xidation of copper-sulphur. matte by submerged gas
TRANSCRIPT
XIDATION OF COPPER-SULPHUR. MATTE BY SUBMERGED GAS INJFCTION
Mass Transfer Rates and Physical Phenornena
RonaId Hiram Schonewille
A thesis submitted in çonfoxmity with the quiremen& for the degree of Doctor of Philosophy
Graduate Department of Chernical Engineering University of Toronto
Copyright by Ronald Hiram Sch~rieWik 1997
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COPPER-SUTPHIJR MAïTE RY S- GAS INJECTION
lVIass Transfer Rates and Physicai Phenornena
Doctor of Philosophy
Ronaid Hiram Schonewille
Depgltment of Chernical Engineering
University of Toronto
1996
Peirce-Smith converters have been used for converthg a variety of base metal
sulphide mattes for most of this centiny. Although they are environmentally undesirable,
their use in the industry is sustained by hi& levels of flexibility and productivity. The
mass transfer rates inside a Peirce-Smith converter are very hi& Air is typically injected
at 0.2 d / s through each of 40 tuyeres at an immersion depth of les than 0.5 m d i l e
exceeding 90% oxygen utilkation. Injection is carried out unda constant flowrate
conditions in the bubbling regime.
Oxygen utilhion and bubble Ikquency were measured on a laborattory sale
while injecting aidoxygen mixtures into molten copper-sulphur melts through a subrnerged
orifice. Purging of the liquid d a c e and vatying lance immersion were used to separate
the extent of reaction into the following stages of gas-liquid contact; bubble growth,
bubble rise and bubble rupture. Bubble rupture is dehed as a combination of the spout
zone on the liquid surfiace and the dispersion zone in the overlying gas.
Gas injection was carried out under constant flowrate conditions in the constant
kcpmcy bubbling regime. Bubble volumes correlated well with semiempirical
relationships specifically for Iiquid metaIs. Changes in the gas and Iiquid phase
composition confirmed gas phase m a s tramfer control. 'The bubble rupture stage was
found to be very important in achieving high levels of oxygen efficiency. n i e extent of
reaction in this stage depends on gas flowrate, orifice orientation and orifice diameter.
For gas injection through a downward facing nozzle, a critical gas flowrate has
been identified as the point at which the mass tramfer coefficient increases substantially.
This critical value was found to decrease with decreasing nozzIe diameter, and x-ray
imaghg of the liquid sinface indiates the formation of an eqanded spout zone. This is
analogous to the transition h m a packed bed to a f l u i d a bed in a gas-solid system.
The expanded spout may also be thought of as a foarn, resulting fkom the gas injection
rate exceeding the bubble rupture rate in the absence of an expanded spout.
'The influence of tempaatine above 1300°C suggests a p i b l e transition in the
rnass transfa mechanism. This requires fkther investigation
Table of Cbnten@ page
Abstract . . 11-
Table of Contents iv. List of Figures vii. List of Tables xi. 1.0 Researchobjectives 1 2.0 Introduction 3
2.1 Process Details 3 2.2 Knowledge Base 4
3.0 Litaahire S w q 7 3.1 Thermodynamics of the (Xi-S-û System 7 3.2 Rate Measurements of Molten MetaVGas Reactions 9
3.2.1 Copper-Sulphur Matte Chidation 9 3.2.2 Related Kinetic Studies 15
3.3 Gas-Liquid Dynamics 20 3.3.1 Bubble Formation Characteristics 20 3 -3.2 Bubble Interactions 21 3.3.3 Bubble Velocity and Shape 25 3.3.4 Bubble Rupture 26
3.4 Dynamics of Tuyere Gas Injection 29 3.4.1 Converter Tuyere Pressure Trace Interpretation 3 1 3.4.2 Bubble Rise: Bubble Rupture and Liquid Stimng 35 3.4.3 Anaiogy with Spouted Beds and Incipient Fluidi7Iltion 36
3 -5 Converter Tuyere Modelling 37 3 S. 1 Mathematicai Modelling 37 3.5.2 Physical Modelling 40
3.6 Mass Transfer Coefficient Correlations 42 4.0 Theoretical Aspects 46
4.1 Converting Therm0chemisû-y 4.2 Fluid Dynamics and Mxhg
4.2.1 Liquid Dynamics 4.2.2 hidence T i e M b u t i o n s
4.3 BubbIe F o h o n and Motion 4.3.1 Wetting Wêcts 4.3.2 Bubble Size 4.3.3 Bubble Shape 4.3.4 Bubble Velocity 4.3.5 Dimensiodes Groups
4.4 Physical Phenornena 4.4.1 Transport Mechanisms 4.4.2 Transport Models
Experimntai 5.1 Expenmental Scope 5 2 Apparahis Set-up 5.3 Equipment and Werials Specifications 5.4 Procedure Results 6.1 System Charaderistics 6.2 Experiment.1 Data Tables 6.3 Spreadsheet Calculaiions 6.4 Graphical Resuits Discussion of Results
Bubble Frequency Measurements Effect of Lance Immersion Effict of Temperature Effect of Gas Flowrate Effect of Lance Geometq Efféct of Oxygen Eairichment Effect of Orifice Diameter Chidation of Sulphur Sahrrzited Copper Inert Gas BIanket Tests X-ray Imaging of Gas Injection Mass Transfer Coefficients 7.1 1.1 Bubble Growth 7.1 1.2 Bubble Rise 7.11.3 BubbleRupture Estimation of Emom Industrial Converter Considerations
Conclusions and Recommendations 8.1 Conclusions 8.2 Recomrnendations Nomenclature Re fer ences Achowledgements
Appendices
Appendices page
Appdix 1: Equipment Profiles 147 Appendix 2: Equipment Schematics 150 Appaidix 3: Calculatd Profiles 152 Appendix 4: Physicai Propeaies of Cu-S Melts at 1523 X 154 Appendix 5: Measured and Calculated Expermental Data 156 Appendix 6: Chernical Analyses 177 Appendix 7: X-ray Images of Gas Injection 181 Appendix 8: Graphitai fresentation of Inert Gas Blanket Test Results 185 Appendix 9: Graphical Presentation of Stagewise Variation of Oxygen 189
Cofl~umption/Driving Force Ratio and Mean Gas Residence Time Appendix 10: Spreadsheet Calculation of Mass Transfer Coefficients 195 Appendix I l : Expenmental Correlations for Growth Stage 21 1
Mass Ttansfer Coefficient Appendix 12: Caldations 215
F i p 2.1.1 - Schernatic of PebSrnith Convert&] Figure 3.1.1 - Cu-S Partial B h y Phase Dia.gra~n['~] Figure 3.1.2 - Partial Ta~iary Diagram for Cu-SO at 1573 K[I41 Figure 3.1.3 - Solubility of Suiphur and Oxygen in Liquid Copper
vs Tempaatine"A Figure 3.7.1.1 - Calculated Profiles for Pm and ~,[91 Figure 3.2.1.2 - Experimental Resuits for Desuiphurization of Figue 3.2.2.1 - Dependence of IgA' on Orifice Reynolds N w Figure 3.3.1.1 - Bubble Volume Variation with Gas Flowrat#'l Figure 3.3.2.1 - Theoretical Pressure Traces for 3 Modes of Injectiodal Figure 3.3.2.2 - Bubble Interactions for Air Injected into M d 2 ] Figure 3 -3.2.3 - Doublet and Pair Fomiation in Gas Injectionm Figure 3.3.2.4 - X-ray Images of Gas tnjection into Irod3l] Figure 3.3.3.1 - Drag Coefficient Variation with Bubble Reynolds No.P31 Figure 3.3 -4.1 - SiIrface Boiling in a Levitated Fe-C Dropld341 Figure 3.3.4.2 - Droplet Ejection as a R d t of Bubble RupturerMi Figure 3.3.4.3 - Bubble Ris,ture Evmt ~ e q u e n d ~ ~ l Figure 3.3.4.4 - Dye Tracer Shuly of Bubble Rupture Ejection~"~' Figure 3.4.1.1 - Pressure D i m c e Frequencies for a Copper con verte^?^] Figure 3.4.1.2 - Schernatic of Bubble Formation at Adjacent Tuyere~[~~] Figure 3.4.1.3 - Effect of Tuyere Immersion on Pressure Disturbance
a) 300 mm and b) 500 dl Figure 3.4.1.4 - Bubble Frequency in Slag Firming Fumace and
Figure 3.4.3.1
Figure 3.5.1.1
Figure 3.5.2.1 Figure 4.1.1 - Figure 4.2.2.1 Figure 4.3.1.1
Figure 4.3.2.1
Figure 4.3.3.1
Copper Convertd8~ - Typical Heat Transfer Coefficient Variation for a) Fixed Ekd and b) Fluidized - Ashman Bubbk Growth Model: Bubble volume, tempemme, 39 gas composition and hquen&q - Enhancement Factor for Mass T r a n ~ f d ~ ~ ] 41 Sulphur and Oxygen Solubilities in Copper at 1473 K 1'" 47 - RTD Curves for BubbIe Growth, Füse and Rupture 50 - Bubble Formation Schematic: Wettuig and 51 Non-Wetting Conditioti~~~~~ - Pressure Variation and Growth Rate for Constant 52 Pressure and Co-t Flow Bubble - Stages of Bubble Formation: Non-weîîing Downward 56 Facing Nozie and Horhntal Orifice
Figure 4.3.3.2 - Bubble Shape Diagram[6a
vii
page Figrne 5.2.1 - Ekperhmtal Apparaîus 67 Figrne 5.3.1 - Crucible and Lanœ Arrangement Schernatic 69 Figure 5.3.2 - Ressure Transducer Elecîricai Cuaiit Diagram 70 Figure 7.1.1 - Experhental Pressure Trace: 77
Downward Facing Nozzie (Rim 17-6) Figure 7.1.2 - Variation of Equivalent Bubble Diameter with Gas F l o ~ e 78
(5.2 mm ID downward n o d e ) Figure 7.1.3 - Variation of Equivalent Bubble Diameter with Gas Flowrate 79
(3.1 mm horizontal orifice) Figure 7.1.4 - Variation of Bubble Frequency with Gas Flowrate 80
and Orifice Diameter Figure 7.2.1 - Variation of Bubble Frequency with Lance Immersion 80
(5.2 mm nozzle) Figrire 7.2.2 - Variation of Bubble Frequency with Lance Immasion 81
(2-3.5 mm orifice) Figure 7.2.3 - Variation of Bubble Frequency with Lance Immersion 81
(varying geomeûy, gas flowrate and oxygen enrichment) Figure 7.2.4 - Expimental Pressure Trace: 82
Effect of Lance Immersion (RLni 3-6, Run 6-1) Figure 7.2.5 - Variation of Oxygen Consumption with Lance Immersion 83
(5.2 mm nozzle) Figure 7.2.6 - Variation of Oxygen Consumption with Lance Immersion 84
(2-3.5 mm orifice) Figure 7.2.7 - Variation of ûxygen Coflsumption with Lance Immersion 84
(varying geometry, gas flowrate and oxygen enrichment) Figure 7.3.1 - Variation of Bubble Frequency with Gas Flowrate 85
and Tenipgdhire (5.2 mm node) Figure 7.3.2 - Variation of Bubble Frequency with Gas Flowrate 86
and Tempaahrre (3.1 mm orifice) Figure 7.3.3 - Variation of SQ Partial Pressure and Ch0 Activity with 89
Oxygen Potaitial at 1623 K Figine 7.4.1 - Variation of Oxygen Consumption with Gas Flowrate 90
and Temperatine (5.2 mm node) Figure 7.4.2 - Variation of Oxygen Consumption with Gas Flo-e 92
and Temperatlrre (3.1 mm orifice) Figure 7.4.3 - Experimental P m Trace: 92
3.1 mm Horizontal Wce (Fùm 3-7) Figure 7.6.1 - Variation of Bubble Fi-equency with Q f i c h e n t 94
in Injected Gas
.a.
vlll
Figure 7.6.2 - Variation of Oxygen CoflSurnption with Q Ennchment in Injected Gas
Figure 7.7.1 - Variation of ûxygen Consumption with Gas Flowrate and (Xifce Diameter (2.6 and 5.2 mm nodes)
Figure 7.7.2 - Variation of Oxygen Cu~lsumption with Gas Flowraîe and Orifice Diameter (2.8, 3.1 and 3.5 mm horizontal orifices)
Figure 7.8.1 - Variation of Melt and O f f j Analysis with Blowing Time (gas flowrate = 1.36 NUmm)
Figure 7.8.2 - Variation of Melt and offgas Analysis with Blowing Tirne (2.66 Numin)
Figure 7.8.3 - Variation of Melt and offjgs M y s i s with Blowing Time (4.0 Wmin)
Figure 7.8.4 - Variation of Oxygen Con~umption with Blowing Time (gas flowrate = 1.36 NUmin)
Figure 7.8.5 - Variation of Oxygen Consumption with Blowing Time (2.66 Numin)
Figure 7.8.6 - Variation of ûxygen Consumption with Blowing Time (4.0 Wmui)
Figure 7.9.1 - Variation of C& Consumption with Air Flowmte During Bubble Stages: 5.2 mm node, 1523 K
Figure 7.9.2 - Variation of Q Consumption with Air Flowrate During Bubble Stages: 2.6 mm node , 1523 K
Figure 7.9.3 - Variation of Q C o q t i o n with Air Flowrate During Bubble Stages: 3.1 mm orince, 1523 K
Figure 7.9.4 - Variation of Q Consumption with Air Flowrate During Bubble Stages: 5.2 mm node, 1623 K
Figure 7.9.5 - Variation of Q Co~lsumption with Air Flowrate During Bubble Stages: 3.1 mm orifice, 1523 K, Q enriched
Figure 7.10.1 - X-ray Image of Quiescent Melt Surface and Nozzle (no injection)
Figure 7.10.2 - X-ray Image of Air Injection at 2.0 Numin 'Through a 3.1 mm Onfice
Figure 7.10.3 - X-ray Image of Air Injection at 4.0 W m i n ïhrough a 5.2 mm Nozzle
Figure 7.1 1.1.1 - Variation of Growth Stage Mass Transfer Coeficient with Gas Flowrate (5.2 mm node)
Figure 7.1 1.1.2 - Variation of Growth Stage Mas Tmfer Coefficient with Gas Flowrate (3.1 mm orifice)
page Figure 7.1 1.1.3 - Variation of Growth Stage M a s Transfer Coefficient wiîh 1 17
Gas Flowrate (varying geomeiq orifice diameter and temp-ature) Figure 7.1 1.1.4 - Vanation of Growth Stage Mass Transfer Coefficient with 1 18
ûxygen &chment Figure 7.1 1.1.5 - l%pmmenental Correlation for Bubble Growth Sherwood No. 1 19 Figure 7.1 1.2.1 - Variation of Rise Stage Mis Transfer Coefficient with 121
Gas Flowrate (5.2 mm node) Figiire 7.112.2 - Variation of Rise Stage Mass Transfer Coefficient with 121
Gas Flowrate (3.1 mm orifice) Figure 7.1 1.2.3 - Variation of Rise Stage Mass Transfer Coefficient with 122
Gas Flowrate (varying geometry, orifice dameter and tempemime) Figure 7.1 1.2.4 - Variation of Rise Stage M&s Transfer Coefficient with 123
Oxygen Enrichent Figure 7.1 1.2.5 - Liquid Film 'Ihickness vs. Gas Flowrate 124 Figure 7.1 1.3.1 - Variation of Rilphrre Stage Uass Tramfer Coefficient with 126
Gas Flowrate (5.2 mm node) Figure 7.1 1.3.2 - Variation of Rupture Stage Mass Transfer Coefficient with 127
Gas Flowrate (2.6 mm and 5.2 mm nozzles, 3.1 mm orifice) Figure 7.1 1.3.3 - Variation of Rupture Stage Mass Tmfer Coefficient with 129
Gas Flowrrite (1 5ZK and 1623K) Figure 7.11.3.4 - Variation o f Wture Stage Mass Tramfer Coefficient with 130
Oxygen Enrichment
List of Tables
Table 3.2.1 - Expenmental Details of Gas Injection Miîss T d e r Investigations
Table 3 S. 1.1 - Sensitivity Analysis of Ashman's Tuyere M~del[~] Table 4.1.1 - Thermodynamic Data for Converting ReactiodBl Table 5.1.1 - Expenmental Parameters Table 5.1.2 - Crucible and Lance Dimensions Table 7.8.1 - Transition Points in DesuiphUrkation Experhents Table 7.12.1 - Estllnated Precision of Measurements
1.0R=ea=h OhctlVes . .
The o v d l objective of this research project is to gain a Mer understanding of
the physical and chernid phenomena associateci with the oxidation of copper-sulphur
matte by gas injection. ûfprimary interest are tuyere injection characteristics, oxygen
utilization and mass transfer rates. Suice the proases taking place in this study are
hdarnental to the operation of converters, some basic knowledge related to the
undaIyîng success of converting shouid be unçovered.
This topic has been chosen for study for two main reasom; it is concemeci with a
processing step that is essential to d l Canadian cupper smelters and although the Peirce-
Smith converter has b e n used for eeating wpper rnattes for over 80 years, the details
regarding its success have not been M y reveald Based upon available heat and mass
tramfer conelations, converters cannot be modelled in agreement with plant performance.
Extremely high mass tramfer rates oaw in converters, but the phenomena supporthg
these rates are not well understd
Converter productivity is presentiy determined by a compromise between hi& air
flowrates and an acceptable de- of splashing in the converter. Converthg rates are not
n d l y controllad by mass transfer, as evidenced by near 100% oxygen eficiencies in
some operations.['l At higher gas flowrates, mass transfer wili likely becorne the rate
determining step. lhis study attempts to determine this ultirnate rate and in doing so,
UnCover the physical and cherniai phenomena leading to the rernarkably hi@ rates of
rnass transfer in a copper converter.
There are additional areas of study that have undergone examination in this
research. 'The reIative importance of the three stages of gas-liquid contact were
investigated; bubble growth, fk bubble rise and bubble rupture. By studying both white
metal (Ch2S) and semi-blister (sulphur saturated copper), the importance of liquid phase
diffusion was uncovered It is ho@ that this investigation will bring us closer to king
able to predict the observeci rates in copper converters mathemafically.
The fwm of e m e n t s was to aeate conditions similar to those in the converter,
and then to change the conditions to promote successively higtier rates of oxidation.
Analysis of the d o n off' for sulphur dioxide and melt sampling were used to
masure oxygen comumption. The relative importance of gas and liquid phase diffiision
was investigated by studying the two systenrs listed above. To gain a better understanding
of the physics of tuyere injection, an x-ray imaging technique was used to andyze spout
shape and gas flow pattern.
The final goal of this investigation was to calculate the mass transfer coefficient
over the range of conditions studied for the three stages of gaç-liquid contact. An
important aspect of this project was establishg experhental conditions that are relevant
to acîuai convater operation. Dirnensionless groups were used to provide some bais for
expimental design, as well as a means of translating any significant d t s to the fidl
scale procesS.
2.0 Introduction
2.1 Process Iletaila
Currently, much of the blister copper deriveci h m sulphide ores is produced by
converting mpper-ion-sulphur mattes with air or slightly oxygaKnriched air in a Peirce-
Smith converter. A schematic of this vesse1 is shown in Figure 2.1.1 .m The mattes
usually originate in bath, electnc or flash smelting opetations." Iron sulphide in the
matte oxidizes preferentially ova copper sdphide, and the resulting iron oxide is fluxed
with silica to produce a fayalite slag. ûnce al1 of the iron has been rernoved the matte is
termed white metal.
PNEUMATIC PUNCHERS
2.1.1 - Sc-c of Peirce Srnith Convertd21
nie next stage of converting is characterized by crossing the Cu-CqS miscibility
gap. Sulphiir in the matte phase is oxidized to SQ f i l e the corresponding copper
reports to the sulphur saturated metal phase. ûnce ail of the matte phase has been
removed the metal is texmed blister copper. This undergoes finther desulphurization in
prepamtion for dïni.ng in the anode fumace. k g the desulphinizaton stage up to 1%
oxygen can be dissolved in the melt.
In the converting of copper-sulphiir m e s , extremely high gas flowrates are used,
resdting in a vay short residence t h e for the oxygen in the blast to react with the
molten bath. A typiical Peirc&hn.ith converter equipped with 42 tuyeres is blown at 500
000 Numin, or 48 000 Umin per tuyere at converthg conditions.['l This resuits in a gas
discharge velocity of about 150 mls at the tuyere tip. Combining this with gas bubble
volumes up to 50 L (due to non-weltable rehctories) and tuyere submergences as low as
300 mm, the mass w f e r rates necessary to achiewe widely reported oygen uîilizations
in excess of 900/d11 are on the order of 10 mol 4/m2/s.
The operation of tuyeres impacts many aspects of the overall converting process.
Tuyeres are continuously king blocked with solid accretions and require regular punching
to maintain adequate gas flowrates. 'The gas issuing fiom the tuyeres results in a great
deai of splashing that builds up a crust around the converta mouth. This requires
chipping once or twice daily. 'The turbulent flow created around the tuyere tip d t s in
accelerated refiactory Wear at the tuyere line, and usually detemiines wtien a converter is
taken out of service for rebricking. During ladle tmsfers the tuyeres cm b m e fùlly
plugged and rnay require drillhg at the end of a converter cycle. ?hm the efficiency of
tuyae operation is v q closely related to converter produdvity.
2.2 Knowiedge Base
Although the chernistry and thennodynamics are well known for copper
C O ~ V - , [ ~ * ~ ~ the physid phenornena relaîed ta their successfiil operation are not as
clear. Vay few theories are available ~gbrduig the nature of the erihanced mass -fer
rates in coppa converters, and none are backed up by hard physical evidence.Eq The
physics of buhble formation in the converter are not fully undersfood due to the
complexity of Mathemafical analysis and the difFidties in direct observation.
'There kas been a gceat deal of debate G"= the natine of gas bubbles issuing h m
a hyere. The 1iteratux-e rnakes reference to bubble sizes as small as 0.001 LI1 and as
large as 300 LI'] (small bubble diaries are king rejected). If the tuyere-line r e m o r y
Wear is extensive, this will pmmote multiple tuyere interactions, resulting in a transition
h m constant flowrate (smaller bubble) to constant pressure (larga bubble) injection.
Changes in bubble s k and shape that may occur after a bubble has been severed h m
the tuyere have rarely been adQessed Reactions taking piace at the bubble surface are
quite violent, and may have an impact on the bubble stability. The nature of bubble
rupture at the bath d a c e may also be important in obtaining the high mass transfer rates
observed in the convexter.
Exphenta i studies to date have not been able to measure the limiting mass
ûansfer rates for oxygen injection into copper-sulphur rnelt~.[~I Conditions have not been
created to obsave oxygen breakthrough at the liquid surface. Theoretid analyses have
beai inadequate due to a lack of heat and rnass transfer correlations that are applicable to
this system, particularly during the bubble growth period of gas injection.[g Based on the
available data, converters m o t be modelled in agreement with plant performance.
There have been mathematical and experhental investigations thaî predict the
mass transfer mtes for srnall, detacfied gas bubbles rishg in wpper matte.P1 Bustos et dlg1
have used tuyere pressure traces to illustrate that copper convaters can operate in three
gas injection modes depending on the state of the tuyere-line refiactory and the tuyere
submagence; classic bubbling, stable horizontal envelope formation and gas channelling.
The fkquency of pressure disturbances for al1 three cases indicate that fully detached
bubble rise time contributes a small portion to the gas residaice tirne, and that gas
bubbles forrned in copper matte converthg are relatively large.
Aluiough thae have been a number of experhental and theoretical studies on
copper rnatte oxidaiion, they have provided little insight into the characteristics of
convates operation, due to a la& of physical similarity. 'The same must be said for
numerous low tempmtux modeis, due to the ciifliculties in matching inatial, buoyancy,
viscous and siirface tension forces, ail of which can be important in gas-matte systems.
There are some significant finding that on be drawn h m the available litexatm
in this field of research. It has beai well esbblished thai the bubble Gequency of a gas
injeded into a liquid increases with increasing gas flowrate, up to a Qitical fhquncy. In this regûne the bubble size is approxhaiely constant. At gas flowraîes beyond that
correspondhg to the critical bubble fkquency, the bubble k p e n c y remains fairly
constant and the bubble size increases. At significantly higher gas flowrates there is a
transition h m bubbling to jetting. Based on the available information in the literatwe,
converters are thought to opaate in the constant fkquency bubbling regime, however the
large bubble volumes are more indicative of constant pressure injection. ïhis is Iikely as
a result of multiple tuyere interactions.
Previous research has shown that there is a definite relationslip between the
maximum bubble fkquency and the orifice diameter. As the orifice diameter decreases,
the bubble fkpency increases. The nature of this comlation depends on several factors
such as liquid properties and the orifice geometry.
'There are a number of mathematical expressions available for predicting bubble
sizes under specific conditions, with application to a variety of controlling mechaniSmS.
Bubble velocity is more diffcult to predict, as well as the rate of acceleraiion in the initial
stages of bubble rise. Many classical velocity and drag coefficient expressions are
inaccurate since they do not account for changes in bubble shape or multiple bubble
interactions.
A major difficulty in physical and mathematid modehg of a copper converter is
deterrnining which forces dominate the process dynamics. The formaiion and subsequent
rise of a bubble in copper matte is subject to inertial, buoyancy, viscous and sudace
tension forces. The relative magnitude of these forces change as the bubble grows and
rises in the !iquid mese forces can be represented by the Reynolds, modified Froude and
Weber numbers.
C m t l y , the processing rate in copper converters is said to be bubble volume
limited; that is, higlier gas flowratg m o t be employed due to increased splashing
arising h m larger b~bbles.["~] If the probkrn of splashing could be ovetwme through
either high pressure injection or altanative converter mouth design, higher converting
rates rnay be possible. At higher gas flowrates, the rates of gas and liquid mass transfer
will eventually limit the converting me. lhis uitimate rate is unknown.
3.0 fiterature S u n q
3.1 Thermodynamics of the CuS-O System
Phase relationships in the copper-sulphur-oxyga systern have received
considerable attention in the past,[H*lznl as reviewed by ~lliott.['~] The Cu-S system has
been treated extensively by researchers such as Schuhmann and ~ o l e s b n d ~ellogg.[l~~
Of most importance to this investigation is the Cu* miscibility gap extending fiom
1.2% S to 19.5% S at 1523 K. This portion of the binary phase diagisun is shown in
Figure 3.1.1.1'41
The partial t e m q diagram for the Cu-S-0 system at 1573 K presented by
ElI i~t t~ '~~ (Fig. 3.1.2) illwiraks the difference in oxygen solubility between CqS and
sulphur sahnaed copper. While crossing the miscibility gap at 1573 K the suiphide phase
can contain up to 1.35% oxygen, whereas the metal phase is limitai to 0.15% oxygen.
Once the sulphide phase has been depleted the oxygen content of the metal phase rises
rapidly. This diagram was based on the infoxmation noted above as well as the thm
binrny systems (Cu-û, Cu-S and S-O).
'The ecplibriurn solubilities of oxygen and sulphur in liquid copper were fùrther
investi@ by Gerlach et alIl7 in 1%3. Using the data of Gerlach and coworkers['~
presented by Biswas and Davenpocm the relationship between sulphur and oxygen in
copper at various temperatures is presented in Figure 3.1.3. From this diagram it can be
deducd thai converting at a higher tempaatlne requk prdting more oxygen into the
metal to achieve the sarne degree of sulphur elimùiation. A typical assay of 0.015%
suiphur and 0.8% oxygen for blister copper produced at
1523 K illustrates that final conversion occm close to equilibrium
i m 3.1.2 - Part a-gram for Cu-S-O at 1 573 K 'l4]
O 0.05 0.1 0.15 0.2 0.25 Weight % Sulphur
3.1.3 - Solubilitv of Sulphur and ûxy-en in Licpd Cop- vs ~emperatud . . . . 171
The solubility of oxygen in Cu2S has &O been studied by Richardsodial. He
reports thaî in the presence of copper and SQ, the solubility of owgen is proportional to
P,O-~, up to 1.4% by weight at 10 1 325 Pa. E s remains constant as the miscibility gap
is crossed, however the total m a s of dissolved oxygen changes gradually with the relative
proportions of the sulphide and metai phases.
The therrnodynamics of copper rnatte oxidation are not an inte@ part of this
study, as this topic bas been covered in great detail by Luraschi and Ellio@, Yaza~a[~l
and in a review by Toguri et A themiodynarnic study by Gerlach et d['I has show
that oxidaîion of cupper sulphide should proceed with minimal exsoluiion of copper oxide,
which is in agreement with an experîmental study by Asaki et alw. B e y observed only a
srnall degree d Cu@ production before sulphin elhimiion was complete.
3.2 Rate Measurements in Molten MeîaYGas Reactions
3-2.1 Copper-Sulphur Mlatte -dation
Kinetic studies on the oxidation of rnolten copper rnatte are not abundant in the
mdlurgical literatllre. In a short papa on copper converthg chemïstry by Quarm12'l in
1967, he emphasizes the need for studies of d o n kinetics to explain the iron oxidation
stage in copper converting. He states that ali recent investigations into the
therrnodynamics of non-ferrous smelting processes have excluded kinetics. Quarm
continues by noting that major &ances will be made only when research efforts are
focused on the relative velocities of the reactions taking place. To stimulate interest in
this area, Quarm gives an alternate reaaion mechanism for blister copper production He
proposes that the intemediate Cu@ is formed by oxidation of metaflic Cu, &er than
oxidation of Cu,S.
Ajersch and ToguriW d e d out oxidation of liquid copper and copper sulphide
under gas phase diffusion control in 1972. Asaki et a1m1 monitored the progressive
oxidation of copper-iron suiphide mattes, also under gas diffusion control in 1988.
Although 16 years had passed, reference was only made to the work of Ajersch and
Toguri regardmg previous hetic investigations. The oxidation reactions in a
dispersed copper smelting system have ken studied by Yannopoulos et al.p1 Most
m t l y , Fdamaka et al" and Alyaser and ~rimacombeN have studied the oxidation of
semi-blista COpper.
In the work of Ajersch and T ~ g u r i , ~ ] oxygedargon gas mixtum were pas& over
a srnall quartz tube cuntaining p m copper sulphide rnatte. &dation was monitored by
measuling the change in weight of the sample using a calibrated helical quartz s p ~ g .
nie reaction rate was manipuiated by changing the diffusion path laigth inside the sarnple
tube and the &on gas composition. The calculateci sulphur dioxide flux was fomd to
be relatively insensitive to teqxmtm, confirrning gas phase control in their exprîments
canied out above 1338 K
InitiaIly, the oxidation rate was variable as steady-state conditions were king
established. This was soon followed by a constant rate of weight loss cortesponding to
crossing the rniscibility gap. ïhk rate was used to calculate the flux of SQ away fkom
the melt Quite abruptly, the sample weight loss slowed, followed by attainment of a
minimum weight and thai a constant rate of weight gain indicating the formation of
copper oxide. sudden change h m copper desuiphunzation to copper oxidation
dernonstrates that these pmcesses take place in two nearly distinct stages.
The variation of oxidation rate with tube length exhibited a linear inverse
relationship, connmllng gas diflciision control as predicted by FicKs first law. The
oxidation rate was found to vay linearly with the oxygen composition of the reaction gas
up to 60% oxygen, at which point it remained constant up to pure oxygen. At high
oxygen concentmiions some splashing was observeci at the liquid gas interface as
evidenced by rnatte on the tube wall.
This work demonstrated that under gas phase diffusion contrai, the oxidation of
copper dphide to copper oxide takes place in two disaefe steps. The only kinetic
information derived fiom this work is the diflkivity of S Q through argon-oxygen gis
mùbures. ï h i s gravimeûic rnethod for following the progres of a reaction requires a
very sensitive balance, given tliat the maximum weight change 'uk~iigho~e a typical
expriment is only 0.02 g. 'The Wpment used in this work appean to have provideci the
required acamcy, based on the caiibration and the smooth naaire of the weight change
Curves.
Yannopouios et alml have studied some kuietic aspects of rnatte droplet oxidation
relating to dispersed cupper smelting. In their experiments, molten matte droplets between
0.8 mm and 2.5 mm in diameter were oxidized in air for duraiions ranging h m 10
seconds to 2 minutes. Variations in the initial matte composition showed thaî the rate of
oxidation of Cu+S is much slowa than that of FeS. Their results also illustrated that
cuprite (Cu@) formaton is a possible intermediaie step in the production of copper f b m
matte. nie production of cuprite as an intennediate is an important observation, however
in an agitaid lîquid systern the conditions rnay not be favoinable for its formation. For
mtîe dmplets 1 mm in diameter containing 75% C q S , over 80% sdphur elirnination was
achieved in the fkst 20 seconds of oxidation
The validity of the obsetvation that Cu20 is an intermediate reaction product
depends on the method used to quaich the samples. Rapidly quenched samples are more
likely to p m e the high tempei?mne state, whereas samples cooled too slowly rnay
undergo changes in the phase constituents. The details of the sample collection were not
reported for this work
Fukunaka et al" have m e a s d the kinetics of desulphinizaion of molten copper
by gas injection. Argon-oxygen gas mUdures were injected through a 4 mm diameter
submerged n o d e into 200 g of copper containing initidy 0.74% sulphur. Gas flowrates
up to 1.5 Umin were used, with oxygen partial pressures ranghg fiom
5 000 to 30 000 Pa Lance immersion mged from 18 to 33 mm The reaction rate was
found to Vary sigruficantly 6 t h the oxygen partial pressure and the gas flowrate, but was
nearly independent of the lance position Monitoring the reaction progress by both melt
sampling and offgas analysis yielded good agreement.
These acperiments reveaied minimal evolution of SQ in the initial 10 seconds of
oxidation, followed by evolldion of SQ at a nearly constant rate. ïhe partial pressure of
SQ decreased as ddphiirization neared completion. Lower rates of sulphur dioxide
production are explained by hcreased dissolution of oxygen into the melt. Miss balance
dculations indicate that virtually al1 of the oxygen blown into the melt was c o m e d
either by reaction with sulphrir or by dissolution in the cupper.
Using available thermodynamic data and gas and liquid mass transfer expressions,
a mathematical mode1 was developed to follow the reaction progress. The calculateci
profiles of P, and Pm as desulphurkation progresses are shown in Figure 3.2.1.1. The
formation of SQ was proposed to occur only between sulphur and oxygen dissolved in
the melt. Assuming an equilibrium systern under combUled gas and liquid diffusion
control, they were able to adequately predict the observed results, as shown in Figure
3.2.1 2 At a dissolved oxygen concentration of 1 %, the mathemafical model predicts that
only 3% of the overall resistance to m a s tramfer is in the liquid phase. It ivas also
deteLTnined that reaction W e e n a single gas bubble and the melt is nearly complete after
the bubble has risen 10 mm.
1 - Calculated Profiles for Pm and PSOtf91
Tirne ( S 1
2 - F m R e d k f h Desulphunzation of Co& . .
91
'These expiments demonstrated that the kuietics of oxidaîion of copper-sulphur
melts are rapid However, the range of expimental conditions and the sinq>listic nature
of the mathematicai model limit the meaning of the results. The range of gas flowraîes
and immenions çovered led to coqlete utilization of oxygen in neariy al1 expiments
This only pemits calculating the minimum mass transfer rates, rather than the actual rates.
The mathemaiid model is based on discrete, fully detached bubbles rising through
a liquid unda the force of buoyancy. This analysis fully disregards m a s tramfer taking
place during both bubble growth and bubble rupture. in adaddition, the results are quite
sensitive to the assumai bubble diameter, which was estimated h m the correlation
provided by Sano and Mori.r3'1 This dcdation depends on the d a c e tension of the
liquid phase, and Fukunaka et d91 negfected the eEècts of oxygen and sulphur, both of
which are highly surface active. 'The d t i n g bubble diameten compond to bubble
hquencies of 20 to 23 Hz for a downward facing orifice with an outer diameter of 6 mm.
This is lower than published data for other liquid metal systems (=30 H Z ) . ~ ~ ~ ]
The bubble velocity is equally important in determinhg the accuracy of the model.
'Ihis was estimateci based on the equation proposed by Davis and Taylor.[w The
resulting bubble velocities are in the m g e 0.22 to 0.25 d s , which are about 30% lower
than the values predicted by the exprhentally based mmlation of E l o ~ i k o v . ~ ~ ~ ~ He
m e a d the rise velocity of helium bubbles in both m m u y and pig iron and derived an
experimental relationship between the drag coefficient and the bubble Reynolds number.
The main limitation of the Fukiniaka d e l is that it treats the bubbles as fully detached,
disaete and staîic, wfien in reality they are highly dynamic and spend very littie tirne in
the fully detached state. In addition, the bubbles are Iikely still acceleraîing d e n they
reach the liquid surface, as a result of the low immersion depth.
Their expimental work is not without problans either. ?he extent of reaction
was detennined by both chernical assay and off= analysis. Metal pin saniples were
quaiched in water and d y z e d by titration and Leco oxygen analysis. The nwnber of
repeat samples were not staied, which is important due to the variability of oxygen
analysis. The reaction offgas was absorbed into a 1% solution of H a and tiûated
against a 0.01 N NaOH solution. The overall accountability of S based on the offgas
d y s i s rneasurements ranged between 90 and 120% indicating a potaitial20% relative
anx in the off= analysis. 'This brin@ the arxnnaçy of the d t s based on offgas
analysis into question.
