performance of a dense-medium cyclone when beneficiating fine coal

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Performance of a Dense-Medium Cyclone WhenBeneficiating Fine CoalR. P. KING a & A. H. JUCKES aa Department of Metallurgy and Materials Engineering, University of the Witwatersrand,Johannesburg, 2050, U.S.APublished online: 27 Apr 2007.

To cite this article: R. P. KING & A. H. JUCKES (1988): Performance of a Dense-Medium Cyclone When Beneficiating Fine Coal,Coal Preparation, 5:3-4, 185-210

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Coal Preparation, 1988, Vol. 5, pp. 185-210Photocopying permitted by license only© 1988 Gordon and Breach Science Publishers S.A.Printed in the United Kingdom

Performance of aDense-Medium Cyclone WhenBeneficiating Fine CoalR. P. KING and A. H. JUCKES

Department of Metallurgy and Materials Engineering. University of theWitwatersrand. Johannesburg. 2050. S.A.

(Received January 23, 1987; in final form June 8. 1987)

The partition function has been determined for fine coal in a dense-medium cyclone. Thepartition curve is characterised by four parameters; the cut point, the separation efficiency, the short circuit to underflow and the short circuit to overflow. Each of theseparameters is a strong function of particle size for fine coal. The effect of slimes in the feedis shown to have only a small effect on the measured partition curves.

INTRODUCTION

There has been considerable renewed interest worldwide since 1980 inthe processing of fine coal. This interest seems to have its origin in anoticeable increase in the production of fine coal by mining methodsthat rely more heavily on mechanised stoping techniques together withan ever-increasing demand for higher processing efficienciesso that lessdiscard coal is produced in washing operations.

Technologies for the beneficiation of fine coal have been available formany years and the state of technical development up to 1982 has beencomprehensively reviewed by Osborne' in this journal. Developmentssince the early part of this decade have been reported in detail at the9th' and lOth:' International Coal Preparation Congresses and an entireissue of the Journal Powder Technology (Volume 40, Nos. 1-3, 1984)was devoted to the technology of fine coal processing. Consequently agood deal of information is available on the problems associated withthe processing of fine coal. However many technical problems remainto be solved before the beneficiation and further processing of fine coalcan become an economically attractive propostion.

185

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186 R. P. KING and A. H. JUCKES

A few industrial plants have been operated for some time but thereare no universally accepted processing routes and most authors agreethat process optimization is essential if fine coal beneficiation is to beeconomically viable.

The study reported in this paper was undertaken specifically toestablish the operating performance characteristics of the densemedium cyclone when processing fine coal. Data available in the literature is very sparse and it would not be possible to predict with anyaccuracy the performance of the dense-medium cyclone when processing fine coal using present available data without extensive plant testsand process optimization would be virtually impossible. The approachtaken in this study was to measure accurately the partition curves undera variety of operating conditions to permit accurate calculations ofbeneficiation performance.

A primary motivation for this study was the current practice ofdumping unbeneficiated fine coal at many South African Collieries withthe consequent loss of a valuable energy resource as well as the cost ofcontrol of dumping procedures to limit environmental damage.

FINE COAL BENEFICIATION

In the context of beneficiation technology, fine coal is usually considered to be smaller than I mm although most plants separate at anominal size of 0.5 mm. Particles as small as this sometimes start toapproach the liberation size of the ash and increased ash liberation canbe exploited to improve beneficiation performance. However, in manycoals, ash liberation size is very much smaller and the beneficiation ofultrafines (particles smaller than 50 11m) has become a separate beneficiation technology. The significant increase in ash liberation at ultra finesizes has opened the possibility for the production of ultra clean coal byflotation" or oil agglomeration.'

The significant variation of behaviour with particle size is a dominantfeature of fine coal beneficiation technology and the characterisation ofperformance as a function of particle size is of paramount importanceif optimal processing routes are to be determined.

The performance of any coal benefication unit operation is mosteffectively presented in terms of the partition curve and this approachis used in this study. Not much data is available in the literature on thepartition curves to be expected from fine coal washing operations in adense-medium cyclone. Geer et al" and Deurbrock? have publishedsome data on partition functions determined experimentally but these

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PERFORMANCE OF A DENSE-MEDIUM CYCLONE 187

are very sparse and do not permit the evaluation of all parameters.Mengelers and Dogge," Osborne" and Fourie et al," have presentedresults obtained in pilot and operating plants but only in terms of thebehaviour of composite material over all particle sizes.

