classification of fine coal with a hydrocyclone

In ternational Journal o f M infffal Processing, 12 ( 1984 ) 213--237 213 Elsevier Science Publishers B.V., Amsterdam --Pr inted in The Netherlands

C L A S S I F I C A T I O N O F F I N E C O A L W I T H A H Y D R O C Y C L O N E

J. SLECHTA and B.A. FIRTH*

BHP Central Research Laboratories, Shortland, N.S.W. 2307 (Australia)

(Received December 6, 1982; revised and accepted July 7, 1983)

ABSTRACT

Slechta, J. and Firth, B.A., 1984. Classification of fine coal with a hydrocyclone. Int. J. Miner. Process., 12: 213--237.

The classification performance of a 225-mm hydrocyclone has been investigated. Coal slimes of a nominal 0.5 mm size consist were classified in the sepvxation-range of 0.070 mm to 0.250 mm at solids contents from 6 to 35% by mass, and flow rates of 200 to 700 1 min- 1.

The partition curves obtained were analysed in terms of the water split to the oversize flowstream, the corrected separation size and the reduced partition curve.

The results can be summarised as follows: (1) The water split to the oversize flowstream was found to be dependent upon the

vortex finder and spigot diameters of the hydrocyclone and the flow rate and pulp density of the feed slurry.

(2) The corrected separation size was dependent on the solids content of the feed, and the vortex finder and spigot diameters. The hydraulic pressure (or flowrate) of the feed slurry did not have a significant effect. This phenomenon could be explained using the crowding theory of Fahlstrom.

(3) The reduced partition curve obtained for this coal sample was independent of the hydraulic pressure and solids content of the feed slurry, the diameters of the vortex finder and spigot, and the proportion of near-size material. This reduced partition curve was similar to that found by Lynch and Rao for silica and limestone.

The solids content of the slurry was the major factor in determining the partition curve of the hydrocyclone.

INTRODUCTION

T h e i n c r e a s e d va lue o f c l ean coa l has r e s u l t e d in an i nc rea sed e m p h a s i s o n t h e p r e p a r a t b n o f f ine coal . I n A u s t r a l i a s o m e seams b e i n g m i n e d have a c o n s i d e r a b l e c lay s l imes c o n t e n t w h i c h can cause p r o b l e m s in t he p repa ra - t i o n o f t he f i ne coal , a n d i n v a r i a b l y r e su l t in an inc rease in f ine coal p r o d u c t ash (LePage a n d Po l l a rd , 1976) . T h e h y d r o p h o b i c i t y o f a n u m b e r o f A us t r a - l i an coals is n o t h igh a n d th i s has led to a r e - e v a l u a t i o n o f m o r e c o m p l e x rio-

*Present address: Port Melbourne Research Laboratory, B.P. Australia Limited, G.P.O. Box 5222 BB, Melbourne, Vic. 3001, Australia.

0301-7516/84/$03.00 © 1984 Elsevier Science Publishers B.V.

214

tation circuits for the preparation of fine coal (Glembotskii et al., 1974; Williamson and Arnold, 1977; Firth et al., 1979). It has been shown that the presence of ultrafine coal (minus 0.063 mm) can severely limit the amount of collector available to adhere to the coarse particles (particularly the plus 0.250 mm fraction; Smitham and Firth, 1982) with the consequent loss of coarse coal. Several of these flotation circuits require a classification stage (Williamson and Arnold, 1977; Firth et al., 1979) and the efficiency of this operation will influence the recovery of the fine clean coal (Firth et al., 1979).

A National Energy Research, Development and Demonstrat ion Council funded project, "Wet Classification of Fine Coal with Particular Reference to Flotat ion Feeds", was designed to assess the performance of various commercially available units for wet classifying fine coal into a coarse fine fraction (minus 0.5 mm plus 0.075 to 0.150 mm) and an ultra-fine fraction (minus 0.075 to 0.150 mm). This paper discusses the operation of a 225-mm hydrocyclone.

Over the past 30 years, hydrocyclones have become an accepted method for classifying fine coal. The populari ty of the hydrocyclone has been due mainly to the simplicity and flexibility of its operation, and its high capacity per unit volume of plant space. Despite its simplicity, the principles which determine the performance of the hydrocyclone are quite complex and not well understood. In fact, there is little information in the literature on the performance of hydrocyclones as classifiers for fine coal.

Centrifugal classification was intensively studied and commercially applied in the decade following 1945. The Dutch State Mines were the first to realise the potential of hydrocylones and they demonstrated conclusively that pumping a stream of water and solids tangentially into a stationary cyclone produced a consistent and reasonably sharp two-product separation (Hitzsot, 1957). In a hydrocyclone a dual spiral flow pattern is developed resulting in the larger and heavier particles being discharged through the spigot and the smaller and lighter particles leaving via the vortex finder. The performance of a hydrocylone is influenced by both the design variables, for example, vortex finder diameter, feed pipe diameter and spigot diameter (Bradley, 1965; Lynch, 1977) and by the operating variables, such as the flow rate and solids content of the slurry and the size distribution of the feed {Lynch, 1977).

Fundamental and applied research on the factors which control the operation of hydrocyclones has been carried out since 1949 when Dahlstrom {1949) was the first to investigate the effect of the dimensions of the hydrocyclone on the pressure drop across the hydrocyclone, the capacity and the separation size. The flow patterns and velocity profiles within a hydrocyclone were defined by Kellsall (1952; 1953) in 1952. This work provided the basis for the development of the equilibrium orbit theory. In this theory it is assumed that the particles with a 50% probabili ty of reporting to the oversize flowstream are at equilibrium with respect to the fluid drag force and the centrifugal force at some point in the hydrocyclone. The equilibrium

215

orbit theory was the basis for the majority of the research work done in the period before Bradley (1965) published his review, on the theory and prac- tice of operating hydrocyclones, in 1965. It must be noted that the majority of the experimental work in this period was done with slurries of low solids content (less than 2% by volume) and with small diameter hydrocyclones.

