a mechanistic model to predict matte temperatures during the smelting of ug2-rich blends of platinum...

Minerals Engineering 24 (2011) 676–687

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Minerals Engineering

journal homepage: www.elsevier .com/ locate/mineng

A mechanistic model to predict matte temperatures during the smeltingof UG2-rich blends of platinum group metal concentrates

J.J. Eksteen ⇑Lonmin (Western Platinum Ltd.), Private Bag X508, Marikana 0284, South Africa

a r t i c l e i n f o a b s t r a c t

Article history:Available online 4 December 2010

Keywords:Precious metal oresSulphide oresPyrometallurgyModelling

0892-6875/$ - see front matter � 2010 Elsevier Ltd. Adoi:10.1016/j.mineng.2010.10.017

⇑ Address: Department of Process Engineering, StAfrica. Tel.: +27 823766055; fax: +27 115161310.

E-mail address: [email protected]

High matte temperatures can be related to numerous catastrophic furnace failures in the platinum groupmetal (PGM) industry where chromite-rich upper group 2 (UG2) concentrates are smelted. Chromite richconcentrates require high slag temperatures as well as sufficient mixing to suspend the chromite spinelparticles in the slag and prevent settling in a so-called ‘‘mushy’’ layer consisting of a three phase emulsionof slag, matte and chromite particles. To achieve sufficient bath mixing and to melt and suspend chromitespinel build-up, high hearth power densities are utilised. However, high hearth power densities in con-junction with a heat-isolating concentrate layer, leads to high side wall heat fluxes which motivated theuse of intensive cooling in the furnace side wall so that a slag freeze lining can be formed. If matte tem-peratures are above the slag liquidus temperature, any matte that comes into contact with the freeze lin-ing can destroy the freeze lining. Moreover, if the matte temperature exceeds ca. 1500 �C, chemicalthermodynamics indicate that matte has the ability to sulfidise MgO–FexO–Cr2O3 refractories, leadingto rapid wear of refractories exposed to high temperature flowing matte. Models are derived for the con-centrate-to-matte and slag-to-matte droplet heat transfer. Calculations using the derived models, phys-ical properties and furnace operating conditions give realistic matte temperatures and show that mattetemperatures rapidly increase as the concentrate bed becomes matte drainage rate limiting. It is shownthat for each concentrate blend mean particle size and mineralogy, there is a maximum smelting rateabove which the concentrate bed becomes rate limiting with regards matte drainage, thereby signifi-cantly contributing to matte preheating, prior to further heat absorption from the slag layer.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Matte temperatures, while not normally problematic during thesmelting of traditional Ni–Cu sulphide concentrates, have beenexperienced to be problematically high when UG2-rich blends ofPGM concentrates are smelted in high intensity electric furnaces.This problem is particularly endemic to some South African PGMsmelters where the chromite rich UG2 ores are smelted in high ra-tios to Merensky or Platreef based concentrates, such as at AngloPlatinum’s Polokwane smelter and at Lonmin’s Western Platinumsmelter in Marikana. The industry practice to date has been tonot micro-agglomerate the concentrates prior to smelting, a factorthat will be explored in more detail in this research. Pelletizing tofairly coarse sizes (larger than 1 mm) were used in the past, but hascaused furnace blow-backs due to moist pellet-cores. It is foreseenthat high matte temperatures will become an increasing problemin the future when more of the smaller PGM producers on the

ll rights reserved.

ellenbosch University, South

Eastern Limb of the Bushveld Igneous Complex (BIC) smelt theirores or deliver it for toll smelting elsewhere.

UG2 concentrates are characterised by relatively high chromitecontents, low base metal contents (relative to Merensky and Pla-treef concentrates) and are particularly rich in hydroxylated ultra-fine soft minerals such as talc. Modal analyses of concentratemineralogy based on QEMScan analyses of Western Platinum con-centrates and a typical repulped revert recycle stream, are pre-sented in Table 1.

Repulped and/or floated reverts which may make up 15–30% ofthe overall feed of a furnace. UG2 concentrate blends are smeltedin circular, 3-electrode, or rectangular, 6-in-line alternating currentelectrical furnaces. When the Cr2O3 content in the concentrate feedis above its solubility limit in slag at 1450–1650 �C (about 1.8%Cr2O3 in a non-reducing environment), the chromite spinel miner-als will not dissolve and needs to be tapped out at the same rate asthey enter the furnace to prevent accumulation which leads tochromite build-up in the hearth, in front of tap holes, or in athree-phase ‘‘mushy’’ layer suspension at the slag–matte interface.Suspension of solids is achieved through sufficient mixing which,in turn, is obtained through sufficiently deep electrode immersionand operating at hearth power densities in excess of 160 kW/m2.

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Table 1Sulphide and gangue mineralogy of Merensky and UG2 concentrates.

Mineral Eastern UG2concentrate

Western UG2concentrate

Western Merenskyconcentrate

Repulped reverts andslag plant conc.*

Pentlandite (or Heazlewoodite for reverts*) 2.0 3.6 15.1 9.8Chalcopyrite (or Chalcocite for reverts*) 1.1 1.7 9.1 6.4Pyrrhotite 0.4 0.8 16.7 3.7Pyrite 0.9 0.9 0.9 –Other sulphides 0.3 0.3 0.8 2.1Orthopyroxene 51.0 50.3 35.4 22.2Clinopyroxene 4.6 6.1 6.1 –Olivine (or amorphous glass for reverts) 0.2 0.2 0.1 42.6Plagioclase/Anorthite 9.9 5.4 4.6 –Amphibole/Tremolite/Actinolite 2.5 2.3 4.1 –Talc 11.0 16.7 2.7 –Serpentine 2.1 2.6 0.1 –Chlorite 1.9 1.7 0.4 –Biotite/Phlogopite 0.8 0.8 0.5 –Quartz 0.7 0.4 0.5 –Chromite spinel 8.2 4.1 0.6 2.5Magnetite spinel 0.1 0.3 0.2 1.1Carbonates and other minor minerals* 0.1 0.4 0.3 9.3

J.J. Eksteen / Minerals Engineering 24 (2011) 676–687 677

As the slag at the operating temperature of 1550–1680 �C wouldrapidly dissolve the furnace side-wall refractories, a slag freeze lin-ing is utilised to protect the refractories. This freeze lining isformed using deep cooled copper waffle or copper plate coolerswhich can sustain high side-wall heat fluxes. The principal weak-ness of most furnaces is the slag–matte tidal zone (interface zone)where the slag–matte interface moves up and down along therefractory contact zone due to the intermittent nature of mattetapping and matte accumulation between taps. When the mattetemperature is higher than the liquidus temperature of the slagfreeze lining, flowing matte will transfer heat to the freeze liningat a higher rate than the copper coolers can remove it and effec-tively destroy the freeze lining. The high heat transfer rate is dueto high matte superheats and the fact that matte has a much higherthermal conductivity, lower viscosity and higher density than slag.

