnetite in the chargedmaterials is not considered in the calculations. This increases the calculated values of354.3.2 Material Deportmentiron oxidized, and hence the calculated oxygen efficiencies. The magnitude of this effectcould be large, since the magnetite content in the reverberatory matte can be over 8%.Unfortunately, insufficient magnetite assays were carried out at the time of the testing toallow the inclusion of this in the oxygen efficiency calculations.4.3.2 Material Deportment4.3.2.1 Major componentsThere are four major components in the copper converter; copper, iron, sulphur, andsilica. These materials are distributed between the slag, blister copper, dust, and gas inthe proportions given in Table IV-XV. From the table it can be seen that the removal ofiron and sulphur from the matte is almost complete, with the majority of the iron beingremoved in the slag, and the sulphur reporting to the gas. It appears that almost all of thesilica added is also removed in the slag, but the amount of flux added is not known withany accuracy, so the input silica was calculated based on the outputs to the slag and dust.This does not include the flux which is collected in the dusts beyond the flue, or is blownout to the atmosphere as the converter turns into stack after flux addition.Between 80 and 85% of the copper fed to the converters reports to the blistercopper, with the majority of the remainder being removed in the slag. Of the copper inthe slag, about 60% is in the slag removed at the end of the copper blow. This material isrecycled directly to another converter, while the remaining slags and dust are returned tothe reverberatory furnace. The amount of copper in the skimmed slag is relativelyconstant, due to the practice of blowing to \u201ccopper high\u201d before skimming. Since thecopper content in the matte is approximately the same at each skim, the copper in the slagis also. However, the sulphur content of all slags sampled, with the exception of thecopper slags, was more than sufficient to allow all the copper to be present as suiphide,364.3.2 Material DeportmentCharge Stream Cu Fe S Si02Blister Copper 85.2 0.2 - -Slag Total 12.0 99.1 4.1 99.4586 Slag Blows 3.9 82.6 3.7 81.7Copper Blow 8.1 16.5 0.4 17.7Dust 2.8 0.6 2.5 0.6Gas - - 93.4 -Blister Copper 83.8 1.5 - -Slag Total 12.3 97.9 4.8 99.8588 Slag Blows 5.2 86.3 4.5 84.1CopperBiow 7.1 11.6 0.3 15.7Dust 3.9 0.6 2.9 0.2Gas - - 92.3 -Blister Copper 79.6 0.12 - -Slag Total 17.8 98.7 4.4 99.0595 Slag Blows 6.3 86.0 4.0 85.6Copper Blow 11.5 12.7 0.4 13.4Dust 2.6 1.2 1.9 1.0Gas - - 93.7 -Table IV-XV Distribution of major components between output streams of thecopper converter.either dissolved or entrained. An indication of the amount of entrainment can be seenfrom the slags with a low silica content in charge 595. In these slags the copper contentis close to double the usual amount. This will be almost entirely due to entrainment, andis caused by the high slag viscosity.In nickel converting there are two major output streams, the slag and the Bessemermatte, and one minor stream, the dust. Ideally, all the copper, nickel, and cobalt willreport to the Bessemer matte, while the iron will be removed to the slag. The results of374.3.2 Material Deportmentan analysis of the data collected from the nickel converter are shown in Table IV-XVI.This shows that the recovery of nickel and copper to the matte is over 90%, while over95% of the iron reports to the slag.Charge Phase Cu Ni Co FeSlag 4.9 5.3 58.2 97.7105 Bessemer Matte 91.7 91.1 39.2 0.9Dust 3.4 3.6 2.7 1.4Slag 2.8 3.2 48.6 95.4106 Bessemer Matte 94.4 93.9 48.2 2.2Dust 2.8 2.9 3.2 2.4Slag 6.0 6.0 44.3 96.9107 Bessemmer Matte 91.4 91.2 53.2 1.9Dust 2.6 2.8 2.5 1.5Slag 4.8 4.6 49.4 96.0108 Bessemmer Matte 91.2 92.1 47.6 1.8Dust 4.0 3.3 3.0 2.2Table IV-XVI Distribution of major components in nickel converting.Figure 4.2 shows that the amount of valuable metals lost to the slag increases withmatte grade. The usual explanation for this relates to increased oxidic dissolution of thevaluable metals at higher oxygen partial pressures, which is seen in equilibriumexperiments. However, when the total mole fraction of copper, nickel and cobalt in theslag is plotted against the oxygen potential of the slag calculated from theFe2\/F3ratio,the result is Figure 4.3, which does not show any evidence that oxygen potential has aneffect. This suggests that there is another explanation for the increased metal losses. It ispossible that, at lower concentrations of iron in the matte, liquid-phase mass-transferbecomes important. As the amount of iron decreases there will be a point at which themass-transfer rate of iron to the gas-liquid interface becomes less than the rate of oxygen384.3.2 Material Deportmentmass-transfer to the interface. Below this concentration cobalt and nickel will begin toreact, and since both cobalt and nickel oxides are thermodynamically favoured over themetals, they will report to the slag. Table IV-XVI also shows that close to half of thecobalt is lost to the slag. However, the relatively small amounts of cobalt present maylead to considerable errors in these numbers..08.07z0I\u2014.06UIIo .05Ui0.04Li)z.01.5 .55 6 .65 .7 .75Cu+Ni+Co IN MATtE (WEIGHT FRACTION)Figure 4.2 Variation of total copper, nickel, and cobalt in slag with nickelconverter matte grade.394.3.2 Material Deportment0.130.12\u2014j 0.11\u2019W 01\u2022 .0.09\u20190.08 10.07LI.o 0.06\u2019zQ 0.05I\u2014. . I0.04\u20190.03\u20190.02\u20190.01\u20190 \u2022 ,. . .\u2014,\u202211 -9 -7 -5LOG(PARTIAL PRESSURE OF OXYGEN)Figure 4.3 Variation of total copper, nickel, and cobalt in slag with slag oxygenpotential.4.3.2.2 Minor elementsThe most important minor elements present at the Fun Flon smelter are lead andzinc. Of the other minor elements usually associated with copper ores, arsenic is the onlyone which is present in any appreciable amount. While antimony and bismuth arepresent, their concentrations are not sufficient to cause any problems.The distributions of lead, zinc, and arsenic between the three output streams aregiven in Figure 4.4. These values are calculated from the overall mass balances of theseparate charges. For the minor elements, it is assumed that all of the input materialswhich are not accounted for in the blister copper or the slag, report to the dusts. In thiscase the dusts include those collected in the cottrell precipitators and the baghouse. Bothlead and zinc are removed effectively, with less than 0.5% of the lead and 0.1% of thezinc reporting to the blister copper. Approximately 10% of the zinc and up to 35% of the404.3.2 Material Deportmentlead are removed in the dusts, with the remainder reporting to the slag. The arsenicdistribution is notably different, with about 10% of the input arsenic reporting to theblister copper, and 60% being concentrated in the dusts. A similar distribution can beseen for bismuth in Figure 4.5, while the same figure shows that the proportion ofantimony reporting to the gas is considerably lower, with a correspondingly largerproportion reporting to the slag.100Zn Pb As90 CHARG\u2022 586+80 + 588Lii 0 59570_____+:i:400. \u2022Ui3020\u20221-10 100 I I \u2022I I I ISLAG BLISTER DUST SLAG BLISTER DUST SLAG BLISTER DUSTFigure 4.4 Minor element distribution in Hudson\u2019s Bay Mining and Smeltingcopper converters, charges 586, 588, and 595, February 1994.414.3.2 Material Deportment10090 ELEMENT+ Bi +80 SbuJ7020010\u2022 +0SLAG BLISTER DUSTFigure 4.5 Antimony and bismuth distribution in Hudson\u2019s Bay Mining andSmelting copper converter charge 595, February 1994.As is the case of copper converting at Flin Flon, the only minor elements present inappreciable quantities in the Copper Cliff nickel converters were lead, zinc, and arsenic.Of these, lead is the most abundant, but in many cases the concentration of the minorelements is close to, or below, the lower threshold of the assay technique. Thedistributions of these elements between the output streams are given in Figure 4.6. Onlythree of the four charges could be used in this case, due to problems with the massbalance on charge 106. These problems relate to a complete lack of knowledge of theweight and composition of the \u201cmush\u201d which is initially present in the converter.Normally the mass balances can be carried out by assuming that the weight andcomposition of the \u201cmush\u201d is essentially the same after each charge. However, forcharge 106 the amount of every element removed from the converter was considerably424.3.2 Material Deportmenthigher than the amount charged, leading to the conclusion that an unusually largequantity of \u201cmush\u201d was present at the beginning, or an unusually small quantity remainedat the end.9080- Pb CHARGE Zn As70 - + 107Lu 0 108 + 104:I0.o .1\u2014 500z400.30 ++20 -10 .0I0 I I I ISLAG MATTE DUST SLAG MATTE DUST SLAG MATTE DUSTFigure 4.6 Minor element distribution in Inco nickel converter (#3 converter,charges 105, 107, and 108, May 1988).Figure 4.6 shows that the distribution of the lead is relatively even between thethree output streams, with a slightly higher proportion reporting to the dust and a slightlylower proportion reporting to the slag. This is similar to the distribution in the copperconverter at the end of the slag blows. The zinc distribution is also similar to the copperconverter, with the majority of the zinc being removed in the slag. The arsenicdistribution, however, is quite different, with between 50 and 70% reporting to the matte,while under 20% is removed with the dust. This is the reverse of the copper converterdistribution, and may suggest that arsenic has a greater affinity for nickel mattes than forcopper mattes. Unfortunately, the accuracy of the assays is not sufficient to allow anyfirm conclusions to be drawn.434.3.3 Converter Dusts4.3.3 Converter DustsThe analysis of the minor element distribution in the copper converter indicates thatthey are concentrated to a certain extent in the converter dusts. During the plant trials aset of dust samples was obtained. Flue dust samples were taken after each charge, andduring charge 590 four samples were taken from different points along the length of thebank of Cottrell precipitators, and a sample of baghouse dust was also obtained.Figure 4.7 shows a schematic of the dust collection system at Flin Flon, and indicates theapproximate location where the Cottrell samples were taken. The assays of thesematerials are given in Table IV-XVII. Some interesting trends can be seen in this table.The concentration of copper drops continuously with distance from the converter, whilethose of zinc, lead, arsenic, antimony, and bismuth all increase. The silica content of thedusts increases initially, with a peak in the two samples taken from the middle of theCottrells.Sample Cu Fe S 5i02 Zn Pb As Sb BiFlue Dust (c586) 66.7 4.13 18.6 2.19 1.18 1.72 0.03 - -Flue Dust (c588) 70.5 3.9 20.0 0.97 1.63 0.78 0.05 - -Flue Dust (c595) 53.6 12.4 19.1 5.12 2.18 1.94 0.019 - -Flue Dust 62.6 4.81 16.8 5.1 0.95 1.16 0.023 .0081 .0026Cottrell Dust 1 51.1 4.43 13.1 17.7 1.68 2.0 0.059 .0039 .0027Cottrell Dust 2 35.5 4.17 10.4 28.7 2.23 5.4 0.12 - -CottrellDust3 22.2 3.55 8.4 31.8 3.78 5.37 0.145 .0108 .0141CottrellDust4 20.5 5.52 11.3 15.0 8.72 5.33 0.33Baghouse Dust 8.28 4.26 14.2 4.0 16.4 12.3 1.01 .0294 .064Table IV-XVII Compositions of converter dust samples.444.3.3 Converter DustsSince a large proportion of some of the minor elements report to the dusts, it isimportant to gain a better understanding of how the dusts are formed. It has beenreported that there are four mechanisms by which dusts can be formed in a steelmakingvessel;99 vapourization, metal and slag ejection due to bubbling, and solids entrainment.To this should be added mechanical ejection due to slopping in the converter. Differentmechanisms will be responsible for the removal of different elements. The dust sampleshave been analyzed using optical and scanning electron microscopy to aid in determiningwhich mechanisms are responsible for the removal of the various elements.Figure 4.7 Schematic of the dust collection system at Hudson\u2019s Bay Mining andSmelting\u2019s Flin Flon smelter. Numbers indicate approximate position from whichCottrell dust samples were taken.4.3.3.1 Flue dustThe wide variation in the flue dust assays shown in Table IV-XVII is related to thestage of the charge they were formed at. The large amount of flue dust generated doesFLUE DUST COTTRELL DUSTCONVERTERBAGHOUSE DUST454.3.3 Converter Dustsnot allow the collection of a sample representative of the entire charge, but the separatesamples show the differences which occur during the charge. Generally, samples withlow iron and silica contents will have been produced during the copper blow, while thosewith higher silica contents will have been produced during the slag blows.The converter flue dust is primarily composed of spherical particles mixed with afew grains of flux. Figure 4.8 is a micrograph of the flue dust and shows a number ofinteresting features. It is evident that there is a wide range of particle sizes present, butmost of the particles have diameters between 0.25 and 1 mm. Also, some of the particlescan be seen to have a coating of a white powder, while another shows evidence of a pore.These features become more evident at higher magnifications. Figure 4.9a shows aparticle coated with what appears to be a layer of condensed fume, while Figure 4.9bshows a pore in a lightly coated particle. If the particles are mounted and sectioned,(Figure 4.10) it can be seen that the majority of the spheres are, in fact, hollow. Thesepores are most likely caused by dissolved gas coming out of solution during freezing, butmay also be a coating held on small bubbles by surface tension.464.3.3 Converter DustsFigure 4.8 Copper converter flue dust, x25.474.3.3 Converter Dustsa.b.Figure 4.9 Copper converter flue dust, a. coated particle, x150, b. particle withpore, x300.484.3.3 Converter DustsFigure 4.10 Copper converter flue dust, mounted and sectioned, x25.At higher magnifications, the polished sections show some other features.Figure 4.11 a shows a non-porous particle which contains entrained particles of flux andwhat appears to be copper droplets which may have separated out as the material cooled.Figures 4.1 lb and 4.1 ic also show particles which contain copper. In Figure 4.1 lb. thecopper forms a single droplet at the edge of a larger particle. This is probably a particleejected during the copper blow. Figure 4.1 ic shows a slightly porous particle whichappears to be fractured. The central pore and the fractures contain copper, whichprobably separated out during solidification. The primary material in this particle alsoappears to be a different colour from the particles around it. Wavelength dispersive x-ray(WDX) analysis of a similar particle (Figure 4.11 d) shows that the darker phase is slag494.3.3 Converter Dustswith an iron-copper ratio of 3.91. This is considerably higher than is found in the slagsfrom the slag blows, and lower than slags from the copper blows. However, thecontained particle is almost pure copper, with trace amounts of lead, zinc, and sulphur,and no measurable iron. This suggests that the material is slag ejected during the copperblow.In general, this analysis indicates that the flue dusts are predominantly materialejected from the bath. The assays show that it is primarily matte, with smaller amountsof slag, copper and white metal. The differences in the compositions shown inTable IV-XVII are caused by variations in the proportions of each of these materialspresent. The relatively low zinc assays and the lead assays which are slightly higher thanfound in matte, suggest that the fume seen is lead based. X-ray diffraction analysis of theflue dusts showed the presence of lead sulphate, which thermodynamics predicts to be thepredominant phase.\u2019\u00b0\u00b0504.3.3 Converter Dustsc. d.Figure 4.11 Copper converter flue dust, mounted and sectioned, a. particlecontaining entrained slag and copper droplets, x125, b. particle containing copperdroplets, xlOO, c. fractured particle containing copper, x125, d. slag particle containingcopper droplet, x80.-\u2018 \u2022.4.,,&. s\u2022...eS., -\u2022 \u20221SI\u201d .1a. b.514.3.3 Converter Dusts4.3.3.2 Cottrell dustThe Cottrell dust assays indicate that there is an increase in minor element contentwith distance from the converter. Figure 4.12 shows samples of the dust from threepositions along the bank of Cottrells. The dust appears to be a mixture of sphericalparticles and angular flux particles surrounded by a matrix of fine, powdery material.The samples taken farther away from the converter show an increase in the proportion offine material present, as well as a decrease in the size of the larger particles. This lastpoint can be seen more clearly in Figure 4.13, which shows the samples with the finematerial removed. While all samples contain small diameter particles, the maximumparticle diameter decreases from 0.5 to 0.1 mm with distance from the converter. Thelarger number of angular flux particles in the second Cottrell sample, corresponding tothe increased silica assay, can also be seen in Figure 4. 13b. X-ray diffraction analysis ofthe Cottrell dusts shows a predominance of silica and lead sulphate, with a small amountofAs203possibly present.A previous analysis of Cottrell dusts from the Kidd Creek Mines\u2019 copper smeltershowed a much higher proportion of lead and zinc than were found in the present case.\u2019\u00b0\u00b0These dusts were produced by the Mitsubishi process, so may be considerably differentfrom converter dusts, however there may still be some similarities, particularly in themineralization. It was determined that PbSO4was the primary form of lead present,while zinc was present as oxide, sulphide, and a ferrite. Copper was present in oxide,ferrite, and arsenide forms. It is possible that the ferrites are present in the copperconverter dusts, although the measured magnetite content of the dusts was below 4% inall cases. The iron content of the dusts is also low, and, since the zinc and copper ferritesare also magnetic, they would increase the value of \u2018magnetite\u2019 measured. The sulphur524.3.3 Converter Dustscontents of the converter Cottrell dusts also indicates that the copper is primarilycombined with sulphur, and x-ray diffraction indicates that it is present as coppersulphide, which was not found in the Mitsubishi process dusts. It is probable that theconverter dusts contain a much higher proportion of ejected and entrained material thanthe Mitsubishi process dusts, which contain more condensed fume leading to higherminor element contents.Scanning electron microscopy of the converter Cottrell dusts shows that all of theparticles are coated with the fine material, (Figure 4.14a). As well as the spherical andangular particles, other small, irregular particles are present. Figure 4. 14b shows one ofthese at high magnification. It appears to be an agglomeration of the fine material. WDXdot-mapping of the Cottrell dusts shows that the majority of the dusts are covered withzinc oxide, with some areas also showing high concentrations of lead and sulphur. Thisconfirms that the matrix material is condensed vapour, which has formed on the larger,ejected particles. The increased amount of fine material with distance from the converteris caused by a combination of the reduction in gas temperature, causing more material tocondense, and the reduced number of ejected particles which are small enough to remainentrained in the gas. This conclusion is supported by the assays, and indicates thatvapourization is the primary mechanism for removal of both lead and zinc. The similartrends in arsenic, antimony, and bismuth concentrations suggests that they are removedby the same mechanism.534.3.3 Converter DustsFigure 4.12 Copper converter Cottrell dust, a. sample 1, xlOO, b. sample 2, xlOO,c. sample 4, xl 60. Numbers refer to sample positions shown in Figure 4.7.C.544.3.3 Converter DustsFigure 4.13 Copper converter Cottrell dust with \u2018matrix\u2019 removed, a. sample 1,xlOO, b. sample 2, x160, c. sample 3, x160. Numbers refer to sample positions shown inFigure 4.7.C.554.3.3 Converter DustsFigure 4.14 Copper converter Cottrell dust, a. sample 2, x300, b. sample 1,agglomerated fume, x2000. Numbers refer to sample positions shown in Figure 4.7.b.564.3.3 Converter DustsThe form of the silica present in the Cottrell dusts indicates that it is removed by the\u2018solids entrainment\u2019 mechanism. This is also evident from observations of converteroperation. At Fun Flon, flux is added by ladle through the mouth, and a portion of it canbe seen to be blown out of the converter as it turns back into the blowing position. Thedistribution of the silica along the Cottrell bank can be attributed to the variation in fluxsize fraction.4.3.3.3 Baghouse dustThe baghouse dust is very similar to the Cottrell dusts in appearance, and followsthe same pattern as was seen in the Cottrells. In fact, the baghouse dust is almost entirelymade up of the fine condensed vapour, with only a very small proportion of silica andejected bath material. This can be seen in Figure 4.15. It should be noted that the dustcollected in the baghouse comes from the reverberatory furnace as well as the converters.However, there does not appear to be a considerable difference between the dustsreaching the baghouse. Both x-ray diffraction and WDX indicate that the predominantmaterials present in the baghouse dust are zinc oxide and lead sulphate, with some silicastifi present.574.3.3 Converter DustsFigure 4.15 Smelter baghouse dust, x1500.585.1 Basic Bubble Growth5 GAS FLOWj THE BATHIn order to properly model the gas\/liquid reaction and mass-transfer it is essential tohave a reasonable representation of the average bubble surface area present at any time.Unfortunately, little information is available on this subject, particularly with respect tohorizontal injection. While some experimental work has been carried out, in all cases thelumped parameter \u2018kA\u2019 is the end result. This value is not transferable between systems,so can only be used to give an idea of trends. However, there is a large body oftheoretical work available concerning vertical injection which can be modified torepresent horizontal injection. This chapter will develop the theory required to give anadequate representation of the bubble growth and rise in the bath.5.1 Basic Bubble GrowthIn past mathematical models, the gas has been assumed to form either a jet orbubbles at the tuyere tip. The simplest modelling technique is to assume the gas flows ina specific, calculable trajectory, and from that derive an average surface area.101\u201d\u00b02Unfortunately, the assumption upon which it is based is not valid at the gas flow rates incopper converters. It also neglects the period of bubble growth on the tuyere whichaccounts for a considerable portion of the mass-transfer,37\u2019103\u201d\u00b04and does not deal wellwith \u2018jet break-up\u2019.A number of theoretical equations have been developed to represent bubble growthand detachment,35\u2019105\u00b0and the basic principles of these can be transferred to the situationof the copper converter. In almost every case the models are developed for verticalinjection, so a direct transfer to this process may not be valid. These models consideronly isothermal and non-reactive conditions so the validity of their direct use would be595.1 Basic Bubble Growthquestionable. A modification of a force-balance type model to the copper converter hasbeen developed by Ashman et al.35 which does include both the reaction and heatingeffects.A comparison of the predicted bubble size at detachment and bubble frequencyfrom a number of different models is given in Table V-TI. The bubble sizes arecalculated for the typical copper converter conditions used by Ashman et al.35 and aregiven in Table V-I.Air flow rate per tuyere (m3sj 0.25Inlet air temperature (K) 298Tuyere diameter (m) 0.04Tuyere submergence (m) 0.4Bath velocity (m s\u2019) 1.8Bath temperature (K) 1450Matte density (kgm3) 4200Matte surface tension (Nm1) 0.4Gas velocity (m s\u2019) 198.94Fr(-) 2.83Table V-I Typical copper converting conditions used for bubble size calculations.35Physical modelling, however, has shown that for the conditions prevalent in theconverter neither the jet nor the single bubble assumptions are valid. Instead, acombination of the two appears to be more correct. A schematic of the process observedfor the injection of air into water, with a high Froude number, is shown in Figure 5.1The figure indicates that there is a short jet formed, from which a bubble breaks offperiodically, as well as bubbles forming above the jet at the tuyere tip. Physical605.1 Basic Bubble GrowthBubble Bubble Bubble Ref.volume diameter frequency(ms) (m) (s\u2019)Ashman et al. (with heating) 0.045 0.441 10.78 35Ashman et al. (without heating) 0.019 0.331 13.16 35Davidson et al. 0.066 0.502 3.77 105Mersmann (K=10) 0.026 0.370 9.46 107Mersmann (K=26) 0.042 0.433 5.87 107Wraith 0.052 0.465 4.76 108Wraith et al. 0.074 0.52 1 3.38 109Calderbank 0.0125 0.288 20 110Table V-TI Bubble size at detachment calculated from different models.modelling studies at lower Froude numbers also show an elliptical gas volume fractiondistribution in the horizontal plane. To allow the modelling of this process the simplebubbling assumption must be modified. At low Froude numbers it is unlikely that the gaswill have sufficient momentum to form a significant jet. However, there should besufficient to distort the bubble to an ellipsoidal shape.112 Thus in the followingdevelopment it will be assumed that the bubble is an ellipsoid, with the axesperpendicular to the tuyere being equal.To calculate the penetration of the bubble into the bath (2b) a simple force balancemay be carried out:615.1 Basic Bubble Growth1=0 O.013s.0.026s. 0.039s.0.078s. O.091s.Figure 5.1 Schematic of high Froude number injection of air into water.11\u2019d dbPgQ\u201do =(Mv)+6ivjir--wheredbVdtand\u201d2a(8b2+3a) ...[5.31M PBQt8b2(3b \u2014a)Combining these results in the second order differential equation625.1 Basic Bubble Growtht+(KpBQ+6\u201di_P-_o ...[5.4]dt2 dt1 KPBQ ) PBKwhereKa(8b2+3a)\u2014 8b2(3b \u2014a)is assumed to be constant. If it is also assumed that the viscosity term is negligible, thegeneral solutionpvtb= .