THE PARTITION CURVE

The partition curves for fine particles differ significantly from thosefound for coarse (;, 0.5 mm) coal in larger dense-medium cyclones.Firstly the partition curves for different size fractions in the compositefeed differ significantly from each other. The separation efficiency fallsquite quickly as size decreases leading to relatively flat partition curves.The cut point varies with size also - small sizes having larger cutpoints. Secondly the partition curves give definite evidence of shortcircuit flows that take feed directly to underflow or overflow withoutsubjecting the coal particles to the separating force of the centrifugalfield within the body of the cyclone. This effect, which is almost neverobserved in larger dense-medium cyclones, manifests itself by producing a partition curve that does not have low and high density asymptotes at 100% and 0% recovery to overflow. These features of thepartitioning behaviour of fine coal in the dense-medium cyclone areillustrated schematically in Fig. I.

TL-_--'-__-""_~~ _=:::""'"_:..~~_=.,_.:._.:.::.::.=::.:=j-.IShortcircuit to ovelflow

Shortcircuit 10underflow

'\..~

01-

0,8

~0,7

£ 0,6

C0,50

~ 0,40c,

0,3 -

0,2Medium de~slty

0,1

Relotive Density

FIGURE I Schematic representation of the partition function for finecoal beneficationin a dense-medium cyclone. The four operating characteristics are shown: cutpoint shift,separation efficiency (EPM), and the two short circuit flows.

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Four parameters characterise the partition curve in a dense-mediumcyclone: the imperfection, the cutpoint shift, short circuit to underflowand short circuit to overflow. The effects of these parameters are shownin Fig. 1which shows a typical sequence of partition curves for particlesof three different sizes in the range 50 Ilm-l mm. The most strikingfeature of the partition curves for fine coal is the rapid change in shapeand shift of the curve to the right as particle size decreases. This is insharp contrast to the behaviour of coarse coal (+ 10mm) in largedense-medium cyclones where the variation of performance with sizecan be neglected without serious error and a single partition functioncan be used for all particles in the feed. Thus when treating fine coalthere is an entire envelope of partition curves effective over the sizerange of particle sizes in the feed and each particle size is separated ata different effective cutpoint which is higher than the medium density.In addition, the efficiency of separation falls off rapidly as the particlesize decreases.

It is usual to normalise the partition curve by plotting against theratio x = relative density/cut point and the normalised curve is foundto be independent of the medium density and the cut point. However,the normalised curve is strongly dependent on particle size. Thephenomenon of short circuiting to underflow and overflow is a significant feature of the partition functions for fine coal. These short-circuitflows have a significant effect on the performance of the dense-mediumcyclone when treating fine coal and they can lead to serious fall off inperformance. Consequently the short-circuit flows must be accuratelymeasured and modelled if a useful model for dense-medium cyclonebehaviour is to be developed.

The experimental facility that was used in this study has been described elsewhere" and the experimental data is fully described inRef. II. The cyclone used was 150mm in diameter, having a cone angleof 150. Two typical sets of measured partition curves are shown inFigs. 2 and 3. Figure 2 shows the variation of partition curve withparticle size at a single medium density and Fig. 3 illustrates the variation of partition function with medium density for a single particle size.The effectiveness of the normalisation procedure can be clearly seen inFig.3b.

A number of suitable empirical functional forms for the partitioncurve are available in the literature and several of these have beenexamined critically by Reid et al," None of the useful functional formshave any theoretical basis and all seek to describe the shape of thepartition curve with the smallest number of parameters. In the case offine coal beneficiation at least four parameters are required to provide

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1,71.61,51,41,3

oL-__--'-__L-_---'-__'--_--'--__'--_--'--_-'"------"'LL__

1,2

10

100 •-500+425 micron •90 -300+250 micron-150+125 micron.

- 90+ 75 micron

0..~l2c:0

~ 40ll.

30

20

Particle specific gravity

FIGURE 2a Measured partition function for four different particle sizes. The partitionfunction varies significantly with particle size. The lines show the best fit to Eqs. (I)and (2).

1,21,11.0Reduced speciftc gravity

0,9

-500+425 micron •-300--250 micron-150+125·

micron

100.-----,-----;;,,----.--------,----,----,---,-----,

..~l2 50c0Et 40ll.

30

20

10

00,8

FIGURE 2b The data of Fig. 2 normalised by plotting against the reduced specificgravity.

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1,7


100

90 ••80

•...Q 60oSl 50c.Q'"te

30

20-150+125 mIcron

10 Medium: Coal 3 :

01,2 1,3 1,4 1.5 1,6

Particle specific gravity

FIGURE 3a Measured partition function at 3 different medium densities. The linesshow the best fit to Eqs. (I) and (2).