The phase transition of a typical slag freeze lining (of slag chem-istry as seen at Western Platinum’s smelter) in the presence andabsence of matte is illustrated in Fig. 1. The phase transition is asmodelled using the thermodynamic modelling software FactSage �.The one case presents the equilibrium% liquid melt of a typicalsmelter slag in the absence of matte. Another curve is presented

% Liquid slag pre

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

900 1000 1100 1200 1300 1

Tempe

Wei

ght %

liqu

id p

ortio

n

Slag onlySlag/Matte (1:1)

Fig. 1. Phase transition of a slag freeze linin

of a slag in equilibrium with a matte of equal area (or volume withunit thickness). As the slag has some ability to dissolve sulphur assulphide and matte has the ability to dissolve some oxygen, thespeciation of the melt and solid phases are slightly shifted. Matteappears to cause a slight lowering of the solidus, while not signif-icantly affecting the liquidus.

From Fig. 1 it is clear that the slag starts melting between 1050and 1100 �C depending if matte is present or not and has essen-tially completed melting by 1450 �C when all (95%) slag basedfreeze line has melted, except for the chromite spinel mineral thatdoes not completely dissolve/melt until a temperature of close to1800 �C is reached. Therefore, matte at temperatures greater than1450 �C will destroy a slag freeze lining completely.

Moreover, matte at temperatures above 1500 �C also becomeschemically aggressive to refractory bricks. Lonmin uses a RHI Ra-dex H60 brick in its furnace hearth with the composition: 58%MgO, 19% Cr2O3, 6.5% Al2O3, 14%Fe2O3, 1.4% CaO, 0.6% SiO2. Above1500 �C matte has a significant capacity to sulfidise MgO–FexO–Cr2O3 refractories. Matte has a significant solubility for oxygen(shown in the discussion below) and can ferry oxygen betweenoxide bricks and slag at sufficiently high temperatures:

sent at Temperature

400 1500 1600 1700 1800 1900

rature (C)

g in the absence and presence of matte.

678 J.J. Eksteen / Minerals Engineering 24 (2011) 676–687

ðFeCr2O4Þrefractory þ 2½S�matte þ 3½Fe�matte ¼ 2½CrS�matte þ 4½FeO�matte

with DG� ¼ �8:478 kJ=mol at T ¼ 1500 �CðDG� < 0;when T > 1450�CÞ; or

ð1aÞ

ðMgCr2O4Þrefractory þ 2½S�matte þ 3½Fe�matte ¼ 2½CrS�matte þ 3½FeO�matte

þ ðMgOÞrefractorywith DG� ¼ þ11:03 kJ=mol at T ¼ 1500 �C

ðDG� < 0;when T > 1650 �CÞ ð1bÞ

The FeO has been shown to be partially soluble in matte as dis-cussed below and it is reflected as such in the above expressions.

Analysis of Lonmin Furnace matte have shown that, afterassociating sulphur with Cu, Ni and Co as Cu2S, Ni3S2 and CoSrespectively according to their decreasing thermodynamicstabilities, there is a significant molar excess of Fe to S when allremaining S is allocated to Fe, making the excess of Fe to S plausi-ble in Reactions (1a) and (1b).

Moreover, Kwatara (2006) and Du Preez (2010) both haveshown that Cr solubility in matte (as sulphide) significantly in-crease with increasing temperature, shifting the equilibria in Eqs.(1a) and (1b) further to the right hand side of the stated reactions.

The combination of high temperature and sulfidation thereforeprimarily attacks the FexO–Cr2O3 ceramic binder (as is apparentfrom the Gibbs Free Energies in Eqs. (1a) and (1b)) which leadsto gradual disintegration in the areas exposed to flowing, high tem-perature matte, such as in the matte–slag tidal zone.

The molten FeO is fully miscible in all proportions with FeS inthe absence of other slag forming components. Fonseca et al.(2008) studied the oxygen solubility and speciation in sulphide-rich mattes in the temperature range 1200–1400 �C and oxygenpartial pressures. They report the results of an experimental studyof the solubility of O in mattes as a function of pS2, pO2, tempera-ture, and composition. They confirm previous observations that Niand Cu have a negative effect on the solubility of oxygen in mattes.They further show evidence for the existence of FeSO as a struc-tural constituent of mattes in the Fe–S–O system. Oxygen wasshown to be fairly soluble in matte (1–9 mass%), even at verylow gaseous O2 partial pressures (pO2 between 10�8 and 10�12

atmosphere). Increasing Ni and Cu both decrease the solubility ofoxygen, but not to the order of magnitude level. They also studiedthe base metal sulphide ores from the Sudbury Igneous Complex,Canada and the Kambalda sulphide ores from Western Australia

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

4.5%

1200 1250 1300 1350 1400 1

Equi

libriu

m R

efra

ctor

y %

Mas

s Lo

ss

Temp

Fig. 2. The FactSage� predicted weight loss due to brick wear (combined sulphidatio

and found the sulphide-rich matte likely lost much of its dissolvedO through diffusion towards the overlying silicate melt. They con-clude that the diffusion of O, out of the sulphide-rich matte andinto the silicate melt, may have led to the precipitation of magne-tite and/or chromite near or on the boundaries between the matteand the silicate melt. They further conclude that most massive sul-phide-rich mattes represent open systems in relation to their Ocontent. Tshilombo and Pistorius (2007) measured the oxygen par-tial pressures in a simulated converter matte throughout the matteblow as the FeS decreases throughout the blow from furnace matteto the final white matte and they have shown that oxygen activityin the matte was sensitive to the iron content of the matte. Theyclaim that the experimental results approximate FactSage predic-tions quite well.

Fig. 2 shows the simulated weight loss due to combined partialmelting and sulphidation when a RHI Radex H60 refractory isequilibrated on an equal area basis with a typical furnace matteas the temperature increases. The results are based on FactSage�

simulations. The establishment of thermodynamic equilibrium isaccelerated by flowing matte, such as matte in the tap hole regionand matte in the tidal region.

To find a way to mitigate the formation of matte with high tem-peratures a mechanistic model has been developed to understandthe heat transfer from all heat sources as the base metal sulphide(BMS) minerals decomposes, liquefies in the concentrate bed andforms matte droplets that settle through the slag bath.

2. Formation of liquid matte in the concentrate bed above theslag

The concentrate feed consists of a blend of the four concentratetypes mentioned in Table 1. The blend depends on mine produc-tion of the various reefs and the reprocessing of recycled material.Table 1 indicates that the BMS portion of Merensky (around 42%) ismuch more than for UG2 concentrates (4.5–7.3%), and that UG2concentrates contains predominantly the hard mineral orthopy-roxene at around 50%, with talc, one of the softest of minerals, atbetween 11% and 17%. The softness (relative hardness of typicalminerals in PGM concentrates listed in Appendix Table A1) and fri-ability of talc potentially leads to over grinding of this mineral sothat it is recovered in the flotation circuits entrained in the waterthat deports to the froth. Talc is also a naturally floating mineral,making depression much more difficult than other predominant

450 1500 1550 1600 1650 1700erature (C)

n and melting) of Radex H60 bricks in the presence of high temperature matte.


silicate minerals such as plagioclase and those from the pyroxenegroup. The median particle sizes vary quite much between the var-ious main concentrate types. From a laser diffraction particle sizeanalysis, it was shown that a typical Merensky concentrate had ad50 of 25 lm, a ‘‘Western’’ UG2 concentrate had a d50 of 16 lmand an ‘‘Eastern’’ UG2 concentrate a d50 of 30 lm. The slag plant(and repulped reverts) recycle had a d50 of 8 lm.