Most m t l y Alyaser and Brimacomber25i have studied the oxidation of molten
Cu2S by top lancing with oxygenkirgon gas mixiues. They varied the gas composition,
flowrate, bath te- and bath mixing (by introducing a very low flowrate of stining
gas). They were able to observe surfiace dynamics which were explaineci based on the
Marangoni e f f i 'The oxidation of Cu$ was observeci to progress in two distinct stages,
initially by simultaneous satlnation with oxygen and copper in a single phase and
secondly by the production of a separate semi-blister copper phase. ïhroughout both
stages the kinetics were found to be controlled by gas phase rnass transfa, proven by little
change in the systern with the introduction of a small amount of stirring gas to the bath.
An electrochemical model of the oxidation reactions was proposed to explain their
experimental results. 'The main bais for the model was the observation of a change in
the rnolar ratio of oxygen consumecl to sdphur rernoved fiom around 1.5 in the primary
stage to 0.95 in the secondas, stage. The transition point was found to correspond closely
to the composition of copper-sulphur matte on the edge of the miscibility gap in
eqdîbrium with semi-biister copper. Durhg the first stage desulphinizaton was only
fomd to take place at the free liquid surface, whereas in the second stage this is
accornpanied by the evolution of SQ gas bubbles below the melt surface.
There are sorne inconsistencies in the resuits of this work that are worth noting.
Although the system was identifid as operating under gas phase dinusion control, the
omet of bubble rupture at the free liquid sril-face (via either gas injection or the onset of
the second stage) did not enhance the kinetics. Both the gas-liquid interfacial a m and the
degree of turbulence in this region are increased substantially by the presence of ruphning
bubbles. 'Ihe effect of terripgatrrre was not observeci either in the olcuiated mass tramfer
coefficiaits. A 100 K rise in the system te- should lead to 10% increase in the
gas phase dihivity, which wodd be reflected in the m a s tramfer coefficient. Finally,
the mass transfa coefficients are not meaningful to interpret since the interfacial area
upon which they are based was not stated.
The observation that the ratio of oxygen consurnecl to suiphur removed is about
0.95 diuing the second stage of oxidaîion is an interesthg one, however Alyasa and
Brimacumber~ do not attempt to reconcile this with the oxygen that is king l i M
h m the melt as a remit of copper king transferred fiam the "Cu2S" phase mgher
oxgyen content) to the "Cu" phase (lower oxygen content). If these two phases contain
1.4% O and 0.16% O by weight respectively as staîed in their work, then the oxidation of
100 mol of S (correspondhg to the transfa of 200 mol of Cu to the metai phase) will
result in the release of 2.5 mol of Q. This accounts for half of the observeci difference
between the oxygen coll~umption rate and the sulphur production rate.
3.2.2 Related Kinetic Studies
Themelis and ~chrnidt[w canied out deoxidation of Iiquid copper by submerged
injection of CO gas jets under gas phase difihion control. Since they were unable to
determine the natirte of the jet dispersion (ie. bubble size), their rnass trcinsfa
measurements were expresd as the product of the mass transfer coefficient and the
interfacial a r a per unit liquid depth (& A). The dependence of this parameter on the
orifice Reynolds nurnber is show in Figure 3.2.2.1. Their r d t s show that this
pafameter is neariy independent of the orifice depth. This indicates two possible
phenornena; e i k the gas jet characteristics (bubble size, velocity) becurne constant
airnost immediately d e r gas Leaves the orifice or as the gas jet e)9)ilnds the bubble
velocity decreases resulting in a decrease in k, and a proportional increase in the value of
A'. The former expianation is most likely correct.
Both of these explanaiions requke that the gas bubbles behave independently,
which was probably the case since the gas as injinjeaed through small orifices (6rnm)
and at deph ranging from 40 to 200 mm 'Therefore the mass transfer rates measured in
this investigation were for detached bubbles rising in liquid copper. Using the jethg
criteria proposed by Zhao and ~ . O I I S [ ~ ~ these expiments were d e d out in the bubbling
regime. Gas phase mass transfer was found to be rate controlling for dissolved oxygen
concentnitions Iess than O. 1%
In this work, a nitrogen blanket was used in selected ex@ments to inhibit d a c e
reaction with CO originating in the rupturing bubbles. Although the resdts of these tests
are not given, this rnay also be an appropriate rnethod for inhibiting d a c e oxidaîion
wtien injecting air into Cu-S melts.
The rates obswed in this expairnent are difficult to compare to those reported by
Fukunaka et since the gas raidaice time was not reporte& For a gas injection
flowrate of 20 Wmin, an injection depth of 80 mm was necessay to achieve 95Y0 CO
utîiization Based on a bubble diameter estimation of 50 mm and a gas bubble velocity
estimation of 0.66 mk, this corresponds to a molar flux of 0.104 moles/d/s, slightly
higher than that reported in the work of Fulnirüika et al (0.088 moledm%) for the sarne
gas phase partial pressure. The respective diffusivities of CO in CQ (2.8 cm%) and Q
in SQ (2.44 cm2/s) at the operating temperatures account for most of this diffmce.[q
The accuracy of the results obtained in this work depends d y on the accuracy
of the analytical equipment Gas d y s i s was conducta! by taking gas samples at two
minute intervals and passing through a gas chromatograph. Although the accuracy of their
specific apparatus was not staîed, this type of equipment usually provides quality results
wtien the gas species are al1 knom
Mas transfer mea~u~ements for a water model of a c o r n convater have been
k e d out by Brimacombe et al.Iq Gas cuntaining 1% SQ in air was injeded into a
0.3% aqueous solution of H A . The product of the mass transfer coefficient and the
interfacial ara per mit length of jet trajectory was found to increase linearly with
increasing Reynolds number and to be a m n g finidon of the orifice diameter. The
dependence on Reynolds number is similar to thaî observed by Themelis anci Schmidd~,
although they found a weak dependence on orifice diameîer.
Extrapolation of the experitnental d t s to conditions in a copper converter
illustrate that a converter should operate at nearly 10% oxygen efficiency. However, this
exkaplation was based on the ratio k&Q remaining constant fiom the experhent to
the converter, where Q is the gas flowrate. ?bis assumes that the gas tmjectory in a
converter is the sarne as in a water bath and that the differences in liqyid properties do not
have any effect More recent d e s have dernollstrafed that gas injected into a converta
behaves radically different h m observations made on water models. 'Ihis new insight
into the behaviour of gas injecte. into molten metals d e s the direct extraplation of
mass irasfer rates h m water models to copper converten invalid
Fruehan[281 has studied the oxidation of small melts of silver and the dmxidation of
copper under liquid diffusion control. He bubbled Q or CO through a single submerged
orifice and measured the product of the rnass transfa coefficient and intedacial area per
unit depth &-A') to Vary £iom i to 3 d / s for gas flowxaies ranging fiom 0.6 to 1.8
Umin (SV). The value of this parameter in the work of Fukioiaka et al['] mged h m 40
to 50 d / s , indicating signifiouitly hi@ rates under gas phase mass transfer control.
Of sigriificance, it was found that this prameter i n d linearly with increasing
depth of immersion, indicating that bubbles of a particular size are formed very near the
orifice and above this location their surface area does not change significantly. F1uehad~~1
also found thai the orifice diameter had vety little effect except close to the orifice. niey
measured the mass transfer rates for detached bubbles rising in liquid copper, and
indved mass iransfm rates much lower than those observecl under gas phase diffusion
conîrol.
The condition for liquid phase rnass tramfer diffusion control during the oxidation
of molten silver was a dissolved oxygen content greater than 0.25% Sirnilady the
maximum oxygen content for liquid phase conml in the d e d a t i o n of Cu with CO was
0.025%. Ekyond these limits the rates were fond to be so fast that the mass transfer rate
was nearly equai to the gas flowrate. Based on these results, it would be e m e d that
the desulphurization of Cu would change fiom gas phase to liquid phase mntrol at a
relatively low S content.
The d t s obtained by rueb ban^^ are more meaningful to interpret since some
bubble dimeta mea~urements were made. A stainless steel wire probe placed just above
the orifice was used to set up an eledcal circuit with the melt. As each bubble passed
through the probe, contact with the melt was broken and the bubble fiquency could be
i n f d The only danger in using this method for masurhg bubble Seguency is that the
probe must be placed very close to the orifice to preclude doublet formation (in this work
the probe tip was 2 to 4 mm above the orifice). The proxhity of the probe to the orifice
likely i n t e r f i with bubble formiion, since bubbles were formed with a diameter up to
12 mm. The p e n c e of a maferid with different suface properties ( d a c e tension,
wettability) inside the bubble during growth could change the bubble size.
To summarize the current state of research into mass tramfer rates in gas injection
systems, Table 3.2.1 has been constructed bas& on reporte. d t s . Some of the data
had to be eshaîed using available com1ations. The results shown in this table are
generally those for the higtiest mass transfa rates observed. Included are the
corresponding parameten for a typic. 4000 mm x 9000 mm Peùre-Smith copper
converter. The dimensionless g r o q s are calculated for the gas phase at the orifice, and as
a rneans of simplification the physical properties have been evaluated at the bath
t-
33 Gas-IiqUidDynamics
33.1 Bub ble Formation Characteristics
The size of bubbles f o n d in molten metals has beai studied by a nurnber of
researchers.m Mi Typically, bubble volumes are correlated with the dimensioniess
Capacitance nurnber and the gas flowraîe. This type of wrrelation is in agreement
with the existence of a constant bubble volume regime at low gas flowrates followed
by a constant bubble Gequency regirne at hi- flowrates. Irons and Guthrid311 have
compileci expimenital and serniempirical data to yield the following expression:
A plot of the correlation in equation 1 dong with the experimental data fkom
three researchers is given in Figure 3.3.3.1. The agreement between the come1ation
and laboratory measurements is good, akhough the limitation of such a correlation is
that the parameters m and K are empirical and Vary with systern properties and
geometry. The multiplier K tends to be least sensitive to these effects and the
following correlation has been proposeci for the constant kquency regime:
Vb=O. 0 8 ~ ~ . ~ ~ d ~ ~ * ~ ~ (2)
This w o n corresponds to substituîing a value of 10 for K, changing the expnent
on the last two t e m h m 0.5 to 0.44 and neglecting capacitance numba terms.
The inclined portion of this graph fdls on the constant flowrate boundary
(minimum bubble diameter for a given gas flowrate), *le the horizontal branches
correspond to conditions intermediate between constant flowrate and constant pressure
injection The constant fiowrate boundary corresponds to bubble Seguencies in the
range 15 to 25 Hz 'Ihis graph does not include data h m tnie constant pressure
injection conditions, as these lines wouid fdl to the left of the constant flow lines.
h n s and have studied the aspects of bubble formation at subrnerged
nodes by injecting argon through a ceramic tube into indium-gallium melts using an
x-ray imaging technique to obtain images of growhg bubbles. They observed the
formation of bubbles at the outer diameter of the n o d e due to non-wetting of the
3.3.1.1 -e Vanahon with Cm F l o w . . d3
liquid metal on the tube. Bubble diameter was found to rernain constant with
increasing gas flowrate until a limiting fkpency was reached, at wtüch point the
bubble diametedgas flowrate relationship became expondal. Measured bubble
diameters were found to depend only on the Capacitance number of Sano and MoriPol
in the flowrate independent regirne. In part due to the non-weaing conditions, they
found it c.Wicuit to produce small bubbles, even at low gas flowrates.
They also observed a great ciifference in bubble s k depending on the
orientation of the ceramic tube when injecting in the surfàce tension controlled regime.
When the tube orifice was pointed downwards the bubbles formed were up to 10 times
srnaller than when the orifice pointed upwards under the same flow conditions. In the
inertia controlled regime the bubble size was nearly independent of n o d e orientation.
3.3.2 Bubble Interactions
During the submerged injection of a gas into a liquid, the pressure fiuctuations
observed immediately qstmm of the onfice can be used to charactterize the injection.
In partidar, deviations firom the theoretical bubbling pressure trace shown in Figure
3.3.2.1 can be used to assess bubble interactions. Classic bubbling is characterized by
a gradual decrease in bubble pressure drrring bubble p w t h followed by a rapid
increase in pressure during detachment. Unstable envelope formation results in a
much steeper pressure trace dining the growth stage. ChaMeling is identified by very
short duration, steep interuptions in the pressure trace as the gas channel to the surface
intermittently collapses.
I Classic
3 Channeiing
&gme 3.3.2.1 - Theoretical Pressure Traces for 3 Modes of Iniectiontgl
ChaUdey and ~ r a i t h t ~ ~ l used high speed cine photography synchronized with
tuyere pressure measurements wliile injecting air into mercuxy. Cornparison of the
results with those obtained h m a similar air-water systern revealed rnany cornmon
feahires.
The pressure traces illustraieci in the figure do not necessarily apply to al1
injection conditions. The horizontal time sale indicates a bubble fkquency of about
10 I-lz, somewtiere in the transition between constant pressure and constant flowrate
gas injection. However, these pressure traces are still instructive in depicting the
possible deviation h m the theoreticai pressure traces shown in Figure 3.3.2.1.
Figure 3.3.2.2p2] illustrates three modes of dispersion behaviour that lead to
three distinct pressure traces. The first diagram depicts triplet formation in the
pressure trace. ïhe first peak is due to detachrnent of the praious bubble. The
second peak is aitributed to a slight disniption in the gas supply at point C, at the
instant when a sphericai bubble has beai fomed. A thîrd peak is observai at point E
due to momentary detachment of the bubble fiom the orifice, followed by a minimum
pressure condition as a comecting tube foxms just pnor to M bubble detachment.
The second diagram in Figure 3.3.2.2 is for a similar dispersion phenornenon
except that the gas supply is not interrupted at point C. 'Ihis resuits in a much srnaller
second peak in the pressure trace. Bubble formation with these characîeristics has
b m termed binary d e s c e n c e with stem formaton A diird gas dispasion
mectianism leading to ody two peaks in the pressure tmce is show in the thkd
diagram. In this case the second peak is not apparent at al1 in part due to the third
peak at point E occirning sooner. This phenornenon, termed stem codescence, is
characterized by no intemiptions in the gas supply except between distinct bubbles.
Triplet Formation Binary Coalesculœ with Stem Formation
-3.3.2.2 - Rubble Interactions for Air bjected into Me~:t.qh~~]
Interactions between subsequent bubbles can take place depending on the size
of the sub-node chamber volume, the gas flowrate and the wettability of the lance.
Irons and Guthrip] have summarized the charactensti * . cs and conditions responsible
for doublet and pair formaîion As can be seen in Figure 3.3.2.3, doublets are
charactaized by coalescence of two bubbles irnrnediately above the orifice. 'This is
caused by rapid acceleration of the second bubble away h m the orifice due to
reduced presnùe in the wake of the fht bubble. Diiring foxmaiion the first bubble is
flattened wIiile the second is elongaîed. This occurs when the sub-node chamber
volume is srndl and the flowrate is moderate to high. 'The result is the formation of a
single, larger bubble.
3.3.2.3 - Doublet and Pair Formation in CmJnjectionpl
Alternatively, pair formation is the texm given to the case when a second
bubble f o m a connecting tube between the orifice and the first bubble. This is
cause. by residual pressure in the gas chamber upstream of the orifice and requires a
large sub-node chamber volume. The connecting tube or tail increases in size with
increasing gas flowrate, and rnay becorne detached. The pair has approximately the
sarne volume as would be predicted for a single bubble.
Lance wettability cm also determine the extent of bubble interactions, as is
illustraîed in Figirre 3.3.2.4 taken fiom the work of Irons and ûuhr@'1. The X-ray
photographs and schematic tracings show in this diagram indiate that the injected
gas can acaially move back dong a horizontal node. Their expimental systern was
comprised of an ~ndik&allium alloy and a non-wetting lance. Thae is an obvious
possibility for bubbles to d e s c e as they travel back dong the lance.
3.2.4 - Xrav - hmggs of- Iqledion mto Ind' ium-Cdlium ~ e l t s ~ ' 1 . . .
3.33 Bubble Velocity and Shape
Bubble rise velocity in liquid met& has received little attention, and most of
the drag coefficient expressions available for bubbles are based on aqueous
e>tpeMients and do not account for bubble deformatons. Elovik0~~~1 has correlateci
cross-sectional diameter with equîvalent diamaer by photographing bubbles in a
varîety of low temperatlrre systems, including the air-mercury system This comlation
is nearly linear over the range 0.2<4<1.6 cm and is given by:
d b = l . 58d,-0.153 (3)
Secondly, Elovikov measured the steady state rise velocity of heliurn bubbles in
pig iron. His apparatus cunsisted of two electncal circuit metering devices, one to
detect bubble detachment and another to record the instant when the bubble reached
the melt surfiace. The resuits have been pmented by correlating the drag coefficient
Cd with the Reynolds number basecl on the mss-sectional bubble diameter. The drag
coefficient is defineci by the following equation:
As seen in Figure 3.3.3.1, the drag coefficient reaches an asymptotic value of about 0.57 for Reynolds numbers greater tban 4000. 'The h g coefficient correlation
is given by:
Cd=O. 568+1.112exp (-8.96 *lO"N,,) ( 5 )
To test the validity of this comlation for other liquid metais, the rise velocity
of helim bubbles was measured in both liquid tin and r n w . The predicted
velocities were 5 to 10% higher than those observai expirnentally.
3.3.3.1 - Dng Coefficient Variation with Bubble Reynolds
3.3.4 Bubble Rupture
When a bubble rises to the kee surface of a liquid, the ensuing sequence of
events can have a signifïcant impact on the amount of m a s transfer that takes place at
and above the liquid surfixe. Distin et alw1 have studied reactions between levitated
iron droplets and flowing gases. While fuming iron in oxygen, surface boiling was
obsexved after the formation of an oxide s k i n As can be seai in Figure 3.3.4.1, a
number of metal droplets are ejected into the gas phase as a result of the release of a
bubble. Figure 3.3.4.2 dernomtraies the ejection of metai droplets following the burst
of 4.6 mm diameter nitrogen bubble injected into a 10 mm diameter mercury &op.
. . Fimire 3.3.4.2 - Drmlet F~ecticu, as a Result of Bubble R U D ~ U ~ ? ~ ~
nie squence of events that lead to the above obsavations are show
sch'emaîicaliy in Figure 3.3.4.3. As a bubble encounters the fke liquid surfiace a
hemispherical dorne is fomed and liquid drallis away. Localized weakening near the
top of the dome results in the formation of a thin secondary cap. This cap bursts and
produces very h e droplets that are carried upwards by the gas escaphg fkom the
bubble. This release of pressure results in a series of standing waves on the liquid
sirrfaçe surroundhg a Crater. As the aster fills in, the liquid flow produces a jet
wtiich rises ai a high velocity. Relaîively large drops of liquid may detach at the apex
of the jet, and rnay subsequently fom srnaller droplets as a result of explosions arising
eorn reaction with the gas phase.
The source of the large droplets e j d h m the centrcil liquid jet has been
studied in detail by MacIntyd? Using doured dye as a tracer, he found that the
liquid contained in the large droplets originates in spherical liquid shells adjaumt to
the bubble surfâce. R e f d g to Figure 3.3.4.4, the top jet drop was originally spread
over the interior bubble surfàce at a mean thickness of 0.05% of the bubble diameter.
Based on zero-order boundary layer theory, the mornentum boundary layer thickness
around a sphaical bubble is about 10% of the bubble diameter. A mornentum balance
indicates that the portion of the flow entering the upward jet is 10 to 20% of this
boundary layer.
.................................... - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - .................. - ........... - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
( vii )
3.3.4.3 - Bubble Rmture Event Sapen~x?~~
h4iicIntyd~ okrved that a single bubble typically results in 3 to 5 droplets
ejected into the gas phase. The liquid chplet diameter is appmximately one tenth of
the original bubble diameter. These results have been confhmed by Kientzler et al[". They also fomd that optimum droplet production was achieved from bubbles less than
2 mm in diameter7 and that these droplets were ejected to heigtts much mer than
the original bubble diameter. The quantity of liquid ejected into the overlying gas
phase for larger bubbles has not been rneaslired
'The bubble rupture zone locafed at and above the fke liquid sinface should be
thought of as two distinct sub-regions7 the spout m e and the dispersion zone. The
spout zone is a dome of gas and iiquid that protrudes into the overlying gas phase.
The dispersion zone is thai volume of gas above the melt that exhibits some degree of
gas liquid contact due to the liquid droplets thaî are ejected out of the spout me.
Sahajwella et alpq have studied the ctiaracteristics of spout formation diiring
the injection of air into water. Over a wide range of operathg conditions the spout
boinidary always corresponded to a gas fiaction of aboui 0.85. Their work also
attempted to define a aitical specific input power density corresponding to the critical
gas flowrate. At flowrates lower than this critical value, more efficient mixing of the
bulk liquid is obtained At flowrafes greater than this value, a greater proportion of
the kinetic energy is transferred to the spout. 'Ihe aiticai gas flowrate represents the
injection conditions *ch maximk the tramfer of energy h m the gas to the 1iquid
phase relative to the energ released at the fixe sur f . . .
By cornpiling the experhental work of Hirasawa et al'381 and Haida and
E3rimacom@9~ with his own results, ~ahajwellP7 calculated a aitical specific input
power daisity of 80 W/g. Using the expression of Sano and Mori@OJ relating input
power density to gas flowrate, this value corresponds to a critical gas flowraie of 84
NUmin/tuyere for a copper converter. This is much lower than typical blowing rates
of 12000 Wdtuyae, resulting in a large amount of energy king rdeased at the
bath suffàce.
3.4 Dynamics of Tuyere Gas Injection
In this section, research pertaining to the dynamics of gas injection thugh
tuyeres into liquid metals will be examined Non-fmus pyrometailurgical processes
widely enqloy gas injection to contad a reactive gas with rnatte or rnetal, such as in
copper converthg and refining.
Recently, thae have beai two thorough rwiews of the physics and chemistry
of gas injection At the Elliott Symposium in June 1990, Brimacombe et
presented a papa entitled 'Process Dynamics: Gas-Liquid which covered gas
dispersion, transport phenomena and metallurgical applications of gas injection. At the
more mit Savard-Lee International Symposium on Bath Smelting, papers written by
Themelis and Mi?~key'~ll and Sano and dealt with hdamentals of gas
injection. These reviews discuss both bubble formation and mass transfer. 'The
phenomena leading to the hi@ rates achieved in copper converting are dl1 unclear.
Predicting the size of bubbles fomed under submerged injection is difficult due
to changes in the contmlling mechanisms with changing gas flowrate. At low
flowrates, surface tension and buoyancy forces dominate, while at higher flo~fafes
viscous and inertial forces becorne more important. These factos make the use of
water models questionable, since the relative magnitude of the buoyancy and surfâce
tension forces are much smaller than in a gas-metal system.
An additional problem encomtemi when using models based on arnbient
te- experiments for rnetal systems is the difference in heat transfer between
the two systems. 'The tempemhm at which the gas properties are evaluated greatly
innuences the bubble size, particuiarly the gas densiîy, -ch rnay Vary by a factor of
5 fiom the injection conditions to the bath conditions.
Some insight into injection phenornena bas been gained by studying air injected
into mercwy at ambient temperature. Oryall and ~rimacOmbe[~~l used an
electroresistivity probe to detamine the volume fiaction of air at various locations in
the bath The d t s bard no resemb1anc.e to those obtained when injecting air into
water. Gas discharging h m the tuyere tip expanded v q rapidly and was seen to
grow behind the tuyere as well as in the direction of flow. The measured expansion
angle was around 150°, compared to 20' for water. Based on these resultsy it was
proposed that since the converter tuyere tip is flush with the refhdory, the extensive
back penetmtion should cause the gas to rise in close proximity to the back wail.
The applicability of these results to the copper converter is uncertain. The
similarity criteria used by Oryall and ~rimaCornbe[~~] was based on the modified
Froude number (N,,). In the convata, the liquid density is one third of that of
merciny and the liquid teniperahtre is 1473 K higtier than the injectecl air. Although
these two differences have opposing effects concaning gas expansion, their relative
magnitudes are unequai. Also, the effect of surfàce tension and wetting is not
quivalent in these two systems, since it is not incorporateci into the caiculation of N,,.
3.4.1 Converter Tuyere Pressure Trace Interpretation
Injection phenornena in the nonferrous industries has been studied by Hoefele
and Brimacombd44] as well as by Bustos et al."] Both these shidies employed a
pressure û=ansducer attached to a cupper or nickel converter tuyere to monitor the
debchrnent of gas bubbles at the hryere tip. The pressure traces can be used to
evduate the gas flow regime as well as the bubble six.
Hoefele and ~rimacornbd*~ me& the pressure disturbance k p e n c y under
both low pressure (normal converter operation) and high pressure injection Their
resuIts are shown in Figure 3.4.1.1. When blowing at gauge pressure of 103 400 Pa
(low), the ttyeres were found to opadte in the bubbling mode with a bubble fkquency
of 10 H i This is the same vaiue obtained when injecting air into merctrry at the same
40) 0-10 MPo (15 psi)
M 0.34 $0 ( 5 0 psi l 0.55 MPo (80 psi
3.4.1.1 - Ressure nisturhance Frgpenciesfor a Convertda]
Tests at higha gas pressures (344 600 Pa, gauge) exhibited very fiat pressure
traces, indicative of stable jethg. Under these conditions, the gas penetrates into the
bath Mer and the tuyae tip is alrnost always surrounded by gas. This can
potentialy lead to reduced tuyere-line rehctory wear and minimal accretion formation.
The position of the tuyere in the convater did not influence the pressure trace
characteristics
Based on a mercury-air system that exhibited sirnilar pressure traces to low
pressure converter operaiion, they conciuded that the bubbles rise almost verticaily in
the converter and irnpinge on the back Wall. Based on the bubbling fkquency, the
bubbles fomed by adjacent tuyaes m u t be connectai even if the gas remains at
ambient temperahire, milees they becorne extremely elongated. ïhis cm be visualized
in Figure 3.4.1.2.
Matte bath (1200 O C )
Refroctory wall
Air
Erpure 3.4.1.2 - Schematic of Fubble Formation at Adjacent ~ u v e r e s [ ~ ~ ]
These two results indicate that the assumption of discrete, spherid bubble
formation in the converter is poor. Hoefele and Brimacombd441 comment that
although large, individual bubbles may form at the tuyere tip, they are likely unstable
in the turbulent liquid and break up to form a swarm of smaller bubbles. They
recognize that this increase in gas-liquid interfiid area is necessary to support the
hi& oxygen efficiencies that are realized in the convater.
Studies of bubble disintegmtion have k e n primarily qualitative, although the
Rayleigh-Taylor instability aiterion has ken used to predict the maximum bubble size
for air in various liquids under stagnant conditions. Brimacombe et alwl report that
the equivalent diameter for an air bubble in water cannot exceed 49 mm and for air in
mercury the value is 34 mm. Bubble Oreakup is thought to result h m a number of
m e c ~ s n i s aside h m Rayleigh-Taylor instability; such as wake phenornena, intemal
turbulence due to the momentum of the injected gas, monance on the bubble surface
and tirrbdence in the liquid 80w field.
Bustos et also paformed plant tests to obtain pressure traces for a copper
convata tuyere. They measured a bubble fhquency of about 4 & much lower than
tliat in the previous work From the shape of the pressure d i m c e s , they deduced
that a copper converter with a tuyere submergence of 50 mm must be discharging gas
into a horhntal gas envelope. The gas envelope then rdeases gas bubbles at mobile
nodes, whose spacing can be analyzed using the Rayleigh-Taylor instability criterion
discussed earlier.
This type of opaation was attributai to the stabilizing V-notch thai had formed
in the reWory ai the tuyere line as a d t of the 250 charges that had aireaciy been
processed in this converter. nÜs is in contrast to the k h l y relined nickel wnvexta
used in the study by Hoefele and Brimac~rnbe.[~~]
The resuits of the testwork of Bustos et for shallow and deep tuyere
submagence are shown in Figure 3.4.1.3 (horizaontal time scale = 1 second). W e
results can be compared with the idealized pressure traces for gas discharge f?om
horizontal, closely spaced tuyeres in Figure 3.3 -2.1. In the case of shallow (30 mm)
tuyere submergenice, pressure disturbances are vay-steep and infkpent. This
indicates the presence of a gas charnel h m the tuyere tip to the bath surface,
periodidy interrupted as the turbulent bath sevas the chininel at the tuyere.
Thae is liale tuyere interaction in this case, milike the horizontal gas envelope
that may connect many tuyem in the deeper submerged operation. Comparative
saidies in a zinc slag fimiing fumace indicate that the liquid viscosity is a h important
in determinhg the degree of tuyere interaction
Vmus forces also appa to have an effèct on tuyere bubbling fkquency.
Figure 3.4.1.4 compares the pressure traces observeci in a slag fuming and a copper
converter. The high viscosity of the zinc fûming slag prevents coalescence of bubbles
fiom neighbouring tuyeres, as is evidenced by the high fkpency pressure fluctuations
that are similar to ihat for classic bubbling. It is possible that the combination of a
low viscosity liquid and V-notch development at the tuyere line are both necessary for
stable gas envelope fomiation
(4 @)
3. 4.1.3 - Eff'ect O f Tuym Immersion on Pressure Disturbance a)330 - -181
Although the converter studies discussed above do give a great deal of insight
into gas injection up to the t h e of detachent h m the tuyere, the nature of the gas
fkom this point until the gas escapes fkom the bath requires another means of study.
3.4.2 Bubble Rise: Bubble Rupture and Liquid Stirring
F~uehan[~~] has Camed out mass transfer e>cperiments discussed earlier that
provided insight into the size of bubbles forrned within liquid m d s . Based on
electronic-probe measments , the calculated bubble fiquency led to a bubble
diarneter estimate of 18 mm. However, visual observation of the bubbles ernerging
from the melt surfiace indicaiecl that they were much srnaller. nie accuracy of visual
observations above the melt surface is questionable, therefore Fruehan followed this up
with some m a s transfa based calculations of bubble size.
As a quantitative means of checkhg the bubble size, he coqared the mass
transfer measurements with those predicted mafhernatidly with a liquid film m a s
transfer coefficient estirnated fiom the Calderbank equation. Based on the observed
mass transfer rates, he concluded that the bubble diameter m u t have been about 10
mm This calculaied bubble diarneter is also subject to error due to the simplicity of
the equation used for calculating the mass û-ansfer coefficient (excludes bubble
EToWth). Sahai and ûuthrid451 report that for argon injectai into molten iron at 6 Umin
the maximum bubble diameter was about 30 mm, compared to the same air flow in
water where the bubbles would only grow to 21 mm. This is &buteci to a higher
surfàce tension, non wetting of the orifice and a lower gas momentum to liquid density
ratio in the metal system 'Ihey concluded that such large bubbles are unstable and
disintegrae above the node into an anay of srnaIler bubbles.
Although there is general agreement that the large bubbles fomed during
submerged gas injection into metals must disintegrate to fom srnaller bubbles, there is
no explmation for the mechanism and littie information regardmg the ultimate bubble
diameter. ïhe relative proportions of the gas residence tirne for which the large and
smali bubbles exist is also unknown.
3.43 Anaiogy with Spouted Beds and Incipient Fluidization
The injection of gas into a shallow liquid can be compared with spouted beds
or fluidized beds at the omet of fluidization Spouted beds are characterized by a hi&
velocity jet of gas and solids surrounded by a siower moving annulus compriseci
rnainly of solids. In gas-solid systems, a relatively narrow range of conditions are
reqwed to generate a spouted bed. At low gas flowrates, the bed rernains static,
while at higher gas flo~rafes and large height to diamefer ratios the bed becornes fùlly
fluidized. Spoiuing is also f a v o d by srnall orifice diarnetm, relaîively large
pattïcle sizes and a namw particle six distribution. An important f w of spouted
beds is the fact that the heat and mass transfer coefficients increase with increasing
particle diameter, the oppsite trend fkom a fluidkd bed. For particle diameter; in
excess of a few mm, spouted beds lead to higher tramfer coefficients than fluidized
beds under sirnilm conditions.
Fixed Bed and b) FIuidized Red . . PO1
Nmerous analogies between fluidized beds and liquids have been drawn in the
past. In particda., the behaviour of bubbles rupturing on a liquid slirface can be
compared with a bed of solids at the point of incipient f l u i ~ o n As the gas
flowrate through a fixed bed is inaeased, the pressure drop m s s the bed increases
until it equals the gravitational force on the bed At this point the particles begh to
move and the bed rnay expand slightly. Furîher i n m e s in the gas flowrate result in
coqlete fluidization accompcniied by m e r bed expansion without any change in the
k d pressure &P. The transition to a fluidized state in a gas-liquid system is typically
accompanied by an increase in the tramfer coefficients of 1 to 2 orders of magnitude.
This is due to the hi& degree of turbulence and hi& rate of suface renewal that
accompanies fluidization Figure 3.4.3.1 scherntically illustrates the typical variation
in heat transfa coefficient during the transition fiom a fixed bed to a fluidizd bed.
The identical behaviour can be expected when plotting mass tramfer coeficients.
3.5 Converter Tuyere Modeiiing
3-51 Mathematid Modelling
Theoretical modelling of the heat and rnass transfer processes occuning inside
a converter is a cornplex task Ashman et aI[q have developed a mathematical mode1
for a copper converta tuyere up to the point of bubble detachment. ïheir mode1
incurporated heat and mass tramfer at the bubble surfiace, chernical reaction with the
liquid, fluid circulation in the converta bath and drag forces acting on the bubble.
'Ihey considered the bubbles to be sphericai and to act discretely, based on the results
of the work of Hoefele and ~nmaCOrnbe.[~~]
A major difficulty in developing such a model is the estimation of necesSay
physical parameters. A sensitivity anaiysis induded with the model, shown in Table
3.5.1.1, illustrates the uncertainty in these values. The heat and mass transfer
coefficients investigated ranged by a factor of 100 and the bath circulation velocity
was estimaîed to be between O and 2.4 mk. The sensitivity analysis yielded the
following results: The range of heat transfer coefficients predict a bubble tempeniture
between 362 and 1380 K at the point of detachment. The range of mass transfer
coefficients predict an oxygen consumption between 5 and 60%. The range of bath
velocities predict a bubble volume between 27 and 254 L.
Ashman et alm constructed a base case model using the medians of most of the
paramder mges listed in Table 3.5.1.1. 'Ihe model predicts that the gas bubble
grows to a volume of 45 L upon detachent, At this point the bubble tempemtm is
575 K and the ovgen consumption is 40% The bubble growth period extends over a
d d o n of about 0.1 S. The following mode1 predictions for the base case bubble
growth p&od are illu~trated in Figure 3.6.1.1, bubble volume, bubble temperature and
gas composition. Figure 3 S. 1.1 also includes the variation of bubble fkquency
bath circulation velocity.
Variable Valuc Frcqucncy fs - ' ) \'olumc ( 1 . ) Tcmperaturc (KI P ~ , ( i ~ t n a )
Baih orculaiion vclocity icm/s)
Air flow raie (Ils1
Air prchcar tcmperaiure (KI
Pcr clni oxygcn in blzt
Tuycrc diameter (cm 1
le 3.5.1.1 - Sensitivity Analysis of Ashman's Tuym ~ o d e l [ ~ ]
The heat and mass tramfa correIations were likely considered to be least
accurate due to their bais of calculation. 'The correlation used was derived fiom
calculaiions for a gas jet impinging on a solid surfiace developed by
S e ~ ~ n d l y ~ the gas velocity LE& in this correlation, *ch is intended to be the mean
gas velociîy striking the solid surfacey was estimated to be the gas velociiîy at the
tuyere tip. ïhis wodd appear to ovecestirnate the transfer coefficients, since the gas
loses momentum in the bath.
Based on their rnass trruisfer equations, criteria were developed for determining
the rate limiting step. Throughout the entire converhg cycle, the reactions were
shown to be limited by nmss ûansfer in the gas phase. Ashman et alis1 amibute the
hi@ converter oxygen efficiencies to the great deal of turbulence in the gas phase.
3.5.1.1 - Ashman Bubble Growth Model: Rubble Volume. Tmperature,
on and ~reauencd~
The bath circulation velocity is important since it cornes into the momentum
balance which serves as the criteria for bubble detachment. In accordance with the
measurements of Hoefele and ~ r i m a c o m b d ~ , the appropriate velocity appzars to be
1.8 d s . This yields a bubble volume of 46 L and a bubble fquency of 10 H z
The mechanisms responsible for heat and rnass transfer afkr the bubble has been
severed fiom the tuyere are equally cornplex At this instance the bubble diameter
e x d the tuyere submergence. If the mode1 is accinrie to this point, which is .
questionable given the Iack of ;;appropriate correlations for bubble growth heat and
mass transfer, fllrther investigation is required to determine precisely how the
rernaining 60% of the oxygen cornes into contact with the matte and reacts before the
gas leaves the convater.
Fukmaka at al191 developed a mathematical model for cornparison with the
results of thei. mass transfer shdy into the injection of oxygen-argon gas mi>bures ùao
copper containing sulphur below saturation. The parameters for this model could be
evaluaîed more accurately since it was based on mass tramfer taking place as the
bubbles are Mly detached and rising. For this situation there are numerous
correlations for evaluating mass transfa coefficients in both the gas and liquid phase.