In the later experimental work of Fahlstrom (1963), slurries of high solids concentration (up to 20% by volume) were considered. The results from this work were explained in terms of a crowding theory for the operation of hydrocyclones. This theory states that, except for hydrocyclone operations with low feed solids contents, the separation size is primarily determined by the spigot diameter and by the solids content and size distribution of the feed. The larger particles of the feed are discharged through the spigot up to its capacity limit, and the remaining finer particles are discharged through the vortex finder. Fahlstrom's experimental results suggest that this effect is controlling when a hydrocyclone is operating with oversize flowstream solids contents greater than 40% by volume.

In the past 15 years, the emphasis of research into hydrocyclones has been directed towards the development of empirical equations which describe the behaviour of large commercial hydrocyclones. The major contributors in this area have been Lynch and Rao (Lynch and Rao, 1975; Lynch, 1977) and Plitt (1971, 1976). Plitt (1976) points out that the empirical equations developed by Lynch (Lynch and Rao, 1975; Lynch, 1977), require the determination of constants which must be experimentally evaluated for every application and then usually apply over a relatively narrow range of operating conditions. Plitt (1976) derived a set of equations from the com- posite of his results on small cyclones and Lynch's data for a large (508 mm) cyclone. He claimed that these equations have a more catholic application since they require no experimental data.

The centrifugal force acting on a particle is dependent upon the "effective" density of the particle in the suspending fluid. Plitt developed his equations using silica of relative density 2.60, while Lynch and Rao considered minerals with relative densities ranging from 2.2 to 7.5. Coal of relative density 1.4 in water has an "effective" density of 0.4 while silica has an "effective" density of 1.6 or four times that of coal. The consequence of coal having this low "effective" density on the performance of commercially available hydrocyclones has not been investigated in detail. The following experimental work was aimed at providing the necessary information so that the classification of fine coal by hydrocyclones could be described to the same degree of confidence as minerals with higher densities.

EXPERIMENTAL PROCEDURE

225 m m L I N A T E X h y d r o c y c l o n e

The standard 225 mm Linatex cyclone is shown schematically in Fig. 1. The cyclone is of fabricated construction with replaceable vortex finders and

216

VENT PIPE - -

. I - I

OUTLET 4 76

T -

INLET .... 47 \' ~ R T E X '[

T " FINDER uc (I.D. 50 ," 38 )

-4' ~I0.4 °

SPIGOT

SPIGOT I.D 16.19 * 25

Fig. 1. 225 mm Linatex hydrocyclone. All dimensions are in millimetres.

spigots, the entire unit being lined with Linatex rubber. Two vortex finders, 50 mm and 38 mm and three spigots, 16 ram, 19 mm and 25 mm were used in various combinations during the evaluation of the cyclone. A 0--150 kPa pressure gauge mounted on a diaphragm was placed just prior to the entry pipe into the cyclone.

Experimental conditions

The 225 mm hydrocyclone was evaluated with slurries of nominally minus 0.5 mm coal (see Fig. 2 for a typical size distribution) with solids contents ranging from 6.4% to 35% by mass. Combinations of the 3 spigots (16, 19 and 25 mm) and the two vortex finders (38 and 50 mm) were used over a range of pressures and flowrates. The hydrocyclone performance, measured in terms of separation size and the partition curve was assessed as a function of slurry solids content , feed rate pressure and the various spigot and vortex finder combinations.

Sampling procedure and analysis

A schematic diagram of the 225 mm hydrocyclone test circuit is shown in Fig. 3. Slurry was pumped around the circuit by a 4-3 Warman centrifugal

217 ROSIN RAMMLER GRAPH

99 1

~5 ~ 5

9 c _ - ~ " I / / / _ - ~ :

~o , 20

~- NORNALISED-FEED-SIZE f -

5060 .~" ~ / ,~ / - DISTR BUTIO 4 - - _1 o _ , / - / _

/*0 \ ,......-I _ \ i j , , / _ -o9

30 _ I ~ " : " - " / - - -08

_ ~ 2 0 _ _

15-- , - -

# 1- _ / . - -o 6 D

~ S ) - - \ MODIFIED SIZE DISTRII~UTION ~--" ( ~ - - 05

=~ 6 _ USED IN TESTS 42,43 4 4 , 4 5 , 4 6 5 95

6~ = -- -- ~- z

97 _~S

2 98 ~o _ L,

J 99

• OL5 .063 .090 .125 .180 ,250 .355 .500 .710

SIZE mm

Fig. 2. Typical and modified size distributions used in cyclone tests.

'~ ~ [ 225 mm

\ HYDROCYCLONE

ULTRASONIC .FLOWMETER

CHART UNDERSIZE RSIZE [__~CORDER

~.PLER \ / \ , L , /

Y 4 - 3 CENTRIFUGAL PUMP

Fig. 3. Schematic diagram of the hydrocyclone test circuit.

218

pump powered by a 10-kW variable speed Reeves drive unit. This allowed flow rates in the range 200 to 720 1 min -1 to be considered. The flow rate was moni tored with an ultrasonic f lowmeter coupled to a conventional pen chart recorder in order to determine when the system reached a steady state. The sampling method used incorporated two main features, firstly both the entire undersize and oversize flowstreams were sampled, and secondly, both streams were cut at precisely the same time. Attr i t ion of the coal occurred during the experiments, but this effect was mitigated by continual replacement of the solids removed from the circuit by the sampling procedure. The initial and replacement solids came from the same previously prepared stock of minus 0.5 mm coal.

Prior to taking a sample for analysis, the following procedure was adopted. Slurry was circulated through the hydrocyclone and the flowrate was progressively increased until the roping discharge mode of operation was attained (that is, the cone shaped discharge of the oversize flowstream changed to a tight winding stream), or the maximum pressure (flow rate) of the pump was reached. The pressure was then noted and a series of tests were performed at lower pressure values. All of the tests were typically made under conditions of spray discharge except in the few instances where roping is specified.