100

90 • • •80

70...Q 60cSlc: 50.Q'"t~ 40

30

20

10

00,8 0,9 1,0

Reduced specific gravity

-150+125 micronMedium: Coal 3 :

1,1 1,2

FIGURE 3b Data of Fig. 3a normalised by plotting against the reduced specificgravity. The regression lines of Fig. 3a are perfectly superimposed in Fig. Jb. showing theefficacy of the normalisation procedure.

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PERFORMANCE OF A DENSE·MEDIUM CYCLONE 191

an adequate description of the partition curve. One parameter isrequired to describe each of the following performance characteristics:

the cut point shift,the separation efficiency,the short-circuit flow to underflow,the short-circuit flow to overflow.

In practice it was not possible to measure the partition curves sufficiently accurately to justify using more than four parameters tocharacterise the partition curves such as those illustrated in Figs. 2and 3.

The Short-circuit FlowsThe real dense-medium cyclone may be considered to act as a separating device which processes only a fraction of the feed - the remainderof the feed passes directly to the overflow or underflow without beingsubjected to the separating action of the cyclone. The portion of thefeed that passes through the centrifugal separating field is split according to a corrected partition function R,.(x), which has the followingproperties

RJO)

R,(I)

R(oo)

1.0

0.5

0.0

(I)

Fractions ex and f3 of the feed short circuit direct to the underflow andoverflow respectively. Then the actual partition function for particles ofa particular size is related to the corrected partition function by

R(x) = f3 + (I - ex - f3)RJx) (2)

(3)

A number of suitable empirical functional forms for the correctedpartition function RJc) are available in the literature. We have used thefollowing form

ebx _ IR,(x) = ebx + eb _ 2

originally due to Lynch, because it is easy to use and fit to experimentaldata. It also has the correct asymptotic behaviour at x = 0 andx = 00.

When Eq. (3) is substituted into Eq. (2) a four-parameter function forthe partition function is obtained as required with each of the fourparameters s., b, ex and f3 having a one-to-one relationship with the four

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operating characteristics of the dense medium cyclone. These cantherefore be determined directly from the measured partition curve.

The cut point s; is most effectively correlated with the particle sizeand operating conditions in terms of the normalised cut point shift(NCPS) defined by

(4)

where s; is the specific gravity of the medium feed to the hydrocyclone.The separating efficiency is commonly expressed in terms of the

imperfection I defined by

I = X 25 - x"2

where R(x,,) = 0.25 and R(x,,) = 0.75. The parameter b in equation (3) is related to the imperfection by

I = 0.5 I (a - 0.75)(0.75 - fJ)b n (a - 0.25) (0.25 - fJ)

(5)

However, it is better in practice to correlate the behaviour of the densemedium cyclone in terms of the imperfection of the corrected partitionfunction

I = 0.5 In (0.75)(0.75)c b (0.25) (0.25)

1.099b

(6)

I,. is called the corrected imperfection.The parameters are easy to estimate if an adequately measured

partition curve is available. We have measured partition curves undera wide variety of conditions in an experimental pilot-scale rig and thedata are available in Ref. II. Figures 2 and 3 are merely typicalexamples of the many that have been measured during this study. Inparticular the partition curves were measured for four narrow sizefractions of coal in each experiment and the four parameters NCPS, I"a and fJ were estimated by non-linear regression as a function of coalparticle size.

THE EFFECT OF SLIMES IN THE FEED

The empirical relationship Eq. (2) may be used to calculate the composition of the two products from the dense-medium cyclone for any

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feed material provided that the particle size distribution and thewashability is known as a function of size. However, fairly largequantities of slimes will be present in the feed if this is not deslimed. Itis not clear what effect such slimes will have on the behaviour of thecoarser particles in the cyclone. In order to determine this effect severalexperiments were run using fine coal from the Landau Colliery. Thecoal was obtained as deslimed fines from the desliming hydrocyclone

TABLE I

Summary of conditions for experiments included in this paper

ExperimentOrigin of coal Slimes content Medium sp. Flowrategr.

Run Sample %-75 I'm in feed Ijmin

5 I Greenside 2.5 1.32 1586 I Greenside 2.5 1.37 1587 I Greenside 2.5 1.46 1728 I Greenside 2.5 1.42 1575 4 Greenside 2.5 1.32 1216 2 Greenside 2.5 1.37 1147 2 Greenside 2.5 1.46 1088 2 Greenside 2.5 1.42 115

12 I Greenside 2.5 1.42 16513 I Greenside 2.5 1.42 16014 1 Greenside 2.5 1.32 155IS I Greenside 2.5 1.32 17116 I Greenside 2.5 1.37 16217 I Landau 10 1.42 16318 I Landau 10 1.32 17919 I Landau 20 1.42 16720 I Landau 30 1.42 15423 I Landau 50 1.42 16329 I Landau 10 1.50 16532 I Greenside 2.5 1.42 19832 2 Greenside 2.5 1.42 13632 3 Greenside 2.5 1.42 112