It is not hown how well the mode1 predicted the observeci mass tramfer rates,
since the low injection rates and relatively deep submagence used in the experiments
always resulted in complete consumption of oxygen The mode1 predictions did agree
satisfaorily with melt sample assays, so it can be concluded that both the model and
experimental mass tramfer rates were fasta than the gas injection rates. However,
due to the simplistic nature of the model, it is not very useful.
3-12 Physical Modeiiing
Kim and ~niehan[~'l have monneci physicd rnodelling of rnass transfer in a
gas s t k d ladle by injecting CQ into an aqueous NaOH sollition. Although the mass
ûansfer rates in this system are quite different than those in a gas-metal system, a
valuable observation was made in this study. Even though the gas was injected f?om a
depth of 430 mm, the resdts indicated that almost 50% of the m a s transfa took place
as the gas bubbles nrptured at the k liquid d a c e , in in they refa to as the
plume eye. It was also detennined üiat a significant mass ûansfer rate could be
obtained by injecting an inert gas while maintaining a d i v e gas in the ovalying gas
phase. These are both very signifiant observations, aithough similar obsavations
have not been reported elsewhere in the literature. Surfàce d o n is likely also very
important in the opemtion of converters, since the residence tirne of a gas bubble in
the bath is very short.
Adjei and Ri~hards[~1 have &ed out physid modelling of the rnass transfer
in a copper converter on a 114 scale Plexiglas model containing five tuyeres. The
SO,H,O, system was used to simulate a gas phase controlled irreversibie reaction.
Injection conditions were deterrnined on the bais of the Froude number to simulate
bubbling in a converter. As a basis of cornparison, a mathematical model was dso
The limitations of such a model are readily apparent. 'The injection phenornena
are quite different from those in a real copper converter, with regards to gas trajectory,
bubble size and bubble shape. Bubble size and shape detemine the volume to surfàce
area ratio for the gas phase, as well as the gas midence time in the liquid. ïhe
obsexved or calculated bubble diarneters were not stated in their report. Part of their
analysis was based on the 20° spreading angle observed in airlwater systems, which is
very different from obsexvations in aidmetal systems.
Power~Unit Mass (w/kg) (Thousands)
Factor for Mass T r a n ~ f d ~ ]
This study did bring to light the importance of mass trmisfer in the bubble
formation stage of gas injection, lhey found that up to 60% of the r d v e gas was
coflsumed before bubble detachment. To accuunt for this observation, they modelled
the mass transfer during bubble fommtion by adding an enhancement factor to the
msteady state diffusion equaîion. This parameter has beai correlateci with the power
of the injectai gas per unît mass of gas in the bubble, as shown in Figure 3 S.2.l. The
use of this enhancement factor has provided &acto~~ predictions for various copper
converter efficiencies.
Brimacombe et al" have also attempted to construct a physical mode1 of a
copper converter ushg the H&SQ systern Swfhx absorption was investigated by
injecting air bene& the liquid sinface in a horizontal jet and blowing SQ onto the
liquid surfàce about 10 cm above the spout at 1% of the air flowate. For air injected
at 4.5 Numin, the spout height was measured to be about 5 cm The extent of S Q
absorption ont0 the liquid surfiace varied between 5 and 12% depending rnainly on the
height of the top lance. It is noted in this work that the m e a d mass transfer
coefficients are l e s than one sDdh of those reporteci by Themelis and Schmidt[m for
the deoxidation of copper by CO injection under similar conditions. The following
explanations for the differences were put forth by Brimacombe et al".
It was speculated that the breakup of a CO jet in copper may result in srnaller
diameter bubbles, however there is no evidence to support this theory. It was also
suggested that circulation (and therefore mass transfa) inside bubbles onginating in
vertical jets rnay be &reater than those h m horizontal jets, since the jet momentum is
aligned with the path of rising bubbles. ïhis is more likely to lead to a subtle
diffmce in rnass transfer coefficient, since the horizontal jet becornes vertical a short
distance h m the lance. A thûd explanafion is based on spontaneous interfacial
turbulence? which was not obsexved in the aqueous systern but is suspectai to be
presait in the Cu-O system as a result of the SuTf'dce active nature of oxygen.
ïhe effect of orifice diameter on the rnass transfer coefficient was also found
to be differait for the two systenis. It was concluded that the mode1 for bubble size
determination in the aqueous work, which was based on obsexvations in aqueous
systerns, was likely unsuitable as a means of interpreting the expainenta1 data of
niemelis and Schmidt." 'rhis coqarison higtiligtas the cautions that must be taken
when extmpolating h m aqueous systems to moltai matte/md systems.
3.6 Mass Transfer Coefficient Correlations
Since the m a s transfer mechanisms taking place are differait during bubble
growth, rise and rupture, it is reasonable to expect that separate mass transfer
coefficients are necessary to describe eadi stage of gas-liquid contact. The litemture
does not rnake direct reference to comlations that are based on precisely the above
stages, although it may be possible to adapt some expressions derived fiom sunila.
physical conditions.
WakeIi~[~~] has studied the m a s transfer rates for an oxygen jet impinging on
the surf" of liquid silva at 1273 K in evaluating his experhental results he
assumed that niass transfer only took place at the gas-liquid interface in the cavity
f o d on the liquid surface by the rnomentum of the gas jet
nie following expression for the local mass transfer coefficient was developed
based on the d a c e r e n d theory:
This expression rnay be diaficult to apply to other cases as it requires the radial liquid
veiocity 4 The above model exhibited adequate agreement with the observeci results.
This model is vay limiteci since it is only valid for non-splashing cases.
The m a s transfer coefficient for a gas jet impingïng on a liquid suface has
also beai studied by oh&^]. He correlated the Sherwood number for mass transfer
between an air jet and water with the jet Reynolds number and modifieci Froude
number, for jet momenturns below the splashing regime. The length sale used in
evaluating the Shmood and Reynolds numbers was the radius of the cavity, while
that for the modifiai Froude nurnber was the orifice diameter. ?he second term
involving Ni is a correction factor diat represents enhanced m a s transfer due to
sudiace wave f o r d o n .
Although this relaîionship is usefbl over a wider range of physical conditions, it is still
limited since it is based on a water model.
Huang4q has studied the heat transfer characteristics for a gas jet impinging on
a solid surface. ~shman[~I used this correlation for the average Nusselt nurnber over
the impingement surface dong with a heat and rnass &asfer analogy in modelling the
rnass transfer in the bubble growth stage for a copper converta. By combining the
empirical expression dweloped by Hùanfj] with the Chilton-Colbum analopy, one
arrives at the following equation for the mass transfer coefficient:
The Reynolds number is evaluated at the orifice conditions in this con-elation. The
applicability of this model to a fluid-fluid system is questioriable.
For bubbles rishg under gas phase rnass h-ansfer control, a correlation could
not be fond in the literature. However, expressions are available for this system
under liquid phase cuntrol. Calderbankrsf] has studied the m a s transfer between high
Reynolds number bubbles and the srarounding liquid For large spherical cap bubbles
possessing Reynolds numbers in excess of 400, the following expression is proposed
relating the Shmood number to the Reynolds and Schmidt n u m k :
*,=1-28J= (9)
Altematively, it rnay be more appropriate to d y z the gas phase as flow
hide a cylinQical channel smunded by fluid Gilliland and ~hervvood~~~ have
studied the vaporization of nine ciifferait liquid into air under this geometry. Their
proposed w o n for the Sherwood number in the gas phase is valid over the
following ranges of conditions; 2000 < N, < 35000 and 0.6 < N, < 2.5.
As discussed earlier, the bubble rupture region can be thought of as consisting
of a plume zone and a dispasion zone. nie plume zone is very dif£ïcult to model due
to the complex fluid flow at the fke liquid sUTface. The dispersion zone can be
regardeci as a spray chamber, with continuou flowing gas and a liquid phase of fine
droplets that is continuously king replenished by the bubbles cupturing in the spout.
Fr~esslin&~I has studied the mas transfer ~ o m liquid droplet to a flowhg gas stream
under gas phase control. His Sherwood nurnber correlation is valid for droplet
Reynolds numbes ranging h m 2 to 1300 and Schmidt numbers ranging from 0.6 to
2.7. 'Ihis expression illustrates the theoretical minimum Sherwood number of 2 for
molecuiar diffiision done.
4.0 Theoretical As-
4.1 Converting Thermochemistry
The chernisûy associated with copper converting has beai well d~cumented,[~l
consisting p M l y of &S oxidation to fonn either Cu@ or metallic Cu. The
copper oxide that does form reacts rapidly with additional copper sulphide to fom
blister copper. 'Ihe primsny teactions are listed below. Since most of the cupper
converthg stage takes place under the Cu-Cu,S miscibility gap, the subscrîpts 1 and 2
are used to refer to the sulphide and metallic phases respectively. Due to the p e n c e
of the miscibility gap, the activities of Cu,S and Cu are approxhnaîely 1.
-- -
As conveision n e m completion, at about 1.5% dphur in the melf the systern
leaves the two phase region and the assumption of unit activity for Cu,S is no longer
valid Assirmuig an ideal solution forms between the t h e species present (Cu, S and
O), therrnodynamics indicate that the sulphur content can be lowered to 0.0 13 %
(~rpical S in blister) *le the level of oxygen rises to 0.35% under a SQ partial
pressure of 10133 Pa. 'This is M e r illustrated in Figure 4.1.1 .r5q Since this oxygen
(3J2sfl.1, + q, = 2 CU021 + SQ!o (12)
@SO.*) + 1.5 Qa& = fi&*, C r 2, + sa, (13)
fi2s0*1, + 2 ~ z ~ o , , or 2) = 6 %, + s o (14) Table 4.1.1 - Thermodynamic Data for Converting Reacti~ns[~~
Data
Er (12) ('cal)
E r (13) @cal)
ffir (14) ( k W
PWcrit (Pa)
activity (-0)
Te- (K) I
1473
-40.3
-55.0
-10.8
0.106
O. 158
1523
-39.7
-53.5
- 12.2
0.204
O. 133
1573 1623
-39.2
-5 1.9
-13.6
0.363
0.1 14
-38.6
-50.4
-15.1
0.642
0.096
content is well below the solubility Iimit for Cu@ in Cu,['l it is possible to produce
blister copper without oxide exsolution under equilibrium conditions.
Once the Cu,S phase has ken eliminated the reaction mechanism for
desulphwimtion follows a slightly different path than the reactions occwing aaoss
the rniscibility gap. Oxygen in the gas phase is thought to dissolve v q rapidly into
the melt in the fom of aîomic oxygen. f i s is followed by reaction with sdphur in
the melt producing S Q according to reactions 15 and 16.
0 = 2 O(dirr) (15)
S(,, + 2 ~~~) = (16) nie equilibnum constant for reaction 16 at 1473 K is 3. 1-1O6.W Copper at
1473 K containhg 1% by weight dissolved sulphur unda an oxygen pressure of 0.2
atm yields an equilibriurn gas phase with a SC+ partial pressure of aboui 101 Pa This
can be compareci with that for S, of 1.0 Pa taken h m the work of Schuhmann and
moles.['^
4.2 Nuid Dynamics and Mixing
The injection of gas through tuyeres m e s a great deal of turbulence in the
converter and d e s analysis of the liquid flow field very difficult. Liquid likely rises
directly in fiont of the tuyere-line, travels across the top of the bath towards the fiont
of the converter and then back down to the tuyeres dong the reli-actory. The
mathematical mode1 of Ashman et allS predicts that the bath circulation velocity is
about 2 mk.
4.2.1 Liquid Dynamics
The degree of mixïng impaaed to a liquid systern by injected gas can be
p t i f i e d by the rate of energy dissipation h m the gas to the liqUid[q The work W
done by a single bubble over a differentiai distance dz is a combination of buoyancy
force work and volurneûic expansion work, where V is the bubble volume, 0 is the
liquid density and P is the pressure inside the bubble.
dW=Vbplgdz+PdVb (17)
Equation 17 can be integrated over the liquid height Z and sumfned over al1 the
bubbles released at a
of energy dissipation
total f l o w e of Q Umin. The resulting expression for the rate
E, is:
where T is the bath temperature and m, is the total bath rnass. This a n be compared
with the specific energy input rate (EJ dculated as the ratio of the potential energy of
the rising gas to the liquid mas, where R, is the vesse1 radius.
This is the energy input rate used in the correlation derived by Sahajwella et al13q for
detennining whether the rnajority of the energy possessed by the gds is released in the
bulk melt or at the melt suffixe.
It is interesthg to compare these two measures of power input with the power
input due to the initial kinetic aiergy of the injected gas. 'This can be calculated h m
the gas density p, the entry velocity u, and the orifice cross sectional are. 4. Based
on the following equation:
It on be show that the powa input due to the entry velocity of the gas is less than
1% of the power dissipated by the rising gas bubbles in a converter.
4.2.2 Residence Time Distributions
nie residence time distribution for each stage of gas-liquid contact depends in
part on the fluid dynamics of the gas phase. Figure 4.2.2.1 depicts the likely shape of
residence tirne distribution (RTD) curves for the three stages; growth, rise and rupture.
During bubble growth the shape of the residence t h e distribution depends on
the injection conditions. For constant flowraîe injection the plot is flat with the mean
residence tirne equal to one half the bubble period. Under constant pressure injection,
the gas flowrate varies slightly as bubble growth progresses, resulting in a slight cuve
in the graph. More importantly, thae is approximately 10% dead tirne, during which
no flow takes place. This results in a decrease in the mean residence time, as gas
must flow through the orifice at a higher rate for the same bubble fiquency as in
constant flowrate injection
DLning bubble rise the residence tirne is equivaient for al1 gas elements and is
calculated as the time to asoend from the point of gmwth to the fixe liquid s ~ a c e a c e
However, if the gas flows to the suffice in a cylindrical channel, this will result in a
slight broadening of the residence time distribution. It is noted thai not al1 gas
elements may corne into contact with the gas liquid intaface by buk flow, and thus
the residence time represents the tirne interval in *ch there is an opportunity for
diffusion to take place.
The bubble rupture stage. and prirnarily the dispersion mne, can be represented
by a fluid flow mode1 between back-mixed and plug flow. The axial dispersion mode1
can be used to more âccuraie1y predict where the a d residence t h e distribution
hct ion lies between these limiting cases. The dispasion parameter Q/(kL) is used
to characterize the fluid flow, however the physical property Q is an effective axial
diaisivity and is ciifficuit to predict. ïhe dispersion zone is likely closer to back-
mixed flow as a result of the turbulence impiirted to the gas phase by the ejected
liquid droplets.
Bubble Growth
Bubble Rise
Bubbie Rupture
This work
D L l W ) 0.044.13
4.2.2.1 - RTD Clwves for Hubble Cmwth. Rise and Rupture
4.3 Bubble Formation and Motion
Sano and ~ o r i [ ~ ~ ~ sumPnanze the three regions of bubble formaiion bas& on
gas f l o ~ e as follows:
1) at low gas f l o ~ e s , the bubble size is independent of gas flowmte and is
detamined by the nozzle diameter and liquid physid pmperties.
2) at intennediate gas flowrafes, the bubble size depends on both the gas flowrate and
the nozzie diameta,
3) at hi& gas flowrates, s d l bubbles are f o d about 100 mm above the n o d e by
disintegration of large kguiar bubbles.
43.1 Wetting EffecfS
Weeiability of the n o d e material by the liquid has a definite e f f i on bubble
shape and size. Figure 4.3.1.1 provides a schematic illusimiion of the differences in
bubble formation between wetted and non-wetted nozzles, orifices and porous plugs.
In the case of bubble formation on a non-wetted d a c e , the base of the bubble
spreads much wida than the aoss-sectional a r a of the gas outlet.
Wetted
NozzIe Orifice Porous plug
n S~han2.k Wettino and No &pre 4.3.1.1 - Rubble Fomtio n-Wetting Conditions[42]
4.3.2 Bubble Size
When a gas is injectai into a liquid, the size of the bubbles fomed rnay be
controlled by a variety of mechanisrns. Gas injection is classified as occurring under
either constaqt flow or constant pressure conditions. Hughes et alLsq suggest using the
system Capacitance nurnber, No to determine the mode of injection.
The variables in this equation are: the interphase density ciiffierence (eniq- pd, the subnozzle chamber volume (v, the gas der~~ity (QJ and the orifice cross-
sectional area (&), while the constant C is the sonic velocity. The gas injection
system is considerd to operate at constant flow if Nccl and constant pressure ZNc*.
If the volume of the gas chamber immediately upstream of the orifice (but
downstrram of any large pressure dmps) is rnuch larger than the bubble volume, the
charnber pressure will not fluctuate significantly over tirne. As the subnozie chamber
volume demeases, a transition occurs fkom constant pressure to constant flowraîe
injection and the bubble fkpency increases. Under constant flowrate injection, the
subnonle charnber pressure varies widely in the initial stage of bubble growth and the
gas flowrate into the growing bubble is essentially constant. At high flowrates and for
small orifice diameters, the pressure drop is large and there is no detectable effect of
subnozzie charnber volume.
Alternatively a dimensionless Capacitance nurnber bas been defined to account
for the inner nozzie diameter as well as wettability.
Since most metallurgical gas injection systerns are operated with srnall subnozzle
chambers, they are cornrnonly modelled as constant flow systems. Figure 4.3.2.1
illustrates the theoretical pressure û x e and bubble growth rate as they Vary during
bubble growth under both injection
- 3000 l i i ~ i i l
O 20 4 0 60 80 100 lm 140
Time (msl
4.3.2.1 - Pressure Vanation and Cirowth &îe for Constant Flo . . w and
'Ihe figure above i l l m e s an order of magnitude difference in the pressure
fluctuation in the chamber as well as a 60% difference in bubble fi-equency between
constant pressure and constant flowrate injection.
For constant flow bubble formation at low f l o ~ e s , the bubble volume is
daermined by a balance of buoyancy and surface tension for~es.l~~1 ïhe bubble
volume V, depends on the orifice diameter & the s d i tension o, the contact angle
p and the density diffèrence between the liquid and gas phases Ap.
This equation is most applicable to capillq injection where nonle flooding is
x-rhhd.
If viscous forces are more important than stirface tension forces, the bubble is
assumed to move a . Stoke's velocity (typically at low gas flowmte~).~~~j This yields
the following equation for the bubble volume upon detachment fkom the orifice:
where p, is the liquid viscosity, is the liquid density and Q is the gas flowrate.
For higher rates of injection, it is more appropriate to use a two-stage mode1 such as
that proposed by The bubble volume at the end of the first stage (expansion)
is derived fimm a force balance involving viscous ternis, sdace tension, inertia and
buoyancy. The dimensionles bubble volume V,' is obtained by solving equation 25:
The second stage dimensionles volume acquired between bubble lift-off and
eventual ddachrnent is obtained h m an empincal correlation:
v;=JQ1+4 ( ~ ' p ' ) -" (26)
and the terminal bubble volume is then given by:
V I = v: + v: (27)
ïhe dimensionles quantities in equations 25 through 27 are defmed by eguations 28
to 30.
A limitation of this model is that it does not account for the liquid and gas
velocities, which can be quite significant in tuyere injection. A liquid updraught
results in the d bubble volume k ing srnaller than would be predicted by Rutf~[~ ' ]
twestage model. A graphical representation of the Ruff mode1 results in a plot that is
very simila. to the e m e n t a l bubble volume data compiled by Sano and ~ori[~*I,
shown previously in Figure 3.3.1.1.
Ashman et dlS] used a simple bubble formation model developed by Davidson
and c ~ w o r k e r s ~ ~ ~ ~ ~ ~ which is based on inertial and buoyancy forces. To adapt this
model to a system where the cuflowing bath has an impact on bubble formation, two
changes were required. A h g term was added to the force balance and the inertid
term was transfomed so that it is calculated relative to the bath velocity instead of
stationary co-ordinates. The resulting equation of motion haî s m e s as the criteria for
bubble detachment is:
The parameters in equation 31 are; the bubble volume V, the bubble diameter
a, the bath velocity v and the bubble velocity W. Numerical constants are the
acceierafion due to gravity g, the drag ooefficiait Cd and the virtuai mass constant Cm.
This last variable depends on the geometry of the system and has a theoretical value
of 0.5 for a sphere moving parailel to a wall and 0.69 for a sphere moving n o r d to a
wall. The first value is more appropriate for a copper converter.
' k i s mode1 for gas bubble formation is more detailed than that of s&
it takes into account the motion of the surroundhg fluid However, it is lùnited suice
it neglects the presence of sirrface tension forcg and requires an estimate of the liquid
velocity. The solution is also more complex since it req- a finite difference
method to calculate the terminal bubble s k .
As a bubble forrns at a non-wetted orifice, the orifce s tab i lk the large
bubble s k . After detachment, the bubble may shatter due to d a c e instability.
Based on the Rayleigh-Taylor instability critena and some empirical da@ Grace et
alrwi provide the following estimate for the maximum bubble size of gases in liquids:
It should be noted that this criteria does not account for the tirne necessary for the
process of bubble shatter to take place. Based on the above equation, the maximum
bubble sizes for air in Cu,S and Cu are 48 and 57 mm respectively.
43.3 Bubble Shape
'The mechanisms for bubble formation at a non-wetiing orifice depend on the
systern geumee. The stages of bubble growth for a downward facing n o d e and a
horizontal orifice are depicteù in Figure 4.3.3.1. For a vertical nozzle, the bubble
forms initially dong the inner diameter. Since the upper limit of the Gibbs' ùiequality
is reached before a hemisphere is formed, it must spread to the outer n o d e diameter
for M e r growtk Once the bubble reaches the outer edge, it increases in s ix until
the buoyancy forces exceed the consûahing forces and the bubble escapes up the side
of the node. The actual profile of the bubble diiring growth may be slightly flattened
in the vertical direction due to the v d c a i pressure gradient.
For bubble forniaton at a horizontal orifice the initial stage of bubble growth is
the same. Upon reaching the upper limit of the Gibbs' inequality the bubble grows
upward dong the lance and the contact angle remains constant at the equilibrium or
advancing contact angle. The maximum spreading diameta is given by the following
expression:
The bubble will then continue to grow and detachment will take place when the
inertial and buoyancy forces exceed the sur fke tension force. Again the bubble is
likely to becorne distorted in the 1- stages of growîh due to pressure gradients.
fi \Dm 4 ion: Non-wettin ward Facing Nozzle
and Horizontal ORfice
The shape that a bubble assumes after it has detached fiom the orifice a n be
predicted using the bubble shape diagram provided by Clifk et al". Shown in Figure
4.3.3.2, this graph is coqrised of a number of bubble shape regions on a plot of
Reynolds number vs. Eotvos number. The Eotvos number indicates the relative
magnitude of gravity and surfkce tension forces. Lines of constant Morton numba are
provided on the graph. 'This dirnensiodess group is strictly a finiciion of the liquid
properties.
This graph can dso be used to estimate the bubble velocity. By first
deterrnining the equivalent bubble diameter, the Eotvos number can be calculated,
'This, in combinaiion with the Morton number, fixes the position on the bubble shape
diagram and detemwnes the Reynolds number. The bubble velocity can then be
calcuiated directiy h m N,.
4.3.4 Bu bble Velocity
ûnce a bubble is released h m a tuyere, it reaches its steaciy state velociq
quickly due to the large interphase density diff'ce and the relatively low viscosity
of the liquid.
Davis and TayIo*W have determined the speed of a rising spherical cap bubble
by calculating the velocity that satisfies the Bernoulli quaiion at the fiontal stagnation
point. The d t i n g expression depends on the bubble radius &, according to the
following expression:
From a balance of the hoyancy, gravitational and drag forces
rising bubble, the terminai velocity of a sphericat bubble is relateci to
and fluid properties by equation 35.i67
acting on a
the bubble size
The drag coefficient, C, can be caicuiaîed fi-om Stoke's Iaw at low Reynolds
numbers ( R d ) or Newton's law at hi& Reynolds numbers (Re1 000). Under
intermediate flow conditions the drag coefficient can be obtained by graphical
methods, multing in an iterative solution since the drag coefficient depends on the
velocity. For dl cases the resulting drag force (FJ on the bubble can be cornputeci
fkom equation 36.
4.3.5 Dimensionles Groups
Two dllnensionless parameten are primanly used to chaxacterize submerged
gas injection nie Weber number (We) takes into account inertial and d a c e tension
forces while the modifiecl Froude number (Fi) is the ratio of inertial to buoyancy
forces for gasfliquid systems. These dirnensionless groups are calculated accurding to
equations 37 and 38; where p, is the gas density, y, is the gas velocity at the orifice
tip, dp is the liquidlgas dmity differaice, d,, is the orifice diameter, O is the surface
tension and g is the gravitaiional constant.
If viscous forces are important they can also be inciuded by using the Reynolds
number, and some auhors characterize hi& velocity injection by the nominal Mich
number for under-expanded flow.
Once a bubble detaches h m the orifice, the inertial force decreases rapidly
and buoyancy and surface tension forces are likely to dominate its motion and s k .
nese two phenornena can be represented by the modified Bond number:
4.4 Physid Phenornena
4.4.1 Transport Mechanhm
DLning tuyere injection converting of copper matte, the physical processes
taking place are those concernai with gas and liquid phase diffusion. The two
necessary reactants, liquid cupcous sulphide and gaseous oxygen, must corne into
contact. This is most likely to mur at the gas-liquid interface.
ûxygen arrives near the interface by bulk transport, Cameci by its momentum
as it leaves the tuyere. The oxygen must then diffuse through a gas film consisting
primarily of sulphin dioxide to arrive at the gas-liquid interface. nie momentum of
the gas issuing fiom the tuyere during bubble formation aids in thinning the stagnant
film and shortens the diffusion pah Oxygen then either reacts heterogeneously with
liquid Cu,S at the gas-liquid intaface or dissolves directly into the liquid
The proportion of oxygen following these paths depends on the solubility
(temperature? % S) and readon and dissolution kinetics. Oxygen that has entered the
bath will then react with either copper suiphide or dissolved sulphur directly in the
liquid, usually near the gas-liquid interfàce. The proportion of oqgen following this
path is likely quite small while aossing the miscibility gap.
Cuprous suiphide amives near the bubble s d k e by buik transport as well,
&ed by the circulation rreafed by gas rising dong the back wall of the converter.
While crossing the miscibility gap? diffusional resistance in the liquid is minimal, since
the rnetallic copper formed moves downward and joins the metallic phase by virtue of
its pater density. Once the matte phase is gone, liquid diffusion may becorne
important since dissolved sulphur must d i f i e through a stagnant film of metallic
copper to reach the gas-liquid interfàce.
Dissolveci oxygen may also diffuse into the liquid to react with dissolved
sulphur. The stagnant liquid film may be vay thin in places due to d d y penetration,
as a result of the converter turbulence. This fiindamental difference between white
metal and semi-blister converting may be useful in determining the importance of
liquid mWng and the e m t of liquid phase diffusion control.
Once both reacfants are presait near the i n t e r f i they must ranain in contact
for sirfficient t h e to overcome the requred activation energy and react. This tirne
requinment depends on the intrinsic kinetics of the conversion reaction (reaction 12,
13 or 16) and is veiy small. Mer the reaction is compkte, the suiphur dioxide
evolved must detach itself fkom the liquid and diaise into the bulk gas phase to be
carrieci away. The condense. phase producf either Cu,O or metallic Cu., mixes into
the liquid by a combination of diffusion and bulk transport, becoming part of the buik
liquid phase. Any copper oxide that f o m will corne into subsequent contact with
aiprous sulphide sornewfiere in the bulk liquid phase and react according to the
kinetics of reaction 14. Bubbles containhg evolved SC& and unreacfed b& nse and are
released at the interface.
4.4.2 Transport Modeis
(Xdinary diffusion for an ideal gas is described by Fick's first law for mass
transport, where the molar flux of specie A (Nd is relaîed to the difhsivity Dm, the
intafacial area 4 and the partial pressure gradient dPA/dz by:
Diffusion is enhance. by mWng near the interface due to a shortening of the
diffusion path, increasing the partial pressure gradient. If a solid f o m at the gas-
liquid interfàce, d i h i o n rates are generaiiy slower due to lower difhsivities in soli&
compared to liquids.
Since the fom of the pressure gradient is unlaiown, the concept of a rnass
transfer coefficient is typically used to evduate experimental mass -fer data The
mass transfer rate is relatecl to the mass ûansfer coefficient k, by the expression:
For the copper-air system the gas phase can be assumed to be in equilibrium
with the liquid at the bubble surface, and consequently the partial pressure of Q at the
surfàce is negligible compared to that in the b u k The bdk partial pressure of C& in
the bubble changes as the bubble ascends the liquid due to its consumption at the
d a c e . A log mean value for POZhiik is most appropriate, and is calculaied according
to the following equation. The vanables Pozi and Pa, are the initial and finai values
for the partial pressure of oxygen respectively.
Mass ûansfer coefficients can be related to the three primary theories for mass
tramfer, the film theory, the penetration theory and the boinidary laya theory. The
film theory proposes that the entire resistance to m a s transfer cm be represented by a
thin laminar filrn of constant thichess 6 adjacent to the intaface. Merior to this
filrn the concentration of the difbing specie is equal to the buk concentration and the
gradient moss the filrn is assumed linear. Only moldar difIùsion leads to mass
transport within 6 and turbulence in the fke stream ai& in reducing 6. For equimolar
conter diffusion, the film thickness can be calcdated £iom the mass tramfer
coefficient accordhg to the following expression:
The penetration theory, proposed by Higbie in 1935, applies when the diffusing
component only d i f i e s a short distance into the phase of interest due to a rapid
chernicd reaction or a short contact tirne. 'This theory postdates that the interface is
constantly in a state of renewal due to eddies penetrating fiom the bulk to the suface.
The rate of sucface r e n d is constant for a given degree of !urhlence and cm be
fepre~ented by sudiace age distribution fiuictions. While at the interface, m a s transfer
occm as though the liquid were stagnant and hfinitely deep and the rate depends on
the eqsure tirne, or rate of surfiace renewaI, S. The mass transfer coefficient is
related to this surface r e n d rate by:
Thirdly, the boundaxy layer theory is used to desaibe mass transfer for cases
where the velocity M e n t across the interface is substantial. For systerns involving
momentum, heat and mass transfer, here are tbree correspondhg boundary layas.
The thickness of the individual boundary layen are related to one anotha by the
following dimensionles grot~ps: momentum - Iç = 1, t h d - II, = N, and
mncentration - 4 = N,. For equimolar coiniter diffusion, the boundary layer
thickness is related to the panmeter 4 accordhg to:
Based on the Blasius soluîion for flow over a flat plate the ercponent F
theoreticai value of 0.33.
4 has a
For sulphur dioxide at 1523 K, the concentration boundary layer is smallest
followed by the thermal and the momentum boundary layes. A correlation of the
following type is consistent with boundary layer theory.
hilass transfer coefficients are often correlated by means of dirnensionless
number expressions. The most common parameter used for relating k, is the
Shmood nurnber for mass transfer, N,. For sphaical geornetry the definition is:
Since it is not always possible to separate the rnass transfer coefficik fkom the
interfacial area for expimental measurements, the Sherwood n u m k can also be
based on the d a c e area of an equivalent sphere.
Correlations for N, have beai developed by direct addition of terms
representing ûansfer by purey molecula. diffusion and tramfer by for& convection.
It c m be shown theoretically that the former shouid approach a value of 2. The
second t m is usually represented by the produd of the Reynolds n u m k (Re) and
the Schmidt numba (Sc). 'The Schmidt number is the ratio of momentum to mass
dBÛsivity.
Consequently, nearly al1 comlations for mass transfer fiom a sphere take the fom of
equation 46. nie value of the constants C, and x depend on the ranges of N, and
N, over which the correlation is applicable.
5.0 -rimental Work
5.1 Experimental Scope
The primary objective of this research was to perform laboratoxy sale
oxidation of copper-sulphur mattes under conditions of gas phase mass transfer
control. nie expairnatal system was made up of a vertical qlindricd crucible with
a ceramic lance i m m d into the melt. To investigaie orifice orientation, both open-
ended lances and closed-ended lances with a small horizontal hole nea. the closed end
wae used. Melts consisting of white metal ("as") and semi-blister (S saturated Cu)
were blown Lmda similar injection conditions. Intemittent melt sampling d o r
offw analysis was used to detemiine the degree of conversion and oxygen utilkation.
A pressure ûmsducer connected to the air supply was used to calculate bubble
Seguency and to chamcterize the gas flow reghe. The experimental conditions were
rnanipulated to produœ discrete bubbling and gas channeIling, since both of these
regimes have been observed in operaîing converters. Selected e-ents were
performed inside an x-ray imaging fumace to observe the dynamcs of bubble rupture
at the melt sufiace.
Table 5.1.1 lists the parameters that were rnanipulated to obsewe varying mass
transfer rates.
Table 5.1.1 - ExDerimental Parameters
II Gas injection rate
II Lance imasion @th
II Melt Composition
II Orifice orientaiion
'The resdts have been used to danonstrate the effect of the experimentai
conditions on bubble Sequency, oxygen efficiency and the gas phase rnass transfer
coefficient. The results of varying the melt composition and the oxygen concentration
in the injected gas were important in confirrning the rate controlling mechanism.
Numerous experiments were canied out with an inert gas blanket to investigate surface
-ion ocming d e r a gas bubble breaks away h m the liquid
Table 5.1.2 lists the aucible and lance dimensions used in the experimental
work The crucible diameter was chosen as the largest size appropriate for the
available fumace and the melt depth was limited by the crucible height and the
necessity for sdficient head space to contain splashing. The resuiting sample size was
about 750 g of white metal or lûûû g of semi-blister.
Table 5.1.2 - Crucible and Lance Dimensions
Prelimiraary experiments conducted by blowing air at 4 NUrnin into Cu,S
through a 2.0 mm diameter horizontal orifice at 1523 K exhibited splashing that could
not be contained by the crucible walis. Ceramic covers for the crucibles were
machined out of refktory brick with a hole drillecl through the centre slightly Iarga
than the lance diarneter, successfully containhg the molten metal.
The gas flowrate necessary to provide rneaningful d t s was calculateci using
two methods; based on the e-ed bubbling fÎ-equency to produce gas bubbles that
are close in diarneter to the tuyere depth and based on a modifiai Froude nuinber of
20 (sirnilar to a converter). 'The correspondhg air flowmtes are 1.2 and 10.1 Wrnin.
Both of these criteria provide some similarity with copper converters.
Dimension
crucible diameter
bath depth
lance submergence
orifice diarneter
Magnitude
55 mm
50 to 60 mm
O to 30 mm
2to7mm
5.2 Apparatus Set-up
A schernatic of the expimental apparatus is show in Figure 5.2.1. The
apparatus a n be broken down into the following sections; gas pretreatrnenc h c e
and miction charnber, measurement devices and gas pst-treannent. The setup of the
gas train was designed to provide mixing and to aeate the desired injection conditions.
Gas pretreatment involved filtering, drykg, oxygen removal and mixhg.
Nitmgen used for flushing the reaction chamber was passai through a drierite column
and then over titanium tumings at 773 K Air taken directly fiom the labomory
bench was pas& through glas wool for oil removal. ûxygen h m a cylinder was
mixed with the air in a beaded column and then passed through a drierite culurnn. A
swge tank was pl& in the injection gas supply line to prevent the pressure
fluctuations thaî arise due to bubbling Iiom disturbing the gas flowmeters. Al1 gases
were delivered to the reaction chamber via a cerarnic lance.
The fumace t- was maintaineci by an odoff switching controller
receiving a tempmtm signal h m a type R themocouple within the firmace and a
setpoint located on the controller dial. 'The melt t e q m a t m was measured by
inserthg a thermocouple down the caamic lance and holding the tip jut above the
orifice.
The arrangement of the fumace components is depicted in Figure A 2 1. The
melt tempemm is typically about 100 K lower than the temperature indicated by the
controller thefinocouple under expimental conditions (see Figure A1.4). ïhe
d o n chamber temperature is set by correlaiing with the fianace controller
temperatine and then fine nnied by direct measunment with a thermocouple directly in
the melt. The tempasiaire variation withh the crucible location of the reaction tube
was about I2 K, howeva this rapidly vanished once gas injection bem.
The measured variables were: gas flowrate, o f f w composition, orifice
diameter, lance immersion, bubble fkcpency and reaction chamber temperatirre. 'The
orifice diarneter was masured using a microscope both before and after a blowing
test The depth of immersion was meas& relative to the quiescent bath surîace,
which was detamineci by observing the lance position at which pressure fluctuations
began on the oscilloscope saeen. Gas flowrates were controlled by adjusting variable
area rotameters.
The sulphur dioxide concentration of the off- was measured by filling a gas
sarnple bottle with the fumace o f f w and then absorbing as H$Q in a 2% H a
solution. The bubble fkquency was measured by a pressure transducer ~ 0 ~ e C t e d to
the gas supply line irnmediately upstream of the lance. The pressure transduca signal
was sent to an oscilloscope to provide a visual trace of the pressure fluctuations, which
was photographed for later evaluation-
Gas p s t - m e n t was a necessity for dealing with the sulphur dioxide
producd The off' was first bubbled into a weak sulphuric acid solution followed
by a weak base to prevent the rnajority of the SQ produced fiom going up the
fùmehood
5.3 Equipment and Materials Specifications
nie main pieces of equipment used in this expimental work were: the firmace
and reaction tube, the crucible and lance, the pressure transducer/oscilloscope setup
and the o f f p scnibbing system The fumace containecl six spiral silicon carbide
heating elements, with a hot zone 140 mm in length The reaction tube was composed
of hi& temperame, non-stoichiometric mullite (closed one end) with the following
dimensions; 79 mm inside diameter, 89 mm outside diameter and 610 mm length.