Samples were taken by activating the sampling trolley to cut the undersize and oversize streams, the sampling time being obtained with the aid of a stopwatch. The volume of undersize and the mass to oversize were measured. The ratio of a mass of oversize to total sample volume was calculated and sampling repeated. This was continued until the ratio varied by no more than 2--3%.

The undersize samples were subdivided to ~ 30 1 with the aid of a slurry sample splitter developed by the Central Research Laboratories of BHP. All samples were then subsampled manually by taking increments f rom an agitated tank by pumping the contents out and cutting the slurry stream at regular intervals to fill a one litre sample container, until the tank was empty.

A spear sampler was used to take head samples at regular intervals for solids content and size distribution determinat ion in order to moni tor any breakdown of feed or loss of water. Four increments were taken and com- bined to form a sample. Reproducibi l i ty with this sampling technique was very good and gave good correlation to recombined size distributions as calculated from the undersize and oversize samples. It should be noted that this method is only effective in a well agitated tank where little stratification occurs. The absence of stratification was shown by the similarity of spear samples taken at the top and bo t tom corners of the tank.

All trials were done in duplicate to check reproducibil i ty. Flow rate mea- surements were calculated from the sampling time and total sample volume which was then correlated to the flow meter reading. This ensured the reli- ability of the flow rate measurement.

219

Once the bulk sample has been subsampled into one-litre containers, the sample slurry mass was determined and the sample was wet screened at 0.045 ram. The sample was dried to determine solids content and the plus 0.045 mm fraction dry screened using a x/2 sieving ratio with sieve apertures from 0.710 to 0.045 ram.

The methods used to calculate the uncertainties in derived quantities (e.g. oversize mass recovery, partition coefficient for the ith size fraction) have been described previously (Slechta et al., 1981). The uncertainties in the measured quantities, obtained by repeat sampling, are given in Table I.

TABLE I

Typical uncertainties associated with derived quantities

Quantity Average order of uncertaint~y*

O/S mass recovery 6% Reconstituted feed for the ith size fraction 7% Partition coefficient for the ith size fraction 8% Separation size 8%

*Relative percent.

Preparation o f a different size distribution

To determine the effect of the size distribution of the feed on the classification process, the feed size distribution was artificially adjusted. The operating conditions of the hydrocyclone were adjusted to give separation sizes between 0.040 mm and 0.190 mm and the undersize streams collected and then repulped to approximately 10% solids content. By this method the size distribution was altered as shown in Fig. 2.

RESULTS AND DISCUSSION

Analysis o f results

The analysis of the 54 duplicate experiments used the procedure specified by the Australian Standard AS1634 (1979). The experimental results pre- sented in this paper are those necessary to illustrate particular points in the discussion; the detailed results from the 54 duplicate experiments are available elsewhere (Firth and Slechta, 1982).

Small variations of the feed size distribution were observed during the course of the experimental work. This was mainly noticeable in the amount of minus 0.045 mm material, which varied from 20 to 30% by mass. This variation was due to degradation caused by the slurry handling system. To allow a meaningful comparison of feed specific results such as mass % solids

220

t o o v e r s i z e , t h e s e r e s u l t s m u s t b e a d j u s t e d t o a c o m m o n base , r e f e r r e d h e r e - in as t h e n o r m a l i s e d f e e d . A d j u s t m e n t is m a d e v ia t h e a s s u m p t i o n t h a t fo r s m a l l v a r i a t i o n s in t h e f e e d size d i s t r i b u t i o n t h e p a r t i t i o n c o e f f i c i e n t f o r a p a r t i c u l a r s ize f r a c t i o n d o e s n o t c h a n g e . T h u s f e e d a d j u s t e d va lue s f o r m a s s r e c o v e r y t o o v e r s i z e , M0, a re c a l c u l a t e d b y t h e d i s c r e t e a n a l o g y of :

Mo =fo f(x)Po (x) dx (1)

w h e r e f(x) r e f e r s t o t h e n o r m a l i s e d f e e d d i s t r i b u t i o n w h i c h a p p e a r s in a c u m u l a t i v e f o r m in F ig . 2 a n d P0 is t h e p a r t i t i o n c o e f f i c i e n t o f t h e o v e r s i z e f o r s ize (x) .

Rope discharge

A m a r k e d c h a n g e in t h e p e r f o r m a n c e o f t h e h y d r o c y c l o n e o c c u r r e d w h e n t h e o v e r s i z e f l o w s t r e a m c h a n g e d f r o m t h e v o r t e x d i s c h a r g e m o d e t o r o p i n g d i s c h a r g e m o d e o f o p e r a t i o n . F i g u r e 4 c o m p a r e s t h e p a r t i t i o n c u r v e s f o r a s l u r r y w i t h 9 .5% b y m a s s o f s o l i d s c o n t e n t w i t h v o r t e x f i n d e r a n d s p i g o t d ia - m e t e r s 50 a n d 19 m m r e s p e c t i v e l y . T h e m a r k e d i n c r e a s e in t h e s e p a r a t i o n s ize a n d m i s p l a c e d o v e r s i z e m a t e r i a l f o r t h e r o p e d i s c h a r g e m o d e i n d i c a t e d an i n e f f i c i e n t c l a s s i f i c a t i o n p r o c e s s .

T a b l e I I s h o w s t h e p r e s s u r e s a t w h i c h r o p e d i s c h a r g e m o d e Of o p e r a t i o n was e n c o u n t e r e d f o r a n u m b e r o f v o r t e x f i n d e r a n d s p i g o t d i a m e t e r s . I n s o m e cases ( r a t i o s o f s p i g o t d i a m e t e r t o v o r t e x f i n d e r d i a m e t e r e q u a l t o o r g r e a t e r t h a n 0 .5 ) t h e p u m p was n o t c a p a b l e o f r e a c h i n g t h e p r e s s u r e a t w h i c h r o p e d i s c h a r g e w o u l d c o m m e n c e . T h e p r e s s u r e , a t w h i c h r o p e d i s c h a r g e ap- p e a r e d , d e c r e a s e d w i t h d e c r e a s i n g s p i g o t d i a m e t e r a n d w i t h i n c r e a s i n g so l i d s c o n t e n t f o r s o l i d s c o n t e n t s g r e a t e r t h a n 10% b y m a s s o f so l ids .