TABLE II

Experimental conditions for experiments with slime in feed

Amount of - 75 I'm Ash content of Sp. gr.Experiment material in feed Medium sp. gr. clean coal differential

17/1 10% 1.419 7.3 0.3418/1 10% 1.320 6.4 0.2319/1 20% 1.422 7.6 0.2520/1 30% 1.414 7.5 0.2623/1 50% 1.440 7.8 0.2329/1 10% 1.505 9.9 0.32

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TABLE V

Particle size distribution of the magnetite medium

Used in experiments Used in experiments Used in experiments6-8 9-25 26-32

Size JIm % undersize Size ,urn % undersize Size Jlm % undersize

23.7 77.9 22.9 90.3 26.1 90.217.1 70.8 16.5 84.7 18.8 84.911.9 62.0 11.5 77.4 13.1 78.07.9 49.7 7.6 65.5 8.7 67.76.2 42.9 6.0 57.3 6.9 59.9

underflow. A sample of the slimes from the hydrocyclone overflow wasobtained and varying amounts of the slimes were added to the deslimedfines to make up feed for the dense medium cyclone tests.

The partition curve for each of four size fractions was determined fordeslimed feed and with additions of 10%, 20%, 30% and 50% 75 jjm

slimes in the feed. Typical examples of the measured partition curvesare shown in Figs. 2 and 3. The four parameters, s,., b, Ci and f3 wereestimated by the method of least squares and the resulting equationsshown as the solid line in the figures. The data shown in these figuresis typical of many partition curves that were measured in the course ofthis study. The complete set, together with all information relating tothe experimental conditions, is available in Ref. II. The experimentalconditions are summarised in Tables I and II. The least-squares bestestimates of the normalised cut point shift and of the imperfection aregiven in Tables III and IV.

The particle size distribution of the magnetite medium is given inTable V.

These data do not give any indication that the presence of increasingamounts of the slime in the feed has any effect on the separationcharacteristics of the coarser particles.

The effect of the addition of viscosity modifier to the medium in thepresence and absence of slimes were investigated experimentally andthese results are reported in Ref. 14.

SHORT CIRCUITING

The two parameters Ci and f3 which characterise the short circuiting tounderflow and overflow are difficult to characterise accurately unlessthe upper and lower asymptotes of the partition curves are established

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with considerable precision. This requires the measurement of thewashability of overflow and underflow over a wide range of particledensities at small intervals. Results averaged over several experiments,from our pilot plant are summarised in Figs. 4 and 5 where the shortcircuit flows are shown as a function of particle size.

Short circuiting is dependent on particle size and is significant up toa size of 600Jim. Short circuiting to underflow is more significant thanshort circuiting to overflow. These short-circuit flows are adequately

100 200 300 400 500 600(Particle size) fJm

800

FIGURE 4 Measured short circuit flow to underflow. The graph extrapolates backclose to the water recovery to underflow. This indicates that very fine particles will followthe water rather than separate by density.

c.P.-c

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20 r-----,---,---.---,------r--...,

• landau coal with slimes

~ Greenside coal

100 600500200 300 400Particle size 11m

FIGURE 5 Short circuit flow to overflow.

o

modelled by the following relationships (d, in J1m):

Short circuiting to underflow:

IX =0.4 exp ( - 0.00543dp ) (7)

The data in Fig. 4 confirm that the presence of up to 50% of ultra fineslimes in the feed does not significantly affect the amount of shortcircuiting to underflow.

Short circuiting to overflow without slimes:

{3 0.08 - 1.33 x 10- 4d, for d, ,,:; 600 J1m (8)

0.0 for d, ;;, 600 J1m

Short circuiting to overflow with slimes present:

{3 0.04 - 6.67 x 10- 5d, for dp ,,:; 600 J1m (9)

0.0 for d, ;;, 600 J1m

Although the presence of slimes does not appear to significantly influence the short circuit to underflow it does reduce the short circuit tooverflow by a small but significant amount. It is interesting that in thelimit as d, --+ 0 the short circuit to underflow approaches quite closelyto the fractional recovery of water to underflow. This result is notunexpected and it indicates that the very fine coal particles tend tofollow the water. Other factors which influence the short circuiting suchas the geometry of the cyclone will be reported in a separate paper.