It is not the bulk concentrate particle size distribution that isas much of importance as the amount of BMS and the way theBMS is distributed compared to silicaceous gangue per particlesize interval. Depending on the distribution of base metal sulp-hides among the particle size classes, and the total amount ofBMS present, the particle size distribution after BMS meltingcan shift towards coarser distributions. The exact shift can be pre-dicted if a mineral liberation analysis (MLA) has been performedon all concentrates types that enter a furnace. MLA’s are normallynot performed on concentrates but rather on flotation tails andfeed streams. It is evident therefore that MLA has much valuein aiding the engineer in the understanding of concentrate bedmelting behaviour prior to slag formation. Lacking an MLA analy-sis at the time of writing, the median particle sizes will be used toindicate the order of magnitude of the mean of some of Lonmin’sconcentrates.

Once the BMS has entered the concentrate bed or ‘‘black top’’,the BMS (Pentlandite) starts to convert to matte componentsaround 650 �C associated with partial desulfurisation. The furnacefreeboard, the gas region above the concentrate layer, typically isaround 550–650 �C, but can be as high as 950 �C, depending on in-gress air flow rate, concentrate mineralogy, and the operatingpower of the furnace. Post combustion in the freeboard will nor-mally contribute to heat transfer to the top of the bed and radiationto the concentrate bed. On the other hand, should the concentratebed melt away in localised regions of the furnace, radiation fromthe slag to the freeboard will rather take place. Concentrate bedheights above the slag layer in electrical furnaces varies between0.2 m and 0.6 m.

As the silicate portion of the bed only starts to melt at 1100 �C,matte has the ability to drain from the silicate bed before the sili-cate minerals can melt. The BMS decomposes according to the fol-lowing set of reactions, where the temperatures indicate theinitiation temperature:

Fig. 3. Equilibrium crystallisation/melting curve for a typical matte

� Ni9Fe8S15ðPentlandite; sÞ ! 8FeSðsÞ þ 3Ni3S2ðsÞþ 1=2S2ðgÞ at 650 �C ð2Þ

� 2CuFeS2ðChalcopyrite; sÞ ! 2FeSðsÞ þ Cu2SðlÞþ 1=2S2ðgÞ at 700 �C ð3Þ

� FeS2ðPyrite; sÞ ! FeSðsÞ þ 1=2S2ðgÞ complete at 796 �C ð4Þ� Fe7S8ðPyrrhotite; sÞ ! Fe7S8ðlÞ between 1150�C and

1200 �C;only when pure ð5Þ� xFe7S8ðlÞ þ yNi3S2ðlÞ þ zCu2SðlÞ !MatteðNi; Fe;Cu; SÞ ð6Þ

From the reaction scheme above is clear that Pentlandite is the firstto convert to Heazlewoodite followed by Chalcopyrite to Chalcocite.Chalcocite will melt first, followed by Heazlewoodite and Pyrrho-tite. Higher melting BMS will become liquid when the molten sulp-hides that melted earlier can dissolve it. The dissolution rate ofPyrrhotite into molten Chalcopyrite–Pentlandite based BMS, andits contribution to matte droplet composition of early drainingmatte is therefore expected to be mass transfer/diffusion controlled.A part of the silicate-locked Pyrrhotite can therefore be expected tobe released only when the concentrate bed melts en-masse. Fromphase diagram modelling (Fig. 3), a typical Cu–Ni–Fe–S matte ap-pears to be completely molten by from 850 to 875 �C. Pyrrhotiteis the last phase to disappear, but does so at a temperature muchlower than the pure component melting point. Fig. 3 does not usethe original minerals as starting point but rather looks at the phaseequilibrium behaviour of a typical PGM smelting matte.

The sulphides of Co and Pb also contribute small amounts to thematte formation. Cr is slightly soluble in matte under slightlyreducing conditions found in electrical furnaces and proceeds sim-ilarly to Eq. (1) for refractory bricks. The hydroxylated and fluori-nated minerals will decompose and lose their hydroxyl andhalide groups to form steam and volatile metal halides at temper-atures slightly below matte forming reactions. For example, talcdecomposes and releases one mole of water for every mole of talcand the solid converts to Enstatite at �700 �C. It is therefore clearthat, over and above electrode consumption to produce CO andCO2, a significant amount of H2O and S2 vapours are released atvarious depths within the concentrate bed as the temperature in-creases. These vapours will escape when the bed is porous, butin the case of a concentrate bed with a sintered surface can move

composed of 17% Ni, 10.5% Cu, 42.5% Fe, 0.5% Co and 29.5% S.


sideways and recondense on the furnace copper coolers to causesulphide and halide attack of the copper coolers.

In the presence of a larger proportion of fines, sintering hasbeen observed to be associated with gas release via localised viagas spouts and concentrate fluid-bed boiling is observed in theproximity of the electrodes (observed as multiple little volcanoeson top of the concentrate bed and much churning of the concen-trate particles close to the electrodes based on video recordingthrough one of the ports in the furnace sidewalls).

Post-oxidation of CO and S2 gases with ingress air to form CO2

and SO2/SO3 respectively can lead to additional heating in the free-board region and is particularly a problem when a partially closedoff-gas damper position can lead to too high S2 and CO concentra-tions and high heat accumulation due to post combustion in thefreeboard. Sufficient ingress air will provide sufficient excess airto reduce the freeboard temperature and dilute the concentrationof the combustible gases (CO and S2) and their combustion prod-ucts. CO2, SOx and H2O vapour dramatically changes the gas emis-sivity and radiation properties. While it is realised the freeboardgas may radiate heat to the top surface of the concentrate bed thiseffect is not modelled quantitatively in this paper. Future work hasto address gas-to-concentrate radiation effects. However, it shouldbe clear that, for a given ingress air flow associated with a specificdamper setting in the off gas ducts, higher gas temperatures will begenerated by:

� higher electrode consumption which occurs at higher furnacepower (forming CO gas);� the presence of increasing quantities of pyrite in the concen-

trate (forming sulphur vapour);� the presence of large talc concentrations (of which the steam

contributes significantly to increased gas emissivity);� CO2, H2O, SO2 and ultrafine dust particulates all contribute sig-

nificantly to increase the emissivity of the gas (Incropera and DeWitt, 1990) and therefore heat transfer to the concentrate bed,the freeboard sidewalls and roof refractories. Whereas a cleanair mixture will not radiate heat, it is therefore clear that:

Tfreeboard ¼ f concentrate mineralogy; particle size;ðexcess ingress air; kW=m2

hearth area

�ð7Þ

The explicit relationship is uncertain although the relationship canqualitatively be described in terms of the factors. Normal freeboardtemperatures range from 550 �C to 650 �C, as long as the concen-trate provides full coverage of the slag.

It is clear from Eqs. (2)–(4) that the BMS decomposes to lose asignificant amount of sulphur to the vapour phase (sometimes re-ferred to as ‘‘labile’’ sulphur) in order to form a matte with a den-sity between 4800 and 5200 kg/m3. The matte fall (defined as themass% of concentrate that reports as matte) can vary between 7%and 50% depending on concentrate blend composition.