The rnajority of the experiments were carried out in crucibles with an inside
diameter of 55 mm, an outside diameter of 63 mm and a height of 205 mm The
crucible material was hi& purity, hi& density dumina Two differait lances were
used in the experimental work Al1 horizontal injection tests were carried out using a
lance with an inside diameta of 5.2 mm and an outside diameter of 7.3 m m
Downward injection tests wae &ed out using this lance as well as a lance with an
insi& diameter of 2.6 mm and an outside diameter of 5.3 mni. Both lance sizes were
also composed of hi& punty alirmina
Al1 of the rotameten used in the expimental work were calibrateci using a
soap bubble colum with a gas volume of 5 L. This pamitted bubble residence times
between 30 and 60 seconds, rninimizing the human m r in t h e measurements. The
calibration cwes found in Appendix 1 contain data points that m e n t the averages
of five measurements.
Inert gas blowing ont0 the melt di was accomplished by enlarghg the
hole in the ceramic cover and Uiserting a 2.6 mm open en& alumina lance next to
the injection lance. The location of this secondary lance was also measured relative to
the quiescent bath sudace. A schematic of the crucible and lance anangement is
shown in Figure 5.3.1.
Refractory Cover
Alumina Lances
Crucibla
2 0 c m
ic 5.3.1 - Crucible and Lance -t S m
I I I I 1 I
1 I
The gases used in the experimental work were of the following purity; ultra
high purity oxygen (c0.0001 WûJ and high purity nitmgen (4.001 Y.9). In
addition, the nitmgen was passe. o v a titanium turnings to lower the oxygen content M e r .
I I
Head Spoce
'Ihe pressure transducer used was a S t a î h n @ mode1 PL283TC-2.5-350, which
measured the differential system pressure relative to ambient pressure. The range of
this transducer was O to 17000 Pa, providing a 1.6 Volt signal at full sale. Excitation
was provided in the form of a 6 Volt lantern battery. 'The tmnsducer output was
conditioned by placing a 1.5 Volt type D battexy in opposite polaiity with the low
voltage signal since the output had an ofkt of about 1.5 Volts at O Pa This aliowed
s&g the oscilloscope at a hi& sensitivity to obtain good resolution of the relatively
weak transducer signal. The maximum change in local pressure when forrning a 2
mm diameta bubble in Cu,S is less than 1200 Pa (4.005 V signal change). A diode
was placed between the transducer and the conditionhg battery to prevent any
electrical darnage to the transducer circuit. A circuit diagrarn is provided in Figure
Transducer E . . . Eimrre 5.3.2 - Pressure lectncal C m t Dia-im
The oscilloscope used to visualize the pressure fluctuations at the lance tip was
a Hewlett-PackardB mode1 1200B, with a maximum vertical sensitivity of 0.001 V per
full d e . The horizontal scan rate was typidly set at 0.1 to 0.3 seconds per full
screen, approximately one third of the bubble fkqmcy. Photographs were taken
using an e)qlsUTe tirne slightly less than the full scanning period of the oscilloscope.
The system t- was rnaintained at the target setting by monitoring the
t h m m u p l e inside the lance and adjusting the pwer -1 as necessary. This
rnaintained the system tempemhm reading witfiin +/-2 K of the target temperatrire.
Type R thennocouples (Pt-W13%Rh) were used for al1 temperature measurements
with an accinacy of +/-3 K, as specifïed by the supplier and conflinned by calibration.
Gas samples were taken by passing the offgas through a glas sample bottle
with a volume of 0.472 L. The gas sample bottle was sded after approxirnately 10
minutes of steady state injection. Upon completion of a test the gas sample was
injectecl into a 2% aqueous solution of H2Q using air as a carrier gas. ïhe
concenûation of SQ in the gas sample was determined by titrating the fomed
with a 0.5 M NaOH solution. This solution was piirchased from Fisher Scientific and
certified to be accurate within 0.005 M.
The gas absorption systan consistecl of a single scrubbing chamber, with a
glas fiit on the end of the gas inlet tube which extends to the bottom of the vessel.
This creafed a very high interfacial area to aid in oomplete~absorption of S 0 2
accordhg to the following reaction:
sQ?o + H 2 0 = H,SO,, (50)
Testing of this apparatus with a secondary scrubber proved that in excess of 99.8% of
the SC$ in the gas sample is typically captured in the first scrubbing unit Fukunaka
et ailg1 have used a similar setup for scrubbing gas streams flowing at 1.5 Urnin
containing up to 2W S Q into a 1% solution of H2Q and reported high accuracy
results based on the initial quantity of sdphur in their samples.
Cuprous sulphide matte was prepared synthetidly in the following manner.
Elec~rolytic copper turnings (YB.99%) were thomughly rnixed with USP grade
sulphur powder (r99.P) using about 10% in excess of the stoichiometric sulphur
requkment for Cu2S. The mixture was placed into a fîreclay crucible and allowed to
react inside a small pot fumace at 598 K for 1 hour. Accordhg to the vapour
plessine-temperature diagram for sulphur shown in Figure A3.1, at this temperature
the suiphur will melt and maintain a vapour pressme of about lûûûû Pa The reaction
betweai sulphur and copper proceded as a remit of the pool of liquid sulphur that
f o m in the bottom of the crucible, generaîing S, gas thai rises inside the aucible to
react with the copper lirming.
Afta this profedrrre was comp1ete the cmcible was ûansferred duectly to a box
fumace at 1473 K and the cli ,S was melted to produce a sample with higher bulk
density. Most of the excess sulphur bumed off in this stage and the resulting mattes
were close to copper saîurated Cu2S at 1473OC. If excessive sulphur burned O& a
srna11 bution of copper was found in the bottom of the aucible and was removed.
Typical assays for the synthetic Cu,S can be found in Table A6.1 in Appendix 6.
Sdphur saturated copper was prepared directiy in the experimental fumace by
charging electrolytic copper wire and synthetic Cu,S into the crucible. A 20% excess
of copper sulphide was used since some d p h u r is lost during the heating of the
system and any remaining matte on be reradily removed in the initial oxidation stage.
5.4 Procedure
&dation was carried out by injecting air or oxygen-enriched air into the melt
and sulphur was rernoved as SQ. The following data collection took place; injected
gas flowrate, % Q in injected gas, resacton c h b e r t- depth of orifice
immersion, % SQ in the offgas and the bubble fîquency. 'The concentraiion of S Q
in the offgas was determined by the method described above. nie bubble fkpaicy
was measured by photographing the oscilloscope screen with a camera exposure tirne
slightly less than the scanning period of the oscilloscope. Knowing the gas flowrate
and the t h e scale of the screen, both the bubble hquency and diameter were
calculated.
ExpmmentaI nins begdn by charging the appropriate rnass of copper sulphide
or copper and cupper sulphide into a crucible. A cgdmic cuver was placed on the
nucible and both were. placed inside a cold reaction tube. The lance was then lowered
into position just inside the hole in the cover and the reacîion tube was sealed with a
Mer cooled copper cap. The tube was then lowered into the cold fumace and power
to the fumace was m e d on. At this tirne the combustion tube was purged with
nitrogen flowing at 2.5 Umin for a d d o n of 10 minuies. This procedure was
typically canied out late in the day, ailowing the sarnple to reach the appropriate
tempaature for experiments by the next moming. Ody a small amount of oxidation
took place overnight, measured by absorbing the gas produced during the heatup
Oxidation experiments were commenced by starting the air/oxygen flow at a
predetermined ratio and total gas flowrate with the lance still above the molten
sample. The lance was then slowly lowered into the melt while monitoring the
oscilloscope screen. 'The first indication of pressure fluctuations was used as a
reference for the liquid level, and the depth of immersion was measured fi-orn this
position. The total melt depth did not change si@cantly durhg a single test. ûver
the duration of a series of tests the liquid lwel did drop by as much as 15 mm due to
the decrease in overall sample mass and increase in bulk melt density.
Mer the lance had beai lowered to a predetennuled depth of immersion, the
systern was monitored as it reached steady state. This was very rapid and after which
the necessary data was collected. 'This aitailed reading the rotameters, the immersion
depth scale and monitoring the system t e m . The oscilloscope screen was set at
an appropriate scan rate which was also morded, Two photographs were then taken
of the oscilloscope screen. Mer the entire gas system had b m purged with at least
fifteen volumes of offgas, the gas botele was seded, the lance was raised and the gas
injection valves were closed. 'The lance was Mly removed ffom the fùmace
occasionally to check for erosion or plugging at the orifice.
To insure maximum accuracy in the offgas analysis, the following procedure
was used. The scnibbing solution was prepared ahead of time in 2 L batches by
diluting technical grade H2Q (30 wt%) d o m to a 2% solution with distilled mer.
Afta methyl red indicator was added to the solution, it was titraid with 0.5 M NaOH
to the fust solid yellow adpoint. Wgas samples were then absorbed into about 0.25
L of this solution by purging a filled gas sangde bottle with air flowing at 2 Numin
for 5 minutes. ïhe resulting solution was then titrated once again with 0.5 M NaOH
back to the same yellow endpoint.
When converthg sulphur samahi copper, a melt sample was taken with a
quartz tube imrnediately afta each oxidation stage and the time of oxidation was
recorded A continuous record was kept of the amount of sulphur removed h m the
sample. When working with C&S, the sulphur inventory was monitored to maintain at
least 20 mm of the Cu$ phase below the orifice position A graphical representation
of the change in matte and overall melt depth with increasing desulphurization can be
referred to in Figure A3.2 of Appendix 3. The typical tamination point for
experiments was at 40% conversion of -S.
For ruos involving siilphw saturad copper, the sulphw invento~y was even
more important to prevent total depletion of sulphur in the metal. Based on other
researchers' wo* it is well hown that Cu20 will rapidly attack alunina crucibles,
likely due to its low viscosity and weaability towards refktoxy materials.
6.0 Experimental Results
6.1 System Characteristics
A number of prelirninary measurements were made to aid in characterizing the
exprimatal setup and in the mathematical treatment of the data.
ïhe sub-node chamber volume, rneasured as the volume of gas between the
orifice and the gas ssupply, was 3.34 L for nuis 1 through 10. The m g e tank was
removed h m the gas inlet line for al1 subsequent MIS, reducing the SutFnozzie
chamber volume to 1.08 L. This was done in an attempt to alleviate the problern of
tance plugging. However, since the sysiern was aiready operaîing unda constant flow
injection conditions, this goal was met with limited SUCC~SS. This change did not
affect the bubble fkquency characteristics of the system,
The pressure inside the gas sample bottie was measured using a m e r
manometer as a hc t i on of the gas flowxaîe, for incorporation into the calculation of
the total quantity of gas in the sample bottle. Figure A1.6 illusûaks the smail
increase in absolute system pressure as the gas flowrate increases, and the resulting
impact on the above caiculation is minimal. The gas inside the sample bottle was
always found to be at room temperatue as a d t of the copper coolhg coi1 attacheci
to the fumace gas outlet port.
The tempahm inside the lance just above the orifice was also rneasured as a
fùnction of gas flowrate. As is shown in Figure A1.6, the gas is essentially preheated
to the system t m as it flows down the lance for the range of gas flowrates
studied. This removes any doubt in calculating the bubble volume based on the
system temperatme. 'The ultimate gas temperature inside the growing bubble is
somewhat higher due to the e x o t h d c reaction betweai the gas and the melt.
6.2 Experimental Data Tables
The raw experimental data collected dining the course of the expiments was
combined with the bubble £kquency data obtained h m analyzhg the photographs of
the oscilloscope saeen and has been tabulated in Appaidix 5. lhese daîa tables also
contain the percent oxygen consumed dcuiated h m the offw SQ concentration
and the rectant gas Q concentration For e>cperiments perforrned with suiphur
saturatecl copper, the sulphur and oxygai assays are also included and have been used
together with the offw analysis in caiculating the oxygen co~lsu~llption.
Chernical analyses of selected melt samples taken over the course of the
e>q>erimental work are tabulated in Table A6.1 l~cafed in Appendix 6.
6.3 Spreadsheet Calculations
The experimental d t s have beai used primanly to evaluate the mass transfer
coefficient in the gas phase durhg each stage of gas-liquid contact. A varïety of
spreadsheets have b m constructed to perform both direct and iterative dcdations.
Appendÿr 10 contains detailed flowcharts illustratuig the caldation methodology and
the spreadsheets used in the following calcdations; the mass tramfer coefficient during
the bubble growth stage (iteraîive), the rnass û=ansfa coefficient during the gas rise
stage (direct) and the mass transfer coefficient - interfacial area product during the
bubble rupture stage (iteraîive). These two temis could not be separafed for the
bubble rupture stage due to the large uncertaixlty in the intafaciai area
6.4 Graphical Results
'The measured experimental results, namely the bubble fiequency and
percentage oxygen consumption, have been grapheci to illustrate their variation with
changes in the system conditions. 'These d t s can be referred to in the Figures
located in Chapter 7. The caldated mass ûansfer coefficients have also been
represented graphically and are l m e d in the following section
The rnelt and offgas analyses for the experiments conducted with sulphur
satumted copper are also m h e d in section 7, h g with the calculated ovgen
ço~l~umption. X-ray images of the melt surfiace during gas injection are found in
Appendix 7. The resdts of the inert gas blanket tests are illusbrated in Appendix 8, by
plotting the oygen efficiency as a hc t ion of the top gas flowrate. Appendix 9
wntains graphs thaî illustrate how the consumption to driving force ratio and gas
residence time Vary for each stage of gas-liquid contact as a fùnction of gis flowrate.
A sumrrÿiry of the expimental resdts is plotted in the five graphs l~cafed in
section 7.9. These graphs illustrate the distribution of o q y p uîilization between the
three stages of gas-liquid contact, and are r e f d to in earlier sections of Chapter 7.
7.0 Jlïscussion of Results
7.1 Bubble Frequency Measurements
The expimental injection conditions al1 led to constant flowraîe injection, as
evidenced by the bubble ikeqwncy range of 15 to 35 tIz Although the subnozzie
chamber volume was reduced fkom 3.34 L to 1 .O8 L afta the first 10 expaimental
nuis, this only served to decrease the capacitance number, rnaintaining constant
flowrate conditions. Assimiing a contact angle of 105" between Cu3 and Ai&, the
caidated dimensionles capacibnce number was in the range 20 to 61. These values
would indicate constant p-gsure injection conditions, therefore the a d contact angle
betweai the rnatte and the lance rnay have been much closer to 180".
The oscilloscope s a e e n photographs used to extract the bubble kquency and
size data did not always exhibit the classic bubblhg pressure d i b c e illusfrafed in
Figure 3.3.2.1. For d o m d facing nozzies, the pressure peaks were not always
evenly spaced, which is shown in Figure 7.1.1. This is likely due to the influence of
residual pressure in the upstream gas chamber. This type of bubble interaction is
illustrated in Figure 3.3.2.2, and aui lead to a cycling in the bubble volume as
observeci in îhe photograph in Figure 7.1.1. The bubble volume cycles were found to
repeat themselves every 2 or 3 bubbles and the ciifference in volume between the
largest and smallest bubble in the cycle was up to 30%.
Egwe 7.1.1 - Experirnent.1 Ressure Trace: Downward Facirg N o d e mun 17-61
The measured bubble fkquencies conf'rrmed that dl the acperiments were
carried out in the constant h p e n c y regirne for bubble formation. Thus the above
changes in the subnozzle chamber volume had no effect on bubble formation.
Ideally, the volume is expected to increase lineady with increasing gas flowrate
(constant frequency), evidenced by the order 1.0 dependence of bubble volume on gas
flowrate in equation 1. The measured bubble volumes for an open-ended lance with
intemal and exiemd diameters of 5.2 and 7.3 rmn respectively have ben correlated
with the gas flowrate and the extemal diameter accordhg to the form of &on 2.
A least squares regression analysis leads to the following expression:
Figure 7.1.2 contains the expimental equivalent bubble diameters dong with
the regression Iine. The maximum observai emr between the measured and
conrelaiecl diameten is 6% conresponding to an error of 19% in bubble volume.
Gas Flowrate (cm3/s at injection conditions) * . Fi-= 7.1.2 - Vanahon of FM valent Bubble Diameter with Gas F1owr;rte
m 'Ihe r n d bubble volumes for a 3.1 mm horizontal orifice exhibit a slightly
higher dependence on gas flowmte, indicating l e s variation in the bubble fkpency.
Equation 52 is plotted in Figure 7.1.3 dong with the experhental data
2 ! 100
5
Gas Flowrate (cm3/s at injection conditions)
1-mrre 7.1.3 - Vanation O . .
f Fquivalent Bubble Diameter with Gas Flowrate
(3.1 daneter horizontal orificel The variation of bubble kquency with orifice diameter for downward facing
nozzles was found to exhibit a higher order dependence than is typically reporteci in
the litaahrre for horizontal or vertical nozzies. Based on the data for a 5.4 mm OD
n o d e and a 7.3 mm OD nozzle, the dependence on orifice diarneter is proportional to
a power of 1.3, however if the intemal diameter for these two nozzles is used this
parameter assumes a value of 0.6, rnuch closer to the theoretical value of '/z This
indicaies that the intemal n o d e diarneter rnay be more appropriate in characterizing
the effect of nozle diameter on bubble fkquency for downward injection in the
c o i i s t kquency regime. - Bubble fkquency was found to decrease only slightly with deaeasing orifice
diarneter for injection through a horizontal orifice. As ilIustrated in Figure 7.1.4, the
average bubble fkquency for a 2 mm orifice is 27 HZ while that for a 3.5 mm orifce
is 22 Hz This is attributal to spreading of the bubble dong the lance as it grows due
to the non-wettability of CL@ on alumina 'The maximum spreading diameter
calculateci kom equation 33 is 95 mm, and is independent of the orifice diameter. A
slight increase in bubble fkquency with decreasing orifice diameter is not une-
since the increased orifiœ velocity muid inhibit spreading of the bubble base (neither
orifice is close to maximum spreading in the expeximental work).
Air into Cu2S 1 .O cm immersion
1523 K 1 Orifice Oiameter
. -
Fi-mire 7.1.4 - Variation of Bubble Freqllency with Gas Flowrate and Orifice Diameter
The effect of the remahhg expimental conditions on bubble fkquency will
be discussed in the sections that follow.
7.2 Effect of Lance Immeision
hcreasing lance immersion had a negligible effect on bubble fkquency, for
immersions of at least 5 mm (see Figures 7.2.1 to 7.2.3).
O 0.5 1 1 -5 2 2.5 Lance Immersion (cm)
7.2.1 - Vmatim of Bubble Freauençv with 1- Imersion ( . .. -5.2 mm nozzle)
8 - -
.
15 r I rn rn rn rn l I a
O 0.5 I
1 1.5 2 2 Lance Immersion (an)
I Open ended lances
2.0 NUrnh. 3.1 mm
Lance Immersion (cm)
of I ance Immersion - Al1 immersion depths were meanired relative to the lance position where
pressure distlnbances were ht noticed on the oscilloscope screen. ï h i s location has
been designated as an immersion depth of O mm. At this position the bubble
kcpency was fotmd to inaease substantially, as indicated in Figure 7.2.2, since the
injection conditions were in transition between top blowing and full submersion. The
shape of the pressure disturbance was significantly differait for a O mm imrnasion as
well. Figure 7.2.4 illusûates that at a depth of 10 mm the pressure trace is sirnilar to
classic bubbling, while that corresponding to a O mm immersion is close to
channell hg.
Oxygen consumption is also a very weak fiuzction of immersion depth. Figures
7.2.5, 7.2.6 and 7.2.7 illustrate thaî an increase in the immersion depth of 10 mm
results in an increase in Q uîilization of 1 to 2 % depending on the injection
conditions. However, this is the increase in utilization observed at the end of the
bubble rupture process, and must be indexed back to the bubble rise stage. This is
done by making use of the fact that the ratio of the m a s transfer rate to the driving
force for rnass transfer for the entire bubble ruptvre stage is independent of the
immersion depth. This leads to the following relationship in terrns of the partial
presme of oxygen:
=CORS t a n t ' A '4 ' 1 ogmean
This can be simplified to yield ir1(P~,/P~3~ = in(P&'Pa&, h e r e the
subscripts b and e refer to conditions at the beginning and end of the bubble rupture
stage, and 1 and 2 refer to two different depths of immersion. ?le calculated
ciifference in P,, for the two immersion depths is the true ciiffierence in oxygen
utilization attributable to this change in the immersion depth.
This dcuiation results in an observed oxygen utilization change of 1Ydrnm
componding to an a d change of 40/dmm. The quantity of oxygen trzinsf-
durhg the bubble rise stage does not Vary greatly with the injection conditions, and is
an indication that the gas isvels through the melt in a sùnilar manner regardless of the
original bubble size or injection conditions (orifice diameter, gas flowrate).
1 O0 5 2 mm nonle - Air into Cu2S
Lance Immersion (cm)
J&UR 7.2.5 - Vanaîlon of Oxygen C o ~ u m ~ t ' o n 1 with ]Lance Imers' ion . *
M
Lance Immersion (cm)
Fipure 7.2.6 - Variation of Oxveen Consumption with Lance Immersion
injection Conditions
1 2 5 NUmin. 2 mm
2.1 NUmin. 2.8 mm
3.35 NUmin. 3.1 mm
1.65 Numin, 35 mm
90
Y Open ended lances
-
A
Injection Conditia + 125 Numin. 3.1 mm + 2.0 NUmin. 3.1 mm ++ 1% Numin. 2.6 mm
43 - 3.1 NUmin. 2.6 mm
Air int0 Cu2S 1523 K
Lance Immersion (cm)
Figure 72 .7 - Variation of Oxvgen C~nsumption with unce l m m e r s i o ~
85- C O .- C
- 3
801 C
C a a % ,x 75
(varyina sometry. g&lowrate and -gnrichment)
-
70 1 1 1 1 1 1 1 1 1
O 0.5 1 1.5 2 2.5
Lance immersion only affects the residence time of the gas in contact with the
melt durhg bubble rise. The caldateci increase in oxygen consumption with
increasing immersion has been used in constnicting the bubble rise portion of the
graphs in Figures 7.9.1 through 7.9.5. Refming to these graphs, it is clear that bubble
rise does not contribute greatly to the overall oxygen mnsumption, and is not an
important aspect of the overall m a s transfa characteristics of the system 'This is not
unexpected since the gas residence tirne is the shortest in the bubble rise stage and the
gas phase is also the least turbulent.
73 Effect of Temperature
The e f f i of injection tanperahrre on bubble fbquency is vay slight, within
the experimental m r of its masurement. Referring to Figures 7.3.1 and 7.3.2, there
is no signifiant change in the bubble fkquency for both a 5.2 mm open-ended lance
and a 3.1 mm horizontal orifice.
Air into Cu2S 1 .O cm immersion
O 1 2 3 4 5 6 Gas F lowrate (Numin)
Gas Flowrate (Numin)
45-
35-
25-
-
15 O
. . 7.3.2 - Vanation of Rubbk F w c y with Gas Flowrate and Temperature
Imm orifice)
One series of data points in Figure 7.3.2 for the 3.1 mm orifice at 1473 K
illusûaîes a dramatic increase in bubble kcpency as the gas flowrate is increased.
ïhis effect may be due to narrowing of the orifice, since it was completely blocked
afkr the experiment performed at the highest gas flowrate. As solid Cu and Cu,S
begin to plug the orifice, they change the system wettability characteristics and the
orifice diameter. If the orifice becornes weaable with respect to molten Cu,S, radial
spreading of the bubble base is les likely to take place, resulting in srnaller bubbles
and a higher bubble fkquency.
Based on equation 1, it is expected that the bubble volume should increase
slightly with increasing tempaahire, due to an increstse in the gas flowmte at the
injection conditions. ï h i s would be o h e d as a sligFt dea~ase in the bubble
kquency. Howeveq since the gas temperature inside the bubble is increased by the
same factor, a anstant observed fkpency does çorrespond to a caiculated increase in
bubble volume.
Air into Cu2S 1 .O cm immersion 1-1 3.1 mm onfice
m
1473 K
1573 K
m
-4-
O - 4 + + C1 - a m i i (
* +
+ 0 , + + I
* I I I 1 1
2 1
4 6
The efféct of tempaatlire on oxygen consumption was found to be insignifiant
over the range 1473 K to 1573 K At 1623 K the oxygen efficiency increasesy to a
lesser extent for a 3.1 mm horizontal orifice and very sharply for a 5.2 mm downward
nozzle. At 1473 K some of the m d oxygen consurnptions are significantly
lower, although these data points correspond with higher bubble fiquaicies due to
orifice plugging, as explained above.
Compazing Figures 7.9.1 and 7.9.4 which illustrate the stageWise oxygen
conswipton for a 5.2 mm downward n o d e at 1523 K and 1623 K, the increase in
oxygen consumption appears to be concentratecl in the bubble nrpture stage. The
bubble gcowth stage also exhibits a slight increase in oxygen efficiency, although thk
can likely be amibuted to the effect of t- on oxygen diffusivity. A 100 K increase corresponds to a 10% increase in the gas phase diffusivity (Dm cc T'a5). 'This
is approximately the relative increase in oxygen comumption observed in the bubble
growth stage between the two temperatlireS.
The abrupt increase in consumption observeci in the bubble rupture stage at
1623 K could be an indication of a change in the oxidation mechanism. It is generdly
agreed that the overall mnverting chemisûy is represented by:
C u 2 S + Q = 2 c U + S Q (54)
However, the possibility for the forniaton of Cu,O as a short lived intermediate is still
king debaîed. Copper oxide fomiation is dikely to take place in the presence of
copper sdphide, since Cu2S will preferentidly consume any available a. The most
probable location for depletion of Cu3 is in the dispersion of fine dmplets above the
melt.
Based on experimental studies in wat&%d mokn ironp], and making use
of the following relationship, the size of the Ch2S droplets formed in the initial stage
of bubble rupture are on the order of 0.00 1 5 mm
d d r , = { 5 (55)
The terminal velocity of these droplets is rnuch lower than the gas rise velocity in the
crucible, and consequmtly the clroplets are Camed upwards at approximately the gas
velocity. The initial droplet trajectory will detamine where it strikes the crucible wall
or mm.
The Reynolds n u m k relative to the coflowing gas for these droplets is very
srnall, thus the Shmood number is equal to the minimum lirniting value of 2. This
corresponds to a mas transfer coefficient of 325 rnk Therefore a dmplet containing
initiaily pine Cu2S will becorne completely depleted of sulphur in 170 ps if the
reaction rate is controlled by gas phase diffusion For an injection f lome of 4
Numin the maxirnum residence time for such droplets in the ovalying gas phase is
3 -3 S. In addition, it is Iikely that some of the droplets will initially be sulphur
deficient since they origjnate in the thin liquid film in contact with the bubble pnor to
its rupture. This liquid film is probably a mixture of Cu,S and sulphur saturateci
-Pa-
Once a droplet has becorne depleted in sulphur, fùrther contact with oxygen
will d t in copper oxide formation according to the following reaction:
4cu+Q=2cu20 (56)
The Cu20 formed in the above reaction will be consumed by the following reaction as
soon as it cornes into contact with Cu2S.
2Cu,O+C@=6Cu+SQ (57)
This sequence c m lead to S Q partial pressures greater than 101325 Pa, resulting in a
violent reaction, as explained by the followùig analysis.
Figure 7.3.3 illustrates the variation of S Q partial pressure and Cu20 activity
with oxygen potential for d o n s 54, 56 and 57 at 1623 K The dotted line in
Figure 7.3.3 is for reaction 54 and the solid line is for reaction 57, assuming unit
activities for Cu and Cu-$. If the converthg chernisûy is conttolled by reaction 54,
the partial pressure of SQ is lirnited to 101325 Pa, corresponding to an oxygen
potential of 0.71 Pa and an equilibrium activity of 0.1 for Cu20. At this activity, the
partial pressme of SC& for reaction 57 is also 101 325 Pa. However, if Cu,S is
depleted locally, it does not dictate the converthg chemistry and the activity of Cu20
may increase, for example to 0.4. 'Ihis corresponds to a higher oxygen potential and a
partial pressure for SQ of aboui 1520000 Pa.
mire 7.3.3 - Variation of SC& Partial Pressure and Cu20 Activity with
Ihe abrupt influence of temperature at 1623 K rnay be as a result of a kinetic
effect that enhances the extent of reaction 56 or a physical effect thai increases the
extent of reaction 57. A possible explanation of the latter is the influence of a higher
temperahire on the transfer of Cu20 back into the melt after it has beai formed in the
dispersed phase.
Some of the fine droplets resulting h m mptured bubbles strike the crucible
wall and cover where they accumulate until forming a large enough drop to run Sack
into the bulk melt. If the local tanpetrihrre is lower than the melting point of Cu20
(1508 K), the subsequent d o n with will take place on the aucible wall above
the melt. However, if the C h 0 mnahs liquid, it a n ru. down the aucible wall and
react with Cu,S on the surface of the buik melt This will provide turbulence at the
melt surfâce and enhance SUTface reaction. 'The aucible wall temperatrae above the
rnelt is lower than that of bulk rnelt, as seen in the temparihae profile in Figure AIS.
7.4 Effect of Gas Fiowiate
The idluaice of gas flowrate on bubble Wency has ken discussed in
section 7.1 and will not be discussed firrther in this section nie effêci of gas flowrate
on oxygen consinrqtion was found to depend on lance geometry and tempaature.
Figure 7.4.1 illustrates the variation of oxygen consumption with gas flowrate
for a 5.2 mm diameter downwad facing nozzle. Over the tempitmz range 1473 to
1573 K, the oxygen consumption decreases with increasing gas flowrate, up to a
criticai gas flowrate. Beyond this point, the oxygen cunswiption be@ to increase
and appears to be appcoaching a limiting value. For a 5.2 mm ID nozzie, the
transition occm at about 2.5 Wrnin, wtiereas for a 2.6 mm ID nozzle this value is
about 1.7 Numin. At higher temperahtres, this trend is only slighty apparent.
. . i m 7.4.1 - Vanation of k g e n C o m t i o n with Gas Flowrate and Temmatme
The explanaiion for this behaviour can be derived h m Figure 7.9.1, which
separates the oxygen consumption into the three stages of gis-liquid contact for the 5.2
h
90- C O .- + d
E 3
80- C
8 - t 0 m )r
i; 70-
-
60
mm ID node. nie consumption of oxygen in the bubble p w t h stage follows a
k ++ m + + m
I %€ +
I m
t + + + - - mf p&izr] 9 1473 K
Air into Cu2S 1 .O cm immersion 5.2 mm noule 1623 K
1 I a 1 1 1 1 1 1 1 1
consistent downward trend as the gas flowrate is increased, but it is in the bubble
O 1 2 3 4 5 1
Gas Flowrate (NLImin)
rupture stage where the increase in oxygen COI]SUII~P~~O~ is observed
It is expxted that consumption during bubble growth shouid demase with
increasing gas flo- since both the gas velocity tfuough the orifice and the bubble
diameta increase. nie increase in oxygen coflsu~llption in the bubble rupture stage
can be explained by an increase in the qwntity of liquid matkirnetal ejected into the
dispersion zone as well as a larger spout zone. 'Ihe mechanism of expansion of the
spout zone will be discussed in later sections.
Both of these phenornena resdt in greater interfacial area and more turbulence
in the bubble rupture stage. This results in inQeased consumption in spite of the fact
that higha gas flo~rafes result in a proportional deaease in the gas residence tirne. It
is also possible that increased splashuig reSuiting h m h i g k gas flo~rar.es enhance
the formation of su££iciently large droplets on the crucible wall that will run back into
the melt, mlliimizing the absorption of CuzO into the crucible.
For a horizontal orifice, there is no enhancement in oxygen consumption at
higtia gas flowrates, illu~frated in Figures 7.4.2 and 7.9.3. The oxygen consurnption
taking place in the bubble rupture stage fdls off slightly as the gas flowrate is
increased This must be as a r d t of les splashing into the ovedyïng gas phase and
lower expansion of the spout zone, compared to the downward k i n g nozzle.
Splashing could be reduced by the gas flowing in an unstable channel dong the lance,
resulting in less fiquent bubble ruptures at the liquid surface. Since the lance
rnaterial is non-wetting with respect to Cu$, the bubbles are iikely to remain attached
to the lance wtien fomed at a horizontal orifice. I f the gas bubbles rernain attached to
the lance during their ascent to the surface, disengagernent of the gas fiom the liquid
will proceed more rapidly, limiting expansion of the p u t on the liquid surface. For a
downward facing node, the 90' angle a . the end of the lance increases the likelihood
of conqilete detachment at the end of the p w t h stage.
The pressure trace photographs for the 3.1 mm horizontal orifice also suggest
that gas channelling may be taking place. The pressure trace shown in Figure 7.4.3
illustrates a sharp second peak just prior to detachment of a bubble. This is an
indication that a comecting tube is formed just after detachment of the bubble base
h m the orifice. Figure 3.4.3 illustrates three scenarios where a sbarp supplemental
peak corresponds directly to this phenornena. 'This connecting hibe d d provide a
pas channel to the liquid d a c e .
100 Air into Cu2S 1 .O cm immersion 3.1 mm orifice
75 ! l I 1 4 l
O 2 4
Gas Flowrate (NUmin)
fice (Run 3-71
7.5 Effet of Lance Geometry
As has been mentioned in sorne of the above sections, significantly diffèrent
expximental resuits were observeci for a horizontal orifice and a downward facing
node. ïhe bubble kquency was f o n d to be a weak hct ion of the horizontal
orifice diarneter and close to inversely proportional to the outer n o d e diarneter for a
downward facing lance. In the bubble rupture stage the lower oxygen consurnptions
obsexved for a horizontal orifice are atîributed to decreased splashing arising fkom gas
channelling. The mass transfer measurements obtained in the bubble growth stage
could also be interpreted as resulting h m gas channelling.
Consider the bubble growth stage for air injected at 3 Numin through a) a 5.2
mm downward fxing n o d e and b) a 3.1 mm horizontal orifice. In both cases the
bubble Gequency is about 21 Hz, so the bubble s k is the sarne. Referring to Figures
7.9.1 and 7.9.3, the oxygen consumption in the growth stage is around 55% for both
the orifice and the node. However, the srnaller orifice lads to an orifice Reynolds
number of about 545, compared to a value of 325 for the larger nozzle.
It is expected thaî the mass transfer coefficient in the bubble growth stage
shodd be proportionai to the orifice Reynolds number to some positive power. Since
the hi* Reynolds number for the horizontal orifice does not lead to a higher
consumption of oxygq sornething must be occuxring that is inhibithg m a s transfer
in the gas phase. ï h i s could be due to channelling of the gas that entas the bubble
just pnor to detachment, which results in some of this gas bypassing the bubble
growîh stage.
7.6 Effect of Oxygen Enrichment
Oxygen entichent experiments were carried out at a constant total gas
flowrate of 2.0 Wmin with both a 3.1 mm horizontal orifice and a 5.2 mm
downward facing nozzie. Figure 7.6.1 illustrates the effect of increasing the injected
gas oxygen content on the bubble fkpency. It was expected that bubble formaiion
would not be significantly affected by oxygen enrichment, however this graph
illustrates that increasing the oxygai content h m 21% tu 60% results in a 25%
deaease in bubble Seguency for the nozzle and 15% for the orifice.
'The reason for this phenornenon is unclear. 1ncrea~ing.the oxygen content of
the injected gas increases the m a s transfer rate as a lesult of a higha driving force.
'Ibis could lead to changes in the oxidation mechanism. I f sulphur is depleted locally
at the bubble surfàce, ooxidation will pro& with the formation of copper oxide. The
copper oxide will react with copper sulphide afkr e g with the buk melt. The
SQ evolved fiom this -ion rnay form a separate bubble fiom the injected gas,
resulting in much srnaller bubbles attachai to the orifice during bubble growth. This
would be expected to decrease the bubble fiequency: such that the a d bubble
volume at detachment h m the orifice is unchanged.
Altematively, increased oxygen enrichment rnay change the contact angle
between liquid rnatte and the alitmina lance. I f this lowered the wettability of the
rnatte ont0 the lance, the bubble size would increase, lowering the bubble kquency.
Figure 7.6.2 illustrates an increasing trend in meaired oxygen consumption
with increasing degree of oqgen auichrnent in the injected gas for both the lance and
the node. Refaring to Figure 7.9.5, the breakdown of oxygen consumption into the
stages of gas-liquid contact for the 5.2 mm n o d e illutrates that a small portion of
the increstse at higher enrichment levels is obswed in the bubble growth stage, with
the balance in the bubble rupture stage.
15 1 I I I b I I I I I
20 30 40 50 60 1
% 02 Injected
30
- n N z
25- O t Q) 3 rn - 22 IL al
20- .Q 3 m
7.6.1 - Vanation of Bubble F-cy with û,,chment in hjected G a . .
If the i n d coflsumption of oxygen is also attributable to a localized
increase in te- at the gas-liquid interface, this would explain why more
cu2s 1523 K 1 .O cm immersion Total gas flowrate = 2.0 NUmin
5.2 mm (OE)
9
+ -+ m
I 4-
+ + m
+
signifiant effects are obsmed in the rupture stage. DLiring bubble growth, the gas
phase is in direct contact with a large m a s of liquid copper and copper sulphide. The
hi& thermal conductivity and heaî capacity of these iiquids creates a large thermal
mass that will dissipate most of the heat generaîed at the interface.