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THE CUTPOINT SHIFT

Various attempts have been made to relate the cut point shift to theoperating conditions and the geometry of the cyclone. Probably themost successful theoretical approach to the problem of predicting thecut point is based on the concept of the equilibrium orbit. In simpleterms this can be explained as follows. The feed to the cyclone entersat the wall and a portion of the flow leaves the cyclone through thevortex finder in the centre. Thus there is a net inward flow of fluid whichwill tend to drag all particles inwards. At the same time all particlesexperience a centrifugal force outwards if they have a density exceedingthat of the medium. Some particles can experience an equilibriumbetween these two forces at a radius between that of the vortex finderand the wall. In the absence of any disturbances to the flow suchparticles remain at that radius and circulate with the fluid. Hence thename equilibrium orbit. In reality the motion of a particle in thehydrocyclone is much more complex than the simple picture presentedabove and any attempt to calculate the cutpoint from the behaviour ofindividual particles must consider the complex hydrodynamic field thatexists inside the hydrocyclone. For present purposes we are interestedonly in establishing the parameters that have a major influence on thecutpoint in order to develop an empirical correlation from which thecutpoint can be predicted on the basis of existing experimental data.Thus we investigate the effect of particle size and density on the equilibrium orbit.

The Drag ForceThe key to the equilibrium orbit theory is the drag force experienced bya particle due to the relative motion between it and the fluid. It is knownthat these relative velocities are small and the particle Reynolds numberis usually so low that it is commonly assumed that the drag force canbe calculated from the formula for the slow relative motion between asphere and a Newtonian fluid. This is the well-known Stokes formula.This approach neglects two very important phenomena: the highlyturbulent nature of the fluid inside the hydrocyclone and the relativelyhigh concentration of particles. Thus the use of Stokes flow theorieswhich assumes that only a single isolated particle is present is not veryrealistic.

We consider here four limiting cases: isolated particles in a laminarflow field (Stokes regime), isolated particles in a turbulent flow field(Newton regime), interacting particles in a laminar flow field (BlakeKozeny regime) and interacting particles in a turbulent flow field

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(Burke-Plummer) regime). Of these the last seems to correspond mostclosely to the experimental observations.

If v, is the radial velocity of the fluid at a point in the hydrocycloneand u, the radial velocity of the particle, the drag force is given by

Drag force = 0.5CD(v, - u,)2I!mA" (10)

where I!m is the medium density, If" the cross-sectional area of theparticle and CD is the drag coefficient. It is not difficult to show that,within the time taken for a particle to make a single orbit in the cyclone,the drag force is balanced by the centrifugal force due to the circulatingmotion. The centrifugal force is given by

V2

Centrifugal force = -!. v,,(I!, - I!m)r

(11)

where Ve is the tangential component of the particle velocity vector, r theradius of the tangential motion, v" the volume of the particle and I!, thedensity of the solid. Balancing these forces

(12)

The Equilibrium OrbitIt is usually assumed that particles that have a 50% chance of passingto overflow will establish an equilibrium orbit somewhere within thecyclone. The position of this equilibrium orbit is not precisely definedalthough some authors claim that it is at the point where the locus ofzero vertical velocity meets the spigot opening. The uncertainty regarding the actual position of the equilibrium orbit of the 50% particle isnot important since we are interested only in establishing a functionalform of the relationship among the particle properties that give it a 50%chance of leaving in either the overflow or underflow. All particles thathave combinations of density and size that produce a 50% split in thecyclone are assumed to have equilibrium orbits at the same location inthe cyclone and this assumption allows a very useful correlation to bedeveloped for the normalised cutpoint shift as shown in the followinganalysis.

On an equilibrium orbit u, = 0 and Eq. (12) can be written for aparticle having a 50% chance of passing to overflow. This defines thespecific gravity of separation or cut point I!, as follows

(13)

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(], is the cut point, (], - (]m the cut point shift, «(], - (]m)/(]m the normalised cut point shift (NCPS) and (Jp is the cross-section area per unitvolume of particle. For a particular cyclone the particles that have a50% chance of passing to overflow will satisfy Eq. (13) at a particularvalue of

These particles define the midpoint of the partition curve as shown inFig. I and Eq. (13) provides a correlation for the normalised cut pointshift as a function of particle properties.

The drag coefficient in Eq. (13) is a function of the particle size andshape and the environment that the particle finds on its equilibriumorbit. Each of the four environments defined above give differentexpressions for CD as follows:

Stokes RegimeIn this regime the particles do not interact with each other and aresurrounded by fluid in laminar motion.

24Jlm

24Jlm ( b'-d-- on an eqm. or It)pV,Qm

d, particle size and 11m is the viscosity of the medium.