The porosity of the bed can be measured in terms of its specificsurface area (in m2/m3), S, and the bed void fraction, e. It is clearfrom the discussion above that the volume of liquid flow is deter-mined by the volume of matte post BMS decomposition and thatthe void fraction of the bed would be more after decompositionand BMS liquefaction than before. For the purposes of the modeldevelopment, spherical particles are assumed. For spheres, the spe-cific surface area for a particle with diameter dp is:

S ¼pd2

p

p d3p=6

� � ¼ 6dp

ð8Þ

The void fraction ‘‘e’’ for spheres is of the order of 0.3–0.4 and variesbetween 0.2 and 0.4 for cubes, depending on the packing density.Minerals such as talc and its decomposition and the melting of base

metal sulphides before silicaceous gangue will change the void frac-tion as temperature increases throughout the concentrate bed. Theinclusion of these void fraction changes are omitted in the model.

The pressure drop DP available to drive a liquid column of li-quid matte of density q from the surface of the concentrate bedto the concentrate–slag interface over a bed height of H is:

ðDPÞ ¼ qmgH ð9Þ

which gives liquid pressure drops in the range of 10–40 kPa for con-centrates beds, depending on concentrate bed height. If the top ofthe concentrate bed is in thermal equilibrium with the freeboard,one can expect that melting will commence from the top of thebed. Steam, CO and S2 gases will further heat-up the upper regionsof the concentrates as the gases are released from the hotter lowerregions. For the purpose of the model developed below, a lineartemperature gradient is assumed throughout the depth of the blacktop.

The matte drainage velocity, assuming laminar flow of thematte through the concentrate bed can be determined by the Car-man–Cozeny equation (where the subscript m refers to the matte):

u ¼ 15

� �e3

S2ð1� eÞ2

!1lm� ð�DPÞHconcbed

¼ 1Afurnace;free

� �dVm

dtð10Þ

where dV/dt is the volume of matte (V) and viscosity l flowingthrough the bed in time t, and Afurnace,free is furnace free flow areain the horizontal plane, defined as:

Afurnace;free ¼ Afurnace;hearth � nelectrode � Aelectrode ð11Þ

where Afurnace,hearth is the projected internal furnace hearth area inthe horizontal plane, nelectrode is the number of electrodes immersedinto the slag (typically 3 for a circular furnace and 6 for a rectangu-lar furnace) and Aelectrode is the electrode cross sectional area in thehorizontal plane.

As the height of the liquid matte column over the concentratebed appears both in Eqs. (9) and (10), the equation can be simpli-fied to:

u ¼ 15

� �e3

S2ð1� eÞ2

!qmglm¼ 1

Afurnace;free

� �dVm

dtð10Þ

with g = 9.81 m s�2 and substituting Eq. (8) into Eq. (10), the equa-tion becomes:

u ¼ 0:0545 � d2p �

qm

lm� e3

ð1� eÞ2

!¼ dVm

Afurnace;freedtð12Þ

If the matte drainage velocity through the bed (u) is lower than thesuperficial production velocity of liquid BMS, the matte drainagevelocity through the bed becomes rate limiting and significant pre-heating of the matte in the concentrate bed can take place. Con-versely, should matte drainage through the bed not be ratelimiting, the slag properties will dominate the heat transfer to thematte.

Fig. 4 shows the effect of mean gangue particle size and voidfraction on the limiting superficial matte velocity. Fig. 5 gives theformation rate of matte for different smelting rates per m2 heartharea and matte fall ranges seen within Western Platinum (Lonmin).These two graphs should be read in combination. It is clear that,depending on the mean particle size of the gangue portion of theconcentrates, the bed characteristics can either dominate matteretention and preheating, or have little influence on it when itdrains rapidly. From the median particle sizes it is clear that,depending on the blend of concentrates from different sources, thiscritical velocity can easily be breached to either operate in a regimeof (A) concentrate bed limits matte drainage and heat-up, or (B)

-

3

6

9

12

15

18

21

24

27

30

5 8 10 13 15 18 20 23 25 28 30 33 35 38 40 43 45 48 50

Con

c. b

edlim

iting

mat

te s

uper

ficia

l

vel

ocity

(mm

/hr)

Average Gangue Particle Size (micron)Bed Void Fraction = 0.20 Bed Void Fraction = 0.25Bed Void Fraction = 0.30 Bed Void Fraction = 0.35Bed Void Fraction = 0.40 Bed Void Fraction = 0.45

Fig. 4. The bed limiting superficial velocity for fluid matte for different particle sizes and void fractions. The lines indicate the concentrate bed limiting matte velocity forvarious gangue particle sizes and bed void fractions. The critical drainage rate for a ‘‘Western’’ type UG2 concentrate is indicated (d50 = 16 lm) and the slag plant recycle(d50 = 8 lm) are indicated. No sintering assumed.

-

3

6

9

12

15

18

21

24

27

30

100 125 150 175 200 225 250 275 300 325

Supe

rfici

al m

atte

vel

ocity

in c

onc

bed

regi

on (m

m/h

r)

Specific Concentrate Feed Rate (kg/hr/m2 conc bed free area, excluding electrode area)

Matte Fall =10% Matte Fall =15% Matte Fall =20%Matte Fall =25% Matte Fall =30% Matte Fall =35%Matte Fall =40% Matte Fall =35% Matte Fall =50%

Fig. 5. The effect of specific concentrate smelting rate in kg concentrate smelted per h per m2 free area (excluding electrode area) and% matte fall on the matte superficialvelocity.


where drainage is rapid enough so that only slag phase heat trans-fer has to be taken into account.

From d50’s provided, it is quite clear that a blend of WesternPlatinum concentrates, taking into account recycled reverts whichcan constitute up to 30% of the furnace feed blend, span the criticalparticle size where the concentrate bed may become rate limitingwith regards to matte drainage. For example, two extremes areindicated in Fig. 5 for repulped and recycled reverts (lower hori-zontal line) and for Western UG2 (higher horizontal line) assumingno sintering. Therefore a blend of these two concentrate streamscan shift the allowable smelting rate before the concentrate be-comes matte drainage limiting over a very wide range. Lonmin’sNo. 1 furnace is designed to be able to process in excess of325 kg/h/m2. The blend has therefore a significant impact on safesmelting capacity which is very adversely affected by excessiveamounts of recycled reverts at the stated grind size.

There will be times when the matte drains rapidly enough sothat slag-to-matte droplet heat transfer is predominant, ratherthan concentrate-to-matte heat transfer. Sintering of UG2 concen-trates would lead to a void fraction reduction below 0.2 whichwould lower the critical drainage rate to very low rates and essen-

tially lead to matte lock-up in the gangue of the concentrate bedand only be released upon gangue smelting.

The most challenging aspect of concentrate bed modelling isto model sintering in the bed and to predict when it will occurand when not. While sintering could reduce the void fractionfrom an initial typical value 0.30–0.40 in a free flowing beddown to 0.07 in a sintered bed, it will have the most significanteffect on particle surface area reduction, and therefore reductionof the heat transfer area between BMS and sintered particles.The area reduction associated with sintering is reviewed byCho and Biswas (2006) who derived closed form solutions forvarious sintering models (depending if it is based on surface dif-fusion, grain boundary diffusion, volume diffusion, overall diffu-sion or viscous flow). The exact situation for PGM flotationconcentrates is not known, and would require laboratory quanti-fication. However, sintering locks up the BMS/matte into thestructure so that they can only be released to the slag once bulkmelting of the bed occurs and the melt viscosity approaches thebulk slag viscosity.