TABLE II

Pressures at which rope discharge of oversize material occurs

Vortex Spigot Solids content, % by mass finder diameter diameter (mm) 6.4 7.8 8.5 9.5 12.5 15.0 25.0 35.0 (mm)

38 16 185 R -- - - 180 R 120 R 100 a -- - - 38 25 . . . . x - - - - - - 50 16 65 R 65 R 65 R 65 R -- 30 R -- - - 50 19 105 R -- - - 100 R - - 25 R -- - - 50 25 x -- - - x - - x x x

- - = no data x = pulp had reached the maximum pressure without rope discharge occurring. R= approximate pressure (in kPa) at which rope discharge occurred.

221

100

o~ 80

~ m,n -I Q

Z.0 o _ 697 z • _ _ / .89 _o * _ _ 4 7 2

e _ _ 331 • _ _ 212

i i 1

0.1 0 .2 0.3

GEOMETRIC M E A N SIZE m m

Fig. 4. C o m p a r i s o n of p a r t i t i o n curves at var ious f low ra tes of a 9.5% solids c o n t e n t s lurry using a 50- ram d i a m e t e r vo r t ex f inder and a 19-ram spigot .

Effect o f pressure on f low rate

The centrifugal force, which provides the classification capability of the hydrocyclone, comes from the fluid pressure (Dahlstrom, 1949). The resulting loss in pressure, P, is a significant operating variable for the hydrocyclone. The majority of pressure loss/flow rate relationships, which have been derived, assume a fully turbulent f low regime (Bradley, 1965). That is:

Q ~ p0.s (2)

where Q = slurry flow rate (1 min-1), and P = pressure loss (kPa). In Fig. 5, the flow rate of slurry through the hydrocyclone was plot ted

against the pressure loss for a number of vortex finder and spigot diameter combinations. The lines were drawn with a gradient of 0.5. The position of the data points to the lines indicate that the above relationship is obeyed.

The diameter of the vortex finder also had a significant effect on the relationship of the flow rate of slurry with respect to pressure loss (Fig. 5). This was expected since the majori ty of the water exits from the hydro.. cyclone via the vortex finder. The dependence of the flowrate on vortex finder diameter for constant pressure loss was linear within experimental error, that is

Q cc D v F (3)

where DVF = inside diameter of the vortex finder. This effect has been observed previously (Dahlstrom, 1949; Lynch and Rao, 1965).

222

VORTEX FINDER SPIGOT SOLIDS CONTENT SYMBOL DIAMETER (ram) DIAIvt:_TER (% by mass)

38 16 9 5 .. 38 16 15 0 38 25 12 0 o 50 25 9.5 x 50 25 15 0 o

1000 50 1 9 9 5 50 16 9.5 ®

see .c_ zOO E

300 ./ ~

200 / o LL

100 ~ , i ~ A i 10 20 ZO 60 " 80 100 200

PRESSURE LOSS kPa

Fig. 5. Pressure loss versus f l o w rate.

Part i t ion curves

A complete description of the ability of a classification unit to size the solids in a slurry is given by the partition curve which is the mass percent of material in one size fraction of the feed reporting to the oversize. For hydrocyclones, the partition curve is the result of a combination of two factors, a classification process and a by-pass effect (Kellsall, 1953). The water reporting with the oversize particles (hydrocyclone underflow) en- trains feed solids of all sizes which by-pass the classification process. By dis- counting the effect of these by-pass particles from the partition curve, a corrected partition curve is obtained. The corrected partition curve is claimed to describe the effect of the centrifugal force, in the hydrocyclone, on the classification of the particulate material in the slurry.

The corrected partition curve is given by the following:

Po(x) = [P0(x) - Rf ] / (100 - Rf) (4)

where Rf is the mass percent of the water reporting with the oversize material, and Po(x) is the corrected partition coefficient.

223

Partitioning of the slurry

It has been shown that the value of Rf is primarily determined by the vortex finder and spigot diameters, and the flow rate and solids contents of the slurry (Bradley, 1965; Lynch and Rao, 1975; Plitt, 1976). The increase in Rf with increasing solids content of the feed slurry is shown in Fig. 6. This figure also shows that both the vortex finder and spigot diameters significantly affect the Rf value. An increase in the spigot diameter results in an increase in Rf while an increase in the vortex finder diameter reduces Rf. In Fig. 7, the decrease in Rf with increasing flow rate is demonstrated for a number of different slurry solids contents.

The dependence of Rf on these factors has only been expressed with empirically derived relationships. The derivation of theoretically based equations is hindered by the presence of an air core where diameter is dependent on the geometry of the hydrocyclone, and it is known to expand with in-

VORTEX FINDER SPIGOT Ds/Dvf SYMBOL DIAMETER (turn) OIAMETER

Dvf (ram) Ds 50 16 0 33 x 50 19 0 38 ,,.

30 50 25 0 50 • 38 1 5 0 .z,2 o

38 25 0 55 o D

Rf% 20

10 o ~

i l I

5 10 20 30

SOLIDS CONTENT {% by mass)

Fig. 6. Effect o f solids content and cyc lone geometry on the value o f Rf ( f l ow rate is approximate ly 250 1 rain -z ).

224

SOLIDS CONTENT % by mass SYMBOL

6z. x g.S o

150 • 25 0 ~, 35.0

Rj %

10

l I I 200 400 • 600 500

FLOW RATE ~ min -1

Fig. 7. Effect of flow rate on Rf (vortex finder and spigot diameters, 50 and 25 ram, respectively).

creasing flow rate (Bradley, 1965). Also, a variation in the solids content of the feed slurry will result in a change in the rheological properties of the material in the hydrocyclone. This change will influence the geometry of the air core.