\u00b0\u2014k1lnt+k2is obtained, where k1 and k2 are integration constants. Unfortunately this solution is notvalid at t=O, so is not very useful.To provide a useful solution to equation 5.4 a numerical approach may be used.Figure 5.2 shows the calculated growth of a bubble under the conditions given inTable V-I, neglecting the effects of temperature and buoyancy.To include temperature and buoyancy, the model of Ashman et al.35 provides agood basis. Although the model was developed assuming spherical bubbles it may bealtered to reflect the variation in bubble shape. Other modifications will also be requiredto give a more accurate representation of bubble growth.In the original model it was assumed that the drag coefficient was a constant withthe value 0.4. This was based on correlations for a solid sphere at a high Reynold\u2019snumber. In the case of the copper converter this choice of correlation is not valid.However, the sensitivity analysis did indicate that the drag coefficient had little effect onthe bubble size at detachment, so the assumption may not be important. What is more635.1 Basic Bubble Growth5 cmSFigure 5.2 Ellipsoidal bubble growth.important is the main implication of this; that the drag term in the overall equation isnegligible. This result is probably caused by the high value of bath circulation velocityused in the model. In the equation used by Ashman et al.35Vg + CD \u2014 VB) =K- [V(vb \u2014 yB)1the overall drag term is a function of (yb-yB)2which will be very small at high bathvelocities. Measurements of fluid flow in a 1:4 scale water model of the Peirce-Smithconverter using Laser Doppler Velocimetry have determined that the maximum flow rateoccurs at the bath surface, with the flow rate close to the tuyere being approximately halfof the maximum value.113 In the water model, the highest reported velocity was.163 ms, with a gas velocity at the tuyere of 79.2 ms1. This indicates that, while thebath velocity in the actual converter will be higher than the measured value, it is unlikelyto reach the 3.6 ms required to give a velocity of 1.8 ms\u2019 at the tuyereline.645.1 Basic Bubble GrowthOther aspects of the model which must be modified are the apparent lack ofconsideration of horizontal motion, and the bubble detachment criterion. In particular,the absence of horizontal motion results in the erroneous equationdswhere s is the distance from the centre of the tuyere tip to the centre of the bubble. Thisequation is valid for vertical injection, where the bubble rises directly above the centre ofthe tuyere, but this is not the case in horizontal injection, particularly with an ellipsoidalbubble. Figure 5.3 compares the two cases, and it is evident that for a rapidly expandingbubble equation 5.8 cannot be used, unless it is only considering the vertical componentof the velocity in which case s should be replaced by h, the height of the bubble centreabove the tuyere centreline. While this differentiation may appear trivial, it may causeconsiderable errors in the determination of the bubble height, which will affect the bubbledetachment calculation.Figure 5.3 Comparison of horizontal and vertical injection conditions.A. B.655.1 Basic Bubble GrowthIf the above considerations are taken into account the model of Ashman et at.35 canbe used as a basis for a more complex model. In doing so a number of the assumptionsmade in the original model must be carried through to the new one, however, some maybe discarded or altered. Those which are still required are:35\u201d\u00b041) the bubbles are not affected by those forming on adjacent tuyeres;2) there is no coalescence of bubbles from the same tuyere;3) the gas flow through the tuyeres is constant;4) at detachment a volume of gas equal to a hemisphere of diameter d remains on thetuyere;5) the bath viscosity and turbulence result in a drag force on the bubble;6) gas surface tension effects are negligible;7) the gas is ideal;8) the bubble wall is a black body and9) only hydrostatic pressure is exerted on the bubble.The assumption of no interaction between adjacent tuyeres is obviously incorrect, as ithas been ascertained that there is tuyere interaction during converting,\u201d4but thisinteraction appears to take place primarily during the copper blow and rarely involvesmore than two tuyeres.\u201d5 The effect of interaction on bubble growth and detachment arenot well known, however observations of interacting tuyeres in both physical models andoperating converters indicate that interaction has little effect on bubble frequency. Thetuyeres have a common gas feed, so the pressures in the bubbles will be the sameregardless of whether they are coalesced or not. With the only force working to alter thebubble shape being the surface tension, which is very small in comparison to the otherforces involved, it is not unreasonable to assume that bubble coalescence during growth665.2 Bubble Detachment Criterionhas no noticeable effect on the growth and detachment process.The assumptions which will be replaced are:1) the gas inside the bubble is backmixed;2) the bubble detaches when its base reaches the top of the tuyere and3) the drag coefficient has a constant value of 0.4.The replacement for the first assumption will be discussed later. The original dragcoefficient will be replaced by a value calculated from4tpgdz,D- PB Vj,This correlation has been developed for spherical drops and bubbles in pure systems.116 Itshould be noted that surface active components within the bath will cause this to be anunderestimate particularly at high Reynold\u2019 s numbers.\u201d7 The bubble detachmentcriterion will be discussed in the following section.5.2 Bubble Detachment CriterionIn previous models, the point at which the bubble detaches from the tuyere isgenerally calculated as a simple relationship between the bubble radius and the distanceof the bubble centre from the tuyere. These simple equations can be used for verticalinjection, but not for horizontal injection. Ashman et at.35 assumed that the bubbledetached when its base reached the top of the tuyere. This is similar in general form tothe vertical injection correlations. However, using the assumption that a volume of gasequal to a hemisphere of diameter d, remains on the tuyere at detachment, a bettercriterion can be determined. This assumption was introduced by Davidson and SchUler\u2019\u00b05based on observations of vertical injection systems. The exact volume of gas remainingon the tuyere is not known, so an assumption must be made.675.2 Bubble Detachment CriterionFigure 5.4 shows the assumed process of detachment and Figure 5.5 shows thegeometry of the system at detachment. For this purpose it is assumed that the bubblereverts to a spherical shape once necking has occurred, since gas momentum no longeraffects it. The geometry can be used to determine the position of the bubble whendetachment occurs as follows.Figure 5.4 Bubble detachment process.The gas remaining on the tuyere at detachment forms part of a sphere as shown inFigure 5.5. If it is assumed that the detaching bubble is touching the wall directelyabove the tuyere, then at detachmentB.C. D68Figure 5.5 Bubble detachment geometry.5.2 Bubble Detachment Criterion...[5.10]Values of h and s for a range of bubble sizes at a tuyere diameter of 0.05 m areplotted in Figure 5.6. It can be seen from the figure that, especially for larger bubblesizes, detachment takes place considerably before the base of the bubble reaches the topof the tuyere. This point can be seen more clearly from Figure 5.7. In this case it ispossible that the new bubble growing on the tuyere may punch through into the detachedbubble, causing further growth.h =(s2_r)2695.2 Bubble Detachment Criterion0.450.40.350.3Ew 0.25C)z0.20.150.10.0500BUBBLE RADIUS (m)Figure 5.6 Variation of the height of the bubble centre above the tuyere centreline(h) and the distance of the bubble centre from the tuyere centre (s) with bubble radius atdetachment.0.1 0.2 0.3 0.4705.3 Bubble Break-up During Growth10.15.3 Bubble Break-up During GrowthThe growth and detachment equations outlined above are still not sufficient tocompletely model the bubbling phenomenon. In particular, the predicted size of thebubbles at detachment is much larger than can be considered reasonable. Therefore,there must be some other mechanism which reduces bubble size at work. It has beennoted that large bubbles rising in a liquid are unstable and have a tendency to break up,and this is likely to be the case for the bubbles growing on the tuyere. Thus it is proposedbathFigure 5.7 Variation of bubble position at detachment with bubble diameter.715.3 Bubble Break-up During Growththat as a bubble grows on the tuyere it reaches a size where it becomes unstable andbreaks into two bubbles, one of which is still attached to the tuyere while the other is freeto rise.To calculate the minimum bubble diameter at which breakup will occur acombination of Kelvin-Helmolz and Rayleigh-Taylor instability theory is used.\u201d8 Thistheory has recently been applied to the bubbling\/jetting transition in submergedinjection,\u201919but is more applicable to the present application. It assumes that an initialperturbation with amplitude q, produces a travelling wave with the equation1 =q,exp[kc,t+ik(x Crt)] ...[5.1l]Which can be rewritten as11 Th exp[kctJ cos(k(x \u2014 Crt)) ...[5. 12]This equation indicates that c represents the disturbance propagation speed, and kc, is theamplitude growth factor. The model of Kitscha and Kocamustafaogullari predicts thebreakup of fluid particles using a relationship between these two quantities.\u201d8 For thecase of a bubble rising in a fluid (Figure 5.8) the propagation speed is given by_( PBVBSifl8O \u2018 ...[5.13]c\u2014I2pB+pbcoth(khb)and the growth factor is given by! ...[5.14]k \u2014 f PBPb coth(khb)k2(l.5VB Sfl9)2\u2014 ak3 \u2014 g I Ap I k1. (PB + Pb coth(khb))2 PB + Pb coth(khb) JFrom Figure 5.8 it can be shown that for spherical bubbles725.3 Bubble Break-up During GrowthB.VBVBFigure 5.8 Schematic illustration of flow around a bubble.118db ...[5.15]hb =--(cos80\u2014cos8)while for an ellipsoidal bubble...[5.16]hb=(a2+ b\u2014)cos90cosO0\u2014(a2+(b)cose) cos9where e0 is the point where the disturbance originates and e is the wake angle. Both ofthese forms of the equation will be required since the cross-section perpendicular to thetuyere axis will be circular.From the above equations the breakup criterion may be derived asEpB+pbcoth(khb)ld 1Eitan()i I ppcoth(khb)k2(1.5vsinO) ak3\u2014g IApIk l>...[5.17][ 3PBVB J b Itan()I 1 (PB+PbCOthQthb)) PB+PbcothQthb)S \u2014and for rising bubbles Cg is given by735.3 Bubble Break-up During Growth...[5.18]Cg =+ Pb coth(khb)J2To calculate the minimum bubble diameter at which breakup will occur values arerequired for the wake angle and the wavenumber. The wake angle is given by theempirical correlation12\u00b05it l9it 04 ...[5.19]e =+-jj-exp(\u2014O.62Re.)To determine the wavenumber which will cause the most unstable wave growth,equation 5.14 is differentiated with respect to k and set to zero. This results in theequationk3apbhbcsch2(khb)+k2{3a[pB + p coth(kh)] \u2014 PBPJ1.51\u2019B 0jJ2[2hbpbcsch(k )coth(khb)h csch2(khb)]}[5 20]_k{2PBPb1.5vBsin[ coth(khb) +gpph csch2(khb)} gpB(pR + Pb coth(khb)) = 0If the value of khb is large it can be assumed that coth(khb) is equal to one, and that termsinvolving csch2(khb) are negligible. Using these simplifications equation 5.20 can bereduced to( ( 2 ...[5.21]3ak_2Pbl.5vBsinJJ _PB=0This indicates that, for a given bath composition, the critical wavenumber is a function ofthe velocity alone, and that it has a minimum value when the velocity is equal to zero. Ifthese assumptions are applied to equation 5.17 the maximum bubble diameter can becalculated as745.3 Bubble Break-up During Growth3vB ,..[5.22]db= c{*2252k2i23k}where[Itan)I ...[5.23][Itan)Iand* Pb ...[5.241PPBHowever, at low velocities, application of the above equations results in values ofthe wavenumber which are considerably smaller than the minimum wavenumber whichcould cause breakup:k\u2014 2it ...[5.25]mill C ,iAlso, at low velocities the simplifying assumptions are not valid. For this case, when thecalculated values of wavenumber which should give the most rapid breakup are less thank., it follows thatk should be used in equation 5.17. After considerable manipulationthis gives the equation*...[5.26]PB 8W I (1 + p) Ow) \u2018 2 ) J PB \u00b0w755.3 Bubble Break-up During Growthfor the maximum bubble size. Equation 5.26 can be solved using the standard procedurefor quadratic equations. lii all of these calculations the bath velocity used must be thevelocity of the top surface of the bubble relative to the bath. It is important to note thatall of these derivations are for spherical bubbles. For the elliptical cross-section of thebubble db must be replaced with 2b(l-e), where! ...[5.27](b2\u2014 a228=1i b2is the eccentricity of the ellipse.Figure 5.9 shows the variation of predicted maximum bubble sizes usingequations 5.22 and 5.26. This shows that equation 5.26 is only valid at very lowvelocities (less than .33 ms\u2019), which are not likely to occur under injection conditions.Using equation 5.22 for the conditions given in Table V-I gives a maximum bubblediameter of approximately .2 m. This is considerably smaller than the diameter predictedby the growth models. Figure 5.9 shows that there is a strong dependence on the bathvelocity, with a higher velocity allowing a larger bubble. This result is expected, as thecriterion by which the occurrence of breakup is determined, is based on a comparison ofthe rate of disturbance growth with the rate the disturbance passes over the bubblesurface. If the disturbance reaches the side of the bubble before it is large enough tocause breakup then it is swept off the bubble without any effect. Equation 5.13 indicatesthat if the bath velocity is faster, the disturbance propagation speed (Cr) is also faster,allowing a larger bubble to form.760.90.80.7ELU 0.8I-LU0.5ULU-JD0.30.20.1105.4 Bubble Rise350300250200LUDzLU>100500 0Figure 5.9 Variation of maximum bubble diameter and wavenumber with bathvelocity.5.4 Bubble RiseAfter the bubbles detach, either from the tuyere or the growing bubble, they willrise due to both the buoyancy force and the bath motion. For modelling, the assumptionthat the bubbles rise at their terminal velocity should not introduce a significant error.Thus the bubble rise velocity is given by\u20192\u2019! ...[5.28](2(g lAp Idb\u201dVT)L 2P80.5 1 1.5 2BATH VELOCITY (me)775.4 Bubble RiseThe assumption that the bubble rise velocity relative to the bath can be represented by therise velocity of a bubble in a stagnant bath has recently been shown to be valid under gasinjection conditions.122Further breakup of the bubbles may occur as they rise, and the same theory asdetailed in the previous section may be applied. In this case the velocity to be consideredis the bubble rise velocity with respect to the bath. From equation 5.28 it can bedetermined that any bubble with a diameter less than 0.05 m will have a tenninal velocityunder 0.33 ms\u2019, and so will have a maximum bubble size as determined fromequation 5.26. For bubbles in this size range combining the bubble breakup criterionwith the terminal velocity expression givesf a (2w3l ...[5.29]d2\u2014b{+\u00e7)sin2J_22}For a bubble rising at its terminal velocity with a high Reynold\u2019s number-. 5 ...[5.301\u2014 18and for the large density difference in bubbling systems it can be assumed thatlAp ...[5.31]PBand that the term involving p is negligible. Using these assumptions the equilibriumbubble size can be calculated as...[5.32]d,, = 3.258951--i PB785.5 Bubble RecombinationFor larger bubbles the introduction of the terminal velocity equation does not resultin the same degree of simplification. Equation 5.21 becomes3ak2\u20140.l786gpdk\u2014gp=0 ...[5.33]The assumption that the term involving the bubble diameter is negligible introduces amaximum error of under 0.1%, and leads to the simplified equation1 [534]k=1.8083JApplying equations 5.28 and 5.34 to equation 5.22 results in...[5.3510.96868pbd+ 1.333d4PiJ \u20144a=0The actual minimum bubble size will be determined by equation 5.35 if it is greaterthan 0.05 m. Otherwise it will be calculated using equation 5.32. The bubbles will breakup progressively until the minimum diameter is reached. It is important to note that thesecondary and lower order bubbles formed by this procedure will also undergo breakup,leading to the formation of a very large number of bubbles.5.5 Bubble RecombinationWith the large number of bubbles formed within the relatively small plume area,bubble coalescence is inevitable. Unfortunately, it is also very difficult to modeltheoretically. Instead an semi-empirical measure is required to determine whetherrecombination occurs. The work of Sano and Mon\u201923 regarding the size of bubbles in aplume gives the following equation for bubble size.0.5 ...[5.36]dvs=6.903\u2014J v10795.5 Bubble RecombinationThis shows that the effect of the surface tension\/density ratio, as discussed above, ismodified by the superficial gas velocity. The surface tension\/density ratio represents theequilibrium bubble size, while the effect of superficial gas velocity is due to bubblecoalescence. It is evident from equation 5.36, that at high superficial gas velocitiescoalescence occurs more frequently, resulting in larger bubbles.\u2019The effect of the superficial gas velocity appears to be important, but it has receivedlittle attention, with only low values being used in physical modelling; ranging from0.0065 ms1 120 to 0.4 ms\u2019.\u201d\u00b0 The superficial gas velocity in the copper converter can beover 3 ms\u2019, so it is probable that there will be considerably more coalescence thanobserved in the physical models. In order for the gas volume flow through the bath to besufficient to give the required superficial velocity, the average bubble rise velocity mustbe greater than the superficial velocity. Since the bubbles have been determined to berising at their terminal velocity relative to the bath, it follows that a high superficial gasvelocity will require larger bubble sizes to achieve the required volume throughput.Therefore, in the model it is assumed that bubbles will coalesce until the average bubblevelocity is greater than the gas superficial velocity.806.2.1 Bath Velocity and Gas Holdup6 MODEL DEVELOPMENT6.1 IntroductionIn the past, models of copper and nickel converters have assumed that thermal andthermodynamic equilibrium prevailed throughout the system. However, one study raisedsome doubts as to whether the matte, slag and gas were at the same temperature.97 Thiswould imply that interphase equilibrium was not attained, and this implication issupported by gas temperature measurements carried out in a nickel converter.\u201925 Afurther analysis of composition data obtained from a nickel converter97confirms that thematte and slag are not in equilibrium. Therefore, to properly model the converter akinetic approach is required.6.2 Preliminary Considerations6.2.1 Bath Velocity and Gas HoldupAt least an approximate knowledge of the bath velocity is required, both for the gasflow calculations, and for the calculation of mass and heat-transfer coefficients. The onlymathematical model of fluid flow in the copper converter determined that the maximumbath velocity was 0.022ms1.26 However, this model did not consider the effect of theslag layer, or calculate the velocity of the liquid in the plume. The calculated velocityappears to be quite low, but it is explained by the large bath\/refractory contact area andlow tuyere submergences, which are dictated by the form of the converter.126 Physicalmodelling of the Peirce-Smith converter has reported bath velocities of up to 0.168 ms\u2019in a 1:4 scale water model.113An approximate estimate of the maximum bath velocity in the bubble column canbe obtained from the spout height. Applying an energy balance to the spout, consideringenergy per unit volume, gives816.2.1 Bath Velocity and Gas HoldupEnergy input = bath kinetic energyPBV(1 \u2014P)andEnergy output = bath potential energy .. . [6.2]= pBgh8(l\u2014where \u00d8 is the gas fraction in the plume and \u00f8, is the gas fraction in the spout. Equatinginput to output gives.[6.3]2PBVB(l \u2014Pr) = pgh,(1or...[6.4]_((l_\u00d8p)12VB \u2014 2ghgp(1\u2014))The gas holdup values can also be calculated from the spout height, by assumingthat the overall bath level is unaffected by gas injection. This implies that the volume ofgas in the plume is equal to the volume of liquid in the spout. With the assumption thatthe basal radius of the spout is double the plume radius, based on time lapse photographyof the spout in a water model of a Peirce-Smith converter,Ah4 =Ah(l \u2014\u00d8)orh3h\u00d8\u2014 8(1 \u2014\u00d8)Substituting equation 6.6 into equation 6.4 gives826.2.1 Bath Velocity and Gas Holdup[67]2yE =h(1)JThis equation shows that the maximum bath velocity is independent of the value chosenfor the spout gas fraction, so only the spout height will be affected by.An estimate of the gas holdup and liquid velocity in the plume can be obtained byconsidering the volume of gas within the plume,Vgp=Qtrwhere tr is the average residence time of a bubble in the plume. The total plume volume,is given byV=Ah,soVgpQtr ...[6.10]\u2014 V Ah,With...[6.ll]and\u2014\u2014 ...[6.12]= + VTrequation 6.10 becomes\u2014_____...[6.13]\u2014 VB + VTThe average height reached by the liquid in the spout will be the centre of mass, so...[6.14]\u2014 ( 4 \u201c2I\u2019Bcp))836.2.2 Converter GeometryCombining equations 6.13 and 6.14 and rearranging gives\u2014 \u2014 ...[6.15]4Ijht+,J \u2014 +2vupv) + +2vSUPvT) \u2014 4=0If it is assumed that the average bubble is the equilibrium size calculated fromequation 5.33, then equation 6.15 may be solved numerically for q. It should beemphasized that this is very approximate because the validity of some of the assumptionsis uncertain.6.2.2 Converter GeometryFor mass and heat-transfer calculations within the converter, interfacial areasbetween phases and solid\/liquid contact areas are required. The horizontal cylinder formof the converter adds some complication to this. Figures 6.1 and 6.2 show schematiccross-sections of a converter, idle and blowing respectively.The idle case is the easiest to deal with, so will be considered first. The matte\/slaginterfacial area is given by! ...[6.16]1 2 22AM\/s = 2(r \u2014 (r \u2014 hM) ) LSimilarly, the slag\/gas interfacial area is given by...[6.17]1 2 22As,G = 2(r \u2014 (r \u2014 hM \u2014h5) ) LUnfortunately, values for hM and h are not directly calculable. Given the mass of matte,MM, and slag, M, present in the converter, hM can be determined fromMM (7r 2 _j r \u2014 JiM \u2018 (r \u2014 hM) 2 ...[6. 18]\u2014 = LL\u2014i\u2014 \u2014 r sin\u2014 2(2rChM \u2014 hM)and h is calculated from846.2.2 Converter Geometry2 _l(rc\u2014hs(rc\u2014hs)( 221Ps PM 2r sin rh \u2014h5)Figure 6.1 Schematic cross-section of an idle converter.The matte\/refractory contact area is given byAM,R 2. _\/r\u2014hM](rc\u2014hM)1-r 2 ChM- h)2]sin I (2r...[6.19].[6.20]where the second term in the equation represents the end-wall contact area. Similarly, theslag\/refractory contact area is given byASIR = Lr[1c 2siif\u2019\u2014\u2018 2 (r\u2014h5)(2rh3\u2014 h)2]_AM\/R...[6.21]11+2rcr ),)856.2.2 Converter GeometryWhen air is being blown into the converter a spout is formed. The possiblevariations in spout form are shown schematically in Figure 6.2. If the spout height isgreater than the slag thickness (Figure 6.2a), only the slag thickness and matte\/slaginterfacial area are affected. The value of h must be modified to account for the spoutvolume= L[rc2sin-{r _iis] \u2014 (r \u2014h5)(2rh5 hJ\u2014ntabh8...[6.221Values of a and b can be determined from the bubble formation calculations outlined inSection 5. If the modified slag thickness is greater than the spout height, then theconfiguration conforms to Figure 6.2b. To calculate the slag\/matte interfacial area theextra area due to the spouts must be included. Unfortunately, the surface area of anellipsoid is calculable only for a few special cases, so an approximation must be used.Therefore, it is assumed that the spout has a surface area equal to a regular ellipsoid, withminor axes equal to the average of the maximum bubble width and the spout height, soI N ...[6.23]= 2(r\u2014 (r \u2014 \u2014 ntab \u2014a2\u2014 s\u2014 sin\u2019 EJwhere\u2014 b+h ...[6.24]b=2If the matte spout height is less than the slag thickness (Figure 6.2b) the slag willform part of the spout. The slag spout height can be calculated in a similar manner to thematte spout height, using the value (hshspMhM) as the submergence. In this calculationh will be given by equation 6.22 to account for the matte spout volume. The matte\/slaginterfacial area is still given by equation 6.23, but the slag\/gas interfacial area must be866.2.2 Converter Geometrysph,Figure 6.2 Schematic cross-sections of an operating converter: a. no gas flowthrough the slag, b. gas flow through matte and slag, c. gas flow through slag only.876.2.2 Converter Geometrymodified to give! ( ...[6.25]= 2(r\u2014 (r \u2014 h + hM+h,,j2)L\u2014n1t; ab \u2014 a2__.sin_1 cA third possibility is shown in Figure 6.2c. In this case the gas is blowing directlyinto the slag, which may occur near the end of a blow when there is a relatively large slagvolume present. Under these conditions the matte\/slag interfacial area will be given byequation 6.20, and the slag\/gas interfacial area will be given by equation 6.25. Whenblister copper is present it is also possible that the gas will pass through it as well. In thiscase the above equations must be modified.The values of interfacial areas calculated in this fashion will be an underestimate inmost cases. Generally there will be a certain amount of wave formation, with theextreme case being slopping, when the bath surface can be approximated by a standingwave. In this case it is likely that the extent of inter-phase mixing will be increasedconsiderably. To obtain a better estimate of the matte\/slag interfacial area duringblowing, a theoretical model of emulsion formation at the edge of the spout is used.\u201927This model uses a force balance approach to determine the radius of the slag dropletsformed, and gives2 1 ! ...[6.26]r r l28Gg(pMpS)Co5d_l6g(pM_ps)cos31l_[l__P2sV. jwhere v1 is the velocity at the matte\/slag interface and is the angle shown in Figure 6.3.To calculate the interfacial velocity, the equation2 1 -2 1627(PMN( VMXS (VMXS \u2018V .-.. 1K =0.13671\u2014 II II I [(1 \u2014K)(0.1108\u20140.0693K)]\u20195Ps} V ) V )was derived, where88V.K=\u20146.2.2 Converter Geometry...[6.281and x is the slag thickness.127Finally, an energy balance is carried out to determine the rate of droplet generation.For the present case it is assumed that the combined spouts produce a linear interface fordroplet formation, stretching the length of the converter. This gives the number ofdroplets formed per second as\u201927= O.83O8L(pvx)2v\u2014 Ps)COS f000 0o 000000r0QL 0000000000Figure 6.3 Schematic of emulsion formation during submerged injection.\u201927...