Fig. 6 gives a schematic diagram of an idealised sintering pro-cess for two equal sized particles prior and during sintering:


The initial surface area of the two spheres is 2 4pr2p;0

� �where

rp,0 represents the initial particle radius. The surface area at anytime is 2 4pr2

p � 2prph� �

, a decrease from the initial surface areadue to overlapping spheres. The radius of the particle is rp at timet, and will increase from its initial value rp,0 as the total volume isconserved. The normalised surface area is therefore expressed as:

a� af

a0 � af¼

rpð2rp � hÞ � r2p;f

2r2p;0 � r2

p;f

ð13Þ

where h is a dimension (Fig. 6) that depends on x, the neck radius. Inthis expression, if rp and h are known as a function of time, the areachange with time is also known. Cho and Biswas (2006) shows thatif the expression is expressed as a normalised surface area change, itis also applicable to an agglomerate where a, a0, and af refer to thesurface area at any time, the initial surface area and the final surfacearea of the entire agglomerate. The volume conservation equationfor sintering spheres is:

43pr3

p;0 ¼43pr3

p �13ph2 3rp � h

� �ð14Þ

If rp is made the object of this cubic equation, then:

rp ¼12� h2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

h3 � 4r3p;0 þ 2

ffiffiffi2p�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2r6

p;0 � h3r3p;0

q� �3

s266664

�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih3 � 4r3

p;0 þ 2ffiffiffi2p�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2r6

p;0 � h3r3p;0

q3

r377775 ð15Þ

Based on the geometry of overlapping spheres, h is expressed as:

h ¼ rp �ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffir2

p � x2q

ð16Þ

Sintering models determine how x varies with time, and a numberof expressions are available from literature. Neck growth rates fordifferent rates of diffusion are given below:

xrp

� �6

¼ 25dDSXVckTr4

p

!t ð17Þ

xrp

� �6

¼ 192bDbXVckTr4

p

!t ð18Þ

xrp

� �5

¼ 120DVXVckTr3

p

!t ð19Þ

x2

2¼ 16DXVc

kTrp

� �t ð20Þ

x2 ¼ 3rpc2l

t ð21Þ

where k is the Boltzmann constant (J/K), T is the absolute tempera-ture (K), rp is the radius of the primary particle, d is the surface

Fig. 6. Schematic diagram of two equal sized primary p

thickness (m), b is the grain boundary thickness (m), Ds, Db, Dv

and D are the surface, grain boundary, volume and apparent diffu-sion coefficient (m2/s), c is the surface tension (J/m2), X is the atom-ic volume, (m3) and l is the viscosity (Pa s). A generalised form forthe neck growth expression, summarising the sintering expressionabove is:

xmrnp ¼ Ait ð22Þ

Therefore,

h ¼ rp �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffir2

p �Aitrn

p

!2=mvuut ð23Þ

Substituting Eq. (23) into Eq. (15). gives an expression in terms ofthe material characteristics, the particle radius rp after a given sin-tering time, the initial particle size prior to sintering rp,0. One there-fore has to solve for rp numerically. Once h and rp has beencalculated, the area reduction can be calculated using Eq. (13).The exact neck growth rate mechanism between particles is notknown for concentrates, neither is it known how variations in con-centrate mineralogy will influence the dominating mechanism.

The available time for sintering is determined by the length oftime a particle spends in the concentrate bed at temperaturesabove glass transition temperature (about 0.6Tliq of the slag withthe temperature in K). For a typical slag, this temperature wouldbe around 1000–1100 K or 727–827 �C. Sintering can therefore oc-cur between 727 �C and 1100 �C (slag solidus temperature), espe-cially in the presence of recycled premelted slag reverts, whichalready has a glassy nature. Above the solidus, bulk melting occursgradually between the solidus and the liquidus.

The residence time of a gangue particle in the bed, assumingplug flow in the bed as the concentrate melts, is:

t ¼ Vconc

_Vconc

¼ AfreeHð _mconc=qbulkÞ

ð24Þ

where _mconc is the mass smelting rate (kg/s) of concentrate and qbulk

is the bulk density of the concentrate (1300–1600 kg/m3). Typicalvalues for the residence time vary between 1.5 and 4 h dependingon smelting rate and concentrate bed height. For the purposes ofsintering a sintering time of 1.5 h can be allowed for. Where the vis-cous flow mechanism of neck growth is assumed, one would requirethe viscosity and surface tension of molten or partially molten sili-cates. The viscosity of silicates (of which magnesium silicates pre-dominate) can vary with 10 orders of magnitude between theglass transition temperature (where the viscosity is 1012 Pa s) andthe liquidus temperature. For a di-magnesium silicate (forsterite)the glass transition temperature is 1000 K (727 �C) according to My-sen and Richet (2005). At a mean temperature between the solidusof a typical slag (1373 K) and the glass transition temperature, theviscosity of di-magnesium silicate takes on a value of 106 so that,while still no bulk melting occurs, viscous flow of the surfaces canoccur. The surface tension tends to approach 0.35 J/m2 (Slag Atlas,1995). Gangue mineral contaminants such as Na2O, K2O, P2O5 andhalides will lower the surface tension. Eq. (21) indicates that the

articles just prior to sintering and during sintering.


larger second term in the square root, the larger the final size thatparticles can sinter to. The role of temperature is significant as theviscosity factor varies so much with temperature in Eq. (21). It isclear that due to the temperature gradient in the packed bed and theconcurrent chemical changes taking place decomposition of miner-als such as talc, chlorite, dolomite etc., the extent of sintering is ex-tremely difficult to predict quantitatively and consequently also thearea reduction that can be anticipated. In sintered beds, the remain-ing porous area can reduce with 99.999% whilst the void fractioncan decrease to the volume% matte in the concentrate (correspond-ing to a void fraction of 7–12% for low matte-fall concentrates).

For packed beds such as the concentrate bed, the heat transfercoefficient can be estimated from a correlation of the Colburnj-factor:

jH ¼ St � Pr2=3 ¼ 2:06e� Re�0:575

d ¼ 2:06e� qmumdp

lm

� ��0:575

ð25Þ

Or, in terms of the Stanton number as a function of Reynolds andPrandtl numbers:

St ¼ 2:06e� Re�0:575

d � Pr�2=3

¼ 2:06e� qmumdp

lm

� ��0:575 Cpmlm

km

� ��0:667

ð26Þ

where, according to definition:

St ¼ NuRe � Pr

¼�h

qm � um � Cpmð27Þ

Therefore

Nu ¼ 2:06e� Re0:425 � Pr0:333 ð28Þ

Or, in terms of �h, the convective heat transfer coefficient:

�h ¼ 2:06e� Re0:425 � Pr0:333 � km

dP

� �

¼ 2:06e

� �um � dp � qm

lm

� �0:425 Cpmlm

km

� �0:333 km

dp

� �ð29Þ

where k refers to thermal conductivity, Cp to heat capacity, and allother symbols were defined earlier.

�h ¼ 2:06e

� �ðu0:425k0:667q0:425Cp0:333Þm

l0:092d0:575p

ð30Þ

The properties are estimated at the arithmetic mean temperaturesof the fluid entering and leaving the bed, the mean particle size(dp) and the superficial velocity of matte as it flows through thebed (u), therefore the volumetric matte production rate per unitcross sectional area of the furnace excluding the immersed elec-trode cross sectional area.