70 1 I 1 I 1 I I I I 1
20 30 40 50 60 1
% 02 lnjected
1 O0 -
g5-
C
90-
E 3 cn c 85-7 O O d ' 80- 8
75-
. . & & p r 3 p r 3 e ~ l 1 c k x ~ u m ~ t * ion wth C& h c h m e n t in Iniected Gas
In the bubble rupture zone, the s d l liquid droplets have a lirnited heat sink
effect, consequently the gas-iiquid interface will be hotter. The mechanistjc effects
that could arise h m increasing temperature in the bubble rupture zone discussed in
section 7.3 apply in thk section as well.
An alternative explanation for the increase in oxygen consumption at higher
IeveIs of oxygen enrichment is the localized formation of Cu20 in the bubble rupture
zone. Higher gas phase mas tramfa rates increase the Iikelihood of copper oxide
formation. This could increase the overall oxygen cofl~umption as a result of an
inaease in the extent of reaction 57. SufEciently hi& gas phase mass transfer rates
could even lead to oxide formaiion in the liquid spout, which would result in explosive
Cu2S f523K 1 .O cm immersion m
Total gas flowrate = 2.0 NUmin + I
I + m ? +
5.2 mm (O€)
conditions resulting b r n d o n 57 directly on the fk liquid d a c e .
A third explanaiion is based on the theory of sufixe tension eEects in the
oxidation of copper matte. I f Marangoni effects are present, increasing the oxygen
concentration in the injected gas may increase the magnitude of these forces, leading
to increased turbulence at the gas liqyid interface.
7.7 Effect of Orifice Diameter
'The effect of orifice dimeter on bubble fkquency has been disnissed in
section 7.1, and this section will attempt to bring together the obsexved effects on
oxygen consurnption. Refening to Figure 7.7.1 for open ended nodes, there is a
signdicant increase in oqgen mnsumption when the nozzle diameter is increased
h m 2.6 mm to 5.2 mm, particularly at low gas flowraîes. At higtier gas flowrates the
difference is not as large.
7.7.1 - Vanagion of 0 - r ~ Consurnption with Gas F * . lowrate
1 00
- n
C 90- c O .- u - i? 3
80- C O O C
- a a %
70- 6 -
60
Figures 7.9.1 and 7.9.2 ilk~strate that oxygen con~umption is only slightly
Air into Cu2S 1523 K O
o o O O O O
CF3 O c 0 u
O
a O = @ A 0 a
A
piz%Gq * A
5.2 mm (OE) A
1 1 1 1 1 1 1
srnaller in the bubble growth stage for the srnalla node, while in the bubble rupture
stage it is sigrilficantly smalla. The lower comumption in the growth stage will be
O 1 2 3 4 5 I
Gas Flowrate (Numin)
dealt with in section 7.1 1.1 whai discussing mass transfer coefficients. The
substantially Iowa oxygen consumption in the rupture stage indicates that when
srnaller bubbles nrptlrre at the surfàce of a liquid, les reaction takes place in either the
spout zone or the dispersion zone.
The effect of orifice velocity can be seni in the Figure 7.7.1 as well. To
achieve the same orifice velocity, a gas flowraîe foiir times greater is requred whai
using the 5.2 mm diameter n o d e (CO@ to the 2.6 mm diameter node). Under
conditions of equivalent orifice velocity, both the 5.2 mm and 2.6 mm nodes result
in the same extent of oxygen utilkition during bubble g . w h
Although the srnalier bubbles created by the 2.6 mm n o d e will result in a
srnaller diameter liquid film just prior to ruphring (the source of the fine droplets), the
fieqyency of bubble rupture at the liquid surfàce is almost double tbat for the 5.2 mm
nozzle. ?hm the quantity of fine droplets ejected into the ovalying gas phase should
not be sigriificanîly different for the two nodes. Therefore, the s k of the liquid
spout must be sigrilficantly smalla for injection through a 2.6 mm nozzle. This a n
be explained by smaller bubbles rupturing fasta than larger bubbles after the omet of
expansion of the spout zone. Assuming that the expnded spout is compised of a
f&ly wide size distribution of bubbles and the srnaller bubbles escape fiom the
expandeci spout quicker than larger bubbles, bubbles generated by a srnaller nozzle
will escape fiom the spout quicker, decreasing the spout volume.
Tnierefore the difference in oxygen C O I ] S U I T I P ~ ~ O ~ in the bubble rupture stage is
probably attributable to a decrease in the interfacial area in the spoa zone. At higher
gas flowmtes the bubble frequency for the 2.6 mm nozzie was found to decrease
slightly, unlike that for the 5.2 mm node. This will have the effect of increasing the
spout zone for the smaller node, and explains why the difference observeci between
the 2.6 mm and 5.2 mm nozzles is not as great at higher gas flowmtes.
'Ihis would explain why the addition of a srnall amount of stimng gas in the
work of Alyaser and Brimacomberu] did not increase the degree of oxygen
consumption. The stirring gas flowrate was oniy 0.08 NUmin, wtiich pl& the gis
injection in the constant bubble size regime. This small increase in the gas flowrate
was insufficiait to promote expansion of the spout, therefore the interfaciai area was
essentially unchanged and the extent of reaction did not increase.
As discussed in d o n 7.1, the orifice diarneter has relatively little effect on
bubble k q e n c y for injection through a horizontal orifice, for orifices ranging ffom
2.0 mm to 3.5 mm in diarneter. It was also observai thai the oxygen consurnption
was essentidy independent of the orifice diameter, since the bubble diarneter was
nearly the same (see Figure 7.7.2).
and Orifice Diameter (2.8. 3.1 and 3.5 mm hori7,gntaI orifices)
1 O0
-
90-
-
However, a s d l a orifice diameter does lead to a larga orifice Reynolds
Air into Cu2S 1523 K
m - i-
+ + % +
36 + M I +€
?C; +
nurnber, which wouid be expected to inaease the oxygen collsumption d u ~ g bubble
R + x
a x
2.8 mm 70
3.1 mm
3.5 mm
60 1 1 1 1 1 1 1 1 1 1 i
O 1 2 3 4 5 6 Gas Flowrate (Numin)
growth. The lack of increase may be related to the presence of gas channeIling, discussed in previous sections. S d e r orifices lead to inaeased gas velocity in the
orifice. This is iikely to increase the degree of channeIling, by means of cormecting
tubes that are able to project further into the W. Thus the effect of increasing
orifice Reynolds numba may be ne@ by more signifiant gas channelling.
To establish the importance of mîxing in the liquid phase, and to confinri gas
phase control in the e>rperiments perfonned with WS, three experimental runs were
conducted by starhg with copper containing sulphur at the solubility lirnit. At 1523
K the solubility of sulphur in molten copper is about 1.2% by weight. Al1 three nins
were c&ed out using a 5.2 mm downward n o d e at an immersion of 10 mm and
with a gas flowrate that remained constant during a single m.
Figures 7.8.1, 7.8.2 and 7.8.3 illustrate that the o f f p SO, content remains
constant at the same value o b s d for Cu$ with decreasing sulphur content in the
. melt, down to quite a low sulphur level. At this point the evolution of SQ decreases
sharply and oxygen begins to dissolve into the rnelt. This change is quite abrupt and
uidicates a rapid ûmsition fkom gas phase control to Iiquid phase control. There aiso
exists a short period of mixed phase diffusion control. The point at &ch the
transition fiom gas phase control to mixed phase control occm depends to some
extent on the gas flowrate. Over the flowrate range studied (1.36 to 4.0 NUmin), this
transition takg place h m 0.4 to 0.8% sulphur in the melt.
Blowing time (min)
1 S in melt * OinmeR S02inoffgasl
7.8.1 - Vanation of Me . . lt and Offgas rnvs i s wth Rlom . . p Time
- -
Blowing time (min)
1 S in met * O inmeit Y ~ 0 2 in offgas 1
Blowing üme (min)
1 0 Sin meit * O in me& S02 in offgas 1
From a processing point of view, desuiphrirization canied out with a Iowa gas
flowrate is more desirable, since the sulphiir target for the blister copper can be
achieved at a Iowa oxygen content, reducing the refhing CO&. However, this is
ofk t by longer desulphurization blows. The following table surnrnarizes the
~ i t i o n points in the d e s u i p h d i o n expiments
Table 7.81 - Transition Points in Desuiphurization Earperiments
The dination of the e e d phase control region deaeases as the gas flowmte is
inaeased, although when this is normalized with respect to the gas flowrate and
sample mass the result is v e y close for d l three expiments (r0.05 NL aidg Cu).
For a standard Peirce-Smith converter blowing at 480 000 Numin, this corresponds to
a mixed phase control period of 8 minutes.
The graphs in Figures 7.8.4, 7.8.5 and 7.8.6 illustrate the variation in oxygen
c~nsumption as desulphurization progresses to cornpletion, followed by oxygen
dissolution Oxygen consurnption is attributed to either evolution as SQ or by
dissolution into the melt The o v d l oxygen cofl~umption is maintaineci close to the
value obtained under gas phase cuntrol throughout the region of rnixed phase control.
At the Iowa gas flowrate (1.36 Numin), the oxygen consumption under liquid
phase difbion control is rnaintained at the same measured vdue as obsewed under
&as phase control, ri@ up to the lîmit of ovgen saairation. However, at a gas
flowrate of 4.0 Wrnin, the efficiency b e g h to drop off as liquid phase control takes
over. This is due to the decreasing ability of the liquid phase to transfer oxygen away
h m the gas-liquid interface relative to the rate of injection.
Air Flowraîe (Nvmin)
1.36
2.66
4.0
% Oxygen ai Sdphur target
of 0.01%
0.50
0.59
0.8
% S u l p h at onset of mixeci phase control
0.4
0.5
O. 8
% ûxygen at end of mixed phase control
1.1
0.75
0.84
This indicates that increasing the gas flowrate fiom 1.36 to 4.0 Numin does
not re-suit in a proportional increase in the degree of turbulence ( m a s transfer
coeEcient) in the liquid phase. This is explaineci by the Iiquid phase aiready king
very well rnixed at the lower rate of gas stimng.
Mixed control +
m Liquid phase control
Air 8 1.36 NUmii 52 mm nonk I
1 - I
I f 1 ? - i: 1 523 K 0 - 0 4 -- 1 I
O 20 40 60 80 100 Blowing time (min)
= EvolvedasS02 + Dissolved in mit Total I Fi-pre 7.8.4 - Variation of û m ~ e n Consumption with Blowin~ Time
flowrate = 1.36 Wrnin)
control I I I I I
Air 8 26ô NUmin 1 1
5 2 mm nom I I 1 1 I
Blowing tirne (min)
0 Evoivedas S02 + Dii ived in melt Total
. . imire 7.8.5 - Vanatiqnof ûq!,gen Cons me (2.66 Nl /mi4
1 02
100 *
s - 80- C O .- CI
2 60- 3 a C
6 40-
0 Evolved as S02 Dissolved in melt * Total
BCB I 34
+ . t )W 4 I O l : * * I I I
* I I
O I I
I a 1 1
Gas phase + I Liquid phase control I
I I 1 Mixed control
I control I
I
1 I
I I I
c - Q)
20- 0 -
e (4.0 N U m )
7.9 Inert Gas Blanket Tests
To separate the extent of reaction into the t i r e stages of gis-liquid contact,
expiments were performed while purging the sufiace of the melt with nitrogen to
inhibit Surface d o n . This technique has b e n used in mass transfer investigations
of aqueous systems (also by placing an oil layer on top of the liquid ~urface).[~q
Although a slag layer would Save the same pinpose as a layer of oil, it d d also
seme as an ovgen transport medium, complicaîing the systern. Therefore nitrogen
purging of the liquid stnfàce was chosen as the method for inhibithg surface miction.
The mass transfer paxameter for slirface d o n has dso b e n evaluated by
injecting an hert gas into the liquid while blowing a reactive gas ont0 the fk liquid
surface. This technique was tested for the air-Cu2S system, but the previous method
led to much more reliable d t s , and was chosai for s e p d g the transfm of oxygen
into the three stages of gas-liquid contact,
Figures A8.1 t h u g h A8.5 display typical plots of oxygen consunqition with
increasing flowfate of nitrogen ont0 the melt surface. Thae is a signifiant reducîion
1 I I I
1
f I Air O 41) NLhin
I I f * 1
5 2 mmnozzie I I I
1523 K 1 l *
O-: c i m m m
I I I I 1 I
O 1 O 20 30 L
Blowing tirne (min)
in the qyantity of oxygen reacted with the melt, which is a clear indication thar a large
proportion of the reaction takes place above the £ke liquid surface. As a result of the
inert gas jet hpinging on the liquid surface, high nitmgai flowrates resdt in a slight
increase in the oxygen consumption This is likely due to the increasing inertia of the
"trogen jet displacing Liqyid droplets into the overlying gas phase. This observaiion
serves to underscore the sigdicance of mass tramfer in the bubble rupture stage.
it may be argued that the lowest level of oxygen consumption observed with
inaeasing flowraîe of nitrogen onto the melt surfiace still contains some reaction
taking place in the bubble rupture stage, since incaeasing nitrogen flowraîes are
obsefved to resdt in a slight in- in the oxygen coflsumption. Therefore the lines
drawn in the Figures in Appendix 8 should be taken as an upper lirnit for the oxygen
consumption taking place in the bubble growth and rise stages. Consequently, the
evaluation of rnass transfer coefficients for the bubble rupture stage in section 7.1 1.3
should be taken as lower lirnits. 'Ibis method of purging the liquid sudace with
nitmgen has proven to be successfùl for inhibithg a sigdcant portion of the surface
reaction.
The total oxygen utilizaîion that is achieved in the absence of nitrogen purging
is amibuted to bubble growth, rise and nrphù.e. The oxygen utildion that still
pxvails during inert gds purging is amibuted to bubble growth and bubble rise. The
portion subtracted off during nitmgen purging is aitributecl to bubble rupture. As
d i d in section 7.2, the amount of readion taking place diiring bubble rise was
assessed by obsaving the i n m e in oxygen coflsumption with incremental increases
in lance immersion. This quantity was then indexed up to the partial pressure of
oxygen where bubble rise actudly takes place. Atter subtracting off the extent of
reaction taking place in bubble rupture, the balance of the oxygen utilization must be
occuning in the bubble p w t h stage.
The accorripanying gr;y,hs in Figures 7.9.1 to 7.9.5 illustrate the separation of
oqgen utilization into the bubble p w t h , rise and rupture stages. It is immediately
apparent that bubble growth and rupture are much more important than bubble rise in
determinhg the high overall oxygen Ldilizations measlired Comparuig Figures 7.9.1
and 7.9.2, the extent of &on in the bubble rupture zone is enhan& by injecting
hugh a larger diameter node. Injection through a smalla nozzle results in smaller
bubbles, which in tum lead to a smaller gas-liquid spout on the d a c e of the melt.
At intemediate gas flowrates this ciifference is partially oBet since the transition to
an expded spout condition oaws at a lower gas flowrate for the srnaller node.
Comparing Figures 7.9.1 and 7.9.3, oxygen ibilization during bubble rupture is
comparable for a downward faicing nozzle and a horizontal orifice at low gas
flowrates, however at higher gas flowrates the n o d e results in higher values.
Injection through a d o m d facing n o d e le& to an expanded spout condition,
which was not observed when injeding through a horizontal orifice. Gas channeling
almg the lance is believed to be responsible for this diffefence. It is possible thaî an
expanded spout condition is achieved with horizontal injection, although at higher gas
velocities.
Figure 7.9.4 illustrates that an increase in kmpemhm to 1623 K results in
increased oxygen Iuilization, in partiailar at low gas flowrates. This indiCates a
possible meaianistic change in the oxidaîion process. Figure 7.9.5 illustrates that an
inaease in the oxygen concentration of the injectai gas leads to an increase in oxygen
utilkatien. This increase is observed to be m d y in the bubble growth stage, and is
likely related to the corresponding decrease in bubble fkqency. Formation of copper
oxide followed by sulphur dioxide evolution in a separate bubble is a possible
explanation for these observations.
1 Bubble Rupture + -k
Bubble Rise
Bubble Growth
O f 1 1 1 1 1 1
1 2 4
3 4 5 Air Flowrate (Numin)
8ol-- - Bubble ----' Rupture
Bubble Rise 40
8u bble Growth 20-
-
O
1523 K 26 mm ~Wice (OE) Cu2S
1 1 1 t 1
1 2 1
3 4 Air Flowrate (Numin)
Bubble Growth
-
60-
-
40-
Bu bble Rupture
_i
Bubble Rise
Bubble Rupture
20J
-
O
. Bubble Rise
1523 K 3.1 mm orifice CU2S
1 1 I 1 1 I I
Bubble Growth
1 2 3 4 Air Flowrate (Numin)
1623K 5 2 mm m œ (O€) CU2S
1 1 I 1 1 1 1
2 3 4 Air Flowrate (Numin)
. . tion with Air Flowmte Dunn &me 7.9.4 - Vmation of Q Consuma g Bubble Stage
Bubbfe Rupture
Bubble Gr&
7.9.5 - Vanatior~ of 0, Co- with 0, &chment Dining Bubble Stage . .
- 0.1 mm orin=- 1523 L2.0 N h h totdgas flowrate)
7.10 X-ray Imaging of Gas Injection
To gain fùrther insight into the mechanisrns responsible for the tramfer of
oxygen durhg oxidation of molten Cu$ by air injection, a series of e e e n t s were
pafomed inside an x-ray imaging fumace. Due to the ability of liquid copper and
Cu$ to absorb x-rays, nothing muid be seen below the stnfiace of the melt The
images in this section and Appaidix 7 were produced by videotaping the idormation
processed by the x-ray detector, and then using fiame isolating software to download
still photographs to a cornputer.
nie dark areas indicate hi& absorption of rc-rays, typical of metal. Light areas
are due to high transmission of x-rays, and correspond to gases or cerarnics. The scale
for these photographs is about 1 :2 (the oiber lance diameter is 9.1 mm). Hand drawn
tracings of the images have also been provided due to dinicdties in obtaining good
contrast and resolution in the images.
Figure 7.10.1 displays both the lance and the quiescent bath surfàce. This
- 3.1 mm orifice ClQS 2.0 Nifmin (Air + 02)
Om 1 I a I l 1 I I 1
30 40 50 60 Oxygen lnjected (%)
image is useIùl for referencing the IOcafion of the k liqpid surfàce in the other
photographs. The dark spots above the melt are liquid droplets adhering to the
aucible wall fiom previous experiments. ïhe lance immersion for dl x-ray irnaging
tests was 10 mm.
e (no injection)
Figure 7.10.2 is for air injected at 2 W m i n through a 3.1 mm horizontal
orifice. nie orifice is l~cafed on the left hand side of the lance in a plane
perpendicular to the plane of the photograph. The image show is for a typicai bubble
just prior to rupture at the melt surfàce. 'The bubble diameter measured h m this
photograph is about 22 mm, indicating that the gas phase nearly fills the distance
between the lance and the aucible wall(23 mm). It appears that the bubble is
adhering to the lance, evidenced by the p w t h of the bubble back dong the lance.
The x-ray vida demoiistrated that al1 of the bubbles were rising dong the left side of
the lance and that the spout was essentially comprised of single bubbles prior to
rupture-
Figure A7.1 is for air at 4 NUrnin through the same onfice. As in the
previous image, the melt surface is undi- except for a bubble about to ruphre on
the left side of the lance. 'The bubbles observed in this v ida typically ext
firrtha out of the melt before rupîuring, but still always on the left side of
Occasionally a droplet on the order of 3 mm in diameter was observeci for
as it was ejected into the ovedying gas phase.
ended
'the lm
an inst
.ce.
ant
Quiescent melt surface
7.10.2 Xray I w e for u e c t e d at 2.0 NU- a 3.1 mm orifice . . - -
110
Figure A7.2 mtak an image obtained while injedng air at 2 Wmin
through a downward nozzle with an inna diameter of 6.8 mm. The liquid spout
show on both sides of the lance is typical of the videos obtained for al1 injection tests
utilizing a downward nozzle. The melt level has risen slightly relative to that
indicated in Figure 7.10.1, suggesting the development of a gas-liquid phase above the
quiescent melt surEàce (aside h m rupturing bubbles). ûccasiondly a liquid droplet
aromd 3 mm in diarneter was seen above the melt as it was ejecîed h m the liquid,
buî no fine droplets d d be detected, since they are only a few microns in diarneter.
The photographs in Figures 7.10.3 and A7.3 were taken while injecting air at 4
Wmin through the same n o d e used above. The melt lwel is observed to have risen
substantially and thae is a large quantity of liquid above the quiescent melt surfaceaceace
Although gas appears to be escaphg h m the melt on both sides of the lance, the
vida showed that there exists an oscillation in the liquid plume fiam side to side.
Numerous liquid droplets are observed in the overlyirig gas phase, as they are ejected
from the melt or nnining d o m the crucible wall before king aigulfed by the spout.
The generation of an expanded gas-liqyid spout above the level of the
quiescent melt surfiace is an important observation. 'Ihis region may be thought of as
rnatte in a state of incipient fluidhtion, or possibly as a f o m The cause of the
generaîion of this additional gas-liquid phase is not clear. For a foam to be generated
in rnatte, solid particles or an emulsion of two liquids would be required to raise the
viscosity. Although Cu@ d d precipitate at some of the temperatirres employed, this
would be consurned by the melt very quickly and could not substantially increase the
system viscosity. The effective viscosity of an ernulsion increases to approxhately
two tunes that of the mntinuous phase with the addition of 25% of a second phase.
This quantity of an additional phase d d easily be gene~afed in the liquid film during
bubble rupture, suice the gas to liquid ratio is quite hi&
However, the transition to a fluidized state could result fiom the gas injection
rate ex&g bubble rupture kinetics. The process of film thinning and rupture
requires a finite amount of time, and the grneration of a fluidized zone on the surface
of the melt inmases the number of locations where gas can escape h m the liquid
This series of x-ray images indicates that injection through a horizontal orifice
is more likely to lead to gas channelling than injection through a downward facing
nozzle. The nozzie also q p e m to resuit in the generation of a gas-liquid phase on
the Strrface of the melt Inaeasing gas flowrate is seen to increase the volume of this
additional phase, however only for injedion through a downward facing node.
I l Rlass Transfer Coefficients
The best masure of mass ûansfkr opability in the three stages of gas-liquid
contact is the use of a mass transfer coefficient Graphs such as those in Figures 7.9.1
to 7.9.5 illustrate the proportion of oxygen transferred in each stage, but do not give
an indication of the true potential for m a s transfer. AiAltugh Figure 7.9.1 shows that
nearly twice as much mass transfer takes place in the growth stage relative to the
rupture stage, it does not m u n t for the degeased driving force or differences in
residence time during each stage.
M~ISS transfer coeficients are calcuiated fiom the following equation, with the
interfacial area 4 king the most dinicuit parameter to quanti@.
The molar flux of oxygen, Nm is calculated fiom the measured extent of reaction
(offjps analysis) and the estimated residence time. The log mean dnving force is
based on the inlet and outlet partial pressures of oqgen, calculated h m the
composition of the injected gas and the offgas analysis.
To gain a better understanding of how the dcuiated mass transfer coefficients
are behg driven by the individual terms in equation 58, the following parameters have
been plotted individually in Appendix 9; the oxygen collsumption to driving force ratio
and the gas-liquid contact the.
Figures Ag. 1, A9.3, A9.5, A9.7 and A9.9 dernonsaate that the consqt ion to
driwig force ratio is generally highest in the bubble rupture stage, paiticularly at high
gas flowrafes. For bubble rise this parameta is on the order of one tenth of that for
bubble growth and bubble rupture. 'This incorporates the decreasing dnving force as
gas p r d fkom the growth stage to eventuai rupture.
The gas-liquid contact time (residence time) cannot be measured as diredy as
the above parameta. For the bubble growtfi stage this is caldateci based on the
m e a d bubble fkpency. ïhe residence tirne diaing bubble rise is calculated
assuming that the gas passes through the liquid in a qlindrical channel, with a
diameter that is appmxirnately equal to the distance between the lance and the mcible
wall. The contact tirne in the bubble rupture stage is calculaid f?om the gas flowate
(at the melt te-) and the crucible head space volume. Splashing was observed
dl the way up the crucible wall and on the undemide of the cover, so it could be
assume. that the entire head space has the potential for gas-liquid contact.
Figures A9.2, A9.4 A9.6, A9.8 and A9.10 are plots of the residence time in
each stage as a fùnction of gas flowrate. The left sale corresponds to bubble growth
and rise while the ri@ de, which is a factor of 100 greater than the le&
corresponds to bubble rupture. These graphs illustrate that bubble rise constitutes the
smallest portion of the total gas-liquid contact time. Bubble growth time is on the
same order as that for bubble rise, but the mean gas-liquid contact t h e in the bubble
rupture stage is at least 40 times greata than that for bubble growth. This begins to
explain why a significant portion of the reaction takes place above the melt surface.
7.11.1 Bubble Growth
The average mass transfer coefficient for the bubble growth stage has been
calcuiated for a variety of experimental conditions using a hite difference method
The bubble is assurned to start as a hernisphericai cap with an oxygen partial pressure
equal to that of the injected gas. 'Ihe duration of bubble p w t h calculated fiom rhe
pressure trace was broken d o m into 100 time increments.
During each tirne inmement the bubble expands as air enters it, increasing the
interfacial area, and the composition changes as oxygen reacts nt the bubble surface.
nie mean mass tr;uisfer coefficient ova the entire growth stage was found by iterating
until the partial pressure of oxygen at the end of the p w t h stage was equivalent to
that measured experhentally. The spreadsheet used to perfonn these calculations is
located in Appendix 10.
ïhe bubble growth m a s transfer coefficient for air injectai through a 5.2 mm
downward fxhg n o d e is plotted in Figure 7.11.1.1 as a fimction of gas flowrate. As
expected, increased turbulence resultuig h m inaeasing gas velocity leads to a slight
increase in the mass -fer coefficient. Although the bubble diameter increases as
well, which wodd tend to decrease the rnass transfer coefficient due to loss of gas
momentum with increasing distance h m the orifice, the following analysis is made.
- 1 2 3 4 5 Gas Flowrate (Numin)
1 . 1 - Variation O . .
& p e 7.1 1. f Growth Stage Miss Transfa Coefficient
with Gas Flowrafe (5.2 mm nozzle)
Since bubble fiequency is nearly constant with increasing gas flowate, bubble
diameter a gas f l o~ l~ i t e*~~ . However, the mass tramfa d c i e n t typically depends
on the orifice Reynolds number to a power of 0.5 to 1. Since the orifice Reynolds
number is linearly proportional to the gas flowrate, the dependence of the mass
transfer coefficient on gas flowrate will be on the order of 0.5 to 1. The higher order
dependence of the mass ûansfer coefficient over the bubble diameta results in the
slight increase in the mass ûansfer coefficient that is o b s d with increasing gas
flowrate. As a means of comprison, the mass transfa coefficient has b e n predicted
using a nurnber of theoretical and empirical correlations fond in the literatlrre.
The correlation provided by for a gas jet impinging on a liquid d a c e
undenstimates the m a s tramfer coefficient by a faor of nearly 10. This is likely
due to the fact that this correlation is based on low gas flowrate experîments, wtiere
the gas-liquid interfice is a srnooth dimple creafed by the low momentun gas jet. ïhe
gas flowmtes used in this investigation are inappropriate for this type of correlation.
ïhe correlation for a gas jet impinging on a solid surEiâce accoKling to
H ~ a n g ! ~ yields adequate (although lower) estimates for the measured mass -fer
coefficient, except at the higha gas flowrates studied here the agreement is very
g d 'The aror in using this correlation to predict the o b s d results can be
35] 51 mm onfice (O€) A UJ Air into Cu2S 2 30- 1 5 n ~
Zheleznyak (1967)
.- O
O O & 15 .c v,
% 20- Gar let irnpingmg on a wilid wiilace
C Empincal intemal arailation mode1 !!! 10- Siskovic and Narsimhan (1970)
l- tn * 5- Gas jet impinging on a Iiquid suriace
2 Lohe (1966)
attnbuted to the physical differences between jetiing a gas ont0 a flat, solid sinface
and into a deforniable liquid medium. The empincal intemal circulation rnodel
developed by Siskovic and Nar~irnhan[~~1 provides similar values for the mass transfer
coefficient (to Huang4q). nie m r in this prediction arises because it is system
specific, and contains an empincal constant-
Zhelez~yak~~~~ has developed a theoretical circulation model, although it
predicts rnass transfer coefficients that are nearly double that which were measirred in
this w o k This model is suggested for use b i d e a growing bubble, although it is
based on extemal circulation. This is a questionable matter, since the effects of
recirdation are much more signifiant on the inside of a bubble.
Figure 7.1 1.1.2 is a similar plot for a 3.1 mm horizontal orifice. As for the 5.2
mm node, the cornlaiion of Luhdml predicts much lower rnass transfer coefficients
and the model developed by Zhele~nyak~~~] overeStimates this parameter- The
influence of gas flowrate is also much different than that predicted by Huandq and
Siskovic and Nar~irnhad~~~, and agreement is found at the lowest gas flowrate studied
rather tban the highest. lhis is consistent with observations discussed in previous
sections *ch indicate that gas channelling may be reducing the effectiveness of the
bubble growth stage for gas injected througti a horizontal non-wetting orifice.
3.1 mm onfice Air into CuZS
60
Gas let irnpinging on a sdid surface
Empiricai internai cilaihiion modei Siikovic and Narslmhan (1 970)
This work
/ Gas jet impinging on a liquid surface
Lohe (1966)
3 Gas Flowrate (NUmin)
7.1 1.1.2 - Vanation pf Growth Sw Mass T m . . fer Coefficient
Flowrate (3.1 mm orifice)
Figure 7.1 1.1.3 , w m a r k the e f f i of temperature> gas flowratey nozzle
diameter and lance geometry on the growth stage rnass transfer coefficient Increasing
the system ternperaaire h m 1523 K to 1623 K resdts in an approximate increase of
30% in the measlired value of k, This is pater than the expected increase in gas
phase diffusivity, (Dm = Tl5, predicts a 10% increase) and may be amibutable to a
higher gas velocity through the orifice, and a curresponding higher rate of intanal
recirculation The effect of increasing tempemhm is a linear increase in gas flowrate,
resulting in a linear increase in the orifice ReynoIds nurnber.
Inlemon Conditions
I O i 8 1
2 3 4 Gas F lowrate (NUmin)
Fi-- 7.1 1.1.3 - Variation of Growth Stage Mius Transfer Coefficient
Flowrate (~axying-geornetq~ onfice diameter and ternernperahire)
Decreasing the n o d e diameter f?om 5.2 to 2.6 mm has a signifiant effect on
the rnass ûansfa coefficient, and is the result of a twefold mechaniSm, A smaller
node diameter d t s in both a smaller bubble diameta and a higher orifice
Reynolds number. Both of these changes would be expected tu enhance mass transfer,
reSuIting in the observed dependence on nozzle diameta.
The effect of changing h m a downward facing 5.2 mm diameter nozzie to a
horizontal 3.1 mm diameter ori.fice supports previous observations tbaî gas chamelhg
is present in the horizontal orifice system. 'The bubble fkquency, and cof~esponding
bubble size, is approximately the same for these two systems. However, the smaller orifice results in a 2 fold increase in the o%ce Reynolds number at the sarne gas
floumie, *ch should yield a higher mass ûansfa coefficient. However, the mass
transfer d c i e n t for these IWO systems is about the same, with that for the 3.1 mm
orifice leveling off at higher gas flowraîes. Thus channelling likely becornes more
prevdent wiîh inaeasing gas flowrate.
Oxygen lnjected (%)
7.1 1.1.4 Vanahon of Growth Staye Ii4ass T m . . - fer Coefficient
The influence of e~ching the injected gas with oxygen on the growth stage
rnass tramfa coefficient is illustrated in Figure 7.1 1.1.4. The observed variation is
within experhental enor. This is in spite of the fact that the bubble diameter was
found to increase slightly with increasing oxygen enrichment. The constant nature of
the mass tramfer coefficient may be aîtributed to the excess heat generated by higher
reaction rates that arise h m oxygen enrichment. Most of the excess heat is likely to
be rapidly absorbed by the melt, limiting the effect on the mass transfer coefficient
during bubble gowth.
The Sherwood number for the bubble growth stage has been correlated with the
orXce Reynolds and modified Froude numbers as well as the Schmidt number for
SQ. nie general form of the correlation is shown below, and was chosen since it
incoprates both the influence of turbulence (N,,) and the e f f i of an mistable gas-
liquid intaface (1+N,,,.). The dependence on N, was chosen as a power of 0.33,
which is commonly used in gas phase mass transfer coefficient comlations.
b 0.33 N&=a [N,,* ( 1 +Nm; 1 1 N,, (59)
Figure 7.1 1.1.5 is a plot of the bubble Sherwood number varying with the
parameter goup Ne0(I+N,,,.). For a 5.2 mm diameta downward node, the
expnent b is 0.366 at 1523 K while the cocresponding value at 1623 K is 0.360. This
relatively low order dependence is a d t of inwrporating two dimensionless groups
into a single parameter.
40 . . . . . . . . . . . General' form: Sh,= a(Re,(l i-Fr',)lnSCOJI
gure 7.1 1.1.5 - Experimental Correlation for Bubble Growth Shmood Number
A Iowa order dependence (b-0.184) is calculated for a 3.1 mm horizontal
orifice at 1523 K This is consistent with previous explanaiions of gas channelling. It
was hoped that the data for the 2.6 mm nozzle wodd fdl close to the line for the 5.2
mm node. Figure 7.1 1.1.5 illustrates that there is a large discrepancy between these
two correlations.
This difference cm be telated to the effect of bubble diameter on the
correlation presented in -ion 59. By evaluating the dimensionles groups at the
orifice conditions, the right hand side of this equation does not reflect changes in
bubble size as a resuit of changing the node diameter. nie data for both the 2.6 and
5.2 mm nodes have been comlated together accordhg to the following expression
(which incorporates bubble diameter): c 0.33
N&, =a [ N& ( 1 +N,,; 1 bdb N S ~ (60)
The variables in equation 60 were detennined in the following m e r . A
value was assumed for the dependence on bubble diameter (c). Linear regression kvas
&ed out to deterrnine the value of the remaining exponent (b) and the constant (a).
The value used for exponent c was adjusted to minimiLe the sum of the square of the
residuals (8). It was found that the best value for c is 1. 'The resulting correlation is:
Nab=360 [NReo(l+N,,o) j 0 - 0 8 9 d b SC (6 1)
Since the Sherwood number is also linearly proportional to the bubble
diarneter, the net result is that the mass transfer coefficient is essentially independent
of the bubble diarneter, over the range studied in this investigation (18 to 32 mm).
This correlation is based'on experimental data c o v e ~ g the ranges 600 < N, < 970 ,
0.02 < N, < 8 and N, = 0.82.
7.11.2 Bubble Rise
The mass tramfer coefficient for the bubble rise stage has been calculated
using the following two methods. In the fkt rnethod the gas is assumed to flow in a
cylindncal slug surrounded by liquid, extending ffom the lance to the crucible wall.
The velocity of the gas is determined by the injected gas flowrate and the cross-
sectional area of the gas slug. Gas-liquid contact is assumed to be limited to the
pairneter of the gas slug. The mass tranrfet coeEcient for the gis phase can be
predicted using correlations available in the lit- for gas flowing through a
cylindrid tube.
The second method assumes that the bubbles behave independently once
detached f?om the orifice. A bubble shape diagram has been used to detamine the
appropriate intafacial area, and the bubble velocity has been estimated using an
available comlation for the drag coefficient.
Figures 7.1 1.2.1 and 7.1 1.2.2 display the dcuiated mas transfa coefficients
in the bubble rise stage for a 5.2 mm downward nozzie and a 3.1 mm horizontal
orifice respectively. Using the second method described above, the calcuiated mass
transfer coefficient decreases slightly with increasing gas flowrate, for both systems.
This is an unexpected ûend, and indicates that this analytical rnethod may be incorrect.
O f r I , 1 L
1 2 3 4 5 Air flowrate (NUmin)
. . i m 7.1 1.2.1 - Vanation of Rise Sta~e Mass Transfer Coefficient with Gas Flowrate
3 Air flowrate (NUrnin)
7.1 1.2.2 - Vanation of Rise S w h&ss Tmqfer W c i e n t with & Flowrate * .
0.1 mm orifice) Further examination of the spreadsheets used to dculate the bubble rise mass
ûansfa coefficients reveals thai the predicted bubble velocities are inconsistent with
the total gas flowrate of injection. To travel at these low velocities, the bubbles would
be nmning into one another. Therefore either the residence tirne of the gas in the nse
stage or the interfacial ara is overestimated
ïhe fkt method used to mode1 the bubble rise stage is a much more redistic
way of analyzing this systern. The mass transfer coeEcient increases nearly linearly
with increasing gas flowraîe, as is ptedicted for gas flowing in a cylindncal channel.
However, as the gas flowraîe increases, the deviation between the expimental and
predicted mass transfer coefficients increases.