[6.291DROPLETSMATTEGAS896.3.1 Equilibrium Within Phases6.3 Mass Balance6.3.1 Equilibrium Within PhasesIt is assumed for the calculations that each phase is in internal equilibrium. Assuch, each must be considered separately.6.3.1.1 Blister copperThe copper phase is the easiest to deal with, since it only contains components intheir elemental forms. Thus, there are no reactions and the composition will be governedonly by mass-transfer considerations.6.3.1.2 MatteThe matte is considerably more complex, since it contains a mixture of sulphides,oxides and elements. The equilibrium composition within the matte will be governed bythe sulphur potential. If it is assumed that all oxygen is present as magnetite, and all FeOproduced by reaction is carried directly to the slag by the rising bubbles, then no reactionsinvolve oxygen and an oxygen potential is not required. The reacting components of thematte are given in Table VT-I, and the equations required to calculate the equilibriumcomposition are given in Table VT-TI. All other components are considered non-reacting,so are not subject to equilibrium calculations. The equilibrium calculations are combinedwith mass balances for each element to give the final composition.Elements Cu, Ni, Fe, Co, Pb, Zn, SCompounds Cu2S, NiS, Ni2S, FeS,CoS, PbS, ZnSTable VI-I. Reacting components of the matte.906.3.1 Equilibrium Within PhasesNumber Reaction1 2Cu + 1\/2S2 Cu2S2 Ni+112S=NiS3 2Ni + 1\/2S2=Ni2S4 Fe+1\/2S=FeS5 Co + 1\/2S2= CoS6 Pb+112S=PbS7 Zn+112S2=ZnSTable VT-il Reactions required to calculate the equilibrium composition of thematte.6.3.1.3 White metalThe white metal is a special case of the matte phase, in which Cu2S is the onlyremaining sulphide component. As such its sulphur potential will be governed byreaction 1 in Table VT-TI.6.3.1.4 SlagWhile the slag is a complex mixture of oxides, it can be assumed that iron is theonly component which has more than one oxide form present. As such, the oxygenpotential of the slag will be controlled by the reaction3FeO + 1\/202 = Fe304 ...[6.30]and the composition is determined by the iron and oxygen mass balances.6.3.1.5 GasLike the slag, the equilibrium composition within the gas is dominated by a singlereaction112S2+0=S0 ...[6.31]916.3.2 Gas-Liquid Mass-transferCombining this with sulphur and oxygen mass balances and setting the total pressure toatmospheric, allows the composition to be cakulated.6.3.1.6 Calculation TechniqueFor each of the phases, with the exception of the blister copper, there is a system ofsimultaneous equations which must be solved. In some cases these will be solveddirectly. In the case of the matte the system is more complex and requires the use of anon-linear equation solving routine. As in a previous work, a Quasi-Newton technique isused.97\u201d28 Model flow charts are given in the Appendix.6.3.2 Gas-Liquid Mass-transferOver the majority of a cycle the gas within the bath will only be in contact with thematte. However, reactions with the slag may also take place within the spout and on thesurface of the bath. Within the matte the rate of the gas-matte reaction is controlled bygas-phase mass transfer. This suggests that the reaction will beFeS+3\/202=FeO+S ...[6.32Jbecause the partial pressure of oxygen at the bubble surface will be very low, favouringthe least oxidized iron compound. Minor element removal may be controlled bygas-phase, or liquid-phase mass-transfer, or by evaporation at the gas\/liquid interface. Tocalculate these rates a representation of the gas flow within the bath is required.6.3.2.1 Gas flowThe basic theory regarding the gas flow within the bath has been developed inSection 5. What remains is its implementation in a computer model. Two stages of themodel are required: bubble growth on the tuyeres and bubble rise. It is necessary thatthese models also consider heat transfer to the bubble, so all aspects will be considered926.3.2 Gas-Liquid Mass-transfertogether.For the bubble growth calculations, the basic model of Ashman et al.35 is followed,with the modifications noted in Section 5. Assuming that the minor elements are presentin the gas in very small quantities, the mole balance within the bubble is given bydn QP0 (x \u2014 1 \u201c 2...[6.33]where Ab is the bubble surface area given by2 2tab . - ...[6.34]Ab=2ta + sin e6e is the bubble eccentricity, and x is the ratio of 02 reacted to SO2 produced in thereaction. It has a value of 1.5 for reaction with matte, 1 for reaction with white metal,and will be infinite for reaction with slag and blister copper. In the latter case, to avoidthe numerical problems introduced by the us of infinity in the model, 10,000 is used sothat the term (x-1)\/x in equation 6.33 is approximately equal to one.The heat balance is given bydTb QP dn ...[6.35]nC---=CT3+hbAb(TB -Tb)+Ab(cLT-61)-CPTl,---This accounts for heating by convection and radiation. The heat of reaction is assumed toreport entirely to the bath. The bubble volume depends on the moles of gas and gastemperature, according todVRTidn vT\u2019...[6.36]dtP dt+ dtThe upwards motion of the bubble is given by936.3.2 Gas-Liquid Mass-transferdw 2 dV ...[6.37]V-j--=2V+CDitabw -w-whereWVbVB ...[6.38]The change in oxygen content of the bubble can be calculated fromdC2\u2014 JQP0 k A C\u2019\u2019 C\u201d dV...[6.39]dt RTO) b 02 \u00b02 dtand the sulphur dioxide content is given bydC0 dV[6.40]dtThese equations determine the size and position of the growing bubble. In themodel the equation governing the bubble shape (equation 5.4) is solved by a fmitedifference technique, while the above equations are solved simultaneously using aRunge-Kutta solution technique. At the end of each time step the bubble stability isdetermined according to equation 5.31 or 5.35, depending on the interfacial velocity, Ifthe bubble is unstable then it is assumed to break up into two bubbles, one of which isstill attached to the tuyere. The size of the free (secondary) bubble will depend on thesize of the initial bubble at breakup, and must be used as a fitting parameter.The equations relating to the motion and breakup of the bubble as it rises throughthe bath have been developed in Section 5. What must be considered here is the heat andmass balance within the rising bubble. The same basic equations can be used as in theprevious analysis, modified to account for the different conditions. Thus the molebalance and heat balance become946.3.2 Gas-Liquid Mass-transferdri (x\u20141, p...[6.41]dtl YQAbRTanddT,, dn ...[6.42]respectively.The equations governing the volume variation and sulphur dioxide concentration(6.36 and 6.40) remain unchanged, while the change in oxygen concentration is given bydC dV .. . [6.43]2_ i A ,-b (-bd \u2014 O2b\u2019-\u2019O \u2018\u00b0 dThe modified equations can then be solved by the same technique. By calculating thepassage of a primary bubble and all its related secondary bubbles through the bath, anumber of different parameters may be determined. The gas composition andtemperature at the bath surface are calculated, along with the amount of oxygen reactedand, therefore, the moles of FeO formed. From the amount of oxygen reacted, the heatgenerated by the reaction can be calculated for use in the heat balance. Also, bycombining the gas flow model with a mass-transfer model for the minor elements, therate of minor element volatilization may be calculated. This will by dealt with in thefollowing section.6.3.2.2 Mass transfer from liquid to gas bubblesThe mass transfer of the minor elements from any of the liquid phases to the gasbubbles may be controlled by one of three transport steps, or by a combination of thesteps. These are the liquid phase transport from the bulk of the bath to the bubble956.3.2 Gas-Liquid Mass-transfersurface, vapourization at the bubble surface, and gas phase transport from the bubblesurface to the bulk of the gas. The mass-transfer rate for each step may be detenninedseparately, and the three combined to give an overall rate equation.By assuming quasi steady state conditions, mass-transfer in the liquid phase can becharacterized by the equation1i = kA(Cf \u2014C1*) ...[6.44]or, replacing concentrations with mole fractions to give compatibility with thethermodynamic modelnI=kLAbp(Xr_X,*) ...[6.45]The vapourization rate can be calculated using the Langmuir-Knudsen equation.129aAb * ...[6.46](Pt\u2014P.)2itRTM,It is important to note that this equation was derived from the kinetic theory of gases forvapourization of a solid into a vacuum,13\u00b0and so some error may be introduced due to thegas pressure within the bubble. This equation is also modified to allow for integrationwith the equilibrium model usingp+po. ...[6.47]which gives_________*...[6.48](P\u00b0y.X. \u2014P. )-\u2018J2iR7MMass-transfer within the bubble can be characterized by the equationkQAb * B ...[6.49]n =\u2014--(P \u2014P1)966.3.2 Gas-Liquid Mass-transferAn overall equation for the mass transport rate to the gas bubbles can be obtainedby combining equations 6.45, 6.48, and 6.49. Rearranging equations 6.48 and 6.49 gives...[6.50]and* (RT B ...[6.51]P1 ni1jAJ+Pirespectively. These equations can then be combined to give= .(I2RTMI +z+PB...[6.52]Ac kGA)Rearranging equation 6.45 gives*______...[6.53]X. =XB, mLbPBwhich, when combined with equation 6.52 and rearranged gives,i. 1 1 pB ...[6.54]\u2014-=I i 1 1 1x7\u2014Ab kkkpm1 j:Oywhere...[6.55]k=-\u2018j2iuRTM,andkkP10y, ...[6.561g RT976.3.3 Mass Transfer Between Liquid PhasesThis equation is very similar to that derived for vacuum refining models, with differencesbeing due to the gas pressure within the bubble.131\u201d32 The one exception to thisformulation is the behaviour of the zinc in matte. Zinc oxide is thermodynamically morestable than iron oxide, so the zinc reaching the gas\/liquid interface will react. Thus, thevapourizing zinc species will be zinc oxide, and any oxide which does not vapourize willreport to the slag.6.3.3 Mass Transfer Between Liquid PhasesWithin any phase, I, the mass-transfer rate of component i to an interface is givenbyri * ...[6.57]= k[(C[ \u2014 C[)or, converting to mole fractions...[6.58]It is important to note that the interfacial concentration of a component will be differenton either side of the interface. At steady state, the rate of mass-transfer to the interfacewill be equal to the rate of mass-transfer away from the interface in the other phase.In general, at an interface between two liquid phases, I and J, there is a relationship(assuming instantaneous chemical kinetics)= K(X*)n .. .[6.59]where K is a constant determined by equilibrium considerations. In the second phase, J,the mass transfer rate of i away from the interface isri * ...[6.601j=kfp(Xi \u2014X!)986.3.3 Mass Transfer Between Liquid Phasesor, rearrangingri 1 ...[6.61]\u2014 Ak\u2019pCombining equations 6.58, 6.59 and 6.61, and rearranging, assuming n=1, gives( 1 ...[6.62]kp1 ?pThis is a general equation which can be used for mass-transfer between any two liquidphases, including cases where there is a reaction. If n is not equal to one the equationbecomes more complex. However, this does not occur in the present case.With no reaction, n=1 and...[6.63]K=LWhere there is a reaction at the interface, for example1 1 ...[6.641Cu2S)+ =Cu20(s)+ Sthe equilibrium constant is calculated as...[6.65]\u2014Ycu2oxcP.KR\u2014CU2SXCUPso n=1 and...[6.66]ycu2oPs996.4.1 Energy LossIn these equations the partial pressures of sulphur and oxygen represent the sulphur andoxygen potentials of the matte and slag respectively, and do not imply the presence ofgaseous species. The equilibrium constant is calculated at the average temperature of thetwo phases.6.4 Energy BalanceWithout the assumption of thermal equilibrium each of the component phaseswithin the converter may be at different temperatures. While this adds to the complexityof the model, the temperature variation may be significant. Heat transfer from the bath tothe gas is calculated as part of the overall gas flow model, so does not need to beconsidered further. However, the cooling effect of the gas on the bath is important.To calculate the temperature of each phase an energy balance must be carried out.That isenergy accumulated = energy input + energy generated .. . [6.67]- energy loss - energy consumedEach of the terms on the right hand side of equation 6.67 will be considered separately.6.4.1 Energy LossEnergy losses come from three sources, materials leaving the converter, conductionthrough the walls, and radiation through the mouth. A thermodynamic model of thenickel converter determined that, during blowing, energy leaving the converter as thesensible heat of the gas accounted for almost 90% of the total energy losses, whileradiation accounted for the majority of the remaining losses.\u201951006.4.1 Energy LossEnergy lost with the gas leaving the converter is calculated as part of the energyconsumption term, so will be considered there. The sensible heat of skimmed or castliquids does not affect the temperature of the remaining materials, so is not required forthe model.Radiation losses from the slag are assumed to be only to the mouth of the converter.As such they will be dependent on either the hood temperature during blowing, or theambient temperature (no mouth cover) while the converter is idle. The rate of energy losswill be given by...[6.68]The emissivity of the slag must be assumed.Allowing the different phases to be at different temperatures adds complexity to thecalculation of energy loss through the walls. The losses are not uniform over the entireconverter, and the outer wall of the converter is not at a uniform temperature. This wasdetermined by radiation pyrometer measurements carried out on an operating nickelconverter, which indicated that there was a considerable temperature variation over theconverter shell.\u201933However, since the wall losses are very small compared to the energy removed withthe gas and the radiation losses, a relatively simple calculation technique can be used.Thus, for the end walls97k, ...[6.69]4ew = 2\u2014ACf (TB \u2014 T)+--(T \u2014 T)]and for the barrel section2k1L r 1 .. .[6.70]q cb = R I (TB \u2014 T) +\u2014 (T \u2014 T)ln(JL 21016.4.2 Energy Consumptionwhere the constants k1 and k2 are due to the variation of refractory thermal conductivitywith temperature according to134kR =k1(1+k2T)= 1.08(1 +4.5(10)T) ...[6.71]for chrome-magnesite refractory.6.4.2 Energy ConsumptionIn the model the consumed energy is that which is required to bring all chargedmaterials up to the temperature of the phase to which it reports. This value is calculatedas=J CP(T)dT+Ae12] ...[6.72]TThe integral in equation 6.72 has been pre-calculated for use in the model, and gives afinal equationI I d. i\u2019 ...[6.73]q0 = Eai+biTB+ciT+_!JJTBValues of the constants in this equation are given in Table VT-HI.971026.4.2 Energy ConsumptionjCin J mor\u2019i a b, cx103 d1x105 NotesFe 7841.02 24.476 4.226Ni -6529.9 25.104 3.766Cu -141.3 31.38Co -3940.3 13.807 12.259FeS -8925.9 51.045 4.979 T<1468KFeS 4664.09 71.128 T>1468KNi2S -25182.5 20.318NiS -12784.5 38.911 13.389Cu2S -6958.62 84.935CoS -13682.7 44.35 5.251Fe304 -52247.3 200.832FeO -32218.8 68.199NiO -9589.16 46.777 4.226Cu20 -19636.7 62.342 11.924 T.<1509KCu20 -38545.1 96.274 .293 -1.925 T>1509KCoO -14205.8 48.283 4.268 -1.674S2 -12165.7 36.484 .355 3.76602 -9507.5 29.957 2.092 1.674SO2 -15407.7 43.43 5.314 5.941N2 -8493.394 27.865 2.134Si02 -29666.3 58.911 5.021Table VT-HI Integrated values of C for use in equation 6.73.1351036.4.3 Energy Generation6.4.3 Energy GenerationThe only sources of generated energy in the converter are the reactions. Since therates of the main reactions are controlled by oxygen mass-transfer within the gas, thetotal energy generated within a time step is approximated byqgen = flO2A1RAt ...[6.741The value of AHR will depend on the phase in which the reaction occurs. The reactionswhich may occur are: in blister copper2Cu + 1\/202 = Cu20 ...[6.751in white metalCu2S+ 02= 2Cu + SO2 ...[6.76]in matteFeS + 3\/202 = FeO + SO2 .. .[6.77]and in slag3FeO + 1\/202 Fe304 ...[6.78]Values of the enthalpies of reaction for each of these are given in Table VI-TV. Theactual reaction heat is also dependent on the temperature, so the values in Table VT-TVare modified accordingly. Some energy generation or consumption may also result fromenthalpies of solution, but this will be small in comparison to the main reaction enthalpy.Reaction AHR(klmor1)6.75 -166.76.76 -190.46.77 -463.46.78 -317.6Table VI-IV Enthalpies of reaction required for energy generation calculation. 1361046.5.1 Physical and Thermal Properties6.4.4 Interphase Heat-transferEnergy will be transferred between phases by convection and mass-transfer. Theconvective heat-transfer will be given by411=hA!,(T\u2014T) ...[6.79]and the heat transferred with materials passing between phases is given by= ...[6.80]It should be noted that in cases where there is a reaction at the interface the heatgenerated by the reaction is assumed to be contained in the metal-containing product, andwill report to its corresponding phase.6.5 DataIn a model of this sort a wide range of data is required. Unfortunately, much of thisdata is unavailable in the literature, or only present for a narrow range of temperaturesand\/or compositions. Therefore, it is necessary to assume that whatever data is availableis valid over the entire range of conditions present in the model and, if nothing isavailable, required values must be assumed or fitted.6.5.1 Physical and Thermal PropertiesData concerning the physical and thermal properties is required for the gas and thethree condensed phases. Most of these properties vary considerably with compositionand temperature, but it is unusual to find a study which considers both together. Therequired properties and the equations used to calculate them are given in Table VT-V.The equation for the slag viscosity given in Table VT-V is derived directly frommeasured viscosities,\u201940while the equations for matte and blister copper viscosities areestimated from measured diffusivities. The constants used in the gas viscosity equationin Table VT-V are given in Table VT-VT.1056.5.1 Physical and Thermal PropertiesPhase Property Ref.Density_(kgm3)Slag 3297 + 128.45[FeO] \u20140.1 1454T[SiO2 137Matte 3880 + 403.6[Cu]M + 4589[Cu] \u2014 3750[Cu] 138Blister Copper 7800 139G\u201d -Gas3.469(103)_JViscosity_(kg_rn_i s1)[Fej \u2018V\u2019 140Slag\u2014 0.7l43[s.QJ ,JJ2.063(105000 139Matte3.36(loiexp(TM JBlister Copper 4866\u2019 1417.688(105)exPL\\ TBGas Co+ClTG+C2T+C34 142Surface Tension (Nm1)Slag 0.7148\u20143.17(10\u2019)(T\u2014273) 138Matte ( X4 (2.271\u20141.673x ( X, (1.149+1.188Xg\u2019 143XF+XCJL 5\u20143X JXF+XcuJ1 3+2XN JBlister Copper 1.136\u2014 1.6(105)TB 144Thermal_Conductivity_(W rn_i K1)Slag 2.09 77Matte 13.399\u2014 17.875[Cu]M+25.551[CU1\u2014 13.74[Cu] 138Blister Copper 133.9 139Table VT-V Physical and thermal properties of the gas and condensed phases.1066.5.2 Thermodynamic DataCo C, C2 C3 C4(x105) (x107) (x109) (xlO\u20192) (xlO\u20196)7.164 -5.083 1.578 -1.785 6.667Table VT-VT Coefficients for gas viscosity equation (air).\u2019426.5.2 Thermodynamic Data6.5.2.1 Free energyTo calculate the equilibrium composition of the matte the free energies of thereactions given in Table VT-il must be known. Values of these are given in Table VI-Vil.Reaction AG(Jmo11)2Cu + 1\/2S2=Cu2S -147 100+42.05TNi + 112S2= NiS -l29300+54.06T2Ni + 112S2=Ni2S -152500+46.06TFe+ 1\/2S2=Fe -115300+30.63TCo + 1\/2S2= CoS -125000+48.12TPb+ 112S2=PbS -138400+64.14TZn + 1\/2S2= ZnS -264800+98.20TTable VT-Vil Free energy of formation of matte compounds.\u201942In addition, free energy data is required to calculate the equilibrium constants usedto determine rates of interphase mass-transfer. The reactions and their corresponding freeenergies are given in Table VI-VITI.Finally, to calculate the compositions of the slag and gas phases, free energies oftwo further reactions are required. These are given in Table VT-TX.1076.5.2 Thermodynamic DataReaction AG(J_mor\u2019)Cu2S + 1\/202 = Cu20+ 1\/2S2 28360-2.59TNiS + 1\/20 = NiO + 112S2 -122800+41.67TFeS + 1\/202 = FeO + 112S2 -128200+21.13TCoS + 1\/202 = CoO + 1\/2S2 -107800+22.6 iTPbS + 1\/202 = PbO + 1\/2S2 -57950+21.38TZnS + 1\/202 = ZnO + 1\/2S2 -80330-3.35TReaction AG(Jmol\u2019)3FeO + 1\/202 = Fe304 -402000+169.77T1\/2S2+ 02 = SO2 -363000+72.42TTable VI-IX Free energy of reaction for slag and gas reactions.\u201935The data available regarding the free energies the minor elements presents someproblems. While the agreement for reactions involving single elements in the gas phaseis not bad (Figure 6.4), the free energy of formation of the oxides and suiphides of arsenicand antimony do not appear to be consistent. Figure 6.5 shows the variation of AG withtemperature for the formation of SbO and SbS, and Figure 6.6 shows the values for AsOand AsS. It is obvious that a problem exists, particularly in the case of SbO, where twopapers, published in the same year and having one author in common,30\u2019use vastlydifferent equations for the free energy of the reaction1 1 ...[6.811Sb2(g) + 02(g) = SbO (g)Table VT-Vu Free energy of reaction for matte-slag reactions.\u2019351086.5.2 Thermodynamic Data50403020C)100-10-201000 2000Figure 6.4 Comparison of reported values of free energy of reaction.1200 1400 1600 1800TEMPERATURE (K)1096.5.2 Thermodynamic Data5SbSChaubal et al. [291Seo and Sohn [30]\u2022 -10 - Nagamori and Chaubal [26]Hino et al. [144]Kim and Sohn [31]\u2014.\u2014-----20 --25 I I1000 1200 1400 1600 1800 2000TEMPERATURE (K)20SbO100\u20220-10-20 I1000 1200 1400 1600 1800 2000TEMPERATURE (K)Figure 6.5 Comparison of reported values of free energy of formation of SbS andSbO.1105AsS6.5.2 Thermodynamic Data01400 1600 1800 2000TEMPERATURE (K)Figure 6.6 Comparison of reported values of free energy of formation of AsS andAsO.6.5.2.2 Enthalpy of ReactionValues required to calculate the heat produced by the reactions are given inTable VI-IV.0-5-10-15Chaubal et al. [29]Sea and Sohn [30]\u2014\u2014\u2014\u2014 Nagamori and Chaubal [2611400 1600TEMPERATURE (K)1800 2000-20-25-5AsO-20-25-30 \u20141000 12001116.5.2 Thermodynamic Data6.5.2.3 Activity coefficientsThe equilibrium calculations within each phase and the mass-transfer calculationsbetween phases, require values for activity coefficients. Equations for calculating thesefor most of the major constituents can be found from the literature, and those used aregiven in Table VI-X.Phase i Ref.Slag FeO exp()log(l.42Xp\u20aco \u2014 .2)) 20Fe304 0.69 +56.8XFeO + 5.45X0 17NiO exp(()\u2014 1.62) 146Cu20 9 147CoO 0.66 148Matte Fe 40 149Ni 15 97Cu 14 17Co 25 149FeS exp((8)ln(.54 + + .52XFeS)) 20(1 1840 \u2018II I j I\u2014.6Ni2S 10 M) 150NiS 1 97Cu2S 1 17CoS .4 151Fe304 (1573\u201d\\ 20expqTM J (4.96 + 9.9 logX +7.43(logX)2+2.55(logX)3)Table VI-X Activity coefficients of the major constituents of the matte and slag.1126.5.2 Thermodynamic DataLead is a common contaminant in copper mattes, and is often present in relativelylarge concentrations. Copper is also an important contaminant in lead, so there isconsiderable information available.15261 Azuma et al. have determined that the activitycoefficient of lead in copper mattes is equal to one at 1473 K.\u201952 However, the data ofEric and Timu\u00e7in suggest that there is a considerable negative deviation from ideality,particularly at high matte grades.\u201958 The same study indicates that the activity coefficientof PbS at infinite dilution in white metal is 0.035,158 and in dilute solutionsln\u2019y = 6.970Xpbs \u2014 3.344 ...[6.82]at 1473 K. Rome and Jailcanen calculated a value of 0.155 for the same parameter, andsuggest that it is relatively constant down toX2 = 0.7.160 Their results also indicate thatthe activity coefficient of lead in white metal is approximately 4, but is quite sensitive tothe sulphur activity.The activity coefficient of lead in copper metal has been calculated by a number ofresearchers,162468 and there is fairly good agreement between the various studies. A valueof 5.7 is used in the model. The activity coefficient of PbO in slag in zinc slag-fuming isgiven by169(\u20143926 ...[6.83]T Jand this agrees well with measurements in copper smelting slags.\u20197\u00b0 This value appearsto be unaffected by the oxygen partial pressure.There is considerably less information available regarding zinc. However, there issufficient data to give values for activity coefficients in the three phases. In copper, zincis reported to be a regular solution with\u2019631136.5.2 Thermodynamic Datar\u201464O0X1 ...[6.84]Yzn=exP[RT jFor dilute solutions of ZnS in matte, the activity coefficient has been calculated as25= 6.8 \u2014 O.02(T \u2014 1523)\u2014 [Cu]M ...[6.85]while at 1523 K it is reported to be represented by the polynomial33= 14.21 \u2014 136.6X + 437.3X \u2014 405X ...[6.861In slag the ZnO activity coefficient can be calculated from26E9201 ...[6.87]Unlike lead and zinc, antimony is generally thought to dissolve in atomic form in allthree condensed phases present in copper converting. The activity coefficient ofantimony in copper is very low, with reported values ranging from 3.7x10 to1 .4x102\u201960\u201d2\u201972The higher of these values are considered to be the more accurate.The activity coefficient of antimony in matte and white metal is considerably higherthan for copper, with the value for white metal being 0.44 and the value in mattecalculated from173=exp[4.8584\u2014 l.936X] ...[6.88]at 1473 K. However, both of these values are very sensitive to the sulphur activity whenthe matte is sulphur deficient. The activity coefficient of antimony in matte is alsosensitive to the oxygen potential of the system, indicating that some oxide may be formedat high oxygen partial pressures.93There is relatively little data concerning antimony dissolution in slags.170\u20194 What isavailable is given in the form of distribution ratios, which must be converted to activitycoefficients. An analysis of the data of Nagamori et al. indicates that there is a1146.5.2 Thermodynamic Dataconsiderable scatter in the experimental results.\u20197\u00b0 The distribution ratio (Lsb) was givenas 30, with the oxygen potential having no apparent effect. This results in an activitycoefficient of 0.4 for antimony in slag.The behavior of arsenic in copper converting systems is similar to antimony. As inthe case of antimony there is a wide variety of information available concerning arsenicdissolution inmatte,160\u20191735and copper,27\u2019162375181 with much less availableregarding the slag.\u201970\u2019182 There is a very wide range of reported values of; from5x107 167 to 1x102.8\u2019 Some variation with temperature is seen, but it is not consistentbetween experimenters. It is probable that the lower values of arsenic activity coefficientare incorrect due to the values of free energy and gas vapour pressures used in theircalculation.181The activity coefficient of arsenic in white metal is reported to be in the range 0.2 to0.12, dropping to l.2x10 as sulphur is removed.176 Variation of the iron content of thematte has been found to cause a considerable change in the arsenic activitycoefficient.160\u2019173 At 1473 Klog\u2019 = 1.35 \u20140.848X2 ...[6.89]but sulphur deficiency in the matte causes a considerable reduction in the valuecalculated from this equation.\u201973There is significant scatter in measured data regarding arsenic in slags, althoughthere is agreement that the dissolved form is monatomic As. Lynch and Schwartzemeasured values of varying from 1 to 10 depending on slag composition.\u201982 Nagamoriet al. reported an average value of LAS\u201d of 300, indicating that dissolution of arsenic inslag equilibrated with molten copper is very small.