The heat transfer rate from the concentrate bed to the matteflowing through the bed can be estimated by:

q ¼ �hAp;tDTlm ¼ �hAp;t �ðTcfi � TBMSÞ � ðTcsi � TmcsÞ

ln Tcai�TBMSTcsi�Tmcs

� � ð31Þ

where Tcfi, Tcsi, TBMS, Tmcs are the temperatures at the concentrate–freeboard interface, the concentrate–slag interface, the Base MetalsSulphides at the concentrate–freeboard interface and the matte atthe concentrate–slag interface respectively.

The heat balance therefore is:

�hAp;t �ðTcfi � TBMSÞ � ðTcsi � TmcsÞ

ln Tcfic�TBMS

Tcsic�Tmcs

� �¼ um � Afurnace;free � qm � CpmðTmcs � TBMSÞ ð32Þ

Assuming that the concentrate at the freeboard–concentrate inter-face and the initial concentrate–slag interface is equal, and substi-tuting Eq. (30) into Eq. (32) gives:

2:06e

� �ðu0:425k0:667q0:425Cp0:333Þm

l0:092d0:575p

" #Ap;total �

ðTcfi � TcsiÞ � ðTcsi � TmcsÞln Tcfi�Tcsi

Tcsi�Tmcs

� �¼ ðu � q � CpÞmAfurnace;freeðTmcs � TcsiÞ ð33Þ

Or

2:06e

� �ðu�0:575k0:667q�0:575Cp�0:667Þm

l0:092d0:575p

" #� Ap;total

Afurnace;free

¼ðTmcs � TcsiÞ ln

Tcfi�Tcsi

Tcsi�Tmcs

� �ðTcfi � TcsiÞ � ðTcsi � TmcsÞ

ð34Þ

where Ap,t is the total surface area of all the particles in the bedwhich can be estimated if the particle size distribution is known.Again, this increases markedly as the particle size decreases.

And

Vconc ¼ H � Afurnace;free � ð1� eÞ ð35Þ

np ¼Vconc

Vp¼ H � Afurnace;free � ð1� eÞ

p=6d3p

ð36Þ

Therefore, Ap,total is:

Ap;total ¼ Ap � np ¼ pd2p

H � Afurnace;free � ð1� eÞp=6d3

p

" #

¼ 6dp

H � Afurnace;free � ð1� eÞ ð37Þ

So that:

1u0:575

k0:667

l0:092Cp0:667q0:575

!m

� 12:36

d1:575p

H � ð1� eÞe


Tcfi�Tcsi

Tcsi�Tmcs


ð38Þ

Substituting Eq. (12) for the matte drainage velocity in Eq. (38)gives:

65:855l483k0:667

Cp0:667q1:15

!m

� H

d2:725p

ð1� eÞ2:15

e2:725


Tcfi�Tcsi

Tcsi�Tmcs


ð39Þ

Eq. (39) is an equation solely in terms of bed properties (dp, e and H),matte properties (Cp, l, q and k) and the temperatures at the topand the bottom of the bed. The sensitivity to the mean particle sizeis apparent in the equation. The only controllable parameter, once aconcentrate with a given mineralogy and grind size has entered thefurnace, is concentrate bed height.

The mean particle size can be affected, but only through unitoperations prior to smelting, such as through the appropriate dry-ing technology (spray drying versus flash fluid bed drying) or mi-cro-agglomeration of ultra fines, or through an appropriateconcentrate blend. In the unsintered state, (dp, and e) will tend tovary independently with e in the range 0.25–0.45 irrespective ofparticle size. Once sintering commences, e can shrink (to a mini-mum of where the silicates fully encapsulates the BMS) as dp in-creases to a maximum grain size. Once mass sintering occurs, thematte is locked into the sinter and can only be released once thesilicate minerals release them during melting at 1450 �C.


The matte temperature at the bottom of the concentrate bed,Tmcs, is initially guessed and iteratively solved for until convergenceis obtained for Eq. (39). While some minor error is introduced byassuming Tcfi = Tfreeboard and Tcsi = Tslag,liquidus, these are minor com-pared to the uncertainty inherent in the underpinning correlationsand the inaccuracies introduced through the exclusion of gas radi-ation effects.

For situations where concentrate bed drainage is rate limiting,Eqs. (12) and (39) can be used to estimate the flow velocity atwhich matte reaches the slag–concentrate interface and the tem-perature of the matte as it arrives at the slag–concentrate interface,respectively. Subsequently, it can only obtain further heat from theslag, as explained in the following paragraph. For situations wherebed drainage is not rate limiting, the concentrate bed plays aninsignificant role in bed-to-matte heat transfer. In the absence ofsintering the matte temperature cannot exceed the solidus of thegangue particles/slag of around 1100 �C as it would this wouldautomatically lead to gangue particle fusion and inhibition ofmatte drainage.

3. Matte droplet formation and slag–matte heat transfer

The droplets that form below unsintered concentrate can ide-ally be visualised as droplets forming below a porous plate or sieveplate where the pore/tube sizes are of a similar size to the hydrau-lic mean diameter between touching particles. It is apparent thatthis is an idealised case that is not truly achieved as the particlesin the lower regions of the concentrate pass through a transitionzone of partially molten silicates and the precursors of the liquidslag. One would therefore expect a very viscous (and rheologicallycomplex) fluid environment. The objective of the analysis given be-low is to derive a simple model for slag-zone heat transfer to thedroplets. It is conceded that very little can be accurately predictedin the multiphase zone at the slag–concentrate interface as this isnot a sharp interface and has no clear rheological properties.

Seibert and Fair (1988) derived the maximum stable Sautermean diameter to which droplets can coalesce in a laminar flowfield, as found in spray/drip liquid–liquid extraction columns(essentially ‘‘empty’’ columns without a packing material). Theyhave shown that:

dm ¼ 1:15 � g �ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

rsm

g � ðqm � qsÞ

rð40Þ

where g is the correction factor for cases where mass transfer oc-curs to or from the continuous phases to the droplet. It takes on avalue of 1.0 for no mass transfer or mass transfer from the contin-uous phase to the dispersed phase (as is the case in the furnace).In analyses below, the subscript s refers to slag (the continuousmedium) and m refers to matte (the dispersed medium), whereassm refer to a slag–matte interfacial property at the matte dropletinterface.

The interfacial tension between matte and slag is given by rsm.It is most sensitive to the FeO concentration in the slag and the FeSconcentration in the matte (increases in either of the FeO or FeSconcentration tend to decrease rsm, increasing burnt lime (CaO)addition tends to increase rsm. For single droplets that fall throughanother fluid, Incropera and De Witt (1990) suggest the followingcorrelation for estimating the heat transfer coefficient:

Nus ¼ 2þ 0:6Re0:5s Pr0:333

s 25Hs

dm

� ��0:7" #

ð41Þ

where Hs is the slag height through which the droplets settle.Seibert and Fair (1988) suggests that for multiple droplets with

interaction, the heat transfer correlations be modified with the dis-persed phase (matte) hold-up as follows:

Nus ¼ 2þ 0:6Re0:5s Pr0:333

s 25Hs

dm

� ��0:7" #( )

ð1� /mÞ ð42Þ

and the dimensionless numbers are defined as:

Re ¼ qsum;slipdms

ls; Pr ¼ Cpsls

ks; Nu ¼ h � dm

ksð43Þ

where qs are ls, ks are the density and viscosity of the slag respec-tively, um,slip is the relative velocity of the matte droplets to the slag(the slip velocity).