A large number of these empirically derived relationships have been published. The volume split of slurry (Z = oversize flowrate/undersize flowrate), which is a parameter closely related to Rf, was given by Moder and Dahl- strom (1952) as:

Z = C ( D s / D v F ) 4 " 4 Q -°'44 (5)

where DS = inside diameter of the spigot, and C = a constant. In Fig. 8, log Z is plotted against log Q for four different pulp densities

and vortex finder-spigot combinations the gradients of the straight lines compared favourably with the --0.44 value used in eq. 5. The gradients of the lines were calculated using the method of least squares. The power, to which the ratio D s / D v F was raised was found to overemphasise the effect of this ratio by a factor of about 2. Also, eq. 5 contains no solids content term and from Fig. 8 it is clear that solids content does influence Z.

225

SOLIDS CONTENT VORTEX FINDER SPIGOT

(% by mass) DIAMETER(mm) DIAMETER(mm) SYMBOL

9 5 50 19 • 35 0 50 25 o

9 5 50 25 x 12 0 38 25 []

Z.0

30 ~ COADIENT OF LINE

-0 A7

-OZ./-.

30 I I I ! I I I 1 1 100 200 500 1000

FLOW RATE I rain-1

Fig. 8. Ef fec t of slurry f low r a t e o n t h e f low split, Z. Z = oversize f low rate /unders ize f low r a t e .

A linear relationship has been observed between the amount of water reporting to the undersize flowstream and the amount of water in the feed (Lynch and Rao, 1975; Lynch, 1977). This linear relationship was also observed for the data obtained in this paper, see Fig. 9. It had been previously found that the spigot diameter had the greatest influence on the linear relationship (Lynch, 1977), but the data in Fig. 9 suggests that this dependence occurs when the ratio of Ds/DvF is greater than 0.5. All of the tests with a solids content of about 10% by mass have a similar relationship except for the tests with a DVF of 38 mm and a DS of 25 mm. Solids content also af- fects this linear relationship. As the solids content increases the amount of water reporting to the undersize flowstream decreases.

Reduced partition curve

From the corrected partition curve a new separation size can be obtained. It is claimed that this corrected separation size, S~0, is the size of particle in the feed slurry which has a 50% probability of reporting to the oversize flow-

226

SOLIDS CONTENT VORTEX FINDER SPIGOT SYMBOL % by mass DIANETER (turn) DIAMETER(ram)

6.4 50 25 o 1 5 0 50 25 o 25 0 50 25 35. 0 50 25

g 5 38 16 x 1 2 0 38 25 • 9 5 50 19 • 9 5 50 16 •

7 / c_ 600 E

500 LO rY

400 D~

t.U U

300 LO 0 Z

z 200

or

100

i i oio i I I I(3(3 20(3 3 400 500 600

WATER IN FEED ~ rain -I

Fig. 9. The linear relationship be tween the amount o f water reporting to the undersize f lowstream and the a m o u n t o f water in the feed.

stream due to the action of the centrifugal and fractional drag in the hydrocyclone (Lynch and 1%o, 1975; Plitt, 1976). A reduced partition curve can be obtained by plotting the corrected partition coefficient for a particular size fraction against the geometric mean size of the size fraction, x , divided by the correction separation size (i.e. x/S'5o). The marked similarity in the shape of reduced partition curves for a particular material being treated by hydrocyclones of different sizes and operating conditions was first observed by Yoshioka and Hotta (1955) .

The extensive experimental work of Lynch and Rao (1975) with silica and limestone slurries showed that the reduced partition curve is constant for a wide range of slurry f low rates and solid contents, and vortex finder and spigot diameters of the hydrocyclone. However, the diameter of a hydrocyclone has an effect on the reduced partition curve, if the diameter is less than 15 mm (Bradley, 1965). Bradley suggested that the variation was due to

227

turbulent diffusion of the particles in the slurry which increase with decreasing hydrocyclone diameter.

The concept of a constant reduced partition curve for a material is ex- tremely useful since it provides a method with which a large amount of experimental data can be summarised and used for predictions. A number of empirical equations have been prepared to represent the reduced partition curve. Lynch (1977) found that the following equation fitted his experimental data:

exp (olx/S'so) -- 1 P0 (x) = (6)

exp (oLx/S'so) + exp a -- 2

The term a is a constant which acts as a measure of the sharpness of classification. For low values of a (less than 3) a poor classification is indicated, while for high values (greater than 4), a sharp classification is shown.

A Rosin-Rammler type of equation has also been used to represent the reduced partition curve (Plitt, 1971):

Po ( x ) = 1 - e x p [ - O . 6 9 3 ( x / S ' s o ) m ] (7)

where m is another measure of the sharpness of the classification. From a multiple regression analysis of his data Plitt produced the following equation (Plitt, 1976):

rn = 1.94 exp( -1 .58 RV) • (Dc 2 h / Q ) T M (8)

where D c = inside diameter of a hydrocyclone measured at the bot tom of the vortex finder; h = the distance from the bot tom of the vortex finder to the spigot; and R V = recovery of feed volume to the oversize flowstream.

Plitt (1976) has claimed that the RV term, which is dependent upon the ratio D s / D v F , shows that as D s / D v F increases the sharpness of the separation deteriorates. He has also claimed that the term Dc 2 h / Q , which is a measure of the residence time of material in a hydrocyclone, shows that the larger residence time of a particle in a hydrocyclone, the greater the probability of that particle reporting to the correct flowstream.

The effect of flow rate on the reduced partition curves obtained for a coal slurry is shown in Fig. 10. These reduced partition curves are identical for flow rates less than 490 1 min -1 . The reduced partition curve obtained for a flow rate of 697 1 min -~ is not as sharp as that obtained for the lower flow rates. This was expected since, at this high flow rate, rope discharge of the oversize material was observed. The independence of the reduced partition curve from the slurry flow rate agrees with the findings of Lynch and Rao (1975), and suggests that the residence time effect of Plitt is insignificant for this hydrocyclone under normal operating conditions (Q < 490 1 min-~).