\u20197\u00b01156.5.2 Thermodynamic DataLike antimony and arsenic, it is generally accepted that bismuth dissolves inmonatomic form in all phases concerned in copper converting, although there is someevidence of sulphide formation at high sulphur activities.\u201960 However, its behaviour doesnot follow the same trends. The activity of bismuth in copper shows a positive deviationfrom ideality,\u201963\u201d8 with an activity coefficient given by\u20197\u00b0c 43751 ...[6.91]= exp[\u20142.04+ T j51001 ...[6.92]YB=exp \u20142.45+TBoth of these equations give values which agree well with the results of otherInformation on bismuth in white metal and matte is limited, and the studiesavailable show very poor However, the difference can be explainedby the value of bismuth vapour pressure used.\u201985 Oxygen has no noticeable effect on theactivity of bismuth in matte, and BiS vapour is formed in preference to BiO, which iscloser to the behavior of lead than arsenic and antimony.\u20196\u2019Anumber of studies have been carried out concerning the distribution of bismuthbetween slag and copper ormatte.161\u201d708192 Most of these calculate distributioncoefficients, and there is considerable disagreement regarding the form of bismuth in theslag. However, the most recent studies\u20196\u201d92report that oxygen partial pressure has aneffect on the amount of bismuth reporting to slag, and one gives activity coefficients inslag of 1500 and 1.1(108) for Bi and BiO respectively at 1458K and PBI=7.5(104).\u201992At1166.5.2 Thermodynamic Datahigher temperatures the activity coefficient of Bi is increased and that of BiO is reduced.However, the magnitude of these numbers indicates that very little bismuth will report tothe slag.Table VI-XI summarizes the activity coefficients of the minor elements used in themodel.MattePb 23PbS exp(.2008\u2014 2.3245X)Zn 25ZnS 6.8\u2014O.02(TM\u2014 1523) \u2014 [CuJMAs1(1.35_ o.848x)Sb exp(4.8584\u2014 l.936X5)Bi 13.6White MetalPb 4PbS exp(6.97XPbS \u2014 3.344)Zn 3ZnS 6.8 \u2014O.02(TM\u2014lS23)\u2014[CuJMAs 0.12Sb 0.44Bi 6.1Table VI-XI Minor element activity coefficients used in the model.1176.5.2 Thermodynamic DataSlagPbO (\u20143926expiZnO (920expi \u2014T8As 5Sb .4Bi 1500Blister CopperPb 5.7Zn (\u20146400XexpiRTBAs 1(102)Sb 1.4(102)Bi exp_2.04+4?5JTable VI-XI Minor element activity coefficients used in the model (continued).6.5.2.4 Equilibrium vapour pressuresEquilibrium vapour pressures of the minor elements are required to calculateliquid-gas mass-transfer rates. The values used are given in Table V-Xll.118Specie Vapour Pressure Ref.As exp((_)+ 10.62) 31Bi exp((_22)+ 11.75) 31Sb exp((_)+12.336) 29(\u2018 23325Pb exp_\u2014\u2014)+l9.O65_0.985lnT) 29PbO exp((\u2014)+13.843) 29PbS exp((_6)+12.977) 29I\u2019( 15243Zn exp(_\u2014--)+21.782_1.255lnT) 26ZnO exp((_2)+4.651) 266.5.3 Kinetic Data...[6.92]Table VI-Xll Equilibrium vapour pressures of the minor elements.6.5.3 Kinetic Data6.5.3.1 DiffusivitiesThe diffusivity of each species in each phase is required for the mass-transfercalculations. Unfortunately, very little data is available for the system underconsideration. Therefore, a theoretical approach must be used. Assuming sphericalparticles following Stokes\u2019 law in a viscous liquid, the Nernst-Einstein relation for thediffusivity is193kT6iitrwhere r is the atomic\/molecular radius of the particle and k is the Boltzman constant.1196.5.3 Kinetic DataThis equation requires atomic or molecular radii of the diffusing species, whichposes another problem: while the minor elements and blister copper constituents arepresent in elemental form, the other species are present as compounds. The radius valuesused to calculate the diffusivity in the matte and slag will depend on the nature of thesolution, If the solution is ionic then the ionic radii of the diffusing elements must beused, whereas, if the solution is covalent then the molecular radius of the diffusingspecies should be used. To determine which case should be used the approximate degreeof ionic bonding can be found using the Pauling electronegativity scale. This suggeststhat the bonding in mattes is less than 12% ionic, while that in slags is closer to 50%.136It is important to note that these numbers are for solid compound, and there may be somedifferences for liquids. In fact, it has been suggested that the molten matte is completelyionic,\u201994but there is no direct evidence of this. The relatively low amount of ionicbonding in mattes suggests that the diffusing species will be covalent molecules, while inslags diffusion of ions is likely to predominate. Based on this assumption the requiredradii are given in Table VI-XllI. Values of diffusivity caluculated using equation 6.92for Fe2 diffusion in slag and matte can be compared with measured values. A diffusivityof 1 .4( 10h1)m2c\u2019 is calculated for Fe2 diffusion in a slag with an iron to silica ratio of0.25 at 1400 K, while a value of 1.13(1O)m2s\u2019 is obtained for Pe2 diffusion in matte atthe same temperature. These are lower than reported values, which range between5(10h1)m2s\u2019 and 5(108)m2s\u2019 in slag\u201995\u20198and between 2.9(10)m2s\u2019 and 1.4(10)m2s\u2019inIn the gas phase oxygen is the primary diffusing species and its diffusivity is givenby4\u00b01206.5.3 Kinetic DataSpecie\/ion radius Specie\/ion radius(nm) (nm)As 0.125 Cu4\u2019 0.096Bi 0.17 Pb24 0.12Sb 0.145 Zn24\u2019 0.074Cu 0.128 Fe24 0.076Pb 0.175 Fe3 0.064Zn 0.133 Ni2 0.072FeS 0.241 Co24\u2019 0.074Cu2S 0.35 1 NiS 0.237CoS 0.239 Ni2S 0.303PbS 0.285 5i02 0.299ZnS 0.239Table VI-XllI Atomic\/ionic\/molecular radii of matte, slag and bullionconstituents.\u201936=3.754(10\u201d)T\u20142.31(10\u2019j ...[6.93]This equation is actually for oxygen diffusivity in argon, but calculations based on anequation derived from the kinetic theory of gases indicate that the error involved in usingthis equation is less than five percent.20\u00b06.5.3.2 Mass-Transfer CoefficientsThe mass-transfer coefficient between the liquid and gas for rising bubbles iscalculated from\u201942k1d,. ( dbw\u2014= 1+1 l+q3i121...[6.9416.5.3 Kinetic DataUnfortunately, there are no correlations available for mass-transfer on the gas side duringbubble rise, so it is assumed that equation 6.94 holds for both sides of the gas-liquidinterface. However, an equation for mass-transfer during drop formation has beenderived,20\u201915...[6.95](v0D)\u2018rbk =2.312gUbwhich can be applied to the bubble formation section of the model.The liquid-liquid mass-transfer coefficient can be given as...[6.961k, =where 8 is the boundary layer thickness. While values of boundary layer thickness arenot known, they can be approximately calculated if it is assumed that they arecomparable to the velocity boundary layer.6.5.3.3 Heat-Transfer CoefficientsThe gas-liquid heat-transfer coefficient is calculated from143Nu =2+O.6Rep). [6.97]and the liquid-liquid heat-transfer coefficient between phases I and J is calculated fromh1 ...[6.98]h=6h1+61h1227.1.1 Bubble Growth7 MODEL VALIDATION7.1 Bubble Model Validation7.1.1 Bubble GrowthThere is a limited amount of data available concerning bubble growth duringhorizontal injection for comparing with the model predictions, however some validationcan be carried out. Oryall and Brimacombe have reported the gas fraction distribution inhorizontal injection of air into mercury.\u20191\u2019From this an approximate maximum bubblepenetration can be determined for comparison with the model. Table Vu-I compares themodel predicted maximum bubble penetration for four different injection conditions withthe 1% gas fraction line reported by Oryall and Brimacombe.\u201d1The maximumdifference is 6 mm, indicating a relatively good fit.Gas Flow Tuyere Predicted Measured Predicted MeasuredRate diameter Penetration Penetration Width Width(Nm3s1) (m) (m) (m) (m) (m)0.002676 .00325 .076 .07 .047 .0460.001615 .00325 .058 .064 .039 -0.001844 .00476 .054 .055 .042 -0.000710 .00325 .037 .043 .029 -Table Vll-I Comparison of measured\u20191\u2019and predicted gas penetration in mercury.Further validation can be obtained from the bubble frequency. Hoefele andBrimacombe have reported a bubble formation frequency of between 10 and 12 s_i in anickel converter.202 The model predicts a variation in bubble formation frequency, with arange of 9.5 - 10.5 s\u2019. Other studies have determined that the bubble frequency in copperconverters is affected by the extent of refractory wear.\u201d5\u2019203 The bubble frequency in anewly relined converter was found to be between 8 and 14 s_I, but this value droppedrapidly to a steady value close to 4 The rapid decrease in bubble frequency is1237.1.2 Bubble Riseexplained by the accelerated refractory wear around the tuyereline, which usually resultsin the formation of a notch. There are two main mechanisms by which the notch reducesbubble frequency; by reducing the bath flow rate at the tuyere tip, and by preventing thesection of the bubble close to the tuyere from rising. The notch may also increase tuyereinteraction, but this does not appear to affect the bubble frequency.\u201915 The modelassumes that there is no notch, so the agreement is good when compared to the newlyrelined converter.7.1.2 Bubble RiseVerification of the bubble rise portion of the model is even more difficult. Only asmall amount of information relating to horizontal injection is available. The physicalmodelling carried out by Adjei gives some data which can be used, but it can only give arough validation due to its imprecise nature.37The formula derived for calculating the bath velocity within the plume, gas holdup,and spout height can be tested by comparing measured and predicted spout heights andgas fractions. Figure 7.1 shows a comparison of calculated spout heights with thosemeasured by Adjei37. It can be seen that the model predicts a shorter spout height thanwas measured. However, this is to be expected, as the spout heights were measured fromtime lapse photographs, which tend to include the liquid ejected from the spout in thespout itself, thus increasing the apparent size. This suggests that the predicted values areat least approximately correct.Physical modelling in bottom injection systems also provides some data which maybe used for verification. Table Vil-il shows a comparison of measured values of gasfraction, bath velocity in the plume, and spout height with those predicted by the model.It can be seen that the predicted spout heights are slightly higher than those measured,1247.1.2 Bubble Rise018 -0.17- V0.16 -0.15 -0.14 -0.13 -II 0.12 - \u2014\u201400.11 - \u2014\u2014\u2014\u20140 \u2014\u2014-\u2014\u2014\u2014\u2014\u2014\u2014\u2014-\u2014-\u2014\u2014----\u2014\u2014-\u2014----\u2014\u2014-\u2014---\u20140.08 -0.070.06 -0.050.04- I I0.001 0.005 0.007 0.009GAS FLOW RATE m1 sFigure 7.1. Comparison of measured37and predicted spout height.while the predicted gas fractions are high at the low flow rate and low at the high flowrate. However, the values of superficial gas velocity are not precise, due to uncertaintiesin the cross-sectional area of the plume. Also, the data of Castillejos andBrimacombe204\u20195indicate that the average gas fraction varies with height above thetuyere in bottom injection, while Oryall and Brimacombe report that the gas fraction isrelatively constant in the plume region for horizontal injection.11\u2019The predicted bubble surface area and gas-phase mass-transfer can be tested by acomparison of predicted and measured gas utilization. However, there is a problem withthe measured data, since Adjei37 did not consider the effect of a surface reaction. In thiscase the model calculates a considerably lower gas utilization than was measured.Unfortunately there is not sufficient information available to calculate the extent of thesurface reaction. In particular, the diffusion boundary layer thickness on the bath surfaceTUYERE SUBMERGENCE (m)086 A MEASUREDPREDICTED.117 v MEASUREDPREDICTEDVVVA0.0031257.1.2 Bubble RiseGas Approximate Approximate Predicted Approximate Predicted Approximate Predicted Ref.flow superficial gas fraction gas bath velocity bath spout height spoutrate gas velocity fraction (ms1) velocity (cm) height(cm3s\u2019) (ms\u2019) (ms1) (cm) \u2014371 .11 .12 .16 - - - - 2041257 .18 .25 .22 - - - - 204371 .11 - .16 4 4.7 206876 .17 - .21 - - 6 6.9 2061257 .18 - .22 - - 7 7.4 2061630 .21 - .25 - - 8 9 206167(1) .11 .26 .2 207500(1) .32 .54 .39 2071000(1) .66 .61 .57 207167(2) .059 .15 .13 V 207500(2) .17V.26 .27 2071000(2) .45 .42 .41 207100 .03 .05-.3 .08 .2-.3 .235 - - 122(1) nozzle diameter = .28 cm(2) nozzle diameter = .5 cmTable VU-TI Comparison of measured and predicted gas fraction, bath velocity,and spout height in vertical injection systems.and the total bath surface area are required, but are not calculable. The diffusionboundary layer thickness wifi be inversly proportional to the square root of the gasvelocity over the bath surface208,so will be reduced by increasing both the gas flow rateand the tuyere submergence. Both of these factors will also increase the bath surfacearea, and so have a large effect on the surface mass-transfer. If it is assumed that the bathsurface is flat and that the surface boundary layer thickness is a function of the gas flowrate and tuyere submergence, then the predicted overall gas utilization can be fitted to themeasured values usingo = (.2374 \u2014 20.06Q + .00256 J (1.621 (l0) + 4.023(10-5)]1267.1.2 Bubble Riseand Figures 7.2 and 7.3 show the fit obtained. While these curves are fitted, they showthat the model is at least able to predict the general trends in gas utilization. It shouldalso be noted that some of the errors in gas utilization may be caused by the uncertaintyin the gas-phase mass\u2014transfer coefficient.099 -o \u00f7LU +0.95- .\u2014&. __\u2014+ \u2014-\u2014\u2014\u2014a: ---pLUQ o. ---.o -a:D -TUYERE SUBMERGENCE (m)X MEASURED0.85- .057 PREDICTED:0.001 0.003 0.005 0.007 0.009GAS FLOW RATE (ms)Figure 7.2 Variation of fraction sulphur dioxide reacted with gas flow rateincluding the fitted effect of surface reaction.1277.2.1 Bath Temperature0.95CuJ0.9wa: 0.85(iiC0.8Ca: 0.75D\u2014j 0.7DCl)0.65___________F0a:LI0.550.5 I I I I I I0.01 0.03 0.05 0.07 0.09 0.11 0.13BATH DEPTH (m)Figure 7.3 Variation of fraction sulphur dioxide reacted with tuyere submergenceincluding the fitted effect of surface reaction.7.2 Copper Converter ValidationThe charges followed in the plant trials were simulated using the model. Thevalidity of the model can be tested by comparing predicted temperatures andcompositions.7.2.1 Bath TemperatureThe temperature variation for the three charges are given in Figures 7.4-7.6.Although there are only a small number of measured temperatures, it can be seen that themodel predictions are reasonable in the slag blows. The matte and slag temperaturespredicted in the copper blows are generally low, but the blister copper temperature fitsthe measured temperatures well.+\u00f7\u00f7 MEASUREDPREDICTED128LUa:DIa:LU0LUI-LUDUJaLUI-7.2.1 Bath Temperature100 200 300 400170016001500140013001200110010000 500TIME (mm)Figure 7.4 Comparison of measured and predicted copper converter temperaturescharge 586, February, 1994.1600150014001300120011000 500TIME (mm)Figure 7.5 Comparison of measured and predicted copper converter temperaturescharge 588, February, 1994.100 200 300 4001297.2.2 Slag Composition160015501500Uia:D1450a:UiaLUI\u2014U 1400135013000 100 200 300 400 500TIME (mm)Figure 7.6 Comparison of measured and predicted copper converter temperaturescharge 595, February, 1994.7.2.2 Slag CompositionA comparison of the measured and predicted slag compositions are given inTables Vil-ifi - VII-V, and Figure 7.7 shows a comparison of the measured and predictedslag iron and silica contents. The iron contents of the slags are predicted well for charges586 and 595, but not as well for charge 588. Tn most cases, the amount of silica in theslag is overpredicted. There are two factors which contribute to this overprediction: themodel includes all inert materials with the silica and a large, but unknown, quantity offlux is lost as the converter begins blowing after a flux addition. This latter reason willalso explain some of the discrepancies in the iron assays.The amount of copper in the slags is underpredicted in almost every case. Theexceptions being in charge 595, following the addition of copper slag to the converter. In1307.2.2 Slag Compositionone of these slags the copper content is overpredicted, while in the other it is very close tothe measured value. Zinc in slags is generally overpredicted, while lead is usuallyoverpredicted for the slags early in the charge, and underpredicted for later slags. Thearsenic content of the slags is underpredicted for charges 586 and 588, but is quite closefor charge 595, for which more accurate assays were available.Slag Fe Cu Zn Pb Si02 As1 Model 45.4 2.81 4.62 .55 27.9 .02Assay 41.6 7.13 3.97 0.7 17.6 .042 Model 40.0 0.85 4.55 0.18 38.0 .010Assay 39.2 6.46 3.89 .73 22.0 .043 Model 38.7 0.78 4.29 0.16 39.5 .01Assay 37.4 6.13 4.00 1.28 22.8 .04Table Vil-ifi Comparison of model predicted slag compositions with assays,(weight percent), #1 converter charge 586, Feb., 1994.Slag Fe Cu Zn Pb Si02 As[ 1 Model 40.9 3.41 6.18 1.54 29.8 .0252L_________ Assay 45.1 5.35 4.51 .67 21.8 .052 Model 49.7 2.19 5.38 .372 21.2 .021Assay 36.5 7.04 3.82 .95 23.2 .05Table Vll-IV Comparison of model predicted slag compositions with assays,(weight percent), #1 converter charge 588, Feb., 1994.1317.2.2 Slag CompositionSlag Fe Cu Zn Pb Si02 As Sb Bi1 Model 36.9 13.9 4.19 1.41 26.3 .0241Assay 39.8 8.1 3.93 0.8 18.8 .0152 Model 39.5 12.6 4.61 1.27 23.8 .0218 .0019 .0002Assay 38.3 12.4 3.80 0.7 17.8 .022 .0058 .00073 Model 44.1 6.44 3.72 0.645 26.2 .0113Assay 38.2 4.16 4.38 1.45 25.5 .0124 Model 48.7 2.43 3.68 0.239 24.9 .0044 .0014 .0003Assay 40.6 3.52_- 4.44 2.06 24.3 .016 .0057 .0002Table Vll-V Comparison of model predicted slag compositions with assays,(weight percent), #1 converter charge 595, Feb., 1994.60I\u2014Z 40 -uJC.)Lu0I\u2014z(!3ij 30- AAALuIR0NA A SILICA20 -10 I10 20 30 40 50MEASURED (WEIGHT PERCENT)Figure 7.7 Comparison of measured and predicted iron and silica contents incopper converter slags, charges 586, 588, and 595, Feb. 1994.1327.2.3 Matte Composition7.2.3 Matte CompositionMatte and blister copper compositions are compared in Tables Vil-VI - Vil-VIll,and Figure 7.8 shows a comparison of the measured and predicted iron and coppercontents of all sampled mattes. The tables and the figure show that the predicted iron,copper and sulphur in the matte are close to the measured values, up until the formationof white metal. The one sample of \u201cmetal\u201d taken during the copper blow of charge 586(sample 4, Table Vil-VI) has a much higher copper content and correspondingly lowersulphur content than is predicted by the model, this sample is not included in Figure 7.8.This is most likely explained by entrainment of blister copper in the matte. The predictedcompositions of three mattes reported in the tables, one in Table Vil-Vil and two inTable Vil-Vifi, are actually a combination of matte and slag in the correct proportions togive the assayed silica content of the mattes. Even with this correction, however, themodel predictions are not good. Some later mattes in charge 595 also had a relativelyhigh silica content, (see Table IV-TV), but the model predicted silica contents close to theassayed values so no correction was made.Zinc is predicted reasonably well for charges 586 and 588, but is consistentlyunderpredicted for charge 595. The lead content of the mattes is overpredicted for almostevery sample. This, combined with the underprediction of lead content in the slags,indicates that there is more oxidation of lead from the matte, particularly at higher mattegrades. Matte arsenic contents are predicted well for all charges, and the antimony andbismuth predictions for charge 595 are also reasonable, with the exception of the bismuthin sample 9 which is too high.1337.2.3 Matte CompositionMatte Fe Cu Zn Pb S As1 Model 6.24 68.6 1.1 2.21 19.3 .032Assay 4.1 70.9 .83 2.89 20.2 .032 Model 4.18 71.4 .69 2.38 19.0 .031Assay 3.09 71.0 .59 2.63 21.6 .023 Model 1.13 74.9 .093 3.24 18.1 .033Assay 1.1 74.7 .3 .65 19.8 .014 Model .62 73.9 .125 4.38 17.7 .045Assay .49 90.1 .13 .23 5.55 .04Blister Model - 99.707 .1449 .145 1 - .0020Assay - 99.04 .002 1 .0072 - .0073Table Vil-VI Comparison of model predicted matte and blister coppercompositions with assays, (weight percent), #1 converter charge 586, Feb., 1994.__Matte Fe Cu Zn Pb S As1 Model* 22.7 40.2 1.41 3.0 12.3 .0351Assay 38.6 23.2 4.82 .47 7.7 .032 Model 4.03 71.5 .42 1.21 18.9 .0365Assay 2.87 70.3 .66 .51 20.8 .033 Model 1.11 73.9 .19 1.11 18.3 .0346Assay 1.43 74.0 .28 .4 19.7 .02Blister Model - 99.68 .1729 .1731 - .0006Assay - 97.89 .0044 .0072 - .0096Table Vu-Vu Comparison of model predicted matte and blister coppercompositions with assays, (weight percent), #1 converter charge 588, Feb., 1994.Asterisk indicates combined matte and slag to bring the matte silica content up to assayedvalue.1347.2.3 Matte CompositionMatte Fe Cu Zn Pb S As Sb Bi1 Model* 17.1 52.2 1.81 1.38 16.8 .0248Assay 23.3 37.3 2.75 1.00 15.1 .0222 Model* 18.4 49.3 1.9 1.43 14.8 .0221Assay 25.6 31.2 2.95 .8 11.1 .0193 Model 9.29 62.0 .973 1.5 18.2 .0202 .0026 .0016Assay 11.8 57.1 1.6 1.17 17.9 .014 .0028 .00134 Model 10.9 60.8 .747 1.56 18.4 .0188Assay 14.5 49.8 1.83 1.01 17.1 .025 Model 10.3 62.0 .451 1.62 18.4 .0147Assay 9.01 58.4 1.31 1.13 18.4 .0146 Model 10.6 62.1 .292 1.7 18.9 .0156 .0021 .0014Assay 7.43 63.2 1.33 1.21 20.1 .018 .0022 .00147 Model 12.0 60.9 .395 1.7 19.5 .0172Assay 8.89 58.5 1.48 1.18 20.0 .0168 Model 10.7 62.6 .22 1.69 19.4 .0171Assay 8.45 59.0 1.45 1.32 21.2 .0159 Model 8.2 65.6 .0658 1.79 19.2 .0167 .0022 .0015Assay 7.87 62.7 1.3 1.15 20.3 .015 .0019 .000210 Model 6.28 68.1 .172 1.84 19.3 .0182Assay 4.15 65.7 .75 .89 19.9 .01211 Model 2.59 72.5 .0315 1.98 18.7 .0175Assay 4.39 62.8 .82 .73 17.3 .01Table Vil-Vill Comparison of model predicted matte compositions with assays,(weight percent), #1 converter charge 595, Feb., 1994. Asterisk indicates combinedmatte and slag to bring the matte silica content up to assayed value.1357.3 Nickel Converter Validation5 10MEASURED (WEIGHT PERCENT)15a. 15Izwb.702uJII 65uJI\u2014I0ij 604545 55 60 65 75MEASURED (WEIGHT PERCENT)Figure 7.8 Comparison of measured and predicted a. iron and b. copper contents incopper converter mattes, charges 586, 588, and 595, Feb. 1994.7.3 Nickel Converter ValidationAs with the copper converter, there is phase composition and temperature dataavailable for the nickel converter which may be compared to the model predictions. Inthis case, however, there is considerably more temperature data available, but the13650 707.3.1 Bath Temperaturecompositions are less accurate.7.3.1 Bath TemperatureA comparison of the measured and predicted bath temperatures are given inFigures 7.9-7.12. The measured temperatures were obtained using a two colourpyrometer mounted in the hood and aimed at the bath surface, so in most cases shouldgive the slag temperature. However, the figures contain both the predicted matte and slagtemperatures, because, at the beginning of a blow, there is usually only a thin layer ofslag present so, depending on where the pyrometer is aimed, the measured temperaturemay be matte rather than slag.It can be seen from the figures that the temperature fit is quite good, especiallyconsidering the lack of accurate weights of the materials charged to and skimmed fromthe converter. In most cases, the largest disparity between the measured and predictedtemperatures are at the beginning of the charge. This is most likely caused by theunknown quantity of \u2018mush\u2019 remaining in the converter from the previous charge.Generally, the \u2018mush\u2019 is a very high silica slag with a large amount of entrainedBessemer matte. It usually provides all the silica for the first blow of the followingcharge, but its composition, weight, and temperature are all unknown. It is interesting tonote that in a number of cases the matte temperature is close at the beginning of the blow,and the slag temperature is close at the end of the blow. This suggests that at some pointduring the blow, the slag thickness becomes sufficient to completely cover the bathsurface, including the spout. There is often an abrupt change in the slope of the measuredtemperatures, and this coincides with the change from matte temperature to slagtemperature. This is particularly evident at the beginning of charge 106 and in the secondblow of charge 108.137UiDIctUi0.LUI-1600DUiaLUI-7.3.1 Bath Temperature160015501500145014001350TIME (miii)Figure 7.9 Comparison of model predicted matte and slag temperatures with plantdata, #3 converter charge 105, May 1988.15500 100 200 300 400 500 600 700 800145014001350100 200 300 400TIME (mm)Figure 7.10 Comparison of model predicted matte and slag temperatures with plantdata, #3 converter charge 106, May 1988.138wDw0wI-LiiDILiiawI\u20147.3.1 Bath Temperature0 100 200 300 400 500 600 70015501500145014001350TIME (mm)Figure 7.11 Comparison of model predicted matte and slag temperatures with plantdata, #3 converter charge 107, May 1988.155015001450140013500TIME (mm)Figure 7.12 Comparison of model predicted matte and slag temperatures with plantdata, #3 converter charge 108, May 1988.100 200 300 400 5001397.3.2 Slag Composition7.3.2 Slag CompositionA comparison of measured and predicted slag compositions are given inTables Vil-IX - VII-XII, and Figure 7.13 shows a comparison of the measured andpredicted iron and silica contents of the slags. Of the minor elements, only lead and zincare included in the tables, because the measured concentrations of arsenic, antimony, andbismuth were below the lower threshold of the assay technique. Also, the \u2018Si02\u2019 includesthe other inert materials, such as alumina and lime. In all charges the \u2018Si02\u2019valuespredicted are close to the measured, as are the iron contents up until the \u2018miss\u2019 blow; thepenultimate blow, before which furnace matte is not added. After this point the predictediron content is considerably lower than the measured value and the nickel and cobaltcontents are considerably higher. There are a number of possible reasons for this,including insufficient iron being added to the model, the model predicting more reactionthan is actually occurring, and the value of liquid-phase diffusivity of iron being too low.The model generally underpredicts the amount of copper, nickel, and cobalt in theearly slags. This discrepancy, for the most part, can be explained by the entrainment ofmatte in the slag, which is not accounted for in the model. Tables IV-Vffl - IV-XIindicate that there is a relatively large amount of sulphur in the early slags, whichindicates a correspondingly large amount of entrainment. The amounts of lead and zincin the slag are predicted fairly well, but the zinc predictions are high for the last slags.The reason for this is most likely for the same as for the increased nickel and