Therefore, after substitution,

h¼ ksð1�/mÞdm

2þ0:6qsum;slipdm

ls

� �0:5 Cpsls

ks

� �0:333

25Hs

dm

� ��0:7" #( )

ð44Þ

The time that the droplet takes to settle through the slag layer isgiven by:

t ¼ Hs

um;slipð45Þ

The slip velocity of a single droplet can be approximated by theStokes terminal settling velocity:

Restokes ¼qsðqs � qmÞgd3

m

18l2s

for which ð46Þ

um;slip ¼ðqs � qmÞgd2

m

18ls¼ Re � ls

dm � qsonly when the Stokes

regime is valid: ð47Þ

For typical values of slag and matte properties and matte dropletsizes greater than 1.5 mm the Stokes regime conditions do not holdwith the norm being 2 < Restokes < 20. For this region Godfrey andSlater (1991) reviews a few slip velocity–hold-up relationshipsdeveloped slip velocity relationships for 7 < Restokes < 2450.

A characteristic velocity is defined (similar to the terminalvelocity):

uk ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2:725dmgðqm � qsÞ

qs

sð48Þ

The slip velocity (Godfrey and Slater, 1991) is dependent on the vol-umetric dispersed phase (matte) hold-up where there is possibleinteraction between droplets:

um;slip ¼ uk1� /

1þ /0:33

� �0:917

ð49Þ

It is clear that as the hold-up approximates zero, the slip velocityapproaches the characteristic velocity. Conversely, the deviation in-creases with increased hold-up due to a shift from a regime of non-interacting droplets to a regime of disturbed settling.

Seibert and Fair (1988) derived an expression for the dispersedphase (matte) hold-up in open liquid–liquid system and packedtowers which, when simplified for the absence of packing (wherethe expression is also valid) is for a superficial matte velocity of um:

/m ¼um

um;slip � usð50Þ

us is the superficial slag velocity defined by:

us ¼_msð1�mf Þ

qs

� �Afurnace;free

or;more accurately through bulk circulation

predicted by CFD modelling: ð51Þ

_ms is the smelting rate of concentrate in (kg/s) and mf is the mattefall (% of furnace feed reporting as matte). The superficial mattevelocity is:


um ¼_ms �mfqm


ð52Þ

Substitution of Eqs. (49), (51), and (52) into Eq. (50) gives:

/m ¼

_ms �mfqmð Þ

Afurnace;free

uk1�/

1þ/0:33

� �0:917�

_ms ð1�mf Þqs


ð53Þ

Eq. (53) can be solved through iteration. Once the volumetric hold-up of matte in slag is determined, it is substituted into Eq. (49) tocalculate the slip velocity of interacting droplets.

In the case of a 3-electrode circular furnace, this may be furtherrefined by splitting the slag bath in two annular zones, one beingthe area circumscribed by the pitch circle of the electrodes, whereslag flows are predominantly vertically upwards (countercurrentto matte droplets) at a relatively higher velocity, and the annularzone between the pitch circle and the furnace wall where slagflows are predominantly downwards (co-current to matte drop-lets) at a relatively slower velocity. These flow patterns have beenwell modelled in recent computational fluid dynamic studies(Ritchie and Eksteen, 2010; Bezuidenhout et al., 2009). In this casethe hold-up is different for the different regions and two new areasneed to be defined:

APCD;free ¼ APCD � 3� Aelectrode ð54ÞAannulus ¼ Ahearth � APCD ð55Þ

where the annular zone essentially is the settling zone in thefurnace.

As a rule of thumb, for optimal reaction zone overlapping, thediameter of the pitch circle, dPCD is:

dPCD ¼4ffiffiffi3p � delectrode and APCD ¼ 5:34

p4

d2electrode: ð56Þ

APCD;free ¼ 2:34p4

d2electrode ð57Þ

Therefore the slag superficial velocities can now be calculated for acirculatory flow in two regions.

The amount of circulation is dependent on furnace hearthpower density (kW/m2) and electrode immersion, as demonstratedCFD models for round furnaces by Ritchie and Eksteen (2010). Theyhave shown that typical bulk slag circulation velocities vary be-tween 0.062 (at 15% electrode immersion) and 0.131 m/s (at 50%electrode immersion) at a heart power density of 225 kW/m2.

With the droplet slip velocities and hold-up known, the heattransfer coefficient can be calculated, using Eq. (44).

The matte temperature Tmsm, as it reaches the slag–matte inter-face in the tidal zone, is given by:

Tmsm ¼ Ts � ðTs � TmcsÞ exp�6ht

q � Cp � dm

� �ð58Þ

or

Tmsm ¼ Ts � ðTs � TmcsÞ exp�6h � Hs

qs � Cps � dm � um;slip

� �ð59Þ

Table 2Typical slag and matte properties at typical smelting operating conditions.

lm (Pa s) ls (Pa s) qm (kg/m3) qs (kg/m3) rsm (N/m)

0.00204 0.088 4800 2960 0.35

Table 3Typical furnace dimensions and operating conditions.

e H (m) Hs (m) dhearth (m) delectro

0.40 0.35 1.20 10.65 1.40

Substituting the heat transfer coefficient Eq. (44) into Eq. (59) gives:

Tmsm ¼ Ts � ðTs � TmcsÞ exp�6ks � Hsð1� /mÞd2

mqs � Cps � um;slip

� 2þ 0:6qsum;slipdm

ls

� �0:5 Cpsls

ks

� �0:333

25dm

Hs

� �0:7" #( )!

ð60Þ

Therefore, once the temperature of matte Tmcs at the concentrate–slag interface is known through Eq. (39), the droplet size throughEq. (40), the matte hold-up is calculated using Eq. (53), the slipvelocity through Eq. (49), the matte temperature Tmsm at the topof the matte–slag interface can be calculated using Eq. (60). If theStokes law estimate is used as a rough estimate for um,slip, the sen-sitivity towards droplet size is apparent – the denominator in theexponent becomes dependent on dm to the 4th power. This in turndepends mostly on variation in the slag–matte interfacial tensionand the density difference. For variations in feed chemistry it isfound that the interfacial tension will vary much more significantlythan the slag–matte density difference.

The matte temperature derivation presented above is for amatte droplet arriving at the bulk matte pool below the bulk slag.The tapping temperature of the matte is further influenced by theheat transfer from the stirred bulk slag (primarily a function ofelectrode immersion as shown by Ritchie and Eksteen (2010)) tothe bulk matte, with higher interfacial velocities contributing toimproved heat transfer between the two melts. Heat loss fromthe bulk matte pool occurs via the hearth refractories. Furnace de-sign aspects such the hearth radius, the type of hearth refractories,the height of the matte tap hole and the depth of the tidal zone willaffect the tapped matte temperature. Ritchie and Eksteen (2010)and Bezuidenhout et al. (2009) have showed that the matte tendsto be very poorly mixed below the matte tapping level and that thematte heel often takes on a thermal profile of a solid with a signif-icant thermal gradient from the slag–matte interface down to thehearth refractories.

4. Example

For the purposes of this example it is assumed that mean parti-cle sizes are sufficiently large that the concentrate bed does not be-comes rate limiting with regards to matte drainage and heat-up. Insuch a case, it is assumed that all the sulphide components havemelted before a temperature of 1100 �C has been reached, as ex-plained in Eqs. (2)–(6). The matte will therefore drain rapidly fromthe concentrate bed, once completely molten (i.e. at its liquidus).The heat transfer mode is therefore slag-to-matte droplet heattransfer rather than concentrate bed-to-matte heat transfer.