This on be atiributed to the fact that the method used for calculating the
experimental m a s tramfer coefficients assumes a srnooth gas liquid interfa at the
perimeter of the gas slug. In redity this may be rippled, leading to an increase in the
degree of turbulence near the interface as well as an increase in the intexfacial am.. -
n e difference between the two values is the enhancement in mass ûansfer that cm be
related back to these two phenornena that result ffom rippling at the gas-liquid
interfàce. It is reasonable that this effect would be more pronounced at higher gas
flowrafes, which is observed in Figures 7.1 1.2.1 and 7.1 1.2.2. 6-
4, into C U ~ S /A
F 5 -
5 - Y /- C
6 4- - O f -
52 mm (OE) , 1523 K
26 mm (OE), 1523 K
5 2 mm (OE), 1623 K
I 1 1 I 1 1 I
1 2 3 4 Air Flowrate (NUmin)
7.1 1.2.3 - Variation of Rise Stage Mass Tramfer Coefficient with Gas Flowrate
ametet- and tem-1
RefeRing to Figure 7.1 1.2.3, the influence of tempaahrre, nozzle diameter and
lance geomm on the nse stage mass -fer coefficient are aU quite small. This is
to be expeaed, since the nozIe/orifice characteristics do not significantly impact on
bubble rise. These results support the theury that the gas travels through the liquid as
a series of cylindrical slug, the diameter of which is detexmined by the proximity of
the lance to the aucible wall, not by the orifice properties. The inrrea~e in mass
transfer coefficient with increasing temperatrne çorresponds to the predicted inaease
in gas phase diffusivity (D, cc TlJ).
Finally, the effect of oxygen enrichment on the bubble rise stage mass transfer
coefficient is presented in Figure 7.1 1-2.4. nere is essentially no e f f i since the
corriposition of the gas phase does not influence the m a s -fer propaties. I f there
is excess heat produced as a result of a higher reaction rate, it is iikely absorbed by
the liquid smounding the gas slug.
7.11. . . 2.4 - Vanation of Rise Sta~e Mass Transfa Coefficient
- '-
5 - Y
c. s 4- - O m -
3- 8 - - VI c - 2 * Ci
VI - V)
2 1 -
O 20
The formation of a gas slug smounded by a liquid film has been addrPssed
rnathdcal ly in the following manner. The maîhemaficai solution for the vetocity
distribution for gas flowing inside a cylindncal tube bas been supaunposed on the
solution for liquid flowing in a wetted wail column The d t i n g expression relates
the liquid flowrate in the £ïim to; the maximum gas slug diameter, the film thickness,
the gas flowrate and the physid properties of the gas and liquid
C"2S 20 NUrnin (Air + 02) 3.1 mm oniice lS23K
e
'* x 31C
1 1 1 1 # 1 I 1
30 40 50 60 Oxygen lnjected (%)
n e gas f l o ~ e is equivalent to the flowrate of injection. The maximum
diameter of the gas slug is assumed to be the disbnce between the lance and the
crucible wail. Since the upward flow of gas displaces a maXllTlum volume of liquid
equal to the gas flowmte, the flowrate in the liquid film is limited by Q I Q.
Howeva, the volume of liquid to be displad will be reduced by the prwious gas
slug. Equation 62 has been solved iteratively for the liquid film thickness and plotted
in Figure 7.1 1.2.5 for two different liquid fiadons flowing in the film
0.5 i 1.5 2 2.5 3 3.5 4 4.5 5
Gas FIowrate (NUmin)
1.2.5 - Liquid Film 'Ihickness vs. Gas Flowrate
Even at the uppa limiting value where the liquid flowfate in the film is equal
to the gas flowrate, the film thickness is less than 5% of the maximum slug diameter
at the highest gas flowrate studied If the liquid film flowrate is 50% of the gas
flowrate the liquid film thickness is about 0.8 mm, which is les than 3% of the slug
diameter. Therefore it is safe to approximate the gas slug diameter with the distance
bdween the lance and the aucible wall.
7.113 Bubble Rupture
The bubble q t u r e stage can be seplu?ited into two distinct zones; the l i e d
spout M y on top of the melt surface and the dispersion zone that was found to
occupy the entire head spaœ of the crucible. Sine the extent of reaction between
Cu3 and Q cannot be rneasured individually for these regions, a bulk rnass transfer
parameter is used to descfibe the complete bubble rupture stage. It has ben assurned
that the tests perfonned with an inert gas blanket eliminaîed the majority of the
d o n taking place in both the p u t and dispasion zones.
Sinae the interfacial area of both the zones in the bubble rupture stage cannot
be m e a d experimentally or predicted with any confidence, the rnass transfer r d t s
are e x p d as a lu+ mass transfi coefficient-interfacial area parameter &*A,)
which is averaged over both zones of gas-liquid contact. It is recognized that the
behaviour in the spout (highly turbulent, short gas asidence tirne) is quite diffèrent
f?om that in the dispersion zone. An estimate for the mass transfer coefficient will be
made aftexwards, and the corresponding interfacial area will be checked to confcirm
that it is a reasonable value.
'The mas transfer paxmeter for the bubble rupture stage depends on the
residence tirne distribution that is assumeci for the gas phase as it travels through the
head space of the crucible. I f the gas phase is desaibed by plug flow, the parameter
k*A, can be calculated directly fiom the expimental measurements. ~owever, if the
gas is assumed to behave as back-mixed flow, the solution requins iteration.
For the latter case the residence time distribution for back-mixed flow is
broken d o m into 100 elernents, each with its own residence time. nie mean value
for k*q is then iterated until the mean composition of the gas phase is equivalent to
that measured experhentally. ïhese two Scenanos provide limiting cases that bracket
the tme solution, although the crucible head space is likely to behave closer to back-
mixed 80w (as a result of turbulence created by the ejected liquid droplets).
Figure 7.1 1.3.1 is a plot of the rnass fer parameter for the bubble rupture
stage as a fiinction of gas flowmte for a 5.2 mm downward n o d e at 1523 K As the
gas flowrate is increased, the parameter increases rapidly. ûne would expect the value
of k*A, to be a f'unction of the degree of turbulence in the gas phase (k, = mk)) and the rnass of liquid ejected into the overlying gas phase (4 = f(dmp1et s iz , # of
droplets)). The observed increase in &*A, with increasing gas flowrate is likely as a
result of increases in both these cpantities. The x-ray images rwealed that higher gas
flowrates lead to a larger spout zone, and it is misonable to expect that larger slugs
nq!&g at the sirrface will lead to more liquid ejected into the dispersion zone. ïhe
rapid inaease in the mass transfa coefficient is not inilike the increase in heat transfer
coefficient illustraîed in Chapter 3 in Figure 3 -4.3.1 .['O1
3000 1 Air into Cu25 5.2 mm onlice (OE)
O ! I b 1 I I I
1 2 3 4 Gas Flowrate (Numin)
7.1 1.3.1 - Vanation of Rupture Stag . .
e Mass Transfer Coefficient
Flowrate !5.2 mm node)
As a means of estimating the interficial area in the bubble rupture stage, the
spout zone can be temporarily neglected and the Limiting value for the Sherwood
number can be used to calculate the mass transfer coefficient. Droplets in the
dispersion zone are on the orda of 0.0015 mm in diameter. These droplets have a
terminal velocity that is much smailer than the upward gas velocity inside the crucible
head space, and as a r d t the Reynolds number of the droplets relative to the gas will
be srnall. The minimum Sherwood nurnber for a sphere is 2 (for N, = O), which
leads to a rnass transfer coefficient of 325 m/s. At a gas flowrate of 2 Wmin the
interfacial area is caldated to be 0.67 d. This ~ ~ r z e ~ p ~ n d s to 95000 droplets in
the dispersion zone, with a total mass of 9.7*1û7 g. For a gas flowrate of 5 NUrnin
the rnass of liquid droplets in the dispersion zone is calculaîed to be 1.0*10-5 g.
'Ihis calculation, based entirely on the dispersion zone, is subject to a great
deal of uncertainty due to the presence of the spout une. In the spout the Reynolds
number is significantly higher and the effecrive diameter is larger, leading to an error
in the estimated mass transfer coefficient. As well, a portion of the calculated
intafacial a r a is in the spout zone. Since the caiculated parameter %*A, is the
weighted average of &*A,),, and &,*A,)dispcrsim the pmprtiom of which are
unknown, it is difficult to separ;ite the mass transfa coefficient and interfacial area for
the bubble rupture stage.
Considering only the spout zone, the interfacial area is likely on the orda of
1Oûûû mm2 and the gas-liquid contact t h e is about 10% of the total residence tirne
above the quiescent melt surfiace. The d t i n g mass tramfer coefficient is about 0.2
mis, which seerns reasonable for the nature of contact within the liquid spout.
The assumption of back-mixed flow results in a higher value for the mass
transfa parameter over plug flow. All fiathet- disaission will pertain to dculations
based on back-rnixed flow, which may slightly over-estirnate the value of h*A,. Figure '7.11.3.2 presents the effects of n o d e diameter and lance geometry on
the mass transfer parameter. ïhe trend with increasing gas flowrate is sirnilar for both
the 2.6 and 5.2 mm downward nozzles, although the 5.2 mm node leads to
significantly higher values for VA,. Differences can be attributed to a higher bubble
fkqumcy and correspondhg lower bubble volume for the snzaller nozzle. This likely
rnanifests itself as a lower interfacial area, rdting fiom a srnaller spout zone and
fewer liquid droplets ejected into the overlying gas phase. The rnass transfer
coefficient is probably quite close for these two systems. 3000 1 Injection Conditions
-a- 5.2 mm orifice (O€)
UI 3.1 mm orifice
Gas flowrate (Numin)
. . * 2 - F i d m 7.1 1 3. Vanat~on of lbpture Stage M&s Tmfer Coeficient
127
The observed inmase in the m a s trwsfer parameter for a 3.1 mm horizontal
orifice with increasing gas flowrate is nearly linear. Compared to the results for the
5.2 mm node, the value of Ig*A, is lower, particularly at higher gis flowrates. This
is consistent with the e f f i of gas channelling, since fewer droplets would be ejected
into the dispersion zone and expansion of the spout is not as signifiant.
A linear increase in the mass tramfa parameter could resdt fkom changes in
the spout zone. xray images mealecl an increasing spout mne volume with
increasing gas flowrate, and the turbulence in the spout zone is likely increasing as
well. The dispersion zone may have les of an impact on $*q with increasing gas
flowrate for the 3-1 mm horizontal orifice.
The innuence of temperatuce on the mass iransfer parameter is presented in
Figure 7.11 -3.3. The value of &*Ai has been plotted for a 5.2 mm nozzle at both
1523 K and 1623 K as a hc î ion of gas flowrate. 'The trend at 1623 K is similar to
that at 1523 K, but the increase with increasing tempemtm is too large to be
atttibuted to an increase in gas phase di£fiisivity- This substantial increase suggests a
change in the o v d l converthg mechanism
The fine droplets ejected into the overlying gas phase as a result of the bursting
liquid film are on the order of 0.001 mm in diameter. These dmplets will be d e d
upwards by the rising gas, and continue to react with oxygen with a minimum mass
transfer d c i e n t of 325 m/s (N, = 2). If a droplet initially contains pure Cu$, the
maximum time for total sulphur depletion is 60 p, much l e s than the typical
residence t h e of a âroplet in the dispersion zone. Once the droplet contains pure
copper, M e r contact with owgen will result in formation of CUZOO This can lead to
the explosive reauion between copper oxide and wpper sulphide, which can enhance
rnass transfer by creating turbulence directly at the gas-liquid interface.
For the sequence of events described above to occur, the copper oxide that
f o m in the dispasion mne must be reintroduced into the melt. ïhis is most likely to
occur by droplets collecting on the aucible wall and then flowing back d o m onto the
melt surfàce. However, since the aucible material is highly wettable widi respect to
&,O, droplets of copper oxide can becorne physically trapped in the pores of the
cmcible wall if given sufficiait tirne. Crucibles removed f?om the fumace upon
cooling were found to contain a srnaIl arnount of red material absorkd in the cmcible
wall directly above the melt, \hiiich upon analysis was found to be copper oxide.
However, droplets adhering to the aucible wall and the underside of the crucible
cover were found to contain only Cu2S a . metallic copper.
5000- k r into C U ~ S
- 5.2 mm orifice (OE)
4000-
h U)
2 3000- E U V - x
1623 K 1 I I 1 I 1
Gas flowrate (Numin)
fer Coefficient,
with Gas Flowraîe (1 523K and 1623K)
Increasing the system temperature would be expected to decrease the necessary
droplet size for flow to occur down the crucible wall back into the melt, although it
could also speed up the kinetics of absorption into the pores of the aucible wail. At
1523 K the following expllanation can be put fortk At a distance of 6 cm above the
melt the temperatlrre is 30 K cooler (1493 K) than the melt itself, slightly Iowa than
the melting point of Q O . Therefore any droplets of oxide that strike the aucible
d l above this height may solidi@ and be prevented h m noUiing back down into the
melt It is recogruzed that the droplets are likely hotter than this tempaature prior to
hitting the cmcible wall as a result of the exothermic reaction with oxygen, therefore
the heat transfer properties of the cmcible and droplet becorne important.
The increase in the mass transfer parameter with increasing oxygen enrichment
depicted in Figure 7.1 1.3.4 may also be related to the phenomenon of oxide formafion.
A higher partial pressure of oxygen in the'gas phase not only leads to proportionaîe1y
higher rates of mass tramfer, buî the obsaved decrease in bubble fkquency results in
more liquid droplets ejected into the dispersion zone. Both of these processes will
lead to increased formation of Cu,O.
0 ! 1 I 1 1 5 1 1 1
20 30 40 50 60 Oxygen lnjected (%)
S .
mire 7.1 1.3.4 - Vanation of Rmture Stage Mas Tmfer Coefficient -
The potential for oxygen enrichment to lead to higher temperatures in the
bubble rupture zone also exists. If the supply of oxygen to the droplet sufiace is rate
limiting then increasing the oxygen enrichment will resuit in greater heat evolution
and a subsequent increase in t-. However, if the rate of copper oxide
formation is limited by the mass of copper ejected into the overlying gas phase (ie.
droplets are completely oxidized), then oxygen enrichment shouid have no effect on
the temperatlire of the dispasion m e . The detemiuiui . -
g factor is the ment of
reaction in the spout m e (the bulk partial pressure of oxygen as the gas e n t a the
dispersion zone), whkh cannot be quantifid in this work
7.12 Estimation of Emrs
The following table identifies the precision of the measurements made
throughout the experhental work Some of these items are estirnated based on the
type of measurement device or the observed level of reproducibility during mlibration.
me levels of precîsion reported below are maxirnum values (ie. when the parameter
king measured is at a minimum). 'Ihese precision levels have ken used to estirnate
the magnitude of the error in the caldateci nmss hansfa parametm.
Table 7.12.1 -J%tirnated Precision of Measuremena
Precision
Air f l o ~ e
Gas sample volume
Bubble fhpency 1 +2.5%
NaOH concentration
NaOH volume titrated
In addition to these quantifiable errors in rneasuremenf some subjective mors
are introduced when interpreting the oscilloscope photographs. As illustrated in Figure
3.3.2. single bubbles oui be represented by multiple peaks in the upstrearn pressure
signal. The m r in air flowrate measurement is slightly greater than that for nitrogen
and oxygen since the air flowmeter had a larger range.
ïhe m o n associated with the caiculated mass transfer parameters have k e n
detenniRed by applyhg the following d e for propagation of mrs:
Errer in x*y = Error in x + Error in y + (Emr in x*Emor in y) (63) Using this method, the emor in the calculated growth and rise stage mass transfer
coefficients are estimated to be M% and &14% respectively. 'The cuccesponding error
in the calculation of the mass -fer coefficient-intafacal area parameter for the
bubble rupture stage is S%. Since growth and rupture contribute nearly equally and
rise cortributes little to the o v d l oxygen coflsumption, the overd1 error in oxygen
comtmption is approximately U/a This compares well with the observed variation
in measurements, illwtmted by the data for a 5.2 mm n o d e in Figure 7.7.1.
7.13 Industrial Converter Considerations
The fùndarnentai qystion b e h d explainhg the success of the Peirce-Smith
convater is the distribution of oxygen co~lsumption between the three stages of gas-
liquid contact. The oxygen co~l~umption at the end of the entire process is typically
about W?'i and a mathematical analysis perforrned by Ashrnan et al["reûicts that
40% conversion occurs in the bubble growth stage.
The relative importance of bubble growth, rise and rupture are likely to exhibit
some degree of scale dependence. Under œrtain conditions in this e><perimental work,
the gas bubbles wae rupturing fiom the entire liquid surface. Therefore the walls of
the crucible may have played a role in establishg an expanded p u t , which
enhanced mass tramfer in the bubble rupture stage. However, the specific gas
flowrate per unit area of bath silrface is 6 times greater in a converter when compared
to the highest gas flowrate used in this work (bas& on the full converter bath d a c e ) .
Since the tuyeres of a converter are al1 located dong the back of the converter, only a
portion of the liquid surfhce may be an active site for bubble rupture. Therefore there
exists a great likelihood for the generation of an expanded bubble rupture zone in a
converter as well.
It is known that bubble growth tirne is vay short, l e s than 0.2 seconds.
Bubble rise time is likely even shorter, since the non-wetting conditions inside the
converter probably Iead to gas flow in a thin, flat sheet between the molten bath and
the back of the converter. If the gas is assumed to flow in a thichess of 200 mm, the
residence tirne in the rise stage has a 0.02 second duraiion. For a converter that is one
third full of liquid, the gas phase residence time in the bubble rupture stage is about
1.4 seconds. This yields a ratio of 10: 1:70 for b:L:b. The formation of a gas envelope could provide a slight incrase in the
residaice t h e during the bubble rise stage, although the gas flowrate is so large
relative to the size of the gas envelope, this is likely insigriificant. It seems logical
that most of the remainllig 50% conversion takes place in the bubble rupture stage.
The degree of splashing inside a converter is substantial. 'The nust that builds up
around the mouth of a converter requires chipping back every 4 to 5 blowing hours.
It is d i f f id t to rnake quantitative predictions for a PeirceSmith converter
based on this research due to the a c u l t y in achieving high injection rates on a
laboraiory d e . In the bubble growth stage, the Sherwood number was fomd to
c o d a t e well with the following variables; N, NF,, N, and the bubble diameter.
Applying the correlation in equation 61 to a converter blowing 12 000 Numin of air
through each 50 mm diameter tuyere, the calcuiated mass transfer coefficient is 0.4
mis. Although this correlation has been used outside of the range in which it was
developed, this is a reasonable estimate for the rnass transfer coefficient. Applying the
f i t e ciifference method used in analyzing the bubble growth rnass transfer resdts, the
corresponding oxygen consurnption in the growth stage is 3 1% (close to the prediction
of ~shmaniq et al).
The bubble rise stage can be analyzed by considering gas flowing through a
relatively thin sheet dong the back of the convater. If the gas film is assumed to be
approximately 200 mm in thickness, the corresponding mass transfer coefficient in the
gas phase is 0.12 m/s (based on a correlation for 80w dong a flat surface). 'The
calculated oxygen consirmption for a converter operaîing with a 400 mm tuyere
immersion is only 0.7%. If the fiIm thickness is assumed to be only 100 mm, the
corresponding oxygen consumption in the bubble rise stage increases to 1%.
The rernaining 55 to 60% of the oxygen consumption must take place in the
bubble rupture stage. A large portion of this likely takes place in the liquid spout,
where the interfacial area can be very high and conditions are highly turbuient. The
dispersion zone rnay be equaliy important, since there is evidence thai a large m a s of
liquid is ejected into the overlying gas phase inside a converter. Although this study
m o t distinguish between the relative importance of the spout and dispasion zones
in a converter, it is evident rhat mass tramfer taking place above the level of the
quiescent bath is very important in determinhg the overdl hi@ oxygen efficiaicy
observed in a Peirce-Smith converter.
&O Conclusions and Recommendations
8.1 Conclusions
1. Bubble growth and bubble rupture are equally important in determining the
high oxygen utilizations observeci in the oxidation of copper matte by submerged gas
injection, while bubble rise is relatively unimportant. This observation is pnrnarily as
a resdt of the highly turbulent nature of the gas phase during bubble growth and the
hi@ interfacial area dining bubble rupture.
2. Increasing gas flowrate leads to a decrease in oxygen efficiency for gas
injection through a horizontal orifice. However, when a downward facing node is
used this trend is revened at higher gas flowrafes and a maximum o q g m efficiency
is approached It appears that a transition occm as the gas fiowrate is increased,
resuiting in an observeci expansion in the spout zone. This is analogous to the onset
of foam genaation or incipient fluidization and rnay be as a result of gas release f5om
the melt king limited by the kinetics of bubble rupture.
3. ïhe omet of an apianded bubble rupture zone occm at lower gas flowrates
as the nozzle diameter decreases. This is due to the fact that a srnalla diameter
orifice results in a higher bubble fkquency.
4. Injection through a downward facing n o d e was found to exhibit
significantly d i f f m t rnass tramfer characteristics fiom those genmed by a
horizontai orifice. In general, a downward nozzie leads to higher oxygen utilization,
particularly in the bubble rupture zone. This is explaineci by the presence of gas
chanelling wiien injecting through a horizontal orifice, which decreases the gas-Iiquid
contact time and also prevents the gaieration of an eqanded spout.
5. The following empirical correlation for the bubble growth Sherwd
number was derived based on the expimental data for downward facing nozzles
(over the bubble diameter range 18 to 32 mm).
Nab=360 [NRe0(1+N';) ] 0 0 0 a 9 d b N ~ ' ~ ~ Sc
This correlation is was developed fiom (and is valid over) the following ranges of
dimensionless parameters; 600 < NRc < 9700,0.02 < NF, < 8 and N, = O. 82.
6. Increasing nozzle diameta leads to increased oxygen utilization,
predominantly in the bubble rupture stage. This is due to the generation of a Iarger
spout on the sudiace of the liquid
7. The influence of temperature on the m a s transfer characteristics of copper
matte oxidaîion by gas injection is insignificant below 1573 K At 1623 K a
substantiai increase in oxygen efficiency is observed, which may be as a result of a
mechanistic change that involves formation of CuZO above the melt dace.
8. 'The oxidation of copper-suiphur melts p r d under gas phase control
through evolution of SC& dom to a d p h w content below saturation, followed by
sirnultanmus sulphur elimination and ovgen dissolution under mixed phase control.
8.2 Recommendations
1 . Altemative converthg methods will be successfùl if they take advantage of
either a bubble growth or bubble rupture stage. An exarnple of this is the top blown - bottom stirred f inishg of sulphur satlrrated copper in c m t practice at n\M3(Ys
Copper C li ff Smelter.
2. Further research is reqiilred to explain the increased influence of tempermre
above 1573 K *ch may be as a result of a mechanistic change.
3. The method of inert gas purping of the liquid siirface can be used in fimire
investigations where it is desirable to efiminaîe the extent of reaction taking place
above the fk liquid surface.
4. A fùture investigation utilking a pressure transducer for characterizhg
bubbie growth while injecting through multiple lances could be useful in identiQing
the importance of gas envelope fomiation.
9.0 Nomenclature
a - variable in equation 60 A, - equivalent spherical bubble surfkce area (m? A, - interfacial area (m2) & - orifice cross-sectional ara (m2) b - variable in equation 60 c - variable in equation 60 Cp - P capacity (J/'g -0 C - sonic velocity (320 d s ) Cd - drag coefficient cm - Wtuai mass constant (4.5) C, - constant in mass tr;uisfer correlations d, - bubble diameter (m) 4 - liquid cavity diameter (m) & - liquid droplet diameter (m) 4 - +valent spherical bubble dianieta (m)
- fnaximm equivalent bubble diameta (rn) 4, - inner n o d e diameter (m) 4, - outer n o d e diameta (m) d,, - orifice diameter (m) dz - differential distance (m) Dm - diffusivity of A in B (mk) Dm - maximum spreading diameter (m) E, - specific energy input rate (W/kg) Fd - drag force (N) g - acceleration due to gravity (9.8 1 mls2) y - depth of liquid cavity (m) k - gas thermal conductivity (W/m -K) K - constant in equation (1) k, - mass transfa coefficient ( d s ) b, - mass transfer coefficient in liquid cavity ( d s ) k, - gas phase mass tramfer coefficient (ds) m - expnent in equation (1) NA - molar flux of p i e A (moles/d/s) Nw - modined Bond number Ne - Capacitance number N, - dimensionless Capacitance number Nw - modified Froude number Nd - modifiai Froude number evaluated at orifice conditions IV, - Prandtl number N, - Reynolds number
Nb - Reynolds numba evaluated at orifice conditions N, - ScIimidt number N, - Sherwood number for mass -fer N, - Sherwood numba based on equivalent sphere surface area N,, - Weber ninnber P - bubble pressure (Pa) PA,, - partial pressure of specie A in bulk of bubble (Pa) PM= - partial pressure of v i e A at bubble surfiace (Pa) P& - carrier gas partial pressure (Pa) P, - power input as a result of hetic energy (W) Pa, - initial buLk @al pressure of oxygen in bubble (Pa) P, - final bulk partial pressure of oxygen in bubble (Pa) Q - gas flowrate, typically at STP (dis) Q - liquid flowraie, (m3/s) Q' - chensionles gas flowrate r - radial distance (m) r, - cavity radius (m) R - gas constant (8.3 14 J/(mole-K)) & - bubble radius (m) R, - vesse1 radius (m) s - surfâce r e n d rate (SI)
t - bubble rise t h e (s) T - SYstem tenipaature (KI u - bubble velocity (rnk) u, - gas velocity at orifice (mk) y - radial liquid velocity ( d s ) v - bath velocity (mis) V,, - bubble volume (m3) V, - subnozzle chamber volume (m3) V,' - first stage dirnensionless bubble vo!ume V; - second stage dimensionles bubble volume \f - temiinal dimensiodess bubble volume w - bubble velocity ( d s ) W - work done by a rising bubble (J) x - Reynolds number exponent in mass ttsuisfer correlations Z - liquid height (m)
P - apparent contact angle (O)
6 - film thickness for rnass transfer (m) Ap - intexphase density ciifference, liquid density - gas density (kg/m?) cl, - gas Viscosity (Pas) p, - liqyid viscoSity (Pa-s) p' - dimemionless viscosity P, - F d=itY
- liquid densiiy (kg/m3) O - surface tension (J/&) 4 - dimensiodes parameter for characterizing heaî, mass and momentum transfer.
mass length velocity area voIume pressure flowrate diffusivity mass transfa coefficient rnass transfer coefficient- interfacial area voltage m e n c y
1. R.E. Johnson, N . J . Themelis and G.A. Eltringham: in mper and ickel Converters, R.E. Johnson ed., 'IIVIS-AIME, New York, 1979,
m. 1-32. 2. A.K. Biswas and W.G. Davenport: mractive Metgllyyw of Copper , 2& ed. , Pergamon Press, Oxford, England, 1980 .-a
3 . A. Luraschi and J.F. Elliott: Trans. Inst. M i n . Met., vol. 89, 1980, pp. C14-25.
4. A. Yazawa, Y. Takeda and Y. Waseda: Can. Met. Quarterly, vol. 2 0 , no. 2, 1981, pp. 129-34.
5. D.W. Ashmn, J.W. McKelliget and J . K . Brimacombe: Can. Met. Quarterly, vol. 20, no. 4, 1981, pp. 387-95.
6. J.K. Brimaccmbe, E.S. Stratigakos and P. Tarassoff: Met . mall~. , vol. 5 , March -1974, pp. 763-71.
7. G. G. ROY, N. Qlakraborti and T. Sundararaj an: Met. Tram. B, vol. 21B, D ~ c . 1990, pp. 1075-9.
8. A.A. Bustos, G.G. Richards, N.B. Gray and J.K. Brimacombe: Met. 'Iliram. BI vol. 15B, March 1984, pp. 77-89.
9. Y. Rilninaka, K. Nishikawa, H.S. Sohn and 2 . Asaki: Met. Trans. BI vol. 22Bf Feb. 1991, pp. 5-11.
10. K.H. Kellogg and C. Diaz: "Bath Smelting Processes in Non- Ferrous Pyrometallurgy: An OveMew", proceedings of the Savard/~ee I n t l . m. on Bath Smelting, J.K. Brimacombe, P.J. Mackey, G.J.W. Kor, C. Bickert and M.G. Ranade edç., Montreal, P.Q., Ott. 1992, T M S f pp. 39-65.
11. U. Kuxmann and T. Benecke: Z. Ertmietall., vol. 19, 1966, pp. 215-21.
12. H. Schmiedl, M. Stofko and V. Repcak: Neue Huette, vol. 16, 1971, pp. 390-4.
13. A. Yazawa and M. Kameda: Technol. Rep. Tohoku Univ., vol. 19, no. 1, 1953, pp. 40-58.
14. J.F. Elliott: Met. Tuanç. BI vol. 7B, March 1976, pp. 17-33.
15. R. Schuhmnn Jr. and O.W. Moles: Lrans. AIME, vol. 191, 1951, m. 235-41.
16. H.H. Kellogg: Can. M e t . Quar t . , vol. 8 , 1969, pp. 3-23.
17. J. Gerlach, K . P . Kantzer and F. Pawlek: Metallwissenschaft und T M , vol. 17, no. 11, 1963, pp. 1096-9.
18. F.D. Richardson: vol. 2, Academic Pre
n M e t a l l w ,
19. J . M . Toguri, N . J . Themelis and P.H. Jennhgs: Can. Met. Quart., vol. 3, 1964, p ~ . 197-220.
20. Z. Asaki, S. Ando and Y. Kmdo: Met. Trans. B, vol. 19B, Feb. 1988, pp. 47-52.
21. T.A. Quarm: M i n . Mag., vol. 117, no. 1, J u l y 1 9 6 7 , pp. 4-7.
22. F. Ajersch and J . M . Toguri: M e t . Trans., vol. 3 , Aug. 1972, pp. 2187-93.
23. J - C . Ymopoulos, C.E. Swanson and LW. Ahlricha: in of Cogper , vol. 1, J . C . Yannopoulos and
J - C . Agarwal e h . , TWS-AIME, New York, 1976, pp. 49-75.
24. R.J. Adreini, %S. Foster an6 R.W. Calkn: M e t . Trans. B, vol. 8B, 1977, pp. 625-31.
25. A.H. Alyaser and J.K. Brimacombe: llOxidation Kinetics of Molten Copper SulphideI1, to be publ ished in M e t . Trans . B , 19% . 26. N . J . Themelis and P.R. Schmidt: Trans. 'IMS-AIME, vol. 239, Sept . 1967, pp. 1313-8.
27 . Y.F. Zhao and G.A. Irons: Met. Tram. B, vol. 21B, Dec. 1990, pp. 997-1003.
28. R . J . mehan: Metals Technology, vol. 7, part 3 , 1980, pp. 95-101 . 29. G.A. Irons and R.I .L. Guthrie: M e t . Trans. B, vol. 9B, March 1978, pp. 101-10.
30. M. Sano and K. Mori: Trans. JIM, vol. 17, 1976, pp. 344-52.
31. G.A. Irons and R.1.L Guthrie: Can. Met. Quart., vol. 19 , no. 4, 1981, pp. 381-7.
32. M.E. Chalkley andA.E. Wraith: TYans. IMM, vol. 87, 1978, pp. C266-71.
33. G.N. Elovikov: Russian Metallurgy, 1977, pp. 90-3.
34. P.A. Distin, G.D. Hallett and F.D. Richardson: Jrnl. ISI, m g . 1968, p ~ . 821-32.
35. F. MacIntyre: Jrnl. Geophyscl. Rsrch., vol. 77, no. 27, 1972, pp. 5211-28.
3 6. C . F . f ient zler , A. B. Arons , D . C . Blanchard and A. H . Woodcock: Tellus, vol. 6, no. 1, 1954, pp. 1-7.
37. V. Sahajweila, %K. Brimacombe and M.E. Salcudean: mut on at the Free Surface of a Gas - St , short
course on Injection Phenomna in Peirce-Smith Con"t"ing, TMS- AIME Annual Meeting, New Orleans, Feb. 17, 1991.
38. M. Hirasawa, K. Mori, M. Sano, A. Hatanaka, Y. Shimatani and Y. Okazaki: Tranç. ISIJ, vol. 27, 1987, p. 277.
39. 0. Haida and %K. Brimacombe: Tram. ISIJ, vol. 25, 1985, pp. 14-20.
40. J.K. BrimaccPnbe, K. Nakanishi, P.E. Anagbo and G.G. Richards: in n e a l i o t t h si^, ISS-XME, Cambridge, MA, June 1990, pp. 304-72.
41. N.J. Thel is and P.J. Mackey: "Solid-Liquid and Gas-Liquid Interactions in a Bath Smelting Reactoru, proceedings of the ~avard/~ee Intl. m. on Bath Smelting, J.K. Brimacombe, P.J. Mackey, G. J.W. Kor, C. Bickert and M.G. Ranade eds., TMS, ûct.
42. M. Sano and K. M o r i : wFundamentals of Gas Injection in Re£ ining Processesn , proceedings of the Savard/~ee Intl . Çymp. on Bath Smelting, J.K. BrimaccPnbe, P.J. Mackey, G.J.W. Kor, C. Bickert and M.G. Ranade eds., TMS, ûct. 1992, Montreal, P.Q., pp. 465-92.
43. G.N. -11 and %K. Brirraccmbe: Met. Trans. B, vol. 7B, 1976, pp. 391-403.
44. E.O. Hoefele and J.K. Brimaccmbe: Met. Trans. B, vol. 10B, 1979, pp. 631-48.
45. Y. Sahai and R.I.L. Guthrie: Intl. Çymp. on Steelmaking, Jamshedpur, India, 1981.
46. G.C. Huang: J. Heat Transfer, vol. 85, 1963, p. 237.
47. S.H. Kim and R . J . mehan: Met. Trans. B, vol. 18B. Dec. 1987, pp. 673-9.
48. E. Adjei and G.G. Richards: llPhysical Mode1 of Mass Tramfer in a Peirce Smith Converter", in &gper 91 , C. Diaz, C. Landolt , A. Luraschi and C. J. Newman eds . , Pergmn Press, New York, 1991, pp. 377-88.
49. D. H. Wakelin: Ph. D . Thesis, Imperia1 College, University of London, 1966.
5 0 . H. Lohe: Chem. Ing. Tech., vol. 38, 1966, p. 309.
51. P.H. Calderbank: The Chemical Engineer, CE220, 1968.
and T.K. Shemood: Ind. Eng. Chem., vol. 26,
Gerlands Beitr. Geophys., vol. 52, 1939, p.
54. 0. Kubaschewski, E.L. Evans and C.B. Alcock: Metallumicd s t y , 4& ed., Peryamon Press, London, 1967.
55. P. Goyal, N.J. Themelis and W.A. Zanchuk: J. Metals, vol. 34, D ~ c . 1982, pp. 22-8.
56. N.J. Themelis and P. Goyal: Can. Met. Quart., vol. 22, no. 3, 1983, pp. 313-20.
57. R.R. Hughes, A.E. Handlos, H.D. hmns and R.L. Maycock: Chem. hg. Sci., vol. 51, 1955, pp. 557-63.
58. J.L. Liow and N.B. Gray: Chem. mg. Sci., vol. 43, no. 12, 1988, pp. 3129-39.
59 . R. K m and M.R. Kuloor: Adv. oiem. hg., vol. 8, 1970, pp. 255-368.
60. J.F. Davidson and B.O.G. Schuler: Trans. Instn. Chem. Engrs., vol. 38, 1960, pp. 145-54.
61. K. R u f f : Chem.-Ing-Tech., vol. 44, 1972, pp. 1360-6.
62. J.K. Walters and J.F. Davidson: J. Fluid Mech., vol. 12, 1962, p. 408.
63. J. F. Davidson and D. Harrison: Fluid~zed P m i c l es I . , Cambridge University Press, London, 1963.
64. J.R. Grace, T. Wairegi and J. Brophy: Can. J. Chem. Eng., vol. 56, 1978, pp. 3-8.
65. R. Clift, J.R. Grace and M.E. Weber: -Mes. Draps and -, Academic Press, New York, 1978.
66. R.M. D a v i s and G.I. Taylor: Proc. Roy. Soc. London, vol. 200A, 1950, pp. 375-90.
67. W.L. McCabe, J - C . Smith and P. Harriott: mit &rations in 4
erlng, 4& ed., McGraw-Hill, New ~ork-, 1985.
68 . N. Siskovic and G. Narsimhari: Proc. Chemca170, Mehume, AUS, vol. 1, 1970, p ~ . 63-75.
69 . A.S. Zhelemyak: J. -1. Chem. USSR, vol. 40, 1967, pp. 834-7.
70. N. 1. Gelperin and V. G. Einstein: IIHeat Tramfer in Fluidized Bedçl', in w a t i o n , Chapter 10, J.F. Davidson and D. Harrison eds., Academic Press, New York, 1971, p. 472.
The cornpletion of my dodorate is the third most signifiant event in my 29
year life. The rnost significant event is my birth, for which 1 must than. my parents.
The second most signifiant event is the marriage to my wife and best fiiend Tracey,
which brings me great happiness. As the third most important event, the completion
of my thesis was made possible by the support of those involved in the previous two
This reseach would not have been possible without the guidance of Professor
J.M Toguri, whose insight into pyrometallurgical processes is an asset to any student.