cobalt.1407.3.2 Slag CompositionSlag Fe Ni Cu Co 0 Pb Zn \u2018 Si02\u20191 Model 54.5 .58 .37 .35 21.0 .052 .061 22.7Assay 51.1 .97 .57 .59 22.2 .042 .055 24.42 Model 52.4 .24 .09 .05 19.8 .021 .061 26.9Assay 51.7 .77 .48 .53 17.6 .035 .057 28.63 Model 49.3 .3 .08 .04 18.7 .021 .05 31.1Assay 50.6 1.02 .49 .6 16.3 .041 .055 31.04 Model 47.5 .29 .09 .04 16.3 .025 .15 35.0Assay 49.7 .9 .44 .67 14.7 .05 .052 33.65 Model 33.6 10.7 .08 5.23 17.0 .022 .54 32.3Assay 48.6 3.39 1.43 1.14 15.3 .059 .047 30.16 Model 21.0 17.4 .11 3.12 13.6 .032 .26 43.8Assay 44.6 3.35 1.07 1.55 15.5 .078 .04 34.0Table Vil-IX Comparison of model predicted slag compositions with assays takenat the end of the blow, (weight percent), #3 converter charge 105, May 1988.Slag Fe Ni Cu Co 0 Pb Zn \u2018Si02\u20191 Model 49.0 .82 .64 .51 18.7 .071 .052 29.9Assay 49.8 2.28 1.1 .79 17.6 .049 .054 28.42 Model 51.1 .78 .59 .46 19.7 .064 .052 26.9Assay 51.1 2.6 .86 1.37 13.6 .061 .044 30.53 Model 47.2 1.76 1.62 2.69 19.3 .017 .286 26.2Assay 55.6 1.17 .71 .51 17.4 .036 .079 24.64 Model 25.9 21.1 2.33 2.13 16.4 .014 .153 30.7Assay 46.0 3.95 1.23 1.56 16.7 .0833 .0418 30.56Table Vll-X Comparison of model predicted slag compositions with assays takenat the end of the blow, (weight percent), #3 converter charge 106, May 1988.1417.3.2 Slag CompositionSlag Fe Ni Cu Co 0 Pb Zn \u2018Si02\u20191 Model 55.5 .84 .32 .22 20.8 .041 .044 21.9Assay 55.2 1.39 .75 .54 16.2 .033 .061 25.92 Model 51.9 .83 .42 .06 19.5 .014 .04 25.8Assay 52.6 .99 .54 .60 16.3 .035 .051 29.03 Model 49.5 .88 .45 .038 18.7 .01 .036 28.7Assay 48.6 4.37 1.72 .75 15.0 .038 .044 29.64 Model 46.4 .61 .29 3.45 18.7 .011 .29 29.2Assay 48.0 3.46 1.32 .78 15.3 .042 .047 31.15 Model 30.5 12.1 .47 3.93 16.0 .014 .15 35.1Assay 42.7 4.79 1.85 1.09 14.3 .064 .036 35.36 Model 22.6 21.9 .33 2.35 15.1 .015 .096 36.2Assay 39.3 6.0 2.22 1.36 13.9 .067 .033 37.2Table VII-XI Comparison of model predicted slag compositions with assays takenat the end of the blow, (weight percent), #3 converter charge 107, May 1988.Slag Fe Ni Cu Co 0 Pb Zn \u2018Si02\u20191 Model 56.4 1.56 .47 .46 21.8 .033 .057 18.5Assay 50.4 2.27 .95 .66 15.9 .046 .05 26.52 Model 51.4 .73 .33 .654 19.4 .011 .046 27.4Assay 49.2 1.54 .63 .78 15.2 .054 .047 32.63 Model 37.5 7.85 .16 2.87 17.1 .013 .095 33.9Assay 46.8 2.82 .86 1.31 14.8 .064 .043 33.4Table Vll-XII Comparison of model predicted slag compositions with assaystaken at the end of the blow, (weight percent), #3 converter charge 108, May 1988.1427.3.3 Matte Composition60IZ 50wC-)ccw0I\u2014C3i:i 40wI\u201400wcc02020 30 40 50 60MEASURED (WEIGHT PERCENT)Figure 7.13 Comparison of measured and predicted iron and silica contents innickel converter slags, #3 converter, charges 105, 106, 107, and 108, May 1988.7.3.3 Matte CompositionA comparison of predicted and assayed matte compositions are given inTables VII-XIll - Vll-XVI, and a comparison of measured and predicted iron, nickel, andcopper contents of all matte samples is given in Figure 7.14. The tables and the figureindicate that the model predictions are relatively close for the major elements, althoughthe relative amounts of nickel and copper do not always correspond. This will be due touncertainties in the feed compositions. Of the minor elements, zinc is generally predictedwell, but lead and arsenic are consistently overpredicted. This could be the result ofuncertainties in the diffusion coefficients, or an underprediction of the matte\/slaginterfacial area.1437.3.3 Matte CompositionMatte Fe Ni Cu Co 0 S Pb Zn As1 Model 16.2 38.2 14.6 1.61 1.52 27.3 .1 .016 .02Assay 16.9 38.8 13.8 1.60 3.54 25.2 .08 .012 .022 Model 9.76 43.9 15.9 1.82 .88 26.9 .52 .005 .049Assay 11.4 42.5 15.4 1.45 3.97 24.9 .071 .004 .022F Model .82 50.8 22.4 .15 .29 24.1 .7 .001 .137Assay .792 48.3 23.5 .949 3.34 22.4 .0625 .003 .025Table VII-XIII Comparison of model predicted matte compositions with assays,(weight percent), #3 converter charge 105, May 1988._Matte Fe Ni Cu Co 0 S Pb Zn As1 Model 9.89 41.9 20.9 1.37 .715 24.35 .082 .011 .044Assay 9.83 42.5 18.4 1.27 3.64 24.1 .069 - .0172 Model 2.42 48.1 24.1 .919 .834 22.3 1.1 .001 .044Assay 5.79 46.8 21.7 1.03 1.91 22.5 .085 - .017F Model .8 50.7 27.6 .28 .28 21.1 .686 .0002 .133Assay .96 51.4 24.1 .79 .83 21.8 .058 - .023Table VII-XIV Comparison of model predicted matte compositions with assays,(weight percent), #3 converter charge 106, May 1988.Matte Fe Ni Cu Co 0 S Pb Zn As1 Model 16.4 37.7 14.6 1.33 1.72 27.5 .39 .007 .02Assay 14.6 42.8 14.7 1.53 .66 25.5 .085 .004 .02F Model .78 50.2 22.8 .134 .293 24.1 .4 .0004 .33Assay 1.17 51.7 21.9 1.10 .8 23.0 .063 - .035Table VII-XV Comparison of model predicted matte compositions with assays,(weight percent), #3 converter charge 107, May 1988.1447.3.3 Matte CompositionMatte Fe Ni Cu Co 0 S Pb Zn As1 Model 12.0 41.9 13.7 1.58 1.02 27.1 .19 .01 .041Assay 12.5 45.5 14.8 1.53 .09 25.5 .0916 .005 .02632 Model 8.02 45.3 14.4 1.78 .796 27.0 .89 .003 .061Assay 12.4 44.9 14.9 1.39 .71 24.5 .0813 .0074 .0243F Model 1.15 50.7 18.7 .366 .431 25.1 1.38 .0001 .105Assay 1.10 55.6 19.5 1.05 - 23.0 .061 - .033Table VII-XVI Comparison of model predicted matte compositions with assays,(weight percent), #3 converter charge 108, May 1988.I\u2014zwC)waI-.(5w0w0wa:a.60A A60-AA40-A30 -x-x-20 -\u00d8_ IRON4__ A NICKEL10 - X COPPERw_______ I I00 10 20 30 40 50 60MEASURED (WEIGHT PERCENT)Figure 7.14 Comparison of measured and predicted iron, nickel and coppercontents in nickel converter mattes, #3 converter, charges 105, 106, 107, and 108, May1988.1457.4.1 Phase Compositions7.4 Discussion7.4.1 Phase CompositionsThe overall compositions of the condensed phases are generally predicted well forboth the copper and nickel converters, with some errors in the minor elementcompositions. There are a number of possible sources for these errors, includingproblems with the activity coefficients, diffusivities, interfacial areas, and assayedcompositions. Certain assumptions made in the modelling may also add to the errors.7.4.1.1 Error in assaysErrors in assayed compositions are a particular problem in the nickel converteranalysis, because of the assay technique used. This point is best illustrated by comparingtwo sets of assays for the same material. These are available for slag samples obtainedfrom charge 110 during the plant trials at Copper Cliff. Table VII-XVII shows acomparison of assay results for the major components obtained using the standard ICPtechnique, by which all other assays of the nickel converter samples were obtained, with\u2018wet\u2019 assay techniques. It is evident that there are some large differences between thevalues, so the model predicted values are, for the most part, within the accuracy of theassays.1467.4.1 Phase CompositionsSlag Assay technique Cu Ni Co Fe Si021 ICP 1.34 3.10 0.718 54.2 21.9\u2018wet\u2019 0.9 2.3 0.74 52.1 22.72 ICP 0.54 1.1 0.586 55.4 23.8\u2018wet\u2019 0.53 1.32 0.62 50.9 24.43 ICP 0.673 1.58 0.712 53.4 25.6\u2018wet\u2019 0.59 1.58 0.75 50.1 25.94 ICP 0.784 2.12 0.839 51.6 27.8\u2018wet\u2019 1.41 4.33 0.95 45.5 29.05 ICP 0.911 2.99 1.37 48.7 29.6\u2018wet\u2019 0.92 3.23 1.6 45.8 28.7Table VII-XVII Comparison of slag assays obtained using ICP and \u2018wet\u2019 assaytechniques.7.4.1.2 Sulphur in slagNeglecting the presence of sulphur in the slag will have some effect on thepredicted slag compositions. The sulphur content of the slags will be mainly due to matteentrainment, because the slags were skimmed while in contact with a high grade matteand so should have a dissolved sulphur content under 0.9%.89 There are two mainmechanisms by which matte entrainment may occur; emulsification of matte in slag andsplashing from the spout. The former mechanism is not usually reported in physicalmodelling studies, but has been reported in one experimental system,209 and is found intop blowing and combined blowing systems.210\u2019This suggests that the majority ofentrained matte is produced by splashing from the spout, that is, matte which is eithercarried out of the spout by its own momentum, or ejected from the spout by collapsingbubb1es. The extent of this will vary considerably with the injection conditions, and theresidence time of the matte in the slag will also depend on the slag viscosity. Thus, a1477.4.1 Phase Compositionssingle value of a \u2018suspension index\u2019 as used by Nagamori and Mackey for the Norandareactor will not be valid for this system. While it may be possible to produce a formulafor suspension indices to give a better fit between the predicted and assayed slagcompositions, it would not be particularly meaningful considering the other inaccuraciesinvolved in the plant trials.7.4.1.3 Oxygen in matteFor the modelling it was assumed that all of the oxygen in the matte was in the formofFe304,however, it is probable that there is also some FeO present. The equilibriummole fraction of FeO in matte may be obtained from the reaction1 ...[7.3]3FeO+O2=Fe304The oxygen potential of the matte may be obtained from the magnetite formationreaction, and the activity coefficient of FeO in matte is given by2\u00b0\u2018YFeO = exp{ J (5.1 + 6.2 logX + 6.41 (1ogX )2+ 2.8(logXcus)3)}The resulting variation ofFe304and FeO with time, calculated by the model for charge586, are given in Figure 7.15. While the mole fraction of FeO is as high as 50% of themagnetite mole fraction, the relative proportions of iron and oxygen present as FeO willbe considerably less. The effect of including FeO will be to increase the iron content inthe matte slightly.1487.4.1 Phase Compositions0.0350.030.025z00.020.01500.010.005500TIME (mm)Figure 7.15 Calculated variation of mole fractions ofFe304and FeO in matte.7.4.1.4 Minor element distributionThe magnitude of the errors in the assays, along with the uncertainties inherent inindustrial scale tests raises some questions regarding the validity of any analysis of minorelement behaviour. However, for the purpose of the analysis of the copper converter,precise values are not as important as overall distributions. If the model predicts themeasured distributions correctly, then the transport mechanisms assumed are likely to becorrect. If this is the case, then the model should still predict the effects of changes inoperation on the minor element distribution correctly.Figure 7.16 shows a comparison of the measured and model predicted distributionsof lead, zinc and arsenic in the copper converter. From the figure it can be seen that themodel predicts the distribution of zinc and arsenic quite well. The amount of leadreporting to the matte\/blister copper is also predicted well, but the lead distributionbetween the slag and gas is not close. The most likely cause of this is the behaviour oflead at the gas\/liquid interface. The model assumes that it vapourizes, in a manner0 100 200 300 4001497.4.1 Phase Compositionssimilar to arsenic, while it appears from the distributions that at least part of the leadreaching the interface is oxidized and reports to the slag. The comparisons of predictedand assayed slag compositions suggest that the majority of this oxidation takes placetowards the end of a charge. The free energies of formation of lead and copper oxides arevery close over the temperature range seen in converters, so it is likely that some of thelead will oxidize towards the end of the slag blows and during the copper blow.A comparison of the measured and predicted antimony and bismuth distributionsfor charge 595 is given in Figure 7.17. This shows that the model can predict thesedistributions well, particularly the proportion reporting to the matte. The differencebetween the predicted and actual antimony in the slag indicates that some oxidation maybe occurring.The predicted minor element distributions in the nickel converter are not as close asfor the copper converter. Figure 7.18 shows that, while the arsenic distribution ispredicted reasonably, the amount of lead and zinc reporting to the slag is underpredicted.The most likely explanation for this is that the activity coefficients of the minor elementsused in the model are for copper mattes, and may be considerably different for nickelmattes.1507.4.1 Phase Compositions100Pb \u00b1 Zn Ase x_____80MEASURED +586\u2022 588w A595C\/) +< 60 PREDICTED0 x586+588i5954000w+o- A20x0 -I______________SLAG MATTE GAS SLAG MATTE GAS SLAG MATTE GASFigure 7.16 Comparison of model predicted lead, zinc and arsenic distributionswith measured values, copper converter charges 586, 588, and 595, Fun Flon, February1994. Solid lines indicate commercially observed range.311517.4.1 Phase Compositions100MEASURED +Sb \u2022 Bi80 PREDICTEDw XSb Bi(I)I60 \u20140I\u2014(DzI\u2014o x40x20 -+0 ISLAG MATTE GASFigure 7.17 Comparison of model predicted antimony and bismuth distributionswith measured values, copper converter charge 595, Fun Flon, February 1994.152Iii(I):i:00I\u2014zI\u2014a::0awcrPb7.4.2 Copper BlowAsMEASURED0 105\u2022 107108PREDICTEDx 105+ 107..\u2018 108\u00b1100806040200x++ xAx*\u00b1+-I.\u00b1+-I.SLAG MATTE GAS SLAG MATTE GAS SLAG MATTE GASFigure 7.18 Comparison of model predicted lead, zinc and arsenic distributionswith measured values, nickel converter charges 105, 107, and 108, Copper Cliff, May1988.7.4.2 Copper BlowOverall, the model is able to predict the bath temperature reasonably well for boththe copper and nickel converters, although the measured matte and slag temperaturesduring the copper blow are suspect. Towards the end of the copper blow it is probablethat the small amounts of matte and slag remaining are well mixed, increasing the extentof matte-slag reaction. Since the slag at this stage is highly oxidized, the increasedreaction will reduce the sulphur content of the matte significantly.1537.4.2 Copper BlowTo determine the reaction products of the matte-slag reaction, the most stablespecies can be found from a predominance area diagram. Figure 7.19 showspredominance area diagrams for the iron-copper-sulphur-oxygen system at 1300 K and1500 K. These are equilibrium diagrams which assume an ideal solution, but should givea good idea of which species will be produced by the reaction. It is interesting to notethat Cu20is not stable at either temperature, with the oxidized copper being in a copperferrite form. In fact, the formation of the ferrite considerably reduces the range ofstability of copper metal at lower temperatures. The composition of the copper slagsindicates that their oxygen potential is higher than 0.05, so the product of the matte-slagreaction is most likely to beCu20.Fe3This suggests that the main reaction between the matte and the slag at this stage islikely to beCu2S +4Fe3O=Cu20.Fe3+ lOFeO + SO2This reaction will reduce both the oxygen and sulphur potentials of the mixture, and willcontinue until one of these values drops below a level at which the copper ferrite is nolonger stable. Whether or not any reaction occurs beyond this point will depend on thesulphur potential of the system. The presence of the ferromagnetic copper ferrite alsoexplains the high values measured for magnetite content in the copper slags, since there isinsufficient iron present to form the amount of magnetite measured. Its presence has alsobeen found in accretions formed during the copper blow of a test converter.211The formation of a matte-slag emulsion will also have a stabilizing effect on thetemperature of the two phases. During the majority of the copper blow, the predictedslag temperature is very low due to a combination of the radiation losses and absence of areaction with the gas. In the actual converter it is probable that the radiation losses would154LOG(OXYGEN PARTIAL PRESSURE)-2-4a:D-6 (1)U)Liia:-8 0-J-10a--12:i:a--14U)(!3- 0-j-18-200Figure 7.19 Predominance area diagrams for the iron-copper-sulphur-oxygensystem; a. 1300 K, b. 1500 K. Dashed lines indicate partial pressure of sulphur dioxide.1557.4.2 Copper Blow0-20 -18 -16 -14 -12 -10 -8 -6 -4 -2LOG(OXYGEN PARTIAL PRESSURE)0-2-4 ii;a:-6 U)(I)wa:-8 a--J-10a--12a--14U)-IQ 0-j-18-20-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 07.4.2 Copper Blowbe from the emulsion rather than just the slag. Also, the presence of the slag within thematte would allow some gas-slag contact and, hence, reaction. The increased matte-slagreaction will also produce extra heat which is not included in the model.1568.1 Gas Flow Model8 MODEL PREDICTIONS AND DISCUSSION8.1 Gas Flow ModelThe predictions of the gas flow section of the model are of interest by themselves,and so are considered separately here. The following discussion will consider a singlebubbling event, and only follow the gas phase. However, the results of this portion of themodel will be useful in discussing the predictions of the complete model.The model predicted gas temperature is shown in Figure 8.1, for the standardconditions shown in Table V-I. All reaction heat is assumed to report to the liquid phase,so before detachment the gas temperature is controlled by a balance between the heatinput from the bath and the cooling effect of the injected gas. Initially, the heat inputpredominates, but as the bubble grows the two factors become more equal. This causesthe gas temperature to level out below the bath temperature. In some cases, as the bubblegrows the gas temperature starts to decrease until breakup occurs and the temperaturestarts to rise again. This effect is small, and does not show on Figure 8.1. Afterdetachment at 0.107 s, the gas temperature rises quickly to the bath temperature, and theprimary bubble exits the bath 0.113 s after detachment.A comparison of the temperatures predicted by the present model with thosepredicted by Ashman et al.35 shows that the changes made in the initial assumptionscause considerable differences. The present model predicts a much faster temperatureincrease, due both to the bubble shape and the heat-transfer coefficient. An ellipticalbubble has more surface area than a spherical one of equal volume (Figure 8.2) giving anincreased area available for heat transfer. Also, Ashman et al.35 used a constantheat-transfer coefficient of 290Wm2K1which is considerably lower than that predictedby equation 6.97, and does not account for variations with bubble size. Bubble breakup1578.1 Gas Flow Model1400w1200Lu1000E :::4000TIME (s)Figure 8.1 Variation of primary bubble temperature with time for injectionconditions given in Table V-I.during growth will also affect the gas temperature, because larger bubbles heat up moreslowly than small bubbles. Figure 8.3 shows that four bubbles break off from theprimary bubble before detachment, and that the primary bubble breaks up one more timebefore leaving the bath. At the bath surface the primary bubble has a volume of 0.05 m3and represents approximately 34% of the gas input during a single bubbling event.Figure 8.4 shows that there is an initial rapid decrease in the total bubble oxygencontent during bubble growth, but the rate of decrease drops off before detachment. Thisis caused by the reduced mass-transfer rate due to increased bubble size. Afterdetachment the oxygen content of the gas decreases more rapidly, but does not reach theinitial rate, since there is no longer enhancement of the mass-transfer rate due to the gasinjection. After 0.22 s the oxygen partial pressure becomes essentially constant. This isbecause only small bubbles are remaining in the bath. These bubbles contain a relatively0.05 0.1 0.15 0.21588.1 Gas Flow Modelsmall proportion of the total gas and, due to their size, already have a low oxygen partialpressure. Therefore, the amount of oxygen removed from these bubbles is insignificantwhen compared to the oxygen which has already exited the bath in the larger bubbles. Itis evident that a relatively large proportion of the oxygen is not reacted (11.5%), whichappears to contradict the high oxygen efficiencies reported for converters. If the tuyeresubmergence is increased to 0.7 m the partial pressure of oxygen remaining decreasesslightly to 0.015 atm. This value is approximately half of that reported by Rodoiff andRana98 for a copper converter with a tuyere submergence of 0.76 m and a Froude numberof 10.92. This difference may be related to the amount of slag present in the actualconverter, or could indicate that the gas-phase mass-transfer coefficient used in the modelis too high.The effect of changing the tuyere diameter on the primary bubble temperature issmall, with the main difference being caused by slightly different detachment times.However, decreasing the tuyere diameter causes a significant increase in oxygen use, asshown in Figure 8.5. This is caused by the increased gas velocity which increases therate of mass transfer during bubble formation. A similar trend was reported by Rodolffand Rana98 and is also predicted for changes in flow rate. The effect of tuyere diameteron the extent of bubble break up during growth is large. Figure 8.6 shows that increasingthe tuyere diameter significantly increases the number of times the bubble breaks up.This is caused by the reduced gas velocity which reduces the equilibrium bubble size asexplained in Section 5.3. The reduced slope of the oxygen in gas curves afterdetachment at lower tuyere diameters (Figure 8.5) is a result of the reduced break up aswell as the lower oxygen concentration. Mass-transfer of oxygen from the bubbles isreduced both by the larger bubble size and the lower driving force.1598.1 Gas Flow Model0 0.2 0.4 0.6 0.8ECCENTRICITYFigure 8.2 Effect of ellipse eccentricity on surface area at constant volume, shadedarea indicates range of eccentricity predicted by the model.0.07\u2014 0.060.050.04D0.03- 0.020.0100 0.05 0.1 0.15 0.2TIME (s)Figure 8.3 Variation of primary bubble volume with time for injection conditionsgiven in Table V-I.2.521.5160zUI>-><00UIDCl)C\u2019)UIa:a--JI-a:0.Uia:UIzUI(>-x0U0UIa:DCl)Cl)UIa:a--JI\u2014a:a-UI(3a:UI>8.1 Gas Flow Model0 0.1 0.2 0.30.20.150.10.0500.4TIME (s)Figure 8.4 Variation of average oxygen partial pressure with tuyere submergencefor injection conditions given in Table V-I.0.20.150.10.050Figure 8.5 Variation of average oxygen partial pressure with tuyere diameter, allother conditions given in Table V-I.0 0.1 0.2 0.3TIME (s)1618.1 Gas Flow Model0.080.070.06wD_i 0.050>w0.04D>. 0.030.02a-0.0100 0.05 0.1 0.15 0.2TIME (s)Figure 8.6 Variation of primary bubble volume with tuyere diameter, all otherconditions given in Table V-I.Increasing the oxygen content of the gas results in an increase in the oxygen partialpressure of the off gas. However, Figure 8.7 shows that the actual amount of oxygenreacted is also increased. There is also a corresponding increase in the partial pressure ofsulphur dioxide in the off gas. These are the result of a higher oxygen mass-transfer ratecaused by the higher partial pressure of oxygen in the bulk of the gas.The model predicts a slightly higher oxygen utilization in the copper blow than inthe slag blow, which was also found by Rodoiff and Rana.98 However, the lowest valueof oxygen remaining was attained for the case of blowing directly into slag. The primaryreasons for this can be seen from Figures 8.8 and 8.9. When blowing into slag the gastemperature rises slowly, due to the low slag thermal conductivity, Also, the higher1628.1 Gas Flow Modelviscosity of the slag reduces the bubble velocity, allowing increased bubble breakup.These result in the formation of a larger number of smaller bubbles, which increases theamount of mass-transfer, as well as the total bubble residence time.The effect of tuyere interaction can be approximated by artificially doubling the gasinput to the bubble, while keeping the gas flow rate through the tuyere constant. Themodel predicts that tuyere interaction will have a small effect on the primary bubbletemperature. The initial heating rate is lower than with no interaction, due to the largerbubble size, but the bath temperature is still attained shortly after detachment. Theoxygen utilization, however, is reduced considerably, as shown in Figure 8.10. Thiseffect is also caused by the increased bubble size during the formation stage,(Figure 8.11) which reduces the mass-transfer rate. This indicates that heat and masstransfer effects are not exactly analogous. Figure 8.11 also shows that even with theincreased bubble size, the primary bubble still breaks up only four times beforedetachment. This effect is again caused by the increased growth velocity which allows alarger bubble to form.163Cl)w-J00UiI0a:zUi0>-><08.1 Gas Flow Model0.250.20.150.10.0500 0.05 0.1 0.15 0.2 0.25 0.3TIME (s)Figure 8.7 Variation of total oxygen reacted with inlet gas oxygen content, all otherconditions given in Table V-I.160014001200Ui1000Ui0UiF-6004002000 0.05 0.1 0.15 0.2 0.25 0.3 0.35TIME (s)Figure 8.8 Variation of primary bubble temperature with bath material, all otherconditions given in Table V-I.164zUici,0U0UiccDCOCOUicc0-JI-ccUiUi>8.1 Gas Flow Model0 0.05 0.1 0.15 0.2 0.25252015Ui-JLULUDLU10500.3 0.35TIME (s)Figure 8.9 Variation of number of bubbles formed with bath material, all otherconditions given in Table V-I.0.20.150.10.0500TIME (s)Figure 8.10 Effect of tuyere interaction on average oxygen partial pressure , allother conditions given in Table V-I.0.05 0.1 0.15 0.2 0.25 0.31658.2.1 Introduction0.15COSwD0>w-J\u2018XIDm>_0.05ci00TIME (s)Figure 8.11 Effect of tuyere interaction on primary bubble volume, all otherconditions given in Table V-I.8.2 Converter Model8.2.1 IntroductionFor the purposes of this discussion, a single copper converter charge is used to testthe effects of variations of model and operating parameters. While none of the industrialcharges followed were \u2018normal\u2019, charge 586 can be considered as representing the finaltwo slag blows and the copper blow of a normal charge, because the transferred mattewas an initial charge to the converter. As in a previous work, the discussion will focus onthe matte temperature and iron content,98but other properties will be discussed asrequired.0.05 0.1 0.15 0.21668.2.2 Copper Converter Charge8.2.2 Copper Converter ChargeThe predicted matte temperature from charge 586 is shown in Figure 8.12.Although there are some similarities between the temperature variations of copper andnickel converter charges, the temperature of the copper charge does not follow the regularpattern exhibited by the nickel converter temperature (Figure 4.1). While the figure doesshow the same rapid temperature increase during blowing, there is not the initialtemperature decrease that is seen in the nickel converter. This difference is caused by thefluxing methods used. At Copper Cliff, the flux is added through the mouth of theconverter while it is blowing, usually over the first ten to fifteen minutes of each blow.At Flin Ron, flux is added from ladles as it is needed throughout the charge. Thus,instead of one initial, large temperature drop, there are a few small drops throughout theblow (marked F on Figure 8.12). The weight of flux required is also much lower at FlinFlon, due to the smaller converter size and the higher initial matte grade.The matte temperature falls only slightly during idle periods. This is caused by theinsulating effect of the slag, which prevents radiation losses. The only heat losses fromthe matte are through the walls and to the slag, both of which are small. Some probablecauses of the low predicted temperatures during the slag blow have been discussed inSection 7.4, but a further examination is required. A temperature decrease, as predictedduring the copper blow, can be caused by material additions or reduced heat inputs to thebath. Since extra material is only added at the times indicated in Figure 8.12, it followsthat the heat input has been reduced. There are two further reasons for this decline inheat production. In the copper blow, copper suiphide is being oxidized rather than ironsulphide, so the principle reaction is1678.2.2 Copper Converter Charge160015001400D1300120011000 500TIME (mm)Figure 8.12 Predicted matte temperature, charge 586. F-flux addition, M-matteaddition, I-idle period start, I*idle period end, S-slag skimmed, Sc-scrap added,C-copper blow start.Cu2S+O= 2Cu + SO2 AHR = \u2014190.4kJ moF\u2019whereas, in the slag blows, the reaction isFeS+O2=FeO SO AIIR =\u2014308.9kJmoF1Thus the heat produced per mole of oxygen reacting is reduced by 38 percent.The second reason can be seen in Figure 8.13. This shows that the oxygen use isconsiderably lower in the copper blow than in the slag blows. It is important to note thatthe graph shows oxygen use, not oxygen efficiency. For the purpose of this discussion,oxygen use is defined as100 200 300 4001688.2.2 Copper Converter Charge( , ( pp ...