Substituting in Eq. (13)

(14)

Normalised cut point shift(], - (]m

(]m

K1 rv,-d' "2"

p (]m Ve

12l1m (Jp rv,

----;;:- dp v~

(15)

Newtonian RegimeIn this regime isolated particles are surrounded by fluid in turbulentmotion

CD = 0.43

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Substituting in equation (\3)

NCPS =rv'

0.2211p -+v.

(16)

(\ 7)

Hindered SettlingThe interaction between the particle and others in its neighbourhood istaken into account by considering the behaviour of the particle as if itwere settling under conditions of hindered settlings. The force exertedon a single particle under these conditions is equal to the pressure.gradient in the bed of particles multiplied by the product of the crosssectional area of the particle and the particle diameter. The pressuregradient can be calculated from the well-established correlations forpressure drop in a fluid which flows through a packed bed."

8PDrag force = .- dp~

oX

f(!m(v, - u,)' ~ Ap

where f is the friction factor in the particle bed and d, is the hydraulicmean diameter of the open channels between particles in the neighbourhood of the particle.

The hydraulic mean diameter is calculated as follows: Consider eachparticle to be influenced by the fluid in its region of influence which hasvolume

nd;6(1 - s]

where 0 is the local voidage

4 x cross-sectional area available for flowd, =

wetted perimeter

4 x volume of voidswetted surface

The wetted surface in the neighbourhood of the particle is made up ofthe surface of the particle and the surface of all particles that are whollyor partially in the volume of the region of influence. Let S, represent the

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surface area of a particle per unit volume of particle

, ) (red} re d 3 )Wetted surface = nd; + Sp(l - E 6(1 _ E) -"6 p

4Ered}

6(1 _ )[ d' SpE1Cd}]E 1C p + 6

(18)

In Eq. (18) S, should represent the average surface area per unit volumeof particles in the region of influence. This can be related to the averageparticle size by S, = 6/J

d" =

6(1

4Ered}

) [ d' Ered}]-E 1C +-p J

where

4Jx6(1 - E)(I + x)

(19)

Equation (19) can be usefully approximated by

where n has a value between 0 and I.Comparing Eqs. (17) and (10)

Co = 2fdpd,

(20)

(2 I)

Blake-Kozeny RegimeIf laminar flow conditions exist in between the particles on an equilibrium orbit,"

f1200(1 - E)

Rep1200(1 - E)J.lm

d"V,1Im

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Substituting this in Eqs. (21) and 13)

NCPS = Q, - Qm

Qm

K 3 rv,-d2 2Qm h Vo

(22)

(23)

Burke-Plummer RegimeIf turbulent conditions prevail around the particle ' S

f = 14.0

and

NCPS = Q, - Qm = K4 rv;e; dh Vo

The four expressions derived above for the normalised cut point shiftcan be tested by experiment in terms of the predicted variation of theNCPS with feed rate and particle size. Kelsall's experiments revealedthat over the normal operating range of the hydrocyclone, the flowpattern and therefore the ratio v,lvo remains unchanged as the flowvaries. Consequently Eqs. (16) and (23), which are based on theassumption of a turbulent flow field inside the cyclone, predict that thenormalized cut point shift should be independent of flowrate. In ourexperimental programme flowratc was varied from 114 Ilmin to 196 IImin. In spite of this variation in flow-rate no systematic variation wasfound in NCPS for any of the particle sizes investigated. On the otherhand Eqs. (15) and (22), which are based on the assumption of alaminar flow field, predict that NCPS should vary approximately as theinverse of the flowrate. Consequently it is concluded that the turbulent

. flow field inside the hydrocyclone dominates the momentum transferprocess between medium and coal particles in spite of the low relativevelocities between the two.

lt is possible to distinguish between Eqs. (16) and (23) on the basisof the effect of coal particle size on the cut point shift. The isolatedparticle theory (Eq, (16» predicts that NCPS should be proportional todp-

I while the hindered settling theory (Eq. (23» predicts that NCPSshould be proportional to dp- ' with 0 ,,:; n < I.

The experimental data are shown in Fig. 6 and they lend support tothe hindered settling theory. The data are well correlated by

NCPS = Q, - Qm = 0.402dp-

0 32 with d, in JIm. (24)Om

Eq. (24) can be used to predict the cut point for each size of coal particlein the feed to the cyclone. The constant will be a function of the cyclone

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0,3

0,2

0,1

0,08

0,06

0,04

0,02

~ Greenside cool

+tonccu coal

NCPS O.4D2dp -!U2

10 100Particle sizeJ.lrn

1000

FIGURE 6 Normalised cut point shift as a function of particle size.

size and geometry and can also be affected by abnormal operatingconditions such as large specific gravity differentials between underflowand overflow,

If the expression for d, given by Eq. (20) is used in Eq. (23)

NCPS = Q, - Qm =Qm

which is of the form of Eq. (24).