I would also like to note the input of Dr. S.W. Minmon, whose attention to detail I
hope cornes out in this work The feedback pmvided by my cornmitte m e m h is
also appreciated The first 2 years of this work were firnded by NSERC, wtiich is
pat ly appreciated. The analytical services provided by Falconbridge Limited of
Sudbury, Ontario are also recognized 1 would also like to thank my colleagues at
Falconbridge Ltd. for their support in my efforts to cornplete this w o k
The permission obtained fiom the following publishers to reproduce seiected
figures and tables fkom previously published journals/books is acknowledged:
Transactions of the Institirte for Mining and Metallurgy, London, U.K American Geophysicai Union, Washington, D.C. Academic Press, San Diego, CA The Metallurgical Society Publishing, Warrendale, PA Elsevier Science inc., Tarrytown, NY Pergarnon Ress, Elmsford, NY Joumai of the lron and Steel lnstihrte, London, U.K
Appdix 1 : Equiprnent Profiles Appendix 2: Equiprnent Schernatics Appendix 3: Calcuiated Profiles Appendix 4: Physical Properties of Cu-S Melts at 1250°C Appendix 5: Measured and Caicuiated Expenmentai Data Appaidix 6: Chernid Analyses Appendk 7: X-ray Images of Gas Injection Appendix 8: Graphitai Presentation of hert Gas Blanket Test Results Appendix 9: Graphical Presentatiion of Stagewise Variation of Oxygen
Consumptionn>riving Force Ratio and Mean Gas Residence Tirne Appendix 10: Spreadsheet Cdculation of Mass Transfer Coeficients Appendix 1 1 : Expimental Correlations for Growth Stage
Mass Transfer Coefficient Appendur 12: Calculations
Appendix 1: Measureà Equipment Profdes
Furnace Cantroller Temperature ("C)
A 1.4 - Measured Relationship Between Fumace and Sarnple Temoerature
l t 6 O 0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00
Distance from bottom of crucible (cm)
Fi mire A1.5 - Fumace Ternemperaiure Profi le 1 260- 6 103
I 1 255- - 102.6
CC 2 1250- CU A h
2 -102.2 -g
3 5 1245- 2 iii m
a 3 Q )
g -101.8 2 $! 1240- a ?
1
1235- -101.4
1 2304 t 1 O1 O 2 4 6 8
Gas Flowrate (Numin)
Fimire A1.6 - Variation of Onfice Tempaature and Gas Samnle Bottle Ressure
Appendix 2: Equipment Schematics
AII dimensions in cm.
Mullite Tube
Sade View Front V iew
Fiemire A21 - Fumace Schematic
Isolation Valves
Air from Lab L r Gas Sampie Bottle
To Vent
Titrate scru bbing solution with 0.5 M NaOH
ing Vessel
Appendix 3: Calculated Profiles
/'
1
P = 0.1 1 atm t
l 0.001
2, ' 2 h ' 3b ! 3M ' 460 ' 4 b ' 5 ~ )
Temperature C'C)
Fi-mire A3.1 - Variation of Sulphur Partial Pressure with Temmture
- Metal Phase Hetght - Tord Meli Height - X S in üulk Melt
Fime A3.2 - Variation of Melt Levels with Degee of Cu,S Conversion
Appendix 4: Physical Properties of Cu4 Melts at 12WC
Table A4.1 - Physical Properties of Cu4 Melts at 12500C
II at 1250°C I ("Cu2SW) 1 (S saturatai Cu)
Viscosity (Pas)
Surface Tension (J/rd)
Melting Point (OC)
Suiphur Content (wt %)
-
Contact Angle, with Alumina (O)
0.005
0.395
1127
19.6
0.003
0.750
1077
1.2
- -
105 -
na
Appendix 5: Measured and Calculated Experimental Data
Table A 5 . L - Experimental MeIt S h
Run #
1
2
3
4
5
6
7
8
9
1 O r
11
12
13
2 4
15
16
17
18
19
20
21
22
23
24 "
25
26
27
C r u a i l e Diameter
(IDIOD) (mm)
41/50
48/53
54/59
54/59
54/59
54/59
55/63
54/59
55/63
55/63
55/63
55/63
55/63
55/63
55/63
55/63
55/63
55/63
55/63
55/63
55/63
55/63
55/63
55/63
55/63
55/63
55/63
Crucible Matenal
Graphite
Alumina
Alumina
Alumina
Numina
Alumina
Aiumina
Aiumina
Aiumina
Aiumina
Aiumina
Alumina
Alumina
Aiumina
Aiumina
Aiumina
Alumina
Alumina
Alumina
Alumina
Aiumina
Aiumina
Aiumina
Alumina
Aumina
Alumina
Alumina
Cruçil>le Heigh t (cm)
14
10
10.4
10.4
10.4
10.4
20.5
10.4
20.5
20.5
20.5
20.5
20.5
20.5
20.5
20.5
20.5
Sample Mass (g)
320
385
515
577
582
450
703
432
591
769
634
976
723
6 10
588
674
1224
Liquid Phase
Cu+
Cu2S
Cu2s
Cu+
Cu2S
Cu$
CU$
Cu+
Cu2S
Cu+
Cu2S
S sat'd Cu
Cu2S
Cu2S
Cu2S
Cu$
S sat'd Cu
Melt Heigh t (cm)
4.4
3.7
3.9
4.3
4.4
3.4
5.1
3.3
4.3
5.6
4.6
5.3
5.3
4.4
4.3
4.9
6.6
4.7
5.1
5.9
53
5.5
5 3
4.4
4.8
4.9
5.1
20.5
20.5
20.5
20.5
20.5
20.5
20.5
20.5
205
20.5
Cu2S
Cu2S
S sat'd Cu
643
705
1089
Cu2S
Cu2S
Cu+
Cu2s
Cu+
a,S
Cu+
730
754
738
610
675
682
705
Air Fiowrate 02 Fbwrate Orifice Diameter Temperature Immersion Bubbie Frequency 02 Effiency f l&\ I' fM !Hz) (%I
1-1 1.6 O 5.2 (OE) 1523 1 203 91.4 1 -2 5.8 O 5.2 (OE) 1 523 0.5 232 94.87 1 -3 5.8 O 5.2 (OE) 1523 1 23,9 95.2 1
Air Flowrate (I /min\
2.1 2.1 2.1 2.1 2.1 3.4 2.1 2.1 2.1 3.25
02 Flowrate Onfice Dimler
O 2 O 2.8 O 2.8 O 2.8 O 2.8 O 2.8 O 5.2 (OE) O 5.2 (O€) O 5.2 (OE) O 5.2 (OE)
(KI 1523 1 523 1523 1523 1523 1523 1523 1 523 1523 1523
Immersion Bubbie Fmq~lency 02 Efficiency 1 !Hz\ 1%)
1 27.8 80.01 1 22.4 82.93
1.5 231 83.56 O. 5 22.8 82.04 O 52.9 81.14 1 23.5 80
1.5 20,1 89.17 1 21 88.6
0.5 20.9 87.73 1 21.6 90.1
Air Flomte 0 2 Romte Fxot. (Umin) n) 3-1 1.25 O 3-2 1.25 O 3-3 1.25 O 3-4 1.25 O 3-5 1.25 O 3 6 1.25 O 3-7 2.1 5 O 3 8 3.05 O 3-9 1.25 O 3-10 2.35 O 3-1 1 3.05 O
Orifice Diameter Ternpemture h m Y t rn
2 1523 2 1523
3.05 1 523 3.05 1523 3.05 1523 3.05 1523 3.05 1523 3.05 1 523 3.05 1473 3.05 1473 3.05 1473
Immersion Bubble Frequency 0 2 Efiiiency (cm) t Hz) t%)
2 25.5 79.8 t .5 26.6 75.9 1.5 221 85.4 1 22 84.8
0.5 24.9 84.1 O 31.9 82.5 1 22.1 85.2 1 22.2 87.1 1 30.7 82.4 1 21.6 84.9 1 ' 21.4 81 -3
' (O€) = open ended norde
Table A5.5 - Experimental Run #4 t- -
$ 4 ~ #4 Cu2S Varying gas flowrate, orifice diameter, geometry and temperature. 06- 1 O-!
Air Flowrate 0 2 Flowrate Orifce Diameter Temperature Immersion Bubble Frequency 0 2 Eii icieni Exd. IUmin) (Umin) (mmY (KI (cm1 (Hz1 (%) 4-1 1.25 O 3.1 1 473 1 30.3 83.6 4-2 1.85 O 3.1 1 473 1 36.1 76.7 4-3 2.7 O 3.1 1473 1 41.3 74.8 4-4 3.6 O 3.1 1 473 1 44 72.4 4-5 1.1 O 5.2 (OE) 1473 1 19.9 92.4 4-6 1.7 O 5.2 (OE) 1 473 1 20.9 86.2 4-7 2.65 O 5.2 (OE) 1 473 1 20.4 82.1 4-8 3.75 O 5.2 (OE) 1 473 1 21.7 86.2 4-9 1.15 O 5.2 (OE) 1 573 1 20.7 91.4 4-1 O 1.8 O 5.2 (OE) 1 573 1 20.9 88.2 4-1 1 2.9 O 5.2 (OE) 1 573 1 21.5 86.5 4-1 2 3.85 O 5.2 (O€) 1 573 1 22.3 89.6 4-1 3 4.35 O - 5.2 IOE) 1573 1 22.4 94.3
Air Flowrate 0 2 R o m e Orifice Diameter Temperature Immersion Bubble Frequency 02 Efficiency Mot. ) furnid !rnml' (KI (cm) il+\ ("/O\
5-1 1.25 O 2 1 523 0.5 25.8 74.4 2
3.1 3.1 3.1 3.5 3.5 3.5 3.5 3.5
5.2 (OE) 5.2 (OE)
' (OE) = open ended noule
Table A57 - Werimental Run #6 #6 Cu2$ Varying gas flowrate. 22-1 0-93
Air Flowrate 02 Rowrate Orifice Diameter Temperature Immersion Bubble Frequency 02 Eff iciency Bflq lUminl (Uminl (mm)' 6-1 1.25 O 5.2 (O€) 1 473 6-2 2.1 7 O 5.2 (OE) 1 473 19.7 82.4 6-3 3.35 O 5.2 (OE) 1473 19.3 757
Air Ftowrate 0 2 flowrate Orifice Diameler Temperature lmnersion Bubble Frequency 02 Eff iciency Expt. (ifmin) (Urnin) (mm)' IK) (cm) (Hz) (Yo) 7- 1 1.5 O 2.8 1 523 1 27.1 88.3
Ah Flowraîe 02 Romte Odice Diameter Tenpeaiure l m r s i o n Bubble Frequency 02 Eff iciency Expi. (Uminl (Umin) (mm)' (KI (cm) (Hz) (%) 8-1 1.25 O 2.6 (OE) 1 523 1 37.2 70.5 8-2 2.3 O 2.6 (O€) 1 523 1 31.7 71.9 8-3 1.75 O 2.6 (OE) 1 523 1 31.3 65.7 8-4 3.4 O 2.6 (OE) 1523 1 35.4 79.8 8-5 3.95 O 2.6 (OE) 1 523 1 28.9 85 8-6 2 O 5.2 (OE) 1 573 1 22,3 84.8 8-7 4.9 O 5.2 (OE) 1 573 1 22.1 95.7 8-8 1.5 O 5.2 (OE) 1 523 1 1 8.6 90.7 8-9 4.9 O 5.2 (OE) 1473 1 1 8.3 91.3 8-1 0 1.45 O 3.1 1 473 1 1 7.8 885 8-1 1 3.95 O 3.1 1 573 1 22 81.9 8-1 2 3.95 O 3.1 1 523 1 19.3 80.8
Air Flowraîe O2 Flowrate Orifice Diameter Tempemture Immersion Bubble Frequency 02 Efficiency Expt. (Umin) (Umin) (mm)* (fl (cm) (Hz) (%) 9-1 2 O 5.2 (OE) 1 523 1 21.6 85.5 9-2 1.8 0.2 5.2 (OE) 1523 1 24,2 08.4 9-3 1.6 0.4 5.2 (OE) 1523 1 23.4 88.5 9-4 1.4 0.6 5.2 (OE) 1523 1 22.1 90.6 9-5 1.2 0.8 5.2 (OE) 1523 t 19.6 92.1 9-6 1 1 5.2 (OE) 1523 1 16.3 96.1 9-7 1.2 O 5.2 (OE) 1523 1 21.3 91.7 9-8 2.7 O 5.2 (OE) 1523 1 18.6 84.9 9-9 3.5 O 5.2 (OE) 1523 1 17 85.3 9-1 O 2 O 3.1 1 523 1 24.9 86.2
Air Flowrate 02 Flowrate Orifiie Diameter Tempemture Immersion Bubble Frequency 0 2 Eff iciency b t . IUmin) (Umin) (mm)* (K) (cm) (Hz1 (%) 10-1 1.1 O 5.2 (OE) 1523 1 20.2 93.9 10-2 2.1 O 5.2 (OE) 1523 1 18 84 10-3 2.9 O 5.2 (OE) 1523 1 21.6 85.3 10-4 3.65 O 5.2 (OE) 1523 1 24.9 89.8 10-5 4.5 O 5.2 (OE) 1523 1 24.3 95 10-6 1.15 O 3.5 7 523 1 18.1 88.1 10-7 1.75 O 3.5 1523 1 23.1 85.2 10-8 1.15 O 3.1 1523 1 18.8 87.4 10-9 2 O 3.1 1523 1 19 84 10-10 2.9 O 3.5 1 523 1 21.5 84.7
* (OE) = open eded noule
I
Varying gas Rowrate, N2 Rowrate and N2 lance location. 11-01-94
Air Romte N2 Flowrate Orib Diameter Otifiœ Dimeter Temperature Immersion ' Immersion Bubble Freqency Offgas Conc. 02 Elficienq in) Air I ancehmY NP I ance Imml' (M Ai&me (un1 N2 Lance (ml [HA Sa?) 1%)
1 1 - 1 1.36 0.51 5.2 (OE) 2.6 (OE) 1 523 1 -2 17.7 12.41 81.26 'il-2 1 .36 1 .a3 5.2 (O€) 2.6 (OE) 1523 1 -2 19.3 9.48 79.33 113 1 .36 1.5 5.2 (OE) 2.6 (OE) 1 523 1 -2 17.5 6.6 66.09 1 1 -4 1.36 2.02 5.2 (OE) 2.6 (OE) 1523 1 -2 17.3 5,43 64.26 11-5 1.36 2.5 5 2 (OE) 2.6 (OE) 1523 1 -2 17.6 4.28 57.85 11-6 1.36 3.97 5.2 (O€) 2.6 (OE) 1 523 1 -2 18.6 4.34 81 .O0 11-7 1.18 1 36 2.6 (OE) 5.2 (O€) 1 523 -2 1 17.7 7.47 76.57 11-8 1 .71 1 -36 2.6 (OE) 5.2 (OE) 1 523 -2 1 8.72 74.55 11-9 2.42 1 36 2.6 (O€) 5.2 (O€) 1 523 -2 1 9.85 73.26 1 1-10 3.36 1.36 2-6 (OE) 5.2 (OE) 1523 -2 1 10,19 68.16 11-11 4.19 1 36 2.6 (OE) 5.2 (OE) 1 523 -2 1 1 1.48 72.4 1 11-12 1 .71 1.81 2.6 (OE) 5.2 (O€) 1 523 -2 1 21.6 8.2 80.38 11-13 1.71 2 .S 2.6 (OE) 5.2 (OE) 1 523 -2 1 18.8 6.55 79.53 11-14 1.71 0.62 2.6 (OE) 5.2 (OE) 1 523 -2 1 1 1.24 72.93 11-15 1 .71 3.20 2.6 (OE) 5.2 (O€) 1523 -2 1 5.86 81.43
(OE) a open ended nonle, Negative immersion idkates orifice dstance above men surface.
Table A5.14 - Exwrimental Run Uî3 un 113 CI@ Varyhg gas Ibwrate, N2 Ibwrele and Imrnemlon. 19-01 -94
(Vmin) n) (mm)' (K) 131 1.18 O 5 2 (W 1523 132 1.18 O 52 (E) 1 523 133 1.18 O 52 (m) 1 5 a 1 3-4 1.18 O 52 1523 13-5 2.03 O 52 (a) 15n 136 325 O 5 2 (ml 1 523 157 4.07 O 52 (ml 1 523 13-8 1.18 O 52 (W 1623 139 1.95 O 52 (w 1 623 13-10 32 O 52 (w 1623 13-11 395 O 52 (El 1623
A t Fiowrate 02Flowrale ûf(iœMamoler Tenpwalure lmnerskn 8&ôieFrequency 02Eîfkiency (Umin) n) (mm)' (Ici (an) (Hz) ph)
14.1 0.9 O 2.6 (O€) 1523 1 35 2 70.9 14-2 49 O 2.6 (OE) 1523 1 31.3 87.1 14-3 5.1 O 3.1 1523 1 21 8 81.3 14-4 4.8 O 3.5 1 523 1 20.5 79.5 14-5 2 O 3.1 1 523 1 22 5 W.5 14-6 1.8 02 3.1 1523 1 22 .a 86.7 14-7 1.6 0.4 3.1 1 523 1 21 2 87.8 1 4 4 1.4 0.6 3.1 1 523 1 20.3 90.3 14-9 12 OB 3.1 1 523 1 20.1 90.7
AirFbwmîe 02nowrale ûIlceDlameler Tenperalure lmmerslon BltiMeFrecpmcy 02Etildency Rlmh) Rrhihl [mm). (KI (cm) (Hz) (%]
151 1 2 O 3.1 16î3 1 22.3 93.4 152 195 O 3.1 1 623 1 19.9 91.7 153 2 8 O 3.1 1623 1 21 2 87.3 154 3.65 O 3.1 1623 1 23.7 85.2
r bwrate b wrete t n* tmmersion e m (Umh) mh) A t Lance (mm)' N2 Lance (mm)' {K) A t lance (cm) N2 Lance (cm) (HZ) (% S02) es)
156 2 9 0.64 5 2 (W 2.6 (Of) 1 5 n 1 -2 18.3 13.56 78.82 157 2 9 12 5 2 (W 2.6 (O€) 1 523 1 -2 18.6 11.31 76.14 158 2.9 2.12 52 (W 2.6 (CE) 1 5 n 1 -2 17.4 8.74 72.04 159 29 3.03 5 2 (W 2.6 (OE) 1523 1 -2 19.1 6.35 6 1.83 15-10 2 9 3.81 5 2 (W 2.6 (OE) 1 523 1 -2 18.8 4 .96 5 4 . a 1511 23 4.55 52 (W 2.6 (Of) 1 523 1 -2 1 0 2 4.6 5627
2.6 (OE) 1 523 1 -2 18.9 5.13 70.76 -
TaMe AS.17 - Experlmental Run 616 Cu2S Varying gas flowrale and N2 Ilowaîe.
WL~~$etmrnY Ml A t l m N2 (Hz1 1% 5021 196) 161 3.7 0.7 52 (W 2.6 (OE) 1523 1 -2 195 14.70 83.70 162 3.7 1 .15 5 2 (W 2.6 (CE) 1 523 1 -2 18.1 1 1.88 74.15 163 3.7 22 52 (W 2.8 (O€) 1 523 1 -2 20.1 9 2 89.88 1 6-4 3.7 3.1 5 2 (W 2.6 (OE) 1 523 1 -2 10.6 7.33 64.15 165 3.7 3.75 52 (OE) 2.8 (Of) 1523 1 -2 178 5.86 57.15 188 3.7 4.62 52 (W 2.6 (O€) 1 523 1 -2 20.3 5.14 55.04 167 3.7 5.38 5 2 (a) 2.6 (O€) 1 523 1 -2 20.8 4.91 57,s 168 4 .a 0.7 5 2 (W 2.6 (CE) 1 523 1 -2 222 1626 89.08 16-9 4.65 1 2 5 2 (W 2.6 (Of) 1 523 1 .2 21.3 14.05 84.17 16-10 4.65 2.15 5 2 (W 2.0 (OE) 1 523 1 -2 20.9 10.7 74.51 1611 4.65 3.3 52 (W 2.6 (OE) 1 523 1 -2 19.8 8.47 68.96 ' 1612 4.65 395 52 (m) 2.6 (CE) 1 523 1 -2 21.6 6.48 57.07
1 1613 4.65 4.8 5 2 (E) 2.6 (OE) 1 523 1 -2 22.4 5.39 52.16
Table A548 - Experimental Run #17 Varying S content of copper melt. Air flowrate = 2.66 NUmin Initial % S in melt = 3.5 Oriiice diameter = 5.2 mm (OE) Temperature = 1523 K Dimensionless t = titime for total S removal Immersion = 1 .O cm Time for total S removal = (0.0349'rnelt mass*inital %S)/Air flowrate
l ime Weight % S Weight Oh O BU^ (min)
O 1 3 4 0.03 18.3 O 4 1.61 0.12 19.1 16.46 0.07
7.5 0,987 0.13 17 18.14 0.1 3 I l 1 .O6 O. 16 15.5 19.1 1 0.19
14.5 1.28 0.1 3 1 8.7 19.24 0.25 21.5 - - 17.1 18.98 0.37 28.5 - - 16.7 19.24 0.49 35.5 0.72 0.19 - 19.95 O. 62 42.5 - - - 19.17 0.74 50.5 - - 18.08 O. 88 55 O. 169 0.23 18.6 15.88 0.96
59.5 0.065 0.36 16.3 9.75 1 .O3 63.5 0.01 5 0.62 17.7 2.32 1.10 66 0.005 0.78 19 O. 39 1.15
Air Flowrate Wîninl
1.2 1.2 1.2 1.2 1.2 1.2
2.35 2.35 2.35 2.35 2.35
Orifice Diameter Air Lance (mmY
3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1
Orifice Diameter N2 L a m (mmY
2.6 (OE) 2.6 (OE) 2,6 (OE) 2.6 (OE) 2.6 (OE) 2.6 (OE) 2.6 (OE) 2.6 (OE) 2.6 (OE) 2.6 (O€) 2.6 (OE)
Immersion ' Immersion ' Bubbie Frequency AirLance(cm1 N2Lance(an) (Hz)
1 -2 22.3 1 -2 23.5 1 -2 22.4 1 -2 21.6 1 -2 21.9 1 -2 21.7 1 -2 23.5 1 -2 23.1 1 -2 22.6 1 -2 23.6 1 -2 21.9
Air flowrate
3.4 3.4 3.4 3.4 3.4 3.4 4.5 4.5 4 s 4.5 4.5 4.5
Orifice D ' i t e r Air
3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1
Onfiœ Diameter
2.6 (OE) 2.6 (O€) 2.6 (O€) 2.6 (OE) 2.6 (O€) 2.6 (OE) 2.6 (OE) 2.6 (OE) 2,6 (OE) 2.6 (OE) 2.6 (OE) 2.6 (O€)
Immersion ' Immersion ' Bubbie Frequency Offgas Conc. Airlance(cml N 2 I m (H7) (% S02\
1 -2 23.7 12.64 1 -2 23.8 10.05 1 -2 22.6 8.3 1 -2 23.4 6.55 1 -2 22.5 5.8 1 -2 21.4 5.67 1 -2 23.1 12.89 1 -2 23.6 10.23 1 -2 22.1 8.61 1 -2 23.6 7.03 1 -2 24.1 6.2 1 1 -2 22.3 6.28
(O€) = open mded nonle Negative immersion indicabs orifice distance above meii sulfsce.
Table A5-21 - Experimental Run #20 Varying S content of copper meit. Air flowrate = 4.0 NUmin Initial % S in mek = 2.2 Orifice diameter = 5.2 mm (OE) Temperature = 1523 K Dimensionless t = titime for total S removal Immersion = 1 .O cm Time for total S removal = (0.0349*melt mass*inital %S)/Air flowrate Mass of Cu =1066(i
Time Weight % S Weight % O Bubble Frequency % S02 in offgas Dimensionless timi
- 34 O 1.58 17.8 0.13 1.63 Vote: Gas samples are 24.4 seconds prior to meit samples.
Calculation of Time Differenoe Between Melt and Gas Samples - Run MO
Ramp Input into Gas Sarnple Bottle
Gas Fbwrate (Nûmin) 562 conc. at GO (%) Sû2 mc. at b t (%) Tirne diration t (min) Conc. gradient ( m i n ) Output function-
Sam* Bottle: IO = L = Vol = u =
0.004 Much closer to piug ibw than csm Row.
4 .O0 Plug Flow 19 Time ~May midence time within reacbr tube + coppercdl+ plastic tubing + 0.5 ' gas sample bottle 15 5 Reaction tube vol: 1.49 NL
0,8 C~abia gas îemp: 1523 K 19-O.8t Gas temp at glas9 htbe: 1000 K
Reçidence time in tube: 5.28 sec Copper and plastic îubing vol: 0.039 NL Mean ga9 temp in tubing: 323 K Residence time in îubing: 0.54 sec Residence lime in sample botlie: 7.08 sec
Toial residenco lime: 9.36 sec
Time between gas and rnelt sample: 15 sec
Residem time indeperident of gradient in m p input, only essumpibn is a linear variation over the time t
Mam Balance: Run ü20
Total O edded to grstem as air. Totai O rie'moved fm system as air: TOM S remwed hwn system as Sû Total O remwed fm system as SO Initiai S contsnt of meit Initial O content of met Finai S content of melt Find O content of meit
2.548 moles 0.255 moles 0.712 moles 1.425 moles 0.749 moles 0.071 d e s 0.000 mdes 1.070 d e s
Total tirne dtference: 24.4 sec
Air flomte n)
21 -1 1.25 21 -2 1.25 21 -3 1.25 21 -4 1.25 21 -5 1.25 21 8 1.25 21 -7 1.9 21 4 1.9 21 -9 1.9 21-10 1.9
Orifice D i i t e r I'
2.6 (OE) 2.6 (OE) 2.6 (OE) 2.6 (OE) 2.6 (OE) 2.6 (OE) 2.6 (OE) 2.6 (OE) 2.6 (OE) 2.6 (OE)
Orifice Diameter N2
2.6 (OE) 2.6 (OE) 2.6 (OE) 2.6 (OE) 2.6 (OE) 2.6 (OE) 2.6 (OE) 2.6 (OE) 2.6 (OE) 2.6 (OE)
Temperature Immersion Immersion IKl Ar-l N2 LEVIce~I
1 523 1 -2 1 523 1 -2 1 523 1 -2 1 523 1 -2 1 523 1 -2 1 523 1 -2 1 523 1 -2 1 523 1 -2 1 523 1 -2 1 523 1 -2
Bubble Frerplency
IHzl 36.3 37.1 35.8 35.6 33.7 34.1 35
33.7 33.1 34
Air flowrate N2 Flowrate Orifice Diameter
2.6 (OE) 2.6 (OE) 2.6 (OE) 2.6 (OE) 2.6 (OE) 2.6 (OE) 2.6 (OE) 2.6 (OE) 2.6 (OE) 2,6 (OE) 2.6 (OE)
Orifiw D i e t e r
2.6 (OE) 2.6 (OE) 2.6 (OE) 2.6 (OE) 2.6 (OE) 2.6 (0 E) 2.6 (OE) 2.6 (OE) 2.6 (OE) 2.6 (OE) 2.6 (OE)
Immersion ' Immersion ' Bubble Frequency N? I -\ (Hd
1 -2 32.1 1 -2 31.9 1 -2 324 1 -2 31.3 1 -2 30,7 1 -2 32 1 -2 31.8 1 -2 30.3 1 -2 31.4 1 -2 29.9 1 -2 3 1
02 Efficiency (%1
75.48 68-16 63.88 58.31 Q.51 64.24 76.81 67.30 60.03 56.45 63.78
(0E)P open ended mnle Negative immersion indites o r i b d s t m above melt surface,
Tabk A524 - Exaerlrnental Run UZ3 Cu2S , Varyhg gas fbwrete, orïke diamelgr, fpomelry and Immersion.
isn
Table A525 - Buerimental Run a4 C Varylng gas IbHnaie and N2 Ibwrale. 22-0591
Ortflce D W l e r N2 Lance (rml).
2.6 (OE) 2.6 (OE) 2.6 (E) 2.6 (E) 2.6 (CE) 2.6 (CE) 2.6 (OE) 2.6 (OE) 2.6 (OE) 2.6 (OE) 2.6 (OE) 2.6 (OE)
Tenpereture Immersion' M A t L a m {cm)
1623 1 1623 1 1623 1 1623 1 1823 1 1623 1 1623 1 1623 1 1623 1 1623 1 1623 1 1623 1
Immersion' N2 Lance (an)
-2 -2 -2 -2 -2 -2 .2 -2 -2 -2 -2 -2
Cu2S Varying gas Ilornale and N2 Ibmale. 25-03-44
AtFlowrale @Romale Omceûbmeter OrXkaûiarrmter Ttaqmîaîw0 Immersbn' Immersion' Blibble F m Ollgas Conc. 02 EHldency (l~tnh) (LMn) A t Lanae (mm)' N2 Lance (mm)' (KI A t LBnca (on) N2 Lance (cm) (HZ) (%S02) (%)
251 3.5 O 5 2 (W 2.6 (OE) 1 623 1 -2 21.4 19.91 94.81 252 3.5 0.85 52 (CE) 2.6 (CE) 1623 1 253 3.5 1.65 5 2 (w 2.6 (a) 1623 1 254 3.5 2.15 5 2 (ml 2.6 (m) 1623 1 255 3.5 2.75 5 2 (E) 2.6 (CE) 1623 1 258 3.5 3.6 5 2 (a) 2.6 (CE) 1623 1 257 3.5 425 5 2 (E) 2.6 (OE) 1623 1 258 4.6 O 5 2 (w 2.6 (CE) 1623 1 25.9 4.6 0.9 5 2 ( E l 2.6 (CE) 1623 1 2510 4.6 1.7 5 2 (W 2.6 (O€) 1623 1 -2 21.1 12.08 78.78 25-11 4.6 2.35 52 2.6 (CE) 1623 1 -2 22 9.86 70.94 2512 4.6 2.9 5 2 (E) 2.6 (CE) 1623 1 -2 19.6 8.72 67.70 2513 4.6 3.7 5 2 (0'3 2.6 (a) 1 623 1 -2 20.8 7.63 65.56
m p s an ~ ~ k i o w n a t e o z t t t ~ n c y m a t n r s n y ( & a ) r d a i u z ~ ~ ~ulp)ur- fmn, (w(40 (-1 6) (91 K ) W) ml fw O 1.67 O21 lae0.0 4 s IP 021 20.71 roe2.1 4.000 8862 aoo 98.62 9 1.07 0 2 1 19.17 1077.5 4 . W 9120 0.00 912Q IMB) 125 Q82 O21 19.34 10728 4.000 gZ10 0.00 0210 11825 16 0.643 (123 16.02 1Q67.1 3951 B1.m 5.œ BBS8 1MA 19.5 a180 O= la13 lW.9 3.673 74.37 1515 88.52 74.a 24 0.m 0.6 612 1-4 3- 2542 6U.m s.22 81 29 2a5 am33 (X86 1 .O3 1W7.9 3229 3.Q6 81.75 9571 6326 29 O 1.11 0.29 1061.6 329 1.13 ml8 89.31 8693 31.5 O 135 022 1057.1 3.2m 0.W M.&? a48
Appendix 6: Chernical Analyses
Table A6.1 - Chernical Analysis of Melt Ssmples
na - not anrilyzed. * - small amount of solid residue afier Aqua Regia dissolution.
Smplc Id.
1 -S-A
# - visible contamination with mattc.
Description
Syndictic Cu,S
C
3
Wt % Copper (A.A.')
79.68
- assays performed at MTC Lab by Falconbridge.
1-S-B
2 4
3-12
4 4
4-13
4-E
4-F
5 -E
5-F
5-C
6-S
6-4
9-E
12-S
12- 1
12-2
12-3
1 2-4 holes:
Wt % Sulpliiir (~eco' f ixco*)
20.75119.8
Wt %Oxygcn (1xco2)
0.40
S yn Wtic Cu,S
Melt sample taken &ter expt 2-4.
Mclt saniple îaken rtfter expt 3-12.
Mctal phase sarnple taken after expt 44 .
Metal phase sample taken aftcr expt 4- 13.
Solid bulk matte sample taken after run #4.
Solid sample taken from surface aftcr run #4.
Solid bulk matte sample taken after mn #S.
Solid m p l e taken from surface after run #5.
Solid sample taken h m underside of cover afkr run #5.
Melt s'ample taken at start of run #6.
Mclt smple iriken after expt 6-4.
Solid bulk matte sample taken aftcr nin #9.
Melt sample taken rit sm of nin # 12.
Melt smplc uken after expt 12-1,
Mclt srui~plc triken 1îTicr cxpt 12-2.
Melt stuiiple tilken nfter cxpt 12-3.
Melt sample taken after cxpt 12-4. - assays performed at L?urenlian University by autlior.
76.02'
80.95
na
na
80.46
82.55
81.38
82.24
na
79.25
78.40'
80.99
na
na
11 a
na
na
19.601na
19.53lna
1.65'1na
1.65%. 10
20.05118.4
17.00115.6
18.50lna
16.521na
18.6Ol17.3
19.69118.5
19.4611 8.2
I8.9llna
0.68410.50
0.43410.42
0.22410.24
0.05910.W6
0.01810.019
na
na
na
0.12
0.79
1.14
na
na 0.93
0.86
0.92
na
O. 14
0,16
0.20
0.29
0.42
Table A6.1 - continued
Description Wt % Copper I (*.A')
Wt % Sulphur Wt %Oxygen (Leco'/Lecoz)
1 12-7
12-8
12-9
11 12-12 i I 1 I
Melt sample taken after expt 12-12. 1 na I nd4.001 I 2,19
12-5
12-6
12-10
12-1 1
11 12-13 1 Melt sample taken after expt 12-13. nd4.00 1 2.47 I na I
Melt stample t i e n after expt 12-7.
Melt sample taken after expi 12-8.
Melt sample [,*en after expt 12-9.
11 12-14 1 Melt sample t i e n after expt 12-14. I na I ndd.001 I 2.73
Melt s,mple tiien after expt 12-5.
Melt sample t'lken after expt 12-6.
Melt sample taken after expt 12-10.
Melt sample ~ i e n after expt 12-1 1.
na
na
na
It 12-0 i I I I
Solid sample taken from oxide layer after run #12. I 86.48' I ndna I 9.9
na
na
na
na
I
na/#.OOl
nd4.001
naM.00 1
na - not andyzcd.
0.00310.001
nd4.001
0.97
1.23
1.44
nal4.00 1
nd4.001
12-15
12-E
17-S
17-1
17-2
17-3
17-4-A
17-4-8
* - small amount of solid rcsidue aftcr Aqua Regia dissolution.
0.59
0.76
1.68
1.93
# - visible contunination with nlattc.
Melt sample taken after expt 12-15.
Solid metal sample taken after run #12.
hotcs: ' - ,assays perfomred nt Laurenti'm University by author. - assays pcrfomwd at MTC Lab by Falconbridge.
Melt sample raken at start of run #17.
Melt sample taken after expt 17-1.
Melt sample taken after expt 17-2.
Melt stample t i e n after cxpt 17-3.
Matte phase sample taken after expt 17-4.
Metal phase sampIe taken after expt 17-4.
na
na
na
na
na
na
na
na
natd.00 1
na/<0.00 1
1.34'/1.22
1.61'11.53
0.98711.88'
1.061 1.94'
19.42/17.9
1.28"I .30
2.78
2..9 1
0.1 1
0.13
0.13
0.13
1.01
0.13
Table A6.1 - continued
17-10 1 Mclt s'ample haken drcr expt 17-10. 1 na 1 0.16910. 17 1 0.17
Srunplc I D .
17-7
17-11 1 Mclt s,mplc taken aftcr expt 17-1 1. 1 na 1 0.065/0.0 17 1 0.30
17-12 1 Mclt s'ample taken aftcr cxpi 17-12. 1 na 1 0.0 1510.00 1 1 0.52
Description
Mclt srimplc cqken dtcr expt 17-7.
17-13 1 Melt smple triken afkr expt 17-13. 1 na 1 0.0051~0.00 1 1 0.66
Wt % Copper (A,A.')
na
I
20-S 1 Melt saiiplc ~ i c n at slm of run #20. 1 na 1 1.76"/ 1.67 1 0.2 1
17- 14
17-E
Wt % Sulphur (Leco'/Leco2)
0,7210.756
Wt %Oxygen (Leco2)
0.13
Melt sample Irikcn after expt 17-14.
Solid metiil s'ample iaken d'ter run #17.
20- i
20-2
20-8 1 Melt smplc triken aftcr expt 20-8. 1 na 1 na.dMû 1 1 1.1 1
-
20-3
20-4
20-5
20-6
20-7
20-9 1 Mclt smple nkcn aftcr expt 20-9. 1 na 1 n,?/<O.ûû 1 1 1.35
na
na
Mc1 t s,unple taken afier expt 20- 1.
Melt simple taken d e r cxpt 20-2. - - - -- -- --
Mclt sarnple taken after expt 20-3.
Melt s,ample taken after expt 204.
Melt smple triken after expt 20-5.
Melt sample taken after expt 20-6.