[8.3]oxygen use = I 1 \u2014----s x 100% = I 1 \u2014 2 2 x 100%L \u00b02 iThe nitrogen partial pressure terms in equation 8.3 are to account for the change in totalmoles of gas present due to reaction, the total moles of nitrogen being unchanged. Thereare two main reasons for the reduction in oxygen use during the copper blow; low slagvolume and reduced tuyere submergence. The rapid heating rate of the slag during slagblows (Figures 7.7-7.9) indicates that there is a considerable amount of slag oxidationoccurring, and this accounts for a large proportion of the total heat input to the converter.However, slag is routinely skimmed just prior to the copper blow, to reduce copperlosses. This leaves approximately five tonnes of slag, which is barely sufficient to coverthe surface of the bath. If the slag remains as a separate phase when a spout is formedthere will be very little contact between the gas and the slag, but it is likely that the slag iscompletely emulsified in the matte. Under either of these conditions there will be littlereaction of the slag with the gas, causing a reduction in the total heat generated.Also, as copper is produced, the total volume of material in the converter isreduced. The resulting reduction in tuyere submergence is shown in Figure 8.14. Forexample, if 120 tomies of white metal is reacted to produce blister copper, there is a 45percent reduction in volume, which results in a 0.5 m decrease in tuyere submergence.At Flin Ron the tuyere submergence can not be increased during the copper blow due tothe requirement for almost continuous tuyere punching, which can only be carried out ata specific converter position. Figure 8.4 shows that decreasing the tuyere submergencereduces oxygen use, leading to the considerably lower heat generation. This point isemphasized in Figure 8.15, which shows that there is a definite relationship betweentuyere submergence and oxygen use. However, the scatter in Figure 8.15 indicates that1698.2.2 Copper Converter ChargewCl)Dzw(30Ew0zw(3IiimDCl)ww>-DI\u201401009080706050100 200 300TIME (mm)Figure 8.13 Predicted variation of oxygen use with time.other variables also contribute to determining the total oxygen use.0.90.80.70.60.50.40.30.2400 5000 100 200 300 400 500TIME (mm)Figure 8.14 Predicted variation of tuyere submergence (including spout) with time.1708.2.3 Sensitivity Analysis100H NH90\u2014N NH NLii HU,zLii070060\u2022IlN50 II0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9TUVERE SUBMERGENCE (m)Figure 8.15 Predicted variation of oxygen use with tuyere submergence (includingspout), charge 586, Feb. 1994.8.2.3 Sensitivity AnalysisIn the development and operation of the model there are a number of parameters forwhich accurate values or equations are not available. It is important to determine theeffects of these parameters on the model predictions. This process can identify areaswhere further work is required to obtain better values, and may also aid in understandingwhat is happening in the converter. Table V1ll-I gives the parameters analyzed and therange of values used.A shorter time step should increase the accuracy of the model predictions, butincreases the total running time. Figure 8.16 shows that reducing the time step to oneminute only has a small effect on the matte temperature and iron content. While runningtime is not a serious problem for the model, the inaccuracies involved in the plant trials1718.2.3 Sensitivity AnalysisParameter low base highTime step (mm) 1 2 -Gas flow calculation frequency (time steps) 1 5 -Initial bath temperature (K) 1350 1400 1450Hood temperature (K) 623 823 1023Slag emissivity .5 .7Liquid-phase diffusivity base\/lO eq. 6.92 basexl0Gas-phase diffusivity base-l0% eq. 6.93 base+10%Gas-phase mass-transfer coefficient base-10% eq. 6.94 base+l0%Matte ladle size (tonnes) 14.4 16 17.6Water in flux (%) 2.5 5 7.5. . .Spout gas fraction multiplier -J - 1.1 1.5Table Vu-I Parameters tested in the sensitivity analysis.and other parameters are sufficiently large to make the difference essentiallyinsignificant. The most time consuming section of the model is the gas flow calculation.To avoid long running times this calculation was only carried out every five time steps(10 minutes), or immediately following an idle period. This could represent a significantsource of error for the model, particularly when the temperature is changing rapidly.However, Figure 8.17 shows that the difference between carrying out the gas flowcalculation every time step and every five time steps is small.1728.2.3 Sensitivity Analysis16001500wa:Da: 1400w01300120098600 100 200 300 400 500TIME (ml,,)Figure 8.16 Effect of model time step on the predicted variation of mattetemperature and iron content (weight percent) with time.The initial bath temperature is not known, but can be estimated based on measuredmatte temperatures at the end of a slag blow. This basis is used because the initial mattefor charge 586 was transferred from another converter, rather than from the reverberatoryfurnace. Figure 8.18 shows that an increase in the initial temperature only has an effecton the first blow temperature and iron content, with the difference at later stages of the1738.2.3 Sensitivity Analysis16001500wD 14001300wI\u2014w 1200I\u201411001000876I54z03200 500TIME (mm)Figure 8.17 Effect of gas flow calculation frequency on the predicted variation ofmatte temperature and iron content (weight percent) with time.charge being negligible. The temperature difference is reduced throughout the first blow,with the difference in the higher initial temperature case being reduced faster due tohigher heat losses. The difference in iron content is primarily due to the temperaturedependance of the magnetite activity coefficient. A lower temperature increases theactivity coefficient and so reduces the iron content. This can be seen from the variationof matte oxygen content given in Figure 8.19.100 200 300 400174120011000.080.070.06LUI\u20140.050.04z00.030.020.010500TIME (mm)Figure 8.18 Effect of initial bath temperature on the predicted variation of mattetemperature and iron content (weight percent) with time.Variations in the hood temperature and slag emissivity have only a small effect onthe matte temperature, and even less on the matte iron content. The slag emissivity,8.2.3 Sensitivity Analysis1600150014001300LUDLU0LUI\u2014LUI\u20140 100 200 300 4001758.2.3 Sensitivity AnalysisTIME (mm)Figure 8.19 Effect of initial bath temperature on the predicted variation of matteoxygen content (weight percent) with time.however, has a relatively large effect on the slag temperature (Figure 8.20). An increasein the hood temperature has a larger effect on slag temperature than a decrease, but it issmall compared to the effect of emissivity. Neither of these parameters has a significanteffect on the slag composition.The liquid-phase diffusivities are calculated from a theoretical equation and, asshown in Section 6.5.3.1, may be too low. However, if the system is under gas-phasediffusion mass-transfer control, diffusivities in the liquid should not have a significanteffect on the model predictions. Figure 8.21, however, indicates that there is an effect,both to the matte temperature and iron content. The effect of an increase in diffusivity iscaused by an increased amount of zinc reacting. Figure 8.22 shows that with the higherdiffusivity the zinc removal from the matte is very rapid. This is because the zincconcentration is low enough to be under liquid-phase diffusion control, so an increase in1.50.500 100 200 300 400 5001768.2.3 Sensitivity Analysis170016001500UI0 1400D1300UIF-1200110010000 500TIME (mm)Figure 8.20 Effect of slag emissivity on the predicted variation of slag temperaturewith time.the diffusivity allows more zinc to reach the gas\/liquid interface. All of the zinc arrivingat the interface should react, because ZnO is thermodynamically more stable than FeO.This reduces the amount of iron oxidized and, to a lesser extent, the heat generated.The increased iron content of the matte during the slag blows caused by a decreasein liquid-phase diffusivity indicates that the reaction of iron has also become controlledby diffusion in the liquid. That is, there is insufficient iron reaching the gas\/liquidinterface to react with all the oxygen. This should not affect the amount of oxygenreacting, so there is an increase in the amount of copper reacting. This causes the copperphase to be formed at an early stage of the process. This reduced iron removal andincreased copper removal combine to produce the large increase in matte iron contentseen in Figure 8.21, particularly at the end of the first blow. After this point the effect ofan increase in diffusivity is reduced, due to the lower levels of zinc in the matte. The100 200 300 4001778.2.3 Sensitivity Analysis18001700160015001400I\u2014w130012001100980 500TIME (mm)Figure 8.21 Effect of liquid-phase diffusivity on the predicted variation of mattetemperature and iron content (weight percent) with time.rapid increase in matte temperature seen at the end of the low diffusivity case inFigure 8.21 corresponds to an increase in the matte magnetite content. The heatgenerated to produce the magnetite combined with the small amount of matte remainingcause the very rapid temperature increase. The effect of changing the liquid-phase100 200 300 4001788.2.3 Sensitivity Analysisdiffusivity on the oxygen content of the slag (Figure 8.23) reveals another interestingpoint. Reducing the diffusivity has a considerable effect on the slag oxygen content,again indicating that the oxidation reaction in the slag is under liquid-phase diffusioncontrol. However, there is no other component in the slag to react, so there is a reductionin the overall oxygen use (Figure 8.24). Increasing the liquid-phase diffusivity had noeffect on the oxygen content of the slag over the first ten minutes of the first blow.However, after this time there is an increase in the slag oxygen content, indicating that inthe base case there is a change in the reaction controlling mechanism from gas-phasediffusion to liquid-phase diffusion. This same pattern is repeated in the second blow, andthe decreased oxygen use is evident in Figure 8.24. This figure also shows thatincreasing the liquid-phase diffusivity has a slight effect on the oxygen use, suggestingthat the gas\/slag reaction is under mixed control throughout the charge.21.50.50500TIME (mm)Figure 8.22 Effect of liquid-phase diffusivity on the predicted variation of mattezinc content (weight percent) with time.0 100 200 300 400179(3a)zzw(3>-><08.2.3 Sensitivity Analysis100 200 300 4002019181716151413120 500TIME (mm)Figure 8.23 Effect of liquid-phase diffusivity on the predicted variation of slagoxygen content (weight percent) with time.1009080wC,)Dz 70LLI(3>-x6050400 500TIME (mm)Figure 8.24 Effect of liquid-phase diffusivity on the predicted variation of oxygenuse with time.100 200 300 4001808.2.3 Sensitivity AnalysisThe effects of changing the gas-phase diffusivity and the gas-phase mass-transfercoefficient are essentially the same. Figure 8.25 shows that increasing the gas-phasemass-transfer coefficient increases the matte temperature and reduces its iron content.These results are what would be expected for a system controlled by gas-phase diffusion.The increased mass-transfer coefficient results in more oxygen reaching the gas\/liquidinterface, allowing more reaction to occur which produces more heat and removes moreiron from the matte. The magnitude of the effect on iron content increases with timeduring the slag blows. In the initial stages of the first blow, the difference between thecases is too small to show in Figure 8.25, but becomes evident 46 minutes into the blow.At the beginning of the copper blow the case with the higher gas-phase mass-transfercoefficient has a higher matte iron content than the other cases. This is caused by thereaction between the gas and iron suiphide coming under liquid-phase control at a higheriron content in the matte, which is caused by the increased amount of oxygen reachingthe reaction site. It is important to note that the model is very sensitive to the gas-phasediffusivity, with a very high value causing extreme temperatures. This is indicative of aprocess under gas phase mass transfer control. However, since the model appears topredict the converter temperatures reasonably well, it can be argued that either the valueused is close to the actual, or the gas surface area is under or over predicted andcompensates for an error in the mass transfer coefficient.The effect of increasing the gas-phase mass-transfer coefficient on the slag,however, is very small. Figure 8.26 shows that the oxygen content of the slag is changedvery little by the increase, again indicating that the reaction in the slag is controlled byliquid-phase diffusion. The fact that a reduction in the gas-phase mass-transfercoefficient does reduce the slag oxygen content again suggests that the gas\/slag reaction18112001100B7500TIME (mm)Figure 8.25 Effect of gas-phase mass-transfer coefficient on the predicted variationof matte temperature and iron content (weight percent) with time.in the base case is under mixed gas-phase and liquid-phase mass-transfer control.1828.2.3 Sensitivity Analysis1600150014001300wIxDwwI\u20140 100 200 300 400TIME (mm)Figure 8.26 Effect of gas-phase mass-transfer coefficient on the predicted variationof slag oxygen content (weight percent) with time.The amount of weight added in a ladle can be calculated approximately based onthe ladle volume. However, the shape of the ladle is such that a large proportion of theweight is in the top section. This means that a small difference in the height to which it isfilled will have a large effect on the actual amount of matte added. Generally, the weightof matte added will average out to calculated amount. Figure 8.27 shows that an increasein the amount of matte added results in an increase in matte temperature and iron content,although the iron content is not increased by as much as may be expected. The increasein matte temperature is caused by the increased tuyere submergence due to the greatertotal volume of matte in the converter. The increased amount of reaction occurringbecause of the extra tuyere submergence is the reason for the lower than expected ironcontent; more iron is being added, but more is also being removed.8.2.3 Sensitivity AnalysisC!,-JCl)zzw>-x019181716151413120 100 200 300 400 5001838.2.3 Sensitivity AnalysisThe flux used at Fun Hon is sand taken from a local sand pit and brought to thesmelter by truck. The water content of the flux is quite variable, and will often depend onthe weather conditions. A variation of the water content of the flux, however, has nonoticeable effect on the matte, and only a slight effect on the slag temperature and silicacontent. The effect of the assumed spout gas fraction-plume gas fraction ratio is alsosmall. This value only affects the calculated spout height, and so represents a smallportion of the total tuyere submergence. As such, an increase in the ratio does increasethe matte temperature slightly due to the slightly increased extent of reaction. This alsoreduces the iron content of the matte by a small amount. The size of these variations isinsignificant when compared to the other uncertainties in the system.1848.2.3 Sensitivity Analysis11008654320TIME (mm)500Figure 8.27 Effect of weight of matte in a ladle on the predicted variation of mattetemperature and iron content (weight percent) with time.16001500w1400ccLii1300120070 100 200 300 4001858.2.4 Converter Operation8.2.4 Converter OperationThere are very few operating parameters which can be changed on a copperconverter. This is probably one of the reasons it has continued, relatively unchanged, forso long: a copper converter will run by itself with very little control and only intermittentoperator intervention required. In the past, there have been suggestions made of ways toimprove operation, and these almost always relate to gas injection. Unfortunately,changes to the gas injection can seriously affect the overall heat balance. To determinethe effect of changes on the length of a charge, the time taken to produce 72 tonnes ofblister copper will be compared. This approach is required because the actual end pointof a charge depends on the extent of the matte\/slag reaction during the copper blow,which can not be predicted by the model. The particular weight chosen is the amountpredicted to have been produced after 400 minutes of the base charge.8.2.4.1 Gas flow ratePerhaps the most direct method to improve converter operation is to increase thegas flow rate. This should shorten the total charge time without altering the heat balance,but is limited by the onset of slopping and causes increased splash from the spout. Themodel predicts that increasing the gas flow rate does increase the rate of iron removalfrom the bath, but Figure 8.28 also shows that it will reduce the matte temperature. Thiseffect is caused by a decrease in the total oxygen use. The amount of heat obtained fromthe reaction per unit volume of gas is decreased, while the heat lost per unit volume ofgas is unchanged. Since the overall heat balance of the converter is essentially controlledby these two factors, decreasing the heat input without changing the heat removed willresult in a reduction in the heat accumulated in the matte. Thus, even though there ismore oxygen reacting, the matte temperature is reduced by the increased heat lost to the186gas.1000865430TIME (mm)8.2.4 Converter Operation500Figure 8.28 Effect of gas flow rate on the predicted variation of matte temperatureand iron content (weight percent) with time.16001500w 1400a:D1300012001100720 100 200 300 4001878.2.4 Converter Operation8.2.4.2 Oxygen enrichmentOxygen enrichment of the injected gas is used in some installations to reducecharge times and allow an increased amount of cold charge addition. The extra scrapburning capability is available because the use of oxygen enrichment affects the heatbalance. The effects of oxygen enrichment can be analyzed in two different ways;keeping the total moles of oxygen added constant by reducing the number of tuyeresused, or increasing the total amount of oxygen added. The latter is what is carried out inindustry, but the former may prove interesting.Figure 8.29 shows the results of using oxygen enrichment while keeping the totaloxygen input constant using a reduced number of tuyeres. The matte temperature isconsiderably higher than without oxygen enrichment, but the iron content of the matte isalso increased. However, the oxygen content of the matte is higher, indicating that theincreased iron content is mainly caused by the reduction of the magnetite activitycoefficient in the matte at the higher temperatures. If the weight percent of iron asmagnetite is subtracted from the total iron content, (Figure 8.30) it can be seen that thereis a small improvement in iron removal with increasing oxygen enrichment, which resultsin a two minute reduction in charge time at 30% oxygen in the gas. This is the result ofan increase in mass-transfer rate within the bubble, which is just sufficient to overcomethe reduction in the number of tuyeres used.If the total oxygen input to the converter is increased the temperature rise is evenlarger than in the previous case. The increased mass-transfer rate through the regularnumber of tuyeres increases the iron removal, and, hence, the temperature. Figure 8.31shows that, even with the large increase in temperature, which will increase the mattemagnetite content, the total iron in the matte is reduced. This figure also shows that the1888.2.4 Converter Operationcase with 30% oxygen in the gas took about 80 minutes less to complete the charge. Theimprovement was only 10 minutes for oxygen enrichment to 25%, and in both cases isdue to the increased rate of mass-transfer to the gas\/liquid interface. This effect isenhanced by higher temperatures, which is the explanation for the large differences incharge times. The higher temperatures are also the cause of the high iron content in thematte during the copper blow, as explained in Section 8.2.2.18986543208.2.4 Converter Operation500TIME (mm)Figure 8.29 Effect of gas oxygen content, with total oxygen input constant, on thepredicted variation of matte temperature and iron content (weight percent) with time.1800- 1700w16001500Lii 140013001200110070 100 200 300 4001908.2.4 Converter Operation20500TIME (mm)Figure 8.30 Effect of gas oxygen content, with total oxygen input constant, on thepredicted variation of matte iron content with iron as magnetite removed (weight percent)with time.To further analyze the effects of oxygen enrichment, the model can be modified tokeep the temperatures of each phase constant. This allows higher gas oxygen contents tobe studied, while removing the complications introduced by the high temperaturesnormally produced. For this analysis the total oxygen input to the converter was alsokept constant, with the number of tuyeres used being reduced in proportion to theincreases in oxygen content. This technique significantly reduces the total gas\/liquidinterfacial area, but the liquid-phase kinetics around a single tuyere are not altered.Figure 8.32 shows the predicted effect of increasing the oxygen enrichment on thematte iron content. It is evident that there is an initial increase in iron removal rate withincreasing oxygen enrichment, but at some point between oxygen contents of 35% and42% the rate of iron removal begins to decrease, and at high oxygen enrichments the65430 100 200 300 4001918.2.4 Converter Operation220020001800wftD1600ftw01400I1200100087654320500TIME (mm)Figure 8.31 Effect of gas oxygen content, with increased oxygen input, on thepredicted variation of matte temperature and iron content (weight percent) with time.0 100 200 300 4001928.2.4 Converter Operationmatte iron content remains higher than the base case (21% oxygen). A possibleexplanation for this is that the reduced interfacial area may be reducing the total amountof reaction occurring. However, Figure 8.33 shows that, while the total oxygen use isreduced during the slag blows at higher oxygen enrichments, the magnitude of thereduction is not large, indicating that the overall amount of reaction occurring in thematte has increased. This suggests that at some point during the charge the reaction ofiron is coming under liquid-phase mass-transfer control, and copper suiphide is alsoreacting.Figure 8.34 shows that there is some reaction with copper sulphide occurring duringthe slag blows. The amount of copper suiphide reacting, however, is not sufficient toaccount for all of the increase in iron content. The effect of the oxygen enrichment on theweight of blister copper produced is shown in Figure 8.35. This figure shows that there iscopper production throughout the charge, even when there is no direct reaction of the gaswith copper sulphide. The prediction that there is copper produced early in the charge,even for the base case, is unexpected, and can be explained by the sulphur potential of thematte. Figure 8.36 shows that the sulphur potential of the matte varies between iO7 and10.6.8, but is not significantly affected by increasing the oxygen enrichment. It can beseen from a potential area diagram of the system (Figure 7.13) that these values are closeto the boundary between copper and copper sulphide, which is why some copper is beingproduced. This effect will be greater at higher temperatures, where the copper phase isstable at higher sulphur potentials.The reduction in charge time achieved with oxygen enrichment to 84% at 1400 K is28 minutes. However, the total amount of copper produced after the full 450 minutes is1938.2.4 Converter Operationincreased by 20 tonnes, while the weight and copper content of the matte remaining issignificantly reduced. This is not likely to occur in the actual process due to thematte\/slag reaction, which forms the copper slag.This analysis indicates that, in general, increasing the oxygen content of the gas willreduce the overall charge time by a combination of mechanisms. Increasing the totalamount of oxygen supplied to the bath allows more reaction to take place, and increasesthe rate of mass-transfer to the gas-liquid interface, however, the percent of the oxygenused is reduced. At very high oxygen enrichments, or with the use of tonnage oxygen,rates of liquid-phase mass-transport begin to become important, and some reaction withcopper sulphide is possible at lower matte grades. However, at the oxygen enrichmentlevels usable under the temperature constraints of the converter, the reduction in chargetime achieved is relatively small, but could be improved if the temperature is controlledusing high grade scrap. It should be noted that, while this increased copper oxidationwould be advantageous in copper converting, it represents a limit to oxygen enrichmentin the nickel converter. In nickel converting, this form of liquid-phase mass-transportcontrol would cause increased cobalt and nickel oxidation, and result in higher slaglosses.194wU)Dzw00109878.2.4 Converter Operation6543200 100 200 300 400 500TIME (mm)Figure 8.32 Effect of gas oxygen content on the predicted variation of matte ironcontent (weight percent) with time at 1400 K.1009080706050400 500TIME (mm)Figure 8.33 Effect of gas oxygen content on the predicted variation of oxygen usewith time at 1400 K.100 200 300 400195z0I\u20140wa:-JI\u20140I.LL0Izw0a:w08.2.4 Converter Operation0 100 200 300 400100806040200500TIME (mm)Figure 8.34 Variation of the predicted amount of iron and copper suiphidesreacting, as a percentage of the total reaction in the matte, with time at 1400 K and 84%oxygen in the injected gas.12010080Liizz0b 60Fw40200500TIME (mm)Figure 8.35 Effect of gas oxygen content on the predicted variation of copperproduced with time at 1400 K.1960 100 200 300 4008.2.4 Converter Operation-6.6-6.7-6.8-6.9-JI.