The reduced partition curves had little dependence on the solids content of the slurry for values of 35% or less, see Fig. 11. The data do suggest that the classification of the ultrafine particles is slightly inhibited for feed slur-

228

100 •

l rain -1 SYMBOL

80 212 x 331 A 472 • / m / / ~ o = 45 , , 489 [a / / - exp( ~cc/£-A }- 1

, -bU 697 • / / P~ I x ) : ~ 0 - - " 60 )÷exp~ 2

I / / /,o

02 0'4 0'6 018 1'0 1!2 1'.4 116 1!8

/s Iso

Fig. 10. The e f fec t o f f low rate on the reduced par t i t ion curves. Solids c o n t e n t o f the slurry was 9.5% and the vor t ex f inder and spigot d iameters were 50 and 19 ram, respectively.

100

SOLIDS CONTENT % by mess SYMBOL ~ x

6.z, x 80 15,0 • J . i ~-- 4.5

7 " 25.0 [] / " I

Po 35.0 z~

60

L0

20 • * e e / /

A X A Q []

I I 0.2 0!z. 0'.6 0'.8 1'.0 1!2 1.z. 1!6 1.8

~ / S l s 0

Fig. 11. The e f fec t o f solids c o n t e n t on the reduced par t i t ion curve. The slurry f low rate was app rox ima te ly 2 5 0 1 rain -1 and the vor tex f inder and spigot d iameters were 50 and 25 ram, respect ively.

229

ties with high solids content. Figures 12 and 13 show that a variation of the vortex finder and/or spigot diameters also has no effect on the reduced partition curve. This implies that the exp(-1.58 RV) term in eq. 8 is suspect. If the spigot diameter was increased it would be expected that, as it closely ap- proached the diameter of the vortex finder, the sharpness of classification must be affected.

In Figs. 10, 11, 12 and 13, the curve line was calculated from eq. 7 with = 4.5. This curve closely fits all of the reduced partition curves obtained

with this coal slurry for a 225 mm hydrocyclone under normal operating conditions. Lynch (1977) has found that the reduced partition curves for limestone and silica were essentially identical, but noted that data, supplied by Tart (Lynch and Rao, 1978), for coal was different. This difference was attributed to difference in the relative density of the materials. In Fig. 14 it is clear that the reduced partition curve obtained from this experimental data is nearly as sharp as those for limestone and silica. This suggests that the effect of relative density on the reduced partition curve is not as significant as previously thought. The difference between the present results and those of Tart may be due to the effect of having particles with a range of relative densities within the feed solids. Unfortunately a relative density analysis of Tarr's coal was not published. The majority (approximately 80% of the coal used in this study had a relative density less than 1.40, so the influence of this effect would be small.

VORTEX FINDER SPIGOT 100 DIAMETER (ram) DIAMETER (ram) SYMBOL

50 16 • ~ • 38 16 x

BO 50 25 mm /

38 25 ~: 4 5 P'o A x

60

40 x

02 014 06 O'.B I!0 1!2 14 1!6 l!e, ac/sJ50

Fig. 12. The effect o f vortex f inder diameter on the reduced partit ion curve.

230

100

SPIGOT DIAMETER SYMBOL ~ " (mm} ~ f 16 x e j BO 19 o ,/.,4 - ~, = 4.5

Pol 60 25 • x ~

2G

G

0.2 0 I/-, 0!6 0'-8 1.0 1!2 1.1/, 1'.6 118 =/sl50

Fig. 13. The effect of spigot diameter on the reduced partition curve. The slurry flow rate was approximately 500 l rain -I, the solids content 9.5% by mass and the vortex finder was 50 mm diameter.

100

8 0 -

2 70 -

~ 6O

~ s0

,,, 1,0 G

30- .2 ' L "/'"/7 20 ./. //

O ~ - - - ' ~ " ~ " ~ 1 I 1 1 I I I I I I I I I I 0.4 0.8 1-2 1-6 2.0 2./. 2.B 3-2

X

Fig. 14. Reduced par t i t ion curves for l imestone (,,), silica (,,) (Lynch, 1977); coal (Tarr 's data) ( - ) (Lynch and Rao, 1975) and coal data f rom this evaluat ion (X).

231

Size of separation

From the previous sections it is clear that both the separation size, Ss0, and the corrected separation size, S;0, are influenced by the operating conditions of the hydrocyclone. A marked change in Ss0 and S'so was observed when the f low rate was increased to the value at which rope discharge of the oversize flowstream occurred. Apart from this effect, the solids content of the feed slurry was the factor which had the largest effect on the separation size. Figure 15 shows the effect of increasing the solids content from 6.4% to 35% by mass (4.7 to 27.8% by volume) on S~0. The marked increase in S;0 with increasing solids content is evident.

T 03 T i

J" } T 3 5 % S C T I I I

..L

"T" o 0 2 T i~t

- ~ ~ ~ 7- 25 % SC

E

z o

0 1

~J

o ~D

I I l I I I l I 200 300 ~.00 500 600 700 B00

FLOW RATE ~ rnin'- 1

Fig. 15 . The e f f e c t o f f l o w rate o n the corrected separat ion size, S's0, at various sol ids contents ( 5 0 m m vor tex f inder, 25 m m spigot) .

Figures 16 and 17 show the effect of vortex finder and spigot diameters on the corrected separation size respectively. From these figures it can be seen that increasing the vortex finder diameter or decreasing the spigot diameter increases the corrected separation size. The magnitude of this effect is dependent upon the solids content of the feed.