Melt sample cîken aftcr expt 20-7.
na/<O.W 1
na/<O.ûû 1
na na
20- 1 0
20-E
0.84
1.84
2.13% -22 2.07'1 1 .O7
. - -
0.2 1
0.23
0.29
0.60
0.86
- --
na
na
na
na
na
lotes: ' - assays performed at Laurentian University by autiior. - rissays performed ai MTC Analyticai Lab by Palconbridge.
na - not andyzed, * - small amount of solid residuc a fw Aqua Regia dissolution. # - visible conmination with matte.
--
Melt sample &en afkr expi 20%). Solid s net al simple triken after nin #20.
0.2 1
0.2 1 - -
1.22/0,92
0.64310,46
O. 18810.06
0.023/0.0 1
0.003310.001
-
na na
nd<0.00 1
na/<O.OOl
-- -
1 .58
2.22
Appendix 7: X-ray Images of Gas Injection
Quiescent melt surface
A7.1 - 3.1 mm orifice. Air IiZ! 4.0 Numin -
Quiescent melt surface
F-A7.2 - 5.2 mm nozzle. Air (a% 2.0 Wmin
Quiescent melt surface
A7.3 - 5.2 mm noda Air m. 4.0 W r n i n
1 84
Appendix 8: Graphical Presentation of Inert Gas Blanket Test Results
100 1523 K GAS 1-n Orifice n i a w r
- Air @ 1.36 NUmin Air 1 cm below 5.2 mm (O€) Cu2S Nitrogen 2 cm above 2.6 mm (OE)
90
80 rn
I Bubble growth and bubble rise
N2 Flowrate (Numin)
A8.1 - Variation of O,ficiencv with N2 Flowrate onto Melt Surface (Air flowrate - - 1.36 W m i n )
1523 K G ~ s L - r n w i g n Air @ 2.03 Umin Air 1 cm below 5.2 mm (OE) Cu2S Nitrogen 2cmabove 2.6 mm (OE)
Nitrogen Flowrate (Numin)
Bubble rupture
1 O0
m
Bubble growth and bubble rise 50 1 1 1 1 1 t 1 1 1 1
-
an,
O 1 2 3 4 5 Nitrogen Flowrate (Numin)
. . gure A8.3 - Vanation of Q Efficiencv with N, Flowrate onto Melt Surface
{Air flowrate - 2.9MIm' in) - -
1523 K Ar@ 29NUmin Cu2S
'O0 1523K GAS l a n c e n o - Air @ 3.7 NUmin Air 1 cm below 5.2 mm (OE) Cu2S Nitrogen 2 cm above 2.6 mm (O€)
90i I
C 0- Air 1 cm below 5.2 mm (OE)
Nitrogen 2 cm above 2.6 mm (OE) 1
1 Bubble Rupture 1
1 50 ! I I I I I J
O 1 6 I 1 I 1 I I
2 3 4 5 6 Nitrogen Flowrate (NUmin)
en- with N2 FIowrate onto Melt Surf'ace {Air flomte = 3.7 NUmin)
- - - - .- - .. Orifice Diameter
I 1 cm below 5.2 mm (OE) Nitrogen 2 cm above 2.6 mm (O€)
1 Bubble rupture 1
40 ! I 1 1 l 1 1 l I I I i
O 1 2 3 4 5 Nitrogen Flowrate (NLfmin)
-I
1523 K 60- Air @ 4.65 NUmin m
- cu2s m (I --
&me A8.5 - Variation of O, Eficiency with N, Flowrate ont0 Melt Surface
50- -
-
{Air flowrate = 4.65 Wrnin)
Bubble growth and bubble rise
Appendix 9: Graphical Presentation of Stagewise Variation of Oxygen Consumption/Dnving Force Ratio and Mean Gas Residence Tirne
5.2 mm orifice (OE) cu2s
I
Growth -t
Rise ;r
Rupture
Air Flowrate (Numin)
K m e Ag. 1 - Variation of Consumpt 'on t o . D n m ~ Fo - *
I rce Ratio with Air Flowrate 15-2 mm orifice (û
1 Growth
3 ( Rupture
3 Air Flowrate (Numin)
-. . A9.2 - Vanation of Mean Gas Residence Time with Air Flowrate
Growth
Rise
Rupture
Air Flowrate (Numin)
Growth
Rise
Rupture
0.05
-
0.04- V) Y
$' -
0.03- 0 O C O - 73 .- % 0.02- Cf C (O
- a
= 0.01 - -
O 1
1523 K 1 .O cm immersion 2.6 mm orifice (O€) Cu2S
\ '. \.
1 1 I I I
2 I
5
-
-4
-
-3
-
-2
-
- 1
-
3 4 O
Air Flowrate (Numin)
I
Growth t
Rise +5
Rupture
2 3 4 Air Flowrate (Numin)
1 .O cm immersion
2 3 Air Flowrate (NL/min)
5
Growth
Rise
2 3 4 Air Flowrate (NL/min)
- 12-
- 10-
- 8-
Rupture 1623K 5.2 mm orifice (OE) cu2S
A9.7 - Variation of Consumption to Drivin~ Force Ratio with AU. Flomte (5.2 mm orifice (OE). 1623 Q
1623 K 5
1 .O cm immersion 5 2 mm orifice (OE) - Cu2S
-4
-
-3
-
-2
-
- 1
-
Air Flowrate (Numin)
Growth --
Rise - Rupture
R
Growth +
Rise -+
Rupture
O 8 - Ci
2 i.u' - II c 6- m s -
Fi-gure Ag. 9 - Variati O n O f Consmtion to Driving Force Ratio with O/dX Injected 0.1 mm orifice. 1523 K. 2 NUmin A i W
1523 K 3.1 mm orifice Cu2S 20NL/min(Air+02)
1 .O cm immersion
0 I 1 1 1 1 1 1
20 1
30 40 50 60 Oxygen lnjected (%)
0 O
$ 4- O *- c.
E - Y
3 V )
S 2-
3 1 Rupture
O t a, - C3)
C o '
. . .10 - Variation of Mean Gas Raid
194
1
1 I 1 a I I l I
20 30 40 50 60 Oxygen lnjected (%)
Appendix 10: Spreadsheet Calculation of Mass Transfer Coefllcients
Table Aî0.1 - Calculated Bubble Growth Stage Mass Transfer Coefficients
P(QJ Injecteci (atm)
0.2 1
0.2 1
0.21
0.2 1
0.2 1
0.2 1
0.2 1
0.2 1
0.2 1
0.2 1
Gas Flowrate wmw
1.35
2.05 v
2.90
3.70
4.65
1 .25
1 -90
3.10
4.30
1.20
2.35
3 -40
4.50
1.40
2.60
3.50
4.60
2.0
2.0
2.0
1- only tor
System Temperature
(KI
1523
1523
1523
1523
1523
1523
1523
1523
1523
1523
1523
1523
1523
1623
1623
1623
1623
1523
1523
1523
open-ended nodes
Orifice ID (mm)
5.2
5.2
5.2
5.2
5.2
2.6
-
Orifice OD (mm)'
7.3
7.3
7.3
7.3
7.3
5.6
2.6
0.2 1 3.1
5.6
na
2.6
0.2 1 3.1
5.6
na
2.6 1 5.6
0.2 1 3.1
3.1
na
na
5.2 7.3 0.2 1 I 5.2 7.3 0.2 1
0.2 1 5.2 7.3
0.2 1 5.2 7.3
3.1 na I 0.29
0.45 3.1
3.1 I I na 0.6 1
(na indicales homntal oniice)
na
Specrfy gas flowrate, temperature, inner orifice diameter, outer onfice diameter, final % conversion obiained. oxygen pzrtial pressure in injected gas. bubble frequency
f Set time(O)=O
Set bubble diameter(0) = internai orifice diameter Set bubble height(0) = O.Sginternal orifice diameter
Set time increment = 0.011bubble frequency Set bubble volume increment = gas flowrate x time increment
Set initial oxygen partial pressure = oxygen partial pressure in injected gas
1
fialculale initial bubble volume(Oj)
f Set I = 1
t ) Calculate time(i) = time (i-1) + time increment
Calculate bubble volume(i) = bubble volume (i-1) + bubble volume increment Calcubte equivalent hemispherical bubble diarneter(i)
I
II equivalent hemispherical diameter c h e r orifice diarneter
Bubble shape is a spherical cap Spherical cap base diameter = inner orifice dimeter
Calculate spherical cap height from diameter and volume Calculate bubble surface area
If equivalent hemispherical bubble diameten outer orifice diameter
True
False
Ficure A 1 O, 1 - Calculation Merhodology Fiowchan & R ubble Grnwth S t w Mass Transfer Coefficients
Bubble shape is a hemispherical cap Cakubte bubble diarneter irom bubble volume
Bubbte diarneter at base of truncation = outer orifce diarneter Cakulate height of truncation baseci on bubble volume
Cakulate bubble sudace area
* Cakulate new partial pressure of oxygen in bubble based on gas entering over the duration t(i-1) to t(i)
based on mass transfer through gas film over the duration t(i-1) ta t(i)
see
experim,, ,.,, ,,,,,, , ,,,, the mass transfer coefficient (increase k to decrease P(02)
Calculatlon of kg for bubble growth stage.
Gan Flowrate 1.35 NL/mln Temperature 1523 K lnslde OrHlce Oiameter 5.2 mm Outslde Orifice Diameter 7.3 mm Final Conversion 58 % P(02) Injecteci 0.21 atm Bubble Frequency 20 Hz
Number of elemenls Time Increment Final Bubble Vol. Final Equlv. Dlameter
kg Target Flnal P(02) Actual Final P(02) Initial Hemlsphere Vol.
1 O0 0.00050 8
5.750 cm3 2.221 cm 13.28 cm18
0.0882 atm 0.0882 atm 0,0368 cm3
Element Bubble Vol. Equlvalent Dlameter Est. Bubble Diameter Actual Bubble Dlameter Spherical Cap Height Interiaclal Area P(02) M a l P(O2) final No. cm3 cm cm cm cm cm2 atm atm
lnitially 0.0368 0.4131 0.52 0.52 0.2600 0.4247 0.21 O0 0.21 O0
Table A10.2 - Calculated Bubble Rise Stage Mass Transfer Coefficients
bA
3- based on a cylindncal gas channel
t
Gas Flowrate (NUmin)
1.35
2.05
2.90
3 .70
4.65
1.25
1.90
3.10
4.30
1.20
2.35
3.40
4.5 O
1.40
2.60
3 .50
4.60
2.0
2.0
2 .O
1- only for 2- based on oblate spheroidal bubble geometry
S ystem Temperature
(KI
1533
1523
1523
1523
1523
1523
1523
1523
1523
1523
1523
1523
1523
1623
1623
1623
1623
1523
1523
1523
open-ended nozzles
Orifice ID
(mm)
5.2
5.2
5.2
5.2
5.2
2.6
2.6
2.6
2 -6
3.1
3.1
3.1
3.1
5.2
5.2
5 -2
5 -2
3. i
3.1
3.1
(na indicates
Orifice OD
(mm)'
7.3
7 -3
7.3
7.3
7 -3
5.6
5.6
5.6
5.6
na
na
na
na
7.3
7.3
7.3
7.3
na
na
na
horizontal
P(OJ Injected (atm)
0.2 1
0.2 1
0.2 1
0.2 1
0.2 1
0.2 1
0.2 1
0.2 1
0.2 1
0.2 1
0.2 1
0.2 1
0.2 1
0.2 1
0.2 1
0.2 1
0.2 1
0.29
0.45
0.6 1
orifice)
Rise Stage k (crn/~) '~
1.12
0.97
0.84
0.74
O -67
1.3 1
1.12
0.90
0.78
0.75
0.77
0.74
0.68
1.22
0.92
0.78
0.67
0.98
0.9 1
0.88
Rise Stage kg (cm/s)'
1.67
2.5 1
3.38
4.17
5.12
1.87
2.45-
3 -45
4.68
1.1 1
2.30
3 -5 8
4.77
2.04
3.55
4.52
5.86
2.36
2.30
2.26
Specify gas flowrate. temperature, orifice immersion, bubble volume, maximum diameter. liquid film thickness,
initial Oh conversion obtained, final % conversion obtained, oxygen partial pressure in injected gas
I
( Calculate initial and final partial pressures of oxygen )
Assume oblate spheroidal bubble shape Assume a cylindrical gas channel
lculate minor axis length Calculate gas channel diameter Calculate major axis lengt h Calculate gas channel cross-sectional area
Calculate eccentricity Calculate gas channel surface area ulate bubble surface ar I
Calculate Morton number From bubble shape diagrarn,
Calculate bubble rise velocity Calculate rise stage residence time
Calculate molar flux of oxygen
Calculate mass transfer coefficient
Calculate gas velocity
--
( Cakulate mass transfer coefficient 3
F i y e A 10.2 - Calculation Methodolo y Flowchart &r Rubhle Rise Stace Mass Transfer Coefficient
Calculation of kg During Bubble Rise
Gas Flowrate Temperature Initial converslon Final conversion Bubble volume Equivalent diameter Immersion Orifice diameter
Geometry :
Eccentricity 0.29
Mass Transfer Coefficient
1.35 1 523
58
62 5.7496
2.22 1
5.2 (OE)
NL/min Initial P(02) K Final P(02) % Log mean P(02)
% cm 3 Maximum diarneter cm Liquid film thickness cm mm
Oblate Spheroidal Bubble
Volume Minor a i s Major axis Surface Area Eotvos No. Morton No. Reynolds No. Rise Velocity Rise time Molar flux
kg
Oblate Spheroidal Bubbte Cylindrical Gas Channel
0.0882 atm 0,0798 atm
0.0839299533 atm
Cylindrical Gas Channel
Diameter X- Area Gas Veloclty Surface Area Rise time Molar flux
kg
Table A
Gas Flowrate (NUmin)
- 1.35
2.05
2.90
3.70
4.65
1.25
L .90
3.10
4.30
1.20
2.35
2- based on plug flow in gas phase of crucible head space 3- based on back-mixed tlow in gas phase of crucible head space
4.50
1.40
2.60
3 -50
4.60
2.0
2.0
2.0
10.3 - Calculated
System Temperature
( K )
1523
1523
1523
1523
1523
1523
1523
1523
1523
1523
1523
only for open-ended nozzles (na indicates horizontal orifice)
1523
1623
1623
1623
1623
1523
1523
1523
Bubble
Orifice ID
(mm)
5.2
5.2
5 -2
5.2
5.2
2.6
2.6
2.6
2.6
3.1
3.1
3.1
5.2
5.2
5.2
5.2
3.1
3.1
3.1
Rupture
Orifice OD
(mm)'
7 -3
7.3
7.3
7.3
7.3
5.6
5.6
5 -6
5.6
na
na
na
7.3
7.3
7.3
7.3
na
na
na
Stage Mass Transfer Coefficients
P(0,) Injected
(atm)
0.2 1
0.2 1
0.2 1
0.2 1
0.2 1
0.2 1
0.2 1
0.2 1
0.2 1
0.2 1
0.2 1
0.2 1
0.2 1
0.2 1
0.2 1
0.2 1
0.29
0.45
0.6 1
Rupture k;Ai
(crn3/s)'
142
157
265
454
833
3 5.3
37.6
145
402
105
209
357
344
445
609
1100
185
232
295
Rupture k8+Ai
265
252
457
950
2510
4 1.7
42.5-
191
70 1
176
352
570
1440
1190
1650
4370
320
465
723
Specdy gas flowrate, temperature. crucible head space height, crucible diameter. initial % anversion obtained,
1 Oh conversion obtained, oxygen partial pressure in injected
I ( Cakulate the initial and final oxygen partial pressures )
Assume gas phase plug flaw in the crucible head space
I Cakulate the crucible cross-sectional area
Calculate the head space volume
rnass transfer coetfiiient- interfacial area (use plug MW value)
Cakulate the mean gas residence tirne Calculate the rnolar flux of oxygen
interiacial area parameter for plug fiow
Set i = 1 Set number of elements = 100
Caiculate lower residence tirne for element i Cakulate upper residence tirne for element i Cakulate mean residence tirne for element i
Calculate rnolar flux of oxygen for element i Cakulate final oxygen partial pressure for element i +
Caiculate fraction of gas in elements<element i Cakulate incremental fraction of gas in
elernent i only + Calculate incremental weighted final oxygen
Fieure A 10.3 - Calculation Methodoloçv Flowchart for Rubble Rupture Stace Mass Transfer Coefficient
Set i = i+l Q see previous page l
/ Calculate weigMed average final oxyge; 7 partial pressure by sumrning the incremental ( weighted values over all 100 elernents
Adjust the lumped interfacial area- final oxygen partial pressures mass transfer coefficient
are within 0.1% (increase k'A to decrease P(02)
Appendix 11: Experimental Comiations for Bubble Growth Stage Mass Transfer Coefficient
Ro(1t Fi']
Conalan1 Sid En al Y E a fl hwlmd No. ol Obrnarkr i r
Gas Flowrate 12000 NiJmin
Temperature 1523 K lnslde Orifice Diameter 50 mm Outslde Orifice Dlarneter 200 mm Final Conversion 30.5 %
P(02) Injected 0.21 atm
Bubble Frequency 5 Hz
Nurnber of elemenls Time lncrement Flnal Bubble Vol. Flnal Equiv. Diameter
kg Target Final P(02) Actual Final P(02) lnilial Hemlsphere Vol.
100 0.00200 s
204429,530 cm3
72.775 cm 40.00 cmis
0.1460 atm 0.1460 atm
32.7249 cm3
Liquid density = 5.8 k a :. specific volume = 25ûO/S. 8 = 430 Utuyere
Lance submergence: typically 1 = 30 to 60 cm 1* = 1/15 :. l(mode1) = 30/15 = 2 cm
Orifice diarneter: typicdly d, = 5 cm l* = 1/15 .'. $(model) = 5/15 = 3.3 mm
a) based on expected bubble fi-equency In the converter3 d, = 4 To achieve this in the model, cl,, = 2 cm Based on previous research, for a 3 mm orifice, bubble rieguency = 25 Hz For d, = 2 cm, Vb = N3/6 = 7P23/6 = 4.2 ad This is the bubble volume at 1523 K .'. at 298 K Vb = 4.2*298/1523 = 0.82 cm' .O. $ at 298 K = V&, = 0.82*25 = 20.5 m 3 s = 1.23 W m i n
b) based on the Modified Froude Number Modified Froude Number = FI' = gq.,2/(g&dJ
For the converter, e, = PM(R'T) P = Pa + egti = 101325 + 5800*9.81*0.3 = 118394 Pa M = 0.029 kgIrno1 R = 8.314 J/(mol K)
Now to achieve Ff=21 in the experirnental scale,
Qn = 7~4,cl,,~/4 = 7c*120*(0.003)2/4 = 8.52*104 d s :. at 298 K and 10 1325 Pa, $ = 8S2* 104*(298/1 523)*(lO2463ilOl325) = 10.1wmin
a) Gas train #1, with surge tank
Subnode chamber volume = supply nibing volume + surge tank volume :. V, = 1.08 + 2.26 = 3.34 L
b) Gas train #2, without surge tank
Subnonle chamber volume = supply tubing v, = 1-08 L
Oxygen utilization m e a d at end of bubble rupture stage Must index back to bubble rise stage Assume bubble rupture is immersion independent :. the difference between two levels of immersion is attributable to the bubble rise *.- mass transfer rate ac dnWig force .'. mass transfer rate/driving force = constant (for 2 different immersions)
In terms of Pm this is expressed as: Mass transfer rate = NA cc Pm Driving force =
Mm = change in Pm over bubble ruphrre stage .'. for the bubble rupture stage, APaJ(bp&,, = constant (for both immersions)
Now mm = Pa, - Pa, where Wginning of rupture stage and e.end of rupture stage
For example, for a 1 cm immesion, the oxygen utilization at the end of the bubble fll~mstage=90% .'. Pm&, = (100-90)/100*(0.21 *lOl325) = 2128 Pa From inert gas blanket tests, for a 1 cm immersion, conversion at the beginning of the bubble rupture stage = 60%
.O. Pa,, = (10060)/100*(0.21* 101325) = 85 1 1 Pa
Now for the same conditions for a 2 cm immersion, the conversion at the end of the bubble rupture stage = 89%
.O. Pa, = (100-89)/100*(0.21*101325) = 2341 Pa
:. using the equation derived above, Pau = 8511*2341/2128 = 9361 Pa This corresponds to an oqgm utilization = 10-(9361*100/(0.21* 101325)) = 56%
.*. a difference of 90-89=10/dcm at the end of the rupture stage corresponds to a dflerence of SO-56=40/dcm at the beginning of the rupture stage
&a Oc (a/(&? E3ased on experiments with molten iron, ket = 2.5 pm O= 1.5 N/m AQ 7200 kg/m3
Assume = k*(~d(&))O.~ .'. 2.5*1@ = k*(1.5/(9.81*7200))05
Now for O = 0.395 N/m and AQ = 5800 kdm3 .*. &, = O.ûOO542*(0.395/(9.8l *5800))05 = 1.4*104 m = 1.4 pm
A. 1 2.6 Proolet Terminal Velocitv vs. Gas Rise Velocity
a) Gas rise velocity in crucible head space %=a$* A = fl/4 D = 5.5 cm
.O. A = 5c*(5.5)2/4 = 0.00238 IY?
Minimum $ = 1 Numin .'. $ = lNUmin * lm3/looOL * 1523/298 * 1 mini60 sec = 8.52*10e5 d / s :. up = 8S2* 1 05/0.0ûW8 = 0.036 m / s
b) Droplet terminal velocity u, = (4& b d ( 3 e AQ = 5800 ks/m3 &, = 1.4*104
eg = 0.23 kg/m' C,: assume Stokes Law applies, check N, lakr .'. CD = 16/NR, NR, = egu,(bopldb -'= C, = 16q(egu,&3
= 5.4* 1 O Pas
Check N, Nk = ~ ~ & , , u J p ~ = 0.23*1.5*10~*1.98*10~/(5.4*10~~) = 1.3*104 -.- Nk (< l :. Stokes Law applies :. u, = l.98* IO4
u, (< u, .O. the droplets are carried upwards by the gas (with % = q,)
NA = ~ ( R ~ * ( P ~ b ~ l k - P~drop l$ $ 3 b2,drop1~< WTL = O (thennodynamic Mt) P,,, = Pm in bubble rupture stage Assume average gas in rupture stage has .*. Pm,, = 0.1*0.21*101325 = 2128 Pa 4 = nd2&(,&
already undergone 90Y0 utilkation
Droplet contents: Vwd = ddroplJ6 = ?iC(1.5*1O6)V6 = 1.8*10"8 m? %, = eiVwa = 58OO*1.8* 1018 = l.02*10-14 kg mol of S in droplet = mol of Cu,S in droplet mol of Cu$ in dmplet = -J(MWm) MW- = O. 159 kgIrno1 .'. mol of Cu,S = 1.02* 1 (r14/0. 159 = 6Atl O-l4 mol .O. mol of S = 6.44*10'14 mol
In SQ, S:Q molar ratio = i : 1 .'. require 6.44*10-I4 mol of Q NA = mol S/reaction tirne .'. C, = mol S / N , = 6.44*1014/(3.87*10-'0) = 1.7*l@ s = 170 p
Check droplet residence time in rupture zone: 4 = W-et h,=12cm ~~=maximmwhen$=4NUmin=14.4cm/s :. 4 = 1244.4 = 0.83 sec
-: & a 6 :. complete desulphurization of the droplets will take place
Based on experjmental d t s , mixed phase control d d o n is estirnaîed to be equivalent to 50 NL airkg Cu
Converter: bath mass = 80 te Cu = 80000 kg
Gas flowrate = 18000 SCFM = 180ûû SC~~*(O.305dfi~*1ûûûUm~ = 510707 Numin
Mixed phase control time = %*bath mass/gas flowrate = 50*80000/510707 = 7.8 mùi
&112.9 Number of Dropl& in Bubble Rupture 7 ~ n e
For $ = 2.0 Numin and d, = 5.1 mm: From expimental renilts, Ig =A, = 0.0002 1 8 d / s Shce the droplets are vexy srnall, N, « 1 :. N, = 2.0 and k, = 325 m / s :. A, = 0.000218325 = 6.7*1C7 II? = 0.67 rmd
SIiTface Area/droplet = x &-, = x*(0.0015)2 = 7.07*104 mxd :. # of droplets = A,/Surface Area per droplet = O.67/(7.07* lo6) = 94786
Mass/dropla = e,?td3w&5 = ~8ûû*n*(lS* 106)Y6 = 1 .03*10*14 kg .*. total mass of droplets in head spacec # of droplets*droplet mass
= 94786* 1 .O3* 10-14 = 9.7* 1 O-'' kg = 0.97 pg
Bubble growth residence tirne: bubble fkquency = 5 Hz :. = I / f , = 1/5 = 0.2 s
Bubble rise residence tirne: & = rishg gas volurne/gas flowraîe Assume gas rises in a sheet dong the back of the convetter assume gis sheet thickness = 20 cm tuyere subrnergence = 40 cm converter length = 10 m :. rising gas volume = thichess*submergmce*len~ = 0.2*0.4* 10 = 0.8 m3 Gas flowrate = 1 8 0 SCFM = 1800 SCFM*(0.305m/A~*(lmin/6ûs)* 1 ~ u / 2 9 8 * Vl.2
= 33.5 m'ls (at converter bath T and P) .O. t, = 0.8/33.5 = 0.024 s
Bubble rupture residence tirne: Empty converta volume = a u 4 D = 3 m L=lOrn .'. converter volume = @32*10/4 = 70.7 m3 Typically converter is l/3 full of liquid :. volume for gas = 2/3*70.7 = 47 II? Gas flowrate = 33.5 m3/s .'. firarr = gas volumelgas flowrate = 47/33.5 = 1.4 s
BubbIe Rise rnass tramfer coefficient:
For gas flowing dong a flat surface, Na, = 0 . 6 6 4 N R c , ~ 5 ~ ~ 3 3 for Ne, < 3* 1@ Nw= egu3 eg = 0.23 kg/ u = = 0.4/0.024 = 16.7 mls L = 2 0 m q = 5.4*10" Pas .*. Nw = 0.23 * 1 6.7*0.20/(5.4* 1 04) = 1 4226 Nk = 0.82 .-. N, = O.664*(1 4226)0-5*(0.82)033 = 74.0
7 74*2.44* 1 04/0.20 = 0.09 mis
Mass transfer rate:
N A = -pl@T)*&, , and NA = Ad& = APQ/(RT) .*. APQ/(R" = -l+/(RT)*APh(Pdpi) .: ypdpi) = -k&Q .'. Pr = Pi exp(-k&Q) k, = 0.09 m,s 4 = I*h = 10*0.4 = 4 m2 Q = 33.4 d / s Q utilkation = 30% (estimatecl)
.O. P, = (100-30)l100)*0.21*101325 = 14985 Pa .O. P, = 14895*exp(-û.09*4/33.4) = 14735 Pa :. Q utilhtiorq = 100-14735*100/(0.21*101325) = 30.70/0 :. A Q utilkation during gas rise = 30.7-30.0 = 0.7%
A.. 12.1 1 Melt h e l Variation During Cu2S Conversion
Initially, al1 Cu$ .O. &=h,andh,=Oat time=O Let x be the fiactional convasion of Cu$ Reaaion chernistry: Cu3 + Q = 2 Cu + SQ Height of CuzS = h& 1 -x) Height of Cu = Q ~ / Q ~ * ( M W ~ ~ / M W ~ ) * ~ I , , X e- = 5800 kg/m3
- 7800 k9/rn3 e a - M W m = 2*63.5 = 127 glrnol M W , , = 127+32.1 = 159.1 g/mol :. height of Cu = (58Oû/î8oO)*(l27/159. I ) ~ J c = 0.59hd(
Let the volume Faction of oxygen in the injected gas = x Let the fiactional oxygen utilhion = y
.O. NJQ = (1-x)/x (in the injected gas)
Reaction chemistry: Cu2S + l/y Q + (1-x)/(x~) N2 = 2 Cu + S@ + (1-y)/y Q + (1-x)/(x~) N2 Inputs: outputs: 1 moi Cu$ (1523 K) 2 mol Cu (1523 K) 1/y mol 0, (298 K) 1 moi SQ (1523 K) (1-x)/(xy) mol N, (298 K) (1-x)/(xy) mol N, (1523 K)
(1-y)/y mol C& (1523 K) T, = 298 K
For autogenous operation, net heat = O .'. H, - H, = O .'. Mm +1 2Z*cpm - [2450*CpQ + AHm +1225*Cpm
+ (1-y)/y*1225*Cpa + (1-y)/(xy)*122Sf Cp* = O Insertllig al1 values for AH! and C, -> l/y = 54168/(10038+9441(1-x)/x)
.'. y = 0.1853 + O. 1742*(l-x)/x For air at 2 1 % oxygen, x = 0.21 .O. y = 0.1853 + 0.1742*(1-0.21)/0.21 = 0.841 :. requred oxygen utilization for autogenous operaiion = 84%
% SQ = mol of S a in sampleltotal mol of gas in ample * 100%
Mol of S q : Scnibbing reaction H2S04 + 2 NaOH = Na,SO, + 2 H20 . *. NaOWSQ mtio = 24 .-. mol of S Q = 0.5*mol of NaOH used
= 0.5*NaOH molarity (moVL)* volume titrated(rnL)/(1000mUL) = 0.0005*&*Vti,,
Mol of Off-: PVs=nRT V, = gas -le volume(ml)* IO4 @ STP, n = PV'(RT) = 101325*V,*1O4/(8.314*298) = 4.1*10'5*Vs @ Praiple and Tm n = 4.1 *1~5*Vs*(298/T,)*(PsaniplJ1~ 1325) :. n = 1 . 2 1 * 1 0 ' 7 * V , ~ ~ ~ d
Mass of S rernoved = A mol S/MW, A mol S = PV&RT) V, = ~ ~ 1 0 0 0 * bdrnin) * YSQ in offgasi100 P = 101325 Pa (STP) R = 8.3 14 J / (~o~*K) T = 298 K (STP) MW, = 32.1 dm01 :. mol S Q = 101325/(8.314*298) * Q%,,*0/aS4/100000
= 4.W* 1 0-4*QtMm?hSQ
:. M k of S rernoved = 32.*4.û9*104*Qt,,,0W%SQ = O.O13*&,o/aSQ New %!3 in melt = rnass of S in melthotai meit m a s * 100%
= rnass of S/(rnass of Cu + m a s of S) * 100% mas of S = initiai m a s of S - IMSS of S rernoved m a s of Cu = initial rnass of Cu = constant
:. New %SQ in melt = (initial mass of S - m a s of S removed)/(initial mass of Cu + inital rnass of S - mass of S rernoved) * 100
New starting mass of S = previous swing m a s of S - rnass of S removed % Q utiiization = %SQ in off@?/oq injected * 100% ?4Q injecîed = (21 *% + loO*Q&G + Q&)
ar = air flowrate Q, = nitrogen flowrate %Q injecîed= ( 2 P Q +O*&)/(% + Qa) =2lW(Q, + Q.a) Y YiiQ utilization = %S@ in offgasl%Q injected * 100 .'. % C& utiiization = lOû*(Q, + Q&)*O/oSQ in offM(2lQ)
= 4.8*(4, + QJ*%SQ in off@(&
A. 12.16 Erne for Total S Remova1
For S-saturated melts Based on 1W? C& utilizaîion Mass of S in melt = melt mas*% in melt/100
Mol of S in melt = melt mass/MWS * %S in melt/100 Molar rate of S rernoval= molar rate of q injection (moi/&) .*. Molar rate of S removal = PQoJ(RT)
= 1 O1 325*0.21*Q&Jmin)/(8.3 14*298* 1000) = 0.00859Q,, T ï e for S removal = mol of S in melt/molar rate of S removal
= melt mas*?& in melt/(32.1* 1 ûû*O.O0859&) = O.O349*melt mass*Y& in melt/Q,
M e t gas flowrate = inlet gas flowfafe- Q dissoluîion .'.Q, = Q - W.9 in melt * melt mass/(lûû%m*MWd* (22.4Umol) MWm = 32.0 gh01
.O. Q, = - O.ûûï*AP/oq in melt * melt mas&,,, melt mass = initial melt mass - S removed + O dissolved
= Uitial melt mass + (AW + W&)/lûû * melt mass
% Q utilization (->S9) = (%SQ in off@/i injected)*(QJQ* 100% % Q utilization (dissolved) = mol of Q dissolved~mol of @ injected * 100% = (A%û in melt*melt madMW&)/(Q*%Q injected/lOO* 1 moV22.4L*t,)* 100 = 7ûûû*A0/oO in melt*melt m a d ( ~ * % Q injectai%,)
Total q utilizaîion = % Q ldilization (->Sq) + YiiQ utilization (dissolved)
Sulphur Accountability = S in offgas as SO/S removed f?om melt % S Acc. = (%SQ in offp*G%J(100*22.4))/(AY& in melt*melt masslEvTW~*100 :. O/aS Acc. = 1.43*%SQ in offgas*&*t+,,J(A%S in rnelt*melt mas)
A 12.1 8 Crfowth SBge Mass Tmfer Coefficient
V, = bubble volume at t + h = bubble volume at t + %*At 4 = quivalent diameter = (~*v, , /x)O~~ Actual bubble diameter d,,
a) when d, < 4, bubble shape is close to hernispherical (Y p is close to 90') .O. 4 = ( ~ / I P V J ~ ) O ~ ~ = ( 3 v d ~ ) O ~ ~
b) when 4 > 4, shape is betwen hemispherical and spherical full sphere volume = 7 ~ & ~ / 6 .*. lUdb3/6 = actuai bubble volume + sphericai cap volume adual bubble volume = V, sphericai cap volume = V,
Solve by iterating with respect to 4
Spherical cap height: h by the pythagorean relaîionship, (~iJ2)~ = (dd2-hy + (d# .: (dd2 - h)2 = 4*/4 - a2/4 .'. w2 - h = (42/4 - (b2/4)0-5 .'. h = 412 - (4,/4 - 42/4)0+5
Interfacial Am: a) Surface area = sinface a m of hemisphere
.O. SA = 114,~/2
b) Surfàce area = sud!ace area of sphae - surface area of spherical 01, .O. SA = a2 - 2fl(h/244)(~&h-h3 + h2/8*~s-'(1-2*W&)]
To find Ig: iterate with repect to k, until the value for paf at the end of the intire bubble growth stage is equal to paf determuied expimentally.
A. 12.1 9 Rubble Füse Mass Tmfer CoeScient
a) for an oblate sphaoidal bubble Ekpivalent bubble diameta = 4 = (6Vd7~)O~~ b = minor âxis length = msilcimum diarneter - liquid film thichess maximum diameter = (aiscible diameter - lance diametery2 a = major axis Iength = 3Vd(4m e = eccentricity = (Va)*($- 610J d a c e rilea = Ai = 2 d + 7QJe*ln[(l+e)ll-e)] Eotvos Numbea = Na = Morton Number = NM = gp&d) Reynolds Nmber = N, = elu,4/p, From Nb and N,, obtain Nk fiom the bubble shape diagram then 4 = C L I N R / ( ~ ~ J Gas rise time = t = irnmersiodq,
b) for a cylhdrical gas charnel D = chan.net diarneter = maximum diameta - liquid film thickness maximum diamter = (crucible diarneter - lance diameter@ Cross-sectionai area = 4 = */4 Gas velociîy = Qdq, = < Sudiace area = A, = IrD*imrnersion
A12.20 Bubble Rupture M a s Transfer Coefficient
a) gas described by plug flow aucible diameter = d, crucible head space height = h,
Head space volume = (~!4)*4~*h, Mean & velocity = u, = QbA, - 4Q$(7~4~) Mean residence time = hju,
b) gas described by back-mixed flow Separate residence tirne distribution fùnction into 120 elements F(t) = 1-exp(t.t,) t, = mean residence tirne = wu, For each elemenî, NA = -l@,/(RT)*APIOg ,, NA = AdAt = APaLQJ(RT)
='- &2QpJ(RT) = -Igq~v*~oJln(P02f/P02i) :. in(Pm/P&) = -kB4/Qt .: P,' = Pa' * exp(-wQJ for each elernent of the RTD
Cumulative weight m i o n = F(t) = 1-exp(t/t,) ha-emental weight Main = F(t) - F(t-At) Incremental weighted Paf = inmental weight M o n *Pmf :. Final weighted Pm = &mental weight M o n *Pm? Note: Q, = (weight M o n with residence time=t)*$ Iterate with respect to until the final weighted Pm equals the value for Po, determirid experimen y ly pmf = (lOeO/iQ utiliZation)Ilûû* lOl325*(0/oq injected/lOo)
For gas phase: Flow in a cylindrical duct r, = APl(2L) * W2 Hagen-Poisselle equation for laminar flow
.O. 't, = = 32w 8*
For liquid phase: Flow in a weaed wall colunni L = e~gt + CI Let r = O at the gs liquid interface At r = O, .à, = LIidiid
.O. eig(û) + ci = 8*Q@ :. c, = 8 * w .*. for liquid phase, r, = Q ,gr + 8$&D
Check for laminar flow in gas phase: N, < 2100 N e g = e Up = 4QJ7m -'- Nkg = 4egQ,@@) D = 0.5*(Dc4-46) -.- Nkg = 8 e g Q B i ~ g @ C - 4 ~ l Worst case: maximum liquid flow, Q = $ Solve the previous equation between Q and 6 iteratively for 6, setting using the above worst case condition. :. at $ = 5 Wrnin, 6 = 0.8 mm :. N,, = 107 .*. assu~ption of laminar gas flow is correct
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