-_.-. -7ZE-7.1-7.2j_J 7.3DCl)-7.4-7.5-7.6-7.70 500TIME (ml,,)Figure 8.36 Effect of gas oxygen content on the predicted variation of sulphurpotential with time at 1400 K.8.2.4.3 Tuyere submergence and diameterThe tuyere submergence in a Peirce-Smith converter is usually limited both by thedesign of the converter and by the requirement for tuyere punching. However, in asystem which is controlled by gas-phase mass-transfer, increasing the total contact areabetween the gas and liquid-phases, by increasing the tuyere submergence, shouldimprove the overall process efficiency. Figure 8.37 shows that it does increase theamount of reaction and, since there is no additional cooling, the matte temperature.Increasing the tuyere submergence by 0.1 m reduces the time required to produce72 tonnes of blister copper by 20 minutes, while a similar decrease in tuyeresubmergence increases the time by 12 minutes. It should be noted that the tuyeresubmergence varies throughout the charge (Figure 8.14), based on the volume of material100 200 300 4001978.2.4 Converter Operationin the bath, so the base submergence can not be given as a number.The use of a reduced tuyere diameter, to increase the velocity of the gas leaving thetuyere, has been tested. This removes the need to punch the tuyeres, and reducetuyereline refractory wear. Figure 8.38 indicates that there is another advantage to usingsmaller diameter tuyeres. The increased tuyere velocity produces a more elongatedbubble, and enhances mixing in the bubble during growth. Both of these lead to moreefficient mass-transfer during bubble growth, and an overall increase in the iron removal,such that charge time is reduced by 18 minutes.Both reducing the tuyere diameter and increasing the tuyere submergence improvethe kinetics of converting, so combining the two offers the possibility of making aconsiderable improvement to the operation. There is, however, one possible drawback.Figure 8.39 shows that, while the rapid decrease in iron is as desired, the increase inmatte temperature is considerable. If a reliable source of high grade scrap material isavailable, then this may be an asset rather than a drawback, but if the scrap is notavailable the increased temperatures may seriously degrade the refractory.198wDw0wI\u2014LUI\u20148.2.4 Converter Operation170016001500140013001200110087\u2014 6LUI\u20145zz0320TIME (mm)Figure 8.37 Effect of tuyere submergence on the predicted variation of mattetemperature and iron content (weight percent) with time.1990 100 200 300 400 500190018001700W 1600ccD1500cc1400wI\u2014 13001200110010006508.2.4 Converter Operation0 100 200 300 400TIME (mm)Figure 8.38 Effect of tuyere diameter on the predicted variation of mattetemperature and iron content (weight percent) with time.50087432200gwDI\u2014Ui0UII\u20148643210TIME (mm)8.2.4 Converter OperationFigure 8.39 Effect of a combined reduction in tuyere diameter and increase intuyere submergence on the predicted variation of matte temperature and iron content(weight percent) with time.500190018001700160015001400130012001100750 100 200 300 4002018.2.4 Converter Operation8.2.4.4 Slag skimming procedureSlag skimming is usually carried out at the end of each blow, before the addition ofmatte. This results in a low initial slag cover, which increases throughout the blow. Theeffect of altering this practice to provide either an increase or decrease in the slagthickness during blowing is shown in Figure 8.40. In the low slag cover case, after theinitial skim at 38 minutes, slag is skimmed as soon as 12.5 toimes (one ladle) is present,while in the high slag cover case, the base amount of slag skimmed is reduced by onehalf. In all cases the slag cover in the copper blow is the same.It is evident from Figure 8.40 that a low slag cover reduces the matte temperature.This is primarily caused by a large reduction in the slag temperature due to the absence ofa gas\/slag reaction, and the low thermal mass of the slag. The absence of the gas\/slagreaction can be clearly seen from the reduction in oxygen use shown in Figure 8.41. Asmall part of this reduction is also caused by the lower temperatures, which reduce theoxygen mass-transfer rate and, hence, the extent of the gas\/matte reaction. This results ina 12 minute increase in the charge time, and is the cause of the higher amount of iron inmatte during the slag blows.2028.2.4 Converter Operation.-. 1600w1500I140001300120011001000876543200 500TUYERE SUBMERGENCE (m)Figure 8.40 Effect of skimming procedure on the predicted variation of mattetemperature and iron content (weight percent) with time.1100 200 300 4002038.2.5 Minor Element Removal1009080C,)DzwC!370060500 500TIME (mm)Figure 8.41 Effect of skimming procedure on the predicted variation of oxygen usewith time.8.2.5 Minor Element Removal8.2.5.1 IntroductionThe removal of minor elements from the matte is an important factor which must beconsidered when operating variables are to be changed. The effects of changing the sameoperating variables as in the previous section will be considered. For this purpose thedistribution of the minor elements between the phases will be considered, although thereare occasions when the actual predicted concentrations are required. In particular, ifchanging a variable results in the formation of a greater amount of any particular phasethe percentage of the total input reporting to that phase may increase, even though theactual concentrations within the phase are reduced.100 200 300 4002048.2.5 Minor Element RemovalFor the purposes of calculating distributions, the copper slag is considered as beinga mixture of the remaining matte and slag at the end of the charge. In an actual converterthe two phases will be well mixed, and there will be a considerable reaction betweenthem, removing the majority of the sulphur from the matte. This reaction has not beenincluded in the model due to insufficient data concerning the mixing and reaction. This isparticularly important for lead and, to a lesser extent, zinc, as a relatively large proportionof these are removed in the copper slag. For this analysis, distributions will be calculatedat a constant weight of blister produced. This provides a constant basis for thecomparisons.8.2.5.2 Minor element behaviour in the base chargeWhile the minor element distributions give an overall indication of the minorelement behaviour, the variation of the minor element content of each phase with timecan give a better idea of what is actually happening. The discussion of distributions willfocus on the proportions of the minor elements reporting to the blister copper and thedust. The base distributions to these phases are given in Table VIlI-IlElement Distribution (%)Blister DustPb 3.93 36.7Zn 3.61 9.90As 2.28 61.5Sb 0.568 40.1Bi 1.20 37.7Table VIlI-Il Predicted distribution of minor elements to the blister copper anddust after 400 minutes of charge 586 (72 tonnes of blister copper produced).2058.2.5 Minor Element RemovalFigures 8.42, 8.44, and 8.45 show the variation with time of the concentration ofminor elements in the blister copper, matte and slag respectively, while Figure 8.46shows the variation of their partial pressures in the off gas. The concentrations of all ofthe minor elements in the blister copper follow the same pattern. There is an initial rapidincrease in minor element content, caused by the large surface area to volume ratio of theblister copper (Figure 8.43). The rate of change of minor element concentration in theblister copper is directly proportional to this ratio, so it can be seen that at deeper depthsof blister copper the rate of change will be reduced. At higher volumes of copper the rateof minor element transfer does not keep pace with the rate of copper production, causingthe levelling off of the curve in Figure 8.42. When the copper blow begins, the minorelement content in the blister copper begins to drop, because the rate of copperproduction is considerably higher than the minor element mass-transfer rate. The suddenincreases in minor element content during the copper blow correspond to the addition ofscrap, which has a higher minor element content than the blister copper. Otherwise, theminor element content decreases during the copper blow. However, this does not implythat the minor elements are being transferred from the blister to the matte. In fact, thetotal weight of the minor elements in the copper is increasing slightly, but not as quicklyas the total weight of copper. The magnitude of the effect of the cold charge addition isrelated to the concentration of the particular minor element in the cold charge.Concentrations of lead, zinc, and arsenic are relatively large, so the cold charge additionhas a larger effect on their concentrations. However, for antimony and bismuth, theconcentrations in the cold charge are not much higher than their concentrations in theblister copper, so the effect is smaller.2068.2.5 Minor Element Removal200.4nI.Jv000C)100 CtwIC\/)-J50C)zN100 200 300 400TIME (mm)050030a. 200ciciCtw 150000C)100F-Cl)-J50Uw-j00cih ciItw000C)Ct 20wI\u2014C\/):i 15zz 100a:Izwo 0z 0 5000O TIME (mm)Figure 8.42 Predicted variation of minor element concentrations in blister copperwith time, a. lead and zinc, b. arsenic, antimony, and bismuth.100 200 300 4002078.2.5 Minor Element Removal1.91.81.60 0.1 0.2 0.3 0.4DEPTH (m)Figure 8.43 Variation of surface area-to-volume ratio of blister copper with depth.The variation of the minor element content of the matte (Figure 8.44) shows thatarsenic, antimony, and bismuth follow the same basic pattern, while the lead and zincbehave differently. Figure 8.44a shows that the zinc content in matte decreases duringblowing, with sudden increases when matte is added. The rate of the decrease of zinccontent becomes much smaller during the copper blow. The behaviour of the lead inmatte is the opposite of this. The lead content increases continuously throughout thecharge, except for the abrupt decreases caused by matte addition. The increase continuesthroughout the copper blow, as lead is concentrated in the matte. The concentrations ofthe other minor elements in the matte are relatively constant throughout the slag blows(Figure 8.44b), but increase slightly during the copper blow. This concentrating effect inthe matte occurs because the rate of copper removal from the matte is considerably fasterthan the rate of minor element removal.2.32.22.121.72088.2.5 Minor Element RemovalThe behaviour of the minor elements in the slag is shown in Figure 8.45. Thisshows that all of the minor elements except for zinc behave in a similar manner;decreasing during the slag blows and remaining relatively constant during the copperblow. The zinc behaviour is quite different. During the slag blows the zinc content tendsto increase, but is subject to rapid drops when flux is added. The increasing zinc contentis caused by the reaction of ZnS in the matte with oxygen to form ZnO. The extent ofthis reaction becomes very small during the copper blow, when the high concentration ofzinc oxide in the slag causes a fairly rapid rate of mass-transfer to the matte\/slaginterface. The oxide reacts with sulphur at the interface, and the zinc is returned to thematte. This causes the reduction of the zinc content during the copper blow.The variations of the minor element partial pressures in the gas, shown inFigure 8.46, all follow the same basic pattern; increasing during the slag blows anddecreasing during the copper blow. The extent of the decrease at the beginning of thecopper blow is related to the difference in activity coefficients between matte and whitemetal. Thus, arsenic and antimony partial pressures drop significantly, while the partialpressures of lead, zinc, and bismuth are only slightly decreased. The increase in partialpressure during the slag blows is caused by the increasing bath temperatures, andlikewise, the decrease during the copper blow is caused by the decreasing temperatures.2098.2.5 Minor Element Removal4\u2014.3.5UI2.5zUI-J0.5a.b.11.41.2__0.80.6z0.4N0.205000 100 200 300 400TIME (mm)900800F-F600Z 5004003001t 200I\u2014Z 100Lu00Z 000100 200 300 400 500TIME (mm)Figure 8.44 Predicted variation of minor element concentrations in matte withtime, a. lead and zinc, b. arsenic, antimony, and bismuth.2108.2.5 Minor Element RemovalCD-JC,)z0LU-JTIME (mm)A\u2018+.c: o04-JCl)3.5z0z3RiFigure 8.45 Predicted variation of minor element concentrations in slag with time,a. lead and zinc, b. arsenic, antimony, and bismuth.a.521.510.500 100 200 300 400TIME (mm)b.-5OOCD 400-JCl)300z0200FzLU 1000z0000 100 200 300 400 500211\u201418.2.5 Minor Element Removal(\/ -2 -<0 100 200 300 400 500TIME (mm)-10-3-4-5-6-7-8-9-10\u201411-fC),zUi_1\u20140-JI-J0 100 200 300 400 500-12TIME (mm)Figure 8.46 Predicted variation of minor element partial pressures in gas withtime, a. lead and zinc, b. arsenic, antimony, and bismuth.2128.2.5 Minor Element Removal8.2.5.3 Model predictions8.2.5.3.1 Gas flow rateIncreasing the gas flow rate should increase the total gas\/liquid interfacial area, aswell as the total gas throughput. Both of these factors should improve the removalkinetics of the minor elements to the gas, and this is predicted by the model. Figure 8.47shows that there is an increase in the distribution of all of the minor elements to the dust.This is particularly evident for lead, the proportion of which reporting to the dust isincreased by 33%. The increase in arsenic, antimony, and bismuth in the low gas flowrate case is unexpected, but can be explained by the increased time required to reach theend point and the increased tuyere submergences due to the reduced iron removal rate.These combine to increase the overall surface area available for mass-transfer. Thedistribution of minor elements to the blister is not significantly affected by the gas flowrate.2138.2.5 Minor Element Removala.::-b.961.5561.45d. ::-10% BASE +10%GAS FLOW RATEFigure 8.47 Predicted variation of minor element distribution to the dust with gasflow rate, a. lead b. zinc, c. arsenic, d. antimony, and e. bismuth.8.2.5.3.2 Oxygen enrichmentUsing oxygen enrichment, while keeping the total volume of oxygen constant, willreduce the total gas flow rate, and so may be expected to reduce removal to the dust.This effect is predicted by the model, as shown in Figure 8.48. There is also an increasein the distribution to the slag by all materials except zinc. The reduction of zinc reportingto the slag is caused by the reduced gas\/liquid interfacial area. The increases in the otherminor elements in the slag are caused by the higher concentrations in the matte, which2148.2.5 Minor Element Removalincrease the driving force for mass-transfer between the liquid phases. This effect is alsoseen in the increased concentration of minor elements in the blister copper. In particular,increasing the oxygen content to 30% causes the concentration of antimony in blistercopper to increase by 27%, while arsenic and bismuth are increased by 10%(Figure 8.49). The differences in the magnitude of these increases is related to theactivity coefficients in the matte and copper.If the total gas flow rate is not changed while oxygen enrichment is used there aresome significant differences. Figure 8.50 shows that there is an increase in the proportionof minor elements reporting to the dust. The primary explanation for these differences isthe bath temperature. At higher gas oxygen contents the bath temperature is dramaticallyincreased, which increases the rate of mass-transfer to the gas\/liquid interface. Theresulting increase in vapourization (Figure 8.51) more than makes up for the slightdecrease in off-gas volume caused by the increased oxygen content.\u2018While there is a slight increase in the proportion of minor elements reporting to theblister copper at 24% oxygen, Figure 8.52 shows that only the antimony concentration isincreased at 30% oxygen in the gas. The explanation of this is more complicated. At24% oxygen enrichment the increase is caused by the higher mass-transfer rates atincreased temperatures and this is also the case for the antimony at 30% oxygen.However, for the other minor elements the composition of the cold charge becomesimportant.2158.2.5 Minor Element Removala.C.61.2-d.40.1 -Sb::e. - Bi37.65 -37.5521 25 30GAS OXYGEN CONTENT (%)Figure 8.48 Predicted variation of minor element distribution to the dust with gasoxygen content with constant total oxygen input, a. lead b. zinc, c. arsenic, d. antimony,and e. bismuth.2168.2.5 Minor Element Removala. Pb3.963.92b. Zn3.643.62 -3.6 -2.5 As2 2.42.3d.Sb0.70.6-1.32 . Bie.1.28 -1.24 -25301.2 -GAS OXYGEN CONTENT (%)Figure 8.49 Predicted variation of minor element distribution to the blister copperwith gas oxygen content with constant total oxygen input, a. lead b. zinc, c. arsenic,d. antimony, and e. bismuth.2178.2.5 Minor Element RemovalC.E\u2014. 61.4d. 41.2 Sbe.37.521 25 30GAS OXYGEN CONTENT (%)Figure 8.50 Predicted variation of minor element distribution to the dust with gasoxygen content with increased total oxygen input, a. lead b. zinc, c. arsenic, d. antimony,and e. bismuth.218LUIIDU)U)wU:0-JI-U:000-J8.2.5 Minor Element Removal-3-4-5-6-7-8-9-10\u201411\/.-\u2022\u2018L r\u2019 \/\u2014\u2014GAS OXYGEN CONTENT (%)21 (BASE)24\u2014\u2014\u2014\u2014\u2014300 100 200 300 400 500TIME (mm)Figure 8.51 Effect of gas oxygen content with increased total oxygen input, onpredicted variation of arsenic partial pressure in the off gas with time.At an oxygen enrichment of 30%, there are some significant differences in theminor element behaviour in the blister copper, as shown in Figure 8.53. The increasedtemperatures cause the arsenic content in the copper to rise more quickly, but there is arapid drop close to the end of the first blow. This is because essentially all of the ironsuiphide has been removed from the matte, causing the production of copper, as well as aconsiderable drop in the arsenic activity coefficient. In this case the direction ofmass-transfer is reversed and, when combined with the initial small volume of copperpresent and the production of additional copper, the effect is quite large. Following theaddition of matte, the arsenic content begins to increase again, until copper begins to beproduced. After this point the curve follows the same pattern as the base curve.However, copper is produced faster at the higher oxygen content, so when the scrap isadded it has a smaller effect on the minor element concentrations, due to the larger total2198.2.5 Minor Element RemovalC. 2.4 Asd.0.562 25 30GAS OXYGEN CONTENT (%)Figure 8.52 Predicted variation of minor element distribution to the blister copperwith gas oxygen content with increased total oxygen input, a. lead b. zinc, c. arsenic,d. antimony, and e. bismuth.mass of copper present. Thus the arsenic concentration in the blister copper remainslower at the higher oxygen enrichment. If the effect of the scrap is overestimated,however, the final arsenic content of the blister copper in the oxygen enriched case mayactually be higher than the base case.2208.2.5 Minor Element RemovalThis is actually seen for the antimony, as shown in Figure 8.54. While the samepattern is followed for the behaviour of the antimony concentration in the base charge,there is considerably less antimony in the scrap. In this case, the increased initialantimony content caused by the higher temperatures is not reduced to the level of thebase charge, and the scrap additions to the base charge do not bring its antimony contentabove the oxygen enriched case. This emphasizes the importance of obtaining goodexpressions for transport properties.2520z1510500 500TIME (mm)Figure 8.53 Effect of gas oxygen content, with increased total oxygen input, on thepredicted variation of arsenic content in blister copper with time.If the model is run using oxygen enrichment, but assuming that the temperature isconstant, some interesting results are obtained. Increasing the oxygen content underthese conditions reduces the distribution of minor elements to the blister copper, asshown in Figure 8.55. The lower concentrations are primarily caused by the increasedrate of copper production early in the charge (Figure 8.56). The increased amount of100 200 300 4002218.2.5 Minor Element Removal2015SzIQ1:00 500TIME (mm)Figure 8.54 Effect of gas oxygen content, with increased total oxygen input, on thepredicted variation of antimony content in blister copper with time.copper reduces the interfacial area to volume ratio, so while the mass-transfer rate isessentially unchanged, the actual concentrations in the copper remain lower. Theincreased weight of copper also reduces the effect of the cold charge addition asexplained above.While increasing the oxygen enrichment to 42% causes a small decrease in theproportions of arsenic, antimony, and bismuth reporting to the dust, Figure 8.57 showsthat increasing the oxygen content to 84% increases the proportions of all of the minorelements reporting to the dust. This result is not expected, and requires someexplanation. The off gas volume, at 84% oxygen in the injected gas, will be reduced byconsiderably more than a factor of four, so to increase the distribution to the dust, thepartial pressures of these minor elements must increase by even more. Figure 8.58 showsthat the arsenic partial pressure is increased at high oxygen contents, and remains100 200 300 4002228.2.5 Minor Element Removalrelatively high, even through the copper blow. Most of the increase in arsenic partialpressure will be directly related to the reduced off-gas volume. It is important to note,however, that the volume of gas injected through a single tuyere is unchanged by theoxygen enrichment. This means that, for the bubble growth and early in the bubble rise,the surface area available for mass-transfer per tuyere is only slightly reduced.Therefore, there is little change in the initial mass-transfer of arsenic to the gas around asingle tuyere. As the oxygen is removed from the gas by reaction there is a concentratingeffect which causes the higher partial pressure.This effect alone will not increase the total amount of minor elements removed tothe dust, so some other mechanism must be involved. The explanation of this can be seenin Figure 8.59. This figure shows that, for the slag blows, there is a very slight increasein the arsenic content of the matte at 84% oxygen in the gas. During the slag blows thearsenic content of the matte drops quite quickly, but during the copper blow the removalrate is very low. This is because the activity coefficients of the minor elements are muchlower in white metal, reducing the driving force for mass transfer. The compositiondependence of the activity coefficients in the matte is also the reason the matte arseniccontent in the case with a high gas oxygen content remains close to the base case duringthe slag blows. The difference between the two cases occurs at the end of the second slagblow. Throughout the charge, the mole fraction of copper suiphide is lower at the highgas oxygen content, and this effectively prolongs the slag blow, allowing the increasedremoval rate to continue for a longer time. This results in the lower final arsenic contentin the matte seen in Figure 8.59. The reason the effect is not seen for lead is that itsactivity coefficient is not as sensitive to matte grade, so its mass-transfer rate is notincreased significantly over the base charge. It should be noted that the formation of2238.2.5 Minor Element Removalwhite metal is determined by the iron suiphide content of the matte. Theoretically, \u2018whitemetal\u2019 is Cu2S, but it is actually a matte with a very low iron sulphide content. Thepresence of lead and zinc suiphides cause the white metal to have a Cu2Smole fractionbetween 0.8 and 0.9.2248.2.5 Minor Element Removala.::z -0 -I\u2014Dm 1.7-1.5-0d.::Sb214284GAS OXYGEN CONTENT (%)Figure 8.55 Predicted variation of minor element distribution to the blister copperwith gas oxygen content with constant total oxygen input and temperature, a. lead b. zinc,c. arsenic, d. antimony, and e. bismuth.2.11.9225Ez0I\u2014zuJ()z0C-)8.2.5 Minor Element Removal2520Is1050500TIME (mm)Figure 8.56 Effect of gas oxygen content, with constant total oxygen input, on thepredicted variation of arsenic content in blister copper with time at 1400 K.0 100 200 300 4002268.2.5 Minor Element Removala. 33-Pb32.8 -32.6-32.4 -32.2 -32 -b. 16Zn14 -2-10 -As65Q63-D61-C\u2019)d. Sb41-39-Bie. 41393721 42 84GAS OXYGEN CONTENT (%)Figure 8.57 Predicted variation of minor element distribution to the dust with gasoxygen content with constant total oxygen input and temperature, a. lead b. zinc,c. arsenic, d. antimony, and e. bismuth.2278.2.5 Minor Element Removal2(U2(U.4-5-6.7-8GAS OXYGEN CONTENT (%)_________ 218411I I I I0 100 200 300 400 500500wi 450TIME (mm)Figure 8.58 Effect of gas oxygen content, with constant total oxygen input, on thepredicted variation of arsenic partial pressure in the off gas with time at 1400 K.550 0.9C00.8 (aa)0Ew0.7zw00.60.-JDC\u2019)Ui00.5C)0.4500400350100 200 300 400TIME (mm)Figure 8.59 Effect of gas oxygen content, with constant total oxygen input, on thepredicted variation of moles of arsenic and mole fraction of copper sulphide in matte withtime at 1400 K.2288.2.5 Minor Element Removal8.2.5.3.3 Tuyere submergence and diameterThe predicted distributions of the minor elements to the dust and copper for changesin tuyere submergence are shown in Figures 8.60 and 8.61 respectively. Increasing thetuyere submergence is predicted to increase the amount of minor elements reporting tothe dusts and reduce the amount of minor elements (with the exception of zinc) reportingto the slag. The increased concentration in the dust is caused by an increase in thegas\/liquid interfacial area, which allows more vapourization to occur. The increasedinterfacial area also increases the amount of zinc oxidized and, hence, the zinc content ofthe slag.During the copper blow the rate of removal of the minor elements from the matte isconsiderably slower than the rate of copper fonnation. This causes them to beconcentrated in the matte remaining at the end of the charge, which forms the copper\u2018slag\u2019. Figure 8.61 shows that the use of tuyere submergences less than the base valuehas little effect on the lead and zinc reporting to the blister copper. However, thedistributions of all of the minor elements to the copper is reduced by an increase in thetuyere submergence. Reducing the tuyere submergence also decreases the proportions ofarsenic, antimony, and bismuth in the blister. Figure 8.62 shows the variation of arsenicconcentration in the blister copper up to the point where 72 tonnes of copper have beenproduced. Although the higher bath temperature causes a more rapid increase in thearsenic content of the copper, the reduction in total concentration begins earlier, and therate of copper production is greater. The larger weight of copper present at scrapadditions reduces the effect of the added arsenic, so the arsenic content at deeper tuyeresubmergences is lower throughout the copper blow. The reduced distribution to thecopper seen for arsenic, antimony, and bismuth is caused by the length of time between2298.2.5 Minor Element Removalthe last scrap addition and the end point. Figure 8.62 shows that the increased timebetween the addition of the scrap and the end point at the reduced tuyere submergenceallows the arsenic content of the blister copper to drop below the final arsenic content ofthe base case, causing the reduced distribution. This indicates that scrap should not beadded close to the end of a charge.The effect of reducing the tuyere diameter follows the same basic pattern asincreasing the tuyere submergence. The increased temperatures and gas\/liquid interfacialarea tend to increase the removal of zinc to the slag and the other minor elements to thedust. As might be expected, combining a high tuyere submergence with a low tuyerediameter has the same effect as each of the separate changes. The overall effect,however, is slightly larger, with a lower final concentration of minor elements in theblister copper, and a higher percentage reporting to the dust.2308.2.5 Minor Element Removala. Pb3.5 -b Zn3-2.5 -c. - As2.2-z 2-D 1.8 -m1 1.6 -- Sb0.56 -0.54 -0:::- Bi1.2 -.BSE+.m0.9Figure 8.60 Predicted variation of minor element distribution to the blister copperwith tuyere submergence, a. lead b. zinc, c. arsenic, d. antimony, and e. bismuth.2318.2.5 Minor Element Removala.z 2-F\u2014 =1.8-ci:1.6-d.