THE SEPARATION EFFICIENCY

K,d(n-I)

dnp

(25)

No adequate theoretical procedures have been developed to relate theseparation efficiency to the operating parameters of the dense mediumcyclone. It has been known for many years that separation efficiency isaffected by particle size but Horsfall" was the first worker to attempta quantitative correlation between the imperfection and the particlesize, Using the data then at his disposal he showed that the product ofimperfection and particle size was close to a constant value, He calledthis constant the "compensated imperfection", The postulated relationship can be tested by appeal to experimental data, The experimental

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206

0,10

0.09

0,08

0,07

<:i 0,06

f 0,05

0,04

0,03

0,02

0,01

R. P. KING and A. H. JUCKES

+ J. Mengelers and C. OoggeTertre Plant 350 mm cyclone

It Deurbrack USBM R179B2 200 mm cyclone

~ This work Greenside coal 150 mm cyclone

+Thiswork Landau coal with slimes •150 mm cyclone

+

o 0,002 0,004 0,006 0.008 0.010 0.012 0.014 0,016(Particle slzej-' Ilm-1

FIGURE 7 Measured imperfection as a function of particle size.

conditions and data from this investigation are summarized in Tables Iand II.

The imperfection and corrected imperfection were obtained from themeasured partition function for 4 narrow size classes in each experiment. The parameters in Eqs. (2) and (3) were estimated by non-linearregression and typical fitted curves are shown in Figs. 2 and 3. Theimperfection and the corrected imperfection were obtained from theparameter busing Eqs. (5) and (6) and the values obtained for thecorrected imperfection are given in Tables III and IV.

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T

¢ Greenside coal (no slimes)

+ landau coal with slimes

Error bars at ± 1 std.devn.

0,07

0,06

....I' --c: 0,05 -- ~-0 -- ,

i --0,04a.§u 0,03~0

~0 0,02U

0,01

o 0,002 0,004 0,006. 0,008 0,010 0,012 0,014 0,016

(Porticle slze)" I1m-'

FIGURE 8 Measured corrected imperfection as a function of particle size.

This data together with previous results'<":" reported from thisproject indicate that the corrected imperfection is not a strong functionof total flowrate of medium and coal through the cyclone and is not afunction of the density of the medium.

The data are summarized in Figs. 7 and 8. In Fig. 7 the imperfectionis shown as a function of particle size with the data plotted as imperfection against the reciprocal of particle size. This set of axes is suggested byHorsfall's postulate of the constancy of the "compensated imperfection"which would require the data in Fig. 6 to fail on a straight line thatpasses through the origin. All other data from the Iiterature" areshown in Fig. 7 as well.

In spite of the inevitable scatter of the data a linear relationship canbe justified although it does not pass through the origin but intersectsthe imperfection axis at a value of 0.0 I. This is evidently the lowestvalue of imperfection that could be obtained in a dense-medium cyclone.

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The data support an empirical relationship

(l - O.OI)dp = 5.75 (26)

with d, in /lm

Thus Horsfall's compensated imperfection must be modified slightly toaccommodate this lower limit. The data obtained by Deurbrock' andMengelers and Dogge" compares reasonably well with the data obtainedin this study.

The scatter in the experimental data that is evident in Fig. 7 is duein large part to the effect of the short circuit flows, particularly at smallparticle sizes. The measured imperfection is significantly affected by thevalues of the short circuit asymptotes on the measured partition curve.In fact, when either short circuit flow approaches 25% the measuredimperfect becomes infinitely large and is not defined at all if either shortcircuit flow exceeds 25%. The corrected imperfection does not sufferfrom this disadvantage since the effect of the short circuit is removedentirely before the corrected imperfection is measured and consequentlya better correlation between corrected imperfection and size can beestablished. The data are shown in Fig. 8 and for feed coal containingnatural slimes the corrected imperfection shows a strong linear variationwith the reciprocal of the particle size. The data are well correlated bythe relationship

I, = 0.013 + 3.8dp-1 (27)

The absence of slimes in the feed material has, at most, a small butsignificant effect on the separation efficiency. This is most readily seenin Fig. 8 where the corrected efficiency for the finer sizes of coal is some10% to 20% smaller than for the same particles in the presence ofslimes. Clearly the presence of slimes does hinder the motion of the veryfine particles to a certain extent.

CONCLUSIONS

An empirical equation has been found to give an excellent fit to measuredpartition factors for the beneficiation of fine coal in a dense mediumcyclone. Four characteristics determine the operating performance ofthe dense-medium cyclone when processing fine coal:

the cut point,the separation efficiency,the short circuit to underflow,the short circuit to overflow.