Figure 15 also shows that there does not appear to be any significant dependence of the value of S~0 on the f low rate. There have been a large number of theoretical and experimental studies (Bradley, 1965; Plitt, 1976)

232

VORTEX FINDER DIAMETER (ram) SYMBOL

0-200 50 •

38 o

o

S

z 0.I00 •-'~'• 0

t.~

D LtJ

UJ n,"

O I I

0 I0 20

SOLIDS CONTENT (% by MASSI

Fig. 16. Ef fec t o f vor tex f inder d iameter o n the Linatex h y d r o c y c l o n e f i t ted w i th a 16 m m spigot . ( f l o w rate ~ 2 5 0 1 min- l ) .

SPIGOT DIAMETER SYMBOL

(ram)

W N

o 0.100

UJ

121

I.,-

O

10 20

SOLIDS CONTENT (% by MASS)

Fig. 17. Ef fec t o f spigot d iameter on the Linatex h y d r o c y c l o n e f i t ted w i th a 50-ram vor tex f inder (slurry f l o w rate ~ 2 5 0 1 rain-l) .

233

which showed tha t S~0 is linearly dependent upon the inverse of the square root of the slurry flow rate, Q-0.s. The theoretical derivations of this relationship neglected particle/particle interactions and the experimental studies only considered dilute suspensions where particle/particle interactions would be minimal. The original work of Dahlstrom (1949) indicated that the un- corrected size of separation was a function of Q-0.s3. This work used a silt and clay feed material and most of the separation sizes were found to be less than 0.030 mm. Since particles of this size are particularly sensitive to the water split between the oversize and undersize flowstreams, the above dependence can be principally explained in terms of the influence of flow rate on the water split, see eq. 5.

For a number of tests, with constant solids content, and vortex finder and spigot diameter, the S~0 value at Q = 300 1 min -1 was calculated by inter- polation. This value was then set at 1 and all other S~0 values at different Q values were adjusted with respect to this point. In Fig. 18 the relative S's0 values are compared with curves calculated from S's0 ~ Q-0.s and Lynch and Rao's empirically derived equation:

SOLIDS 1 . 6 - CONTENT Dvf Ds SYMBOL

(% by mass) (rnm) (ram)

9.5 3~ 16 o \ 15.0 38 16 •

1.z, \ 25.0 50 25 x \ 9.5 50 25 o

9.5 50 19

1 -2 RELATIVE

• ~ Lynch and Rao's i

S50

1.0

0.8 ~ ~ -05

0.6 I I J 1 I 100 200 300 /430 500 600

0 t rain -1

Fig. 18. Relative S's0 values from this study are compared with calculated curves from Lynch and Rao's (1975) equation 9 and S'50 = Q-O.5.

234

Log10 S~0 = 0.040 DVF -- 0.0576 DS + 0 .0366DI + 0.0299 SC

- 0 . 0 0 0 1 Q (9)

SC = solids contents of the solids, percent by mass. There is a correspondence between the relative S's0 data points obtained

in this study and the curve calculated from Lynch and Rao which was obtained from limestone slurries with solids contents in the range 15 to 70% by mass, approximately 6 to 46% by volume. The volume fractions of solids used in this s tudy are comparable, approximately 5 to 28% by volume. Also, the experimental work of Fahlstrom (1963), on slurries with 8.5% by volume solids content , showed no dependence of the separation size on the slurry flow rate.

The volume fractions of the particles in the oversize flowstream for the experiments in this paper have been estimated to lie between 35% and 50%, that is, in the range where Fahlstrom considered the crowding effect to be dominant. The above effects may thus be explained in terms of crowding theory for the operation by hydrocyclones developed by Fahlstrom (1963). The larger particles of the feed are discharged through the spigot up to its capacity limit, and the remaining particles are discharged through the vortex finder. This implies that an increase in solids content or a decrease in the diameter of the spigot will result in an increase of the separation size. By increasing the diameter of the vortex finder, the hydraulic pressure pushing the oversize flowstream through the spigot will be reduced, so the capacity limit of the spigot will be reduced and the separation size will be increased. An increase in the hydraulic pressure of the slurry entering the hydrocyclone (that is an increase in slurry flow rate) leads to an increase in the hydraulic pressure pushing the oversize flowstream through the spigot. This results in the capacity limit of the spigot increasing which accommodates the increased mass flow of material in the oversize flowstream. So the increase in slurry flow rate does not result in a significant increase in the separation size.

Mass split to oversize

The mass recovery of solids to oversize, M0, has been corrected to com- pensate for the slight feed variations which occurred during the experiments. This correction procedure assumes that the partition coefficients do not vary with minor variations in the size distribution of the feed solids, see eq. 1.

Figure 19 shows the systematic decrease in M0 with the increase in separation size for all of the data points in which the vortex finder diameter varied between 50 mm and 38 mm, spigot diameter varied between 25 mm, 19 mm and 16 mm, and solids content varied between 6.4% and 35% by mass. This effect is expected from the crowding theory of hydrocyclone operation (Fahlstrom, 1963).

235

70

% NORMALISED

MASS TO • • • OVERSIZE 60

FLOWSTREAM ~ •

50

30 I I 0 0.100 0.200

SEPARATION SIZE ( mm)

Fig. 19. Effect of separation size on the normalised mass percent of solids reporting to the oversize flowstream (all data points).

The effect o f size distribution

The altered size distribution prepared by the method described previously is shown in Fig. 2. For this size distribution the amount of near size material for Ss0 values in the range 0.090 mm to 0.150 mm is significantly larger than that of the size distribution used in the previous trials. This material was classified in the hydrocyclone with a vortex finder diameter of 50 mm and spigot diameters of 25 mm and 16 mm. The Rf values obtained for the altered size distribution were similar to those found for the original size distribution. A small increase in S~0 was found for a spigot diameter of 25 mm (approximately 0.010 mm), but, for a spigot diameter of 16 mm, there was a marked increase (approximately 0.040 mm). The capacity limit of the spigot can magnify the effect of near size material on separation size.