-.lm BASE +.1mFigure 8.61 Predicted variation of minor element distribution to the dust withtuyere submergence, a. lead b. zinc, c. arsenic, d. antimony, and e. bismuth.232Eccw0000ccwI\u2014Cl)-Jz0zwC,)cc8.2.5 Minor Element Removal100 200 300 4003025201510500 500TIME (mm)Figure 8.62 Effect of tuyere submergence on the predicted variation of arseniccontent in blister copper with time.8.2.5.4 SummaryIn general, factors which increase the extent of oxygen use or the total gas flowthrough the bath will increase the minor element removal to the dust and reduce thedistribution to the blister copper. The same factors which have the greatest effect onoxygen use, gas\/liquid interfacial area, temperature, and, to a lesser extent, gas injectionvelocity, also affect the rate of minor element transport to the gas. Low levels of oxygenenrichment are detrimental to minor element removal, due to the lower gas volumeproduced, but this may be overcome by the effect of temperature. Very high levels ofoxygen enrichment have a large effect on the distributions to the dust and blister copper,increasing the former and decreasing the latter. These effects are directly related to theprocess kinetics. The timing of scrap additions is also predicted to have a large effect on2338.2.6 Comparison with Previous Workthe amount of minor elements reporting to the blister copper. The scrap provides a largeproportion of the total amount of minor elements in the blister copper, but its effect canbe reduced by increasing the time between the final scrap addition and the end of thecharge.8.2.6 Comparison with Previous Work8.2.6.1 Overall modelWhile the publications regarding most previous models do not contain sufficientdata to allow a reasonable comparison, a comparison may be made with the results of anequilibrium model of the nickel converter.97 In fact, the data obtained from the previousstudy has been used in the verification of the present model, so there is a good basis forcomparison. The equilibrium model assumed that the two condensed phases were at thesame temperature, and that they were in equilibrium with the gas exiting the bath. Anoverall oxygen efficiency of 95% was used.A direct comparison of the temperatures and compositions predicted by bothmodels for the Copper Cliff nickel charges, shows that the predictive ability of the twomodels is similar. The temperatures in the equilibrium model, however, did require somefitting at the beginning of each charge to account for the shape of the temperature curve.This fitting was carried out by assuming that the mush dissolved slowly and removedheat continuously throughout the first part of the first blow. Fitting of this nature is notrequired in the kinetic model, because the abrupt change in the slope of the measuredtemperatures matched the crossover between matte and slag temperatures in most cases(see Section 7.3.1). This also occurred in later blows, where the equilibrium model againfailed to match the lower initial temperatures.2348.2.6 Comparison with Previous WorkThe compositions predicted by both models are also comparable, and generallywithin the error of the measurements. The equilibrium model is closer for slags at theends of the charges, but the kinetic model is better for most slags at other times. Thekinetic model is also better able to predict the Bessemer matte composition. In general,however, both models are able to predict the measured temperatures and compositions towithin the accuracy of the measurements, although minor elements were not included inthe equilibrium model, so no comparison of them may be made.It is in the predictions regarding operating parameters that the models differ. Bothmodels do predict the same trends for increases in oxygen enrichment and gas flow rate,but such variables as tuyere submergence and tuyere diameter have no effect on theequilibrium model. These are parameters which affect the process kinetics, so have nobearing on the system if equilibrium is assumed. Perhaps the most important differencebetween the two models is that, using the equilibrium model, it was determined that therewas little which could be done to improve the chemistry of the converter.97 However, thekinetic model indicates that there are some variables which may be altered to improveconverter kinetics.8.2.6.2 Minor element distributionPrevious modelling work on minor element distribution has been limited to anumber of versions of a single model. These concentrate on determining the effects ofoxygen use and initial matte grade.\u20196\u2019263113 In all cases it has also been assumed thatthe three condensed phases were in equilibrium with each other and the gas. Thedistribution of minor elements between phases was calculated using distributioncoefficients and the volatilization of minor elements was also based on equilibrium2358.2.6 Comparison with Previous Workconsiderations. It was assumed that the oxygen efficiency was 100%, with all of theoxygen reacting with FeS until white metal was formed, at which point reaction withCu2Sbegan. The models also assumed isothermal conditions.The results of these models, for converting conditions, indicate that the amount ofminor element removal is almost entirely determined by the total volume of off gasproduced during smelting and\/or converting. As such, increasing oxygen enrichment andinitial matte grade both reduce the amount of minor element removal to the dust. Theoxygen dependence of the distribution coefficients does suggest that there will beincreased slagging of minor elements at higher oxygen enrichments, but the extent of thisis much smaller than the reduction in volatilization. One of the papers did note that theincrease in temperature accompanying oxygen enrichment would counteract the reducedgas volume.213The large differences in the basic assumptions between the previous models and thepresent case make a comparison difficult. While some of the same trends are predicted inboth cases, in particular, the basic effect of total off gas volume and the effect ofincreasing temperature, the effects caused by general kinetic considerations andespecially variations in matte composition due to kinetic effects, are completelyoverlooked by the equilibrium models. With respect to the comparative validity of thetwo models, the present case appears to able to calculate the minor element distributionsin a copper converter charge quite well, whereas Table VIll-ilI shows that thevolatilization models have some difficulties. While the present model does appear tohave difficulty predicting the bismuth distribution, this arises only during the copperblow. Predictions up to the end of the slag blows are close to measured values. Theequilibrium model predictions of lead and arsenic are outside of the observed range, and2368.2.6 Comparison with Previous Workthe distributions of antimony and bismuth to the gas are very close to the top of the range.The fact that all of the predicted distributions to the gas, with the exception of zinc,appear to be high is an indication that the removal kinetics are controlling thevolatilization rates, rather than the thermodynamics.Phase I Pb I Zn As I Sb BiCommercially Observed16slag 40-80 70-90 10-50 30-70 5-20gas 20-55 10-30 20-70 5-50 70-90Equilibrium Model\u20196slag 29 82 8 33 6gas 64 18 80 48 85Kinetic Modelslag 59 86 36 59 45gas 37 10 62 40 54Table Vu-Ill Comparison of equilibrium and kinetic model predicted minorelement distributions with commercially observed ranges.2379.1 Introduction9 MODEL APPLICATION9.1 IntroductionThe kinetic model developed here can be applied to determine improved operatingconditions for the Peirce-Smith converter in its present form, or to indicate a direction forthe development of a new process.9.2 Converter OptimizationThere are three primary factors to be considered when trying to optimize theperformance of the Peirce-Smith converter: process time, oxygen efficiency, and minorelement deportment. Any optimization must also be carried out within the constraints setby bath temperature and bath motion considerations. The variables which may be usedare tuyere submergence and diameter, gas flow rate, gas oxygen content, slag skimmingpractice, and number of tuyeres used. Each of these will affect the primary factors indifferent ways, both beneficial and detrimental. It is important to note that if only oxygenefficiency and the process time are considered, equilibrium operation should be optimal.However, under equilibrium conditions the amount of minor elements reporting to theblister copper will be high, so the kinetics become important.Oxygen enrichment is not available in many installations, and its effect on the bathtemperature generally limits its use to situations where extra scrap is available. At lowlevels, it has a detrimental effect on minor element removal, and the extent of oxygenenrichment usable is limited by its effect on the tuyere-line refractory. All of thesefactors suggest that oxygen enrichment contributes little to the process, and so should notbe considered further.2389.2 Converter OptimizationOf the remaining variables, a reduced tuyere diameter and an increased tuyeresubmergence both increase the oxygen use and reduce the total charge time, as well ashaving a beneficial effect on the minor element removal to the dust. Increasing the tuyeresubmergence also allows a higher gas flow rate to be used without initiating bathslopping.9 Reducing the tuyere diameter increases the gas exit velocity, which has beenshown to remove the need for tuyere punching due to the formation of stable,non-blocking accretions on the tuyeres.8 The increased gas velocity also reduces theextent of tuyere interaction,115 and does not affect the bath motion, which is related to thebuoyant power per unit mass of the bath.9 All of these factors suggest that a small tuyerediameter in a deep bath will provide the optimum operation. However, both of thesevariables also cause an increase in the bath temperature, so there is a limit to their use.Increasing the gas flow rate was also found to reduce the total charge time and thedistribution of the minor elements to the blister copper. Unlike the changes in tuyeresubmergence and diameter, an increased gas flow reduces the oxygen use and the bathtemperature. Increasing the gas flow rate may also cause bath slopping, but this may becontrolled by an increased tuyere submergence.9Reducing the slag cover increases thetotal charge time slightly and reduces both the oxygen use and the matte temperature.These factors indicate that present converter operations can be improvedconsiderably by using a smaller tuyere diameter at a deeper tuyere submergence and ahigher gas flow rate. The increased gas flow rate will aid in controlling the temperatureincrease, and may be aided by altering the skimming practice. The reduced tuyere sizeshould remove the need for tuyere punching, and so extend refractory life. The increasedtuyere submergence will reduce the likelihood of bath slopping, even at the higher gasflow rate. In addition to this a reduced number of tuyeres could be used to further2399.2 Converter Optimizationincrease the gas exit velocity and reduce the amount of tuyere interaction.To illustrate this, Figure 9.1 shows the results of an \u2018improved\u2019 version of the basecharge used in Section 8. The conditions used for this prediction are given in Table IX-I.the lengths of the slag blows are reduced, but all idle times are unchanged. Figure 9.1shows that the total charge time is reduced by 70 minutes, while the bath temperature iskept within the range of the base charge. Figure 9.2 shows that the oxygen use in the\u2018improved\u2019 charge is lower than the base charge during the slag blows, but is higherduring the copper blow. This suggests that there is still room for improvements, but theymay be limited by the bath temperature. In fact, it is quite possible that 100% oxygen useis not attainable because of the temperature constraints.Variable ValueTuyere submergence base+0.05 mTuyere diameter 0.03 8 mGas flow rate base+10%Slag cover \u2018low\u2019Table IX-I Conditions used in the \u2018improved\u2019 charge.2409.2 Converter Optimization17001600w150014001300120011001000987Lii 6I\u201454z0 3Cl200 500Figure 9.1 Effect of modifications given in Table IX-I on the predicted variation ofmatte temperature and iron content (weight percent) with time.241100 200 300 400TIME (miri)9.3 New Process Development1009080C\/)Dzw(370060500 500TIME (mm)Figure 9.2 Effect of modifications given in Table IX-I on the predicted variation ofoxygen use with time.9.3 New Process DevelopmentThe results of the model runs using a very high oxygen content in the gas at aconstant temperature indicate a possible direction for process development. In thestandard converter, equilibrium represents the limit to operating efficiency, which can beapproached by altering variables to improve the kinetics. At high levels of oxygenenrichment the kinetics of the system can be used to give considerable improvements inoperation. Unfortunately, high levels of oxygen in the gas also cause a large increase inthe bath temperature.100 200 300 4002429.3 New Process DevelopmentThe Peirce-Smith converter, like most other pyrometallurgical reactors, is designedto keep heat in. This is the opposite of what is required to allow process improvement. Ifthe reactor walls are designed to remove heat, rather than retain it, then higher levels ofoxygen could be used. For example, the use of water cooled panels would increase theheat lost through the walls considerably, and give a certain degree of control over thebath temperature. The bath temperature can also be controlled by the addition of coldmaterials such as flux, concentrate, or solidified matte.The primary improvement available using a high gas oxygen content is the directproduction of copper from matte. This is possible if the extent of the reaction of ironsulphide becomes controlled by liquid-phase mass-transfer. Under these circumstancesthe excess oxygen at the gas\/liquid interface will react with copper suiphide to formcopper. A process designed to utilize this would have the added advantages of low gasvolumes and an off gas with a high SO2 content.To provide an example of such a process, the model has been modified to increasethe heat flux through the walls. The initial conditions of the base charge are used subjectto the modifications given in Table DC-il. The composition of the matte added is given inTable TX-ill. Both solidified matte and flux are added continuously throughout the runand 15 tonnes of slag is skimmed every 10 minutes. Figure 9.3 shows the predictedvariation of matte temperature and iron content for this process. Following an initialdecrease, the bath temperature increases up to the end of the run. This could becontrolled by increasing the heat removal through the walls, to provide an essentiallyisothermal system. The weight percent of iron in the matte drops initially, but begins tolevel out towards the end of the run. This could also be controlled by altering the ironcontent of the added matte, the rate of matte addition, the gas flow rate, or the gas oxygen2439.3 New Process Developmentcontent, to provide a constant value.Figure 9.4 shows that the oxygen use in this system is very high. Even with thehigh oxygen content in the gas, the oxygen use is higher than the model preducts for anyof the regular converter charges. Finally, Figure 9.5 indicates that the rate of blistercopper production is almost one tonne per minute. This is considerably higher than thePeirce-Smith converter, which can produce about 10 tonnes per hour.98Variable ValueTuyere submergence base+0.3 mTuyere diameter 0.03 mGas flow rate\/tuyere 0.2325 Nm3s\u2019Gas oxygen content 95%Number of tuyeres 20Flux addition rate 0.5 tonnes min1Matte addition rate 2.75 tonnes min1Table TX-il Conditions used in the \u2018new process\u2019.Element Fe Cu 0 S Pb ZnContent (wt.%) 24.7 43.8 3.4 24.1 1.16 2.66Table TX-ill Composition of matte added in the \u2018new process\u2019.2449.3 New Process Development1650w1600w1550wI\u20141500\u2014 1450Figure 9.3 Predicted variation of matte temperature and iron content (weightpercent) with time for the \u2018new process\u2019.TIME (mm)245(I)a>CC.2Ui0D00UI0000cxUIFigure 9,3the \u2018new process\u2019Predicted variation of weight of blister copper produced with time for9.3 New Process Development0 10 20 30 40TIME (mm)1009998UI(I,DzUI0970969560Figure 9.4 Predicted variation of oxygen use with time for the \u2018new process\u2019.504030201000 10 20 30 40TIME (mm)5024610 CONCLUSIONS AND FURTHERWORK10 CONCLUSIONS AND FURTHER WORKThe kinetic model of the Peirce-Smith converter developed here, has been shown tobe able to predict both temperatures and compositions of the condensed phases to withinthe accuracy of the measurements. A number of conclusions may be drawn based on thepredictions of both the gas flow model and the overall model, but it must be recognizedthat there are still considerable inaccuracies involved with some of the data used.The apparent success of the gas flow model indicates that it is possible totheoretically model the formation and rise of gas bubbles through a liquid bath. Whilethe fluid flow portion of the model is far from rigorous, it is effective, and able to predictgas fractions within the plume and spout heights with reasonable accuracy. Perhaps moreimportant is that gas\/liquid interfacial areas are predicted well enough to use for kineticmodelling purposes, however the almost complete lack of information regardinggas-phase mass-transfer in bubbles does add some doubt to the accuracies of thepredictions.Using the gas flow model, it can be concluded that increases in the tuyeresubmergence and the gas exit velocity would increase the amount of oxygen available forreaction. While increasing the oxygen content of the gas produces more reaction, it alsoleaves a larger amount of unreacted oxygen because the increase in the mass-transfer rateis not sufficient to react all of the extra oxygen. The material properties of the liquidphase also have an effect on the rate of bubble growth, and tuyere interactionsignificantly reduces the amount of oxygen available for reaction due to the largerbubbles produced.The increased oxygen use with increased tuyere submergence and gas exit velocityreported in an operating converter98can only be explained if the converter is kinetically24710 CONCLUSIONS AND FURTHER WORKcontrolled. These phenomena were predicted by the gas flow model, and are directlytransferred to the overall model. Thus, to properly model the converting process, thekinetics of the system must be considered.The effects of many of the process variables on the major components in theconverter follow directly from the results of the gas flow model. Any variable whichincreases the oxygen use will increase the rates of iron removal and temperature increasein the matte. What cannot be predicted by the gas flow model are the relative amounts ofreaction in the matte and slag, and the behaviour of the minor elements. The separationof the reactions with the matte and slag are an important part of the kinetic model, whichis not possible with the assumption that all of the phases are in equilibrium.A number of important conclusions may be drawn from the overall model. Theeffects of tuyere submergence and gas exit velocity (controlled by the tuyere diameterand the gas flow rate) have already been mentioned. As well, it has been determined thatthe reaction between the gas and slag is at least partially controlled by liquid-phasemass-transfer. As such it may be possible to alter the amount of reaction occurring bychanging the physical properties of the slag. In particular, the slag viscosity will have adirect effect on the liquid-phase diffusivities, and can be altered by changing the iron tosilica ratio. It has also been determined that small amounts of copper are producedthroughout the converting cycle.Oxygen enrichment does not necessarily cause an increase in the amount of minorelements reporting to the blister copper. The higher temperatures associated with oxygenenrichment increase the mass-transfer rates within the liquid phases as well as theequilibrium vapour pressures, so more of the minor elements are vapourized. At veryhigh oxygen enrichments it is predicted that white metal is formed later in the converting24810 CONCLUSIONS AND FURTHERWORKcycle, with copper being produced directly from a high grade matte. This could have abearing on future process design, as it also increases the amount of minor elementvapourization.There is still insufficient data regarding these, particularly with respect tomass-transport, so the predictions regarding them must be considered to be tentative. Theinaccuracies involved in the overall model may also fairly large. Measurements made onoperating equipment are far from precise, and make any validation uncertain. Toimprove on this carefully controlled cold modelling could be used, or, ideally a smallscale test converter could be used. Some tests have been carried out, but insufficient datahas been reported to allow their use in the present case.Some other physical modelling studies could provide information which would beuseful in improving the kinetic model. These would primarily involve injection into twoand three phase systems, to obtain a better understanding of the behaviour of theinterfaces involved. Ideally these would also involve mass-transfer measurements.Perhaps most important is the development of an expression relating to gas-phasemass-transfer coefficient in rising bubbles. Such an expression is essential to improvingour understanding of all gas injection processes.24911 NOMENCLATURE11 NOMENCLATUREA Area (m2)a Minor axis of ellipse (m)b Maj or axis of effipse (m)C Concentration (molm3)CD Drag coefficientHeat capacity (J kg KjDisturbance propagation speed (eq. 4.22)Diffusivity (m2 s\u2019)d Diameter (m)F Force (N)Fr\u2019 Modified Froude numberf Fraction 02 in gasg Acceleration due to gravity (9.81 m 2)h Height (m)h Heat-transfer coefficient (W m2K1)hB Height shown in Figure. 4.7K Constantk Mass-transfer coefficient (m sjk Wave number (ma) (2tkc1 Growth factor (eq. 4.23)L Converter length (m)L1\u2019 Distribution coefficient between copper and slag1 Length (m)M Molecular weight (g mor\u2019)M Mass (kg)[M] Weight percent of element MNu Nusselt numbern Number, Molesii Molar flux (mol sj25011 NOMENCLATUREP Pressure (Pa)P\u00b0 Equilibrium vapor pressure of pure substance (Pa)Pr Prandtl numberp Partial pressure (Pa)Q Volume flow rate (m3 s1)4 Heat flux (J s\u2019)R Gas ConstantRe Reynold\u2019s numberr Radius (m)s Distance from tuyere centre to bubble centre (m)T Temperature (K)t Time (s)V Volume (m3)v Velocity (m s\u2019)w Relative velocity of bubble with respect to the bath (m 1)X Mole fractionx Thickness (m)x Reaction constant (equation 6.34)Greek lettersAccommodation coefficient in Langmuir-Knudsen equationThermal diffusivity (m2 s\u2019)Absorptivity of gasAngle (Figure 5.4 or Figure 6.3)Activity coefficientboundary layer thickness (m)8 Eccentricity of ellipse8 Emissivityln[([Itan(\u2019IPerterbation amplitude (m)25111 NOMENCLATURE00 Disturbance initiation angleWake angleWavelength (m)Dynamic viscosity (kg m1 s1)v Kinematic viscosity (m2 s\u2019)p Density (kgm3),rn Molar density (mol m3)Dimensionless densitya Surface tension (Nm1)a Stefan-Boltzman constant, 5.67(108) W m2K4Gas holdup25211 NOMENCLATURESubscriptsamb AmbientB BathBu Buoyancyb Bubblec convertercb converter barrelcon ConsumedD Dragd droplete Evaporationew End wallext ExternalG Gas-phaseg Gasgp Gas in plumegen GeneratedH Hoodi Specie, Initial, Interfacialmt InternalL Liquid-phaseM Matte-phasem Mouthmm Minimummt Mass-transfero Orifacep PlumeR Reaction, Refractoryr Remaining, Residencerad RadiationS Slag-phase, Spheres Surface tensionsp Spout25311 NOMENCLATUREsup superficialT Temina1t Tuyerew Wallx Cross-sectionSuperscriptsB BulkC CopperI InterfacialI,J PhaseM MatteS SlagW White metal* Interfacial (actual)+ Interfacial (equilibrium)25412 REFERENCES12 REFERENCES1. 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With this exception, it is assumed thatall interphase heat and mass-transfer can be calculated based on the temperatures andcompositions at the end of the previous time step.26613 APPENDIXINPUT OPERATING PARAMETERSCALCULATE PHASE DEPTHSGAS FLOW CALCULATIONMASS BALANCE CALCULATION* I MODIFYHEAT BALANCE CALCULATIONI_TEMPERATUREAT>r)YESNONOt=t+At t>tYESENDFigure 13.1 Simplified flow chart of the overall model.267INPUTBLOWING PARAMETERS13 APPENDIXBUBBLE GROWTH CALCUlATIONSTABILITY CALCULATIONNODETACHMENT?YBSt=t+At4PLUMB CHARACTERISTICSSTABILITY Cl LCULATIONFigure 13.2 Flow chart of the gas flow calculation.268BUBBLE RISE CALCULATIONOUThUT13 APPENDIXLUTMAJOR COMPONENTS REACTION CALCULATIONMINOR COMPONENTS MASS-TRANSFER CALCULATIONLIQUID\/LIQUID MASS-TRANSFEREQUILIBRIUM CALCULATIONSOUTPUTFigure 13.3 Flow chart of the mass balance calculation.26913 APPENDIXINPUTMATTE HEAT BALANCE CALCULATIONSLAG HEAT BALANCE CALCULATIONBLISTERYESBLISTER HEAT BALANCE CALCULATIONFigure 13.4 Flow chart of the heat balance calculation.270","attrs":{"lang":"en","ns":"http:\/\/www.w3.org\/2009\/08\/skos-reference\/skos.html#note","classmap":"oc:AnnotationContainer"},"iri":"http:\/\/www.w3.org\/2009\/08\/skos-reference\/skos.html#note","explain":"Simple Knowledge Organisation System; Notes are used to provide information relating to SKOS concepts. 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