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Consequently a four-parameter model is required with each parameteraccounting for one of these characteristics.

The variation of each of these parameters with particle size has beendetermined and empirical models are proposed (Eqs. 7, 8,9,24 and 27)for each of the operating characteristics.

Horsfall's concept of compensated imperfection is found to describethe present data very well after a slight refinement.

The presence of up to 50%-75 J1.m slimes in the feed was found tohave no significant effect on the behaviour ofcoarser coal particles withrespect to the cut point shift and the short circuit flow to overflow.

The presence of slimes shows a small but significant effect on theshort circuit to underflow and on the corrected imperfection.

The model developed is entirely predictive and has been found to bevery useful for the simulation of fine coal beneficiation flowsheets.

Acknowledgements

Mrs P. Stirling carried out the dense-liquid washability analyses with great precision,from which the partition curves were determined. Mr B. Mothibeli assisted with theexperiments and sample analyses.

This work was supported by the Foundation for Research Development and by VanEck and Lurie. This support is gratefully acknowledged.

References

I. D. G. Osborne, "Fine coal cleaning by gravity methods. A review of modernmethods". Coal Preparation 2. 207-242 (1986).

2. S. Ranga Raja Rao, ed., Coal Preparation and Use: A World Review. A. A. Balkema,Rotterdam (1982).

3. Anonymous. Proceedings of the 10th International Coal Preparation Congress.Canadian Institute of Mining and Metallurgy (1986), Vol. I.

4. E. T. Woodburn, S. A. Flynn, B. A. Cressey and G. Cressy, "The effect of frothstability on the beneficiation of low-rank coal by flotation". Powder Technology 40,167-177 (1984).

5. B. C. J. Labuschagne, "Relationships between oil agglomeration and surfaceproperties ofcoal: Effect of pH and oil composition". Coal Preparation 3 1-13 (1986).

6. M. R. Greer, M. Sokaski, P. S. Jacobsen and H. F. Yancey, "Performance ofdense-medium cyclone in cleaning fine coal", u.s. Bureau of Mines, RI 5732 (1960).

7. A. W. Deurbrock, "Washing of fine size coal in a dense-medium cyclone". U.S.Bureau of Mines, RI 7982 (1974).

8. J. Mengelers and C. Dogge, "A new technique for the treatment 010-1 mm fine coalby means of heavy medium cyclones". 8th Int. Coal Preparation Congress, Donetsk(1979), Paper BI.

9. R. A. Lathioor and D. G. Osborne, "Dense medium cyclone cleaning of fine coal".2nd Int. Conference on Hydrocyclones. Bath, pp. 233-252 (1984).

10. P. J. F. Fourie, P. J. van der Walt and L. M. Falcon, "The beneficiation of fine coalby dense-medium cyclone". 1.S. Afr. Inst. of Mining and Metallurgy 80, 357-361(1980).

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210 R. P. KING and A. H JUCKES

II. R. P. King and A. H. Juckes, "Performance characteristics of dense-medium cyclonesprocessing fine coal: Experimental data". Dept. of Metallurgy and Materials Engineering, University of the Witwatersrand, Report CSPCOAL-J5 (1987) 356pp.

12. R. P. KingandA. H. Juckes, "Cleaning of finecoal by dense-medium hydrocyclone",Powder Technology 40, 147-160 (1984).

13. K. J. Reid, Maixi Lee and Shenggui Shang. "Coal preparation distribution curves".Coal Preparation I, 231-250 (1985).

14. R. P. King and A. H. Juckes, "The effect of viscosity modification on the cleaningof finecoal by dense medium hydrocyclone", University of the Witwatersrand, Dept.of Metallurgy. Report CSPCOAL-2 (1983) 9 pp.

15. R. B. Bird, W. E. Stewart and E. N. Lightfoot, Transport Phenomena, Wiley,New York (1969) p. 196.

16. D. W. Horsfall, "Pilot plant data for fine coal beneficiation". Paper presented atS. Afr. Inst. Mining and Metallurgy Colloquium (1978).

17. R. P. King and A. H. Juckes, "Cleaning of fine coals by dense medium hydrocyclone". University of Witwatersrand, Dept. of Metallurgy, .Report CSPCOAL-J(1983) 32pp.

18. R. P. King and A. H. Juckes, "Beneficiation of fine coal in a dense medium cyclone:The effect of slimes in the feed". University of the Witwatersrand, Dept. ofMetallurgy. Report CSPCOAL-6 (1986) 61 pp.

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performance of a dense-medium cyclone when beneficiating fine coal

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