In Fig. 20 the reduced partition curves obtained for the classification trials with the altered size distribution are shown. Again eq. 6, with ~ = 4.5, closely fits all of the data points. This implies that the increased amount of near size material does not affect the classification capability of the hydrocyclone. However, the amount of misplaced material is increased. This is due to the increased amount of material near the separation size. The values of the partition coefficients for this material are such that a portion of this material will be misplaced.

236

100

80 expC4.5 :~S'so ) -1 , , ~ " , - - . & 5 ~ , ~ - . , . £ SYMBOL SPIGOT DIAMETER FLOW _F_F~TE

expL--S-:--,b50 I+expl4 bJ-z ..//" (ram) l min x 15 355

60 / o 16 279 ' x/ • 25 570

$50 / " 25 416 40 / a 25 225

/ 20 / e

I I I I I 0 0-4 08 1.2 1.6 2.0

X/s~ 0

Fig. 20. Ef fec t of increased near-s ized mater ia l o n the r educed p a r t i t i o n curve.

C O N C L U S I O N S

The effects of the operational variables on the classifying performance of a 225-mm diameter hydrocyclone have been analysed in terms of their effect on the water split to oversize, Rf , the corrected separation size, S's0, and the reduced partition curve:

(1) The Rf value was found to be dependent upon the vortex finder and spigot diameter of the hydrocyclone and the flowrate and solids content of the feed slurry.

(2) The S'~0 value is determined by the solids content of the feed, and the vortex finder and spigot diameter. The hydraulic pressure (or flow rate) of the feed slurry does not have a significant effect. This phenomenon can be explained with the crowding theory of Fahlstrom (1963).

(3) The reduced partition curve obtained for this coal sample was independent of the hydraulic pressure and solids content of the feed slurry, the diameters of the vortex finder and spigot and near size material. This reduced partition curve was similar to that found by Lynch and Rao (1975) for silica and limestone.

A C K N O W L E D G E M E N T S

The authors gratefully acknowledge the support of the National Energy Research and Development Council who supplied a grant for the assessment

237

of various pieces of commercially available equipment for wet classification of fine coal of which this work is part.

The considerable task of sampling and analysing the samples from the experiments was performed by Gary Burgin, Andrew Walker, and Dale Witchard.

REFERENCES

Australian Standard AS1634, 1979. Recommended Procedures for Expression and Presentation of Results of Tests of Coal Size Classifying Equipment.

Bradley, D., 1965. The Hydrocyclone. Pergamon Press, Oxford. Dahlstrom, D.A., 1949. Cyclone operating factors and capacities on coal and refuse

slurries. Trans. AIME, 184: 331--344. Fahlstrom, P.H., 1963. Studies of the Hydrocyclone as a Classifier. Proc. 6th Int. Miner.

Process. Congr., Cannes, pp. 87--113. Firth, B.A., Swanson, A.R. and Nicol, S.K., 1979. Flota t ion circuits for poorly float-

ing coals. Int. J. Miner. Process., 5: 321--324. Firth, B.A. and Slechta, J.J., 1982. The Wet Classification of Fine Coal 'wi th Particular

Reference to Flota t ion Feeds. National Energy Research, Development and Demon- stration Council, Final Report . Available from Research Policy and Programme Branch, Department of National Development and Energy, P.O. Box 5, Canberra, ACT 2600, Australia.

Glembotskii , V.A., Zaikin, S.A., Panova, A.A. and Rubinshtein, Yu.B., 1974. Research into the possibilities for separate conditioning in coal-slurry flotation. Koko Khim., 6: 8--10.

Hitzsot, H.W., 1957. The newer classification tools - - their evolution and recent applica- tions. In: Int. "Mineral Dressing Congress, Stockholm. S. Gruvforeningen (Editor). Alto qvist and Wiksell, Stockholm, pp. 141--159.

Kellsall, D.F., 1952. A study of the motion of solid particles in a hydraulic cyclone. Trans. Ind. Chem. Eng., 30: 87.

Kellsall, D.F., 1953. A further s tudy of the hydraulic cyclone. Chem. Eng. Sci., 2: 254-- 273.

LePage, A. and Pollard, F., 1976. Methods for providing reliable data for coal prepara- t ion plant design. In: A.C. Partridge (Editor), Proceedings, Seventh International Coal Preparation Congress, D2.

Lynch, A.J. and Rao, T.C., 1965. Digital computer simulation of comminution system. Proc. 8th Comm. Min. Metall. Congr., Aust., 6: 597--606.

Lynch, A.J. and Rao, T.C., 1975. Modelling and scale-up of hydrocyclone classifiers. Proc. l l t h Int. Miner. Process. Congr., Cagliari, pp. 246--269.

Lynch, A.J., 1977. Mineral Crushing and Grinding Circuits, Their Simulation, Optimisa- t ion, Design and Control. Elsevier, Amsterdam, 342 pp.

Moder, J.J. and Dahlstrom, D.A., 1952. Chem. Eng. Progr., 48: 75. Plitt, L.R., 1971. The analysis of solid-solid separations in classifiers. C.I.M., Bull., 64:

42--47. Plitt, L.R., 1976. A mathematical model of the hydrocyclone classifier, C.I.M. Bull., 69:

114--123. Slechta, J., Taggart, I., Gallagher, E. and Firth, B.A., 1981. An evaluation of a novel

vibrating screen. Proc. First Australian Coal Preparation Conference, Newcastle, pp. 319--340.

Smitham, J. and Firth, B.A., 1982. The distr ibution of an insoluble f lotat ion collector on fine coal particles. Aust. I.M.M., 283: 29--35.

Williamson, M.M. and Arnold, J.J., 1977. The application of bore core data to coal pre- parat ion plant design. Aust. I.M.M. Symposium on Coal Borehole Evaluation, p. 114.

Yoshioka, N. and Hotta, Y., 1955. Liquid cyclone as a hydraulic classifier. Chem. Eng. Jpn., 19: 632--640.

classification of fine coal with a hydrocyclone

Documents