The matte and slag properties (which will vary with tempera-ture and chemistry, but is held fixed for this example) are pre-sented in Table 2. The furnace dimensions and operatingconditions are given in Table 3.

The operating conditions and furnace specific dimensions are:The average droplet size, according to Eq. (40) is:

Cps (J/kg K) Cpm (J/kg K) km (W/m2 K) ks (W/m2 K)

1394 774 17 0.5

de (m) Tcfi (K) Tmcs (K) Ts (K)

923 1123 (850 �C) 1893 (1620 �C)

Table 4The effect of concentrate bed drainage on matte temperature (same concentratechemistry).

Concentrate bed condition Resultant matte temperature atslag–bulk matte interface (�C)

Concentrate bed is not rate limiting withregards to matte drainage

1491

Concentrate bed is rate limiting withregards to matte drainage

1536

Concentrate bed has experienced bulksintering at some point in the bedvolume

1592

Table A1Selected mineral properties for minerals found in PGM concentrates.

Mineral Moh’shardness

Brinellhardness

Density(s.g.)

Pentlandite [(Ni,Fe)9S8] 3.5 120–150 4.7Chalcopyrite [CuFeS2] 3.7 120–150 4.2Pyrrhotite [Fe7S8] 4.0 160 4.6Pyrite [FeS2] 6.0 400 5.1Other sulphides (galena, bornite, etc.) 3.0 120–150 7.0Orthopyroxene [(Mg,Fe)SiO3] 5.5 120–150 3.5Clinopyroxene

[(Ca,Mg,Fe)(Mg,Fe)(Fe3+,Al)Si2O6]6.0 120–150 3.4

Olivine [(Mg,Fe)2SiO4] 7.0 120–150 3.5Plagioclase/Anorthite [Ca(Al2Si2O8)] 6.2 450 2.7Amphibole/Tremolite/

Actinolite[Ca2(Mg,Fe)5Si8O22(OH,F)2]6.0 110 3.0

Talc [Mg3(Si4O10)(OH)2] 1.0 2 2.7Serpentine [Mg6(Si4O10)(OH)8] 3.5 120–150 2.6Chlorite

[(Fe,Al)2(OH)6,Mg(Al,Si)4O10)(OH)2]2.1 25 2.6

Biotite/Phlogopite[K(Mg,Fe)3(AlSi3O10)(OH,F)2]

2.5 60 2.9

Quartz [SiO2] 7.0 650 2.65Chromite spinel [(Mg,Fe)(Cr,Al)2O4] 5.5 400 4.5Magnetite spinel [Fe3O4] 6.5 500 5.2Carbonates [(Mg,Ca)CO3] 3.5 120–150 2.9


dm ¼ 0:0053 m or 5:3 mm:

According to Eq. (48), the characteristic velocity therefore is0.296 m/s.

With a slag circulation velocity 0.1 m/s and a superficial mattevelocity of 3.0 � 10�6 m/s (10.8 mm/h or 296 kgconcentrate/h/m2 at18% matte fall), the equilibrium volumetric hold-up of matte inslag is very low:

/m ¼ 0:0016%

The slip velocity, based on Eq. (49) is therefore 0.289 m/s.The Prandtl number of the slag is 245 which, with a Reynolds

number of 51.3, give a Nusselt number of 16.8 using Eq. (42). This,in turn, gives a film heat transfer coefficient of 1591 W/m2 K at thematte droplet slag interface.

The settling time for a matte droplet under the conditions spec-ified above is 4.15 s.

Using Eq. (60), with a slag temperature of 1620 �C and an initialmatte temperature at the concentrate–slag interface of 850 �C, theresultant matte temperature of a matte droplet arriving at theslag–bulk matte pool interface is 1491 �C. Should the concentratebed rate limiting with regards to matte drainage and the matteapproaches the solidus of gangue particles (1100 �C), the mattetemperature increases to 1536 �C. Should the concentrate bed sin-ter, and release the matte droplets only upon bulk melting at1450 �C, the matte temperature increases to 1592 �C. In all cases,some cooling of the bulk matte pool will occur via heat transferthrough the hearth to slightly lower the observed tapping temper-ature, although this effect will be fairly similar for all cases, irre-spective of concentrate, slag bath or chemical changes. Thecomparison of the different drainage scenarios are given in Table 4.

Therefore, while slag properties play the overriding role whenthe concentrate bed is not rate limiting with regards to mattedrainage, matte temperatures (even for a very hot slag at1620 �C), are still below the point that major refractory attackcan occur. However, as soon as either the bed becomes rate limit-ing, or when it experience bulk sintering, the temperatures rapidlyescalates above the refractory sulfidation temperature, causing ra-pid refractory wear thereby compromising the furnace integrity.

5. Conclusions

Models have been derived and presented for concentrate–matteand slag–matte droplet heat transfer. These are contextualisedwithin the concentrate smelting environments found at WesternPlatinum’s Marikana operations. It has been shown that, dependingon the grind of recycled reverts and the mineralogy and grind ofMerensky and UG2 concentrates, and on the blend of the varioustypes of concentrates and recycles streams, the concentrate bedcan become rate limiting with regards to matte drainage. Whenthis happens (and even more so for sintered concentrate beds),the matte temperature can rapidly rise to temperature which could

compromise the integrity of furnace. In such cases the mattetemperature will exceed the critical temperature where the extentof sulfidation and melting of the refractory rapidly increases. Theeffect of electrode immersion and general furnace design and lay-out on matte temperature as tapped has not been explored in thispaper. The research made it clear that there are upper limits inhearth power density and smelting rates per m2 hearth area ifexceedingly high matte temperatures are to be avoided, and thatthese are primarily determined by the particle size distributionand the mineralogy of the blended furnace feed, all other furnacedesign and operating parameters being equal.

Understanding the role of particle size and mineralogy (by sizeclass) will aid the metallurgical engineer to decide upon agglomer-ation and drying options prior to smelting. For instance, drycycloning and micro-agglomeration can shift the particle size dis-tribution to coarser particle sizes that aid bed porosity. Alterna-tively, the drying technology employed may also have significantimpacts. From a particle size and concentrate bed porosity per-spective, it is better to utilise spray driers which can give agglom-erated products rather that fluidised bed flash dryers, despite thelatter being thermally more efficient from a drying perspective.The way furnace dusts are pre-treated before recycle, the particlesize are specified for fluxes, or how fine the reverts are milled be-fore recycling, all can be adapted to shift the particle size distribu-tion to coarser particle sizes. Over and above the benefit foreseenfor lowering matte temperature, dust losses from the furnace canbe lowered or, alternatively, more ingress air can be allowed tolower furnace freeboard temperatures for a given dust loss.

In some cases, hot converter slag return to the furnace, ratherthan recycled and floated or repulped reverts, would be beneficial.However this is constrained up to a point where chromite spinelsmight become problematic.

Future work will explore the role of changing mineralogy, feedchemistry and electrode immersion on the matte temperatures astapped.

Appendix A

See Table A1.


References

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a mechanistic model to predict matte temperatures during the smelting of ug2-rich blends of platinum...

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